From 53884109790df35cf666acf7694701ec0efa4ce9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 7 Mar 2022 12:33:37 +0100 Subject: fix page numbering --- .../B/3 - Verallgemeinerte Potenzreihen.pdf | Bin 2377226 -> 2385923 bytes .../MSE/2 - Gamma- und Beta-Funktion.pdf | Bin 4698780 -> 4710774 bytes 2 files changed, 0 insertions(+), 0 deletions(-) diff --git a/vorlesungsnotizen/B/3 - Verallgemeinerte Potenzreihen.pdf b/vorlesungsnotizen/B/3 - Verallgemeinerte Potenzreihen.pdf index 780b958..b6c280b 100644 Binary files a/vorlesungsnotizen/B/3 - Verallgemeinerte Potenzreihen.pdf and b/vorlesungsnotizen/B/3 - Verallgemeinerte Potenzreihen.pdf differ diff --git a/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf b/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf index 1475e2d..667ac4b 100644 Binary files a/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf and b/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf differ -- cgit v1.2.1 From 3851cc9b2f67b7caef62a700e107e7c80dbd7eeb Mon Sep 17 00:00:00 2001 From: Nicolas Tobler Date: Mon, 7 Mar 2022 15:46:37 +0100 Subject: Added title and author --- buch/papers/ellfilter/main.tex | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/buch/papers/ellfilter/main.tex b/buch/papers/ellfilter/main.tex index f81451f..26aaec1 100644 --- a/buch/papers/ellfilter/main.tex +++ b/buch/papers/ellfilter/main.tex @@ -1,12 +1,12 @@ % -% main.tex -- Paper zum Thema +% main.tex -- Paper zum Thema Elliptische Filter % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:ellfilter}} -\lhead{Thema} +\chapter{Elliptische Filter\label{chapter:ellfilter}} +\lhead{Elliptische Filter} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Nicolas Tobler} Ein paar Hinweise für die korrekte Formatierung des Textes \begin{itemize} @@ -15,14 +15,14 @@ Absätze werden gebildet, indem man eine Leerzeile einfügt. Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. \item Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. +Optionen werden gelöscht. Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. \item -Beginnen Sie jeden Satz auf einer neuen Zeile. +Beginnen Sie jeden Satz auf einer neuen Zeile. Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt +in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt anzuwenden. -\item +\item Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. \end{itemize} -- cgit v1.2.1 From 403b8888ab0702f4d4cf4c7df24adc8c3fa45ab0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Mon, 7 Mar 2022 17:19:47 +0100 Subject: Start paper about Laguerre polynomials --- buch/papers/laguerre/definition.tex | 48 +++++++++++++++++++++++++++++++++ buch/papers/laguerre/eigenschaften.tex | 8 ++++++ buch/papers/laguerre/main.tex | 36 +++++++------------------ buch/papers/laguerre/packages.tex | 2 +- buch/papers/laguerre/quadratur.tex | 29 ++++++++++++++++++++ buch/papers/laguerre/transformation.tex | 31 +++++++++++++++++++++ buch/papers/laguerre/wasserstoff.tex | 29 ++++++++++++++++++++ 7 files changed, 156 insertions(+), 27 deletions(-) create mode 100644 buch/papers/laguerre/definition.tex create mode 100644 buch/papers/laguerre/eigenschaften.tex create mode 100644 buch/papers/laguerre/quadratur.tex create mode 100644 buch/papers/laguerre/transformation.tex create mode 100644 buch/papers/laguerre/wasserstoff.tex diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex new file mode 100644 index 0000000..5f6d8bd --- /dev/null +++ b/buch/papers/laguerre/definition.tex @@ -0,0 +1,48 @@ +% +% definition.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Definition +\label{laguerre:section:definition}} +\rhead{Definition} + +\begin{align} + x y''(x) + (1 - x) y'(x) + n y(x) + = + 0 + \label{laguerre:dgl} +\end{align} + +\begin{align} + L_n(x) + = + \sum_{k=0}^{n} + \frac{(-1)^k}{k!} + \begin{pmatrix} + n \\ + k + \end{pmatrix} + x^k + \label{laguerre:polynom} +\end{align} + +\begin{align} + x y''(x) + (\alpha + 1 - x) y'(x) + n y(x) + = + 0 + \label{laguerre:generell_dgl} +\end{align} + +\begin{align} + L_n^\alpha (x) + = + \sum_{k=0}^{n} + \frac{(-1)^k}{k!} + \begin{pmatrix} + n + \alpha \\ + n - k + \end{pmatrix} + x^k + \label{laguerre:polynom} +\end{align} diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex new file mode 100644 index 0000000..b7597e5 --- /dev/null +++ b/buch/papers/laguerre/eigenschaften.tex @@ -0,0 +1,8 @@ +% +% eigenschaften.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Eigenschaften +\label{laguerre:section:eigenschaften}} +\rhead{Eigenschaften} \ No newline at end of file diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex index 207e8d7..1fe0f8b 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -1,36 +1,20 @@ % -% main.tex -- Paper zum Thema +% main.tex -- Paper zum Thema Laguerre-Polynome % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:laguerre}} -\lhead{Thema} +\chapter{Laguerre-Polynome\label{chapter:laguerre}} +\lhead{Laguerre-Polynome} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Patrik Müller} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} +Hier kommt eine Einleitung. -\input{papers/laguerre/teil0.tex} -\input{papers/laguerre/teil1.tex} -\input{papers/laguerre/teil2.tex} -\input{papers/laguerre/teil3.tex} +\input{papers/laguerre/definition} +\input{papers/laguerre/eigenschaften} +\input{papers/laguerre/quadratur} +\input{papers/laguerre/transformation} +\input{papers/laguerre/wasserstoff} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/laguerre/packages.tex b/buch/papers/laguerre/packages.tex index 6fbe890..ab55228 100644 --- a/buch/papers/laguerre/packages.tex +++ b/buch/papers/laguerre/packages.tex @@ -6,5 +6,5 @@ % if your paper needs special packages, add package commands as in the % following example -%\usepackage{packagename} +\usepackage{derivative} diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex new file mode 100644 index 0000000..8ab1af5 --- /dev/null +++ b/buch/papers/laguerre/quadratur.tex @@ -0,0 +1,29 @@ +% +% quadratur.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Gauss-Laguerre Quadratur +\label{laguerre:section:quadratur}} + +\begin{align} + \int_a^b f(x) w(x) + \approx + \sum_{i=1}^N f(x_i) A_i + \label{laguerre:gaussquadratur} +\end{align} + +\begin{align} + \int_{0}^{\infty} f(x) e^{-x} dx + \approx + \sum_{i=1}^{N} f(x_i) A_i + \label{laguerre:laguerrequadratur} +\end{align} + +\begin{align} + A_i + = + \frac{x_i}{(n + 1)^2 \left[ L_{n + 1}(x_i)\right]^2} + \label{laguerre:quadratur_gewichte} +\end{align} + diff --git a/buch/papers/laguerre/transformation.tex b/buch/papers/laguerre/transformation.tex new file mode 100644 index 0000000..4de86b6 --- /dev/null +++ b/buch/papers/laguerre/transformation.tex @@ -0,0 +1,31 @@ +% +% transformation.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Laguerre Transformation +\label{laguerre:section:transformation}} +\begin{align} + L \left\{ f(x) \right\} + = + \tilde{f}_\alpha(n) + = + \int_0^\infty e^{-x} x^\alpha L_n^\alpha(x) f(x) dx + \label{laguerre:transformation} +\end{align} + +\begin{align} + L^{-1} \left\{ \tilde{f}_\alpha(n) \right\} + = + f(x) + = + \sum_{n=0}^{\infty} + \begin{pmatrix} + n + \alpha \\ + n + \end{pmatrix}^{-1} + \frac{1}{\Gamma(\alpha + 1)} + \tilde{f}_\alpha(n) + L_n^\alpha(x) + \label{laguerre:inverse_transformation} +\end{align} \ No newline at end of file diff --git a/buch/papers/laguerre/wasserstoff.tex b/buch/papers/laguerre/wasserstoff.tex new file mode 100644 index 0000000..caaa6af --- /dev/null +++ b/buch/papers/laguerre/wasserstoff.tex @@ -0,0 +1,29 @@ +% +% wasserstoff.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Radialer Schwingungsanteil eines Wasserstoffatoms +\label{laguerre:section:radial_h_atom}} + +\begin{align} + \nonumber + - \frac{\hbar^2}{2m} + & + \left( + \frac{1}{r^2} \pdv{}{r} + \left( r^2 \pdv{}{r} \right) + + + \frac{1}{r^2 \sin \vartheta} \pdv{}{\vartheta} + \left( \sin \vartheta \pdv{}{\vartheta} \right) + + + \frac{1}{r^2 \sin^2 \vartheta} \pdv[2]{}{\varphi} + \right) + u(r, \vartheta, \varphi) + \\ + & - + \frac{e^2}{4 \pi \epsilon_0 r} u(r, \vartheta, \varphi) + = + E u(r, \vartheta, \varphi) + \label{laguerre:pdg_h_atom} +\end{align} -- cgit v1.2.1 From 98036160c9165dbef0fcb237d5cdcf7f804748c3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Mon, 7 Mar 2022 17:22:21 +0100 Subject: Change title, name, added some formulas and structured paper --- buch/papers/laguerre/teil0.tex | 22 ----------------- buch/papers/laguerre/teil1.tex | 55 ------------------------------------------ buch/papers/laguerre/teil2.tex | 40 ------------------------------ buch/papers/laguerre/teil3.tex | 40 ------------------------------ 4 files changed, 157 deletions(-) delete mode 100644 buch/papers/laguerre/teil0.tex delete mode 100644 buch/papers/laguerre/teil1.tex delete mode 100644 buch/papers/laguerre/teil2.tex delete mode 100644 buch/papers/laguerre/teil3.tex diff --git a/buch/papers/laguerre/teil0.tex b/buch/papers/laguerre/teil0.tex deleted file mode 100644 index a0a215b..0000000 --- a/buch/papers/laguerre/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{laguerre:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{laguerre:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/laguerre/teil1.tex b/buch/papers/laguerre/teil1.tex deleted file mode 100644 index 744d505..0000000 --- a/buch/papers/laguerre/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{laguerre:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{laguerre:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{laguerre:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{laguerre:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{laguerre:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/laguerre/teil2.tex b/buch/papers/laguerre/teil2.tex deleted file mode 100644 index d514042..0000000 --- a/buch/papers/laguerre/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{laguerre:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{laguerre:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/laguerre/teil3.tex b/buch/papers/laguerre/teil3.tex deleted file mode 100644 index 120067d..0000000 --- a/buch/papers/laguerre/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{laguerre:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{laguerre:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - -- cgit v1.2.1 From 63a61e6c7f7383bfff291573526a5160c9e71690 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 7 Mar 2022 21:13:34 +0100 Subject: fix laguerre/Makefile.inc --- buch/papers/laguerre/Makefile.inc | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/buch/papers/laguerre/Makefile.inc b/buch/papers/laguerre/Makefile.inc index e83a069..1eb5034 100644 --- a/buch/papers/laguerre/Makefile.inc +++ b/buch/papers/laguerre/Makefile.inc @@ -7,8 +7,10 @@ dependencies-laguerre = \ papers/laguerre/packages.tex \ papers/laguerre/main.tex \ papers/laguerre/references.bib \ - papers/laguerre/teil0.tex \ - papers/laguerre/teil1.tex \ - papers/laguerre/teil2.tex \ - papers/laguerre/teil3.tex + papers/laguerre/definition.tex \ + papers/laguerre/eigenschaften.tex \ + papers/laguerre/quadratur.tex \ + papers/laguerre/transformation.tex \ + papers/laguerre/wasserstoff.tex + -- cgit v1.2.1 From b2975538a4f250b286c5bf0fee910ace5deb4887 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 07:02:38 +0100 Subject: nlwave -> parzyl --- buch/papers/common/Makefile.inc | 6 ++-- buch/papers/common/addbibresources.tex | 2 +- buch/papers/common/addpackages.tex | 2 +- buch/papers/common/addpapers.tex | 2 +- buch/papers/common/includes.inc | 4 +-- buch/papers/common/paperlist | 2 +- buch/papers/nlwave/Makefile | 9 ------ buch/papers/nlwave/Makefile.inc | 14 --------- buch/papers/nlwave/main.tex | 36 ---------------------- buch/papers/nlwave/packages.tex | 10 ------- buch/papers/nlwave/references.bib | 35 ---------------------- buch/papers/nlwave/teil0.tex | 22 -------------- buch/papers/nlwave/teil1.tex | 55 ---------------------------------- buch/papers/nlwave/teil2.tex | 40 ------------------------- buch/papers/nlwave/teil3.tex | 40 ------------------------- buch/papers/parzyl/Makefile | 9 ++++++ buch/papers/parzyl/Makefile.inc | 14 +++++++++ buch/papers/parzyl/main.tex | 36 ++++++++++++++++++++++ buch/papers/parzyl/packages.tex | 10 +++++++ buch/papers/parzyl/references.bib | 35 ++++++++++++++++++++++ buch/papers/parzyl/teil0.tex | 22 ++++++++++++++ buch/papers/parzyl/teil1.tex | 55 ++++++++++++++++++++++++++++++++++ buch/papers/parzyl/teil2.tex | 40 +++++++++++++++++++++++++ buch/papers/parzyl/teil3.tex | 40 +++++++++++++++++++++++++ 24 files changed, 270 insertions(+), 270 deletions(-) delete mode 100644 buch/papers/nlwave/Makefile delete mode 100644 buch/papers/nlwave/Makefile.inc delete mode 100644 buch/papers/nlwave/main.tex delete mode 100644 buch/papers/nlwave/packages.tex delete mode 100644 buch/papers/nlwave/references.bib delete mode 100644 buch/papers/nlwave/teil0.tex delete mode 100644 buch/papers/nlwave/teil1.tex delete mode 100644 buch/papers/nlwave/teil2.tex delete mode 100644 buch/papers/nlwave/teil3.tex create mode 100644 buch/papers/parzyl/Makefile create mode 100644 buch/papers/parzyl/Makefile.inc create mode 100644 buch/papers/parzyl/main.tex create mode 100644 buch/papers/parzyl/packages.tex create mode 100644 buch/papers/parzyl/references.bib create mode 100644 buch/papers/parzyl/teil0.tex create mode 100644 buch/papers/parzyl/teil1.tex create mode 100644 buch/papers/parzyl/teil2.tex create mode 100644 buch/papers/parzyl/teil3.tex diff --git a/buch/papers/common/Makefile.inc b/buch/papers/common/Makefile.inc index d32c902..1e699cc 100644 --- a/buch/papers/common/Makefile.inc +++ b/buch/papers/common/Makefile.inc @@ -11,7 +11,7 @@ PAPERFILES = \ papers/000template/main.tex \ papers/lambertw/main.tex \ papers/fm/main.tex \ - papers/nlwave/main.tex \ + papers/parzyl/main.tex \ papers/fresnel/main.tex \ papers/kreismembran/main.tex \ papers/sturmliouville/main.tex \ @@ -99,7 +99,7 @@ PAPER_DIRECTORIES = \ 000template \ lambertw \ fm \ - nlwave \ + parzyl \ fresnel \ kreismembran \ sturmliouville \ @@ -117,7 +117,7 @@ PAPER_MAKEFILEINC = \ papers/000template/Makefile.inc \ papers/lambertw/Makefile.inc \ papers/fm/Makefile.inc \ - papers/nlwave/Makefile.inc \ + papers/parzyl/Makefile.inc \ papers/fresnel/Makefile.inc \ papers/kreismembran/Makefile.inc \ papers/sturmliouville/Makefile.inc \ diff --git a/buch/papers/common/addbibresources.tex b/buch/papers/common/addbibresources.tex index be4802c..0d60231 100644 --- a/buch/papers/common/addbibresources.tex +++ b/buch/papers/common/addbibresources.tex @@ -6,7 +6,7 @@ \addbibresource{papers/000template/references.bib} \addbibresource{papers/lambertw/references.bib} \addbibresource{papers/fm/references.bib} -\addbibresource{papers/nlwave/references.bib} +\addbibresource{papers/parzyl/references.bib} \addbibresource{papers/fresnel/references.bib} \addbibresource{papers/kreismembran/references.bib} \addbibresource{papers/sturmliouville/references.bib} diff --git a/buch/papers/common/addpackages.tex b/buch/papers/common/addpackages.tex index 00e564a..c97ce85 100644 --- a/buch/papers/common/addpackages.tex +++ b/buch/papers/common/addpackages.tex @@ -6,7 +6,7 @@ \input{papers/000template/packages.tex} \input{papers/lambertw/packages.tex} \input{papers/fm/packages.tex} -\input{papers/nlwave/packages.tex} +\input{papers/parzyl/packages.tex} \input{papers/fresnel/packages.tex} \input{papers/kreismembran/packages.tex} \input{papers/sturmliouville/packages.tex} diff --git a/buch/papers/common/addpapers.tex b/buch/papers/common/addpapers.tex index 6327dc3..9e53036 100644 --- a/buch/papers/common/addpapers.tex +++ b/buch/papers/common/addpapers.tex @@ -6,7 +6,7 @@ \input{papers/000template/main.tex} \input{papers/lambertw/main.tex} \input{papers/fm/main.tex} -\input{papers/nlwave/main.tex} +\input{papers/parzyl/main.tex} \input{papers/fresnel/main.tex} \input{papers/kreismembran/main.tex} \input{papers/sturmliouville/main.tex} diff --git a/buch/papers/common/includes.inc b/buch/papers/common/includes.inc index e5b4a63..ad8af23 100644 --- a/buch/papers/common/includes.inc +++ b/buch/papers/common/includes.inc @@ -1,7 +1,7 @@ include papers/000template/Makefile.inc include papers/lambertw/Makefile.inc include papers/fm/Makefile.inc -include papers/nlwave/Makefile.inc +include papers/parzyl/Makefile.inc include papers/fresnel/Makefile.inc include papers/kreismembran/Makefile.inc include papers/sturmliouville/Makefile.inc @@ -19,7 +19,7 @@ TEXFILES = \ $(dependencies-000template) \ $(dependencies-lambertw) \ $(dependencies-fm) \ - $(dependencies-nlwave) \ + $(dependencies-parzyl) \ $(dependencies-fresnel) \ $(dependencies-kreismembran) \ $(dependencies-sturmliouville) \ diff --git a/buch/papers/common/paperlist b/buch/papers/common/paperlist index e2ef4c3..6eab61d 100644 --- a/buch/papers/common/paperlist +++ b/buch/papers/common/paperlist @@ -1,7 +1,7 @@ 000template lambertw fm -nlwave +parzyl fresnel kreismembran sturmliouville diff --git a/buch/papers/nlwave/Makefile b/buch/papers/nlwave/Makefile deleted file mode 100644 index d2c7958..0000000 --- a/buch/papers/nlwave/Makefile +++ /dev/null @@ -1,9 +0,0 @@ -# -# Makefile -- make file for the paper nlwave -# -# (c) 2020 Prof Dr Andreas Mueller -# - -images: - @echo "no images to be created in nlwave" - diff --git a/buch/papers/nlwave/Makefile.inc b/buch/papers/nlwave/Makefile.inc deleted file mode 100644 index e9d59b2..0000000 --- a/buch/papers/nlwave/Makefile.inc +++ /dev/null @@ -1,14 +0,0 @@ -# -# Makefile.inc -- dependencies for this article -# -# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -# -dependencies-nlwave = \ - papers/nlwave/packages.tex \ - papers/nlwave/main.tex \ - papers/nlwave/references.bib \ - papers/nlwave/teil0.tex \ - papers/nlwave/teil1.tex \ - papers/nlwave/teil2.tex \ - papers/nlwave/teil3.tex - diff --git a/buch/papers/nlwave/main.tex b/buch/papers/nlwave/main.tex deleted file mode 100644 index 12fccc2..0000000 --- a/buch/papers/nlwave/main.tex +++ /dev/null @@ -1,36 +0,0 @@ -% -% main.tex -- Paper zum Thema -% -% (c) 2020 Hochschule Rapperswil -% -\chapter{Thema\label{chapter:nlwave}} -\lhead{Thema} -\begin{refsection} -\chapterauthor{Hans Muster} - -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} - -\input{papers/nlwave/teil0.tex} -\input{papers/nlwave/teil1.tex} -\input{papers/nlwave/teil2.tex} -\input{papers/nlwave/teil3.tex} - -\printbibliography[heading=subbibliography] -\end{refsection} diff --git a/buch/papers/nlwave/packages.tex b/buch/papers/nlwave/packages.tex deleted file mode 100644 index 7f5be16..0000000 --- a/buch/papers/nlwave/packages.tex +++ /dev/null @@ -1,10 +0,0 @@ -% -% packages.tex -- packages required by the paper nlwave -% -% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil -% - -% if your paper needs special packages, add package commands as in the -% following example -%\usepackage{packagename} - diff --git a/buch/papers/nlwave/references.bib b/buch/papers/nlwave/references.bib deleted file mode 100644 index 976d046..0000000 --- a/buch/papers/nlwave/references.bib +++ /dev/null @@ -1,35 +0,0 @@ -% -% references.bib -- Bibliography file for the paper nlwave -% -% (c) 2020 Autor, Hochschule Rapperswil -% - -@online{nlwave:bibtex, - title = {BibTeX}, - url = {https://de.wikipedia.org/wiki/BibTeX}, - date = {2020-02-06}, - year = {2020}, - month = {2}, - day = {6} -} - -@book{nlwave:numerical-analysis, - title = {Numerical Analysis}, - author = {David Kincaid and Ward Cheney}, - publisher = {American Mathematical Society}, - year = {2002}, - isbn = {978-8-8218-4788-6}, - inseries = {Pure and applied undegraduate texts}, - volume = {2} -} - -@article{nlwave:mendezmueller, - author = { Tabea Méndez and Andreas Müller }, - title = { Noncommutative harmonic analysis and image registration }, - journal = { Appl. Comput. Harmon. Anal.}, - year = 2019, - volume = 47, - pages = {607--627}, - url = {https://doi.org/10.1016/j.acha.2017.11.004} -} - diff --git a/buch/papers/nlwave/teil0.tex b/buch/papers/nlwave/teil0.tex deleted file mode 100644 index cbbf458..0000000 --- a/buch/papers/nlwave/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{nlwave:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{nlwave:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/nlwave/teil1.tex b/buch/papers/nlwave/teil1.tex deleted file mode 100644 index f64aee9..0000000 --- a/buch/papers/nlwave/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{nlwave:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{nlwave:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{nlwave:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{nlwave:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{nlwave:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/nlwave/teil2.tex b/buch/papers/nlwave/teil2.tex deleted file mode 100644 index b93d8b4..0000000 --- a/buch/papers/nlwave/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{nlwave:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{nlwave:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/nlwave/teil3.tex b/buch/papers/nlwave/teil3.tex deleted file mode 100644 index c28424a..0000000 --- a/buch/papers/nlwave/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{nlwave:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{nlwave:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/parzyl/Makefile b/buch/papers/parzyl/Makefile new file mode 100644 index 0000000..d2c7958 --- /dev/null +++ b/buch/papers/parzyl/Makefile @@ -0,0 +1,9 @@ +# +# Makefile -- make file for the paper nlwave +# +# (c) 2020 Prof Dr Andreas Mueller +# + +images: + @echo "no images to be created in nlwave" + diff --git a/buch/papers/parzyl/Makefile.inc b/buch/papers/parzyl/Makefile.inc new file mode 100644 index 0000000..e9d59b2 --- /dev/null +++ b/buch/papers/parzyl/Makefile.inc @@ -0,0 +1,14 @@ +# +# Makefile.inc -- dependencies for this article +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +dependencies-nlwave = \ + papers/nlwave/packages.tex \ + papers/nlwave/main.tex \ + papers/nlwave/references.bib \ + papers/nlwave/teil0.tex \ + papers/nlwave/teil1.tex \ + papers/nlwave/teil2.tex \ + papers/nlwave/teil3.tex + diff --git a/buch/papers/parzyl/main.tex b/buch/papers/parzyl/main.tex new file mode 100644 index 0000000..12fccc2 --- /dev/null +++ b/buch/papers/parzyl/main.tex @@ -0,0 +1,36 @@ +% +% main.tex -- Paper zum Thema +% +% (c) 2020 Hochschule Rapperswil +% +\chapter{Thema\label{chapter:nlwave}} +\lhead{Thema} +\begin{refsection} +\chapterauthor{Hans Muster} + +Ein paar Hinweise für die korrekte Formatierung des Textes +\begin{itemize} +\item +Absätze werden gebildet, indem man eine Leerzeile einfügt. +Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. +\item +Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende +Optionen werden gelöscht. +Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. +\item +Beginnen Sie jeden Satz auf einer neuen Zeile. +Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen +in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt +anzuwenden. +\item +Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren +Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. +\end{itemize} + +\input{papers/nlwave/teil0.tex} +\input{papers/nlwave/teil1.tex} +\input{papers/nlwave/teil2.tex} +\input{papers/nlwave/teil3.tex} + +\printbibliography[heading=subbibliography] +\end{refsection} diff --git a/buch/papers/parzyl/packages.tex b/buch/papers/parzyl/packages.tex new file mode 100644 index 0000000..7f5be16 --- /dev/null +++ b/buch/papers/parzyl/packages.tex @@ -0,0 +1,10 @@ +% +% packages.tex -- packages required by the paper nlwave +% +% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil +% + +% if your paper needs special packages, add package commands as in the +% following example +%\usepackage{packagename} + diff --git a/buch/papers/parzyl/references.bib b/buch/papers/parzyl/references.bib new file mode 100644 index 0000000..976d046 --- /dev/null +++ b/buch/papers/parzyl/references.bib @@ -0,0 +1,35 @@ +% +% references.bib -- Bibliography file for the paper nlwave +% +% (c) 2020 Autor, Hochschule Rapperswil +% + +@online{nlwave:bibtex, + title = {BibTeX}, + url = {https://de.wikipedia.org/wiki/BibTeX}, + date = {2020-02-06}, + year = {2020}, + month = {2}, + day = {6} +} + +@book{nlwave:numerical-analysis, + title = {Numerical Analysis}, + author = {David Kincaid and Ward Cheney}, + publisher = {American Mathematical Society}, + year = {2002}, + isbn = {978-8-8218-4788-6}, + inseries = {Pure and applied undegraduate texts}, + volume = {2} +} + +@article{nlwave:mendezmueller, + author = { Tabea Méndez and Andreas Müller }, + title = { Noncommutative harmonic analysis and image registration }, + journal = { Appl. Comput. Harmon. Anal.}, + year = 2019, + volume = 47, + pages = {607--627}, + url = {https://doi.org/10.1016/j.acha.2017.11.004} +} + diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex new file mode 100644 index 0000000..cbbf458 --- /dev/null +++ b/buch/papers/parzyl/teil0.tex @@ -0,0 +1,22 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 0\label{nlwave:section:teil0}} +\rhead{Teil 0} +Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +erat, sed diam voluptua \cite{nlwave:bibtex}. +At vero eos et accusam et justo duo dolores et ea rebum. +Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum +dolor sit amet. + +Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +erat, sed diam voluptua. +At vero eos et accusam et justo duo dolores et ea rebum. Stet clita +kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit +amet. + + diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex new file mode 100644 index 0000000..f64aee9 --- /dev/null +++ b/buch/papers/parzyl/teil1.tex @@ -0,0 +1,55 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 1 +\label{nlwave:section:teil1}} +\rhead{Problemstellung} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. +Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +aut fugit, sed quia consequuntur magni dolores eos qui ratione +voluptatem sequi nesciunt +\begin{equation} +\int_a^b x^2\, dx += +\left[ \frac13 x^3 \right]_a^b += +\frac{b^3-a^3}3. +\label{nlwave:equation1} +\end{equation} +Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +consectetur, adipisci velit, sed quia non numquam eius modi tempora +incidunt ut labore et dolore magnam aliquam quaerat voluptatem. + +Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +Quis autem vel eum iure reprehenderit qui in ea voluptate velit +esse quam nihil molestiae consequatur, vel illum qui dolorem eum +fugiat quo voluptas nulla pariatur? + +\subsection{De finibus bonorum et malorum +\label{nlwave:subsection:finibus}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. + +Et harum quidem rerum facilis est et expedita distinctio +\ref{nlwave:section:loesung}. +Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +impedit quo minus id quod maxime placeat facere possimus, omnis +voluptas assumenda est, omnis dolor repellendus +\ref{nlwave:section:folgerung}. +Temporibus autem quibusdam et aut officiis debitis aut rerum +necessitatibus saepe eveniet ut et voluptates repudiandae sint et +molestiae non recusandae. +Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +voluptatibus maiores alias consequatur aut perferendis doloribus +asperiores repellat. + + diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex new file mode 100644 index 0000000..b93d8b4 --- /dev/null +++ b/buch/papers/parzyl/teil2.tex @@ -0,0 +1,40 @@ +% +% teil2.tex -- Beispiel-File für teil2 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 2 +\label{nlwave:section:teil2}} +\rhead{Teil 2} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +velit, sed quia non numquam eius modi tempora incidunt ut labore +et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +reprehenderit qui in ea voluptate velit esse quam nihil molestiae +consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +pariatur? + +\subsection{De finibus bonorum et malorum +\label{nlwave:subsection:bonorum}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +est et expedita distinctio. Nam libero tempore, cum soluta nobis +est eligendi optio cumque nihil impedit quo minus id quod maxime +placeat facere possimus, omnis voluptas assumenda est, omnis dolor +repellendus. Temporibus autem quibusdam et aut officiis debitis aut +rerum necessitatibus saepe eveniet ut et voluptates repudiandae +sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +sapiente delectus, ut aut reiciendis voluptatibus maiores alias +consequatur aut perferendis doloribus asperiores repellat. + + diff --git a/buch/papers/parzyl/teil3.tex b/buch/papers/parzyl/teil3.tex new file mode 100644 index 0000000..c28424a --- /dev/null +++ b/buch/papers/parzyl/teil3.tex @@ -0,0 +1,40 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 3 +\label{nlwave:section:teil3}} +\rhead{Teil 3} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +velit, sed quia non numquam eius modi tempora incidunt ut labore +et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +reprehenderit qui in ea voluptate velit esse quam nihil molestiae +consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +pariatur? + +\subsection{De finibus bonorum et malorum +\label{nlwave:subsection:malorum}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +est et expedita distinctio. Nam libero tempore, cum soluta nobis +est eligendi optio cumque nihil impedit quo minus id quod maxime +placeat facere possimus, omnis voluptas assumenda est, omnis dolor +repellendus. Temporibus autem quibusdam et aut officiis debitis aut +rerum necessitatibus saepe eveniet ut et voluptates repudiandae +sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +sapiente delectus, ut aut reiciendis voluptatibus maiores alias +consequatur aut perferendis doloribus asperiores repellat. + + -- cgit v1.2.1 From 1caf2628298cf35f88025d348954efa6243a8a34 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 07:42:33 +0100 Subject: fix cover --- buch/common/teilnehmer.tex | 16 ++++++++-------- buch/papers/parzyl/Makefile | 4 ++-- buch/papers/parzyl/Makefile.inc | 16 ++++++++-------- buch/papers/parzyl/main.tex | 12 ++++++------ buch/papers/parzyl/packages.tex | 2 +- buch/papers/parzyl/references.bib | 8 ++++---- buch/papers/parzyl/teil0.tex | 4 ++-- buch/papers/parzyl/teil1.tex | 10 +++++----- buch/papers/parzyl/teil2.tex | 4 ++-- buch/papers/parzyl/teil3.tex | 4 ++-- cover/backcover.jpg | Bin 903962 -> 803111 bytes cover/backcover.png | Bin 858440 -> 866099 bytes cover/buchcover.jpg | Bin 1182986 -> 1085847 bytes cover/buchcover.png | Bin 1606730 -> 1616028 bytes cover/buchcover.tex | 16 ++++++++-------- 15 files changed, 48 insertions(+), 48 deletions(-) diff --git a/buch/common/teilnehmer.tex b/buch/common/teilnehmer.tex index c8a28fc..ec6e915 100644 --- a/buch/common/teilnehmer.tex +++ b/buch/common/teilnehmer.tex @@ -4,21 +4,21 @@ % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % Joshua Bär, % E -Selvin Blöchlinger, % E +%Selvin Blöchlinger, % E Marc Benz, % MSE -Manuel Cattaneo%, % MSE -\\ +Manuel Cattaneo, % MSE Fabian Dünki, % E -Robin Eberle, % E +\\ +%Robin Eberle, % E Enez Erdem, % B -Nilakshan Eswararajah%, % B +Nilakshan Eswararajah, % B +Réde Hadouche%, % E \\ -Réde Hadouche, % E David Hugentobler, % E Alain Keller, % E -Yanik Kuster%, % E +Yanik Kuster, % E +Marc Kühne%, % B \\ -Marc Kühne, % B Erik Löffler, % E Kevin Meili, % M-I Andrea Mozzini Vellen%, % E diff --git a/buch/papers/parzyl/Makefile b/buch/papers/parzyl/Makefile index d2c7958..3578f26 100644 --- a/buch/papers/parzyl/Makefile +++ b/buch/papers/parzyl/Makefile @@ -1,9 +1,9 @@ # -# Makefile -- make file for the paper nlwave +# Makefile -- make file for the paper parzyl # # (c) 2020 Prof Dr Andreas Mueller # images: - @echo "no images to be created in nlwave" + @echo "no images to be created in parzyl" diff --git a/buch/papers/parzyl/Makefile.inc b/buch/papers/parzyl/Makefile.inc index e9d59b2..fc182e1 100644 --- a/buch/papers/parzyl/Makefile.inc +++ b/buch/papers/parzyl/Makefile.inc @@ -3,12 +3,12 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -dependencies-nlwave = \ - papers/nlwave/packages.tex \ - papers/nlwave/main.tex \ - papers/nlwave/references.bib \ - papers/nlwave/teil0.tex \ - papers/nlwave/teil1.tex \ - papers/nlwave/teil2.tex \ - papers/nlwave/teil3.tex +dependencies-parzyl = \ + papers/parzyl/packages.tex \ + papers/parzyl/main.tex \ + papers/parzyl/references.bib \ + papers/parzyl/teil0.tex \ + papers/parzyl/teil1.tex \ + papers/parzyl/teil2.tex \ + papers/parzyl/teil3.tex diff --git a/buch/papers/parzyl/main.tex b/buch/papers/parzyl/main.tex index 12fccc2..250d170 100644 --- a/buch/papers/parzyl/main.tex +++ b/buch/papers/parzyl/main.tex @@ -1,9 +1,9 @@ % -% main.tex -- Paper zum Thema +% main.tex -- Paper zum Thema % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:nlwave}} +\chapter{Thema\label{chapter:parzyl}} \lhead{Thema} \begin{refsection} \chapterauthor{Hans Muster} @@ -27,10 +27,10 @@ Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. \end{itemize} -\input{papers/nlwave/teil0.tex} -\input{papers/nlwave/teil1.tex} -\input{papers/nlwave/teil2.tex} -\input{papers/nlwave/teil3.tex} +\input{papers/parzyl/teil0.tex} +\input{papers/parzyl/teil1.tex} +\input{papers/parzyl/teil2.tex} +\input{papers/parzyl/teil3.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/parzyl/packages.tex b/buch/papers/parzyl/packages.tex index 7f5be16..f6844a6 100644 --- a/buch/papers/parzyl/packages.tex +++ b/buch/papers/parzyl/packages.tex @@ -1,5 +1,5 @@ % -% packages.tex -- packages required by the paper nlwave +% packages.tex -- packages required by the paper parzyl % % (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil % diff --git a/buch/papers/parzyl/references.bib b/buch/papers/parzyl/references.bib index 976d046..494ff7c 100644 --- a/buch/papers/parzyl/references.bib +++ b/buch/papers/parzyl/references.bib @@ -1,10 +1,10 @@ % -% references.bib -- Bibliography file for the paper nlwave +% references.bib -- Bibliography file for the paper parzyl % % (c) 2020 Autor, Hochschule Rapperswil % -@online{nlwave:bibtex, +@online{parzyl:bibtex, title = {BibTeX}, url = {https://de.wikipedia.org/wiki/BibTeX}, date = {2020-02-06}, @@ -13,7 +13,7 @@ day = {6} } -@book{nlwave:numerical-analysis, +@book{parzyl:numerical-analysis, title = {Numerical Analysis}, author = {David Kincaid and Ward Cheney}, publisher = {American Mathematical Society}, @@ -23,7 +23,7 @@ volume = {2} } -@article{nlwave:mendezmueller, +@article{parzyl:mendezmueller, author = { Tabea Méndez and Andreas Müller }, title = { Noncommutative harmonic analysis and image registration }, journal = { Appl. Comput. Harmon. Anal.}, diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index cbbf458..09b4024 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -3,11 +3,11 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{nlwave:section:teil0}} +\section{Teil 0\label{parzyl:section:teil0}} \rhead{Teil 0} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{nlwave:bibtex}. +erat, sed diam voluptua \cite{parzyl:bibtex}. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex index f64aee9..9ea60e2 100644 --- a/buch/papers/parzyl/teil1.tex +++ b/buch/papers/parzyl/teil1.tex @@ -4,7 +4,7 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Teil 1 -\label{nlwave:section:teil1}} +\label{parzyl:section:teil1}} \rhead{Problemstellung} Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa @@ -19,7 +19,7 @@ voluptatem sequi nesciunt \left[ \frac13 x^3 \right]_a^b = \frac{b^3-a^3}3. -\label{nlwave:equation1} +\label{parzyl:equation1} \end{equation} Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit, sed quia non numquam eius modi tempora @@ -32,7 +32,7 @@ esse quam nihil molestiae consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla pariatur? \subsection{De finibus bonorum et malorum -\label{nlwave:subsection:finibus}} +\label{parzyl:subsection:finibus}} At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non @@ -40,11 +40,11 @@ provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. Et harum quidem rerum facilis est et expedita distinctio -\ref{nlwave:section:loesung}. +\ref{parzyl:section:loesung}. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus -\ref{nlwave:section:folgerung}. +\ref{parzyl:section:folgerung}. Temporibus autem quibusdam et aut officiis debitis aut rerum necessitatibus saepe eveniet ut et voluptates repudiandae sint et molestiae non recusandae. diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex index b93d8b4..75ba259 100644 --- a/buch/papers/parzyl/teil2.tex +++ b/buch/papers/parzyl/teil2.tex @@ -4,7 +4,7 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Teil 2 -\label{nlwave:section:teil2}} +\label{parzyl:section:teil2}} \rhead{Teil 2} Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa @@ -22,7 +22,7 @@ consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla pariatur? \subsection{De finibus bonorum et malorum -\label{nlwave:subsection:bonorum}} +\label{parzyl:subsection:bonorum}} At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non diff --git a/buch/papers/parzyl/teil3.tex b/buch/papers/parzyl/teil3.tex index c28424a..72c23ca 100644 --- a/buch/papers/parzyl/teil3.tex +++ b/buch/papers/parzyl/teil3.tex @@ -4,7 +4,7 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Teil 3 -\label{nlwave:section:teil3}} +\label{parzyl:section:teil3}} \rhead{Teil 3} Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa @@ -22,7 +22,7 @@ consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla pariatur? \subsection{De finibus bonorum et malorum -\label{nlwave:subsection:malorum}} +\label{parzyl:subsection:malorum}} At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non diff --git a/cover/backcover.jpg b/cover/backcover.jpg index fbde01f..acb8678 100644 Binary files a/cover/backcover.jpg and b/cover/backcover.jpg differ diff --git a/cover/backcover.png b/cover/backcover.png index 741d5a7..514e4fb 100644 Binary files a/cover/backcover.png and b/cover/backcover.png differ diff --git a/cover/buchcover.jpg b/cover/buchcover.jpg index f941169..d9beff9 100644 Binary files a/cover/buchcover.jpg and b/cover/buchcover.jpg differ diff --git a/cover/buchcover.png b/cover/buchcover.png index 994f1ac..a787c91 100644 Binary files a/cover/buchcover.png and b/cover/buchcover.png differ diff --git a/cover/buchcover.tex b/cover/buchcover.tex index 0afcd01..49519af 100644 --- a/cover/buchcover.tex +++ b/cover/buchcover.tex @@ -76,36 +76,36 @@ {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont Joshua Bär, % E - Selvin Blöchlinger, % E + %Selvin Blöchlinger, % E Marc Benz, % MSE - Manuel Cattaneo%, % MSE + Manuel Cattaneo, % MSE + Fabian Dünki%, % E }}; \node at ({\einschlag+2*\gelenk+\ruecken+1.5*\breite},17.75) [color=white,scale=1] {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont - Fabian Dünki, % E - Robin Eberle, % E + %Robin Eberle, % E Enez Erdem, % B - Nilakshan Eswararajah%, % B + Nilakshan Eswararajah, % B + Réda Haddouche%, % E }}; \node at ({\einschlag+2*\gelenk+\ruecken+1.5*\breite},17.1) [color=white,scale=1] {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont - Réda Hadouche, % E David Hugentobler, % E Alain Keller, % E - Yanik Kuster%, % E + Yanik Kuster, % E + Marc Kühne%, % B }}; \node at ({\einschlag+2*\gelenk+\ruecken+1.5*\breite},16.45) [color=white,scale=1] {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont - Marc Kühne, % B Erik Löffler, % E Kevin Meili, % M-I Andrea Mozzini Vellen%, % E -- cgit v1.2.1 From c33458fa86e17af60065df9d973e17e07dba1039 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 07:46:14 +0100 Subject: Korrekturen Teilnehmerliste --- buch/common/teilnehmer.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/common/teilnehmer.tex b/buch/common/teilnehmer.tex index ec6e915..c14790a 100644 --- a/buch/common/teilnehmer.tex +++ b/buch/common/teilnehmer.tex @@ -7,12 +7,12 @@ Joshua Bär, % E %Selvin Blöchlinger, % E Marc Benz, % MSE Manuel Cattaneo, % MSE -Fabian Dünki, % E +Fabian Dünki%, % E \\ %Robin Eberle, % E Enez Erdem, % B Nilakshan Eswararajah, % B -Réde Hadouche%, % E +Réda Haddouche%, % E \\ David Hugentobler, % E Alain Keller, % E -- cgit v1.2.1 From 689d22c8c63b3e9d9735e08882d1bd9425c28f6e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 08:08:06 +0100 Subject: fix cover --- cover/backcover.jpg | Bin 803111 -> 903962 bytes cover/backcover.png | Bin 866099 -> 858440 bytes cover/buchcover.jpg | Bin 1085847 -> 1160870 bytes cover/buchcover.png | Bin 1616028 -> 1604134 bytes 4 files changed, 0 insertions(+), 0 deletions(-) diff --git a/cover/backcover.jpg b/cover/backcover.jpg index acb8678..fbde01f 100644 Binary files a/cover/backcover.jpg and b/cover/backcover.jpg differ diff --git a/cover/backcover.png b/cover/backcover.png index 514e4fb..6425910 100644 Binary files a/cover/backcover.png and b/cover/backcover.png differ diff --git a/cover/buchcover.jpg b/cover/buchcover.jpg index d9beff9..52d17d1 100644 Binary files a/cover/buchcover.jpg and b/cover/buchcover.jpg differ diff --git a/cover/buchcover.png b/cover/buchcover.png index a787c91..1fbf03a 100644 Binary files a/cover/buchcover.png and b/cover/buchcover.png differ -- cgit v1.2.1 From e24dd73e5b6fdc4d23781b45f5cfa5de964e4df3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 08:13:15 +0100 Subject: fix buchcover --- cover/Makefile | 2 ++ cover/buchcover.png | Bin 1604134 -> 1604134 bytes 2 files changed, 2 insertions(+) diff --git a/cover/Makefile b/cover/Makefile index 128e5a3..34ca109 100644 --- a/cover/Makefile +++ b/cover/Makefile @@ -13,6 +13,8 @@ buchcover.png: buchcover.pdf Makefile buchcover.png buchcover.jpg: buchcover.png convert buchcover.png buchcover.jpg +buchcover-small.jpg: buchcover.jpg + convert buchcover.jpg -scale 50% buchcover-small.jpg backcover.png: buchcover.pdf Makefile convert -density 300 -extract 2054x2900+192+190 buchcover.pdf \ backcover.png diff --git a/cover/buchcover.png b/cover/buchcover.png index 1fbf03a..02590e0 100644 Binary files a/cover/buchcover.png and b/cover/buchcover.png differ -- cgit v1.2.1 From ed0a70c80e7a8c9915f53edbfeb4daf19e030dd8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 16:27:37 +0100 Subject: add some theory --- buch/papers/common/Makefile.inc | 7 + buch/papers/common/addbibresources.tex | 1 + buch/papers/common/addpackages.tex | 1 + buch/papers/common/addpapers.tex | 1 + buch/papers/common/includes.inc | 2 + buch/papers/common/paperlist | 1 + buch/papers/dreieck/Makefile | 9 ++ buch/papers/dreieck/Makefile.inc | 14 ++ buch/papers/dreieck/main.tex | 26 ++++ buch/papers/dreieck/packages.tex | 10 ++ buch/papers/dreieck/references.bib | 35 +++++ buch/papers/dreieck/teil0.tex | 9 ++ buch/papers/dreieck/teil1.tex | 261 +++++++++++++++++++++++++++++++++ buch/papers/dreieck/teil2.tex | 9 ++ buch/papers/dreieck/teil3.tex | 10 ++ 15 files changed, 396 insertions(+) create mode 100644 buch/papers/dreieck/Makefile create mode 100644 buch/papers/dreieck/Makefile.inc create mode 100644 buch/papers/dreieck/main.tex create mode 100644 buch/papers/dreieck/packages.tex create mode 100644 buch/papers/dreieck/references.bib create mode 100644 buch/papers/dreieck/teil0.tex create mode 100644 buch/papers/dreieck/teil1.tex create mode 100644 buch/papers/dreieck/teil2.tex create mode 100644 buch/papers/dreieck/teil3.tex diff --git a/buch/papers/common/Makefile.inc b/buch/papers/common/Makefile.inc index 1e699cc..eb8b8a7 100644 --- a/buch/papers/common/Makefile.inc +++ b/buch/papers/common/Makefile.inc @@ -24,6 +24,7 @@ PAPERFILES = \ papers/kugel/main.tex \ papers/hermite/main.tex \ papers/ellfilter/main.tex \ + papers/dreieck/main.tex \ buch1-blx.bbl: buch1-blx.aux bibtex buch1-blx @@ -76,6 +77,9 @@ buch16-blx.bbl: buch16-blx.aux buch17-blx.bbl: buch17-blx.aux bibtex buch17-blx +buch18-blx.bbl: buch18-blx.aux + bibtex buch18-blx + BLXFILES = buch.bbl \ buch1-blx.bbl \ buch2-blx.bbl \ @@ -94,6 +98,7 @@ BLXFILES = buch.bbl \ buch15-blx.bbl \ buch16-blx.bbl \ buch17-blx.bbl \ + buch18-blx.bbl \ PAPER_DIRECTORIES = \ 000template \ @@ -112,6 +117,7 @@ PAPER_DIRECTORIES = \ kugel \ hermite \ ellfilter \ + dreieck \ PAPER_MAKEFILEINC = \ papers/000template/Makefile.inc \ @@ -130,4 +136,5 @@ PAPER_MAKEFILEINC = \ papers/kugel/Makefile.inc \ papers/hermite/Makefile.inc \ papers/ellfilter/Makefile.inc \ + papers/dreieck/Makefile.inc \ diff --git a/buch/papers/common/addbibresources.tex b/buch/papers/common/addbibresources.tex index 0d60231..6e354b5 100644 --- a/buch/papers/common/addbibresources.tex +++ b/buch/papers/common/addbibresources.tex @@ -19,3 +19,4 @@ \addbibresource{papers/kugel/references.bib} \addbibresource{papers/hermite/references.bib} \addbibresource{papers/ellfilter/references.bib} +\addbibresource{papers/dreieck/references.bib} diff --git a/buch/papers/common/addpackages.tex b/buch/papers/common/addpackages.tex index c97ce85..31f7455 100644 --- a/buch/papers/common/addpackages.tex +++ b/buch/papers/common/addpackages.tex @@ -19,3 +19,4 @@ \input{papers/kugel/packages.tex} \input{papers/hermite/packages.tex} \input{papers/ellfilter/packages.tex} +\input{papers/dreieck/packages.tex} diff --git a/buch/papers/common/addpapers.tex b/buch/papers/common/addpapers.tex index 9e53036..dd2b07a 100644 --- a/buch/papers/common/addpapers.tex +++ b/buch/papers/common/addpapers.tex @@ -19,3 +19,4 @@ \input{papers/kugel/main.tex} \input{papers/hermite/main.tex} \input{papers/ellfilter/main.tex} +\input{papers/dreieck/main.tex} diff --git a/buch/papers/common/includes.inc b/buch/papers/common/includes.inc index ad8af23..3e064d9 100644 --- a/buch/papers/common/includes.inc +++ b/buch/papers/common/includes.inc @@ -14,6 +14,7 @@ include papers/kra/Makefile.inc include papers/kugel/Makefile.inc include papers/hermite/Makefile.inc include papers/ellfilter/Makefile.inc +include papers/dreieck/Makefile.inc TEXFILES = \ $(dependencies-000template) \ @@ -32,4 +33,5 @@ TEXFILES = \ $(dependencies-kugel) \ $(dependencies-hermite) \ $(dependencies-ellfilter) \ + $(dependencies-dreieck) \ diff --git a/buch/papers/common/paperlist b/buch/papers/common/paperlist index 6eab61d..d4e5c20 100644 --- a/buch/papers/common/paperlist +++ b/buch/papers/common/paperlist @@ -14,3 +14,4 @@ kra kugel hermite ellfilter +dreieck diff --git a/buch/papers/dreieck/Makefile b/buch/papers/dreieck/Makefile new file mode 100644 index 0000000..f0cb602 --- /dev/null +++ b/buch/papers/dreieck/Makefile @@ -0,0 +1,9 @@ +# +# Makefile -- make file for the paper dreieck +# +# (c) 2020 Prof Dr Andreas Mueller +# + +images: + @echo "no images to be created in dreieck" + diff --git a/buch/papers/dreieck/Makefile.inc b/buch/papers/dreieck/Makefile.inc new file mode 100644 index 0000000..843da8d --- /dev/null +++ b/buch/papers/dreieck/Makefile.inc @@ -0,0 +1,14 @@ +# +# Makefile.inc -- dependencies for this article +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +dependencies-dreieck = \ + papers/dreieck/packages.tex \ + papers/dreieck/main.tex \ + papers/dreieck/references.bib \ + papers/dreieck/teil0.tex \ + papers/dreieck/teil1.tex \ + papers/dreieck/teil2.tex \ + papers/dreieck/teil3.tex + diff --git a/buch/papers/dreieck/main.tex b/buch/papers/dreieck/main.tex new file mode 100644 index 0000000..75ba410 --- /dev/null +++ b/buch/papers/dreieck/main.tex @@ -0,0 +1,26 @@ +% +% main.tex -- Paper zum Thema +% +% (c) 2020 Hochschule Rapperswil +% +\chapter{Dreieckstest und Beta-Funktion\label{chapter:dreieck}} +\lhead{Dreieckstest und Beta-Funktion} +\begin{refsection} +\chapterauthor{Andreas Müller} + +\noindent +Mit dem Dreieckstest kann man feststellen, wie gut ein Geruchs- +oder Geschmackstester verschiedene Gerüche oder Geschmäcker +unterscheiden kann. +Seine wahrscheinlichkeitstheoretische Erklärung benötigt die Beta-Funktion, +man kann die Beta-Funktion als durchaus als die mathematische Grundlage +der Weindegustation +bezeichnen. + +\input{papers/dreieck/teil0.tex} +\input{papers/dreieck/teil1.tex} +\input{papers/dreieck/teil2.tex} +\input{papers/dreieck/teil3.tex} + +\printbibliography[heading=subbibliography] +\end{refsection} diff --git a/buch/papers/dreieck/packages.tex b/buch/papers/dreieck/packages.tex new file mode 100644 index 0000000..fd4ebce --- /dev/null +++ b/buch/papers/dreieck/packages.tex @@ -0,0 +1,10 @@ +% +% packages.tex -- packages required by the paper dreieck +% +% (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil +% + +% if your paper needs special packages, add package commands as in the +% following example +%\usepackage{packagename} + diff --git a/buch/papers/dreieck/references.bib b/buch/papers/dreieck/references.bib new file mode 100644 index 0000000..d2bbe08 --- /dev/null +++ b/buch/papers/dreieck/references.bib @@ -0,0 +1,35 @@ +% +% references.bib -- Bibliography file for the paper dreieck +% +% (c) 2020 Autor, Hochschule Rapperswil +% + +@online{dreieck:bibtex, + title = {BibTeX}, + url = {https://de.wikipedia.org/wiki/BibTeX}, + date = {2020-02-06}, + year = {2020}, + month = {2}, + day = {6} +} + +@book{dreieck:numerical-analysis, + title = {Numerical Analysis}, + author = {David Kincaid and Ward Cheney}, + publisher = {American Mathematical Society}, + year = {2002}, + isbn = {978-8-8218-4788-6}, + inseries = {Pure and applied undegraduate texts}, + volume = {2} +} + +@article{dreieck:mendezmueller, + author = { Tabea Méndez and Andreas Müller }, + title = { Noncommutative harmonic analysis and image registration }, + journal = { Appl. Comput. Harmon. Anal.}, + year = 2019, + volume = 47, + pages = {607--627}, + url = {https://doi.org/10.1016/j.acha.2017.11.004} +} + diff --git a/buch/papers/dreieck/teil0.tex b/buch/papers/dreieck/teil0.tex new file mode 100644 index 0000000..bcf2cf8 --- /dev/null +++ b/buch/papers/dreieck/teil0.tex @@ -0,0 +1,9 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Testprinzip\label{dreieck:section:testprinzip}} +\rhead{Testprinzip} + + diff --git a/buch/papers/dreieck/teil1.tex b/buch/papers/dreieck/teil1.tex new file mode 100644 index 0000000..255c5d0 --- /dev/null +++ b/buch/papers/dreieck/teil1.tex @@ -0,0 +1,261 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Ordnungsstatistik und Beta-Funktion +\label{dreieck:section:ordnungsstatistik}} +\rhead{Ordnungsstatistik und Beta-Funktion} +In diesem Abschnitt ist $X$ eine Zufallsvariable mit der Verteilungsfunktion +$F_X(x)$, und $X_i$, $1\le i\le n$ sei ein Stichprobe von unabhängigen +Zufallsvariablen, die wie $X$ verteilt sind. +Ziel ist, die Verteilungsfunktion und die Wahrscheinlichkeitsdichte +des grössten, zweitgrössten, $k$-t-grössten Wertes in der Stichprobe +zu finden. + +\subsection{Verteilung von $\operatorname{max}(X_1,\dots,X_n)$ und +$\operatorname{min}(X_1,\dots,X_n)$ +\label{dreieck:subsection:minmax}} +Die Verteilungsfunktion von $\operatorname{max}(X_1,\dots,X_n)$ hat +den Wert +\begin{align*} +F_{\operatorname{max}(X_1,\dots,X_n)}(x) +&= +P(\operatorname{max}(X_1,\dots,X_n) \le x) +\\ +&= +P(X_1\le x\wedge \dots \wedge X_n\le x) +\\ +&= +P(X_1\le x) \cdot \ldots \cdot P(X_n\le x) +\\ +&= +P(X\le x)^n += +F_X(x)^n. +\end{align*} +Für die Gleichverteilung ist +\[ +F_{\text{equi}}(x) += +\begin{cases} +0&\qquad x< 0 +\\ +x&\qquad 0\le x\le 1 +\\ +1&\qquad 1 X_1\wedge \dots \wedge x > X_n) +\\ +&= +1- +(1-P(x\le X_1)) \cdot\ldots\cdot (1-P(x\le X_n)) +\\ +&= +1-(1-F_X(x))^n, +\end{align*} +Im Speziellen für im Intervall $[0,1]$ gleichverteilte $X_i$ ist die +Verteilungsfunktion des Minimums +\[ +F_{\operatorname{min}(X_1,\dots,X_n)}(x) += +\begin{cases} +0 &\qquad x<0 \\ +1-(1-x)^n&\qquad 0\le x\le 1\\ +1 &\qquad 1 < x +\end{cases} +\] +mit Wahrscheinlichkeitsdichte +\[ +\varphi_{\operatorname{min}(X_1,\dots,X_n)} += +\frac{d}{dx} +F_{\operatorname{min}(X_1,\dots,X_n)} += +\begin{cases} +n(1-x)^{n-1}&\qquad 0\le x\le 1\\ +0 &\qquad \text{sonst} +\end{cases} +\] +und Erwartungswert +\begin{align*} +E(\operatorname{min}(X_1,\dots,X_n) +&= +\int_{-\infty}^\infty x\varphi_{\operatorname{min}(X_1,\dots,X_n)}(x)\,dx += +\int_0^1 x\cdot n(1-x)^{n-1}\,dx +\\ +&= +\bigl[ -x(1-x)^n \bigr]_0^1 + \int_0^1 (1-x)^n\,dx += +\biggl[ +- +\frac{1}{n+1} +(1-x)^{n+1} +\biggr]_0^1 += +\frac{1}{n+1}. +\end{align*} +Es ergibt sich daraus als natürlich Verallgemeinerung die Frage nach +der Verteilung des zweitegrössten oder zweitkleinsten Wertes unter den +Werten $X_i$. + +\subsection{Der $k$-t-grösste Wert} +Sie wieder $X_i$ eine Stichprobe von $n$ unabhängigen wie $X$ verteilten +Zufallsvariablen. +Diese werden jetzt der Grösse nach sortiert, die sortierten Werte werden +mit +\[ +X_{1:n} \le X_{2:n} \le \dots \le X_{(n-1):n} \le X_{n:n} +\] +bezeichnet. +Die Grössen $X_{k:n}$ sind Zufallsvariablen, sie heissen die $k$-ten +Ordnungsstatistiken. +Die in Abschnitt~\ref{dreieck:subsection:minmax} behandelten Zufallsvariablen +$\operatorname{min}(X_1,\dots,X_n)$ +und +$\operatorname{max}(X_1,\dots,X_n)$ +sind die Fälle +\begin{align*} +X_{1:n} &= \operatorname{min}(X_1,\dots,X_n) \\ +X_{n:n} &= \operatorname{max}(X_1,\dots,X_n). +\end{align*} + +Um den Wert der Verteilungsfunktion von $X_{k:n}$ zu berechnen, müssen wir +die Wahrscheinlichkeit bestimmen, dass $k$ der $n$ Werte $X_i$ $x$ nicht +übersteigen. +Es muss also eine Partition von $[n]=\{1,\dots,n\}$ in eine +$k$-elementige $I=\{i_1,\dots,i_k\}$ Teilmenge und ihre +$(n-k)$-elementige Komplementmenge $[n]\setminus I$ geben +derart, dass die $X_{i} \le x$ sind für $i\in I$ und $X_{j}> x$ für +$j\in [n]\setminus I$. +Daraus kann man ablesen, dass +\begin{align*} +F_{X_{k:n}}(x) +&= +P\biggl( +\bigvee_{I\subset[n]\wedge |I|=k} +\bigwedge_{i\in I} (X_i\le x) +\wedge +\bigwedge_{j\in [n]\setminus I} (X_i > x) +\biggr). +\intertext{Da die verschiedenen $k$-elementigen Teilmengen $I\subset[n]$ +zu disjunkten Ereignissen gehören, ist die Wahrscheinlichkeit eine Summe} +&= +\sum_{I\subset[n]\wedge |I|=k} +P\biggl( +\bigwedge_{i\in I} (X_i\le x) +\wedge +\bigwedge_{j\in [n]\setminus I} (X_i > x) +\biggr) +\\ +&= +\sum_{I\subset[n]\wedge |I|=k} +\prod_{i\in I} +P(X_i\le x) +\cdot +\prod_{j\in [n]\setminus I} +P(X_j > x) +\\ +&= +\sum_{I\subset[n]\wedge |I|=k} +F_X(x)^k +(1-F_X(x))^{n-k}. +\intertext{Die Anzahl solcher Teilmengen $I$ ist gegeben durch den +Binomialkoeffizienten gebeben, die Verteilungsfunktion ist daher} +F_{X_{k:n}}(x) +&= +\binom{n}{k} +F_X(x)^k +(1-F_X(x))^{n-k}. +\end{align*} +Für im Intervall $[0,1]$ gleichverteilte $X_i$ ist die Verteilungsfunktion +der $k$-ten Ordnungsstatistik +\[ +F_{X_{k:n}}(x) += +\binom{n}{k} x^k(1-x)^{n-k}. +\] +Ihre Ableitung nach $x$ ist die Wahrscheinlichkeitsdichte und damit +wird es jetzt auch möglich, den Erwartungswert zu ermitteln: +\begin{align*} +E(X_{k:n}) +&= +\int_{0}^1 +\underbrace{x\llap{\phantom{\bigg|}}\mathstrut}_{\downarrow} +\underbrace{\frac{d}{dx}\binom{n}{k}x^k(1-x)^{n-k}}_{\uparrow} +\,dx += +\biggl[ +x\binom{n}{k}x^k(1-x)^{n-k} +\biggr]_0^1 +- +\int_0^1 +\binom{n}{k}x^k(1-x)^{n-k} +\,dx +\\ +&= +\binom{n}{k} +\biggl( +0^{n-k} +- +\int_0^1 x^k(1-x)^{n-k}\,dx +\biggr) +\end{align*} + + + + + diff --git a/buch/papers/dreieck/teil2.tex b/buch/papers/dreieck/teil2.tex new file mode 100644 index 0000000..83ea3cb --- /dev/null +++ b/buch/papers/dreieck/teil2.tex @@ -0,0 +1,9 @@ +% +% teil2.tex -- Beispiel-File für teil2 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Wahrscheinlichkeiten im Dreieckstest +\label{dreieck:section:wahrscheinlichkeiten}} +\rhead{Wahrscheinlichkeiten} + diff --git a/buch/papers/dreieck/teil3.tex b/buch/papers/dreieck/teil3.tex new file mode 100644 index 0000000..e2dfd6b --- /dev/null +++ b/buch/papers/dreieck/teil3.tex @@ -0,0 +1,10 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Erweiterungen +\label{dreieck:section:erweiterungen}} +\rhead{Erweiterungen} + + -- cgit v1.2.1 From 3157b81b70673659b27edbd680af7ef5a4485a22 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 8 Mar 2022 16:53:48 +0100 Subject: add new files --- buch/papers/dreieck/images/Makefile | 8 ++++++++ buch/papers/dreieck/images/order.tex | 34 ++++++++++++++++++++++++++++++++++ 2 files changed, 42 insertions(+) create mode 100644 buch/papers/dreieck/images/Makefile create mode 100644 buch/papers/dreieck/images/order.tex diff --git a/buch/papers/dreieck/images/Makefile b/buch/papers/dreieck/images/Makefile new file mode 100644 index 0000000..02be1bb --- /dev/null +++ b/buch/papers/dreieck/images/Makefile @@ -0,0 +1,8 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +order.pdf: order.tex + pdflatex order.tex + diff --git a/buch/papers/dreieck/images/order.tex b/buch/papers/dreieck/images/order.tex new file mode 100644 index 0000000..826f48c --- /dev/null +++ b/buch/papers/dreieck/images/order.tex @@ -0,0 +1,34 @@ +% +% order.tex -- Verteilungsfunktion für Ordnungsstatistik +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{8} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\draw[color=red,line width=1.4pt] ({-0.1/\skala},0) + -- + plot[domain=0:1,samples=100] ({\x},{0.5*\x*\x*\x*\x*\x*\x}) + -- + ({1+0.1/\skala},0.5); + +\draw[color=red,line width=1.4pt] ({-0.1/\skala},0) + -- + plot[domain=0:1,samples=100] ({\x},{0.5*(\x*\x*\x*\x)}) + -- + ({1+0.1/\skala},0.5); + +\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$1$}]; +\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$F(X)$}]; + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1 From 100498089783148753f2862c4dbfba04f110727f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 9 Mar 2022 09:42:50 +0100 Subject: add order statistics graph --- buch/papers/dreieck/images/Makefile | 4 +- buch/papers/dreieck/images/order.m | 79 ++++++++++++++++++++++++++++++++++ buch/papers/dreieck/images/order.pdf | Bin 0 -> 31044 bytes buch/papers/dreieck/images/order.tex | 81 +++++++++++++++++++++++++++++++---- 4 files changed, 155 insertions(+), 9 deletions(-) create mode 100644 buch/papers/dreieck/images/order.m create mode 100644 buch/papers/dreieck/images/order.pdf diff --git a/buch/papers/dreieck/images/Makefile b/buch/papers/dreieck/images/Makefile index 02be1bb..3907d13 100644 --- a/buch/papers/dreieck/images/Makefile +++ b/buch/papers/dreieck/images/Makefile @@ -3,6 +3,8 @@ # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -order.pdf: order.tex +order.pdf: order.tex orderpath.tex pdflatex order.tex +orderpath.tex: order.m + octave order.m diff --git a/buch/papers/dreieck/images/order.m b/buch/papers/dreieck/images/order.m new file mode 100644 index 0000000..d37a258 --- /dev/null +++ b/buch/papers/dreieck/images/order.m @@ -0,0 +1,79 @@ +# +# order.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global N; +N = 10; +global subdivisions; +subdivisions = 100; +global P; +P = 0.5 + +function retval = orderF(p, n, k) + retval = 0; + for i = (k:n) + retval = retval + nchoosek(n,i) * p^i * (1-p)^(n-i); + end +end + +function retval = orderd(p, n, k) + retval = 0; + for i = (k:n) + s = i * p^(i-1) * (1-p)^(n-i); + s = s - p^i * (n-i) * (1-p)^(n-i-1); + retval = retval + nchoosek(n,i) * s; + end +end + +function orderpath(fn, k, name) + fprintf(fn, "\\def\\order%s{\n\t(0,0)", name); + global N; + global subdivisions; + for i = (0:subdivisions) + p = i/subdivisions; + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", + p, orderF(p, N, k)); + end + fprintf(fn, "\n}\n"); +end + +function orderdpath(fn, k, name) + fprintf(fn, "\\def\\orderd%s{\n\t(0,0)", name); + global N; + global subdivisions; + for i = (1:subdivisions-1) + p = i/subdivisions; + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", + p, orderd(p, N, k)); + end + fprintf(fn, "\n\t-- ({1*\\dx},0)"); + fprintf(fn, "\n}\n"); +end + +fn = fopen("orderpath.tex", "w"); +orderpath(fn, 0, "zero"); +orderdpath(fn, 0, "zero"); +orderpath(fn, 1, "one"); +orderdpath(fn, 1, "one"); +orderpath(fn, 2, "two"); +orderdpath(fn, 2, "two"); +orderpath(fn, 3, "three"); +orderdpath(fn, 3, "three"); +orderpath(fn, 4, "four"); +orderdpath(fn, 4, "four"); +orderpath(fn, 5, "five"); +orderdpath(fn, 5, "five"); +orderpath(fn, 6, "six"); +orderdpath(fn, 6, "six"); +orderpath(fn, 7, "seven"); +orderdpath(fn, 7, "seven"); +orderpath(fn, 8, "eight"); +orderdpath(fn, 8, "eight"); +orderpath(fn, 9, "nine"); +orderdpath(fn, 9, "nine"); +orderpath(fn, 10, "ten"); +orderdpath(fn, 10, "ten"); +fclose(fn); + + diff --git a/buch/papers/dreieck/images/order.pdf b/buch/papers/dreieck/images/order.pdf new file mode 100644 index 0000000..6d9c8c0 Binary files /dev/null and b/buch/papers/dreieck/images/order.pdf differ diff --git a/buch/papers/dreieck/images/order.tex b/buch/papers/dreieck/images/order.tex index 826f48c..083f014 100644 --- a/buch/papers/dreieck/images/order.tex +++ b/buch/papers/dreieck/images/order.tex @@ -12,22 +12,87 @@ \usetikzlibrary{arrows,intersections,math} \begin{document} \def\skala{8} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\input{orderpath.tex} \begin{tikzpicture}[>=latex,thick,scale=\skala] -\draw[color=red,line width=1.4pt] ({-0.1/\skala},0) - -- - plot[domain=0:1,samples=100] ({\x},{0.5*\x*\x*\x*\x*\x*\x}) - -- - ({1+0.1/\skala},0.5); +\def\dx{1} +\def\dy{0.5} -\draw[color=red,line width=1.4pt] ({-0.1/\skala},0) +\def\pfad#1#2{ +\draw[color=#2,line width=1.4pt] ({-0.1/\skala},0) -- - plot[domain=0:1,samples=100] ({\x},{0.5*(\x*\x*\x*\x)}) + #1 -- ({1+0.1/\skala},0.5); +} -\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$1$}]; +\pfad{\orderzero}{darkgreen!20} +\pfad{\orderone}{darkgreen!20} +\pfad{\ordertwo}{darkgreen!20} +\pfad{\orderthree}{darkgreen!20} +\pfad{\orderfour}{darkgreen!20} +\pfad{\orderfive}{darkgreen!20} +\pfad{\ordersix}{darkgreen!20} +\pfad{\ordereight}{darkgreen!20} +\pfad{\ordernine}{darkgreen!20} +\pfad{\orderten}{darkgreen!20} +\pfad{\orderseven}{darkgreen} + +\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$x$}]; \draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$F(X)$}]; +\foreach \x in {0,0.2,0.4,0.6,0.8,1}{ + \draw (\x,{-0.1/\skala}) -- (\x,{0.1/\skala}); + \node at (\x,{-0.1/\skala}) [below] {$\x$}; +} +\foreach \y in {0.5,1}{ + \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); + \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; +} + +\node[color=darkgreen] at (0.65,{0.5*\dy}) [above,rotate=55] {$k=7$}; + +\begin{scope}[yshift=-0.7cm] +\def\dy{0.125} + +\def\pfad#1#2{ + \draw[color=#2,line width=1.4pt] ({-0.1/\skala},0) + -- + #1 + -- + ({1+0.1/\skala},0.0); +} + +\begin{scope} +\clip ({-0.1/\skala},{-0.1/\skala}) + rectangle ({1+0.1/\skala},{0.56+0.1/\skala}); +\pfad{\orderdzero}{red!20} +\pfad{\orderdone}{red!20} +\pfad{\orderdtwo}{red!20} +\pfad{\orderdthree}{red!20} +\pfad{\orderdfour}{red!20} +\pfad{\orderdfive}{red!20} +\pfad{\orderdsix}{red!20} +\pfad{\orderdeight}{red!20} +\pfad{\orderdnine}{red!20} +\pfad{\orderdten}{red!20} +\pfad{\orderdseven}{red} +\end{scope} + +\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$x$}]; +\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$\varphi(X)$}]; +\foreach \x in {0,0.2,0.4,0.6,0.8,1}{ + \draw (\x,{-0.1/\skala}) -- (\x,{0.1/\skala}); + \node at (\x,{-0.1/\skala}) [below] {$\x$}; +} +\foreach \y in {1,2,3,4}{ + \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); + \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; +} + +\node[color=red] at (0.67,{2.7*\dy}) [above] {$k=7$}; + +\end{scope} \end{tikzpicture} \end{document} -- cgit v1.2.1 From 293c84dfc5ec8511af15d699ccc9140c8b9b3679 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 9 Mar 2022 11:22:17 +0100 Subject: add sample slides and presentations --- vorlesungen/01_0f1/0f1-handout.tex | 11 ++ vorlesungen/01_0f1/Makefile | 33 +++++ vorlesungen/01_0f1/MathSem-01-0f1.tex | 14 ++ vorlesungen/01_0f1/common.tex | 16 +++ vorlesungen/01_0f1/slides.tex | 6 + vorlesungen/02_parzyl/Makefile | 33 +++++ vorlesungen/02_parzyl/MathSem-02-parzyl.tex | 14 ++ 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create mode 100644 vorlesungen/14_kra/slides.tex create mode 100644 vorlesungen/15_laguerre/Makefile create mode 100644 vorlesungen/15_laguerre/MathSem-15-laguerre.tex create mode 100644 vorlesungen/15_laguerre/common.tex create mode 100644 vorlesungen/15_laguerre/laguerre-handout.tex create mode 100644 vorlesungen/15_laguerre/slides.tex create mode 100644 vorlesungen/16_transfer/Makefile create mode 100644 vorlesungen/16_transfer/MathSem-16-transfer.tex create mode 100644 vorlesungen/16_transfer/common.tex create mode 100644 vorlesungen/16_transfer/slides.tex create mode 100644 vorlesungen/16_transfer/transfer-handout.tex create mode 100644 vorlesungen/17_zeta/Makefile create mode 100644 vorlesungen/17_zeta/MathSem-17-zeta.tex create mode 100644 vorlesungen/17_zeta/common.tex create mode 100644 vorlesungen/17_zeta/slides.tex create mode 100644 vorlesungen/17_zeta/zeta-handout.tex create mode 100644 vorlesungen/slides/0f1/Makefile.inc create mode 100644 vorlesungen/slides/0f1/chapter.tex create mode 100644 vorlesungen/slides/0f1/test.tex create mode 100644 vorlesungen/slides/dreieck/Makefile.inc create mode 100644 vorlesungen/slides/dreieck/chapter.tex create mode 100644 vorlesungen/slides/dreieck/minmax.tex create mode 100644 vorlesungen/slides/dreieck/ordnungsstatistik.tex create mode 100644 vorlesungen/slides/dreieck/stichprobe.tex create mode 100644 vorlesungen/slides/dreieck/test.tex create mode 100644 vorlesungen/slides/ellfilter/Makefile.inc create mode 100644 vorlesungen/slides/ellfilter/chapter.tex create mode 100644 vorlesungen/slides/ellfilter/test.tex create mode 100644 vorlesungen/slides/fm/Makefile.inc create mode 100644 vorlesungen/slides/fm/chapter.tex create mode 100644 vorlesungen/slides/fm/test.tex create mode 100644 vorlesungen/slides/fresnel/Makefile.inc create mode 100644 vorlesungen/slides/fresnel/chapter.tex create mode 100644 vorlesungen/slides/fresnel/test.tex create mode 100644 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vorlesungen/slides/lambertw/test.tex create mode 100644 vorlesungen/slides/nav/Makefile.inc create mode 100644 vorlesungen/slides/nav/chapter.tex create mode 100644 vorlesungen/slides/nav/test.tex create mode 100644 vorlesungen/slides/parzyl/Makefile.inc create mode 100644 vorlesungen/slides/parzyl/chapter.tex create mode 100644 vorlesungen/slides/parzyl/test.tex create mode 100644 vorlesungen/slides/sturmliouville/Makefile.inc create mode 100644 vorlesungen/slides/sturmliouville/chapter.tex create mode 100644 vorlesungen/slides/sturmliouville/test.tex create mode 100644 vorlesungen/slides/transfer/Makefile.inc create mode 100644 vorlesungen/slides/transfer/chapter.tex create mode 100644 vorlesungen/slides/transfer/test.tex create mode 100644 vorlesungen/slides/zeta/Makefile.inc create mode 100644 vorlesungen/slides/zeta/chapter.tex create mode 100644 vorlesungen/slides/zeta/test.tex diff --git a/vorlesungen/01_0f1/0f1-handout.tex b/vorlesungen/01_0f1/0f1-handout.tex new file mode 100644 index 0000000..993f4ec --- /dev/null +++ b/vorlesungen/01_0f1/0f1-handout.tex @@ -0,0 +1,11 @@ +% +% 0f1-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/01_0f1/Makefile b/vorlesungen/01_0f1/Makefile new file mode 100644 index 0000000..054a635 --- /dev/null +++ b/vorlesungen/01_0f1/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- 0f1 +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: 0f1-handout.pdf MathSem-01-0f1.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-01-0f1.pdf: MathSem-01-0f1.tex $(SOURCES) + pdflatex MathSem-01-0f1.tex + +0f1-handout.pdf: 0f1-handout.tex $(SOURCES) + pdflatex 0f1-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-01-0f1.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-01-0f1.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-01-0f1.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-01-0f1.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/01_0f1/MathSem-01-0f1.tex b/vorlesungen/01_0f1/MathSem-01-0f1.tex new file mode 100644 index 0000000..e13603f --- /dev/null +++ b/vorlesungen/01_0f1/MathSem-01-0f1.tex @@ -0,0 +1,14 @@ +% +% MathSem-01-0f1.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/01_0f1/common.tex b/vorlesungen/01_0f1/common.tex new file mode 100644 index 0000000..3c6a194 --- /dev/null +++ b/vorlesungen/01_0f1/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[$\mathstrut_0F_1$]{$\mathstrut_0F_1$} +\author[F.~Dünki]{Fabian Dünki} +\date[]{2.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/01_0f1/slides.tex b/vorlesungen/01_0f1/slides.tex new file mode 100644 index 0000000..d404040 --- /dev/null +++ b/vorlesungen/01_0f1/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- 0f1 +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{0f1/test.tex} diff --git a/vorlesungen/02_parzyl/Makefile b/vorlesungen/02_parzyl/Makefile new file mode 100644 index 0000000..c27b7c9 --- /dev/null +++ b/vorlesungen/02_parzyl/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- parzyl +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: parzyl-handout.pdf MathSem-02-parzyl.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-02-parzyl.pdf: MathSem-02-parzyl.tex $(SOURCES) + pdflatex MathSem-02-parzyl.tex + +parzyl-handout.pdf: parzyl-handout.tex $(SOURCES) + pdflatex parzyl-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-02-parzyl.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-02-parzyl.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-02-parzyl.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-02-parzyl.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/02_parzyl/MathSem-02-parzyl.tex b/vorlesungen/02_parzyl/MathSem-02-parzyl.tex new file mode 100644 index 0000000..4ae611b --- /dev/null +++ b/vorlesungen/02_parzyl/MathSem-02-parzyl.tex @@ -0,0 +1,14 @@ +% +% MathSem-02-parzyl.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/02_parzyl/common.tex b/vorlesungen/02_parzyl/common.tex new file mode 100644 index 0000000..885ea19 --- /dev/null +++ b/vorlesungen/02_parzyl/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[ParZyl]{Parabolische Zylinderfunktionen} +\author[T.~S.~und~A.~K.]{Thierry Schwaller und Alain Keller} +\date[]{2.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/02_parzyl/parzyl-handout.tex b/vorlesungen/02_parzyl/parzyl-handout.tex new file mode 100644 index 0000000..5647a18 --- /dev/null +++ b/vorlesungen/02_parzyl/parzyl-handout.tex @@ -0,0 +1,11 @@ +% +% parzyl-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/02_parzyl/slides.tex b/vorlesungen/02_parzyl/slides.tex new file mode 100644 index 0000000..9258394 --- /dev/null +++ b/vorlesungen/02_parzyl/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- parzyl +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{parzyl/test.tex} diff --git a/vorlesungen/03_lambertw/Makefile b/vorlesungen/03_lambertw/Makefile new file mode 100644 index 0000000..e5ffcf0 --- /dev/null +++ b/vorlesungen/03_lambertw/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- lambertw +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: lambertw-handout.pdf MathSem-03-lambertw.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-03-lambertw.pdf: MathSem-03-lambertw.tex $(SOURCES) + pdflatex MathSem-03-lambertw.tex + +lambertw-handout.pdf: lambertw-handout.tex $(SOURCES) + pdflatex lambertw-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-03-lambertw.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-03-lambertw.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-03-lambertw.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-03-lambertw.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/03_lambertw/MathSem-03-lambertw.tex b/vorlesungen/03_lambertw/MathSem-03-lambertw.tex new file mode 100644 index 0000000..9b88b28 --- /dev/null +++ b/vorlesungen/03_lambertw/MathSem-03-lambertw.tex @@ -0,0 +1,14 @@ +% +% MathSem-03-lambertw.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/03_lambertw/common.tex b/vorlesungen/03_lambertw/common.tex new file mode 100644 index 0000000..23fb4b7 --- /dev/null +++ b/vorlesungen/03_lambertw/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Lambert $W$]{Verfolgungskurven und Lambert $W$-Funktion} +\author[D.~H.~und~Y.~K.]{David Hugentobler und Yanik Kuster} +\date[]{9.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/03_lambertw/lambertw-handout.tex b/vorlesungen/03_lambertw/lambertw-handout.tex new file mode 100644 index 0000000..2dba9a8 --- /dev/null +++ b/vorlesungen/03_lambertw/lambertw-handout.tex @@ -0,0 +1,11 @@ +% +% lambertw-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/03_lambertw/slides.tex b/vorlesungen/03_lambertw/slides.tex new file mode 100644 index 0000000..42113e2 --- /dev/null +++ b/vorlesungen/03_lambertw/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- lambertw +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{lambertw/test.tex} diff --git a/vorlesungen/04_fresnel/Makefile b/vorlesungen/04_fresnel/Makefile new file mode 100644 index 0000000..2b76cd7 --- /dev/null +++ b/vorlesungen/04_fresnel/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- fresnel +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: fresnel-handout.pdf MathSem-04-fresnel.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-04-fresnel.pdf: MathSem-04-fresnel.tex $(SOURCES) + pdflatex MathSem-04-fresnel.tex + +fresnel-handout.pdf: fresnel-handout.tex $(SOURCES) + pdflatex fresnel-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-04-fresnel.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-04-fresnel.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-04-fresnel.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-04-fresnel.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/04_fresnel/MathSem-04-fresnel.tex b/vorlesungen/04_fresnel/MathSem-04-fresnel.tex new file mode 100644 index 0000000..eae6242 --- /dev/null +++ b/vorlesungen/04_fresnel/MathSem-04-fresnel.tex @@ -0,0 +1,14 @@ +% +% MathSem-04-fresnel.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/04_fresnel/common.tex b/vorlesungen/04_fresnel/common.tex new file mode 100644 index 0000000..418b7a5 --- /dev/null +++ b/vorlesungen/04_fresnel/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Klothoide]{Klothoide} +\author[N.~Eswararajah]{Nilakshan Eswararajah} +\date[]{9.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/04_fresnel/fresnel-handout.tex b/vorlesungen/04_fresnel/fresnel-handout.tex new file mode 100644 index 0000000..fc84f67 --- /dev/null +++ b/vorlesungen/04_fresnel/fresnel-handout.tex @@ -0,0 +1,11 @@ +% +% fresnel-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/04_fresnel/slides.tex b/vorlesungen/04_fresnel/slides.tex new file mode 100644 index 0000000..5a7cce2 --- /dev/null +++ b/vorlesungen/04_fresnel/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- fresnel +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{fresnel/test.tex} diff --git a/vorlesungen/05_nav/Makefile b/vorlesungen/05_nav/Makefile new file mode 100644 index 0000000..8cdb5b4 --- /dev/null +++ b/vorlesungen/05_nav/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- nav +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: nav-handout.pdf MathSem-05-nav.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-05-nav.pdf: MathSem-05-nav.tex $(SOURCES) + pdflatex MathSem-05-nav.tex + +nav-handout.pdf: nav-handout.tex $(SOURCES) + pdflatex nav-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-05-nav.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-05-nav.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-05-nav.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-05-nav.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/05_nav/MathSem-05-nav.tex b/vorlesungen/05_nav/MathSem-05-nav.tex new file mode 100644 index 0000000..334865d --- /dev/null +++ b/vorlesungen/05_nav/MathSem-05-nav.tex @@ -0,0 +1,14 @@ +% +% MathSem-05-nav.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/05_nav/common.tex b/vorlesungen/05_nav/common.tex new file mode 100644 index 0000000..7aad073 --- /dev/null +++ b/vorlesungen/05_nav/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Navigation]{Sphärische Navigation} +\author[E.~E.~und~M.~K.]{Enez Erdem und Marc Kühne} +\date[]{16.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/05_nav/nav-handout.tex b/vorlesungen/05_nav/nav-handout.tex new file mode 100644 index 0000000..2cce5fa --- /dev/null +++ b/vorlesungen/05_nav/nav-handout.tex @@ -0,0 +1,11 @@ +% +% nav-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/05_nav/slides.tex b/vorlesungen/05_nav/slides.tex new file mode 100644 index 0000000..d7826b1 --- /dev/null +++ b/vorlesungen/05_nav/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- nav +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{nav/test.tex} diff --git a/vorlesungen/06_fm/Makefile b/vorlesungen/06_fm/Makefile new file mode 100644 index 0000000..12ba284 --- /dev/null +++ b/vorlesungen/06_fm/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- fm +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: fm-handout.pdf MathSem-06-fm.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-06-fm.pdf: MathSem-06-fm.tex $(SOURCES) + pdflatex MathSem-06-fm.tex + +fm-handout.pdf: fm-handout.tex $(SOURCES) + pdflatex fm-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-06-fm.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-06-fm.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-06-fm.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-06-fm.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/06_fm/MathSem-06-fm.tex b/vorlesungen/06_fm/MathSem-06-fm.tex new file mode 100644 index 0000000..6809d78 --- /dev/null +++ b/vorlesungen/06_fm/MathSem-06-fm.tex @@ -0,0 +1,14 @@ +% +% MathSem-06-fm.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/06_fm/common.tex b/vorlesungen/06_fm/common.tex new file mode 100644 index 0000000..525d6fd --- /dev/null +++ b/vorlesungen/06_fm/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[FM]{Frequenzspektrum eines frequenzmodulierten Signals} +\author[Joshua Bär]{Joshua Bär} +\date[]{16.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/06_fm/fm-handout.tex b/vorlesungen/06_fm/fm-handout.tex new file mode 100644 index 0000000..9e5a7c1 --- /dev/null +++ b/vorlesungen/06_fm/fm-handout.tex @@ -0,0 +1,11 @@ +% +% fm-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/06_fm/slides.tex b/vorlesungen/06_fm/slides.tex new file mode 100644 index 0000000..ad92b00 --- /dev/null +++ b/vorlesungen/06_fm/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- fm +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{fm/test.tex} diff --git a/vorlesungen/07_kreismembran/Makefile b/vorlesungen/07_kreismembran/Makefile new file mode 100644 index 0000000..ab1762f --- /dev/null +++ b/vorlesungen/07_kreismembran/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kreismembran +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kreismembran-handout.pdf MathSem-07-kreismembran.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-07-kreismembran.pdf: MathSem-07-kreismembran.tex $(SOURCES) + pdflatex MathSem-07-kreismembran.tex + +kreismembran-handout.pdf: kreismembran-handout.tex $(SOURCES) + pdflatex kreismembran-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-07-kreismembran.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-07-kreismembran.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-07-kreismembran.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-07-kreismembran.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/07_kreismembran/MathSem-07-kreismembran.tex b/vorlesungen/07_kreismembran/MathSem-07-kreismembran.tex new file mode 100644 index 0000000..9f4e524 --- /dev/null +++ b/vorlesungen/07_kreismembran/MathSem-07-kreismembran.tex @@ -0,0 +1,14 @@ +% +% MathSem-07-kreismembran.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/07_kreismembran/common.tex b/vorlesungen/07_kreismembran/common.tex new file mode 100644 index 0000000..7eefaaf --- /dev/null +++ b/vorlesungen/07_kreismembran/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Kreis]{Schwingungen einer kreisförmigen Membran} +\author[A.~M.~V.~und~T.~T.]{Andrea Mozzini Vellen und Tim Tönz} +\date[]{16.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/07_kreismembran/kreismembran-handout.tex b/vorlesungen/07_kreismembran/kreismembran-handout.tex new file mode 100644 index 0000000..03e14fa --- /dev/null +++ b/vorlesungen/07_kreismembran/kreismembran-handout.tex @@ -0,0 +1,11 @@ +% +% kreismembran-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/07_kreismembran/slides.tex b/vorlesungen/07_kreismembran/slides.tex new file mode 100644 index 0000000..be00745 --- /dev/null +++ b/vorlesungen/07_kreismembran/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kreismembran +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kreismembran/test.tex} diff --git a/vorlesungen/08_sturmliouville/Makefile b/vorlesungen/08_sturmliouville/Makefile new file mode 100644 index 0000000..7d777b2 --- /dev/null +++ b/vorlesungen/08_sturmliouville/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- sturmliouville +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: sturmliouville-handout.pdf MathSem-08-sturmliouville.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-08-sturmliouville.pdf: MathSem-08-sturmliouville.tex $(SOURCES) + pdflatex MathSem-08-sturmliouville.tex + +sturmliouville-handout.pdf: sturmliouville-handout.tex $(SOURCES) + pdflatex sturmliouville-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-08-sturmliouville.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-08-sturmliouville.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-08-sturmliouville.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-08-sturmliouville.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/08_sturmliouville/MathSem-08-sturmliouville.tex b/vorlesungen/08_sturmliouville/MathSem-08-sturmliouville.tex new file mode 100644 index 0000000..ce26b7f --- /dev/null +++ b/vorlesungen/08_sturmliouville/MathSem-08-sturmliouville.tex @@ -0,0 +1,14 @@ +% +% MathSem-08-sturmliouville.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/08_sturmliouville/common.tex b/vorlesungen/08_sturmliouville/common.tex new file mode 100644 index 0000000..d0021eb --- /dev/null +++ b/vorlesungen/08_sturmliouville/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Titel]{Sturm-Liouville-Problem} +\author[R.~H.~und~E.~L.]{Réda Haddouche und Erik Löffler} +\date[]{23.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/08_sturmliouville/slides.tex b/vorlesungen/08_sturmliouville/slides.tex new file mode 100644 index 0000000..dcb2124 --- /dev/null +++ b/vorlesungen/08_sturmliouville/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- sturmliouville +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{sturmliouville/test.tex} diff --git a/vorlesungen/08_sturmliouville/sturmliouville-handout.tex b/vorlesungen/08_sturmliouville/sturmliouville-handout.tex new file mode 100644 index 0000000..4c8eb03 --- /dev/null +++ b/vorlesungen/08_sturmliouville/sturmliouville-handout.tex @@ -0,0 +1,11 @@ +% +% sturmliouville-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/09_hermite/Makefile b/vorlesungen/09_hermite/Makefile new file mode 100644 index 0000000..4e185e6 --- /dev/null +++ b/vorlesungen/09_hermite/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- hermite +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: hermite-handout.pdf MathSem-09-hermite.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-09-hermite.pdf: MathSem-09-hermite.tex $(SOURCES) + pdflatex MathSem-09-hermite.tex + +hermite-handout.pdf: hermite-handout.tex $(SOURCES) + pdflatex hermite-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-09-hermite.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-09-hermite.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-09-hermite.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-09-hermite.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/09_hermite/MathSem-09-hermite.tex b/vorlesungen/09_hermite/MathSem-09-hermite.tex new file mode 100644 index 0000000..59d9213 --- /dev/null +++ b/vorlesungen/09_hermite/MathSem-09-hermite.tex @@ -0,0 +1,14 @@ +% +% MathSem-09-hermite.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/09_hermite/common.tex b/vorlesungen/09_hermite/common.tex new file mode 100644 index 0000000..a4ee31f --- /dev/null +++ b/vorlesungen/09_hermite/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[QM]{Rodrigues-Formeln und harmonischer Oszillator} +\author[K.~Meili]{Kevin Meili} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/09_hermite/hermite-handout.tex b/vorlesungen/09_hermite/hermite-handout.tex new file mode 100644 index 0000000..65941da --- /dev/null +++ b/vorlesungen/09_hermite/hermite-handout.tex @@ -0,0 +1,11 @@ +% +% hermite-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/09_hermite/slides.tex b/vorlesungen/09_hermite/slides.tex new file mode 100644 index 0000000..d74d191 --- /dev/null +++ b/vorlesungen/09_hermite/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- hermite +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{hermite/test.tex} diff --git a/vorlesungen/10_kugel/Makefile b/vorlesungen/10_kugel/Makefile new file mode 100644 index 0000000..cd35320 --- /dev/null +++ b/vorlesungen/10_kugel/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kugel +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kugel-handout.pdf MathSem-10-kugel.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-10-kugel.pdf: MathSem-10-kugel.tex $(SOURCES) + pdflatex MathSem-10-kugel.tex + +kugel-handout.pdf: kugel-handout.tex $(SOURCES) + pdflatex kugel-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-10-kugel.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-10-kugel.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-10-kugel.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-10-kugel.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/10_kugel/MathSem-10-kugel.tex b/vorlesungen/10_kugel/MathSem-10-kugel.tex new file mode 100644 index 0000000..779ac8f --- /dev/null +++ b/vorlesungen/10_kugel/MathSem-10-kugel.tex @@ -0,0 +1,14 @@ +% +% MathSem-10-kugel.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/10_kugel/common.tex b/vorlesungen/10_kugel/common.tex new file mode 100644 index 0000000..1662568 --- /dev/null +++ b/vorlesungen/10_kugel/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Kugel]{Auf- und Absteigeoperatoren und Kugelfunktionen} +\author[Naoki Pross]{Naoki Pross} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/10_kugel/kugel-handout.tex b/vorlesungen/10_kugel/kugel-handout.tex new file mode 100644 index 0000000..a7973fc --- /dev/null +++ b/vorlesungen/10_kugel/kugel-handout.tex @@ -0,0 +1,11 @@ +% +% kugel-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/10_kugel/slides.tex b/vorlesungen/10_kugel/slides.tex new file mode 100644 index 0000000..885fd87 --- /dev/null +++ b/vorlesungen/10_kugel/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kugel +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kugel/test.tex} diff --git a/vorlesungen/11_kugel2/Makefile b/vorlesungen/11_kugel2/Makefile new file mode 100644 index 0000000..8fd817c --- /dev/null +++ b/vorlesungen/11_kugel2/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kugel2 +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kugel2-handout.pdf MathSem-11-kugel2.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-11-kugel2.pdf: MathSem-11-kugel2.tex $(SOURCES) + pdflatex MathSem-11-kugel2.tex + +kugel2-handout.pdf: kugel2-handout.tex $(SOURCES) + pdflatex kugel2-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-11-kugel2.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-11-kugel2.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-11-kugel2.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-11-kugel2.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/11_kugel2/MathSem-11-kugel2.tex b/vorlesungen/11_kugel2/MathSem-11-kugel2.tex new file mode 100644 index 0000000..a474bb3 --- /dev/null +++ b/vorlesungen/11_kugel2/MathSem-11-kugel2.tex @@ -0,0 +1,14 @@ +% +% MathSem-11-kugel2.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/11_kugel2/common.tex b/vorlesungen/11_kugel2/common.tex new file mode 100644 index 0000000..002e71e --- /dev/null +++ b/vorlesungen/11_kugel2/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Kugel]{Auf- und Absteigeoperatoren und Kugelfunktionen} +\author[M.~Cattaneo]{Manuel Cattaneo} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/11_kugel2/kugel2-handout.tex b/vorlesungen/11_kugel2/kugel2-handout.tex new file mode 100644 index 0000000..cb6664a --- /dev/null +++ b/vorlesungen/11_kugel2/kugel2-handout.tex @@ -0,0 +1,11 @@ +% +% kugel2-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/11_kugel2/slides.tex b/vorlesungen/11_kugel2/slides.tex new file mode 100644 index 0000000..f73034e --- /dev/null +++ b/vorlesungen/11_kugel2/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kugel2 +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kugel/test.tex} diff --git a/vorlesungen/12_dreieck/Makefile b/vorlesungen/12_dreieck/Makefile new file mode 100644 index 0000000..c790f0c --- /dev/null +++ b/vorlesungen/12_dreieck/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- dreieck +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: dreieck-handout.pdf MathSem-12-dreieck.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-12-dreieck.pdf: MathSem-12-dreieck.tex $(SOURCES) + pdflatex MathSem-12-dreieck.tex + +dreieck-handout.pdf: dreieck-handout.tex $(SOURCES) + pdflatex dreieck-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-12-dreieck.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-12-dreieck.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-12-dreieck.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-12-dreieck.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/12_dreieck/MathSem-12-dreieck.tex b/vorlesungen/12_dreieck/MathSem-12-dreieck.tex new file mode 100644 index 0000000..7dbc42a --- /dev/null +++ b/vorlesungen/12_dreieck/MathSem-12-dreieck.tex @@ -0,0 +1,14 @@ +% +% MathSem-12-dreieck.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/12_dreieck/common.tex b/vorlesungen/12_dreieck/common.tex new file mode 100644 index 0000000..9414e42 --- /dev/null +++ b/vorlesungen/12_dreieck/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Dreieckstest]{Dreieckstest} +\author[A.~Müller]{Prof. Dr. Andreas Müller} +\date[]{30.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/12_dreieck/dreieck-handout.tex b/vorlesungen/12_dreieck/dreieck-handout.tex new file mode 100644 index 0000000..010bcef --- /dev/null +++ b/vorlesungen/12_dreieck/dreieck-handout.tex @@ -0,0 +1,11 @@ +% +% dreieck-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/12_dreieck/slides.tex b/vorlesungen/12_dreieck/slides.tex new file mode 100644 index 0000000..211a105 --- /dev/null +++ b/vorlesungen/12_dreieck/slides.tex @@ -0,0 +1,8 @@ +% +% slides.tex -- dreieck +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{dreieck/stichprobe.tex} +\folie{dreieck/minmax.tex} +\folie{dreieck/ordnungsstatistik.tex} diff --git a/vorlesungen/13_ellfilter/Makefile b/vorlesungen/13_ellfilter/Makefile new file mode 100644 index 0000000..dd4395a --- /dev/null +++ b/vorlesungen/13_ellfilter/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- ellfilter +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: ellfilter-handout.pdf MathSem-13-ellfilter.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-13-ellfilter.pdf: MathSem-13-ellfilter.tex $(SOURCES) + pdflatex MathSem-13-ellfilter.tex + +ellfilter-handout.pdf: ellfilter-handout.tex $(SOURCES) + pdflatex ellfilter-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-13-ellfilter.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-13-ellfilter.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-13-ellfilter.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-13-ellfilter.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/13_ellfilter/MathSem-13-ellfilter.tex b/vorlesungen/13_ellfilter/MathSem-13-ellfilter.tex new file mode 100644 index 0000000..82198f9 --- /dev/null +++ b/vorlesungen/13_ellfilter/MathSem-13-ellfilter.tex @@ -0,0 +1,14 @@ +% +% MathSem-13-ellfilter.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/13_ellfilter/common.tex b/vorlesungen/13_ellfilter/common.tex new file mode 100644 index 0000000..7789019 --- /dev/null +++ b/vorlesungen/13_ellfilter/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Filter]{Elliptische Filter} +\author[N.~Tobler]{Nicolas Tobler} +\date[]{3.~Juni 2022} +\newboolean{presentation} + diff --git a/vorlesungen/13_ellfilter/ellfilter-handout.tex b/vorlesungen/13_ellfilter/ellfilter-handout.tex new file mode 100644 index 0000000..c39a956 --- /dev/null +++ b/vorlesungen/13_ellfilter/ellfilter-handout.tex @@ -0,0 +1,11 @@ +% +% ellfilter-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/13_ellfilter/slides.tex b/vorlesungen/13_ellfilter/slides.tex new file mode 100644 index 0000000..44e0388 --- /dev/null +++ b/vorlesungen/13_ellfilter/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- ellfilter +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{ellfilter/test.tex} diff --git a/vorlesungen/14_kra/Makefile b/vorlesungen/14_kra/Makefile new file mode 100644 index 0000000..3bf22af --- /dev/null +++ b/vorlesungen/14_kra/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- kra +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: kra-handout.pdf MathSem-14-kra.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-14-kra.pdf: MathSem-14-kra.tex $(SOURCES) + pdflatex MathSem-14-kra.tex + +kra-handout.pdf: kra-handout.tex $(SOURCES) + pdflatex kra-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-14-kra.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-14-kra.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-14-kra.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-14-kra.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/14_kra/MathSem-14-kra.tex b/vorlesungen/14_kra/MathSem-14-kra.tex new file mode 100644 index 0000000..f6beb19 --- /dev/null +++ b/vorlesungen/14_kra/MathSem-14-kra.tex @@ -0,0 +1,14 @@ +% +% MathSem-14-kra.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/14_kra/common.tex b/vorlesungen/14_kra/common.tex new file mode 100644 index 0000000..0d8d23a --- /dev/null +++ b/vorlesungen/14_kra/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[KRA]{Kalman, Riccati, Abel} +\author[S.~Niederer]{Samuel Niederer} +\date[]{3.~Juni 2022} +\newboolean{presentation} + diff --git a/vorlesungen/14_kra/kra-handout.tex b/vorlesungen/14_kra/kra-handout.tex new file mode 100644 index 0000000..87dc3a6 --- /dev/null +++ b/vorlesungen/14_kra/kra-handout.tex @@ -0,0 +1,11 @@ +% +% kra-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/14_kra/slides.tex b/vorlesungen/14_kra/slides.tex new file mode 100644 index 0000000..bdd1d44 --- /dev/null +++ b/vorlesungen/14_kra/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- kra +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{kra/test.tex} diff --git a/vorlesungen/15_laguerre/Makefile b/vorlesungen/15_laguerre/Makefile new file mode 100644 index 0000000..4dea30b --- /dev/null +++ b/vorlesungen/15_laguerre/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- laguerre +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: laguerre-handout.pdf MathSem-15-laguerre.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-15-laguerre.pdf: MathSem-15-laguerre.tex $(SOURCES) + pdflatex MathSem-15-laguerre.tex + +laguerre-handout.pdf: laguerre-handout.tex $(SOURCES) + pdflatex laguerre-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-15-laguerre.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-15-laguerre.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-15-laguerre.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-15-laguerre.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/15_laguerre/MathSem-15-laguerre.tex b/vorlesungen/15_laguerre/MathSem-15-laguerre.tex new file mode 100644 index 0000000..3c48315 --- /dev/null +++ b/vorlesungen/15_laguerre/MathSem-15-laguerre.tex @@ -0,0 +1,14 @@ +% +% MathSem-15-laguerre.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/15_laguerre/common.tex b/vorlesungen/15_laguerre/common.tex new file mode 100644 index 0000000..5db4f95 --- /dev/null +++ b/vorlesungen/15_laguerre/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Laguerre]{Laguerre Polynome} +\author[P.~Müller]{Patrik Müller} +\date[]{3.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/15_laguerre/laguerre-handout.tex b/vorlesungen/15_laguerre/laguerre-handout.tex new file mode 100644 index 0000000..8ba2101 --- /dev/null +++ b/vorlesungen/15_laguerre/laguerre-handout.tex @@ -0,0 +1,11 @@ +% +% laguerre-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/15_laguerre/slides.tex b/vorlesungen/15_laguerre/slides.tex new file mode 100644 index 0000000..7b6b91b --- /dev/null +++ b/vorlesungen/15_laguerre/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- laguerre +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{laguerre/test.tex} diff --git a/vorlesungen/16_transfer/Makefile b/vorlesungen/16_transfer/Makefile new file mode 100644 index 0000000..bc704e5 --- /dev/null +++ b/vorlesungen/16_transfer/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- transfer +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: transfer-handout.pdf MathSem-16-transfer.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-16-transfer.pdf: MathSem-16-transfer.tex $(SOURCES) + pdflatex MathSem-16-transfer.tex + +transfer-handout.pdf: transfer-handout.tex $(SOURCES) + pdflatex transfer-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-16-transfer.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-16-transfer.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-16-transfer.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-16-transfer.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/16_transfer/MathSem-16-transfer.tex b/vorlesungen/16_transfer/MathSem-16-transfer.tex new file mode 100644 index 0000000..d975f11 --- /dev/null +++ b/vorlesungen/16_transfer/MathSem-16-transfer.tex @@ -0,0 +1,14 @@ +% +% MathSem-16-transfer.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/16_transfer/common.tex b/vorlesungen/16_transfer/common.tex new file mode 100644 index 0000000..61fc97f --- /dev/null +++ b/vorlesungen/16_transfer/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[Transferfunktionen]{Transferfunktionen} +\author[Marc Benz]{Marc Benz} +\date[]{} +\newboolean{presentation} + diff --git a/vorlesungen/16_transfer/slides.tex b/vorlesungen/16_transfer/slides.tex new file mode 100644 index 0000000..bcfeb20 --- /dev/null +++ b/vorlesungen/16_transfer/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- transfer +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{transfer/test.tex} diff --git a/vorlesungen/16_transfer/transfer-handout.tex b/vorlesungen/16_transfer/transfer-handout.tex new file mode 100644 index 0000000..7e48e0b --- /dev/null +++ b/vorlesungen/16_transfer/transfer-handout.tex @@ -0,0 +1,11 @@ +% +% transfer-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/17_zeta/Makefile b/vorlesungen/17_zeta/Makefile new file mode 100644 index 0000000..ca4da07 --- /dev/null +++ b/vorlesungen/17_zeta/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- zeta +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: zeta-handout.pdf MathSem-17-zeta.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-17-zeta.pdf: MathSem-17-zeta.tex $(SOURCES) + pdflatex MathSem-17-zeta.tex + +zeta-handout.pdf: zeta-handout.tex $(SOURCES) + pdflatex zeta-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-17-zeta.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-17-zeta.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-17-zeta.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-17-zeta.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/17_zeta/MathSem-17-zeta.tex b/vorlesungen/17_zeta/MathSem-17-zeta.tex new file mode 100644 index 0000000..aa2d2dc --- /dev/null +++ b/vorlesungen/17_zeta/MathSem-17-zeta.tex @@ -0,0 +1,14 @@ +% +% MathSem-17-zeta.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/17_zeta/common.tex b/vorlesungen/17_zeta/common.tex new file mode 100644 index 0000000..a5571fb --- /dev/null +++ b/vorlesungen/17_zeta/common.tex @@ -0,0 +1,16 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[$\zeta$]{Riemann $\zeta$-Funktion} +\author[R.~Unterer]{Raphael Unterer} +\date[]{3.~Mai 2022} +\newboolean{presentation} + diff --git a/vorlesungen/17_zeta/slides.tex b/vorlesungen/17_zeta/slides.tex new file mode 100644 index 0000000..88ff0e7 --- /dev/null +++ b/vorlesungen/17_zeta/slides.tex @@ -0,0 +1,6 @@ +% +% slides.tex -- XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{zeta/test.tex} diff --git a/vorlesungen/17_zeta/zeta-handout.tex b/vorlesungen/17_zeta/zeta-handout.tex new file mode 100644 index 0000000..73d33cd --- /dev/null +++ b/vorlesungen/17_zeta/zeta-handout.tex @@ -0,0 +1,11 @@ +% +% zeta-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/slides/0f1/Makefile.inc b/vorlesungen/slides/0f1/Makefile.inc new file mode 100644 index 0000000..a37ccfc --- /dev/null +++ b/vorlesungen/slides/0f1/Makefile.inc @@ -0,0 +1,7 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapter0f1 = \ + ../slides/0f1/test.tex diff --git a/vorlesungen/slides/0f1/chapter.tex b/vorlesungen/slides/0f1/chapter.tex new file mode 100644 index 0000000..1dadad6 --- /dev/null +++ b/vorlesungen/slides/0f1/chapter.tex @@ -0,0 +1,6 @@ +% +% chapter.tex -- slides for chapter 0f1 +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{0f1/test.tex} diff --git a/vorlesungen/slides/0f1/test.tex b/vorlesungen/slides/0f1/test.tex new file mode 100644 index 0000000..c212802 --- /dev/null +++ b/vorlesungen/slides/0f1/test.tex @@ -0,0 +1,19 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Template für $\mathstrut_0F_1$} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/Makefile.inc b/vorlesungen/slides/Makefile.inc index 16e3048..dc5a538 100644 --- a/vorlesungen/slides/Makefile.inc +++ b/vorlesungen/slides/Makefile.inc @@ -4,25 +4,41 @@ # (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil # include ../slides/0/Makefile.inc -#include ../slides/1/Makefile.inc -#include ../slides/2/Makefile.inc -#include ../slides/3/Makefile.inc -#include ../slides/4/Makefile.inc -#include ../slides/5/Makefile.inc -#include ../slides/6/Makefile.inc -#include ../slides/7/Makefile.inc -#include ../slides/8/Makefile.inc +include ../slides/0f1/Makefile.inc +include ../slides/dreieck/Makefile.inc +include ../slides/ellfilter/Makefile.inc +include ../slides/fm/Makefile.inc +include ../slides/fresnel/Makefile.inc +include ../slides/hermite/Makefile.inc +include ../slides/kra/Makefile.inc +include ../slides/kreismembran/Makefile.inc +include ../slides/kugel/Makefile.inc +include ../slides/laguerre/Makefile.inc +include ../slides/lambertw/Makefile.inc +include ../slides/nav/Makefile.inc +include ../slides/parzyl/Makefile.inc +include ../slides/sturmliouville/Makefile.inc +include ../slides/transfer/Makefile.inc +include ../slides/zeta/Makefile.inc slides = \ $(chapter0) \ - $(chapter1) \ - $(chapter2) \ - $(chapter3) \ - $(chapter4) \ - $(chapter5) \ - $(chapter6) \ - $(chapter7) \ - $(chapter8) + $(chapter0f1) \ + $(chapterdreieck) \ + $(chapterellfilter) \ + $(chapterfm) \ + $(chapterfresnel) \ + $(chapterhermite) \ + $(chapterkra) \ + $(chapterkreismembran) \ + $(chapterkugel) \ + $(chapterlaguerre) \ + $(chapterlambertw) \ + $(chapternav) \ + $(chapterparzyl) \ + $(chaptersturmliouville) \ + $(chaptertransfer) \ + $(chapterzeta) diff --git a/vorlesungen/slides/dreieck/Makefile.inc b/vorlesungen/slides/dreieck/Makefile.inc new file mode 100644 index 0000000..0575397 --- /dev/null +++ b/vorlesungen/slides/dreieck/Makefile.inc @@ -0,0 +1,9 @@ +# +# Makefile.inc +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +chapterdreieck = \ + ../slides/dreieck/minmax.tex \ + ../slides/dreieck/ordnungsstatistik.tex \ + ../slides/dreieck/test.tex diff --git a/vorlesungen/slides/dreieck/chapter.tex b/vorlesungen/slides/dreieck/chapter.tex new file mode 100644 index 0000000..2c91eb5 --- /dev/null +++ b/vorlesungen/slides/dreieck/chapter.tex @@ -0,0 +1,8 @@ +% +% chapter.tex -- slides for chapter dreieck +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\folie{dreieck/test.tex} +\folie{dreieck/minmax.tex} +\folie{dreieck/ordnungsstatistik.tex} diff --git a/vorlesungen/slides/dreieck/minmax.tex b/vorlesungen/slides/dreieck/minmax.tex new file mode 100644 index 0000000..9ef8d1a --- /dev/null +++ b/vorlesungen/slides/dreieck/minmax.tex @@ -0,0 +1,65 @@ +% +% minmax.tex -- Minimum und Maximum +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Minimum und Maximum} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Maximum} +Verteilungsfunktion von +\[ +Z=\operatorname{max}(X_1,\dots,X_n) +\] +\begin{align*} +F_Z(x) +&= +P(Z\le x) +\\ +&= +P(X_1\le x\wedge\dots\wedge X_n\le x) +\\ +&= +P(X_1\le x)\cdot \ldots\cdot P(X_n\le x) +\\ +&= +F_X(x)^n +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Minimum} +Verteilungsfunktion von +\[ +Z=\operatorname{min}(X_1,\dots,X_n) +\] +\begin{align*} +F_Z(x) +&= +P(Z\le x) +\\ +&=P(\overline{ +X_1\le x\wedge\dots\wedge X_n \le x +}) +\\ +&= +1-P( +X_1> x\wedge\dots\wedge X_n > x +) +\\ +&= +1-(P(X_1>x)\cdot\ldots\cdot P(X_n>x)) +\\ +&= +1-(1-F_X(x))^n +\end{align*} +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/ordnungsstatistik.tex b/vorlesungen/slides/dreieck/ordnungsstatistik.tex new file mode 100644 index 0000000..6346953 --- /dev/null +++ b/vorlesungen/slides/dreieck/ordnungsstatistik.tex @@ -0,0 +1,19 @@ +% +% ordnungsstatistik.tex -- Ordnungsstatistik +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Ordnungstatistik} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\end{column} +\begin{column}{0.48\textwidth} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/stichprobe.tex b/vorlesungen/slides/dreieck/stichprobe.tex new file mode 100644 index 0000000..da3a20e --- /dev/null +++ b/vorlesungen/slides/dreieck/stichprobe.tex @@ -0,0 +1,60 @@ +% +% stichprobe.tex -- Stichprobe +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Stichprobe} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Zufallsvariable} +Gegeben eine Zufallsvariable $X$ mit +Verteilungsfunktion +\[ +F_X(x) += +P(X\le x) +\] +und +Wahrscheinlichkeitsdichte +\[ +\varphi_X(x) += +\frac{d}{dx} F_X(x) +\] +\end{block} +\begin{block}{Gleichverteilung} +\[ +F(x) = \begin{cases} +0&\qquad x<0\\ +x&\qquad 0\le x \le 1\\ +1&\qquad 1 Date: Wed, 9 Mar 2022 12:46:49 +0100 Subject: Name und Titel --- buch/papers/parzyl/main.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/buch/papers/parzyl/main.tex b/buch/papers/parzyl/main.tex index 250d170..ff21c9f 100644 --- a/buch/papers/parzyl/main.tex +++ b/buch/papers/parzyl/main.tex @@ -3,10 +3,10 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:parzyl}} -\lhead{Thema} +\chapter{Parabolische Zylinderfunktionen\label{chapter:parzyl}} +\lhead{Parabolische Zylinderfunktionen} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Thierry Schwaller, Alain Keller} Ein paar Hinweise für die korrekte Formatierung des Textes \begin{itemize} -- cgit v1.2.1 From 62d7a414606babe3a5230b233be84cd272061cfc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 10 Mar 2022 21:08:01 +0100 Subject: fix lecture notes --- .../MSE/2 - Gamma- und Beta-Funktion.pdf | Bin 4710774 -> 4710819 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf b/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf index 667ac4b..1fd469a 100644 Binary files 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fixes session MSE 2 --- .../MSE/2 - Gamma- und Beta-Funktion.pdf | Bin 4710819 -> 4710818 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf b/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf index 1fd469a..e0d26be 100644 Binary files a/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf and b/vorlesungsnotizen/MSE/2 - Gamma- und Beta-Funktion.pdf differ -- cgit v1.2.1 From ced982f32f430b7e3b82b3cc062411b8130b0bfd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 11 Mar 2022 22:34:32 +0100 Subject: Bohr-Mollerup und Eindeutigkeit der Gamma-Funktion --- buch/chapters/040-rekursion/Makefile.inc | 2 + buch/chapters/040-rekursion/bohrmollerup.tex | 196 +++++++++++++++++++++++++++ buch/chapters/040-rekursion/gamma.tex | 2 + buch/chapters/040-rekursion/integral.tex | 103 ++++++++++++++ 4 files changed, 303 insertions(+) create mode 100644 buch/chapters/040-rekursion/bohrmollerup.tex create mode 100644 buch/chapters/040-rekursion/integral.tex diff --git a/buch/chapters/040-rekursion/Makefile.inc b/buch/chapters/040-rekursion/Makefile.inc index c5887f7..ed8fd51 100644 --- a/buch/chapters/040-rekursion/Makefile.inc +++ b/buch/chapters/040-rekursion/Makefile.inc @@ -6,6 +6,8 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/040-rekursion/gamma.tex \ + chapters/040-rekursion/bohrmollerup.tex \ + chapters/040-rekursion/integral.tex \ chapters/040-rekursion/beta.tex \ chapters/040-rekursion/linear.tex \ chapters/040-rekursion/hypergeometrisch.tex \ diff --git a/buch/chapters/040-rekursion/bohrmollerup.tex b/buch/chapters/040-rekursion/bohrmollerup.tex new file mode 100644 index 0000000..96897be --- /dev/null +++ b/buch/chapters/040-rekursion/bohrmollerup.tex @@ -0,0 +1,196 @@ +% +% bohrmollerup.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\subsection{Der Satz von Bohr-Mollerup +\label{buch:rekursion:subsection:bohr-mollerup}} +Die Integralformel und die Grenzwertdefinition für die Gamma-Funktion +zeigen beide, dass das Problem der Ausdehnung der Fakultät zu einer +Funktion $\mathbb{C}\to\mathbb{C}$ eine Lösung hat, aber es ist noch +nicht klar, in welchem Sinn dies die einzig mögliche Lösung ist. +Der Satz von Bohr-Mollerup gibt darauf eine Antwort. + +\begin{satz} +\label{buch:satz:bohr-mollerup} +Eine Funktion $f\colon \mathbb{R}^+\to\mathbb{R}$ mit den Eigenschaften +\begin{enumerate}[i)] +\item $f(1)=1$, +\item $f(x+1)=xf(x)$ für alle $x\in\mathbb{R}^+$ und +\item die Funktion $\log f(t)$ ist konvex +\end{enumerate} +ist die Gamma-Funktion: $f(t)=\Gamma(t)$. +\end{satz} + +Für den Beweis verwenden wir die folgende Eigenschaft einer konvexen +Funktion $g(x)$. +Sei +\begin{equation} +S(y,x) = \frac{g(y)-g(x)}{y-x} +\qquad\text{für $y-x$} +\end{equation} +die Steigung der Sekante zwischen den Punkten $(x,g(x))$ und $(y,g(y))$ +des Graphen von $g$. +Da $g$ konvex ist, ist $S(y,x)$ eine monoton wachsende Funktion +der beiden Variablen $x$ und $y$, solange $y>x$. + +\begin{proof}[Beweis] +Wir halten zunächst fest, dass die Bedingungen i) und ii) zur Folge haben, +dass $f(n+1)=n!$ ist für alle positiven natürlichen Zahlen. +Für die Steigung einer Sekante der Funktion $g(x)=\log f(x)$ kann damit +für natürliche Argumente bereits berechnet werden, es ist +\[ +S(n,n+1) += +\frac{\log n! - \log (n-1)!}{n+1-n} += +\frac{\log n + \log (n-1)! - \log(n-1)!}{1} += +\log n +\] +und entsprechend auch $S(n-1,n) = \log(n-1)$. + +\begin{figure} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\draw (-6,0) -- (6,0); + +\node at (-5,0) [above] {$n-1\mathstrut$}; +\node at (0,0) [above] {$n\mathstrut$}; +\node at (3,0) [above] {$n+x\mathstrut$}; +\node at (5,0) [above] {$n+1\mathstrut$}; + +\node[color=blue] at (-5,-2.3) {$S(n-1,n)\mathstrut$}; +\node[color=red] at (-1.666,-2.3) {$S(n-1,n+x)\mathstrut$}; +\node[color=darkgreen] at (1.666,-2.3) {$S(n,n+x)\mathstrut$}; +\node[color=orange] at (5,-2.3) {$S(n,n+1)\mathstrut$}; + +\node at (-3.333,-2.3) {$<\mathstrut$}; +\node at (0,-2.3) {$<\mathstrut$}; +\node at (3.333,-2.3) {$<\mathstrut$}; + +\draw[color=blue] (-5,0) -- (-5,-2) -- (0,0); +\draw[color=red] (-5,0) -- (-1.666,-2) -- (3,0); +\draw[color=darkgreen] (0,0) -- (1.666,-2) -- (3,0); +\draw[color=orange] (0,0) -- (5,-2) -- (5,0); + +\fill (-5,0) circle[radius=0.08]; +\fill (0,0) circle[radius=0.08]; +\fill (3,0) circle[radius=0.08]; +\fill (5,0) circle[radius=0.08]; + +\draw[double,color=blue] (-5,-2.5) -- (-5,-3.0); +\draw[double,color=orange] (5,-2.5) -- (5,-3.0); + +\node[color=blue] at (-5,-3.3) {$\log (n-1)\mathstrut$}; +\node[color=orange] at (5,-3.3) {$\log (n)\mathstrut$}; + +\end{tikzpicture} +\end{center} +\caption{Für den Beweis des Satzes von Bohr-Mollerup wird die +Sekantensteigung $S(x,y)$ für die Argumente $n-1$, $n$, $n+x$ und $n+1$ +verwendet. +\label{buch:rekursion:fig:bohr-mollerup}} +\end{figure} +Wir wenden jetzt die eben erwähnte Tatsache, dass $S(x,y)$ monoton +wachsend ist, auf die Punkte $n-1$, $n$, $n+x$ und $n+1$ wie +in Abbildung~\ref{buch:rekursion:fig:bohr-mollerup} an, wobei +$0 Date: Sun, 13 Mar 2022 11:05:56 +0100 Subject: add beta distribution graphs --- buch/chapters/040-rekursion/bohrmollerup.tex | 2 +- buch/chapters/040-rekursion/gamma.tex | 25 ++- buch/papers/dreieck/images/Makefile | 8 + buch/papers/dreieck/images/beta.pdf | Bin 0 -> 100791 bytes buch/papers/dreieck/images/beta.tex | 214 +++++++++++++++++++++ buch/papers/dreieck/images/betadist.m | 50 +++++ buch/papers/dreieck/images/order.m | 40 ++++ buch/papers/dreieck/images/order.pdf | Bin 31044 -> 32692 bytes buch/papers/dreieck/images/order.tex | 52 +++-- buch/papers/dreieck/teil1.tex | 273 +++++++++++++++++++++------ 10 files changed, 586 insertions(+), 78 deletions(-) create mode 100644 buch/papers/dreieck/images/beta.pdf create mode 100644 buch/papers/dreieck/images/beta.tex create mode 100644 buch/papers/dreieck/images/betadist.m diff --git a/buch/chapters/040-rekursion/bohrmollerup.tex b/buch/chapters/040-rekursion/bohrmollerup.tex index 96897be..cd9cadc 100644 --- a/buch/chapters/040-rekursion/bohrmollerup.tex +++ b/buch/chapters/040-rekursion/bohrmollerup.tex @@ -172,7 +172,7 @@ erhalten wir (x)_n f(x) < n^x (n-1)! -\\ +\intertext{oder nach Division durch $(x)_n$} %\underbrace{ \frac{(n-1)^x (n-1)!}{(x)_n} %}_{\displaystyle\to \Gamma(x)} diff --git a/buch/chapters/040-rekursion/gamma.tex b/buch/chapters/040-rekursion/gamma.tex index af5d572..7d4453b 100644 --- a/buch/chapters/040-rekursion/gamma.tex +++ b/buch/chapters/040-rekursion/gamma.tex @@ -651,8 +651,11 @@ Abschnitt~\ref{buch:funktionentheorie:section:fortsetzung} beschrieben wird, kann die Funktion auf ganz $\mathbb{C}$ ausgedehnt werden, mit Ausnahme einzelner Pole. Die Funktionalgleichung gilt natürlich für alle $z\in\mathbb{C}$, -für die $\Gamma(z)$ definiert ist. -In einer Umgebung von $z=-n$ gilt +für die $\Gamma(z)$ definiert ist, nicht nur für diejenigen $z$, für +die das Integral konvergiert. +Wir können Sie daher verwenden, um das Argument in den Bereich +zu bringen, wo das Integral zur Berechnung verwendet werden kann. +Dazu berechnen wir \[ \Gamma(z) = @@ -665,12 +668,20 @@ In einer Umgebung von $z=-n$ gilt \dots = \frac{\Gamma(z+n)}{z(z+1)(z+2)\cdots(z+n-1)} += +\frac{\Gamma(z+n)}{(z)_n}. \] -Keiner der Faktoren im Nenner verschwindet in der Nähe von $z=-n$, der -Zähler hat aber einen Pol erster Ordnung an dieser Stelle. -Daher hat auch der Quotient einen Pol erster Ordnung. -Abbildung~\ref{buch:rekursion:fig:gamma} zeigt die Pole bei den -nicht negativen ganzen Zahlen. +Dies gilt für jedes natürlich $n$. +Für $n$ gross genug, genauer für +$n\ge |\operatorname{Re}z|$, +ist $\operatorname{Re}(z+n)=\operatorname{Re}z + n>0$ und damit +kann $\Gamma(z+n)$ mit der Integralformel berechnet werden. + +Die Gamma-Funktion hat keine Nullstellen, aber in der Nähe von $z=-n$ +hat der Nenner eine Nullstelle erster Ordnung. +Somit hat $\Gamma(z)$ Pole erster Ordnung bei den negativen +ganzen Zahlen und bei $0$, wie sie in +Abbildung~\ref{buch:rekursion:fig:gamma} gezeigt werden. \subsubsection{Numerische Berechnung} \begin{table} diff --git a/buch/papers/dreieck/images/Makefile b/buch/papers/dreieck/images/Makefile index 3907d13..c979599 100644 --- a/buch/papers/dreieck/images/Makefile +++ b/buch/papers/dreieck/images/Makefile @@ -3,8 +3,16 @@ # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # +all: order.pdf beta.pdf + order.pdf: order.tex orderpath.tex pdflatex order.tex orderpath.tex: order.m octave order.m + +beta.pdf: beta.tex betapaths.tex + pdflatex beta.tex + +betapaths.tex: betadist.m + octave betadist.m diff --git a/buch/papers/dreieck/images/beta.pdf b/buch/papers/dreieck/images/beta.pdf new file mode 100644 index 0000000..c3ab4f6 Binary files /dev/null and b/buch/papers/dreieck/images/beta.pdf differ diff --git a/buch/papers/dreieck/images/beta.tex b/buch/papers/dreieck/images/beta.tex new file mode 100644 index 0000000..50509ee --- /dev/null +++ b/buch/papers/dreieck/images/beta.tex @@ -0,0 +1,214 @@ +% +% beta.tex -- display some symmetric beta distributions +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\input{betapaths.tex} +\begin{document} +\def\skala{12} +\definecolor{colorone}{rgb}{1.0,0.6,0.0} +\definecolor{colortwo}{rgb}{1.0,0.0,0.0} +\definecolor{colorthree}{rgb}{0.6,0.0,0.6} +\definecolor{colorfour}{rgb}{0.6,0.0,1.0} +\definecolor{colorfive}{rgb}{0.0,0.0,1.0} +\definecolor{colorsix}{rgb}{0.4,0.6,1.0} +\definecolor{colorseven}{rgb}{0.0,0.0,0.0} +\definecolor{coloreight}{rgb}{0.0,0.8,0.8} +\definecolor{colornine}{rgb}{0.0,0.8,0.2} +\definecolor{colorten}{rgb}{0.2,0.4,0.0} +\definecolor{coloreleven}{rgb}{1.0,0.8,0.4} + +\def\achsen{ + \foreach \x in {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9}{ + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; + } + \foreach \y in {1,2,3,4}{ + \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); + \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; + } + \def\x{1} + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; + \def\x{0} + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; + + \draw[->] ({-0.1/\skala},0) -- ({1*\dx+0.4/\skala},0) + coordinate[label={$x$}]; + \draw[->] (0,{-0.1/\skala}) -- (0,{\betamax*\dy+0.4/\skala},0) + coordinate[label={right:$\beta(a,b,x)$}]; +} + +\def\farbcoord#1#2{ + ({\dx*(0.7+((#1-1)/4)*0.27)},{\dx*(0.15+((#2-1)/4)*0.27)}) +} +\def\farbviereck{ + \foreach \x in {1,2,3,4,5}{ + \draw[color=gray!30] \farbcoord{\x}{1} -- \farbcoord{\x}{5}; + \draw[color=gray!30] \farbcoord{1}{\x} -- \farbcoord{5}{\x}; + } + \draw[->] \farbcoord{1}{1} -- \farbcoord{5.4}{1} + coordinate[label={$a$}]; + \draw[->] \farbcoord{1}{1} -- \farbcoord{1}{5.4} + coordinate[label={left: $b$}]; + \foreach \x in {1,2,3,4,5}{ + \node[color=gray] at \farbcoord{5}{\x} [right] {\tiny $b=\x$}; + \fill[color=white,opacity=0.7] + \farbcoord{(\x-0.1)}{4.3} + rectangle + \farbcoord{(\x+0.1)}{5}; + \node[color=gray] at \farbcoord{\x}{5} [left,rotate=90] + {\tiny $a=\x$}; + } +} +\def\farbpunkt#1#2#3{ + \fill[color=#3] \farbcoord{#1}{#2} circle[radius={0.1/\skala}]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\dx{1} +\def\dy{0.1} +\def\opa{0.1} + +\def\betamax{4.2} + +\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betabb -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betacc -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betadd -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betaff -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betagg -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betahh -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaii -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betajj -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaaa; +\draw[color=colortwo] \betabb; +\draw[color=colorthree] \betacc; +\draw[color=colorfour] \betadd; +\draw[color=colorfive] \betaee; +\draw[color=colorsix] \betaff; +\draw[color=colorseven] \betagg; +\draw[color=coloreight] \betahh; +\draw[color=colornine] \betaii; +\draw[color=colorten] \betajj; +\draw[color=coloreleven] \betakk; + +\achsen + +\farbviereck + +\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven} +\farbpunkt{\alphaten}{\betaten}{colorten} +\farbpunkt{\alphanine}{\betanine}{colornine} +\farbpunkt{\alphaeight}{\betaeight}{coloreight} +\farbpunkt{\alphaseven}{\betaseven}{colorseven} +\farbpunkt{\alphasix}{\betasix}{colorsix} +\farbpunkt{\alphafive}{\betafive}{colorfive} +\farbpunkt{\alphafour}{\betafour}{colorfour} +\farbpunkt{\alphathree}{\betathree}{colorthree} +\farbpunkt{\alphatwo}{\betatwo}{colortwo} +\farbpunkt{\alphaone}{\betaone}{colorone} + + +\def\betamax{4.9} + +\begin{scope}[yshift=-0.6cm] +\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betaab -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betaac -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betaad -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaae -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betaaf -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betaag -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betaah -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaai -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betaaj -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaaa; +\draw[color=colortwo] \betaab; +\draw[color=colorthree] \betaac; +\draw[color=colorfour] \betaad; +\draw[color=colorfive] \betaae; +\draw[color=colorsix] \betaaf; +\draw[color=colorseven] \betaag; +\draw[color=coloreight] \betaah; +\draw[color=colornine] \betaai; +\draw[color=colorten] \betaaj; +\draw[color=coloreleven] \betaak; + +\achsen + +\farbviereck + +\farbpunkt{\alphaone}{\betaeleven}{coloreleven} +\farbpunkt{\alphaone}{\betaten}{colorten} +\farbpunkt{\alphaone}{\betanine}{colornine} +\farbpunkt{\alphaone}{\betaeight}{coloreight} +\farbpunkt{\alphaone}{\betaseven}{colorseven} +\farbpunkt{\alphaone}{\betasix}{colorsix} +\farbpunkt{\alphaone}{\betafive}{colorfive} +\farbpunkt{\alphaone}{\betafour}{colorfour} +\farbpunkt{\alphaone}{\betathree}{colorthree} +\farbpunkt{\alphaone}{\betatwo}{colortwo} +\farbpunkt{\alphaone}{\betaone}{colorone} + +\end{scope} + +\begin{scope}[yshift=-1.2cm] +\fill[color=colorone,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betabk -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betack -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betadk -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaek -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betafk -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betagk -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betahk -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaik -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betajk -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaak; +\draw[color=colortwo] \betabk; +\draw[color=colorthree] \betack; +\draw[color=colorfour] \betadk; +\draw[color=colorfive] \betaek; +\draw[color=colorsix] \betafk; +\draw[color=colorseven] \betagk; +\draw[color=coloreight] \betahk; +\draw[color=colornine] \betaik; +\draw[color=colorten] \betajk; +\draw[color=coloreleven] \betakk; + +\achsen + +\farbviereck + +\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven} +\farbpunkt{\alphaten}{\betaeleven}{colorten} +\farbpunkt{\alphanine}{\betaeleven}{colornine} +\farbpunkt{\alphaeight}{\betaeleven}{coloreight} +\farbpunkt{\alphaseven}{\betaeleven}{colorseven} +\farbpunkt{\alphasix}{\betaeleven}{colorsix} +\farbpunkt{\alphafive}{\betaeleven}{colorfive} +\farbpunkt{\alphafour}{\betaeleven}{colorfour} +\farbpunkt{\alphathree}{\betaeleven}{colorthree} +\farbpunkt{\alphatwo}{\betaeleven}{colortwo} +\farbpunkt{\alphaone}{\betaeleven}{colorone} + +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/dreieck/images/betadist.m b/buch/papers/dreieck/images/betadist.m new file mode 100644 index 0000000..9ff78ed --- /dev/null +++ b/buch/papers/dreieck/images/betadist.m @@ -0,0 +1,50 @@ +# +# betadist.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global N; +N = 201; +global n; +n = 11; + +t = (0:n-1) / (n-1) +alpha = 1 + 4 * t.^2 + +#alpha = [ 1, 1.03, 1.05, 1.1, 1.25, 1.5, 2, 2.5, 3, 4, 5 ]; +beta = alpha; +names = [ "one"; "two"; "three"; "four"; "five"; "six"; "seven"; "eight"; + "nine"; "ten"; "eleven" ] + +function retval = Beta(a, b, x) + retval = x^(a-1) * (1-x)^(b-1) / beta(a, b); +end + +function plotbeta(fn, a, b, name) + global N; + fprintf(fn, "\\def\\beta%s{\n", name); + fprintf(fn, "\t({%.4f*\\dx},{%.4f*\\dy})", 0, Beta(a, b, 0)); + for x = (1:N-1)/(N-1) + X = (1-cos(pi * x))/2; + fprintf(fn, "\n\t--({%.4f*\\dx},{%.4f*\\dy})", + X, Beta(a, b, X)); + end + fprintf(fn, "\n}\n"); +end + +fn = fopen("betapaths.tex", "w"); + +for i = (1:n) + fprintf(fn, "\\def\\alpha%s{%f}\n", names(i,:), alpha(i)); + fprintf(fn, "\\def\\beta%s{%f}\n", names(i,:), beta(i)); +end + +for i = (1:n) + for j = (1:n) + printf("working on %d,%d:\n", i, j); + plotbeta(fn, alpha(i), beta(j), + char(['a' + i - 1, 'a' + j - 1])); + end +end + +fclose(fn); diff --git a/buch/papers/dreieck/images/order.m b/buch/papers/dreieck/images/order.m index d37a258..762f458 100644 --- a/buch/papers/dreieck/images/order.m +++ b/buch/papers/dreieck/images/order.m @@ -26,6 +26,10 @@ function retval = orderd(p, n, k) end end +function retval = orders(p, n, k) + retval = k * nchoosek(n, k) * p^(k-1) * (1-p)^(n-k); +end + function orderpath(fn, k, name) fprintf(fn, "\\def\\order%s{\n\t(0,0)", name); global N; @@ -51,29 +55,65 @@ function orderdpath(fn, k, name) fprintf(fn, "\n}\n"); end +function orderspath(fn, k, name) + fprintf(fn, "\\def\\orders%s{\n\t(0,0)", name); + global N; + global subdivisions; + for i = (1:subdivisions-1) + p = i/subdivisions; + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", + p, orders(p, N, k)); + end + fprintf(fn, "\n\t-- ({1*\\dx},0)"); + fprintf(fn, "\n}\n"); +end + fn = fopen("orderpath.tex", "w"); + orderpath(fn, 0, "zero"); orderdpath(fn, 0, "zero"); +orderspath(fn, 0, "zero"); + orderpath(fn, 1, "one"); orderdpath(fn, 1, "one"); +orderspath(fn, 1, "one"); + orderpath(fn, 2, "two"); orderdpath(fn, 2, "two"); +orderspath(fn, 2, "two"); + orderpath(fn, 3, "three"); orderdpath(fn, 3, "three"); +orderspath(fn, 3, "three"); + orderpath(fn, 4, "four"); orderdpath(fn, 4, "four"); +orderspath(fn, 4, "four"); + orderpath(fn, 5, "five"); orderdpath(fn, 5, "five"); +orderspath(fn, 5, "five"); + orderpath(fn, 6, "six"); orderdpath(fn, 6, "six"); +orderspath(fn, 6, "six"); + orderpath(fn, 7, "seven"); orderdpath(fn, 7, "seven"); +orderspath(fn, 7, "seven"); + orderpath(fn, 8, "eight"); orderdpath(fn, 8, "eight"); +orderspath(fn, 8, "eight"); + orderpath(fn, 9, "nine"); orderdpath(fn, 9, "nine"); +orderspath(fn, 9, "nine"); + orderpath(fn, 10, "ten"); orderdpath(fn, 10, "ten"); +orderspath(fn, 10, "ten"); + fclose(fn); diff --git a/buch/papers/dreieck/images/order.pdf b/buch/papers/dreieck/images/order.pdf index 6d9c8c0..98a5fbe 100644 Binary files a/buch/papers/dreieck/images/order.pdf and b/buch/papers/dreieck/images/order.pdf differ diff --git a/buch/papers/dreieck/images/order.tex b/buch/papers/dreieck/images/order.tex index 083f014..9a2511c 100644 --- a/buch/papers/dreieck/images/order.tex +++ b/buch/papers/dreieck/images/order.tex @@ -13,10 +13,25 @@ \begin{document} \def\skala{8} \definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\n{10} +\def\E#1#2{ + \draw[color=#2] + ({\dx*#1/(\n+1)},{-0.1/\skala}) -- ({\dx*#1/(\n+1)},{4.4*\dy}); + \node[color=#2] at ({\dx*#1/(\n+1)},{3.2*\dy}) + [rotate=90,above right] {$k=#1$}; +} +\def\var#1#2{ + \pgfmathparse{\dx*sqrt(#1*(\n-#1+1)/((\n+1)*(\n+1)*(\n+2)))} + \xdef\var{\pgfmathresult} + \fill[color=#2,opacity=0.5] + ({\dx*#1/(\n+1)-\var},0) rectangle ({\dx*#1/(\n+1)+\var},{4.4*\dy}); +} + \input{orderpath.tex} \begin{tikzpicture}[>=latex,thick,scale=\skala] -\def\dx{1} +\def\dx{1.6} \def\dy{0.5} \def\pfad#1#2{ @@ -24,7 +39,7 @@ -- #1 -- - ({1+0.1/\skala},0.5); + ({1*\dx+0.1/\skala},0.5); } \pfad{\orderzero}{darkgreen!20} @@ -39,11 +54,11 @@ \pfad{\orderten}{darkgreen!20} \pfad{\orderseven}{darkgreen} -\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$x$}]; -\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$F(X)$}]; +\draw[->] ({-0.1/\skala},0) -- ({1.03*\dx},0) coordinate[label={$x$}]; +\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={right:$F(X)$}]; \foreach \x in {0,0.2,0.4,0.6,0.8,1}{ - \draw (\x,{-0.1/\skala}) -- (\x,{0.1/\skala}); - \node at (\x,{-0.1/\skala}) [below] {$\x$}; + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; } \foreach \y in {0.5,1}{ \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); @@ -55,17 +70,25 @@ \begin{scope}[yshift=-0.7cm] \def\dy{0.125} +\foreach \k in {1,2,3,4,5,6,8,9,10}{ + \E{\k}{blue!30} +} +\def\k{7} +\var{\k}{orange!40} +\node[color=blue] at ({\dx*\k/(\n+1)},{4.3*\dy}) [above] {$E(X_{7:n})$}; + \def\pfad#1#2{ \draw[color=#2,line width=1.4pt] ({-0.1/\skala},0) -- #1 -- - ({1+0.1/\skala},0.0); + ({1*\dx+0.1/\skala},0.0); } \begin{scope} \clip ({-0.1/\skala},{-0.1/\skala}) - rectangle ({1+0.1/\skala},{0.56+0.1/\skala}); + rectangle ({1*\dx+0.1/\skala},{0.56+0.1/\skala}); + \pfad{\orderdzero}{red!20} \pfad{\orderdone}{red!20} \pfad{\orderdtwo}{red!20} @@ -76,21 +99,24 @@ \pfad{\orderdeight}{red!20} \pfad{\orderdnine}{red!20} \pfad{\orderdten}{red!20} +\E{\k}{blue} \pfad{\orderdseven}{red} + \end{scope} -\draw[->] ({-0.1/\skala},0) -- (1.1,0) coordinate[label={$x$}]; -\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={left:$\varphi(X)$}]; +\draw[->] ({-0.1/\skala},0) -- ({1.03*\dx},0) coordinate[label={$x$}]; +\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={right:$\varphi(X)$}]; \foreach \x in {0,0.2,0.4,0.6,0.8,1}{ - \draw (\x,{-0.1/\skala}) -- (\x,{0.1/\skala}); - \node at (\x,{-0.1/\skala}) [below] {$\x$}; + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; } \foreach \y in {1,2,3,4}{ \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; } -\node[color=red] at (0.67,{2.7*\dy}) [above] {$k=7$}; +\node[color=red] at ({0.67*\dx},{2.7*\dy}) [above] {$k=7$}; + \end{scope} diff --git a/buch/papers/dreieck/teil1.tex b/buch/papers/dreieck/teil1.tex index 255c5d0..5e7090b 100644 --- a/buch/papers/dreieck/teil1.tex +++ b/buch/papers/dreieck/teil1.tex @@ -12,6 +12,8 @@ Zufallsvariablen, die wie $X$ verteilt sind. Ziel ist, die Verteilungsfunktion und die Wahrscheinlichkeitsdichte des grössten, zweitgrössten, $k$-t-grössten Wertes in der Stichprobe zu finden. +Wir schreiben $[n]=\{1,\dots,n\}$ für die Menge der natürlichen +Zahlen von zwischen $1$ und $n$. \subsection{Verteilung von $\operatorname{max}(X_1,\dots,X_n)$ und $\operatorname{min}(X_1,\dots,X_n)$ @@ -176,86 +178,243 @@ X_{n:n} &= \operatorname{max}(X_1,\dots,X_n). Um den Wert der Verteilungsfunktion von $X_{k:n}$ zu berechnen, müssen wir die Wahrscheinlichkeit bestimmen, dass $k$ der $n$ Werte $X_i$ $x$ nicht übersteigen. -Es muss also eine Partition von $[n]=\{1,\dots,n\}$ in eine -$k$-elementige $I=\{i_1,\dots,i_k\}$ Teilmenge und ihre -$(n-k)$-elementige Komplementmenge $[n]\setminus I$ geben -derart, dass die $X_{i} \le x$ sind für $i\in I$ und $X_{j}> x$ für -$j\in [n]\setminus I$. -Daraus kann man ablesen, dass +Der $k$-te Wert $X_{k:n}$ übersteigt genau dann $x$ nicht, wenn +mindestens $k$ der Zufallswerte $X_i$ $x$ nicht übersteigen, also +\[ +P(X_{k:n} \le x) += +P\left( +|\{i\in[n]\,|\, X_i\le x\}| \ge k +\right). +\] + +Das Ereignis $\{X_i\le x\}$ ist eine Bernoulli-Experiment, welches mit +Wahrscheinlichkeit $F_X(x)$ eintritt. +Die Anzahl der Zufallsvariablen $X_i$, die $x$ übertreffen, ist also +Binomialverteilt mit $p=F_X(x)$. +Damit haben wir gefunden, dass mit Wahrscheinlichkeit +\begin{equation} +F_{X_{k:n}}(x) += +P(X_{k:n}\le x) += +\sum_{i=k}^n \binom{n}{i}F_X(x)^i (1-F_X(x))^{n-i} +\label{dreieck:eqn:FXkn} +\end{equation} +mindestens $k$ der Zufallsvariablen den Wert $x$ überschreiten. + +\subsubsection{Wahrscheinlichkeitsdichte der Ordnungsstatistik} +Die Wahrscheinlichkeitsdichte der Ordnungsstatistik kann durch Ableitung +von \eqref{dreieck:eqn:FXkn} gefunden, werden, sie ist \begin{align*} +\varphi_{X_{k:n}}(x) +&= +\frac{d}{dx} F_{X_{k:n}}(x) +\\ &= -P\biggl( -\bigvee_{I\subset[n]\wedge |I|=k} -\bigwedge_{i\in I} (X_i\le x) -\wedge -\bigwedge_{j\in [n]\setminus I} (X_i > x) -\biggr). -\intertext{Da die verschiedenen $k$-elementigen Teilmengen $I\subset[n]$ -zu disjunkten Ereignissen gehören, ist die Wahrscheinlichkeit eine Summe} +\sum_{i=k}^n +\binom{n}{i} +\bigl( +iF_X(x)^{i-1}\varphi_X(x) (1-F_X(x))^{n-i} +- +F_X(x)^k +(n-i) +(1-F_X(x))^{n-i-1} +\varphi_X(x) +\bigr) +\\ &= -\sum_{I\subset[n]\wedge |I|=k} -P\biggl( -\bigwedge_{i\in I} (X_i\le x) -\wedge -\bigwedge_{j\in [n]\setminus I} (X_i > x) +\sum_{i=k}^n +\binom{n}{i} +\varphi_X(x) +F_X(x)^{i-1}(1-F_X(x))^{n-i-1} +\bigl( +iF_X(x)-(n-i)(1-F_X(x)) +\bigr) +\\ +&= +\varphi_X(x) +\biggl( +\sum_{i=k}^n i\binom{n}{i} F_X(x)^{i-1}(1-F_X(x))^{n-i} +- +\sum_{j=k}^n (n-j)\binom{n}{j} F_X(x)^{j}(1-F_X(x))^{n-j-1} \biggr) \\ &= -\sum_{I\subset[n]\wedge |I|=k} -\prod_{i\in I} -P(X_i\le x) -\cdot -\prod_{j\in [n]\setminus I} -P(X_j > x) +\varphi_X(x) +\biggl( +\sum_{i=k}^n i\binom{n}{i} F_X(x)^{i-1}(1-F_X(x))^{n-i} +- +\sum_{i=k+1}^{n+1} (n-i+1)\binom{n}{i-1} F_X(x)^{i-1}(1-F_X(x))^{n-i} +\biggr) \\ &= -\sum_{I\subset[n]\wedge |I|=k} -F_X(x)^k -(1-F_X(x))^{n-k}. -\intertext{Die Anzahl solcher Teilmengen $I$ ist gegeben durch den -Binomialkoeffizienten gebeben, die Verteilungsfunktion ist daher} -F_{X_{k:n}}(x) +\varphi_X(x) +\biggl( +k\binom{n}{k}F_X(x)^{k-1}(1-F_X(x))^{n-k} ++ +\sum_{i=k+1}^{n+1} +\left( +i\binom{n}{i} +- +(n-i+1)\binom{n}{i-1} +\right) +F_X(x)^{i-1}(1-F_X(x))^{n-i} +\biggr) +\end{align*} +Mit den wohlbekannten Identitäten für die Binomialkoeffizienten +\begin{align*} +i\binom{n}{i} +- +(n-i+1)\binom{n}{i-1} &= -\binom{n}{k} -F_X(x)^k -(1-F_X(x))^{n-k}. +n\binom{n-1}{i-1} +- +n +\binom{n-1}{i-1} += +0 +\end{align*} +folgt jetzt +\begin{align*} +\varphi_{X_{k:n}}(x) +&= +\varphi_X(x)k\binom{n}{k} F_X(x)^{k-1}(1-F_X(x))^{n-k}(x). +\intertext{Im Speziellen für gleichverteilte Zufallsvariablen $X_i$ ist +} +\varphi_{X_{k:n}}(x) +&= +k\binom{n}{k} x^{k-1}(1-x)^{n-k}. \end{align*} -Für im Intervall $[0,1]$ gleichverteilte $X_i$ ist die Verteilungsfunktion -der $k$-ten Ordnungsstatistik +Dies ist die Wahrscheinlichkeitsdichte einer Betaverteilung \[ -F_{X_{k:n}}(x) +\beta(k,n-k+1)(x) += +\frac{1}{B(k,n-k+1)} +x^{k-1}(1-x)^{n-k}. +\] +Tatsächlich ist die Normierungskonstante +\begin{align} +\frac{1}{B(k,n-k+1)} +&= +\frac{\Gamma(n+1)}{\Gamma(k)\Gamma(n-k+1)} += +\frac{n!}{(k-1)!(n-k)!}. +\label{dreieck:betaverteilung:normierung1} +\end{align} +Andererseits ist +\[ +k\binom{n}{k} += +k\frac{n!}{k!(n-k)!} = -\binom{n}{k} x^k(1-x)^{n-k}. +\frac{n!}{(k-1)!(n-k)!}, \] -Ihre Ableitung nach $x$ ist die Wahrscheinlichkeitsdichte und damit -wird es jetzt auch möglich, den Erwartungswert zu ermitteln: +in Übereinstimmung mit~\eqref{dreieck:betaverteilung:normierung1}. +Die Verteilungsfunktion und die Wahrscheinlichkeitsdichte der +Ordnungsstatistik sind in Abbildung~\ref{dreieck:fig:order} dargestellt. + +\begin{figure} +\centering +\includegraphics{papers/dreieck/images/order.pdf} +\caption{Verteilungsfunktion und Wahrscheinlichkeitsdichte der +Ordnungsstatistiken $X_{k:n}$ einer gleichverteilung Zuvallsvariable +mit $n=10$. +\label{dreieck:fig:order}} +\end{figure} + +\subsubsection{Erwartungswert} +Mit der Wahrscheinlichkeitsdichte kann man jetzt auch den Erwartungswerte +der $k$-ten Ordnungsstatistik bestimmen. +Die Rechnung ergibt: \begin{align*} E(X_{k:n}) &= -\int_{0}^1 -\underbrace{x\llap{\phantom{\bigg|}}\mathstrut}_{\downarrow} -\underbrace{\frac{d}{dx}\binom{n}{k}x^k(1-x)^{n-k}}_{\uparrow} -\,dx +\int_0^1 x\cdot k\binom{n}{k} x^{k-1}(1-x)^{n-k}\,dx = -\biggl[ -x\binom{n}{k}x^k(1-x)^{n-k} -\biggr]_0^1 -- +k +\binom{n}{k} \int_0^1 -\binom{n}{k}x^k(1-x)^{n-k} -\,dx -\\ +x^{k}(1-x)^{n-k}\,dx. +\intertext{Dies ist das Beta-Integral} &= -\binom{n}{k} -\biggl( -0^{n-k} -- -\int_0^1 x^k(1-x)^{n-k}\,dx -\biggr) +k\binom{n}{k} +B(k+1,n-k+1) +\intertext{welches man durch Gamma-Funktionen bzw.~durch Fakultäten wie in} +&= +k\frac{n!}{k!(n-k)!} +\frac{\Gamma(k+1)\Gamma(n-k+1)}{n+2} += +k\frac{n!}{k!(n-k)!} +\frac{k!(n-k)!}{(n+1)!} += +\frac{k}{n+1} \end{align*} +ausdrücken kann. +Die Erwartungswerte haben also regelmässige Abstände, sie sind in +Abbildung~\ref{dreieck:fig:order} als blaue vertikale Linien eingezeichnet. +\subsubsection{Varianz} +Auch die Varianz lässt sich einfach berechnen, dazu muss zunächst +der Erwartungswert von $X_{k:n}^2$ bestimmt werden. +Er ist +\begin{align*} +E(X_{k:n}^2) +&= +\int_0^1 x^2\cdot k\binom{n}{k} x^{k-1}(1-x)^{n-k}\,dx += +k +\binom{n}{k} +\int_0^1 +x^{k+1}(1-x)^{n-k}\,dx. +\intertext{Auch dies ist ein Beta-Integral, nämlich} +&= +k\binom{n}{k} +B(k+2,n-k+1) += +k\frac{n!}{k!(n-k)!} +\frac{(k+1)!(n-k)!}{(n+2)!} += +\frac{k(k+1)}{(n+1)(n+2)}. +\end{align*} +Die Varianz wird damit +\begin{align} +\operatorname{var}(X_{k:n}) +&= +E(X_{k:n}^2) - E(X_{k:n})^2 +\notag +\\ +& += +\frac{k(k+1)}{(n+1)(n+2)}-\frac{k^2}{(n+1)^2} += +\frac{k(k+1)(n+1)-k^2(n+2)}{(n+1)^2(n+2)} += +\frac{k(n-k+1)}{(n+1)^2(n+2)}. +\label{dreieck:eqn:ordnungsstatistik:varianz} +\end{align} +In Abbildung~\ref{dreieck:fig:order} ist die Varianz der +Ordnungsstatistik $X_{k:n}$ für $k=7$ und $n=10$ als oranges +Rechteck dargestellt. +\begin{figure} +\centering +\includegraphics[width=0.84\textwidth]{papers/dreieck/images/beta.pdf} +\caption{Wahrscheinlichkeitsdichte der Beta-Verteilung +$\beta(a,b,x)$ +für verschiedene Werte der Parameter $a$ und $b$. +Die Werte des Parameters für einen Graphen einer Beta-Verteilung +sind als Punkt im kleinen Quadrat rechts +im Graphen als Punkt mit der gleichen Farbe dargestellt. +\label{dreieck:fig:betaverteilungn}} +\end{figure} +Die Formel~\eqref{dreieck:eqn:ordnungsstatistik:varianz} +besagt auch, dass die Varianz der proportional ist zu $k((n+1)-k)$. +Dieser Ausdruck ist am grössten für $k=(n+1)/2$, die Varianz ist +also grösser für die ``mittleren'' Ordnungstatistiken als für die +extremen $X_{1:n}=\operatorname{min}(X_1,\dots,X_n)$ und +$X_{n:n}=\operatorname{max}(X_1,\dots,X_n)$. -- cgit v1.2.1 From f5047d4d780e996a8b8f7738c1ac7c884a07f135 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 13 Mar 2022 23:26:58 +0100 Subject: new stuff about beta, test2 --- buch/aufgaben2.tex | 4 + buch/chapters/040-rekursion/Makefile.inc | 1 + buch/chapters/040-rekursion/beta.tex | 104 ++------- buch/chapters/040-rekursion/images/Makefile | 16 +- buch/chapters/040-rekursion/images/beta.pdf | Bin 0 -> 109772 bytes buch/chapters/040-rekursion/images/beta.tex | 236 +++++++++++++++++++++ buch/chapters/040-rekursion/images/betadist.m | 58 +++++ buch/chapters/040-rekursion/images/order.m | 119 +++++++++++ buch/chapters/040-rekursion/images/order.pdf | Bin 0 -> 32692 bytes buch/chapters/040-rekursion/images/order.tex | 125 +++++++++++ buch/chapters/070-orthogonalitaet/Makefile.inc | 1 + buch/chapters/070-orthogonalitaet/chapter.tex | 2 +- .../070-orthogonalitaet/uebungsaufgaben/701.tex | 137 ++++++++++++ buch/chapters/090-pde/Makefile.inc | 1 + buch/chapters/090-pde/chapter.tex | 12 +- buch/chapters/090-pde/kreis.tex | 2 +- buch/chapters/090-pde/uebungsaufgaben/901.tex | 82 +++++++ buch/papers/dreieck/images/beta.pdf | Bin 100791 -> 109717 bytes buch/papers/dreieck/images/beta.tex | 208 ++++++++++-------- buch/papers/dreieck/images/betadist.m | 24 ++- 20 files changed, 938 insertions(+), 194 deletions(-) create mode 100644 buch/chapters/040-rekursion/images/beta.pdf create mode 100644 buch/chapters/040-rekursion/images/beta.tex create mode 100644 buch/chapters/040-rekursion/images/betadist.m create mode 100644 buch/chapters/040-rekursion/images/order.m create mode 100644 buch/chapters/040-rekursion/images/order.pdf create mode 100644 buch/chapters/040-rekursion/images/order.tex create mode 100644 buch/chapters/070-orthogonalitaet/uebungsaufgaben/701.tex create mode 100644 buch/chapters/090-pde/uebungsaufgaben/901.tex diff --git a/buch/aufgaben2.tex b/buch/aufgaben2.tex index bed14fb..f98562e 100644 --- a/buch/aufgaben2.tex +++ b/buch/aufgaben2.tex @@ -8,4 +8,8 @@ %\input chapters/40-eigenwerte/uebungsaufgaben/4004.tex %\item %\input chapters/40-eigenwerte/uebungsaufgaben/4005.tex +\item +\input{chapters/090-pde/uebungsaufgaben/901.tex} +\item +\input{chapters/070-orthogonalitaet/uebungsaufgaben/701.tex} diff --git a/buch/chapters/040-rekursion/Makefile.inc b/buch/chapters/040-rekursion/Makefile.inc index ed8fd51..a222b1c 100644 --- a/buch/chapters/040-rekursion/Makefile.inc +++ b/buch/chapters/040-rekursion/Makefile.inc @@ -9,6 +9,7 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/040-rekursion/bohrmollerup.tex \ chapters/040-rekursion/integral.tex \ chapters/040-rekursion/beta.tex \ + chapters/040-rekursion/betaverteilung.tex \ chapters/040-rekursion/linear.tex \ chapters/040-rekursion/hypergeometrisch.tex \ chapters/040-rekursion/uebungsaufgaben/401.tex \ diff --git a/buch/chapters/040-rekursion/beta.tex b/buch/chapters/040-rekursion/beta.tex index ea847bc..ff59bad 100644 --- a/buch/chapters/040-rekursion/beta.tex +++ b/buch/chapters/040-rekursion/beta.tex @@ -3,11 +3,17 @@ % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % -\subsection{Die Beta-Funktion -\label{buch:rekursion:gamma:subsection:beta}} +\section{Die Beta-Funktion +\label{buch:rekursion:gamma:section:beta}} Die Eulersche Integralformel für die Gamma-Funktion in -Definition~\ref{buch:rekursion:def:gamma} wurde bisher nicht -gerechtfertigt. +Definition~\ref{buch:rekursion:def:gamma} wurde in +Abschnitt~\ref{buch:subsection:integral-eindeutig} +mit dem Satz von Mollerup gerechtfertigt. +Man kann Sie aber auch als Grenzfall der Beta-Funktion verstehen, +die in diesem Abschnitt dargestellt wird. + + +\subsection{Beta-Integral} In diesem Abschnitt wird das Beta-Integral eingeführt, eine Funktion von zwei Variablen, welches eine Integral-Definition mit einer reichaltigen Menge von Rekursionsbeziehungen hat, die sich direkt auf @@ -233,6 +239,16 @@ B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} berechnet werden. \end{satz} +% +% Info über die Beta-Verteilung +% +\input{chapters/040-rekursion/betaverteilung.tex} + +\subsection{Weitere Eigenschaften der Gamma-Funktion} +Die nahe Verwandtschaft der Gamma- mit der Beta-Funktion ermöglicht +nun, weitere Eigenschaften der Gamma-Funktion mit Hilfe der Beta-Funktion +herzuleiten. + \subsubsection{Nochmals der Wert von $\Gamma(\frac12)$?} Der Wert von $\Gamma(\frac12)=\sqrt{\pi}$ wurde bereits in \eqref{buch:rekursion:gamma:wert12} @@ -484,83 +500,3 @@ Setzt man $x=\frac12$ in die Verdoppelungsformel ein, erhält man in Übereinstimmung mit dem aus \eqref{buch:rekursion:gamma:gamma12} bereits bekannten Wert. -\subsubsection{Beta-Funktion und Binomialkoeffizienten} -Die Binomialkoeffizienten können mit Hilfe der Fakultät als -\begin{align*} -\binom{n}{k} -&= -\frac{n!}{(n-k)!\,k!} -\intertext{geschrieben werden. -Drückt man die Fakultäten durch die Gamma-Funktion aus, erhält man} -&= -\frac{\Gamma(n+1)}{\Gamma(n-k+1)\Gamma(k+1)}. -\intertext{Schreibt man $x=k-1$ und $y=n-k+1$, wird daraus -wegen $x+y=k+1+n-k+1=n+2=(n+1)+1$} -&= -\frac{\Gamma(x+y-1)}{\Gamma(x)\Gamma(y)}. -\intertext{Die Rekursionsformel für die Gamma-Funktion erlaubt, -den Zähler umzuwandeln in $\Gamma(x+y-1)=\Gamma(x+y)/(x+y-1)$, so dass -der Binomialkoeffizient schliesslich} -&= -\frac{\Gamma(x+y)}{(x+y-1)\Gamma(x)\Gamma(y)} -= -\frac{1}{(n-1)B(n-k+1,k+1)} -\label{buch:rekursion:gamma:binombeta} -\end{align*} -geschrieben werden kann. -Die Rekursionsbeziehung -\[ -\binom{n+1}{k} = \binom{n}{k-1} + \binom{n}{k} -\] -der Binomialkoeffizienten erzeugt das vertraute Pascal-Dreieck, -die Formel \eqref{buch:rekursion:gamma:binombeta} für die -Binomialkoeffizienten macht daraus -\[ -\frac{n-1}{B(n-k,k-1)} -= -\frac{n-2}{B(n-k,k-2)} -+ -\frac{n-2}{B(n-k-1,k-1)}, -\] -die für ganzzahlige Argumente gilt. -Wir wollen nachrechnen, dass dies für beliebige Argumente gilt. -\begin{align*} -\frac{(n-1)\Gamma(n-1)}{\Gamma(n-k)\Gamma(k-1)} -&= -\frac{(n-2)\Gamma(n-2)}{\Gamma(n-k)\Gamma(k-2)} -+ -\frac{(n-2)\Gamma(n-2)}{\Gamma(n-k-1)\Gamma(k-1)} -\\ -\frac{\Gamma(n)}{\Gamma(n-k)\Gamma(k-1)} -&= -\frac{\Gamma(n-1)}{\Gamma(n-k)\Gamma(k-2)} -+ -\frac{\Gamma(n-1)}{\Gamma(n-k-1)\Gamma(k-1)} -\intertext{Durch Zusammenfassen der Faktoren im Zähler mit Hilfe -der Rekursionsformel für die Gamma-Funktion und Multiplizieren -mit dem gemeinsamen Nenner -$\Gamma(n-k)\Gamma(k-1)=(n-k-1)\Gamma(n-k-1)(k-2)\Gamma(k-2)$ wird daraus} -\Gamma(n) -&= -(k-2) -\Gamma(n-1) -+ -(n-k-1) -\Gamma(n-1) -\intertext{Indem wir die Rekursionsformel für die Gamma-Funktion auf -die rechte Seite anwenden können wir erreichen, dass in allen Termen -ein Faktor -$\Gamma(n-1)$ auftritt:} -(n-1)\Gamma(n-1) -&= -(k-2)\Gamma(n-1) -+ -(n+k-1)\Gamma(n-1) -\\ -n-1 -&= -k-2 -+ -n-k-1 -\end{align*} - diff --git a/buch/chapters/040-rekursion/images/Makefile b/buch/chapters/040-rekursion/images/Makefile index 9608a94..86dfa1e 100644 --- a/buch/chapters/040-rekursion/images/Makefile +++ b/buch/chapters/040-rekursion/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: gammaplot.pdf fibonacci.pdf +all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf gammaplot.pdf: gammaplot.tex gammapaths.tex pdflatex gammaplot.tex @@ -16,3 +16,17 @@ fibonaccigrid.tex: fibonacci.m fibonacci.pdf: fibonacci.tex fibonaccigrid.tex pdflatex fibonacci.tex + +order.pdf: order.tex orderpath.tex + pdflatex order.tex + +orderpath.tex: order.m + octave order.m + +beta.pdf: beta.tex betapaths.tex + pdflatex beta.tex + +betapaths.tex: betadist.m + octave betadist.m + + diff --git a/buch/chapters/040-rekursion/images/beta.pdf b/buch/chapters/040-rekursion/images/beta.pdf new file mode 100644 index 0000000..0e6567b Binary files /dev/null and b/buch/chapters/040-rekursion/images/beta.pdf differ diff --git a/buch/chapters/040-rekursion/images/beta.tex b/buch/chapters/040-rekursion/images/beta.tex new file mode 100644 index 0000000..1e1a1b3 --- /dev/null +++ b/buch/chapters/040-rekursion/images/beta.tex @@ -0,0 +1,236 @@ +% +% beta.tex -- display some symmetric beta distributions +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\input{betapaths.tex} +\begin{document} +\def\skala{12} +\definecolor{colorone}{rgb}{1.0,0.6,0.0} +\definecolor{colortwo}{rgb}{1.0,0.0,0.0} +\definecolor{colorthree}{rgb}{0.6,0.0,0.6} +\definecolor{colorfour}{rgb}{0.6,0.0,1.0} +\definecolor{colorfive}{rgb}{0.0,0.0,1.0} +\definecolor{colorsix}{rgb}{0.4,0.6,1.0} +\definecolor{colorseven}{rgb}{0.0,0.0,0.0} +\definecolor{coloreight}{rgb}{0.0,0.8,0.8} +\definecolor{colornine}{rgb}{0.0,0.8,0.2} +\definecolor{colorten}{rgb}{0.2,0.4,0.0} +\definecolor{coloreleven}{rgb}{0.6,1.0,0.0} +\definecolor{colortwelve}{rgb}{1.0,0.8,0.4} + +\def\achsen{ + \foreach \x in {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9}{ + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; + } + \foreach \y in {1,2,3,4}{ + \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); + \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; + } + \def\x{1} + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; + \def\x{0} + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; + + \draw[->] ({-0.1/\skala},0) -- ({1*\dx+0.4/\skala},0) + coordinate[label={$x$}]; + \draw[->] (0,{-0.1/\skala}) -- (0,{\betamax*\dy+0.4/\skala},0) + coordinate[label={right:$\beta(a,b,x)$}]; +} + +\def\farbcoord#1#2{ + ({\dx*(0.63+((#1)/5)*0.27)},{\dx*(0.18+((#2)/5)*0.27)}) +} +\def\farbviereck{ + \foreach \x in {1,2,3,4}{ + \draw[color=gray!30] \farbcoord{\x}{0} -- \farbcoord{\x}{4}; + \draw[color=gray!30] \farbcoord{0}{\x} -- \farbcoord{4}{\x}; + } + \draw[->] \farbcoord{0}{0} -- \farbcoord{4.4}{0} + coordinate[label={$a$}]; + \draw[->] \farbcoord{0}{0} -- \farbcoord{0}{4.4} + coordinate[label={left: $b$}]; + \foreach \x in {1,2,3,4}{ + \node[color=gray] at \farbcoord{4}{\x} [right] {\tiny $b=\x$}; + %\fill[color=white,opacity=0.7] + % \farbcoord{(\x-0.1)}{3.3} + % rectangle + % \farbcoord{(\x+0.1)}{4}; + \node[color=gray] at \farbcoord{\x}{4} [right,rotate=90] + {\tiny $a=\x$}; + } +} +\def\farbpunkt#1#2#3{ + \fill[color=#3] \farbcoord{#1}{#2} circle[radius={0.1/\skala}]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\dx{1.15} +\def\dy{0.1} +\def\opa{0.1} + +\def\betamax{4.9} + +\begin{scope} +\clip (0,0) rectangle ({1*\dx},{\betamax*\dy}); +\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betabb -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betacc -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betadd -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betaff -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betagg -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betahh -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaii -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betajj -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle; +\fill[color=colortwelve,opacity=\opa] (0,0) -- \betall -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaaa; +\draw[color=colortwo] \betabb; +\draw[color=colorthree] \betacc; +\draw[color=colorfour] \betadd; +\draw[color=colorfive] \betaee; +\draw[color=colorsix] \betaff; +\draw[color=colorseven] \betagg; +\draw[color=coloreight] \betahh; +\draw[color=colornine] \betaii; +\draw[color=colorten] \betajj; +\draw[color=coloreleven] \betakk; +\draw[color=colortwelve] \betall; + +\end{scope} + +\achsen + +\farbviereck + +\farbpunkt{\alphatwelve}{\betatwelve}{colortwelve} +\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven} +\farbpunkt{\alphaten}{\betaten}{colorten} +\farbpunkt{\alphanine}{\betanine}{colornine} +\farbpunkt{\alphaeight}{\betaeight}{coloreight} +\farbpunkt{\alphaseven}{\betaseven}{colorseven} +\farbpunkt{\alphasix}{\betasix}{colorsix} +\farbpunkt{\alphafive}{\betafive}{colorfive} +\farbpunkt{\alphafour}{\betafour}{colorfour} +\farbpunkt{\alphathree}{\betathree}{colorthree} +\farbpunkt{\alphatwo}{\betatwo}{colortwo} +\farbpunkt{\alphaone}{\betaone}{colorone} + + +\def\betamax{4.9} + +\begin{scope}[yshift=-0.6cm] + +\begin{scope} +\clip (0,0) rectangle ({1*\dx},{\betamax*\dy}); +\fill[color=colorone,opacity=\opa] (0,0) -- \betaea -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betaeb -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betaec -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betaed -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betaef -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betaeg -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betaeh -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaei -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betaej -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaek -- (\dx,0) -- cycle; +\fill[color=colortwelve,opacity=\opa] (0,0) -- \betael -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaea; +\draw[color=colortwo] \betaeb; +\draw[color=colorthree] \betaec; +\draw[color=colorfour] \betaed; +\draw[color=colorfive] \betaee; +\draw[color=colorsix] \betaef; +\draw[color=colorseven] \betaeg; +\draw[color=coloreight] \betaeh; +\draw[color=colornine] \betaei; +\draw[color=colorten] \betaej; +\draw[color=coloreleven] \betaek; +\draw[color=colortwelve] \betael; +\end{scope} + +\achsen + +\farbviereck + +\farbpunkt{\alphafive}{\betatwelve}{colortwelve} +\farbpunkt{\alphafive}{\betaeleven}{coloreleven} +\farbpunkt{\alphafive}{\betaten}{colorten} +\farbpunkt{\alphafive}{\betanine}{colornine} +\farbpunkt{\alphafive}{\betaeight}{coloreight} +\farbpunkt{\alphafive}{\betaseven}{colorseven} +\farbpunkt{\alphafive}{\betasix}{colorsix} +\farbpunkt{\alphafive}{\betafive}{colorfive} +\farbpunkt{\alphafive}{\betafour}{colorfour} +\farbpunkt{\alphafive}{\betathree}{colorthree} +\farbpunkt{\alphafive}{\betatwo}{colortwo} +\farbpunkt{\alphafive}{\betaone}{colorone} + +\end{scope} + +\begin{scope}[yshift=-1.2cm] + +\begin{scope} +\clip (0,0) rectangle ({1*\dx},{\betamax*\dy}); +\fill[color=colorone,opacity=\opa] (0,0) -- \betaal -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betabl -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betacl -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betadl -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betael -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betafl -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betagl -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betahl -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betail -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betajl -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakl -- (\dx,0) -- cycle; +\fill[color=colortwelve,opacity=\opa] (0,0) -- \betall -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaal; +\draw[color=colortwo] \betabl; +\draw[color=colorthree] \betacl; +\draw[color=colorfour] \betadl; +\draw[color=colorfive] \betael; +\draw[color=colorsix] \betafl; +\draw[color=colorseven] \betagl; +\draw[color=coloreight] \betahl; +\draw[color=colornine] \betail; +\draw[color=colorten] \betajl; +\draw[color=coloreleven] \betakl; +\draw[color=colortwelve] \betall; +\end{scope} + +\achsen + +\farbviereck + +\farbpunkt{\alphatwelve}{\betatwelve}{colortwelve} +\farbpunkt{\alphaeleven}{\betatwelve}{coloreleven} +\farbpunkt{\alphaten}{\betatwelve}{colorten} +\farbpunkt{\alphanine}{\betatwelve}{colornine} +\farbpunkt{\alphaeight}{\betatwelve}{coloreight} +\farbpunkt{\alphaseven}{\betatwelve}{colorseven} +\farbpunkt{\alphasix}{\betatwelve}{colorsix} +\farbpunkt{\alphafive}{\betatwelve}{colorfive} +\farbpunkt{\alphafour}{\betatwelve}{colorfour} +\farbpunkt{\alphathree}{\betatwelve}{colorthree} +\farbpunkt{\alphatwo}{\betatwelve}{colortwo} +\farbpunkt{\alphaone}{\betatwelve}{colorone} + +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/040-rekursion/images/betadist.m b/buch/chapters/040-rekursion/images/betadist.m new file mode 100644 index 0000000..5b466a6 --- /dev/null +++ b/buch/chapters/040-rekursion/images/betadist.m @@ -0,0 +1,58 @@ +# +# betadist.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global N; +N = 201; +global nmin; +global nmax; +nmin = -4; +nmax = 7; +n = nmax - nmin + 1 +A = 3; + +t = (nmin:nmax) / nmax; +alpha = 1 + A * t .* abs(t) +#alpha(1) = 0.01; + +#alpha = [ 1, 1.03, 1.05, 1.1, 1.25, 1.5, 2, 2.5, 3, 4, 5 ]; +beta = alpha; +names = [ "one"; "two"; "three"; "four"; "five"; "six"; "seven"; "eight"; + "nine"; "ten"; "eleven"; "twelve" ] + +function retval = Beta(a, b, x) + retval = x^(a-1) * (1-x)^(b-1) / beta(a, b); + if (retval > 100) + retval = 100 + end +end + +function plotbeta(fn, a, b, name) + global N; + fprintf(fn, "\\def\\beta%s{\n", strtrim(name)); + fprintf(fn, "\t({%.4f*\\dx},{%.4f*\\dy})", 0, Beta(a, b, 0)); + for x = (1:N-1)/(N-1) + X = (1-cos(pi * x))/2; + fprintf(fn, "\n\t--({%.4f*\\dx},{%.4f*\\dy})", + X, Beta(a, b, X)); + end + fprintf(fn, "\n}\n"); +end + +fn = fopen("betapaths.tex", "w"); + +for i = (1:n) + fprintf(fn, "\\def\\alpha%s{%f}\n", strtrim(names(i,:)), alpha(i)); + fprintf(fn, "\\def\\beta%s{%f}\n", strtrim(names(i,:)), beta(i)); +end + +for i = (1:n) + for j = (1:n) + printf("working on %d,%d:\n", i, j); + plotbeta(fn, alpha(i), beta(j), + char(['a' + i - 1, 'a' + j - 1])); + end +end + +fclose(fn); diff --git a/buch/chapters/040-rekursion/images/order.m b/buch/chapters/040-rekursion/images/order.m new file mode 100644 index 0000000..762f458 --- /dev/null +++ b/buch/chapters/040-rekursion/images/order.m @@ -0,0 +1,119 @@ +# +# order.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global N; +N = 10; +global subdivisions; +subdivisions = 100; +global P; +P = 0.5 + +function retval = orderF(p, n, k) + retval = 0; + for i = (k:n) + retval = retval + nchoosek(n,i) * p^i * (1-p)^(n-i); + end +end + +function retval = orderd(p, n, k) + retval = 0; + for i = (k:n) + s = i * p^(i-1) * (1-p)^(n-i); + s = s - p^i * (n-i) * (1-p)^(n-i-1); + retval = retval + nchoosek(n,i) * s; + end +end + +function retval = orders(p, n, k) + retval = k * nchoosek(n, k) * p^(k-1) * (1-p)^(n-k); +end + +function orderpath(fn, k, name) + fprintf(fn, "\\def\\order%s{\n\t(0,0)", name); + global N; + global subdivisions; + for i = (0:subdivisions) + p = i/subdivisions; + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", + p, orderF(p, N, k)); + end + fprintf(fn, "\n}\n"); +end + +function orderdpath(fn, k, name) + fprintf(fn, "\\def\\orderd%s{\n\t(0,0)", name); + global N; + global subdivisions; + for i = (1:subdivisions-1) + p = i/subdivisions; + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", + p, orderd(p, N, k)); + end + fprintf(fn, "\n\t-- ({1*\\dx},0)"); + fprintf(fn, "\n}\n"); +end + +function orderspath(fn, k, name) + fprintf(fn, "\\def\\orders%s{\n\t(0,0)", name); + global N; + global subdivisions; + for i = (1:subdivisions-1) + p = i/subdivisions; + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", + p, orders(p, N, k)); + end + fprintf(fn, "\n\t-- ({1*\\dx},0)"); + fprintf(fn, "\n}\n"); +end + +fn = fopen("orderpath.tex", "w"); + +orderpath(fn, 0, "zero"); +orderdpath(fn, 0, "zero"); +orderspath(fn, 0, "zero"); + +orderpath(fn, 1, "one"); +orderdpath(fn, 1, "one"); +orderspath(fn, 1, "one"); + +orderpath(fn, 2, "two"); +orderdpath(fn, 2, "two"); +orderspath(fn, 2, "two"); + +orderpath(fn, 3, "three"); +orderdpath(fn, 3, "three"); +orderspath(fn, 3, "three"); + +orderpath(fn, 4, "four"); +orderdpath(fn, 4, "four"); +orderspath(fn, 4, "four"); + +orderpath(fn, 5, "five"); +orderdpath(fn, 5, "five"); +orderspath(fn, 5, "five"); + +orderpath(fn, 6, "six"); +orderdpath(fn, 6, "six"); +orderspath(fn, 6, "six"); + +orderpath(fn, 7, "seven"); +orderdpath(fn, 7, "seven"); +orderspath(fn, 7, "seven"); + +orderpath(fn, 8, "eight"); +orderdpath(fn, 8, "eight"); +orderspath(fn, 8, "eight"); + +orderpath(fn, 9, "nine"); +orderdpath(fn, 9, "nine"); +orderspath(fn, 9, "nine"); + +orderpath(fn, 10, "ten"); +orderdpath(fn, 10, "ten"); +orderspath(fn, 10, "ten"); + +fclose(fn); + + diff --git a/buch/chapters/040-rekursion/images/order.pdf b/buch/chapters/040-rekursion/images/order.pdf new file mode 100644 index 0000000..cc175a9 Binary files /dev/null and b/buch/chapters/040-rekursion/images/order.pdf differ diff --git a/buch/chapters/040-rekursion/images/order.tex b/buch/chapters/040-rekursion/images/order.tex new file mode 100644 index 0000000..9a2511c --- /dev/null +++ b/buch/chapters/040-rekursion/images/order.tex @@ -0,0 +1,125 @@ +% +% order.tex -- Verteilungsfunktion für Ordnungsstatistik +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{8} +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\n{10} +\def\E#1#2{ + \draw[color=#2] + ({\dx*#1/(\n+1)},{-0.1/\skala}) -- ({\dx*#1/(\n+1)},{4.4*\dy}); + \node[color=#2] at ({\dx*#1/(\n+1)},{3.2*\dy}) + [rotate=90,above right] {$k=#1$}; +} +\def\var#1#2{ + \pgfmathparse{\dx*sqrt(#1*(\n-#1+1)/((\n+1)*(\n+1)*(\n+2)))} + \xdef\var{\pgfmathresult} + \fill[color=#2,opacity=0.5] + ({\dx*#1/(\n+1)-\var},0) rectangle ({\dx*#1/(\n+1)+\var},{4.4*\dy}); +} + +\input{orderpath.tex} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\dx{1.6} +\def\dy{0.5} + +\def\pfad#1#2{ +\draw[color=#2,line width=1.4pt] ({-0.1/\skala},0) + -- + #1 + -- + ({1*\dx+0.1/\skala},0.5); +} + +\pfad{\orderzero}{darkgreen!20} +\pfad{\orderone}{darkgreen!20} +\pfad{\ordertwo}{darkgreen!20} +\pfad{\orderthree}{darkgreen!20} +\pfad{\orderfour}{darkgreen!20} +\pfad{\orderfive}{darkgreen!20} +\pfad{\ordersix}{darkgreen!20} +\pfad{\ordereight}{darkgreen!20} +\pfad{\ordernine}{darkgreen!20} +\pfad{\orderten}{darkgreen!20} +\pfad{\orderseven}{darkgreen} + +\draw[->] ({-0.1/\skala},0) -- ({1.03*\dx},0) coordinate[label={$x$}]; +\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={right:$F(X)$}]; +\foreach \x in {0,0.2,0.4,0.6,0.8,1}{ + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; +} +\foreach \y in {0.5,1}{ + \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); + \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; +} + +\node[color=darkgreen] at (0.65,{0.5*\dy}) [above,rotate=55] {$k=7$}; + +\begin{scope}[yshift=-0.7cm] +\def\dy{0.125} + +\foreach \k in {1,2,3,4,5,6,8,9,10}{ + \E{\k}{blue!30} +} +\def\k{7} +\var{\k}{orange!40} +\node[color=blue] at ({\dx*\k/(\n+1)},{4.3*\dy}) [above] {$E(X_{7:n})$}; + +\def\pfad#1#2{ + \draw[color=#2,line width=1.4pt] ({-0.1/\skala},0) + -- + #1 + -- + ({1*\dx+0.1/\skala},0.0); +} + +\begin{scope} +\clip ({-0.1/\skala},{-0.1/\skala}) + rectangle ({1*\dx+0.1/\skala},{0.56+0.1/\skala}); + +\pfad{\orderdzero}{red!20} +\pfad{\orderdone}{red!20} +\pfad{\orderdtwo}{red!20} +\pfad{\orderdthree}{red!20} +\pfad{\orderdfour}{red!20} +\pfad{\orderdfive}{red!20} +\pfad{\orderdsix}{red!20} +\pfad{\orderdeight}{red!20} +\pfad{\orderdnine}{red!20} +\pfad{\orderdten}{red!20} +\E{\k}{blue} +\pfad{\orderdseven}{red} + +\end{scope} + +\draw[->] ({-0.1/\skala},0) -- ({1.03*\dx},0) coordinate[label={$x$}]; +\draw[->] (0,{-0.1/\skala}) -- (0,0.6) coordinate[label={right:$\varphi(X)$}]; +\foreach \x in {0,0.2,0.4,0.6,0.8,1}{ + \draw ({\x*\dx},{-0.1/\skala}) -- ({\x*\dx},{0.1/\skala}); + \node at ({\x*\dx},{-0.1/\skala}) [below] {$\x$}; +} +\foreach \y in {1,2,3,4}{ + \draw ({-0.1/\skala},{\y*\dy}) -- ({0.1/\skala},{\y*\dy}); + \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; +} + +\node[color=red] at ({0.67*\dx},{2.7*\dy}) [above] {$k=7$}; + + +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/070-orthogonalitaet/Makefile.inc b/buch/chapters/070-orthogonalitaet/Makefile.inc index 48e5356..286ab2e 100644 --- a/buch/chapters/070-orthogonalitaet/Makefile.inc +++ b/buch/chapters/070-orthogonalitaet/Makefile.inc @@ -13,4 +13,5 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/070-orthogonalitaet/jacobi.tex \ chapters/070-orthogonalitaet/sturm.tex \ chapters/070-orthogonalitaet/gaussquadratur.tex \ + chapters/070-orthogonalitaet/uebungsaufgaben/701.tex \ chapters/070-orthogonalitaet/chapter.tex diff --git a/buch/chapters/070-orthogonalitaet/chapter.tex b/buch/chapters/070-orthogonalitaet/chapter.tex index 5ebb795..4756844 100644 --- a/buch/chapters/070-orthogonalitaet/chapter.tex +++ b/buch/chapters/070-orthogonalitaet/chapter.tex @@ -25,7 +25,7 @@ \rhead{Übungsaufgaben} \aufgabetoplevel{chapters/070-orthogonalitaet/uebungsaufgaben} \begin{uebungsaufgaben} -%\uebungsaufgabe{0} +\uebungsaufgabe{701} %\uebungsaufgabe{1} \end{uebungsaufgaben} diff --git a/buch/chapters/070-orthogonalitaet/uebungsaufgaben/701.tex b/buch/chapters/070-orthogonalitaet/uebungsaufgaben/701.tex new file mode 100644 index 0000000..dad489f --- /dev/null +++ b/buch/chapters/070-orthogonalitaet/uebungsaufgaben/701.tex @@ -0,0 +1,137 @@ +Für Funktionen auf dem Interval $(-\frac{\pi}2,\frac{\pi}2)$ ist +\[ +\langle f,g\rangle += +\frac12\int_{-\frac{\pi}2}^{\frac{\pi}2} f(x)g(x)\cos x\,dx +\] +ein Skalarprodukt. +Bestimmen Sie bezüglich dieses Skalarproduktes orthogonale Polynome +bis zum Grad $2$. + +\begin{hinweis} +Verwenden Sie +\begin{align*} +\int_{-\frac{\pi}2}^{\frac{\pi}2} 1\cos x\,dx +&= +1, +& +\int_{-\frac{\pi}2}^{\frac{\pi}2} x^2\cos x\,dx +&= +\frac{\pi^2-8}{2}, +& +\int_{-\frac{\pi}2}^{\frac{\pi}2} x^4\cos x\,dx +&= +\frac{\pi^4-48\pi^2+384}{8}. +\end{align*} +\end{hinweis} + +\begin{loesung} +Wir müssen den Gram-Schmidt-Orthogonalisierungsprozess für die +Polynome $f_0(x)=1$, $f_1(x)=x$ und $f_2(x)=x^2$ durchführen. +Zunächst halten wir fest, dass +\[ +\langle f_0,f_0\rangle += +\frac12 +\int_{-\frac{\pi}2}^{\frac{\pi}2} \cos x\,dx += +1, +\] +das Polynom $g_0(x)=f_0(x)$ ist hat also Norm $1$. + +Ein dazu orthogonales Polynom ist +\( +f_1(x) - \langle g_0,f_1\rangle g_0(x), +\) +wir müssen also das Skalarprodukt +\[ +\langle g_0,f_1\rangle += +\frac{1}{2} +\int_{-\frac{\pi}2}^{\frac{\pi}2} +x\cos x\,dx +\] +bestimmen. +Es verschwindet, weil die Funktion $x\cos x$ ungerade ist. +Somit ist die Funktion $f_1(x)=x$ orthogonal zu $f_0(x)=1$, um sie auch zu +normieren berechnen wir das Integral +\[ +\| f_1\|^2 += +\frac12\int_{-\frac{\pi}2}^{\frac{\pi}2} x^2\cos x\,dx += +\frac{\pi^2-8}{4}, +\] +und +\[ +g_1(x) += +\frac{2}{\sqrt{\pi^2-8}} x. +\] + +Zur Berechnung von $g_2$ müssen wir die Skalarprodukte +\begin{align*} +\langle g_0,f_2\rangle +&= +\frac{1}{2} +\int_{-\frac{\pi}2}^{\frac{\pi}2} +x^2 +\cos x +\,dx += +\frac{\pi^2-8}{4} +\\ +\langle g_1,f_2\rangle +&= +\frac{1}{2} +\int_{-\frac{\pi}2}^{\frac{\pi}2} +\frac{2}{\sqrt{\pi^2-8}} +x +\cdot x^2 +\cos x +\,dx += +0 +\end{align*} +bestimmen. +Damit wird das dritte Polynom +\[ +f_2(x) +- g_0(x)\langle g_0,f_2\rangle +- g_1(x)\langle g_1,f_2\rangle += +x^2 - \frac{\pi^2-8}{4}, +\] +welches bereits orthogonal ist zu $g_0$ und $g_1$. +Wir können auch noch erreichen, obwohl das nicht verlangt war, +dass es normiert ist, indem wir die Norm berechnen: +\[ +\left\| x^2-\frac{\pi^2-8}{4} \right\|^2 += +\frac12 +\int_{-\frac{\pi}2}^{\frac{\pi}2} +\biggl(x^2-\frac{\pi^2-8}{4}\biggr)^2 +\cos x\,dx += +20-2\pi^2 +\] +woraus sich +\[ +g_2(x) += +\frac{1}{\sqrt{20-2\pi^2}} +\biggl( +x^2 - \frac{\pi^2-8}{4} +\biggr). +\] +Damit haben wir die ersten drei bezüglich des obigen Skalarproduktes +orthogonalen Polynome +\begin{align*} +g_0(x)&=1, +& +g_1(x)&=\frac{2x}{\sqrt{\pi^2-8}}, +& +g_2(x)&=\frac{1}{\sqrt{20-2\pi^2}}\biggl(x^2-\frac{\pi^2-8}{4}\biggr) +\end{align*} +gefunden. +\end{loesung} diff --git a/buch/chapters/090-pde/Makefile.inc b/buch/chapters/090-pde/Makefile.inc index a9ef74a..c64af06 100644 --- a/buch/chapters/090-pde/Makefile.inc +++ b/buch/chapters/090-pde/Makefile.inc @@ -10,4 +10,5 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/090-pde/rechteck.tex \ chapters/090-pde/kreis.tex \ chapters/090-pde/kugel.tex \ + chapters/090-pde/uebungsaufgaben/901.tex \ chapters/090-pde/chapter.tex diff --git a/buch/chapters/090-pde/chapter.tex b/buch/chapters/090-pde/chapter.tex index db909ee..a393da5 100644 --- a/buch/chapters/090-pde/chapter.tex +++ b/buch/chapters/090-pde/chapter.tex @@ -21,11 +21,11 @@ deren Lösungen spezielle Funktionen sind. \input{chapters/090-pde/kreis.tex} \input{chapters/090-pde/kugel.tex} -%\section*{Übungsaufgaben} -%\rhead{Übungsaufgaben} -%\aufgabetoplevel{chapters/020-exponential/uebungsaufgaben} -%\begin{uebungsaufgaben} -%\uebungsaufgabe{0} +\section*{Übungsaufgaben} +\rhead{Übungsaufgaben} +\aufgabetoplevel{chapters/090-pde/uebungsaufgaben} +\begin{uebungsaufgaben} +\uebungsaufgabe{901} %\uebungsaufgabe{1} -%\end{uebungsaufgaben} +\end{uebungsaufgaben} diff --git a/buch/chapters/090-pde/kreis.tex b/buch/chapters/090-pde/kreis.tex index a24b6bb..b4ce8d7 100644 --- a/buch/chapters/090-pde/kreis.tex +++ b/buch/chapters/090-pde/kreis.tex @@ -120,7 +120,7 @@ für $\Phi(\varphi)$. Die Gleichung für $\Phi$ hat für $\mu\ne 0$ die Lösungen \begin{align*} \Phi(\varphi) &= \cos\mu\varphi -\text{und}\qquad +&&\text{und}& \Phi(\varphi) &= \sin\mu\varphi. \end{align*} Die Lösung muss aber auch stetig sein, d.~h.~es muss $\Phi(0)=\Phi(2\pi)$ diff --git a/buch/chapters/090-pde/uebungsaufgaben/901.tex b/buch/chapters/090-pde/uebungsaufgaben/901.tex new file mode 100644 index 0000000..67fa8e5 --- /dev/null +++ b/buch/chapters/090-pde/uebungsaufgaben/901.tex @@ -0,0 +1,82 @@ +Die Differentialgleichung +\begin{equation} +\frac{\partial u}{\partial t} = \kappa \frac{\partial^2 u}{\partial x^2} +\qquad +\text{im Gebiet} +\qquad +(t,x)\in \Omega=\mathbb{R}^+\times (0,l) +\label{505:waermeleitungsgleichung} +\end{equation} +beschreibt die Änderung der Temperatur eines Stabes der Länge $l$. +Die homogene Randbedingung +\begin{equation} +u(t,0)= +u(t,l)=0 +\label{505:homogene-randbedingung} +\end{equation} +besagt, dass der Stab an seinen Enden auf Temperatur $0$ gehalten. +Zur Lösung dieser Differentialgleichung muss auch die Temperatur +zur Zeit $t=0$ in Form einer Randbedingung +\[ +u(0,x) = T_0(x) +\] +gegeben sein. +Führen Sie Separation für die +Differentialgleichung~\eqref{505:waermeleitungsgleichung} +durch und bestimmen Sie die zulässigen Werte der Separationskonstanten. + +\begin{loesung} +Man verwendet den Ansatz $u(t,x)= T(t)\cdot X(x)$ und setzt diesen +in die Differentialgleichung ein, die dadurch zu +\[ +T'(t)X(x) = \kappa T(t) X''(x) +\] +wird. +Division durch $T(t)X(x)$ wird dies zu +\[ +\frac{T'(t)}{T(t)} += +\kappa +\frac{X''(x)}{X(x)}. +\] +Da die linke Seite nur von $t$ abhängt, die rechte aber nur von $x$, müssen +beide Seiten konstant sein. +Wir bezeichnen die Konstante mit $-\lambda^2$, so dass wir die beiden +gewöhnlichen Differentialgleichungen +\begin{align*} +\frac{1}{\kappa} +\frac{T'(t)}{T(t)}&=-\lambda^2 +& +\frac{X''(x)}{X(x)}&=-\lambda^2 +\\ +T'(t)&=-\lambda^2\kappa T(t) +& +X''(x) &= -\lambda^2 X(x) +\intertext{welche die Lösungen} +T(t)&=Ce^{-\lambda^2\kappa t} +& +X(x)&= A\cos\lambda x + B\sin\lambda x +\end{align*} +haben. +Die Lösung $X(x)$ muss aber auch die homogene Randbedingung +\eqref{505:homogene-randbedingung} erfüllen. +Setzt man $x=0$ und $x=l$ ein, folgt +\begin{align*} +0 = X(0)&=A\cos 0 + B\sin 0 = A +& +0 = X(l)&=B\sin \lambda l, +\end{align*} +woraus man schliessen kann, dass $\lambda l$ ein ganzzahliges +Vielfaches von $\pi$ ist, wir schreiben $\lambda l = k\pi$ oder +\[ +\lambda = \frac{k\pi}{l}. +\] +Damit sind die möglichen Werte $\lambda$ bestimmt und man kann jetzt +auch die möglichen Lösungen aufschreiben, sie sind +\[ +u(t,x) += +\sum_{k=1}^\infty b_k e^{-k^2\pi^2\kappa t/l^2}\sin\frac{k\pi x}{l}. +\qedhere +\] +\end{loesung} diff --git a/buch/papers/dreieck/images/beta.pdf b/buch/papers/dreieck/images/beta.pdf index c3ab4f6..cd5ed80 100644 Binary files a/buch/papers/dreieck/images/beta.pdf and b/buch/papers/dreieck/images/beta.pdf differ diff --git a/buch/papers/dreieck/images/beta.tex b/buch/papers/dreieck/images/beta.tex index 50509ee..f0ffdf0 100644 --- a/buch/papers/dreieck/images/beta.tex +++ b/buch/papers/dreieck/images/beta.tex @@ -23,7 +23,8 @@ \definecolor{coloreight}{rgb}{0.0,0.8,0.8} \definecolor{colornine}{rgb}{0.0,0.8,0.2} \definecolor{colorten}{rgb}{0.2,0.4,0.0} -\definecolor{coloreleven}{rgb}{1.0,0.8,0.4} +\definecolor{coloreleven}{rgb}{0.6,1.0,0.0} +\definecolor{colortwelve}{rgb}{1.0,0.8,0.4} \def\achsen{ \foreach \x in {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9}{ @@ -47,24 +48,24 @@ } \def\farbcoord#1#2{ - ({\dx*(0.7+((#1-1)/4)*0.27)},{\dx*(0.15+((#2-1)/4)*0.27)}) + ({\dx*(0.63+((#1)/5)*0.27)},{\dx*(0.18+((#2)/5)*0.27)}) } \def\farbviereck{ - \foreach \x in {1,2,3,4,5}{ - \draw[color=gray!30] \farbcoord{\x}{1} -- \farbcoord{\x}{5}; - \draw[color=gray!30] \farbcoord{1}{\x} -- \farbcoord{5}{\x}; + \foreach \x in {1,2,3,4}{ + \draw[color=gray!30] \farbcoord{\x}{0} -- \farbcoord{\x}{4}; + \draw[color=gray!30] \farbcoord{0}{\x} -- \farbcoord{4}{\x}; } - \draw[->] \farbcoord{1}{1} -- \farbcoord{5.4}{1} + \draw[->] \farbcoord{0}{0} -- \farbcoord{4.4}{0} coordinate[label={$a$}]; - \draw[->] \farbcoord{1}{1} -- \farbcoord{1}{5.4} + \draw[->] \farbcoord{0}{0} -- \farbcoord{0}{4.4} coordinate[label={left: $b$}]; - \foreach \x in {1,2,3,4,5}{ - \node[color=gray] at \farbcoord{5}{\x} [right] {\tiny $b=\x$}; - \fill[color=white,opacity=0.7] - \farbcoord{(\x-0.1)}{4.3} - rectangle - \farbcoord{(\x+0.1)}{5}; - \node[color=gray] at \farbcoord{\x}{5} [left,rotate=90] + \foreach \x in {1,2,3,4}{ + \node[color=gray] at \farbcoord{4}{\x} [right] {\tiny $b=\x$}; + %\fill[color=white,opacity=0.7] + % \farbcoord{(\x-0.1)}{3.3} + % rectangle + % \farbcoord{(\x+0.1)}{4}; + \node[color=gray] at \farbcoord{\x}{4} [right,rotate=90] {\tiny $a=\x$}; } } @@ -74,23 +75,26 @@ \begin{tikzpicture}[>=latex,thick,scale=\skala] -\def\dx{1} +\def\dx{1.1} \def\dy{0.1} \def\opa{0.1} -\def\betamax{4.2} - -\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle; -\fill[color=colortwo,opacity=\opa] (0,0) -- \betabb -- (\dx,0) -- cycle; -\fill[color=colorthree,opacity=\opa] (0,0) -- \betacc -- (\dx,0) -- cycle; -\fill[color=colorfour,opacity=\opa] (0,0) -- \betadd -- (\dx,0) -- cycle; -\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle; -\fill[color=colorsix,opacity=\opa] (0,0) -- \betaff -- (\dx,0) -- cycle; -\fill[color=colorseven,opacity=\opa] (0,0) -- \betagg -- (\dx,0) -- cycle; -\fill[color=coloreight,opacity=\opa] (0,0) -- \betahh -- (\dx,0) -- cycle; -\fill[color=colornine,opacity=\opa] (0,0) -- \betaii -- (\dx,0) -- cycle; -\fill[color=colorten,opacity=\opa] (0,0) -- \betajj -- (\dx,0) -- cycle; +\def\betamax{4.9} + +\begin{scope} +\clip (0,0) rectangle ({1*\dx},{\betamax*\dy}); +\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betabb -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betacc -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betadd -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betaff -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betagg -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betahh -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaii -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betajj -- (\dx,0) -- cycle; \fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle; +\fill[color=colortwelve,opacity=\opa] (0,0) -- \betall -- (\dx,0) -- cycle; \draw[color=colorone] \betaaa; \draw[color=colortwo] \betabb; @@ -103,11 +107,15 @@ \draw[color=colornine] \betaii; \draw[color=colorten] \betajj; \draw[color=coloreleven] \betakk; +\draw[color=colortwelve] \betall; + +\end{scope} \achsen \farbviereck +\farbpunkt{\alphatwelve}{\betatwelve}{colortwelve} \farbpunkt{\alphaeleven}{\betaeleven}{coloreleven} \farbpunkt{\alphaten}{\betaten}{colorten} \farbpunkt{\alphanine}{\betanine}{colornine} @@ -124,88 +132,102 @@ \def\betamax{4.9} \begin{scope}[yshift=-0.6cm] -\fill[color=colorone,opacity=\opa] (0,0) -- \betaaa -- (\dx,0) -- cycle; -\fill[color=colortwo,opacity=\opa] (0,0) -- \betaab -- (\dx,0) -- cycle; -\fill[color=colorthree,opacity=\opa] (0,0) -- \betaac -- (\dx,0) -- cycle; -\fill[color=colorfour,opacity=\opa] (0,0) -- \betaad -- (\dx,0) -- cycle; -\fill[color=colorfive,opacity=\opa] (0,0) -- \betaae -- (\dx,0) -- cycle; -\fill[color=colorsix,opacity=\opa] (0,0) -- \betaaf -- (\dx,0) -- cycle; -\fill[color=colorseven,opacity=\opa] (0,0) -- \betaag -- (\dx,0) -- cycle; -\fill[color=coloreight,opacity=\opa] (0,0) -- \betaah -- (\dx,0) -- cycle; -\fill[color=colornine,opacity=\opa] (0,0) -- \betaai -- (\dx,0) -- cycle; -\fill[color=colorten,opacity=\opa] (0,0) -- \betaaj -- (\dx,0) -- cycle; -\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle; -\draw[color=colorone] \betaaa; -\draw[color=colortwo] \betaab; -\draw[color=colorthree] \betaac; -\draw[color=colorfour] \betaad; -\draw[color=colorfive] \betaae; -\draw[color=colorsix] \betaaf; -\draw[color=colorseven] \betaag; -\draw[color=coloreight] \betaah; -\draw[color=colornine] \betaai; -\draw[color=colorten] \betaaj; -\draw[color=coloreleven] \betaak; +\begin{scope} +\clip (0,0) rectangle ({1*\dx},{\betamax*\dy}); +\fill[color=colorone,opacity=\opa] (0,0) -- \betaea -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betaeb -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betaec -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betaed -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betaee -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betaef -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betaeg -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betaeh -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betaei -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betaej -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betaek -- (\dx,0) -- cycle; +\fill[color=colortwelve,opacity=\opa] (0,0) -- \betael -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaea; +\draw[color=colortwo] \betaeb; +\draw[color=colorthree] \betaec; +\draw[color=colorfour] \betaed; +\draw[color=colorfive] \betaee; +\draw[color=colorsix] \betaef; +\draw[color=colorseven] \betaeg; +\draw[color=coloreight] \betaeh; +\draw[color=colornine] \betaei; +\draw[color=colorten] \betaej; +\draw[color=coloreleven] \betaek; +\draw[color=colortwelve] \betael; +\end{scope} \achsen \farbviereck -\farbpunkt{\alphaone}{\betaeleven}{coloreleven} -\farbpunkt{\alphaone}{\betaten}{colorten} -\farbpunkt{\alphaone}{\betanine}{colornine} -\farbpunkt{\alphaone}{\betaeight}{coloreight} -\farbpunkt{\alphaone}{\betaseven}{colorseven} -\farbpunkt{\alphaone}{\betasix}{colorsix} -\farbpunkt{\alphaone}{\betafive}{colorfive} -\farbpunkt{\alphaone}{\betafour}{colorfour} -\farbpunkt{\alphaone}{\betathree}{colorthree} -\farbpunkt{\alphaone}{\betatwo}{colortwo} -\farbpunkt{\alphaone}{\betaone}{colorone} +\farbpunkt{\alphafive}{\betatwelve}{colortwelve} +\farbpunkt{\alphafive}{\betaeleven}{coloreleven} +\farbpunkt{\alphafive}{\betaten}{colorten} +\farbpunkt{\alphafive}{\betanine}{colornine} +\farbpunkt{\alphafive}{\betaeight}{coloreight} +\farbpunkt{\alphafive}{\betaseven}{colorseven} +\farbpunkt{\alphafive}{\betasix}{colorsix} +\farbpunkt{\alphafive}{\betafive}{colorfive} +\farbpunkt{\alphafive}{\betafour}{colorfour} +\farbpunkt{\alphafive}{\betathree}{colorthree} +\farbpunkt{\alphafive}{\betatwo}{colortwo} +\farbpunkt{\alphafive}{\betaone}{colorone} \end{scope} \begin{scope}[yshift=-1.2cm] -\fill[color=colorone,opacity=\opa] (0,0) -- \betaak -- (\dx,0) -- cycle; -\fill[color=colortwo,opacity=\opa] (0,0) -- \betabk -- (\dx,0) -- cycle; -\fill[color=colorthree,opacity=\opa] (0,0) -- \betack -- (\dx,0) -- cycle; -\fill[color=colorfour,opacity=\opa] (0,0) -- \betadk -- (\dx,0) -- cycle; -\fill[color=colorfive,opacity=\opa] (0,0) -- \betaek -- (\dx,0) -- cycle; -\fill[color=colorsix,opacity=\opa] (0,0) -- \betafk -- (\dx,0) -- cycle; -\fill[color=colorseven,opacity=\opa] (0,0) -- \betagk -- (\dx,0) -- cycle; -\fill[color=coloreight,opacity=\opa] (0,0) -- \betahk -- (\dx,0) -- cycle; -\fill[color=colornine,opacity=\opa] (0,0) -- \betaik -- (\dx,0) -- cycle; -\fill[color=colorten,opacity=\opa] (0,0) -- \betajk -- (\dx,0) -- cycle; -\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakk -- (\dx,0) -- cycle; -\draw[color=colorone] \betaak; -\draw[color=colortwo] \betabk; -\draw[color=colorthree] \betack; -\draw[color=colorfour] \betadk; -\draw[color=colorfive] \betaek; -\draw[color=colorsix] \betafk; -\draw[color=colorseven] \betagk; -\draw[color=coloreight] \betahk; -\draw[color=colornine] \betaik; -\draw[color=colorten] \betajk; -\draw[color=coloreleven] \betakk; +\begin{scope} +\clip (0,0) rectangle ({1*\dx},{\betamax*\dy}); +\fill[color=colorone,opacity=\opa] (0,0) -- \betaal -- (\dx,0) -- cycle; +\fill[color=colortwo,opacity=\opa] (0,0) -- \betabl -- (\dx,0) -- cycle; +\fill[color=colorthree,opacity=\opa] (0,0) -- \betacl -- (\dx,0) -- cycle; +\fill[color=colorfour,opacity=\opa] (0,0) -- \betadl -- (\dx,0) -- cycle; +\fill[color=colorfive,opacity=\opa] (0,0) -- \betael -- (\dx,0) -- cycle; +\fill[color=colorsix,opacity=\opa] (0,0) -- \betafl -- (\dx,0) -- cycle; +\fill[color=colorseven,opacity=\opa] (0,0) -- \betagl -- (\dx,0) -- cycle; +\fill[color=coloreight,opacity=\opa] (0,0) -- \betahl -- (\dx,0) -- cycle; +\fill[color=colornine,opacity=\opa] (0,0) -- \betail -- (\dx,0) -- cycle; +\fill[color=colorten,opacity=\opa] (0,0) -- \betajl -- (\dx,0) -- cycle; +\fill[color=coloreleven,opacity=\opa] (0,0) -- \betakl -- (\dx,0) -- cycle; +\fill[color=colortwelve,opacity=\opa] (0,0) -- \betall -- (\dx,0) -- cycle; + +\draw[color=colorone] \betaal; +\draw[color=colortwo] \betabl; +\draw[color=colorthree] \betacl; +\draw[color=colorfour] \betadl; +\draw[color=colorfive] \betael; +\draw[color=colorsix] \betafl; +\draw[color=colorseven] \betagl; +\draw[color=coloreight] \betahl; +\draw[color=colornine] \betail; +\draw[color=colorten] \betajl; +\draw[color=coloreleven] \betakl; +\draw[color=colortwelve] \betall; +\end{scope} \achsen \farbviereck -\farbpunkt{\alphaeleven}{\betaeleven}{coloreleven} -\farbpunkt{\alphaten}{\betaeleven}{colorten} -\farbpunkt{\alphanine}{\betaeleven}{colornine} -\farbpunkt{\alphaeight}{\betaeleven}{coloreight} -\farbpunkt{\alphaseven}{\betaeleven}{colorseven} -\farbpunkt{\alphasix}{\betaeleven}{colorsix} -\farbpunkt{\alphafive}{\betaeleven}{colorfive} -\farbpunkt{\alphafour}{\betaeleven}{colorfour} -\farbpunkt{\alphathree}{\betaeleven}{colorthree} -\farbpunkt{\alphatwo}{\betaeleven}{colortwo} -\farbpunkt{\alphaone}{\betaeleven}{colorone} +\farbpunkt{\alphatwelve}{\betatwelve}{colortwelve} +\farbpunkt{\alphaeleven}{\betatwelve}{coloreleven} +\farbpunkt{\alphaten}{\betatwelve}{colorten} +\farbpunkt{\alphanine}{\betatwelve}{colornine} +\farbpunkt{\alphaeight}{\betatwelve}{coloreight} +\farbpunkt{\alphaseven}{\betatwelve}{colorseven} +\farbpunkt{\alphasix}{\betatwelve}{colorsix} +\farbpunkt{\alphafive}{\betatwelve}{colorfive} +\farbpunkt{\alphafour}{\betatwelve}{colorfour} +\farbpunkt{\alphathree}{\betatwelve}{colorthree} +\farbpunkt{\alphatwo}{\betatwelve}{colortwo} +\farbpunkt{\alphaone}{\betatwelve}{colorone} \end{scope} diff --git a/buch/papers/dreieck/images/betadist.m b/buch/papers/dreieck/images/betadist.m index 9ff78ed..5b466a6 100644 --- a/buch/papers/dreieck/images/betadist.m +++ b/buch/papers/dreieck/images/betadist.m @@ -5,24 +5,32 @@ # global N; N = 201; -global n; -n = 11; +global nmin; +global nmax; +nmin = -4; +nmax = 7; +n = nmax - nmin + 1 +A = 3; -t = (0:n-1) / (n-1) -alpha = 1 + 4 * t.^2 +t = (nmin:nmax) / nmax; +alpha = 1 + A * t .* abs(t) +#alpha(1) = 0.01; #alpha = [ 1, 1.03, 1.05, 1.1, 1.25, 1.5, 2, 2.5, 3, 4, 5 ]; beta = alpha; names = [ "one"; "two"; "three"; "four"; "five"; "six"; "seven"; "eight"; - "nine"; "ten"; "eleven" ] + "nine"; "ten"; "eleven"; "twelve" ] function retval = Beta(a, b, x) retval = x^(a-1) * (1-x)^(b-1) / beta(a, b); + if (retval > 100) + retval = 100 + end end function plotbeta(fn, a, b, name) global N; - fprintf(fn, "\\def\\beta%s{\n", name); + fprintf(fn, "\\def\\beta%s{\n", strtrim(name)); fprintf(fn, "\t({%.4f*\\dx},{%.4f*\\dy})", 0, Beta(a, b, 0)); for x = (1:N-1)/(N-1) X = (1-cos(pi * x))/2; @@ -35,8 +43,8 @@ end fn = fopen("betapaths.tex", "w"); for i = (1:n) - fprintf(fn, "\\def\\alpha%s{%f}\n", names(i,:), alpha(i)); - fprintf(fn, "\\def\\beta%s{%f}\n", names(i,:), beta(i)); + fprintf(fn, "\\def\\alpha%s{%f}\n", strtrim(names(i,:)), alpha(i)); + fprintf(fn, "\\def\\beta%s{%f}\n", strtrim(names(i,:)), beta(i)); end for i = (1:n) -- cgit v1.2.1 From 9f0ff73d26b3e096d848abfd20cd124433e2a4a7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 13 Mar 2022 23:27:43 +0100 Subject: cleanup --- buch/aufgaben2.tex | 4 ---- 1 file changed, 4 deletions(-) diff --git a/buch/aufgaben2.tex b/buch/aufgaben2.tex index f98562e..8073f26 100644 --- a/buch/aufgaben2.tex +++ b/buch/aufgaben2.tex @@ -4,10 +4,6 @@ % (c) 2022 Prof. Dr. Andreas Mueller, OST % -%\item -%\input chapters/40-eigenwerte/uebungsaufgaben/4004.tex -%\item -%\input chapters/40-eigenwerte/uebungsaufgaben/4005.tex \item \input{chapters/090-pde/uebungsaufgaben/901.tex} \item -- cgit v1.2.1 From 18e46179f2da76a3147d3f3b466206c6b5405859 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 14 Mar 2022 08:20:28 +0100 Subject: describe link between Jacobi-weights and Beta-distribution --- buch/chapters/070-orthogonalitaet/jacobi.tex | 22 ++ buch/chapters/070-orthogonalitaet/orthogonal.tex | 51 +++ buch/papers/dreieck/teil1.tex | 411 +---------------------- 3 files changed, 74 insertions(+), 410 deletions(-) diff --git a/buch/chapters/070-orthogonalitaet/jacobi.tex b/buch/chapters/070-orthogonalitaet/jacobi.tex index 042d466..f776c03 100644 --- a/buch/chapters/070-orthogonalitaet/jacobi.tex +++ b/buch/chapters/070-orthogonalitaet/jacobi.tex @@ -189,6 +189,28 @@ rechten Rand haben. \label{buch:orthogonal:fig:jacobi-parameter}} \end{figure} +\subsection{Jacobi-Gewichtsfunktion und Beta-Verteilung +\label{buch:orthogonal:subsection:beta-verteilung}} +Die Jacobi-Gewichtsfunktion entsteht aus der Wahrscheinlichkeitsdichte +der Beta-Verteilung, die in +Abschnitt~\ref{buch:rekursion:subsection:beta-verteilung} +eingeführt wurde mit Hilfe der Variablen-Transformation $x = 2t-1$ +oder $t=(x+1)/2$. +Das Integral mit der Jacobi-Gewichtsfunktion $w^{(\alpha,\beta)}(x)$ +kann damit umgeformt werden in +\[ +\int_{-1}^1 +f(x)\,w^{(\alpha,\beta)}(x)\,dx += +\int_0^1 +f(2t-1) w^{(\alpha,\beta)}(2t-1)\,2\,dt += +\int_0^1 +f(2t-1) +(1-(2t-1))^\alpha (1+(2t-1))^\beta +\,2\,dt +\] + % % % diff --git a/buch/chapters/070-orthogonalitaet/orthogonal.tex b/buch/chapters/070-orthogonalitaet/orthogonal.tex index d06f46e..a84248a 100644 --- a/buch/chapters/070-orthogonalitaet/orthogonal.tex +++ b/buch/chapters/070-orthogonalitaet/orthogonal.tex @@ -737,6 +737,57 @@ rechten Rand haben. \label{buch:orthogonal:fig:jacobi-parameter}} \end{figure} +\subsubsection{Jacobi-Gewichtsfunktion und Beta-Verteilung +\label{buch:orthogonal:subsection:beta-verteilung}} +Die Jacobi-Gewichtsfunktion entsteht aus der Wahrscheinlichkeitsdichte +der Beta-Verteilung, die in +Abschnitt~\ref{buch:rekursion:subsection:beta-verteilung} +eingeführt wurde mit Hilfe der Variablen-Transformation $x = 2t-1$ +oder $t=(x+1)/2$. +Das Integral mit der Jacobi-Gewichtsfunktion $w^{(\alpha,\beta)}(x)$ +kann damit umgeformt werden in +\begin{align*} +\int_{-1}^1 +f(x)\,w^{(\alpha,\beta)}(x)\,dx +&= +\int_0^1 +f(2t-1) w^{(\alpha,\beta)}(2t-1)\,2\,dt +\\ +&= +\int_0^1 +f(2t-1) +(1-(2t-1))^\alpha (1+(2t-1))^\beta +\,2\,dt +\\ +&= +2^{\alpha+\beta+1} +\int_0^1 +f(2t-1) +\, +t^\beta +(1-t)^\alpha +\,dt +\\ +&= +2^{\alpha+\beta+1} +B(\alpha+1,\beta+1) +\int_0^1 +f(2t-1) +\, +\frac{ +t^\beta +(1-t)^\alpha +}{B(\alpha+1,\beta+1)} +\,dt. +\end{align*} +Auf der letzten Zeile steht ein Integral mit der Wahrscheinlichkeitsdichte +der Beta-Verteilung. +Orthogonale Funktionen bezüglich der Jacobischen Gewichtsfunktion +$w^{(\alpha,\beta)}$ werden mit der genannten Substitution also +zu orthogonalen Funktionen bezüglich der Beta-Verteilung mit +Parametern $\beta+1$ und $\alpha+1$. + + % % Tschebyscheff-Gewichtsfunktion % diff --git a/buch/papers/dreieck/teil1.tex b/buch/papers/dreieck/teil1.tex index 5e7090b..4abe2e1 100644 --- a/buch/papers/dreieck/teil1.tex +++ b/buch/papers/dreieck/teil1.tex @@ -5,416 +5,7 @@ % \section{Ordnungsstatistik und Beta-Funktion \label{dreieck:section:ordnungsstatistik}} -\rhead{Ordnungsstatistik und Beta-Funktion} -In diesem Abschnitt ist $X$ eine Zufallsvariable mit der Verteilungsfunktion -$F_X(x)$, und $X_i$, $1\le i\le n$ sei ein Stichprobe von unabhängigen -Zufallsvariablen, die wie $X$ verteilt sind. -Ziel ist, die Verteilungsfunktion und die Wahrscheinlichkeitsdichte -des grössten, zweitgrössten, $k$-t-grössten Wertes in der Stichprobe -zu finden. -Wir schreiben $[n]=\{1,\dots,n\}$ für die Menge der natürlichen -Zahlen von zwischen $1$ und $n$. +\rhead{} -\subsection{Verteilung von $\operatorname{max}(X_1,\dots,X_n)$ und -$\operatorname{min}(X_1,\dots,X_n)$ -\label{dreieck:subsection:minmax}} -Die Verteilungsfunktion von $\operatorname{max}(X_1,\dots,X_n)$ hat -den Wert -\begin{align*} -F_{\operatorname{max}(X_1,\dots,X_n)}(x) -&= -P(\operatorname{max}(X_1,\dots,X_n) \le x) -\\ -&= -P(X_1\le x\wedge \dots \wedge X_n\le x) -\\ -&= -P(X_1\le x) \cdot \ldots \cdot P(X_n\le x) -\\ -&= -P(X\le x)^n -= -F_X(x)^n. -\end{align*} -Für die Gleichverteilung ist -\[ -F_{\text{equi}}(x) -= -\begin{cases} -0&\qquad x< 0 -\\ -x&\qquad 0\le x\le 1 -\\ -1&\qquad 1 X_1\wedge \dots \wedge x > X_n) -\\ -&= -1- -(1-P(x\le X_1)) \cdot\ldots\cdot (1-P(x\le X_n)) -\\ -&= -1-(1-F_X(x))^n, -\end{align*} -Im Speziellen für im Intervall $[0,1]$ gleichverteilte $X_i$ ist die -Verteilungsfunktion des Minimums -\[ -F_{\operatorname{min}(X_1,\dots,X_n)}(x) -= -\begin{cases} -0 &\qquad x<0 \\ -1-(1-x)^n&\qquad 0\le x\le 1\\ -1 &\qquad 1 < x -\end{cases} -\] -mit Wahrscheinlichkeitsdichte -\[ -\varphi_{\operatorname{min}(X_1,\dots,X_n)} -= -\frac{d}{dx} -F_{\operatorname{min}(X_1,\dots,X_n)} -= -\begin{cases} -n(1-x)^{n-1}&\qquad 0\le x\le 1\\ -0 &\qquad \text{sonst} -\end{cases} -\] -und Erwartungswert -\begin{align*} -E(\operatorname{min}(X_1,\dots,X_n) -&= -\int_{-\infty}^\infty x\varphi_{\operatorname{min}(X_1,\dots,X_n)}(x)\,dx -= -\int_0^1 x\cdot n(1-x)^{n-1}\,dx -\\ -&= -\bigl[ -x(1-x)^n \bigr]_0^1 + \int_0^1 (1-x)^n\,dx -= -\biggl[ -- -\frac{1}{n+1} -(1-x)^{n+1} -\biggr]_0^1 -= -\frac{1}{n+1}. -\end{align*} -Es ergibt sich daraus als natürlich Verallgemeinerung die Frage nach -der Verteilung des zweitegrössten oder zweitkleinsten Wertes unter den -Werten $X_i$. - -\subsection{Der $k$-t-grösste Wert} -Sie wieder $X_i$ eine Stichprobe von $n$ unabhängigen wie $X$ verteilten -Zufallsvariablen. -Diese werden jetzt der Grösse nach sortiert, die sortierten Werte werden -mit -\[ -X_{1:n} \le X_{2:n} \le \dots \le X_{(n-1):n} \le X_{n:n} -\] -bezeichnet. -Die Grössen $X_{k:n}$ sind Zufallsvariablen, sie heissen die $k$-ten -Ordnungsstatistiken. -Die in Abschnitt~\ref{dreieck:subsection:minmax} behandelten Zufallsvariablen -$\operatorname{min}(X_1,\dots,X_n)$ -und -$\operatorname{max}(X_1,\dots,X_n)$ -sind die Fälle -\begin{align*} -X_{1:n} &= \operatorname{min}(X_1,\dots,X_n) \\ -X_{n:n} &= \operatorname{max}(X_1,\dots,X_n). -\end{align*} - -Um den Wert der Verteilungsfunktion von $X_{k:n}$ zu berechnen, müssen wir -die Wahrscheinlichkeit bestimmen, dass $k$ der $n$ Werte $X_i$ $x$ nicht -übersteigen. -Der $k$-te Wert $X_{k:n}$ übersteigt genau dann $x$ nicht, wenn -mindestens $k$ der Zufallswerte $X_i$ $x$ nicht übersteigen, also -\[ -P(X_{k:n} \le x) -= -P\left( -|\{i\in[n]\,|\, X_i\le x\}| \ge k -\right). -\] - -Das Ereignis $\{X_i\le x\}$ ist eine Bernoulli-Experiment, welches mit -Wahrscheinlichkeit $F_X(x)$ eintritt. -Die Anzahl der Zufallsvariablen $X_i$, die $x$ übertreffen, ist also -Binomialverteilt mit $p=F_X(x)$. -Damit haben wir gefunden, dass mit Wahrscheinlichkeit -\begin{equation} -F_{X_{k:n}}(x) -= -P(X_{k:n}\le x) -= -\sum_{i=k}^n \binom{n}{i}F_X(x)^i (1-F_X(x))^{n-i} -\label{dreieck:eqn:FXkn} -\end{equation} -mindestens $k$ der Zufallsvariablen den Wert $x$ überschreiten. - -\subsubsection{Wahrscheinlichkeitsdichte der Ordnungsstatistik} -Die Wahrscheinlichkeitsdichte der Ordnungsstatistik kann durch Ableitung -von \eqref{dreieck:eqn:FXkn} gefunden, werden, sie ist -\begin{align*} -\varphi_{X_{k:n}}(x) -&= -\frac{d}{dx} -F_{X_{k:n}}(x) -\\ -&= -\sum_{i=k}^n -\binom{n}{i} -\bigl( -iF_X(x)^{i-1}\varphi_X(x) (1-F_X(x))^{n-i} -- -F_X(x)^k -(n-i) -(1-F_X(x))^{n-i-1} -\varphi_X(x) -\bigr) -\\ -&= -\sum_{i=k}^n -\binom{n}{i} -\varphi_X(x) -F_X(x)^{i-1}(1-F_X(x))^{n-i-1} -\bigl( -iF_X(x)-(n-i)(1-F_X(x)) -\bigr) -\\ -&= -\varphi_X(x) -\biggl( -\sum_{i=k}^n i\binom{n}{i} F_X(x)^{i-1}(1-F_X(x))^{n-i} -- -\sum_{j=k}^n (n-j)\binom{n}{j} F_X(x)^{j}(1-F_X(x))^{n-j-1} -\biggr) -\\ -&= -\varphi_X(x) -\biggl( -\sum_{i=k}^n i\binom{n}{i} F_X(x)^{i-1}(1-F_X(x))^{n-i} -- -\sum_{i=k+1}^{n+1} (n-i+1)\binom{n}{i-1} F_X(x)^{i-1}(1-F_X(x))^{n-i} -\biggr) -\\ -&= -\varphi_X(x) -\biggl( -k\binom{n}{k}F_X(x)^{k-1}(1-F_X(x))^{n-k} -+ -\sum_{i=k+1}^{n+1} -\left( -i\binom{n}{i} -- -(n-i+1)\binom{n}{i-1} -\right) -F_X(x)^{i-1}(1-F_X(x))^{n-i} -\biggr) -\end{align*} -Mit den wohlbekannten Identitäten für die Binomialkoeffizienten -\begin{align*} -i\binom{n}{i} -- -(n-i+1)\binom{n}{i-1} -&= -n\binom{n-1}{i-1} -- -n -\binom{n-1}{i-1} -= -0 -\end{align*} -folgt jetzt -\begin{align*} -\varphi_{X_{k:n}}(x) -&= -\varphi_X(x)k\binom{n}{k} F_X(x)^{k-1}(1-F_X(x))^{n-k}(x). -\intertext{Im Speziellen für gleichverteilte Zufallsvariablen $X_i$ ist -} -\varphi_{X_{k:n}}(x) -&= -k\binom{n}{k} x^{k-1}(1-x)^{n-k}. -\end{align*} -Dies ist die Wahrscheinlichkeitsdichte einer Betaverteilung -\[ -\beta(k,n-k+1)(x) -= -\frac{1}{B(k,n-k+1)} -x^{k-1}(1-x)^{n-k}. -\] -Tatsächlich ist die Normierungskonstante -\begin{align} -\frac{1}{B(k,n-k+1)} -&= -\frac{\Gamma(n+1)}{\Gamma(k)\Gamma(n-k+1)} -= -\frac{n!}{(k-1)!(n-k)!}. -\label{dreieck:betaverteilung:normierung1} -\end{align} -Andererseits ist -\[ -k\binom{n}{k} -= -k\frac{n!}{k!(n-k)!} -= -\frac{n!}{(k-1)!(n-k)!}, -\] -in Übereinstimmung mit~\eqref{dreieck:betaverteilung:normierung1}. -Die Verteilungsfunktion und die Wahrscheinlichkeitsdichte der -Ordnungsstatistik sind in Abbildung~\ref{dreieck:fig:order} dargestellt. - -\begin{figure} -\centering -\includegraphics{papers/dreieck/images/order.pdf} -\caption{Verteilungsfunktion und Wahrscheinlichkeitsdichte der -Ordnungsstatistiken $X_{k:n}$ einer gleichverteilung Zuvallsvariable -mit $n=10$. -\label{dreieck:fig:order}} -\end{figure} - -\subsubsection{Erwartungswert} -Mit der Wahrscheinlichkeitsdichte kann man jetzt auch den Erwartungswerte -der $k$-ten Ordnungsstatistik bestimmen. -Die Rechnung ergibt: -\begin{align*} -E(X_{k:n}) -&= -\int_0^1 x\cdot k\binom{n}{k} x^{k-1}(1-x)^{n-k}\,dx -= -k -\binom{n}{k} -\int_0^1 -x^{k}(1-x)^{n-k}\,dx. -\intertext{Dies ist das Beta-Integral} -&= -k\binom{n}{k} -B(k+1,n-k+1) -\intertext{welches man durch Gamma-Funktionen bzw.~durch Fakultäten wie in} -&= -k\frac{n!}{k!(n-k)!} -\frac{\Gamma(k+1)\Gamma(n-k+1)}{n+2} -= -k\frac{n!}{k!(n-k)!} -\frac{k!(n-k)!}{(n+1)!} -= -\frac{k}{n+1} -\end{align*} -ausdrücken kann. -Die Erwartungswerte haben also regelmässige Abstände, sie sind in -Abbildung~\ref{dreieck:fig:order} als blaue vertikale Linien eingezeichnet. - -\subsubsection{Varianz} -Auch die Varianz lässt sich einfach berechnen, dazu muss zunächst -der Erwartungswert von $X_{k:n}^2$ bestimmt werden. -Er ist -\begin{align*} -E(X_{k:n}^2) -&= -\int_0^1 x^2\cdot k\binom{n}{k} x^{k-1}(1-x)^{n-k}\,dx -= -k -\binom{n}{k} -\int_0^1 -x^{k+1}(1-x)^{n-k}\,dx. -\intertext{Auch dies ist ein Beta-Integral, nämlich} -&= -k\binom{n}{k} -B(k+2,n-k+1) -= -k\frac{n!}{k!(n-k)!} -\frac{(k+1)!(n-k)!}{(n+2)!} -= -\frac{k(k+1)}{(n+1)(n+2)}. -\end{align*} -Die Varianz wird damit -\begin{align} -\operatorname{var}(X_{k:n}) -&= -E(X_{k:n}^2) - E(X_{k:n})^2 -\notag -\\ -& -= -\frac{k(k+1)}{(n+1)(n+2)}-\frac{k^2}{(n+1)^2} -= -\frac{k(k+1)(n+1)-k^2(n+2)}{(n+1)^2(n+2)} -= -\frac{k(n-k+1)}{(n+1)^2(n+2)}. -\label{dreieck:eqn:ordnungsstatistik:varianz} -\end{align} -In Abbildung~\ref{dreieck:fig:order} ist die Varianz der -Ordnungsstatistik $X_{k:n}$ für $k=7$ und $n=10$ als oranges -Rechteck dargestellt. - -\begin{figure} -\centering -\includegraphics[width=0.84\textwidth]{papers/dreieck/images/beta.pdf} -\caption{Wahrscheinlichkeitsdichte der Beta-Verteilung -$\beta(a,b,x)$ -für verschiedene Werte der Parameter $a$ und $b$. -Die Werte des Parameters für einen Graphen einer Beta-Verteilung -sind als Punkt im kleinen Quadrat rechts -im Graphen als Punkt mit der gleichen Farbe dargestellt. -\label{dreieck:fig:betaverteilungn}} -\end{figure} - -Die Formel~\eqref{dreieck:eqn:ordnungsstatistik:varianz} -besagt auch, dass die Varianz der proportional ist zu $k((n+1)-k)$. -Dieser Ausdruck ist am grössten für $k=(n+1)/2$, die Varianz ist -also grösser für die ``mittleren'' Ordnungstatistiken als für die -extremen $X_{1:n}=\operatorname{min}(X_1,\dots,X_n)$ und -$X_{n:n}=\operatorname{max}(X_1,\dots,X_n)$. -- cgit v1.2.1 From 8ecf2cd93564d76aee7dd81736d3cd5908b273cd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 14 Mar 2022 12:41:22 +0100 Subject: move command configuration to common/Makefile.inc --- buch/Makefile | 28 ++++++++++++++-------------- buch/common/Makefile.inc | 8 +++++++- 2 files changed, 21 insertions(+), 15 deletions(-) diff --git a/buch/Makefile b/buch/Makefile index e2ad4c0..00fcf42 100755 --- a/buch/Makefile +++ b/buch/Makefile @@ -18,15 +18,15 @@ ALLTEXFILES = $(TEXFILES) $(CHAPTERFILES) # Buchblock für Druckerei # buch.pdf: buch.tex $(TEXFILES) buch.ind $(BLXFILES) - pdflatex buch.tex - bibtex buch + $(pdflatex) buch.tex + $(bibtex) buch buch.idx: buch.tex $(TEXFILES) images - touch buch.ind - pdflatex buch.tex + $(touch) buch.ind + $(pdflatex) buch.tex buch.ind: buch.idx - makeindex buch.idx + $(makeindex) buch.idx # # Papers in einzelne PDF-Files separieren für digitales Feedback @@ -39,16 +39,16 @@ separate: buch.aux buch.pdf # SeminarSpezielleFunktionen.pdf: SeminarSpezielleFunktionen.tex $(TEXFILES) \ SeminarSpezielleFunktionen.ind $(BLXFILES) - pdflatex SeminarSpezielleFunktionen.tex - bibtex SeminarSpezielleFunktionen + $(pdflatex) SeminarSpezielleFunktionen.tex + $(bibtex) SeminarSpezielleFunktionen SeminarSpezielleFunktionen.idx: SeminarSpezielleFunktionen.tex $(TEXFILES) \ images - touch SeminarSpezielleFunktionen.ind - pdflatex SeminarSpezielleFunktionen.tex + $(touch) SeminarSpezielleFunktionen.ind + $(pdflatex) SeminarSpezielleFunktionen.tex SeminarSpezielleFunktionen.ind: SeminarSpezielleFunktionen.idx - makeindex SeminarSpezielleFunktionen + $(makeindex) SeminarSpezielleFunktionen # # This Makefile can also construct the short tests @@ -56,17 +56,17 @@ SeminarSpezielleFunktionen.ind: SeminarSpezielleFunktionen.idx tests: test1.pdf test2.pdf test3.pdf test1.pdf: common/test-common.tex common/test1.tex aufgaben1.tex - pdflatex common/test1.tex + $(pdflatex) common/test1.tex test2.pdf: common/test-common.tex common/test1.tex aufgaben2.tex - pdflatex common/test2.tex + $(pdflatex) common/test2.tex test3.pdf: common/test-common.tex common/test1.tex aufgaben3.tex - pdflatex common/test3.tex + $(pdflatex) common/test3.tex # # Errata # errata.pdf: errata.tex - pdflatex errata.tex + $(pdflatex) errata.tex diff --git a/buch/common/Makefile.inc b/buch/common/Makefile.inc index c8b0f6e..b9461e5 100755 --- a/buch/common/Makefile.inc +++ b/buch/common/Makefile.inc @@ -4,9 +4,15 @@ # (c) 2021 Prof Dr Andreas Mueller, OST Ostschweizer Fachhochschule # - SUBDIRECTORIES = chapters +# change the following variables to suit your environment + +pdflatex = pdflatex +bibtex = bibtex +makeindex = makeindex +touch = touch + .PHONY: images images: -- cgit v1.2.1 From bfaa02edc586b384691399c81aad54d92b5de986 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Tue, 15 Mar 2022 09:48:35 +0100 Subject: kugel: Add paper title and notes --- buch/papers/kugel/Makefile.inc | 8 ++---- buch/papers/kugel/main.tex | 57 ++++++++++++++++++++++-------------------- buch/papers/kugel/teil0.tex | 22 ---------------- buch/papers/kugel/teil1.tex | 55 ---------------------------------------- buch/papers/kugel/teil2.tex | 40 ----------------------------- buch/papers/kugel/teil3.tex | 40 ----------------------------- 6 files changed, 32 insertions(+), 190 deletions(-) delete mode 100644 buch/papers/kugel/teil0.tex delete mode 100644 buch/papers/kugel/teil1.tex delete mode 100644 buch/papers/kugel/teil2.tex delete mode 100644 buch/papers/kugel/teil3.tex diff --git a/buch/papers/kugel/Makefile.inc b/buch/papers/kugel/Makefile.inc index d926229..50d6825 100644 --- a/buch/papers/kugel/Makefile.inc +++ b/buch/papers/kugel/Makefile.inc @@ -4,11 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # dependencies-kugel = \ - papers/kugel/packages.tex \ + papers/kugel/packages.tex \ papers/kugel/main.tex \ - papers/kugel/references.bib \ - papers/kugel/teil0.tex \ - papers/kugel/teil1.tex \ - papers/kugel/teil2.tex \ - papers/kugel/teil3.tex + papers/kugel/references.bib diff --git a/buch/papers/kugel/main.tex b/buch/papers/kugel/main.tex index 0e632ec..06368af 100644 --- a/buch/papers/kugel/main.tex +++ b/buch/papers/kugel/main.tex @@ -1,36 +1,39 @@ % + % main.tex -- Paper zum Thema % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:kugel}} -\lhead{Thema} +\chapter{Recurrence Relations for Spherical Harmonics in Quantum Mechanics\label{chapter:kugel}} +\lhead{Recurrence Relations in Quantum Mechanics} \begin{refsection} -\chapterauthor{Hans Muster} - -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} - -\input{papers/kugel/teil0.tex} -\input{papers/kugel/teil1.tex} -\input{papers/kugel/teil2.tex} -\input{papers/kugel/teil3.tex} +\chapterauthor{Manuel Cattaneo, Naoki Pross} + +\begin{verbatim} + +Ideas and current research goals +-------------------------------- + +- Recurrence relations for spherical harmonics +- Associated Legendre polynomials +- Rodrigues' type formula aka Rodrigues' formula +- Applications: + * Quantization of angular momentum + * Gravitational field measurements (NASA ebb and flow, ESA goce) + * Literally anything that needs basis functions on the surface of a sphere + +Literature +---------- + +- Nichtkommutative Bildverarbeitung, T. Mendez, p57+ +- Linear Algebra Done Right, S. Axler, p212,221,231,237 +- Introduction to Quantum Mechanics, D. J. Griffith, p201+ +- Seminar Quantenmechanik, A. Müller, p101,106,114,121 +- Introduction to Partial Differential Equations, J. Oliver, p510+ +- Partial Differential Equations in Engineering Problems, K. Miller, p175,190 + +\end{verbatim} + \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/kugel/teil0.tex b/buch/papers/kugel/teil0.tex deleted file mode 100644 index f921a82..0000000 --- a/buch/papers/kugel/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{kugel:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{kugel:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/kugel/teil1.tex b/buch/papers/kugel/teil1.tex deleted file mode 100644 index e56bb18..0000000 --- a/buch/papers/kugel/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{kugel:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{kugel:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{kugel:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{kugel:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{kugel:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/kugel/teil2.tex b/buch/papers/kugel/teil2.tex deleted file mode 100644 index cb9e427..0000000 --- a/buch/papers/kugel/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{kugel:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{kugel:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/kugel/teil3.tex b/buch/papers/kugel/teil3.tex deleted file mode 100644 index 734fff9..0000000 --- a/buch/papers/kugel/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{kugel:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{kugel:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - -- cgit v1.2.1 From 9f542be91a61e6eb1fcb3c29e8a908eb9e5b8949 Mon Sep 17 00:00:00 2001 From: Marc Benz Date: Tue, 15 Mar 2022 14:00:47 +0100 Subject: initial commit from Marc Benz --- buch/papers/transfer/main.tex | 23 ++--------------------- 1 file changed, 2 insertions(+), 21 deletions(-) diff --git a/buch/papers/transfer/main.tex b/buch/papers/transfer/main.tex index 2aae635..ed16998 100644 --- a/buch/papers/transfer/main.tex +++ b/buch/papers/transfer/main.tex @@ -3,29 +3,10 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:transfer}} +\chapter{Transferfunktionen\label{chapter:transfer}} \lhead{Thema} \begin{refsection} -\chapterauthor{Hans Muster} - -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} +\chapterauthor{Marc Benz} \input{papers/transfer/teil0.tex} \input{papers/transfer/teil1.tex} -- cgit v1.2.1 From e32ae87f92309dc6034fef9323ba058754b0e486 Mon Sep 17 00:00:00 2001 From: David Hugentobler Date: Tue, 15 Mar 2022 14:10:29 +0100 Subject: Titel und Autor wurde in paper lambertw geaendert --- buch/papers/lambertw/main.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/papers/lambertw/main.tex b/buch/papers/lambertw/main.tex index c125c33..e58ed5a 100644 --- a/buch/papers/lambertw/main.tex +++ b/buch/papers/lambertw/main.tex @@ -3,10 +3,10 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:lambertw}} +\chapter{Verfolgungskurven\label{chapter:lambertw}} \lhead{Thema} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{David Hugentobler und Yanik Kuster} Ein paar Hinweise für die korrekte Formatierung des Textes \begin{itemize} -- cgit v1.2.1 From 4b8e2383962955bcd6419d855e5c38df36e7d067 Mon Sep 17 00:00:00 2001 From: David Hugentobler Date: Tue, 15 Mar 2022 14:20:01 +0100 Subject: commit after adding main.log --- buch/papers/lambertw/main.log | 749 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 749 insertions(+) create mode 100644 buch/papers/lambertw/main.log diff --git a/buch/papers/lambertw/main.log b/buch/papers/lambertw/main.log new file mode 100644 index 0000000..4b0af4d --- /dev/null +++ b/buch/papers/lambertw/main.log @@ -0,0 +1,749 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.23 (TeX Live 2021/W32TeX) (preloaded format=pdflatex 2021.11.16) 15 MAR 2022 13:23 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**main.tex +(./main.tex +LaTeX2e <2021-11-15> +L3 programming layer <2021-11-12> +! 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LaTeX Error: File `papers/lambertw/teil0.tex' not found. + +Type X to quit or to proceed, +or enter new name. (Default extension: tex) + +Enter file name: +! Emergency stop. + + +l.30 \input{papers/lambertw/teil0.tex} + ^^M +*** (cannot \read from terminal in nonstop modes) + + +Here is how much of TeX's memory you used: + 36 strings out of 478371 + 593 string characters out of 5852527 + 296836 words of memory out of 5000000 + 18242 multiletter control sequences out of 15000+600000 + 403598 words of font info for 28 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 23i,1n,32p,120b,183s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! -- cgit v1.2.1 From 3381bfe1e6ebcd66249cd4c6f49bdd820643a5be Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 15 Mar 2022 17:35:00 +0100 Subject: add some stuff about separation --- buch/chapters/090-pde/kreis.tex | 2 +- buch/chapters/090-pde/kugel.tex | 146 ++++++++++++++++++++++++++++++++++++++ buch/papers/000template/main.tex | 5 +- buch/papers/000template/teil0.tex | 3 + buch/papers/000template/teil1.tex | 3 + buch/papers/000template/teil2.tex | 3 + buch/papers/000template/teil3.tex | 3 + 7 files changed, 163 insertions(+), 2 deletions(-) diff --git a/buch/chapters/090-pde/kreis.tex b/buch/chapters/090-pde/kreis.tex index b4ce8d7..c60fd44 100644 --- a/buch/chapters/090-pde/kreis.tex +++ b/buch/chapters/090-pde/kreis.tex @@ -32,7 +32,7 @@ Der Laplace-Operator hat in Polarkoordinaten die Form \frac1r \frac{\partial}{\partial r} + -\frac{1}{r 2} +\frac{1}{r^2} \frac{\partial^2}{\partial\varphi^2}. \label{buch:pde:kreis:laplace} \end{equation} diff --git a/buch/chapters/090-pde/kugel.tex b/buch/chapters/090-pde/kugel.tex index 0e3524f..c081029 100644 --- a/buch/chapters/090-pde/kugel.tex +++ b/buch/chapters/090-pde/kugel.tex @@ -5,4 +5,150 @@ % \section{Kugelfunktionen \label{buch:pde:section:kugel}} +Kugelsymmetrische Probleme können oft vorteilhaft in Kugelkoordinaten +beschrieben werden. +Die Separationsmethode kann auf partielle Differentialgleichungen +mit dem Laplace-Operator angewendet werden. +Die daraus resultierenden gewöhnlichen Differentialgleichungen führen +einerseits auf die Laguerre-Differentialgleichung für den radialen +Anteil sowie auf Kugelfunktionen für die Koordinaten der +geographischen Länge und Breite. + +\subsection{Kugelkoordinaten} +Wir verwenden Kugelkoordinaten $(r,\vartheta,\varphi)$, wobei $r$ +der Radius ist, $\vartheta$ die geographische Breite gemessen vom +Nordpol der Kugel und $\varphi$ die geographische Breite. +Der Definitionsbereich für Kugelkoordinaten ist +\[ +\Omega += +\{(r,\vartheta,\varphi) +\;|\; +r\ge 0\wedge +0\le \vartheta\le \pi\wedge +0\le \varphi< 2\pi +\}. +\] +Die Entfernung eines Punktes von der $z$-Achse ist $r\sin\vartheta$. +Daraus lassen sich die karteischen Koordinaten eines Punktes mit Hilfe +von +\[ +\begin{pmatrix}x\\y\\z\end{pmatrix} += +\begin{pmatrix} +r\cos\vartheta\\ +r\sin\vartheta\cos\varphi\\ +r\sin\vartheta\sin\varphi +\end{pmatrix}. +\] +Man beachte, dass die Punkte auf der $z$-Achse keine eindeutigen +Kugelkoordinaten haben. +Sie sind charakterisiert durch $r\sin\vartheta=0$, was $\cos\vartheta=\pm1$ +impliziert. +Entsprechend führen alle Werte von $\varphi$ auf den gleichen Punkt +$(0,0,\pm r)$. + +\subsection{Der Laplace-Operator in Kugelkoordinaten} +Der Laplace-Operator in Kugelkoordinaten lautet +\begin{align} +\Delta +&= +\frac{1}{r^2} \frac{\partial}{\partial r}r^2\frac{\partial}{\partial r} ++ +\frac{1}{r^2\sin\vartheta}\frac{\partial}{\partial\vartheta} +\sin\vartheta\frac{\partial}{\partial\vartheta} ++ +\frac{1}{r^2\sin^2\vartheta}\frac{\partial^2}{\partial\varphi^2}. +\label{buch:pde:kugel:laplace1} +\intertext{Dies kann auch geschrieben werden als} +&= +\frac{\partial^2}{\partial r^2} ++ +\frac{2}{r}\frac{\partial}{\partial r} ++ +\frac{1}{r^2\sin\vartheta}\frac{\partial}{\partial\vartheta} +\sin\vartheta\frac{\partial}{\partial\vartheta} ++ +\frac{1}{r^2\sin^2\vartheta}\frac{\partial^2}{\partial\varphi^2} +\label{buch:pde:kugel:laplace2} +\intertext{oder} +&= +\frac{1}{r} +\frac{\partial^2}{\partial r^2} r ++ +\frac{1}{r^2\sin\vartheta}\frac{\partial}{\partial\vartheta} +\sin\vartheta\frac{\partial}{\partial\vartheta} ++ +\frac{1}{r^2\sin^2\vartheta}\frac{\partial^2}{\partial\varphi^2}. +\label{buch:pde:kugel:laplace3} +\end{align} +Dabei ist zu berücksichtigen, dass mit der Notation gemeint ist, +dass ein Ableitungsoperator auf alles wirkt, was rechts im gleichen +Term steht. +Der Operator +\[ +\frac{1}{r} +\frac{\partial^2}{\partial r^2}r +\quad\text{wirkt daher als}\quad +\frac{1}{r} +\frac{\partial^2}{\partial r^2}rf += +\frac{1}{r} +\frac{\partial}{\partial r}\biggl(f + r\frac{\partial f}{\partial r}\biggr) += +\frac{1}{r} +\frac{\partial f}{\partial r} ++ +\frac{1}{r} +\frac{\partial f}{\partial r} ++ +\frac{\partial^2f}{\partial r^2}. += +\frac{2}{r}\frac{\partial f}{\partial r} ++ +\frac{\partial^2f}{\partial r^2}, +\] +was die Äquivalenz der beiden Formen +\eqref{buch:pde:kugel:laplace2} +und +\eqref{buch:pde:kugel:laplace3} +rechtfertigt. +Auch die Äquivalenz mit +\eqref{buch:pde:kugel:laplace1} +kann auf ähnliche Weise verstanden werden. + +Die Herleitung dieser Formel ist ziemlich aufwendig und soll hier +nicht dargestellt werden. +Es sei aber darauf hingewiesen, dass sich für $\vartheta=\frac{\pi}2$ +wegen $\sin\vartheta=\sin\frac{\pi}2=1$ +der eingeschränkte Operator +\[ +\Delta += +\frac{1}{r^2}\frac{\partial }{\partial r} r^2\frac{\partial}{\partial r} ++ +\frac{1}{r^2}\frac{\partial^2}{\partial\varphi^2} +\] +ergibt. +Wendet man wie oben die Produktregel auf den ersten Term an, entsteht die +Form +\[ +\frac{\partial^2}{\partial r^2} ++ +\frac{2}{r} +\frac{\partial}{\partial r} ++ +\frac{1}{r^2}\frac{\partial^2}{\partial\varphi^2} +\] +die {\em nicht} übereinstimmt mit dem Laplace-Operator in +Polarkoordinaten~\eqref{buch:pde:kreis:laplace}. +Der Unterschied rührt daher, dass der Laplace-Operator die Krümmung +der Koordinatenlinien berücksichtigt, in diesem Fall der Meridiane. + + +\subsection{Separation} + + + + diff --git a/buch/papers/000template/main.tex b/buch/papers/000template/main.tex index 87a5685..91b6d6e 100644 --- a/buch/papers/000template/main.tex +++ b/buch/papers/000template/main.tex @@ -1,7 +1,10 @@ % % main.tex -- Paper zum Thema <000template> % -% (c) 2020 Hochschule Rapperswil +% (c) 2020 Autor, OST Ostschweizer Fachhochschule +% +% !TEX root = ../../buch.tex +% !TEX encoding = UTF-8 % \chapter{Thema\label{chapter:000template}} \lhead{Thema} diff --git a/buch/papers/000template/teil0.tex b/buch/papers/000template/teil0.tex index 7b9f088..65d7ae1 100644 --- a/buch/papers/000template/teil0.tex +++ b/buch/papers/000template/teil0.tex @@ -3,6 +3,9 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % +% !TEX root = ../../buch.tex +% !TEX encoding = UTF-8 +% \section{Teil 0\label{000template:section:teil0}} \rhead{Teil 0} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam diff --git a/buch/papers/000template/teil1.tex b/buch/papers/000template/teil1.tex index 00d3058..0f8dfae 100644 --- a/buch/papers/000template/teil1.tex +++ b/buch/papers/000template/teil1.tex @@ -3,6 +3,9 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % +% !TEX root = ../../buch.tex +% !TEX encoding = UTF-8 +% \section{Teil 1 \label{000template:section:teil1}} \rhead{Problemstellung} diff --git a/buch/papers/000template/teil2.tex b/buch/papers/000template/teil2.tex index 471adae..496557f 100644 --- a/buch/papers/000template/teil2.tex +++ b/buch/papers/000template/teil2.tex @@ -3,6 +3,9 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % +% !TEX root = ../../buch.tex +% !TEX encoding = UTF-8 +% \section{Teil 2 \label{000template:section:teil2}} \rhead{Teil 2} diff --git a/buch/papers/000template/teil3.tex b/buch/papers/000template/teil3.tex index 4697813..ef2aa75 100644 --- a/buch/papers/000template/teil3.tex +++ b/buch/papers/000template/teil3.tex @@ -3,6 +3,9 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % +% !TEX root = ../../buch.tex +% !TEX encoding = UTF-8 +% \section{Teil 3 \label{000template:section:teil3}} \rhead{Teil 3} -- cgit v1.2.1 From 61202dbd7a7762ceeee673cf27da26e47d72b966 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 16 Mar 2022 09:42:00 +0100 Subject: Kugelfunktionen --- buch/chapters/090-pde/kugel.tex | 237 +++++++++++++++++++++++++++++++++++++++- 1 file changed, 236 insertions(+), 1 deletion(-) diff --git a/buch/chapters/090-pde/kugel.tex b/buch/chapters/090-pde/kugel.tex index c081029..d466e26 100644 --- a/buch/chapters/090-pde/kugel.tex +++ b/buch/chapters/090-pde/kugel.tex @@ -145,8 +145,243 @@ Polarkoordinaten~\eqref{buch:pde:kreis:laplace}. Der Unterschied rührt daher, dass der Laplace-Operator die Krümmung der Koordinatenlinien berücksichtigt, in diesem Fall der Meridiane. - \subsection{Separation} +In Abschnitt~\ref{buch:pde:subsection:eigenwertproblem} +wurde bereits gzeigt, wie die Wellengleichung +\[ +\frac{1}{c^2} +\frac{\partial^2 U}{\partial t^2} +-\Delta U += +0 +\] +durch Separation der Zeit auf ein Eigenwertproblem für eine +Funktion $u$ reduziert werden kann, die nur von den Ortskoordinaten +abhängt. +Es geht also nur noch darum, dass Eigenwertproblem +\[ +\Delta u = -\lambda^2 u +\] +mit geeigneten Randbedingungen zu lösen. +Dazu gehören einerseits eventuelle Gebietsränder, die im Moment +nicht interessieren. +Andererseits muss sichergestellt sein, dass die Lösungsfunktionen +stetig und differentierbar sind an den Orten, wo das Koordinatensystem +singulär ist. +So müssen $u(r,\vartheta,\varphi)$ $2\pi$-periodisch in $\varphi$ sein. +% XXX Ableitungen + +\subsubsection{Separation des radialen Anteils} +Für das Eigenwertproblem verwenden wir den Ansatz +\[ +u(r,\vartheta,\varphi) += +R(r) \Theta(\vartheta) \Phi(\varphi), +\] +den wir in die Differentialgleichung einsetzen. +So erhalten wir +\[ +\biggl(\frac{1}{r^2}R''(r)+\frac{2}{r}R'(r) \biggr) +\Theta(\vartheta)\Phi(\varphi) ++ +R(r) +\frac{1}{r^2\sin\vartheta} +\frac{\partial}{\partial\vartheta}(\sin\vartheta \Theta'(\vartheta)) +\Phi(\varphi) ++ +R(r)\Theta(\vartheta) +\frac{1}{r^2\sin\vartheta} \Phi''(\varphi) += +-\lambda^2 R(r)\Theta(\vartheta)\Phi(\varphi). +\] +Die Gleichung lässt sich nach Multiplikation mit $r^2$ und +Division durch $u$ separieren in +\begin{equation} +\frac{R''(r)+2rR'(r)+\lambda^2r^2}{R(r)} ++ +\frac{1}{\Theta(\vartheta) \sin\vartheta} +\frac{\partial}{\partial\vartheta}\sin\vartheta\Theta'(\vartheta) ++ +\frac{1}{\sin^2\vartheta}\frac{\Phi''(\varphi)}{\Phi(\varphi)} += +0 +\label{buch:pde:kugel:separiert2} +\end{equation} +Der erste Term hängt nur von $r$ ab, die anderen nur von $\vartheta$ und +$\varphi$, daher muss der erste Term konstant sein. +Damit ergbit sich für den Radialanteil die gewöhnliche Differentialgleichung +\[ +R''(r) + 2rR'(r) +\lambda^2 r^2 = \mu^2 R(r), +\] +die zum Beispiel mit der Potenzreihenmethode gelöst werden kann. +Sie kann aber durch eine geeignete Substition nochmals auf die +Laguerre-Differentialgleichung reduziert werden, wie in +Kapitel~\ref{chapter:laguerre} dargelegt wird. + +\subsubsection{Kugelflächenanteil} +Für die Separation der verbleibenden winkelabhängigen Teile muss die +Gleichung +\[ +\frac{1}{\Theta(\vartheta) \sin\vartheta} +\frac{\partial}{\partial\vartheta}\sin\vartheta\Theta'(\vartheta) ++ +\frac{1}{\sin^2\vartheta}\frac{\Phi''(\varphi)}{\Phi(\varphi)} += +-\mu^2 +\] +mit $\sin^2\vartheta$ multipliziert werden, was auf +\[ +\frac{\sin\vartheta}{\Theta(\vartheta)} +\frac{\partial}{\partial\vartheta}\sin\vartheta\Theta'(\vartheta) ++ +\frac{\Phi''(\varphi)}{\Phi(\varphi)} += +-\mu^2\sin^2\vartheta +\quad\Rightarrow\quad +\frac{\sin\vartheta}{\Theta(\vartheta)} +\frac{\partial}{\partial\vartheta}\sin\vartheta\Theta'(\vartheta) ++ +\mu^2\sin^2\vartheta += +- +\frac{\Phi''(\varphi)}{\Phi(\varphi)} +\] +führt. +Die linke Seite der letzten Gleichung hängt nur von $\vartheta$ +ab, die rechte nur von $\varphi$, beide Seiten müssen daher +konstant sein, wir bezeichnen diese Konstante mit $\alpha^2$. +So ergibt sich die Differentialgleichung +\[ +\alpha^2 += +-\frac{\Phi''(\varphi)}{\Phi(\varphi)} +\] +für die Abhängigkeit von $\varphi$, mit der allgemeinen Lösung +\[ +\Phi(\varphi) += +A\cos\alpha \varphi ++ +B\sin\alpha \varphi. +\] +Die Randbedingungen verlangen, dass $\Phi(\varphi)$ eine $2\pi$-periodische +Funktion ist, was genau dann möglich ist, wenn $\alpha=m$ ganzzahlig ist. +Damit ergibt sich für die $\vartheta$-Abhängigkeit die Differentialgleichung +\begin{equation} +\frac{\sin\vartheta}{\Theta(\vartheta)} +\frac{\partial}{\partial\vartheta}\sin\vartheta\Theta'(\vartheta) ++ +\mu^2\sin^2\vartheta += +m^2. +\label{buch:pde:kugel:eqn:thetaanteil} +\end{equation} + +\subsubsection{Abhängigkeit von $\vartheta$} +Die Differentialgleichung~\eqref{buch:pde:kugel:eqn:thetaanteil} +ist etwas unhandlich, daher verwenden wir die Substitution $z=\cos\vartheta$, +um die trigonometrischen Funktionen los zu werden. +Wegen +\[ +\frac{dz}{d\vartheta} = -\sin\vartheta =-\sqrt{1-z^2} +\] +können die Ableitungen nach $\vartheta$ auch durch Ableitungen nach $z$ +ausgedrückt werden. +Wir schreiben dazu $Z(z)=\Theta(\vartheta)$ und berechnen +\[ +\Theta'(\vartheta) += +\frac{d\Theta}{d\vartheta} += +\frac{dZ}{dz}\frac{dz}{d\vartheta} += +- +\sqrt{1-z^2} +Z'(z). +\] +Dies bedeutet auch, dass +\[ +\sin\vartheta\frac{d}{d\vartheta} += +- +(1-z^2)\frac{d}{dz}, +\] +damit lässt sich die Differentialgleichung für $\Theta(\vartheta)$ umschreiben +in eine Differentialgleichung für $Z(z)$, nämlich +\[ +(1-z^2)\frac{d}{dz}(1-z^2)\frac{d}{dz} Z(z) ++ +\mu^2 +(1-z^2) +Z(z) += +m^2 +Z(z). +\] +Indem man die Ableitung im ersten Term mit Hilfe der Produktregel +ausführt, kann man die Gleichung +\[ +(1-z^2)\biggl( +-2zZ'(z) + (1-z^2)Z''(z) +\biggr) ++ +\mu^2(1-z^2)Z(z) += +-m^2 Z(z) +\] +bekommen. +Division durch $1-z^2$ ergibt die +{\em Legendre-Differentialgleichung} +\begin{equation} +(1-z^2)Z''(z) +-2zZ'(z) ++ +\biggl( +\mu^2 - \frac{m^2}{1-z^2} +\biggr) +Z(z) += +0. +\label{buch:pde:kugel:eqn:legendre-dgl} +\end{equation} +Eine Diskussion der Lösungen dieser Differentialgleichung erfolgt im +Kapitel~\ref{chapter:kugel}. + +\subsection{Kugelfunktionen} +Die Legendre-Differentialgleichung~\eqref{buch:pde:kugel:eqn:legendre-dgl} +hat Lösungen für Werte von $\mu$ derart, dass $\mu^2=l(l+1)$ für natürliche +Zahlen $l$. +Die Lösungen sind sogar Polynome, die wir mit $P_l^{(m)}(z)$ +bezeichnen, dabei ist $m$ eine ganze Zahl mit $-l\le m\le l$. +Die Funktionen $P_l^{(m)}(\cos\vartheta)e^{im\varphi}$ +sind daher alle Lösungen des von $\vartheta$ und $\varphi$ +abhängigen Teils der Lösungen des Eigenwertproblems. +Mit einer geeigneten Normierung kann man zudem eine Familie von +bezüglich des Skalarproduktes +\[ +\langle f,g\rangle_{S^2} += +\int_{-\pi}^{\pi} +\int_{0}^{\pi} +\overline{f(\vartheta,\varphi)} +g(\vartheta,\varphi) +\sin\vartheta +\,d\vartheta +\,d\varphi +\] +orthonormiete Funktionen auf der Kugeloberfläche erhalten, die +man normalerweise als +\[ +Y_{lm}(\vartheta,\varphi) += +\frac{1}{\sqrt{2\pi}} +\sqrt{ +\frac{2l+1}{2}\cdot +\frac{(l-m)!}{(l+m)!} +} +P_{l}^{(m)}(\cos\vartheta)e^{im\varphi} +\] +bezeichnet. -- cgit v1.2.1 From fd8e4b595f3f2c4245e7ba201a727585e34cfc82 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 16 Mar 2022 14:36:37 +0100 Subject: add missing file --- buch/chapters/040-rekursion/betaverteilung.tex | 487 +++++++++++++++++++++++++ buch/chapters/090-pde/gleichung.tex | 1 + buch/chapters/090-pde/kreis.tex | 1 + buch/chapters/090-pde/kugel.tex | 1 + buch/chapters/090-pde/rechteck.tex | 1 + buch/chapters/090-pde/separation.tex | 1 + 6 files changed, 492 insertions(+) create mode 100644 buch/chapters/040-rekursion/betaverteilung.tex diff --git a/buch/chapters/040-rekursion/betaverteilung.tex b/buch/chapters/040-rekursion/betaverteilung.tex new file mode 100644 index 0000000..979d04c --- /dev/null +++ b/buch/chapters/040-rekursion/betaverteilung.tex @@ -0,0 +1,487 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\subsection{Ordnungsstatistik und Beta-Funktion +\label{buch:rekursion:ordnung:section:ordnungsstatistik}} +\rhead{Ordnungsstatistik und Beta-Funktion} +In diesem Abschnitt ist $X$ eine Zufallsvariable mit der Verteilungsfunktion +$F_X(x)$, und $X_i$, $1\le i\le n$ sei ein Stichprobe von unabhängigen +Zufallsvariablen, die wie $X$ verteilt sind. +Ziel ist, die Verteilungsfunktion und die Wahrscheinlichkeitsdichte +des grössten, zweitgrössten, $k$-t-grössten Wertes in der Stichprobe +zu finden. +Wir schreiben $[n]=\{1,\dots,n\}$ für die Menge der natürlichen +Zahlen von zwischen $1$ und $n$. + +\subsubsection{Verteilung von $\operatorname{max}(X_1,\dots,X_n)$ und +$\operatorname{min}(X_1,\dots,X_n)$ +\label{buch:rekursion:ordnung:subsection:minmax}} +Die Verteilungsfunktion von $\operatorname{max}(X_1,\dots,X_n)$ hat +den Wert +\begin{align*} +F_{\operatorname{max}(X_1,\dots,X_n)}(x) +&= +P(\operatorname{max}(X_1,\dots,X_n) \le x) +\\ +&= +P(X_1\le x\wedge \dots \wedge X_n\le x) +\\ +&= +P(X_1\le x) \cdot \ldots \cdot P(X_n\le x) +\\ +&= +P(X\le x)^n += +F_X(x)^n. +\end{align*} +Für die Gleichverteilung ist +\[ +F_{\text{equi}}(x) += +\begin{cases} +0&\qquad x< 0 +\\ +x&\qquad 0\le x\le 1 +\\ +1&\qquad 1 X_1\wedge \dots \wedge x > X_n) +\\ +&= +1- +(1-P(x\le X_1)) \cdot\ldots\cdot (1-P(x\le X_n)) +\\ +&= +1-(1-F_X(x))^n, +\end{align*} +Im Speziellen für im Intervall $[0,1]$ gleichverteilte $X_i$ ist die +Verteilungsfunktion des Minimums +\[ +F_{\operatorname{min}(X_1,\dots,X_n)}(x) += +\begin{cases} +0 &\qquad x<0 \\ +1-(1-x)^n&\qquad 0\le x\le 1\\ +1 &\qquad 1 < x +\end{cases} +\] +mit Wahrscheinlichkeitsdichte +\[ +\varphi_{\operatorname{min}(X_1,\dots,X_n)} += +\frac{d}{dx} +F_{\operatorname{min}(X_1,\dots,X_n)} += +\begin{cases} +n(1-x)^{n-1}&\qquad 0\le x\le 1\\ +0 &\qquad \text{sonst} +\end{cases} +\] +und Erwartungswert +\begin{align*} +E(\operatorname{min}(X_1,\dots,X_n) +&= +\int_{-\infty}^\infty x\varphi_{\operatorname{min}(X_1,\dots,X_n)}(x)\,dx += +\int_0^1 x\cdot n(1-x)^{n-1}\,dx +\\ +&= +\bigl[ -x(1-x)^n \bigr]_0^1 + \int_0^1 (1-x)^n\,dx += +\biggl[ +- +\frac{1}{n+1} +(1-x)^{n+1} +\biggr]_0^1 += +\frac{1}{n+1}. +\end{align*} +Es ergibt sich daraus als natürlich Verallgemeinerung die Frage nach +der Verteilung des zweitegrössten oder zweitkleinsten Wertes unter den +Werten $X_i$. + +\subsubsection{Der $k$-t-grösste Wert} +Sie wieder $X_i$ eine Stichprobe von $n$ unabhängigen wie $X$ verteilten +Zufallsvariablen. +Diese werden jetzt der Grösse nach sortiert, die sortierten Werte werden +mit +\[ +X_{1:n} \le X_{2:n} \le \dots \le X_{(n-1):n} \le X_{n:n} +\] +bezeichnet. +Die Grössen $X_{k:n}$ sind Zufallsvariablen, sie heissen die $k$-ten +Ordnungsstatistiken. +Die in Abschnitt~\ref{buch:rekursion:ordnung:subsection:minmax} behandelten Zufallsvariablen +$\operatorname{min}(X_1,\dots,X_n)$ +und +$\operatorname{max}(X_1,\dots,X_n)$ +sind die Fälle +\begin{align*} +X_{1:n} &= \operatorname{min}(X_1,\dots,X_n) \\ +X_{n:n} &= \operatorname{max}(X_1,\dots,X_n). +\end{align*} + +Um den Wert der Verteilungsfunktion von $X_{k:n}$ zu berechnen, müssen wir +die Wahrscheinlichkeit bestimmen, dass $k$ der $n$ Werte $X_i$ $x$ nicht +übersteigen. +Der $k$-te Wert $X_{k:n}$ übersteigt genau dann $x$ nicht, wenn +mindestens $k$ der Zufallswerte $X_i$ $x$ nicht übersteigen, also +\[ +P(X_{k:n} \le x) += +P\left( +|\{i\in[n]\,|\, X_i\le x\}| \ge k +\right). +\] + +Das Ereignis $\{X_i\le x\}$ ist eine Bernoulli-Experiment, welches mit +Wahrscheinlichkeit $F_X(x)$ eintritt. +Die Anzahl der Zufallsvariablen $X_i$, die $x$ übertreffen, ist also +Binomialverteilt mit $p=F_X(x)$. +Damit haben wir gefunden, dass mit Wahrscheinlichkeit +\begin{equation} +F_{X_{k:n}}(x) += +P(X_{k:n}\le x) += +\sum_{i=k}^n \binom{n}{i}F_X(x)^i (1-F_X(x))^{n-i} +\label{buch:rekursion:ordnung:eqn:FXkn} +\end{equation} +mindestens $k$ der Zufallsvariablen den Wert $x$ überschreiten. + +\subsubsection{Wahrscheinlichkeitsdichte der Ordnungsstatistik} +Die Wahrscheinlichkeitsdichte der Ordnungsstatistik kann durch Ableitung +von \eqref{buch:rekursion:ordnung:eqn:FXkn} gefunden, werden, sie ist +\begin{align*} +\varphi_{X_{k:n}}(x) +&= +\frac{d}{dx} +F_{X_{k:n}}(x) +\\ +&= +\sum_{i=k}^n +\binom{n}{i} +\bigl( +iF_X(x)^{i-1}\varphi_X(x) (1-F_X(x))^{n-i} +- +F_X(x)^k +(n-i) +(1-F_X(x))^{n-i-1} +\varphi_X(x) +\bigr) +\\ +&= +\sum_{i=k}^n +\binom{n}{i} +\varphi_X(x) +F_X(x)^{i-1}(1-F_X(x))^{n-i-1} +\bigl( +iF_X(x)-(n-i)(1-F_X(x)) +\bigr) +\\ +&= +\varphi_X(x) +\biggl( +\sum_{i=k}^n i\binom{n}{i} F_X(x)^{i-1}(1-F_X(x))^{n-i} +- +\sum_{j=k}^n (n-j)\binom{n}{j} F_X(x)^{j}(1-F_X(x))^{n-j-1} +\biggr) +\\ +&= +\varphi_X(x) +\biggl( +\sum_{i=k}^n i\binom{n}{i} F_X(x)^{i-1}(1-F_X(x))^{n-i} +- +\sum_{i=k+1}^{n+1} (n-i+1)\binom{n}{i-1} F_X(x)^{i-1}(1-F_X(x))^{n-i} +\biggr) +\\ +&= +\varphi_X(x) +\biggl( +k\binom{n}{k}F_X(x)^{k-1}(1-F_X(x))^{n-k} ++ +\sum_{i=k+1}^{n+1} +\left( +i\binom{n}{i} +- +(n-i+1)\binom{n}{i-1} +\right) +F_X(x)^{i-1}(1-F_X(x))^{n-i} +\biggr) +\end{align*} +Mit den wohlbekannten Identitäten für die Binomialkoeffizienten +\begin{align*} +i\binom{n}{i} +- +(n-i+1)\binom{n}{i-1} +&= +n\binom{n-1}{i-1} +- +n +\binom{n-1}{i-1} += +0 +\end{align*} +folgt jetzt +\begin{align*} +\varphi_{X_{k:n}}(x) +&= +\varphi_X(x)k\binom{n}{k} F_X(x)^{k-1}(1-F_X(x))^{n-k}(x). +\intertext{Im Speziellen für gleichverteilte Zufallsvariablen $X_i$ ist +} +\varphi_{X_{k:n}}(x) +&= +k\binom{n}{k} x^{k-1}(1-x)^{n-k}. +\end{align*} +Dies ist die Wahrscheinlichkeitsdichte einer Betaverteilung +\[ +\beta(k,n-k+1)(x) += +\frac{1}{B(k,n-k+1)} +x^{k-1}(1-x)^{n-k}. +\] +Tatsächlich ist die Normierungskonstante +\begin{align} +\frac{1}{B(k,n-k+1)} +&= +\frac{\Gamma(n+1)}{\Gamma(k)\Gamma(n-k+1)} += +\frac{n!}{(k-1)!(n-k)!}. +\label{buch:rekursion:ordnung:betaverteilung:normierung1} +\end{align} +Andererseits ist +\[ +k\binom{n}{k} += +k\frac{n!}{k!(n-k)!} += +\frac{n!}{(k-1)!(n-k)!}, +\] +in Übereinstimmung mit~\eqref{buch:rekursion:ordnung:betaverteilung:normierung1}. +Die Verteilungsfunktion und die Wahrscheinlichkeitsdichte der +Ordnungsstatistik sind in Abbildung~\ref{buch:rekursion:ordnung:fig:order} dargestellt. + +\begin{figure} +\centering +\includegraphics{chapters/040-rekursion/images/order.pdf} +\caption{Verteilungsfunktion und Wahrscheinlichkeitsdichte der +Ordnungsstatistiken $X_{k:n}$ einer gleichverteilung Zuvallsvariable +mit $n=10$. +\label{buch:rekursion:ordnung:fig:order}} +\end{figure} + +% +% Die Beta-Funktion +% +\subsection{Die Beta-Verteilung +\label{buch:rekursion:subsection:beta-verteilung}} +Die Wahrscheinlichkeitsdichte, die im +Abschnitt~\ref{buch:rekursion:ordnung:section:ordnungsstatistik} +gefunden worden ist, ist nicht nur für ganzzahlige Exponenten +definiert. + +\begin{figure} +\centering +\includegraphics[width=0.92\textwidth]{chapters/040-rekursion/images/beta.pdf} +\caption{Wahrscheinlichkeitsdichte der Beta-Verteilung +$\beta(a,b,x)$ +für verschiedene Werte der Parameter $a$ und $b$. +Die Werte des Parameters für einen Graphen einer Beta-Verteilung +sind im kleinen Quadrat rechts im Graphen +als Punkt mit der gleichen Farbe dargestellt. +\label{buch:rekursion:ordnung:fig:betaverteilungn}} +\end{figure} + +\begin{definition} +Die Beta-Verteilung ist die Verteilung mit der Wahrscheinlichkeitsdichte +\[ +\beta_{a,b}(x) += +\begin{cases} +\displaystyle +\frac{1}{B(a,b)} +x^{a-1}(1-x)^{b-1}&\qquad 0\le x \le 1\\ +0&\qquad\text{sonst.} +\end{cases} +\] +\end{definition} + +Die Beta-Funktion ist also die Normierungskonstante der Beta-Verteilung. +Die wichtigsten Kennzahlen der Beta-Verteilung wie Erwartungswert und +Varianz lassen sich alle ebenfalls als Werte der Beta-Funktion ausdrücken. + +\subsubsection{Erwartungswert} +Mit der Wahrscheinlichkeitsdichte kann man jetzt auch den Erwartungswerte +der $k$-ten Ordnungsstatistik bestimmen. +Die Rechnung ergibt: +\begin{align*} +E(X_{k:n}) +&= +\int_0^1 x\cdot k\binom{n}{k} x^{k-1}(1-x)^{n-k}\,dx += +k +\binom{n}{k} +\int_0^1 +x^{k}(1-x)^{n-k}\,dx. +\intertext{Dies ist das Beta-Integral} +&= +k\binom{n}{k} +B(k+1,n-k+1) +\intertext{welches man durch Gamma-Funktionen bzw.~durch Fakultäten wie in} +&= +k\frac{n!}{k!(n-k)!} +\frac{\Gamma(k+1)\Gamma(n-k+1)}{n+2} += +k\frac{n!}{k!(n-k)!} +\frac{k!(n-k)!}{(n+1)!} += +\frac{k}{n+1} +\end{align*} +ausdrücken kann. +Die Erwartungswerte haben also regelmässige Abstände, sie sind in +Abbildung~\ref{buch:rekursion:ordnung:fig:order} als blaue vertikale Linien eingezeichnet. + +Für die Beta-Verteilung lässt sich die Rechnung noch allgemeiner +durchführen. +Der Erwartungswert einer $\beta_{a,b}$-verteilten Zufallsvariablen $X$ +ist +\begin{align*} +E(X) +&= +\int_0^1 x \beta_{a,b}(x)\,dx += +\frac{1}{B(a,b)} +\int_0^1 x\cdot x^{a-1}(1-x)^{b-1}\,dx += +\frac{B(a+1,b)}{B(a,b)} += +\frac{a}{a+b}. +\end{align*} +Durch Einsetzen von $a=k+1$ und $b=n-k+1$ lassen sich die für die +Ordnungsstatistik berechneten Werte wiederfinden. + +\subsubsection{Varianz} +Auch die Varianz lässt sich einfach berechnen, dazu muss zunächst +der Erwartungswert von $X_{k:n}^2$ bestimmt werden. +Er ist +\begin{align*} +E(X_{k:n}^2) +&= +\int_0^1 x^2\cdot k\binom{n}{k} x^{k-1}(1-x)^{n-k}\,dx += +k +\binom{n}{k} +\int_0^1 +x^{k+1}(1-x)^{n-k}\,dx. +\intertext{Auch dies ist ein Beta-Integral, nämlich} +&= +k\binom{n}{k} +B(k+2,n-k+1) += +k\frac{n!}{k!(n-k)!} +\frac{(k+1)!(n-k)!}{(n+2)!} += +\frac{k(k+1)}{(n+1)(n+2)}. +\end{align*} +Die Varianz wird damit +\begin{align} +\operatorname{var}(X_{k:n}) +&= +E(X_{k:n}^2) - E(X_{k:n})^2 +\notag +\\ +& += +\frac{k(k+1)}{(n+1)(n+2)}-\frac{k^2}{(n+1)^2} += +\frac{k(k+1)(n+1)-k^2(n+2)}{(n+1)^2(n+2)} += +\frac{k(n-k+1)}{(n+1)^2(n+2)}. +\label{buch:rekursion:ordnung:eqn:ordnungsstatistik:varianz} +\end{align} +In Abbildung~\ref{buch:rekursion:ordnung:fig:order} ist die Varianz der +Ordnungsstatistik $X_{k:n}$ für $k=7$ und $n=10$ als oranges +Rechteck dargestellt. + +Auch die Varianz kann ganz allgemein für die Beta-Verteilung +bestimmt werden. +Dazu berechnen wir zunächst +\begin{align*} +E(X^2) +&= +\frac{1}{B(a,b)} +\int_0^1 +x^2\cdot x^{a-1}(1-y)^{b-1}\,dx += +\frac{B(a+2,b)}{B(a,b)}. +\end{align*} +Daraus folgt dann +\[ +\operatorname{var}(X) += +E(X^2)-E(X)^2 += +\frac{B(a+2,b)B(a,b)-B(a+1,b)^2}{B(a,b)^2}. +\] + +Die Formel~\eqref{buch:rekursion:ordnung:eqn:ordnungsstatistik:varianz} +besagt auch, dass die Varianz der proportional ist zu $k((n+1)-k)$. +Dieser Ausdruck ist am grössten für $k=(n+1)/2$, die Varianz ist +also grösser für die ``mittleren'' Ordnungstatistiken als für die +extremen $X_{1:n}=\operatorname{min}(X_1,\dots,X_n)$ und +$X_{n:n}=\operatorname{max}(X_1,\dots,X_n)$. + diff --git a/buch/chapters/090-pde/gleichung.tex b/buch/chapters/090-pde/gleichung.tex index 7f65f06..583895d 100644 --- a/buch/chapters/090-pde/gleichung.tex +++ b/buch/chapters/090-pde/gleichung.tex @@ -5,6 +5,7 @@ % \section{Gleichungen und Randbedingungen \label{buch:pde:section:gleichungen-und-randbedingungen}} +\rhead{Gebiete, Gleichungen und Randbedingungen} \subsection{Gebiete, Differentialoperatoren, Randbedingungen} diff --git a/buch/chapters/090-pde/kreis.tex b/buch/chapters/090-pde/kreis.tex index c60fd44..a8cab3e 100644 --- a/buch/chapters/090-pde/kreis.tex +++ b/buch/chapters/090-pde/kreis.tex @@ -5,6 +5,7 @@ % \section{Kreisförmige Membran \label{buch:pde:section:kreis}} +\rhead{Kreisförmige Membran} In diesem Abschnitt soll die Differentialgleichung einer kreisförmigen Membran mit Hilfe der Separationsmethode gelöst werden. Dabei werden die Bessel-Funktionen als Lösungsfunktionen diff --git a/buch/chapters/090-pde/kugel.tex b/buch/chapters/090-pde/kugel.tex index d466e26..ee56316 100644 --- a/buch/chapters/090-pde/kugel.tex +++ b/buch/chapters/090-pde/kugel.tex @@ -5,6 +5,7 @@ % \section{Kugelfunktionen \label{buch:pde:section:kugel}} +\rhead{Kugelfunktionen} Kugelsymmetrische Probleme können oft vorteilhaft in Kugelkoordinaten beschrieben werden. Die Separationsmethode kann auf partielle Differentialgleichungen diff --git a/buch/chapters/090-pde/rechteck.tex b/buch/chapters/090-pde/rechteck.tex index 72e2806..b7dfe11 100644 --- a/buch/chapters/090-pde/rechteck.tex +++ b/buch/chapters/090-pde/rechteck.tex @@ -5,6 +5,7 @@ % \section{Rechteckige Membran \label{buch:pde:section:rechteck}} +\rhead{Rechteckige Membran} Als Beispiel für die Lösung des in Abschnitt~\ref{buch:pde:subsection:eigenwertproblem} aus der Wellengleichung abgeleiteten Eigenwertproblems diff --git a/buch/chapters/090-pde/separation.tex b/buch/chapters/090-pde/separation.tex index 6faceaa..e5e144a 100644 --- a/buch/chapters/090-pde/separation.tex +++ b/buch/chapters/090-pde/separation.tex @@ -5,6 +5,7 @@ % \section{Separationsmethode \label{buch:pde:section:separation}} +\rhead{Separationsmethode} Die Existenz der Lösung einer gewöhnlichen Differentialgleichung ist unter einigermassen milden Bedingungen in der Nähe der Anfangsbedingung garantiert. -- cgit v1.2.1 From e245386805c7bb6d7515154f2bd50aba3a7713a8 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 18 Mar 2022 08:45:05 +0100 Subject: typos --- buch/chapters/070-orthogonalitaet/gaussquadratur.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index 55f9700..b7a5643 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -135,7 +135,7 @@ p(x)&=x^2\colon& \frac23 &= A_0x_0^2 + A_1x_1^2\\ p(x)&=x^3\colon& 0 &= A_0x_0^3 + A_1x_1^3. \end{aligned} \] -Dividiert man die zweite und vierte Gleichung in der Form +Dividiert man die zweite und dritte Gleichung in der Form \[ \left. \begin{aligned} @@ -155,7 +155,7 @@ x_1=-x_0. \] Indem wir dies in die zweite Gleichung einsetzen, finden wir \[ -0 = A_0x_0 + A_1x_1 = A_0x_1 -A_1x_0 = (A_0-A_1)x_0 +0 = A_0x_0 + A_1x_1 = A_0x_0 -A_1x_0 = (A_0-A_1)x_0 \quad\Rightarrow\quad A_0=A_1. \] -- cgit v1.2.1 From 8ea715ed37adfbaf6369c7fbd889380857b574e0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 18 Mar 2022 08:56:45 +0100 Subject: fix Gauss quadrature example --- buch/chapters/070-orthogonalitaet/gaussquadratur.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index b7a5643..acfdb1a 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -135,12 +135,12 @@ p(x)&=x^2\colon& \frac23 &= A_0x_0^2 + A_1x_1^2\\ p(x)&=x^3\colon& 0 &= A_0x_0^3 + A_1x_1^3. \end{aligned} \] -Dividiert man die zweite und dritte Gleichung in der Form +Dividiert man die vierte durch die zweite Gleichung in der Form \[ \left. \begin{aligned} -A_0x_0 &= -A_1x_1\\ -A_0x_0^2 &= -A_1x_1^2 +A_0x_0^3 &= -A_1x_1^3 &\qquad&\text{(vierte Gleichung)}\\ +A_0x_0 &= -A_1x_1 &\qquad&\text{(zweite Gleichung)} \end{aligned} \quad \right\} -- cgit v1.2.1 From b1033012ad434fb6ac2dbeb09d6c9fcd5f6cedb6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 20 Mar 2022 21:22:31 +0100 Subject: add orthogonal polynomials lecture notes --- vorlesungsnotizen/B/5 - Orthogonale Polynome.pdf | Bin 0 -> 2996979 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 vorlesungsnotizen/B/5 - Orthogonale Polynome.pdf diff --git a/vorlesungsnotizen/B/5 - Orthogonale Polynome.pdf b/vorlesungsnotizen/B/5 - Orthogonale Polynome.pdf new file mode 100644 index 0000000..8e9ab51 Binary files /dev/null and b/vorlesungsnotizen/B/5 - Orthogonale Polynome.pdf differ -- cgit v1.2.1 From e44c12611872cd540933b023ff393edd6c2fcd99 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 24 Mar 2022 21:26:54 +0100 Subject: add MSE lecture 3 --- vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf | Bin 0 -> 6230218 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf diff --git a/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf b/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf new file mode 100644 index 0000000..2150320 Binary files /dev/null and b/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf differ -- cgit v1.2.1 From 3ad9b64931ff50477c1eb99cd5fa4d4930ac9f77 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 25 Mar 2022 16:15:42 +0100 Subject: Fehlerbereinigungen --- .../MSE/3 - Differentialgleichungen.pdf | Bin 6230218 -> 6237222 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf b/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf index 2150320..9ce44bb 100644 Binary files a/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf and b/vorlesungsnotizen/MSE/3 - Differentialgleichungen.pdf differ -- cgit v1.2.1 From 9b8e3f91862b5acd367cf7bbf9d52cb17563390d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 26 Mar 2022 22:08:42 +0100 Subject: add new lecture notes --- buch/chapters/110-elliptisch/images/jacobiplots.pdf | Bin 57192 -> 56975 bytes buch/chapters/110-elliptisch/images/jacobiplots.tex | 2 +- vorlesungsnotizen/B/6 - Elliptische Funktionen.pdf | Bin 0 -> 3388898 bytes 3 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 vorlesungsnotizen/B/6 - Elliptische Funktionen.pdf diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index d11bde8..88cf119 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.tex b/buch/chapters/110-elliptisch/images/jacobiplots.tex index 4fc572e..fec04fc 100644 --- a/buch/chapters/110-elliptisch/images/jacobiplots.tex +++ b/buch/chapters/110-elliptisch/images/jacobiplots.tex @@ -31,7 +31,7 @@ \fill[color=gray!50] (-0.2,1.65) rectangle (7.0,2.3); \draw[line width=0.5pt] (-0.2,-6) rectangle (7.0,2.3); \begin{scope}[scale=0.5] -\node at (6.5,{\dy+2}) {$m = #1$}; +\node at (6.5,{\dy+2}) {$k^2 = #1$}; \end{scope} } \def\jacobiplot#1#2#3#4{ diff --git a/vorlesungsnotizen/B/6 - Elliptische Funktionen.pdf b/vorlesungsnotizen/B/6 - Elliptische Funktionen.pdf new file mode 100644 index 0000000..1b0b73a Binary files /dev/null and b/vorlesungsnotizen/B/6 - Elliptische Funktionen.pdf differ -- cgit v1.2.1 From 4a49ccec57384ba582c1c132a33942c938bc1b43 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 28 Mar 2022 13:26:54 +0200 Subject: new stuff about bessel --- buch/chapters/075-fourier/2d.tex | 19 + buch/chapters/075-fourier/Makefile.inc | 2 + buch/chapters/075-fourier/bessel.tex | 620 +++++++++++++++++++++++++++++++++ buch/chapters/075-fourier/chapter.tex | 3 +- 4 files changed, 643 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/075-fourier/2d.tex create mode 100644 buch/chapters/075-fourier/bessel.tex diff --git a/buch/chapters/075-fourier/2d.tex b/buch/chapters/075-fourier/2d.tex new file mode 100644 index 0000000..cc019c7 --- /dev/null +++ b/buch/chapters/075-fourier/2d.tex @@ -0,0 +1,19 @@ +% +% 2d.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\section{Zweidimensionale Fourier-Transformation +\label{buch:fourier:section:2d}} +\rhead{Zweidimensionale Fourier-Transformation} + +\subsection{Fourier-Transformation und partielle Differentialgleichungen} + +\subsection{Fourier-Transformation in kartesischen Koordinaten} + +\subsection{Basisfunktionen in Polarkoordinaten} + + + + + diff --git a/buch/chapters/075-fourier/Makefile.inc b/buch/chapters/075-fourier/Makefile.inc index ee9641c..c153dc4 100644 --- a/buch/chapters/075-fourier/Makefile.inc +++ b/buch/chapters/075-fourier/Makefile.inc @@ -5,4 +5,6 @@ # CHAPTERFILES = $(CHAPTERFILES) \ + chapters/075-fourier/bessel.tex \ + chapters/075-fourier/2d.tex \ chapters/075-fourier/chapter.tex diff --git a/buch/chapters/075-fourier/bessel.tex b/buch/chapters/075-fourier/bessel.tex new file mode 100644 index 0000000..7e978f7 --- /dev/null +++ b/buch/chapters/075-fourier/bessel.tex @@ -0,0 +1,620 @@ +% +% bessel.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\section{Fourier-Transformation und Bessel-Funktionen +\label{buch:fourier:section:fourier-und-bessel}} +\rhead{Fourier-Transformation und Bessel-Funktionen} + +Sei $f\colon \mathbb{R}^2\to\mathbb{C}$ eine auf $\mathbb{R}$ definierte +Funktion. +Die Fourier-Transformation von $f$ ist das Integral +\begin{equation} +(\mathscr{F}f)(u,v) += +F(u,v) += +\frac{1}{2\pi} +\int_{-\infty}^\infty +\int_{-\infty}^\infty +f(x,y) e^{i(xu+yv)} +\,dx\,dy. +\label{buch:fourier:eqn:2dfourier} +\end{equation} +Die Funktionen $e_{u,v}\colon (x,y)\mapsto e^{i(xu+yv)}$ +sind die Eigenfunktionen des Laplace-Operators in kartesischen Koordinaten, +sie erfüllen +\[ +\Delta e_{u,v} = (u^2+v^2) \Delta e_{u,v}. +\] +Die Fourier-Integrale sind die Skalarprodukte +\[ +(\mathscr{F}f)(u,v) += +\langle +e_{u,v}, +f +\rangle, +\] +wobei das Skalarprodukt durch +\[ +\langle f,g\rangle += +\int_{-\infty}^\infty +\int_{-\infty}^\infty +\overline{f(x)} g(x) +\,dx\,dy +\] +definiert ist. + +Jede Funktion in der Ebene kann auch in Polarkoordinaten ausgedrückt werden. +Die kartesischen Koordinaten können mittels +\begin{align*} +x&=r\cos\varphi +y&=r\sin\varphi +\end{align*} +durch die Polarkoordinaten $(r,\varphi)$ ausgedrückt werden. +Wir schreiben +\[ +\tilde{f}(r,\varphi) += +f(r\cos\varphi,r\sin\varphi) +\] +für die Funktion $f$ ausgedrückt in Polarkoordinaten. + +In Polarkoordinaten wird das Skalarprodukt +\[ +\langle f,g\rangle += +\int_0^\infty \int_{0}^{2\pi} e^{in\varphi} +\overline{ +\tilde{f}(r,\varphi) +} +\tilde{g}(r,\varphi) +r\,dr\,d\varphi. +\] +Auch die Fouriertransformation kann jetzt durch Berechnung eines +doppelten Integrals in Polarkoordinaten ermittelt werden. +Ziel dieses Abschnitts ist zu zeigen, dass auch diese Berechnung auf +Bessel-Funktionen führt. +Im Gegenzug werden sich neue Eigenschaften und Darstellungen derselben +ergeben. + + +\subsection{Berechnung der Fourier-Transformation in Polarkoordinaten} +Die Fourier-Transformation $(\mathscr{F}f)(u,v)$ ist eine Funktion +$\mathbb{R}^2\to\mathbb{C}$, die vom Wellenvektor $(u,v)$ abhängt. +Auch dieser Vektor kann in Polarkoordinaten ausgedrückt werden. +Für die Polarkoordinaten in der Wellenvektor-Ebene soll die Bezeichnung +$(R,\vartheta)$ verwendet werden, was auf die Transformationsgleichungen +\begin{align*} +u&=R\cos\vartheta\\ +v&=R\sin\vartheta +\end{align*} +führt. +Im Exponenten der Exponentialfunktion +des Fourier-Integrals~\eqref{buch:fourier:eqn:2dfourier} +steht der Ausdruck +\[ +xu+yv += +r\cos\varphi\cdot R\cos\vartheta ++ +r\sin\varphi\cdot R\sin\vartheta += +rR\cos(\varphi-\vartheta). +\] +Mit diesen Bezeichnungen wird das +Fourier-Integral~\eqref{buch:fourier:eqn:2dfourier} +zu +\begin{align} +\tilde{F}(R,\vartheta) +&= +\frac{1}{2\pi} +\int_{0}^{\infty} +\int_{0}^{2\pi} +f(r\cos\varphi,r\sin\varphi) +e^{irR\cos(\varphi-\vartheta)} +\,d\varphi\,r\, dr +\notag +\\ +&= +\frac{1}{2\pi} +\int_{0}^{\infty} +\int_{0}^{2\pi} +\tilde{f}(r,\varphi) +e^{irR\cos(\varphi-\vartheta)} +\,d\varphi\,r\, dr. +\label{buch:fourier:eqn:fouriertrafopolar} +\end{align} +Die partielle Funktion $\varphi\mapsto \tilde{f}(r,\varphi)$ +ist eine $2\pi$-periodische Funktion, sie lässt sich also als +komplexe Fourier-Reihe +\begin{equation} +\tilde{f}(r,\varphi) += +\sum_{n\in\mathbb{Z}} \hat{f}_n(r) e^{in\varphi} +\label{buch:fourier:eqn:fourierkoef} +\end{equation} +schreiben, die Funktionen $\hat{f}_n(r)$ sind die komplexen +Fourier-Koeffizienten. +Setzt man \eqref{buch:fourier:eqn:fourierkoef} in die Fourier-Transformation +\eqref{buch:fourier:eqn:fouriertrafopolar} ein, erhält man +\begin{align*} +\tilde{F}(R,\vartheta) +&= +\sum_{n\in\mathbb{Z}} +\int_0^\infty +\hat{f}_n(r) +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi+irR\cos(\varphi-\vartheta)} +\,d\varphi +\, +r\,dr. +\end{align*} +Der Exponent im inneren Integral kann als +\[ +in\varphi+irR\cos(\varphi-\vartheta) += +i(n(\varphi-\vartheta)+rR\cos(\varphi-\vartheta)) ++ +in\vartheta, +\] +oder im Integral als +\[ +\tilde{F}(R,\vartheta) += +\sum_{n\in\mathbb{Z}} +\int_0^\infty +\hat{f}_n(r) +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in(\varphi-\vartheta)+irR\cos(\varphi-\vartheta)} +e^{in\vartheta} +\,d\varphi +\, +r\,dr +\] +geschrieben werden. +Der zweite Exonentialfaktor hängt nicht von $\varphi$ ab und kann daher +aus dem Integral herausgezogen werden. +Der erste Exponentialfaktor hängt nur von $\varphi-\vartheta$ ab. +Da die Exponentialfunktion $2\pi$-periodisch ist, hat die Verschiebung +um $\vartheta$ keinen Einfluss auf den Wert des Integrals. +Die Fourier-Transformation ist daher auch +\[ +\tilde{F}(R,\vartheta) += +\sum_{n\in\mathbb{Z}} +\int_0^\infty +\hat{f}_n(r) +e^{in\vartheta} +\underbrace{ +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi+irR\cos\varphi} +\,d\varphi +}_{\displaystyle =:F_n(rR)} +\, +r\,dr. +\] +Die Beziehung zu den Besselfunktionen können wir daraus herstellen, +indem wir zunächst $\xi = rR$ abkürzen und dann das innere Integral +\begin{equation} +F_n(\xi) += +\frac{1}{2\pi} +\int_{0}^{2\pi} +e^{in\varphi+i\xi\cos\varphi} +\,d\varphi += +\frac{1}{2\pi} +\int_{0}^{2\pi} +e^{in\varphi}e^{i\xi\cos\varphi} +\,d\varphi +\label{buch:fourier:eqn:Fncosphi} +\end{equation} +auswerten. +Exponentialfunktion als Potenzreihe entwickeln: +\[ +F_n(\xi) += +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi} +\sum_{k=0}^\infty +\frac{ +i^k\xi^k \cos^k\varphi +}{k!} +\,d\varphi += +\sum_{k=0}^\infty +\frac{i^k\xi^k}{k!} +\underbrace{ +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi} +\cos^k\varphi +\,d\varphi}_{\displaystyle =c_{n,k}}. +\] +Das Integral auf der rechten Seite ist im Wesentlichen ein +Fourier-Koeffizient der Funktion $\varphi\mapsto \cos^k\varphi$. + +\subsubsection{Berechnung der Fourier-Koeffizienten von $\cos^k\varphi$} +Indem man die Kosinus-Funktion als die Linearkombination +\[ +\cos\varphi += +\frac{e^{i\varphi}+e^{-i\varphi}}2 +\] +von Exponentialfunktionen ausdrückt, kann man auch die $k$-te Potenz +mit Hilfe des binomischen Satzes als +\[ +\cos^k\varphi += +\sum_{m=0}^k +\frac{1}{2^k} +\binom{k}{m} +e^{im\varphi}e^{i(m-k)\varphi} += +\sum_{m=0}^k +\frac{1}{2^k} +\binom{k}{m} +e^{i(2m-k)\varphi} +\] +ausdrücken. +Der Fourier-Koeffizient von $\cos^k\varphi$ ist daher das Integral +\begin{align*} +c_{n,k} +&= +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi}\cos^k\varphi\,d\varphi +\\ +&= +\frac{1}{2^k} +\sum_{m=0}^k +\binom{k}{m} +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi}e^{i(2m-k)\varphi} +\,d\varphi +\\ +&= +\frac{1}{2^k} +\sum_{m=0}^k +\binom{k}{m} +\frac{1}{2\pi} +\int_0^{2\pi} +e^{i(2m-k+n)\varphi} +\,d\varphi. +\end{align*} +Für $2m-k+n=0$ ist das Integral ein Integral der Funktion $1$ über +ein Intervall der Länge $2\pi$, zusammen mit dem Faktor $1/2\pi$ hat +es daher den Wert $1$. +Für $2m-k+n\ne 0$ ist das Integral +\[ +\frac{1}{2\pi} +\int_0^{2\pi} +e^{i(2m-k+n)\varphi} +\,d\varphi += +\frac{1}{i} +\biggl[ +\frac{e^{i(2m-k+n)\varphi}}{2m-k+n} +\biggr]_0^{2\pi} += +0 +\] +weil die Exponentialfunktion $2\pi$-periodisch ist. +Nur für $k=2m+n$ ergibt sich ein nicht verschwindender +Fourier-Koeffizient. +Eine Summe über $k\in\mathbb{N}$ kann daher auch als Summe über +$m\in\mathbb{N}$ interpretiert werden, in der $k$ durch die Formel +$k=2m+n$ gegeben wird. +Mit dieser Konvention wird +\[ +c_{n,k} += +c_{n,2m+n} +%= +%\frac{1}{2\pi} +%\int_0^{2\pi} +%e^{-i(2m+n)\varphi} +%\cos^{2m+n}\varphi +%\,d\varphi += +\frac{1}{2^{2m+n}} +\binom{2m+n}{m} +\] +schreiben lässt. + +\subsubsection{Berechnung von $F_n(\xi)$} +Die Reihe für $F_n(\xi)$ lässt sich weiter vereinfachen. +Wir verwenden wieder die Tatsache, dass sich nur für $n=-2m-k$ +ein Beitrag ergibt. +Dies bedeutet, dass $k=2m+n$ sein muss, die Summe kann damit als +Summe über $m$ statt über $k$ geschrieben werden. +Somit ist +\begin{align*} +F_n(\xi) +&= +\sum_{k=0}^\infty +\frac{i^k\xi^k}{k!} +c_{n,k} += +\sum_{m=0}^\infty +\frac{i^{2m+n}\xi^{2m+n}}{(2m+n)!} +c_{n,2m+n} +\\ +&= +\sum_{m=0}^\infty +\frac{1}{2^{2m+n}} +\binom{2m+n}{m} +\frac{i^{2m+n}\xi^{2m+n}}{(2m+n)!} +\\ +&= +i^n +\sum_{m=0}^\infty +\frac{(-1)^m}{(2m+n)!} +\frac{(2m+n)!}{m!\,(2m+n-m)!} +\biggl(\frac{\xi}{2}\biggr)^{2m+n} +\\ +&= +i^n +\sum_{m=0}^\infty +\frac{(-1)^m} +{m!\,\Gamma(m+n+1)} +\biggl(\frac{\xi}{2}\biggr)^{2m+n} += +i^n J_n(\xi). +\end{align*} +Die Funktionen $F_n(\xi)$ sind daher bis auf einen Phasenfaktor der +Wert $J_n(\xi)$ einer Bessel-Funktion. + +\subsubsection{Berechnung der Fourier-Transformation mit Bessel-Funktionen} +Mit allen oben zusammengestellten Notationen kann die Fourier-Transformation +jetzt in Polarkoordinaten als +\[ +\tilde{F}(R,\vartheta) += +\sum_{n\in\mathbb{Z}} +e^{in\vartheta} +\int_0^\infty +\hat{f}_n(r) +i^n +J_n(rR) +r\,dr +\] +geschrieben werden. +Dies hat tatsächlich die Form eines Skalarproduktes der Funktion +$\tilde{f}(r,\varphi)$ mit einer Funktion der Form +\[ +\tilde{e}_{n,R}(r,\varphi) += +e^{in\varphi} +J_n(rR). +\] +Letzeres sind die in Abschnitt~\ref{buch:fourier:section:2d} +versprochenen Basisfunktionen. + +\subsubsection{Fourier-Reihe von $e^{i\xi\cos\varphi}$} +Die Funktionen $F_n(\xi)$ sind wegen +\[ +F_n(\xi) += +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi} +e^{i\xi\cos\varphi} +\,d\varphi, +\] +daraus kann man die Fourier-Reihe von $e^{i\xi\cos\varphi}$ +berechnen, dies wird im folgenden Satz durchgeführt. + + +\begin{satz} +\label{buch:fourier:satz:expinphi} +Die komplexe Fourier-Reihe der Funktion +$\varphi\mapsto \exp(i\xi\cos\varphi)$ +ist +\begin{align} +e^{i\xi\cos\varphi} +&= +J_0(\xi) ++ +2\sum_{n=1}^\infty i^n J_n(\xi) \cos n\varphi. +\label{buch:fourier:eqn:expinphicomplex}. +\intertext{Real- und Imaginärteil davon sind die Fourier-Reihen} +\cos(\xi\cos\varphi) +&= +J_0(\xi) + 2\sum_{m=1}^\infty (-1)^m J_{2m}(\xi) \cos2m\varphi +\label{buch:fourier:eqn:expinphireal} +\\ +\sin(\xi\cos\varphi) +&= +2\sum_{m=0}^\infty (-1)^m J_{2m+1}(\xi) \cos(2m+1)\varphi. +\label{buch:fourier:eqn:expinphiimaginary} +\end{align} +\end{satz} + +\begin{proof}[Beweis] +Die Fourier-Koeffizienten $F_n(\xi)$ der Funktion $e^{i\xi\cos\varphi}$ +führen auf die Fourier-Reihe +\begin{align*} +e^{i\xi\cos\varphi} +&= +\sum_{n\in\mathbb{Z}} F_n(\xi) e^{in\varphi} += +\sum_{n\in\mathbb{Z}} i^n J_n(\xi) e^{in\varphi}. +\end{align*} +Terme mit $\pm n$ können wegen +\[ +\left. +\begin{aligned} +J_{-n}(\xi) &= (-1)^n J_n(\xi) +\\ +i^{-n}&=(-1)^n i^n +\end{aligned} +\quad +\right\} +\qquad\Rightarrow\qquad +i^{-n}J_{-n}(\xi) = i^n J_n(\xi) +\] +zusammengefasst werden, auf diese Weise erhält man +\begin{align*} +e^{i\xi\cos\varphi} +&= +J_0(\xi) ++ +\sum_{n=1}^\infty i^n J_n(\xi) (e^{in\varphi}+e^{-in\varphi}) += +2\sum_{n=1}^\infty i^n J_n(\xi) \cos n\varphi. +\end{align*} +Dies beweist +\eqref{buch:fourier:eqn:expinphicomplex}. + +Indem man Real- und Imaginärteil trennt, kann man daraus auch +die Fourier-Reihen von $\cos(\xi\cos\varphi)$ und +$\sin(\xi\cos\varphi)$ gewinnen, sie sind +\begin{align*} +\exp(\xi\cos\varphi) +&= +J_0(\xi) + 2\sum_{n=1}^\infty i^{n} J_{n}(\xi) \cos n\varphi +\\ +&= +J_0(\xi) ++ +2\sum_{m=1}^\infty i^{2m}J_{2m}(\xi)\cos 2m\varphi ++ +2\sum_{m=0}^\infty i^{2m+1}J_{2m+1}(\xi)\cos(2m+1)\varphi +\\ +&= +J_0(\xi) ++ +2\sum_{m=1}^\infty (-1)^{m}J_{2m}(\xi)\cos 2m\varphi ++ +2i\sum_{m=0}^\infty (-1)^{m}J_{2m+1}(\xi)\cos(2m+1)\varphi +\\ +\cos(\xi\cos\varphi) +&= +J_0(\xi) ++ +2\sum_{m=1}^\infty (-1)^{m}J_{2m}(\xi)\cos 2m\varphi +\\ +\sin(\xi\cos\varphi) +&= +2\sum_{m=0}^\infty (-1)^m J_{2m+1}(\xi) \cos(2m+1)\varphi. +\end{align*} +Damit sind auch die Formeln +\eqref{buch:fourier:eqn:expinphireal} +und +\eqref{buch:fourier:eqn:expinphiimaginary} +für die reellen Fourier-Reihen bewiesen. +\end{proof} + +% +% Integraldarstellung der Bessel-Funktion +% +\subsection{Integraldarstellung der Bessel-Funktion} +Aus \eqref{buch:fourier:eqn:Fncosphi} kann jetzt die Integraldarstelltung +der Bessel-Funktionen gewonnen werden. +Dazu substituiert man $\varphi$ durch $\tau$ mit +$\varphi = \frac{\pi}2-\tau$ +oder +$\tau=\frac{\pi}2-\varphi$ +und $d\tau = -d\varphi$ +im Integral und berechnet +\begin{align*} +J_n(\xi) +&= +(-i)^n +\frac{1}{2\pi} +\int_0^{2\pi} +e^{in\varphi+i\xi \cos\varphi} +\,d\varphi +\\ +&= +- +(-i)^n +\frac{1}{2\pi} +\int_{\frac{\pi}2}^{-\frac{3\pi}2} +e^{in(\frac{\pi}2-\tau) + i\xi\cos(\frac{\pi}2-\tau)} +\,d\tau +\\ +&= +(-i)^n +\frac{1}{2\pi} +\int^{\frac{\pi}2}_{-\frac{3\pi}2} +i^n +e^{-in\tau + i\xi\sin\tau)} +\,d\tau. +\intertext{Da der Integrand $2\pi$-periodisch ist, kann das +Integrationsintervall auf $[-\pi,\pi]$ verschoben werden, was} +&= +\frac{1}{2\pi} +\int_{-\pi}^{\pi} +e^{-in\tau + i\xi\sin\tau)} +\,d\tau. +\intertext{ergibt. +Das Integral kann in zwei Integrale} +&= +\frac{1}{2\pi} +\int_0^\pi +e^{-in\tau + i\xi\sin\tau} +\,d\tau ++ +\frac{1}{2\pi} +\int_0^\pi +e^{in\tau - i\xi\sin\tau} +\,d\tau +\intertext{aufgeteilt werden, +} +&= +\frac{1}{\pi} +\int_0^\pi +\frac{ +e^{-in\tau + i\xi\sin\tau} ++ +e^{in\tau - i\xi\sin\tau} +}{2} +\,d\tau +\\ +&= +\frac{1}{\pi} +\int_0^\pi +\frac{ +e^{i(-n\tau + \xi\sin\tau)} ++ +e^{-i(-n\tau + \xi\sin\tau)} +}{2} +\,d\tau +\\ +&= +\frac{1}{\pi} +\int_0^\pi +\cos(n\tau - \xi\sin\tau) +\,d\tau. +\end{align*} +Damit haben wir den folgenden Satz bewiesen: + +\begin{satz}[Integraldarstelltung der Bessel-Funktionen] +\label{buch:fourier:satz:bessel-integraldarstellung} +Die Bessel-Funktionen $J_n$ mit ganzzahliger Ordnung $n$ haben +die Integraldarstellung +\begin{equation} +J_n(\xi) += +\frac{1}{\pi} +\int_0^\pi +\cos(n\tau - \xi\sin\tau) +\,d\tau. +\label{buch:fourier:eqn:bessel-integraldarstellung} +\end{equation} +\end{satz} + + + + diff --git a/buch/chapters/075-fourier/chapter.tex b/buch/chapters/075-fourier/chapter.tex index 341d8df..681a1c0 100644 --- a/buch/chapters/075-fourier/chapter.tex +++ b/buch/chapters/075-fourier/chapter.tex @@ -13,7 +13,8 @@ führen zu neuen speziellen Funktionen. In diesem Kapitel soll als Beispiel die Fourier-Transformation der Bessel-Funktionen untersucht werden. -%\input{chapters/075-fourier/bessel.tex} +\input{chapters/075-fourier/2d.tex} +\input{chapters/075-fourier/bessel.tex} %\section{TODO} %\begin{itemize} -- cgit v1.2.1 From 45241da09f3dc8b8d700d505edea2d38a26a517c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 1 Apr 2022 17:45:58 +0200 Subject: add Vorlesung Komplexe Funktionen --- buch/chapters/110-elliptisch/Makefile.inc | 1 + buch/chapters/110-elliptisch/chapter.tex | 12 ++++++------ vorlesungsnotizen/B/7 - Komplexe Funktionen.pdf | Bin 0 -> 2772838 bytes 3 files changed, 7 insertions(+), 6 deletions(-) create mode 100644 vorlesungsnotizen/B/7 - Komplexe Funktionen.pdf diff --git a/buch/chapters/110-elliptisch/Makefile.inc b/buch/chapters/110-elliptisch/Makefile.inc index 0ca1392..538db68 100644 --- a/buch/chapters/110-elliptisch/Makefile.inc +++ b/buch/chapters/110-elliptisch/Makefile.inc @@ -8,4 +8,5 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/110-elliptisch/ellintegral.tex \ chapters/110-elliptisch/jacobi.tex \ chapters/110-elliptisch/lemniskate.tex \ + chapters/110-elliptisch/uebungsaufgaben/001.tex \ chapters/110-geometrie/chapter.tex diff --git a/buch/chapters/110-elliptisch/chapter.tex b/buch/chapters/110-elliptisch/chapter.tex index a03ce24..e09fa53 100644 --- a/buch/chapters/110-elliptisch/chapter.tex +++ b/buch/chapters/110-elliptisch/chapter.tex @@ -20,11 +20,11 @@ aufgebaute Integrale in dieser Familie zu finden. \input{chapters/110-elliptisch/jacobi.tex} \input{chapters/110-elliptisch/lemniskate.tex} -%\section*{Übungsaufgaben} -%\rhead{Übungsaufgaben} -%\aufgabetoplevel{chapters/020-exponential/uebungsaufgaben} -%\begin{uebungsaufgaben} +\section*{Übungsaufgaben} +\rhead{Übungsaufgaben} +\aufgabetoplevel{chapters/110-elliptisch/uebungsaufgaben} +\begin{uebungsaufgaben} %\uebungsaufgabe{0} -%\uebungsaufgabe{1} -%\end{uebungsaufgaben} +\uebungsaufgabe{1} +\end{uebungsaufgaben} diff --git a/vorlesungsnotizen/B/7 - Komplexe Funktionen.pdf b/vorlesungsnotizen/B/7 - Komplexe Funktionen.pdf new file mode 100644 index 0000000..179aa5c Binary files /dev/null and b/vorlesungsnotizen/B/7 - Komplexe Funktionen.pdf differ -- cgit v1.2.1 From f4ce26a24fbb50621ca52316209bbffd25a60794 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 2 Apr 2022 08:38:00 +0200 Subject: add missing exercise --- buch/chapters/110-elliptisch/uebungsaufgaben/1.tex | 312 +++++++++++++++++++++ .../110-elliptisch/uebungsaufgaben/Makefile | 8 + .../uebungsaufgaben/anharmonisch.pdf | Bin 0 -> 19279 bytes .../uebungsaufgaben/anharmonisch.tex | 62 ++++ 4 files changed, 382 insertions(+) create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/1.tex create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/Makefile create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.pdf create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex new file mode 100644 index 0000000..8e4b39f --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex @@ -0,0 +1,312 @@ +In einem anharmonische Oszillator oszilliert eine Masse $m$ unter dem +Einfluss einer Kraft, die nach dem Gesetz +\[ +F(x) = -\kappa x + \delta x^3 +\] +von der Auslenkung aus der Ruhelage abhängt. +Nehmen Sie im Folgenden an, dass $\delta >0$ ist, +dass also die rücktreibende Kraft $F(x)$ kleiner ist als bei einem +harmonischen Oszillator. +Ziel der folgenden Teilaufgaben ist, die Lösung $x(t)$ schrittweise +dadurch zu bestimmen, dass die Bewegungsgleichung in die Differentialgleichung +der Jacobischen elliptischen Funktion $\operatorname{sn}(u,k)$ umgeformt +wird. +\begin{teilaufgaben} +\item +Berechnen Sie die Auslenkung $x_0$, bei der die rücktreibende Kraft +verschwindet. +Eine beschränkte Schwingung kann diese Amplitude nicht überschreiten. +\item +Berechnen Sie die potentielle Energie in Abhängigkeit von der +Auslenkung. +\item +\label{buch:1101:basic-dgl} +Formulieren Sie den Energieerhaltungssatz für die Gesamtenergie $E$ +dieses Oszillators. +Leiten Sie daraus eine nichtlineare Differentialgleichung erster Ordnung +for den anharmonischen Oszillator ab, die sie in der Form +$\frac12m\dot{x}^2 = f(x)$ schreiben. +\item +Die Amplitude der Schwingung ist derjenige $x$-Wert, für den die +Geschwindigkeit verschwindet. +Leiten Sie die Amplitude aus der Differentialgleichung von +\ref{buch:1101:basic-dgl} ab. +Sie erhalten zwei Werte $x_{\pm}$, wobei der kleinere $x_-$ +die Amplitude einer beschränkten Schwingung beschreibt, +während die $x_+$ die minimale Ausgangsamplitude einer gegen +$\infty$ divergenten Lösung ist. +\item +Rechnen Sie nach, dass +\[ +\frac{x_+^2+x_-^2}{2} += +x_0^2 +\qquad\text{und}\qquad +x_-^2x_+^2 += +\frac{4E}{\delta}. +\] +\item +Faktorisieren Sie die Funktion $f(x)$ in der Differentialgleichung +von Teilaufgabe c) mit Hilfe der in Teilaufgabe d) bestimmten +Nullstellen $x_{\pm}^2$. +\item +Dividieren Sie die Differentialgleichung durch $x_-^2$, schreiben +Sie $X=x/x_-$ und bringen Sie die Differentialgleichung in die +Form +\begin{equation} +A \dot{X}^2 += +(1-X^2) +(1-k^2X^2), +\label{buch:1101:eqn:dgl3} +\end{equation} +wobei $k^2=x_-^2/x_+^2$ und $A$ geeignet gewählt werden müssen. +\item +\label{buch:1101:teilaufgabe:dgl3} +Verwenden Sie $t(\tau) = \alpha\tau$ +und +$Y(\tau)=X(t(\tau))$ um eine Differentialgleichung für die Funktion +$Y(\tau)$ zu gewinnen, die die Form der Differentialgleichung +von $\operatorname{sn}(u,k)$ hat, für die also $A=0$ in +\eqref{buch:1101:eqn:dgl3} ist. +\item +Verwenden Sie die Lösung $\operatorname{sn}(u,k)$ der in +\ref{buch:1101:teilaufgabe:dgl3} erhaltenen Differentialgleichung, +um die Lösung $x(t)$ der ursprünglichen Gleichung aufzuschreiben. +\end{teilaufgaben} + +\begin{loesung} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/uebungsaufgaben/anharmonisch.pdf} +\caption{Rechte Seite der Differentialgleichung +\eqref{buch:1101:eqn:dglf}. +Eine beschränkte Lösung bewegt sich im Bereich $xx_+$ die Kraft abstossend ist und zu einer +divergenten Lösung führt. +\label{buch:1101:fig:potential} +} +\end{figure} +\begin{teilaufgaben} +\item +Wegen +\[ +F(x) += +-\kappa x\biggl(1-\frac{\delta}{\kappa}x^2\biggr) += +-Ix +\biggl(1-\sqrt{\frac{\delta}{\kappa}}x\biggr) +\biggl(1+\sqrt{\frac{\delta}{\kappa}}x\biggr) +\] +folgt, dass die rücktreibende Kraft bei der Auslenkung $\pm x_0$ mit +\[ +x_0^2 += +\frac{\kappa}{\delta} +\qquad\text{oder}\qquad +x_0 = \sqrt{\frac{\kappa}{\delta}} +\] +verschwindet. +\item +Die potentielle Energie ist die Arbeit, die gegen die rücktreibende Kraft +geleistet wird, um die Auslenkung $x$ zu erreichen. +Sie entsteht durch Integrieren der Kraft über +das Auslenkungsinterval, also +\[ +E_{\text{pot}} += +- +\int_0^x F(\xi) \,d\xi += +\int_0^x \kappa\xi-\delta\xi^3\,d\xi += +\biggl[ +\kappa\frac{\xi^2}{2} +- +\delta +\frac{\xi^4}{4} +\biggr]_0^x += +\kappa\frac{x^2}{2} +- +\delta\frac{x^4}{4}. +\] +\item +Die kinetische Energie ist gegeben durch +\[ +E_{\text{kin}} += +\frac12m\dot{x}^2. +\] +Die Gesamtenergie ist damit +\[ +E += +\frac12m\dot{x}^2 ++ +\kappa +\frac{x^2}{2} +- +\delta +\frac{x^4}{4}. +\] +Die verlangte Umformung ergibt +\begin{align} +\frac12m\dot{x}^2 +&= +E +- +\kappa\frac{x^2}{2} ++ +\delta\frac{x^4}{4} +\label{buch:1101:eqn:dglf} +\end{align} +als Differentialgleichung für $x$. +Die Ableitung $\dot{x}$ hat positives Vorzeichen wenn die Kraft +abstossend ist und negatives Vorzeichen dort, wo die Kraft anziehend ist. +% +\item +Die Amplitude der Schwingung ist derjenige $x$-Wert, für den +die Geschwindigkeit verschwindet, also eine Lösung der Gleichung +\[ +0 += +\frac{2E}{m} -\frac{\kappa}{m}x^2 + \frac{\delta}{2m}x^4. +\] +Der gemeinsame Nenner $m$ spielt offenbar keine Rolle. +Die Gleichung hat die zwei Lösungen +\[ +x_{\pm}^2 += +\frac{\kappa \pm \sqrt{\kappa^2-4E\delta}}{\delta} += +\frac{\kappa}{\delta} +\pm +\sqrt{ +\biggl(\frac{\kappa}{\delta}\biggr)^2 +- +\frac{4E}{\delta} +}. +\] +Die Situation ist in Abbildung~\ref{buch:1101:fig:potential} +Für $x>x_+$ ist die Kraft abstossend, die Lösung divergiert. +Die Lösung mit dem negativen Zeichen $x_-$ bleibt dagegen beschränkt, +dies ist die Lösung, die wir suchen. + +\item +Die beiden Formeln ergeben sich aus den Regeln von Vieta für die +Lösungen einer quadratischen Gleichungg der Form $x^4+px^2+q$. +Die Nullstellen haben den Mittelwert $-p/2$ und das Produkt $q$. + +\item +Die rechte Seite der Differentialgleichung lässt sich mit Hilfe +der beiden Nullstellen $x_{\pm}^2$ faktorisieren und bekommt die Form +\[ +\frac12m\dot{x}^2 += +\frac{\delta}{4}(x_+^2-x^2)(x_-^2-x^2). +\] + +\item +Indem die ganze Gleichung durch $x_-^2$ dividiert wird, entsteht +\[ +\frac12m +\biggl(\frac{\dot{x}}{x_-}\biggr)^2 += +\frac{\delta}{4} +(x_+^2-x^2) +\biggl(1-\frac{x^2}{x_-^2}\biggr). +\] +Schreiben wir $X=x/x_-$ wird daraus +\[ +\frac1{2}m\dot{X}^2 += +\frac{\delta}{4} +\biggl(x_+^2-x_-^2 X^2\biggr) +(1-X^2). +\] +Durch Ausklammern von $x_+^2$ im ersten Faktor wir daraus +\[ +\frac1{2}m\dot{X}^2 += +\frac{\delta}{4} +x_+^2 +\biggl(1-\frac{x_-^2}{x_+^2} X^2\biggr) +(1-X^2). +\] +Mit der Schreibweise $k^2 = x_-^2/x_+^2$ wird die Differentialgleichung +zu +\begin{equation} +\frac{2m}{\delta x_+^2} \dot{X}^2 += +(1-X^2)(1-k^2X^2), +\label{buch:1101:eqn:dgl2} +\end{equation} +was der Differentialgleichung für die Jacobische elliptische Funktion +$\operatorname{sn}(u,k)$ bereits sehr ähnlich sieht. +\item +Bis auf den Faktor vor $\dot{X}^2$ ist +\eqref{buch:1101:eqn:dgl2} +die Differentialgleichung +von +$\operatorname{sn}(u,k)$. +Um den Faktor zum Verschwinden zu bringen, schreiben wir +$t(\tau) = \alpha\tau$. +Die Ableitung von $Y(\tau)=X(t(\tau))$ nach $\tau$ ist +\[ +\frac{dY}{d\tau} += +\dot{X}(t(\tau))\frac{dt}{d\tau} += +\alpha +\dot{X}(t(\tau)) +\qquad\Rightarrow\qquad +\frac{1}{\alpha^2}\frac{dY}{d\tau} += +\dot{X}(t(\tau)). +\] +Die Differentialgleichung für $Y(\tau)$ ist +\[ +\frac{2mk^2}{\delta x_+^2\alpha^2} +\frac{dY}{d\tau} += +(1-Y^2)(1-k^2Y^2). +\] +Der Koeffizient vor der Ableitung wird $1$, wenn man +\[ +\alpha^2 += +\frac{2mk^2}{\delta x_+^2} +\] +wählt. +Diese Differentialgleichug hat die Lösung +\[ +Y(\tau) = \operatorname{sn}(\tau,k). +\] +\item +Indem man die gefunden Grössen einsetzt kann man jetzt die Lösung +der Differentialgleichung in geschlossener Form als +\begin{align*} +x(t) +&= +x_- X(t) += +x_- \operatorname{sn}\biggl( +t\sqrt{\frac{\delta x_+^2}{2mk^2} } +,k +\biggr) +\end{align*} +Das Produkt $\delta x_+^2$ kann auch als +\[ +\delta x_+^2 += +\kappa+\sqrt{\kappa -4\delta E} +\] +geschrieben werden. +\qedhere +\end{teilaufgaben} +\end{loesung} + + diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/Makefile b/buch/chapters/110-elliptisch/uebungsaufgaben/Makefile new file mode 100644 index 0000000..0ca5234 --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/Makefile @@ -0,0 +1,8 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# + +anharmonisch.pdf: anharmonisch.tex + pdflatex anharmonisch.tex diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.pdf b/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.pdf new file mode 100644 index 0000000..4b00f4d Binary files /dev/null and b/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.pdf differ diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex new file mode 100644 index 0000000..a00c393 --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/anharmonisch.tex @@ -0,0 +1,62 @@ +% +% anharmonisch.tex -- Potential einer anharmonischen Schwingung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\E{3} +\def\K{0.2} +\def\D{0.0025} + +\pgfmathparse{sqrt(\K/\D)} +\xdef\xnull{\pgfmathresult} + +\pgfmathparse{sqrt((\K+sqrt(\K*\K-4*\E*\D))/\D)} +\xdef\xplus{\pgfmathresult} +\pgfmathparse{sqrt((\K-sqrt(\K*\K-4*\E*\D))/\D)} +\xdef\xminus{\pgfmathresult} + +\def\xmax{13} + +\fill[color=darkgreen!20] (0,-1.5) rectangle (\xminus,4.7); +\node[color=darkgreen] at ({0.5*\xminus},4.7) [below] {anziehende Kraft\strut}; + +\fill[color=orange!20] (\xplus,-1.5) rectangle (\xmax,4.7); +\node[color=orange] at ({0.5*(\xplus+\xmax)},4.7) [below] {abstossende\strut}; 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+0200 Subject: add notes for MSE session 4 --- .../MSE/4 - Hypergeometrische Funktionen.pdf | Bin 0 -> 4954963 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 vorlesungsnotizen/MSE/4 - Hypergeometrische Funktionen.pdf diff --git a/vorlesungsnotizen/MSE/4 - Hypergeometrische Funktionen.pdf b/vorlesungsnotizen/MSE/4 - Hypergeometrische Funktionen.pdf new file mode 100644 index 0000000..e0d3bf1 Binary files /dev/null and b/vorlesungsnotizen/MSE/4 - Hypergeometrische Funktionen.pdf differ -- cgit v1.2.1 From a43b5d2e05d2b0f467c897fe29d7060b4ee9f526 Mon Sep 17 00:00:00 2001 From: David Hugentobler Date: Mon, 4 Apr 2022 23:26:25 +0200 Subject: =?UTF-8?q?File=20teil4.tex=20hinzugef=C3=BCgt=20und=20darin=20ges?= =?UTF-8?q?chrieben?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/lambertw/main.tex | 1 + 1 file changed, 1 insertion(+) diff --git a/buch/papers/lambertw/main.tex b/buch/papers/lambertw/main.tex index e58ed5a..6e9bbe0 100644 --- a/buch/papers/lambertw/main.tex +++ b/buch/papers/lambertw/main.tex @@ -31,6 +31,7 @@ Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren \input{papers/lambertw/teil1.tex} \input{papers/lambertw/teil2.tex} \input{papers/lambertw/teil3.tex} +\input{papers/lambertw/teil4.tex} \printbibliography[heading=subbibliography] \end{refsection} -- cgit v1.2.1 From 301b946bc51b69cd72c8860f0ff3632c57decb22 Mon Sep 17 00:00:00 2001 From: David Hugentobler Date: Mon, 4 Apr 2022 23:29:52 +0200 Subject: erneut versuchen teil4.tex zu commiten --- buch/papers/lambertw/teil4.log | 1620 ++++++++++++++++++++++++++++++++++++++++ buch/papers/lambertw/teil4.tex | 81 ++ 2 files changed, 1701 insertions(+) create mode 100644 buch/papers/lambertw/teil4.log create mode 100644 buch/papers/lambertw/teil4.tex diff --git a/buch/papers/lambertw/teil4.log b/buch/papers/lambertw/teil4.log new file mode 100644 index 0000000..63894e5 --- /dev/null +++ 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+Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! 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Emergency stop. +<*> teil4.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 16 strings out of 478371 + 382 string characters out of 5852527 + 296836 words of memory out of 5000000 + 18226 multiletter control sequences out of 15000+600000 + 403430 words of font info for 27 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 13i,0n,12p,83b,18s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex new file mode 100644 index 0000000..74b6b02 --- /dev/null +++ b/buch/papers/lambertw/teil4.tex @@ -0,0 +1,81 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Beispiel Verfolgungskurve +\label{lambertw:section:teil4}} +\rhead{Beispiel Verfolgungskurve} +In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve beschreiben. + +\subsection{Ziel bewegt sich auf einer Gerade +\label{lambertw:subsection:malorum}} +Das zu verfolgende Ziel \(Z\) wandert auf einer Gerade, wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(V\) startet auf einem beliebigen Punkt auf dem ersten Quadrant. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: +\begin{equation} + Z + = + \left( \begin{array}{c} 0 \\ t \end{array} \right) + ; + V + = + \left( \begin{array}{c} x \\ y \end{array} \right) + \label{lambertw:equation2} +\end{equation} +Wenn man diese Startpunkte in die Gleichung der Verfolgungskurve einfügt ergibt sich folgender Ausdruck: +\begin{equation} + \frac{\left( \begin{array}{c} 0-x \\ t-y \end{array} \right)}{\sqrt{x^2 + (t-y)^2}} + \circ + \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) + = + 1 + \label{lambertw:equation3} +\end{equation} +Macht man den linken Term Bruchfrei und löst das Skalarprodukt auf, dann ergibt sich folgende DGL: +\[ + \left( \begin{array}{c} 0-x \\ t-y \end{array} \right) + \circ + \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) + = \sqrt{x^2 + (t-y)^2}\\ +\] +\begin{equation} + -x \cdot \dot{x} + (t-y) \cdot \dot{y} + = \sqrt{x^2 + (t-y)^2} + \label{lambertw:equation4} +\end{equation} +Im nächsten Schritt quadriert man beide Seiten, erweitert den neu entstandenen quadratischen Term, bringt alles auf die linke Seite und klammert gemeinsames aus. +\begin{align*} + ((t-y) \dot{y} - x \dot{x})^2 + &= x^2 + (t-y)^2 \\ + x^2 \dot{x}^2 - 2x(t-y) \dot{x} \dot{y} + (t-y)^2 \dot{y} + &= x^2 + (t-y)^2 \\ + \dot{x}^2 x^2 - x^2 - 2x(t-y) \dot{x} \dot{y} + \dot{y}^2 (t-y)^2 - (t-y)^2 + &= 0 \\ + (\dot{x}^2 - 1) \cdot x^2 - 2x(t-y) \dot{x} \dot{y} + (\dot{y}^2 - 1) \cdot (t-y)^2 + &= 0 +\end{align*} +Der letzte Ausdruck kann mittels folgender Beziehung \(\dot{x}^2 + \dot{y}^2 = 1\) vereinfacht werden und anschliessend mit \(-1\) multiplizieren: +\[ + \underbrace{(\dot{x}^2 - 1)}_{\mathclap{-\dot{y}^2}} \cdot x^2 - 2x(t-y) \dot{x} \dot{y} + \underbrace{(\dot{y}^2 - 1)}_{\mathclap{-\dot{x}^2}} \cdot (t-y)^2 + = 0 +\] +\begin{align*} + - \dot{y}^2 \cdot x^2 - 2x(t-y) \dot{x} \dot{y} - \dot{x}^2 \cdot (t-y)^2 + &= 0 \\ + \dot{y}^2 \cdot x^2 + 2x(t-y) \dot{x} \dot{y} + \dot{x}^2 \cdot (t-y)^2 + &= 0 +\end{align*} +Im letzten Ausdruck erkennt man das Muster einer binomischen Formel, was den Ausdruck wesentlich vereinfacht: +\begin{align*} + x^2 \dot{y}^2 + 2 \cdot x \dot{y} \cdot (t-y) \dot{x} + (t-y)^2 \dot{x}^2 + &= 0 \\ + (x \dot{y} + (t-y) \dot{x})^2 + &= 0 +\end{align*} +Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich zu \eqref{lambertw:equation4} eine wesentlich einfachere DGL: +\begin{equation} + x \dot{y} + (t-y) \dot{x} + = 0 + \label{lambertw:equation5} +\end{equation} + + -- cgit v1.2.1 From 670555039265d83945b0d3e205aefb020425585b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Wed, 6 Apr 2022 08:00:09 +0200 Subject: Start definition.tex --- buch/.gitignore | 37 ++ buch/papers/laguerre/definition.tex | 150 +++++-- buch/papers/laguerre/images/wasserstoff_model.tex | 58 +++ buch/papers/laguerre/main.tex | 4 +- buch/papers/laguerre/packages.tex | 1 - buch/papers/laguerre/scripts/gamma_approx.ipynb | 431 +++++++++++++++++++++ buch/papers/laguerre/scripts/laguerre_plot.py | 39 ++ .../laguerre/scripts/lanczos_approximation.py | 47 +++ buch/papers/laguerre/scripts/quadrature_gama.py | 178 +++++++++ buch/papers/laguerre/wasserstoff.tex | 147 ++++++- buch/standalone.tex | 35 ++ 11 files changed, 1077 insertions(+), 50 deletions(-) create mode 100644 buch/.gitignore create mode 100644 buch/papers/laguerre/images/wasserstoff_model.tex create mode 100644 buch/papers/laguerre/scripts/gamma_approx.ipynb create mode 100644 buch/papers/laguerre/scripts/laguerre_plot.py create mode 100644 buch/papers/laguerre/scripts/lanczos_approximation.py create mode 100644 buch/papers/laguerre/scripts/quadrature_gama.py create mode 100644 buch/standalone.tex diff --git a/buch/.gitignore b/buch/.gitignore new file mode 100644 index 0000000..4d056e5 --- /dev/null +++ b/buch/.gitignore @@ -0,0 +1,37 @@ +*.acn +*.acr +*.alg +*.aux +*.bbl +*.blg +*.dvi +*.fdb_latexmk +*.glg +*.glo +*.gls +*.idx +*.ilg +*.ind +*.ist +*.lof +*.log +*.lot +*.maf +*.mtc +*.mtc0 +*.nav +*.nlo +*.out +*.pdfsync +.vscode/* +*.fls +*.xdv +*.ps +*.snm +*.synctex.gz +*.toc +*.vrb +*.xdy +*.tdo +*-blx.bib +*.synctex \ No newline at end of file diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index 5f6d8bd..84a26cf 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -6,43 +6,133 @@ \section{Definition \label{laguerre:section:definition}} \rhead{Definition} - +Die Laguerre-Differentialgleichung ist gegeben durch \begin{align} - x y''(x) + (1 - x) y'(x) + n y(x) - = - 0 - \label{laguerre:dgl} +x y''(x) + (1 - x) y'(x) + n y(x) += +0 +, \quad +n \in \mathbb{N}_0 +, \quad +x \in \mathbb{R} +. +\label{laguerre:dgl} \end{align} - +Zur Lösung der Gleichung \eqref{laguerre:dgl} +verwenden wir einen Potenzreihenansatz. +Setzt man nun den Ansatz +\begin{align*} +y(x) +&= +\sum_{k=0}^\infty a_k x^k +\\ +y'(x) +& = +\sum_{k=1}^\infty k a_k x^{k-1} += +\sum_{k=0}^\infty (k+1) a_{k+1} x^k +\\ +y''(x) +&= +\sum_{k=2}^\infty k (k-1) a_k x^{k-2} += +\sum_{k=1}^\infty (k+1) k a_{k+1} x^{k-1} +\end{align*} +in die Differentialgleichung ein, erhält man: +\begin{align*} +\sum_{k=1}^\infty (k+1) k a_{k+1} x^k ++ \sum_{k=0}^\infty (k+1) a_{k+1} x^k +- \sum_{k=0}^\infty k a_k x^k ++ n \sum_{k=0}^\infty a_k x^k +&= +0\\ +\sum_{k=0}^\infty +\left[ (k+1) k a_{k+1} + (k+1) a_{k+1} - k a_k + n a_k \right] x^k +&= +0. +\end{align*} +Daraus lässt sich die Rekursionsbeziehung +\begin{align*} +a_{k+1} +&= +\frac{k-n}{(k+1) ^ 2} a_k +\end{align*} +ableiten. +Für ein konstantes $n$ erhalten wir als Potenzreihenlösung ein Polynom vom Grad $n$, +denn für $k=n$ wird $a_{n+1} = 0$ und damit auch $a_{n+2}=a_{n+3}=\ldots=0$. +Aus der Rekursionsbeziehung ist zudem ersichtlich, +dass $a_0 \neq 0$ beliebig gewählt werden kann. +Wählen wir nun $c_0 = 1$, dann folgt für die Koeffizienten $a_1, a_2, a_3$ +\begin{align*} +a_1 += +-\frac{n}{1^2} +,&& +a_2 += +\frac{(n-1)n}{1^2 2^2} +,&& +a_3 += +-\frac{(n-2)(n-1)n}{1^2 2^2 3^2} +\end{align*} +und allgemein +\begin{align*} +k&\leq n: +& +a_k +&= +(-1)^k \frac{n!}{(n-k)!} \frac{1}{(k!)^2} += +\frac{(-1)^k}{k!} +\begin{pmatrix} +n +\\ +k +\end{pmatrix} +\\ +k&>n: +& +a_k +&= +0. +\end{align*} +Somit haben wir die Laguerre-Polynome $L_n(x)$ erhalten: \begin{align} - L_n(x) - = - \sum_{k=0}^{n} - \frac{(-1)^k}{k!} - \begin{pmatrix} - n \\ - k - \end{pmatrix} - x^k - \label{laguerre:polynom} +L_n(x) += +\sum_{k=0}^{n} +\frac{(-1)^k}{k!} +\begin{pmatrix} +n \\ +k +\end{pmatrix} +x^k +\label{laguerre:polynom} \end{align} +\subsection{Assoziierte Laguerre-Polynome +\label{laguerre:subsection:assoz_laguerre} +} \begin{align} - x y''(x) + (\alpha + 1 - x) y'(x) + n y(x) - = - 0 - \label{laguerre:generell_dgl} +x y''(x) + (\alpha + 1 - x) y'(x) + n y(x) += +0 +\label{laguerre:generell_dgl} \end{align} \begin{align} - L_n^\alpha (x) - = - \sum_{k=0}^{n} - \frac{(-1)^k}{k!} - \begin{pmatrix} - n + \alpha \\ - n - k - \end{pmatrix} - x^k - \label{laguerre:polynom} +L_n^\alpha (x) += +\sum_{k=0}^{n} +\frac{(-1)^k}{k!} +\begin{pmatrix} +n + \alpha \\ +n - k +\end{pmatrix} +x^k +\label{laguerre:polynom} \end{align} + +% https://www.math.kit.edu/iana1/lehre/hm3phys2012w/media/laguerre.pdf +% http://www.physics.okayama-u.ac.jp/jeschke_homepage/E4/kapitel4.pdf diff --git a/buch/papers/laguerre/images/wasserstoff_model.tex b/buch/papers/laguerre/images/wasserstoff_model.tex new file mode 100644 index 0000000..fe838c3 --- /dev/null +++ b/buch/papers/laguerre/images/wasserstoff_model.tex @@ -0,0 +1,58 @@ +\documentclass{standalone} + +\usepackage{pgfplots} +\usepackage{tikz-3dplot} + +\tdplotsetmaincoords{60}{115} +\pgfplotsset{compat=newest} + +\begin{document} + +\newcommand{\drawcircle}[4]{ +\shade[ball color=#3, opacity=#4] (#1) circle (#2 cm); +\tdplotsetrotatedcoords{0}{0}{0}; +\draw[dashed, tdplot_rotated_coords, #3!40!black] (#1) circle (#2); +} + +\begin{tikzpicture}[tdplot_main_coords, scale = 2] +\def\r{1.0} +\def\rp{0.2} +\def\rn{0.05} +\def\rvec{1.0} +\def\thetavec{45} +\def\phivec{60} + +\coordinate (O) at (0, 0, 0); +\tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec} + +% Labels +\node[inner sep=1pt] at (0, -4.0*\rp, 1.0*\r) (plabel){Proton}; +\draw (plabel) -- (O); +\node[inner sep=1pt] at (-0.*\r, 1.0*\r, 1.3*\r) (elabel){Elektron}; +\draw (elabel) -- (P); +% Draw proton +\drawcircle{O}{\rp}{red}{1.0} + +% Draw spherical coordinates of electron +\draw (O) -- node[anchor=north west, yshift=4pt]{$r$} (P); +\draw[dashed] (O) -- (Pxy); +\draw[dashed] (P) -- (Pxy); +\tdplotdrawarc{(O)}{0.6}{0}{\phivec}{anchor=north}{$\varphi$} +\tdplotsetthetaplanecoords{\phivec} +\tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{0}% +{\thetavec}{anchor=south west, xshift=-2pt, yshift=-2pt}{$\vartheta$} + +% Draw electron +\drawcircle{P}{\rn}{blue}{1.0} + +% Draw surrounding sphere +\drawcircle{O}{\r}{gray}{0.3} + +% Draw cartesian coordinate system +\draw[-stealth, thick] (O) -- (1.8*\r,0,0) node[below left] {$x$}; +\draw[-stealth, thick] (O) -- (0,1.3*\r,0) node[below right] {$y$}; +\draw[-stealth, thick] (O) -- (0,0,1.3*\r) node[above] {$z$}; + +\end{tikzpicture} + +\end{document} \ No newline at end of file diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex index 1fe0f8b..3db67d5 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -13,8 +13,8 @@ Hier kommt eine Einleitung. \input{papers/laguerre/definition} \input{papers/laguerre/eigenschaften} \input{papers/laguerre/quadratur} -\input{papers/laguerre/transformation} -\input{papers/laguerre/wasserstoff} +% \input{papers/laguerre/transformation} +% \input{papers/laguerre/wasserstoff} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/laguerre/packages.tex b/buch/papers/laguerre/packages.tex index ab55228..4ebc172 100644 --- a/buch/papers/laguerre/packages.tex +++ b/buch/papers/laguerre/packages.tex @@ -7,4 +7,3 @@ % if your paper needs special packages, add package commands as in the % following example \usepackage{derivative} - diff --git a/buch/papers/laguerre/scripts/gamma_approx.ipynb b/buch/papers/laguerre/scripts/gamma_approx.ipynb new file mode 100644 index 0000000..9a1fee6 --- /dev/null +++ b/buch/papers/laguerre/scripts/gamma_approx.ipynb @@ -0,0 +1,431 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gauss-Laguerre Quadratur für die Gamma-Funktion\n", + "\n", + "$$\n", + " \\Gamma(z)\n", + " = \n", + " \\int_0^\\infty t^{z-1}e^{-t}dt\n", + "$$\n", + "\n", + "$$\n", + " \\int_0^\\infty f(x) e^{-x} dx \n", + " \\approx \n", + " \\sum_{i=1}^{N} f(x_i) w_i\n", + " \\qquad\\text{ wobei }\n", + " w_i = \\frac{x_i}{(n+1)^2 [L_{n+1}(x_i)]^2}\n", + "$$\n", + "und $x_i$ sind Nullstellen des Laguerre Polynoms $L_n(x)$\n", + "\n", + "Der Fehler ist gegeben als\n", + "\n", + "$$\n", + " E \n", + " =\n", + " \\frac{(n!)^2}{(2n)!} f^{(2n)}(\\xi) \n", + " = \n", + " (-2n + z)_{2n} \\frac{(n!)^2}{(2n)!} \\xi^{z - 2n - 1}\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from cmath import exp, pi, sin, sqrt\n", + "import scipy.special\n", + "\n", + "EPSILON = 1e-07\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "lanczos_p = [\n", + " 676.5203681218851,\n", + " -1259.1392167224028,\n", + " 771.32342877765313,\n", + " -176.61502916214059,\n", + " 12.507343278686905,\n", + " -0.13857109526572012,\n", + " 9.9843695780195716e-6,\n", + " 1.5056327351493116e-7,\n", + "]\n", + "\n", + "\n", + "def drop_imag(z):\n", + " if abs(z.imag) <= EPSILON:\n", + " z = z.real\n", + " return z\n", + "\n", + "\n", + "def lanczos_gamma(z):\n", + " z = complex(z)\n", + " if z.real < 0.5:\n", + " y = pi / (sin(pi * z) * lanczos_gamma(1 - z)) # Reflection formula\n", + " else:\n", + " z -= 1\n", + " x = 0.99999999999980993\n", + " for (i, pval) in enumerate(lanczos_p):\n", + " x += pval / (z + i + 1)\n", + " t = z + len(lanczos_p) - 0.5\n", + " y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x\n", + " return drop_imag(y)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "zeros = np.array(\n", + " [\n", + " 1.70279632305101000e-1,\n", + " 9.03701776799379912e-1,\n", + " 2.25108662986613069e0,\n", + " 4.26670017028765879e0,\n", + " 7.04590540239346570e0,\n", + " 1.07585160101809952e1,\n", + " 1.57406786412780046e1,\n", + " 2.28631317368892641e1,\n", + " ]\n", + ")\n", + "\n", + "weights = np.array(\n", + " [\n", + " 3.69188589341637530e-1,\n", + " 4.18786780814342956e-1,\n", + " 1.75794986637171806e-1,\n", + " 3.33434922612156515e-2,\n", + " 2.79453623522567252e-3,\n", + " 9.07650877335821310e-5,\n", + " 8.48574671627253154e-7,\n", + " 1.04800117487151038e-9,\n", + " ]\n", + ")\n", + "\n", + "\n", + "def pochhammer(z, n):\n", + " return np.prod(z + np.arange(n))\n", + "\n", + "\n", + "def find_shift(z, target):\n", + " factor = 1.0\n", + " steps = int(np.floor(target - np.real(z)))\n", + " zs = z + steps\n", + " if steps > 0:\n", + " factor = 1 / pochhammer(z, steps)\n", + " elif steps < 0:\n", + " factor = pochhammer(zs, -steps)\n", + " return zs, factor\n", + "\n", + "\n", + "def laguerre_gamma(z, x, w, target=11):\n", + " # res = 0.0\n", + " z = complex(z)\n", + " if z.real < 1e-3:\n", + " res = pi / (\n", + " sin(pi * z) * laguerre_gamma(1 - z, x, w, target)\n", + " ) # Reflection formula\n", + " else:\n", + " z_shifted, correction_factor = find_shift(z, target)\n", + " res = np.sum(x ** (z_shifted - 1) * w)\n", + " res *= correction_factor\n", + " res = drop_imag(res)\n", + " return res\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def eval_laguerre(x, target=12):\n", + " return np.array([laguerre_gamma(xi, zeros, weights, target) for xi in x])\n", + "\n", + "\n", + "def eval_lanczos(x):\n", + " return np.array([lanczos_gamma(xi) for xi in x])\n", + "\n", + "\n", + "def eval_mean_laguerre(x, targets):\n", + " return np.mean([eval_laguerre(x, target) for target in targets], 0)\n", + "\n", + "\n", + "def calc_rel_error(x, y):\n", + " return (y - x) / x\n", + "\n", + "\n", + "def evaluate(x, target=12):\n", + " lanczos_gammas = eval_lanczos(x)\n", + " laguerre_gammas = eval_laguerre(x, target)\n", + " rel_error = calc_rel_error(lanczos_gammas, laguerre_gammas)\n", + " return rel_error\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Test with real values" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "targets = np.arange(8, 15)\n", + "mean_targets = ((11, 12),)\n", + "x = np.linspace(EPSILON, 1 - EPSILON, 101)\n", + "_, axs = plt.subplots(\n", + " 2, sharex=True, clear=True, constrained_layout=True, figsize=(12, 12)\n", + ")\n", + "\n", + "lanczos = eval_lanczos(x)\n", + "for mean_target in mean_targets:\n", + " vals = eval_mean_laguerre(x, mean_target)\n", + " rel_error_mean = calc_rel_error(lanczos, vals)\n", + " axs[0].plot(x, rel_error_mean, label=mean_target)\n", + " axs[1].semilogy(x, np.abs(rel_error_mean), label=mean_target)\n", + "\n", + "for target in targets:\n", + " rel_error = evaluate(x, target)\n", + " axs[0].plot(x, rel_error, label=target)\n", + " axs[1].semilogy(x, np.abs(rel_error), label=target)\n", + "# axs[0].set_ylim(*(np.array([-1, 1]) * 3.5e-8))\n", + "\n", + "axs[0].set_xlim(x[0], x[-1])\n", + "axs[1].set_ylim(1e-10, 2e-7)\n", + "for ax in axs:\n", + " ax.legend()\n", + " ax.grid(which=\"both\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(-7.5, 25.0)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "targets = (11, 12)\n", + "xmax = 15\n", + "x = np.linspace(-xmax + EPSILON, xmax - EPSILON, 1000)\n", + "\n", + "mean_lag = eval_mean_laguerre(x, targets)\n", + "lanczos = eval_lanczos(x)\n", + "rel_error = calc_rel_error(lanczos, mean_lag)\n", + "rel_error_simple = evaluate(x, targets[-1])\n", + "# rel_error = evaluate(x, target)\n", + "\n", + "_, axs = plt.subplots(\n", + " 2, sharex=True, clear=True, constrained_layout=True, figsize=(12, 12)\n", + ")\n", + "axs[0].plot(x, rel_error, label=targets)\n", + "axs[1].semilogy(x, np.abs(rel_error), label=targets)\n", + "axs[0].plot(x, rel_error_simple, label=targets[-1])\n", + "axs[1].semilogy(x, np.abs(rel_error_simple), label=targets[-1])\n", + "axs[0].set_xlim(x[0], x[-1])\n", + "# axs[0].set_ylim(*(np.array([-1, 1]) * 4.2e-8))\n", + "axs[1].set_ylim(1e-10, 5e-8)\n", + "for ax in axs:\n", + " ax.legend()\n", + "\n", + "x2 = np.linspace(-5 + EPSILON, 5, 4001)\n", + "_, ax = plt.subplots(constrained_layout=True, figsize=(8, 6))\n", + "ax.plot(x2, eval_mean_laguerre(x2, targets))\n", + "ax.set_xlim(x2[0], x2[-1])\n", + "ax.set_ylim(-7.5, 25)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Test with complex values" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "targets = (11, 12)\n", + "vals = np.linspace(-5 + EPSILON, 5, 100)\n", + "x, y = np.meshgrid(vals, vals)\n", + "mesh = x + 1j * y\n", + "input = mesh.flatten()\n", + "\n", + "mean_lag = eval_mean_laguerre(input, targets).reshape(mesh.shape)\n", + "lanczos = eval_lanczos(input).reshape(mesh.shape)\n", + "rel_error = np.abs(calc_rel_error(lanczos, mean_lag))\n", + "\n", + "lag = eval_laguerre(input, targets[-1]).reshape(mesh.shape)\n", + "rel_error_simple = np.abs(calc_rel_error(lanczos, lag))\n", + "# rel_error = evaluate(x, target)\n", + "\n", + "fig, axs = plt.subplots(\n", + " 2,\n", + " 2,\n", + " sharex=True,\n", + " sharey=True,\n", + " clear=True,\n", + " constrained_layout=True,\n", + " figsize=(12, 10),\n", + ")\n", + "_c = axs[0, 1].pcolormesh(x, y, np.log10(np.abs(lanczos - mean_lag)), shading=\"gouraud\")\n", + "_c = axs[0, 0].pcolormesh(x, y, np.log10(np.abs(lanczos - lag)), shading=\"gouraud\")\n", + "fig.colorbar(_c, ax=axs[0, :])\n", + "_c = axs[1, 1].pcolormesh(x, y, np.log10(rel_error), shading=\"gouraud\")\n", + "_c = axs[1, 0].pcolormesh(x, y, np.log10(rel_error_simple), shading=\"gouraud\")\n", + "fig.colorbar(_c, ax=axs[1, :])\n", + "_ = axs[0, 0].set_title(\"Absolute Error\")\n", + "_ = axs[1, 0].set_title(\"Relative Error\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# TODO: Macht kei Sinn!\n", + "n = 8\n", + "ms = np.arange(4, 5)\n", + "xi = np.linspace(EPSILON, 20, 201)[:, None]\n", + "z = np.arange(6, 16)[None]+0.1\n", + "c = scipy.special.factorial(n) ** 2 / scipy.special.factorial(2 * n)\n", + "\n", + "\n", + "_, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(12, 8))\n", + "ax.grid(1)\n", + "for m, color in zip(ms, ['r', 'b', 'g', 'c', 'm', 'y']):\n", + " e = np.abs(\n", + " scipy.special.poch(z - 2 * n, 2 * n)\n", + " / scipy.special.poch(z - m, m)\n", + " * c\n", + " * xi ** (z - 2 * n + m - 1)\n", + " )\n", + " # ax.semilogy(xi, e, color=color)\n", + " ax.semilogy(xi, e)\n", + " ax.set_xticks(np.arange(xi[-1] +1))\n", + " ax.set_ylim(1e-8, 1e5)\n", + " _ = ax.legend([f'z={zi}' for zi in z[0]])\n" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "767d51c1340bd893661ea55ea3124f6de3c7a262a8b4abca0554b478b1e2ff90" + }, + "kernelspec": { + "display_name": "Python 3.8.10 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/buch/papers/laguerre/scripts/laguerre_plot.py b/buch/papers/laguerre/scripts/laguerre_plot.py new file mode 100644 index 0000000..cd90df1 --- /dev/null +++ b/buch/papers/laguerre/scripts/laguerre_plot.py @@ -0,0 +1,39 @@ +#!/usr/bin/env python3 +# -*- coding:utf-8 -*- +"""Some plots for Laguerre Polynomials.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np +import scipy.special as ss + +N = 1000 +t = np.linspace(0, 12.5, N)[:, None] +root = str(Path(__file__).parent) + +fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) +for n in np.arange(0, 10): + k = np.arange(0, n + 1)[None] + L = np.sum((-1) ** k * ss.binom(n, k) / ss.factorial(k) * t ** k, -1) + ax.plot(t, L, label=f"n={n}") +ax.set_xticks(np.arange(1, t[-1])) +ax.set_xlim(t[0], t[-1] + 0.1*(t[1] - t[0])) +ax.set_ylim(-20, 20) +ax.legend(ncol=2) +# set the x-spine +ax.spines['left'].set_position('zero') +ax.spines['right'].set_visible(False) +ax.spines['bottom'].set_position('zero') +ax.spines['top'].set_visible(False) +ax.xaxis.set_ticks_position('bottom') +ax.yaxis.set_ticks_position('left') + +# make arrows +# ax.plot((1), (0), ls="", marker=">", ms=10, color="k", +# transform=ax.get_yaxis_transform(), clip_on=False) +# ax.plot((0), (1), ls="", marker="^", ms=10, color="k", +# transform=ax.get_xaxis_transform(), clip_on=False) +# ax.grid(1) +fig.savefig(f'{root}/laguerre_polynomes.pdf') +# plt.show() diff --git a/buch/papers/laguerre/scripts/lanczos_approximation.py b/buch/papers/laguerre/scripts/lanczos_approximation.py new file mode 100644 index 0000000..3c48266 --- /dev/null +++ b/buch/papers/laguerre/scripts/lanczos_approximation.py @@ -0,0 +1,47 @@ +from cmath import exp, pi, sin, sqrt + +p = [ + 676.5203681218851, + -1259.1392167224028, + 771.32342877765313, + -176.61502916214059, + 12.507343278686905, + -0.13857109526572012, + 9.9843695780195716e-6, + 1.5056327351493116e-7, +] + +EPSILON = 1e-07 + + +def drop_imag(z): + if abs(z.imag) <= EPSILON: + z = z.real + return z + + +def gamma(z): + z = complex(z) + if z.real < 0.5: + y = pi / (sin(pi * z) * gamma(1 - z)) # Reflection formula + else: + z -= 1 + x = 0.99999999999980993 + for (i, pval) in enumerate(p): + x += pval / (z + i + 1) + t = z + len(p) - 0.5 + y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x + return drop_imag(y) + + +""" +The above use of the reflection (thus the if-else structure) is necessary, even though +it may look strange, as it allows to extend the approximation to values of z where +Re(z) < 0.5, where the Lanczos method is not valid. +""" + +print(gamma(1)) +print(gamma(5)) +print(gamma(0.5)) +print(gamma(0.5* (1 + 1j))) +print(gamma(-0.5)) diff --git a/buch/papers/laguerre/scripts/quadrature_gama.py b/buch/papers/laguerre/scripts/quadrature_gama.py new file mode 100644 index 0000000..37a9cd8 --- /dev/null +++ b/buch/papers/laguerre/scripts/quadrature_gama.py @@ -0,0 +1,178 @@ +#!/usr/bin/env python3 +# -*- coding:utf-8 -*- +"""Use Gauss-Laguerre quadrature to calculate gamma function.""" +# import sympy +from cmath import exp, pi, sin, sqrt + +import matplotlib.pyplot as plt +import numpy as np +import scipy.special as ss + +p = [ + 676.5203681218851, + -1259.1392167224028, + 771.32342877765313, + -176.61502916214059, + 12.507343278686905, + -0.13857109526572012, + 9.9843695780195716e-6, + 1.5056327351493116e-7, +] + +EPSILON = 1e-07 + + +def drop_imag(z): + if abs(z.imag) <= EPSILON: + z = z.real + return z + + +def gamma(z): + z = complex(z) + if z.real < 0.5: + y = pi / (sin(pi * z) * gamma(1 - z)) # Reflection formula + else: + z -= 1 + x = 0.99999999999980993 + for (i, pval) in enumerate(p): + x += pval / (z + i + 1) + t = z + len(p) - 0.5 + y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x + return drop_imag(y) + + +zeros = np.array( + [ + 3.22547689619392312e-1, + 1.74576110115834658e0, + 4.53662029692112798e0, + 9.39507091230113313e0, + ], + np.longdouble, +) +weights = np.array( + [ + 6.03154104341633602e-1, + 3.57418692437799687e-1, + 3.88879085150053843e-2, + 5.39294705561327450e-4, + ], + np.longdouble, +) + +zeros = np.array( + [ + 1.70279632305101000e-1, + 9.03701776799379912e-1, + 2.25108662986613069e0, + 4.26670017028765879e0, + 7.04590540239346570e0, + 1.07585160101809952e1, + 1.57406786412780046e1, + 2.28631317368892641e1, + ], + np.longdouble, +) + +weights = np.array( + [ + 3.69188589341637530e-1, + 4.18786780814342956e-1, + 1.75794986637171806e-1, + 3.33434922612156515e-2, + 2.79453623522567252e-3, + 9.07650877335821310e-5, + 8.48574671627253154e-7, + 1.04800117487151038e-9, + ], + np.longdouble, +) + + +def calc_gamma(z, n, x, w): + res = 0.0 + z = complex(z) + for xi, wi in zip(x, w): + res += xi ** (z + n - 1) * wi + for i in range(int(n)): + res /= z + i + res = drop_imag(res) + return res + +small = 1e-3 +Z = np.linspace(small, 1-small, 101) + +# Z = [-3/2, -1/2, 1/2, 3/2] +# target = +# targets = np.array([gamma(z) for z in Z]) +targets1 = ss.gamma(Z) +targets2 = np.array([gamma(z) for z in Z]) +approxs = np.array([calc_gamma(z, 11, zeros, weights) for z in Z]) +rel_error1 = np.abs(targets1 - approxs) / targets1 +rel_error2 = np.abs(targets2 - approxs) / targets2 + +_, axs = plt.subplots(2, num=1, clear=True, constrained_layout=True) +axs[0].plot(Z, rel_error1) +axs[1].semilogy(Z, rel_error1) +axs[0].plot(Z, rel_error2) +axs[1].semilogy(Z, rel_error2) +axs[1].semilogy(Z, np.abs(targets1-targets2)/targets1) +plt.show() +# values = np.array([calc_gamma]) +# _ = [ +# print( +# n, +# [ +# float( +# f"{np.abs((calc_gamma(z, n, zeros, weights) - gamma(z)) / gamma(z)):.3g}" +# ) +# for z in Z +# ], +# ) +# for n in range(21) +# ] + + +# target = ss.gamma(z) +# target = np.sqrt(np.pi) + +# _, ax = plt.subplots(num=1, clear=True, constrained_layout=True) +# for i, degree in enumerate(degrees): +# samples_points, weights = np.polynomial.laguerre.laggauss(degree) +# values = np.sum( +# samples_points[:, None] ** (z + shifts[None] - 1) * weights[:, None], 0 +# ) / ss.poch(z, shifts) +# # print(np.abs(target - values)) +# print(values) +# ax.plot(shifts, values, label=f"N={degree}") +# ax.legend() +# plt.show() + + +# def count_equal_digits(x, y): +# for i in range(1, 13): +# try: +# np.testing.assert_almost_equal(x, y, i) +# except AssertionError: +# break +# return i + + +# Z = np.linspace(1.0, 11.0, 11) +# # degrees = [2, 4, 8, 16, 32, 64, 100] +# d = 100 +# X = np.zeros(len(Z)) +# for i, z in enumerate(Z): +# samples_points, weights = np.polynomial.laguerre.laggauss(d) +# X[i] = np.sum(samples_points ** (z - 1) * weights) +# # X[i] = np.sum(np.sin(z * samples_points) * weights) +# Y = ss.gamma(Z) +# # Y = Z / (Z ** 2 + 1) +# ed = [count_equal_digits(x, y) for x, y in zip(X, Y)] +# for x,y in zip(X,Y): +# print(x,y) + +# _, ax = plt.subplots(num=1, clear=True, constrained_layout=True) +# ax.plot(Z, ed) +# plt.show() diff --git a/buch/papers/laguerre/wasserstoff.tex b/buch/papers/laguerre/wasserstoff.tex index caaa6af..0da8be3 100644 --- a/buch/papers/laguerre/wasserstoff.tex +++ b/buch/papers/laguerre/wasserstoff.tex @@ -6,24 +6,137 @@ \section{Radialer Schwingungsanteil eines Wasserstoffatoms \label{laguerre:section:radial_h_atom}} +Das Wasserstoffatom besteht aus einem Proton im Kern +mit Masse $M$ und Ladung $+e$. +Ein Elektron mit Masse $m$ und Ladung $-e$ umkreist das Proton +(vgl. Abbildung~\ref{laguerre:fig:wasserstoff_model}). +Für das folgende Model werden folgende Annahmen getroffen: + +\begin{figure} +\centering +\includegraphics{papers/laguerre/images/wasserstoff_model.pdf} +\caption{Skizze eines Wasserstoffatoms. +Kartesische, wie auch Kugelkoordinaten sind eingezeichnet. +} +\label{laguerre:fig:wasserstoff_model} +\end{figure} + +\begin{enumerate} +\item +Das Elektron wird als nicht-relativistisches Teilchen betrachtet, +das heisst, +relativistische Effekte sind vernachlässigbar. +\item +Der Spin des Elektrons und des Protons +und das damit verbundene magnetische Moment +wird vernachlässigt. +\item +Fluktuationen des Vakuums werden nicht berücksichtigt. +\item +Wechselwirkung zwischen Elektron und Proton +ist durch die Coulombwechselwirkung gegeben. +Somit entspricht die potentielle Energie der Coulombenergie $V_C(r)$ +und nimmt damit die folgende Form an +\begin{align} + V_C(r) + = + -\frac{e^2}{4 \pi \epsilon_0 r} + \text{ mit } + r + = + \lvert\vec{r}\rvert + = + \sqrt{x^2 + y^2 + z^2} + . + \label{laguerre:coulombenergie} +\end{align} +Im Falle das der Kern einen endlichen Radius $r_0$ besitzt, +ist die $1/r$-Abhängigkeit in Gleichung \eqref{laguerre:coulombenergie} +als Näherung zu betrachten. +Diese Näherung darf nur angewendet werden, wenn die +Aufenthaltswahrscheinlicheit des Elektrons +innerhalb $r_0$ vernachlässigbar ist. +Für das Wasserstoffatom ist diese Näherung für alle Zustände gerechtfertigt. +\item +Da $M \gg m$, kann das Proton als in Ruhe angenommen werden. +\end{enumerate} + +\subsection{Herleitung zeitunabhängige Schrödinger-Gleichung} +\label{laguerre:subsection:herleitung_schroedinger} +Das Problem ist kugelsymmetrisch, +darum transformieren wir das Problem in Kugelkoordinaten. +Somit gilt: + +\begin{align*} + r + & = + \sqrt{x^2 + y^2 + z^2}\\ + \vartheta + & = + \arccos\left(\frac{z}{r}\right)\\ + \varphi + & = + \arctan\left(\frac{y}{x}\right) +\end{align*} + +Die potentielle Energie $V_C(r)$ hat keine direkte Zeitabhängigkeit. +Daraus folgt, dass die konstant ist Gesamtenergie $E$ +und es existieren stationäre Zustände + \begin{align} - \nonumber - - \frac{\hbar^2}{2m} - & - \left( - \frac{1}{r^2} \pdv{}{r} - \left( r^2 \pdv{}{r} \right) - + - \frac{1}{r^2 \sin \vartheta} \pdv{}{\vartheta} - \left( \sin \vartheta \pdv{}{\vartheta} \right) - + - \frac{1}{r^2 \sin^2 \vartheta} \pdv[2]{}{\varphi} - \right) - u(r, \vartheta, \varphi) - \\ - & - - \frac{e^2}{4 \pi \epsilon_0 r} u(r, \vartheta, \varphi) + \psi(r, \vartheta, \varphi, t) + = + u(r, \vartheta, \varphi) e^{-i E t / h}, +\end{align} +wobei $u(r, \vartheta, \varphi)$ +die zeitunabhängige Schrödinger-Gleichung erfüllt. + +\begin{align} + -\frac{\hbar^2}{2m} \Delta u(r, \vartheta, \varphi) + + V_C(r) u(r, \vartheta, \varphi) = E u(r, \vartheta, \varphi) - \label{laguerre:pdg_h_atom} + \label{laguerre:schroedinger} +\end{align} + +Für Kugelkoordinaten hat der Laplace-Operator $\Delta$ die Form + +\begin{align} + \Delta + = + \frac{1}{r^2} \pdv{}{r} \left( r^2 \pdv{}{r} \right) + + \frac{1}{r^2 \sin\vartheta} \pdv{}{\vartheta} + \left(\sin\vartheta \pdv{}{\vartheta}\right) + + \frac{1}{r^2 \sin^2\vartheta} \pdv[2]{}{\varphi} + \label{laguerre:laplace_kugel} \end{align} + +Setzt man nun +\eqref{laguerre:coulombenergie} und \eqref{laguerre:laplace_kugel} +in \eqref{laguerre:schroedinger} ein, +erhält man die zeitunabhängige Schrödinger-Gleichung für Kugelkoordinaten + +\begin{align} +\nonumber +- \frac{\hbar^2}{2m} +& +\left( +\frac{1}{r^2} \pdv{}{r} +\left( r^2 \pdv{}{r} \right) ++ +\frac{1}{r^2 \sin \vartheta} \pdv{}{\vartheta} +\left( \sin \vartheta \pdv{}{\vartheta} \right) ++ +\frac{1}{r^2 \sin^2 \vartheta} \pdv[2]{}{\varphi} +\right) +u(r, \vartheta, \varphi) +\\ +& - +\frac{e^2}{4 \pi \epsilon_0 r} u(r, \vartheta, \varphi) += +E u(r, \vartheta, \varphi). +\label{laguerre:pdg_h_atom} +\end{align} + +\subsection{Separation der Schrödinger-Gleichung} +\label{laguerre:subsection:seperation_schroedinger} diff --git a/buch/standalone.tex b/buch/standalone.tex new file mode 100644 index 0000000..e681460 --- /dev/null +++ b/buch/standalone.tex @@ -0,0 +1,35 @@ +% +% packages.tex -- common packages +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass{book} +\def\IncludeBookCover{0} +\input{common/packages.tex} +% additional packages used by the individual papers, add a line for +% each paper +\input{papers/common/addpackages.tex} + +% workaround for biblatex bug +\makeatletter +\def\blx@maxline{77} +\makeatother +\addbibresource{chapters/references.bib} + +% Bibresources for each article +\input{papers/common/addbibresources.tex} + +% make sure the last index starts on an odd page +\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} +\makeindex + +%\pgfplotsset{compat=1.12} +\setlength{\headheight}{15pt} % fix headheight warning +\DeclareGraphicsRule{*}{mps}{*}{} + +\begin{document} + \input{common/macros.tex} + \def\chapterauthor#1{{\large #1}\bigskip\bigskip} + + \input{papers/laguerre/main} +\end{document} \ No newline at end of file -- cgit v1.2.1 From d36a701a0538df37ab8389925011c9f33fcd4cbd Mon Sep 17 00:00:00 2001 From: Yanik Kuster Date: Wed, 6 Apr 2022 11:20:25 +0200 Subject: added a picture to visualize example problem --- buch/papers/lambertw/Bilder/something.svg | 1 + 1 file changed, 1 insertion(+) create mode 100644 buch/papers/lambertw/Bilder/something.svg diff --git a/buch/papers/lambertw/Bilder/something.svg b/buch/papers/lambertw/Bilder/something.svg new file mode 100644 index 0000000..e9d5656 --- /dev/null +++ b/buch/papers/lambertw/Bilder/something.svg @@ -0,0 +1 @@ +–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888000OAOAOAOPOPOPPAPAPAPPPAAA \ No newline at end of file -- cgit v1.2.1 From d2a5fa34c505f498845f3c8ab8335c090bd1bfec Mon Sep 17 00:00:00 2001 From: Yanik Kuster Date: Wed, 6 Apr 2022 11:30:37 +0200 Subject: derivation of pursuerproblem DGL --- buch/papers/lambertw/packages.tex | 2 + buch/papers/lambertw/teil0.tex | 21 +++----- buch/papers/lambertw/teil1.tex | 109 +++++++++++++++++++++++++++++++++++++- 3 files changed, 118 insertions(+), 14 deletions(-) diff --git a/buch/papers/lambertw/packages.tex b/buch/papers/lambertw/packages.tex index 6581a5a..366de78 100644 --- a/buch/papers/lambertw/packages.tex +++ b/buch/papers/lambertw/packages.tex @@ -8,3 +8,5 @@ % following example %\usepackage{packagename} +\usepackage{graphicx} +\usepackage{float} \ No newline at end of file diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 2b83d59..ca172e5 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -3,20 +3,15 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{lambertw:section:teil0}} +\section{Was sind Verfolgungskurven? \label{lambertw:section:teil0}} \rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{lambertw:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. + +Verfolgungskurven entstehen immer, dann wenn ein Verfolger sein Ziel verfolgt. +Nämlich ist eine Verfolgungskurve die Kurve, die ein Verfolger abfährt während er sein Ziel verfolgt. + +Zum Beispiel + + diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 7b545c3..493ec05 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -3,9 +3,116 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 1 +\section{Beispiel () \label{lambertw:section:teil1}} \rhead{Problemstellung} + + + +%\begin{figure}[H] +% \centering +% \includegraphics[width=0.5\textwidth]{.\Bilder\something.pdf} +% \label{pursuer:grafik1} +%\end{figure} + + + +Je nach Verfolgungsstrategie die der Verfolger verwendet, entsteht eine andere DGL. +Für dieses konkrete Beispiel wird einfachheitshalber die simpelste Strategie gewählt. +Bei dieser Strategie bewegt sich der Verfolger immer direkt auf sein Ziel hinzu. +Womit der Geschwindigkeitsvektor des Verfolgers zu jeder Zeit direkt auf das Ziel zeigt. + +Um die DGL dieses Problems herzuleiten wird der Sachverhalt in der Grafik \eqref{pursuer:grafik1} aufgezeigt. +Der Punkt $P$ ist der Verfolger und der Punkt $A$ ist sein Ziel. + +Um dies mathematisch beschreiben zu können, wird der Richtungsvektor +\begin{equation} + \frac{A-P}{|A-P|} + = + \frac{\dot{P}}{|\dot{P}|} +\end{equation} +benötigt. Durch die Subtraktion der Ortsvektoren $\overrightarrow{OP}$ und $\overrightarrow{OA}$ entsteht ein Vektor der vom Punkt $P$ auf $A$ zeigt. +Da die Länge dieses Vektors beliebig sein kann, wird durch Division mit dem Betrag, die Länge auf eins festgelegt. +Aus dem Verfolgungsproblem ist auch ersichtlich, dass die Punkte $A$ und $P$ nicht am gleichen Ort starten und so eine Division durch Null ausgeschlossen ist. +Wenn die Punkte $A$ und $P$ trotzdem am gleichen Ort starten, ist die Lösung trivial. + +Nun wird die Gleichung mit deren rechten Seite skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. +\begin{equation} + \label{pursuer:pursuerDGL} + \frac{A-P}{|A-P|}\cdot \frac{\dot{P}}{|\dot{P}|} + = + 1 +\end{equation} +Diese DGL ist der Kern des Verfolgungsproblems, insofern sich der Verfolger immer direkt auf sein Ziel zubewegt. + + +\subsection{Beispiel} +Das Verfolgungsproblem wird mithilfe eines konkreten Beispiels veranschaulicht. Dafür wird die einfachste Strategie verwendet, bei der sich der Verfolger direkt auf sein Ziel hinzu bewegt. Für dieses Problem wurde bereits die DGL \eqref{pursuer:pursuerDGL} hergeleitet. + +Um dieses Beispiel einfach zu halten, wird für den Verfolger und das Ziel jeweils eine konstante Geschwindigkeit von eins gewählt. Das Ziel wiederum startet im Ursprung und bewegt sich linear auf der positiven Y-Achse. + +\begin{align} + v_P^2 + &= + \dot{P}\cdot\dot{P} + = + 1 + \\[5pt] + v_A + &= + 1 + \\[5pt] + A + &= + \begin{pmatrix} + 0 \\ + v_A\cdot t + \end{pmatrix} + = + \begin{pmatrix} + 0 \\ + t + \end{pmatrix} + \\[5pt] + P + &= + \begin{pmatrix} + x \\ + y + \end{pmatrix} +\end{align} + +Die Anfangsbedingungen dieses Problems sind. + +\begin{align} + y(t)\bigg|_{t=0} + &= + y_0 + \\[5pt] + x(t)\bigg|_{t=0} + &= + x_0 \\[5pt] + \frac{\,dy}{\,dx}(t)\bigg|_{t=0} + &= + \frac{y_A(t) -y_P(t)}{x_A(t)-x_P(t)}\bigg|_{t=0} +\end{align} + +Mit den vorangegangenen Definitionen kann nun die DGL \eqref{pursuer:pursuerDGL} gelöst werden. +Dafür wird als erstes das Skalarprodukt ausgerechnet. + +\begin{equation} + \dfrac{-x\cdot\dot{x}+(t-y)\cdot\dot{y}}{\sqrt{x^2+(t-y)^2}} = 1 +\end{equation} + + + + + + + + + + Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae -- cgit v1.2.1 From dc51fe760249ea37d410599690df96c94f6d808d Mon Sep 17 00:00:00 2001 From: daHugen Date: Wed, 6 Apr 2022 11:36:23 +0200 Subject: made some changes in teil4.tex --- buch/papers/lambertw/teil4.tex | 22 ++++++++++++++++++---- 1 file changed, 18 insertions(+), 4 deletions(-) diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 74b6b02..d3269ee 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -10,13 +10,15 @@ In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve beschre \subsection{Ziel bewegt sich auf einer Gerade \label{lambertw:subsection:malorum}} -Das zu verfolgende Ziel \(Z\) wandert auf einer Gerade, wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(V\) startet auf einem beliebigen Punkt auf dem ersten Quadrant. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: +Das zu verfolgende Ziel \(A\) wandert auf einer Gerade, wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(P\) startet auf einem beliebigen Punkt auf dem ersten Quadrant.Um die Rechnungen zu vereinfachen wir die Geschwindigkeit \(v\) auf 1 gesetzt. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: \begin{equation} - Z + A + = + \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) = \left( \begin{array}{c} 0 \\ t \end{array} \right) ; - V + P = \left( \begin{array}{c} x \\ y \end{array} \right) \label{lambertw:equation2} @@ -53,7 +55,7 @@ Im nächsten Schritt quadriert man beide Seiten, erweitert den neu entstandenen (\dot{x}^2 - 1) \cdot x^2 - 2x(t-y) \dot{x} \dot{y} + (\dot{y}^2 - 1) \cdot (t-y)^2 &= 0 \end{align*} -Der letzte Ausdruck kann mittels folgender Beziehung \(\dot{x}^2 + \dot{y}^2 = 1\) vereinfacht werden und anschliessend mit \(-1\) multiplizieren: +Der letzte Ausdruck kann mittels folgender Beziehung \(\dot{x}^2 + \dot{y}^2 = 1\) vereinfacht werden, anschliessend wird die Gleichung mit \(-1\) multipliziert: \[ \underbrace{(\dot{x}^2 - 1)}_{\mathclap{-\dot{y}^2}} \cdot x^2 - 2x(t-y) \dot{x} \dot{y} + \underbrace{(\dot{y}^2 - 1)}_{\mathclap{-\dot{x}^2}} \cdot (t-y)^2 = 0 @@ -77,5 +79,17 @@ Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich z = 0 \label{lambertw:equation5} \end{equation} +Um die Ableitung nach der Zeit wegzubringen wird beidseitig mit \(\dot{x}\) dividiert, wobei \(\frac{\dot{y}}{\dot{x}} = \frac{dy}{dt}/\frac{dx}{dt} = \frac{dy}{dx}\) entspricht. +\[ + x \frac{\dot{y}}{\dot{x}} + (t-y) \frac{\dot{x}}{\dot{x}} + = 0 +\] +Nach dem kürzen ergibt sich folgende DGL: +\begin{equation} + x y^{\prime} + t - y + = 0 + \label{lambertw:equation6} +\end{equation} +Hier wäre es passend wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen muss man -- cgit v1.2.1 From 8b5a486a6a2cd7b5c9b07053fe9857e399e65f63 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 6 Apr 2022 20:32:40 +0200 Subject: FIrst Commit Name added --- buch/papers/fm/main.tex | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 1e75235..de3e10a 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -3,10 +3,13 @@ % % (c) 2020 Hochschule Rapperswil % +% !TeX root = /.../...buch.tex +%\begin {document} \chapter{Thema\label{chapter:fm}} \lhead{Thema} \begin{refsection} -\chapterauthor{Hans Muster} + +\chapterauthor{Joshua Bär} Ein paar Hinweise für die korrekte Formatierung des Textes \begin{itemize} @@ -34,3 +37,5 @@ Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren \printbibliography[heading=subbibliography] \end{refsection} + +%\end {document} -- cgit v1.2.1 From 77e1d7652711e18ab381f0eaf2059675689d7304 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 9 Apr 2022 12:48:35 +0200 Subject: Singularitaeten --- buch/chapters/050-differential/besselhyper.maxima | 37 ++ buch/chapters/080-funktionentheorie/Makefile.inc | 1 + .../chapters/080-funktionentheorie/anwendungen.tex | 1 + .../080-funktionentheorie/images/operator-1.pdf | Bin 0 -> 6228 bytes .../080-funktionentheorie/images/operator.mp | 46 +++ .../080-funktionentheorie/singularitaeten.tex | 427 +++++++++++++++++++++ 6 files changed, 512 insertions(+) create mode 100644 buch/chapters/050-differential/besselhyper.maxima create mode 100644 buch/chapters/080-funktionentheorie/images/operator-1.pdf create mode 100644 buch/chapters/080-funktionentheorie/images/operator.mp create mode 100644 buch/chapters/080-funktionentheorie/singularitaeten.tex diff --git a/buch/chapters/050-differential/besselhyper.maxima b/buch/chapters/050-differential/besselhyper.maxima new file mode 100644 index 0000000..0a67819 --- /dev/null +++ b/buch/chapters/050-differential/besselhyper.maxima @@ -0,0 +1,37 @@ +/* + * besselhyper.maxima + */ +gradef(y(x), yp(x)); +gradef(yp(x), ypp(x)); + +w(x) := x^alpha * y(-x^2/4); + +/* Zusammenhang zwischen Y und W */ +Y: x^(-alpha) * W; + +/* erste Ableitung Yp ausgedrückt durch W und W' */ +e: Wp=diff(w(x),x) $ +e: ratsimp(e); +e: subst(W * x^(-alpha), y(-x^2/4), e) $ +e: subst(Yp, yp(-x^2/4), e) $ +s: solve(e, Yp) $ +Yp: rhs(s[1]) $ +Yp: ratsimp(Yp); +ratsimp(subst(0,W,Yp)); +ratsimp(subst(0,Wp,Yp)); + +/* zweite Ableitung Yp ausgedrückt durch W, W' und W'' */ +e: Wpp = ratsimp(diff(diff(w(x),x),x)); +e: subst(W * x^(-alpha), y(-x^2/4), e) $ +e: subst(Yp, yp(-x^2/4), e) $ +e: subst(Ypp, ypp(-x^2/4), e) $ +e: ratsimp(e) $ +Ypp: rhs(solve(e, Ypp)[1]) $ +Ypp: ratsimp(Ypp); +ratsimp(subst(0, W, subst(0, Wp, Ypp))); +ratsimp(subst(0, W, subst(0, Wpp, Ypp))); +ratsimp(subst(0, Wp, subst(0, Wpp, Ypp))); + + +B: (-x^2/4) * Ypp + (alpha+1)*Yp - Y; +expand(-x^(alpha+2) * B); diff --git a/buch/chapters/080-funktionentheorie/Makefile.inc b/buch/chapters/080-funktionentheorie/Makefile.inc index 813865f..affaa94 100644 --- a/buch/chapters/080-funktionentheorie/Makefile.inc +++ b/buch/chapters/080-funktionentheorie/Makefile.inc @@ -12,6 +12,7 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/080-funktionentheorie/anwendungen.tex \ chapters/080-funktionentheorie/gammareflektion.tex \ chapters/080-funktionentheorie/carlson.tex \ + chapters/080-funktionentheorie/singularitaeten.tex \ chapters/080-funktionentheorie/uebungsaufgaben/1.tex \ chapters/080-funktionentheorie/uebungsaufgaben/2.tex \ chapters/080-funktionentheorie/chapter.tex diff --git a/buch/chapters/080-funktionentheorie/anwendungen.tex b/buch/chapters/080-funktionentheorie/anwendungen.tex index e02fb3e..4cdf9be 100644 --- a/buch/chapters/080-funktionentheorie/anwendungen.tex +++ b/buch/chapters/080-funktionentheorie/anwendungen.tex @@ -8,3 +8,4 @@ \input{chapters/080-funktionentheorie/gammareflektion.tex} \input{chapters/080-funktionentheorie/carlson.tex} +\input{chapters/080-funktionentheorie/singularitaeten.tex} diff --git a/buch/chapters/080-funktionentheorie/images/operator-1.pdf b/buch/chapters/080-funktionentheorie/images/operator-1.pdf new file mode 100644 index 0000000..4ba1346 Binary files /dev/null and b/buch/chapters/080-funktionentheorie/images/operator-1.pdf differ diff --git a/buch/chapters/080-funktionentheorie/images/operator.mp b/buch/chapters/080-funktionentheorie/images/operator.mp new file mode 100644 index 0000000..35f4303 --- /dev/null +++ b/buch/chapters/080-funktionentheorie/images/operator.mp @@ -0,0 +1,46 @@ +% +% operatormp -- Seitz-Kull-Operator in Metapost +% +% (c) 2016 Prof Dr Andreas Mueller, Hochschule Rapperswil +% +verbatimtex +\documentclass{book} +\usepackage{times} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{amsfonts} +\usepackage{txfonts} +\begin{document} +etex; + +beginfig(1) + +label(btex $A$ etex, (0,0)); + +path circle; + +numeric r; +r := 4.7; +numeric b; +b := 0.45; + +circle := r * (cosd(40), sind(40)); + +for alpha = 41 step 1 until 370: + circle := circle--(r * (cosd(alpha), sind(alpha))); +endfor; + +path head; +head := (0,0)--(5,-3)--(0,6)--(-5,-3)--cycle; + +z1 = (-0.3,-0.4); + +pickup pencircle scaled b; +draw circle shifted z1; +fill head scaled 0.2 rotated 10 shifted (r,0) rotated 10 shifted z1; + +endfig; + +end + + diff --git a/buch/chapters/080-funktionentheorie/singularitaeten.tex b/buch/chapters/080-funktionentheorie/singularitaeten.tex new file mode 100644 index 0000000..71d1844 --- /dev/null +++ b/buch/chapters/080-funktionentheorie/singularitaeten.tex @@ -0,0 +1,427 @@ +% +% singularitaeten.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\newcommand*\sk{\vcenter{\hbox{\includegraphics[scale=0.8]{chapters/080-funktionentheorie/images/operator-1.pdf}}}} + +\subsection{Lösungen von linearen Differentialgleichungen mit Singularitäten +\label{buch:funktionentheorie:subsection:dglsing}} +Die Potenzreihenmethode hat ermöglicht, mindestens eine Lösung gewisser +linearer Differentialgleichungen zu finden. +Bei Differentialgleichungen wie der Besselschen Differentialgleichung, +deren Koeffizienten Singularitäten aufweisen, konnte aber nur eine +Lösung gefunden werden, während die Theorie verlangt, dass eine +Differentialgleichung zweiter Ordnung zwei linear unabhängige Lösungen +haben muss. + +Ziel dieses Abschnitts ist zu zeigen, warum dies nicht möglich war und +wie diese Schwierigkeit mit Hilfe der analytischen Fortsetzung überwunden +werden kann. + +\subsubsection{Differentialgleichungen mit Singularitäten} +Mit der Besselschen +Differentialgleichung~\eqref{buch:differentialgleichungen:eqn:bessel} +ist es nicht möglich, die zweite Ableitung $y''(0)$ an der Stelle $x=0$ +zu bestimmen. +Die Differentialgleichung kann an der Stelle $x=0$ nicht nach $y''$ +aufgelöst werden. +Wenn man die Differentialgleichung in ein Differntialgleichungssystem +\[ +\frac{d}{dx} +\begin{pmatrix} +y_1\\y_2 +\end{pmatrix} += +\begin{pmatrix} +0&1\\ +1-\frac{\alpha^2}{x^2} +& +-\frac{1}{x} +\end{pmatrix} +\begin{pmatrix} +y_1\\y_2 +\end{pmatrix} +\] +erster Ordnung umwandelt, zeigt sich an der Stelle $x=0$ eine +Singularität in der Matrix, die Ableitung kann also für $x=0$ +nicht bestimmt werden. +In einer Umgebung von $x=0$ erfüllt die Differentialgleichung +die Voraussetzungen bekannter Existenz- und Eindeutigkeitssätze +für gewöhnliche Differentialgleichungen nicht. + +Ein ähnliches Problem tritt bei jeder hypergeometrischen +Differentialgleichung auf. +Diese werden gemäss Abschnitt +\ref{buch:differentialgleichungen:section:hypergeometrisch} +aus den Differentialoperatoren +\[ +D_a=z\frac{d}{dz} + a +\] +zusammengesetzt. +Die Ableitung höchster Ordnung eines Produktes solcher Operationen ist +\[ +D_{a_1} +\cdots +D_{a_p} += +z^p\frac{d^p}{dz^p} + \text{Ableitungen niedrigerer Ordnung}. +\] +Dies zeigt, dass für $p>0$ oder $q>0$ ein Faktor $x$ bei der +Ableitung höchster Ordnung unvermeidlich ist, die Differentialgleichung +kann also wieder nicht nach dieser Ableitung aufgelöst werden und +erfüllt die Voraussetzungen der Existenz- und Eindeutigkeitssätze +in einer Umgebung von $x=0$ wieder nicht. + +Die Besselsche Differentialgleichung +hat auch nicht die Form $y''+p(x)xy'+q(x)=0$, die der Theorie der +Indexgleichung zugrunde lag. +Daher kann es auch keine Garantie geben, dass die Methode der +verallgemeinerten Potenzreihen zwei linear unabhängige Lösungen +liefern kann. +Tatsächlich wurde für ganzzahlige $n$ wegen $J_n(x) = (-1)^n J_{-n}(x)$ +nur eine Lösung statt der erwarteten zwei linear unabhängigen +Lösungen gefunden. + +Sind die Koeffizienten einer linearen Differentialgleichungen wie +in den genannten Beispielen singulär bei $x=0$, kann man auch nicht +erwarten, dass die Lösungen singulär sind. +Dies war schliesslich die Motivation, einen Lösungsansatz mit einer +verallgemeinerten Potenzreihe zu versuchen. +Mit den Funktion $x^\varrho$ lässt sich bereits eine recht grosse +Klasse von Singularitäten beschreiben, aber es ist nicht klar, +welche weiteren Arten von Singularitäten berücksichtigt werden sollten. +Dies soll im Folgenden geklärt werden. + +\subsubsection{Der Lösungsraum einer Differentialgleichung zweiter Ordnung} +Eine Differentialgleichung $n$-ter Ordnung hat lokal einen $n$-dimensionalen +Vektorraum als Lösungsraum. + +\begin{definition} +Sei +\begin{equation} +\sum_{k=0}^n a_k(x) y^{(n)}(x) = 0 +\label{buch:funktionentheorie:singularitaeten:eqn:defdgl} +\end{equation} +eine Differentialgleichung $n$-ter Ordnung mit analytischen Koeffizienten +und $x_0\in \mathbb{C}$. +Dann ist +\[ +\mathbb{L}_{x_0} += +\left\{ +y(x) +\;\left|\; +\begin{minipage}{6cm} +$y$ ist Lösung der Differentialgleichung +\eqref{buch:funktionentheorie:singularitaeten:eqn:defdgl} +in einer Umgebung von $x_0$ +\end{minipage} +\right. +\right\} +\] +der Lösungsraum der Differentialgleichung +\eqref{buch:funktionentheorie:singularitaeten:eqn:defdgl}. +Wenn der Punkt $x_0$ aus dem Kontext klar ist, kann er auch weggelassen +werden: $\mathbb{L}_{x_0}=\mathbb{L}$. +\end{definition} + +\subsubsection{Analytische Fortsetzung auf einem Weg um $0$} +Die betrachteten Differentialgleichungen haben holomorphe +Koeffizienten, Lösungen der Differentialgleichung lassen sich +daher immer in die komplexe Ebene fortsetzen, solange man die +Singularitäten der Koeffizienten vermeidet. +Hat eine Funktion $y(z)$ eine Laurent-Reihe +\[ +y(z) = \sum_{k=-\infty}^\infty a_kz^k, +\] +dann ist sie automatisch in einer Umgebung von $0$ definiert +ausser in $0$. +Die analytische Fortsetzung entlang eines Pfades, der $0$ +umschliesst, ist die Funktion $y(z)$ selbst. + +Für die Wurzelfunktion $y(z)=z^{\frac1n}$ ist dies nicht möglich. +Die analytische Fortsetzung von $\sqrt[n]{x}$ auf der positiven reellen +Achse entlang einer Kurve, die $0$ umschliesst, +produziert die Funktion +\[ +\sqrt[n]{z} += +\sqrt[n]{re^{i\varphi}} += +\sqrt[n]{r}e^{i\frac{\varphi}n}, +\] +die für $\varphi=2\pi$ zu $e^{i\frac{2\pi}n}\sqrt{x}$ wird. +Verallgemeinerte Potenzreihen als Lösungen zeigen daher, dass +die analytische Fortsetzung der Lösung entlang eines Pfades um +eine Singularität nicht mit der Lösung übereinstimmen muss. +Das Studium dieser analytischen Fortsetzung dürfte daher zusätzliche +Informationen über die Lösung hervorbringen. + +\begin{definition} +Der {\em Fortsetzungsoperator} $\sk$ ist der lineare Operator, der eine +in einem Punkt $x\in\mathbb{R}^+$ analytische Funktion $f(x)$ entlang eines +geschlossenen Weges fortsetzt, der $0$ im Gegenuhrzeigersinn umläuft. +Die Einschränkung der analytischen Fortsetzung auf $\mathbb{R}^+$ wird +mit $\sk f(x)$ bezeichnet. +\end{definition} + +Die obengenannten Beispiele lassen sich mit dem Operator $\sk$ als +\[ +\begin{aligned} +\sk z^n +&= +z^n +&\qquad& n \in \mathbb{Z} +\\ +\sk +\sum_{k=-\infty}^\infty a_kz^k +&= +\sum_{k=-\infty}^\infty a_kz^k +\\ +\sk z^\varrho +&= +e^{2\pi i\varrho} z^\varrho +\end{aligned} +\] +schreiben. + +\subsubsection{Rechenregeln für die analytische Fortsetzung} +Der Operator $\sk$ ist ein Algebrahomomorphismus, d.~h.~für zwei analytische +Funktionen $f$ und $g$ gilt +\[ +\begin{aligned} +\sk(\lambda f + \mu g) +&= +\lambda \sk f + \mu \sk g +\\ +\sk(fg) +&= +(\sk f)(\sk g) +\end{aligned} +\] +für beliebige $\lambda,\mu\in\mathbb{C}$. +Ist $f$ eine in ganz $\mathbb{C}$ holomorphe Funktion, dann lässt sie +sich mit Hilfe einer Potenzreihe berechnen. +Der Wert $f(g(z))$ entsteht durch Einsetzen von $g(z)$ in die Potenzreihe. +Analytische Fortsetzung mit $\sk$ reproduziert jeden einzelnen Term +der Potenzreihe, es folgt +$\sk f(g(z)) = f(\sk g(z))$. +Ebenso folgt auch, dass der Operator $\sk$ mit der Ableitung +vertauscht, dass also +\[ +\frac{d^n}{dz^n}(\sk f) += +\sk(f^{(n)}). +\] + + +\subsubsection{Analytische Fortsetzung von Lösungen einer Differentialgleichung} +Wir untersuchen jetzt die Wirkung des Operators $\sk$ auf +den Lösungsraum $\mathbb{L}$ einer Differentialgleichung mit +analytischen Koeffizienten, die in einer Umgebung von $0$ +definiert sind. +Auf den Koeffizienten wirkt $\sk$ als die Identität. +Ist $y(x)$ eine Lösung der Differentialgleichung, dann gilt +\[ +0 += +\sk\biggl( +\sum_{k=0}^n a_k(x) y^{(n)}(x) +\biggr) += +\sum_{k=0}^n (\sk a_k)(x) \cdot (\sk y)^{(n)}(x) += +\sum_{k=0}^n a_k(x) \cdot (\sk y)^{(n)}(x), +\] +somit ist $\sk y$ ebenfalls eine Lösung. +Wir schliessen daraus, dass $\sk$ eine lineare Abbildung +$\mathbb{L}\to\mathbb{L}$ ist. + +Der Lösungsraum einer Differentialgleichung $n$-ter Ordnung +ist $n$-dimensional. +Nach Wahl einer Basis des Lösungsraums kann der Operator $\sk$ +mit Hilfe einer Matrix $A\in M_{n\times n}(\mathbb{C})$ beschrieben werden. +Sei $\mathscr{W}=\{w_1,\dots,w_n\}$ eine Basis des Lösungsraums, dann +kann $\sk w_j$ wieder eine Lösung der Differentialgleichung +und kann daher geschrieben werden als Linearkombination +\begin{equation} +\sk w_j += +\sum_{k=1}^n +a_{jk} w_k +\end{equation} +der Funktionen in $\mathscr{W}$. + +Die Matrix $A$ mit den Einträgen $a_{jk}$ kann durch Wahl einer +geeigneten Basis in besonders einfache Form gebracht. +Wir führen diese Diskussion im folgenden nur für eine Differentialgleichung +zweiter Ordnung $n=2$. + + +\subsubsection{Fall $A$ diagonalisierbar: verallgemeinerte Potenzreihen} +In diesem Fall kann man die Lösungsfunktionen $w_1$ und $w_2$ so +wählen, dass die Matrix +\[ +A=\begin{pmatrix}\lambda_1&0\\0&\lambda_2\end{pmatrix} +\] +diagonal wird mit Eigenwerten $\lambda_j$, $j=1,2$. +Dies bedeutet, dass $\sk w_j = \lambda_j w_j$. +Wir schreiben +\[ +\varrho_j = \frac{1}{2\pi i} \log\lambda_j. +\] +Der Logarithmus ist nicht eindeutig, er ist nur bis auf ein Vielfaches +von $2\pi i$ bestimmt. +Folglich aus auch $\varrho_j$ nicht eindeutig bestimmt, eine +andere Wahl des Logarithmus ändert $\varrho_j$ aber um eine ganze Zahl. + +Die Funktion $z^{\varrho_j}$ wird unter der Wirkung von $\sk$ zu +\[ +\sk z^{\varrho_j} += +e^{2\pi i\varrho_j} z^{\varrho_j} += +e^{\log \lambda_j} z^{\varrho_j} += +\lambda_j z^{\varrho_j}. +\] +Auf den Funktionen $z^{\varrho_j}$ und $w_j$ wirkt der Operator $\sk$ +also die gleich durch Multiplikation mit $\lambda_j$. +Deren Quotient +\[ +f(z) = \frac{w_j(z)}{z^{\varrho_j}} +\qquad\text{erfüllt}\qquad +\sk f += +\frac{\sk w_j}{\sk z^{\varrho_j}} += +\frac{\lambda_j w_j}{\lambda_j z^{\varrho_j}} += +\frac{w_j}{z^{\varrho_j}} += +f. +\] +Die Funktion $f$ kann daher als Laurent-Reihe +\[ +f(z) += +\sum_{k=-\infty}^\infty a_kz^k +\] +geschrieben werden. +Die Lösung $w_2(z)$ muss daher die Form +\begin{equation} +w_j(z) += +z^{\varrho_j} f(z) += +z^{\varrho_j} \sum_{k=-\infty}^\infty a_kz^k +\end{equation} +haben, also die einer verallgemeinerten Potenzreihe. +Auch hier zeigt sich, dass die Wahl des Logarithmus in der Definition +von $\varrho_j$ unbedeutend ist, sie äussert sich nur in einer +Verschiebung der Koeffizienten $a_k$. + +Falls der Operator $\sk$ also diagonalisierbar ist, dann gibt es +zwei linear unabhängige Lösungen der Differentialgleichung in der +Form einer verallgemeinerten Potenzreihe. + +\subsubsection{Fall $A$ nicht diagonalisierbar: logarithmische Lösungen} +Falls die Matrix $A$ nicht diagonalisierbar ist, hat sie nur einen +Eigenwert $\lambda$ und kann durch geeignete Wahl einer Basis in +Jordansche Normalform +\[ +A += +\begin{pmatrix} +\lambda & 1 \\ + 0 & \lambda +\end{pmatrix} +\] +gebracht werden. +Dies bedeutet, dass +\begin{align*} +\sk w_1 &= \lambda w_1 + w_2 +\\ +\sk w_2 &= \lambda w_2. +\end{align*} +Die Funktion $w_2$ hat unter $\sk$ die gleichen Eigenschaften +wie im diagonalisierbaren Fall, man kann also wieder schliessen, +dass $w_2$ durch eine verallgemeinerte Potenzreihe mit +\[ +\varrho=\frac{1}{2\pi i} \log \lambda +\] +dargestellt werden kann. + +Für den Quotienten $w_1/w_2$ findet man jetzt das Bild +\begin{equation} +\sk \frac{w_1}{w_2} += +\frac{\sk w_1}{\sk w_2} += +\frac{\lambda w_1+w_2}{\lambda w_2} += +\frac{w_1}{w_2} + \frac{1}{\lambda} +\label{buch:funktionentheorie:singularitaeten:sklog} +\end{equation} +Das Verhalten von $w_1$ unter $\sk$ in +\eqref{buch:funktionentheorie:singularitaeten:sklog} +ist dasselbe wie bei $\log(z)/\lambda$, denn +\[ +\sk \frac{\log(z)}{\lambda} += +\frac{\log(z)}{\lambda} + 1. +\] +Die Differenz $w_1-\log(z)/\lambda$ wird bei der analytischen +Fortsetzung zu +\[ +\sk\biggl( +\frac{w_1}{w_2}-\frac{\log(z)}{\lambda} +\biggr) += +\sk \frac{w_1}{w_2} - \sk\frac{\log(z)}{\lambda} += +\frac{w_1}{w_2} + \frac{1}{\lambda} +- +\frac{\log(z)}{\lambda} +-\frac{1}{\lambda} += +\frac{w_1}{w_2}-\frac{\log(z)}{\lambda}. +\] +Die Differenz ist daher wieder als Laurent-Reihe +\[ +\frac{w_1}{w_2}-\frac{\log(z)}{\lambda} += +\sum_{k=-\infty}^\infty b_kz^k +\] +darstellbar, was nach $w_1$ aufgelöst +\[ +w_1(z) += +\frac{1}{\lambda} \log(z) w_2(z) ++ +w_2(z) \sum_{k=-\infty}^\infty b_kz^k +\] +ergibt. +Da $w_2$ eine verallgemeinerte Potenzreihe ist, kann man dies auch +als +\begin{equation} +w_1(z) += +c \log(z) w_2(z) ++ +z^{\varrho} +\sum_{k=-\infty}^{\infty} c_kz^k +\label{buch:funktionentheorie:singularitäten:eqn:w1} +\end{equation} +schreiben, wobei Konstanten $c$ und $c_k$ noch bestimmt werden müssen. +Setzt man +\eqref{buch:funktionentheorie:singularitäten:eqn:w1} +in die ursprüngliche Differentialgleichung ein, verschwindet der +$\log(z)$-Term und für die verbleibenden Koeffizienten kann die +bekannte Methode des Koeffizientenvergleichs verwendet werden. + +\subsubsection{Bessel-Funktionen zweiter Art} + + + -- cgit v1.2.1 From 5312bb1779adb029f6a115d0ea6fe065b4c878c0 Mon Sep 17 00:00:00 2001 From: daHugen Date: Mon, 18 Apr 2022 22:11:56 +0200 Subject: made some changes and added some things to teil4.txt --- buch/papers/lambertw/teil4.tex | 87 ++++++++++++++++++++++++++++++++++++++---- 1 file changed, 79 insertions(+), 8 deletions(-) diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index d3269ee..598a57e 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -21,7 +21,7 @@ Das zu verfolgende Ziel \(A\) wandert auf einer Gerade, wobei diese Gerade der \ P = \left( \begin{array}{c} x \\ y \end{array} \right) - \label{lambertw:equation2} + \label{lambertw:Anfangspunkte} \end{equation} Wenn man diese Startpunkte in die Gleichung der Verfolgungskurve einfügt ergibt sich folgender Ausdruck: \begin{equation} @@ -30,7 +30,7 @@ Wenn man diese Startpunkte in die Gleichung der Verfolgungskurve einfügt ergibt \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) = 1 - \label{lambertw:equation3} + \label{lambertw:eqMitAnfangspunkte} \end{equation} Macht man den linken Term Bruchfrei und löst das Skalarprodukt auf, dann ergibt sich folgende DGL: \[ @@ -42,7 +42,7 @@ Macht man den linken Term Bruchfrei und löst das Skalarprodukt auf, dann ergibt \begin{equation} -x \cdot \dot{x} + (t-y) \cdot \dot{y} = \sqrt{x^2 + (t-y)^2} - \label{lambertw:equation4} + \label{lambertw:eq1BspVerfolgKurve} \end{equation} Im nächsten Schritt quadriert man beide Seiten, erweitert den neu entstandenen quadratischen Term, bringt alles auf die linke Seite und klammert gemeinsames aus. \begin{align*} @@ -73,7 +73,7 @@ Im letzten Ausdruck erkennt man das Muster einer binomischen Formel, was den Aus (x \dot{y} + (t-y) \dot{x})^2 &= 0 \end{align*} -Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich zu \eqref{lambertw:equation4} eine wesentlich einfachere DGL: +Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich zu \eqref{lambertw:eq1BspVerfolgKurve} eine wesentlich einfachere DGL: \begin{equation} x \dot{y} + (t-y) \dot{x} = 0 @@ -88,8 +88,79 @@ Nach dem kürzen ergibt sich folgende DGL: \begin{equation} x y^{\prime} + t - y = 0 - \label{lambertw:equation6} + \label{lambertw:DGLmitT} \end{equation} -Hier wäre es passend wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen muss man - - +Hier wäre es passend wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen muss man auf die Definition der Bogenlänge aus Analysis 2 zurückgreifen: +\begin{equation} + s + = + v \cdot t + = + t + = + \int_{x_0}^{x_{end}}\sqrt{1+y^{\prime\, 2}} \: dx + \label{lambertw:eqZuBogenlaenge} +\end{equation} +Nicht gerade auffällig ist die Richtung in welche hier integriert wird. Wenn der Verfolger sich wie vorgesehen am Anfang im ersten Quadranten befindet, dann muss sich dieser nach links bewegen, was nicht der üblichen Integrationsrichtung entspricht. Um eine Integration wie üblich von links nach rechts ausführen zu können, müssen die Integrationsgenerzen vertauscht werden, was in einem Vorzeichenwechsel resultiert. Wenn man nun \eqref{lambertw:eqZuBogenlaenge} in die DGL \eqref{lambertw:DGLmitT} einfügt, dann ergibt sich folgender Ausdruck: +\begin{equation} + x y^{\prime} - \int\sqrt{1+y^{\prime\, 2}} \: dx - y + = 0 + \label{lambertw:DGLohneT} +\end{equation} +Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambertw:DGLohneT} nach \(x\) ab: +\begin{align*} + y^{\prime}+ xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} - y^{\prime} + &= 0 \\ + xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} + &= 0 +\end{align*} +Mittels der Substitution \(y^{\prime} = u\) kann vorherige DGL in eine erster Ordnung umgewandelt werden: +\begin{equation*} + xu^{\prime} - \sqrt{1+u^2} + = 0 + \label{lambertw:DGLmitU} +\end{equation*} +Welche mittels Separation gelöst werden kann: +\begin{align*} + arsinh(u) + C_L + &= + ln(x) + C_R \\ + arsinh(u) + &= + ln(x) + C \\ + u + &= + sinh(ln(x) + C) +\end{align*} +In dem man die Substitution rückgängig macht, erhält man eine weitere DGL erster Ordnung die bereits separiert ist: +\begin{equation} + y^{\prime} + = + sinh(ln(x) + C) +\end{equation} +Diese kann mit den selben Methoden gelöst werden, diesmal in Kombination mit der exponentiellen Definition der \(sinh\)-Funktion: +\begin{align*} + y + &= + \int sinh(ln(x) + C) \\ + &= + \int \frac{1}{2} (e^{ln(x)+C} - e^{-(ln(x)+C)}) \\ + &= + C_1 + C_2 x^2 - C_3 ln(x) +\end{align*} +Das Resultat wie ersichtlich ist folgende Funktion welche mittels Anfangsbedingungen parametrisiert werden kann: +\begin{equation} + y(x) + = + C_1 + C_2 x^2 - C_3 ln(x) + \label{lambertw:funkLoes} +\end{equation} +Für die Koeffizienten \(C_1, C_2\) und \(C_3\) ergibt sich ein Anfangswertproblem, welches für deren Bestimmung gelöst werden muss. Zuerst soll aber eine qualitative Intuition, oder Idee für das Aussehen der Funktion \(\bf{y(x)}\) geschaffen werden: +\begin{itemize} + \item + Für grosse \(x\)-Werte welche in der Regel in der Nähe von \(x_0\) sein sollten, ist der quadratisch Term in der Funktion dominant und somit für immer kleiner werdende \(x\) geht der Verfolger in Richtung \(y\)-Achse wobei seine Steigung stetig sinkt, was Sinn macht wenn der Verfolgte entlang der \(y\)-Achse steigt. + \item + Für \(x\)-Werte in der Nähe von \(0\) ist das asymptotische Verhalten des Logarithmus dominant, dies macht auch Sinn da sich der Verfolgte auf der \(y\)-Achse bewegt und der Verfolger im nachgeht. + \item + Aufgrund des Monotoniewechsels in der Kurve muss die Kurve auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? Durch eine logische Überlegung kann eine Abschätzung darüber getroffen werden und zwar, dass dieser dann entsteht, wenn \(A\) und \(P\) die gleiche \(y\)-Koordinaten besitzen. In diesem Moment ändert die Richtung der \(y\)-Komponente der Geschwindigkeit und somit auch sein Vorzeichen. +\end{itemize} -- cgit v1.2.1 From 0344a846c083c11e9ed93ddc5898dd55c6dd1022 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 20 Apr 2022 10:30:56 +0200 Subject: lemniscate sine stuff --- buch/chapters/110-elliptisch/Makefile.inc | 3 + buch/chapters/110-elliptisch/chapter.tex | 21 +- buch/chapters/110-elliptisch/ellintegral.tex | 208 +- buch/chapters/110-elliptisch/images/Makefile | 9 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/lemniskate.pdf | Bin 9914 -> 14339 bytes buch/chapters/110-elliptisch/images/lemniskate.tex | 15 +- buch/chapters/110-elliptisch/images/slcl.cpp | 128 + buch/chapters/110-elliptisch/images/slcl.pdf | Bin 0 -> 28269 bytes buch/chapters/110-elliptisch/images/slcl.tex | 88 + buch/chapters/110-elliptisch/jacobi.tex | 3264 ++++++++++---------- buch/chapters/110-elliptisch/lemniskate.tex | 299 +- 12 files changed, 2431 insertions(+), 1604 deletions(-) create mode 100644 buch/chapters/110-elliptisch/images/slcl.cpp create mode 100644 buch/chapters/110-elliptisch/images/slcl.pdf create mode 100644 buch/chapters/110-elliptisch/images/slcl.tex diff --git a/buch/chapters/110-elliptisch/Makefile.inc b/buch/chapters/110-elliptisch/Makefile.inc index 538db68..b23df52 100644 --- a/buch/chapters/110-elliptisch/Makefile.inc +++ b/buch/chapters/110-elliptisch/Makefile.inc @@ -7,6 +7,9 @@ CHAPTERFILES = $(CHAPTERFILES) \ chapters/110-elliptisch/ellintegral.tex \ chapters/110-elliptisch/jacobi.tex \ + chapters/110-elliptisch/elltrigo.tex \ + chapters/110-elliptisch/dglsol.tex \ + chapters/110-elliptisch/mathpendel.tex \ chapters/110-elliptisch/lemniskate.tex \ chapters/110-elliptisch/uebungsaufgaben/001.tex \ chapters/110-geometrie/chapter.tex diff --git a/buch/chapters/110-elliptisch/chapter.tex b/buch/chapters/110-elliptisch/chapter.tex index e09fa53..e05f3bd 100644 --- a/buch/chapters/110-elliptisch/chapter.tex +++ b/buch/chapters/110-elliptisch/chapter.tex @@ -10,18 +10,33 @@ \rhead{} Der Versuch, die Länge eines Ellipsenbogens zu berechnen, hat -in Abschnitt~\ref{buch:geometrie:subsection:hyperbeln-und-ellipsen} +in Abschnitt~\ref{buch:geometrie:subsection:kegelschnitte} zu Integralen geführt, die nicht in geschlossener Form ausgewertet werden können. Neben den dort gefundenen Integralen sind noch weitere, ähnlich aufgebaute Integrale in dieser Familie zu finden. +Auf die trigonometrischen Funktionen stösst man, indem man Funktion +der Bogenlänge umkehrt. +Ein analoges Vorgehen bei den elliptischen Integralen führt auf +die Jacobischen elliptischen Funktionen, die in +Abschnitt~\ref{buch:elliptisch:section:jacobi} allerdings auf +eine eher geometrische Art eingeführt werden. +Die Verbindung zu den elliptischen Integralen wird dann in +Abschnitt~\ref{buch:elliptisch:subsection:differentialgleichungen} +wieder hergestellt. + \input{chapters/110-elliptisch/ellintegral.tex} + \input{chapters/110-elliptisch/jacobi.tex} +\input{chapters/110-elliptisch/elltrigo.tex} +\input{chapters/110-elliptisch/dglsol.tex} +\input{chapters/110-elliptisch/mathpendel.tex} + \input{chapters/110-elliptisch/lemniskate.tex} -\section*{Übungsaufgaben} -\rhead{Übungsaufgaben} +\section*{Übungsaufgabe} +\rhead{Übungsaufgabe} \aufgabetoplevel{chapters/110-elliptisch/uebungsaufgaben} \begin{uebungsaufgaben} %\uebungsaufgabe{0} diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 46659cd..4cb2ba3 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -7,7 +7,7 @@ \label{buch:elliptisch:section:integral}} \rhead{Elliptisches Integral} Bei der Berechnung des Ellipsenbogens in -Abschnitt~\ref{buch:geometrie:subsection:hyperbeln-und-ellipsen} +Abschnitt~\ref{buch:geometrie:subsection:kegelschnitte} sind wir auf ein Integral gestossen, welches sich nicht in geschlossener Form ausdrücken liess. Um solche Integrale in den Griff zu bekommen, ist es nötig, sie als @@ -172,7 +172,188 @@ die {\em Jacobi-Normalform} heisst. \subsubsection{Vollständige elliptische Integrale als hypergeometrische Funktionen} -XXX Als hypergeometrische Funktionen \url{https://www.youtube.com/watch?v=j0t1yWrvKmE} \\ +%XXX Als hypergeometrische Funktionen \url{https://www.youtube.com/watch?v=j0t1yWrvKmE} \\ +Das vollständige elliptische Integral $K(k)$ kann mit Hilfe der +Binomialreihe umgeformt werden in eine hypergeometrische Reihe. +Da im Integral nur $k^2$ auftaucht, wird sich $K(k)$ als +hypergeometrische Funktion von $k^2$ ausdrücken lassen. + +\begin{satz} +\label{buch:elliptisch:satz:hyperK} +Das vollständige elliptische Integral $K(k)$ lässt sich durch die +hypergeometrische Funktion $\mathstrut_2F_1$ als +\[ +K(k) += +\frac{\pi}2 +\cdot +\mathstrut_2F_1\biggl( +\begin{matrix}\frac12,\frac12\\1\end{matrix};1;k^2 +\biggr) +\] +ausdrücken. +\end{satz} + +\begin{proof}[Beweis] +Zunächst ist das vollständige elliptische Integral in der Legendre-Form +\begin{align} +K(k) +&= +\int_0^{\frac{\pi}2} +\frac{d\vartheta}{\sqrt{1-k^2\sin^2\vartheta}} +%\notag +%\\ +%& += +\int_0^{\frac{\pi}2} +\bigl( +1-(k\sin\vartheta)^2 +\bigr)^{-\frac12}\,d\vartheta. +\notag +\intertext{Die Wurzel im letzten Integral kann mit Hilfe der binomischen +Reihe vereinfacht werden zu} +&= +\sum_{n=0}^\infty +(-1)^n k^2\binom{-\frac12}{n} +\int_0^{\frac{\pi}2} +\sin^{2n}\vartheta +\,d\vartheta. +\label{buch:elliptisch:beweis:ellharm2} +\end{align} +Der verallgemeinerte Binomialkoeffizient lässt sich nach +\begin{align*} +\binom{-\frac12}{n} +&= +\frac{(-\frac12)(-\frac32)(-\frac52)\cdot\ldots\cdot(-\frac12-n+1)}{n!} += +(-1)^n +\cdot +\frac{1}{n!} +\cdot +\frac12\cdot\frac32\cdot\frac52\cdot\ldots\cdot\biggl(\frac12+n-1\biggr) += +(-1)^n\frac{(\frac12)_n}{n!} +\end{align*} +vereinfachen. +Setzt man dies in \eqref{buch:elliptisch:beweis:ellharm2} ein, erhält +man +\begin{align*} +K(k) +&= +\sum_{n=0}^\infty +(-1)^n k^{2n} +\cdot +(-1)^n +\frac{(\frac12)_n}{n!} +\cdot +\int_0^{\frac{\pi}2} \sin^{2n}\vartheta\,d\vartheta += +\sum_{n=0}^\infty +\frac{(\frac12)_n}{n!} +\int_0^{\frac{\pi}2} \sin^{2n}\vartheta\,d\vartheta +\cdot (k^2)^n. +\end{align*} +Es muss jetzt also nur noch das Integral von $\sin^{2n}\vartheta$ +berechnet werden. +Mit partieller Integration kann man +\begin{align*} +\int \sin^m\vartheta\,d\vartheta +&= +\int +\underbrace{\sin \vartheta}_{\uparrow} +\underbrace{\sin^{m-1}\vartheta}_{\downarrow} +\,d\vartheta +\\ +&= +-\cos\vartheta\sin^{m-1}\vartheta ++ +\int \cos^2\vartheta (m-1)\sin^{m-2}\vartheta\,d\vartheta +\\ +&= +-\cos\vartheta \sin^{m-1}\vartheta ++ +(m-1) +\int +(1-\sin^2\vartheta) +\sin^{m-2}\vartheta\,d\vartheta. +\end{align*} +Wegen $\sin 0=0$ und +$\cos\frac{\pi}2=0$ verschwindet der erste Term im bestimmten Integral +und der zweite wird +\begin{align*} +\int_0^{\frac{\pi}2} +\sin^{m} \vartheta +\,d\vartheta +&= +(m-1) +\int_0^{\frac{\pi}2} +\sin^{m-2}\vartheta\,d\vartheta +- +(m-1) +\int_0^{\frac{\pi}2} +\sin^m \vartheta\,d\vartheta +\\ +m +\int_0^{\frac{\pi}2} +\sin^{m} \vartheta\,d\vartheta +&= +(m-1) +\int_0^{\frac{\pi}2} +\sin^{m-2} \vartheta\,d\vartheta +\\ +\int_0^{\frac{\pi}2} +\sin^{m} \vartheta\,d\vartheta +&= +\frac{m-1}{m} +\int_0^{\frac{\pi}2} +\sin^{m-2} \vartheta\,d\vartheta. +\end{align*} +Mit dieser Rekursionsformel kann jetzt das Integral berechnet werden. +Es folgt +\begin{align*} +\int_0^{\frac{\pi}2} +\sin^{2n}\vartheta\,d\vartheta +&= +\frac{2n-1}{2n} +\int_0^{\frac{\pi}2} +\sin^{2n-2}\vartheta\,d\vartheta +\\ +&= +\frac{2n-1}{2n} +\frac{2n-3}{2n-2} +\frac{2n-5}{2n-4} +\cdots +\frac{2n-(2n-1)}{2(n-1)} +\int_0^{\frac{\pi}2} +\sin^{2n-4}\vartheta\,d\vartheta +\\ +&= +\frac{ +(n-\frac12)(n-\frac32)(n-\frac52)\cdot\ldots\cdot\frac32\cdot\frac12 +}{ +n! +} +\int_0^{\frac{\pi}2} 1\,d\vartheta +\\ +&= +\frac{(\frac12)_n}{n!} +\cdot +\frac{\pi}2. +\end{align*} +Damit wird die Reihenentwicklung für $K(k)$ jetzt zu +\[ +K(k) += +\frac{\pi}2 +\sum_{n=0}^\infty +\frac{(\frac12)_n(\frac12)_n}{n!} \cdot \frac{(k^2)^n}{n!} += +\frac{\pi}2 +\cdot +\mathstrut_2F_1\biggl(\begin{matrix}\frac12,\frac12\\1\end{matrix};k^2\biggr), +\] +dies beweist die Behauptung. +\end{proof} @@ -247,6 +428,29 @@ Für den extremen Wert $\varepsilon=0$ entsteht der Umfang einer Ellipse, also $E(0)=\frac{\pi}2$. Für $\varepsilon=1$ ist $a=0$, es entsteht eine Strecke mit Länge $E(1)=1$. +\begin{satz} +\label{buch:elliptisch:satz:hyperE} +Das volständige elliptische Integral $E(k)$ ist +\[ +E(k) += +\int_0^{\frac{\pi}2} \sqrt{1-k^2\sin^2\vartheta}\,d\vartheta += +\frac{\pi}2 +\cdot +\mathstrut_2F_1\biggl( +\begin{matrix}-\frac12,\frac12\\1\end{matrix}; +k^2 +\biggr). +\] +\end{satz} + +\begin{proof}[Beweis] +Die Identität kann wie im Satz~\ref{buch:elliptisch:satz:hyperK} mit +Hilfe einer Entwicklung der Wurzel mit der Binomialreihe gefunden +werden. +\end{proof} + \subsubsection{Komplementäre Integrale} \subsubsection{Ableitung} diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 68322b6..a7c9e74 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -5,7 +5,7 @@ # all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ - sncnlimit.pdf + sncnlimit.pdf slcl.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex @@ -71,3 +71,10 @@ jacobi12.pdf: jacobi12.tex sncnlimit.pdf: sncnlimit.tex pdflatex sncnlimit.tex +slcl: slcl.cpp + g++ -O -Wall -std=c++11 slcl.cpp -o slcl `pkg-config --cflags gsl` `pkg-config --libs gsl` + +slcldata.tex: slcl + ./slcl --outfile=slcldata.tex --a=0 --b=13.4 --steps=200 +slcl.pdf: slcl.tex slcldata.tex + pdflatex slcl.tex diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 88cf119..f0e6e78 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/lemniskate.pdf b/buch/chapters/110-elliptisch/images/lemniskate.pdf index 063a3e1..9e02c3c 100644 Binary files a/buch/chapters/110-elliptisch/images/lemniskate.pdf and b/buch/chapters/110-elliptisch/images/lemniskate.pdf differ diff --git a/buch/chapters/110-elliptisch/images/lemniskate.tex b/buch/chapters/110-elliptisch/images/lemniskate.tex index f74a81f..fe90631 100644 --- a/buch/chapters/110-elliptisch/images/lemniskate.tex +++ b/buch/chapters/110-elliptisch/images/lemniskate.tex @@ -27,13 +27,16 @@ \draw[color=red,line width=2.0pt] plot[domain=45:\a,samples=100] ({\x}:{sqrt(2*cos(2*\x))}); -\draw[->] (-1.5,0) -- (1.5,0) coordinate[label={$x$}]; -\draw[->] (0,-0.7) -- (0,0.7) coordinate[label={right:$y$}]; +\draw[->] (-1.5,0) -- (1.7,0) coordinate[label={$X$}]; +\draw[->] (0,-0.7) -- (0,0.7) coordinate[label={right:$Y$}]; \fill[color=white] (1,0) circle[radius=0.02]; \draw (1,0) circle[radius=0.02]; +\node at ({1},0) [below] {$\displaystyle a\mathstrut$}; + \fill[color=white] (-1,0) circle[radius=0.02]; \draw (-1,0) circle[radius=0.02]; +\node at ({-1},0) [below] {$\displaystyle\llap{$-$}a\mathstrut$}; \node[color=blue] at (\a:{0.6*sqrt(2*cos(2*\a))}) [below] {$r$}; \node[color=red] at ({\b}:{sqrt(2*cos(2*\b))}) [above] {$s$}; @@ -41,6 +44,14 @@ \fill[color=white] (\a:{sqrt(2*cos(2*\a))}) circle[radius=0.02]; \draw[color=red] (\a:{sqrt(2*cos(2*\a))}) circle[radius=0.02]; +\draw ({sqrt(2)},{-0.1/\skala}) -- ({sqrt(2)},{0.1/\skala}); +\node at ({sqrt(2)},0) [below right] + {$\displaystyle a\mathstrut\sqrt{2}$}; +\draw ({-sqrt(2)},{-0.1/\skala}) -- ({-sqrt(2)},{0.1/\skala}); +\node at ({-sqrt(2)},0) [below left] + {$\displaystyle -a\mathstrut\sqrt{2}$}; + + \end{tikzpicture} \end{document} diff --git a/buch/chapters/110-elliptisch/images/slcl.cpp b/buch/chapters/110-elliptisch/images/slcl.cpp new file mode 100644 index 0000000..8584e94 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/slcl.cpp @@ -0,0 +1,128 @@ +/* + * slcl.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace slcl { + +static struct option longopts[] { +{ "outfile", required_argument, NULL, 'o' }, +{ "a", required_argument, NULL, 'a' }, +{ "b", required_argument, NULL, 'b' }, +{ "steps", required_argument, NULL, 'n' }, +{ NULL, 0, NULL, 0 } +}; + +class plot { + typedef std::pair point_t; + typedef std::vector curve_t; + curve_t _sl; + curve_t _cl; + double _a; + double _b; + int _steps; +public: + double a() const { return _a; } + double b() const { return _b; } + int steps() const { return _steps; } +public: + plot(double a, double b, int steps) : _a(a), _b(b), _steps(steps) { + double l = sqrt(2); + double k = 1 / l; + double m = k * k; + double h = (b - a) / steps; + for (int i = 0; i <= steps; i++) { + double x = a + h * i; + double sn, cn, dn; + gsl_sf_elljac_e(x, m, &sn, &cn, &dn); + _sl.push_back(std::make_pair(l * x, k * sn / dn)); + _cl.push_back(std::make_pair(l * x, cn)); + } + } +private: + std::string point(const point_t p) const { + char buffer[128]; + snprintf(buffer, sizeof(buffer), "({%.4f*\\dx},{%.4f*\\dy})", + p.first, p.second); + return std::string(buffer); + } + std::string path(const curve_t& curve) const { + std::ostringstream out; + auto i = curve.begin(); + out << point(*(i++)); + do { + out << std::endl << " -- " << point(*(i++)); + } while (i != curve.end()); + out.flush(); + return out.str(); + } +public: + std::string slpath() const { + return path(_sl); + } + std::string clpath() const { + return path(_cl); + } +}; + +/** + * \brief Main function for the slcl program + */ +int main(int argc, char *argv[]) { + int longindex; + int c; + double a = 0; + double b = 10; + int steps = 100; + std::ostream *out = &std::cout; + while (EOF != (c = getopt_long(argc, argv, "a:b:o:n:", + longopts, &longindex))) + switch (c) { + case 'a': + a = std::stod(optarg); + break; + case 'b': + b = std::stod(optarg) / sqrt(2); + break; + case 'n': + steps = std::stol(optarg); + break; + case 'o': + out = new std::ofstream(optarg); + break; + } + + plot p(a, b, steps); + (*out) << "\\def\\slpath{ " << p.slpath(); + (*out) << std::endl << " }" << std::endl; + (*out) << "\\def\\clpath{ " << p.clpath(); + (*out) << std::endl << " }" << std::endl; + + out->flush(); + //out->close(); + return EXIT_SUCCESS; +} + +} // namespace slcl + +int main(int argc, char *argv[]) { + try { + return slcl::main(argc, argv); + } catch (const std::exception& e) { + std::cerr << "terminated by exception: " << e.what(); + std::cerr << std::endl; + } catch (...) { + std::cerr << "terminated by unknown exception" << std::endl; + } + return EXIT_FAILURE; +} diff --git a/buch/chapters/110-elliptisch/images/slcl.pdf b/buch/chapters/110-elliptisch/images/slcl.pdf new file mode 100644 index 0000000..493b5fa Binary files /dev/null and b/buch/chapters/110-elliptisch/images/slcl.pdf differ diff --git a/buch/chapters/110-elliptisch/images/slcl.tex b/buch/chapters/110-elliptisch/images/slcl.tex new file mode 100644 index 0000000..08241ac --- /dev/null +++ b/buch/chapters/110-elliptisch/images/slcl.tex @@ -0,0 +1,88 @@ +% +% tikztemplate.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\input{slcldata.tex} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +% add image content here +\def\lemniscateconstant{2.6220575542} +\pgfmathparse{(3.1415926535/2)/\lemniscateconstant} +\xdef\scalechange{\pgfmathresult} + +\pgfmathparse{\scalechange*(180/3.1415926535)} +\xdef\ts{\pgfmathresult} + +\def\dx{1} +\def\dy{3} + +\draw[line width=0.3pt] + ({\lemniscateconstant*\dx},0) + -- + ({\lemniscateconstant*\dx},{1*\dy}); +\draw[line width=0.3pt] + ({2*\lemniscateconstant*\dx},0) + -- + ({2*\lemniscateconstant*\dx},{-1*\dy}); +\draw[line width=0.3pt] + ({3*\lemniscateconstant*\dx},0) + -- + ({3*\lemniscateconstant*\dx},{-1*\dy}); +\draw[line width=0.3pt] + ({4*\lemniscateconstant*\dx},0) + -- + ({4*\lemniscateconstant*\dx},{1*\dy}); +\draw[line width=0.3pt] + ({5*\lemniscateconstant*\dx},0) + -- + ({5*\lemniscateconstant*\dx},{1*\dy}); + +\draw[color=red!20,line width=1.4pt] + plot[domain=0:13,samples=200] ({\x},{\dy*sin(\ts*\x)}); +\draw[color=blue!20,line width=1.4pt] + plot[domain=0:13,samples=200] ({\x},{\dy*cos(\ts*\x)}); + +\draw[color=red,line width=1.4pt] \slpath; +\draw[color=blue,line width=1.4pt] \clpath; + +\draw[->] (0,{-1*\dy-0.1}) -- (0,{1*\dy+0.4}) coordinate[label={right:$r$}]; +\draw[->] (-0.1,0) -- (13.7,0) coordinate[label={$s$}]; + +\foreach \i in {1,2,3,4,5}{ + \draw ({\lemniscateconstant*\i},-0.1) -- ({\lemniscateconstant*\i},0.1); +} +\node at ({\lemniscateconstant*\dx},0) [below left] {$ \varpi\mathstrut$}; +\node at ({2*\lemniscateconstant*\dx},0) [below left] {$2\varpi\mathstrut$}; +\node at ({3*\lemniscateconstant*\dx},0) [below right] {$3\varpi\mathstrut$}; +\node at ({4*\lemniscateconstant*\dx},0) [below right] {$4\varpi\mathstrut$}; +\node at ({5*\lemniscateconstant*\dx},0) [below left] {$5\varpi\mathstrut$}; + +\node[color=red] at ({1.6*\lemniscateconstant*\dx},{0.6*\dy}) + [below left] {$\operatorname{sl}(s)$}; +\node[color=red!50] at ({1.5*\lemniscateconstant*\dx},{sin(1.5*90)*\dy*0.90}) + [above right] {$\sin \bigl(\frac{\pi}{2\varpi}s\bigr)$}; + +\node[color=blue] at ({1.4*\lemniscateconstant*\dx},{-0.6*\dy}) + [above right] {$\operatorname{cl}(s)$}; +\node[color=blue!50] at ({1.5*\lemniscateconstant*\dx},{cos(1.5*90)*\dy*0.90}) + [below left] {$\cos\bigl(\frac{\pi}{2\varpi}s\bigr)$}; + +\draw (-0.1,{1*\dy}) -- (0.1,{1*\dy}); +\draw (-0.1,{-1*\dy}) -- (0.1,{-1*\dy}); +\node at (0,{1*\dy}) [left] {$1\mathstrut$}; +\node at (0,0) [left] {$0\mathstrut$}; +\node at (0,{-1*\dy}) [left] {$-1\mathstrut$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/110-elliptisch/jacobi.tex b/buch/chapters/110-elliptisch/jacobi.tex index f1e0987..e1fbc00 100644 --- a/buch/chapters/110-elliptisch/jacobi.tex +++ b/buch/chapters/110-elliptisch/jacobi.tex @@ -22,1597 +22,1743 @@ dann muss man die Umkehrfunktionen der elliptischen Integrale dafür ins Auge fassen. +%% +%% elliptische Funktionen als Trigonometrie +%% +%\subsection{Elliptische Funktionen als Trigonometrie} +%\begin{figure} +%\centering +%\includegraphics{chapters/110-elliptisch/images/ellipse.pdf} +%\caption{Kreis und Ellipse zum Vergleich und zur Herleitung der +%elliptischen Funktionen von Jacobi als ``trigonometrische'' Funktionen +%auf einer Ellipse. +%\label{buch:elliptisch:fig:ellipse}} +%\end{figure} +%% based on Willliam Schwalm, Elliptic functions and elliptic integrals +%% https://youtu.be/DCXItCajCyo % -% ellpitische Funktionen als Trigonometrie +%% +%% Geometrie einer Ellipse +%% +%\subsubsection{Geometrie einer Ellipse} +%Eine {\em Ellipse} ist die Menge der Punkte der Ebene, für die die Summe +%\index{Ellipse}% +%der Entfernungen von zwei festen Punkten $F_1$ und $F_2$, +%den {\em Brennpunkten}, konstant ist. +%\index{Brennpunkt}% +%In Abbildung~\ref{buch:elliptisch:fig:ellipse} eine Ellipse +%mit Brennpunkten in $F_1=(-e,0)$ und $F_2=(e,0)$ dargestellt, +%die durch die Punkte $(\pm a,0)$ und $(0,\pm b)$ auf den Achsen geht. +%Der Punkt $(a,0)$ hat die Entfernungen $a+e$ und $a-e$ von den beiden +%Brennpunkten, also die Entfernungssumme $a+e+a-e=2a$. +%Jeder andere Punkt auf der Ellipse muss ebenfalls diese Entfernungssumme +%haben, insbesondere auch der Punkt $(0,b)$. +%Seine Entfernung zu jedem Brennpunkt muss aus Symmetriegründen gleich gross, +%also $a$ sein. +%Aus dem Satz von Pythagoras liest man daher ab, dass +%\[ +%b^2+e^2=a^2 +%\qquad\Rightarrow\qquad +%e^2 = a^2-b^2 +%\] +%sein muss. +%Die Strecke $e$ heisst auch {\em (lineare) Exzentrizität} der Ellipse. +%Das Verhältnis $\varepsilon= e/a$ heisst die {\em numerische Exzentrizität} +%der Ellipse. % -\subsection{Elliptische Funktionen als Trigonometrie} -\begin{figure} -\centering -\includegraphics{chapters/110-elliptisch/images/ellipse.pdf} -\caption{Kreis und Ellipse zum Vergleich und zur Herleitung der -elliptischen Funktionen von Jacobi als ``trigonometrische'' Funktionen -auf einer Ellipse. -\label{buch:elliptisch:fig:ellipse}} -\end{figure} -% based on Willliam Schwalm, Elliptic functions and elliptic integrals -% https://youtu.be/DCXItCajCyo - +%% +%% Die Ellipsengleichung +%% +%\subsubsection{Ellipsengleichung} +%Der Punkt $P=(x,y)$ auf der Ellipse hat die Entfernungen +%\begin{equation} +%\begin{aligned} +%\overline{PF_1}^2 +%&= +%y^2 + (x+e)^2 +%\\ +%\overline{PF_2}^2 +%&= +%y^2 + (x-e)^2 +%\end{aligned} +%\label{buch:elliptisch:eqn:wurzelausdruecke} +%\end{equation} +%von den Brennpunkten, für die +%\begin{equation} +%\overline{PF_1}+\overline{PF_2} +%= +%2a +%\label{buch:elliptisch:eqn:pf1pf2a} +%\end{equation} +%gelten muss. +%Man kann nachrechnen, dass ein Punkt $P$, der die Gleichung +%\[ +%\frac{x^2}{a^2} + \frac{y^2}{b^2}=1 +%\] +%erfüllt, auch die Eigenschaft~\eqref{buch:elliptisch:eqn:pf1pf2a} +%erfüllt. +%Zur Vereinfachung setzen wir $l_1=\overline{PF_1}$ und $l_2=\overline{PF_2}$. +%$l_1$ und $l_2$ sind Wurzeln aus der rechten Seite von +%\eqref{buch:elliptisch:eqn:wurzelausdruecke}. +%Das Quadrat von $l_1+l_2$ ist +%\[ +%l_1^2 + 2l_1l_2 + l_2^2 = 4a^2. +%\] +%Um die Wurzeln ganz zu eliminieren, bringt man das Produkt $l_1l_2$ alleine +%auf die rechte Seite und quadriert. +%Man muss also verifizieren, dass +%\[ +%(l_1^2 + l_2^2 -4a^2)^2 = 4l_1^2l_2^2. +%\] +%In den entstehenden Ausdrücken muss man ausserdem $e=\sqrt{a^2-b^2}$ und +%\[ +%y=b\sqrt{1-\frac{x^2}{a^2}} +%\] +%substituieren. +%Diese Rechnung führt man am einfachsten mit Hilfe eines +%Computeralgebraprogramms durch, welches obige Behauptung bestätigt. % -% Geometrie einer Ellipse +%% +%% Normierung +%% +%\subsubsection{Normierung} +%Die trigonometrischen Funktionen sind definiert als Verhältnisse +%von Seiten rechtwinkliger Dreiecke. +%Dadurch, dass man den die Hypothenuse auf Länge $1$ normiert, +%kann man die Sinus- und Kosinus-Funktion als Koordinaten eines +%Punktes auf dem Einheitskreis interpretieren. % -\subsubsection{Geometrie einer Ellipse} -Eine {\em Ellipse} ist die Menge der Punkte der Ebene, für die die Summe -\index{Ellipse}% -der Entfernungen von zwei festen Punkten $F_1$ und $F_2$, -den {\em Brennpunkten}, konstant ist. -\index{Brennpunkt}% -In Abbildung~\ref{buch:elliptisch:fig:ellipse} eine Ellipse -mit Brennpunkten in $F_1=(-e,0)$ und $F_2=(e,0)$ dargestellt, -die durch die Punkte $(\pm a,0)$ und $(0,\pm b)$ auf den Achsen geht. -Der Punkt $(a,0)$ hat die Entfernungen $a+e$ und $a-e$ von den beiden -Brennpunkten, also die Entfernungssumme $a+e+a-e=2a$. -Jeder andere Punkt auf der Ellipse muss ebenfalls diese Entfernungssumme -haben, insbesondere auch der Punkt $(0,b)$. -Seine Entfernung zu jedem Brennpunkt muss aus Symmetriegründen gleich gross, -also $a$ sein. -Aus dem Satz von Pythagoras liest man daher ab, dass -\[ -b^2+e^2=a^2 -\qquad\Rightarrow\qquad -e^2 = a^2-b^2 -\] -sein muss. -Die Strecke $e$ heisst auch {\em (lineare) Exzentrizität} der Ellipse. -Das Verhältnis $\varepsilon= e/a$ heisst die {\em numerische Exzentrizität} -der Ellipse. - +%Für die Koordinaten eines Punktes auf der Ellipse ist dies nicht so einfach, +%weil es nicht nur eine Ellipse gibt, sondern für jede numerische Exzentrizität +%mindestens eine mit Halbeachse $1$. +%Wir wählen die Ellipsen so, dass $a$ die grosse Halbachse ist, also $a>b$. +%Als Normierungsbedingung verwenden wir, dass $b=1$ sein soll, wie in +%Abbildung~\ref{buch:elliptisch:fig:jacobidef}. +%Dann ist $a=1/\varepsilon>1$. +%In dieser Normierung haben Punkte $(x,y)$ auf der Ellipse $y$-Koordinaten +%zwischen $-1$ und $1$ und $x$-Koordinaten zwischen $-a$ und $a$. % -% Die Ellipsengleichung +%Im Zusammenhang mit elliptischen Funktionen wird die numerische Exzentrizität +%$\varepsilon$ auch mit +%\[ +%k +%= +%\varepsilon +%= +%\frac{e}{a} +%= +%\frac{\sqrt{a^2-b^2}}{a} +%= +%\frac{\sqrt{a^2-1}}{a}, +%\] +%die Zahl $k$ heisst auch der {\em Modulus}. +%Man kann $a$ auch durch $k$ ausdrücken, durch Quadrieren und Umstellen +%findet man +%\[ +%k^2a^2 = a^2-1 +%\quad\Rightarrow\quad +%1=a^2(k^2-1) +%\quad\Rightarrow\quad +%a=\frac{1}{\sqrt{k^2-1}}. +%\] % -\subsubsection{Ellipsengleichung} -Der Punkt $P=(x,y)$ auf der Ellipse hat die Entfernungen -\begin{equation} -\begin{aligned} -\overline{PF_1}^2 -&= -y^2 + (x+e)^2 -\\ -\overline{PF_2}^2 -&= -y^2 + (x-e)^2 -\end{aligned} -\label{buch:elliptisch:eqn:wurzelausdruecke} -\end{equation} -von den Brennpunkten, für die -\begin{equation} -\overline{PF_1}+\overline{PF_2} -= -2a -\label{buch:elliptisch:eqn:pf1pf2a} -\end{equation} -gelten muss. -Man kann nachrechnen, dass ein Punkt $P$, der die Gleichung -\[ -\frac{x^2}{a^2} + \frac{y^2}{b^2}=1 -\] -erfüllt, auch die Eigenschaft~\eqref{buch:elliptisch:eqn:pf1pf2a} -erfüllt. -Zur Vereinfachung setzen wir $l_1=\overline{PF_1}$ und $l_2=\overline{PF_2}$. -$l_1$ und $l_2$ sind Wurzeln aus der rechten Seite von -\eqref{buch:elliptisch:eqn:wurzelausdruecke}. -Das Quadrat von $l_1+l_2$ ist -\[ -l_1^2 + 2l_1l_2 + l_2^2 = 4a^2. -\] -Um die Wurzeln ganz zu eliminieren, bringt man das Produkt $l_1l_2$ alleine -auf die rechte Seite und quadriert. -Man muss also verifizieren, dass -\[ -(l_1^2 + l_2^2 -4a^2)^2 = 4l_1^2l_2^2. -\] -In den entstehenden Ausdrücken muss man ausserdem $e=\sqrt{a^2-b^2}$ und -\[ -y=b\sqrt{1-\frac{x^2}{a^2}} -\] -substituieren. -Diese Rechnung führt man am einfachsten mit Hilfe eines -Computeralgebraprogramms durch, welches obige Behauptung bestätigt. - +%Die Gleichung der ``Einheitsellipse'' zu diesem Modulus ist +%\[ +%\frac{x^2}{a^2}+y^2=1 +%\qquad\text{oder}\qquad +%x^2(k^2-1) + y^2 = 1. +%\] % -% Normierung +%% +%% Definition der elliptischen Funktionen +%% +%\begin{figure} +%\centering +%\includegraphics{chapters/110-elliptisch/images/jacobidef.pdf} +%\caption{Definition der elliptischen Funktionen als Trigonometrie +%an einer Ellipse mit Halbachsen $a$ und $1$. +%\label{buch:elliptisch:fig:jacobidef}} +%\end{figure} +%\subsubsection{Definition der elliptischen Funktionen} +%Die elliptischen Funktionen für einen Punkt $P$ auf der Ellipse mit Modulus $k$ +%können jetzt als Verhältnisse der Koordinaten des Punktes definieren. +%Es stellt sich aber die Frage, was man als Argument verwenden soll. +%Es soll so etwas wie den Winkel $\varphi$ zwischen der $x$-Achse und dem +%Radiusvektor zum Punkt $P$ +%darstellen, aber wir haben hier noch eine Wahlfreiheit, die wir später +%ausnützen möchten. +%Im Moment müssen wir die Frage noch nicht beantworten und nennen das +%noch unbestimmte Argument $u$. +%Wir kümmern uns später um die Frage, wie $u$ von $\varphi$ abhängt. % -\subsubsection{Normierung} -Die trigonometrischen Funktionen sind definiert als Verhältnisse -von Seiten rechtwinkliger Dreiecke. -Dadurch, dass man den die Hypothenuse auf Länge $1$ normiert, -kann man die Sinus- und Kosinus-Funktion als Koordinaten eines -Punktes auf dem Einheitskreis interpretieren. - -Für die Koordinaten eines Punktes auf der Ellipse ist dies nicht so einfach, -weil es nicht nur eine Ellipse gibt, sondern für jede numerische Exzentrizität -mindestens eine mit Halbeachse $1$. -Wir wählen die Ellipsen so, dass $a$ die grosse Halbachse ist, also $a>b$. -Als Normierungsbedingung verwenden wir, dass $b=1$ sein soll, wie in -Abbildung~\ref{buch:elliptisch:fig:jacobidef}. -Dann ist $a=1/\varepsilon>1$. -In dieser Normierung haben Punkte $(x,y)$ auf der Ellipse $y$-Koordinaten -zwischen $-1$ und $1$ und $x$-Koordinaten zwischen $-a$ und $a$. - -Im Zusammenhang mit elliptischen Funktionen wird die numerische Exzentrizität -$\varepsilon$ auch mit -\[ -k -= -\varepsilon -= -\frac{e}{a} -= -\frac{\sqrt{a^2-b^2}}{a} -= -\frac{\sqrt{a^2-1}}{a}, -\] -die Zahl $k$ heisst auch der {\em Modulus}. -Man kann $a$ auch durch $k$ ausdrücken, durch Quadrieren und Umstellen -findet man -\[ -k^2a^2 = a^2-1 -\quad\Rightarrow\quad -1=a^2(k^2-1) -\quad\Rightarrow\quad -a=\frac{1}{\sqrt{k^2-1}}. -\] - -Die Gleichung der ``Einheitsellipse'' zu diesem Modulus ist -\[ -\frac{x^2}{a^2}+y^2=1 -\qquad\text{oder}\qquad -x^2(k^2-1) + y^2 = 1. -\] - +%Die Funktionen, die wir definieren wollen, hängen ausserdem auch +%vom Modulus ab. +%Falls der verwendete Modulus aus dem Zusammenhang klar ist, lassen +%wir das $k$-Argument weg. % -% Definition der elliptischen Funktionen +%Die Punkte auf dem Einheitskreis haben alle den gleichen Abstand vom +%Nullpunkt, dies ist gleichzeitig die definierende Gleichung $r^2=x^2+y^2=1$ +%des Kreises. +%Die Punkte auf der Ellipse erfüllen die Gleichung $x^2/a^2+y^2=1$, +%die Entfernung der Punkte $r=\sqrt{x^2+y^2}$ vom Nullpunkt variert aber. % -\begin{figure} -\centering -\includegraphics{chapters/110-elliptisch/images/jacobidef.pdf} -\caption{Definition der elliptischen Funktionen als Trigonometrie -an einer Ellipse mit Halbachsen $a$ und $1$. -\label{buch:elliptisch:fig:jacobidef}} -\end{figure} -\subsubsection{Definition der elliptischen Funktionen} -Die elliptischen Funktionen für einen Punkt $P$ auf der Ellipse mit Modulus $k$ -können jetzt als Verhältnisse der Koordinaten des Punktes definieren. -Es stellt sich aber die Frage, was man als Argument verwenden soll. -Es soll so etwas wie den Winkel $\varphi$ zwischen der $x$-Achse und dem -Radiusvektor zum Punkt $P$ -darstellen, aber wir haben hier noch eine Wahlfreiheit, die wir später -ausnützen möchten. -Im Moment müssen wir die Frage noch nicht beantworten und nennen das -noch unbestimmte Argument $u$. -Wir kümmern uns später um die Frage, wie $u$ von $\varphi$ abhängt. - -Die Funktionen, die wir definieren wollen, hängen ausserdem auch -vom Modulus ab. -Falls der verwendete Modulus aus dem Zusammenhang klar ist, lassen -wir das $k$-Argument weg. - -Die Punkte auf dem Einheitskreis haben alle den gleichen Abstand vom -Nullpunkt, dies ist gleichzeitig die definierende Gleichung $r^2=x^2+y^2=1$ -des Kreises. -Die Punkte auf der Ellipse erfüllen die Gleichung $x^2/a^2+y^2=1$, -die Entfernung der Punkte $r=\sqrt{x^2+y^2}$ vom Nullpunkt variert aber. - -In Analogie zu den trigonometrischen Funktionen setzen wir jetzt für -die Funktionen -\[ -\begin{aligned} -&\text{sinus amplitudinis:}& -{\color{red}\operatorname{sn}(u,k)}&= y \\ -&\text{cosinus amplitudinis:}& -{\color{blue}\operatorname{cn}(u,k)}&= \frac{x}{a} \\ -&\text{delta amplitudinis:}& -{\color{darkgreen}\operatorname{dn}(u,k)}&=\frac{r}{a}, -\end{aligned} -\] -die auch in Abbildung~\ref{buch:elliptisch:fig:jacobidef} -dargestellt sind. -Aus der Gleichung der Ellipse folgt sofort, dass -\[ -\operatorname{sn}(u,k)^2 + \operatorname{cn}(u,k)^2 = 1 -\] -ist. -Der Satz von Pythagoras kann verwendet werden, um die Entfernung zu -berechnen, also gilt -\begin{equation} -r^2 -= -a^2 \operatorname{dn}(u,k)^2 -= -x^2 + y^2 -= -a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2 -\quad -\Rightarrow -\quad -a^2 \operatorname{dn}(u,k)^2 -= -a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2. -\label{buch:elliptisch:eqn:sncndnrelation} -\end{equation} -Ersetzt man -$ -a^2\operatorname{cn}(u,k)^2 -= -a^2-a^2\operatorname{sn}(u,k)^2 -$, ergibt sich -\[ -a^2 \operatorname{dn}(u,k)^2 -= -a^2-a^2\operatorname{sn}(u,k)^2 -+ -\operatorname{sn}(u,k)^2 -\quad -\Rightarrow -\quad -\operatorname{dn}(u,k)^2 -+ -\frac{a^2-1}{a^2}\operatorname{sn}(u,k)^2 -= -1, -\] -woraus sich die Identität -\[ -\operatorname{dn}(u,k)^2 + k^2 \operatorname{sn}(u,k)^2 = 1 -\] -ergibt. -Ebenso kann man aus~\eqref{buch:elliptisch:eqn:sncndnrelation} -die Funktion $\operatorname{cn}(u,k)$ eliminieren, was auf -\[ -a^2\operatorname{dn}(u,k)^2 -= -a^2\operatorname{cn}(u,k)^2 -+1-\operatorname{cn}(u,k)^2 -= -(a^2-1)\operatorname{cn}(u,k)^2 -+1. -\] -Nach Division durch $a^2$ ergibt sich -\begin{align*} -\operatorname{dn}(u,k)^2 -- -k^2\operatorname{cn}(u,k)^2 -&= -\frac{1}{a^2} -= -\frac{a^2-a^2+1}{a^2} -= -1-k^2 =: k^{\prime 2}. -\end{align*} -Wir stellen die hiermit gefundenen Relationen zwischen den grundlegenden -Jacobischen elliptischen Funktionen für später zusammen in den Formeln -\begin{equation} -\begin{aligned} -\operatorname{sn}^2(u,k) -+ -\operatorname{cn}^2(u,k) -&= -1 -\\ -\operatorname{dn}^2(u,k) + k^2\operatorname{sn}^2(u,k) -&= -1 -\\ -\operatorname{dn}^2(u,k) -k^2\operatorname{cn}^2(u,k) -&= -k^{\prime 2}. -\end{aligned} -\label{buch:elliptisch:eqn:jacobi-relationen} -\end{equation} -zusammen. -So wie es möglich ist, $\sin\alpha$ durch $\cos\alpha$ auszudrücken, -ist es mit -\eqref{buch:elliptisch:eqn:jacobi-relationen} -jetzt auch möglich jede grundlegende elliptische Funktion durch -jede anderen auszudrücken. -Die Resultate sind in der Tabelle~\ref{buch:elliptisch:fig:jacobi-relationen} -zusammengestellt. - -\begin{table} -\centering -\renewcommand{\arraystretch}{2.1} -\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} -\hline -&\operatorname{sn}(u,k) -&\operatorname{cn}(u,k) -&\operatorname{dn}(u,k)\\ -\hline -\operatorname{sn}(u,k) -&\operatorname{sn}(u,k) -&\sqrt{1-\operatorname{cn}^2(u,k)} -&\frac1k\sqrt{1-\operatorname{dn}^2(u,k)} -\\ -\operatorname{cn}(u,k) -&\sqrt{1-\operatorname{sn}^2(u,k)} -&\operatorname{cn}(u,k) -&\frac{1}{k}\sqrt{\operatorname{dn}^2(u,k)-k^{\prime2}} -\\ -\operatorname{dn}(u,k) -&\sqrt{1-k^2\operatorname{sn}^2(u,k)} -&\sqrt{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} -&\operatorname{dn}(u,k) -\\ -\hline -\end{tabular} -\caption{Jede der Jacobischen elliptischen Funktionen lässt sich -unter Verwendung der Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} -durch jede andere ausdrücken. -\label{buch:elliptisch:fig:jacobi-relationen}} -\end{table} - +%In Analogie zu den trigonometrischen Funktionen setzen wir jetzt für +%die Funktionen +%\[ +%\begin{aligned} +%&\text{sinus amplitudinis:}& +%{\color{red}\operatorname{sn}(u,k)}&= y \\ +%&\text{cosinus amplitudinis:}& +%{\color{blue}\operatorname{cn}(u,k)}&= \frac{x}{a} \\ +%&\text{delta amplitudinis:}& +%{\color{darkgreen}\operatorname{dn}(u,k)}&=\frac{r}{a}, +%\end{aligned} +%\] +%die auch in Abbildung~\ref{buch:elliptisch:fig:jacobidef} +%dargestellt sind. +%Aus der Gleichung der Ellipse folgt sofort, dass +%\[ +%\operatorname{sn}(u,k)^2 + \operatorname{cn}(u,k)^2 = 1 +%\] +%ist. +%Der Satz von Pythagoras kann verwendet werden, um die Entfernung zu +%berechnen, also gilt +%\begin{equation} +%r^2 +%= +%a^2 \operatorname{dn}(u,k)^2 +%= +%x^2 + y^2 +%= +%a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2 +%\quad +%\Rightarrow +%\quad +%a^2 \operatorname{dn}(u,k)^2 +%= +%a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2. +%\label{buch:elliptisch:eqn:sncndnrelation} +%\end{equation} +%Ersetzt man +%$ +%a^2\operatorname{cn}(u,k)^2 +%= +%a^2-a^2\operatorname{sn}(u,k)^2 +%$, ergibt sich +%\[ +%a^2 \operatorname{dn}(u,k)^2 +%= +%a^2-a^2\operatorname{sn}(u,k)^2 +%+ +%\operatorname{sn}(u,k)^2 +%\quad +%\Rightarrow +%\quad +%\operatorname{dn}(u,k)^2 +%+ +%\frac{a^2-1}{a^2}\operatorname{sn}(u,k)^2 +%= +%1, +%\] +%woraus sich die Identität +%\[ +%\operatorname{dn}(u,k)^2 + k^2 \operatorname{sn}(u,k)^2 = 1 +%\] +%ergibt. +%Ebenso kann man aus~\eqref{buch:elliptisch:eqn:sncndnrelation} +%die Funktion $\operatorname{cn}(u,k)$ eliminieren, was auf +%\[ +%a^2\operatorname{dn}(u,k)^2 +%= +%a^2\operatorname{cn}(u,k)^2 +%+1-\operatorname{cn}(u,k)^2 +%= +%(a^2-1)\operatorname{cn}(u,k)^2 +%+1. +%\] +%Nach Division durch $a^2$ ergibt sich +%\begin{align*} +%\operatorname{dn}(u,k)^2 +%- +%k^2\operatorname{cn}(u,k)^2 +%&= +%\frac{1}{a^2} +%= +%\frac{a^2-a^2+1}{a^2} +%= +%1-k^2 =: k^{\prime 2}. +%\end{align*} +%Wir stellen die hiermit gefundenen Relationen zwischen den grundlegenden +%Jacobischen elliptischen Funktionen für später zusammen in den Formeln +%\begin{equation} +%\begin{aligned} +%\operatorname{sn}^2(u,k) +%+ +%\operatorname{cn}^2(u,k) +%&= +%1 +%\\ +%\operatorname{dn}^2(u,k) + k^2\operatorname{sn}^2(u,k) +%&= +%1 +%\\ +%\operatorname{dn}^2(u,k) -k^2\operatorname{cn}^2(u,k) +%&= +%k^{\prime 2}. +%\end{aligned} +%\label{buch:elliptisch:eqn:jacobi-relationen} +%\end{equation} +%zusammen. +%So wie es möglich ist, $\sin\alpha$ durch $\cos\alpha$ auszudrücken, +%ist es mit +%\eqref{buch:elliptisch:eqn:jacobi-relationen} +%jetzt auch möglich jede grundlegende elliptische Funktion durch +%jede anderen auszudrücken. +%Die Resultate sind in der Tabelle~\ref{buch:elliptisch:fig:jacobi-relationen} +%zusammengestellt. % -% Ableitungen der Jacobi-ellpitischen Funktionen -% -\subsubsection{Ableitung} -Die trigonometrischen Funktionen sind deshalb so besonders nützlich -für die Lösung von Schwingungsdifferentialgleichungen, weil sie die -Beziehungen -\[ -\frac{d}{d\varphi} \cos\varphi = -\sin\varphi -\qquad\text{und}\qquad -\frac{d}{d\varphi} \sin\varphi = \cos\varphi -\] -erfüllen. -So einfach können die Beziehungen natürlich nicht sein, sonst würde sich -durch Integration ja wieder nur die trigonometrischen Funktionen ergeben. -Durch geschickte Wahl des Arguments $u$ kann man aber erreichen, dass -sie ähnlich nützliche Beziehungen zwischen den Ableitungen ergeben. - -Gesucht ist jetzt also eine Wahl für das Argument $u$ zum Beispiel in -Abhängigkeit von $\varphi$, dass sich einfache und nützliche -Ableitungsformeln ergeben. -Wir setzen daher $u(\varphi)$ voraus und beachten, dass $x$ und $y$ -ebenfalls von $\varphi$ abhängen, es ist -$y=\sin\varphi$ und $x=a\cos\varphi$. -Die Ableitungen von $x$ und $y$ nach $\varphi$ sind -\begin{align*} -\frac{dy}{d\varphi} -&= -\cos\varphi -= -\frac{1}{a} x -= -\operatorname{cn}(u,k) -\\ -\frac{dx}{d\varphi} -&= --a\sin\varphi -= --a y -= --a\operatorname{sn}(u,k). -\end{align*} -Daraus kann man jetzt die folgenden Ausdrücke für die Ableitungen der -elliptischen Funktionen nach $\varphi$ ableiten: -\begin{align*} -\frac{d}{d\varphi} \operatorname{sn}(u,z) -&= -\frac{d}{d\varphi} y(\varphi) -= -\cos\varphi -= -\frac{x}{a} -= -\operatorname{cn}(u,k) -&&\Rightarrow& -\frac{d}{du} -\operatorname{sn}(u,k) -&= -\operatorname{cn}(u,k) \frac{d\varphi}{du} -\\ -\frac{d}{d\varphi} \operatorname{cn}(u,z) -&= -\frac{d}{d\varphi} \frac{x(\varphi)}{a} -= --\sin\varphi -= --\operatorname{sn}(u,k) -&&\Rightarrow& -\frac{d}{du}\operatorname{cn}(u,k) -&= --\operatorname{sn}(u,k) \frac{d\varphi}{du} -\\ -\frac{d}{d\varphi} \operatorname{dn}(u,z) -&= -\frac{1}{a}\frac{dr}{d\varphi} -= -\frac{1}{a}\frac{d\sqrt{x^2+y^2}}{d\varphi} -\\ -&= -\frac{x}{ar} \frac{dx}{d\varphi} -+ -\frac{y}{ar} \frac{dy}{d\varphi} -\\ -&= -\frac{x}{ar} (-a\operatorname{sn}(u,k)) -+ -\frac{y}{ar} \operatorname{cn}(u,k) -\\ -&= -\frac{x}{ar}(-ay) -+ -\frac{y}{ar} \frac{x}{a} -= -\frac{xy(-1+\frac{1}{a^2})}{r} -\\ -&= --\frac{xy(a^2-1)}{a^2r} -\\ -&= --\frac{a^2-1}{ar} -\operatorname{cn}(u,k) \operatorname{sn}(u,k) -\\ -&=-k^2 -\frac{a}{r} -\operatorname{cn}(u,k) \operatorname{sn}(u,k) -\\ -&= --k^2\frac{\operatorname{cn}(u,k)\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} -&&\Rightarrow& -\frac{d}{du} \operatorname{dn}(u,k) -&= --k^2\frac{\operatorname{cn}(u,k) -\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} -\frac{d\varphi}{du} -\end{align*} -Die einfachsten Beziehungen ergeben sich offenbar, wenn man $u$ so -wählt, dass -\[ -\frac{d\varphi}{du} -= -\operatorname{dn}(u,k) -= -\frac{r}{a} -\] -Damit haben wir die grundlegenden Ableitungsregeln -\begin{align*} -\frac{d}{du}\operatorname{sn}(u,k) -&= -\phantom{-}\operatorname{cn}(u,k)\operatorname{dn}(u,k) -\\ -\frac{d}{du}\operatorname{cn}(u,k) -&= --\operatorname{sn}(u,k)\operatorname{dn}(u,k) -\\ -\frac{d}{du}\operatorname{dn}(u,k) -&= --k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k) -\end{align*} -der elliptischen Funktionen nach Jacobi. - +%\begin{table} +%\centering +%\renewcommand{\arraystretch}{2.1} +%\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} +%\hline +%&\operatorname{sn}(u,k) +%&\operatorname{cn}(u,k) +%&\operatorname{dn}(u,k)\\ +%\hline +%\operatorname{sn}(u,k) +%&\operatorname{sn}(u,k) +%&\sqrt{1-\operatorname{cn}^2(u,k)} +%&\frac1k\sqrt{1-\operatorname{dn}^2(u,k)} +%\\ +%\operatorname{cn}(u,k) +%&\sqrt{1-\operatorname{sn}^2(u,k)} +%&\operatorname{cn}(u,k) +%&\frac{1}{k}\sqrt{\operatorname{dn}^2(u,k)-k^{\prime2}} +%\\ +%\operatorname{dn}(u,k) +%&\sqrt{1-k^2\operatorname{sn}^2(u,k)} +%&\sqrt{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} +%&\operatorname{dn}(u,k) +%\\ +%\hline +%\end{tabular} +%\caption{Jede der Jacobischen elliptischen Funktionen lässt sich +%unter Verwendung der Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} +%durch jede andere ausdrücken. +%\label{buch:elliptisch:fig:jacobi-relationen}} +%\end{table} % -% Der Grenzfall $k=1$ +%% +%% Ableitungen der Jacobi-ellpitischen Funktionen +%% +%\subsubsection{Ableitung} +%Die trigonometrischen Funktionen sind deshalb so besonders nützlich +%für die Lösung von Schwingungsdifferentialgleichungen, weil sie die +%Beziehungen +%\[ +%\frac{d}{d\varphi} \cos\varphi = -\sin\varphi +%\qquad\text{und}\qquad +%\frac{d}{d\varphi} \sin\varphi = \cos\varphi +%\] +%erfüllen. +%So einfach können die Beziehungen natürlich nicht sein, sonst würde sich +%durch Integration ja wieder nur die trigonometrischen Funktionen ergeben. +%Durch geschickte Wahl des Arguments $u$ kann man aber erreichen, dass +%sie ähnlich nützliche Beziehungen zwischen den Ableitungen ergeben. % -\subsubsection{Der Grenzwert $k\to1$} -\begin{figure} -\centering -\includegraphics{chapters/110-elliptisch/images/sncnlimit.pdf} -\caption{Grenzfälle der Jacobischen elliptischen Funktionen -für die Werte $0$ und $1$ des Parameters $k$. -\label{buch:elliptisch:fig:sncnlimit}} -\end{figure} -Für $k=1$ ist $k^{\prime2}=1-k^2=$ und es folgt aus den -Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} -\[ -\operatorname{cn}^2(u,k) -- -k^2 -\operatorname{dn}^2(u,k) -= -k^{\prime2} -= -0 -\qquad\Rightarrow\qquad -\operatorname{cn}^2(u,1) -= -\operatorname{dn}^2(u,1), -\] -die beiden Funktionen -$\operatorname{cn}(u,k)$ -und -$\operatorname{dn}(u,k)$ -fallen also zusammen. -Die Ableitungsregeln werden dadurch vereinfacht: -\begin{align*} -\operatorname{sn}'(u,1) -&= -\operatorname{cn}(u,1) -\operatorname{dn}(u,1) -= -\operatorname{cn}^2(u,1) -= -1-\operatorname{sn}^2(u,1) -&&\Rightarrow& y'&=1-y^2 -\\ -\operatorname{cn}'(u,1) -&= -- -\operatorname{sn}(u,1) -\operatorname{dn}(u,1) -= -- -\operatorname{sn}(u,1)\operatorname{cn}(u,1) -&&\Rightarrow& -\frac{z'}{z}&=(\log z)' = -y -\end{align*} -Die erste Differentialgleichung für $y$ lässt sich separieren, man findet -die Lösung -\[ -\frac{y'}{1-y^2} -= -1 -\quad\Rightarrow\quad -\int \frac{dy}{1-y^2} = \int \,du -\quad\Rightarrow\quad -\operatorname{artanh}(y) = u -\quad\Rightarrow\quad -\operatorname{sn}(u,1)=\tanh u. -\] -Damit kann man jetzt auch $z$ berechnen: -\begin{align*} -(\log \operatorname{cn}(u,1))' -&= -\tanh u -&&\Rightarrow& -\log\operatorname{cn}(u,1) -&= --\int\tanh u\,du -= --\log\cosh u -\\ -& -&&\Rightarrow& -\operatorname{cn}(u,1) -&= -\frac{1}{\cosh u} -= -\operatorname{sech}u. -\end{align*} -Die Grenzfunktionen sind in Abbildung~\ref{buch:elliptisch:fig:sncnlimit} -dargestellt. - +%Gesucht ist jetzt also eine Wahl für das Argument $u$ zum Beispiel in +%Abhängigkeit von $\varphi$, dass sich einfache und nützliche +%Ableitungsformeln ergeben. +%Wir setzen daher $u(\varphi)$ voraus und beachten, dass $x$ und $y$ +%ebenfalls von $\varphi$ abhängen, es ist +%$y=\sin\varphi$ und $x=a\cos\varphi$. +%Die Ableitungen von $x$ und $y$ nach $\varphi$ sind +%\begin{align*} +%\frac{dy}{d\varphi} +%&= +%\cos\varphi +%= +%\frac{1}{a} x +%= +%\operatorname{cn}(u,k) +%\\ +%\frac{dx}{d\varphi} +%&= +%-a\sin\varphi +%= +%-a y +%= +%-a\operatorname{sn}(u,k). +%\end{align*} +%Daraus kann man jetzt die folgenden Ausdrücke für die Ableitungen der +%elliptischen Funktionen nach $\varphi$ ableiten: +%\begin{align*} +%\frac{d}{d\varphi} \operatorname{sn}(u,z) +%&= +%\frac{d}{d\varphi} y(\varphi) +%= +%\cos\varphi +%= +%\frac{x}{a} +%= +%\operatorname{cn}(u,k) +%&&\Rightarrow& +%\frac{d}{du} +%\operatorname{sn}(u,k) +%&= +%\operatorname{cn}(u,k) \frac{d\varphi}{du} +%\\ +%\frac{d}{d\varphi} \operatorname{cn}(u,z) +%&= +%\frac{d}{d\varphi} \frac{x(\varphi)}{a} +%= +%-\sin\varphi +%= +%-\operatorname{sn}(u,k) +%&&\Rightarrow& +%\frac{d}{du}\operatorname{cn}(u,k) +%&= +%-\operatorname{sn}(u,k) \frac{d\varphi}{du} +%\\ +%\frac{d}{d\varphi} \operatorname{dn}(u,z) +%&= +%\frac{1}{a}\frac{dr}{d\varphi} +%= +%\frac{1}{a}\frac{d\sqrt{x^2+y^2}}{d\varphi} +%%\\ +%%& +%\rlap{$\displaystyle\mathstrut +%= +%\frac{x}{ar} \frac{dx}{d\varphi} +%+ +%\frac{y}{ar} \frac{dy}{d\varphi} +%%\\ +%%& +%= +%\frac{x}{ar} (-a\operatorname{sn}(u,k)) +%+ +%\frac{y}{ar} \operatorname{cn}(u,k) +%$} +%\\ +%& +%\rlap{$\displaystyle\mathstrut +%= +%\frac{x}{ar}(-ay) +%+ +%\frac{y}{ar} \frac{x}{a} +%%\rlap{$\displaystyle +%= +%\frac{xy(-1+\frac{1}{a^2})}{r} +%%$} +%%\\ +%%& +%= +%-\frac{xy(a^2-1)}{a^2r} +%$} +%\\ +%&= +%-\frac{a^2-1}{ar} +%\operatorname{cn}(u,k) \operatorname{sn}(u,k) +%%\\ +%%& +%\rlap{$\displaystyle\mathstrut +%= +%-k^2 +%\frac{a}{r} +%\operatorname{cn}(u,k) \operatorname{sn}(u,k) +%$} +%\\ +%&= +%-k^2\frac{\operatorname{cn}(u,k)\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} +%&&\Rightarrow& +%\frac{d}{du} \operatorname{dn}(u,k) +%&= +%-k^2\frac{\operatorname{cn}(u,k) +%\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} +%\frac{d\varphi}{du}. +%\end{align*} +%Die einfachsten Beziehungen ergeben sich offenbar, wenn man $u$ so +%wählt, dass +%\[ +%\frac{d\varphi}{du} +%= +%\operatorname{dn}(u,k) +%= +%\frac{r}{a}. +%\] +%Damit haben wir die grundlegenden Ableitungsregeln % -% Das Argument u +%\begin{satz} +%\label{buch:elliptisch:satz:ableitungen} +%Die Jacobischen elliptischen Funktionen haben die Ableitungen +%\begin{equation} +%\begin{aligned} +%\frac{d}{du}\operatorname{sn}(u,k) +%&= +%\phantom{-}\operatorname{cn}(u,k)\operatorname{dn}(u,k) +%\\ +%\frac{d}{du}\operatorname{cn}(u,k) +%&= +%-\operatorname{sn}(u,k)\operatorname{dn}(u,k) +%\\ +%\frac{d}{du}\operatorname{dn}(u,k) +%&= +%-k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k). +%\end{aligned} +%\label{buch:elliptisch:eqn:ableitungsregeln} +%\end{equation} +%\end{satz} % -\subsubsection{Das Argument $u$} -Die Gleichung -\begin{equation} -\frac{d\varphi}{du} -= -\operatorname{dn}(u,k) -\label{buch:elliptisch:eqn:uableitung} -\end{equation} -ermöglicht, $\varphi$ in Abhängigkeit von $u$ zu berechnen, ohne jedoch -die geometrische Bedeutung zu klären. -Das beginnt bereits damit, dass der Winkel $\varphi$ nicht nicht der -Polarwinkel des Punktes $P$ in Abbildung~\ref{buch:elliptisch:fig:jacobidef} -ist, diesen nennen wir $\vartheta$. -Der Zusammenhang zwischen $\varphi$ und $\vartheta$ ist -\begin{equation} -\frac1{a}\tan\varphi = \tan\vartheta -\label{buch:elliptisch:eqn:phitheta} -\end{equation} - -Um die geometrische Bedeutung besser zu verstehen, nehmen wir jetzt an, -dass die Ellipse mit einem Parameter $t$ parametrisiert ist, dass also -$\varphi(t)$, $\vartheta(t)$ und $u(t)$ Funktionen von $t$ sind. -Die Ableitung von~\eqref{buch:elliptisch:eqn:phitheta} ist -\[ -\frac1{a}\cdot \frac{1}{\cos^2\varphi}\cdot \dot{\varphi} -= -\frac{1}{\cos^2\vartheta}\cdot \dot{\vartheta}. -\] -Daraus kann die Ableitung von $\vartheta$ nach $\varphi$ bestimmt -werden, sie ist -\[ -\frac{d\vartheta}{d\varphi} -= -\frac{\dot{\vartheta}}{\dot{\varphi}} -= -\frac{1}{a} -\cdot -\frac{\cos^2\vartheta}{\cos^2\varphi} -= -\frac{1}{a} -\cdot -\frac{(x/r)^2}{(x/a)^2} -= -\frac{1}{a}\cdot -\frac{a^2}{r^2} -= -\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)}. -\] -Damit kann man jetzt mit Hilfe von~\eqref{buch:elliptisch:eqn:uableitung} -Die Ableitung von $\vartheta$ nach $u$ ermitteln, sie ist -\[ -\frac{d\vartheta}{du} -= -\frac{d\vartheta}{d\varphi} -\cdot -\frac{d\varphi}{du} -= -\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)} -\cdot -\operatorname{dn}(u,k) -= -\frac{1}{a} -\cdot -\frac{1}{\operatorname{dn}(u,k)} -= -\frac{1}{a} -\cdot\frac{a}{r} -= -\frac{1}{r}, -\] -wobei wir auch die Definition der Funktion $\operatorname{dn}(u,k)$ -verwendet haben. - -In der Parametrisierung mit dem Parameter $t$ kann man jetzt die Ableitung -von $u$ nach $t$ berechnen als -\[ -\frac{du}{dt} -= -\frac{du}{d\vartheta} -\frac{d\vartheta}{dt} -= -r -\dot{\vartheta}. -\] -Darin ist $\dot{\vartheta}$ die Winkelgeschwindigkeit des Punktes um -das Zentrum $O$ und $r$ ist die aktuelle Entfernung des Punktes $P$ -von $O$. -$r\dot{\vartheta}$ ist also die Geschwindigkeitskomponenten des Punktes -$P$ senkrecht auf den aktuellen Radiusvektor. -Der Parameter $u$, der zum Punkt $P$ gehört, ist also das Integral -\[ -u(P) = \int_0^P r\,d\vartheta. -\] -Für einen Kreis ist die Geschwindigkeit von $P$ immer senkrecht -auf dem Radiusvektor und der Radius ist konstant, so dass -$u(P)=\vartheta(P)$ ist. - +%% +%% Der Grenzfall $k=1$ +%% +%\subsubsection{Der Grenzwert $k\to1$} +%\begin{figure} +%\centering +%\includegraphics{chapters/110-elliptisch/images/sncnlimit.pdf} +%\caption{Grenzfälle der Jacobischen elliptischen Funktionen +%für die Werte $0$ und $1$ des Parameters $k$. +%\label{buch:elliptisch:fig:sncnlimit}} +%\end{figure} +%Für $k=1$ ist $k^{\prime2}=1-k^2=$ und es folgt aus den +%Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} +%\[ +%\operatorname{cn}^2(u,k) +%- +%k^2 +%\operatorname{dn}^2(u,k) +%= +%k^{\prime2} +%= +%0 +%\qquad\Rightarrow\qquad +%\operatorname{cn}^2(u,1) +%= +%\operatorname{dn}^2(u,1), +%\] +%die beiden Funktionen +%$\operatorname{cn}(u,k)$ +%und +%$\operatorname{dn}(u,k)$ +%fallen also zusammen. +%Die Ableitungsregeln werden dadurch vereinfacht: +%\begin{align*} +%\operatorname{sn}'(u,1) +%&= +%\operatorname{cn}(u,1) +%\operatorname{dn}(u,1) +%= +%\operatorname{cn}^2(u,1) +%= +%1-\operatorname{sn}^2(u,1) +%&&\Rightarrow& y'&=1-y^2 +%\\ +%\operatorname{cn}'(u,1) +%&= +%- +%\operatorname{sn}(u,1) +%\operatorname{dn}(u,1) +%= +%- +%\operatorname{sn}(u,1)\operatorname{cn}(u,1) +%&&\Rightarrow& +%\frac{z'}{z}&=(\log z)' = -y +%\end{align*} +%Die erste Differentialgleichung für $y$ lässt sich separieren, man findet +%die Lösung +%\[ +%\frac{y'}{1-y^2} +%= +%1 +%\quad\Rightarrow\quad +%\int \frac{dy}{1-y^2} = \int \,du +%\quad\Rightarrow\quad +%\operatorname{artanh}(y) = u +%\quad\Rightarrow\quad +%\operatorname{sn}(u,1)=\tanh u. +%\] +%Damit kann man jetzt auch $z$ berechnen: +%\begin{align*} +%(\log \operatorname{cn}(u,1))' +%&= +%\tanh u +%&&\Rightarrow& +%\log\operatorname{cn}(u,1) +%&= +%-\int\tanh u\,du +%= +%-\log\cosh u +%\\ +%& +%&&\Rightarrow& +%\operatorname{cn}(u,1) +%&= +%\frac{1}{\cosh u} +%= +%\operatorname{sech}u. +%\end{align*} +%Die Grenzfunktionen sind in Abbildung~\ref{buch:elliptisch:fig:sncnlimit} +%dargestellt. % -% Die abgeleiteten elliptischen Funktionen +%% +%% Das Argument u +%% +%\subsubsection{Das Argument $u$} +%Die Gleichung +%\begin{equation} +%\frac{d\varphi}{du} +%= +%\operatorname{dn}(u,k) +%\label{buch:elliptisch:eqn:uableitung} +%\end{equation} +%ermöglicht, $\varphi$ in Abhängigkeit von $u$ zu berechnen, ohne jedoch +%die geometrische Bedeutung zu klären. +%Das beginnt bereits damit, dass der Winkel $\varphi$ nicht nicht der +%Polarwinkel des Punktes $P$ in Abbildung~\ref{buch:elliptisch:fig:jacobidef} +%ist, diesen nennen wir $\vartheta$. +%Der Zusammenhang zwischen $\varphi$ und $\vartheta$ ist +%\begin{equation} +%\frac1{a}\tan\varphi = \tan\vartheta +%\label{buch:elliptisch:eqn:phitheta} +%\end{equation} % -\begin{figure} -\centering -\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobi12.pdf} -\caption{Die Verhältnisse der Funktionen -$\operatorname{sn}(u,k)$, -$\operatorname{cn}(u,k)$ -udn -$\operatorname{dn}(u,k)$ -geben Anlass zu neun weitere Funktionen, die sich mit Hilfe -des Strahlensatzes geometrisch interpretieren lassen. -\label{buch:elliptisch:fig:jacobi12}} -\end{figure} -\begin{table} -\centering -\renewcommand{\arraystretch}{2.5} -\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} -\hline -\cdot & -\frac{1}{1} & -\frac{1}{\operatorname{sn}(u,k)} & -\frac{1}{\operatorname{cn}(u,k)} & -\frac{1}{\operatorname{dn}(u,k)} -\\[5pt] -\hline -1& -&%\operatorname{nn}(u,k)=\frac{1}{1} & -\operatorname{ns}(u,k)=\frac{1}{\operatorname{sn}(u,k)} & -\operatorname{nc}(u,k)=\frac{1}{\operatorname{cn}(u,k)} & -\operatorname{nd}(u,k)=\frac{1}{\operatorname{dn}(u,k)} -\\ -\operatorname{sn}(u,k) & -\operatorname{sn}(u,k)=\frac{\operatorname{sn}(u,k)}{1}& -&%\operatorname{ss}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{sn}(u,k)}& -\operatorname{sc}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)}& -\operatorname{sd}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} -\\ -\operatorname{cn}(u,k) & -\operatorname{cn}(u,k)=\frac{\operatorname{cn}(u,k)}{1} & -\operatorname{cs}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{sn}(u,k)}& -&%\operatorname{cc}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{cn}(u,k)}& -\operatorname{cd}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{dn}(u,k)} -\\ -\operatorname{dn}(u,k) & -\operatorname{dn}(u,k)=\frac{\operatorname{dn}(u,k)}{1} & -\operatorname{ds}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{sn}(u,k)}& -\operatorname{dc}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)}& -%\operatorname{dd}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{dn}(u,k)} -\\[5pt] -\hline -\end{tabular} -\caption{Zusammenstellung der abgeleiteten Jacobischen elliptischen -Funktionen in hinteren drei Spalten als Quotienten der grundlegenden -Jacobischen elliptischen Funktionen. -Die erste Spalte zum Nenner $1$ enthält die grundlegenden -Jacobischen elliptischen Funktionen. -\label{buch:elliptisch:table:abgeleitetjacobi}} -\end{table} -\subsubsection{Die abgeleiteten elliptischen Funktionen} -Zusätzlich zu den grundlegenden Jacobischen elliptischen Funktioenn -lassen sich weitere elliptische Funktionen bilden, die unglücklicherweise -die {\em abgeleiteten elliptischen Funktionen} genannt werden. -Ähnlich wie die trigonometrischen Funktionen $\tan\alpha$, $\cot\alpha$, -$\sec\alpha$ und $\csc\alpha$ als Quotienten von $\sin\alpha$ und -$\cos\alpha$ definiert sind, sind die abgeleiteten elliptischen Funktionen -die in Tabelle~\ref{buch:elliptisch:table:abgeleitetjacobi} zusammengestellten -Quotienten der grundlegenden Jacobischen elliptischen Funktionen. -Die Bezeichnungskonvention ist, dass die Funktion $\operatorname{pq}(u,k)$ -ein Quotient ist, dessen Zähler durch den Buchstaben p bestimmt ist, -der Nenner durch den Buchstaben q. -Der Buchstabe n steht für eine $1$, die Buchstaben s, c und d stehen für -die Anfangsbuchstaben der grundlegenden Jacobischen elliptischen -Funktionen. -Meint man irgend eine der Jacobischen elliptischen Funktionen, schreibt -man manchmal auch $\operatorname{zn}(u,k)$. - -In Abbildung~\ref{buch:elliptisch:fig:jacobi12} sind die Quotienten auch -geometrisch interpretiert. -Der Wert der Funktion $\operatorname{nq}(u,k)$ ist die auf dem Strahl -mit Polarwinkel $\varphi$ abgetragene Länge bis zu den vertikalen -Geraden, die den verschiedenen möglichen Nennern entsprechen. -Entsprechend ist der Wert der Funktion $\operatorname{dq}(u,k)$ die -Länge auf dem Strahl mit Polarwinkel $\vartheta$. - -Die Relationen~\ref{buch:elliptisch:eqn:jacobi-relationen} -ermöglichen, jede Funktion $\operatorname{zn}(u,k)$ durch jede -andere auszudrücken. -Die schiere Anzahl solcher Beziehungen macht es unmöglich, sie -übersichtlich in einer Tabelle zusammenzustellen, daher soll hier -nur an einem Beispiel das Vorgehen gezeigt werden: - -\begin{beispiel} -Die Funktion $\operatorname{sc}(u,k)$ soll durch $\operatorname{cd}(u,k)$ -ausgedrückt werden. -Zunächst ist -\[ -\operatorname{sc}(u,k) -= -\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} -\] -nach Definition. -Im Resultat sollen nur noch $\operatorname{cn}(u,k)$ und -$\operatorname{dn}(u,k)$ vorkommen. -Daher eliminieren wir zunächst die Funktion $\operatorname{sn}(u,k)$ -mit Hilfe von \eqref{buch:elliptisch:eqn:jacobi-relationen} und erhalten -\begin{equation} -\operatorname{sc}(u,k) -= -\frac{\sqrt{1-\operatorname{cn}^2(u,k)}}{\operatorname{cn}(u,k)}. -\label{buch:elliptisch:eqn:allgausdruecken} -\end{equation} -Nun genügt es, die Funktion $\operatorname{cn}(u,k)$ durch -$\operatorname{cd}(u,k)$ auszudrücken. -Aus der Definition und der -dritten Relation in \eqref{buch:elliptisch:eqn:jacobi-relationen} -erhält man -\begin{align*} -\operatorname{cd}^2(u,k) -&= -\frac{\operatorname{cn}^2(u,k)}{\operatorname{dn}^2(u,k)} -= -\frac{\operatorname{cn}^2(u,k)}{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} -\\ -\Rightarrow -\qquad -k^{\prime 2} -\operatorname{cd}^2(u,k) -+ -k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) -&= -\operatorname{cn}^2(u,k) -\\ -\operatorname{cn}^2(u,k) -- -k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) -&= -k^{\prime 2} -\operatorname{cd}^2(u,k) -\\ -\operatorname{cn}^2(u,k) -&= -\frac{ -k^{\prime 2} -\operatorname{cd}^2(u,k) -}{ -1 - k^2\operatorname{cd}^2(u,k) -} -\end{align*} -Für den Zähler brauchen wir $1-\operatorname{cn}^2(u,k)$, also -\[ -1-\operatorname{cn}^2(u,k) -= -\frac{ -1 -- -k^2\operatorname{cd}^2(u,k) -- -k^{\prime 2} -\operatorname{cd}^2(u,k) -}{ -1 -- -k^2\operatorname{cd}^2(u,k) -} -= -\frac{1-\operatorname{cd}^2(u,k)}{1-k^2\operatorname{cd}^2(u,k)} -\] -Einsetzen in~\eqref{buch:elliptisch:eqn:allgausdruecken} gibt -\begin{align*} -\operatorname{sc}(u,k) -&= -\frac{ -\sqrt{1-\operatorname{cd}^2(u,k)} -}{\sqrt{1-k^2\operatorname{cd}^2(u,k)}} -\cdot -\frac{ -\sqrt{1 - k^2\operatorname{cd}^2(u,k)} -}{ -k' -\operatorname{cd}(u,k) -} -= -\frac{ -\sqrt{1-\operatorname{cd}^2(u,k)} -}{ -k' -\operatorname{cd}(u,k) -}. -\qedhere -\end{align*} -\end{beispiel} - -\subsubsection{Ableitung der abgeleiteten elliptischen Funktionen} -Aus den Ableitungen der grundlegenden Jacobischen elliptischen Funktionen -können mit der Quotientenregel nun auch beliebige Ableitungen der -abgeleiteten Jacobischen elliptischen Funktionen gefunden werden. -Als Beispiel berechnen wir die Ableitung von $\operatorname{sc}(u,k)$. -Sie ist -\begin{align*} -\frac{d}{du} -\operatorname{sc}(u,k) -&= -\frac{d}{du} -\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} -= -\frac{ -\operatorname{sn}'(u,k)\operatorname{cn}(u,k) -- -\operatorname{sn}(u,k)\operatorname{cn}'(u,k)}{ -\operatorname{cn}^2(u,k) -} -\\ -&= -\frac{ -\operatorname{cn}^2(u,k)\operatorname{dn}(u,k) -+ -\operatorname{sn}^2(u,k)\operatorname{dn}(u,k) -}{ -\operatorname{cn}^2(u,k) -} -= -\frac{( -\operatorname{sn}^2(u,k) -+ -\operatorname{cn}^2(u,k) -)\operatorname{dn}(u,k)}{ -\operatorname{cn}^2(u,k) -} -\\ -&= -\frac{1}{\operatorname{cn}(u,k)} -\cdot -\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)} -= -\operatorname{nc}(u,k) -\operatorname{dc}(u,k). -\end{align*} -Man beachte, dass das Quadrat der Nennerfunktion im Resultat -der Quotientenregel zur Folge hat, dass die -beiden Funktionen im Resultat beide den gleichen Nenner haben wie -die Funktion, die abgeleitet wird. - -Mit etwas Fleiss kann man nach diesem Muster alle Ableitungen -\begin{equation} -%\small -\begin{aligned} -\operatorname{sn}'(u,k) -&= -\phantom{-} -\operatorname{cn}(u,k)\,\operatorname{dn}(u,k) -&&\qquad& -\operatorname{ns}'(u,k) -&= -- -\operatorname{cs}(u,k)\,\operatorname{ds}(u,k) -\\ -\operatorname{cn}'(u,k) -&= -- -\operatorname{sn}(u,k)\,\operatorname{dn}(u,k) -&&& -\operatorname{nc}'(u,k) -&= -\phantom{-} -\operatorname{sc}(u,k)\,\operatorname{dc}(u,k) -\\ -\operatorname{dn}'(u,k) -&= --k^2 -\operatorname{sn}(u,k)\,\operatorname{cn}(u,k) -&&& -\operatorname{nd}'(u,k) -&= -\phantom{-} -k^2 -\operatorname{sd}(u,k)\,\operatorname{cd}(u,k) -\\ -\operatorname{sc}'(u,k) -&= -\phantom{-} -\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) -&&& -\operatorname{cs}'(u,k) -&= -- -\operatorname{ds}(u,k)\,\operatorname{ns}(u,k) -\\ -\operatorname{cd}'(u,k) -&= --k^{\prime2} -\operatorname{sd}(u,k)\,\operatorname{nd}(u,k) -&&& -\operatorname{dc}'(u,k) -&= -\phantom{-} -k^{\prime2} -\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) -\\ -\operatorname{ds}'(d,k) -&= -- -\operatorname{cs}(u,k)\,\operatorname{ns}(u,k) -&&& -\operatorname{sd}'(d,k) -&= -\phantom{-} -\operatorname{cd}(u,k)\,\operatorname{nd}(u,k) -\end{aligned} -\label{buch:elliptisch:eqn:alleableitungen} -\end{equation} -finden. -Man beachte, dass in jeder Identität alle Funktionen den gleichen -zweiten Buchstaben haben. - -\subsubsection{TODO} -XXX algebraische Beziehungen \\ -XXX Additionstheoreme \\ -XXX Perioden -% use https://math.stackexchange.com/questions/3013692/how-to-show-that-jacobi-sine-function-is-doubly-periodic - - -XXX Ableitungen \\ -XXX Werte \\ - +%Um die geometrische Bedeutung besser zu verstehen, nehmen wir jetzt an, +%dass die Ellipse mit einem Parameter $t$ parametrisiert ist, dass also +%$\varphi(t)$, $\vartheta(t)$ und $u(t)$ Funktionen von $t$ sind. +%Die Ableitung von~\eqref{buch:elliptisch:eqn:phitheta} ist +%\[ +%\frac1{a}\cdot \frac{1}{\cos^2\varphi}\cdot \dot{\varphi} +%= +%\frac{1}{\cos^2\vartheta}\cdot \dot{\vartheta}. +%\] +%Daraus kann die Ableitung von $\vartheta$ nach $\varphi$ bestimmt +%werden, sie ist +%\[ +%\frac{d\vartheta}{d\varphi} +%= +%\frac{\dot{\vartheta}}{\dot{\varphi}} +%= +%\frac{1}{a} +%\cdot +%\frac{\cos^2\vartheta}{\cos^2\varphi} +%= +%\frac{1}{a} +%\cdot +%\frac{(x/r)^2}{(x/a)^2} +%= +%\frac{1}{a}\cdot +%\frac{a^2}{r^2} +%= +%\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)}. +%\] +%Damit kann man jetzt mit Hilfe von~\eqref{buch:elliptisch:eqn:uableitung} +%Die Ableitung von $\vartheta$ nach $u$ ermitteln, sie ist +%\[ +%\frac{d\vartheta}{du} +%= +%\frac{d\vartheta}{d\varphi} +%\cdot +%\frac{d\varphi}{du} +%= +%\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)} +%\cdot +%\operatorname{dn}(u,k) +%= +%\frac{1}{a} +%\cdot +%\frac{1}{\operatorname{dn}(u,k)} +%= +%\frac{1}{a} +%\cdot\frac{a}{r} +%= +%\frac{1}{r}, +%\] +%wobei wir auch die Definition der Funktion $\operatorname{dn}(u,k)$ +%verwendet haben. % -% Lösung von Differentialgleichungen +%In der Parametrisierung mit dem Parameter $t$ kann man jetzt die Ableitung +%von $u$ nach $t$ berechnen als +%\[ +%\frac{du}{dt} +%= +%\frac{du}{d\vartheta} +%\frac{d\vartheta}{dt} +%= +%r +%\dot{\vartheta}. +%\] +%Darin ist $\dot{\vartheta}$ die Winkelgeschwindigkeit des Punktes um +%das Zentrum $O$ und $r$ ist die aktuelle Entfernung des Punktes $P$ +%von $O$. +%$r\dot{\vartheta}$ ist also die Geschwindigkeitskomponenten des Punktes +%$P$ senkrecht auf den aktuellen Radiusvektor. +%Der Parameter $u$, der zum Punkt $P$ gehört, ist also das Integral +%\[ +%u(P) = \int_0^P r\,d\vartheta. +%\] +%Für einen Kreis ist die Geschwindigkeit von $P$ immer senkrecht +%auf dem Radiusvektor und der Radius ist konstant, so dass +%$u(P)=\vartheta(P)$ ist. % -\subsection{Lösungen von Differentialgleichungen} -Die elliptischen Funktionen ermöglichen die Lösung gewisser nichtlinearer -Differentialgleichungen in geschlossener Form. -Ziel dieses Abschnitts ist, Differentialgleichungen der Form -\( -\ddot{x}(t) -= -p(x(t)) -\) -mit einem Polynom dritten Grades als rechter Seite lösen zu können. - +%% +%% Die abgeleiteten elliptischen Funktionen +%% +%\begin{figure} +%\centering +%\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobi12.pdf} +%\caption{Die Verhältnisse der Funktionen +%$\operatorname{sn}(u,k)$, +%$\operatorname{cn}(u,k)$ +%udn +%$\operatorname{dn}(u,k)$ +%geben Anlass zu neun weitere Funktionen, die sich mit Hilfe +%des Strahlensatzes geometrisch interpretieren lassen. +%\label{buch:elliptisch:fig:jacobi12}} +%\end{figure} +%\begin{table} +%\centering +%\renewcommand{\arraystretch}{2.5} +%\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} +%\hline +%\cdot & +%\frac{1}{1} & +%\frac{1}{\operatorname{sn}(u,k)} & +%\frac{1}{\operatorname{cn}(u,k)} & +%\frac{1}{\operatorname{dn}(u,k)} +%\\[5pt] +%\hline +%1& +%&%\operatorname{nn}(u,k)=\frac{1}{1} & +%\operatorname{ns}(u,k)=\frac{1}{\operatorname{sn}(u,k)} & +%\operatorname{nc}(u,k)=\frac{1}{\operatorname{cn}(u,k)} & +%\operatorname{nd}(u,k)=\frac{1}{\operatorname{dn}(u,k)} +%\\ +%\operatorname{sn}(u,k) & +%\operatorname{sn}(u,k)=\frac{\operatorname{sn}(u,k)}{1}& +%&%\operatorname{ss}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{sn}(u,k)}& +%\operatorname{sc}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)}& +%\operatorname{sd}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} +%\\ +%\operatorname{cn}(u,k) & +%\operatorname{cn}(u,k)=\frac{\operatorname{cn}(u,k)}{1} & +%\operatorname{cs}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{sn}(u,k)}& +%&%\operatorname{cc}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{cn}(u,k)}& +%\operatorname{cd}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{dn}(u,k)} +%\\ +%\operatorname{dn}(u,k) & +%\operatorname{dn}(u,k)=\frac{\operatorname{dn}(u,k)}{1} & +%\operatorname{ds}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{sn}(u,k)}& +%\operatorname{dc}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)}& +%%\operatorname{dd}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{dn}(u,k)} +%\\[5pt] +%\hline +%\end{tabular} +%\caption{Zusammenstellung der abgeleiteten Jacobischen elliptischen +%Funktionen in hinteren drei Spalten als Quotienten der grundlegenden +%Jacobischen elliptischen Funktionen. +%Die erste Spalte zum Nenner $1$ enthält die grundlegenden +%Jacobischen elliptischen Funktionen. +%\label{buch:elliptisch:table:abgeleitetjacobi}} +%\end{table} +%\subsubsection{Die abgeleiteten elliptischen Funktionen} +%Zusätzlich zu den grundlegenden Jacobischen elliptischen Funktioenn +%lassen sich weitere elliptische Funktionen bilden, die unglücklicherweise +%die {\em abgeleiteten elliptischen Funktionen} genannt werden. +%Ähnlich wie die trigonometrischen Funktionen $\tan\alpha$, $\cot\alpha$, +%$\sec\alpha$ und $\csc\alpha$ als Quotienten von $\sin\alpha$ und +%$\cos\alpha$ definiert sind, sind die abgeleiteten elliptischen Funktionen +%die in Tabelle~\ref{buch:elliptisch:table:abgeleitetjacobi} zusammengestellten +%Quotienten der grundlegenden Jacobischen elliptischen Funktionen. +%Die Bezeichnungskonvention ist, dass die Funktion $\operatorname{pq}(u,k)$ +%ein Quotient ist, dessen Zähler durch den Buchstaben p bestimmt ist, +%der Nenner durch den Buchstaben q. +%Der Buchstabe n steht für eine $1$, die Buchstaben s, c und d stehen für +%die Anfangsbuchstaben der grundlegenden Jacobischen elliptischen +%Funktionen. +%Meint man irgend eine der Jacobischen elliptischen Funktionen, schreibt +%man manchmal auch $\operatorname{zn}(u,k)$. % -% Die Differentialgleichung der elliptischen Funktionen +%In Abbildung~\ref{buch:elliptisch:fig:jacobi12} sind die Quotienten auch +%geometrisch interpretiert. +%Der Wert der Funktion $\operatorname{nq}(u,k)$ ist die auf dem Strahl +%mit Polarwinkel $\varphi$ abgetragene Länge bis zu den vertikalen +%Geraden, die den verschiedenen möglichen Nennern entsprechen. +%Entsprechend ist der Wert der Funktion $\operatorname{dq}(u,k)$ die +%Länge auf dem Strahl mit Polarwinkel $\vartheta$. % -\subsubsection{Die Differentialgleichungen der elliptischen Funktionen} -Um Differentialgleichungen mit elliptischen Funktion lösen zu -können, muss man als erstes die Differentialgleichungen derselben -finden. -Quadriert man die Ableitungsregel für $\operatorname{sn}(u,k)$, erhält -man -\[ -\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 -= -\operatorname{cn}(u,k)^2 \operatorname{dn}(u,k)^2. -\] -Die Funktionen auf der rechten Seite können durch $\operatorname{sn}(u,k)$ -ausgedrückt werden. -\begin{align*} -\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 -&= -\biggl( -1-\operatorname{sn}(u,k)^2 -\biggr) -\biggl( -1-k^2 \operatorname{sn}(u,k)^2 -\biggr) -\\ -&= -k^2\operatorname{sn}(u,k)^4 --(1+k^2) -\operatorname{sn}(u,k)^2 -+1. -\end{align*} -Für die Funktion $\operatorname{cn}(u,k)$ ergibt analoge Rechnung -\begin{align*} -\frac{d}{du}\operatorname{cn}(u,k) -&= --\operatorname{sn}(u,k) \operatorname{dn}(u,k) -\\ -\biggl(\frac{d}{du}\operatorname{cn}(u,k)\biggr)^2 -&= -\operatorname{sn}(u,k)^2 \operatorname{dn}(u,k)^2 -\\ -&= -\biggl(1-\operatorname{cn}(u,k)^2\biggr) -\biggl(1-k^2+k^2 \operatorname{cn}(u,k)^2\biggr) -\\ -&= --k^2\operatorname{cn}(u,k)^4 -- -(1-k^2-k^2)\operatorname{cn}(u,k)^2 -+ -(1-k^2) -\\ -\frac{d}{du}\operatorname{dn}(u,k) -&= --k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k) -\\ -\biggl( -\frac{d}{du}\operatorname{dn}(u,k) -\biggr)^2 -&= -\bigl(k^2 \operatorname{sn}(u,k)^2\bigr) -\bigl(k^2 \operatorname{cn}(u,k)^2\bigr) -\\ -&= -\biggl( -1-\operatorname{dn}(u,k)^2 -\biggr) -\biggl( -\operatorname{dn}(u,k)^2-k^2+1 -\biggr) -\\ -&= --\operatorname{dn}(u,k)^4 -- -2\operatorname{dn}(u,k)^2 --k^2+1. -\end{align*} -\begin{table} -\centering -\renewcommand{\arraystretch}{2} -\begin{tabular}{|>{$}l<{$}|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}>{$}c<{$}>{$}c<{$}|} -\hline -\text{Funktion $y=$}&\text{Differentialgleichung}&\alpha&\beta&\gamma&\multicolumn{3}{c|}{Signatur}\\ -\hline -\operatorname{sn}(u,k) - & y'^2 = \phantom{-}(1-y^2)(1-k^2y^2) - &k^2&1&1 &+&+&+ -\\ -\operatorname{cn}(u,k) - &y'^2 = \phantom{-}(1-y^2)(1-k^2+k^2y^2) - &-k^2 &2k^2-1&1-k^2 &-&&+ -\\ -\operatorname{dn}(u,k) - & y'^2 = -(1-y^2)(1-k^2-y^2) - &1 &1-k^2 &-(1-k^2)&+&+&- -\\ -\hline -\end{tabular} -\caption{Elliptische Funktionen als Lösungsfunktionen für verschiedene -nichtlineare Differentialgleichungen der Art -\eqref{buch:elliptisch:eqn:1storderdglell}. -Die Vorzeichen der Koeffizienten $\alpha$, $\beta$ und $\gamma$ -entscheidet darüber, welche Funktion für die Lösung verwendet werden -muss. -\label{buch:elliptisch:tabelle:loesungsfunktionen}} -\end{table} - -Die elliptischen Funktionen genügen also alle einer nichtlinearen -Differentialgleichung erster Ordnung der selben Art. -Das Quadrat der Ableitung ist ein Polynom vierten Grades der Funktion. -Um dies besser einzufangen, schreiben wir $\operatorname{zn}(u,k)$, -wenn wir eine beliebige der drei Funktionen -$\operatorname{sn}(u,k)$, -$\operatorname{cn}(u,k)$ -oder -$\operatorname{dn}(u,k)$ -meinen. -Die Funktion $\operatorname{zn}(u,k)$ ist also Lösung der -Differentialgleichung -\begin{equation} -\operatorname{zn}'(u,k)^2 -= -\alpha \operatorname{zn}(u,k)^4 + \beta \operatorname{zn}(u,)^2 + \gamma, -\label{buch:elliptisch:eqn:1storderdglell} -\end{equation} -wobei wir mit $\operatorname{zn}'(u,k)$ die Ableitung von -$\operatorname{zn}(u,k)$ nach dem ersten Argument meinen. -Die Koeffizienten $\alpha$, $\beta$ und $\gamma$ hängen von $k$ ab, -vor allem aber haben Sie verschiedene Vorzeichen. -Je nach Vorzeichen sind also eine andere elliptische Funktion als -Lösung zu verwenden. - +%Die Relationen~\ref{buch:elliptisch:eqn:jacobi-relationen} +%ermöglichen, jede Funktion $\operatorname{zn}(u,k)$ durch jede +%andere auszudrücken. +%Die schiere Anzahl solcher Beziehungen macht es unmöglich, sie +%übersichtlich in einer Tabelle zusammenzustellen, daher soll hier +%nur an einem Beispiel das Vorgehen gezeigt werden: % -% Jacobischen elliptische Funktionen und elliptische Integrale +%\begin{beispiel} +%Die Funktion $\operatorname{sc}(u,k)$ soll durch $\operatorname{cd}(u,k)$ +%ausgedrückt werden. +%Zunächst ist +%\[ +%\operatorname{sc}(u,k) +%= +%\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} +%\] +%nach Definition. +%Im Resultat sollen nur noch $\operatorname{cn}(u,k)$ und +%$\operatorname{dn}(u,k)$ vorkommen. +%Daher eliminieren wir zunächst die Funktion $\operatorname{sn}(u,k)$ +%mit Hilfe von \eqref{buch:elliptisch:eqn:jacobi-relationen} und erhalten +%\begin{equation} +%\operatorname{sc}(u,k) +%= +%\frac{\sqrt{1-\operatorname{cn}^2(u,k)}}{\operatorname{cn}(u,k)}. +%\label{buch:elliptisch:eqn:allgausdruecken} +%\end{equation} +%Nun genügt es, die Funktion $\operatorname{cn}(u,k)$ durch +%$\operatorname{cd}(u,k)$ auszudrücken. +%Aus der Definition und der +%dritten Relation in \eqref{buch:elliptisch:eqn:jacobi-relationen} +%erhält man +%\begin{align*} +%\operatorname{cd}^2(u,k) +%&= +%\frac{\operatorname{cn}^2(u,k)}{\operatorname{dn}^2(u,k)} +%= +%\frac{\operatorname{cn}^2(u,k)}{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} +%\\ +%\Rightarrow +%\qquad +%k^{\prime 2} +%\operatorname{cd}^2(u,k) +%+ +%k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) +%&= +%\operatorname{cn}^2(u,k) +%\\ +%\operatorname{cn}^2(u,k) +%- +%k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) +%&= +%k^{\prime 2} +%\operatorname{cd}^2(u,k) +%\\ +%\operatorname{cn}^2(u,k) +%&= +%\frac{ +%k^{\prime 2} +%\operatorname{cd}^2(u,k) +%}{ +%1 - k^2\operatorname{cd}^2(u,k) +%} +%\end{align*} +%Für den Zähler brauchen wir $1-\operatorname{cn}^2(u,k)$, also +%\[ +%1-\operatorname{cn}^2(u,k) +%= +%\frac{ +%1 +%- +%k^2\operatorname{cd}^2(u,k) +%- +%k^{\prime 2} +%\operatorname{cd}^2(u,k) +%}{ +%1 +%- +%k^2\operatorname{cd}^2(u,k) +%} +%= +%\frac{1-\operatorname{cd}^2(u,k)}{1-k^2\operatorname{cd}^2(u,k)} +%\] +%Einsetzen in~\eqref{buch:elliptisch:eqn:allgausdruecken} gibt +%\begin{align*} +%\operatorname{sc}(u,k) +%&= +%\frac{ +%\sqrt{1-\operatorname{cd}^2(u,k)} +%}{\sqrt{1-k^2\operatorname{cd}^2(u,k)}} +%\cdot +%\frac{ +%\sqrt{1 - k^2\operatorname{cd}^2(u,k)} +%}{ +%k' +%\operatorname{cd}(u,k) +%} +%= +%\frac{ +%\sqrt{1-\operatorname{cd}^2(u,k)} +%}{ +%k' +%\operatorname{cd}(u,k) +%}. +%\qedhere +%\end{align*} +%\end{beispiel} % -\subsubsection{Jacobische elliptische Funktionen als elliptische Integrale} -Die in Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} -zusammengestellten Differentialgleichungen ermöglichen nun, den -Zusammenhang zwischen den Funktionen -$\operatorname{sn}(u,k)$, $\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$ -und den unvollständigen elliptischen Integralen herzustellen. -Die Differentialgleichungen sind alle von der Form -\begin{equation} -\biggl( -\frac{d y}{d u} -\biggr)^2 -= -p(u), -\label{buch:elliptisch:eqn:allgdgl} -\end{equation} -wobei $p(u)$ ein Polynom vierten Grades in $y$ ist. -Diese Differentialgleichung lässt sich mit Separation lösen. -Dazu zieht man aus~\eqref{buch:elliptisch:eqn:allgdgl} die -Wurzel -\begin{align} -\frac{dy}{du} -= -\sqrt{p(y)} -\notag -\intertext{und trennt die Variablen. Man erhält} -\int\frac{dy}{\sqrt{p(y)}} = u+C. -\label{buch:elliptisch:eqn:yintegral} -\end{align} -Solange $p(y)>0$ ist, ist der Integrand auf der linken Seite -von~\eqref{buch:elliptisch:eqn:yintegral} ebenfalls positiv und -das Integral ist eine monoton wachsende Funktion $F(y)$. -Insbesondere ist $F(y)$ invertierbar. -Die Lösung $y(u)$ der Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} -ist daher -\[ -y(u) = F^{-1}(u+C). -\] -Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen -der unvollständigen elliptischen Integrale. - -\subsubsection{Differentialgleichung zweiter Ordnung} -Leitet die Differentialgleichung ~\eqref{buch:elliptisch:eqn:1storderdglell} -man dies nochmals nach $u$ ab, erhält man die Differentialgleichung -\[ -2\operatorname{zn}''(u,k)\operatorname{zn}'(u,k) -= -4\alpha \operatorname{zn}(u,k)^3\operatorname{zn}'(u,k) + 2\beta \operatorname{zn}'(u,k)\operatorname{zn}(u,k). -\] -Teilt man auf beiden Seiten durch $2\operatorname{zn}'(u,k)$, -bleibt die nichtlineare -Differentialgleichung -\[ -\frac{d^2\operatorname{zn}}{du^2} -= -\beta \operatorname{zn} + 2\alpha \operatorname{zn}^3. -\] -Dies ist die Gleichung eines harmonischen Oszillators mit einer -Anharmonizität der Form $2\alpha z^3$. - +%\subsubsection{Ableitung der abgeleiteten elliptischen Funktionen} +%Aus den Ableitungen der grundlegenden Jacobischen elliptischen Funktionen +%können mit der Quotientenregel nun auch beliebige Ableitungen der +%abgeleiteten Jacobischen elliptischen Funktionen gefunden werden. +%Als Beispiel berechnen wir die Ableitung von $\operatorname{sc}(u,k)$. +%Sie ist +%\begin{align*} +%\frac{d}{du} +%\operatorname{sc}(u,k) +%&= +%\frac{d}{du} +%\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} +%= +%\frac{ +%\operatorname{sn}'(u,k)\operatorname{cn}(u,k) +%- +%\operatorname{sn}(u,k)\operatorname{cn}'(u,k)}{ +%\operatorname{cn}^2(u,k) +%} +%\\ +%&= +%\frac{ +%\operatorname{cn}^2(u,k)\operatorname{dn}(u,k) +%+ +%\operatorname{sn}^2(u,k)\operatorname{dn}(u,k) +%}{ +%\operatorname{cn}^2(u,k) +%} +%= +%\frac{( +%\operatorname{sn}^2(u,k) +%+ +%\operatorname{cn}^2(u,k) +%)\operatorname{dn}(u,k)}{ +%\operatorname{cn}^2(u,k) +%} +%\\ +%&= +%\frac{1}{\operatorname{cn}(u,k)} +%\cdot +%\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)} +%= +%\operatorname{nc}(u,k) +%\operatorname{dc}(u,k). +%\end{align*} +%Man beachte, dass das Quadrat der Nennerfunktion im Resultat +%der Quotientenregel zur Folge hat, dass die +%beiden Funktionen im Resultat beide den gleichen Nenner haben wie +%die Funktion, die abgeleitet wird. % -% Differentialgleichung des anharmonischen Oszillators +%Mit etwas Fleiss kann man nach diesem Muster alle Ableitungen +%\begin{equation} +%%\small +%\begin{aligned} +%\operatorname{sn}'(u,k) +%&= +%\phantom{-} +%\operatorname{cn}(u,k)\,\operatorname{dn}(u,k) +%&&\qquad& +%\operatorname{ns}'(u,k) +%&= +%- +%\operatorname{cs}(u,k)\,\operatorname{ds}(u,k) +%\\ +%\operatorname{cn}'(u,k) +%&= +%- +%\operatorname{sn}(u,k)\,\operatorname{dn}(u,k) +%&&& +%\operatorname{nc}'(u,k) +%&= +%\phantom{-} +%\operatorname{sc}(u,k)\,\operatorname{dc}(u,k) +%\\ +%\operatorname{dn}'(u,k) +%&= +%-k^2 +%\operatorname{sn}(u,k)\,\operatorname{cn}(u,k) +%&&& +%\operatorname{nd}'(u,k) +%&= +%\phantom{-} +%k^2 +%\operatorname{sd}(u,k)\,\operatorname{cd}(u,k) +%\\ +%\operatorname{sc}'(u,k) +%&= +%\phantom{-} +%\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) +%&&& +%\operatorname{cs}'(u,k) +%&= +%- +%\operatorname{ds}(u,k)\,\operatorname{ns}(u,k) +%\\ +%\operatorname{cd}'(u,k) +%&= +%-k^{\prime2} +%\operatorname{sd}(u,k)\,\operatorname{nd}(u,k) +%&&& +%\operatorname{dc}'(u,k) +%&= +%\phantom{-} +%k^{\prime2} +%\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) +%\\ +%\operatorname{ds}'(d,k) +%&= +%- +%\operatorname{cs}(u,k)\,\operatorname{ns}(u,k) +%&&& +%\operatorname{sd}'(d,k) +%&= +%\phantom{-} +%\operatorname{cd}(u,k)\,\operatorname{nd}(u,k) +%\end{aligned} +%\label{buch:elliptisch:eqn:alleableitungen} +%\end{equation} +%finden. +%Man beachte, dass in jeder Identität alle Funktionen den gleichen +%zweiten Buchstaben haben. % -\subsubsection{Differentialgleichung des anharmonischen Oszillators} -Wir möchten die nichtlineare Differentialgleichung -\begin{equation} -\biggl( -\frac{dx}{dt} -\biggr)^2 -= -Ax^4+Bx^2 + C -\label{buch:elliptisch:eqn:allgdgl} -\end{equation} -mit Hilfe elliptischer Funktionen lösen. -Wir nehmen also an, dass die gesuchte Lösung eine Funktion der Form -\begin{equation} -x(t) = a\operatorname{zn}(bt,k) -\label{buch:elliptisch:eqn:loesungsansatz} -\end{equation} -ist. -Die erste Ableitung von $x(t)$ ist -\[ -\dot{x}(t) -= -a\operatorname{zn}'(bt,k). -\] - -Indem wir diesen Lösungsansatz in die -Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} -einsetzen, erhalten wir -\begin{equation} -a^2b^2 \operatorname{zn}'(bt,k)^2 -= -a^4A\operatorname{zn}(bt,k)^4 -+ -a^2B\operatorname{zn}(bt,k)^2 -+C -\label{buch:elliptisch:eqn:dglx} -\end{equation} -Andererseits wissen wir, dass $\operatorname{zn}(u,k)$ einer -Differentilgleichung der Form~\eqref{buch:elliptisch:eqn:1storderdglell} -erfüllt. -Wenn wir \eqref{buch:elliptisch:eqn:dglx} durch $a^2b^2$ teilen, können wir -die rechte Seite von \eqref{buch:elliptisch:eqn:dglx} mit der rechten -Seite von \eqref{buch:elliptisch:eqn:1storderdglell} vergleichen: -\[ -\frac{a^2A}{b^2}\operatorname{zn}(bt,k)^4 -+ -\frac{B}{b^2}\operatorname{zn}(bt,k)^2 -+\frac{C}{a^2b^2} -= -\alpha\operatorname{zn}(bt,k)^4 -+ -\beta\operatorname{zn}(bt,k)^2 -+ -\gamma\operatorname{zn}(bt,k). -\] -Daraus ergeben sich die Gleichungen -\begin{align} -\alpha &= \frac{a^2A}{b^2}, -& -\beta &= \frac{B}{b^2} -&&\text{und} -& -\gamma &= \frac{C}{a^2b^2} -\label{buch:elliptisch:eqn:koeffvergl} -\intertext{oder aufgelöst nach den Koeffizienten der ursprünglichen -Differentialgleichung} -A&=\frac{\alpha b^2}{a^2} -& -B&=\beta b^2 -&&\text{und}& -C &= \gamma a^2b^2 -\label{buch:elliptisch:eqn:koeffABC} -\end{align} -für die Koeffizienten der Differentialgleichung der zu verwendenden -Funktion. - -Man beachte, dass nach \eqref{buch:elliptisch:eqn:koeffvergl} die -Koeffizienten $A$, $B$ und $C$ die gleichen Vorzeichen haben wie -$\alpha$, $\beta$ und $\gamma$, da in -\eqref{buch:elliptisch:eqn:koeffvergl} nur mit Quadraten multipliziert -wird, die immer positiv sind. -Diese Vorzeichen bestimmen, welche der Funktionen gewählt werden muss. - -In den Differentialgleichungen für die elliptischen Funktionen gibt -es nur den Parameter $k$, der angepasst werden kann. -Es folgt, dass die Gleichungen -\eqref{buch:elliptisch:eqn:koeffvergl} -auch $a$ und $b$ bestimmen. -Zum Beispiel folgt aus der letzten Gleichung, dass -\[ -b = \pm\sqrt{\frac{B}{\beta}}. -\] -Damit folgt dann aus der zweiten -\[ -a=\pm\sqrt{\frac{\beta C}{\gamma B}}. -\] -Die verbleibende Gleichung legt $k$ fest. -Das folgende Beispiel illustriert das Vorgehen am Beispiel einer -Gleichung, die Lösungsfunktion $\operatorname{sn}(u,k)$ verlangt. - -\begin{beispiel} -Wir nehmen an, dass die Vorzeichen von $A$, $B$ und $C$ gemäss -Tabelle~\ref{buch:elliptische:tabelle:loesungsfunktionen} verlangen, -dass die Funktion $\operatorname{sn}(u,k)$ für die Lösung verwendet -werden muss. -Die Tabelle sagt dann auch, dass -$\alpha=k^2$, $\beta=1$ und $\gamma=1$ gewählt werden müssen. -Aus dem Koeffizientenvergleich~\eqref{buch:elliptisch:eqn:koeffvergl} -folgt dann der Reihe nach -\begin{align*} -b&=\pm \sqrt{B} -\\ -a&=\pm \sqrt{\frac{C}{B}} -\\ -k^2 -&= -\frac{AC}{B^2}. -\end{align*} -Man beachte, dass man $k^2$ durch Einsetzen von -\eqref{buch:elliptisch:eqn:koeffABC} -auch direkt aus den Koeffizienten $\alpha$, $\beta$ und $\gamma$ -erhalten kann, nämlich -\[ -\frac{AC}{B^2} -= -\frac{\frac{\alpha b^2}{a^2} \gamma a^2b^2}{\beta^2 b^4} -= -\frac{\alpha\gamma}{\beta^2}. -\qedhere -\] -\end{beispiel} - -Da alle Parameter im -Lösungsansatz~\eqref{buch:elliptisch:eqn:loesungsansatz} bereits -festgelegt sind stellt sich die Frage, woher man einen weiteren -Parameter nehmen kann, mit dem Anfangsbedingungen erfüllen kann. -Die Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} ist -autonom, die Koeffizienten der rechten Seite der Differentialgleichung -sind nicht von der Zeit abhängig. -Damit ist eine zeitverschobene Funktion $x(t-t_0)$ ebenfalls eine -Lösung der Differentialgleichung. -Die allgmeine Lösung der -Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} hat -also die Form -\[ -x(t) = a\operatorname{zn}(b(t-t_0)), -\] -wobei die Funktion $\operatorname{zn}(u,k)$ auf Grund der Vorzeichen -von $A$, $B$ und $C$ gewählt werden müssen. - +%\subsubsection{TODO} +%XXX algebraische Beziehungen \\ +%XXX Additionstheoreme \\ +%XXX Perioden +%% use https://math.stackexchange.com/questions/3013692/how-to-show-that-jacobi-sine-function-is-doubly-periodic % -% Das mathematische Pendel % -\subsection{Das mathematische Pendel -\label{buch:elliptisch:subsection:mathpendel}} -\begin{figure} -\centering -\includegraphics{chapters/110-elliptisch/images/pendel.pdf} -\caption{Mathematisches Pendel -\label{buch:elliptisch:fig:mathpendel}} -\end{figure} -Das in Abbildung~\ref{buch:elliptisch:fig:mathpendel} dargestellte -Mathematische Pendel besteht aus einem Massepunkt der Masse $m$ -im Punkt $P$, -der über eine masselose Stange der Länge $l$ mit dem Drehpunkt $O$ -verbunden ist. -Das Pendel bewegt sich unter dem Einfluss der Schwerebeschleunigung $g$. - -Das Trägheitsmoment des Massepunktes um den Drehpunkt $O$ ist -\( -I=ml^2 -\). -Das Drehmoment der Schwerkraft ist -\(M=gl\sin\vartheta\). -Die Bewegungsgleichung wird daher -\[ -\begin{aligned} -\frac{d}{dt} I\dot{\vartheta} -&= -M -= -gl\sin\vartheta -\\ -ml^2\ddot{\vartheta} -&= -gl\sin\vartheta -&&\Rightarrow& -\ddot{\vartheta} -&=\frac{g}{l}\sin\vartheta -\end{aligned} -\] -Dies ist eine nichtlineare Differentialgleichung zweiter Ordnung, die -wir nicht unmittelbar mit den Differentialgleichungen erster Ordnung -der elliptischen Funktionen vergleichen können. - -Die Differentialgleichungen erster Ordnung der elliptischen Funktionen -enthalten das Quadrat der ersten Ableitung. -In unserem Fall entspricht das einer Gleichung, die $\dot{\vartheta}^2$ -enthält. -Der Energieerhaltungssatz kann uns eine solche Gleichung geben. -Die Summe von kinetischer und potentieller Energie muss konstant sein. -Dies führt auf -\[ -E_{\text{kinetisch}} -+ -E_{\text{potentiell}} -= -\frac12I\dot{\vartheta}^2 -+ -mgl(1-\cos\vartheta) -= -\frac12ml^2\dot{\vartheta}^2 -+ -mgl(1-\cos\vartheta) -= -E -\] -Durch Auflösen nach $\dot{\vartheta}$ kann man jetzt die -Differentialgleichung -\[ -\dot{\vartheta}^2 -= -- -\frac{2g}{l}(1-\cos\vartheta) -+\frac{2E}{ml^2} -\] -finden. -In erster Näherung, d.h. wenn man die rechte Seite bis zu vierten -Potenzen in eine Taylor-Reihe in $\vartheta$ entwickelt, ist dies -tatsächlich eine Differentialgleichung der Art, wie wir sie für -elliptische Funktionen gefunden haben, wir möchten aber eine exakte -Lösung konstruieren. - -Die maximale Energie für eine Bewegung, bei der sich das Pendel gerade -über den höchsten Punkt hinweg zu bewegen vermag, ist -$E=2lmg$. -Falls $E<2mgl$ ist, erwarten wir Schwingungslösungen, bei denen -der Winkel $\vartheta$ immer im offenen Interval $(-\pi,\pi)$ -bleibt. -Für $E>2mgl$ wird sich das Pendel im Kreis bewegen, für sehr grosse -Energie ist die kinetische Energie dominant, die Verlangsamung im -höchsten Punkt wird immer weniger ausgeprägt sein. +%XXX Ableitungen \\ +%XXX Werte \\ +%% +%% Lösung von Differentialgleichungen +%% +%\subsection{Lösungen von Differentialgleichungen +%\label{buch:elliptisch:subsection:differentialgleichungen}} +%Die elliptischen Funktionen ermöglichen die Lösung gewisser nichtlinearer +%Differentialgleichungen in geschlossener Form. +%Ziel dieses Abschnitts ist, Differentialgleichungen der Form +%\( +%\dot{x}(t)^2 +%= +%P(x(t)) +%\) +%mit einem Polynom $P$ vierten Grades oder +%\( +%\ddot{x}(t) +%= +%p(x(t)) +%\) +%mit einem Polynom dritten Grades als rechter Seite lösen zu können. % -% Koordinatentransformation auf elliptische Funktionen +%% +%% Die Differentialgleichung der elliptischen Funktionen +%% +%\subsubsection{Die Differentialgleichungen der elliptischen Funktionen} +%Um Differentialgleichungen mit elliptischen Funktion lösen zu +%können, muss man als erstes die Differentialgleichungen derselben +%finden. +%Quadriert man die Ableitungsregel für $\operatorname{sn}(u,k)$, erhält +%man +%\[ +%\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 +%= +%\operatorname{cn}(u,k)^2 \operatorname{dn}(u,k)^2. +%\] +%Die Funktionen auf der rechten Seite können durch $\operatorname{sn}(u,k)$ +%ausgedrückt werden, dies führt auf die Differentialgleichung +%\begin{align*} +%\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 +%&= +%\bigl( +%1-\operatorname{sn}(u,k)^2 +%\bigr) +%\bigl( +%1-k^2 \operatorname{sn}(u,k)^2 +%\bigr) +%\\ +%&= +%k^2\operatorname{sn}(u,k)^4 +%-(1+k^2) +%\operatorname{sn}(u,k)^2 +%+1. +%\end{align*} +%Für die Funktion $\operatorname{cn}(u,k)$ ergibt die analoge Rechnung +%\begin{align*} +%\frac{d}{du}\operatorname{cn}(u,k) +%&= +%-\operatorname{sn}(u,k) \operatorname{dn}(u,k) +%\\ +%\biggl(\frac{d}{du}\operatorname{cn}(u,k)\biggr)^2 +%&= +%\operatorname{sn}(u,k)^2 \operatorname{dn}(u,k)^2 +%\\ +%&= +%\bigl(1-\operatorname{cn}(u,k)^2\bigr) +%\bigl(k^{\prime 2}+k^2 \operatorname{cn}(u,k)^2\bigr) +%\\ +%&= +%-k^2\operatorname{cn}(u,k)^4 +%+ +%(k^2-k^{\prime 2})\operatorname{cn}(u,k)^2 +%+ +%k^{\prime 2} +%\intertext{und weiter für $\operatorname{dn}(u,k)$:} +%\frac{d}{du}\operatorname{dn}(u,k) +%&= +%-k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k) +%\\ +%\biggl( +%\frac{d}{du}\operatorname{dn}(u,k) +%\biggr)^2 +%&= +%\bigl(k^2 \operatorname{sn}(u,k)^2\bigr) +%\bigl(k^2 \operatorname{cn}(u,k)^2\bigr) +%\\ +%&= +%\bigl( +%1-\operatorname{dn}(u,k)^2 +%\bigr) +%\bigl( +%\operatorname{dn}(u,k)^2-k^{\prime 2} +%\bigr) +%\\ +%&= +%-\operatorname{dn}(u,k)^4 +%+ +%(1+k^{\prime 2})\operatorname{dn}(u,k)^2 +%-k^{\prime 2}. +%\end{align*} % -\subsubsection{Koordinatentransformation auf elliptische Funktionen} -Wir verwenden als neue Variable -\[ -y = \sin\frac{\vartheta}2 -\] -mit der Ableitung -\[ -\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. -\] -Man beachte, dass $y$ nicht eine Koordinate in -Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. - -Aus den Halbwinkelformeln finden wir -\[ -\cos\vartheta -= -1-2\sin^2 \frac{\vartheta}2 -= -1-2y^2. -\] -Dies können wir zusammen mit der -Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ -in die Energiegleichung einsetzen und erhalten -\[ -\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E -\qquad\Rightarrow\qquad -\frac14 \dot{\vartheta}^2 = \frac{E}{2ml^2} - \frac{g}{2l}y^2. -\] -Der konstante Term auf der rechten Seite ist grösser oder kleiner als -$1$ je nachdem, ob das Pendel sich im Kreis bewegt oder nicht. - -Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ -erhalten wir auf der linken Seite einen Ausdruck, den wir -als Funktion von $\dot{y}$ ausdrücken können. -Wir erhalten -\begin{align*} -\frac14 -\cos^2\frac{\vartheta}2 -\cdot -\dot{\vartheta}^2 -&= -\frac14 -(1-y^2) -\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) -\\ -\dot{y}^2 -&= -\frac{1}{4} -(1-y^2) -\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) -\end{align*} -Die letzte Gleichung hat die Form einer Differentialgleichung -für elliptische Funktionen. -Welche Funktion verwendet werden muss, hängt von der Grösse der -Koeffizienten in der zweiten Klammer ab. -Die Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} -zeigt, dass in der zweiten Klammer jeweils einer der Terme -$1$ sein muss. - +%\begin{table} +%\centering +%\renewcommand{\arraystretch}{1.7} +%\begin{tabular}{|>{$}l<{$}|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +%\hline +%\text{Funktion $y=$}&\text{Differentialgleichung}&\alpha&\beta&\gamma\\ +%\hline +%\operatorname{sn}(u,k) +% & y'^2 = \phantom{-}(1-y^2)(1-k^2y^2) +% &k^2&1+k^2&1 +%\\ +%\operatorname{cn}(u,k) &y'^2 = \phantom{-}(1-y^2)(k^{\prime2}+k^2y^2) +% &-k^2 &k^2-k^{\prime 2}=2k^2-1&k^{\prime2} +%\\ +%\operatorname{dn}(u,k) +% & y'^2 = -(1-y^2)(k^{\prime 2}-y^2) +% &-1 &1+k^{\prime 2}=2-k^2 &-k^{\prime2} +%\\ +%\hline +%\end{tabular} +%\caption{Elliptische Funktionen als Lösungsfunktionen für verschiedene +%nichtlineare Differentialgleichungen der Art +%\eqref{buch:elliptisch:eqn:1storderdglell}. +%Die Vorzeichen der Koeffizienten $\alpha$, $\beta$ und $\gamma$ +%entscheidet darüber, welche Funktion für die Lösung verwendet werden +%muss. +%\label{buch:elliptisch:tabelle:loesungsfunktionen}} +%\end{table} % -% Der Fall E < 2mgl +%Die drei grundlegenden Jacobischen elliptischen Funktionen genügen also alle +%einer nichtlinearen Differentialgleichung erster Ordnung der selben Art. +%Das Quadrat der Ableitung ist ein Polynom vierten Grades der Funktion. +%Die Differentialgleichungen sind in der +%Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} zusammengefasst. % -\subsubsection{Der Fall $E<2mgl$} -\begin{figure} -\centering -\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} -\caption{% -Abhängigkeit der elliptischen Funktionen von $u$ für -verschiedene Werte von $k^2=m$. -Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, -$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese -sind in allen Plots in einer helleren Farbe eingezeichnet. -Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig -von den trigonometrischen Funktionen ab, -es ist aber klar erkennbar, dass die anharmonischen Terme in der -Differentialgleichung die Periode mit steigender Amplitude verlängern. -Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass -die Energie des Pendels fast ausreicht, dass es den höchsten Punkt -erreichen kann, was es für $m$ macht. -\label{buch:elliptisch:fig:jacobiplots}} -\end{figure} - - -Wir verwenden als neue Variable -\[ -y = \sin\frac{\vartheta}2 -\] -mit der Ableitung -\[ -\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. -\] -Man beachte, dass $y$ nicht eine Koordinate in -Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. - -Aus den Halbwinkelformeln finden wir -\[ -\cos\vartheta -= -1-2\sin^2 \frac{\vartheta}2 -= -1-2y^2. -\] -Dies können wir zusammen mit der -Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ -in die Energiegleichung einsetzen und erhalten -\[ -\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E. -\] -Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ -erhalten wir auf der linken Seite einen Ausdruck, den wir -als Funktion von $\dot{y}$ ausdrücken können. -Wir erhalten -\begin{align*} -\frac12ml^2 -\cos^2\frac{\vartheta}2 -\dot{\vartheta}^2 -&= -(1-y^2) -(E -mgly^2) -\\ -\frac{1}{4}\cos^2\frac{\vartheta}{2}\dot{\vartheta}^2 -&= -\frac{1}{2} -(1-y^2) -\biggl(\frac{E}{ml^2} -\frac{g}{l}y^2\biggr) -\\ -\dot{y}^2 -&= -\frac{E}{2ml^2} -(1-y^2)\biggl( -1-\frac{2gml}{E}y^2 -\biggr). -\end{align*} -Dies ist genau die Form der Differentialgleichung für die elliptische -Funktion $\operatorname{sn}(u,k)$ -mit $k^2 = 2gml/E< 1$. - +%% +%% Differentialgleichung der abgeleiteten elliptischen Funktionen +%% +%\subsubsection{Die Differentialgleichung der abgeleiteten elliptischen +%Funktionen} +%Da auch die Ableitungen der abgeleiteten Jacobischen elliptischen +%Funktionen Produkte von genau zwei Funktionen sind, die sich wieder +%durch die ursprüngliche Funktion ausdrücken lassen, darf man erwarten, +%dass alle elliptischen Funktionen einer ähnlichen Differentialgleichung +%genügen. +%Um dies besser einzufangen, schreiben wir $\operatorname{pq}(u,k)$, +%wenn wir eine beliebige abgeleitete Jacobische elliptische Funktion. +%Für +%$\operatorname{pq}=\operatorname{sn}$ +%$\operatorname{pq}=\operatorname{cn}$ +%und +%$\operatorname{pq}=\operatorname{dn}$ +%wissen wir bereits und erwarten für jede andere Funktion dass +%$\operatorname{pq}(u,k)$ auch, dass sie Lösung einer Differentialgleichung +%der Form +%\begin{equation} +%\operatorname{pq}'(u,k)^2 +%= +%\alpha \operatorname{pq}(u,k)^4 + \beta \operatorname{pq}(u,k)^2 + \gamma +%\label{buch:elliptisch:eqn:1storderdglell} +%\end{equation} +%erfüllt, +%wobei wir mit $\operatorname{pq}'(u,k)$ die Ableitung von +%$\operatorname{pq}(u,k)$ nach dem ersten Argument meinen. +%Die Koeffizienten $\alpha$, $\beta$ und $\gamma$ hängen von $k$ ab, +%ihre Werte für die grundlegenden Jacobischen elliptischen +%sind in Tabelle~\ref{buch:elliptisch:table:differentialgleichungen} +%zusammengestellt. % -% Der Fall E > 2mgl +%Die Koeffizienten müssen nicht für jede Funktion wieder neu bestimmt +%werden, denn für den Kehrwert einer Funktion lässt sich die +%Differentialgleichung aus der Differentialgleichung der ursprünglichen +%Funktion ermitteln. % -\subsection{Der Fall $E > 2mgl$} -In diesem Fall hat das Pendel im höchsten Punkte immer noch genügend -kinetische Energie, so dass es sich im Kreise dreht. -Indem wir die Gleichung - -XXX Differentialgleichung \\ -XXX Mathematisches Pendel \\ - -\subsection{Soliton-Lösungen der Sinus-Gordon-Gleichung} +%% +%% Differentialgleichung der Kehrwertfunktion +%% +%\subsubsection{Differentialgleichung für den Kehrwert einer elliptischen Funktion} +%Aus der Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} +%für die Funktion $\operatorname{pq}(u,k)$ kann auch eine +%Differentialgleichung für den Kehrwert +%$\operatorname{qp}(u,k)=\operatorname{pq}(u,k)^{-1}$ +%ableiten. +%Dazu rechnet man +%\[ +%\operatorname{qp}'(u,k) +%= +%\frac{d}{du}\frac{1}{\operatorname{pq}(u,k)} +%= +%\frac{\operatorname{pq}'(u,k)}{\operatorname{pq}(u,k)^2} +%\qquad\Rightarrow\qquad +%\left\{ +%\quad +%\begin{aligned} +%\operatorname{pq}(u,k) +%&= +%\frac{1}{\operatorname{qp}(u,k)} +%\\ +%\operatorname{pq}'(u,k) +%&= +%\frac{\operatorname{qp}'(u,k)}{\operatorname{qp}(u,k)^2} +%\end{aligned} +%\right. +%\] +%und setzt in die Differentialgleichung ein: +%\begin{align*} +%\biggl( +%\frac{ +%\operatorname{qp}'(u,k) +%}{ +%\operatorname{qp}(u,k) +%} +%\biggr)^2 +%&= +%\alpha \frac{1}{\operatorname{qp}(u,k)^4} +%+ +%\beta \frac{1}{\operatorname{qp}(u,k)^2} +%+ +%\gamma. +%\end{align*} +%Nach Multiplikation mit $\operatorname{qp}(u,k)^4$ erhält man den +%folgenden Satz. +% +%\begin{satz} +%Wenn die Jacobische elliptische Funktion $\operatorname{pq}(u,k)$ +%der Differentialgleichung genügt, dann genügt der Kehrwert +%$\operatorname{qp}(u,k) = 1/\operatorname{pq}(u,k)$ der Differentialgleichung +%\begin{equation} +%(\operatorname{qp}'(u,k))^2 +%= +%\gamma \operatorname{qp}(u,k)^4 +%+ +%\beta \operatorname{qp}(u,k)^2 +%+ +%\alpha +%\label{buch:elliptisch:eqn:kehrwertdgl} +%\end{equation} +%\end{satz} +% +%\begin{table} +%\centering +%\def\lfn#1{\multicolumn{1}{|l|}{#1}} +%\def\rfn#1{\multicolumn{1}{r|}{#1}} +%\renewcommand{\arraystretch}{1.3} +%\begin{tabular}{l|>{$}c<{$}>{$}c<{$}>{$}c<{$}|r} +%\cline{1-4} +%\lfn{Funktion} +% & \alpha & \beta & \gamma &\\ +%\hline +%\lfn{sn}& k^2 & -(1+k^2) & 1 &\rfn{ns}\\ +%\lfn{cn}& -k^2 & -(1-2k^2) & 1-k^2 &\rfn{nc}\\ +%\lfn{dn}& 1 & 2-k^2 & -(1-k^2) &\rfn{nd}\\ +%\hline +%\lfn{sc}& 1-k^2 & 2-k^2 & 1 &\rfn{cs}\\ +%\lfn{sd}&-k^2(1-k^2)&-(1-2k^2) & 1 &\rfn{ds}\\ +%\lfn{cd}& k^2 &-(1+k^2) & 1 &\rfn{dc}\\ +%\hline +% & \gamma & \beta & \alpha &\rfn{Reziproke}\\ +%\cline{2-5} +%\end{tabular} +%\caption{Koeffizienten der Differentialgleichungen für die Jacobischen +%elliptischen Funktionen. +%Der Kehrwert einer Funktion hat jeweils die Differentialgleichung der +%ursprünglichen Funktion, in der die Koeffizienten $\alpha$ und $\gamma$ +%vertauscht worden sind. +%\label{buch:elliptisch:table:differentialgleichungen}} +%\end{table} +% +%% +%% Differentialgleichung zweiter Ordnung +%% +%\subsubsection{Differentialgleichung zweiter Ordnung} +%Leitet die Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} +%man dies nochmals nach $u$ ab, erhält man die Differentialgleichung +%\[ +%2\operatorname{pq}''(u,k)\operatorname{pq}'(u,k) +%= +%4\alpha \operatorname{pq}(u,k)^3\operatorname{pq}'(u,k) + 2\beta \operatorname{pq}'(u,k)\operatorname{pq}(u,k). +%\] +%Teilt man auf beiden Seiten durch $2\operatorname{pq}'(u,k)$, +%bleibt die nichtlineare +%Differentialgleichung +%\[ +%\frac{d^2\operatorname{pq}}{du^2} +%= +%\beta \operatorname{pq} + 2\alpha \operatorname{pq}^3. +%\] +%Dies ist die Gleichung eines harmonischen Oszillators mit einer +%Anharmonizität der Form $2\alpha z^3$. +% +% +% +%% +%% Jacobischen elliptische Funktionen und elliptische Integrale +%% +%\subsubsection{Jacobische elliptische Funktionen als elliptische Integrale} +%Die in Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} +%zusammengestellten Differentialgleichungen ermöglichen nun, den +%Zusammenhang zwischen den Funktionen +%$\operatorname{sn}(u,k)$, $\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$ +%und den unvollständigen elliptischen Integralen herzustellen. +%Die Differentialgleichungen sind alle von der Form +%\begin{equation} +%\biggl( +%\frac{d y}{d u} +%\biggr)^2 +%= +%p(u), +%\label{buch:elliptisch:eqn:allgdgl} +%\end{equation} +%wobei $p(u)$ ein Polynom vierten Grades in $y$ ist. +%Diese Differentialgleichung lässt sich mit Separation lösen. +%Dazu zieht man aus~\eqref{buch:elliptisch:eqn:allgdgl} die +%Wurzel +%\begin{align} +%\frac{dy}{du} +%= +%\sqrt{p(y)} +%\notag +%\intertext{und trennt die Variablen. Man erhält} +%\int\frac{dy}{\sqrt{p(y)}} = u+C. +%\label{buch:elliptisch:eqn:yintegral} +%\end{align} +%Solange $p(y)>0$ ist, ist der Integrand auf der linken Seite +%von~\eqref{buch:elliptisch:eqn:yintegral} ebenfalls positiv und +%das Integral ist eine monoton wachsende Funktion $F(y)$. +%Insbesondere ist $F(y)$ invertierbar. +%Die Lösung $y(u)$ der Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} +%ist daher +%\[ +%y(u) = F^{-1}(u+C). +%\] +%Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen +%der unvollständigen elliptischen Integrale. +% +% +%% +%% Differentialgleichung des anharmonischen Oszillators +%% +%\subsubsection{Differentialgleichung des anharmonischen Oszillators} +%Wir möchten die nichtlineare Differentialgleichung +%\begin{equation} +%\biggl( +%\frac{dx}{dt} +%\biggr)^2 +%= +%Ax^4+Bx^2 + C +%\label{buch:elliptisch:eqn:allgdgl} +%\end{equation} +%mit Hilfe elliptischer Funktionen lösen. +%Wir nehmen also an, dass die gesuchte Lösung eine Funktion der Form +%\begin{equation} +%x(t) = a\operatorname{zn}(bt,k) +%\label{buch:elliptisch:eqn:loesungsansatz} +%\end{equation} +%ist. +%Die erste Ableitung von $x(t)$ ist +%\[ +%\dot{x}(t) +%= +%a\operatorname{zn}'(bt,k). +%\] +% +%Indem wir diesen Lösungsansatz in die +%Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} +%einsetzen, erhalten wir +%\begin{equation} +%a^2b^2 \operatorname{zn}'(bt,k)^2 +%= +%a^4A\operatorname{zn}(bt,k)^4 +%+ +%a^2B\operatorname{zn}(bt,k)^2 +%+C +%\label{buch:elliptisch:eqn:dglx} +%\end{equation} +%Andererseits wissen wir, dass $\operatorname{zn}(u,k)$ einer +%Differentilgleichung der Form~\eqref{buch:elliptisch:eqn:1storderdglell} +%erfüllt. +%Wenn wir \eqref{buch:elliptisch:eqn:dglx} durch $a^2b^2$ teilen, können wir +%die rechte Seite von \eqref{buch:elliptisch:eqn:dglx} mit der rechten +%Seite von \eqref{buch:elliptisch:eqn:1storderdglell} vergleichen: +%\[ +%\frac{a^2A}{b^2}\operatorname{zn}(bt,k)^4 +%+ +%\frac{B}{b^2}\operatorname{zn}(bt,k)^2 +%+\frac{C}{a^2b^2} +%= +%\alpha\operatorname{zn}(bt,k)^4 +%+ +%\beta\operatorname{zn}(bt,k)^2 +%+ +%\gamma\operatorname{zn}(bt,k). +%\] +%Daraus ergeben sich die Gleichungen +%\begin{align} +%\alpha &= \frac{a^2A}{b^2}, +%& +%\beta &= \frac{B}{b^2} +%&&\text{und} +%& +%\gamma &= \frac{C}{a^2b^2} +%\label{buch:elliptisch:eqn:koeffvergl} +%\intertext{oder aufgelöst nach den Koeffizienten der ursprünglichen +%Differentialgleichung} +%A&=\frac{\alpha b^2}{a^2} +%& +%B&=\beta b^2 +%&&\text{und}& +%C &= \gamma a^2b^2 +%\label{buch:elliptisch:eqn:koeffABC} +%\end{align} +%für die Koeffizienten der Differentialgleichung der zu verwendenden +%Funktion. +% +%Man beachte, dass nach \eqref{buch:elliptisch:eqn:koeffvergl} die +%Koeffizienten $A$, $B$ und $C$ die gleichen Vorzeichen haben wie +%$\alpha$, $\beta$ und $\gamma$, da in +%\eqref{buch:elliptisch:eqn:koeffvergl} nur mit Quadraten multipliziert +%wird, die immer positiv sind. +%Diese Vorzeichen bestimmen, welche der Funktionen gewählt werden muss. +% +%In den Differentialgleichungen für die elliptischen Funktionen gibt +%es nur den Parameter $k$, der angepasst werden kann. +%Es folgt, dass die Gleichungen +%\eqref{buch:elliptisch:eqn:koeffvergl} +%auch $a$ und $b$ bestimmen. +%Zum Beispiel folgt aus der letzten Gleichung, dass +%\[ +%b = \pm\sqrt{\frac{B}{\beta}}. +%\] +%Damit folgt dann aus der zweiten +%\[ +%a=\pm\sqrt{\frac{\beta C}{\gamma B}}. +%\] +%Die verbleibende Gleichung legt $k$ fest. +%Das folgende Beispiel illustriert das Vorgehen am Beispiel einer +%Gleichung, die Lösungsfunktion $\operatorname{sn}(u,k)$ verlangt. +% +%\begin{beispiel} +%Wir nehmen an, dass die Vorzeichen von $A$, $B$ und $C$ gemäss +%Tabelle~\ref{buch:elliptische:tabelle:loesungsfunktionen} verlangen, +%dass die Funktion $\operatorname{sn}(u,k)$ für die Lösung verwendet +%werden muss. +%Die Tabelle sagt dann auch, dass +%$\alpha=k^2$, $\beta=1$ und $\gamma=1$ gewählt werden müssen. +%Aus dem Koeffizientenvergleich~\eqref{buch:elliptisch:eqn:koeffvergl} +%folgt dann der Reihe nach +%\begin{align*} +%b&=\pm \sqrt{B} +%\\ +%a&=\pm \sqrt{\frac{C}{B}} +%\\ +%k^2 +%&= +%\frac{AC}{B^2}. +%\end{align*} +%Man beachte, dass man $k^2$ durch Einsetzen von +%\eqref{buch:elliptisch:eqn:koeffABC} +%auch direkt aus den Koeffizienten $\alpha$, $\beta$ und $\gamma$ +%erhalten kann, nämlich +%\[ +%\frac{AC}{B^2} +%= +%\frac{\frac{\alpha b^2}{a^2} \gamma a^2b^2}{\beta^2 b^4} +%= +%\frac{\alpha\gamma}{\beta^2}. +%\qedhere +%\] +%\end{beispiel} +% +%Da alle Parameter im +%Lösungsansatz~\eqref{buch:elliptisch:eqn:loesungsansatz} bereits +%festgelegt sind stellt sich die Frage, woher man einen weiteren +%Parameter nehmen kann, mit dem Anfangsbedingungen erfüllen kann. +%Die Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} ist +%autonom, die Koeffizienten der rechten Seite der Differentialgleichung +%sind nicht von der Zeit abhängig. +%Damit ist eine zeitverschobene Funktion $x(t-t_0)$ ebenfalls eine +%Lösung der Differentialgleichung. +%Die allgmeine Lösung der +%Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} hat +%also die Form +%\[ +%x(t) = a\operatorname{zn}(b(t-t_0)), +%\] +%wobei die Funktion $\operatorname{zn}(u,k)$ auf Grund der Vorzeichen +%von $A$, $B$ und $C$ gewählt werden müssen. -\subsection{Nichtlineare Differentialgleichung vierter Ordnung} -XXX Möbius-Transformation \\ -XXX Reduktion auf die Differentialgleichung elliptischer Funktionen +%% +%% Das mathematische Pendel +%% +%\subsection{Das mathematische Pendel +%\label{buch:elliptisch:subsection:mathpendel}} +%\begin{figure} +%\centering +%\includegraphics{chapters/110-elliptisch/images/pendel.pdf} +%\caption{Mathematisches Pendel +%\label{buch:elliptisch:fig:mathpendel}} +%\end{figure} +%Das in Abbildung~\ref{buch:elliptisch:fig:mathpendel} dargestellte +%Mathematische Pendel besteht aus einem Massepunkt der Masse $m$ +%im Punkt $P$, +%der über eine masselose Stange der Länge $l$ mit dem Drehpunkt $O$ +%verbunden ist. +%Das Pendel bewegt sich unter dem Einfluss der Schwerebeschleunigung $g$. +% +%Das Trägheitsmoment des Massepunktes um den Drehpunkt $O$ ist +%\( +%I=ml^2 +%\). +%Das Drehmoment der Schwerkraft ist +%\(M=gl\sin\vartheta\). +%Die Bewegungsgleichung wird daher +%\[ +%\begin{aligned} +%\frac{d}{dt} I\dot{\vartheta} +%&= +%M +%= +%gl\sin\vartheta +%\\ +%ml^2\ddot{\vartheta} +%&= +%gl\sin\vartheta +%&&\Rightarrow& +%\ddot{\vartheta} +%&=\frac{g}{l}\sin\vartheta +%\end{aligned} +%\] +%Dies ist eine nichtlineare Differentialgleichung zweiter Ordnung, die +%wir nicht unmittelbar mit den Differentialgleichungen erster Ordnung +%der elliptischen Funktionen vergleichen können. +% +%Die Differentialgleichungen erster Ordnung der elliptischen Funktionen +%enthalten das Quadrat der ersten Ableitung. +%In unserem Fall entspricht das einer Gleichung, die $\dot{\vartheta}^2$ +%enthält. +%Der Energieerhaltungssatz kann uns eine solche Gleichung geben. +%Die Summe von kinetischer und potentieller Energie muss konstant sein. +%Dies führt auf +%\[ +%E_{\text{kinetisch}} +%+ +%E_{\text{potentiell}} +%= +%\frac12I\dot{\vartheta}^2 +%+ +%mgl(1-\cos\vartheta) +%= +%\frac12ml^2\dot{\vartheta}^2 +%+ +%mgl(1-\cos\vartheta) +%= +%E +%\] +%Durch Auflösen nach $\dot{\vartheta}$ kann man jetzt die +%Differentialgleichung +%\[ +%\dot{\vartheta}^2 +%= +%- +%\frac{2g}{l}(1-\cos\vartheta) +%+\frac{2E}{ml^2} +%\] +%finden. +%In erster Näherung, d.h. wenn man die rechte Seite bis zu vierten +%Potenzen in eine Taylor-Reihe in $\vartheta$ entwickelt, ist dies +%tatsächlich eine Differentialgleichung der Art, wie wir sie für +%elliptische Funktionen gefunden haben, wir möchten aber eine exakte +%Lösung konstruieren. +% +%Die maximale Energie für eine Bewegung, bei der sich das Pendel gerade +%über den höchsten Punkt hinweg zu bewegen vermag, ist +%$E=2lmg$. +%Falls $E<2mgl$ ist, erwarten wir Schwingungslösungen, bei denen +%der Winkel $\vartheta$ immer im offenen Interval $(-\pi,\pi)$ +%bleibt. +%Für $E>2mgl$ wird sich das Pendel im Kreis bewegen, für sehr grosse +%Energie ist die kinetische Energie dominant, die Verlangsamung im +%höchsten Punkt wird immer weniger ausgeprägt sein. +% +%% +%% Koordinatentransformation auf elliptische Funktionen +%% +%\subsubsection{Koordinatentransformation auf elliptische Funktionen} +%Wir verwenden als neue Variable +%\[ +%y = \sin\frac{\vartheta}2 +%\] +%mit der Ableitung +%\[ +%\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. +%\] +%Man beachte, dass $y$ nicht eine Koordinate in +%Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. +% +%Aus den Halbwinkelformeln finden wir +%\[ +%\cos\vartheta +%= +%1-2\sin^2 \frac{\vartheta}2 +%= +%1-2y^2. +%\] +%Dies können wir zusammen mit der +%Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ +%in die Energiegleichung einsetzen und erhalten +%\[ +%\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E +%\qquad\Rightarrow\qquad +%\frac14 \dot{\vartheta}^2 = \frac{E}{2ml^2} - \frac{g}{2l}y^2. +%\] +%Der konstante Term auf der rechten Seite ist grösser oder kleiner als +%$1$ je nachdem, ob das Pendel sich im Kreis bewegt oder nicht. +% +%Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ +%erhalten wir auf der linken Seite einen Ausdruck, den wir +%als Funktion von $\dot{y}$ ausdrücken können. +%Wir erhalten +%\begin{align*} +%\frac14 +%\cos^2\frac{\vartheta}2 +%\cdot +%\dot{\vartheta}^2 +%&= +%\frac14 +%(1-y^2) +%\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) +%\\ +%\dot{y}^2 +%&= +%\frac{1}{4} +%(1-y^2) +%\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) +%\end{align*} +%Die letzte Gleichung hat die Form einer Differentialgleichung +%für elliptische Funktionen. +%Welche Funktion verwendet werden muss, hängt von der Grösse der +%Koeffizienten in der zweiten Klammer ab. +%Die Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} +%zeigt, dass in der zweiten Klammer jeweils einer der Terme +%$1$ sein muss. +% +%% +%% Der Fall E < 2mgl +%% +%\subsubsection{Der Fall $E<2mgl$} +%\begin{figure} +%\centering +%\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} +%\caption{% +%Abhängigkeit der elliptischen Funktionen von $u$ für +%verschiedene Werte von $k^2=m$. +%Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, +%$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese +%sind in allen Plots in einer helleren Farbe eingezeichnet. +%Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig +%von den trigonometrischen Funktionen ab, +%es ist aber klar erkennbar, dass die anharmonischen Terme in der +%Differentialgleichung die Periode mit steigender Amplitude verlängern. +%Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass +%die Energie des Pendels fast ausreicht, dass es den höchsten Punkt +%erreichen kann, was es für $m$ macht. +%\label{buch:elliptisch:fig:jacobiplots}} +%\end{figure} +% +% +%Wir verwenden als neue Variable +%\[ +%y = \sin\frac{\vartheta}2 +%\] +%mit der Ableitung +%\[ +%\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. +%\] +%Man beachte, dass $y$ nicht eine Koordinate in +%Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. +% +%Aus den Halbwinkelformeln finden wir +%\[ +%\cos\vartheta +%= +%1-2\sin^2 \frac{\vartheta}2 +%= +%1-2y^2. +%\] +%Dies können wir zusammen mit der +%Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ +%in die Energiegleichung einsetzen und erhalten +%\[ +%\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E. +%\] +%Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ +%erhalten wir auf der linken Seite einen Ausdruck, den wir +%als Funktion von $\dot{y}$ ausdrücken können. +%Wir erhalten +%\begin{align*} +%\frac12ml^2 +%\cos^2\frac{\vartheta}2 +%\dot{\vartheta}^2 +%&= +%(1-y^2) +%(E -mgly^2) +%\\ +%\frac{1}{4}\cos^2\frac{\vartheta}{2}\dot{\vartheta}^2 +%&= +%\frac{1}{2} +%(1-y^2) +%\biggl(\frac{E}{ml^2} -\frac{g}{l}y^2\biggr) +%\\ +%\dot{y}^2 +%&= +%\frac{E}{2ml^2} +%(1-y^2)\biggl( +%1-\frac{2gml}{E}y^2 +%\biggr). +%\end{align*} +%Dies ist genau die Form der Differentialgleichung für die elliptische +%Funktion $\operatorname{sn}(u,k)$ +%mit $k^2 = 2gml/E< 1$. +% +%%% +%%% Der Fall E > 2mgl +%%% +%%\subsection{Der Fall $E > 2mgl$} +%%In diesem Fall hat das Pendel im höchsten Punkte immer noch genügend +%%kinetische Energie, so dass es sich im Kreise dreht. +%%Indem wir die Gleichung +% +% +%%\subsection{Soliton-Lösungen der Sinus-Gordon-Gleichung} +% +%%\subsection{Nichtlineare Differentialgleichung vierter Ordnung} +%%XXX Möbius-Transformation \\ +%%XXX Reduktion auf die Differentialgleichung elliptischer Funktionen diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index 7083b63..e766779 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -22,23 +22,46 @@ elliptischen Funktionen hergestellt werden. \end{figure} Die Lemniskate von Bernoulli ist die Kurve vierten Grades mit der Gleichung \begin{equation} -(x^2+y^2)^2 = 2a^2(x^2-y^2). +(X^2+Y^2)^2 = 2a^2(X^2-Y^2). \label{buch:elliptisch:eqn:lemniskate} \end{equation} Sie ist in Abbildung~\ref{buch:elliptisch:fig:lemniskate} dargestellt. -Die beiden Scheitel der Lemniskate befinden sich bei $x=\pm a/\sqrt{2}$. +Die beiden Scheitel der Lemniskate befinden sich bei $X_s=\pm a\sqrt{2}$. +Dividiert man die Gleichung der Lemniskate durch $X_s^2=4a^4$ entsteht +\begin{equation} +\biggl( +\biggl(\frac{X}{a\sqrt{2}}\biggr)^2 ++ +\biggl(\frac{Y}{a\sqrt{2}}\biggr)^2 +\biggr)^2 += +2\frac{a^2}{2a^2}\biggl( +\biggl(\frac{X}{a\sqrt{2}}\biggr)^2 +- +\biggl(\frac{Y}{a\sqrt{2}}\biggr)^2 +\biggr). +\qquad +\Leftrightarrow +\qquad +(x^2+y^2)^2 = x^2-y^2, +\label{buch:elliptisch:eqn:lemniskatenormiert} +\end{equation} +wobei wir $x=X/a\sqrt{2}$ und $y=Y/a\sqrt{2}$ gesetzt haben. +In dieser Normierung liegen die Scheitel bei $\pm 1$. +Dies ist die Skalierung, die für die Definition des lemniskatischen +Sinus und Kosinus verwendet werden soll. In Polarkoordinaten $x=r\cos\varphi$ und $y=r\sin\varphi$ -gilt nach Einsetzen in \eqref{buch:elliptisch:eqn:lemniskate} +gilt nach Einsetzen in \eqref{buch:elliptisch:eqn:lemniskatenormiert} \begin{equation} r^4 = -2a^2r^2(\cos^2\varphi-\sin^2\varphi) +r^2(\cos^2\varphi-\sin^2\varphi) = -2a^2r^2\cos2\varphi +r^2\cos2\varphi \qquad\Rightarrow\qquad -r^2 = 2a^2\cos 2\varphi +r^2 = \cos 2\varphi \label{buch:elliptisch:eqn:lemniskatepolar} \end{equation} als Darstellung der Lemniskate in Polardarstellung. @@ -46,15 +69,7 @@ Sie gilt für Winkel $\varphi\in[-\frac{\pi}4,\frac{\pi}4]$ für das rechte Blatt und $\varphi\in[\frac{3\pi}4,\frac{5\pi}4]$ für das linke Blatt der Lemniskate. -Für die Definition des lemniskatischen Sinus wird eine Skalierung -verwendet, die den rechten Scheitel im Punkt $(1,0)$. -Dies ist der Fall für $a=1/\sqrt{2}$, die Gleichung der Lemniskate -wird dann zu -\[ -(x^2+y^2)^2 = 2(x^2-y^2). -\] - -\subsubsection{Bogelänge} +\subsection{Bogenlänge} Die Funktionen \begin{equation} x(r) = \frac{r}{\sqrt{2}}\sqrt{1+r^2}, @@ -76,7 +91,7 @@ r^4 \end{align*} sie stellen also eine Parametrisierung der Lemniskate dar. -Mit Hilfe der Parametrsierung~\eqref{buch:geometrie:eqn:lemniskateparam} +Mit Hilfe der Parametrisierung~\eqref{buch:geometrie:eqn:lemniskateparam} kann man die Länge $s$ des in Abbildung~\ref{buch:elliptisch:fig:lemniskate} dargestellten Bogens der Lemniskate berechnen. Dazu benötigt man die Ableitungen nach $r$, die man mit der Produkt- und @@ -123,11 +138,16 @@ s(r) \label{buch:elliptisch:eqn:lemniskatebogenlaenge} \end{equation} -\subsubsection{Darstellung als elliptisches Integral} +% +% Als elliptisches Integral +% +\subsection{Darstellung als elliptisches Integral} Das unvollständige elliptische Integral erster Art mit Parameter -$m=-1$ ist +$k^2=-1$ oder $k=i$ ist \[ -K(r,-1) +K(r,i) += +\int_0^x \frac{dt}{\sqrt{(1-t^2)(1-i^2 t^2)}} = \int_0^x \frac{dt}{\sqrt{(1-t^2)(1-(-1)t^2)}} = @@ -136,11 +156,209 @@ K(r,-1) s(r). \] Der lemniskatische Sinus ist also eine Umkehrfunktion des -ellptischen Integrals erster Art für einen speziellen Wert des -Parameters $m$ +elliptischen Integrals erster Art für den speziellen Wert $i$ des +Parameters $k$. + +Die Länge des rechten Blattes der Lemniskate wird mit $\varpi$ bezeichnet +und hat den numerischen Wert +\[ +\varpi += +2\int_0^1\sqrt{\frac{1}{1-t^4}}\,dt += +2.6220575542. +\] +$\varpi$ ist auch als die {\em lemniskatische Konstante} bekannt. +\index{lemniskatische Konstante}% +Der Lemniskatenbogen zwischen dem Nullpunkt und $(1,0)$ hat die Länge +$\varpi/2$. + +% +% Bogenlängenparametrisierung +% +\subsection{Bogenlängenparametrisierung} +Die Lemniskate mit der Gleichung +\[ +(X^2+X^2)^2=2(X^2-X^2) +\] +(der Fall $a=1$ in \eqref{buch:elliptisch:eqn:lemniskate}) +kann mit Jacobischen elliptischen Funktionen +parametrisiert werden. +Dazu schreibt man +\[ +\left. +\begin{aligned} +X(t) +&= +\sqrt{2}\operatorname{cn}(t,k) \operatorname{dn}(t,k) +\\ +Y(t) +&= +\phantom{\sqrt{2}} +\operatorname{cn}(t,k) \operatorname{sn}(t,k) +\end{aligned} +\quad\right\} +\qquad\text{mit $k=\displaystyle\frac{1}{\sqrt{2}}$} +\] +und berechnet die beiden Seiten der definierenden Gleichung der +Lemniskate. +Zunächst ist +\begin{align*} +X(t)^2 +&= +2\operatorname{cn}(t,k)^2 +\operatorname{dn}(t,k)^2 +\\ +Y(t)^2 +&= +\operatorname{cn}(t,k)^2 +\operatorname{sn}(t,k)^2 +\\ +X(t)^2+Y(t)^2 +&= +2\operatorname{cn}(t,k)^2 +\bigl( +\underbrace{ +\operatorname{dn}(t,k)^2 ++{\textstyle\frac12} +\operatorname{sn}(t,k)^2 +}_{\displaystyle =1} +\bigr) +%\\ +%& += +2\operatorname{cn}(t,k)^2 +\\ +X(t)^2-Y(t)^2 +&= +\operatorname{cn}(t,k)^2 +\bigl( +2\operatorname{dn}(t,k)^2 - \operatorname{sn}(t,k)^2 +\bigr) +\\ +&= +\operatorname{cn}(t,k)^2 +\bigl( +2\bigl({\textstyle\frac12}+{\textstyle\frac12}\operatorname{cn}(t,k)^2\bigr) +- +\bigl(1-\operatorname{cn}(t,k)^2\bigr) +\bigr) +\\ +&= +2\operatorname{cn}(t,k)^4 +\\ +\Rightarrow\qquad +(X(t)^2+Y(t)^2)^2 +&= +4\operatorname{cn}(t,k)^4 += +2(X(t)^2-Y(t)^2). +\end{align*} +Wir zeigen jetzt, dass dies tatsächlich eine Bogenlängenparametrisierung +der Lemniskate ist. +Dazu berechnen wir die Ableitungen +\begin{align*} +\dot{X}(t) +&= +\sqrt{2}\operatorname{cn}'(t,k)\operatorname{dn}(t,k) ++ +\sqrt{2}\operatorname{cn}(t,k)\operatorname{dn}'(t,k) +\\ +&= +-\sqrt{2}\operatorname{sn}(t,k)\operatorname{dn}(t,k)^2 +-\frac12\sqrt{2}\operatorname{sn}(t,k)\operatorname{cn}(t,k)^2 +\\ +&= +-\sqrt{2}\operatorname{sn}(t,k)\bigl( +1-{\textstyle\frac12}\operatorname{sn}(t,k)^2 ++{\textstyle\frac12}-{\textstyle\frac12}\operatorname{sn}(u,t)^2 +\bigr) +\\ +&= +\sqrt{2}\operatorname{sn}(t,k) +\bigl( +{\textstyle \frac32}-\operatorname{sn}(t,k)^2 +\bigr) +\\ +\dot{X}(t)^2 +&= +2\operatorname{sn}(t,k)^2 +\bigl( +{\textstyle \frac32}-\operatorname{sn}(t,k)^2 +\bigr)^2 +\\ +&= +{\textstyle\frac{9}{2}}\operatorname{sn}(t,k)^2 +- +6\operatorname{sn}(t,k)^4 ++2\operatorname{sn}(t,k)^6 +\\ +\dot{Y}(t) +&= +\operatorname{cn}'(t,k)\operatorname{sn}(t,k) ++ +\operatorname{cn}(t,k)\operatorname{sn}'(t,k) +\\ +&= +-\operatorname{sn}(t,k)^2 +\operatorname{dn}(t,k) ++\operatorname{cn}(t,k)^2 +\operatorname{dn}(t,k) +\\ +&= +\operatorname{dn}(t,k)\bigl(1-2\operatorname{sn}(t,k)^2\bigr) +\\ +\dot{Y}(t)^2 +&= +\bigl(1-{\textstyle\frac12}\operatorname{sn}(t,k)^2\bigr) +\bigl(1-2\operatorname|{sn}(t,k)^2\bigr)^2 +\\ +&= +1-{\textstyle\frac{9}{2}}\operatorname{sn}(t,k)^2 ++6\operatorname{sn}(t,k)^4 +-2\operatorname{sn}(t,k)^6 +\\ +\dot{X}(t)^2 + \dot{Y}(t)^2 +&= +1. +\end{align*} +Dies bedeutet, dass die Bogenlänge zwischen den Parameterwerten $0$ und $s$ +\[ +\int_0^s +\sqrt{\dot{X}(t)^2 + \dot{Y}(t)^2} +\,dt += +\int_0^s\,dt += +s, +\] +der Parameter $t$ ist also ein Bogenlängenparameter. + +Die mit dem Faktor $1/\sqrt{2}$ skalierte Standard-Lemniskate mit der +Gleichung +\[ +(x^2+y^2)^2 = x^2-y^2 +\] +hat daher eine Bogenlängenparametrisierung mit +\begin{equation} +\begin{aligned} +x(t) +&= +\phantom{\frac{1}{\sqrt{2}}} +\operatorname{cn}(\sqrt{2}t,k)\operatorname{dn}(\sqrt{2}t,k) +\\ +y(t) +&= +\frac{1}{\sqrt{2}}\operatorname{cn}(\sqrt{2}t,k)\operatorname{sn}(\sqrt{2}t,k) +\end{aligned} +\label{buch:elliptisch:lemniskate:bogenlaenge} +\end{equation} + +\subsection{Der lemniskatische Sinus und Kosinus} +Der Sinus Berechnet die Gegenkathete zu einer gegebenen Bogenlänge des +Kreises, er ist die Umkehrfunktion der Funktion, die der Gegenkathete +die Bogenlänge zuordnet. -\subsubsection{Der lemniskatische Sinus und Kosinus} -Berechnet die Gegenkathete zu einer gegebenen Bogenlänge des Kreises. Daher ist es naheliegend, die Umkehrfunktion von $s(r)$ in \eqref{buch:elliptisch:eqn:lemniskatebogenlaenge} den {\em lemniskatischen Sinus} zu nennen mit der Bezeichnung @@ -150,22 +368,29 @@ Der Kosinus ist der Sinus des komplementären Winkels. Auch für die lemniskatische Bogenlänge $s(r)$ lässt sich eine komplementäre Bogenlänge definieren, nämlich die Bogenlänge zwischen dem Punkt $(x(r), y(r))$ und $(1,0)$. -Die Länge des rechten Blattes der Lemniskate wird mit $\varpi$ bezeichnet -und hat den numerischen Wert + +Da die Parametrisierung~\eqref{buch:elliptisch:lemniskate:bogenlaenge} +eine Bogenlängenparametrisierung ist, darf man $t=s$ schreiben. +Dann kann man aber auch $r(s)$ daraus berechnen, +es ist \[ -\varphi +r(s)^2 = -2\int_0^1\sqrt{\frac{1}{1-t^4}}\,dt +x(s)^2 + y(s)^2 = -2.6220575542. +\operatorname{cn}(s\sqrt{2},k)^2 +\qquad\Rightarrow\qquad +r(s) += +\operatorname{cn}(s\sqrt{2},k) \] -Lemniskatenbogens zwischen dem Nullpunkt und $(1,0)$ hat die Länge -$\varpi/2$. - -Der {\em lemniskatische Kosinus} von $s$ ist derjenige Radiuswert $r$, -für den der Lemniskatenbogen zwischen $(x(r), y(r))$ und $(1,0)$ -die Länge $s$ hat. - -XXX Algebraische Beziehungen \\ -XXX Ableitungen \\ +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/slcl.pdf} +\caption{ +Lemniskatischer Sinus und Kosinus sowie Sinus und Kosinus +mit derart skaliertem Argument, dass die Funktionen die gleichen Nullstellen +haben. +\label{buch:elliptisch:figure:slcl}} +\end{figure} -- cgit v1.2.1 From 4666311b63fb00a3f90d1c9858218e24b14360bc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 20 Apr 2022 10:31:44 +0200 Subject: add missing files --- buch/chapters/110-elliptisch/dglsol.tex | 494 +++++++++++++ buch/chapters/110-elliptisch/elltrigo.tex | 1012 +++++++++++++++++++++++++++ buch/chapters/110-elliptisch/mathpendel.tex | 250 +++++++ 3 files changed, 1756 insertions(+) create mode 100644 buch/chapters/110-elliptisch/dglsol.tex create mode 100644 buch/chapters/110-elliptisch/elltrigo.tex create mode 100644 buch/chapters/110-elliptisch/mathpendel.tex diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex new file mode 100644 index 0000000..7eaab38 --- /dev/null +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -0,0 +1,494 @@ +% +% dglsol.tex -- Lösung von Differentialgleichungen +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% + +% +% Lösung von Differentialgleichungen +% +\subsection{Lösungen von Differentialgleichungen +\label{buch:elliptisch:subsection:differentialgleichungen}} +Die elliptischen Funktionen ermöglichen die Lösung gewisser nichtlinearer +Differentialgleichungen in geschlossener Form. +Ziel dieses Abschnitts ist, Differentialgleichungen der Form +\( +\dot{x}(t)^2 += +P(x(t)) +\) +mit einem Polynom $P$ vierten Grades oder +\( +\ddot{x}(t) += +p(x(t)) +\) +mit einem Polynom dritten Grades als rechter Seite lösen zu können. + +% +% Die Differentialgleichung der elliptischen Funktionen +% +\subsubsection{Die Differentialgleichungen der elliptischen Funktionen} +Um Differentialgleichungen mit elliptischen Funktion lösen zu +können, muss man als erstes die Differentialgleichungen derselben +finden. +Quadriert man die Ableitungsregel für $\operatorname{sn}(u,k)$, erhält +man +\[ +\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 += +\operatorname{cn}(u,k)^2 \operatorname{dn}(u,k)^2. +\] +Die Funktionen auf der rechten Seite können durch $\operatorname{sn}(u,k)$ +ausgedrückt werden, dies führt auf die Differentialgleichung +\begin{align*} +\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 +&= +\bigl( +1-\operatorname{sn}(u,k)^2 +\bigr) +\bigl( +1-k^2 \operatorname{sn}(u,k)^2 +\bigr) +\\ +&= +k^2\operatorname{sn}(u,k)^4 +-(1+k^2) +\operatorname{sn}(u,k)^2 ++1. +\end{align*} +Für die Funktion $\operatorname{cn}(u,k)$ ergibt die analoge Rechnung +\begin{align*} +\frac{d}{du}\operatorname{cn}(u,k) +&= +-\operatorname{sn}(u,k) \operatorname{dn}(u,k) +\\ +\biggl(\frac{d}{du}\operatorname{cn}(u,k)\biggr)^2 +&= +\operatorname{sn}(u,k)^2 \operatorname{dn}(u,k)^2 +\\ +&= +\bigl(1-\operatorname{cn}(u,k)^2\bigr) +\bigl(k^{\prime 2}+k^2 \operatorname{cn}(u,k)^2\bigr) +\\ +&= +-k^2\operatorname{cn}(u,k)^4 ++ +(k^2-k^{\prime 2})\operatorname{cn}(u,k)^2 ++ +k^{\prime 2} +\intertext{und weiter für $\operatorname{dn}(u,k)$:} +\frac{d}{du}\operatorname{dn}(u,k) +&= +-k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k) +\\ +\biggl( +\frac{d}{du}\operatorname{dn}(u,k) +\biggr)^2 +&= +\bigl(k^2 \operatorname{sn}(u,k)^2\bigr) +\bigl(k^2 \operatorname{cn}(u,k)^2\bigr) +\\ +&= +\bigl( +1-\operatorname{dn}(u,k)^2 +\bigr) +\bigl( +\operatorname{dn}(u,k)^2-k^{\prime 2} +\bigr) +\\ +&= +-\operatorname{dn}(u,k)^4 ++ +(1+k^{\prime 2})\operatorname{dn}(u,k)^2 +-k^{\prime 2}. +\end{align*} + +\begin{table} +\centering +\renewcommand{\arraystretch}{1.7} +\begin{tabular}{|>{$}l<{$}|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\hline +\text{Funktion $y=$}&\text{Differentialgleichung}&\alpha&\beta&\gamma\\ +\hline +\operatorname{sn}(u,k) + & y'^2 = \phantom{-}(1-y^2)(1-k^2y^2) + &k^2&1+k^2&1 +\\ +\operatorname{cn}(u,k) &y'^2 = \phantom{-}(1-y^2)(k^{\prime2}+k^2y^2) + &-k^2 &k^2-k^{\prime 2}=2k^2-1&k^{\prime2} +\\ +\operatorname{dn}(u,k) + & y'^2 = -(1-y^2)(k^{\prime 2}-y^2) + &-1 &1+k^{\prime 2}=2-k^2 &-k^{\prime2} +\\ +\hline +\end{tabular} +\caption{Elliptische Funktionen als Lösungsfunktionen für verschiedene +nichtlineare Differentialgleichungen der Art +\eqref{buch:elliptisch:eqn:1storderdglell}. +Die Vorzeichen der Koeffizienten $\alpha$, $\beta$ und $\gamma$ +entscheidet darüber, welche Funktion für die Lösung verwendet werden +muss. +\label{buch:elliptisch:tabelle:loesungsfunktionen}} +\end{table} + +Die drei grundlegenden Jacobischen elliptischen Funktionen genügen also alle +einer nichtlinearen Differentialgleichung erster Ordnung der selben Art. +Das Quadrat der Ableitung ist ein Polynom vierten Grades der Funktion. +Die Differentialgleichungen sind in der +Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} zusammengefasst. + +% +% Differentialgleichung der abgeleiteten elliptischen Funktionen +% +\subsubsection{Die Differentialgleichung der abgeleiteten elliptischen +Funktionen} +Da auch die Ableitungen der abgeleiteten Jacobischen elliptischen +Funktionen Produkte von genau zwei Funktionen sind, die sich wieder +durch die ursprüngliche Funktion ausdrücken lassen, darf man erwarten, +dass alle elliptischen Funktionen einer ähnlichen Differentialgleichung +genügen. +Um dies besser einzufangen, schreiben wir $\operatorname{pq}(u,k)$, +wenn wir eine beliebige abgeleitete Jacobische elliptische Funktion. +Für +$\operatorname{pq}=\operatorname{sn}$ +$\operatorname{pq}=\operatorname{cn}$ +und +$\operatorname{pq}=\operatorname{dn}$ +wissen wir bereits und erwarten für jede andere Funktion dass +$\operatorname{pq}(u,k)$ auch, dass sie Lösung einer Differentialgleichung +der Form +\begin{equation} +\operatorname{pq}'(u,k)^2 += +\alpha \operatorname{pq}(u,k)^4 + \beta \operatorname{pq}(u,k)^2 + \gamma +\label{buch:elliptisch:eqn:1storderdglell} +\end{equation} +erfüllt, +wobei wir mit $\operatorname{pq}'(u,k)$ die Ableitung von +$\operatorname{pq}(u,k)$ nach dem ersten Argument meinen. +Die Koeffizienten $\alpha$, $\beta$ und $\gamma$ hängen von $k$ ab, +ihre Werte für die grundlegenden Jacobischen elliptischen +sind in Tabelle~\ref{buch:elliptisch:table:differentialgleichungen} +zusammengestellt. + +Die Koeffizienten müssen nicht für jede Funktion wieder neu bestimmt +werden, denn für den Kehrwert einer Funktion lässt sich die +Differentialgleichung aus der Differentialgleichung der ursprünglichen +Funktion ermitteln. + +% +% Differentialgleichung der Kehrwertfunktion +% +\subsubsection{Differentialgleichung für den Kehrwert einer elliptischen Funktion} +Aus der Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} +für die Funktion $\operatorname{pq}(u,k)$ kann auch eine +Differentialgleichung für den Kehrwert +$\operatorname{qp}(u,k)=\operatorname{pq}(u,k)^{-1}$ +ableiten. +Dazu rechnet man +\[ +\operatorname{qp}'(u,k) += +\frac{d}{du}\frac{1}{\operatorname{pq}(u,k)} += +\frac{\operatorname{pq}'(u,k)}{\operatorname{pq}(u,k)^2} +\qquad\Rightarrow\qquad +\left\{ +\quad +\begin{aligned} +\operatorname{pq}(u,k) +&= +\frac{1}{\operatorname{qp}(u,k)} +\\ +\operatorname{pq}'(u,k) +&= +\frac{\operatorname{qp}'(u,k)}{\operatorname{qp}(u,k)^2} +\end{aligned} +\right. +\] +und setzt in die Differentialgleichung ein: +\begin{align*} +\biggl( +\frac{ +\operatorname{qp}'(u,k) +}{ +\operatorname{qp}(u,k) +} +\biggr)^2 +&= +\alpha \frac{1}{\operatorname{qp}(u,k)^4} ++ +\beta \frac{1}{\operatorname{qp}(u,k)^2} ++ +\gamma. +\end{align*} +Nach Multiplikation mit $\operatorname{qp}(u,k)^4$ erhält man den +folgenden Satz. + +\begin{satz} +Wenn die Jacobische elliptische Funktion $\operatorname{pq}(u,k)$ +der Differentialgleichung genügt, dann genügt der Kehrwert +$\operatorname{qp}(u,k) = 1/\operatorname{pq}(u,k)$ der Differentialgleichung +\begin{equation} +(\operatorname{qp}'(u,k))^2 += +\gamma \operatorname{qp}(u,k)^4 ++ +\beta \operatorname{qp}(u,k)^2 ++ +\alpha +\label{buch:elliptisch:eqn:kehrwertdgl} +\end{equation} +\end{satz} + +\begin{table} +\centering +\def\lfn#1{\multicolumn{1}{|l|}{#1}} +\def\rfn#1{\multicolumn{1}{r|}{#1}} +\renewcommand{\arraystretch}{1.3} +\begin{tabular}{l|>{$}c<{$}>{$}c<{$}>{$}c<{$}|r} +\cline{1-4} +\lfn{Funktion} + & \alpha & \beta & \gamma &\\ +\hline +\lfn{sn}& k^2 & -(1+k^2) & 1 &\rfn{ns}\\ +\lfn{cn}& -k^2 & -(1-2k^2) & 1-k^2 &\rfn{nc}\\ +\lfn{dn}& 1 & 2-k^2 & -(1-k^2) &\rfn{nd}\\ +\hline +\lfn{sc}& 1-k^2 & 2-k^2 & 1 &\rfn{cs}\\ +\lfn{sd}&-k^2(1-k^2)&-(1-2k^2) & 1 &\rfn{ds}\\ +\lfn{cd}& k^2 &-(1+k^2) & 1 &\rfn{dc}\\ +\hline + & \gamma & \beta & \alpha &\rfn{Reziproke}\\ +\cline{2-5} +\end{tabular} +\caption{Koeffizienten der Differentialgleichungen für die Jacobischen +elliptischen Funktionen. +Der Kehrwert einer Funktion hat jeweils die Differentialgleichung der +ursprünglichen Funktion, in der die Koeffizienten $\alpha$ und $\gamma$ +vertauscht worden sind. +\label{buch:elliptisch:table:differentialgleichungen}} +\end{table} + +% +% Differentialgleichung zweiter Ordnung +% +\subsubsection{Differentialgleichung zweiter Ordnung} +Leitet die Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} +man dies nochmals nach $u$ ab, erhält man die Differentialgleichung +\[ +2\operatorname{pq}''(u,k)\operatorname{pq}'(u,k) += +4\alpha \operatorname{pq}(u,k)^3\operatorname{pq}'(u,k) + 2\beta \operatorname{pq}'(u,k)\operatorname{pq}(u,k). +\] +Teilt man auf beiden Seiten durch $2\operatorname{pq}'(u,k)$, +bleibt die nichtlineare +Differentialgleichung +\[ +\frac{d^2\operatorname{pq}}{du^2} += +\beta \operatorname{pq} + 2\alpha \operatorname{pq}^3. +\] +Dies ist die Gleichung eines harmonischen Oszillators mit einer +Anharmonizität der Form $2\alpha z^3$. + + + +% +% Jacobischen elliptische Funktionen und elliptische Integrale +% +\subsubsection{Jacobische elliptische Funktionen als elliptische Integrale} +Die in Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} +zusammengestellten Differentialgleichungen ermöglichen nun, den +Zusammenhang zwischen den Funktionen +$\operatorname{sn}(u,k)$, $\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$ +und den unvollständigen elliptischen Integralen herzustellen. +Die Differentialgleichungen sind alle von der Form +\begin{equation} +\biggl( +\frac{d y}{d u} +\biggr)^2 += +p(u), +\label{buch:elliptisch:eqn:allgdgl} +\end{equation} +wobei $p(u)$ ein Polynom vierten Grades in $y$ ist. +Diese Differentialgleichung lässt sich mit Separation lösen. +Dazu zieht man aus~\eqref{buch:elliptisch:eqn:allgdgl} die +Wurzel +\begin{align} +\frac{dy}{du} += +\sqrt{p(y)} +\notag +\intertext{und trennt die Variablen. Man erhält} +\int\frac{dy}{\sqrt{p(y)}} = u+C. +\label{buch:elliptisch:eqn:yintegral} +\end{align} +Solange $p(y)>0$ ist, ist der Integrand auf der linken Seite +von~\eqref{buch:elliptisch:eqn:yintegral} ebenfalls positiv und +das Integral ist eine monoton wachsende Funktion $F(y)$. +Insbesondere ist $F(y)$ invertierbar. +Die Lösung $y(u)$ der Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} +ist daher +\[ +y(u) = F^{-1}(u+C). +\] +Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen +der unvollständigen elliptischen Integrale. + + +% +% Differentialgleichung des anharmonischen Oszillators +% +\subsubsection{Differentialgleichung des anharmonischen Oszillators} +Wir möchten die nichtlineare Differentialgleichung +\begin{equation} +\biggl( +\frac{dx}{dt} +\biggr)^2 += +Ax^4+Bx^2 + C +\label{buch:elliptisch:eqn:allgdgl} +\end{equation} +mit Hilfe elliptischer Funktionen lösen. +Wir nehmen also an, dass die gesuchte Lösung eine Funktion der Form +\begin{equation} +x(t) = a\operatorname{zn}(bt,k) +\label{buch:elliptisch:eqn:loesungsansatz} +\end{equation} +ist. +Die erste Ableitung von $x(t)$ ist +\[ +\dot{x}(t) += +a\operatorname{zn}'(bt,k). +\] + +Indem wir diesen Lösungsansatz in die +Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} +einsetzen, erhalten wir +\begin{equation} +a^2b^2 \operatorname{zn}'(bt,k)^2 += +a^4A\operatorname{zn}(bt,k)^4 ++ +a^2B\operatorname{zn}(bt,k)^2 ++C +\label{buch:elliptisch:eqn:dglx} +\end{equation} +Andererseits wissen wir, dass $\operatorname{zn}(u,k)$ einer +Differentilgleichung der Form~\eqref{buch:elliptisch:eqn:1storderdglell} +erfüllt. +Wenn wir \eqref{buch:elliptisch:eqn:dglx} durch $a^2b^2$ teilen, können wir +die rechte Seite von \eqref{buch:elliptisch:eqn:dglx} mit der rechten +Seite von \eqref{buch:elliptisch:eqn:1storderdglell} vergleichen: +\[ +\frac{a^2A}{b^2}\operatorname{zn}(bt,k)^4 ++ +\frac{B}{b^2}\operatorname{zn}(bt,k)^2 ++\frac{C}{a^2b^2} += +\alpha\operatorname{zn}(bt,k)^4 ++ +\beta\operatorname{zn}(bt,k)^2 ++ +\gamma\operatorname{zn}(bt,k). +\] +Daraus ergeben sich die Gleichungen +\begin{align} +\alpha &= \frac{a^2A}{b^2}, +& +\beta &= \frac{B}{b^2} +&&\text{und} +& +\gamma &= \frac{C}{a^2b^2} +\label{buch:elliptisch:eqn:koeffvergl} +\intertext{oder aufgelöst nach den Koeffizienten der ursprünglichen +Differentialgleichung} +A&=\frac{\alpha b^2}{a^2} +& +B&=\beta b^2 +&&\text{und}& +C &= \gamma a^2b^2 +\label{buch:elliptisch:eqn:koeffABC} +\end{align} +für die Koeffizienten der Differentialgleichung der zu verwendenden +Funktion. + +Man beachte, dass nach \eqref{buch:elliptisch:eqn:koeffvergl} die +Koeffizienten $A$, $B$ und $C$ die gleichen Vorzeichen haben wie +$\alpha$, $\beta$ und $\gamma$, da in +\eqref{buch:elliptisch:eqn:koeffvergl} nur mit Quadraten multipliziert +wird, die immer positiv sind. +Diese Vorzeichen bestimmen, welche der Funktionen gewählt werden muss. + +In den Differentialgleichungen für die elliptischen Funktionen gibt +es nur den Parameter $k$, der angepasst werden kann. +Es folgt, dass die Gleichungen +\eqref{buch:elliptisch:eqn:koeffvergl} +auch $a$ und $b$ bestimmen. +Zum Beispiel folgt aus der letzten Gleichung, dass +\[ +b = \pm\sqrt{\frac{B}{\beta}}. +\] +Damit folgt dann aus der zweiten +\[ +a=\pm\sqrt{\frac{\beta C}{\gamma B}}. +\] +Die verbleibende Gleichung legt $k$ fest. +Das folgende Beispiel illustriert das Vorgehen am Beispiel einer +Gleichung, die Lösungsfunktion $\operatorname{sn}(u,k)$ verlangt. + +\begin{beispiel} +Wir nehmen an, dass die Vorzeichen von $A$, $B$ und $C$ gemäss +Tabelle~\ref{buch:elliptische:tabelle:loesungsfunktionen} verlangen, +dass die Funktion $\operatorname{sn}(u,k)$ für die Lösung verwendet +werden muss. +Die Tabelle sagt dann auch, dass +$\alpha=k^2$, $\beta=1$ und $\gamma=1$ gewählt werden müssen. +Aus dem Koeffizientenvergleich~\eqref{buch:elliptisch:eqn:koeffvergl} +folgt dann der Reihe nach +\begin{align*} +b&=\pm \sqrt{B} +\\ +a&=\pm \sqrt{\frac{C}{B}} +\\ +k^2 +&= +\frac{AC}{B^2}. +\end{align*} +Man beachte, dass man $k^2$ durch Einsetzen von +\eqref{buch:elliptisch:eqn:koeffABC} +auch direkt aus den Koeffizienten $\alpha$, $\beta$ und $\gamma$ +erhalten kann, nämlich +\[ +\frac{AC}{B^2} += +\frac{\frac{\alpha b^2}{a^2} \gamma a^2b^2}{\beta^2 b^4} += +\frac{\alpha\gamma}{\beta^2}. +\qedhere +\] +\end{beispiel} + +Da alle Parameter im +Lösungsansatz~\eqref{buch:elliptisch:eqn:loesungsansatz} bereits +festgelegt sind stellt sich die Frage, woher man einen weiteren +Parameter nehmen kann, mit dem Anfangsbedingungen erfüllen kann. +Die Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} ist +autonom, die Koeffizienten der rechten Seite der Differentialgleichung +sind nicht von der Zeit abhängig. +Damit ist eine zeitverschobene Funktion $x(t-t_0)$ ebenfalls eine +Lösung der Differentialgleichung. +Die allgmeine Lösung der +Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} hat +also die Form +\[ +x(t) = a\operatorname{zn}(b(t-t_0)), +\] +wobei die Funktion $\operatorname{zn}(u,k)$ auf Grund der Vorzeichen +von $A$, $B$ und $C$ gewählt werden müssen. + diff --git a/buch/chapters/110-elliptisch/elltrigo.tex b/buch/chapters/110-elliptisch/elltrigo.tex new file mode 100644 index 0000000..d600243 --- /dev/null +++ b/buch/chapters/110-elliptisch/elltrigo.tex @@ -0,0 +1,1012 @@ +% +% elltrigo.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% + +% +% elliptische Funktionen als Trigonometrie +% +\subsection{Elliptische Funktionen als Trigonometrie} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/ellipse.pdf} +\caption{Kreis und Ellipse zum Vergleich und zur Herleitung der +elliptischen Funktionen von Jacobi als ``trigonometrische'' Funktionen +auf einer Ellipse. +\label{buch:elliptisch:fig:ellipse}} +\end{figure} +% based on Willliam Schwalm, Elliptic functions and elliptic integrals +% https://youtu.be/DCXItCajCyo + +% +% Geometrie einer Ellipse +% +\subsubsection{Geometrie einer Ellipse} +Eine {\em Ellipse} ist die Menge der Punkte der Ebene, für die die Summe +\index{Ellipse}% +der Entfernungen von zwei festen Punkten $F_1$ und $F_2$, +den {\em Brennpunkten}, konstant ist. +\index{Brennpunkt}% +In Abbildung~\ref{buch:elliptisch:fig:ellipse} eine Ellipse +mit Brennpunkten in $F_1=(-e,0)$ und $F_2=(e,0)$ dargestellt, +die durch die Punkte $(\pm a,0)$ und $(0,\pm b)$ auf den Achsen geht. +Der Punkt $(a,0)$ hat die Entfernungen $a+e$ und $a-e$ von den beiden +Brennpunkten, also die Entfernungssumme $a+e+a-e=2a$. +Jeder andere Punkt auf der Ellipse muss ebenfalls diese Entfernungssumme +haben, insbesondere auch der Punkt $(0,b)$. +Seine Entfernung zu jedem Brennpunkt muss aus Symmetriegründen gleich gross, +also $a$ sein. +Aus dem Satz von Pythagoras liest man daher ab, dass +\[ +b^2+e^2=a^2 +\qquad\Rightarrow\qquad +e^2 = a^2-b^2 +\] +sein muss. +Die Strecke $e$ heisst auch {\em (lineare) Exzentrizität} der Ellipse. +Das Verhältnis $\varepsilon= e/a$ heisst die {\em numerische Exzentrizität} +der Ellipse. + +% +% Die Ellipsengleichung +% +\subsubsection{Ellipsengleichung} +Der Punkt $P=(x,y)$ auf der Ellipse hat die Entfernungen +\begin{equation} +\begin{aligned} +\overline{PF_1}^2 +&= +y^2 + (x+e)^2 +\\ +\overline{PF_2}^2 +&= +y^2 + (x-e)^2 +\end{aligned} +\label{buch:elliptisch:eqn:wurzelausdruecke} +\end{equation} +von den Brennpunkten, für die +\begin{equation} +\overline{PF_1}+\overline{PF_2} += +2a +\label{buch:elliptisch:eqn:pf1pf2a} +\end{equation} +gelten muss. +Man kann nachrechnen, dass ein Punkt $P$, der die Gleichung +\[ +\frac{x^2}{a^2} + \frac{y^2}{b^2}=1 +\] +erfüllt, auch die Eigenschaft~\eqref{buch:elliptisch:eqn:pf1pf2a} +erfüllt. +Zur Vereinfachung setzen wir $l_1=\overline{PF_1}$ und $l_2=\overline{PF_2}$. +$l_1$ und $l_2$ sind Wurzeln aus der rechten Seite von +\eqref{buch:elliptisch:eqn:wurzelausdruecke}. +Das Quadrat von $l_1+l_2$ ist +\[ +l_1^2 + 2l_1l_2 + l_2^2 = 4a^2. +\] +Um die Wurzeln ganz zu eliminieren, bringt man das Produkt $l_1l_2$ alleine +auf die rechte Seite und quadriert. +Man muss also verifizieren, dass +\[ +(l_1^2 + l_2^2 -4a^2)^2 = 4l_1^2l_2^2. +\] +In den entstehenden Ausdrücken muss man ausserdem $e=\sqrt{a^2-b^2}$ und +\[ +y=b\sqrt{1-\frac{x^2}{a^2}} +\] +substituieren. +Diese Rechnung führt man am einfachsten mit Hilfe eines +Computeralgebraprogramms durch, welches obige Behauptung bestätigt. + +% +% Normierung +% +\subsubsection{Normierung} +Die trigonometrischen Funktionen sind definiert als Verhältnisse +von Seiten rechtwinkliger Dreiecke. +Dadurch, dass man den die Hypothenuse auf Länge $1$ normiert, +kann man die Sinus- und Kosinus-Funktion als Koordinaten eines +Punktes auf dem Einheitskreis interpretieren. + +Für die Koordinaten eines Punktes auf der Ellipse ist dies nicht so einfach, +weil es nicht nur eine Ellipse gibt, sondern für jede numerische Exzentrizität +mindestens eine mit Halbeachse $1$. +Wir wählen die Ellipsen so, dass $a$ die grosse Halbachse ist, also $a>b$. +Als Normierungsbedingung verwenden wir, dass $b=1$ sein soll, wie in +Abbildung~\ref{buch:elliptisch:fig:jacobidef}. +Dann ist $a=1/\varepsilon>1$. +In dieser Normierung haben Punkte $(x,y)$ auf der Ellipse $y$-Koordinaten +zwischen $-1$ und $1$ und $x$-Koordinaten zwischen $-a$ und $a$. + +Im Zusammenhang mit elliptischen Funktionen wird die numerische Exzentrizität +$\varepsilon$ auch mit +\[ +k += +\varepsilon += +\frac{e}{a} += +\frac{\sqrt{a^2-b^2}}{a} += +\frac{\sqrt{a^2-1}}{a}, +\] +die Zahl $k$ heisst auch der {\em Modulus}. +Man kann $a$ auch durch $k$ ausdrücken, durch Quadrieren und Umstellen +findet man +\[ +k^2a^2 = a^2-1 +\quad\Rightarrow\quad +1=a^2(k^2-1) +\quad\Rightarrow\quad +a=\frac{1}{\sqrt{k^2-1}}. +\] + +Die Gleichung der ``Einheitsellipse'' zu diesem Modulus ist +\[ +\frac{x^2}{a^2}+y^2=1 +\qquad\text{oder}\qquad +x^2(k^2-1) + y^2 = 1. +\] + +% +% Definition der elliptischen Funktionen +% +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/jacobidef.pdf} +\caption{Definition der elliptischen Funktionen als Trigonometrie +an einer Ellipse mit Halbachsen $a$ und $1$. +\label{buch:elliptisch:fig:jacobidef}} +\end{figure} +\subsubsection{Definition der elliptischen Funktionen} +Die elliptischen Funktionen für einen Punkt $P$ auf der Ellipse mit Modulus $k$ +können jetzt als Verhältnisse der Koordinaten des Punktes definieren. +Es stellt sich aber die Frage, was man als Argument verwenden soll. +Es soll so etwas wie den Winkel $\varphi$ zwischen der $x$-Achse und dem +Radiusvektor zum Punkt $P$ +darstellen, aber wir haben hier noch eine Wahlfreiheit, die wir später +ausnützen möchten. +Im Moment müssen wir die Frage noch nicht beantworten und nennen das +noch unbestimmte Argument $u$. +Wir kümmern uns später um die Frage, wie $u$ von $\varphi$ abhängt. + +Die Funktionen, die wir definieren wollen, hängen ausserdem auch +vom Modulus ab. +Falls der verwendete Modulus aus dem Zusammenhang klar ist, lassen +wir das $k$-Argument weg. + +Die Punkte auf dem Einheitskreis haben alle den gleichen Abstand vom +Nullpunkt, dies ist gleichzeitig die definierende Gleichung $r^2=x^2+y^2=1$ +des Kreises. +Die Punkte auf der Ellipse erfüllen die Gleichung $x^2/a^2+y^2=1$, +die Entfernung der Punkte $r=\sqrt{x^2+y^2}$ vom Nullpunkt variert aber. + +In Analogie zu den trigonometrischen Funktionen setzen wir jetzt für +die Funktionen +\[ +\begin{aligned} +&\text{sinus amplitudinis:}& +{\color{red}\operatorname{sn}(u,k)}&= y \\ +&\text{cosinus amplitudinis:}& +{\color{blue}\operatorname{cn}(u,k)}&= \frac{x}{a} \\ +&\text{delta amplitudinis:}& +{\color{darkgreen}\operatorname{dn}(u,k)}&=\frac{r}{a}, +\end{aligned} +\] +die auch in Abbildung~\ref{buch:elliptisch:fig:jacobidef} +dargestellt sind. +Aus der Gleichung der Ellipse folgt sofort, dass +\[ +\operatorname{sn}(u,k)^2 + \operatorname{cn}(u,k)^2 = 1 +\] +ist. +Der Satz von Pythagoras kann verwendet werden, um die Entfernung zu +berechnen, also gilt +\begin{equation} +r^2 += +a^2 \operatorname{dn}(u,k)^2 += +x^2 + y^2 += +a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2 +\quad +\Rightarrow +\quad +a^2 \operatorname{dn}(u,k)^2 += +a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2. +\label{buch:elliptisch:eqn:sncndnrelation} +\end{equation} +Ersetzt man +$ +a^2\operatorname{cn}(u,k)^2 += +a^2-a^2\operatorname{sn}(u,k)^2 +$, ergibt sich +\[ +a^2 \operatorname{dn}(u,k)^2 += +a^2-a^2\operatorname{sn}(u,k)^2 ++ +\operatorname{sn}(u,k)^2 +\quad +\Rightarrow +\quad +\operatorname{dn}(u,k)^2 ++ +\frac{a^2-1}{a^2}\operatorname{sn}(u,k)^2 += +1, +\] +woraus sich die Identität +\[ +\operatorname{dn}(u,k)^2 + k^2 \operatorname{sn}(u,k)^2 = 1 +\] +ergibt. +Ebenso kann man aus~\eqref{buch:elliptisch:eqn:sncndnrelation} +die Funktion $\operatorname{cn}(u,k)$ eliminieren, was auf +\[ +a^2\operatorname{dn}(u,k)^2 += +a^2\operatorname{cn}(u,k)^2 ++1-\operatorname{cn}(u,k)^2 += +(a^2-1)\operatorname{cn}(u,k)^2 ++1. +\] +Nach Division durch $a^2$ ergibt sich +\begin{align*} +\operatorname{dn}(u,k)^2 +- +k^2\operatorname{cn}(u,k)^2 +&= +\frac{1}{a^2} += +\frac{a^2-a^2+1}{a^2} += +1-k^2 =: k^{\prime 2}. +\end{align*} +Wir stellen die hiermit gefundenen Relationen zwischen den grundlegenden +Jacobischen elliptischen Funktionen für später zusammen in den Formeln +\begin{equation} +\begin{aligned} +\operatorname{sn}^2(u,k) ++ +\operatorname{cn}^2(u,k) +&= +1 +\\ +\operatorname{dn}^2(u,k) + k^2\operatorname{sn}^2(u,k) +&= +1 +\\ +\operatorname{dn}^2(u,k) -k^2\operatorname{cn}^2(u,k) +&= +k^{\prime 2}. +\end{aligned} +\label{buch:elliptisch:eqn:jacobi-relationen} +\end{equation} +zusammen. +So wie es möglich ist, $\sin\alpha$ durch $\cos\alpha$ auszudrücken, +ist es mit +\eqref{buch:elliptisch:eqn:jacobi-relationen} +jetzt auch möglich jede grundlegende elliptische Funktion durch +jede anderen auszudrücken. +Die Resultate sind in der Tabelle~\ref{buch:elliptisch:fig:jacobi-relationen} +zusammengestellt. + +\begin{table} +\centering +\renewcommand{\arraystretch}{2.1} +\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} +\hline +&\operatorname{sn}(u,k) +&\operatorname{cn}(u,k) +&\operatorname{dn}(u,k)\\ +\hline +\operatorname{sn}(u,k) +&\operatorname{sn}(u,k) +&\sqrt{1-\operatorname{cn}^2(u,k)} +&\frac1k\sqrt{1-\operatorname{dn}^2(u,k)} +\\ +\operatorname{cn}(u,k) +&\sqrt{1-\operatorname{sn}^2(u,k)} +&\operatorname{cn}(u,k) +&\frac{1}{k}\sqrt{\operatorname{dn}^2(u,k)-k^{\prime2}} +\\ +\operatorname{dn}(u,k) +&\sqrt{1-k^2\operatorname{sn}^2(u,k)} +&\sqrt{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} +&\operatorname{dn}(u,k) +\\ +\hline +\end{tabular} +\caption{Jede der Jacobischen elliptischen Funktionen lässt sich +unter Verwendung der Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} +durch jede andere ausdrücken. +\label{buch:elliptisch:fig:jacobi-relationen}} +\end{table} + +% +% Ableitungen der Jacobi-ellpitischen Funktionen +% +\subsubsection{Ableitung} +Die trigonometrischen Funktionen sind deshalb so besonders nützlich +für die Lösung von Schwingungsdifferentialgleichungen, weil sie die +Beziehungen +\[ +\frac{d}{d\varphi} \cos\varphi = -\sin\varphi +\qquad\text{und}\qquad +\frac{d}{d\varphi} \sin\varphi = \cos\varphi +\] +erfüllen. +So einfach können die Beziehungen natürlich nicht sein, sonst würde sich +durch Integration ja wieder nur die trigonometrischen Funktionen ergeben. +Durch geschickte Wahl des Arguments $u$ kann man aber erreichen, dass +sie ähnlich nützliche Beziehungen zwischen den Ableitungen ergeben. + +Gesucht ist jetzt also eine Wahl für das Argument $u$ zum Beispiel in +Abhängigkeit von $\varphi$, dass sich einfache und nützliche +Ableitungsformeln ergeben. +Wir setzen daher $u(\varphi)$ voraus und beachten, dass $x$ und $y$ +ebenfalls von $\varphi$ abhängen, es ist +$y=\sin\varphi$ und $x=a\cos\varphi$. +Die Ableitungen von $x$ und $y$ nach $\varphi$ sind +\begin{align*} +\frac{dy}{d\varphi} +&= +\cos\varphi += +\frac{1}{a} x += +\operatorname{cn}(u,k) +\\ +\frac{dx}{d\varphi} +&= +-a\sin\varphi += +-a y += +-a\operatorname{sn}(u,k). +\end{align*} +Daraus kann man jetzt die folgenden Ausdrücke für die Ableitungen der +elliptischen Funktionen nach $\varphi$ ableiten: +\begin{align*} +\frac{d}{d\varphi} \operatorname{sn}(u,z) +&= +\frac{d}{d\varphi} y(\varphi) += +\cos\varphi += +\frac{x}{a} += +\operatorname{cn}(u,k) +&&\Rightarrow& +\frac{d}{du} +\operatorname{sn}(u,k) +&= +\operatorname{cn}(u,k) \frac{d\varphi}{du} +\\ +\frac{d}{d\varphi} \operatorname{cn}(u,z) +&= +\frac{d}{d\varphi} \frac{x(\varphi)}{a} += +-\sin\varphi += +-\operatorname{sn}(u,k) +&&\Rightarrow& +\frac{d}{du}\operatorname{cn}(u,k) +&= +-\operatorname{sn}(u,k) \frac{d\varphi}{du} +\\ +\frac{d}{d\varphi} \operatorname{dn}(u,z) +&= +\frac{1}{a}\frac{dr}{d\varphi} += +\frac{1}{a}\frac{d\sqrt{x^2+y^2}}{d\varphi} +%\\ +%& +\rlap{$\displaystyle\mathstrut += +\frac{x}{ar} \frac{dx}{d\varphi} ++ +\frac{y}{ar} \frac{dy}{d\varphi} +%\\ +%& += +\frac{x}{ar} (-a\operatorname{sn}(u,k)) ++ +\frac{y}{ar} \operatorname{cn}(u,k) +$} +\\ +& +\rlap{$\displaystyle\mathstrut += +\frac{x}{ar}(-ay) ++ +\frac{y}{ar} \frac{x}{a} +%\rlap{$\displaystyle += +\frac{xy(-1+\frac{1}{a^2})}{r} +%$} +%\\ +%& += +-\frac{xy(a^2-1)}{a^2r} +$} +\\ +&= +-\frac{a^2-1}{ar} +\operatorname{cn}(u,k) \operatorname{sn}(u,k) +%\\ +%& +\rlap{$\displaystyle\mathstrut += +-k^2 +\frac{a}{r} +\operatorname{cn}(u,k) \operatorname{sn}(u,k) +$} +\\ +&= +-k^2\frac{\operatorname{cn}(u,k)\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} +&&\Rightarrow& +\frac{d}{du} \operatorname{dn}(u,k) +&= +-k^2\frac{\operatorname{cn}(u,k) +\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} +\frac{d\varphi}{du}. +\end{align*} +Die einfachsten Beziehungen ergeben sich offenbar, wenn man $u$ so +wählt, dass +\[ +\frac{d\varphi}{du} += +\operatorname{dn}(u,k) += +\frac{r}{a}. +\] +Damit haben wir die grundlegenden Ableitungsregeln + +\begin{satz} +\label{buch:elliptisch:satz:ableitungen} +Die Jacobischen elliptischen Funktionen haben die Ableitungen +\begin{equation} +\begin{aligned} +\frac{d}{du}\operatorname{sn}(u,k) +&= +\phantom{-}\operatorname{cn}(u,k)\operatorname{dn}(u,k) +\\ +\frac{d}{du}\operatorname{cn}(u,k) +&= +-\operatorname{sn}(u,k)\operatorname{dn}(u,k) +\\ +\frac{d}{du}\operatorname{dn}(u,k) +&= +-k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k). +\end{aligned} +\label{buch:elliptisch:eqn:ableitungsregeln} +\end{equation} +\end{satz} + +% +% Der Grenzfall $k=1$ +% +\subsubsection{Der Grenzwert $k\to1$} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/sncnlimit.pdf} +\caption{Grenzfälle der Jacobischen elliptischen Funktionen +für die Werte $0$ und $1$ des Parameters $k$. +\label{buch:elliptisch:fig:sncnlimit}} +\end{figure} +Für $k=1$ ist $k^{\prime2}=1-k^2=$ und es folgt aus den +Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} +\[ +\operatorname{cn}^2(u,k) +- +k^2 +\operatorname{dn}^2(u,k) += +k^{\prime2} += +0 +\qquad\Rightarrow\qquad +\operatorname{cn}^2(u,1) += +\operatorname{dn}^2(u,1), +\] +die beiden Funktionen +$\operatorname{cn}(u,k)$ +und +$\operatorname{dn}(u,k)$ +fallen also zusammen. +Die Ableitungsregeln werden dadurch vereinfacht: +\begin{align*} +\operatorname{sn}'(u,1) +&= +\operatorname{cn}(u,1) +\operatorname{dn}(u,1) += +\operatorname{cn}^2(u,1) += +1-\operatorname{sn}^2(u,1) +&&\Rightarrow& y'&=1-y^2 +\\ +\operatorname{cn}'(u,1) +&= +- +\operatorname{sn}(u,1) +\operatorname{dn}(u,1) += +- +\operatorname{sn}(u,1)\operatorname{cn}(u,1) +&&\Rightarrow& +\frac{z'}{z}&=(\log z)' = -y +\end{align*} +Die erste Differentialgleichung für $y$ lässt sich separieren, man findet +die Lösung +\[ +\frac{y'}{1-y^2} += +1 +\quad\Rightarrow\quad +\int \frac{dy}{1-y^2} = \int \,du +\quad\Rightarrow\quad +\operatorname{artanh}(y) = u +\quad\Rightarrow\quad +\operatorname{sn}(u,1)=\tanh u. +\] +Damit kann man jetzt auch $z$ berechnen: +\begin{align*} +(\log \operatorname{cn}(u,1))' +&= +\tanh u +&&\Rightarrow& +\log\operatorname{cn}(u,1) +&= +-\int\tanh u\,du += +-\log\cosh u +\\ +& +&&\Rightarrow& +\operatorname{cn}(u,1) +&= +\frac{1}{\cosh u} += +\operatorname{sech}u. +\end{align*} +Die Grenzfunktionen sind in Abbildung~\ref{buch:elliptisch:fig:sncnlimit} +dargestellt. + +% +% Das Argument u +% +\subsubsection{Das Argument $u$} +Die Gleichung +\begin{equation} +\frac{d\varphi}{du} += +\operatorname{dn}(u,k) +\label{buch:elliptisch:eqn:uableitung} +\end{equation} +ermöglicht, $\varphi$ in Abhängigkeit von $u$ zu berechnen, ohne jedoch +die geometrische Bedeutung zu klären. +Das beginnt bereits damit, dass der Winkel $\varphi$ nicht nicht der +Polarwinkel des Punktes $P$ in Abbildung~\ref{buch:elliptisch:fig:jacobidef} +ist, diesen nennen wir $\vartheta$. +Der Zusammenhang zwischen $\varphi$ und $\vartheta$ ist +\begin{equation} +\frac1{a}\tan\varphi = \tan\vartheta +\label{buch:elliptisch:eqn:phitheta} +\end{equation} + +Um die geometrische Bedeutung besser zu verstehen, nehmen wir jetzt an, +dass die Ellipse mit einem Parameter $t$ parametrisiert ist, dass also +$\varphi(t)$, $\vartheta(t)$ und $u(t)$ Funktionen von $t$ sind. +Die Ableitung von~\eqref{buch:elliptisch:eqn:phitheta} ist +\[ +\frac1{a}\cdot \frac{1}{\cos^2\varphi}\cdot \dot{\varphi} += +\frac{1}{\cos^2\vartheta}\cdot \dot{\vartheta}. +\] +Daraus kann die Ableitung von $\vartheta$ nach $\varphi$ bestimmt +werden, sie ist +\[ +\frac{d\vartheta}{d\varphi} += +\frac{\dot{\vartheta}}{\dot{\varphi}} += +\frac{1}{a} +\cdot +\frac{\cos^2\vartheta}{\cos^2\varphi} += +\frac{1}{a} +\cdot +\frac{(x/r)^2}{(x/a)^2} += +\frac{1}{a}\cdot +\frac{a^2}{r^2} += +\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)}. +\] +Damit kann man jetzt mit Hilfe von~\eqref{buch:elliptisch:eqn:uableitung} +Die Ableitung von $\vartheta$ nach $u$ ermitteln, sie ist +\[ +\frac{d\vartheta}{du} += +\frac{d\vartheta}{d\varphi} +\cdot +\frac{d\varphi}{du} += +\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)} +\cdot +\operatorname{dn}(u,k) += +\frac{1}{a} +\cdot +\frac{1}{\operatorname{dn}(u,k)} += +\frac{1}{a} +\cdot\frac{a}{r} += +\frac{1}{r}, +\] +wobei wir auch die Definition der Funktion $\operatorname{dn}(u,k)$ +verwendet haben. + +In der Parametrisierung mit dem Parameter $t$ kann man jetzt die Ableitung +von $u$ nach $t$ berechnen als +\[ +\frac{du}{dt} += +\frac{du}{d\vartheta} +\frac{d\vartheta}{dt} += +r +\dot{\vartheta}. +\] +Darin ist $\dot{\vartheta}$ die Winkelgeschwindigkeit des Punktes um +das Zentrum $O$ und $r$ ist die aktuelle Entfernung des Punktes $P$ +von $O$. +$r\dot{\vartheta}$ ist also die Geschwindigkeitskomponenten des Punktes +$P$ senkrecht auf den aktuellen Radiusvektor. +Der Parameter $u$, der zum Punkt $P$ gehört, ist also das Integral +\[ +u(P) = \int_0^P r\,d\vartheta. +\] +Für einen Kreis ist die Geschwindigkeit von $P$ immer senkrecht +auf dem Radiusvektor und der Radius ist konstant, so dass +$u(P)=\vartheta(P)$ ist. + +% +% Die abgeleiteten elliptischen Funktionen +% +\begin{figure} +\centering +\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobi12.pdf} +\caption{Die Verhältnisse der Funktionen +$\operatorname{sn}(u,k)$, +$\operatorname{cn}(u,k)$ +udn +$\operatorname{dn}(u,k)$ +geben Anlass zu neun weitere Funktionen, die sich mit Hilfe +des Strahlensatzes geometrisch interpretieren lassen. +\label{buch:elliptisch:fig:jacobi12}} +\end{figure} +\begin{table} +\centering +\renewcommand{\arraystretch}{2.5} +\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} +\hline +\cdot & +\frac{1}{1} & +\frac{1}{\operatorname{sn}(u,k)} & +\frac{1}{\operatorname{cn}(u,k)} & +\frac{1}{\operatorname{dn}(u,k)} +\\[5pt] +\hline +1& +&%\operatorname{nn}(u,k)=\frac{1}{1} & +\operatorname{ns}(u,k)=\frac{1}{\operatorname{sn}(u,k)} & +\operatorname{nc}(u,k)=\frac{1}{\operatorname{cn}(u,k)} & +\operatorname{nd}(u,k)=\frac{1}{\operatorname{dn}(u,k)} +\\ +\operatorname{sn}(u,k) & +\operatorname{sn}(u,k)=\frac{\operatorname{sn}(u,k)}{1}& +&%\operatorname{ss}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{sn}(u,k)}& +\operatorname{sc}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)}& +\operatorname{sd}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} +\\ +\operatorname{cn}(u,k) & +\operatorname{cn}(u,k)=\frac{\operatorname{cn}(u,k)}{1} & +\operatorname{cs}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{sn}(u,k)}& +&%\operatorname{cc}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{cn}(u,k)}& +\operatorname{cd}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{dn}(u,k)} +\\ +\operatorname{dn}(u,k) & +\operatorname{dn}(u,k)=\frac{\operatorname{dn}(u,k)}{1} & +\operatorname{ds}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{sn}(u,k)}& +\operatorname{dc}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)}& +%\operatorname{dd}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{dn}(u,k)} +\\[5pt] +\hline +\end{tabular} +\caption{Zusammenstellung der abgeleiteten Jacobischen elliptischen +Funktionen in hinteren drei Spalten als Quotienten der grundlegenden +Jacobischen elliptischen Funktionen. +Die erste Spalte zum Nenner $1$ enthält die grundlegenden +Jacobischen elliptischen Funktionen. +\label{buch:elliptisch:table:abgeleitetjacobi}} +\end{table} + +% +% Die abgeleiteten elliptischen Funktionen +% +\subsubsection{Die abgeleiteten elliptischen Funktionen} +Zusätzlich zu den grundlegenden Jacobischen elliptischen Funktioenn +lassen sich weitere elliptische Funktionen bilden, die unglücklicherweise +die {\em abgeleiteten elliptischen Funktionen} genannt werden. +Ähnlich wie die trigonometrischen Funktionen $\tan\alpha$, $\cot\alpha$, +$\sec\alpha$ und $\csc\alpha$ als Quotienten von $\sin\alpha$ und +$\cos\alpha$ definiert sind, sind die abgeleiteten elliptischen Funktionen +die in Tabelle~\ref{buch:elliptisch:table:abgeleitetjacobi} zusammengestellten +Quotienten der grundlegenden Jacobischen elliptischen Funktionen. +Die Bezeichnungskonvention ist, dass die Funktion $\operatorname{pq}(u,k)$ +ein Quotient ist, dessen Zähler durch den Buchstaben p bestimmt ist, +der Nenner durch den Buchstaben q. +Der Buchstabe n steht für eine $1$, die Buchstaben s, c und d stehen für +die Anfangsbuchstaben der grundlegenden Jacobischen elliptischen +Funktionen. +Meint man irgend eine der Jacobischen elliptischen Funktionen, schreibt +man manchmal auch $\operatorname{zn}(u,k)$. + +In Abbildung~\ref{buch:elliptisch:fig:jacobi12} sind die Quotienten auch +geometrisch interpretiert. +Der Wert der Funktion $\operatorname{nq}(u,k)$ ist die auf dem Strahl +mit Polarwinkel $\varphi$ abgetragene Länge bis zu den vertikalen +Geraden, die den verschiedenen möglichen Nennern entsprechen. +Entsprechend ist der Wert der Funktion $\operatorname{dq}(u,k)$ die +Länge auf dem Strahl mit Polarwinkel $\vartheta$. + +Die Relationen~\ref{buch:elliptisch:eqn:jacobi-relationen} +ermöglichen, jede Funktion $\operatorname{zn}(u,k)$ durch jede +andere auszudrücken. +Die schiere Anzahl solcher Beziehungen macht es unmöglich, sie +übersichtlich in einer Tabelle zusammenzustellen, daher soll hier +nur an einem Beispiel das Vorgehen gezeigt werden: + +\begin{beispiel} +Die Funktion $\operatorname{sc}(u,k)$ soll durch $\operatorname{cd}(u,k)$ +ausgedrückt werden. +Zunächst ist +\[ +\operatorname{sc}(u,k) += +\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} +\] +nach Definition. +Im Resultat sollen nur noch $\operatorname{cn}(u,k)$ und +$\operatorname{dn}(u,k)$ vorkommen. +Daher eliminieren wir zunächst die Funktion $\operatorname{sn}(u,k)$ +mit Hilfe von \eqref{buch:elliptisch:eqn:jacobi-relationen} und erhalten +\begin{equation} +\operatorname{sc}(u,k) += +\frac{\sqrt{1-\operatorname{cn}^2(u,k)}}{\operatorname{cn}(u,k)}. +\label{buch:elliptisch:eqn:allgausdruecken} +\end{equation} +Nun genügt es, die Funktion $\operatorname{cn}(u,k)$ durch +$\operatorname{cd}(u,k)$ auszudrücken. +Aus der Definition und der +dritten Relation in \eqref{buch:elliptisch:eqn:jacobi-relationen} +erhält man +\begin{align*} +\operatorname{cd}^2(u,k) +&= +\frac{\operatorname{cn}^2(u,k)}{\operatorname{dn}^2(u,k)} += +\frac{\operatorname{cn}^2(u,k)}{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} +\\ +\Rightarrow +\qquad +k^{\prime 2} +\operatorname{cd}^2(u,k) ++ +k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) +&= +\operatorname{cn}^2(u,k) +\\ +\operatorname{cn}^2(u,k) +- +k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) +&= +k^{\prime 2} +\operatorname{cd}^2(u,k) +\\ +\operatorname{cn}^2(u,k) +&= +\frac{ +k^{\prime 2} +\operatorname{cd}^2(u,k) +}{ +1 - k^2\operatorname{cd}^2(u,k) +} +\end{align*} +Für den Zähler brauchen wir $1-\operatorname{cn}^2(u,k)$, also +\[ +1-\operatorname{cn}^2(u,k) += +\frac{ +1 +- +k^2\operatorname{cd}^2(u,k) +- +k^{\prime 2} +\operatorname{cd}^2(u,k) +}{ +1 +- +k^2\operatorname{cd}^2(u,k) +} += +\frac{1-\operatorname{cd}^2(u,k)}{1-k^2\operatorname{cd}^2(u,k)} +\] +Einsetzen in~\eqref{buch:elliptisch:eqn:allgausdruecken} gibt +\begin{align*} +\operatorname{sc}(u,k) +&= +\frac{ +\sqrt{1-\operatorname{cd}^2(u,k)} +}{\sqrt{1-k^2\operatorname{cd}^2(u,k)}} +\cdot +\frac{ +\sqrt{1 - k^2\operatorname{cd}^2(u,k)} +}{ +k' +\operatorname{cd}(u,k) +} += +\frac{ +\sqrt{1-\operatorname{cd}^2(u,k)} +}{ +k' +\operatorname{cd}(u,k) +}. +\qedhere +\end{align*} +\end{beispiel} + +\subsubsection{Ableitung der abgeleiteten elliptischen Funktionen} +Aus den Ableitungen der grundlegenden Jacobischen elliptischen Funktionen +können mit der Quotientenregel nun auch beliebige Ableitungen der +abgeleiteten Jacobischen elliptischen Funktionen gefunden werden. +Als Beispiel berechnen wir die Ableitung von $\operatorname{sc}(u,k)$. +Sie ist +\begin{align*} +\frac{d}{du} +\operatorname{sc}(u,k) +&= +\frac{d}{du} +\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} += +\frac{ +\operatorname{sn}'(u,k)\operatorname{cn}(u,k) +- +\operatorname{sn}(u,k)\operatorname{cn}'(u,k)}{ +\operatorname{cn}^2(u,k) +} +\\ +&= +\frac{ +\operatorname{cn}^2(u,k)\operatorname{dn}(u,k) ++ +\operatorname{sn}^2(u,k)\operatorname{dn}(u,k) +}{ +\operatorname{cn}^2(u,k) +} += +\frac{( +\operatorname{sn}^2(u,k) ++ +\operatorname{cn}^2(u,k) +)\operatorname{dn}(u,k)}{ +\operatorname{cn}^2(u,k) +} +\\ +&= +\frac{1}{\operatorname{cn}(u,k)} +\cdot +\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)} += +\operatorname{nc}(u,k) +\operatorname{dc}(u,k). +\end{align*} +Man beachte, dass das Quadrat der Nennerfunktion im Resultat +der Quotientenregel zur Folge hat, dass die +beiden Funktionen im Resultat beide den gleichen Nenner haben wie +die Funktion, die abgeleitet wird. + +Mit etwas Fleiss kann man nach diesem Muster alle Ableitungen +\begin{equation} +%\small +\begin{aligned} +\operatorname{sn}'(u,k) +&= +\phantom{-} +\operatorname{cn}(u,k)\,\operatorname{dn}(u,k) +&&\qquad& +\operatorname{ns}'(u,k) +&= +- +\operatorname{cs}(u,k)\,\operatorname{ds}(u,k) +\\ +\operatorname{cn}'(u,k) +&= +- +\operatorname{sn}(u,k)\,\operatorname{dn}(u,k) +&&& +\operatorname{nc}'(u,k) +&= +\phantom{-} +\operatorname{sc}(u,k)\,\operatorname{dc}(u,k) +\\ +\operatorname{dn}'(u,k) +&= +-k^2 +\operatorname{sn}(u,k)\,\operatorname{cn}(u,k) +&&& +\operatorname{nd}'(u,k) +&= +\phantom{-} +k^2 +\operatorname{sd}(u,k)\,\operatorname{cd}(u,k) +\\ +\operatorname{sc}'(u,k) +&= +\phantom{-} +\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) +&&& +\operatorname{cs}'(u,k) +&= +- +\operatorname{ds}(u,k)\,\operatorname{ns}(u,k) +\\ +\operatorname{cd}'(u,k) +&= +-k^{\prime2} +\operatorname{sd}(u,k)\,\operatorname{nd}(u,k) +&&& +\operatorname{dc}'(u,k) +&= +\phantom{-} +k^{\prime2} +\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) +\\ +\operatorname{ds}'(d,k) +&= +- +\operatorname{cs}(u,k)\,\operatorname{ns}(u,k) +&&& +\operatorname{sd}'(d,k) +&= +\phantom{-} +\operatorname{cd}(u,k)\,\operatorname{nd}(u,k) +\end{aligned} +\label{buch:elliptisch:eqn:alleableitungen} +\end{equation} +finden. +Man beachte, dass in jeder Identität alle Funktionen den gleichen +zweiten Buchstaben haben. + +\subsubsection{TODO} +XXX algebraische Beziehungen \\ +XXX Additionstheoreme \\ +XXX Perioden +% use https://math.stackexchange.com/questions/3013692/how-to-show-that-jacobi-sine-function-is-doubly-periodic + + diff --git a/buch/chapters/110-elliptisch/mathpendel.tex b/buch/chapters/110-elliptisch/mathpendel.tex new file mode 100644 index 0000000..d61bcf6 --- /dev/null +++ b/buch/chapters/110-elliptisch/mathpendel.tex @@ -0,0 +1,250 @@ +% +% mathpendel.tex -- Das mathematische Pendel +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% + +\subsection{Das mathematische Pendel +\label{buch:elliptisch:subsection:mathpendel}} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/pendel.pdf} +\caption{Mathematisches Pendel +\label{buch:elliptisch:fig:mathpendel}} +\end{figure} +Das in Abbildung~\ref{buch:elliptisch:fig:mathpendel} dargestellte +Mathematische Pendel besteht aus einem Massepunkt der Masse $m$ +im Punkt $P$, +der über eine masselose Stange der Länge $l$ mit dem Drehpunkt $O$ +verbunden ist. +Das Pendel bewegt sich unter dem Einfluss der Schwerebeschleunigung $g$. + +Das Trägheitsmoment des Massepunktes um den Drehpunkt $O$ ist +\( +I=ml^2 +\). +Das Drehmoment der Schwerkraft ist +\(M=gl\sin\vartheta\). +Die Bewegungsgleichung wird daher +\[ +\begin{aligned} +\frac{d}{dt} I\dot{\vartheta} +&= +M += +gl\sin\vartheta +\\ +ml^2\ddot{\vartheta} +&= +gl\sin\vartheta +&&\Rightarrow& +\ddot{\vartheta} +&=\frac{g}{l}\sin\vartheta +\end{aligned} +\] +Dies ist eine nichtlineare Differentialgleichung zweiter Ordnung, die +wir nicht unmittelbar mit den Differentialgleichungen erster Ordnung +der elliptischen Funktionen vergleichen können. + +Die Differentialgleichungen erster Ordnung der elliptischen Funktionen +enthalten das Quadrat der ersten Ableitung. +In unserem Fall entspricht das einer Gleichung, die $\dot{\vartheta}^2$ +enthält. +Der Energieerhaltungssatz kann uns eine solche Gleichung geben. +Die Summe von kinetischer und potentieller Energie muss konstant sein. +Dies führt auf +\[ +E_{\text{kinetisch}} ++ +E_{\text{potentiell}} += +\frac12I\dot{\vartheta}^2 ++ +mgl(1-\cos\vartheta) += +\frac12ml^2\dot{\vartheta}^2 ++ +mgl(1-\cos\vartheta) += +E +\] +Durch Auflösen nach $\dot{\vartheta}$ kann man jetzt die +Differentialgleichung +\[ +\dot{\vartheta}^2 += +- +\frac{2g}{l}(1-\cos\vartheta) ++\frac{2E}{ml^2} +\] +finden. +In erster Näherung, d.h. wenn man die rechte Seite bis zu vierten +Potenzen in eine Taylor-Reihe in $\vartheta$ entwickelt, ist dies +tatsächlich eine Differentialgleichung der Art, wie wir sie für +elliptische Funktionen gefunden haben, wir möchten aber eine exakte +Lösung konstruieren. + +Die maximale Energie für eine Bewegung, bei der sich das Pendel gerade +über den höchsten Punkt hinweg zu bewegen vermag, ist +$E=2lmg$. +Falls $E<2mgl$ ist, erwarten wir Schwingungslösungen, bei denen +der Winkel $\vartheta$ immer im offenen Interval $(-\pi,\pi)$ +bleibt. +Für $E>2mgl$ wird sich das Pendel im Kreis bewegen, für sehr grosse +Energie ist die kinetische Energie dominant, die Verlangsamung im +höchsten Punkt wird immer weniger ausgeprägt sein. + +% +% Koordinatentransformation auf elliptische Funktionen +% +\subsubsection{Koordinatentransformation auf elliptische Funktionen} +Wir verwenden als neue Variable +\[ +y = \sin\frac{\vartheta}2 +\] +mit der Ableitung +\[ +\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. +\] +Man beachte, dass $y$ nicht eine Koordinate in +Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. + +Aus den Halbwinkelformeln finden wir +\[ +\cos\vartheta += +1-2\sin^2 \frac{\vartheta}2 += +1-2y^2. +\] +Dies können wir zusammen mit der +Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ +in die Energiegleichung einsetzen und erhalten +\[ +\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E +\qquad\Rightarrow\qquad +\frac14 \dot{\vartheta}^2 = \frac{E}{2ml^2} - \frac{g}{2l}y^2. +\] +Der konstante Term auf der rechten Seite ist grösser oder kleiner als +$1$ je nachdem, ob das Pendel sich im Kreis bewegt oder nicht. + +Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ +erhalten wir auf der linken Seite einen Ausdruck, den wir +als Funktion von $\dot{y}$ ausdrücken können. +Wir erhalten +\begin{align*} +\frac14 +\cos^2\frac{\vartheta}2 +\cdot +\dot{\vartheta}^2 +&= +\frac14 +(1-y^2) +\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) +\\ +\dot{y}^2 +&= +\frac{1}{4} +(1-y^2) +\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) +\end{align*} +Die letzte Gleichung hat die Form einer Differentialgleichung +für elliptische Funktionen. +Welche Funktion verwendet werden muss, hängt von der Grösse der +Koeffizienten in der zweiten Klammer ab. +Die Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} +zeigt, dass in der zweiten Klammer jeweils einer der Terme +$1$ sein muss. + +% +% Der Fall E < 2mgl +% +\subsubsection{Der Fall $E<2mgl$} +\begin{figure} +\centering +\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} +\caption{% +Abhängigkeit der elliptischen Funktionen von $u$ für +verschiedene Werte von $k^2=m$. +Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, +$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese +sind in allen Plots in einer helleren Farbe eingezeichnet. +Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig +von den trigonometrischen Funktionen ab, +es ist aber klar erkennbar, dass die anharmonischen Terme in der +Differentialgleichung die Periode mit steigender Amplitude verlängern. +Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass +die Energie des Pendels fast ausreicht, dass es den höchsten Punkt +erreichen kann, was es für $m$ macht. +\label{buch:elliptisch:fig:jacobiplots}} +\end{figure} + + +Wir verwenden als neue Variable +\[ +y = \sin\frac{\vartheta}2 +\] +mit der Ableitung +\[ +\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. +\] +Man beachte, dass $y$ nicht eine Koordinate in +Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. + +Aus den Halbwinkelformeln finden wir +\[ +\cos\vartheta += +1-2\sin^2 \frac{\vartheta}2 += +1-2y^2. +\] +Dies können wir zusammen mit der +Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ +in die Energiegleichung einsetzen und erhalten +\[ +\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E. +\] +Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ +erhalten wir auf der linken Seite einen Ausdruck, den wir +als Funktion von $\dot{y}$ ausdrücken können. +Wir erhalten +\begin{align*} +\frac12ml^2 +\cos^2\frac{\vartheta}2 +\dot{\vartheta}^2 +&= +(1-y^2) +(E -mgly^2) +\\ +\frac{1}{4}\cos^2\frac{\vartheta}{2}\dot{\vartheta}^2 +&= +\frac{1}{2} +(1-y^2) +\biggl(\frac{E}{ml^2} -\frac{g}{l}y^2\biggr) +\\ +\dot{y}^2 +&= +\frac{E}{2ml^2} +(1-y^2)\biggl( +1-\frac{2gml}{E}y^2 +\biggr). +\end{align*} +Dies ist genau die Form der Differentialgleichung für die elliptische +Funktion $\operatorname{sn}(u,k)$ +mit $k^2 = 2gml/E< 1$. + +%% +%% Der Fall E > 2mgl +%% +%\subsection{Der Fall $E > 2mgl$} +%In diesem Fall hat das Pendel im höchsten Punkte immer noch genügend +%kinetische Energie, so dass es sich im Kreise dreht. +%Indem wir die Gleichung + + +%\subsection{Soliton-Lösungen der Sinus-Gordon-Gleichung} + +%\subsection{Nichtlineare Differentialgleichung vierter Ordnung} +%XXX Möbius-Transformation \\ +%XXX Reduktion auf die Differentialgleichung elliptischer Funktionen -- cgit v1.2.1 From e1b65ea3e46bf60fec0d6503b701a84f68138a24 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 21 Apr 2022 22:36:54 +0200 Subject: add lecture notes for session 5 --- buch/chapters/110-elliptisch/images/slcl.pdf | Bin 28269 -> 28233 bytes buch/chapters/110-elliptisch/images/slcl.tex | 20 +- buch/chapters/110-elliptisch/jacobi.tex | 1738 -------------------- buch/chapters/110-elliptisch/lemniskate.tex | 2 +- .../MSE/5 - Elliptische Funktionen.pdf | Bin 0 -> 5607117 bytes 5 files changed, 11 insertions(+), 1749 deletions(-) create mode 100644 vorlesungsnotizen/MSE/5 - Elliptische Funktionen.pdf diff --git a/buch/chapters/110-elliptisch/images/slcl.pdf b/buch/chapters/110-elliptisch/images/slcl.pdf index 493b5fa..c15051b 100644 Binary files a/buch/chapters/110-elliptisch/images/slcl.pdf and b/buch/chapters/110-elliptisch/images/slcl.pdf differ diff --git a/buch/chapters/110-elliptisch/images/slcl.tex b/buch/chapters/110-elliptisch/images/slcl.tex index 08241ac..0af1027 100644 --- a/buch/chapters/110-elliptisch/images/slcl.tex +++ b/buch/chapters/110-elliptisch/images/slcl.tex @@ -47,35 +47,35 @@ -- ({5*\lemniscateconstant*\dx},{1*\dy}); -\draw[color=red!20,line width=1.4pt] +\draw[color=red!40,line width=1.4pt] plot[domain=0:13,samples=200] ({\x},{\dy*sin(\ts*\x)}); -\draw[color=blue!20,line width=1.4pt] +\draw[color=blue!40,line width=1.4pt] plot[domain=0:13,samples=200] ({\x},{\dy*cos(\ts*\x)}); \draw[color=red,line width=1.4pt] \slpath; \draw[color=blue,line width=1.4pt] \clpath; \draw[->] (0,{-1*\dy-0.1}) -- (0,{1*\dy+0.4}) coordinate[label={right:$r$}]; -\draw[->] (-0.1,0) -- (13.7,0) coordinate[label={$s$}]; +\draw[->] (-0.1,0) -- (13.6,0) coordinate[label={$s$}]; \foreach \i in {1,2,3,4,5}{ \draw ({\lemniscateconstant*\i},-0.1) -- ({\lemniscateconstant*\i},0.1); } -\node at ({\lemniscateconstant*\dx},0) [below left] {$ \varpi\mathstrut$}; -\node at ({2*\lemniscateconstant*\dx},0) [below left] {$2\varpi\mathstrut$}; -\node at ({3*\lemniscateconstant*\dx},0) [below right] {$3\varpi\mathstrut$}; -\node at ({4*\lemniscateconstant*\dx},0) [below right] {$4\varpi\mathstrut$}; -\node at ({5*\lemniscateconstant*\dx},0) [below left] {$5\varpi\mathstrut$}; +\node at ({\lemniscateconstant*\dx},0) [below left] {$\frac{\varpi}2\mathstrut$}; +\node at ({2*\lemniscateconstant*\dx},0) [below left] {$\varpi\mathstrut$}; +\node at ({3*\lemniscateconstant*\dx},0) [below right] {$\frac{3\varpi}2\mathstrut$}; +\node at ({4*\lemniscateconstant*\dx},0) [below right] {$2\varpi\mathstrut$}; +\node at ({5*\lemniscateconstant*\dx},0) [below left] {$\frac{5\varpi}2\mathstrut$}; \node[color=red] at ({1.6*\lemniscateconstant*\dx},{0.6*\dy}) [below left] {$\operatorname{sl}(s)$}; \node[color=red!50] at ({1.5*\lemniscateconstant*\dx},{sin(1.5*90)*\dy*0.90}) - [above right] {$\sin \bigl(\frac{\pi}{2\varpi}s\bigr)$}; + [above right] {$\sin \bigl(\frac{\pi}{\varpi}s\bigr)$}; \node[color=blue] at ({1.4*\lemniscateconstant*\dx},{-0.6*\dy}) [above right] {$\operatorname{cl}(s)$}; \node[color=blue!50] at ({1.5*\lemniscateconstant*\dx},{cos(1.5*90)*\dy*0.90}) - [below left] {$\cos\bigl(\frac{\pi}{2\varpi}s\bigr)$}; + [below left] {$\cos\bigl(\frac{\pi}{\varpi}s\bigr)$}; \draw (-0.1,{1*\dy}) -- (0.1,{1*\dy}); \draw (-0.1,{-1*\dy}) -- (0.1,{-1*\dy}); diff --git a/buch/chapters/110-elliptisch/jacobi.tex b/buch/chapters/110-elliptisch/jacobi.tex index e1fbc00..166ea41 100644 --- a/buch/chapters/110-elliptisch/jacobi.tex +++ b/buch/chapters/110-elliptisch/jacobi.tex @@ -22,1743 +22,5 @@ dann muss man die Umkehrfunktionen der elliptischen Integrale dafür ins Auge fassen. -%% -%% elliptische Funktionen als Trigonometrie -%% -%\subsection{Elliptische Funktionen als Trigonometrie} -%\begin{figure} -%\centering -%\includegraphics{chapters/110-elliptisch/images/ellipse.pdf} -%\caption{Kreis und Ellipse zum Vergleich und zur Herleitung der -%elliptischen Funktionen von Jacobi als ``trigonometrische'' Funktionen -%auf einer Ellipse. -%\label{buch:elliptisch:fig:ellipse}} -%\end{figure} -%% based on Willliam Schwalm, Elliptic functions and elliptic integrals -%% https://youtu.be/DCXItCajCyo -% -%% -%% Geometrie einer Ellipse -%% -%\subsubsection{Geometrie einer Ellipse} -%Eine {\em Ellipse} ist die Menge der Punkte der Ebene, für die die Summe -%\index{Ellipse}% -%der Entfernungen von zwei festen Punkten $F_1$ und $F_2$, -%den {\em Brennpunkten}, konstant ist. -%\index{Brennpunkt}% -%In Abbildung~\ref{buch:elliptisch:fig:ellipse} eine Ellipse -%mit Brennpunkten in $F_1=(-e,0)$ und $F_2=(e,0)$ dargestellt, -%die durch die Punkte $(\pm a,0)$ und $(0,\pm b)$ auf den Achsen geht. -%Der Punkt $(a,0)$ hat die Entfernungen $a+e$ und $a-e$ von den beiden -%Brennpunkten, also die Entfernungssumme $a+e+a-e=2a$. -%Jeder andere Punkt auf der Ellipse muss ebenfalls diese Entfernungssumme -%haben, insbesondere auch der Punkt $(0,b)$. -%Seine Entfernung zu jedem Brennpunkt muss aus Symmetriegründen gleich gross, -%also $a$ sein. -%Aus dem Satz von Pythagoras liest man daher ab, dass -%\[ -%b^2+e^2=a^2 -%\qquad\Rightarrow\qquad -%e^2 = a^2-b^2 -%\] -%sein muss. -%Die Strecke $e$ heisst auch {\em (lineare) Exzentrizität} der Ellipse. -%Das Verhältnis $\varepsilon= e/a$ heisst die {\em numerische Exzentrizität} -%der Ellipse. -% -%% -%% Die Ellipsengleichung -%% -%\subsubsection{Ellipsengleichung} -%Der Punkt $P=(x,y)$ auf der Ellipse hat die Entfernungen -%\begin{equation} -%\begin{aligned} -%\overline{PF_1}^2 -%&= -%y^2 + (x+e)^2 -%\\ -%\overline{PF_2}^2 -%&= -%y^2 + (x-e)^2 -%\end{aligned} -%\label{buch:elliptisch:eqn:wurzelausdruecke} -%\end{equation} -%von den Brennpunkten, für die -%\begin{equation} -%\overline{PF_1}+\overline{PF_2} -%= -%2a -%\label{buch:elliptisch:eqn:pf1pf2a} -%\end{equation} -%gelten muss. -%Man kann nachrechnen, dass ein Punkt $P$, der die Gleichung -%\[ -%\frac{x^2}{a^2} + \frac{y^2}{b^2}=1 -%\] -%erfüllt, auch die Eigenschaft~\eqref{buch:elliptisch:eqn:pf1pf2a} -%erfüllt. -%Zur Vereinfachung setzen wir $l_1=\overline{PF_1}$ und $l_2=\overline{PF_2}$. -%$l_1$ und $l_2$ sind Wurzeln aus der rechten Seite von -%\eqref{buch:elliptisch:eqn:wurzelausdruecke}. -%Das Quadrat von $l_1+l_2$ ist -%\[ -%l_1^2 + 2l_1l_2 + l_2^2 = 4a^2. -%\] -%Um die Wurzeln ganz zu eliminieren, bringt man das Produkt $l_1l_2$ alleine -%auf die rechte Seite und quadriert. -%Man muss also verifizieren, dass -%\[ -%(l_1^2 + l_2^2 -4a^2)^2 = 4l_1^2l_2^2. -%\] -%In den entstehenden Ausdrücken muss man ausserdem $e=\sqrt{a^2-b^2}$ und -%\[ -%y=b\sqrt{1-\frac{x^2}{a^2}} -%\] -%substituieren. -%Diese Rechnung führt man am einfachsten mit Hilfe eines -%Computeralgebraprogramms durch, welches obige Behauptung bestätigt. -% -%% -%% Normierung -%% -%\subsubsection{Normierung} -%Die trigonometrischen Funktionen sind definiert als Verhältnisse -%von Seiten rechtwinkliger Dreiecke. -%Dadurch, dass man den die Hypothenuse auf Länge $1$ normiert, -%kann man die Sinus- und Kosinus-Funktion als Koordinaten eines -%Punktes auf dem Einheitskreis interpretieren. -% -%Für die Koordinaten eines Punktes auf der Ellipse ist dies nicht so einfach, -%weil es nicht nur eine Ellipse gibt, sondern für jede numerische Exzentrizität -%mindestens eine mit Halbeachse $1$. -%Wir wählen die Ellipsen so, dass $a$ die grosse Halbachse ist, also $a>b$. -%Als Normierungsbedingung verwenden wir, dass $b=1$ sein soll, wie in -%Abbildung~\ref{buch:elliptisch:fig:jacobidef}. -%Dann ist $a=1/\varepsilon>1$. -%In dieser Normierung haben Punkte $(x,y)$ auf der Ellipse $y$-Koordinaten -%zwischen $-1$ und $1$ und $x$-Koordinaten zwischen $-a$ und $a$. -% -%Im Zusammenhang mit elliptischen Funktionen wird die numerische Exzentrizität -%$\varepsilon$ auch mit -%\[ -%k -%= -%\varepsilon -%= -%\frac{e}{a} -%= -%\frac{\sqrt{a^2-b^2}}{a} -%= -%\frac{\sqrt{a^2-1}}{a}, -%\] -%die Zahl $k$ heisst auch der {\em Modulus}. -%Man kann $a$ auch durch $k$ ausdrücken, durch Quadrieren und Umstellen -%findet man -%\[ -%k^2a^2 = a^2-1 -%\quad\Rightarrow\quad -%1=a^2(k^2-1) -%\quad\Rightarrow\quad -%a=\frac{1}{\sqrt{k^2-1}}. -%\] -% -%Die Gleichung der ``Einheitsellipse'' zu diesem Modulus ist -%\[ -%\frac{x^2}{a^2}+y^2=1 -%\qquad\text{oder}\qquad -%x^2(k^2-1) + y^2 = 1. -%\] -% -%% -%% Definition der elliptischen Funktionen -%% -%\begin{figure} -%\centering -%\includegraphics{chapters/110-elliptisch/images/jacobidef.pdf} -%\caption{Definition der elliptischen Funktionen als Trigonometrie -%an einer Ellipse mit Halbachsen $a$ und $1$. -%\label{buch:elliptisch:fig:jacobidef}} -%\end{figure} -%\subsubsection{Definition der elliptischen Funktionen} -%Die elliptischen Funktionen für einen Punkt $P$ auf der Ellipse mit Modulus $k$ -%können jetzt als Verhältnisse der Koordinaten des Punktes definieren. -%Es stellt sich aber die Frage, was man als Argument verwenden soll. -%Es soll so etwas wie den Winkel $\varphi$ zwischen der $x$-Achse und dem -%Radiusvektor zum Punkt $P$ -%darstellen, aber wir haben hier noch eine Wahlfreiheit, die wir später -%ausnützen möchten. -%Im Moment müssen wir die Frage noch nicht beantworten und nennen das -%noch unbestimmte Argument $u$. -%Wir kümmern uns später um die Frage, wie $u$ von $\varphi$ abhängt. -% -%Die Funktionen, die wir definieren wollen, hängen ausserdem auch -%vom Modulus ab. -%Falls der verwendete Modulus aus dem Zusammenhang klar ist, lassen -%wir das $k$-Argument weg. -% -%Die Punkte auf dem Einheitskreis haben alle den gleichen Abstand vom -%Nullpunkt, dies ist gleichzeitig die definierende Gleichung $r^2=x^2+y^2=1$ -%des Kreises. -%Die Punkte auf der Ellipse erfüllen die Gleichung $x^2/a^2+y^2=1$, -%die Entfernung der Punkte $r=\sqrt{x^2+y^2}$ vom Nullpunkt variert aber. -% -%In Analogie zu den trigonometrischen Funktionen setzen wir jetzt für -%die Funktionen -%\[ -%\begin{aligned} -%&\text{sinus amplitudinis:}& -%{\color{red}\operatorname{sn}(u,k)}&= y \\ -%&\text{cosinus amplitudinis:}& -%{\color{blue}\operatorname{cn}(u,k)}&= \frac{x}{a} \\ -%&\text{delta amplitudinis:}& -%{\color{darkgreen}\operatorname{dn}(u,k)}&=\frac{r}{a}, -%\end{aligned} -%\] -%die auch in Abbildung~\ref{buch:elliptisch:fig:jacobidef} -%dargestellt sind. -%Aus der Gleichung der Ellipse folgt sofort, dass -%\[ -%\operatorname{sn}(u,k)^2 + \operatorname{cn}(u,k)^2 = 1 -%\] -%ist. -%Der Satz von Pythagoras kann verwendet werden, um die Entfernung zu -%berechnen, also gilt -%\begin{equation} -%r^2 -%= -%a^2 \operatorname{dn}(u,k)^2 -%= -%x^2 + y^2 -%= -%a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2 -%\quad -%\Rightarrow -%\quad -%a^2 \operatorname{dn}(u,k)^2 -%= -%a^2\operatorname{cn}(u,k)^2 + \operatorname{sn}(u,k)^2. -%\label{buch:elliptisch:eqn:sncndnrelation} -%\end{equation} -%Ersetzt man -%$ -%a^2\operatorname{cn}(u,k)^2 -%= -%a^2-a^2\operatorname{sn}(u,k)^2 -%$, ergibt sich -%\[ -%a^2 \operatorname{dn}(u,k)^2 -%= -%a^2-a^2\operatorname{sn}(u,k)^2 -%+ -%\operatorname{sn}(u,k)^2 -%\quad -%\Rightarrow -%\quad -%\operatorname{dn}(u,k)^2 -%+ -%\frac{a^2-1}{a^2}\operatorname{sn}(u,k)^2 -%= -%1, -%\] -%woraus sich die Identität -%\[ -%\operatorname{dn}(u,k)^2 + k^2 \operatorname{sn}(u,k)^2 = 1 -%\] -%ergibt. -%Ebenso kann man aus~\eqref{buch:elliptisch:eqn:sncndnrelation} -%die Funktion $\operatorname{cn}(u,k)$ eliminieren, was auf -%\[ -%a^2\operatorname{dn}(u,k)^2 -%= -%a^2\operatorname{cn}(u,k)^2 -%+1-\operatorname{cn}(u,k)^2 -%= -%(a^2-1)\operatorname{cn}(u,k)^2 -%+1. -%\] -%Nach Division durch $a^2$ ergibt sich -%\begin{align*} -%\operatorname{dn}(u,k)^2 -%- -%k^2\operatorname{cn}(u,k)^2 -%&= -%\frac{1}{a^2} -%= -%\frac{a^2-a^2+1}{a^2} -%= -%1-k^2 =: k^{\prime 2}. -%\end{align*} -%Wir stellen die hiermit gefundenen Relationen zwischen den grundlegenden -%Jacobischen elliptischen Funktionen für später zusammen in den Formeln -%\begin{equation} -%\begin{aligned} -%\operatorname{sn}^2(u,k) -%+ -%\operatorname{cn}^2(u,k) -%&= -%1 -%\\ -%\operatorname{dn}^2(u,k) + k^2\operatorname{sn}^2(u,k) -%&= -%1 -%\\ -%\operatorname{dn}^2(u,k) -k^2\operatorname{cn}^2(u,k) -%&= -%k^{\prime 2}. -%\end{aligned} -%\label{buch:elliptisch:eqn:jacobi-relationen} -%\end{equation} -%zusammen. -%So wie es möglich ist, $\sin\alpha$ durch $\cos\alpha$ auszudrücken, -%ist es mit -%\eqref{buch:elliptisch:eqn:jacobi-relationen} -%jetzt auch möglich jede grundlegende elliptische Funktion durch -%jede anderen auszudrücken. -%Die Resultate sind in der Tabelle~\ref{buch:elliptisch:fig:jacobi-relationen} -%zusammengestellt. -% -%\begin{table} -%\centering -%\renewcommand{\arraystretch}{2.1} -%\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} -%\hline -%&\operatorname{sn}(u,k) -%&\operatorname{cn}(u,k) -%&\operatorname{dn}(u,k)\\ -%\hline -%\operatorname{sn}(u,k) -%&\operatorname{sn}(u,k) -%&\sqrt{1-\operatorname{cn}^2(u,k)} -%&\frac1k\sqrt{1-\operatorname{dn}^2(u,k)} -%\\ -%\operatorname{cn}(u,k) -%&\sqrt{1-\operatorname{sn}^2(u,k)} -%&\operatorname{cn}(u,k) -%&\frac{1}{k}\sqrt{\operatorname{dn}^2(u,k)-k^{\prime2}} -%\\ -%\operatorname{dn}(u,k) -%&\sqrt{1-k^2\operatorname{sn}^2(u,k)} -%&\sqrt{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} -%&\operatorname{dn}(u,k) -%\\ -%\hline -%\end{tabular} -%\caption{Jede der Jacobischen elliptischen Funktionen lässt sich -%unter Verwendung der Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} -%durch jede andere ausdrücken. -%\label{buch:elliptisch:fig:jacobi-relationen}} -%\end{table} -% -%% -%% Ableitungen der Jacobi-ellpitischen Funktionen -%% -%\subsubsection{Ableitung} -%Die trigonometrischen Funktionen sind deshalb so besonders nützlich -%für die Lösung von Schwingungsdifferentialgleichungen, weil sie die -%Beziehungen -%\[ -%\frac{d}{d\varphi} \cos\varphi = -\sin\varphi -%\qquad\text{und}\qquad -%\frac{d}{d\varphi} \sin\varphi = \cos\varphi -%\] -%erfüllen. -%So einfach können die Beziehungen natürlich nicht sein, sonst würde sich -%durch Integration ja wieder nur die trigonometrischen Funktionen ergeben. -%Durch geschickte Wahl des Arguments $u$ kann man aber erreichen, dass -%sie ähnlich nützliche Beziehungen zwischen den Ableitungen ergeben. -% -%Gesucht ist jetzt also eine Wahl für das Argument $u$ zum Beispiel in -%Abhängigkeit von $\varphi$, dass sich einfache und nützliche -%Ableitungsformeln ergeben. -%Wir setzen daher $u(\varphi)$ voraus und beachten, dass $x$ und $y$ -%ebenfalls von $\varphi$ abhängen, es ist -%$y=\sin\varphi$ und $x=a\cos\varphi$. -%Die Ableitungen von $x$ und $y$ nach $\varphi$ sind -%\begin{align*} -%\frac{dy}{d\varphi} -%&= -%\cos\varphi -%= -%\frac{1}{a} x -%= -%\operatorname{cn}(u,k) -%\\ -%\frac{dx}{d\varphi} -%&= -%-a\sin\varphi -%= -%-a y -%= -%-a\operatorname{sn}(u,k). -%\end{align*} -%Daraus kann man jetzt die folgenden Ausdrücke für die Ableitungen der -%elliptischen Funktionen nach $\varphi$ ableiten: -%\begin{align*} -%\frac{d}{d\varphi} \operatorname{sn}(u,z) -%&= -%\frac{d}{d\varphi} y(\varphi) -%= -%\cos\varphi -%= -%\frac{x}{a} -%= -%\operatorname{cn}(u,k) -%&&\Rightarrow& -%\frac{d}{du} -%\operatorname{sn}(u,k) -%&= -%\operatorname{cn}(u,k) \frac{d\varphi}{du} -%\\ -%\frac{d}{d\varphi} \operatorname{cn}(u,z) -%&= -%\frac{d}{d\varphi} \frac{x(\varphi)}{a} -%= -%-\sin\varphi -%= -%-\operatorname{sn}(u,k) -%&&\Rightarrow& -%\frac{d}{du}\operatorname{cn}(u,k) -%&= -%-\operatorname{sn}(u,k) \frac{d\varphi}{du} -%\\ -%\frac{d}{d\varphi} \operatorname{dn}(u,z) -%&= -%\frac{1}{a}\frac{dr}{d\varphi} -%= -%\frac{1}{a}\frac{d\sqrt{x^2+y^2}}{d\varphi} -%%\\ -%%& -%\rlap{$\displaystyle\mathstrut -%= -%\frac{x}{ar} \frac{dx}{d\varphi} -%+ -%\frac{y}{ar} \frac{dy}{d\varphi} -%%\\ -%%& -%= -%\frac{x}{ar} (-a\operatorname{sn}(u,k)) -%+ -%\frac{y}{ar} \operatorname{cn}(u,k) -%$} -%\\ -%& -%\rlap{$\displaystyle\mathstrut -%= -%\frac{x}{ar}(-ay) -%+ -%\frac{y}{ar} \frac{x}{a} -%%\rlap{$\displaystyle -%= -%\frac{xy(-1+\frac{1}{a^2})}{r} -%%$} -%%\\ -%%& -%= -%-\frac{xy(a^2-1)}{a^2r} -%$} -%\\ -%&= -%-\frac{a^2-1}{ar} -%\operatorname{cn}(u,k) \operatorname{sn}(u,k) -%%\\ -%%& -%\rlap{$\displaystyle\mathstrut -%= -%-k^2 -%\frac{a}{r} -%\operatorname{cn}(u,k) \operatorname{sn}(u,k) -%$} -%\\ -%&= -%-k^2\frac{\operatorname{cn}(u,k)\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} -%&&\Rightarrow& -%\frac{d}{du} \operatorname{dn}(u,k) -%&= -%-k^2\frac{\operatorname{cn}(u,k) -%\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} -%\frac{d\varphi}{du}. -%\end{align*} -%Die einfachsten Beziehungen ergeben sich offenbar, wenn man $u$ so -%wählt, dass -%\[ -%\frac{d\varphi}{du} -%= -%\operatorname{dn}(u,k) -%= -%\frac{r}{a}. -%\] -%Damit haben wir die grundlegenden Ableitungsregeln -% -%\begin{satz} -%\label{buch:elliptisch:satz:ableitungen} -%Die Jacobischen elliptischen Funktionen haben die Ableitungen -%\begin{equation} -%\begin{aligned} -%\frac{d}{du}\operatorname{sn}(u,k) -%&= -%\phantom{-}\operatorname{cn}(u,k)\operatorname{dn}(u,k) -%\\ -%\frac{d}{du}\operatorname{cn}(u,k) -%&= -%-\operatorname{sn}(u,k)\operatorname{dn}(u,k) -%\\ -%\frac{d}{du}\operatorname{dn}(u,k) -%&= -%-k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k). -%\end{aligned} -%\label{buch:elliptisch:eqn:ableitungsregeln} -%\end{equation} -%\end{satz} -% -%% -%% Der Grenzfall $k=1$ -%% -%\subsubsection{Der Grenzwert $k\to1$} -%\begin{figure} -%\centering -%\includegraphics{chapters/110-elliptisch/images/sncnlimit.pdf} -%\caption{Grenzfälle der Jacobischen elliptischen Funktionen -%für die Werte $0$ und $1$ des Parameters $k$. -%\label{buch:elliptisch:fig:sncnlimit}} -%\end{figure} -%Für $k=1$ ist $k^{\prime2}=1-k^2=$ und es folgt aus den -%Relationen~\eqref{buch:elliptisch:eqn:jacobi-relationen} -%\[ -%\operatorname{cn}^2(u,k) -%- -%k^2 -%\operatorname{dn}^2(u,k) -%= -%k^{\prime2} -%= -%0 -%\qquad\Rightarrow\qquad -%\operatorname{cn}^2(u,1) -%= -%\operatorname{dn}^2(u,1), -%\] -%die beiden Funktionen -%$\operatorname{cn}(u,k)$ -%und -%$\operatorname{dn}(u,k)$ -%fallen also zusammen. -%Die Ableitungsregeln werden dadurch vereinfacht: -%\begin{align*} -%\operatorname{sn}'(u,1) -%&= -%\operatorname{cn}(u,1) -%\operatorname{dn}(u,1) -%= -%\operatorname{cn}^2(u,1) -%= -%1-\operatorname{sn}^2(u,1) -%&&\Rightarrow& y'&=1-y^2 -%\\ -%\operatorname{cn}'(u,1) -%&= -%- -%\operatorname{sn}(u,1) -%\operatorname{dn}(u,1) -%= -%- -%\operatorname{sn}(u,1)\operatorname{cn}(u,1) -%&&\Rightarrow& -%\frac{z'}{z}&=(\log z)' = -y -%\end{align*} -%Die erste Differentialgleichung für $y$ lässt sich separieren, man findet -%die Lösung -%\[ -%\frac{y'}{1-y^2} -%= -%1 -%\quad\Rightarrow\quad -%\int \frac{dy}{1-y^2} = \int \,du -%\quad\Rightarrow\quad -%\operatorname{artanh}(y) = u -%\quad\Rightarrow\quad -%\operatorname{sn}(u,1)=\tanh u. -%\] -%Damit kann man jetzt auch $z$ berechnen: -%\begin{align*} -%(\log \operatorname{cn}(u,1))' -%&= -%\tanh u -%&&\Rightarrow& -%\log\operatorname{cn}(u,1) -%&= -%-\int\tanh u\,du -%= -%-\log\cosh u -%\\ -%& -%&&\Rightarrow& -%\operatorname{cn}(u,1) -%&= -%\frac{1}{\cosh u} -%= -%\operatorname{sech}u. -%\end{align*} -%Die Grenzfunktionen sind in Abbildung~\ref{buch:elliptisch:fig:sncnlimit} -%dargestellt. -% -%% -%% Das Argument u -%% -%\subsubsection{Das Argument $u$} -%Die Gleichung -%\begin{equation} -%\frac{d\varphi}{du} -%= -%\operatorname{dn}(u,k) -%\label{buch:elliptisch:eqn:uableitung} -%\end{equation} -%ermöglicht, $\varphi$ in Abhängigkeit von $u$ zu berechnen, ohne jedoch -%die geometrische Bedeutung zu klären. -%Das beginnt bereits damit, dass der Winkel $\varphi$ nicht nicht der -%Polarwinkel des Punktes $P$ in Abbildung~\ref{buch:elliptisch:fig:jacobidef} -%ist, diesen nennen wir $\vartheta$. -%Der Zusammenhang zwischen $\varphi$ und $\vartheta$ ist -%\begin{equation} -%\frac1{a}\tan\varphi = \tan\vartheta -%\label{buch:elliptisch:eqn:phitheta} -%\end{equation} -% -%Um die geometrische Bedeutung besser zu verstehen, nehmen wir jetzt an, -%dass die Ellipse mit einem Parameter $t$ parametrisiert ist, dass also -%$\varphi(t)$, $\vartheta(t)$ und $u(t)$ Funktionen von $t$ sind. -%Die Ableitung von~\eqref{buch:elliptisch:eqn:phitheta} ist -%\[ -%\frac1{a}\cdot \frac{1}{\cos^2\varphi}\cdot \dot{\varphi} -%= -%\frac{1}{\cos^2\vartheta}\cdot \dot{\vartheta}. -%\] -%Daraus kann die Ableitung von $\vartheta$ nach $\varphi$ bestimmt -%werden, sie ist -%\[ -%\frac{d\vartheta}{d\varphi} -%= -%\frac{\dot{\vartheta}}{\dot{\varphi}} -%= -%\frac{1}{a} -%\cdot -%\frac{\cos^2\vartheta}{\cos^2\varphi} -%= -%\frac{1}{a} -%\cdot -%\frac{(x/r)^2}{(x/a)^2} -%= -%\frac{1}{a}\cdot -%\frac{a^2}{r^2} -%= -%\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)}. -%\] -%Damit kann man jetzt mit Hilfe von~\eqref{buch:elliptisch:eqn:uableitung} -%Die Ableitung von $\vartheta$ nach $u$ ermitteln, sie ist -%\[ -%\frac{d\vartheta}{du} -%= -%\frac{d\vartheta}{d\varphi} -%\cdot -%\frac{d\varphi}{du} -%= -%\frac{1}{a}\cdot\frac{1}{\operatorname{dn}^2(u,k)} -%\cdot -%\operatorname{dn}(u,k) -%= -%\frac{1}{a} -%\cdot -%\frac{1}{\operatorname{dn}(u,k)} -%= -%\frac{1}{a} -%\cdot\frac{a}{r} -%= -%\frac{1}{r}, -%\] -%wobei wir auch die Definition der Funktion $\operatorname{dn}(u,k)$ -%verwendet haben. -% -%In der Parametrisierung mit dem Parameter $t$ kann man jetzt die Ableitung -%von $u$ nach $t$ berechnen als -%\[ -%\frac{du}{dt} -%= -%\frac{du}{d\vartheta} -%\frac{d\vartheta}{dt} -%= -%r -%\dot{\vartheta}. -%\] -%Darin ist $\dot{\vartheta}$ die Winkelgeschwindigkeit des Punktes um -%das Zentrum $O$ und $r$ ist die aktuelle Entfernung des Punktes $P$ -%von $O$. -%$r\dot{\vartheta}$ ist also die Geschwindigkeitskomponenten des Punktes -%$P$ senkrecht auf den aktuellen Radiusvektor. -%Der Parameter $u$, der zum Punkt $P$ gehört, ist also das Integral -%\[ -%u(P) = \int_0^P r\,d\vartheta. -%\] -%Für einen Kreis ist die Geschwindigkeit von $P$ immer senkrecht -%auf dem Radiusvektor und der Radius ist konstant, so dass -%$u(P)=\vartheta(P)$ ist. -% -%% -%% Die abgeleiteten elliptischen Funktionen -%% -%\begin{figure} -%\centering -%\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobi12.pdf} -%\caption{Die Verhältnisse der Funktionen -%$\operatorname{sn}(u,k)$, -%$\operatorname{cn}(u,k)$ -%udn -%$\operatorname{dn}(u,k)$ -%geben Anlass zu neun weitere Funktionen, die sich mit Hilfe -%des Strahlensatzes geometrisch interpretieren lassen. -%\label{buch:elliptisch:fig:jacobi12}} -%\end{figure} -%\begin{table} -%\centering -%\renewcommand{\arraystretch}{2.5} -%\begin{tabular}{|>{$\displaystyle}c<{$}|>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}>{$\displaystyle}c<{$}|} -%\hline -%\cdot & -%\frac{1}{1} & -%\frac{1}{\operatorname{sn}(u,k)} & -%\frac{1}{\operatorname{cn}(u,k)} & -%\frac{1}{\operatorname{dn}(u,k)} -%\\[5pt] -%\hline -%1& -%&%\operatorname{nn}(u,k)=\frac{1}{1} & -%\operatorname{ns}(u,k)=\frac{1}{\operatorname{sn}(u,k)} & -%\operatorname{nc}(u,k)=\frac{1}{\operatorname{cn}(u,k)} & -%\operatorname{nd}(u,k)=\frac{1}{\operatorname{dn}(u,k)} -%\\ -%\operatorname{sn}(u,k) & -%\operatorname{sn}(u,k)=\frac{\operatorname{sn}(u,k)}{1}& -%&%\operatorname{ss}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{sn}(u,k)}& -%\operatorname{sc}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)}& -%\operatorname{sd}(u,k)=\frac{\operatorname{sn}(u,k)}{\operatorname{dn}(u,k)} -%\\ -%\operatorname{cn}(u,k) & -%\operatorname{cn}(u,k)=\frac{\operatorname{cn}(u,k)}{1} & -%\operatorname{cs}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{sn}(u,k)}& -%&%\operatorname{cc}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{cn}(u,k)}& -%\operatorname{cd}(u,k)=\frac{\operatorname{cn}(u,k)}{\operatorname{dn}(u,k)} -%\\ -%\operatorname{dn}(u,k) & -%\operatorname{dn}(u,k)=\frac{\operatorname{dn}(u,k)}{1} & -%\operatorname{ds}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{sn}(u,k)}& -%\operatorname{dc}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)}& -%%\operatorname{dd}(u,k)=\frac{\operatorname{dn}(u,k)}{\operatorname{dn}(u,k)} -%\\[5pt] -%\hline -%\end{tabular} -%\caption{Zusammenstellung der abgeleiteten Jacobischen elliptischen -%Funktionen in hinteren drei Spalten als Quotienten der grundlegenden -%Jacobischen elliptischen Funktionen. -%Die erste Spalte zum Nenner $1$ enthält die grundlegenden -%Jacobischen elliptischen Funktionen. -%\label{buch:elliptisch:table:abgeleitetjacobi}} -%\end{table} -%\subsubsection{Die abgeleiteten elliptischen Funktionen} -%Zusätzlich zu den grundlegenden Jacobischen elliptischen Funktioenn -%lassen sich weitere elliptische Funktionen bilden, die unglücklicherweise -%die {\em abgeleiteten elliptischen Funktionen} genannt werden. -%Ähnlich wie die trigonometrischen Funktionen $\tan\alpha$, $\cot\alpha$, -%$\sec\alpha$ und $\csc\alpha$ als Quotienten von $\sin\alpha$ und -%$\cos\alpha$ definiert sind, sind die abgeleiteten elliptischen Funktionen -%die in Tabelle~\ref{buch:elliptisch:table:abgeleitetjacobi} zusammengestellten -%Quotienten der grundlegenden Jacobischen elliptischen Funktionen. -%Die Bezeichnungskonvention ist, dass die Funktion $\operatorname{pq}(u,k)$ -%ein Quotient ist, dessen Zähler durch den Buchstaben p bestimmt ist, -%der Nenner durch den Buchstaben q. -%Der Buchstabe n steht für eine $1$, die Buchstaben s, c und d stehen für -%die Anfangsbuchstaben der grundlegenden Jacobischen elliptischen -%Funktionen. -%Meint man irgend eine der Jacobischen elliptischen Funktionen, schreibt -%man manchmal auch $\operatorname{zn}(u,k)$. -% -%In Abbildung~\ref{buch:elliptisch:fig:jacobi12} sind die Quotienten auch -%geometrisch interpretiert. -%Der Wert der Funktion $\operatorname{nq}(u,k)$ ist die auf dem Strahl -%mit Polarwinkel $\varphi$ abgetragene Länge bis zu den vertikalen -%Geraden, die den verschiedenen möglichen Nennern entsprechen. -%Entsprechend ist der Wert der Funktion $\operatorname{dq}(u,k)$ die -%Länge auf dem Strahl mit Polarwinkel $\vartheta$. -% -%Die Relationen~\ref{buch:elliptisch:eqn:jacobi-relationen} -%ermöglichen, jede Funktion $\operatorname{zn}(u,k)$ durch jede -%andere auszudrücken. -%Die schiere Anzahl solcher Beziehungen macht es unmöglich, sie -%übersichtlich in einer Tabelle zusammenzustellen, daher soll hier -%nur an einem Beispiel das Vorgehen gezeigt werden: -% -%\begin{beispiel} -%Die Funktion $\operatorname{sc}(u,k)$ soll durch $\operatorname{cd}(u,k)$ -%ausgedrückt werden. -%Zunächst ist -%\[ -%\operatorname{sc}(u,k) -%= -%\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} -%\] -%nach Definition. -%Im Resultat sollen nur noch $\operatorname{cn}(u,k)$ und -%$\operatorname{dn}(u,k)$ vorkommen. -%Daher eliminieren wir zunächst die Funktion $\operatorname{sn}(u,k)$ -%mit Hilfe von \eqref{buch:elliptisch:eqn:jacobi-relationen} und erhalten -%\begin{equation} -%\operatorname{sc}(u,k) -%= -%\frac{\sqrt{1-\operatorname{cn}^2(u,k)}}{\operatorname{cn}(u,k)}. -%\label{buch:elliptisch:eqn:allgausdruecken} -%\end{equation} -%Nun genügt es, die Funktion $\operatorname{cn}(u,k)$ durch -%$\operatorname{cd}(u,k)$ auszudrücken. -%Aus der Definition und der -%dritten Relation in \eqref{buch:elliptisch:eqn:jacobi-relationen} -%erhält man -%\begin{align*} -%\operatorname{cd}^2(u,k) -%&= -%\frac{\operatorname{cn}^2(u,k)}{\operatorname{dn}^2(u,k)} -%= -%\frac{\operatorname{cn}^2(u,k)}{k^{\prime2}+k^2\operatorname{cn}^2(u,k)} -%\\ -%\Rightarrow -%\qquad -%k^{\prime 2} -%\operatorname{cd}^2(u,k) -%+ -%k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) -%&= -%\operatorname{cn}^2(u,k) -%\\ -%\operatorname{cn}^2(u,k) -%- -%k^2\operatorname{cd}^2(u,k)\operatorname{cn}^2(u,k) -%&= -%k^{\prime 2} -%\operatorname{cd}^2(u,k) -%\\ -%\operatorname{cn}^2(u,k) -%&= -%\frac{ -%k^{\prime 2} -%\operatorname{cd}^2(u,k) -%}{ -%1 - k^2\operatorname{cd}^2(u,k) -%} -%\end{align*} -%Für den Zähler brauchen wir $1-\operatorname{cn}^2(u,k)$, also -%\[ -%1-\operatorname{cn}^2(u,k) -%= -%\frac{ -%1 -%- -%k^2\operatorname{cd}^2(u,k) -%- -%k^{\prime 2} -%\operatorname{cd}^2(u,k) -%}{ -%1 -%- -%k^2\operatorname{cd}^2(u,k) -%} -%= -%\frac{1-\operatorname{cd}^2(u,k)}{1-k^2\operatorname{cd}^2(u,k)} -%\] -%Einsetzen in~\eqref{buch:elliptisch:eqn:allgausdruecken} gibt -%\begin{align*} -%\operatorname{sc}(u,k) -%&= -%\frac{ -%\sqrt{1-\operatorname{cd}^2(u,k)} -%}{\sqrt{1-k^2\operatorname{cd}^2(u,k)}} -%\cdot -%\frac{ -%\sqrt{1 - k^2\operatorname{cd}^2(u,k)} -%}{ -%k' -%\operatorname{cd}(u,k) -%} -%= -%\frac{ -%\sqrt{1-\operatorname{cd}^2(u,k)} -%}{ -%k' -%\operatorname{cd}(u,k) -%}. -%\qedhere -%\end{align*} -%\end{beispiel} -% -%\subsubsection{Ableitung der abgeleiteten elliptischen Funktionen} -%Aus den Ableitungen der grundlegenden Jacobischen elliptischen Funktionen -%können mit der Quotientenregel nun auch beliebige Ableitungen der -%abgeleiteten Jacobischen elliptischen Funktionen gefunden werden. -%Als Beispiel berechnen wir die Ableitung von $\operatorname{sc}(u,k)$. -%Sie ist -%\begin{align*} -%\frac{d}{du} -%\operatorname{sc}(u,k) -%&= -%\frac{d}{du} -%\frac{\operatorname{sn}(u,k)}{\operatorname{cn}(u,k)} -%= -%\frac{ -%\operatorname{sn}'(u,k)\operatorname{cn}(u,k) -%- -%\operatorname{sn}(u,k)\operatorname{cn}'(u,k)}{ -%\operatorname{cn}^2(u,k) -%} -%\\ -%&= -%\frac{ -%\operatorname{cn}^2(u,k)\operatorname{dn}(u,k) -%+ -%\operatorname{sn}^2(u,k)\operatorname{dn}(u,k) -%}{ -%\operatorname{cn}^2(u,k) -%} -%= -%\frac{( -%\operatorname{sn}^2(u,k) -%+ -%\operatorname{cn}^2(u,k) -%)\operatorname{dn}(u,k)}{ -%\operatorname{cn}^2(u,k) -%} -%\\ -%&= -%\frac{1}{\operatorname{cn}(u,k)} -%\cdot -%\frac{\operatorname{dn}(u,k)}{\operatorname{cn}(u,k)} -%= -%\operatorname{nc}(u,k) -%\operatorname{dc}(u,k). -%\end{align*} -%Man beachte, dass das Quadrat der Nennerfunktion im Resultat -%der Quotientenregel zur Folge hat, dass die -%beiden Funktionen im Resultat beide den gleichen Nenner haben wie -%die Funktion, die abgeleitet wird. -% -%Mit etwas Fleiss kann man nach diesem Muster alle Ableitungen -%\begin{equation} -%%\small -%\begin{aligned} -%\operatorname{sn}'(u,k) -%&= -%\phantom{-} -%\operatorname{cn}(u,k)\,\operatorname{dn}(u,k) -%&&\qquad& -%\operatorname{ns}'(u,k) -%&= -%- -%\operatorname{cs}(u,k)\,\operatorname{ds}(u,k) -%\\ -%\operatorname{cn}'(u,k) -%&= -%- -%\operatorname{sn}(u,k)\,\operatorname{dn}(u,k) -%&&& -%\operatorname{nc}'(u,k) -%&= -%\phantom{-} -%\operatorname{sc}(u,k)\,\operatorname{dc}(u,k) -%\\ -%\operatorname{dn}'(u,k) -%&= -%-k^2 -%\operatorname{sn}(u,k)\,\operatorname{cn}(u,k) -%&&& -%\operatorname{nd}'(u,k) -%&= -%\phantom{-} -%k^2 -%\operatorname{sd}(u,k)\,\operatorname{cd}(u,k) -%\\ -%\operatorname{sc}'(u,k) -%&= -%\phantom{-} -%\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) -%&&& -%\operatorname{cs}'(u,k) -%&= -%- -%\operatorname{ds}(u,k)\,\operatorname{ns}(u,k) -%\\ -%\operatorname{cd}'(u,k) -%&= -%-k^{\prime2} -%\operatorname{sd}(u,k)\,\operatorname{nd}(u,k) -%&&& -%\operatorname{dc}'(u,k) -%&= -%\phantom{-} -%k^{\prime2} -%\operatorname{dc}(u,k)\,\operatorname{nc}(u,k) -%\\ -%\operatorname{ds}'(d,k) -%&= -%- -%\operatorname{cs}(u,k)\,\operatorname{ns}(u,k) -%&&& -%\operatorname{sd}'(d,k) -%&= -%\phantom{-} -%\operatorname{cd}(u,k)\,\operatorname{nd}(u,k) -%\end{aligned} -%\label{buch:elliptisch:eqn:alleableitungen} -%\end{equation} -%finden. -%Man beachte, dass in jeder Identität alle Funktionen den gleichen -%zweiten Buchstaben haben. -% -%\subsubsection{TODO} -%XXX algebraische Beziehungen \\ -%XXX Additionstheoreme \\ -%XXX Perioden -%% use https://math.stackexchange.com/questions/3013692/how-to-show-that-jacobi-sine-function-is-doubly-periodic -% -% -%XXX Ableitungen \\ -%XXX Werte \\ -%% -%% Lösung von Differentialgleichungen -%% -%\subsection{Lösungen von Differentialgleichungen -%\label{buch:elliptisch:subsection:differentialgleichungen}} -%Die elliptischen Funktionen ermöglichen die Lösung gewisser nichtlinearer -%Differentialgleichungen in geschlossener Form. -%Ziel dieses Abschnitts ist, Differentialgleichungen der Form -%\( -%\dot{x}(t)^2 -%= -%P(x(t)) -%\) -%mit einem Polynom $P$ vierten Grades oder -%\( -%\ddot{x}(t) -%= -%p(x(t)) -%\) -%mit einem Polynom dritten Grades als rechter Seite lösen zu können. -% -%% -%% Die Differentialgleichung der elliptischen Funktionen -%% -%\subsubsection{Die Differentialgleichungen der elliptischen Funktionen} -%Um Differentialgleichungen mit elliptischen Funktion lösen zu -%können, muss man als erstes die Differentialgleichungen derselben -%finden. -%Quadriert man die Ableitungsregel für $\operatorname{sn}(u,k)$, erhält -%man -%\[ -%\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 -%= -%\operatorname{cn}(u,k)^2 \operatorname{dn}(u,k)^2. -%\] -%Die Funktionen auf der rechten Seite können durch $\operatorname{sn}(u,k)$ -%ausgedrückt werden, dies führt auf die Differentialgleichung -%\begin{align*} -%\biggl(\frac{d}{du}\operatorname{sn}(u,k)\biggr)^2 -%&= -%\bigl( -%1-\operatorname{sn}(u,k)^2 -%\bigr) -%\bigl( -%1-k^2 \operatorname{sn}(u,k)^2 -%\bigr) -%\\ -%&= -%k^2\operatorname{sn}(u,k)^4 -%-(1+k^2) -%\operatorname{sn}(u,k)^2 -%+1. -%\end{align*} -%Für die Funktion $\operatorname{cn}(u,k)$ ergibt die analoge Rechnung -%\begin{align*} -%\frac{d}{du}\operatorname{cn}(u,k) -%&= -%-\operatorname{sn}(u,k) \operatorname{dn}(u,k) -%\\ -%\biggl(\frac{d}{du}\operatorname{cn}(u,k)\biggr)^2 -%&= -%\operatorname{sn}(u,k)^2 \operatorname{dn}(u,k)^2 -%\\ -%&= -%\bigl(1-\operatorname{cn}(u,k)^2\bigr) -%\bigl(k^{\prime 2}+k^2 \operatorname{cn}(u,k)^2\bigr) -%\\ -%&= -%-k^2\operatorname{cn}(u,k)^4 -%+ -%(k^2-k^{\prime 2})\operatorname{cn}(u,k)^2 -%+ -%k^{\prime 2} -%\intertext{und weiter für $\operatorname{dn}(u,k)$:} -%\frac{d}{du}\operatorname{dn}(u,k) -%&= -%-k^2\operatorname{sn}(u,k)\operatorname{cn}(u,k) -%\\ -%\biggl( -%\frac{d}{du}\operatorname{dn}(u,k) -%\biggr)^2 -%&= -%\bigl(k^2 \operatorname{sn}(u,k)^2\bigr) -%\bigl(k^2 \operatorname{cn}(u,k)^2\bigr) -%\\ -%&= -%\bigl( -%1-\operatorname{dn}(u,k)^2 -%\bigr) -%\bigl( -%\operatorname{dn}(u,k)^2-k^{\prime 2} -%\bigr) -%\\ -%&= -%-\operatorname{dn}(u,k)^4 -%+ -%(1+k^{\prime 2})\operatorname{dn}(u,k)^2 -%-k^{\prime 2}. -%\end{align*} -% -%\begin{table} -%\centering -%\renewcommand{\arraystretch}{1.7} -%\begin{tabular}{|>{$}l<{$}|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} -%\hline -%\text{Funktion $y=$}&\text{Differentialgleichung}&\alpha&\beta&\gamma\\ -%\hline -%\operatorname{sn}(u,k) -% & y'^2 = \phantom{-}(1-y^2)(1-k^2y^2) -% &k^2&1+k^2&1 -%\\ -%\operatorname{cn}(u,k) &y'^2 = \phantom{-}(1-y^2)(k^{\prime2}+k^2y^2) -% &-k^2 &k^2-k^{\prime 2}=2k^2-1&k^{\prime2} -%\\ -%\operatorname{dn}(u,k) -% & y'^2 = -(1-y^2)(k^{\prime 2}-y^2) -% &-1 &1+k^{\prime 2}=2-k^2 &-k^{\prime2} -%\\ -%\hline -%\end{tabular} -%\caption{Elliptische Funktionen als Lösungsfunktionen für verschiedene -%nichtlineare Differentialgleichungen der Art -%\eqref{buch:elliptisch:eqn:1storderdglell}. -%Die Vorzeichen der Koeffizienten $\alpha$, $\beta$ und $\gamma$ -%entscheidet darüber, welche Funktion für die Lösung verwendet werden -%muss. -%\label{buch:elliptisch:tabelle:loesungsfunktionen}} -%\end{table} -% -%Die drei grundlegenden Jacobischen elliptischen Funktionen genügen also alle -%einer nichtlinearen Differentialgleichung erster Ordnung der selben Art. -%Das Quadrat der Ableitung ist ein Polynom vierten Grades der Funktion. -%Die Differentialgleichungen sind in der -%Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} zusammengefasst. -% -%% -%% Differentialgleichung der abgeleiteten elliptischen Funktionen -%% -%\subsubsection{Die Differentialgleichung der abgeleiteten elliptischen -%Funktionen} -%Da auch die Ableitungen der abgeleiteten Jacobischen elliptischen -%Funktionen Produkte von genau zwei Funktionen sind, die sich wieder -%durch die ursprüngliche Funktion ausdrücken lassen, darf man erwarten, -%dass alle elliptischen Funktionen einer ähnlichen Differentialgleichung -%genügen. -%Um dies besser einzufangen, schreiben wir $\operatorname{pq}(u,k)$, -%wenn wir eine beliebige abgeleitete Jacobische elliptische Funktion. -%Für -%$\operatorname{pq}=\operatorname{sn}$ -%$\operatorname{pq}=\operatorname{cn}$ -%und -%$\operatorname{pq}=\operatorname{dn}$ -%wissen wir bereits und erwarten für jede andere Funktion dass -%$\operatorname{pq}(u,k)$ auch, dass sie Lösung einer Differentialgleichung -%der Form -%\begin{equation} -%\operatorname{pq}'(u,k)^2 -%= -%\alpha \operatorname{pq}(u,k)^4 + \beta \operatorname{pq}(u,k)^2 + \gamma -%\label{buch:elliptisch:eqn:1storderdglell} -%\end{equation} -%erfüllt, -%wobei wir mit $\operatorname{pq}'(u,k)$ die Ableitung von -%$\operatorname{pq}(u,k)$ nach dem ersten Argument meinen. -%Die Koeffizienten $\alpha$, $\beta$ und $\gamma$ hängen von $k$ ab, -%ihre Werte für die grundlegenden Jacobischen elliptischen -%sind in Tabelle~\ref{buch:elliptisch:table:differentialgleichungen} -%zusammengestellt. -% -%Die Koeffizienten müssen nicht für jede Funktion wieder neu bestimmt -%werden, denn für den Kehrwert einer Funktion lässt sich die -%Differentialgleichung aus der Differentialgleichung der ursprünglichen -%Funktion ermitteln. -% -%% -%% Differentialgleichung der Kehrwertfunktion -%% -%\subsubsection{Differentialgleichung für den Kehrwert einer elliptischen Funktion} -%Aus der Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} -%für die Funktion $\operatorname{pq}(u,k)$ kann auch eine -%Differentialgleichung für den Kehrwert -%$\operatorname{qp}(u,k)=\operatorname{pq}(u,k)^{-1}$ -%ableiten. -%Dazu rechnet man -%\[ -%\operatorname{qp}'(u,k) -%= -%\frac{d}{du}\frac{1}{\operatorname{pq}(u,k)} -%= -%\frac{\operatorname{pq}'(u,k)}{\operatorname{pq}(u,k)^2} -%\qquad\Rightarrow\qquad -%\left\{ -%\quad -%\begin{aligned} -%\operatorname{pq}(u,k) -%&= -%\frac{1}{\operatorname{qp}(u,k)} -%\\ -%\operatorname{pq}'(u,k) -%&= -%\frac{\operatorname{qp}'(u,k)}{\operatorname{qp}(u,k)^2} -%\end{aligned} -%\right. -%\] -%und setzt in die Differentialgleichung ein: -%\begin{align*} -%\biggl( -%\frac{ -%\operatorname{qp}'(u,k) -%}{ -%\operatorname{qp}(u,k) -%} -%\biggr)^2 -%&= -%\alpha \frac{1}{\operatorname{qp}(u,k)^4} -%+ -%\beta \frac{1}{\operatorname{qp}(u,k)^2} -%+ -%\gamma. -%\end{align*} -%Nach Multiplikation mit $\operatorname{qp}(u,k)^4$ erhält man den -%folgenden Satz. -% -%\begin{satz} -%Wenn die Jacobische elliptische Funktion $\operatorname{pq}(u,k)$ -%der Differentialgleichung genügt, dann genügt der Kehrwert -%$\operatorname{qp}(u,k) = 1/\operatorname{pq}(u,k)$ der Differentialgleichung -%\begin{equation} -%(\operatorname{qp}'(u,k))^2 -%= -%\gamma \operatorname{qp}(u,k)^4 -%+ -%\beta \operatorname{qp}(u,k)^2 -%+ -%\alpha -%\label{buch:elliptisch:eqn:kehrwertdgl} -%\end{equation} -%\end{satz} -% -%\begin{table} -%\centering -%\def\lfn#1{\multicolumn{1}{|l|}{#1}} -%\def\rfn#1{\multicolumn{1}{r|}{#1}} -%\renewcommand{\arraystretch}{1.3} -%\begin{tabular}{l|>{$}c<{$}>{$}c<{$}>{$}c<{$}|r} -%\cline{1-4} -%\lfn{Funktion} -% & \alpha & \beta & \gamma &\\ -%\hline -%\lfn{sn}& k^2 & -(1+k^2) & 1 &\rfn{ns}\\ -%\lfn{cn}& -k^2 & -(1-2k^2) & 1-k^2 &\rfn{nc}\\ -%\lfn{dn}& 1 & 2-k^2 & -(1-k^2) &\rfn{nd}\\ -%\hline -%\lfn{sc}& 1-k^2 & 2-k^2 & 1 &\rfn{cs}\\ -%\lfn{sd}&-k^2(1-k^2)&-(1-2k^2) & 1 &\rfn{ds}\\ -%\lfn{cd}& k^2 &-(1+k^2) & 1 &\rfn{dc}\\ -%\hline -% & \gamma & \beta & \alpha &\rfn{Reziproke}\\ -%\cline{2-5} -%\end{tabular} -%\caption{Koeffizienten der Differentialgleichungen für die Jacobischen -%elliptischen Funktionen. -%Der Kehrwert einer Funktion hat jeweils die Differentialgleichung der -%ursprünglichen Funktion, in der die Koeffizienten $\alpha$ und $\gamma$ -%vertauscht worden sind. -%\label{buch:elliptisch:table:differentialgleichungen}} -%\end{table} -% -%% -%% Differentialgleichung zweiter Ordnung -%% -%\subsubsection{Differentialgleichung zweiter Ordnung} -%Leitet die Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} -%man dies nochmals nach $u$ ab, erhält man die Differentialgleichung -%\[ -%2\operatorname{pq}''(u,k)\operatorname{pq}'(u,k) -%= -%4\alpha \operatorname{pq}(u,k)^3\operatorname{pq}'(u,k) + 2\beta \operatorname{pq}'(u,k)\operatorname{pq}(u,k). -%\] -%Teilt man auf beiden Seiten durch $2\operatorname{pq}'(u,k)$, -%bleibt die nichtlineare -%Differentialgleichung -%\[ -%\frac{d^2\operatorname{pq}}{du^2} -%= -%\beta \operatorname{pq} + 2\alpha \operatorname{pq}^3. -%\] -%Dies ist die Gleichung eines harmonischen Oszillators mit einer -%Anharmonizität der Form $2\alpha z^3$. -% -% -% -%% -%% Jacobischen elliptische Funktionen und elliptische Integrale -%% -%\subsubsection{Jacobische elliptische Funktionen als elliptische Integrale} -%Die in Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} -%zusammengestellten Differentialgleichungen ermöglichen nun, den -%Zusammenhang zwischen den Funktionen -%$\operatorname{sn}(u,k)$, $\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$ -%und den unvollständigen elliptischen Integralen herzustellen. -%Die Differentialgleichungen sind alle von der Form -%\begin{equation} -%\biggl( -%\frac{d y}{d u} -%\biggr)^2 -%= -%p(u), -%\label{buch:elliptisch:eqn:allgdgl} -%\end{equation} -%wobei $p(u)$ ein Polynom vierten Grades in $y$ ist. -%Diese Differentialgleichung lässt sich mit Separation lösen. -%Dazu zieht man aus~\eqref{buch:elliptisch:eqn:allgdgl} die -%Wurzel -%\begin{align} -%\frac{dy}{du} -%= -%\sqrt{p(y)} -%\notag -%\intertext{und trennt die Variablen. Man erhält} -%\int\frac{dy}{\sqrt{p(y)}} = u+C. -%\label{buch:elliptisch:eqn:yintegral} -%\end{align} -%Solange $p(y)>0$ ist, ist der Integrand auf der linken Seite -%von~\eqref{buch:elliptisch:eqn:yintegral} ebenfalls positiv und -%das Integral ist eine monoton wachsende Funktion $F(y)$. -%Insbesondere ist $F(y)$ invertierbar. -%Die Lösung $y(u)$ der Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} -%ist daher -%\[ -%y(u) = F^{-1}(u+C). -%\] -%Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen -%der unvollständigen elliptischen Integrale. -% -% -%% -%% Differentialgleichung des anharmonischen Oszillators -%% -%\subsubsection{Differentialgleichung des anharmonischen Oszillators} -%Wir möchten die nichtlineare Differentialgleichung -%\begin{equation} -%\biggl( -%\frac{dx}{dt} -%\biggr)^2 -%= -%Ax^4+Bx^2 + C -%\label{buch:elliptisch:eqn:allgdgl} -%\end{equation} -%mit Hilfe elliptischer Funktionen lösen. -%Wir nehmen also an, dass die gesuchte Lösung eine Funktion der Form -%\begin{equation} -%x(t) = a\operatorname{zn}(bt,k) -%\label{buch:elliptisch:eqn:loesungsansatz} -%\end{equation} -%ist. -%Die erste Ableitung von $x(t)$ ist -%\[ -%\dot{x}(t) -%= -%a\operatorname{zn}'(bt,k). -%\] -% -%Indem wir diesen Lösungsansatz in die -%Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} -%einsetzen, erhalten wir -%\begin{equation} -%a^2b^2 \operatorname{zn}'(bt,k)^2 -%= -%a^4A\operatorname{zn}(bt,k)^4 -%+ -%a^2B\operatorname{zn}(bt,k)^2 -%+C -%\label{buch:elliptisch:eqn:dglx} -%\end{equation} -%Andererseits wissen wir, dass $\operatorname{zn}(u,k)$ einer -%Differentilgleichung der Form~\eqref{buch:elliptisch:eqn:1storderdglell} -%erfüllt. -%Wenn wir \eqref{buch:elliptisch:eqn:dglx} durch $a^2b^2$ teilen, können wir -%die rechte Seite von \eqref{buch:elliptisch:eqn:dglx} mit der rechten -%Seite von \eqref{buch:elliptisch:eqn:1storderdglell} vergleichen: -%\[ -%\frac{a^2A}{b^2}\operatorname{zn}(bt,k)^4 -%+ -%\frac{B}{b^2}\operatorname{zn}(bt,k)^2 -%+\frac{C}{a^2b^2} -%= -%\alpha\operatorname{zn}(bt,k)^4 -%+ -%\beta\operatorname{zn}(bt,k)^2 -%+ -%\gamma\operatorname{zn}(bt,k). -%\] -%Daraus ergeben sich die Gleichungen -%\begin{align} -%\alpha &= \frac{a^2A}{b^2}, -%& -%\beta &= \frac{B}{b^2} -%&&\text{und} -%& -%\gamma &= \frac{C}{a^2b^2} -%\label{buch:elliptisch:eqn:koeffvergl} -%\intertext{oder aufgelöst nach den Koeffizienten der ursprünglichen -%Differentialgleichung} -%A&=\frac{\alpha b^2}{a^2} -%& -%B&=\beta b^2 -%&&\text{und}& -%C &= \gamma a^2b^2 -%\label{buch:elliptisch:eqn:koeffABC} -%\end{align} -%für die Koeffizienten der Differentialgleichung der zu verwendenden -%Funktion. -% -%Man beachte, dass nach \eqref{buch:elliptisch:eqn:koeffvergl} die -%Koeffizienten $A$, $B$ und $C$ die gleichen Vorzeichen haben wie -%$\alpha$, $\beta$ und $\gamma$, da in -%\eqref{buch:elliptisch:eqn:koeffvergl} nur mit Quadraten multipliziert -%wird, die immer positiv sind. -%Diese Vorzeichen bestimmen, welche der Funktionen gewählt werden muss. -% -%In den Differentialgleichungen für die elliptischen Funktionen gibt -%es nur den Parameter $k$, der angepasst werden kann. -%Es folgt, dass die Gleichungen -%\eqref{buch:elliptisch:eqn:koeffvergl} -%auch $a$ und $b$ bestimmen. -%Zum Beispiel folgt aus der letzten Gleichung, dass -%\[ -%b = \pm\sqrt{\frac{B}{\beta}}. -%\] -%Damit folgt dann aus der zweiten -%\[ -%a=\pm\sqrt{\frac{\beta C}{\gamma B}}. -%\] -%Die verbleibende Gleichung legt $k$ fest. -%Das folgende Beispiel illustriert das Vorgehen am Beispiel einer -%Gleichung, die Lösungsfunktion $\operatorname{sn}(u,k)$ verlangt. -% -%\begin{beispiel} -%Wir nehmen an, dass die Vorzeichen von $A$, $B$ und $C$ gemäss -%Tabelle~\ref{buch:elliptische:tabelle:loesungsfunktionen} verlangen, -%dass die Funktion $\operatorname{sn}(u,k)$ für die Lösung verwendet -%werden muss. -%Die Tabelle sagt dann auch, dass -%$\alpha=k^2$, $\beta=1$ und $\gamma=1$ gewählt werden müssen. -%Aus dem Koeffizientenvergleich~\eqref{buch:elliptisch:eqn:koeffvergl} -%folgt dann der Reihe nach -%\begin{align*} -%b&=\pm \sqrt{B} -%\\ -%a&=\pm \sqrt{\frac{C}{B}} -%\\ -%k^2 -%&= -%\frac{AC}{B^2}. -%\end{align*} -%Man beachte, dass man $k^2$ durch Einsetzen von -%\eqref{buch:elliptisch:eqn:koeffABC} -%auch direkt aus den Koeffizienten $\alpha$, $\beta$ und $\gamma$ -%erhalten kann, nämlich -%\[ -%\frac{AC}{B^2} -%= -%\frac{\frac{\alpha b^2}{a^2} \gamma a^2b^2}{\beta^2 b^4} -%= -%\frac{\alpha\gamma}{\beta^2}. -%\qedhere -%\] -%\end{beispiel} -% -%Da alle Parameter im -%Lösungsansatz~\eqref{buch:elliptisch:eqn:loesungsansatz} bereits -%festgelegt sind stellt sich die Frage, woher man einen weiteren -%Parameter nehmen kann, mit dem Anfangsbedingungen erfüllen kann. -%Die Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} ist -%autonom, die Koeffizienten der rechten Seite der Differentialgleichung -%sind nicht von der Zeit abhängig. -%Damit ist eine zeitverschobene Funktion $x(t-t_0)$ ebenfalls eine -%Lösung der Differentialgleichung. -%Die allgmeine Lösung der -%Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} hat -%also die Form -%\[ -%x(t) = a\operatorname{zn}(b(t-t_0)), -%\] -%wobei die Funktion $\operatorname{zn}(u,k)$ auf Grund der Vorzeichen -%von $A$, $B$ und $C$ gewählt werden müssen. -%% -%% Das mathematische Pendel -%% -%\subsection{Das mathematische Pendel -%\label{buch:elliptisch:subsection:mathpendel}} -%\begin{figure} -%\centering -%\includegraphics{chapters/110-elliptisch/images/pendel.pdf} -%\caption{Mathematisches Pendel -%\label{buch:elliptisch:fig:mathpendel}} -%\end{figure} -%Das in Abbildung~\ref{buch:elliptisch:fig:mathpendel} dargestellte -%Mathematische Pendel besteht aus einem Massepunkt der Masse $m$ -%im Punkt $P$, -%der über eine masselose Stange der Länge $l$ mit dem Drehpunkt $O$ -%verbunden ist. -%Das Pendel bewegt sich unter dem Einfluss der Schwerebeschleunigung $g$. -% -%Das Trägheitsmoment des Massepunktes um den Drehpunkt $O$ ist -%\( -%I=ml^2 -%\). -%Das Drehmoment der Schwerkraft ist -%\(M=gl\sin\vartheta\). -%Die Bewegungsgleichung wird daher -%\[ -%\begin{aligned} -%\frac{d}{dt} I\dot{\vartheta} -%&= -%M -%= -%gl\sin\vartheta -%\\ -%ml^2\ddot{\vartheta} -%&= -%gl\sin\vartheta -%&&\Rightarrow& -%\ddot{\vartheta} -%&=\frac{g}{l}\sin\vartheta -%\end{aligned} -%\] -%Dies ist eine nichtlineare Differentialgleichung zweiter Ordnung, die -%wir nicht unmittelbar mit den Differentialgleichungen erster Ordnung -%der elliptischen Funktionen vergleichen können. -% -%Die Differentialgleichungen erster Ordnung der elliptischen Funktionen -%enthalten das Quadrat der ersten Ableitung. -%In unserem Fall entspricht das einer Gleichung, die $\dot{\vartheta}^2$ -%enthält. -%Der Energieerhaltungssatz kann uns eine solche Gleichung geben. -%Die Summe von kinetischer und potentieller Energie muss konstant sein. -%Dies führt auf -%\[ -%E_{\text{kinetisch}} -%+ -%E_{\text{potentiell}} -%= -%\frac12I\dot{\vartheta}^2 -%+ -%mgl(1-\cos\vartheta) -%= -%\frac12ml^2\dot{\vartheta}^2 -%+ -%mgl(1-\cos\vartheta) -%= -%E -%\] -%Durch Auflösen nach $\dot{\vartheta}$ kann man jetzt die -%Differentialgleichung -%\[ -%\dot{\vartheta}^2 -%= -%- -%\frac{2g}{l}(1-\cos\vartheta) -%+\frac{2E}{ml^2} -%\] -%finden. -%In erster Näherung, d.h. wenn man die rechte Seite bis zu vierten -%Potenzen in eine Taylor-Reihe in $\vartheta$ entwickelt, ist dies -%tatsächlich eine Differentialgleichung der Art, wie wir sie für -%elliptische Funktionen gefunden haben, wir möchten aber eine exakte -%Lösung konstruieren. -% -%Die maximale Energie für eine Bewegung, bei der sich das Pendel gerade -%über den höchsten Punkt hinweg zu bewegen vermag, ist -%$E=2lmg$. -%Falls $E<2mgl$ ist, erwarten wir Schwingungslösungen, bei denen -%der Winkel $\vartheta$ immer im offenen Interval $(-\pi,\pi)$ -%bleibt. -%Für $E>2mgl$ wird sich das Pendel im Kreis bewegen, für sehr grosse -%Energie ist die kinetische Energie dominant, die Verlangsamung im -%höchsten Punkt wird immer weniger ausgeprägt sein. -% -%% -%% Koordinatentransformation auf elliptische Funktionen -%% -%\subsubsection{Koordinatentransformation auf elliptische Funktionen} -%Wir verwenden als neue Variable -%\[ -%y = \sin\frac{\vartheta}2 -%\] -%mit der Ableitung -%\[ -%\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. -%\] -%Man beachte, dass $y$ nicht eine Koordinate in -%Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. -% -%Aus den Halbwinkelformeln finden wir -%\[ -%\cos\vartheta -%= -%1-2\sin^2 \frac{\vartheta}2 -%= -%1-2y^2. -%\] -%Dies können wir zusammen mit der -%Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ -%in die Energiegleichung einsetzen und erhalten -%\[ -%\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E -%\qquad\Rightarrow\qquad -%\frac14 \dot{\vartheta}^2 = \frac{E}{2ml^2} - \frac{g}{2l}y^2. -%\] -%Der konstante Term auf der rechten Seite ist grösser oder kleiner als -%$1$ je nachdem, ob das Pendel sich im Kreis bewegt oder nicht. -% -%Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ -%erhalten wir auf der linken Seite einen Ausdruck, den wir -%als Funktion von $\dot{y}$ ausdrücken können. -%Wir erhalten -%\begin{align*} -%\frac14 -%\cos^2\frac{\vartheta}2 -%\cdot -%\dot{\vartheta}^2 -%&= -%\frac14 -%(1-y^2) -%\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) -%\\ -%\dot{y}^2 -%&= -%\frac{1}{4} -%(1-y^2) -%\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) -%\end{align*} -%Die letzte Gleichung hat die Form einer Differentialgleichung -%für elliptische Funktionen. -%Welche Funktion verwendet werden muss, hängt von der Grösse der -%Koeffizienten in der zweiten Klammer ab. -%Die Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} -%zeigt, dass in der zweiten Klammer jeweils einer der Terme -%$1$ sein muss. -% -%% -%% Der Fall E < 2mgl -%% -%\subsubsection{Der Fall $E<2mgl$} -%\begin{figure} -%\centering -%\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} -%\caption{% -%Abhängigkeit der elliptischen Funktionen von $u$ für -%verschiedene Werte von $k^2=m$. -%Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, -%$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese -%sind in allen Plots in einer helleren Farbe eingezeichnet. -%Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig -%von den trigonometrischen Funktionen ab, -%es ist aber klar erkennbar, dass die anharmonischen Terme in der -%Differentialgleichung die Periode mit steigender Amplitude verlängern. -%Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass -%die Energie des Pendels fast ausreicht, dass es den höchsten Punkt -%erreichen kann, was es für $m$ macht. -%\label{buch:elliptisch:fig:jacobiplots}} -%\end{figure} -% -% -%Wir verwenden als neue Variable -%\[ -%y = \sin\frac{\vartheta}2 -%\] -%mit der Ableitung -%\[ -%\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. -%\] -%Man beachte, dass $y$ nicht eine Koordinate in -%Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. -% -%Aus den Halbwinkelformeln finden wir -%\[ -%\cos\vartheta -%= -%1-2\sin^2 \frac{\vartheta}2 -%= -%1-2y^2. -%\] -%Dies können wir zusammen mit der -%Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ -%in die Energiegleichung einsetzen und erhalten -%\[ -%\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E. -%\] -%Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ -%erhalten wir auf der linken Seite einen Ausdruck, den wir -%als Funktion von $\dot{y}$ ausdrücken können. -%Wir erhalten -%\begin{align*} -%\frac12ml^2 -%\cos^2\frac{\vartheta}2 -%\dot{\vartheta}^2 -%&= -%(1-y^2) -%(E -mgly^2) -%\\ -%\frac{1}{4}\cos^2\frac{\vartheta}{2}\dot{\vartheta}^2 -%&= -%\frac{1}{2} -%(1-y^2) -%\biggl(\frac{E}{ml^2} -\frac{g}{l}y^2\biggr) -%\\ -%\dot{y}^2 -%&= -%\frac{E}{2ml^2} -%(1-y^2)\biggl( -%1-\frac{2gml}{E}y^2 -%\biggr). -%\end{align*} -%Dies ist genau die Form der Differentialgleichung für die elliptische -%Funktion $\operatorname{sn}(u,k)$ -%mit $k^2 = 2gml/E< 1$. -% -%%% -%%% Der Fall E > 2mgl -%%% -%%\subsection{Der Fall $E > 2mgl$} -%%In diesem Fall hat das Pendel im höchsten Punkte immer noch genügend -%%kinetische Energie, so dass es sich im Kreise dreht. -%%Indem wir die Gleichung -% -% -%%\subsection{Soliton-Lösungen der Sinus-Gordon-Gleichung} -% -%%\subsection{Nichtlineare Differentialgleichung vierter Ordnung} -%%XXX Möbius-Transformation \\ -%%XXX Reduktion auf die Differentialgleichung elliptischer Funktionen diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index e766779..0df27a7 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -387,7 +387,7 @@ r(s) \begin{figure} \centering -\includegraphics{chapters/110-elliptisch/images/slcl.pdf} +\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/slcl.pdf} \caption{ Lemniskatischer Sinus und Kosinus sowie Sinus und Kosinus mit derart skaliertem Argument, dass die Funktionen die gleichen Nullstellen diff --git a/vorlesungsnotizen/MSE/5 - Elliptische Funktionen.pdf b/vorlesungsnotizen/MSE/5 - Elliptische Funktionen.pdf new file mode 100644 index 0000000..8537524 Binary files /dev/null and b/vorlesungsnotizen/MSE/5 - Elliptische Funktionen.pdf differ -- cgit v1.2.1 From f9842b34a2b78bc340b861cc57aa29ccfbb13fd1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 24 Apr 2022 15:35:47 +0200 Subject: Makefile fixes, lecture notes week 8 --- buch/Makefile | 4 ++-- buch/aufgaben3.tex | 4 ++-- buch/chapters/000-einleitung/Makefile.inc | 2 +- buch/chapters/010-potenzen/Makefile.inc | 2 +- buch/chapters/020-exponential/Makefile.inc | 2 +- buch/chapters/030-geometrie/Makefile.inc | 2 +- buch/chapters/040-rekursion/Makefile.inc | 2 +- buch/chapters/050-differential/Makefile.inc | 2 +- buch/chapters/060-integral/Makefile.inc | 6 +----- buch/chapters/070-orthogonalitaet/Makefile.inc | 2 +- buch/chapters/075-fourier/Makefile.inc | 2 +- buch/chapters/080-funktionentheorie/Makefile.inc | 2 +- buch/chapters/090-pde/Makefile.inc | 2 +- buch/chapters/110-elliptisch/Makefile.inc | 6 +++--- buch/chapters/110-elliptisch/uebungsaufgaben/1.tex | 19 ++++++++++++------- buch/common/macros.tex | 4 +++- buch/common/test-common.tex | 1 + buch/common/test3.tex | 1 + .../B/8 - Integration in geschlossener Form.pdf | Bin 0 -> 3984055 bytes 19 files changed, 35 insertions(+), 30 deletions(-) create mode 100644 vorlesungsnotizen/B/8 - Integration in geschlossener Form.pdf diff --git a/buch/Makefile b/buch/Makefile index 00fcf42..af0e1e2 100755 --- a/buch/Makefile +++ b/buch/Makefile @@ -55,13 +55,13 @@ SeminarSpezielleFunktionen.ind: SeminarSpezielleFunktionen.idx # tests: test1.pdf test2.pdf test3.pdf -test1.pdf: common/test-common.tex common/test1.tex aufgaben1.tex +test1.pdf: common/test-common.tex common/test1.tex aufgaben1.tex $(TEXFILES) $(pdflatex) common/test1.tex test2.pdf: common/test-common.tex common/test1.tex aufgaben2.tex $(pdflatex) common/test2.tex -test3.pdf: common/test-common.tex common/test1.tex aufgaben3.tex +test3.pdf: common/test-common.tex common/test1.tex aufgaben3.tex $(CHAPTERFILES) $(pdflatex) common/test3.tex # diff --git a/buch/aufgaben3.tex b/buch/aufgaben3.tex index a39fc19..16288ec 100644 --- a/buch/aufgaben3.tex +++ b/buch/aufgaben3.tex @@ -4,6 +4,6 @@ % (c) 2022 Prof. Dr. Andreas Mueller, OST % -%\item -%\input chapters/60-gruppen/uebungsaufgaben/6001.tex +\item +\input chapters/110-elliptisch/uebungsaufgaben/1.tex diff --git a/buch/chapters/000-einleitung/Makefile.inc b/buch/chapters/000-einleitung/Makefile.inc index a870448..5840050 100644 --- a/buch/chapters/000-einleitung/Makefile.inc +++ b/buch/chapters/000-einleitung/Makefile.inc @@ -4,5 +4,5 @@ # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/000-einleitung/chapter.tex diff --git a/buch/chapters/010-potenzen/Makefile.inc b/buch/chapters/010-potenzen/Makefile.inc index a4505cb..27ccdae 100644 --- a/buch/chapters/010-potenzen/Makefile.inc +++ b/buch/chapters/010-potenzen/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/010-potenzen/loesbarkeit.tex \ chapters/010-potenzen/polynome.tex \ chapters/010-potenzen/tschebyscheff.tex \ diff --git a/buch/chapters/020-exponential/Makefile.inc b/buch/chapters/020-exponential/Makefile.inc index d6b3c7f..4d8f58b 100644 --- a/buch/chapters/020-exponential/Makefile.inc +++ b/buch/chapters/020-exponential/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/020-exponential/zins.tex \ chapters/020-exponential/log.tex \ chapters/020-exponential/lambertw.tex \ diff --git a/buch/chapters/030-geometrie/Makefile.inc b/buch/chapters/030-geometrie/Makefile.inc index 0bf775f..d4940dc 100644 --- a/buch/chapters/030-geometrie/Makefile.inc +++ b/buch/chapters/030-geometrie/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/030-geometrie/trigonometrisch.tex \ chapters/030-geometrie/sphaerisch.tex \ chapters/030-geometrie/hyperbolisch.tex \ diff --git a/buch/chapters/040-rekursion/Makefile.inc b/buch/chapters/040-rekursion/Makefile.inc index a222b1c..cd54c80 100644 --- a/buch/chapters/040-rekursion/Makefile.inc +++ b/buch/chapters/040-rekursion/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/040-rekursion/gamma.tex \ chapters/040-rekursion/bohrmollerup.tex \ chapters/040-rekursion/integral.tex \ diff --git a/buch/chapters/050-differential/Makefile.inc b/buch/chapters/050-differential/Makefile.inc index b72a275..7151c07 100644 --- a/buch/chapters/050-differential/Makefile.inc +++ b/buch/chapters/050-differential/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/050-differential/beispiele.tex \ chapters/050-differential/potenzreihenmethode.tex \ chapters/050-differential/bessel.tex \ diff --git a/buch/chapters/060-integral/Makefile.inc b/buch/chapters/060-integral/Makefile.inc index e19cb0c..d85caad 100644 --- a/buch/chapters/060-integral/Makefile.inc +++ b/buch/chapters/060-integral/Makefile.inc @@ -4,13 +4,9 @@ # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/060-integral/fehlerfunktion.tex \ chapters/060-integral/eulertransformation.tex \ chapters/060-integral/differentialkoerper.tex \ chapters/060-integral/risch.tex \ - chapters/060-integral/orthogonal.tex \ - chapters/060-integral/legendredgl.tex \ - chapters/060-integral/sturm.tex \ - chapters/060-integral/gaussquadratur.tex \ chapters/060-integral/chapter.tex diff --git a/buch/chapters/070-orthogonalitaet/Makefile.inc b/buch/chapters/070-orthogonalitaet/Makefile.inc index 286ab2e..8f58489 100644 --- a/buch/chapters/070-orthogonalitaet/Makefile.inc +++ b/buch/chapters/070-orthogonalitaet/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/070-orthogonalitaet/orthogonal.tex \ chapters/070-orthogonalitaet/rekursion.tex \ chapters/070-orthogonalitaet/rodrigues.tex \ diff --git a/buch/chapters/075-fourier/Makefile.inc b/buch/chapters/075-fourier/Makefile.inc index c153dc4..a762e63 100644 --- a/buch/chapters/075-fourier/Makefile.inc +++ b/buch/chapters/075-fourier/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/075-fourier/bessel.tex \ chapters/075-fourier/2d.tex \ chapters/075-fourier/chapter.tex diff --git a/buch/chapters/080-funktionentheorie/Makefile.inc b/buch/chapters/080-funktionentheorie/Makefile.inc index affaa94..779cd80 100644 --- a/buch/chapters/080-funktionentheorie/Makefile.inc +++ b/buch/chapters/080-funktionentheorie/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/080-funktionentheorie/holomorph.tex \ chapters/080-funktionentheorie/analytisch.tex \ chapters/080-funktionentheorie/cauchy.tex \ diff --git a/buch/chapters/090-pde/Makefile.inc b/buch/chapters/090-pde/Makefile.inc index c64af06..5b52d27 100644 --- a/buch/chapters/090-pde/Makefile.inc +++ b/buch/chapters/090-pde/Makefile.inc @@ -4,7 +4,7 @@ # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/090-pde/gleichung.tex \ chapters/090-pde/separation.tex \ chapters/090-pde/rechteck.tex \ diff --git a/buch/chapters/110-elliptisch/Makefile.inc b/buch/chapters/110-elliptisch/Makefile.inc index b23df52..639cb8f 100644 --- a/buch/chapters/110-elliptisch/Makefile.inc +++ b/buch/chapters/110-elliptisch/Makefile.inc @@ -4,12 +4,12 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -CHAPTERFILES = $(CHAPTERFILES) \ +CHAPTERFILES += \ chapters/110-elliptisch/ellintegral.tex \ chapters/110-elliptisch/jacobi.tex \ chapters/110-elliptisch/elltrigo.tex \ chapters/110-elliptisch/dglsol.tex \ chapters/110-elliptisch/mathpendel.tex \ chapters/110-elliptisch/lemniskate.tex \ - chapters/110-elliptisch/uebungsaufgaben/001.tex \ - chapters/110-geometrie/chapter.tex + chapters/110-elliptisch/uebungsaufgaben/1.tex \ + chapters/110-elliptisch/chapter.tex diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex index 8e4b39f..67d5148 100644 --- a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex @@ -28,9 +28,11 @@ for den anharmonischen Oszillator ab, die sie in der Form $\frac12m\dot{x}^2 = f(x)$ schreiben. \item Die Amplitude der Schwingung ist derjenige $x$-Wert, für den die -Geschwindigkeit verschwindet. +Geschwindigkeit $\dot{x}(t)$ verschwindet. Leiten Sie die Amplitude aus der Differentialgleichung von -\ref{buch:1101:basic-dgl} ab. +%\ref{buch:1101:basic-dgl} +Teilaufgabe c) +ab. Sie erhalten zwei Werte $x_{\pm}$, wobei der kleinere $x_-$ die Amplitude einer beschränkten Schwingung beschreibt, während die $x_+$ die minimale Ausgangsamplitude einer gegen @@ -66,13 +68,16 @@ wobei $k^2=x_-^2/x_+^2$ und $A$ geeignet gewählt werden müssen. \label{buch:1101:teilaufgabe:dgl3} Verwenden Sie $t(\tau) = \alpha\tau$ und -$Y(\tau)=X(t(\tau))$ um eine Differentialgleichung für die Funktion -$Y(\tau)$ zu gewinnen, die die Form der Differentialgleichung -von $\operatorname{sn}(u,k)$ hat, für die also $A=0$ in -\eqref{buch:1101:eqn:dgl3} ist. +$Y(\tau)=X(t(\tau))=X(\alpha\tau)$ um eine Differentialgleichung für +die Funktion $Y(\tau)$ zu gewinnen, die die Form der Differentialgleichung +von $\operatorname{sn}(u,k)$ hat (Abschnitt +\ref{buch:elliptisch:subsection:differentialgleichungen}), +für die also $A=0$ in \eqref{buch:1101:eqn:dgl3} ist. \item Verwenden Sie die Lösung $\operatorname{sn}(u,k)$ der in -\ref{buch:1101:teilaufgabe:dgl3} erhaltenen Differentialgleichung, +Teilaufgabe h) +%\ref{buch:1101:teilaufgabe:dgl3} +erhaltenen Differentialgleichung, um die Lösung $x(t)$ der ursprünglichen Gleichung aufzuschreiben. \end{teilaufgaben} diff --git a/buch/common/macros.tex b/buch/common/macros.tex index 7c82180..bb6e9b0 100644 --- a/buch/common/macros.tex +++ b/buch/common/macros.tex @@ -23,7 +23,9 @@ \vfill\pagebreak} \newenvironment{teilaufgaben}{ \begin{enumerate} -\renewcommand{\labelenumi}{\alph{enumi})} +\renewcommand{\theenumi}{\alph{enumi})} +%\renewcommand{\labelenumi}{\alph{enumi})} +\renewcommand{\labelenumi}{\theenumi} }{\end{enumerate}} % Aufgabe \newcounter{problemcounter}[chapter] diff --git a/buch/common/test-common.tex b/buch/common/test-common.tex index 289e59c..3f49701 100644 --- a/buch/common/test-common.tex +++ b/buch/common/test-common.tex @@ -30,6 +30,7 @@ \usepackage{standalone} \usepackage{environ} \usepackage{tikz} +\usepackage{xr} \input{../common/linsys.tex} \newcounter{beispiel} \newenvironment{beispiele}{ diff --git a/buch/common/test3.tex b/buch/common/test3.tex index 8b24262..22d6b63 100644 --- a/buch/common/test3.tex +++ b/buch/common/test3.tex @@ -4,6 +4,7 @@ % (c) 2021 Prof. Dr. Andreas Mueller, OST % \input{common/test-common.tex} +\externaldocument{buch} \begin{document} {\parindent0pt\hbox to\hsize{% diff --git a/vorlesungsnotizen/B/8 - Integration in geschlossener Form.pdf b/vorlesungsnotizen/B/8 - Integration in geschlossener Form.pdf new file mode 100644 index 0000000..9f06bdc Binary files /dev/null and b/vorlesungsnotizen/B/8 - Integration in geschlossener Form.pdf differ -- cgit v1.2.1 From bc23a25ab1aaa67f78998d34d8bf75afbe70606d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 25 Apr 2022 21:54:35 +0200 Subject: fix typos --- buch/chapters/110-elliptisch/uebungsaufgaben/1.tex | 20 +++++++++++++------- 1 file changed, 13 insertions(+), 7 deletions(-) diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex index 67d5148..694f18a 100644 --- a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex @@ -267,15 +267,21 @@ Die Ableitung von $Y(\tau)=X(t(\tau))$ nach $\tau$ ist = \alpha \dot{X}(t(\tau)) -\qquad\Rightarrow\qquad -\frac{1}{\alpha^2}\frac{dY}{d\tau} +\quad\Rightarrow\quad +\frac{1}{\alpha}\frac{dY}{d\tau} = -\dot{X}(t(\tau)). +\dot{X}(t(\tau)) +\quad\Rightarrow\quad +\frac{1}{\alpha^2}\biggl(\frac{dY}{d\tau}\biggr)^2 += +\dot{X}(t(\tau))^2. \] Die Differentialgleichung für $Y(\tau)$ ist \[ -\frac{2mk^2}{\delta x_+^2\alpha^2} +\frac{2m}{\delta x_+^2\alpha^2} +\biggl( \frac{dY}{d\tau} +\biggr)^2 = (1-Y^2)(1-k^2Y^2). \] @@ -283,7 +289,7 @@ Der Koeffizient vor der Ableitung wird $1$, wenn man \[ \alpha^2 = -\frac{2mk^2}{\delta x_+^2} +\frac{2m}{\delta x_+^2} \] wählt. Diese Differentialgleichug hat die Lösung @@ -299,9 +305,9 @@ x(t) x_- X(t) = x_- \operatorname{sn}\biggl( -t\sqrt{\frac{\delta x_+^2}{2mk^2} } +t\sqrt{\frac{\delta x_+^2}{2m} } ,k -\biggr) +\biggr). \end{align*} Das Produkt $\delta x_+^2$ kann auch als \[ -- cgit v1.2.1 From c771727f3d404d7d79f36b3871e540a8539edfcf Mon Sep 17 00:00:00 2001 From: runterer Date: Sat, 30 Apr 2022 22:03:05 +0200 Subject: wip copying my handwritten stuff to LaTex --- buch/papers/zeta/Makefile.inc | 7 +- buch/papers/zeta/analytic_continuation.tex | 165 +++++++++++++++++++++++++++++ buch/papers/zeta/einleitung.tex | 11 ++ buch/papers/zeta/main.tex | 32 ++---- buch/papers/zeta/teil0.tex | 22 ---- buch/papers/zeta/teil1.tex | 55 ---------- buch/papers/zeta/teil2.tex | 40 ------- buch/papers/zeta/teil3.tex | 40 ------- buch/papers/zeta/zeta_gamma.tex | 53 +++++++++ 9 files changed, 239 insertions(+), 186 deletions(-) create mode 100644 buch/papers/zeta/analytic_continuation.tex create mode 100644 buch/papers/zeta/einleitung.tex delete mode 100644 buch/papers/zeta/teil0.tex delete mode 100644 buch/papers/zeta/teil1.tex delete mode 100644 buch/papers/zeta/teil2.tex delete mode 100644 buch/papers/zeta/teil3.tex create mode 100644 buch/papers/zeta/zeta_gamma.tex diff --git a/buch/papers/zeta/Makefile.inc b/buch/papers/zeta/Makefile.inc index 11c7697..14babe2 100644 --- a/buch/papers/zeta/Makefile.inc +++ b/buch/papers/zeta/Makefile.inc @@ -7,8 +7,7 @@ dependencies-zeta = \ papers/zeta/packages.tex \ papers/zeta/main.tex \ papers/zeta/references.bib \ - papers/zeta/teil0.tex \ - papers/zeta/teil1.tex \ - papers/zeta/teil2.tex \ - papers/zeta/teil3.tex + papers/zeta/einleitung.tex \ + papers/zeta/analytic_continuation.tex \ + papers/zeta/zeta_gamma.tex \ diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex new file mode 100644 index 0000000..943647a --- /dev/null +++ b/buch/papers/zeta/analytic_continuation.tex @@ -0,0 +1,165 @@ +\section{Analytische Fortsetzung} \label{zeta:section:analytische_fortsetzung} +\rhead{Analytische Fortsetzung} + +%TODO missing Text + +\subsection{Fortsetzung auf $\Re(s) > 0$} \label{zeta:subsection:auf_bereich_ge_0} +Zuerst definieren die Dirichletsche Etafunktion als +\begin{equation}\label{zeta:equation:eta} + \eta(s) + = + \sum_{n=1}^{\infty} + \frac{(-1)^{n-1}}{n^s}, +\end{equation} +wobei die Reihe bis auf die alternierenden Vorzeichen die selbe wie in der Zetafunktion ist. +Diese Etafunktion konvergiert gemäss dem Leibnitz-Kriterium im Bereich $\Re(s) > 0$, da dann die einzelnen Glieder monoton fallend sind. + +Wenn wir es nun schaffen, die sehr ähnliche Zetafunktion mit der Etafunktion auszudrücken, dann haben die gesuchte Fortsetzung. +Die folgenden Schritte zeigen, wie man dazu kommt: +\begin{align} + \zeta(s) + &= + \sum_{n=1}^{\infty} + \frac{1}{n^s} \label{zeta:align1} + \\ + \frac{1}{2^{s-1}} + \zeta(s) + &= + \sum_{n=1}^{\infty} + \frac{2}{(2n)^s} \label{zeta:align2} + \\ + \left(1 - \frac{1}{2^{s-1}} \right) + \zeta(s) + &= + \frac{1}{1^s} + \underbrace{-\frac{2}{2^s} + \frac{1}{2^s}}_{-\frac{1}{2^s}} + + \frac{1}{3^s} + \underbrace{-\frac{2}{4^s} + \frac{1}{4^s}}_{-\frac{1}{4^s}} + \ldots + && \text{\eqref{zeta:align1}} - \text{\eqref{zeta:align2}} + \\ + &= \eta(s) + \\ + \zeta(s) + &= + \left(1 - \frac{1}{2^{s-1}} \right)^{-1} \eta(s). +\end{align} + +\subsection{Fortsetzung auf ganz $\mathbb{C}$} \label{zeta:subsection:auf_ganz} +Für die Fortsetzung auf den Rest von $\mathbb{C}$, verwenden wir den Zusammenhang von Gamma- und Zetafunktion aus \ref{zeta:section:zusammenhang_mit_gammafunktion}. +Wir beginnen damit, die Gammafunktion für den halben Funktionswert zu berechnen als +\begin{equation} + \Gamma \left( \frac{s}{2} \right) + = + \int_0^{\infty} t^{\frac{s}{2}-1} e^{-t} dt. +\end{equation} +Nun substituieren wir $t$ mit $t = \pi n^2 x$ und $dt=\pi n^2 dx$ und erhalten +\begin{align} + \Gamma \left( \frac{s}{2} \right) + &= + \int_0^{\infty} + (\pi n^2)^{\frac{s}{2}} + x^{\frac{s}{2}-1} + e^{-\pi n^2 x} + dx + && \text{Division durch } (\pi n^2)^{\frac{s}{2}} + \\ + \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}} n^s} + &= + \int_0^{\infty} + x^{\frac{s}{2}-1} + e^{-\pi n^2 x} + dx + && \text{Zeta durch Summenbildung } \sum_{n=1}^{\infty} + \\ + \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}}} + \zeta(s) + &= + \int_0^{\infty} + x^{\frac{s}{2}-1} + \sum_{n=1}^{\infty} + e^{-\pi n^2 x} + dx. \label{zeta:equation:integral1} +\end{align} +Die Summe kürzen wir ab als $\psi(x) = \sum_{n=1}^{\infty} e^{-\pi n^2 x}$. +%TODO Wieso folgendes -> aus Fourier Signal +Es gilt +\begin{equation}\label{zeta:equation:psi} + \psi(x) + = + - \frac{1}{2} + + \frac{\psi\left(\frac{1}{x} \right)}{\sqrt{x}} + + \frac{1}{2 \sqrt{x}}. +\end{equation} + +Zunächst teilen wir nun das Integral aus \eqref{zeta:equation:integral1} auf als +\begin{equation}\label{zeta:equation:integral2} + \int_0^{\infty} + x^{\frac{s}{2}-1} + \psi(x) + dx + = + \int_0^{1} + x^{\frac{s}{2}-1} + \psi(x) + dx + + + \int_1^{\infty} + x^{\frac{s}{2}-1} + \psi(x) + dx, +\end{equation} +wobei wir uns nun auf den ersten Teil konzentrieren werden. +Dabei setzen wir das Wissen aus \eqref{zeta:equation:integral2} ein und erhalten +\begin{align} + \int_0^{1} + x^{\frac{s}{2}-1} + \psi(x) + dx + &= + \int_0^{1} + x^{\frac{s}{2}-1} + \left( + - \frac{1}{2} + + \frac{\psi\left(\frac{1}{x} \right)}{\sqrt{x}} + + \frac{1}{2 \sqrt{x}}. + \right) + dx + \\ + &= + \int_0^{1} + x^{\frac{s}{2}-\frac{3}{2}} + \psi \left( \frac{1}{x} \right) + + \frac{1}{2} + \left( + x^{\frac{s}{2}-\frac{3}{2}} + - + x^{\frac{s}{2}-1} + \right) + dx + \\ + &= + \int_0^{1} + x^{\frac{s}{2}-\frac{3}{2}} + \psi \left( \frac{1}{x} \right) + dx + + \frac{1}{2} + \int_0^1 + x^{\frac{s}{2}-\frac{3}{2}} + - + x^{\frac{s}{2}-1} + dx. +\end{align} +Dabei kann das zweite integral gelöst werden als +\begin{equation} + \frac{1}{2} + \int_0^1 + x^{\frac{s}{2}-\frac{3}{2}} + - + x^{\frac{s}{2}-1} + dx + = + \frac{1}{s(s-1)}. +\end{equation} + + diff --git a/buch/papers/zeta/einleitung.tex b/buch/papers/zeta/einleitung.tex new file mode 100644 index 0000000..3b70531 --- /dev/null +++ b/buch/papers/zeta/einleitung.tex @@ -0,0 +1,11 @@ +\section{Einleitung} \label{zeta:section:einleitung} +\rhead{Einleitung} + +Die Riemannsche Zetafunktion ist für alle komplexe $s$ mit $\Re(s) > 1$ definiert als +\begin{equation}\label{zeta:equation1} + \zeta(s) + = + \sum_{n=1}^{\infty} + \frac{1}{n^s}. +\end{equation} + diff --git a/buch/papers/zeta/main.tex b/buch/papers/zeta/main.tex index 1d9e059..e0ea8e1 100644 --- a/buch/papers/zeta/main.tex +++ b/buch/papers/zeta/main.tex @@ -3,34 +3,16 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:zeta}} -\lhead{Thema} +\chapter{Riemannsche Zetafunktion\label{chapter:zeta}} +\lhead{Riemannsche Zetafunktion} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Raphael Unterer} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} +%TODO Einleitung -\input{papers/zeta/teil0.tex} -\input{papers/zeta/teil1.tex} -\input{papers/zeta/teil2.tex} -\input{papers/zeta/teil3.tex} +\input{papers/zeta/einleitung.tex} +\input{papers/zeta/zeta_gamma.tex} +\input{papers/zeta/analytic_continuation.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/zeta/teil0.tex b/buch/papers/zeta/teil0.tex deleted file mode 100644 index 56c0b1b..0000000 --- a/buch/papers/zeta/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{zeta:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{zeta:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/zeta/teil1.tex b/buch/papers/zeta/teil1.tex deleted file mode 100644 index 4017ee8..0000000 --- a/buch/papers/zeta/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{zeta:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{zeta:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{zeta:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{zeta:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{zeta:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/zeta/teil2.tex b/buch/papers/zeta/teil2.tex deleted file mode 100644 index 9e8a96e..0000000 --- a/buch/papers/zeta/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{zeta:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{zeta:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/zeta/teil3.tex b/buch/papers/zeta/teil3.tex deleted file mode 100644 index 6610cc3..0000000 --- a/buch/papers/zeta/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{zeta:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{zeta:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/zeta/zeta_gamma.tex b/buch/papers/zeta/zeta_gamma.tex new file mode 100644 index 0000000..59c8744 --- /dev/null +++ b/buch/papers/zeta/zeta_gamma.tex @@ -0,0 +1,53 @@ +\section{Zusammenhang mit Gammafunktion} \label{zeta:section:zusammenhang_mit_gammafunktion} +\rhead{Zusammenhang mit Gammafunktion} + +Dieser Abschnitt stellt die Verbindung zwischen der Gamma- und der Zetafunktion her. + +%TODO ref Gamma +Wenn in der Gammafunkion die Integrationsvariable $t$ substituieren mit $t = nu$ und $dt = n du$, dann können wir die Gleichung umstellen und erhalten den Zusammenhang mit der Zetafunktion +\begin{align} + \Gamma(s) + &= + \int_0^{\infty} t^{s-1} e^{-t} dt + \\ + &= + \int_0^{\infty} n^{s\cancel{-1}}u^{s-1} e^{-nu} \cancel{n}du + && + \text{Division durch }n^s + \\ + \frac{\Gamma(s)}{n^s} + &= + \int_0^{\infty} u^{s-1} e^{-nu}du + && + \text{Zeta durch Summenbildung } \sum_{n=1}^{\infty} + \\ + \Gamma(s) \zeta(s) + &= + \int_0^{\infty} u^{s-1} + \sum_{n=1}^{\infty}e^{-nu} + du. + \label{zeta:equation:zeta_gamma1} +\end{align} +Die Summe über $e^{-nu}$ können wir als geometrische Reihe schreiben und erhalten +\begin{align} + \sum_{n=1}^{\infty}e^{-u^n} + &= + \sum_{n=0}^{\infty}e^{-u^n} + - + 1 + \\ + &= + \frac{1}{1 - e^{-u}} - 1 + \\ + &= + \frac{1}{e^u - 1}. +\end{align} +Wenn wir dieses Resultat einsetzen in \eqref{zeta:equation:zeta_gamma1} und durch $\Gamma(s)$ teilen, erhalten wir +\begin{equation}\label{zeta:equation:zeta_gamma_final} + \zeta(s) + = + \frac{1}{\Gamma(s)} + \int_0^{\infty} + \frac{u^{s-1}}{e^u -1} + du. +\end{equation} -- cgit v1.2.1 From e26f12668c78fab5f0d8c5c9625396fd34970c82 Mon Sep 17 00:00:00 2001 From: runterer Date: Sat, 30 Apr 2022 22:39:22 +0200 Subject: Erster Entwurf der analytischen Fortsetzung geschrieben --- buch/papers/zeta/analytic_continuation.tex | 107 +++++++++++++++++++++++++++-- 1 file changed, 103 insertions(+), 4 deletions(-) diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex index 943647a..f5de6e7 100644 --- a/buch/papers/zeta/analytic_continuation.tex +++ b/buch/papers/zeta/analytic_continuation.tex @@ -110,7 +110,7 @@ Zunächst teilen wir nun das Integral aus \eqref{zeta:equation:integral1} auf al dx, \end{equation} wobei wir uns nun auf den ersten Teil konzentrieren werden. -Dabei setzen wir das Wissen aus \eqref{zeta:equation:integral2} ein und erhalten +Dabei setzen wir das Wissen aus \eqref{zeta:equation:psi} ein und erhalten \begin{align} \int_0^{1} x^{\frac{s}{2}-1} @@ -148,9 +148,9 @@ Dabei setzen wir das Wissen aus \eqref{zeta:equation:integral2} ein und erhalten x^{\frac{s}{2}-\frac{3}{2}} - x^{\frac{s}{2}-1} - dx. + dx. \label{zeta:equation:integral3} \end{align} -Dabei kann das zweite integral gelöst werden als +Dabei kann das zweite Integral gelöst werden als \begin{equation} \frac{1}{2} \int_0^1 @@ -161,5 +161,104 @@ Dabei kann das zweite integral gelöst werden als = \frac{1}{s(s-1)}. \end{equation} - +Das erste Integral aus \eqref{zeta:equation:integral3} mit $\psi \left(\frac{1}{x} \right)$ ist nicht lösbar in dieser Form. +Deshalb substituieren wir $x = \frac{1}{u}$ und $dx = -\frac{1}{u^2}du$. +Die untere Integralgrenze wechselt ebenfalls zu $x_0 = 0 \rightarrow u_0 = \infty$. +Dies ergibt +\begin{align} + \int_{\infty}^{1} + {\frac{1}{u}}^{\frac{s}{2}-\frac{3}{2}} + \psi(u) + \frac{-du}{u^2} + &= + \int_{1}^{\infty} + {\frac{1}{u}}^{\frac{s}{2}-\frac{3}{2}} + \psi(u) + \frac{du}{u^2} + \\ + &= + \int_{1}^{\infty} + x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} + \psi(x) + dx, +\end{align} +wobei wir durch Multiplikation mit $(-1)$ die Integralgrenzen tauschen dürfen. +Es ist zu beachten das diese Grenzen nun identisch mit den Grenzen des zweiten Integrals von \eqref{zeta:equation:integral2} sind. +Wir setzen beide Lösungen ein in Gleichung \eqref{zeta:equation:integral3} und erhalten +\begin{equation} + \int_0^{1} + x^{\frac{s}{2}-1} + \psi(x) + dx + = + \int_{1}^{\infty} + x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} + \psi(x) + dx, + + + \frac{1}{s(s-1)}. +\end{equation} +Dieses Resultat setzen wir wiederum ein in \eqref{zeta:equation:integral2}, um schlussendlich +\begin{align} + \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}}} + \zeta(s) + &= + \int_0^{1} + x^{\frac{s}{2}-1} + \psi(x) + dx + + + \int_1^{\infty} + x^{\frac{s}{2}-1} + \psi(x) + dx + \nonumber + \\ + &= + \frac{1}{s(s-1)} + + + \int_{1}^{\infty} + x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} + \psi(x) + dx, + + + \int_1^{\infty} + x^{\frac{s}{2}-1} + \psi(x) + dx + \\ + &= + \frac{1}{s(s-1)} + + + \int_{1}^{\infty} + \left( + x^{-\frac{s}{2}-\frac{1}{2}} + + + x^{\frac{s}{2}-1} + \right) + \psi(x) + dx + \\ + &= + \frac{-1}{s(1-s)} + + + \int_{1}^{\infty} + \left( + x^{\frac{1-s}{2}} + + + x^{\frac{s}{2}} + \right) + \frac{\psi(x)}{x} + dx, +\end{align} +zu erhalten. +Wenn wir dieses Resultat genau anschauen, erkennen wir dass sich nichts verändert wenn $s$ mit $1-s$ ersetzt wird. +Somit haben wir die analytische Fortsetzung gefunden als +\begin{equation}\label{zeta:equation:functional} + \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}}} + \zeta(s) + = + \frac{\Gamma \left( \frac{1-s}{2} \right)}{\pi^{\frac{1-s}{2}}} + \zeta(1-s). +\end{equation} -- cgit v1.2.1 From 2041283fe8afc6c80451208e239913f52f767d93 Mon Sep 17 00:00:00 2001 From: runterer Date: Sat, 30 Apr 2022 22:46:13 +0200 Subject: minor fix --- buch/papers/zeta/analytic_continuation.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex index f5de6e7..bb95b92 100644 --- a/buch/papers/zeta/analytic_continuation.tex +++ b/buch/papers/zeta/analytic_continuation.tex @@ -194,7 +194,7 @@ Wir setzen beide Lösungen ein in Gleichung \eqref{zeta:equation:integral3} und \int_{1}^{\infty} x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} \psi(x) - dx, + dx + \frac{1}{s(s-1)}. \end{equation} @@ -220,7 +220,7 @@ Dieses Resultat setzen wir wiederum ein in \eqref{zeta:equation:integral2}, um s \int_{1}^{\infty} x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} \psi(x) - dx, + dx + \int_1^{\infty} x^{\frac{s}{2}-1} -- cgit v1.2.1 From ce72c8b27b09ecbf98a454f3b37019aaa948a57e Mon Sep 17 00:00:00 2001 From: Andrea Mozzini Vellen Date: Mon, 2 May 2022 16:02:40 +0200 Subject: Intro chapters --- buch/papers/kreismembran/main.tex | 23 ++---- buch/papers/kreismembran/teil0.tex | 16 +---- buch/papers/kreismembran/teil1.tex | 142 +++++++++++++++++++++++++------------ buch/papers/kreismembran/teil2.tex | 79 ++++++++++++--------- 4 files changed, 148 insertions(+), 112 deletions(-) diff --git a/buch/papers/kreismembran/main.tex b/buch/papers/kreismembran/main.tex index 67b436c..eafec18 100644 --- a/buch/papers/kreismembran/main.tex +++ b/buch/papers/kreismembran/main.tex @@ -3,28 +3,19 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:kreismembran}} -\lhead{Thema} +\chapter{Schwingungen einer kreisförmligen Membran\label{chapter:kreismembran}} +\lhead{Schwingungen einer kreisförmligen Membran} \begin{refsection} -\chapterauthor{Hans Muster} - -Ein paar Hinweise für die korrekte Formatierung des Textes +\chapterauthor{Andrea Mozzini Vellen und Tim Tönz} \begin{itemize} \item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. +Tim ist ein snitch \item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. +ich dachte wir sind gute Freunden \item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. +du schuldest mir ein bier \item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. +auch ein gin tonic \end{itemize} \input{papers/kreismembran/teil0.tex} diff --git a/buch/papers/kreismembran/teil0.tex b/buch/papers/kreismembran/teil0.tex index e4b1711..1552259 100644 --- a/buch/papers/kreismembran/teil0.tex +++ b/buch/papers/kreismembran/teil0.tex @@ -3,20 +3,8 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{kreismembran:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{kreismembran:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. +\section{Einleitung\label{kreismembran:section:teil0}} +\rhead{Einleitung} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. diff --git a/buch/papers/kreismembran/teil1.tex b/buch/papers/kreismembran/teil1.tex index b715075..29a47a6 100644 --- a/buch/papers/kreismembran/teil1.tex +++ b/buch/papers/kreismembran/teil1.tex @@ -2,54 +2,102 @@ % teil1.tex -- Beispiel-File für das Paper % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{kreismembran:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt + +\section{Die Hankel Transformation \label{kreismembran:section:teil1}} +\rhead{Die Hankel Transformation} + +Hermann Hankel (1839-1873) war ein deutscher Mathematiker, der für seinen Beitrag zur mathematischen Analyse und insbesondere für seine namensgebende Transformation bekannt ist. +Diese Transformation tritt bei der Untersuchung von funktionen auf, die nur von der Enternung des Ursprungs abhängen. +Er studierte auch funktionen, jetzt Hankel- oder Bessel- Funktionen genannt, der dritten Art. +Die Hankel Transformation mit Bessel Funktionen al Kern taucht natürlich bei achsensymmetrischen Problemen auf, die in Zylindrischen Polarkoordinaten formuliert sind. +In diesem Kapitel werden die Theorie der Transformation und einige Eigenschaften der Grundoperationen erläutert. + +Wir führen die Definition der Hankel Transformation aus der zweidimensionalen Fourier Transformation und ihrer Umkehrung ein, die durch: +\begin{align} + \mathscr{F}\{f(x,y)\} & = F(k,l)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-i( \bm{\kappa}\cdot \mathbf{r})}f(x,y) dx dy,\label{equation:fourier_transform}\\ + \mathscr{F}^{-1}\{F(x,y)\} & = f(x,y)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{i(\bm{\kappa}\cdot \mathbf{r}))}F(k,l) dx dy \label{equation:inv_fourier_transform} +\end{align} +wo $\mathbf{r}=(x,y)$ und $\bm{\kappa}=(k,l)$. Wie bereits erwähnt, sind Polarkoordinaten für diese Art von Problemen am besten geeignet, also mit, $(x,y)=r(\cos\theta,\sin\theta)$ und $(k,l)=\kappa(\cos\phi,\sin\phi)$, findet man $\bm{\kappa}\cdot\mathbf{r}=\kappa r(\cos(\theta-\phi))$ und danach: +\begin{align} + F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}r dr \int_{0}^{2\pi}e^{-ikr\cos(\theta-\phi)}f(r,\theta) d\phi. + \label{equation:F_ohne_variable_wechsel} +\end{align} +Dann wird angenommen dass, $f(r,\theta)=e^{in\theta}f(r)$, was keine strenge Einschränkung ist, und es wird eine Änderung der Variabeln vorgenommen $\theta-\phi=\alpha-\frac{\pi}{2}$, um \ref{equation:F_ohne_variable_wechsel} zu reduzieren: +\begin{align} + F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}rf(r) dr \int_{\phi_{0}}^{2\pi+\phi_{0}}e^{in(\phi-\frac{\pi}{2})+i(n\alpha-kr\sin\alpha)} d\alpha, + \label{equation:F_ohne_bessel} +\end{align} +wo $\phi_{0}=(\frac{\pi}{2}-\phi)$. + +Unter Verwendung der Integral Darstellung der Besselfunktion vom Ordnung n +\begin{align} + J_n(\kappa r)=\frac{1}{2\pi}\int_{\phi_{0}}^{2\pi + \phi_{0}}e^{i(n\alpha-\kappa r \sin \alpha)} d\alpha + \label{equation:bessel_n_ordnung} +\end{align} +\eqref{equation:F_ohne_bessel} wird sie zu: +\begin{align} + F(k,\phi)&=e^{in(\phi-\frac{\pi}{2})}\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr \label{equation:F_mit_bessel_step_1} \\ + &=e^{in(\phi-\frac{\pi}{2})}\tilde{f}_n(\kappa), + \label{equation:F_mit_bessel_step_2} +\end{align} +wo $\tilde{f}_n(\kappa)$ ist die \textit{Hankel Transformation} von $f(r)$ und ist formell definiert durch: +\begin{align} + \mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)=\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr. + \label{equation:hankel} +\end{align} + +Ähnlich verhält es sich mit der inversen Fourier Transformation in Form von polaren Koordinaten unter der Annahme $f(r,\theta)=e^{in\theta}f(r)$ mit \ref{equation:F_mit_bessel_step_2}, wird die inverse Fourier Transformation \ref{equation:inv_fourier_transform}: + +\begin{align*} + e^{in\theta}f(r)&=\frac{1}{2\pi}\int_{0}^{\infty}\kappa d\kappa \int_{0}^{2\pi}e^{i\kappa r \cos (\theta - \phi)}F(\kappa,\phi) d\phi\\ + &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{0}^{2\pi}e^{in(\phi - \frac{\pi}{2})- i\kappa r \cos (\theta - \phi)} d\phi, +\end{align*} +was durch den Wechsel der Variablen $\theta-\phi=-(\alpha+\frac{\pi}{2})$ und $\theta_0=-(\theta+\frac{\pi}{2})$, + +\begin{align} + &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{\theta_0}^{2\pi+\theta_0}e^{in(\theta + \alpha - i\kappa r \sin\alpha)} d\alpha \nonumber \\ + &= e^{in\theta}\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa,\quad \text{von \eqref{equation:bessel_n_ordnung}} +\end{align} + +Also, die inverse \textit{Hankel Transformation} ist so definiert: +\begin{align} + \mathscr{H}^{-1}_n\{\tilde{f}_n(\kappa)\}=f(r)=\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa. + \label{equation:inv_hankel} +\end{align} + +Anstelle von $\tilde{f}_n(\kappa)$, wird häufig für die Hankel Transformation verwendet, indem die Ordnung angegeben wird. +\eqref{equation:hankel} und \eqref{equation:inv_hankel} Integralen existieren für eine grosse Klasse von Funktionen, die normalerweise in physikalischen Anwendungen benötigt werden. +Alternativ kann auch die berühmte Hankel Transformationsformel verwendet werden, + +\begin{align} + f(r) = \int_{0}^{\infty}\kappa J_n(\kappa r) d\kappa \int_{0}^{\infty} p J_n(\kappa p)f(p) dp, + \label{equation:hankel_integral_formula} +\end{align} +um die Hankel Transformation \eqref{equation:hankel} und ihre Inverse \eqref{equation:inv_hankel} zu definieren. +Insbesondere die Hankel Transformation der nullten Ordnung ($n=0$) und der ersten Ordnung ($n=1$) sind häufig nützlich, um Lösungen für Probleme mit der Laplace Gleichung in einer achsensymmetrischen zylindrischen Geometrie zu finden. + +\subsection{Operative Eigenschaften der Hankel Transformation\label{sub:op_properties_hankel}} +In diesem Kapitel werden die operativen Eigenschaften der Hankel Transformation aufgeführt. Der Beweis für ihre Gültigkeit wird jedoch nicht analysiert. + +\subsubsection{Skalierung \label{subsub:skalierung}} +Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: + +\begin{equation} + \mathscr{H}_n\{f(ar)\}=\frac{1}{a^{2}}\tilde{f}_n \left(\frac{\kappa}{a}\right), \quad a>0. +\end{equation} + +\subsubsection{Persevalsche Relation \label{subsub:perseval}} +Wenn $\tilde{f}(\kappa)=\mathscr{H}_n\{f(r)\}$ und $\tilde{g}(\kappa)=\mathscr{H}_n\{g(r)\}$, dann: + \begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{kreismembran:equation1} + \int_{0}^{\infty}rf(r) dr = \int_{0}^{\infty}\kappa\tilde{f}(\kappa)\tilde{g}(\kappa) d\kappa. \end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{kreismembran:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{kreismembran:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{kreismembran:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. +\subsubsection{Hankel Transformationen von Ableitungen \label{subsub:ableitungen}} +Wenn $\tilde{f}_n(\kappa)=\mathscr{H}_n\{f(r)\}$, dann: +\begin{align} + &\mathscr{H}_n\{f'(r)\}=\frac{\kappa}{2n}\left[(n-1)\tilde{f}_{n+1}(\kappa)-(n+1)\tilde{f}_{n-1}(\kappa)\right], \quad n\geq1, \\ + &\mathscr{H}_1\{f'(r)\}=-\kappa \tilde{f}_0(\kappa), +\end{align} +bereitgestellt dass $[rf(r)]$ verschwindet als $r\to0$ und $r\to\infty=0$. \ No newline at end of file diff --git a/buch/papers/kreismembran/teil2.tex b/buch/papers/kreismembran/teil2.tex index 7ed217f..45357f2 100644 --- a/buch/papers/kreismembran/teil2.tex +++ b/buch/papers/kreismembran/teil2.tex @@ -1,40 +1,49 @@ % -% teil2.tex -- Beispiel-File für teil2 -% % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 -\label{kreismembran:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{kreismembran:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\section{Lösung der partiellen Differentialgleichung + \label{kreismembran:section:teil2}} +\rhead{Lösung der partiellen Differentialgleichung} + +Wie im vorherigen Kapitel gezeigt, lautet die partielle Differentialgleichung, die die Schwingungen einer Membran beschreibt: +\begin{equation*} + \frac{1}{c^2}\frac{\partial^2u}{\partial t^2} = \Delta u +\end{equation*} +Da es sich um eine Kreisscheibe handelt, werden Polarkoordinaten verwendet, so dass sich der Laplaceoperator ergibt: +\begin{equation*} + \Delta + = + \frac{\partial^2}{\partial r^2} + + + \frac1r + \frac{\partial}{\partial r} + + + \frac{1}{r 2} + \frac{\partial^2}{\partial\varphi^2}. + \label{buch:pde:kreis:laplace} +\end{equation*} + +Es wird eine runde elastische Membran berücksichtigt, die den Gebietbereich $\Omega$ abdeckt und am Rand $\Gamma$ befestigt ist. +Es wird daher davon ausgegangen, dass die Membran aus einem homogenen Material von vernachlässigbarer Dicke gefertigt ist. +Die Membran kann verformt werden, aber innere elastische Kräfte wirken den Verformungen entgegen. Es wirken keine äusseren Kräfte. Es handelt sich somit von einer kreisförmligen eigespannten homogenen schwingenden Membran. + +Daher ist die Membranabweichung im Punkt $(r,\theta)$ $\in$ $\overline{\rm \Omega}$ zum Zeitpunkt $t$: +\begin{align*} + u: \overline{\rm \Omega} \times \mathbb{R}_{\geq 0} &\longrightarrow \mathbb{R}\\ + (r,\theta,t) &\longmapsto u(r,\theta,t) +\end{align*} +Da die Membran am Rand befestigt ist, kann es keine Schwingungen geben, so dass die \textit{Dirichlet-Randbedingung} gilt: +\begin{equation*} + u\big|_{\Gamma} = 0 +\end{equation*} + + +Um eine eindeutige Lösung bestimmen zu können, werden die folgenden Anfangsbedingungen festgelegt: + +\begin{align*} + u(r,\theta, 0) &:= f(x,y)\\ + \frac{\partial}{\partial t} u(r,\theta, 0) &:= g(x,y) +\end{align*} +An dieser Stelle könnte man zum Beispiel die bereits in Kapitel (TODO:refKAPITEL) vorgestellte Methode der Separation anwenden. Da es sich in diesem Fall jedoch um einem achsensymmetrischen Problem handelt, das in Polarkoordinaten formuliert ist, wird man die Transformationsmethode verwenden, insbesondere die Hankel Transformation. -- cgit v1.2.1 From 32093bf360c25dded5b3b02f97c5fe8d93dfcd2a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 3 May 2022 21:38:35 +0200 Subject: some fixes --- buch/chapters/070-orthogonalitaet/gaussquadratur.tex | 8 +++++--- buch/chapters/070-orthogonalitaet/sturm.tex | 2 +- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index acfdb1a..2e43cec 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -263,7 +263,7 @@ werden können, muss auch = \int_{-1}^1 q(x)p(x)\,dx = -\sum_{i=0}^n q(x_i)p(x_i) +\sum_{i=0}^n A_iq(x_i)p(x_i) \] für jedes beliebige Polynom $q\in R_{n-1}$ gelten. Da man für $q$ die Interpolationspolynome $l_j(x)$ verwenden @@ -272,9 +272,11 @@ kann, den Grad $n-1$ haben, folgt 0 = \sum_{i=0}^n -l_j(x_i)p(x_i) +A_il_j(x_i)p(x_i) = -\sum_{i=0}^n \delta_{ij}p(x_i), +\sum_{i=0}^n A_i\delta_{ij}p(x_i) += +A_jp(x_j), \] die Stützstellen $x_i$ müssen also die Nullstellen des Polynoms $p(x)$ sein. diff --git a/buch/chapters/070-orthogonalitaet/sturm.tex b/buch/chapters/070-orthogonalitaet/sturm.tex index c9c9cc6..35054ab 100644 --- a/buch/chapters/070-orthogonalitaet/sturm.tex +++ b/buch/chapters/070-orthogonalitaet/sturm.tex @@ -375,7 +375,7 @@ automatisch für diese Funktionenfamilien. \subsubsection{Trigonometrische Funktionen} Die trigonometrischen Funktionen sind Eigenfunktionen des Operators $d^2/dx^2$, also eines Sturm-Liouville-Operators mit $p(x)=1$, $q(x)=0$ -und $w(x)=0$. +und $w(x)=1$. Auf dem Intervall $(-\pi,\pi)$ können wir die Randbedingungen \bgroup \renewcommand{\arraycolsep}{2pt} -- cgit v1.2.1 From 3259e5f02e8a1b8e9fd22038bbbbec2929f8105c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 4 May 2022 08:18:47 +0200 Subject: remove template paper --- buch/papers/common/addpapers.tex | 1 - buch/papers/common/paperlist | 1 - 2 files changed, 2 deletions(-) diff --git a/buch/papers/common/addpapers.tex b/buch/papers/common/addpapers.tex index dd2b07a..eb353d7 100644 --- a/buch/papers/common/addpapers.tex +++ b/buch/papers/common/addpapers.tex @@ -3,7 +3,6 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\input{papers/000template/main.tex} \input{papers/lambertw/main.tex} \input{papers/fm/main.tex} \input{papers/parzyl/main.tex} diff --git a/buch/papers/common/paperlist b/buch/papers/common/paperlist index d4e5c20..f607279 100644 --- a/buch/papers/common/paperlist +++ b/buch/papers/common/paperlist @@ -1,4 +1,3 @@ -000template lambertw fm parzyl -- cgit v1.2.1 From a866d7cd6672474e9376617aadc91424b9ba3506 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 8 May 2022 22:37:45 +0200 Subject: add Fresnel presentation --- vorlesungen/04_fresnel/common.tex | 2 +- vorlesungen/04_fresnel/slides.tex | 5 +- vorlesungen/slides/fresnel/Makefile | 9 +++ vorlesungen/slides/fresnel/Makefile.inc | 5 +- vorlesungen/slides/fresnel/chapter.tex | 5 +- vorlesungen/slides/fresnel/eulerspirale.m | 34 ++++++++++++ vorlesungen/slides/fresnel/integrale.tex | 72 ++++++++++++++++++++++++ vorlesungen/slides/fresnel/klothoide.tex | 61 +++++++++++++++++++++ vorlesungen/slides/fresnel/kruemmung.tex | 91 +++++++++++++++++++++++++++++++ vorlesungen/slides/fresnel/numerik.tex | 83 ++++++++++++++++++++++++++++ 10 files changed, 363 insertions(+), 4 deletions(-) create mode 100644 vorlesungen/slides/fresnel/Makefile create mode 100644 vorlesungen/slides/fresnel/eulerspirale.m create mode 100644 vorlesungen/slides/fresnel/integrale.tex create mode 100644 vorlesungen/slides/fresnel/klothoide.tex create mode 100644 vorlesungen/slides/fresnel/kruemmung.tex create mode 100644 vorlesungen/slides/fresnel/numerik.tex diff --git a/vorlesungen/04_fresnel/common.tex b/vorlesungen/04_fresnel/common.tex index 418b7a5..1134b71 100644 --- a/vorlesungen/04_fresnel/common.tex +++ b/vorlesungen/04_fresnel/common.tex @@ -10,7 +10,7 @@ } \beamertemplatenavigationsymbolsempty \title[Klothoide]{Klothoide} -\author[N.~Eswararajah]{Nilakshan Eswararajah} +\author[A.~Müller]{Andreas Müller} \date[]{9.~Mai 2022} \newboolean{presentation} diff --git a/vorlesungen/04_fresnel/slides.tex b/vorlesungen/04_fresnel/slides.tex index 5a7cce2..32f7233 100644 --- a/vorlesungen/04_fresnel/slides.tex +++ b/vorlesungen/04_fresnel/slides.tex @@ -3,4 +3,7 @@ % % (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil % -\folie{fresnel/test.tex} +\folie{fresnel/integrale.tex} +\folie{fresnel/numerik.tex} +\folie{fresnel/kruemmung.tex} +\folie{fresnel/klothoide.tex} diff --git a/vorlesungen/slides/fresnel/Makefile b/vorlesungen/slides/fresnel/Makefile new file mode 100644 index 0000000..77ad9a2 --- /dev/null +++ b/vorlesungen/slides/fresnel/Makefile @@ -0,0 +1,9 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +all: eulerpath.tex + +eulerpath.tex: eulerspirale.m + octave eulerspirale.m diff --git a/vorlesungen/slides/fresnel/Makefile.inc b/vorlesungen/slides/fresnel/Makefile.inc index c17b654..4ab3b2f 100644 --- a/vorlesungen/slides/fresnel/Makefile.inc +++ b/vorlesungen/slides/fresnel/Makefile.inc @@ -4,4 +4,7 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # chapterfresnel = \ - ../slides/fresnel/test.tex + ../slides/fresnel/integrale.tex \ + ../slides/fresnel/kruemmung.tex \ + ../slides/fresnel/klothoide.tex \ + ../slides/fresnel/numerik.tex diff --git a/vorlesungen/slides/fresnel/chapter.tex b/vorlesungen/slides/fresnel/chapter.tex index dc5d031..ad0c011 100644 --- a/vorlesungen/slides/fresnel/chapter.tex +++ b/vorlesungen/slides/fresnel/chapter.tex @@ -3,4 +3,7 @@ % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % -\folie{fresnel/test.tex} +\folie{fresnel/integrale.tex} +\folie{fresnel/kruemmung.tex} +\folie{fresnel/klothoide.tex} +\folie{fresnel/numerik.tex} diff --git a/vorlesungen/slides/fresnel/eulerspirale.m b/vorlesungen/slides/fresnel/eulerspirale.m new file mode 100644 index 0000000..312541a --- /dev/null +++ b/vorlesungen/slides/fresnel/eulerspirale.m @@ -0,0 +1,34 @@ +# +# eulerspirale.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +# +global n; +n = 10000; +global tmax; +tmax = 10; + +function retval = f(x, t) + retval = [ cos(t*t); sin(t*t) ]; +endfunction + +x0 = [ 0; 0 ]; +t = tmax * (0:n) / n; + +c = lsode(@f, x0, t); + +fn = fopen("eulerpath.tex", "w"); + +fprintf(fn, "\\def\\fresnela{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", c(i,1), c(i,2)); +end +fprintf(fn, "\n}\n"); + +fprintf(fn, "\\def\\fresnelb{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", -c(i,1), -c(i,2)); +end +fprintf(fn, "\n}\n"); + +fclose(fn); diff --git a/vorlesungen/slides/fresnel/integrale.tex b/vorlesungen/slides/fresnel/integrale.tex new file mode 100644 index 0000000..7798932 --- /dev/null +++ b/vorlesungen/slides/fresnel/integrale.tex @@ -0,0 +1,72 @@ +% +% fresnel.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\input{../slides/fresnel/eulerpath.tex} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Fresnel-Integrale} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Definition} +Fresnel-Integrale: +\begin{align*} +S(t) +&= +\int_0^t \sin(\tau^2)\,d\tau +\\ +C(t) +&= +\int_0^t \cos(\tau^2)\,d\tau +\end{align*} +\uncover<2->{% +Können nicht in geschlossener Form ausgewertet werden. +} +\end{block} +\uncover<3->{% +\begin{block}{Kurve} +\[ +\gamma(t) += +\begin{pmatrix} +S(t)\\C(t) +\end{pmatrix} +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<4->{% +\begin{block}{Euler-Spirale} +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=2.7] + +\draw[->] (-1.05,0) -- (1.05,0) coordinate[label={$C(t)$}]; +\draw[->] (0,-1.05) -- (0,1.05) coordinate[label={right:$S(t)$}]; + +\draw[color=red,line width=1.4pt] \fresnela; +\draw[color=red,line width=1.4pt] \fresnelb; + +\fill[color=blue] ({sqrt(3.14159/8)},{sqrt(3.14159/8)}) circle[radius=0.02]; +\fill[color=blue] ({-sqrt(3.14159/8)},{-sqrt(3.14159/8)}) circle[radius=0.02]; + +\draw (1,-0.03) -- (1,0.03); +\node at (1,-0.03) [below] {$1$}; +\draw (-1,-0.03) -- (-1,0.03); +\node at (-1,0.03) [above] {$-1$}; +\draw (-0.03,1) -- (0.03,1); +\node at (-0.03,1) [left] {$1$}; +\draw (-0.03,-1) -- (0.03,-1); +\node at (0.03,-1) [right] {$-1$}; +\node at (0,0) [below right] {$0$}; + +\end{tikzpicture} +\end{center} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/klothoide.tex b/vorlesungen/slides/fresnel/klothoide.tex new file mode 100644 index 0000000..dcf52be --- /dev/null +++ b/vorlesungen/slides/fresnel/klothoide.tex @@ -0,0 +1,61 @@ +% +% klothoide.tex -- Klothoide +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Klothoide} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Krümmung der Euler-Spirale} +\begin{align*} +\frac{d}{dt}\gamma(t) +&= +\begin{pmatrix} +\cos t^2\\ +\sin t^2 +\end{pmatrix} +\intertext{\uncover<2->{Bogenlänge:}} +\uncover<2->{ +|\dot{\gamma}(t)| +&= +\sqrt{\cos^2 t^2 + \sin^2 t^2} += +1 +} +\intertext{\uncover<3->{Polarwinkel:}} +\uncover<3->{ +\varphi&=t^2 +\intertext{\uncover<4->{Krümmung:}} +\uncover<4->{ +\frac{d\varphi}{dt} +&= +2t +} +} +\end{align*} +\uncover<5->{% +$\Rightarrow$ Krümmung ist proportional zur Bogenlänge +} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<6->{% +\begin{block}{Definition} +Eine Kurve, deren Krümmung proportional zur Bogenlänge ist, heisst +{\em Klothoid} +\end{block}} +\uncover<7->{% +\begin{block}{Anwendung} +Strassenbau: Um mit konstanter Geschwindigkeit auf einer +Klothoidenkurve zu fahren, muss man das Lenkrad mit konstanter Geschwindigkeit +drehen +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/kruemmung.tex b/vorlesungen/slides/fresnel/kruemmung.tex new file mode 100644 index 0000000..e75611b --- /dev/null +++ b/vorlesungen/slides/fresnel/kruemmung.tex @@ -0,0 +1,91 @@ +% +% kruemmung.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Krümmung einer Kurve} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Krümmungsradius} +Bogen und Radius: +\[ +s=r\cdot\Delta\varphi +\uncover<2->{ +\quad +\Rightarrow +\quad +r += +\frac{s}{\Delta\varphi} +} +\] +\end{block} +\vspace*{-12pt} +\uncover<3->{ +\begin{block}{Krümmung} +Je grösser der Krümmungsradius, desto kleiner die Krümmung: +\[ +\kappa = \frac{1}{r} +\] +\end{block}} +\vspace*{-12pt} +\uncover<5->{% +\begin{block}{Definition} +Änderungsgeschwindigkeit des Polarwinkels der Tangente +\[ +\kappa += +\frac{1}{r} +\uncover<6->{= +\frac{\Delta\varphi}{s}} +\uncover<7->{= +\frac{d\varphi}{dt}} +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\begin{scope} +\clip (-1,-1) rectangle (4,4); + +\def\r{3} +\def\winkel{30} + +\fill[color=blue!20] (0,0) -- (0:\r) arc (0:\winkel:\r) -- cycle; +\node[color=blue] at ({0.5*\winkel}:{0.5*\r}) {$\Delta\varphi$}; + +\draw[line width=0.3pt] (0,0) circle[radius=\r]; + +\draw[->] (0,0) -- (0:\r); +\draw[->] (0,0) -- (\winkel:\r); + +\uncover<4->{ +\draw[->] (0:\r) -- ($(0:\r)+(90:0.7*\r)$); +\draw[->] (\winkel:\r) -- ($(\winkel:\r)+({90+\winkel}:0.7*\r)$); +} + +\draw[color=red,line width=1.4pt] (0:\r) arc (0:\winkel:\r); +\node[color=red] at ({0.5*\winkel}:\r) [left] {$s$}; +\fill[color=red] (0:\r) circle[radius=0.05]; +\fill[color=red] (\winkel:\r) circle[radius=0.05]; + +\node at (\winkel:{0.5*\r}) [above] {$r$}; +\node at (0:{0.5*\r}) [below] {$r$}; +\end{scope} + +\end{tikzpicture} +\end{center} +\uncover<4->{% +Für $\varphi$ kann man auch den Polarwinkel des Tangentialvektors nehmen +} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/numerik.tex b/vorlesungen/slides/fresnel/numerik.tex new file mode 100644 index 0000000..5c6f96d --- /dev/null +++ b/vorlesungen/slides/fresnel/numerik.tex @@ -0,0 +1,83 @@ +% +% numerik.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Numerik} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Taylor-Reihe} +\begin{align*} +\sin t^2 +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{2k+1}}{(2k+1)!} +\\ +%\int \sin t^2\,dt +\uncover<2->{ +S(t) +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{4k+3}}{(2k+1)!(4n+3)} +} +\\ +\cos t^2 +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{2k}}{(2k)!} +\\ +%\int \sin t^2\,dt +\uncover<3->{ +C(t) +&= +\sum_{k=0}^\infty +(-1)^k \frac{t^{4k+1}}{(2k)!(4k+1)} +} +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<4->{ +\begin{block}{Differentialgleichung} +\[ +\dot{\gamma}(t) += +\begin{pmatrix} +\sin t^2\\ \cos t^2 +\end{pmatrix} +\] +\end{block}} +\uncover<5->{% +\begin{block}{Hypergeometrische Reihen} +\begin{align*} +\uncover<6->{% +S(t) +&= +\frac{\pi z^3}{6}\, +\mathstrut_1F_2\biggl( +\begin{matrix}\frac34\\\frac32,\frac74\end{matrix} +; +-\frac{\pi^2z^4}{16} +\biggr) +} +\\ +\uncover<7->{ +C(t) +&= +z\, +\mathstrut_1F_2\biggl( +\begin{matrix}\frac14\\\frac12,\frac54\end{matrix} +; +-\frac{\pi^2z^4}{16} +\biggr)} +\end{align*} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup -- cgit v1.2.1 From db0fcc225416e260284ffa3a1da5919a2b1ac5a5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 9 May 2022 11:03:14 +0200 Subject: =?UTF-8?q?Fresnel-Pr=C3=A4sentation?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- vorlesungen/04_fresnel/common.tex | 4 +- vorlesungen/04_fresnel/slides.tex | 1 + vorlesungen/slides/fresnel/Makefile.inc | 3 +- vorlesungen/slides/fresnel/apfel.jpg | Bin 0 -> 1125584 bytes vorlesungen/slides/fresnel/apfel.png | Bin 0 -> 525490 bytes vorlesungen/slides/fresnel/apfel.tex | 32 + vorlesungen/slides/fresnel/chapter.tex | 1 + vorlesungen/slides/fresnel/eulerpath.tex | 4012 +++++++++++++++++++++++++++++ vorlesungen/slides/fresnel/eulerspirale.m | 35 +- vorlesungen/slides/fresnel/integrale.tex | 105 +- vorlesungen/slides/fresnel/klothoide.tex | 15 +- vorlesungen/slides/fresnel/kruemmung.tex | 2 +- vorlesungen/slides/fresnel/numerik.tex | 75 +- vorlesungen/slides/fresnel/test.tex | 19 - 14 files changed, 4227 insertions(+), 77 deletions(-) create mode 100644 vorlesungen/slides/fresnel/apfel.jpg create mode 100644 vorlesungen/slides/fresnel/apfel.png create mode 100644 vorlesungen/slides/fresnel/apfel.tex create mode 100644 vorlesungen/slides/fresnel/eulerpath.tex delete mode 100644 vorlesungen/slides/fresnel/test.tex diff --git a/vorlesungen/04_fresnel/common.tex b/vorlesungen/04_fresnel/common.tex index 1134b71..f4d919b 100644 --- a/vorlesungen/04_fresnel/common.tex +++ b/vorlesungen/04_fresnel/common.tex @@ -9,8 +9,8 @@ \usetheme[hideothersubsections,hidetitle]{Hannover} } \beamertemplatenavigationsymbolsempty -\title[Klothoide]{Klothoide} -\author[A.~Müller]{Andreas Müller} +\title[Klothoide]{Fresnel-Integrale und Klothoide} +\author[A.~Müller]{Prof.~Dr.~Andreas Müller} \date[]{9.~Mai 2022} \newboolean{presentation} diff --git a/vorlesungen/04_fresnel/slides.tex b/vorlesungen/04_fresnel/slides.tex index 32f7233..a46fe9e 100644 --- a/vorlesungen/04_fresnel/slides.tex +++ b/vorlesungen/04_fresnel/slides.tex @@ -7,3 +7,4 @@ \folie{fresnel/numerik.tex} \folie{fresnel/kruemmung.tex} \folie{fresnel/klothoide.tex} +\folie{fresnel/apfel.tex} diff --git a/vorlesungen/slides/fresnel/Makefile.inc b/vorlesungen/slides/fresnel/Makefile.inc index 4ab3b2f..b6d11f0 100644 --- a/vorlesungen/slides/fresnel/Makefile.inc +++ b/vorlesungen/slides/fresnel/Makefile.inc @@ -7,4 +7,5 @@ chapterfresnel = \ ../slides/fresnel/integrale.tex \ ../slides/fresnel/kruemmung.tex \ ../slides/fresnel/klothoide.tex \ - ../slides/fresnel/numerik.tex + ../slides/fresnel/numerik.tex \ + ../slides/fresnel/apfel.tex diff --git a/vorlesungen/slides/fresnel/apfel.jpg b/vorlesungen/slides/fresnel/apfel.jpg new file mode 100644 index 0000000..96b975d Binary files /dev/null and b/vorlesungen/slides/fresnel/apfel.jpg differ diff --git a/vorlesungen/slides/fresnel/apfel.png b/vorlesungen/slides/fresnel/apfel.png new file mode 100644 index 0000000..f413852 Binary files /dev/null and b/vorlesungen/slides/fresnel/apfel.png differ diff --git a/vorlesungen/slides/fresnel/apfel.tex b/vorlesungen/slides/fresnel/apfel.tex new file mode 100644 index 0000000..090c3d5 --- /dev/null +++ b/vorlesungen/slides/fresnel/apfel.tex @@ -0,0 +1,32 @@ +% +% apfel.tex -- Apfelschale als Klothoide +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\input{../slides/fresnel/eulerpath.tex} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Apfelschale} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\begin{scope} +\clip(-1,-1) rectangle (7,6); +\uncover<2->{ +\node at (3.1,2.2) [rotate=-3] + {\includegraphics[width=9.4cm]{../slides/fresnel/apfel.png}}; +} +\end{scope} +\draw[color=gray!50] (0,0) rectangle (4,4); +\draw[->] (-0.5,0) -- (7.5,0) coordinate[label={$C(t)$}]; +\draw[->] (0,-0.5) -- (0,6.0) coordinate[label={left:$S(t)$}]; +\uncover<3->{ +\begin{scope}[scale=8] +\draw[color=red,opacity=0.5,line width=1.4pt] \fresnela; +\end{scope} +} +\end{tikzpicture} +\end{center} +\end{frame} +\egroup diff --git a/vorlesungen/slides/fresnel/chapter.tex b/vorlesungen/slides/fresnel/chapter.tex index ad0c011..916a3a9 100644 --- a/vorlesungen/slides/fresnel/chapter.tex +++ b/vorlesungen/slides/fresnel/chapter.tex @@ -7,3 +7,4 @@ \folie{fresnel/kruemmung.tex} \folie{fresnel/klothoide.tex} \folie{fresnel/numerik.tex} +\folie{fresnel/apfel.tex} diff --git a/vorlesungen/slides/fresnel/eulerpath.tex b/vorlesungen/slides/fresnel/eulerpath.tex new file mode 100644 index 0000000..ecd0b2b --- /dev/null +++ b/vorlesungen/slides/fresnel/eulerpath.tex @@ -0,0 +1,4012 @@ +\def\fresnela{ (0,0) + -- (0.0100,0.0000) + -- (0.0200,0.0000) + -- (0.0300,0.0000) + -- (0.0400,0.0000) + -- (0.0500,0.0001) + -- (0.0600,0.0001) + -- (0.0700,0.0002) + -- (0.0800,0.0003) + -- (0.0900,0.0004) + -- (0.1000,0.0005) + -- (0.1100,0.0007) + -- (0.1200,0.0009) + -- (0.1300,0.0012) + -- (0.1400,0.0014) + -- (0.1500,0.0018) + -- (0.1600,0.0021) + -- (0.1700,0.0026) + -- (0.1800,0.0031) + -- (0.1899,0.0036) + -- (0.1999,0.0042) + -- (0.2099,0.0048) + -- (0.2199,0.0056) + -- (0.2298,0.0064) + -- (0.2398,0.0072) + -- (0.2498,0.0082) + -- (0.2597,0.0092) + -- (0.2696,0.0103) + -- (0.2796,0.0115) + -- (0.2895,0.0128) + -- (0.2994,0.0141) + -- (0.3093,0.0156) + -- (0.3192,0.0171) + -- (0.3290,0.0188) + -- (0.3389,0.0205) + -- (0.3487,0.0224) + -- (0.3585,0.0244) + -- (0.3683,0.0264) + -- (0.3780,0.0286) + -- 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(-0.5760,-0.4855) + -- (-0.5771,-0.4955) + -- (-0.5768,-0.5054) + -- (-0.5753,-0.5153) + -- (-0.5725,-0.5249) + -- (-0.5684,-0.5341) + -- (-0.5633,-0.5426) + -- (-0.5570,-0.5504) + -- (-0.5498,-0.5573) + -- (-0.5417,-0.5632) + -- (-0.5329,-0.5680) + -- (-0.5236,-0.5716) + -- (-0.5139,-0.5739) + -- (-0.5040,-0.5749) + -- (-0.4940,-0.5746) + -- (-0.4841,-0.5730) + -- (-0.4746,-0.5700) + -- (-0.4655,-0.5658) + -- (-0.4571,-0.5604) + -- (-0.4494,-0.5540) + -- (-0.4428,-0.5466) + -- (-0.4371,-0.5383) + -- (-0.4327,-0.5294) + -- (-0.4295,-0.5199) + -- (-0.4276,-0.5101) + -- (-0.4270,-0.5001) + -- (-0.4279,-0.4902) + -- (-0.4301,-0.4804) + -- (-0.4336,-0.4711) + -- (-0.4383,-0.4623) + -- (-0.4443,-0.4542) + -- (-0.4512,-0.4471) + -- (-0.4591,-0.4410) + -- (-0.4678,-0.4360) + -- (-0.4771,-0.4323) + -- (-0.4868,-0.4299) + -- (-0.4967,-0.4289) + -- (-0.5067,-0.4293) + -- (-0.5165,-0.4311) + -- (-0.5260,-0.4343) + -- (-0.5350,-0.4387) + -- (-0.5432,-0.4444) + -- (-0.5505,-0.4512) + -- (-0.5568,-0.4590) + -- (-0.5619,-0.4676) + -- (-0.5658,-0.4768) + -- (-0.5683,-0.4864) + -- (-0.5694,-0.4964) + -- (-0.5690,-0.5064) + -- (-0.5672,-0.5162) + -- (-0.5641,-0.5257) + -- (-0.5595,-0.5346) + -- (-0.5538,-0.5427) + -- (-0.5469,-0.5500) + -- (-0.5391,-0.5562) + -- (-0.5304,-0.5611) + -- (-0.5211,-0.5648) + -- (-0.5114,-0.5670) + -- (-0.5014,-0.5678) + -- (-0.4914,-0.5671) + -- (-0.4817,-0.5650) + -- (-0.4723,-0.5615) + -- (-0.4636,-0.5566) + -- (-0.4557,-0.5504) + -- (-0.4488,-0.5432) + -- (-0.4431,-0.5350) + -- (-0.4386,-0.5261) + -- (-0.4355,-0.5166) + -- (-0.4339,-0.5067) + -- (-0.4338,-0.4968) + -- (-0.4352,-0.4869) + -- (-0.4380,-0.4773) + -- (-0.4423,-0.4682) + -- (-0.4479,-0.4600) + -- (-0.4546,-0.4526) + -- (-0.4624,-0.4464) + -- (-0.4711,-0.4414) + -- (-0.4804,-0.4378) + -- (-0.4902,-0.4357) + -- (-0.5002,-0.4351) + -- (-0.5101,-0.4360) + -- (-0.5198,-0.4384) + -- (-0.5290,-0.4423) + -- (-0.5375,-0.4476) + -- (-0.5450,-0.4541) + -- (-0.5515,-0.4618) + -- (-0.5567,-0.4703) + -- (-0.5605,-0.4795) + -- (-0.5628,-0.4892) + -- (-0.5636,-0.4992) + -- (-0.5628,-0.5092) + -- (-0.5605,-0.5189) + -- (-0.5567,-0.5281) + -- (-0.5514,-0.5366) + -- (-0.5449,-0.5442) + -- (-0.5373,-0.5506) + -- (-0.5288,-0.5558) + -- (-0.5195,-0.5595) + -- (-0.5098,-0.5617) + -- (-0.4998,-0.5624) + -- (-0.4898,-0.5614) + -- (-0.4802,-0.5589) + -- (-0.4710,-0.5549) + -- (-0.4627,-0.5494) + -- (-0.4553,-0.5427) + -- (-0.4491,-0.5348) + -- (-0.4443,-0.5261) + -- (-0.4409,-0.5167) + -- (-0.4391,-0.5069) + -- (-0.4389,-0.4969) + -- (-0.4403,-0.4870) + -- (-0.4434,-0.4775) + -- (-0.4479,-0.4686) + -- (-0.4538,-0.4605) + -- (-0.4610,-0.4536) + -- (-0.4692,-0.4479) + -- (-0.4783,-0.4437) + -- (-0.4879,-0.4410) + -- (-0.4978,-0.4399) + -- (-0.5078,-0.4405) + -- (-0.5175,-0.4427) + -- (-0.5268,-0.4465) + -- (-0.5352,-0.4518) + -- (-0.5427,-0.4584) + -- (-0.5490,-0.4662) + -- (-0.5538,-0.4749) + -- (-0.5572,-0.4844) + -- (-0.5589,-0.4942) + -- (-0.5589,-0.5042) + -- (-0.5572,-0.5140) + -- (-0.5539,-0.5235) + -- (-0.5491,-0.5322) + -- (-0.5428,-0.5400) + -- (-0.5354,-0.5466) + -- (-0.5269,-0.5518) + -- (-0.5176,-0.5556) + -- (-0.5078,-0.5576) + -- (-0.4978,-0.5580) + -- (-0.4879,-0.5567) + -- (-0.4784,-0.5537) + -- (-0.4696,-0.5491) + -- (-0.4616,-0.5430) + -- (-0.4548,-0.5357) + -- (-0.4494,-0.5273) + -- (-0.4456,-0.5181) + -- (-0.4434,-0.5083) + -- (-0.4429,-0.4984) + -- (-0.4442,-0.4884) + -- (-0.4471,-0.4789) + -- (-0.4517,-0.4700) + -- (-0.4578,-0.4621) + -- (-0.4652,-0.4554) + -- (-0.4736,-0.4500) + -- (-0.4828,-0.4462) + -- (-0.4926,-0.4442) + -- (-0.5026,-0.4438) + -- (-0.5125,-0.4453) + -- (-0.5219,-0.4484) + -- (-0.5307,-0.4532) + -- (-0.5385,-0.4595) + -- (-0.5450,-0.4671) + -- (-0.5500,-0.4757) + -- (-0.5535,-0.4851) + -- (-0.5552,-0.4949) + -- (-0.5551,-0.5049) + -- (-0.5533,-0.5147) + -- (-0.5496,-0.5240) + -- (-0.5444,-0.5325) + -- (-0.5377,-0.5400) + -- (-0.5298,-0.5460) + -- (-0.5210,-0.5506) + -- (-0.5114,-0.5535) + -- (-0.5015,-0.5546) + -- (-0.4915,-0.5538) + -- (-0.4818,-0.5513) + -- (-0.4728,-0.5470) + -- (-0.4647,-0.5412) + -- (-0.4578,-0.5339) + -- (-0.4524,-0.5256) + -- (-0.4486,-0.5163) + -- (-0.4466,-0.5066) + -- (-0.4464,-0.4966) + -- (-0.4480,-0.4867) + -- (-0.4514,-0.4774) + -- (-0.4566,-0.4688) + -- (-0.4632,-0.4613) + -- (-0.4711,-0.4552) + -- (-0.4800,-0.4507) + -- (-0.4896,-0.4479) + -- (-0.4995,-0.4470) + -- (-0.5095,-0.4479) + -- (-0.5191,-0.4507) + -- (-0.5280,-0.4552) + -- (-0.5358,-0.4614) + -- (-0.5424,-0.4689) + -- (-0.5475,-0.4775) + -- (-0.5508,-0.4869) + -- (-0.5522,-0.4968) + -- (-0.5518,-0.5068) + -- (-0.5495,-0.5165) + -- (-0.5454,-0.5256) + -- (-0.5396,-0.5337) + -- (-0.5324,-0.5406) + -- (-0.5239,-0.5460) + -- (-0.5147,-0.5496) + -- (-0.5048,-0.5514) + -- (-0.4949,-0.5513) + -- (-0.4851,-0.5493) + -- (-0.4759,-0.5454) + -- (-0.4676,-0.5398) + -- (-0.4606,-0.5327) + -- (-0.4550,-0.5244) + -- (-0.4512,-0.5152) + -- (-0.4493,-0.5054) + -- (-0.4493,-0.4954) + -- (-0.4512,-0.4856) + -- (-0.4551,-0.4764) + -- (-0.4606,-0.4681) + -- (-0.4677,-0.4611) + -- (-0.4760,-0.4555) + -- (-0.4852,-0.4518) + -- (-0.4951,-0.4499) + -- (-0.5050,-0.4500) + -- (-0.5148,-0.4520) + -- (-0.5240,-0.4560) + -- (-0.5322,-0.4617) + -- (-0.5391,-0.4689) + -- (-0.5444,-0.4773) + -- (-0.5480,-0.4866) + -- (-0.5496,-0.4965) + -- (-0.5492,-0.5065) + -- (-0.5469,-0.5162) + -- (-0.5426,-0.5252) + -- (-0.5366,-0.5332) + -- (-0.5292,-0.5398) + -- (-0.5205,-0.5448) + -- (-0.5110,-0.5479) + -- (-0.5011,-0.5491) + -- (-0.4912,-0.5482) + -- (-0.4816,-0.5454) + -- (-0.4728,-0.5406) + -- (-0.4652,-0.5342) + -- (-0.4590,-0.5264) + -- (-0.4546,-0.5174) + -- (-0.4520,-0.5078) + -- (-0.4515,-0.4978) + -- (-0.4531,-0.4879) + -- (-0.4566,-0.4786) + -- (-0.4620,-0.4702) + -- (-0.4690,-0.4631) + -- (-0.4773,-0.4575) + -- (-0.4866,-0.4538) + -- (-0.4964,-0.4521) + -- (-0.5064,-0.4525) + -- (-0.5161,-0.4549) + -- (-0.5250,-0.4593) + -- (-0.5329,-0.4654) + -- (-0.5393,-0.4731) + -- (-0.5440,-0.4819) + -- (-0.5467,-0.4915) + -- (-0.5474,-0.5015) + -- (-0.5460,-0.5113) + -- (-0.5425,-0.5207) + -- (-0.5372,-0.5291) + -- (-0.5302,-0.5362) + -- (-0.5218,-0.5417) + -- (-0.5125,-0.5453) + -- (-0.5027,-0.5469) + -- (-0.4927,-0.5463) + -- (-0.4831,-0.5436) + -- (-0.4742,-0.5390) + -- (-0.4666,-0.5326) + -- (-0.4605,-0.5247) + -- (-0.4562,-0.5157) + -- (-0.4539,-0.5060) + -- (-0.4538,-0.4960) + -- (-0.4558,-0.4862) + -- (-0.4598,-0.4771) + -- (-0.4657,-0.4690) + -- (-0.4732,-0.4624) + -- (-0.4820,-0.4576) + -- (-0.4915,-0.4548) + -- (-0.5015,-0.4541) + -- (-0.5114,-0.4556) + -- (-0.5207,-0.4591) + -- (-0.5290,-0.4646) + -- (-0.5359,-0.4718) + -- (-0.5411,-0.4803) + -- (-0.5444,-0.4898) + -- (-0.5455,-0.4997) + -- (-0.5444,-0.5096) + -- (-0.5411,-0.5191) + -- (-0.5359,-0.5276) + -- (-0.5290,-0.5347) + -- (-0.5206,-0.5402) + -- (-0.5112,-0.5437) + -- (-0.5014,-0.5450) + -- (-0.4914,-0.5441) + -- (-0.4819,-0.5411) + -- (-0.4733,-0.5360) + -- (-0.4660,-0.5292) + -- (-0.4605,-0.5209) + -- (-0.4569,-0.5116) + -- (-0.4555,-0.5017) + -- (-0.4563,-0.4918) + -- (-0.4592,-0.4822) + -- (-0.4643,-0.4736) + -- (-0.4711,-0.4664) + -- (-0.4794,-0.4608) + -- (-0.4887,-0.4573) + -- (-0.4986,-0.4559) + -- (-0.5086,-0.4568) + -- (-0.5181,-0.4599) + -- (-0.5266,-0.4650) + -- (-0.5338,-0.4719) + -- (-0.5392,-0.4803) + -- (-0.5426,-0.4897) + -- (-0.5437,-0.4996) + -- (-0.5426,-0.5095) + -- (-0.5393,-0.5189) + -- (-0.5339,-0.5273) + -- (-0.5267,-0.5343) + -- (-0.5182,-0.5394) + -- (-0.5087,-0.5425) + -- (-0.4987,-0.5433) + -- (-0.4889,-0.5418) + -- (-0.4796,-0.5381) + -- (-0.4714,-0.5323) + -- (-0.4648,-0.5249) + -- (-0.4601,-0.5161) + -- (-0.4575,-0.5064) + -- (-0.4573,-0.4965) + -- (-0.4593,-0.4867) + -- (-0.4635,-0.4777) + -- (-0.4697,-0.4698) + -- (-0.4776,-0.4637) + -- (-0.4867,-0.4595) + -- (-0.4964,-0.4576) + -- (-0.5064,-0.4580) + -- (-0.5160,-0.4607) + -- (-0.5247,-0.4656) + -- (-0.5320,-0.4724) + -- (-0.5376,-0.4807) + -- (-0.5410,-0.4900) + -- (-0.5422,-0.4999) + -- (-0.5409,-0.5098) + -- (-0.5374,-0.5192) + -- (-0.5318,-0.5274) + -- (-0.5244,-0.5341) + -- (-0.5156,-0.5389) + -- (-0.5060,-0.5414) + -- (-0.4960,-0.5416) + -- (-0.4863,-0.5394) + -- (-0.4773,-0.5350) + -- (-0.4697,-0.5285) + -- (-0.4638,-0.5205) + -- (-0.4601,-0.5112) + -- (-0.4586,-0.5014) + -- (-0.4595,-0.4914) + -- (-0.4628,-0.4820) + -- (-0.4682,-0.4737) + -- (-0.4755,-0.4668) + -- (-0.4842,-0.4620) + -- (-0.4938,-0.4593) + -- (-0.5038,-0.4591) + -- (-0.5135,-0.4613) + -- (-0.5225,-0.4657) + -- (-0.5300,-0.4722) + -- (-0.5358,-0.4804) + -- (-0.5395,-0.4896) + -- (-0.5408,-0.4995) + -- (-0.5396,-0.5094) + -- (-0.5361,-0.5188) + -- (-0.5304,-0.5270) + -- (-0.5228,-0.5335) + -- (-0.5139,-0.5380) + -- (-0.5042,-0.5402) + -- (-0.4942,-0.5400) + -- (-0.4846,-0.5373) + -- (-0.4760,-0.5323) + -- (-0.4688,-0.5254) + -- (-0.4636,-0.5169) + -- (-0.4606,-0.5074) + -- (-0.4600,-0.4975) + -- (-0.4619,-0.4877) + -- (-0.4662,-0.4787) + -- (-0.4726,-0.4710) + -- (-0.4806,-0.4651) + -- (-0.4899,-0.4615) + -- (-0.4998,-0.4602) + -- (-0.5097,-0.4615) + -- (-0.5190,-0.4651) + -- (-0.5270,-0.4710) + -- (-0.5334,-0.4787) + -- (-0.5376,-0.4877) + -- (-0.5394,-0.4976) + -- (-0.5387,-0.5075) + -- (-0.5356,-0.5170) + -- (-0.5301,-0.5253) + -- (-0.5227,-0.5320) + -- (-0.5139,-0.5367) + -- (-0.5042,-0.5390) + -- (-0.4942,-0.5387) + -- (-0.4847,-0.5360) + -- (-0.4761,-0.5309) + -- (-0.4691,-0.5238) + -- (-0.4641,-0.5151) + -- (-0.4615,-0.5055) + -- (-0.4614,-0.4955) + -- (-0.4638,-0.4859) + -- (-0.4687,-0.4772) + -- (-0.4756,-0.4700) + -- (-0.4841,-0.4648) + -- (-0.4936,-0.4619) + -- (-0.5036,-0.4616) + -- (-0.5133,-0.4638) + -- (-0.5221,-0.4685) + -- (-0.5294,-0.4753) + -- (-0.5348,-0.4837) + -- (-0.5377,-0.4932) + -- (-0.5382,-0.5032) + -- (-0.5360,-0.5129) + -- (-0.5314,-0.5218) + -- (-0.5247,-0.5291) + -- (-0.5163,-0.5345) + -- (-0.5067,-0.5375) + -- (-0.4968,-0.5379) + -- (-0.4870,-0.5357) + -- (-0.4782,-0.5311) + -- (-0.4709,-0.5243) + -- (-0.4656,-0.5158) + -- (-0.4627,-0.5063) + -- (-0.4624,-0.4963) + -- (-0.4647,-0.4866) + -- (-0.4695,-0.4779) + -- (-0.4764,-0.4707) + -- (-0.4850,-0.4656) + -- (-0.4946,-0.4629) + -- (-0.5045,-0.4628) + -- (-0.5142,-0.4653) + -- (-0.5228,-0.4703) + -- (-0.5298,-0.4775) + -- (-0.5347,-0.4862) + -- (-0.5370,-0.4958) + -- (-0.5368,-0.5058) + -- (-0.5339,-0.5153) + -- (-0.5285,-0.5238) + -- (-0.5212,-0.5305) + -- (-0.5123,-0.5350) + -- (-0.5025,-0.5369) + -- (-0.4925,-0.5362) + -- (-0.4831,-0.5329) + -- (-0.4750,-0.5271) + -- (-0.4687,-0.5194) + -- (-0.4647,-0.5103) + -- (-0.4632,-0.5004) + -- (-0.4645,-0.4905) + -- (-0.4684,-0.4813) + -- (-0.4747,-0.4736) + -- (-0.4827,-0.4677) + -- (-0.4921,-0.4643) + -- (-0.5020,-0.4636) + -- (-0.5118,-0.4655) + -- (-0.5207,-0.4700) + -- (-0.5280,-0.4768) + -- (-0.5332,-0.4853) + -- (-0.5359,-0.4949) + -- (-0.5359,-0.5049) + -- (-0.5332,-0.5145) + -- (-0.5280,-0.5229) + -- (-0.5206,-0.5297) + -- (-0.5117,-0.5341) + -- (-0.5019,-0.5360) + -- (-0.4920,-0.5351) + -- (-0.4827,-0.5315) + -- (-0.4747,-0.5255) + -- (-0.4687,-0.5176) + -- (-0.4651,-0.5083) + -- (-0.4642,-0.4983) + -- (-0.4661,-0.4886) + -- (-0.4706,-0.4797) + -- (-0.4774,-0.4724) + -- (-0.4860,-0.4672) + -- (-0.4956,-0.4647) + -- (-0.5056,-0.4649) + -- (-0.5151,-0.4678) + -- (-0.5234,-0.4733) + -- (-0.5299,-0.4809) + -- (-0.5340,-0.4900) + -- (-0.5354,-0.4999) + -- (-0.5340,-0.5097) + -- (-0.5299,-0.5188) + -- (-0.5234,-0.5264) + -- (-0.5150,-0.5318) + -- (-0.5055,-0.5347) + -- (-0.4955,-0.5348) + -- (-0.4859,-0.5322) + -- (-0.4775,-0.5269) + -- (-0.4709,-0.5194) + -- (-0.4666,-0.5104) + -- (-0.4651,-0.5006) + -- (-0.4664,-0.4907) + -- (-0.4704,-0.4816) + -- (-0.4769,-0.4740) + -- (-0.4852,-0.4685) + -- (-0.4947,-0.4657) + -- (-0.5047,-0.4656) + -- (-0.5143,-0.4684) + -- (-0.5226,-0.4738) + -- (-0.5291,-0.4814) + -- (-0.5332,-0.4904) + -- (-0.5345,-0.5003) + -- (-0.5330,-0.5102) + -- (-0.5286,-0.5191) + -- (-0.5219,-0.5265) + -- (-0.5134,-0.5317) + -- (-0.5037,-0.5341) + -- (-0.4938,-0.5337) + -- (-0.4844,-0.5305) + -- (-0.4763,-0.5247) + -- (-0.4702,-0.5168) + -- (-0.4667,-0.5074) + -- (-0.4660,-0.4975) + -- (-0.4682,-0.4878) + -- (-0.4731,-0.4791) + -- (-0.4803,-0.4723) + -- (-0.4892,-0.4678) + -- (-0.4990,-0.4661) + -- (-0.5089,-0.4673) + -- (-0.5180,-0.4713) + -- (-0.5256,-0.4779) + -- (-0.5309,-0.4863) + -- (-0.5335,-0.4959) + -- (-0.5332,-0.5059) + -- (-0.5300,-0.5153) + -- (-0.5242,-0.5234) + -- (-0.5163,-0.5294) + -- (-0.5069,-0.5329) + -- (-0.4970,-0.5334) + -- (-0.4873,-0.5310) + -- (-0.4788,-0.5259) + -- (-0.4721,-0.5184) + -- (-0.4679,-0.5094) + -- (-0.4666,-0.4995) + -- (-0.4683,-0.4897) + -- (-0.4728,-0.4808) + -- (-0.4797,-0.4736) + -- (-0.4885,-0.4688) + -- (-0.4982,-0.4669) + -- (-0.5081,-0.4679) + -- (-0.5173,-0.4718) + -- (-0.5249,-0.4782) + -- (-0.5302,-0.4866) + -- (-0.5328,-0.4962) + -- (-0.5324,-0.5062) + -- (-0.5290,-0.5156) + -- (-0.5230,-0.5235) + -- (-0.5149,-0.5293) + -- (-0.5054,-0.5324) + -- (-0.4955,-0.5325) + -- (-0.4860,-0.5296) + -- (-0.4777,-0.5240) + -- (-0.4716,-0.5162) + -- (-0.4680,-0.5069) + -- (-0.4675,-0.4969) + -- (-0.4700,-0.4873) + -- (-0.4753,-0.4788) + -- (-0.4828,-0.4723) + -- (-0.4920,-0.4685) + -- (-0.5019,-0.4676) + -- (-0.5117,-0.4697) + -- (-0.5203,-0.4747) + -- (-0.5270,-0.4821) + -- (-0.5311,-0.4911) + -- (-0.5323,-0.5010) + -- (-0.5304,-0.5108) + -- (-0.5256,-0.5196) + -- (-0.5184,-0.5264) + -- (-0.5095,-0.5308) + -- (-0.4996,-0.5321) + -- (-0.4898,-0.5305) + -- (-0.4810,-0.5258) + -- (-0.4740,-0.5187) + -- (-0.4695,-0.5098) + -- (-0.4680,-0.5000) + -- (-0.4696,-0.4901) + -- (-0.4741,-0.4813) + -- (-0.4812,-0.4742) + -- (-0.4901,-0.4697) +} + +\def\Cplotright{ (0,0) + -- ({0.0100*\dx},{0.0100*\dy}) + -- ({0.0200*\dx},{0.0200*\dy}) + -- ({0.0300*\dx},{0.0300*\dy}) + -- ({0.0400*\dx},{0.0400*\dy}) + -- ({0.0500*\dx},{0.0500*\dy}) + -- ({0.0600*\dx},{0.0600*\dy}) + -- ({0.0700*\dx},{0.0700*\dy}) + -- ({0.0800*\dx},{0.0800*\dy}) + -- ({0.0900*\dx},{0.0900*\dy}) + -- ({0.1000*\dx},{0.1000*\dy}) + -- ({0.1100*\dx},{0.1100*\dy}) + -- ({0.1200*\dx},{0.1200*\dy}) + -- ({0.1300*\dx},{0.1300*\dy}) + -- ({0.1400*\dx},{0.1400*\dy}) + -- ({0.1500*\dx},{0.1500*\dy}) + -- ({0.1600*\dx},{0.1600*\dy}) + -- ({0.1700*\dx},{0.1700*\dy}) + -- ({0.1800*\dx},{0.1800*\dy}) + -- ({0.1900*\dx},{0.1899*\dy}) + -- ({0.2000*\dx},{0.1999*\dy}) + -- ({0.2100*\dx},{0.2099*\dy}) + -- ({0.2200*\dx},{0.2199*\dy}) + -- ({0.2300*\dx},{0.2298*\dy}) + -- ({0.2400*\dx},{0.2398*\dy}) + -- ({0.2500*\dx},{0.2498*\dy}) + -- ({0.2600*\dx},{0.2597*\dy}) + -- ({0.2700*\dx},{0.2696*\dy}) + -- ({0.2800*\dx},{0.2796*\dy}) + -- ({0.2900*\dx},{0.2895*\dy}) + -- ({0.3000*\dx},{0.2994*\dy}) + -- ({0.3100*\dx},{0.3093*\dy}) + -- ({0.3200*\dx},{0.3192*\dy}) + -- ({0.3300*\dx},{0.3290*\dy}) + -- ({0.3400*\dx},{0.3389*\dy}) + -- ({0.3500*\dx},{0.3487*\dy}) + -- ({0.3600*\dx},{0.3585*\dy}) + -- ({0.3700*\dx},{0.3683*\dy}) + -- ({0.3800*\dx},{0.3780*\dy}) + -- ({0.3900*\dx},{0.3878*\dy}) + -- ({0.4000*\dx},{0.3975*\dy}) + -- ({0.4100*\dx},{0.4072*\dy}) + -- ({0.4200*\dx},{0.4168*\dy}) + -- ({0.4300*\dx},{0.4264*\dy}) + -- ({0.4400*\dx},{0.4359*\dy}) + -- ({0.4500*\dx},{0.4455*\dy}) + -- ({0.4600*\dx},{0.4549*\dy}) + -- ({0.4700*\dx},{0.4644*\dy}) + -- ({0.4800*\dx},{0.4738*\dy}) + -- ({0.4900*\dx},{0.4831*\dy}) + -- ({0.5000*\dx},{0.4923*\dy}) + -- ({0.5100*\dx},{0.5016*\dy}) + -- ({0.5200*\dx},{0.5107*\dy}) + -- ({0.5300*\dx},{0.5198*\dy}) + -- ({0.5400*\dx},{0.5288*\dy}) + -- ({0.5500*\dx},{0.5377*\dy}) + -- ({0.5600*\dx},{0.5466*\dy}) + -- ({0.5700*\dx},{0.5553*\dy}) + -- ({0.5800*\dx},{0.5640*\dy}) + -- ({0.5900*\dx},{0.5726*\dy}) + -- ({0.6000*\dx},{0.5811*\dy}) + -- ({0.6100*\dx},{0.5895*\dy}) + -- ({0.6200*\dx},{0.5978*\dy}) + -- ({0.6300*\dx},{0.6059*\dy}) + -- ({0.6400*\dx},{0.6140*\dy}) + -- ({0.6500*\dx},{0.6219*\dy}) + -- ({0.6600*\dx},{0.6298*\dy}) + -- ({0.6700*\dx},{0.6374*\dy}) + -- ({0.6800*\dx},{0.6450*\dy}) + -- ({0.6900*\dx},{0.6524*\dy}) + -- ({0.7000*\dx},{0.6597*\dy}) + -- ({0.7100*\dx},{0.6668*\dy}) + -- ({0.7200*\dx},{0.6737*\dy}) + -- ({0.7300*\dx},{0.6805*\dy}) + -- ({0.7400*\dx},{0.6871*\dy}) + -- ({0.7500*\dx},{0.6935*\dy}) + -- ({0.7600*\dx},{0.6998*\dy}) + -- ({0.7700*\dx},{0.7058*\dy}) + -- ({0.7800*\dx},{0.7117*\dy}) + -- ({0.7900*\dx},{0.7174*\dy}) + -- ({0.8000*\dx},{0.7228*\dy}) + -- ({0.8100*\dx},{0.7281*\dy}) + -- ({0.8200*\dx},{0.7331*\dy}) + -- ({0.8300*\dx},{0.7379*\dy}) + -- ({0.8400*\dx},{0.7425*\dy}) + -- ({0.8500*\dx},{0.7469*\dy}) + -- ({0.8600*\dx},{0.7510*\dy}) + -- ({0.8700*\dx},{0.7548*\dy}) + -- ({0.8800*\dx},{0.7584*\dy}) + -- ({0.8900*\dx},{0.7617*\dy}) + -- ({0.9000*\dx},{0.7648*\dy}) + -- ({0.9100*\dx},{0.7676*\dy}) + -- ({0.9200*\dx},{0.7702*\dy}) + -- ({0.9300*\dx},{0.7724*\dy}) + -- ({0.9400*\dx},{0.7744*\dy}) + -- ({0.9500*\dx},{0.7760*\dy}) + -- ({0.9600*\dx},{0.7774*\dy}) + -- ({0.9700*\dx},{0.7785*\dy}) + -- ({0.9800*\dx},{0.7793*\dy}) + -- ({0.9900*\dx},{0.7797*\dy}) + -- ({1.0000*\dx},{0.7799*\dy}) + -- ({1.0100*\dx},{0.7797*\dy}) + -- ({1.0200*\dx},{0.7793*\dy}) + -- ({1.0300*\dx},{0.7785*\dy}) + -- ({1.0400*\dx},{0.7774*\dy}) + -- ({1.0500*\dx},{0.7759*\dy}) + -- ({1.0600*\dx},{0.7741*\dy}) + -- ({1.0700*\dx},{0.7721*\dy}) + -- ({1.0800*\dx},{0.7696*\dy}) + -- ({1.0900*\dx},{0.7669*\dy}) + -- ({1.1000*\dx},{0.7638*\dy}) + -- ({1.1100*\dx},{0.7604*\dy}) + -- ({1.1200*\dx},{0.7567*\dy}) + -- ({1.1300*\dx},{0.7526*\dy}) + -- ({1.1400*\dx},{0.7482*\dy}) + -- ({1.1500*\dx},{0.7436*\dy}) + -- ({1.1600*\dx},{0.7385*\dy}) + -- ({1.1700*\dx},{0.7332*\dy}) + -- ({1.1800*\dx},{0.7276*\dy}) + -- ({1.1900*\dx},{0.7217*\dy}) + -- ({1.2000*\dx},{0.7154*\dy}) + -- ({1.2100*\dx},{0.7089*\dy}) + -- ({1.2200*\dx},{0.7021*\dy}) + -- ({1.2300*\dx},{0.6950*\dy}) + -- ({1.2400*\dx},{0.6877*\dy}) + -- ({1.2500*\dx},{0.6801*\dy}) + -- ({1.2600*\dx},{0.6722*\dy}) + -- ({1.2700*\dx},{0.6641*\dy}) + -- ({1.2800*\dx},{0.6558*\dy}) + -- ({1.2900*\dx},{0.6473*\dy}) + -- ({1.3000*\dx},{0.6386*\dy}) + -- ({1.3100*\dx},{0.6296*\dy}) + -- ({1.3200*\dx},{0.6205*\dy}) + -- ({1.3300*\dx},{0.6112*\dy}) + -- ({1.3400*\dx},{0.6018*\dy}) + -- ({1.3500*\dx},{0.5923*\dy}) + -- ({1.3600*\dx},{0.5826*\dy}) + -- ({1.3700*\dx},{0.5728*\dy}) + -- ({1.3800*\dx},{0.5630*\dy}) + -- ({1.3900*\dx},{0.5531*\dy}) + -- ({1.4000*\dx},{0.5431*\dy}) + -- ({1.4100*\dx},{0.5331*\dy}) + -- ({1.4200*\dx},{0.5231*\dy}) + -- ({1.4300*\dx},{0.5131*\dy}) + -- ({1.4400*\dx},{0.5032*\dy}) + -- ({1.4500*\dx},{0.4933*\dy}) + -- ({1.4600*\dx},{0.4834*\dy}) + -- ({1.4700*\dx},{0.4737*\dy}) + -- ({1.4800*\dx},{0.4641*\dy}) + -- ({1.4900*\dx},{0.4546*\dy}) + -- ({1.5000*\dx},{0.4453*\dy}) + -- ({1.5100*\dx},{0.4361*\dy}) + -- ({1.5200*\dx},{0.4272*\dy}) + -- ({1.5300*\dx},{0.4185*\dy}) + -- ({1.5400*\dx},{0.4100*\dy}) + -- ({1.5500*\dx},{0.4018*\dy}) + -- ({1.5600*\dx},{0.3939*\dy}) + -- ({1.5700*\dx},{0.3862*\dy}) + -- ({1.5800*\dx},{0.3790*\dy}) + -- ({1.5900*\dx},{0.3720*\dy}) + -- ({1.6000*\dx},{0.3655*\dy}) + -- ({1.6100*\dx},{0.3593*\dy}) + -- ({1.6200*\dx},{0.3535*\dy}) + -- ({1.6300*\dx},{0.3482*\dy}) + -- ({1.6400*\dx},{0.3433*\dy}) + -- ({1.6500*\dx},{0.3388*\dy}) + -- ({1.6600*\dx},{0.3348*\dy}) + -- ({1.6700*\dx},{0.3313*\dy}) + -- ({1.6800*\dx},{0.3283*\dy}) + -- ({1.6900*\dx},{0.3258*\dy}) + -- ({1.7000*\dx},{0.3238*\dy}) + -- ({1.7100*\dx},{0.3224*\dy}) + -- ({1.7200*\dx},{0.3214*\dy}) + -- ({1.7300*\dx},{0.3211*\dy}) + -- ({1.7400*\dx},{0.3212*\dy}) + -- ({1.7500*\dx},{0.3219*\dy}) + -- ({1.7600*\dx},{0.3232*\dy}) + -- ({1.7700*\dx},{0.3250*\dy}) + -- ({1.7800*\dx},{0.3273*\dy}) + -- ({1.7900*\dx},{0.3302*\dy}) + -- ({1.8000*\dx},{0.3336*\dy}) + -- ({1.8100*\dx},{0.3376*\dy}) + -- ({1.8200*\dx},{0.3420*\dy}) + -- ({1.8300*\dx},{0.3470*\dy}) + -- ({1.8400*\dx},{0.3524*\dy}) + -- ({1.8500*\dx},{0.3584*\dy}) + -- ({1.8600*\dx},{0.3648*\dy}) + -- ({1.8700*\dx},{0.3716*\dy}) + -- ({1.8800*\dx},{0.3788*\dy}) + -- ({1.8900*\dx},{0.3865*\dy}) + -- ({1.9000*\dx},{0.3945*\dy}) + -- ({1.9100*\dx},{0.4028*\dy}) + -- ({1.9200*\dx},{0.4115*\dy}) + -- ({1.9300*\dx},{0.4204*\dy}) + -- ({1.9400*\dx},{0.4296*\dy}) + -- ({1.9500*\dx},{0.4391*\dy}) + -- ({1.9600*\dx},{0.4487*\dy}) + -- ({1.9700*\dx},{0.4584*\dy}) + -- ({1.9800*\dx},{0.4683*\dy}) + -- ({1.9900*\dx},{0.4783*\dy}) + -- ({2.0000*\dx},{0.4883*\dy}) + -- ({2.0100*\dx},{0.4982*\dy}) + -- ({2.0200*\dx},{0.5082*\dy}) + -- ({2.0300*\dx},{0.5181*\dy}) + -- ({2.0400*\dx},{0.5278*\dy}) + -- ({2.0500*\dx},{0.5374*\dy}) + -- ({2.0600*\dx},{0.5468*\dy}) + -- ({2.0700*\dx},{0.5560*\dy}) + -- ({2.0800*\dx},{0.5648*\dy}) + -- ({2.0900*\dx},{0.5734*\dy}) + -- ({2.1000*\dx},{0.5816*\dy}) + -- ({2.1100*\dx},{0.5894*\dy}) + -- ({2.1200*\dx},{0.5967*\dy}) + -- ({2.1300*\dx},{0.6036*\dy}) + -- ({2.1400*\dx},{0.6100*\dy}) + -- ({2.1500*\dx},{0.6159*\dy}) + -- ({2.1600*\dx},{0.6212*\dy}) + -- ({2.1700*\dx},{0.6259*\dy}) + -- ({2.1800*\dx},{0.6300*\dy}) + -- ({2.1900*\dx},{0.6335*\dy}) + -- ({2.2000*\dx},{0.6363*\dy}) + -- ({2.2100*\dx},{0.6384*\dy}) + -- ({2.2200*\dx},{0.6399*\dy}) + -- ({2.2300*\dx},{0.6407*\dy}) + -- ({2.2400*\dx},{0.6408*\dy}) + -- ({2.2500*\dx},{0.6401*\dy}) + -- ({2.2600*\dx},{0.6388*\dy}) + -- ({2.2700*\dx},{0.6368*\dy}) + -- ({2.2800*\dx},{0.6340*\dy}) + -- ({2.2900*\dx},{0.6306*\dy}) + -- ({2.3000*\dx},{0.6266*\dy}) + -- ({2.3100*\dx},{0.6218*\dy}) + -- ({2.3200*\dx},{0.6165*\dy}) + -- ({2.3300*\dx},{0.6105*\dy}) + -- ({2.3400*\dx},{0.6040*\dy}) + -- ({2.3500*\dx},{0.5970*\dy}) + -- ({2.3600*\dx},{0.5894*\dy}) + -- ({2.3700*\dx},{0.5814*\dy}) + -- ({2.3800*\dx},{0.5729*\dy}) + -- ({2.3900*\dx},{0.5641*\dy}) + -- ({2.4000*\dx},{0.5550*\dy}) + -- ({2.4100*\dx},{0.5455*\dy}) + -- ({2.4200*\dx},{0.5359*\dy}) + -- ({2.4300*\dx},{0.5261*\dy}) + -- ({2.4400*\dx},{0.5161*\dy}) + -- ({2.4500*\dx},{0.5061*\dy}) + -- ({2.4600*\dx},{0.4961*\dy}) + -- ({2.4700*\dx},{0.4862*\dy}) + -- ({2.4800*\dx},{0.4764*\dy}) + -- ({2.4900*\dx},{0.4668*\dy}) + -- ({2.5000*\dx},{0.4574*\dy}) + -- ({2.5100*\dx},{0.4483*\dy}) + -- ({2.5200*\dx},{0.4396*\dy}) + -- ({2.5300*\dx},{0.4313*\dy}) + -- ({2.5400*\dx},{0.4235*\dy}) + -- ({2.5500*\dx},{0.4161*\dy}) + -- ({2.5600*\dx},{0.4094*\dy}) + -- ({2.5700*\dx},{0.4033*\dy}) + -- ({2.5800*\dx},{0.3978*\dy}) + -- ({2.5900*\dx},{0.3930*\dy}) + -- ({2.6000*\dx},{0.3889*\dy}) + -- ({2.6100*\dx},{0.3856*\dy}) + -- ({2.6200*\dx},{0.3831*\dy}) + -- ({2.6300*\dx},{0.3814*\dy}) + -- ({2.6400*\dx},{0.3805*\dy}) + -- ({2.6500*\dx},{0.3805*\dy}) + -- ({2.6600*\dx},{0.3812*\dy}) + -- ({2.6700*\dx},{0.3828*\dy}) + -- ({2.6800*\dx},{0.3853*\dy}) + -- ({2.6900*\dx},{0.3885*\dy}) + -- ({2.7000*\dx},{0.3925*\dy}) + -- ({2.7100*\dx},{0.3973*\dy}) + -- ({2.7200*\dx},{0.4028*\dy}) + -- ({2.7300*\dx},{0.4090*\dy}) + -- ({2.7400*\dx},{0.4158*\dy}) + -- ({2.7500*\dx},{0.4233*\dy}) + -- ({2.7600*\dx},{0.4313*\dy}) + -- ({2.7700*\dx},{0.4397*\dy}) + -- ({2.7800*\dx},{0.4487*\dy}) + -- ({2.7900*\dx},{0.4579*\dy}) + -- ({2.8000*\dx},{0.4675*\dy}) + -- ({2.8100*\dx},{0.4773*\dy}) + -- ({2.8200*\dx},{0.4872*\dy}) + -- ({2.8300*\dx},{0.4972*\dy}) + -- ({2.8400*\dx},{0.5072*\dy}) + -- ({2.8500*\dx},{0.5171*\dy}) + -- ({2.8600*\dx},{0.5268*\dy}) + -- ({2.8700*\dx},{0.5362*\dy}) + -- ({2.8800*\dx},{0.5454*\dy}) + -- ({2.8900*\dx},{0.5541*\dy}) + -- ({2.9000*\dx},{0.5624*\dy}) + -- ({2.9100*\dx},{0.5701*\dy}) + -- ({2.9200*\dx},{0.5772*\dy}) + -- ({2.9300*\dx},{0.5836*\dy}) + -- ({2.9400*\dx},{0.5893*\dy}) + -- ({2.9500*\dx},{0.5942*\dy}) + -- ({2.9600*\dx},{0.5983*\dy}) + -- ({2.9700*\dx},{0.6015*\dy}) + -- ({2.9800*\dx},{0.6038*\dy}) + -- ({2.9900*\dx},{0.6053*\dy}) + -- ({3.0000*\dx},{0.6057*\dy}) + -- ({3.0100*\dx},{0.6052*\dy}) + -- ({3.0200*\dx},{0.6038*\dy}) + -- ({3.0300*\dx},{0.6015*\dy}) + -- ({3.0400*\dx},{0.5982*\dy}) + -- ({3.0500*\dx},{0.5941*\dy}) + -- ({3.0600*\dx},{0.5891*\dy}) + -- ({3.0700*\dx},{0.5833*\dy}) + -- ({3.0800*\dx},{0.5767*\dy}) + -- ({3.0900*\dx},{0.5695*\dy}) + -- ({3.1000*\dx},{0.5616*\dy}) + -- ({3.1100*\dx},{0.5531*\dy}) + -- ({3.1200*\dx},{0.5442*\dy}) + -- ({3.1300*\dx},{0.5349*\dy}) + -- ({3.1400*\dx},{0.5253*\dy}) + -- ({3.1500*\dx},{0.5154*\dy}) + -- ({3.1600*\dx},{0.5054*\dy}) + -- ({3.1700*\dx},{0.4954*\dy}) + -- ({3.1800*\dx},{0.4855*\dy}) + -- ({3.1900*\dx},{0.4758*\dy}) + -- ({3.2000*\dx},{0.4663*\dy}) + -- ({3.2100*\dx},{0.4572*\dy}) + -- ({3.2200*\dx},{0.4486*\dy}) + -- ({3.2300*\dx},{0.4405*\dy}) + -- ({3.2400*\dx},{0.4331*\dy}) + -- ({3.2500*\dx},{0.4263*\dy}) + -- ({3.2600*\dx},{0.4204*\dy}) + -- ({3.2700*\dx},{0.4153*\dy}) + -- ({3.2800*\dx},{0.4111*\dy}) + -- ({3.2900*\dx},{0.4079*\dy}) + -- ({3.3000*\dx},{0.4057*\dy}) + -- ({3.3100*\dx},{0.4045*\dy}) + -- ({3.3200*\dx},{0.4043*\dy}) + -- ({3.3300*\dx},{0.4052*\dy}) + -- ({3.3400*\dx},{0.4071*\dy}) + -- ({3.3500*\dx},{0.4100*\dy}) + -- ({3.3600*\dx},{0.4139*\dy}) + -- ({3.3700*\dx},{0.4188*\dy}) + -- ({3.3800*\dx},{0.4246*\dy}) + -- ({3.3900*\dx},{0.4311*\dy}) + -- ({3.4000*\dx},{0.4385*\dy}) + -- ({3.4100*\dx},{0.4465*\dy}) + -- ({3.4200*\dx},{0.4551*\dy}) + -- ({3.4300*\dx},{0.4643*\dy}) + -- ({3.4400*\dx},{0.4738*\dy}) + -- ({3.4500*\dx},{0.4835*\dy}) + -- ({3.4600*\dx},{0.4935*\dy}) + -- ({3.4700*\dx},{0.5035*\dy}) + -- ({3.4800*\dx},{0.5134*\dy}) + -- ({3.4900*\dx},{0.5231*\dy}) + -- ({3.5000*\dx},{0.5326*\dy}) + -- ({3.5100*\dx},{0.5416*\dy}) + -- ({3.5200*\dx},{0.5501*\dy}) + -- ({3.5300*\dx},{0.5579*\dy}) + -- ({3.5400*\dx},{0.5650*\dy}) + -- ({3.5500*\dx},{0.5713*\dy}) + -- ({3.5600*\dx},{0.5767*\dy}) + -- ({3.5700*\dx},{0.5811*\dy}) + -- ({3.5800*\dx},{0.5845*\dy}) + -- ({3.5900*\dx},{0.5868*\dy}) + -- ({3.6000*\dx},{0.5880*\dy}) + -- ({3.6100*\dx},{0.5880*\dy}) + -- ({3.6200*\dx},{0.5869*\dy}) + -- ({3.6300*\dx},{0.5848*\dy}) + -- ({3.6400*\dx},{0.5815*\dy}) + -- ({3.6500*\dx},{0.5771*\dy}) + -- ({3.6600*\dx},{0.5718*\dy}) + -- ({3.6700*\dx},{0.5655*\dy}) + -- ({3.6800*\dx},{0.5584*\dy}) + -- ({3.6900*\dx},{0.5505*\dy}) + -- ({3.7000*\dx},{0.5419*\dy}) + -- ({3.7100*\dx},{0.5329*\dy}) + -- ({3.7200*\dx},{0.5233*\dy}) + -- ({3.7300*\dx},{0.5135*\dy}) + -- ({3.7400*\dx},{0.5036*\dy}) + -- ({3.7500*\dx},{0.4936*\dy}) + -- ({3.7600*\dx},{0.4837*\dy}) + -- ({3.7700*\dx},{0.4741*\dy}) + -- ({3.7800*\dx},{0.4649*\dy}) + -- ({3.7900*\dx},{0.4562*\dy}) + -- ({3.8000*\dx},{0.4481*\dy}) + -- ({3.8100*\dx},{0.4408*\dy}) + -- ({3.8200*\dx},{0.4343*\dy}) + -- ({3.8300*\dx},{0.4289*\dy}) + -- ({3.8400*\dx},{0.4244*\dy}) + -- ({3.8500*\dx},{0.4211*\dy}) + -- ({3.8600*\dx},{0.4189*\dy}) + -- ({3.8700*\dx},{0.4180*\dy}) + -- ({3.8800*\dx},{0.4182*\dy}) + -- ({3.8900*\dx},{0.4197*\dy}) + -- ({3.9000*\dx},{0.4223*\dy}) + -- ({3.9100*\dx},{0.4261*\dy}) + -- ({3.9200*\dx},{0.4311*\dy}) + -- ({3.9300*\dx},{0.4370*\dy}) + -- ({3.9400*\dx},{0.4439*\dy}) + -- ({3.9500*\dx},{0.4516*\dy}) + -- ({3.9600*\dx},{0.4601*\dy}) + -- ({3.9700*\dx},{0.4691*\dy}) + -- ({3.9800*\dx},{0.4786*\dy}) + -- ({3.9900*\dx},{0.4885*\dy}) + -- ({4.0000*\dx},{0.4984*\dy}) + -- ({4.0100*\dx},{0.5084*\dy}) + -- ({4.0200*\dx},{0.5182*\dy}) + -- ({4.0300*\dx},{0.5277*\dy}) + -- ({4.0400*\dx},{0.5368*\dy}) + -- ({4.0500*\dx},{0.5452*\dy}) + -- ({4.0600*\dx},{0.5528*\dy}) + -- ({4.0700*\dx},{0.5596*\dy}) + -- ({4.0800*\dx},{0.5654*\dy}) + -- ({4.0900*\dx},{0.5701*\dy}) + -- ({4.1000*\dx},{0.5737*\dy}) + -- ({4.1100*\dx},{0.5760*\dy}) + -- ({4.1200*\dx},{0.5771*\dy}) + -- ({4.1300*\dx},{0.5768*\dy}) + -- ({4.1400*\dx},{0.5753*\dy}) + -- ({4.1500*\dx},{0.5725*\dy}) + -- ({4.1600*\dx},{0.5684*\dy}) + -- ({4.1700*\dx},{0.5633*\dy}) + -- ({4.1800*\dx},{0.5570*\dy}) + -- ({4.1900*\dx},{0.5498*\dy}) + -- ({4.2000*\dx},{0.5417*\dy}) + -- ({4.2100*\dx},{0.5329*\dy}) + -- ({4.2200*\dx},{0.5236*\dy}) + -- ({4.2300*\dx},{0.5139*\dy}) + -- ({4.2400*\dx},{0.5040*\dy}) + -- ({4.2500*\dx},{0.4940*\dy}) + -- ({4.2600*\dx},{0.4841*\dy}) + -- ({4.2700*\dx},{0.4746*\dy}) + -- ({4.2800*\dx},{0.4655*\dy}) + -- ({4.2900*\dx},{0.4571*\dy}) + -- ({4.3000*\dx},{0.4494*\dy}) + -- ({4.3100*\dx},{0.4428*\dy}) + -- ({4.3200*\dx},{0.4371*\dy}) + -- ({4.3300*\dx},{0.4327*\dy}) + -- ({4.3400*\dx},{0.4295*\dy}) + -- ({4.3500*\dx},{0.4276*\dy}) + -- ({4.3600*\dx},{0.4270*\dy}) + -- ({4.3700*\dx},{0.4279*\dy}) + -- ({4.3800*\dx},{0.4301*\dy}) + -- ({4.3900*\dx},{0.4336*\dy}) + -- ({4.4000*\dx},{0.4383*\dy}) + -- ({4.4100*\dx},{0.4443*\dy}) + -- ({4.4200*\dx},{0.4512*\dy}) + -- ({4.4300*\dx},{0.4591*\dy}) + -- ({4.4400*\dx},{0.4678*\dy}) + -- ({4.4500*\dx},{0.4771*\dy}) + -- ({4.4600*\dx},{0.4868*\dy}) + -- ({4.4700*\dx},{0.4967*\dy}) + -- ({4.4800*\dx},{0.5067*\dy}) + -- ({4.4900*\dx},{0.5165*\dy}) + -- ({4.5000*\dx},{0.5260*\dy}) + -- ({4.5100*\dx},{0.5350*\dy}) + -- ({4.5200*\dx},{0.5432*\dy}) + -- ({4.5300*\dx},{0.5505*\dy}) + -- ({4.5400*\dx},{0.5568*\dy}) + -- ({4.5500*\dx},{0.5619*\dy}) + -- ({4.5600*\dx},{0.5658*\dy}) + -- ({4.5700*\dx},{0.5683*\dy}) + -- ({4.5800*\dx},{0.5694*\dy}) + -- ({4.5900*\dx},{0.5690*\dy}) + -- ({4.6000*\dx},{0.5672*\dy}) + -- ({4.6100*\dx},{0.5641*\dy}) + -- ({4.6200*\dx},{0.5595*\dy}) + -- ({4.6300*\dx},{0.5538*\dy}) + -- ({4.6400*\dx},{0.5469*\dy}) + -- ({4.6500*\dx},{0.5391*\dy}) + -- ({4.6600*\dx},{0.5304*\dy}) + -- ({4.6700*\dx},{0.5211*\dy}) + -- ({4.6800*\dx},{0.5114*\dy}) + -- ({4.6900*\dx},{0.5014*\dy}) + -- ({4.7000*\dx},{0.4914*\dy}) + -- ({4.7100*\dx},{0.4817*\dy}) + -- ({4.7200*\dx},{0.4723*\dy}) + -- ({4.7300*\dx},{0.4636*\dy}) + -- ({4.7400*\dx},{0.4557*\dy}) + -- ({4.7500*\dx},{0.4488*\dy}) + -- ({4.7600*\dx},{0.4431*\dy}) + -- ({4.7700*\dx},{0.4386*\dy}) + -- ({4.7800*\dx},{0.4355*\dy}) + -- ({4.7900*\dx},{0.4339*\dy}) + -- ({4.8000*\dx},{0.4338*\dy}) + -- ({4.8100*\dx},{0.4352*\dy}) + -- ({4.8200*\dx},{0.4380*\dy}) + -- ({4.8300*\dx},{0.4423*\dy}) + -- ({4.8400*\dx},{0.4479*\dy}) + -- ({4.8500*\dx},{0.4546*\dy}) + -- ({4.8600*\dx},{0.4624*\dy}) + -- ({4.8700*\dx},{0.4711*\dy}) + -- ({4.8800*\dx},{0.4804*\dy}) + -- ({4.8900*\dx},{0.4902*\dy}) + -- ({4.9000*\dx},{0.5002*\dy}) + -- ({4.9100*\dx},{0.5101*\dy}) + -- ({4.9200*\dx},{0.5198*\dy}) + -- ({4.9300*\dx},{0.5290*\dy}) + -- ({4.9400*\dx},{0.5375*\dy}) + -- ({4.9500*\dx},{0.5450*\dy}) + -- ({4.9600*\dx},{0.5515*\dy}) + -- ({4.9700*\dx},{0.5567*\dy}) + -- ({4.9800*\dx},{0.5605*\dy}) + -- ({4.9900*\dx},{0.5628*\dy}) +} + +\def\Cplotleft{ (0,0) + -- ({-0.0100*\dx},{-0.0100*\dy}) + -- ({-0.0200*\dx},{-0.0200*\dy}) + -- ({-0.0300*\dx},{-0.0300*\dy}) + -- ({-0.0400*\dx},{-0.0400*\dy}) + -- ({-0.0500*\dx},{-0.0500*\dy}) + -- ({-0.0600*\dx},{-0.0600*\dy}) + -- ({-0.0700*\dx},{-0.0700*\dy}) + -- ({-0.0800*\dx},{-0.0800*\dy}) + -- ({-0.0900*\dx},{-0.0900*\dy}) + -- ({-0.1000*\dx},{-0.1000*\dy}) + -- ({-0.1100*\dx},{-0.1100*\dy}) + -- ({-0.1200*\dx},{-0.1200*\dy}) + -- ({-0.1300*\dx},{-0.1300*\dy}) + -- ({-0.1400*\dx},{-0.1400*\dy}) + -- ({-0.1500*\dx},{-0.1500*\dy}) + -- ({-0.1600*\dx},{-0.1600*\dy}) + -- ({-0.1700*\dx},{-0.1700*\dy}) + -- ({-0.1800*\dx},{-0.1800*\dy}) + -- ({-0.1900*\dx},{-0.1899*\dy}) + -- ({-0.2000*\dx},{-0.1999*\dy}) + -- ({-0.2100*\dx},{-0.2099*\dy}) + -- ({-0.2200*\dx},{-0.2199*\dy}) + -- ({-0.2300*\dx},{-0.2298*\dy}) + -- ({-0.2400*\dx},{-0.2398*\dy}) + -- ({-0.2500*\dx},{-0.2498*\dy}) + -- ({-0.2600*\dx},{-0.2597*\dy}) + -- ({-0.2700*\dx},{-0.2696*\dy}) + -- ({-0.2800*\dx},{-0.2796*\dy}) + -- ({-0.2900*\dx},{-0.2895*\dy}) + -- ({-0.3000*\dx},{-0.2994*\dy}) + -- ({-0.3100*\dx},{-0.3093*\dy}) + -- ({-0.3200*\dx},{-0.3192*\dy}) + -- ({-0.3300*\dx},{-0.3290*\dy}) + -- ({-0.3400*\dx},{-0.3389*\dy}) + -- ({-0.3500*\dx},{-0.3487*\dy}) + -- ({-0.3600*\dx},{-0.3585*\dy}) + -- ({-0.3700*\dx},{-0.3683*\dy}) + -- ({-0.3800*\dx},{-0.3780*\dy}) + -- ({-0.3900*\dx},{-0.3878*\dy}) + -- ({-0.4000*\dx},{-0.3975*\dy}) + -- ({-0.4100*\dx},{-0.4072*\dy}) + -- ({-0.4200*\dx},{-0.4168*\dy}) + -- ({-0.4300*\dx},{-0.4264*\dy}) + -- ({-0.4400*\dx},{-0.4359*\dy}) + -- ({-0.4500*\dx},{-0.4455*\dy}) + -- ({-0.4600*\dx},{-0.4549*\dy}) + -- ({-0.4700*\dx},{-0.4644*\dy}) + -- ({-0.4800*\dx},{-0.4738*\dy}) + -- ({-0.4900*\dx},{-0.4831*\dy}) + -- ({-0.5000*\dx},{-0.4923*\dy}) + -- ({-0.5100*\dx},{-0.5016*\dy}) + -- ({-0.5200*\dx},{-0.5107*\dy}) + -- ({-0.5300*\dx},{-0.5198*\dy}) + -- ({-0.5400*\dx},{-0.5288*\dy}) + -- ({-0.5500*\dx},{-0.5377*\dy}) + -- ({-0.5600*\dx},{-0.5466*\dy}) + -- ({-0.5700*\dx},{-0.5553*\dy}) + -- ({-0.5800*\dx},{-0.5640*\dy}) + -- ({-0.5900*\dx},{-0.5726*\dy}) + -- ({-0.6000*\dx},{-0.5811*\dy}) + -- ({-0.6100*\dx},{-0.5895*\dy}) + -- ({-0.6200*\dx},{-0.5978*\dy}) + -- ({-0.6300*\dx},{-0.6059*\dy}) + -- ({-0.6400*\dx},{-0.6140*\dy}) + -- ({-0.6500*\dx},{-0.6219*\dy}) + -- ({-0.6600*\dx},{-0.6298*\dy}) + -- ({-0.6700*\dx},{-0.6374*\dy}) + -- ({-0.6800*\dx},{-0.6450*\dy}) + -- ({-0.6900*\dx},{-0.6524*\dy}) + -- ({-0.7000*\dx},{-0.6597*\dy}) + -- ({-0.7100*\dx},{-0.6668*\dy}) + -- ({-0.7200*\dx},{-0.6737*\dy}) + -- ({-0.7300*\dx},{-0.6805*\dy}) + -- ({-0.7400*\dx},{-0.6871*\dy}) + -- ({-0.7500*\dx},{-0.6935*\dy}) + -- ({-0.7600*\dx},{-0.6998*\dy}) + -- ({-0.7700*\dx},{-0.7058*\dy}) + -- ({-0.7800*\dx},{-0.7117*\dy}) + -- ({-0.7900*\dx},{-0.7174*\dy}) + -- ({-0.8000*\dx},{-0.7228*\dy}) + -- ({-0.8100*\dx},{-0.7281*\dy}) + -- ({-0.8200*\dx},{-0.7331*\dy}) + -- ({-0.8300*\dx},{-0.7379*\dy}) + -- ({-0.8400*\dx},{-0.7425*\dy}) + -- ({-0.8500*\dx},{-0.7469*\dy}) + -- ({-0.8600*\dx},{-0.7510*\dy}) + -- ({-0.8700*\dx},{-0.7548*\dy}) + -- ({-0.8800*\dx},{-0.7584*\dy}) + -- ({-0.8900*\dx},{-0.7617*\dy}) + -- ({-0.9000*\dx},{-0.7648*\dy}) + -- ({-0.9100*\dx},{-0.7676*\dy}) + -- ({-0.9200*\dx},{-0.7702*\dy}) + -- ({-0.9300*\dx},{-0.7724*\dy}) + -- ({-0.9400*\dx},{-0.7744*\dy}) + -- ({-0.9500*\dx},{-0.7760*\dy}) + -- ({-0.9600*\dx},{-0.7774*\dy}) + -- ({-0.9700*\dx},{-0.7785*\dy}) + -- ({-0.9800*\dx},{-0.7793*\dy}) + -- ({-0.9900*\dx},{-0.7797*\dy}) + -- ({-1.0000*\dx},{-0.7799*\dy}) + -- ({-1.0100*\dx},{-0.7797*\dy}) + -- ({-1.0200*\dx},{-0.7793*\dy}) + -- ({-1.0300*\dx},{-0.7785*\dy}) + -- ({-1.0400*\dx},{-0.7774*\dy}) + -- ({-1.0500*\dx},{-0.7759*\dy}) + -- ({-1.0600*\dx},{-0.7741*\dy}) + -- ({-1.0700*\dx},{-0.7721*\dy}) + -- ({-1.0800*\dx},{-0.7696*\dy}) + -- ({-1.0900*\dx},{-0.7669*\dy}) + -- ({-1.1000*\dx},{-0.7638*\dy}) + -- ({-1.1100*\dx},{-0.7604*\dy}) + -- ({-1.1200*\dx},{-0.7567*\dy}) + -- ({-1.1300*\dx},{-0.7526*\dy}) + -- ({-1.1400*\dx},{-0.7482*\dy}) + -- ({-1.1500*\dx},{-0.7436*\dy}) + -- ({-1.1600*\dx},{-0.7385*\dy}) + -- ({-1.1700*\dx},{-0.7332*\dy}) + -- ({-1.1800*\dx},{-0.7276*\dy}) + -- ({-1.1900*\dx},{-0.7217*\dy}) + -- ({-1.2000*\dx},{-0.7154*\dy}) + -- ({-1.2100*\dx},{-0.7089*\dy}) + -- ({-1.2200*\dx},{-0.7021*\dy}) + -- ({-1.2300*\dx},{-0.6950*\dy}) + -- ({-1.2400*\dx},{-0.6877*\dy}) + -- ({-1.2500*\dx},{-0.6801*\dy}) + -- ({-1.2600*\dx},{-0.6722*\dy}) + -- ({-1.2700*\dx},{-0.6641*\dy}) + -- ({-1.2800*\dx},{-0.6558*\dy}) + -- ({-1.2900*\dx},{-0.6473*\dy}) + -- ({-1.3000*\dx},{-0.6386*\dy}) + -- ({-1.3100*\dx},{-0.6296*\dy}) + -- ({-1.3200*\dx},{-0.6205*\dy}) + -- ({-1.3300*\dx},{-0.6112*\dy}) + -- ({-1.3400*\dx},{-0.6018*\dy}) + -- ({-1.3500*\dx},{-0.5923*\dy}) + -- ({-1.3600*\dx},{-0.5826*\dy}) + -- ({-1.3700*\dx},{-0.5728*\dy}) + -- ({-1.3800*\dx},{-0.5630*\dy}) + -- ({-1.3900*\dx},{-0.5531*\dy}) + -- ({-1.4000*\dx},{-0.5431*\dy}) + -- ({-1.4100*\dx},{-0.5331*\dy}) + -- ({-1.4200*\dx},{-0.5231*\dy}) + -- ({-1.4300*\dx},{-0.5131*\dy}) + -- ({-1.4400*\dx},{-0.5032*\dy}) + -- ({-1.4500*\dx},{-0.4933*\dy}) + -- ({-1.4600*\dx},{-0.4834*\dy}) + -- ({-1.4700*\dx},{-0.4737*\dy}) + -- ({-1.4800*\dx},{-0.4641*\dy}) + -- ({-1.4900*\dx},{-0.4546*\dy}) + -- ({-1.5000*\dx},{-0.4453*\dy}) + -- ({-1.5100*\dx},{-0.4361*\dy}) + -- ({-1.5200*\dx},{-0.4272*\dy}) + -- ({-1.5300*\dx},{-0.4185*\dy}) + -- ({-1.5400*\dx},{-0.4100*\dy}) + -- ({-1.5500*\dx},{-0.4018*\dy}) + -- ({-1.5600*\dx},{-0.3939*\dy}) + -- ({-1.5700*\dx},{-0.3862*\dy}) + -- ({-1.5800*\dx},{-0.3790*\dy}) + -- ({-1.5900*\dx},{-0.3720*\dy}) + -- ({-1.6000*\dx},{-0.3655*\dy}) + -- ({-1.6100*\dx},{-0.3593*\dy}) + -- ({-1.6200*\dx},{-0.3535*\dy}) + -- ({-1.6300*\dx},{-0.3482*\dy}) + -- ({-1.6400*\dx},{-0.3433*\dy}) + -- ({-1.6500*\dx},{-0.3388*\dy}) + -- ({-1.6600*\dx},{-0.3348*\dy}) + -- ({-1.6700*\dx},{-0.3313*\dy}) + -- ({-1.6800*\dx},{-0.3283*\dy}) + -- ({-1.6900*\dx},{-0.3258*\dy}) + -- ({-1.7000*\dx},{-0.3238*\dy}) + -- ({-1.7100*\dx},{-0.3224*\dy}) + -- ({-1.7200*\dx},{-0.3214*\dy}) + -- ({-1.7300*\dx},{-0.3211*\dy}) + -- ({-1.7400*\dx},{-0.3212*\dy}) + -- ({-1.7500*\dx},{-0.3219*\dy}) + -- ({-1.7600*\dx},{-0.3232*\dy}) + -- ({-1.7700*\dx},{-0.3250*\dy}) + -- ({-1.7800*\dx},{-0.3273*\dy}) + -- ({-1.7900*\dx},{-0.3302*\dy}) + -- ({-1.8000*\dx},{-0.3336*\dy}) + -- ({-1.8100*\dx},{-0.3376*\dy}) + -- ({-1.8200*\dx},{-0.3420*\dy}) + -- ({-1.8300*\dx},{-0.3470*\dy}) + -- ({-1.8400*\dx},{-0.3524*\dy}) + -- ({-1.8500*\dx},{-0.3584*\dy}) + -- ({-1.8600*\dx},{-0.3648*\dy}) + -- ({-1.8700*\dx},{-0.3716*\dy}) + -- ({-1.8800*\dx},{-0.3788*\dy}) + -- ({-1.8900*\dx},{-0.3865*\dy}) + -- ({-1.9000*\dx},{-0.3945*\dy}) + -- ({-1.9100*\dx},{-0.4028*\dy}) + -- ({-1.9200*\dx},{-0.4115*\dy}) + -- ({-1.9300*\dx},{-0.4204*\dy}) + -- ({-1.9400*\dx},{-0.4296*\dy}) + -- ({-1.9500*\dx},{-0.4391*\dy}) + -- ({-1.9600*\dx},{-0.4487*\dy}) + -- ({-1.9700*\dx},{-0.4584*\dy}) + -- ({-1.9800*\dx},{-0.4683*\dy}) + -- ({-1.9900*\dx},{-0.4783*\dy}) + -- ({-2.0000*\dx},{-0.4883*\dy}) + -- ({-2.0100*\dx},{-0.4982*\dy}) + -- ({-2.0200*\dx},{-0.5082*\dy}) + -- ({-2.0300*\dx},{-0.5181*\dy}) + -- ({-2.0400*\dx},{-0.5278*\dy}) + -- ({-2.0500*\dx},{-0.5374*\dy}) + -- ({-2.0600*\dx},{-0.5468*\dy}) + -- ({-2.0700*\dx},{-0.5560*\dy}) + -- ({-2.0800*\dx},{-0.5648*\dy}) + -- ({-2.0900*\dx},{-0.5734*\dy}) + -- ({-2.1000*\dx},{-0.5816*\dy}) + -- ({-2.1100*\dx},{-0.5894*\dy}) + -- ({-2.1200*\dx},{-0.5967*\dy}) + -- ({-2.1300*\dx},{-0.6036*\dy}) + -- ({-2.1400*\dx},{-0.6100*\dy}) + -- ({-2.1500*\dx},{-0.6159*\dy}) + -- ({-2.1600*\dx},{-0.6212*\dy}) + -- ({-2.1700*\dx},{-0.6259*\dy}) + -- ({-2.1800*\dx},{-0.6300*\dy}) + -- ({-2.1900*\dx},{-0.6335*\dy}) + -- ({-2.2000*\dx},{-0.6363*\dy}) + -- ({-2.2100*\dx},{-0.6384*\dy}) + -- ({-2.2200*\dx},{-0.6399*\dy}) + -- ({-2.2300*\dx},{-0.6407*\dy}) + -- ({-2.2400*\dx},{-0.6408*\dy}) + -- ({-2.2500*\dx},{-0.6401*\dy}) + -- ({-2.2600*\dx},{-0.6388*\dy}) + -- ({-2.2700*\dx},{-0.6368*\dy}) + -- ({-2.2800*\dx},{-0.6340*\dy}) + -- ({-2.2900*\dx},{-0.6306*\dy}) + -- ({-2.3000*\dx},{-0.6266*\dy}) + -- ({-2.3100*\dx},{-0.6218*\dy}) + -- ({-2.3200*\dx},{-0.6165*\dy}) + -- ({-2.3300*\dx},{-0.6105*\dy}) + -- ({-2.3400*\dx},{-0.6040*\dy}) + -- ({-2.3500*\dx},{-0.5970*\dy}) + -- ({-2.3600*\dx},{-0.5894*\dy}) + -- ({-2.3700*\dx},{-0.5814*\dy}) + -- ({-2.3800*\dx},{-0.5729*\dy}) + -- ({-2.3900*\dx},{-0.5641*\dy}) + -- ({-2.4000*\dx},{-0.5550*\dy}) + -- ({-2.4100*\dx},{-0.5455*\dy}) + -- ({-2.4200*\dx},{-0.5359*\dy}) + -- ({-2.4300*\dx},{-0.5261*\dy}) + -- ({-2.4400*\dx},{-0.5161*\dy}) + -- ({-2.4500*\dx},{-0.5061*\dy}) + -- ({-2.4600*\dx},{-0.4961*\dy}) + -- ({-2.4700*\dx},{-0.4862*\dy}) + -- ({-2.4800*\dx},{-0.4764*\dy}) + -- ({-2.4900*\dx},{-0.4668*\dy}) + -- ({-2.5000*\dx},{-0.4574*\dy}) + -- ({-2.5100*\dx},{-0.4483*\dy}) + -- ({-2.5200*\dx},{-0.4396*\dy}) + -- ({-2.5300*\dx},{-0.4313*\dy}) + -- ({-2.5400*\dx},{-0.4235*\dy}) + -- ({-2.5500*\dx},{-0.4161*\dy}) + -- ({-2.5600*\dx},{-0.4094*\dy}) + -- ({-2.5700*\dx},{-0.4033*\dy}) + -- ({-2.5800*\dx},{-0.3978*\dy}) + -- ({-2.5900*\dx},{-0.3930*\dy}) + -- ({-2.6000*\dx},{-0.3889*\dy}) + -- ({-2.6100*\dx},{-0.3856*\dy}) + -- ({-2.6200*\dx},{-0.3831*\dy}) + -- ({-2.6300*\dx},{-0.3814*\dy}) + -- ({-2.6400*\dx},{-0.3805*\dy}) + -- ({-2.6500*\dx},{-0.3805*\dy}) + -- ({-2.6600*\dx},{-0.3812*\dy}) + -- ({-2.6700*\dx},{-0.3828*\dy}) + -- ({-2.6800*\dx},{-0.3853*\dy}) + -- ({-2.6900*\dx},{-0.3885*\dy}) + -- ({-2.7000*\dx},{-0.3925*\dy}) + -- ({-2.7100*\dx},{-0.3973*\dy}) + -- ({-2.7200*\dx},{-0.4028*\dy}) + -- ({-2.7300*\dx},{-0.4090*\dy}) + -- ({-2.7400*\dx},{-0.4158*\dy}) + -- ({-2.7500*\dx},{-0.4233*\dy}) + -- ({-2.7600*\dx},{-0.4313*\dy}) + -- ({-2.7700*\dx},{-0.4397*\dy}) + -- ({-2.7800*\dx},{-0.4487*\dy}) + -- ({-2.7900*\dx},{-0.4579*\dy}) + -- ({-2.8000*\dx},{-0.4675*\dy}) + -- ({-2.8100*\dx},{-0.4773*\dy}) + -- ({-2.8200*\dx},{-0.4872*\dy}) + -- ({-2.8300*\dx},{-0.4972*\dy}) + -- ({-2.8400*\dx},{-0.5072*\dy}) + -- ({-2.8500*\dx},{-0.5171*\dy}) + -- ({-2.8600*\dx},{-0.5268*\dy}) + -- ({-2.8700*\dx},{-0.5362*\dy}) + -- ({-2.8800*\dx},{-0.5454*\dy}) + -- ({-2.8900*\dx},{-0.5541*\dy}) + -- ({-2.9000*\dx},{-0.5624*\dy}) + -- ({-2.9100*\dx},{-0.5701*\dy}) + -- ({-2.9200*\dx},{-0.5772*\dy}) + -- ({-2.9300*\dx},{-0.5836*\dy}) + -- ({-2.9400*\dx},{-0.5893*\dy}) + -- ({-2.9500*\dx},{-0.5942*\dy}) + -- ({-2.9600*\dx},{-0.5983*\dy}) + -- ({-2.9700*\dx},{-0.6015*\dy}) + -- ({-2.9800*\dx},{-0.6038*\dy}) + -- ({-2.9900*\dx},{-0.6053*\dy}) + -- ({-3.0000*\dx},{-0.6057*\dy}) + -- ({-3.0100*\dx},{-0.6052*\dy}) + -- ({-3.0200*\dx},{-0.6038*\dy}) + -- ({-3.0300*\dx},{-0.6015*\dy}) + -- ({-3.0400*\dx},{-0.5982*\dy}) + -- ({-3.0500*\dx},{-0.5941*\dy}) + -- ({-3.0600*\dx},{-0.5891*\dy}) + -- ({-3.0700*\dx},{-0.5833*\dy}) + -- ({-3.0800*\dx},{-0.5767*\dy}) + -- ({-3.0900*\dx},{-0.5695*\dy}) + -- ({-3.1000*\dx},{-0.5616*\dy}) + -- ({-3.1100*\dx},{-0.5531*\dy}) + -- ({-3.1200*\dx},{-0.5442*\dy}) + -- ({-3.1300*\dx},{-0.5349*\dy}) + -- ({-3.1400*\dx},{-0.5253*\dy}) + -- ({-3.1500*\dx},{-0.5154*\dy}) + -- ({-3.1600*\dx},{-0.5054*\dy}) + -- ({-3.1700*\dx},{-0.4954*\dy}) + -- ({-3.1800*\dx},{-0.4855*\dy}) + -- ({-3.1900*\dx},{-0.4758*\dy}) + -- ({-3.2000*\dx},{-0.4663*\dy}) + -- ({-3.2100*\dx},{-0.4572*\dy}) + -- ({-3.2200*\dx},{-0.4486*\dy}) + -- ({-3.2300*\dx},{-0.4405*\dy}) + -- ({-3.2400*\dx},{-0.4331*\dy}) + -- ({-3.2500*\dx},{-0.4263*\dy}) + -- ({-3.2600*\dx},{-0.4204*\dy}) + -- ({-3.2700*\dx},{-0.4153*\dy}) + -- ({-3.2800*\dx},{-0.4111*\dy}) + -- ({-3.2900*\dx},{-0.4079*\dy}) + -- ({-3.3000*\dx},{-0.4057*\dy}) + -- ({-3.3100*\dx},{-0.4045*\dy}) + -- ({-3.3200*\dx},{-0.4043*\dy}) + -- ({-3.3300*\dx},{-0.4052*\dy}) + -- ({-3.3400*\dx},{-0.4071*\dy}) + -- ({-3.3500*\dx},{-0.4100*\dy}) + -- ({-3.3600*\dx},{-0.4139*\dy}) + -- ({-3.3700*\dx},{-0.4188*\dy}) + -- ({-3.3800*\dx},{-0.4246*\dy}) + -- ({-3.3900*\dx},{-0.4311*\dy}) + -- ({-3.4000*\dx},{-0.4385*\dy}) + -- ({-3.4100*\dx},{-0.4465*\dy}) + -- ({-3.4200*\dx},{-0.4551*\dy}) + -- ({-3.4300*\dx},{-0.4643*\dy}) + -- ({-3.4400*\dx},{-0.4738*\dy}) + -- ({-3.4500*\dx},{-0.4835*\dy}) + -- ({-3.4600*\dx},{-0.4935*\dy}) + -- ({-3.4700*\dx},{-0.5035*\dy}) + -- ({-3.4800*\dx},{-0.5134*\dy}) + -- ({-3.4900*\dx},{-0.5231*\dy}) + -- ({-3.5000*\dx},{-0.5326*\dy}) + -- ({-3.5100*\dx},{-0.5416*\dy}) + -- ({-3.5200*\dx},{-0.5501*\dy}) + -- ({-3.5300*\dx},{-0.5579*\dy}) + -- ({-3.5400*\dx},{-0.5650*\dy}) + -- ({-3.5500*\dx},{-0.5713*\dy}) + -- ({-3.5600*\dx},{-0.5767*\dy}) + -- ({-3.5700*\dx},{-0.5811*\dy}) + -- ({-3.5800*\dx},{-0.5845*\dy}) + -- ({-3.5900*\dx},{-0.5868*\dy}) + -- ({-3.6000*\dx},{-0.5880*\dy}) + -- ({-3.6100*\dx},{-0.5880*\dy}) + -- ({-3.6200*\dx},{-0.5869*\dy}) + -- ({-3.6300*\dx},{-0.5848*\dy}) + -- ({-3.6400*\dx},{-0.5815*\dy}) + -- ({-3.6500*\dx},{-0.5771*\dy}) + -- ({-3.6600*\dx},{-0.5718*\dy}) + -- ({-3.6700*\dx},{-0.5655*\dy}) + -- ({-3.6800*\dx},{-0.5584*\dy}) + -- ({-3.6900*\dx},{-0.5505*\dy}) + -- ({-3.7000*\dx},{-0.5419*\dy}) + -- ({-3.7100*\dx},{-0.5329*\dy}) + -- ({-3.7200*\dx},{-0.5233*\dy}) + -- ({-3.7300*\dx},{-0.5135*\dy}) + -- ({-3.7400*\dx},{-0.5036*\dy}) + -- ({-3.7500*\dx},{-0.4936*\dy}) + -- ({-3.7600*\dx},{-0.4837*\dy}) + -- ({-3.7700*\dx},{-0.4741*\dy}) + -- ({-3.7800*\dx},{-0.4649*\dy}) + -- ({-3.7900*\dx},{-0.4562*\dy}) + -- ({-3.8000*\dx},{-0.4481*\dy}) + -- ({-3.8100*\dx},{-0.4408*\dy}) + -- ({-3.8200*\dx},{-0.4343*\dy}) + -- ({-3.8300*\dx},{-0.4289*\dy}) + -- ({-3.8400*\dx},{-0.4244*\dy}) + -- ({-3.8500*\dx},{-0.4211*\dy}) + -- ({-3.8600*\dx},{-0.4189*\dy}) + -- ({-3.8700*\dx},{-0.4180*\dy}) + -- ({-3.8800*\dx},{-0.4182*\dy}) + -- ({-3.8900*\dx},{-0.4197*\dy}) + -- ({-3.9000*\dx},{-0.4223*\dy}) + -- ({-3.9100*\dx},{-0.4261*\dy}) + -- ({-3.9200*\dx},{-0.4311*\dy}) + -- ({-3.9300*\dx},{-0.4370*\dy}) + -- ({-3.9400*\dx},{-0.4439*\dy}) + -- ({-3.9500*\dx},{-0.4516*\dy}) + -- ({-3.9600*\dx},{-0.4601*\dy}) + -- ({-3.9700*\dx},{-0.4691*\dy}) + -- ({-3.9800*\dx},{-0.4786*\dy}) + -- ({-3.9900*\dx},{-0.4885*\dy}) + -- ({-4.0000*\dx},{-0.4984*\dy}) + -- ({-4.0100*\dx},{-0.5084*\dy}) + -- ({-4.0200*\dx},{-0.5182*\dy}) + -- ({-4.0300*\dx},{-0.5277*\dy}) + -- ({-4.0400*\dx},{-0.5368*\dy}) + -- ({-4.0500*\dx},{-0.5452*\dy}) + -- ({-4.0600*\dx},{-0.5528*\dy}) + -- ({-4.0700*\dx},{-0.5596*\dy}) + -- ({-4.0800*\dx},{-0.5654*\dy}) + -- ({-4.0900*\dx},{-0.5701*\dy}) + -- ({-4.1000*\dx},{-0.5737*\dy}) + -- ({-4.1100*\dx},{-0.5760*\dy}) + -- ({-4.1200*\dx},{-0.5771*\dy}) + -- ({-4.1300*\dx},{-0.5768*\dy}) + -- ({-4.1400*\dx},{-0.5753*\dy}) + -- ({-4.1500*\dx},{-0.5725*\dy}) + -- ({-4.1600*\dx},{-0.5684*\dy}) + -- ({-4.1700*\dx},{-0.5633*\dy}) + -- ({-4.1800*\dx},{-0.5570*\dy}) + -- ({-4.1900*\dx},{-0.5498*\dy}) + -- ({-4.2000*\dx},{-0.5417*\dy}) + -- ({-4.2100*\dx},{-0.5329*\dy}) + -- ({-4.2200*\dx},{-0.5236*\dy}) + -- ({-4.2300*\dx},{-0.5139*\dy}) + -- ({-4.2400*\dx},{-0.5040*\dy}) + -- ({-4.2500*\dx},{-0.4940*\dy}) + -- ({-4.2600*\dx},{-0.4841*\dy}) + -- ({-4.2700*\dx},{-0.4746*\dy}) + -- ({-4.2800*\dx},{-0.4655*\dy}) + -- ({-4.2900*\dx},{-0.4571*\dy}) + -- ({-4.3000*\dx},{-0.4494*\dy}) + -- ({-4.3100*\dx},{-0.4428*\dy}) + -- ({-4.3200*\dx},{-0.4371*\dy}) + -- ({-4.3300*\dx},{-0.4327*\dy}) + -- ({-4.3400*\dx},{-0.4295*\dy}) + -- ({-4.3500*\dx},{-0.4276*\dy}) + -- ({-4.3600*\dx},{-0.4270*\dy}) + -- ({-4.3700*\dx},{-0.4279*\dy}) + -- ({-4.3800*\dx},{-0.4301*\dy}) + -- ({-4.3900*\dx},{-0.4336*\dy}) + -- ({-4.4000*\dx},{-0.4383*\dy}) + -- ({-4.4100*\dx},{-0.4443*\dy}) + -- ({-4.4200*\dx},{-0.4512*\dy}) + -- ({-4.4300*\dx},{-0.4591*\dy}) + -- ({-4.4400*\dx},{-0.4678*\dy}) + -- ({-4.4500*\dx},{-0.4771*\dy}) + -- ({-4.4600*\dx},{-0.4868*\dy}) + -- ({-4.4700*\dx},{-0.4967*\dy}) + -- ({-4.4800*\dx},{-0.5067*\dy}) + -- ({-4.4900*\dx},{-0.5165*\dy}) + -- ({-4.5000*\dx},{-0.5260*\dy}) + -- ({-4.5100*\dx},{-0.5350*\dy}) + -- ({-4.5200*\dx},{-0.5432*\dy}) + -- ({-4.5300*\dx},{-0.5505*\dy}) + -- ({-4.5400*\dx},{-0.5568*\dy}) + -- ({-4.5500*\dx},{-0.5619*\dy}) + -- ({-4.5600*\dx},{-0.5658*\dy}) + -- ({-4.5700*\dx},{-0.5683*\dy}) + -- ({-4.5800*\dx},{-0.5694*\dy}) + -- ({-4.5900*\dx},{-0.5690*\dy}) + -- ({-4.6000*\dx},{-0.5672*\dy}) + -- ({-4.6100*\dx},{-0.5641*\dy}) + -- ({-4.6200*\dx},{-0.5595*\dy}) + -- ({-4.6300*\dx},{-0.5538*\dy}) + -- ({-4.6400*\dx},{-0.5469*\dy}) + -- ({-4.6500*\dx},{-0.5391*\dy}) + -- ({-4.6600*\dx},{-0.5304*\dy}) + -- ({-4.6700*\dx},{-0.5211*\dy}) + -- ({-4.6800*\dx},{-0.5114*\dy}) + -- ({-4.6900*\dx},{-0.5014*\dy}) + -- ({-4.7000*\dx},{-0.4914*\dy}) + -- ({-4.7100*\dx},{-0.4817*\dy}) + -- ({-4.7200*\dx},{-0.4723*\dy}) + -- ({-4.7300*\dx},{-0.4636*\dy}) + -- ({-4.7400*\dx},{-0.4557*\dy}) + -- ({-4.7500*\dx},{-0.4488*\dy}) + -- ({-4.7600*\dx},{-0.4431*\dy}) + -- ({-4.7700*\dx},{-0.4386*\dy}) + -- ({-4.7800*\dx},{-0.4355*\dy}) + -- ({-4.7900*\dx},{-0.4339*\dy}) + -- ({-4.8000*\dx},{-0.4338*\dy}) + -- ({-4.8100*\dx},{-0.4352*\dy}) + -- ({-4.8200*\dx},{-0.4380*\dy}) + -- ({-4.8300*\dx},{-0.4423*\dy}) + -- ({-4.8400*\dx},{-0.4479*\dy}) + -- ({-4.8500*\dx},{-0.4546*\dy}) + -- ({-4.8600*\dx},{-0.4624*\dy}) + -- ({-4.8700*\dx},{-0.4711*\dy}) + -- ({-4.8800*\dx},{-0.4804*\dy}) + -- ({-4.8900*\dx},{-0.4902*\dy}) + -- ({-4.9000*\dx},{-0.5002*\dy}) + -- ({-4.9100*\dx},{-0.5101*\dy}) + -- ({-4.9200*\dx},{-0.5198*\dy}) + -- ({-4.9300*\dx},{-0.5290*\dy}) + -- ({-4.9400*\dx},{-0.5375*\dy}) + -- ({-4.9500*\dx},{-0.5450*\dy}) + -- ({-4.9600*\dx},{-0.5515*\dy}) + -- ({-4.9700*\dx},{-0.5567*\dy}) + -- ({-4.9800*\dx},{-0.5605*\dy}) + -- ({-4.9900*\dx},{-0.5628*\dy}) +} + +\def\Splotright{ (0,0) + -- ({0.0100*\dx},{0.0000*\dy}) + -- ({0.0200*\dx},{0.0000*\dy}) + -- ({0.0300*\dx},{0.0000*\dy}) + -- ({0.0400*\dx},{0.0000*\dy}) + -- ({0.0500*\dx},{0.0001*\dy}) + -- ({0.0600*\dx},{0.0001*\dy}) + -- ({0.0700*\dx},{0.0002*\dy}) + -- ({0.0800*\dx},{0.0003*\dy}) + -- ({0.0900*\dx},{0.0004*\dy}) + -- ({0.1000*\dx},{0.0005*\dy}) + -- ({0.1100*\dx},{0.0007*\dy}) + -- ({0.1200*\dx},{0.0009*\dy}) + -- ({0.1300*\dx},{0.0012*\dy}) + -- ({0.1400*\dx},{0.0014*\dy}) + -- ({0.1500*\dx},{0.0018*\dy}) + -- ({0.1600*\dx},{0.0021*\dy}) + -- ({0.1700*\dx},{0.0026*\dy}) + -- ({0.1800*\dx},{0.0031*\dy}) + -- ({0.1900*\dx},{0.0036*\dy}) + -- ({0.2000*\dx},{0.0042*\dy}) + -- ({0.2100*\dx},{0.0048*\dy}) + -- ({0.2200*\dx},{0.0056*\dy}) + -- ({0.2300*\dx},{0.0064*\dy}) + -- ({0.2400*\dx},{0.0072*\dy}) + -- ({0.2500*\dx},{0.0082*\dy}) + -- ({0.2600*\dx},{0.0092*\dy}) + -- ({0.2700*\dx},{0.0103*\dy}) + -- ({0.2800*\dx},{0.0115*\dy}) + -- ({0.2900*\dx},{0.0128*\dy}) + -- ({0.3000*\dx},{0.0141*\dy}) + -- ({0.3100*\dx},{0.0156*\dy}) + -- ({0.3200*\dx},{0.0171*\dy}) + -- ({0.3300*\dx},{0.0188*\dy}) + -- ({0.3400*\dx},{0.0205*\dy}) + -- ({0.3500*\dx},{0.0224*\dy}) + -- ({0.3600*\dx},{0.0244*\dy}) + -- ({0.3700*\dx},{0.0264*\dy}) + -- ({0.3800*\dx},{0.0286*\dy}) + -- ({0.3900*\dx},{0.0309*\dy}) + -- ({0.4000*\dx},{0.0334*\dy}) + -- ({0.4100*\dx},{0.0359*\dy}) + -- ({0.4200*\dx},{0.0386*\dy}) + -- ({0.4300*\dx},{0.0414*\dy}) + -- ({0.4400*\dx},{0.0443*\dy}) + -- ({0.4500*\dx},{0.0474*\dy}) + -- ({0.4600*\dx},{0.0506*\dy}) + -- ({0.4700*\dx},{0.0539*\dy}) + -- ({0.4800*\dx},{0.0574*\dy}) + -- ({0.4900*\dx},{0.0610*\dy}) + -- ({0.5000*\dx},{0.0647*\dy}) + -- ({0.5100*\dx},{0.0686*\dy}) + -- ({0.5200*\dx},{0.0727*\dy}) + -- ({0.5300*\dx},{0.0769*\dy}) + -- ({0.5400*\dx},{0.0812*\dy}) + -- ({0.5500*\dx},{0.0857*\dy}) + -- ({0.5600*\dx},{0.0904*\dy}) + -- ({0.5700*\dx},{0.0952*\dy}) + -- ({0.5800*\dx},{0.1001*\dy}) + -- ({0.5900*\dx},{0.1053*\dy}) + -- ({0.6000*\dx},{0.1105*\dy}) + -- ({0.6100*\dx},{0.1160*\dy}) + -- ({0.6200*\dx},{0.1216*\dy}) + -- ({0.6300*\dx},{0.1273*\dy}) + -- ({0.6400*\dx},{0.1333*\dy}) + -- ({0.6500*\dx},{0.1393*\dy}) + -- ({0.6600*\dx},{0.1456*\dy}) + -- ({0.6700*\dx},{0.1520*\dy}) + -- ({0.6800*\dx},{0.1585*\dy}) + -- ({0.6900*\dx},{0.1653*\dy}) + -- ({0.7000*\dx},{0.1721*\dy}) + -- ({0.7100*\dx},{0.1792*\dy}) + -- ({0.7200*\dx},{0.1864*\dy}) + -- ({0.7300*\dx},{0.1937*\dy}) + -- ({0.7400*\dx},{0.2012*\dy}) + -- ({0.7500*\dx},{0.2089*\dy}) + -- ({0.7600*\dx},{0.2167*\dy}) + -- ({0.7700*\dx},{0.2246*\dy}) + -- ({0.7800*\dx},{0.2327*\dy}) + -- ({0.7900*\dx},{0.2410*\dy}) + -- ({0.8000*\dx},{0.2493*\dy}) + -- ({0.8100*\dx},{0.2579*\dy}) + -- ({0.8200*\dx},{0.2665*\dy}) + -- ({0.8300*\dx},{0.2753*\dy}) + -- ({0.8400*\dx},{0.2841*\dy}) + -- ({0.8500*\dx},{0.2932*\dy}) + -- ({0.8600*\dx},{0.3023*\dy}) + -- ({0.8700*\dx},{0.3115*\dy}) + -- ({0.8800*\dx},{0.3208*\dy}) + -- ({0.8900*\dx},{0.3303*\dy}) + -- ({0.9000*\dx},{0.3398*\dy}) + -- ({0.9100*\dx},{0.3494*\dy}) + -- ({0.9200*\dx},{0.3590*\dy}) + -- ({0.9300*\dx},{0.3688*\dy}) + -- ({0.9400*\dx},{0.3786*\dy}) + -- ({0.9500*\dx},{0.3885*\dy}) + -- ({0.9600*\dx},{0.3984*\dy}) + -- ({0.9700*\dx},{0.4083*\dy}) + -- ({0.9800*\dx},{0.4183*\dy}) + -- ({0.9900*\dx},{0.4283*\dy}) + -- ({1.0000*\dx},{0.4383*\dy}) + -- ({1.0100*\dx},{0.4483*\dy}) + -- ({1.0200*\dx},{0.4582*\dy}) + -- ({1.0300*\dx},{0.4682*\dy}) + -- ({1.0400*\dx},{0.4782*\dy}) + -- ({1.0500*\dx},{0.4880*\dy}) + -- ({1.0600*\dx},{0.4979*\dy}) + -- ({1.0700*\dx},{0.5077*\dy}) + -- ({1.0800*\dx},{0.5174*\dy}) + -- ({1.0900*\dx},{0.5270*\dy}) + -- ({1.1000*\dx},{0.5365*\dy}) + -- ({1.1100*\dx},{0.5459*\dy}) + -- ({1.1200*\dx},{0.5552*\dy}) + -- ({1.1300*\dx},{0.5643*\dy}) + -- ({1.1400*\dx},{0.5733*\dy}) + -- ({1.1500*\dx},{0.5821*\dy}) + -- ({1.1600*\dx},{0.5908*\dy}) + -- ({1.1700*\dx},{0.5993*\dy}) + -- ({1.1800*\dx},{0.6075*\dy}) + -- ({1.1900*\dx},{0.6156*\dy}) + -- ({1.2000*\dx},{0.6234*\dy}) + -- ({1.2100*\dx},{0.6310*\dy}) + -- ({1.2200*\dx},{0.6383*\dy}) + -- ({1.2300*\dx},{0.6454*\dy}) + -- ({1.2400*\dx},{0.6522*\dy}) + -- ({1.2500*\dx},{0.6587*\dy}) + -- ({1.2600*\dx},{0.6648*\dy}) + -- ({1.2700*\dx},{0.6707*\dy}) + -- ({1.2800*\dx},{0.6763*\dy}) + -- ({1.2900*\dx},{0.6815*\dy}) + -- ({1.3000*\dx},{0.6863*\dy}) + -- ({1.3100*\dx},{0.6908*\dy}) + -- ({1.3200*\dx},{0.6950*\dy}) + -- ({1.3300*\dx},{0.6987*\dy}) + -- ({1.3400*\dx},{0.7021*\dy}) + -- ({1.3500*\dx},{0.7050*\dy}) + -- ({1.3600*\dx},{0.7076*\dy}) + -- ({1.3700*\dx},{0.7097*\dy}) + -- ({1.3800*\dx},{0.7114*\dy}) + -- ({1.3900*\dx},{0.7127*\dy}) + -- ({1.4000*\dx},{0.7135*\dy}) + -- ({1.4100*\dx},{0.7139*\dy}) + -- ({1.4200*\dx},{0.7139*\dy}) + -- ({1.4300*\dx},{0.7134*\dy}) + -- ({1.4400*\dx},{0.7125*\dy}) + -- ({1.4500*\dx},{0.7111*\dy}) + -- ({1.4600*\dx},{0.7093*\dy}) + -- ({1.4700*\dx},{0.7070*\dy}) + -- ({1.4800*\dx},{0.7043*\dy}) + -- ({1.4900*\dx},{0.7011*\dy}) + -- ({1.5000*\dx},{0.6975*\dy}) + -- ({1.5100*\dx},{0.6935*\dy}) + -- ({1.5200*\dx},{0.6890*\dy}) + -- ({1.5300*\dx},{0.6841*\dy}) + -- ({1.5400*\dx},{0.6788*\dy}) + -- ({1.5500*\dx},{0.6731*\dy}) + -- ({1.5600*\dx},{0.6670*\dy}) + -- ({1.5700*\dx},{0.6605*\dy}) + -- ({1.5800*\dx},{0.6536*\dy}) + -- ({1.5900*\dx},{0.6464*\dy}) + -- ({1.6000*\dx},{0.6389*\dy}) + -- ({1.6100*\dx},{0.6310*\dy}) + -- ({1.6200*\dx},{0.6229*\dy}) + -- ({1.6300*\dx},{0.6144*\dy}) + -- ({1.6400*\dx},{0.6057*\dy}) + -- ({1.6500*\dx},{0.5968*\dy}) + -- ({1.6600*\dx},{0.5876*\dy}) + -- ({1.6700*\dx},{0.5782*\dy}) + -- ({1.6800*\dx},{0.5687*\dy}) + -- ({1.6900*\dx},{0.5590*\dy}) + -- ({1.7000*\dx},{0.5492*\dy}) + -- ({1.7100*\dx},{0.5393*\dy}) + -- ({1.7200*\dx},{0.5293*\dy}) + -- ({1.7300*\dx},{0.5194*\dy}) + -- ({1.7400*\dx},{0.5094*\dy}) + -- ({1.7500*\dx},{0.4994*\dy}) + -- ({1.7600*\dx},{0.4895*\dy}) + -- ({1.7700*\dx},{0.4796*\dy}) + -- ({1.7800*\dx},{0.4699*\dy}) + -- ({1.7900*\dx},{0.4603*\dy}) + -- ({1.8000*\dx},{0.4509*\dy}) + -- ({1.8100*\dx},{0.4418*\dy}) + -- ({1.8200*\dx},{0.4328*\dy}) + -- ({1.8300*\dx},{0.4241*\dy}) + -- ({1.8400*\dx},{0.4157*\dy}) + -- ({1.8500*\dx},{0.4077*\dy}) + -- ({1.8600*\dx},{0.4000*\dy}) + -- ({1.8700*\dx},{0.3927*\dy}) + -- ({1.8800*\dx},{0.3858*\dy}) + -- ({1.8900*\dx},{0.3793*\dy}) + -- ({1.9000*\dx},{0.3733*\dy}) + -- ({1.9100*\dx},{0.3678*\dy}) + -- ({1.9200*\dx},{0.3629*\dy}) + -- ({1.9300*\dx},{0.3584*\dy}) + -- ({1.9400*\dx},{0.3545*\dy}) + -- ({1.9500*\dx},{0.3511*\dy}) + -- ({1.9600*\dx},{0.3484*\dy}) + -- ({1.9700*\dx},{0.3462*\dy}) + -- ({1.9800*\dx},{0.3447*\dy}) + -- ({1.9900*\dx},{0.3437*\dy}) + -- ({2.0000*\dx},{0.3434*\dy}) + -- ({2.0100*\dx},{0.3437*\dy}) + -- ({2.0200*\dx},{0.3447*\dy}) + -- ({2.0300*\dx},{0.3462*\dy}) + -- ({2.0400*\dx},{0.3484*\dy}) + -- ({2.0500*\dx},{0.3513*\dy}) + -- ({2.0600*\dx},{0.3547*\dy}) + -- ({2.0700*\dx},{0.3587*\dy}) + -- ({2.0800*\dx},{0.3633*\dy}) + -- ({2.0900*\dx},{0.3685*\dy}) + -- ({2.1000*\dx},{0.3743*\dy}) + -- ({2.1100*\dx},{0.3805*\dy}) + -- ({2.1200*\dx},{0.3873*\dy}) + -- ({2.1300*\dx},{0.3945*\dy}) + -- ({2.1400*\dx},{0.4022*\dy}) + -- ({2.1500*\dx},{0.4103*\dy}) + -- ({2.1600*\dx},{0.4188*\dy}) + -- ({2.1700*\dx},{0.4276*\dy}) + -- ({2.1800*\dx},{0.4367*\dy}) + -- ({2.1900*\dx},{0.4461*\dy}) + -- ({2.2000*\dx},{0.4557*\dy}) + -- ({2.2100*\dx},{0.4655*\dy}) + -- ({2.2200*\dx},{0.4754*\dy}) + -- ({2.2300*\dx},{0.4853*\dy}) + -- ({2.2400*\dx},{0.4953*\dy}) + -- ({2.2500*\dx},{0.5053*\dy}) + -- ({2.2600*\dx},{0.5152*\dy}) + -- ({2.2700*\dx},{0.5250*\dy}) + -- ({2.2800*\dx},{0.5346*\dy}) + -- ({2.2900*\dx},{0.5440*\dy}) + -- ({2.3000*\dx},{0.5532*\dy}) + -- ({2.3100*\dx},{0.5620*\dy}) + -- ({2.3200*\dx},{0.5704*\dy}) + -- ({2.3300*\dx},{0.5784*\dy}) + -- ({2.3400*\dx},{0.5860*\dy}) + -- ({2.3500*\dx},{0.5931*\dy}) + -- ({2.3600*\dx},{0.5996*\dy}) + -- ({2.3700*\dx},{0.6056*\dy}) + -- ({2.3800*\dx},{0.6110*\dy}) + -- ({2.3900*\dx},{0.6157*\dy}) + -- ({2.4000*\dx},{0.6197*\dy}) + -- ({2.4100*\dx},{0.6230*\dy}) + -- ({2.4200*\dx},{0.6256*\dy}) + -- ({2.4300*\dx},{0.6275*\dy}) + -- ({2.4400*\dx},{0.6286*\dy}) + -- ({2.4500*\dx},{0.6289*\dy}) + -- ({2.4600*\dx},{0.6285*\dy}) + -- ({2.4700*\dx},{0.6273*\dy}) + -- ({2.4800*\dx},{0.6254*\dy}) + -- ({2.4900*\dx},{0.6226*\dy}) + -- ({2.5000*\dx},{0.6192*\dy}) + -- ({2.5100*\dx},{0.6150*\dy}) + -- ({2.5200*\dx},{0.6101*\dy}) + -- ({2.5300*\dx},{0.6045*\dy}) + -- ({2.5400*\dx},{0.5983*\dy}) + -- ({2.5500*\dx},{0.5915*\dy}) + -- ({2.5600*\dx},{0.5842*\dy}) + -- ({2.5700*\dx},{0.5763*\dy}) + -- ({2.5800*\dx},{0.5679*\dy}) + -- ({2.5900*\dx},{0.5591*\dy}) + -- ({2.6000*\dx},{0.5500*\dy}) + -- ({2.6100*\dx},{0.5406*\dy}) + -- ({2.6200*\dx},{0.5309*\dy}) + -- ({2.6300*\dx},{0.5210*\dy}) + -- ({2.6400*\dx},{0.5111*\dy}) + -- ({2.6500*\dx},{0.5011*\dy}) + -- ({2.6600*\dx},{0.4911*\dy}) + -- ({2.6700*\dx},{0.4812*\dy}) + -- ({2.6800*\dx},{0.4715*\dy}) + -- ({2.6900*\dx},{0.4621*\dy}) + -- ({2.7000*\dx},{0.4529*\dy}) + -- ({2.7100*\dx},{0.4441*\dy}) + -- ({2.7200*\dx},{0.4358*\dy}) + -- ({2.7300*\dx},{0.4279*\dy}) + -- ({2.7400*\dx},{0.4207*\dy}) + -- ({2.7500*\dx},{0.4140*\dy}) + -- ({2.7600*\dx},{0.4080*\dy}) + -- ({2.7700*\dx},{0.4027*\dy}) + -- ({2.7800*\dx},{0.3982*\dy}) + -- ({2.7900*\dx},{0.3944*\dy}) + -- ({2.8000*\dx},{0.3915*\dy}) + -- ({2.8100*\dx},{0.3895*\dy}) + -- ({2.8200*\dx},{0.3883*\dy}) + -- ({2.8300*\dx},{0.3880*\dy}) + -- ({2.8400*\dx},{0.3886*\dy}) + -- ({2.8500*\dx},{0.3900*\dy}) + -- ({2.8600*\dx},{0.3924*\dy}) + -- ({2.8700*\dx},{0.3956*\dy}) + -- ({2.8800*\dx},{0.3996*\dy}) + -- ({2.8900*\dx},{0.4045*\dy}) + -- ({2.9000*\dx},{0.4101*\dy}) + -- ({2.9100*\dx},{0.4165*\dy}) + -- ({2.9200*\dx},{0.4235*\dy}) + -- ({2.9300*\dx},{0.4312*\dy}) + -- ({2.9400*\dx},{0.4394*\dy}) + -- ({2.9500*\dx},{0.4481*\dy}) + -- ({2.9600*\dx},{0.4572*\dy}) + -- ({2.9700*\dx},{0.4667*\dy}) + -- ({2.9800*\dx},{0.4764*\dy}) + -- ({2.9900*\dx},{0.4863*\dy}) + -- ({3.0000*\dx},{0.4963*\dy}) + -- ({3.0100*\dx},{0.5063*\dy}) + -- ({3.0200*\dx},{0.5162*\dy}) + -- ({3.0300*\dx},{0.5259*\dy}) + -- ({3.0400*\dx},{0.5354*\dy}) + -- ({3.0500*\dx},{0.5445*\dy}) + -- ({3.0600*\dx},{0.5531*\dy}) + -- ({3.0700*\dx},{0.5613*\dy}) + -- ({3.0800*\dx},{0.5688*\dy}) + -- ({3.0900*\dx},{0.5757*\dy}) + -- ({3.1000*\dx},{0.5818*\dy}) + -- ({3.1100*\dx},{0.5872*\dy}) + -- ({3.1200*\dx},{0.5917*\dy}) + -- ({3.1300*\dx},{0.5952*\dy}) + -- ({3.1400*\dx},{0.5979*\dy}) + -- ({3.1500*\dx},{0.5996*\dy}) + -- ({3.1600*\dx},{0.6003*\dy}) + -- ({3.1700*\dx},{0.6001*\dy}) + -- ({3.1800*\dx},{0.5988*\dy}) + -- ({3.1900*\dx},{0.5966*\dy}) + -- ({3.2000*\dx},{0.5933*\dy}) + -- ({3.2100*\dx},{0.5892*\dy}) + -- ({3.2200*\dx},{0.5842*\dy}) + -- ({3.2300*\dx},{0.5783*\dy}) + -- ({3.2400*\dx},{0.5716*\dy}) + -- ({3.2500*\dx},{0.5642*\dy}) + -- ({3.2600*\dx},{0.5562*\dy}) + -- ({3.2700*\dx},{0.5476*\dy}) + -- ({3.2800*\dx},{0.5385*\dy}) + -- ({3.2900*\dx},{0.5290*\dy}) + -- ({3.3000*\dx},{0.5193*\dy}) + -- ({3.3100*\dx},{0.5094*\dy}) + -- ({3.3200*\dx},{0.4994*\dy}) + -- ({3.3300*\dx},{0.4894*\dy}) + -- ({3.3400*\dx},{0.4796*\dy}) + -- ({3.3500*\dx},{0.4700*\dy}) + -- ({3.3600*\dx},{0.4608*\dy}) + -- ({3.3700*\dx},{0.4521*\dy}) + -- ({3.3800*\dx},{0.4439*\dy}) + -- ({3.3900*\dx},{0.4364*\dy}) + -- ({3.4000*\dx},{0.4296*\dy}) + -- ({3.4100*\dx},{0.4237*\dy}) + -- ({3.4200*\dx},{0.4186*\dy}) + -- ({3.4300*\dx},{0.4145*\dy}) + -- ({3.4400*\dx},{0.4114*\dy}) + -- ({3.4500*\dx},{0.4094*\dy}) + -- ({3.4600*\dx},{0.4084*\dy}) + -- ({3.4700*\dx},{0.4085*\dy}) + -- ({3.4800*\dx},{0.4097*\dy}) + -- ({3.4900*\dx},{0.4119*\dy}) + -- ({3.5000*\dx},{0.4152*\dy}) + -- ({3.5100*\dx},{0.4196*\dy}) + -- ({3.5200*\dx},{0.4249*\dy}) + -- ({3.5300*\dx},{0.4311*\dy}) + -- ({3.5400*\dx},{0.4381*\dy}) + -- ({3.5500*\dx},{0.4459*\dy}) + -- ({3.5600*\dx},{0.4543*\dy}) + -- ({3.5700*\dx},{0.4633*\dy}) + -- ({3.5800*\dx},{0.4727*\dy}) + -- ({3.5900*\dx},{0.4824*\dy}) + -- ({3.6000*\dx},{0.4923*\dy}) + -- ({3.6100*\dx},{0.5023*\dy}) + -- ({3.6200*\dx},{0.5122*\dy}) + -- ({3.6300*\dx},{0.5220*\dy}) + -- ({3.6400*\dx},{0.5314*\dy}) + -- ({3.6500*\dx},{0.5404*\dy}) + -- ({3.6600*\dx},{0.5489*\dy}) + -- ({3.6700*\dx},{0.5567*\dy}) + -- ({3.6800*\dx},{0.5637*\dy}) + -- ({3.6900*\dx},{0.5698*\dy}) + -- ({3.7000*\dx},{0.5750*\dy}) + -- ({3.7100*\dx},{0.5791*\dy}) + -- ({3.7200*\dx},{0.5822*\dy}) + -- ({3.7300*\dx},{0.5841*\dy}) + -- ({3.7400*\dx},{0.5849*\dy}) + -- ({3.7500*\dx},{0.5845*\dy}) + -- ({3.7600*\dx},{0.5830*\dy}) + -- ({3.7700*\dx},{0.5803*\dy}) + -- ({3.7800*\dx},{0.5764*\dy}) + -- ({3.7900*\dx},{0.5715*\dy}) + -- ({3.8000*\dx},{0.5656*\dy}) + -- ({3.8100*\dx},{0.5588*\dy}) + -- ({3.8200*\dx},{0.5512*\dy}) + -- ({3.8300*\dx},{0.5428*\dy}) + -- ({3.8400*\dx},{0.5338*\dy}) + -- ({3.8500*\dx},{0.5244*\dy}) + -- ({3.8600*\dx},{0.5147*\dy}) + -- ({3.8700*\dx},{0.5047*\dy}) + -- ({3.8800*\dx},{0.4947*\dy}) + -- ({3.8900*\dx},{0.4848*\dy}) + -- ({3.9000*\dx},{0.4752*\dy}) + -- ({3.9100*\dx},{0.4660*\dy}) + -- ({3.9200*\dx},{0.4573*\dy}) + -- ({3.9300*\dx},{0.4492*\dy}) + -- ({3.9400*\dx},{0.4420*\dy}) + -- ({3.9500*\dx},{0.4357*\dy}) + -- ({3.9600*\dx},{0.4303*\dy}) + -- ({3.9700*\dx},{0.4261*\dy}) + -- ({3.9800*\dx},{0.4230*\dy}) + -- ({3.9900*\dx},{0.4211*\dy}) + -- ({4.0000*\dx},{0.4205*\dy}) + -- ({4.0100*\dx},{0.4211*\dy}) + -- ({4.0200*\dx},{0.4230*\dy}) + -- ({4.0300*\dx},{0.4261*\dy}) + -- ({4.0400*\dx},{0.4304*\dy}) + -- ({4.0500*\dx},{0.4358*\dy}) + -- ({4.0600*\dx},{0.4422*\dy}) + -- ({4.0700*\dx},{0.4495*\dy}) + -- ({4.0800*\dx},{0.4576*\dy}) + -- ({4.0900*\dx},{0.4665*\dy}) + -- ({4.1000*\dx},{0.4758*\dy}) + -- ({4.1100*\dx},{0.4855*\dy}) + -- ({4.1200*\dx},{0.4955*\dy}) + -- ({4.1300*\dx},{0.5054*\dy}) + -- ({4.1400*\dx},{0.5153*\dy}) + -- ({4.1500*\dx},{0.5249*\dy}) + -- ({4.1600*\dx},{0.5341*\dy}) + -- ({4.1700*\dx},{0.5426*\dy}) + -- ({4.1800*\dx},{0.5504*\dy}) + -- ({4.1900*\dx},{0.5573*\dy}) + -- ({4.2000*\dx},{0.5632*\dy}) + -- ({4.2100*\dx},{0.5680*\dy}) + -- ({4.2200*\dx},{0.5716*\dy}) + -- ({4.2300*\dx},{0.5739*\dy}) + -- ({4.2400*\dx},{0.5749*\dy}) + -- ({4.2500*\dx},{0.5746*\dy}) + -- ({4.2600*\dx},{0.5730*\dy}) + -- ({4.2700*\dx},{0.5700*\dy}) + -- ({4.2800*\dx},{0.5658*\dy}) + -- ({4.2900*\dx},{0.5604*\dy}) + -- ({4.3000*\dx},{0.5540*\dy}) + -- ({4.3100*\dx},{0.5466*\dy}) + -- ({4.3200*\dx},{0.5383*\dy}) + -- ({4.3300*\dx},{0.5294*\dy}) + -- ({4.3400*\dx},{0.5199*\dy}) + -- ({4.3500*\dx},{0.5101*\dy}) + -- ({4.3600*\dx},{0.5001*\dy}) + -- ({4.3700*\dx},{0.4902*\dy}) + -- ({4.3800*\dx},{0.4804*\dy}) + -- ({4.3900*\dx},{0.4711*\dy}) + -- ({4.4000*\dx},{0.4623*\dy}) + -- ({4.4100*\dx},{0.4542*\dy}) + -- ({4.4200*\dx},{0.4471*\dy}) + -- ({4.4300*\dx},{0.4410*\dy}) + -- ({4.4400*\dx},{0.4360*\dy}) + -- ({4.4500*\dx},{0.4323*\dy}) + -- ({4.4600*\dx},{0.4299*\dy}) + -- ({4.4700*\dx},{0.4289*\dy}) + -- ({4.4800*\dx},{0.4293*\dy}) + -- ({4.4900*\dx},{0.4311*\dy}) + -- ({4.5000*\dx},{0.4343*\dy}) + -- ({4.5100*\dx},{0.4387*\dy}) + -- ({4.5200*\dx},{0.4444*\dy}) + -- ({4.5300*\dx},{0.4512*\dy}) + -- ({4.5400*\dx},{0.4590*\dy}) + -- ({4.5500*\dx},{0.4676*\dy}) + -- ({4.5600*\dx},{0.4768*\dy}) + -- ({4.5700*\dx},{0.4864*\dy}) + -- ({4.5800*\dx},{0.4964*\dy}) + -- ({4.5900*\dx},{0.5064*\dy}) + -- ({4.6000*\dx},{0.5162*\dy}) + -- ({4.6100*\dx},{0.5257*\dy}) + -- ({4.6200*\dx},{0.5346*\dy}) + -- ({4.6300*\dx},{0.5427*\dy}) + -- ({4.6400*\dx},{0.5500*\dy}) + -- ({4.6500*\dx},{0.5562*\dy}) + -- ({4.6600*\dx},{0.5611*\dy}) + -- ({4.6700*\dx},{0.5648*\dy}) + -- ({4.6800*\dx},{0.5670*\dy}) + -- ({4.6900*\dx},{0.5678*\dy}) + -- ({4.7000*\dx},{0.5671*\dy}) + -- ({4.7100*\dx},{0.5650*\dy}) + -- ({4.7200*\dx},{0.5615*\dy}) + -- ({4.7300*\dx},{0.5566*\dy}) + -- ({4.7400*\dx},{0.5504*\dy}) + -- ({4.7500*\dx},{0.5432*\dy}) + -- ({4.7600*\dx},{0.5350*\dy}) + -- ({4.7700*\dx},{0.5261*\dy}) + -- ({4.7800*\dx},{0.5166*\dy}) + -- ({4.7900*\dx},{0.5067*\dy}) + -- ({4.8000*\dx},{0.4968*\dy}) + -- ({4.8100*\dx},{0.4869*\dy}) + -- ({4.8200*\dx},{0.4773*\dy}) + -- ({4.8300*\dx},{0.4682*\dy}) + -- ({4.8400*\dx},{0.4600*\dy}) + -- ({4.8500*\dx},{0.4526*\dy}) + -- ({4.8600*\dx},{0.4464*\dy}) + -- ({4.8700*\dx},{0.4414*\dy}) + -- ({4.8800*\dx},{0.4378*\dy}) + -- ({4.8900*\dx},{0.4357*\dy}) + -- ({4.9000*\dx},{0.4351*\dy}) + -- ({4.9100*\dx},{0.4360*\dy}) + -- ({4.9200*\dx},{0.4384*\dy}) + -- ({4.9300*\dx},{0.4423*\dy}) + -- ({4.9400*\dx},{0.4476*\dy}) + -- ({4.9500*\dx},{0.4541*\dy}) + -- ({4.9600*\dx},{0.4618*\dy}) + -- ({4.9700*\dx},{0.4703*\dy}) + -- ({4.9800*\dx},{0.4795*\dy}) + -- ({4.9900*\dx},{0.4892*\dy}) +} + +\def\Splotleft{ (0,0) + -- ({-0.0100*\dx},{-0.0000*\dy}) + -- ({-0.0200*\dx},{-0.0000*\dy}) + -- ({-0.0300*\dx},{-0.0000*\dy}) + -- ({-0.0400*\dx},{-0.0000*\dy}) + -- ({-0.0500*\dx},{-0.0001*\dy}) + -- ({-0.0600*\dx},{-0.0001*\dy}) + -- ({-0.0700*\dx},{-0.0002*\dy}) + -- ({-0.0800*\dx},{-0.0003*\dy}) + -- ({-0.0900*\dx},{-0.0004*\dy}) + -- ({-0.1000*\dx},{-0.0005*\dy}) + -- ({-0.1100*\dx},{-0.0007*\dy}) + -- ({-0.1200*\dx},{-0.0009*\dy}) + -- ({-0.1300*\dx},{-0.0012*\dy}) + -- ({-0.1400*\dx},{-0.0014*\dy}) + -- ({-0.1500*\dx},{-0.0018*\dy}) + -- ({-0.1600*\dx},{-0.0021*\dy}) + -- ({-0.1700*\dx},{-0.0026*\dy}) + -- ({-0.1800*\dx},{-0.0031*\dy}) + -- ({-0.1900*\dx},{-0.0036*\dy}) + -- ({-0.2000*\dx},{-0.0042*\dy}) + -- ({-0.2100*\dx},{-0.0048*\dy}) + -- ({-0.2200*\dx},{-0.0056*\dy}) + -- ({-0.2300*\dx},{-0.0064*\dy}) + -- ({-0.2400*\dx},{-0.0072*\dy}) + -- ({-0.2500*\dx},{-0.0082*\dy}) + -- ({-0.2600*\dx},{-0.0092*\dy}) + -- ({-0.2700*\dx},{-0.0103*\dy}) + -- ({-0.2800*\dx},{-0.0115*\dy}) + -- ({-0.2900*\dx},{-0.0128*\dy}) + -- ({-0.3000*\dx},{-0.0141*\dy}) + -- ({-0.3100*\dx},{-0.0156*\dy}) + -- ({-0.3200*\dx},{-0.0171*\dy}) + -- ({-0.3300*\dx},{-0.0188*\dy}) + -- ({-0.3400*\dx},{-0.0205*\dy}) + -- ({-0.3500*\dx},{-0.0224*\dy}) + -- ({-0.3600*\dx},{-0.0244*\dy}) + -- ({-0.3700*\dx},{-0.0264*\dy}) + -- ({-0.3800*\dx},{-0.0286*\dy}) + -- ({-0.3900*\dx},{-0.0309*\dy}) + -- ({-0.4000*\dx},{-0.0334*\dy}) + -- ({-0.4100*\dx},{-0.0359*\dy}) + -- ({-0.4200*\dx},{-0.0386*\dy}) + -- ({-0.4300*\dx},{-0.0414*\dy}) + -- ({-0.4400*\dx},{-0.0443*\dy}) + -- ({-0.4500*\dx},{-0.0474*\dy}) + -- ({-0.4600*\dx},{-0.0506*\dy}) + -- ({-0.4700*\dx},{-0.0539*\dy}) + -- ({-0.4800*\dx},{-0.0574*\dy}) + -- ({-0.4900*\dx},{-0.0610*\dy}) + -- ({-0.5000*\dx},{-0.0647*\dy}) + -- ({-0.5100*\dx},{-0.0686*\dy}) + -- ({-0.5200*\dx},{-0.0727*\dy}) + -- ({-0.5300*\dx},{-0.0769*\dy}) + -- ({-0.5400*\dx},{-0.0812*\dy}) + -- ({-0.5500*\dx},{-0.0857*\dy}) + -- ({-0.5600*\dx},{-0.0904*\dy}) + -- ({-0.5700*\dx},{-0.0952*\dy}) + -- ({-0.5800*\dx},{-0.1001*\dy}) + -- ({-0.5900*\dx},{-0.1053*\dy}) + -- ({-0.6000*\dx},{-0.1105*\dy}) + -- ({-0.6100*\dx},{-0.1160*\dy}) + -- ({-0.6200*\dx},{-0.1216*\dy}) + -- ({-0.6300*\dx},{-0.1273*\dy}) + -- ({-0.6400*\dx},{-0.1333*\dy}) + -- ({-0.6500*\dx},{-0.1393*\dy}) + -- ({-0.6600*\dx},{-0.1456*\dy}) + -- ({-0.6700*\dx},{-0.1520*\dy}) + -- ({-0.6800*\dx},{-0.1585*\dy}) + -- ({-0.6900*\dx},{-0.1653*\dy}) + -- ({-0.7000*\dx},{-0.1721*\dy}) + -- ({-0.7100*\dx},{-0.1792*\dy}) + -- ({-0.7200*\dx},{-0.1864*\dy}) + -- ({-0.7300*\dx},{-0.1937*\dy}) + -- ({-0.7400*\dx},{-0.2012*\dy}) + -- ({-0.7500*\dx},{-0.2089*\dy}) + -- ({-0.7600*\dx},{-0.2167*\dy}) + -- ({-0.7700*\dx},{-0.2246*\dy}) + -- ({-0.7800*\dx},{-0.2327*\dy}) + -- ({-0.7900*\dx},{-0.2410*\dy}) + -- ({-0.8000*\dx},{-0.2493*\dy}) + -- ({-0.8100*\dx},{-0.2579*\dy}) + -- ({-0.8200*\dx},{-0.2665*\dy}) + -- ({-0.8300*\dx},{-0.2753*\dy}) + -- ({-0.8400*\dx},{-0.2841*\dy}) + -- ({-0.8500*\dx},{-0.2932*\dy}) + -- ({-0.8600*\dx},{-0.3023*\dy}) + -- ({-0.8700*\dx},{-0.3115*\dy}) + -- ({-0.8800*\dx},{-0.3208*\dy}) + -- ({-0.8900*\dx},{-0.3303*\dy}) + -- ({-0.9000*\dx},{-0.3398*\dy}) + -- ({-0.9100*\dx},{-0.3494*\dy}) + -- ({-0.9200*\dx},{-0.3590*\dy}) + -- ({-0.9300*\dx},{-0.3688*\dy}) + -- ({-0.9400*\dx},{-0.3786*\dy}) + -- ({-0.9500*\dx},{-0.3885*\dy}) + -- ({-0.9600*\dx},{-0.3984*\dy}) + -- ({-0.9700*\dx},{-0.4083*\dy}) + -- ({-0.9800*\dx},{-0.4183*\dy}) + -- ({-0.9900*\dx},{-0.4283*\dy}) + -- ({-1.0000*\dx},{-0.4383*\dy}) + -- ({-1.0100*\dx},{-0.4483*\dy}) + -- ({-1.0200*\dx},{-0.4582*\dy}) + -- ({-1.0300*\dx},{-0.4682*\dy}) + -- ({-1.0400*\dx},{-0.4782*\dy}) + -- ({-1.0500*\dx},{-0.4880*\dy}) + -- ({-1.0600*\dx},{-0.4979*\dy}) + -- ({-1.0700*\dx},{-0.5077*\dy}) + -- ({-1.0800*\dx},{-0.5174*\dy}) + -- ({-1.0900*\dx},{-0.5270*\dy}) + -- ({-1.1000*\dx},{-0.5365*\dy}) + -- ({-1.1100*\dx},{-0.5459*\dy}) + -- ({-1.1200*\dx},{-0.5552*\dy}) + -- ({-1.1300*\dx},{-0.5643*\dy}) + -- ({-1.1400*\dx},{-0.5733*\dy}) + -- ({-1.1500*\dx},{-0.5821*\dy}) + -- ({-1.1600*\dx},{-0.5908*\dy}) + -- ({-1.1700*\dx},{-0.5993*\dy}) + -- ({-1.1800*\dx},{-0.6075*\dy}) + -- ({-1.1900*\dx},{-0.6156*\dy}) + -- ({-1.2000*\dx},{-0.6234*\dy}) + -- ({-1.2100*\dx},{-0.6310*\dy}) + -- ({-1.2200*\dx},{-0.6383*\dy}) + -- ({-1.2300*\dx},{-0.6454*\dy}) + -- ({-1.2400*\dx},{-0.6522*\dy}) + -- ({-1.2500*\dx},{-0.6587*\dy}) + -- ({-1.2600*\dx},{-0.6648*\dy}) + -- ({-1.2700*\dx},{-0.6707*\dy}) + -- ({-1.2800*\dx},{-0.6763*\dy}) + -- ({-1.2900*\dx},{-0.6815*\dy}) + -- ({-1.3000*\dx},{-0.6863*\dy}) + -- ({-1.3100*\dx},{-0.6908*\dy}) + -- ({-1.3200*\dx},{-0.6950*\dy}) + -- ({-1.3300*\dx},{-0.6987*\dy}) + -- ({-1.3400*\dx},{-0.7021*\dy}) + -- ({-1.3500*\dx},{-0.7050*\dy}) + -- ({-1.3600*\dx},{-0.7076*\dy}) + -- ({-1.3700*\dx},{-0.7097*\dy}) + -- ({-1.3800*\dx},{-0.7114*\dy}) + -- ({-1.3900*\dx},{-0.7127*\dy}) + -- ({-1.4000*\dx},{-0.7135*\dy}) + -- ({-1.4100*\dx},{-0.7139*\dy}) + -- ({-1.4200*\dx},{-0.7139*\dy}) + -- ({-1.4300*\dx},{-0.7134*\dy}) + -- ({-1.4400*\dx},{-0.7125*\dy}) + -- ({-1.4500*\dx},{-0.7111*\dy}) + -- ({-1.4600*\dx},{-0.7093*\dy}) + -- ({-1.4700*\dx},{-0.7070*\dy}) + -- ({-1.4800*\dx},{-0.7043*\dy}) + -- ({-1.4900*\dx},{-0.7011*\dy}) + -- ({-1.5000*\dx},{-0.6975*\dy}) + -- ({-1.5100*\dx},{-0.6935*\dy}) + -- ({-1.5200*\dx},{-0.6890*\dy}) + -- ({-1.5300*\dx},{-0.6841*\dy}) + -- ({-1.5400*\dx},{-0.6788*\dy}) + -- ({-1.5500*\dx},{-0.6731*\dy}) + -- ({-1.5600*\dx},{-0.6670*\dy}) + -- ({-1.5700*\dx},{-0.6605*\dy}) + -- ({-1.5800*\dx},{-0.6536*\dy}) + -- ({-1.5900*\dx},{-0.6464*\dy}) + -- ({-1.6000*\dx},{-0.6389*\dy}) + -- ({-1.6100*\dx},{-0.6310*\dy}) + -- ({-1.6200*\dx},{-0.6229*\dy}) + -- ({-1.6300*\dx},{-0.6144*\dy}) + -- ({-1.6400*\dx},{-0.6057*\dy}) + -- ({-1.6500*\dx},{-0.5968*\dy}) + -- ({-1.6600*\dx},{-0.5876*\dy}) + -- ({-1.6700*\dx},{-0.5782*\dy}) + -- ({-1.6800*\dx},{-0.5687*\dy}) + -- ({-1.6900*\dx},{-0.5590*\dy}) + -- ({-1.7000*\dx},{-0.5492*\dy}) + -- ({-1.7100*\dx},{-0.5393*\dy}) + -- ({-1.7200*\dx},{-0.5293*\dy}) + -- ({-1.7300*\dx},{-0.5194*\dy}) + -- ({-1.7400*\dx},{-0.5094*\dy}) + -- ({-1.7500*\dx},{-0.4994*\dy}) + -- ({-1.7600*\dx},{-0.4895*\dy}) + -- ({-1.7700*\dx},{-0.4796*\dy}) + -- ({-1.7800*\dx},{-0.4699*\dy}) + -- ({-1.7900*\dx},{-0.4603*\dy}) + -- ({-1.8000*\dx},{-0.4509*\dy}) + -- ({-1.8100*\dx},{-0.4418*\dy}) + -- ({-1.8200*\dx},{-0.4328*\dy}) + -- ({-1.8300*\dx},{-0.4241*\dy}) + -- ({-1.8400*\dx},{-0.4157*\dy}) + -- ({-1.8500*\dx},{-0.4077*\dy}) + -- ({-1.8600*\dx},{-0.4000*\dy}) + -- ({-1.8700*\dx},{-0.3927*\dy}) + -- ({-1.8800*\dx},{-0.3858*\dy}) + -- ({-1.8900*\dx},{-0.3793*\dy}) + -- ({-1.9000*\dx},{-0.3733*\dy}) + -- ({-1.9100*\dx},{-0.3678*\dy}) + -- ({-1.9200*\dx},{-0.3629*\dy}) + -- ({-1.9300*\dx},{-0.3584*\dy}) + -- ({-1.9400*\dx},{-0.3545*\dy}) + -- ({-1.9500*\dx},{-0.3511*\dy}) + -- ({-1.9600*\dx},{-0.3484*\dy}) + -- ({-1.9700*\dx},{-0.3462*\dy}) + -- ({-1.9800*\dx},{-0.3447*\dy}) + -- ({-1.9900*\dx},{-0.3437*\dy}) + -- ({-2.0000*\dx},{-0.3434*\dy}) + -- ({-2.0100*\dx},{-0.3437*\dy}) + -- ({-2.0200*\dx},{-0.3447*\dy}) + -- ({-2.0300*\dx},{-0.3462*\dy}) + -- ({-2.0400*\dx},{-0.3484*\dy}) + -- ({-2.0500*\dx},{-0.3513*\dy}) + -- ({-2.0600*\dx},{-0.3547*\dy}) + -- ({-2.0700*\dx},{-0.3587*\dy}) + -- ({-2.0800*\dx},{-0.3633*\dy}) + -- ({-2.0900*\dx},{-0.3685*\dy}) + -- ({-2.1000*\dx},{-0.3743*\dy}) + -- ({-2.1100*\dx},{-0.3805*\dy}) + -- ({-2.1200*\dx},{-0.3873*\dy}) + -- ({-2.1300*\dx},{-0.3945*\dy}) + -- ({-2.1400*\dx},{-0.4022*\dy}) + -- ({-2.1500*\dx},{-0.4103*\dy}) + -- ({-2.1600*\dx},{-0.4188*\dy}) + -- ({-2.1700*\dx},{-0.4276*\dy}) + -- ({-2.1800*\dx},{-0.4367*\dy}) + -- ({-2.1900*\dx},{-0.4461*\dy}) + -- ({-2.2000*\dx},{-0.4557*\dy}) + -- ({-2.2100*\dx},{-0.4655*\dy}) + -- ({-2.2200*\dx},{-0.4754*\dy}) + -- ({-2.2300*\dx},{-0.4853*\dy}) + -- ({-2.2400*\dx},{-0.4953*\dy}) + -- ({-2.2500*\dx},{-0.5053*\dy}) + -- ({-2.2600*\dx},{-0.5152*\dy}) + -- ({-2.2700*\dx},{-0.5250*\dy}) + -- ({-2.2800*\dx},{-0.5346*\dy}) + -- ({-2.2900*\dx},{-0.5440*\dy}) + -- ({-2.3000*\dx},{-0.5532*\dy}) + -- ({-2.3100*\dx},{-0.5620*\dy}) + -- ({-2.3200*\dx},{-0.5704*\dy}) + -- ({-2.3300*\dx},{-0.5784*\dy}) + -- ({-2.3400*\dx},{-0.5860*\dy}) + -- ({-2.3500*\dx},{-0.5931*\dy}) + -- ({-2.3600*\dx},{-0.5996*\dy}) + -- ({-2.3700*\dx},{-0.6056*\dy}) + -- ({-2.3800*\dx},{-0.6110*\dy}) + -- ({-2.3900*\dx},{-0.6157*\dy}) + -- ({-2.4000*\dx},{-0.6197*\dy}) + -- ({-2.4100*\dx},{-0.6230*\dy}) + -- ({-2.4200*\dx},{-0.6256*\dy}) + -- ({-2.4300*\dx},{-0.6275*\dy}) + -- ({-2.4400*\dx},{-0.6286*\dy}) + -- ({-2.4500*\dx},{-0.6289*\dy}) + -- ({-2.4600*\dx},{-0.6285*\dy}) + -- ({-2.4700*\dx},{-0.6273*\dy}) + -- ({-2.4800*\dx},{-0.6254*\dy}) + -- ({-2.4900*\dx},{-0.6226*\dy}) + -- ({-2.5000*\dx},{-0.6192*\dy}) + -- ({-2.5100*\dx},{-0.6150*\dy}) + -- ({-2.5200*\dx},{-0.6101*\dy}) + -- ({-2.5300*\dx},{-0.6045*\dy}) + -- ({-2.5400*\dx},{-0.5983*\dy}) + -- ({-2.5500*\dx},{-0.5915*\dy}) + -- ({-2.5600*\dx},{-0.5842*\dy}) + -- ({-2.5700*\dx},{-0.5763*\dy}) + -- ({-2.5800*\dx},{-0.5679*\dy}) + -- ({-2.5900*\dx},{-0.5591*\dy}) + -- ({-2.6000*\dx},{-0.5500*\dy}) + -- ({-2.6100*\dx},{-0.5406*\dy}) + -- ({-2.6200*\dx},{-0.5309*\dy}) + -- ({-2.6300*\dx},{-0.5210*\dy}) + -- ({-2.6400*\dx},{-0.5111*\dy}) + -- ({-2.6500*\dx},{-0.5011*\dy}) + -- ({-2.6600*\dx},{-0.4911*\dy}) + -- ({-2.6700*\dx},{-0.4812*\dy}) + -- ({-2.6800*\dx},{-0.4715*\dy}) + -- ({-2.6900*\dx},{-0.4621*\dy}) + -- ({-2.7000*\dx},{-0.4529*\dy}) + -- ({-2.7100*\dx},{-0.4441*\dy}) + -- ({-2.7200*\dx},{-0.4358*\dy}) + -- ({-2.7300*\dx},{-0.4279*\dy}) + -- ({-2.7400*\dx},{-0.4207*\dy}) + -- ({-2.7500*\dx},{-0.4140*\dy}) + -- ({-2.7600*\dx},{-0.4080*\dy}) + -- ({-2.7700*\dx},{-0.4027*\dy}) + -- ({-2.7800*\dx},{-0.3982*\dy}) + -- ({-2.7900*\dx},{-0.3944*\dy}) + -- ({-2.8000*\dx},{-0.3915*\dy}) + -- ({-2.8100*\dx},{-0.3895*\dy}) + -- ({-2.8200*\dx},{-0.3883*\dy}) + -- ({-2.8300*\dx},{-0.3880*\dy}) + -- ({-2.8400*\dx},{-0.3886*\dy}) + -- ({-2.8500*\dx},{-0.3900*\dy}) + -- ({-2.8600*\dx},{-0.3924*\dy}) + -- ({-2.8700*\dx},{-0.3956*\dy}) + -- ({-2.8800*\dx},{-0.3996*\dy}) + -- ({-2.8900*\dx},{-0.4045*\dy}) + -- ({-2.9000*\dx},{-0.4101*\dy}) + -- ({-2.9100*\dx},{-0.4165*\dy}) + -- ({-2.9200*\dx},{-0.4235*\dy}) + -- ({-2.9300*\dx},{-0.4312*\dy}) + -- ({-2.9400*\dx},{-0.4394*\dy}) + -- ({-2.9500*\dx},{-0.4481*\dy}) + -- ({-2.9600*\dx},{-0.4572*\dy}) + -- ({-2.9700*\dx},{-0.4667*\dy}) + -- ({-2.9800*\dx},{-0.4764*\dy}) + -- ({-2.9900*\dx},{-0.4863*\dy}) + -- ({-3.0000*\dx},{-0.4963*\dy}) + -- ({-3.0100*\dx},{-0.5063*\dy}) + -- ({-3.0200*\dx},{-0.5162*\dy}) + -- ({-3.0300*\dx},{-0.5259*\dy}) + -- ({-3.0400*\dx},{-0.5354*\dy}) + -- ({-3.0500*\dx},{-0.5445*\dy}) + -- ({-3.0600*\dx},{-0.5531*\dy}) + -- ({-3.0700*\dx},{-0.5613*\dy}) + -- ({-3.0800*\dx},{-0.5688*\dy}) + -- ({-3.0900*\dx},{-0.5757*\dy}) + -- ({-3.1000*\dx},{-0.5818*\dy}) + -- ({-3.1100*\dx},{-0.5872*\dy}) + -- ({-3.1200*\dx},{-0.5917*\dy}) + -- ({-3.1300*\dx},{-0.5952*\dy}) + -- ({-3.1400*\dx},{-0.5979*\dy}) + -- ({-3.1500*\dx},{-0.5996*\dy}) + -- ({-3.1600*\dx},{-0.6003*\dy}) + -- ({-3.1700*\dx},{-0.6001*\dy}) + -- ({-3.1800*\dx},{-0.5988*\dy}) + -- ({-3.1900*\dx},{-0.5966*\dy}) + -- ({-3.2000*\dx},{-0.5933*\dy}) + -- ({-3.2100*\dx},{-0.5892*\dy}) + -- ({-3.2200*\dx},{-0.5842*\dy}) + -- ({-3.2300*\dx},{-0.5783*\dy}) + -- ({-3.2400*\dx},{-0.5716*\dy}) + -- ({-3.2500*\dx},{-0.5642*\dy}) + -- ({-3.2600*\dx},{-0.5562*\dy}) + -- ({-3.2700*\dx},{-0.5476*\dy}) + -- ({-3.2800*\dx},{-0.5385*\dy}) + -- ({-3.2900*\dx},{-0.5290*\dy}) + -- ({-3.3000*\dx},{-0.5193*\dy}) + -- ({-3.3100*\dx},{-0.5094*\dy}) + -- ({-3.3200*\dx},{-0.4994*\dy}) + -- ({-3.3300*\dx},{-0.4894*\dy}) + -- ({-3.3400*\dx},{-0.4796*\dy}) + -- ({-3.3500*\dx},{-0.4700*\dy}) + -- ({-3.3600*\dx},{-0.4608*\dy}) + -- ({-3.3700*\dx},{-0.4521*\dy}) + -- ({-3.3800*\dx},{-0.4439*\dy}) + -- ({-3.3900*\dx},{-0.4364*\dy}) + -- ({-3.4000*\dx},{-0.4296*\dy}) + -- ({-3.4100*\dx},{-0.4237*\dy}) + -- ({-3.4200*\dx},{-0.4186*\dy}) + -- ({-3.4300*\dx},{-0.4145*\dy}) + -- ({-3.4400*\dx},{-0.4114*\dy}) + -- ({-3.4500*\dx},{-0.4094*\dy}) + -- ({-3.4600*\dx},{-0.4084*\dy}) + -- ({-3.4700*\dx},{-0.4085*\dy}) + -- ({-3.4800*\dx},{-0.4097*\dy}) + -- ({-3.4900*\dx},{-0.4119*\dy}) + -- ({-3.5000*\dx},{-0.4152*\dy}) + -- ({-3.5100*\dx},{-0.4196*\dy}) + -- ({-3.5200*\dx},{-0.4249*\dy}) + -- ({-3.5300*\dx},{-0.4311*\dy}) + -- ({-3.5400*\dx},{-0.4381*\dy}) + -- ({-3.5500*\dx},{-0.4459*\dy}) + -- ({-3.5600*\dx},{-0.4543*\dy}) + -- ({-3.5700*\dx},{-0.4633*\dy}) + -- ({-3.5800*\dx},{-0.4727*\dy}) + -- ({-3.5900*\dx},{-0.4824*\dy}) + -- ({-3.6000*\dx},{-0.4923*\dy}) + -- ({-3.6100*\dx},{-0.5023*\dy}) + -- ({-3.6200*\dx},{-0.5122*\dy}) + -- ({-3.6300*\dx},{-0.5220*\dy}) + -- ({-3.6400*\dx},{-0.5314*\dy}) + -- ({-3.6500*\dx},{-0.5404*\dy}) + -- ({-3.6600*\dx},{-0.5489*\dy}) + -- ({-3.6700*\dx},{-0.5567*\dy}) + -- ({-3.6800*\dx},{-0.5637*\dy}) + -- ({-3.6900*\dx},{-0.5698*\dy}) + -- ({-3.7000*\dx},{-0.5750*\dy}) + -- ({-3.7100*\dx},{-0.5791*\dy}) + -- ({-3.7200*\dx},{-0.5822*\dy}) + -- ({-3.7300*\dx},{-0.5841*\dy}) + -- ({-3.7400*\dx},{-0.5849*\dy}) + -- ({-3.7500*\dx},{-0.5845*\dy}) + -- ({-3.7600*\dx},{-0.5830*\dy}) + -- ({-3.7700*\dx},{-0.5803*\dy}) + -- ({-3.7800*\dx},{-0.5764*\dy}) + -- ({-3.7900*\dx},{-0.5715*\dy}) + -- ({-3.8000*\dx},{-0.5656*\dy}) + -- ({-3.8100*\dx},{-0.5588*\dy}) + -- ({-3.8200*\dx},{-0.5512*\dy}) + -- ({-3.8300*\dx},{-0.5428*\dy}) + -- ({-3.8400*\dx},{-0.5338*\dy}) + -- ({-3.8500*\dx},{-0.5244*\dy}) + -- ({-3.8600*\dx},{-0.5147*\dy}) + -- ({-3.8700*\dx},{-0.5047*\dy}) + -- ({-3.8800*\dx},{-0.4947*\dy}) + -- ({-3.8900*\dx},{-0.4848*\dy}) + -- ({-3.9000*\dx},{-0.4752*\dy}) + -- ({-3.9100*\dx},{-0.4660*\dy}) + -- ({-3.9200*\dx},{-0.4573*\dy}) + -- ({-3.9300*\dx},{-0.4492*\dy}) + -- ({-3.9400*\dx},{-0.4420*\dy}) + -- ({-3.9500*\dx},{-0.4357*\dy}) + -- ({-3.9600*\dx},{-0.4303*\dy}) + -- ({-3.9700*\dx},{-0.4261*\dy}) + -- ({-3.9800*\dx},{-0.4230*\dy}) + -- ({-3.9900*\dx},{-0.4211*\dy}) + -- ({-4.0000*\dx},{-0.4205*\dy}) + -- ({-4.0100*\dx},{-0.4211*\dy}) + -- ({-4.0200*\dx},{-0.4230*\dy}) + -- ({-4.0300*\dx},{-0.4261*\dy}) + -- ({-4.0400*\dx},{-0.4304*\dy}) + -- ({-4.0500*\dx},{-0.4358*\dy}) + -- ({-4.0600*\dx},{-0.4422*\dy}) + -- ({-4.0700*\dx},{-0.4495*\dy}) + -- ({-4.0800*\dx},{-0.4576*\dy}) + -- ({-4.0900*\dx},{-0.4665*\dy}) + -- ({-4.1000*\dx},{-0.4758*\dy}) + -- ({-4.1100*\dx},{-0.4855*\dy}) + -- ({-4.1200*\dx},{-0.4955*\dy}) + -- ({-4.1300*\dx},{-0.5054*\dy}) + -- ({-4.1400*\dx},{-0.5153*\dy}) + -- ({-4.1500*\dx},{-0.5249*\dy}) + -- ({-4.1600*\dx},{-0.5341*\dy}) + -- ({-4.1700*\dx},{-0.5426*\dy}) + -- ({-4.1800*\dx},{-0.5504*\dy}) + -- ({-4.1900*\dx},{-0.5573*\dy}) + -- ({-4.2000*\dx},{-0.5632*\dy}) + -- ({-4.2100*\dx},{-0.5680*\dy}) + -- ({-4.2200*\dx},{-0.5716*\dy}) + -- ({-4.2300*\dx},{-0.5739*\dy}) + -- ({-4.2400*\dx},{-0.5749*\dy}) + -- ({-4.2500*\dx},{-0.5746*\dy}) + -- ({-4.2600*\dx},{-0.5730*\dy}) + -- ({-4.2700*\dx},{-0.5700*\dy}) + -- ({-4.2800*\dx},{-0.5658*\dy}) + -- ({-4.2900*\dx},{-0.5604*\dy}) + -- ({-4.3000*\dx},{-0.5540*\dy}) + -- ({-4.3100*\dx},{-0.5466*\dy}) + -- ({-4.3200*\dx},{-0.5383*\dy}) + -- ({-4.3300*\dx},{-0.5294*\dy}) + -- ({-4.3400*\dx},{-0.5199*\dy}) + -- ({-4.3500*\dx},{-0.5101*\dy}) + -- ({-4.3600*\dx},{-0.5001*\dy}) + -- ({-4.3700*\dx},{-0.4902*\dy}) + -- ({-4.3800*\dx},{-0.4804*\dy}) + -- ({-4.3900*\dx},{-0.4711*\dy}) + -- ({-4.4000*\dx},{-0.4623*\dy}) + -- ({-4.4100*\dx},{-0.4542*\dy}) + -- ({-4.4200*\dx},{-0.4471*\dy}) + -- ({-4.4300*\dx},{-0.4410*\dy}) + -- ({-4.4400*\dx},{-0.4360*\dy}) + -- ({-4.4500*\dx},{-0.4323*\dy}) + -- ({-4.4600*\dx},{-0.4299*\dy}) + -- ({-4.4700*\dx},{-0.4289*\dy}) + -- ({-4.4800*\dx},{-0.4293*\dy}) + -- ({-4.4900*\dx},{-0.4311*\dy}) + -- ({-4.5000*\dx},{-0.4343*\dy}) + -- ({-4.5100*\dx},{-0.4387*\dy}) + -- ({-4.5200*\dx},{-0.4444*\dy}) + -- ({-4.5300*\dx},{-0.4512*\dy}) + -- ({-4.5400*\dx},{-0.4590*\dy}) + -- ({-4.5500*\dx},{-0.4676*\dy}) + -- ({-4.5600*\dx},{-0.4768*\dy}) + -- ({-4.5700*\dx},{-0.4864*\dy}) + -- ({-4.5800*\dx},{-0.4964*\dy}) + -- ({-4.5900*\dx},{-0.5064*\dy}) + -- ({-4.6000*\dx},{-0.5162*\dy}) + -- ({-4.6100*\dx},{-0.5257*\dy}) + -- ({-4.6200*\dx},{-0.5346*\dy}) + -- ({-4.6300*\dx},{-0.5427*\dy}) + -- ({-4.6400*\dx},{-0.5500*\dy}) + -- ({-4.6500*\dx},{-0.5562*\dy}) + -- ({-4.6600*\dx},{-0.5611*\dy}) + -- ({-4.6700*\dx},{-0.5648*\dy}) + -- ({-4.6800*\dx},{-0.5670*\dy}) + -- ({-4.6900*\dx},{-0.5678*\dy}) + -- ({-4.7000*\dx},{-0.5671*\dy}) + -- ({-4.7100*\dx},{-0.5650*\dy}) + -- ({-4.7200*\dx},{-0.5615*\dy}) + -- ({-4.7300*\dx},{-0.5566*\dy}) + -- ({-4.7400*\dx},{-0.5504*\dy}) + -- ({-4.7500*\dx},{-0.5432*\dy}) + -- ({-4.7600*\dx},{-0.5350*\dy}) + -- ({-4.7700*\dx},{-0.5261*\dy}) + -- ({-4.7800*\dx},{-0.5166*\dy}) + -- ({-4.7900*\dx},{-0.5067*\dy}) + -- ({-4.8000*\dx},{-0.4968*\dy}) + -- ({-4.8100*\dx},{-0.4869*\dy}) + -- ({-4.8200*\dx},{-0.4773*\dy}) + -- ({-4.8300*\dx},{-0.4682*\dy}) + -- ({-4.8400*\dx},{-0.4600*\dy}) + -- ({-4.8500*\dx},{-0.4526*\dy}) + -- ({-4.8600*\dx},{-0.4464*\dy}) + -- ({-4.8700*\dx},{-0.4414*\dy}) + -- ({-4.8800*\dx},{-0.4378*\dy}) + -- ({-4.8900*\dx},{-0.4357*\dy}) + -- ({-4.9000*\dx},{-0.4351*\dy}) + -- ({-4.9100*\dx},{-0.4360*\dy}) + -- ({-4.9200*\dx},{-0.4384*\dy}) + -- ({-4.9300*\dx},{-0.4423*\dy}) + -- ({-4.9400*\dx},{-0.4476*\dy}) + -- ({-4.9500*\dx},{-0.4541*\dy}) + -- ({-4.9600*\dx},{-0.4618*\dy}) + -- ({-4.9700*\dx},{-0.4703*\dy}) + -- ({-4.9800*\dx},{-0.4795*\dy}) + -- ({-4.9900*\dx},{-0.4892*\dy}) +} + diff --git a/vorlesungen/slides/fresnel/eulerspirale.m b/vorlesungen/slides/fresnel/eulerspirale.m index 312541a..84e3696 100644 --- a/vorlesungen/slides/fresnel/eulerspirale.m +++ b/vorlesungen/slides/fresnel/eulerspirale.m @@ -4,12 +4,15 @@ # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue # global n; -n = 10000; +n = 1000; global tmax; tmax = 10; +global N; +N = round(n*5/tmax); function retval = f(x, t) - retval = [ cos(t*t); sin(t*t) ]; + x = pi * t^2 / 2; + retval = [ cos(x); sin(x) ]; endfunction x0 = [ 0; 0 ]; @@ -23,12 +26,36 @@ fprintf(fn, "\\def\\fresnela{ (0,0)"); for i = (2:n) fprintf(fn, "\n\t-- (%.4f,%.4f)", c(i,1), c(i,2)); end -fprintf(fn, "\n}\n"); +fprintf(fn, "\n}\n\n"); fprintf(fn, "\\def\\fresnelb{ (0,0)"); for i = (2:n) fprintf(fn, "\n\t-- (%.4f,%.4f)", -c(i,1), -c(i,2)); end -fprintf(fn, "\n}\n"); +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); fclose(fn); diff --git a/vorlesungen/slides/fresnel/integrale.tex b/vorlesungen/slides/fresnel/integrale.tex index 7798932..906aec1 100644 --- a/vorlesungen/slides/fresnel/integrale.tex +++ b/vorlesungen/slides/fresnel/integrale.tex @@ -1,10 +1,11 @@ % -% fresnel.tex -- slide template +% integrale.tex -- Definition der Fresnel Integrale % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % \bgroup \input{../slides/fresnel/eulerpath.tex} +\definecolor{darkgreen}{rgb}{0,0.6,0} \begin{frame}[t] \setlength{\abovedisplayskip}{5pt} \setlength{\belowdisplayskip}{5pt} @@ -15,57 +16,103 @@ \begin{block}{Definition} Fresnel-Integrale: \begin{align*} -S(t) +\color{red}S(t) &= -\int_0^t \sin(\tau^2)\,d\tau +\int_0^t \sin\biggl(\frac{\pi\tau^2}2\biggr)\,d\tau \\ -C(t) +\color{blue}C(t) &= -\int_0^t \cos(\tau^2)\,d\tau +\int_0^t \cos\biggl(\frac{\pi\tau^2}2\biggr)\,d\tau \end{align*} -\uncover<2->{% +\uncover<3->{% Können nicht in geschlossener Form ausgewertet werden. } \end{block} -\uncover<3->{% -\begin{block}{Kurve} +\uncover<4->{% +\begin{block}{Euler-Spirale} \[ -\gamma(t) +\gamma_a(t) = \begin{pmatrix} -S(t)\\C(t) +C_a(t)\\S_a(t) +\end{pmatrix} += +\begin{pmatrix} +\displaystyle +\int_0^t \cos (a\tau^2)\,d\tau\\[8pt] +\displaystyle +\int_0^t \sin (a\tau^2)\,d\tau \end{pmatrix} \] \end{block}} \end{column} \begin{column}{0.48\textwidth} -\uncover<4->{% -\begin{block}{Euler-Spirale} +\ifthenelse{\boolean{presentation}}{ +\only<2-4>{% \begin{center} -\begin{tikzpicture}[>=latex,thick,scale=2.7] +\begin{tikzpicture}[>=latex,thick,scale=1] +\def\dx{0.6} +\def\dy{1.5} -\draw[->] (-1.05,0) -- (1.05,0) coordinate[label={$C(t)$}]; -\draw[->] (0,-1.05) -- (0,1.05) coordinate[label={right:$S(t)$}]; +\begin{scope} + \draw[color=gray!50] (0,{0.5*\dy}) -- (3,{0.5*\dy}); + \draw[color=gray!50] (0,{-0.5*\dy}) -- (-3,{-0.5*\dy}); + \draw[->] (-3,0) -- (3.3,0) coordinate[label={$t$}]; + \draw[->] (0,-1.5) -- (0,1.5) coordinate[label={left:$S(t)$}]; + \draw (-0.1,{0.5*\dy}) -- (0.1,{0.5*\dy}); + \node at (-0.1,{0.5*\dy}) [left] {$\frac12$}; + \draw (-0.1,{-0.5*\dy}) -- (0.1,{-0.5*\dy}); + \node at (0.1,{-0.5*\dy}) [right] {$-\frac12$}; + \draw[color=red,line width=1.4pt] \Splotright; + \draw[color=red,line width=1.4pt] \Splotleft; +\end{scope} -\draw[color=red,line width=1.4pt] \fresnela; -\draw[color=red,line width=1.4pt] \fresnelb; +\begin{scope}[yshift=-3.4cm] + \draw[color=gray!50] (0,{0.5*\dy}) -- (3,{0.5*\dy}); + \draw[color=gray!50] (0,{-0.5*\dy}) -- (-3,{-0.5*\dy}); + \draw[->] (-3,0) -- (3.3,0) coordinate[label={$t$}]; + \draw[->] (0,-1.5) -- (0,1.5) coordinate[label={left:$C(t)$}]; + \draw (-0.1,{0.5*\dy}) -- (0.1,{0.5*\dy}); + \node at (-0.1,{0.5*\dy}) [left] {$\frac12$}; + \draw (-0.1,{-0.5*\dy}) -- (0.1,{-0.5*\dy}); + \node at (0.1,{-0.5*\dy}) [right] {$-\frac12$}; + \draw[color=blue,line width=1.4pt] \Cplotright; + \draw[color=blue,line width=1.4pt] \Cplotleft; +\end{scope} -\fill[color=blue] ({sqrt(3.14159/8)},{sqrt(3.14159/8)}) circle[radius=0.02]; -\fill[color=blue] ({-sqrt(3.14159/8)},{-sqrt(3.14159/8)}) circle[radius=0.02]; +\end{tikzpicture} +\end{center} +}}{} +\uncover<5->{% +\begin{center} +\begin{tikzpicture}[>=latex,thick,scale=3.5] + +\draw[color=gray!50] (-0.5,-0.5) rectangle (0.5,0.5); + +\draw[->] (-0.8,0) -- (0.9,0) coordinate[label={$\color{blue}C(t)$}]; +\draw[->] (0,-0.8) -- (0,0.9) coordinate[label={right:$\color{red}S(t)$}]; + +\draw[color=darkgreen,line width=1.0pt] \fresnela; +\draw[color=darkgreen,line width=1.0pt] \fresnelb; + +\fill[color=orange] (0.5,0.5) circle[radius=0.02]; +\fill[color=orange] (-0.5,-0.5) circle[radius=0.02]; -\draw (1,-0.03) -- (1,0.03); -\node at (1,-0.03) [below] {$1$}; -\draw (-1,-0.03) -- (-1,0.03); -\node at (-1,0.03) [above] {$-1$}; -\draw (-0.03,1) -- (0.03,1); -\node at (-0.03,1) [left] {$1$}; -\draw (-0.03,-1) -- (0.03,-1); -\node at (0.03,-1) [right] {$-1$}; -\node at (0,0) [below right] {$0$}; +\draw (0.5,-0.02) -- (0.5,0.02); +\node at (0.5,-0.02) [below right] {$\frac12$}; + +\draw (-0.5,-0.02) -- (-0.5,0.02); +\node at (-0.5,0.02) [above left] {$-\frac12$}; + +\draw (-0.01,0.5) -- (0.02,0.5); +\node at (-0.02,0.5) [above left] {$\frac12$}; + +\draw (-0.02,-0.5) -- (0.02,-0.5); +\node at (0.02,-0.5) [below right] {$-\frac12$}; \end{tikzpicture} \end{center} -\end{block}} +} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/fresnel/klothoide.tex b/vorlesungen/slides/fresnel/klothoide.tex index dcf52be..bf43644 100644 --- a/vorlesungen/slides/fresnel/klothoide.tex +++ b/vorlesungen/slides/fresnel/klothoide.tex @@ -13,15 +13,17 @@ \begin{column}{0.48\textwidth} \begin{block}{Krümmung der Euler-Spirale} \begin{align*} -\frac{d}{dt}\gamma(t) +\frac{d}{dt}\gamma_1(t) &= +\dot{\gamma}_1(t) += \begin{pmatrix} \cos t^2\\ \sin t^2 \end{pmatrix} \intertext{\uncover<2->{Bogenlänge:}} \uncover<2->{ -|\dot{\gamma}(t)| +|\dot{\gamma}_1(t)| &= \sqrt{\cos^2 t^2 + \sin^2 t^2} = @@ -47,13 +49,18 @@ $\Rightarrow$ Krümmung ist proportional zur Bogenlänge \uncover<6->{% \begin{block}{Definition} Eine Kurve, deren Krümmung proportional zur Bogenlänge ist, heisst -{\em Klothoid} +{\em Klothoide} \end{block}} \uncover<7->{% \begin{block}{Anwendung} +\begin{itemize} +\item<8-> Strassenbau: Um mit konstanter Geschwindigkeit auf einer -Klothoidenkurve zu fahren, muss man das Lenkrad mit konstanter Geschwindigkeit +Klothoide zu fahren, muss man das Lenkrad mit konstanter Geschwindigkeit drehen +\item<9-> +Apfel + Sparschäler +\end{itemize} \end{block}} \end{column} \end{columns} diff --git a/vorlesungen/slides/fresnel/kruemmung.tex b/vorlesungen/slides/fresnel/kruemmung.tex index e75611b..06f6b9b 100644 --- a/vorlesungen/slides/fresnel/kruemmung.tex +++ b/vorlesungen/slides/fresnel/kruemmung.tex @@ -1,5 +1,5 @@ % -% kruemmung.tex -- slide template +% kruemmung.tex -- Kruemmung % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % diff --git a/vorlesungen/slides/fresnel/numerik.tex b/vorlesungen/slides/fresnel/numerik.tex index 5c6f96d..0bd4d5a 100644 --- a/vorlesungen/slides/fresnel/numerik.tex +++ b/vorlesungen/slides/fresnel/numerik.tex @@ -1,5 +1,5 @@ % -% numerik.tex -- slide template +% numerik.tex -- numerische Berechnung der Fresnel Integrale % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % @@ -13,27 +13,38 @@ \begin{column}{0.48\textwidth} \begin{block}{Taylor-Reihe} \begin{align*} -\sin t^2 +\sin t^{\uncover<2->{\color<2>{red}2}} &= \sum_{k=0}^\infty -(-1)^k \frac{t^{2k+1}}{(2k+1)!} +(-1)^k \frac{t^{ +\ifthenelse{\boolean{presentation}}{\only<1>{2k+1}}{} +\only<2->{\color<2>{red}4k+2} +} +}{ +(2k+1)! +} \\ %\int \sin t^2\,dt -\uncover<2->{ -S(t) +\uncover<4->{ +S_1(t) &= \sum_{k=0}^\infty (-1)^k \frac{t^{4k+3}}{(2k+1)!(4n+3)} } \\ -\cos t^2 +\cos t^{\uncover<3->{\color<3>{red}2}} &= \sum_{k=0}^\infty -(-1)^k \frac{t^{2k}}{(2k)!} +(-1)^k \frac{t^{ +\ifthenelse{\boolean{presentation}}{\only<-2>{2k}}{} +\only<3->{\color<3>{red}4k}} +}{ +(2k)! +} \\ %\int \sin t^2\,dt -\uncover<3->{ -C(t) +\uncover<5->{ +C_1(t) &= \sum_{k=0}^\infty (-1)^k \frac{t^{4k+1}}{(2k)!(4k+1)} @@ -42,23 +53,34 @@ C(t) \end{block} \end{column} \begin{column}{0.48\textwidth} -\uncover<4->{ +\uncover<6->{ \begin{block}{Differentialgleichung} \[ -\dot{\gamma}(t) +\dot{\gamma}_1(t) = \begin{pmatrix} -\sin t^2\\ \cos t^2 +\cos t^2\\ \sin t^2 \end{pmatrix} +\uncover<7->{ +\; +\to +\; +\gamma_1(t) += +\begin{pmatrix} +C_1(t)\\S_1(t) +\end{pmatrix} +} \] \end{block}} -\uncover<5->{% +\uncover<8->{% \begin{block}{Hypergeometrische Reihen} \begin{align*} -\uncover<6->{% +\uncover<9->{% S(t) &= -\frac{\pi z^3}{6}\, +\frac{\pi z^3}{6} +\cdot \mathstrut_1F_2\biggl( \begin{matrix}\frac34\\\frac32,\frac74\end{matrix} ; @@ -66,10 +88,11 @@ S(t) \biggr) } \\ -\uncover<7->{ +\uncover<10->{ C(t) &= -z\, +z +\cdot \mathstrut_1F_2\biggl( \begin{matrix}\frac14\\\frac12,\frac54\end{matrix} ; @@ -79,5 +102,23 @@ z\, \end{block}} \end{column} \end{columns} +\uncover<11->{% +\begin{block}{Komplexe Fehlerfunktion} +\[ +\left. +\begin{matrix} +S(z)\\ +C(z) +\end{matrix} +\right\} += +\frac{1\pm i}{4} +\left( +\operatorname{erf}\biggl({\frac{1+i}2}\sqrt{\pi}z\biggr) +\mp i +\operatorname{erf}\biggl({\frac{1-i}2}\sqrt{\pi}z\biggr) +\right) +\] +\end{block}} \end{frame} \egroup diff --git a/vorlesungen/slides/fresnel/test.tex b/vorlesungen/slides/fresnel/test.tex deleted file mode 100644 index 6c2f25b..0000000 --- a/vorlesungen/slides/fresnel/test.tex +++ /dev/null @@ -1,19 +0,0 @@ -% -% template.tex -- slide template -% -% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -% -\bgroup -\begin{frame}[t] -\setlength{\abovedisplayskip}{5pt} -\setlength{\belowdisplayskip}{5pt} -\frametitle{Template für Klothoide} -\vspace{-20pt} -\begin{columns}[t,onlytextwidth] -\begin{column}{0.48\textwidth} -\end{column} -\begin{column}{0.48\textwidth} -\end{column} -\end{columns} -\end{frame} -\egroup -- cgit v1.2.1 From a7a12c313b1a4fb528337eb354668e69d6d20942 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 11 May 2022 22:13:59 +0200 Subject: dreiecksgraphik --- buch/papers/nav/images/Makefile | 11 ++++++ buch/papers/nav/images/dreieck.tex | 68 ++++++++++++++++++++++++++++++++++++++ buch/papers/nav/images/macros.tex | 54 ++++++++++++++++++++++++++++++ buch/papers/nav/images/pk.m | 55 ++++++++++++++++++++++++++++++ 4 files changed, 188 insertions(+) create mode 100644 buch/papers/nav/images/Makefile create mode 100644 buch/papers/nav/images/dreieck.tex create mode 100644 buch/papers/nav/images/macros.tex create mode 100644 buch/papers/nav/images/pk.m diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile new file mode 100644 index 0000000..a0d7b34 --- /dev/null +++ b/buch/papers/nav/images/Makefile @@ -0,0 +1,11 @@ +# +# Makefile to build images +# +# (c) 2022 +# + +dreieck.pdf: dreieck.tex dreieckdata.tex macros.tex + pdflatex dreieck.tex + +dreieckdata.tex: pk.m + octave pk.m diff --git a/buch/papers/nav/images/dreieck.tex b/buch/papers/nav/images/dreieck.tex new file mode 100644 index 0000000..55f6a81 --- /dev/null +++ b/buch/papers/nav/images/dreieck.tex @@ -0,0 +1,68 @@ +% +% dreieck.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +\def\punktbeschriftung{ + \node at (A) [above] {$A$}; + \node at (B) [left] {$B$}; + \node at (C) [right] {$C$}; + \node at (P) [below] {$P$}; +} + +\winkelKappa{gray} + +\winkelAlpha{red} +\winkelGamma{blue} +\winkelBeta{darkgreen} + +\winkelOmega{gray} +\winkelBetaEins{brown} + +\seiteC{black} +\seiteB{black} +\seiteA{black} + +\seiteL{gray} +\seitePB{gray} +\seitePC{gray} + +\draw[line width=1.4pt] \kanteAB; +\draw[line width=1.4pt] \kanteAC; +\draw[color=gray] \kanteAP; +\draw[line width=1.4pt] \kanteBC; +\draw[color=gray] \kanteBP; +\draw[color=gray] \kanteCP; + +\punkt{(A)}{black}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{gray}; + +\punktbeschriftung + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/macros.tex b/buch/papers/nav/images/macros.tex new file mode 100644 index 0000000..69a620d --- /dev/null +++ b/buch/papers/nav/images/macros.tex @@ -0,0 +1,54 @@ +\def\winkelAlpha#1{ + \begin{scope} + \clip (A) circle[radius=1.1]; + \fill[color=#1!20] \kanteAB -- \kanteCA -- cycle; + \end{scope} + \node[color=#1] at ($(A)+(222:0.82)$) {$\alpha$}; +} + +\def\winkelOmega#1{ + \begin{scope} + \clip (A) circle[radius=0.7]; + \fill[color=#1!20] \kanteAP -- \kanteCA -- cycle; + \end{scope} + \node[color=#1] at ($(A)+(285:0.50)$) {$\omega$}; +} + +\def\winkelGamma#1{ + \begin{scope} + \clip (C) circle[radius=1.0]; + \fill[color=#1!20] \kanteCA -- \kanteBC -- cycle; + \end{scope} + \node[color=#1] at ($(C)+(155:0.60)$) {$\gamma$}; +} + +\def\winkelKappa#1{ + \begin{scope} + \clip (B) circle[radius=1.2]; + \fill[color=#1!20] \kanteBP -- \kanteAB -- cycle; + \end{scope} + \node[color=#1] at ($(B)+(15:1.00)$) {$\kappa$}; +} + +\def\winkelBeta#1{ + \begin{scope} + \clip (B) circle[radius=0.8]; + \fill[color=#1!20] \kanteBC -- \kanteAB -- cycle; + \end{scope} + \node[color=#1] at ($(B)+(35:0.40)$) {$\beta$}; +} + +\def\winkelBetaEins#1{ + \begin{scope} + \clip (B) circle[radius=0.8]; + \fill[color=#1!20] \kanteBP -- \kanteCB -- cycle; + \end{scope} + \node[color=#1] at ($(B)+(330:0.60)$) {$\beta_1$}; +} + +\def\seiteC#1{ \node[color=#1] at (-1.9,5.9) {$c$}; } +\def\seiteB#1{ \node[color=#1] at (3.2,6.5) {$b$}; } +\def\seiteL#1{ \node[color=#1] at (-0.2,4.5) {$l$}; } +\def\seiteA#1{ \node[color=#1] at (2,3) {$a$}; } +\def\seitePB#1{ \node[color=#1] at (-2.1,1) {$p_b$}; } +\def\seitePC#1{ \node[color=#1] at (2.5,1.5) {$p_c$}; } diff --git a/buch/papers/nav/images/pk.m b/buch/papers/nav/images/pk.m new file mode 100644 index 0000000..6e89e9a --- /dev/null +++ b/buch/papers/nav/images/pk.m @@ -0,0 +1,55 @@ +# +# pk.m -- Punkte und Kanten für sphärisches Dreieck +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# + +A = [ 1, 8 ]; +B = [ -3, 3 ]; +C = [ 4, 4 ]; +P = [ 0, 0 ]; + +global fn; +fn = fopen("dreieckdata.tex", "w"); + +fprintf(fn, "\\coordinate (P) at (%.4f,%.4f);\n", P(1,1), P(1,2)); +fprintf(fn, "\\coordinate (A) at (%.4f,%.4f);\n", A(1,1), A(1,2)); +fprintf(fn, "\\coordinate (B) at (%.4f,%.4f);\n", B(1,1), B(1,2)); +fprintf(fn, "\\coordinate (C) at (%.4f,%.4f);\n", C(1,1), C(1,2)); + +function retval = seite(A, B, l, nameA, nameB) + global fn; + d = fliplr(B - A); + d(1, 2) = -d(1, 2); + # Zentrum + C = 0.5 * (A + B) + l * d; + # Radius: + r = hypot(C(1,1)-A(1,1), C(1,2)-A(1,2)) + # Winkel von + winkelvon = atan2(A(1,2)-C(1,2),A(1,1)-C(1,1)); + # Winkel bis + winkelbis = atan2(B(1,2)-C(1,2),B(1,1)-C(1,1)); + if (abs(winkelvon - winkelbis) > pi) + if (winkelbis < winkelvon) + winkelbis = winkelbis + 2 * pi + else + winkelvon = winkelvon + 2 * pi + end + end + # Kurve + fprintf(fn, "\\def\\kante%s%s{(%.4f,%.4f) arc (%.5f:%.5f:%.4f)}\n", + nameA, nameB, + A(1,1), A(1,2), winkelvon * 180 / pi, winkelbis * 180 / pi, r); + fprintf(fn, "\\def\\kante%s%s{(%.4f,%.4f) arc (%.5f:%.5f:%.4f)}\n", + nameB, nameA, + B(1,1), B(1,2), winkelbis * 180 / pi, winkelvon * 180 / pi, r); +endfunction + +seite(A, B, -1, "A", "B"); +seite(A, C, 1, "A", "C"); +seite(A, P, -1, "A", "P"); +seite(B, C, -2, "B", "C"); +seite(B, P, -1, "B", "P"); +seite(C, P, 2, "C", "P"); + +fclose(fn); -- cgit v1.2.1 From 1067af52a6b066174b7306e96766e9e4e11cbac7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 11 May 2022 22:14:11 +0200 Subject: dreiecksdaten --- buch/papers/nav/images/dreieckdata.tex | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) create mode 100644 buch/papers/nav/images/dreieckdata.tex diff --git a/buch/papers/nav/images/dreieckdata.tex b/buch/papers/nav/images/dreieckdata.tex new file mode 100644 index 0000000..c0fb720 --- /dev/null +++ b/buch/papers/nav/images/dreieckdata.tex @@ -0,0 +1,16 @@ +\coordinate (P) at (0.0000,0.0000); +\coordinate (A) at (1.0000,8.0000); +\coordinate (B) at (-3.0000,3.0000); +\coordinate (C) at (4.0000,4.0000); +\def\kanteAB{(1.0000,8.0000) arc (114.77514:167.90524:7.1589)} +\def\kanteBA{(-3.0000,3.0000) arc (167.90524:114.77514:7.1589)} +\def\kanteAC{(1.0000,8.0000) arc (63.43495:10.30485:5.5902)} +\def\kanteCA{(4.0000,4.0000) arc (10.30485:63.43495:5.5902)} +\def\kanteAP{(1.0000,8.0000) arc (146.30993:199.44003:9.0139)} +\def\kantePA{(0.0000,0.0000) arc (199.44003:146.30993:9.0139)} +\def\kanteBC{(-3.0000,3.0000) arc (-95.90614:-67.83365:14.5774)} +\def\kanteCB{(4.0000,4.0000) arc (-67.83365:-95.90614:14.5774)} +\def\kanteBP{(-3.0000,3.0000) arc (-161.56505:-108.43495:4.7434)} +\def\kantePB{(0.0000,0.0000) arc (-108.43495:-161.56505:4.7434)} +\def\kanteCP{(4.0000,4.0000) arc (-30.96376:-59.03624:11.6619)} +\def\kantePC{(0.0000,0.0000) arc (-59.03624:-30.96376:11.6619)} -- cgit v1.2.1 From b7ee1c1a6836f30d2267cfc9e6dbfa206b2cb737 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 12 May 2022 18:19:49 +0200 Subject: Derive Laguerre-Polynomials from Laguerre-ODE, proof orthogonality with Sturm-Liouville --- buch/.gitignore | 37 ---- buch/papers/laguerre/Makefile | 6 +- buch/papers/laguerre/Makefile.inc | 4 +- buch/papers/laguerre/definition.tex | 160 ++++++++------- buch/papers/laguerre/eigenschaften.tex | 94 ++++++++- buch/papers/laguerre/images/laguerre_polynomes.pdf | Bin 0 -> 16239 bytes buch/papers/laguerre/scripts/gamma_approx.ipynb | 224 +++++++++------------ buch/papers/laguerre/scripts/laguerre_plot.py | 103 ++++++++-- .../laguerre/scripts/lanczos_approximation.py | 47 ----- buch/papers/laguerre/scripts/quadrature_gama.py | 178 ---------------- buch/standalone.tex | 35 ---- 11 files changed, 361 insertions(+), 527 deletions(-) delete mode 100644 buch/.gitignore create mode 100644 buch/papers/laguerre/images/laguerre_polynomes.pdf delete mode 100644 buch/papers/laguerre/scripts/lanczos_approximation.py delete mode 100644 buch/papers/laguerre/scripts/quadrature_gama.py delete mode 100644 buch/standalone.tex diff --git a/buch/.gitignore b/buch/.gitignore deleted file mode 100644 index 4d056e5..0000000 --- a/buch/.gitignore +++ /dev/null @@ -1,37 +0,0 @@ -*.acn -*.acr -*.alg -*.aux -*.bbl -*.blg -*.dvi -*.fdb_latexmk -*.glg -*.glo -*.gls -*.idx -*.ilg -*.ind -*.ist -*.lof -*.log -*.lot -*.maf -*.mtc -*.mtc0 -*.nav -*.nlo -*.out -*.pdfsync -.vscode/* -*.fls -*.xdv -*.ps -*.snm -*.synctex.gz -*.toc -*.vrb -*.xdy -*.tdo -*-blx.bib -*.synctex \ No newline at end of file diff --git a/buch/papers/laguerre/Makefile b/buch/papers/laguerre/Makefile index 606d7e1..0f0985a 100644 --- a/buch/papers/laguerre/Makefile +++ b/buch/papers/laguerre/Makefile @@ -4,6 +4,8 @@ # (c) 2020 Prof Dr Andreas Mueller # -images: - @echo "no images to be created in laguerre" +images: images/laguerre_polynomes.pdf + +images/laguerre_polynomes.pdf: scripts/laguerre_plot.py + python3 scripts/laguerre_plot.py diff --git a/buch/papers/laguerre/Makefile.inc b/buch/papers/laguerre/Makefile.inc index 1eb5034..aae51f9 100644 --- a/buch/papers/laguerre/Makefile.inc +++ b/buch/papers/laguerre/Makefile.inc @@ -9,8 +9,6 @@ dependencies-laguerre = \ papers/laguerre/references.bib \ papers/laguerre/definition.tex \ papers/laguerre/eigenschaften.tex \ - papers/laguerre/quadratur.tex \ - papers/laguerre/transformation.tex \ - papers/laguerre/wasserstoff.tex + papers/laguerre/quadratur.tex diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index 84a26cf..edd2b7b 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -4,11 +4,11 @@ % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % \section{Definition -\label{laguerre:section:definition}} + \label{laguerre:section:definition}} \rhead{Definition} -Die Laguerre-Differentialgleichung ist gegeben durch +Die verallgemeinerte Laguerre-Differentialgleichung ist gegeben durch \begin{align} -x y''(x) + (1 - x) y'(x) + n y(x) +x y''(x) + (\nu + 1 - x) y'(x) + n y(x) = 0 , \quad @@ -18,22 +18,27 @@ x \in \mathbb{R} . \label{laguerre:dgl} \end{align} -Zur Lösung der Gleichung \eqref{laguerre:dgl} -verwenden wir einen Potenzreihenansatz. +Hier wird die verallgemeinerte Laguerre-Differentialgleichung verwendet, +weil die Lösung gleich berechnet werden kann, +aber man zusätzlich die Lösung für den allgmeinen Fall erhält. +Zur Lösung der Gleichung \eqref{laguerre:dgl} verwenden wir einen +Potenzreihenansatz. +Da wir bereits wissen, dass die Lösung orthogonale Polynome sind, +erscheint dieser Ansatz sinnvoll. Setzt man nun den Ansatz \begin{align*} -y(x) -&= +y(x) + & = \sum_{k=0}^\infty a_k x^k \\ y'(x) -& = + & = \sum_{k=1}^\infty k a_k x^{k-1} = \sum_{k=0}^\infty (k+1) a_{k+1} x^k \\ y''(x) -&= + & = \sum_{k=2}^\infty k (k-1) a_k x^{k-2} = \sum_{k=1}^\infty (k+1) k a_{k+1} x^{k-1} @@ -41,98 +46,109 @@ y''(x) in die Differentialgleichung ein, erhält man: \begin{align*} \sum_{k=1}^\infty (k+1) k a_{k+1} x^k -+ \sum_{k=0}^\infty (k+1) a_{k+1} x^k -- \sum_{k=0}^\infty k a_k x^k -+ n \sum_{k=0}^\infty a_k x^k -&= -0\\ -\sum_{k=0}^\infty -\left[ (k+1) k a_{k+1} + (k+1) a_{k+1} - k a_k + n a_k \right] x^k -&= ++ +(\nu + 1)\sum_{k=0}^\infty (k+1) a_{k+1} x^k +- +\sum_{k=0}^\infty k a_k x^k ++ +n \sum_{k=0}^\infty a_k x^k + & = +0 \\ +\sum_{k=1}^\infty +\left[ (k+1) k a_{k+1} + (\nu + 1)(k+1) a_{k+1} - k a_k + n a_k \right] x^k + & = 0. \end{align*} Daraus lässt sich die Rekursionsbeziehung \begin{align*} a_{k+1} -&= -\frac{k-n}{(k+1) ^ 2} a_k + & = +\frac{k-n}{(k+1) (k + \nu + 1)} a_k \end{align*} ableiten. -Für ein konstantes $n$ erhalten wir als Potenzreihenlösung ein Polynom vom Grad $n$, +Für ein konstantes $n$ erhalten wir als Potenzreihenlösung ein Polynom vom Grad +$n$, denn für $k=n$ wird $a_{n+1} = 0$ und damit auch $a_{n+2}=a_{n+3}=\ldots=0$. -Aus der Rekursionsbeziehung ist zudem ersichtlich, +Aus der Rekursionsbeziehung ist zudem ersichtlich, dass $a_0 \neq 0$ beliebig gewählt werden kann. -Wählen wir nun $c_0 = 1$, dann folgt für die Koeffizienten $a_1, a_2, a_3$ +Wählen wir nun $a_0 = 1$, dann folgt für die Koeffizienten $a_1, a_2, a_3$ \begin{align*} -a_1 -= --\frac{n}{1^2} -,&& -a_2 -= -\frac{(n-1)n}{1^2 2^2} -,&& +a_1 += +-\frac{n}{1 \cdot (\nu + 1)} +, & & +a_2 += +\frac{(n-1)n}{1 \cdot 2 \cdot (\nu + 1)(\nu + 2)} +, & & a_3 = --\frac{(n-2)(n-1)n}{1^2 2^2 3^2} +-\frac{(n-2)(n-1)n}{1 \cdot 2 \cdot 3 \cdot (\nu + 1)(\nu + 2)(\nu + 3)} \end{align*} und allgemein \begin{align*} -k&\leq n: -& -a_k -&= -(-1)^k \frac{n!}{(n-k)!} \frac{1}{(k!)^2} -= -\frac{(-1)^k}{k!} -\begin{pmatrix} -n -\\ k -\end{pmatrix} + & \leq +n: + & +a_k + & = +(-1)^k \frac{n!}{(n-k)!} \frac{1}{k!(\nu + 1)_k} += +\frac{(-1)^k}{(\nu + 1)_k} \binom{n}{k} \\ -k&>n: -& +k & >n: + & a_k -&= + & = 0. \end{align*} -Somit haben wir die Laguerre-Polynome $L_n(x)$ erhalten: +Somit erhalten wir für $\nu = 0$ die Laguerre-Polynome \begin{align} L_n(x) = -\sum_{k=0}^{n} -\frac{(-1)^k}{k!} -\begin{pmatrix} -n \\ -k -\end{pmatrix} -x^k +\sum_{k=0}^{n} \frac{(-1)^k}{k!} \binom{n}{k} x^k \label{laguerre:polynom} \end{align} - -\subsection{Assoziierte Laguerre-Polynome -\label{laguerre:subsection:assoz_laguerre} -} +und mit $\nu \in \mathbb{R}$ die verallgemeinerten Laguerre-Polynome \begin{align} -x y''(x) + (\alpha + 1 - x) y'(x) + n y(x) +L_n^\nu(x) = -0 -\label{laguerre:generell_dgl} +\sum_{k=0}^{n} \frac{(-1)^k}{(\nu + 1)_k} \binom{n}{k} x^k. +\label{laguerre:allg_polynom} \end{align} - -\begin{align} -L_n^\alpha (x) +Durch die analytische Fortsetzung erhalten wir zudem noch die zweite Lösung der +Differentialgleichung mit der Form +\begin{align*} +\Xi_n(x) = -\sum_{k=0}^{n} -\frac{(-1)^k}{k!} -\begin{pmatrix} -n + \alpha \\ -n - k -\end{pmatrix} -x^k -\label{laguerre:polynom} -\end{align} +L_n(x) \ln(x) + \sum_{k=1}^\infty d_k x^k +\end{align*} +Nach einigen mühsamen Rechnungen, +die den Rahmen dieses Kapitel sprengen würden, +erhalten wir +\begin{align*} +\Xi_n += +L_n(x) \ln(x) ++ +\sum_{k=1}^n \frac{(-1)^k}{k!} \binom{n}{k} +(\alpha_{n-k} - \alpha_n - 2 \alpha_k)x^k ++ +(-1)^n \sum_{k=1}^\infty \frac{(k-1)!n!}{((n+k)!)^2} x^{n+k}, +\end{align*} +wobei $\alpha_0 = 0$ und $\alpha_k =\sum_{i=1}^k i^{-1}$, +$\forall k \in \mathbb{N}$. +Die Laguerre-Polynome von Grad $0$ bis $7$ sind in +Abbildung~\ref{laguerre:fig:polyeval} dargestellt. +\begin{figure} +\centering +\includegraphics[width=0.7\textwidth]{% + papers/laguerre/images/laguerre_polynomes.pdf% +} +\caption{Laguerre-Polynome vom Grad $0$ bis $7$} +\label{laguerre:fig:polyeval} +\end{figure} % https://www.math.kit.edu/iana1/lehre/hm3phys2012w/media/laguerre.pdf % http://www.physics.okayama-u.ac.jp/jeschke_homepage/E4/kapitel4.pdf diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index b7597e5..c589c92 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -4,5 +4,95 @@ % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % \section{Eigenschaften -\label{laguerre:section:eigenschaften}} -\rhead{Eigenschaften} \ No newline at end of file + \label{laguerre:section:eigenschaften}} +\rhead{Eigenschaften} + +\subsection{Orthogonalität} +Wenn wir die Laguerre\--Differentialgleichung in ein +Sturm\--Liouville\--Problem umwandeln können, haben wir bewiesen, dass es sich +bei +den Laguerre\--Polynomen um orthogonale Polynome handelt (siehe +Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem}). +Der Sturm-Liouville-Operator hat die Form +\begin{align} +S += +\frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right). +\label{laguerre:slop} +\end{align} +Aus der Beziehung +\begin{align} +S + & = +\Lambda +\nonumber +\\ +\frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right) + & = +x \frac{d^2}{dx^2} + (\nu + 1 - x) \frac{d}{dx} +\label{laguerre:sl-lag} +\end{align} +lässt sich sofort erkennen, dass $q(x) = 0$. +Ausserdem ist ersichtlich, dass $p(x)$ die Differentialgleichung +\begin{align*} +x \frac{dp}{dx} += +-(\nu + 1 - x) p, +\end{align*} +erfüllen muss. +Durch Separation erhalten wir dann +\begin{align*} +\int \frac{dp}{p} + & = +-\int \frac{\nu + 1 - x}{x}dx +\\ +\log p + & = +-\log \nu + 1 - x + C +\\ +p(x) + & = +-C x^{\nu + 1} e^{-x} +\end{align*} +Eingefügt in Gleichung~\eqref{laguerre:sl-lag} erhalten wir +\begin{align*} +\frac{C}{w(x)} +\left( +x^{\nu+1} e^{-x} \frac{d^2}{dx^2} + +(\nu + 1 - x) x^{\nu} e^{-x} \frac{d}{dx} +\right) += +x \frac{d^2}{dx^2} + (\nu + 1 - x) \frac{d}{dx}. +\end{align*} +Mittels Koeffizientenvergleich kann nun abgelesen werden, dass $w(x) = x^\nu +e^{-x}$ und $C=1$ mit $\nu > -1$. +Die Gewichtsfunktion $w(x)$ wächst für $x\rightarrow-\infty$ sehr schnell an, +deshalb ist die Laguerre-Gewichtsfunktion nur geeignet für den +Definitionsbereich $(0, \infty)$. +Bleibt nur noch sicherzustellen, dass die Randbedingungen, +\begin{align} +k_0 y(0) + h_0 p(0)y'(0) + & = +0 +\label{laguerre:sllag_randa} +\\ +k_\infty y(\infty) + h_\infty p(\infty) y'(\infty) + & = +0 +\label{laguerre:sllag_randb} +\end{align} +mit $|k_i|^2 + |h_i|^2 \neq 0,\,\forall i \in \{0, \infty\}$, erfüllt sind. +Am linken Rand (Gleichung~\eqref{laguerre:sllag_randa}) kann $y(0) = 1$, $k_0 = +0$ und $h_0 = 1$ verwendet werden, +was auch die Laguerre-Polynome ergeben haben. +Für den rechten Rand ist die Bedingung (Gleichung~\eqref{laguerre:sllag_randb}) +\begin{align*} +\lim_{x \rightarrow \infty} p(x) y'(x) + & = +\lim_{x \rightarrow \infty} -x^{\nu + 1} e^{-x} y'(x) += +0 +\end{align*} +für beliebige Polynomlösungen erfüllt für $k_\infty=0$ und $h_\infty=1$. +Damit können wir schlussfolgern, dass die Laguerre-Polynome orthogonal +bezüglich des Skalarproduktes mit der Laguerre\--Gewichtsfunktion sind. diff --git a/buch/papers/laguerre/images/laguerre_polynomes.pdf b/buch/papers/laguerre/images/laguerre_polynomes.pdf new file mode 100644 index 0000000..3976bc7 Binary files /dev/null and b/buch/papers/laguerre/images/laguerre_polynomes.pdf differ diff --git a/buch/papers/laguerre/scripts/gamma_approx.ipynb b/buch/papers/laguerre/scripts/gamma_approx.ipynb index 9a1fee6..44f3abd 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.ipynb +++ b/buch/papers/laguerre/scripts/gamma_approx.ipynb @@ -28,13 +28,13 @@ " =\n", " \\frac{(n!)^2}{(2n)!} f^{(2n)}(\\xi) \n", " = \n", - " (-2n + z)_{2n} \\frac{(n!)^2}{(2n)!} \\xi^{z - 2n - 1}\n", + " \\frac{(-2n + z)_{2n}}{(z-m)_m} \\frac{(n!)^2}{(2n)!} \\xi^{z + m - 2n - 1}\n", "$$" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -86,35 +86,36 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "zeros = np.array(\n", - " [\n", - " 1.70279632305101000e-1,\n", - " 9.03701776799379912e-1,\n", - " 2.25108662986613069e0,\n", - " 4.26670017028765879e0,\n", - " 7.04590540239346570e0,\n", - " 1.07585160101809952e1,\n", - " 1.57406786412780046e1,\n", - " 2.28631317368892641e1,\n", - " ]\n", - ")\n", - "\n", - "weights = np.array(\n", - " [\n", - " 3.69188589341637530e-1,\n", - " 4.18786780814342956e-1,\n", - " 1.75794986637171806e-1,\n", - " 3.33434922612156515e-2,\n", - " 2.79453623522567252e-3,\n", - " 9.07650877335821310e-5,\n", - " 8.48574671627253154e-7,\n", - " 1.04800117487151038e-9,\n", - " ]\n", - ")\n", + "zeros, weights = np.polynomial.laguerre.laggauss(8)\n", + "# zeros = np.array(\n", + "# [\n", + "# 1.70279632305101000e-1,\n", + "# 9.03701776799379912e-1,\n", + "# 2.25108662986613069e0,\n", + "# 4.26670017028765879e0,\n", + "# 7.04590540239346570e0,\n", + "# 1.07585160101809952e1,\n", + "# 1.57406786412780046e1,\n", + "# 2.28631317368892641e1,\n", + "# ]\n", + "# )\n", + "\n", + "# weights = np.array(\n", + "# [\n", + "# 3.69188589341637530e-1,\n", + "# 4.18786780814342956e-1,\n", + "# 1.75794986637171806e-1,\n", + "# 3.33434922612156515e-2,\n", + "# 2.79453623522567252e-3,\n", + "# 9.07650877335821310e-5,\n", + "# 8.48574671627253154e-7,\n", + "# 1.04800117487151038e-9,\n", + "# ]\n", + "# )\n", "\n", "\n", "def pochhammer(z, n):\n", @@ -149,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -183,27 +184,32 @@ "### Test with real values" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Empirische Tests zeigen:\n", + "- $n=4 \\Rightarrow m=6$\n", + "- $n=5 \\Rightarrow m=7$ oder $m=8$\n", + "- $n=6 \\Rightarrow m=9$\n", + "- $n=7 \\Rightarrow m=10$\n", + "- $n=8 \\Rightarrow m=11$ oder $m=12$\n", + "- $n=9 \\Rightarrow m=13$\n", + "- $n=10 \\Rightarrow m=14$\n", + "- $n=11 \\Rightarrow m=15$ oder $m=16$\n", + "- $n=12 \\Rightarrow m=17$\n", + "- $n=13 \\Rightarrow m=18 \\Rightarrow $ Beginnt numerisch instabil zu werden \n" + ] + }, { "cell_type": "code", - "execution_count": 60, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "targets = np.arange(8, 15)\n", - "mean_targets = ((11, 12),)\n", + "zeros, weights = np.polynomial.laguerre.laggauss(12)\n", + "targets = np.arange(16, 21)\n", + "mean_targets = ((16, 17),)\n", "x = np.linspace(EPSILON, 1 - EPSILON, 101)\n", "_, axs = plt.subplots(\n", " 2, sharex=True, clear=True, constrained_layout=True, figsize=(12, 12)\n", @@ -216,14 +222,18 @@ " axs[0].plot(x, rel_error_mean, label=mean_target)\n", " axs[1].semilogy(x, np.abs(rel_error_mean), label=mean_target)\n", "\n", + "mins = []\n", + "maxs = []\n", "for target in targets:\n", " rel_error = evaluate(x, target)\n", + " mins.append(np.min(np.abs(rel_error[(0.1 <= x) & (x <= 0.9)])))\n", + " maxs.append(np.max(np.abs(rel_error)))\n", " axs[0].plot(x, rel_error, label=target)\n", " axs[1].semilogy(x, np.abs(rel_error), label=target)\n", "# axs[0].set_ylim(*(np.array([-1, 1]) * 3.5e-8))\n", "\n", "axs[0].set_xlim(x[0], x[-1])\n", - "axs[1].set_ylim(1e-10, 2e-7)\n", + "axs[1].set_ylim(np.min(mins), 1.04*np.max(maxs))\n", "for ax in axs:\n", " ax.legend()\n", " ax.grid(which=\"both\")\n" @@ -231,46 +241,11 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(-7.5, 25.0)" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "targets = (11, 12)\n", + "targets = (16, 17)\n", "xmax = 15\n", "x = np.linspace(-xmax + EPSILON, xmax - EPSILON, 1000)\n", "\n", @@ -289,7 +264,7 @@ "axs[1].semilogy(x, np.abs(rel_error_simple), label=targets[-1])\n", "axs[0].set_xlim(x[0], x[-1])\n", "# axs[0].set_ylim(*(np.array([-1, 1]) * 4.2e-8))\n", - "axs[1].set_ylim(1e-10, 5e-8)\n", + "# axs[1].set_ylim(1e-10, 5e-8)\n", "for ax in axs:\n", " ax.legend()\n", "\n", @@ -309,24 +284,11 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "targets = (11, 12)\n", + "targets = (16, 17)\n", "vals = np.linspace(-5 + EPSILON, 5, 100)\n", "x, y = np.meshgrid(vals, vals)\n", "mesh = x + 1j * y\n", @@ -361,45 +323,47 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "# TODO: Macht kei Sinn!\n", - "n = 8\n", - "ms = np.arange(4, 5)\n", - "xi = np.linspace(EPSILON, 20, 201)[:, None]\n", - "z = np.arange(6, 16)[None]+0.1\n", - "c = scipy.special.factorial(n) ** 2 / scipy.special.factorial(2 * n)\n", - "\n", + "z = 0.5\n", + "ns = [4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12] # np.arange(4, 13)\n", + "ms = np.arange(6, 18)\n", + "xi = np.logspace(0, 2, 201)[:, None]\n", + "lanczos = eval_lanczos([z])[0]\n", "\n", "_, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(12, 8))\n", "ax.grid(1)\n", - "for m, color in zip(ms, ['r', 'b', 'g', 'c', 'm', 'y']):\n", + "for n, m in zip(ns, ms):\n", + " zeros, weights = np.polynomial.laguerre.laggauss(n)\n", + " c = scipy.special.factorial(n) ** 2 / scipy.special.factorial(2 * n)\n", " e = np.abs(\n", " scipy.special.poch(z - 2 * n, 2 * n)\n", " / scipy.special.poch(z - m, m)\n", " * c\n", " * xi ** (z - 2 * n + m - 1)\n", " )\n", + " ez = np.sum(\n", + " scipy.special.poch(z - 2 * n, 2 * n)\n", + " / scipy.special.poch(z - m, m)\n", + " * c\n", + " * zeros[:, None] ** (z - 2 * n + m - 1),\n", + " 0,\n", + " )\n", + " lag = eval_laguerre([z], m)[0]\n", + " err = np.abs(lanczos - lag)\n", + " # print(m+z,ez)\n", + " # for zi,ezi in zip(z[0], ez):\n", + " # print(f\"{m+zi}: {ezi}\")\n", " # ax.semilogy(xi, e, color=color)\n", - " ax.semilogy(xi, e)\n", - " ax.set_xticks(np.arange(xi[-1] +1))\n", - " ax.set_ylim(1e-8, 1e5)\n", - " _ = ax.legend([f'z={zi}' for zi in z[0]])\n" + " lines = ax.loglog(xi, e, label=str(n))\n", + " ax.axhline(err, color=lines[0].get_color())\n", + " # ax.set_xticks(np.arange(xi[-1] + 1))\n", + " # ax.set_ylim(1e-8, 1e5)\n", + "_ = ax.legend()\n", + "# _ = ax.legend([f\"z={zi}\" for zi in z[0]])\n", + "# _ = [ax.axvline(x) for x in zeros]\n" ] } ], diff --git a/buch/papers/laguerre/scripts/laguerre_plot.py b/buch/papers/laguerre/scripts/laguerre_plot.py index cd90df1..b9088d0 100644 --- a/buch/papers/laguerre/scripts/laguerre_plot.py +++ b/buch/papers/laguerre/scripts/laguerre_plot.py @@ -2,38 +2,99 @@ # -*- coding:utf-8 -*- """Some plots for Laguerre Polynomials.""" +import os from pathlib import Path import matplotlib.pyplot as plt import numpy as np import scipy.special as ss + +def get_ticks(start, end, step=1): + ticks = np.arange(start, end, step) + return ticks[ticks != 0] + + N = 1000 -t = np.linspace(0, 12.5, N)[:, None] +step = 5 +t = np.linspace(-1.05, 10.5, N)[:, None] root = str(Path(__file__).parent) +img_path = f"{root}/../images" +os.makedirs(img_path, exist_ok=True) + +# fig = plt.figure(num=1, clear=True, tight_layout=True, figsize=(5.5, 3.7)) +# ax = fig.add_subplot(axes_class=AxesZero) fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) -for n in np.arange(0, 10): +for n in np.arange(0, 8): k = np.arange(0, n + 1)[None] L = np.sum((-1) ** k * ss.binom(n, k) / ss.factorial(k) * t ** k, -1) ax.plot(t, L, label=f"n={n}") -ax.set_xticks(np.arange(1, t[-1])) -ax.set_xlim(t[0], t[-1] + 0.1*(t[1] - t[0])) -ax.set_ylim(-20, 20) -ax.legend(ncol=2) + +ax.set_xticks(get_ticks(int(t[0]), t[-1]), minor=True) +ax.set_xticks(get_ticks(0, t[-1], step)) +ax.set_xlim(t[0], t[-1] + 0.1 * (t[1] - t[0])) +ax.set_xlabel(r"$x$", x=1.0, labelpad=-10, rotation=0, fontsize="large") + +ylim = 13 +ax.set_yticks(np.arange(-ylim, ylim), minor=True) +ax.set_yticks(np.arange(-step * (ylim // step), ylim, step)) +ax.set_ylim(-ylim, ylim) +ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large") + +ax.legend(ncol=2, loc=(0.125, 0.01), fontsize="large") + # set the x-spine -ax.spines['left'].set_position('zero') -ax.spines['right'].set_visible(False) -ax.spines['bottom'].set_position('zero') -ax.spines['top'].set_visible(False) -ax.xaxis.set_ticks_position('bottom') -ax.yaxis.set_ticks_position('left') - -# make arrows -# ax.plot((1), (0), ls="", marker=">", ms=10, color="k", -# transform=ax.get_yaxis_transform(), clip_on=False) -# ax.plot((0), (1), ls="", marker="^", ms=10, color="k", -# transform=ax.get_xaxis_transform(), clip_on=False) -# ax.grid(1) -fig.savefig(f'{root}/laguerre_polynomes.pdf') -# plt.show() +ax.spines[["left", "bottom"]].set_position("zero") +ax.spines[["right", "top"]].set_visible(False) +ax.xaxis.set_ticks_position("bottom") +hlx = 0.4 +dx = t[-1, 0] - t[0, 0] +dy = 2 * ylim +hly = dy / dx * hlx +dps = fig.dpi_scale_trans.inverted() +bbox = ax.get_window_extent().transformed(dps) +width, height = bbox.width, bbox.height + +# manual arrowhead width and length +hw = 1.0 / 60.0 * dy +hl = 1.0 / 30.0 * dx +lw = 0.5 # axis line width +ohg = 0.0 # arrow overhang + +# compute matching arrowhead length and width +yhw = hw / dy * dx * height / width +yhl = hl / dx * dy * width / height + +# draw x and y axis +ax.arrow( + t[-1, 0] - hl, + 0, + hl, + 0.0, + fc="k", + ec="k", + lw=lw, + head_width=hw, + head_length=hl, + overhang=ohg, + length_includes_head=True, + clip_on=False, +) + +ax.arrow( + 0, + ylim - yhl, + 0.0, + yhl, + fc="k", + ec="k", + lw=lw, + head_width=yhw, + head_length=yhl, + overhang=ohg, + length_includes_head=True, + clip_on=False, +) + +fig.savefig(f"{img_path}/laguerre_polynomes.pdf") diff --git a/buch/papers/laguerre/scripts/lanczos_approximation.py b/buch/papers/laguerre/scripts/lanczos_approximation.py deleted file mode 100644 index 3c48266..0000000 --- a/buch/papers/laguerre/scripts/lanczos_approximation.py +++ /dev/null @@ -1,47 +0,0 @@ -from cmath import exp, pi, sin, sqrt - -p = [ - 676.5203681218851, - -1259.1392167224028, - 771.32342877765313, - -176.61502916214059, - 12.507343278686905, - -0.13857109526572012, - 9.9843695780195716e-6, - 1.5056327351493116e-7, -] - -EPSILON = 1e-07 - - -def drop_imag(z): - if abs(z.imag) <= EPSILON: - z = z.real - return z - - -def gamma(z): - z = complex(z) - if z.real < 0.5: - y = pi / (sin(pi * z) * gamma(1 - z)) # Reflection formula - else: - z -= 1 - x = 0.99999999999980993 - for (i, pval) in enumerate(p): - x += pval / (z + i + 1) - t = z + len(p) - 0.5 - y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x - return drop_imag(y) - - -""" -The above use of the reflection (thus the if-else structure) is necessary, even though -it may look strange, as it allows to extend the approximation to values of z where -Re(z) < 0.5, where the Lanczos method is not valid. -""" - -print(gamma(1)) -print(gamma(5)) -print(gamma(0.5)) -print(gamma(0.5* (1 + 1j))) -print(gamma(-0.5)) diff --git a/buch/papers/laguerre/scripts/quadrature_gama.py b/buch/papers/laguerre/scripts/quadrature_gama.py deleted file mode 100644 index 37a9cd8..0000000 --- a/buch/papers/laguerre/scripts/quadrature_gama.py +++ /dev/null @@ -1,178 +0,0 @@ -#!/usr/bin/env python3 -# -*- coding:utf-8 -*- -"""Use Gauss-Laguerre quadrature to calculate gamma function.""" -# import sympy -from cmath import exp, pi, sin, sqrt - -import matplotlib.pyplot as plt -import numpy as np -import scipy.special as ss - -p = [ - 676.5203681218851, - -1259.1392167224028, - 771.32342877765313, - -176.61502916214059, - 12.507343278686905, - -0.13857109526572012, - 9.9843695780195716e-6, - 1.5056327351493116e-7, -] - -EPSILON = 1e-07 - - -def drop_imag(z): - if abs(z.imag) <= EPSILON: - z = z.real - return z - - -def gamma(z): - z = complex(z) - if z.real < 0.5: - y = pi / (sin(pi * z) * gamma(1 - z)) # Reflection formula - else: - z -= 1 - x = 0.99999999999980993 - for (i, pval) in enumerate(p): - x += pval / (z + i + 1) - t = z + len(p) - 0.5 - y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x - return drop_imag(y) - - -zeros = np.array( - [ - 3.22547689619392312e-1, - 1.74576110115834658e0, - 4.53662029692112798e0, - 9.39507091230113313e0, - ], - np.longdouble, -) -weights = np.array( - [ - 6.03154104341633602e-1, - 3.57418692437799687e-1, - 3.88879085150053843e-2, - 5.39294705561327450e-4, - ], - np.longdouble, -) - -zeros = np.array( - [ - 1.70279632305101000e-1, - 9.03701776799379912e-1, - 2.25108662986613069e0, - 4.26670017028765879e0, - 7.04590540239346570e0, - 1.07585160101809952e1, - 1.57406786412780046e1, - 2.28631317368892641e1, - ], - np.longdouble, -) - -weights = np.array( - [ - 3.69188589341637530e-1, - 4.18786780814342956e-1, - 1.75794986637171806e-1, - 3.33434922612156515e-2, - 2.79453623522567252e-3, - 9.07650877335821310e-5, - 8.48574671627253154e-7, - 1.04800117487151038e-9, - ], - np.longdouble, -) - - -def calc_gamma(z, n, x, w): - res = 0.0 - z = complex(z) - for xi, wi in zip(x, w): - res += xi ** (z + n - 1) * wi - for i in range(int(n)): - res /= z + i - res = drop_imag(res) - return res - -small = 1e-3 -Z = np.linspace(small, 1-small, 101) - -# Z = [-3/2, -1/2, 1/2, 3/2] -# target = -# targets = np.array([gamma(z) for z in Z]) -targets1 = ss.gamma(Z) -targets2 = np.array([gamma(z) for z in Z]) -approxs = np.array([calc_gamma(z, 11, zeros, weights) for z in Z]) -rel_error1 = np.abs(targets1 - approxs) / targets1 -rel_error2 = np.abs(targets2 - approxs) / targets2 - -_, axs = plt.subplots(2, num=1, clear=True, constrained_layout=True) -axs[0].plot(Z, rel_error1) -axs[1].semilogy(Z, rel_error1) -axs[0].plot(Z, rel_error2) -axs[1].semilogy(Z, rel_error2) -axs[1].semilogy(Z, np.abs(targets1-targets2)/targets1) -plt.show() -# values = np.array([calc_gamma]) -# _ = [ -# print( -# n, -# [ -# float( -# f"{np.abs((calc_gamma(z, n, zeros, weights) - gamma(z)) / gamma(z)):.3g}" -# ) -# for z in Z -# ], -# ) -# for n in range(21) -# ] - - -# target = ss.gamma(z) -# target = np.sqrt(np.pi) - -# _, ax = plt.subplots(num=1, clear=True, constrained_layout=True) -# for i, degree in enumerate(degrees): -# samples_points, weights = np.polynomial.laguerre.laggauss(degree) -# values = np.sum( -# samples_points[:, None] ** (z + shifts[None] - 1) * weights[:, None], 0 -# ) / ss.poch(z, shifts) -# # print(np.abs(target - values)) -# print(values) -# ax.plot(shifts, values, label=f"N={degree}") -# ax.legend() -# plt.show() - - -# def count_equal_digits(x, y): -# for i in range(1, 13): -# try: -# np.testing.assert_almost_equal(x, y, i) -# except AssertionError: -# break -# return i - - -# Z = np.linspace(1.0, 11.0, 11) -# # degrees = [2, 4, 8, 16, 32, 64, 100] -# d = 100 -# X = np.zeros(len(Z)) -# for i, z in enumerate(Z): -# samples_points, weights = np.polynomial.laguerre.laggauss(d) -# X[i] = np.sum(samples_points ** (z - 1) * weights) -# # X[i] = np.sum(np.sin(z * samples_points) * weights) -# Y = ss.gamma(Z) -# # Y = Z / (Z ** 2 + 1) -# ed = [count_equal_digits(x, y) for x, y in zip(X, Y)] -# for x,y in zip(X,Y): -# print(x,y) - -# _, ax = plt.subplots(num=1, clear=True, constrained_layout=True) -# ax.plot(Z, ed) -# plt.show() diff --git a/buch/standalone.tex b/buch/standalone.tex deleted file mode 100644 index e681460..0000000 --- a/buch/standalone.tex +++ /dev/null @@ -1,35 +0,0 @@ -% -% packages.tex -- common packages -% -% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -% -\documentclass{book} -\def\IncludeBookCover{0} -\input{common/packages.tex} -% additional packages used by the individual papers, add a line for -% each paper -\input{papers/common/addpackages.tex} - -% workaround for biblatex bug -\makeatletter -\def\blx@maxline{77} -\makeatother -\addbibresource{chapters/references.bib} - -% Bibresources for each article -\input{papers/common/addbibresources.tex} - -% make sure the last index starts on an odd page -\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} -\makeindex - -%\pgfplotsset{compat=1.12} -\setlength{\headheight}{15pt} % fix headheight warning -\DeclareGraphicsRule{*}{mps}{*}{} - -\begin{document} - \input{common/macros.tex} - \def\chapterauthor#1{{\large #1}\bigskip\bigskip} - - \input{papers/laguerre/main} -\end{document} \ No newline at end of file -- cgit v1.2.1 From 7397861ade0537bf8e501fa87bd57653d932d459 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 12 May 2022 18:21:25 +0200 Subject: Remove deprecated files --- buch/papers/laguerre/images/wasserstoff_model.tex | 58 --------- buch/papers/laguerre/transformation.tex | 31 ----- buch/papers/laguerre/wasserstoff.tex | 142 ---------------------- 3 files changed, 231 deletions(-) delete mode 100644 buch/papers/laguerre/images/wasserstoff_model.tex delete mode 100644 buch/papers/laguerre/transformation.tex delete mode 100644 buch/papers/laguerre/wasserstoff.tex diff --git a/buch/papers/laguerre/images/wasserstoff_model.tex b/buch/papers/laguerre/images/wasserstoff_model.tex deleted file mode 100644 index fe838c3..0000000 --- a/buch/papers/laguerre/images/wasserstoff_model.tex +++ /dev/null @@ -1,58 +0,0 @@ -\documentclass{standalone} - -\usepackage{pgfplots} -\usepackage{tikz-3dplot} - -\tdplotsetmaincoords{60}{115} -\pgfplotsset{compat=newest} - -\begin{document} - -\newcommand{\drawcircle}[4]{ -\shade[ball color=#3, opacity=#4] (#1) circle (#2 cm); -\tdplotsetrotatedcoords{0}{0}{0}; -\draw[dashed, tdplot_rotated_coords, #3!40!black] (#1) circle (#2); -} - -\begin{tikzpicture}[tdplot_main_coords, scale = 2] -\def\r{1.0} -\def\rp{0.2} -\def\rn{0.05} -\def\rvec{1.0} -\def\thetavec{45} -\def\phivec{60} - -\coordinate (O) at (0, 0, 0); -\tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec} - -% Labels -\node[inner sep=1pt] at (0, -4.0*\rp, 1.0*\r) (plabel){Proton}; -\draw (plabel) -- (O); -\node[inner sep=1pt] at (-0.*\r, 1.0*\r, 1.3*\r) (elabel){Elektron}; -\draw (elabel) -- (P); -% Draw proton -\drawcircle{O}{\rp}{red}{1.0} - -% Draw spherical coordinates of electron -\draw (O) -- node[anchor=north west, yshift=4pt]{$r$} (P); -\draw[dashed] (O) -- (Pxy); -\draw[dashed] (P) -- (Pxy); -\tdplotdrawarc{(O)}{0.6}{0}{\phivec}{anchor=north}{$\varphi$} -\tdplotsetthetaplanecoords{\phivec} -\tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{0}% -{\thetavec}{anchor=south west, xshift=-2pt, yshift=-2pt}{$\vartheta$} - -% Draw electron -\drawcircle{P}{\rn}{blue}{1.0} - -% Draw surrounding sphere -\drawcircle{O}{\r}{gray}{0.3} - -% Draw cartesian coordinate system -\draw[-stealth, thick] (O) -- (1.8*\r,0,0) node[below left] {$x$}; -\draw[-stealth, thick] (O) -- (0,1.3*\r,0) node[below right] {$y$}; -\draw[-stealth, thick] (O) -- (0,0,1.3*\r) node[above] {$z$}; - -\end{tikzpicture} - -\end{document} \ No newline at end of file diff --git a/buch/papers/laguerre/transformation.tex b/buch/papers/laguerre/transformation.tex deleted file mode 100644 index 4de86b6..0000000 --- a/buch/papers/laguerre/transformation.tex +++ /dev/null @@ -1,31 +0,0 @@ -% -% transformation.tex -% -% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule -% -\section{Laguerre Transformation -\label{laguerre:section:transformation}} -\begin{align} - L \left\{ f(x) \right\} - = - \tilde{f}_\alpha(n) - = - \int_0^\infty e^{-x} x^\alpha L_n^\alpha(x) f(x) dx - \label{laguerre:transformation} -\end{align} - -\begin{align} - L^{-1} \left\{ \tilde{f}_\alpha(n) \right\} - = - f(x) - = - \sum_{n=0}^{\infty} - \begin{pmatrix} - n + \alpha \\ - n - \end{pmatrix}^{-1} - \frac{1}{\Gamma(\alpha + 1)} - \tilde{f}_\alpha(n) - L_n^\alpha(x) - \label{laguerre:inverse_transformation} -\end{align} \ No newline at end of file diff --git a/buch/papers/laguerre/wasserstoff.tex b/buch/papers/laguerre/wasserstoff.tex deleted file mode 100644 index 0da8be3..0000000 --- a/buch/papers/laguerre/wasserstoff.tex +++ /dev/null @@ -1,142 +0,0 @@ -% -% wasserstoff.tex -% -% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule -% -\section{Radialer Schwingungsanteil eines Wasserstoffatoms -\label{laguerre:section:radial_h_atom}} - -Das Wasserstoffatom besteht aus einem Proton im Kern -mit Masse $M$ und Ladung $+e$. -Ein Elektron mit Masse $m$ und Ladung $-e$ umkreist das Proton -(vgl. Abbildung~\ref{laguerre:fig:wasserstoff_model}). -Für das folgende Model werden folgende Annahmen getroffen: - -\begin{figure} -\centering -\includegraphics{papers/laguerre/images/wasserstoff_model.pdf} -\caption{Skizze eines Wasserstoffatoms. -Kartesische, wie auch Kugelkoordinaten sind eingezeichnet. -} -\label{laguerre:fig:wasserstoff_model} -\end{figure} - -\begin{enumerate} -\item -Das Elektron wird als nicht-relativistisches Teilchen betrachtet, -das heisst, -relativistische Effekte sind vernachlässigbar. -\item -Der Spin des Elektrons und des Protons -und das damit verbundene magnetische Moment -wird vernachlässigt. -\item -Fluktuationen des Vakuums werden nicht berücksichtigt. -\item -Wechselwirkung zwischen Elektron und Proton -ist durch die Coulombwechselwirkung gegeben. -Somit entspricht die potentielle Energie der Coulombenergie $V_C(r)$ -und nimmt damit die folgende Form an -\begin{align} - V_C(r) - = - -\frac{e^2}{4 \pi \epsilon_0 r} - \text{ mit } - r - = - \lvert\vec{r}\rvert - = - \sqrt{x^2 + y^2 + z^2} - . - \label{laguerre:coulombenergie} -\end{align} -Im Falle das der Kern einen endlichen Radius $r_0$ besitzt, -ist die $1/r$-Abhängigkeit in Gleichung \eqref{laguerre:coulombenergie} -als Näherung zu betrachten. -Diese Näherung darf nur angewendet werden, wenn die -Aufenthaltswahrscheinlicheit des Elektrons -innerhalb $r_0$ vernachlässigbar ist. -Für das Wasserstoffatom ist diese Näherung für alle Zustände gerechtfertigt. -\item -Da $M \gg m$, kann das Proton als in Ruhe angenommen werden. -\end{enumerate} - -\subsection{Herleitung zeitunabhängige Schrödinger-Gleichung} -\label{laguerre:subsection:herleitung_schroedinger} -Das Problem ist kugelsymmetrisch, -darum transformieren wir das Problem in Kugelkoordinaten. -Somit gilt: - -\begin{align*} - r - & = - \sqrt{x^2 + y^2 + z^2}\\ - \vartheta - & = - \arccos\left(\frac{z}{r}\right)\\ - \varphi - & = - \arctan\left(\frac{y}{x}\right) -\end{align*} - -Die potentielle Energie $V_C(r)$ hat keine direkte Zeitabhängigkeit. -Daraus folgt, dass die konstant ist Gesamtenergie $E$ -und es existieren stationäre Zustände - -\begin{align} - \psi(r, \vartheta, \varphi, t) - = - u(r, \vartheta, \varphi) e^{-i E t / h}, -\end{align} -wobei $u(r, \vartheta, \varphi)$ -die zeitunabhängige Schrödinger-Gleichung erfüllt. - -\begin{align} - -\frac{\hbar^2}{2m} \Delta u(r, \vartheta, \varphi) - + V_C(r) u(r, \vartheta, \varphi) - = - E u(r, \vartheta, \varphi) - \label{laguerre:schroedinger} -\end{align} - -Für Kugelkoordinaten hat der Laplace-Operator $\Delta$ die Form - -\begin{align} - \Delta - = - \frac{1}{r^2} \pdv{}{r} \left( r^2 \pdv{}{r} \right) - + \frac{1}{r^2 \sin\vartheta} \pdv{}{\vartheta} - \left(\sin\vartheta \pdv{}{\vartheta}\right) - + \frac{1}{r^2 \sin^2\vartheta} \pdv[2]{}{\varphi} - \label{laguerre:laplace_kugel} -\end{align} - -Setzt man nun -\eqref{laguerre:coulombenergie} und \eqref{laguerre:laplace_kugel} -in \eqref{laguerre:schroedinger} ein, -erhält man die zeitunabhängige Schrödinger-Gleichung für Kugelkoordinaten - -\begin{align} -\nonumber -- \frac{\hbar^2}{2m} -& -\left( -\frac{1}{r^2} \pdv{}{r} -\left( r^2 \pdv{}{r} \right) -+ -\frac{1}{r^2 \sin \vartheta} \pdv{}{\vartheta} -\left( \sin \vartheta \pdv{}{\vartheta} \right) -+ -\frac{1}{r^2 \sin^2 \vartheta} \pdv[2]{}{\varphi} -\right) -u(r, \vartheta, \varphi) -\\ -& - -\frac{e^2}{4 \pi \epsilon_0 r} u(r, \vartheta, \varphi) -= -E u(r, \vartheta, \varphi). -\label{laguerre:pdg_h_atom} -\end{align} - -\subsection{Separation der Schrödinger-Gleichung} -\label{laguerre:subsection:seperation_schroedinger} -- cgit v1.2.1 From 155989e49b70a4598dbf3ff3277d9e320f226a83 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Fri, 13 May 2022 12:38:18 +0200 Subject: Add some information about Gauss Quadrature and application to Gamma integral --- buch/papers/laguerre/Makefile.inc | 3 +- buch/papers/laguerre/definition.tex | 5 ++- buch/papers/laguerre/eigenschaften.tex | 25 ++++++++++- buch/papers/laguerre/gamma.tex | 76 +++++++++++++++++++++++++++++++++ buch/papers/laguerre/main.tex | 3 +- buch/papers/laguerre/quadratur.tex | 78 ++++++++++++++++++++++++++++------ buch/papers/laguerre/references.bib | 45 +++++++------------- 7 files changed, 187 insertions(+), 48 deletions(-) create mode 100644 buch/papers/laguerre/gamma.tex diff --git a/buch/papers/laguerre/Makefile.inc b/buch/papers/laguerre/Makefile.inc index aae51f9..12b0935 100644 --- a/buch/papers/laguerre/Makefile.inc +++ b/buch/papers/laguerre/Makefile.inc @@ -9,6 +9,7 @@ dependencies-laguerre = \ papers/laguerre/references.bib \ papers/laguerre/definition.tex \ papers/laguerre/eigenschaften.tex \ - papers/laguerre/quadratur.tex + papers/laguerre/quadratur.tex \ + papers/laguerre/gamma.tex diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index edd2b7b..d111f6f 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -18,8 +18,9 @@ x \in \mathbb{R} . \label{laguerre:dgl} \end{align} +Die klassische Laguerre-Diffentialgleichung erhält man, wenn $\nu = 0$. Hier wird die verallgemeinerte Laguerre-Differentialgleichung verwendet, -weil die Lösung gleich berechnet werden kann, +weil die Lösung mit der selben Methode berechnet werden kann, aber man zusätzlich die Lösung für den allgmeinen Fall erhält. Zur Lösung der Gleichung \eqref{laguerre:dgl} verwenden wir einen Potenzreihenansatz. @@ -117,6 +118,8 @@ L_n^\nu(x) \sum_{k=0}^{n} \frac{(-1)^k}{(\nu + 1)_k} \binom{n}{k} x^k. \label{laguerre:allg_polynom} \end{align} + +\subsection{Analytische Fortsetzung} Durch die analytische Fortsetzung erhalten wir zudem noch die zweite Lösung der Differentialgleichung mit der Form \begin{align*} diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index c589c92..b0cc3a3 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -5,9 +5,21 @@ % \section{Eigenschaften \label{laguerre:section:eigenschaften}} +{ +\large \color{red} +TODO: +Evtl. nur Orthogonalität hier behandeln, da nur diese für die Gauss-Quadratur +benötigt wird. +} + +Die Laguerre-Polynome besitzen einige interessante Eigenschaften \rhead{Eigenschaften} -\subsection{Orthogonalität} +\subsection{Orthogonalität + \label{laguerre:subsection:orthogonal}} +Im Abschnitt~\ref{laguerre:section:definition} haben wir behauptet, +dass die Laguerre-Polynome orthogonale Polynome sind. +Zu dieser Behauptung möchten wir nun einen Beweis liefern. Wenn wir die Laguerre\--Differentialgleichung in ein Sturm\--Liouville\--Problem umwandeln können, haben wir bewiesen, dass es sich bei @@ -95,4 +107,13 @@ Für den rechten Rand ist die Bedingung (Gleichung~\eqref{laguerre:sllag_randb}) \end{align*} für beliebige Polynomlösungen erfüllt für $k_\infty=0$ und $h_\infty=1$. Damit können wir schlussfolgern, dass die Laguerre-Polynome orthogonal -bezüglich des Skalarproduktes mit der Laguerre\--Gewichtsfunktion sind. +bezüglich des Skalarproduktes auf dem Intervall $(0, \infty)$ mit der Laguerre\--Gewichtsfunktion +$w(x)=x^\nu e^{-x}$ sind. + + +\subsection{Rodrigues-Formel} + +\subsection{Drei-Terme Rekursion} + +\subsection{Beziehung mit der Hypergeometrischen Funktion} + diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex new file mode 100644 index 0000000..e3838b0 --- /dev/null +++ b/buch/papers/laguerre/gamma.tex @@ -0,0 +1,76 @@ +% +% gamma.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Anwendung: Berechnung der Gamma-Funktion + \label{laguerre:section:quad-gamma}} +Die Gauss-Laguerre-Quadratur kann nun verwendet werden, +um exponentiell abfallende Funktionen im Definitionsbereich $(0, \infty)$ zu +berechnen. +Dabei bietet sich z.B. die Gamma-Funkion bestens an, wie wir in den folgenden +Abschnitten sehen werden. + +\subsection{Gamma-Funktion} +Die Gamma-Funktion ist eine Erweiterung der Fakultät auf die reale und komplexe +Zahlenmenge. +Die Definition~\ref{buch:rekursion:def:gamma} beschreibt die Gamma-Funktion als +Integral der Form +\begin{align} +\Gamma(z) + & = +\int_0^\infty t^{z-1} e^{-t} dt +, +\quad +\text{wobei Realteil von $z$ grösser als $0$} +, +\label{laguerre:gamma} +\end{align} +welches alle Eigenschaften erfüllt, um mit der Gauss-Laguerre-Quadratur +berechnet zu werden. + +\subsubsection{Funktionalgleichung} +Die Funktionalgleichung besagt +\begin{align} +z \Gamma(z) = \Gamma(z+1). +\label{laguerre:gamma_funktional} +\end{align} +Mittels dieser Gleichung kann der Wert an einer bestimmten, +geeigneten Stelle evaluiert werden und dann zurückverschoben werden, +um das gewünschte Resultat zu erhalten. + +\subsection{Berechnung mittels Gauss-Laguerre-Quadratur} + +Fehlerterm: +\begin{align*} +R_n += +(z - 2n)_{2n} \frac{(n!)^2}{(2n)!} \xi^{z-2n-1} +\end{align*} + +\subsubsection{Finden der optimalen Berechnungsstelle} +Nun stellt sich die Frage, +ob die Approximation mittels Gauss-Laguerre-Quadratur verbessert werden kann, +wenn man das Problem an einer geeigneten Stelle evaluiert und +dann zurückverschiebt mit der Funktionalgleichung. +Dazu wollen wir den Fehlerterm in +Gleichung~\eqref{laguerre:lagurre:lag_error} anpassen und dann minimieren. +Zunächst wollen wir dies nur für $z\in \mathbb{R}$ und $0 Date: Fri, 13 May 2022 12:47:50 +0200 Subject: fix some bugs --- buch/chapters/070-orthogonalitaet/orthogonal.tex | 4 +- buch/chapters/070-orthogonalitaet/rekursion.tex | 10 ++-- buch/papers/nav/images/Makefile | 33 ++++++++++++ buch/papers/nav/images/dreieck1.pdf | Bin 0 -> 11578 bytes buch/papers/nav/images/dreieck1.tex | 59 +++++++++++++++++++++ buch/papers/nav/images/dreieck2.pdf | Bin 0 -> 8812 bytes buch/papers/nav/images/dreieck2.tex | 59 +++++++++++++++++++++ buch/papers/nav/images/dreieck3.pdf | Bin 0 -> 10636 bytes buch/papers/nav/images/dreieck3.tex | 59 +++++++++++++++++++++ buch/papers/nav/images/dreieck4.pdf | Bin 0 -> 13231 bytes buch/papers/nav/images/dreieck4.tex | 64 +++++++++++++++++++++++ buch/papers/nav/images/dreieck5.pdf | Bin 0 -> 8721 bytes buch/papers/nav/images/dreieck5.tex | 64 +++++++++++++++++++++++ buch/papers/nav/images/dreieck6.pdf | Bin 0 -> 10699 bytes buch/papers/nav/images/dreieck6.tex | 64 +++++++++++++++++++++++ buch/papers/nav/images/dreieck7.pdf | Bin 0 -> 11079 bytes buch/papers/nav/images/dreieck7.tex | 64 +++++++++++++++++++++++ 17 files changed, 473 insertions(+), 7 deletions(-) create mode 100644 buch/papers/nav/images/dreieck1.pdf create mode 100644 buch/papers/nav/images/dreieck1.tex create mode 100644 buch/papers/nav/images/dreieck2.pdf create mode 100644 buch/papers/nav/images/dreieck2.tex create mode 100644 buch/papers/nav/images/dreieck3.pdf create mode 100644 buch/papers/nav/images/dreieck3.tex create mode 100644 buch/papers/nav/images/dreieck4.pdf create mode 100644 buch/papers/nav/images/dreieck4.tex create mode 100644 buch/papers/nav/images/dreieck5.pdf create mode 100644 buch/papers/nav/images/dreieck5.tex create mode 100644 buch/papers/nav/images/dreieck6.pdf create mode 100644 buch/papers/nav/images/dreieck6.tex create mode 100644 buch/papers/nav/images/dreieck7.pdf create mode 100644 buch/papers/nav/images/dreieck7.tex diff --git a/buch/chapters/070-orthogonalitaet/orthogonal.tex b/buch/chapters/070-orthogonalitaet/orthogonal.tex index a84248a..677e865 100644 --- a/buch/chapters/070-orthogonalitaet/orthogonal.tex +++ b/buch/chapters/070-orthogonalitaet/orthogonal.tex @@ -842,14 +842,14 @@ bei geeigneter Normierung die {\em Hermite-Polynome}. % % Laguerre-Gewichtsfunktion % -\subsection{Laguerre-Gewichtsfunktion} +\subsubsection{Laguerre-Gewichtsfunktion} Ähnlich wie die Hermite-Gewichtsfunktion ist die {\em Laguerre-Gewichtsfunktion} \index{Laguerre-Gewichtsfunktion}% \[ w_{\text{Laguerre}}(x) = -w^{-x} +e^{-x} \] auf ganz $\mathbb{R}$ definiert, und sie geht für $x\to\infty$ wieder sehr rasch gegen $0$. diff --git a/buch/chapters/070-orthogonalitaet/rekursion.tex b/buch/chapters/070-orthogonalitaet/rekursion.tex index 5ec7fed..dc5531b 100644 --- a/buch/chapters/070-orthogonalitaet/rekursion.tex +++ b/buch/chapters/070-orthogonalitaet/rekursion.tex @@ -30,7 +30,7 @@ Skalarproduktes $\langle\,\;,\;\rangle_w$, wenn für alle $n$, $m$. \end{definition} -\subsection{Allgemeine Drei-Term-Rekursion für orthogonale Polynome} +\subsubsection{Allgemeine Drei-Term-Rekursion für orthogonale Polynome} Der folgende Satz besagt, dass $p_n$ eine Rekursionsbeziehung erfüllt. \begin{satz} @@ -55,7 +55,7 @@ C_{n+1} = \frac{A_{n+1}}{A_n}\frac{h_{n+1}}{h_n}. \end{equation} \end{satz} -\subsection{Multiplikationsoperator mit $x$} +\subsubsection{Multiplikationsoperator mit $x$} Man kann die Relation auch nach dem Produkt $xp_n(x)$ auflösen, dann wird sie \begin{equation} @@ -72,7 +72,7 @@ Die Multiplikation mit $x$ ist eine lineare Abbildung im Raum der Funktionen. Die Relation~\eqref{buch:orthogonal:eqn:multixrelation} besagt, dass diese Abbildung in der Basis der Polynome $p_k$ tridiagonale Form hat. -\subsection{Drei-Term-Rekursion für die Tschebyscheff-Polynome} +\subsubsection{Drei-Term-Rekursion für die Tschebyscheff-Polynome} Eine Relation der Form~\eqref{buch:orthogonal:eqn:multixrelation} wurde bereits in Abschnitt~\ref{buch:potenzen:tschebyscheff:rekursionsbeziehungen} @@ -80,12 +80,12 @@ hergeleitet. In der Form~\eqref{buch:orthogonal:eqn:rekursion} geschrieben lautet sie \[ -T_{n+1}(x) = 2x\,T_n(x)-T_{n-1}(x). +T_{n+1}(x) = 2x\,T_n(x)-T_{n-1}(x), \] also $A_n=2$, $B_n=0$ und $C_n=1$. -\subsection{Beweis von Satz~\ref{buch:orthogonal:satz:drei-term-rekursion}} +\subsubsection{Beweis von Satz~\ref{buch:orthogonal:satz:drei-term-rekursion}} Die Relation~\eqref{buch:orthogonal:eqn:multixrelation} zeigt auch, dass der Beweis die Koeffizienten $\langle xp_k,p_j\rangle_w$ berechnen muss. diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile index a0d7b34..0c1cbc3 100644 --- a/buch/papers/nav/images/Makefile +++ b/buch/papers/nav/images/Makefile @@ -3,9 +3,42 @@ # # (c) 2022 # +all: dreiecke dreieck.pdf: dreieck.tex dreieckdata.tex macros.tex pdflatex dreieck.tex dreieckdata.tex: pk.m octave pk.m + +DREIECKE = \ + dreieck1.pdf \ + dreieck2.pdf \ + dreieck3.pdf \ + dreieck4.pdf \ + dreieck5.pdf \ + dreieck6.pdf \ + dreieck7.pdf + +dreiecke: $(DREIECKE) + +dreieck1.pdf: dreieck1.tex dreieckdata.tex macros.tex + pdflatex dreieck1.tex + +dreieck2.pdf: dreieck2.tex dreieckdata.tex macros.tex + pdflatex dreieck2.tex + +dreieck3.pdf: dreieck3.tex dreieckdata.tex macros.tex + pdflatex dreieck3.tex + +dreieck4.pdf: dreieck4.tex dreieckdata.tex macros.tex + pdflatex dreieck4.tex + +dreieck5.pdf: dreieck5.tex dreieckdata.tex macros.tex + pdflatex dreieck5.tex + +dreieck6.pdf: dreieck6.tex dreieckdata.tex macros.tex + pdflatex dreieck6.tex + +dreieck7.pdf: dreieck7.tex dreieckdata.tex macros.tex + pdflatex dreieck7.tex diff --git a/buch/papers/nav/images/dreieck1.pdf b/buch/papers/nav/images/dreieck1.pdf new file mode 100644 index 0000000..5bdf23d Binary files /dev/null and b/buch/papers/nav/images/dreieck1.pdf differ diff --git a/buch/papers/nav/images/dreieck1.tex b/buch/papers/nav/images/dreieck1.tex new file mode 100644 index 0000000..436314c --- /dev/null +++ b/buch/papers/nav/images/dreieck1.tex @@ -0,0 +1,59 @@ +% +% dreieck.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +\winkelAlpha{red} +\winkelGamma{blue} +\winkelBeta{darkgreen} + +\seiteC{black} +\seiteB{black} +\seiteA{black} + +%\seiteL{gray} +\seitePB{gray} +\seitePC{gray} + +\draw[line width=1.4pt] \kanteAB; +\draw[line width=1.4pt] \kanteAC; +%\draw[color=gray] \kanteAP; +\draw[line width=1.4pt] \kanteBC; +\draw[color=gray] \kanteBP; +\draw[color=gray] \kanteCP; + +\punkt{(A)}{black}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{gray}; + +\node at (A) [above] {$A$}; +\node at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node[color=gray] at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/dreieck2.pdf b/buch/papers/nav/images/dreieck2.pdf new file mode 100644 index 0000000..a872b25 Binary files /dev/null and b/buch/papers/nav/images/dreieck2.pdf differ diff --git a/buch/papers/nav/images/dreieck2.tex b/buch/papers/nav/images/dreieck2.tex new file mode 100644 index 0000000..99aabb7 --- /dev/null +++ b/buch/papers/nav/images/dreieck2.tex @@ -0,0 +1,59 @@ +% +% dreieck2.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +%\winkelAlpha{red} +%\winkelGamma{blue} +%\winkelBeta{darkgreen} + +\seiteC{black} +\seiteB{black} +%\seiteA{black} + +%\seiteL{gray} +\seitePB{gray} +\seitePC{gray} + +\draw[line width=1.4pt] \kanteAB; +\draw[line width=1.4pt] \kanteAC; +%\draw[color=gray] \kanteAP; +\draw[line width=1.4pt] \kanteBC; +\draw[color=gray] \kanteBP; +\draw[color=gray] \kanteCP; + +\punkt{(A)}{black}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{gray}; + +\node at (A) [above] {$A$}; +\node at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node[color=gray] at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/dreieck3.pdf b/buch/papers/nav/images/dreieck3.pdf new file mode 100644 index 0000000..65070c6 Binary files /dev/null and b/buch/papers/nav/images/dreieck3.pdf differ diff --git a/buch/papers/nav/images/dreieck3.tex b/buch/papers/nav/images/dreieck3.tex new file mode 100644 index 0000000..0cf5363 --- /dev/null +++ b/buch/papers/nav/images/dreieck3.tex @@ -0,0 +1,59 @@ +% +% dreieck.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +\winkelAlpha{red} +%\winkelGamma{blue} +%\winkelBeta{darkgreen} + +\seiteC{black} +\seiteB{black} +%\seiteA{black} + +%\seiteL{gray} +\seitePB{gray} +\seitePC{gray} + +\draw[line width=1.4pt] \kanteAB; +\draw[line width=1.4pt] \kanteAC; +%\draw[color=gray] \kanteAP; +\draw[line width=1.4pt] \kanteBC; +\draw[color=gray] \kanteBP; +\draw[color=gray] \kanteCP; + +\punkt{(A)}{black}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{gray}; + +\node at (A) [above] {$A$}; +\node at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node[color=gray] at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/dreieck4.pdf b/buch/papers/nav/images/dreieck4.pdf new file mode 100644 index 0000000..4871a1e Binary files /dev/null and b/buch/papers/nav/images/dreieck4.pdf differ diff --git a/buch/papers/nav/images/dreieck4.tex b/buch/papers/nav/images/dreieck4.tex new file mode 100644 index 0000000..19a7d12 --- /dev/null +++ b/buch/papers/nav/images/dreieck4.tex @@ -0,0 +1,64 @@ +% +% dreieck4.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +%\winkelKappa{gray} + +%\winkelAlpha{red} +%\winkelGamma{blue} +%\winkelBeta{darkgreen} + +%\winkelOmega{gray} +\winkelBetaEins{brown} + +%\seiteC{gray} +%\seiteB{gray} +%\seiteL{gray} + +\seiteA{black} +\seitePB{black} +\seitePC{black} + +\draw[color=gray] \kanteAB; +\draw[color=gray] \kanteAC; +%\draw[color=gray] \kanteAP; +\draw[color=black,line width=1.4pt] \kanteBC; +\draw[color=black,line width=1.4pt] \kanteBP; +\draw[color=black,line width=1.4pt] \kanteCP; + +\punkt{(A)}{gray}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{black}; + +\node[color=gray] at (A) [above] {$A$}; +\node at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/dreieck5.pdf b/buch/papers/nav/images/dreieck5.pdf new file mode 100644 index 0000000..cf686e0 Binary files /dev/null and b/buch/papers/nav/images/dreieck5.pdf differ diff --git a/buch/papers/nav/images/dreieck5.tex b/buch/papers/nav/images/dreieck5.tex new file mode 100644 index 0000000..d1117d1 --- /dev/null +++ b/buch/papers/nav/images/dreieck5.tex @@ -0,0 +1,64 @@ +% +% dreieck4.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +%\winkelKappa{gray} + +%\winkelAlpha{red} +%\winkelGamma{blue} +%\winkelBeta{darkgreen} + +%\winkelOmega{gray} +%\winkelBetaEins{brown} + +%\seiteC{gray} +%\seiteB{gray} +%\seiteL{gray} + +%\seiteA{black} +\seitePB{black} +\seitePC{black} + +\draw[color=gray] \kanteAB; +\draw[color=gray] \kanteAC; +%\draw[color=gray] \kanteAP; +\draw[color=black,line width=1.4pt] \kanteBC; +\draw[color=black,line width=1.4pt] \kanteBP; +\draw[color=black,line width=1.4pt] \kanteCP; + +\punkt{(A)}{gray}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{black}; + +\node[color=gray] at (A) [above] {$A$}; +\node at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/dreieck6.pdf b/buch/papers/nav/images/dreieck6.pdf new file mode 100644 index 0000000..7efd673 Binary files /dev/null and b/buch/papers/nav/images/dreieck6.pdf differ diff --git a/buch/papers/nav/images/dreieck6.tex b/buch/papers/nav/images/dreieck6.tex new file mode 100644 index 0000000..87db1c2 --- /dev/null +++ b/buch/papers/nav/images/dreieck6.tex @@ -0,0 +1,64 @@ +% +% dreieck6.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +\winkelKappa{gray} + +%\winkelAlpha{red} +%\winkelGamma{blue} +%\winkelBeta{darkgreen} + +%\winkelOmega{gray} +%\winkelBetaEins{brown} + +\seiteC{black} +\seiteB{black} +%\seiteA{gray} + +\seiteL{black} +\seitePB{black} +\seitePC{black} + +\draw[color=black,line width=1.4pt] \kanteAB; +\draw[color=black,line width=1.4pt] \kanteAC; +\draw[color=black,line width=1.4pt] \kanteAP; +%\draw[color=gray] \kanteBC; +\draw[color=black,line width=1.4pt] \kanteBP; +\draw[color=black,line width=1.4pt] \kanteCP; + +\punkt{(A)}{black}; +\punkt{(B)}{black}; +\punkt{(C)}{black}; +\punkt{(P)}{black}; + +\node at (A) [above] {$A$}; +\node at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/nav/images/dreieck7.pdf b/buch/papers/nav/images/dreieck7.pdf new file mode 100644 index 0000000..aa83e28 Binary files /dev/null and b/buch/papers/nav/images/dreieck7.pdf differ diff --git a/buch/papers/nav/images/dreieck7.tex b/buch/papers/nav/images/dreieck7.tex new file mode 100644 index 0000000..f084708 --- /dev/null +++ b/buch/papers/nav/images/dreieck7.tex @@ -0,0 +1,64 @@ +% +% dreieck.tex -- sphärische Dreiecke für Positionsbestimmung +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\def\skala{1} + +\def\punkt#1#2{ + \fill[color=#2] #1 circle[radius=0.08]; +} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{dreieckdata.tex} +\input{macros.tex} + +%\winkelKappa{gray} + +%\winkelAlpha{red} +%\winkelGamma{blue} +%\winkelBeta{darkgreen} + +\winkelOmega{gray} +%\winkelBetaEins{brown} + +\seiteC{black} +\seiteB{black} +\seiteA{gray} + +\seiteL{black} +\seitePB{gray} +\seitePC{black} + +\draw[color=gray] \kanteAB; +\draw[color=black,line width=1.4pt] \kanteAC; +\draw[color=black,line width=1.4pt] \kanteAP; +\draw[color=gray] \kanteBC; +\draw[color=gray] \kanteBP; +\draw[line width=1.4pt] \kanteCP; + +\punkt{(A)}{black}; +\punkt{(B)}{gray}; +\punkt{(C)}{black}; +\punkt{(P)}{black}; + +\node at (A) [above] {$A$}; +\node[color=gray] at (B) [left] {$B$}; +\node at (C) [right] {$C$}; +\node at (P) [below] {$P$}; + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1 From 7b3657a77eeec57f2dd21de6fdc36e5240560c8e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 13 May 2022 15:13:30 +0200 Subject: improvements --- buch/papers/fm/anim/Makefile | 12 +++++ buch/papers/fm/anim/animation.tex | 85 +++++++++++++++++++++++++++++++++ buch/papers/fm/anim/fm.m | 98 +++++++++++++++++++++++++++++++++++++++ 3 files changed, 195 insertions(+) create mode 100644 buch/papers/fm/anim/Makefile create mode 100644 buch/papers/fm/anim/animation.tex create mode 100644 buch/papers/fm/anim/fm.m diff --git a/buch/papers/fm/anim/Makefile b/buch/papers/fm/anim/Makefile new file mode 100644 index 0000000..f4c7850 --- /dev/null +++ b/buch/papers/fm/anim/Makefile @@ -0,0 +1,12 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller +# +all: animation.pdf + +parts.tex: fm.m + octave fm.m + +animation.pdf: animation.tex parts.tex + pdflatex animation.tex diff --git a/buch/papers/fm/anim/animation.tex b/buch/papers/fm/anim/animation.tex new file mode 100644 index 0000000..4a6f428 --- /dev/null +++ b/buch/papers/fm/anim/animation.tex @@ -0,0 +1,85 @@ +% +% animation.tex +% +% (c) 2022 Prof Dr Andreas Müller, +% +\documentclass[aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{epic} +\usepackage{color} +\usepackage{array} +\usepackage{ifthen} +\usepackage{lmodern} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{nccmath} +\usepackage{mathtools} +\usepackage{adjustbox} +\usepackage{multimedia} +\usepackage{verbatim} +\usepackage{wasysym} +\usepackage{stmaryrd} +\usepackage{tikz} +\usetikzlibrary{shapes.geometric} +\usetikzlibrary{decorations.pathreplacing} +\usetikzlibrary{calc} +\usetikzlibrary{arrows} +\usetikzlibrary{3d} +\usetikzlibrary{arrows,shapes,math,decorations.text,automata} +\usepackage{pifont} +\usepackage[all]{xy} +\usepackage[many]{tcolorbox} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\begin{document} + +\def\spektrum#1#2{ +\only<#1>{ + \begin{scope} + \color{red} + \input{#2} + \end{scope} +} +} + +\begin{frame} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\def\df{0.37} +\def\da{1} + +\draw[->,color=gray] (0,-0.1) -- (0,6.3) [right] coordinate[label={right:$a$}]; + +\foreach \a in {1,...,5}{ + \draw[color=gray!50] (-6,{(6-\a)*\da}) -- (6,{(6-\a)*\da}); +} +\draw[color=gray!50] (-6,{6*\da}) -- (6,{6*\da}); +\foreach \f in {-15,-10,-5,5,10,15}{ + \draw[color=gray!50] ({\f*\df},0) -- ({\f*\df},{6*\da}); +} + +\input{parts.tex} + +\draw[->] (-6.1,0) -- (6.9,0) coordinate[label={$f$}]; +\foreach \f in {-16,...,16}{ + \draw ({\f*\df},-0.05) -- ({\f*\df},0.05); +} +\foreach \f in {-15,-10,-5,5,10,15}{ + \node at ({\f*\df},-0.1) [below] {$\f f_m$}; + \draw ({\f*\df},-0.1) -- ({\f*\df},0.1); +} +\node at (0,-0.1) [below] {$0$}; + +\foreach \a in {1,...,5}{ + \node at (6,{(6-\a)*\da}) [right] {$-\a$}; +} +\node at (6,{6*\da}) [right] {$\phantom{-}0$}; + +\end{tikzpicture} +\end{center} +\end{frame} + +\end{document} diff --git a/buch/papers/fm/anim/fm.m b/buch/papers/fm/anim/fm.m new file mode 100644 index 0000000..9062818 --- /dev/null +++ b/buch/papers/fm/anim/fm.m @@ -0,0 +1,98 @@ +# +# fm.m -- animation frequenzspektrum +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global fc; +fc = 1e6; +global width; +width = 16; +global fm; +fm = 1000; +global gamma; +gamma = 2; +global resolution; +resolution = 300; + +function retval = spektrum(beta, fm) + global width; + global fc; + retval = zeros(2 * width + 1, 2); + center = width + 1; + for k = (0:width) + retval(center - k, 1) = fc - k * fm; + retval(center + k, 1) = fc + k * fm; + a = besselj(k, beta); + retval(center - k, 2) = a; + retval(center + k, 2) = a; + endfor +endfunction + +function drawspectrum(fn, spectrum, foffset, fscale, beta) + n = size(spectrum)(1,1); + for i = (1:n) + f = (spectrum(i, 1) - foffset)/fscale; + a = log10(spectrum(i, 2)) + 6; + if (a < 0) + a = 0; + end + fprintf(fn, "\\draw[line width=3.5pt] "); + fprintf(fn, "({%.2f*\\df},0) -- ({%.2f*\\df},{%.5f*\\da});\n", + f, f, abs(a)); + fprintf(fn, "\\node at ({-15*\\df},5.5) [right] {$\\beta = %.3f$};", beta); + endfor +endfunction + +function drawhull(fn, beta) + global resolution; + fprintf(fn, "\\begin{scope}\n"); + fprintf(fn, "\\clip ({-16.5*\\df},0) rectangle ({16.5*\\df},{6*\\da});\n"); + p = zeros(resolution, 2); + for k = (1:resolution) + nu = 16.5 * (k - 1) / resolution; + p(k,1) = nu; + y = log10(abs(besselj(nu, beta))) + 6; + p(k,2) = y; + end + fprintf(fn, "\\draw[color=blue] ({%.4f*\\df},{%.5f*\\da})", + p(1,1), p(1,2)); + for k = (2:resolution) + fprintf(fn, "\n -- ({%.4f*\\df},{%.5f*\\da})", + p(k,1), p(k,2)); + endfor + fprintf(fn, ";\n\n"); + fprintf(fn, "\\draw[color=blue] ({%.4f*\\df},{%.5f*\\da})", + p(1,1), p(1,2)); + for k = (2:resolution) + fprintf(fn, "\n -- ({%.4f*\\df},{%.5f*\\da})", + -p(k,1), p(k,2)); + endfor + fprintf(fn, ";\n\n"); + fprintf(fn, "\\end{scope}\n"); +endfunction + +function animation(betamin, betamax, steps) + global fm; + global fc; + global gamma; + fa = fopen("parts.tex", "w"); + for k = (1:steps) + % add entry to parts.tex + fprintf(fa, "\\spektrum{%d}{texfiles/a%04d.tex}\n", k, k); + % compute beta + x = (k - 1) / (steps - 1); + beta = betamin + (betamax - betamin) * (x ^ gamma); + % create a new file + name = sprintf("texfiles/a%04d.tex", k); + fn = fopen(name, "w"); + % write the hull + drawhull(fn, beta); + % compute and write the spectrum + spectrum = spektrum(beta, fm); + drawspectrum(fn, spectrum, fc, fm, beta); + fclose(fn); + endfor + fclose(fa); +endfunction + +animation(0.001,10.1,200) -- cgit v1.2.1 From d223b0ff1fb5364b2b243b8fd4fd7a0e9ffba285 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 13 May 2022 20:12:50 +0200 Subject: 3dimages --- buch/papers/nav/images/Makefile | 66 ++++++++++++++- buch/papers/nav/images/common.inc | 149 ++++++++++++++++++++++++++++++++++ buch/papers/nav/images/dreieck3d1.pov | 58 +++++++++++++ buch/papers/nav/images/dreieck3d1.tex | 53 ++++++++++++ buch/papers/nav/images/dreieck3d2.pov | 26 ++++++ buch/papers/nav/images/dreieck3d2.tex | 53 ++++++++++++ buch/papers/nav/images/dreieck3d3.pov | 37 +++++++++ buch/papers/nav/images/dreieck3d3.tex | 53 ++++++++++++ buch/papers/nav/images/dreieck3d4.pov | 37 +++++++++ buch/papers/nav/images/dreieck3d4.tex | 54 ++++++++++++ buch/papers/nav/images/dreieck3d5.pov | 26 ++++++ buch/papers/nav/images/dreieck3d5.tex | 53 ++++++++++++ buch/papers/nav/images/dreieck3d6.pov | 37 +++++++++ buch/papers/nav/images/dreieck3d6.tex | 55 +++++++++++++ buch/papers/nav/images/dreieck3d7.pov | 39 +++++++++ buch/papers/nav/images/dreieck3d7.tex | 55 +++++++++++++ 16 files changed, 850 insertions(+), 1 deletion(-) create mode 100644 buch/papers/nav/images/common.inc create mode 100644 buch/papers/nav/images/dreieck3d1.pov create mode 100644 buch/papers/nav/images/dreieck3d1.tex create mode 100644 buch/papers/nav/images/dreieck3d2.pov create mode 100644 buch/papers/nav/images/dreieck3d2.tex create mode 100644 buch/papers/nav/images/dreieck3d3.pov create mode 100644 buch/papers/nav/images/dreieck3d3.tex create mode 100644 buch/papers/nav/images/dreieck3d4.pov create mode 100644 buch/papers/nav/images/dreieck3d4.tex create mode 100644 buch/papers/nav/images/dreieck3d5.pov create mode 100644 buch/papers/nav/images/dreieck3d5.tex create mode 100644 buch/papers/nav/images/dreieck3d6.pov create mode 100644 buch/papers/nav/images/dreieck3d6.tex create mode 100644 buch/papers/nav/images/dreieck3d7.pov create mode 100644 buch/papers/nav/images/dreieck3d7.tex diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile index 0c1cbc3..c9dcacc 100644 --- a/buch/papers/nav/images/Makefile +++ b/buch/papers/nav/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2022 # -all: dreiecke +all: dreiecke3d dreieck.pdf: dreieck.tex dreieckdata.tex macros.tex pdflatex dreieck.tex @@ -42,3 +42,67 @@ dreieck6.pdf: dreieck6.tex dreieckdata.tex macros.tex dreieck7.pdf: dreieck7.tex dreieckdata.tex macros.tex pdflatex dreieck7.tex + +DREIECKE3D = \ + dreieck3d1.pdf \ + dreieck3d2.pdf \ + dreieck3d3.pdf \ + dreieck3d4.pdf \ + dreieck3d5.pdf \ + dreieck3d6.pdf \ + dreieck3d7.pdf + +dreiecke3d: $(DREIECKE3D) + +POVRAYOPTIONS = -W1080 -H1080 +#POVRAYOPTIONS = -W480 -H480 + +dreieck3d1.png: dreieck3d1.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d1.png dreieck3d1.pov +dreieck3d1.jpg: dreieck3d1.png + convert dreieck3d1.png -density 300 -units PixelsPerInch dreieck3d1.jpg +dreieck3d1.pdf: dreieck3d1.tex dreieck3d1.jpg + pdflatex dreieck3d1.tex + +dreieck3d2.png: dreieck3d2.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d2.png dreieck3d2.pov +dreieck3d2.jpg: dreieck3d2.png + convert dreieck3d2.png -density 300 -units PixelsPerInch dreieck3d2.jpg +dreieck3d2.pdf: dreieck3d2.tex dreieck3d2.jpg + pdflatex dreieck3d2.tex + +dreieck3d3.png: dreieck3d3.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d3.png dreieck3d3.pov +dreieck3d3.jpg: dreieck3d3.png + convert dreieck3d3.png -density 300 -units PixelsPerInch dreieck3d3.jpg +dreieck3d3.pdf: dreieck3d3.tex dreieck3d3.jpg + pdflatex dreieck3d3.tex + +dreieck3d4.png: dreieck3d4.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d4.png dreieck3d4.pov +dreieck3d4.jpg: dreieck3d4.png + convert dreieck3d4.png -density 300 -units PixelsPerInch dreieck3d4.jpg +dreieck3d4.pdf: dreieck3d4.tex dreieck3d4.jpg + pdflatex dreieck3d4.tex + +dreieck3d5.png: dreieck3d5.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d5.png dreieck3d5.pov +dreieck3d5.jpg: dreieck3d5.png + convert dreieck3d5.png -density 300 -units PixelsPerInch dreieck3d5.jpg +dreieck3d5.pdf: dreieck3d5.tex dreieck3d5.jpg + pdflatex dreieck3d5.tex + +dreieck3d6.png: dreieck3d6.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d6.png dreieck3d6.pov +dreieck3d6.jpg: dreieck3d6.png + convert dreieck3d6.png -density 300 -units PixelsPerInch dreieck3d6.jpg +dreieck3d6.pdf: dreieck3d6.tex dreieck3d6.jpg + pdflatex dreieck3d6.tex + +dreieck3d7.png: dreieck3d7.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d7.png dreieck3d7.pov +dreieck3d7.jpg: dreieck3d7.png + convert dreieck3d7.png -density 300 -units PixelsPerInch dreieck3d7.jpg +dreieck3d7.pdf: dreieck3d7.tex dreieck3d7.jpg + pdflatex dreieck3d7.tex + diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc new file mode 100644 index 0000000..33d9384 --- /dev/null +++ b/buch/papers/nav/images/common.inc @@ -0,0 +1,149 @@ +// +// common.inc -- 3d Darstellung +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.034; + +#declare A = vnormalize(< 0, 1, 0>); +#declare B = vnormalize(< 1, 2, -8>); +#declare C = vnormalize(< 5, 1, 0>); +#declare P = vnormalize(< 5, -1, -7>); + +camera { + location <40, 20, -20> + look_at <0, 0.24, -0.20> + right x * imagescale + up y * imagescale +} + +light_source { + <10, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +// +// draw an arrow from to with thickness with +// color +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro grosskreis(normale, staerke) +union { + #declare v1 = vcross(normale, ); + #declare v1 = vnormalize(v1); + #declare v2 = vnormalize(vcross(v1, normale)); + #declare phisteps = 100; + #declare phistep = pi / phisteps; + #declare phi = 0; + #declare p1 = v1; + #while (phi < 2 * pi - phistep/2) + sphere { p1, staerke } + #declare phi = phi + phistep; + #declare p2 = v1 * cos(phi) + v2 * sin(phi); + cylinder { p1, p2, staerke } + #declare p1 = p2; + #end +} +#end + +#macro seite(p, q, staerke) + #declare n = vcross(p, q); + intersection { + grosskreis(n, staerke) + plane { -vcross(n, q) * vdot(vcross(n, q), p), 0 } + plane { -vcross(n, p) * vdot(vcross(n, p), q), 0 } + } +#end + +#macro winkel(w, p, q, staerke) + #declare n = vnormalize(w); + #declare pp = vnormalize(p - vdot(n, p) * n); + #declare qq = vnormalize(q - vdot(n, q) * n); + intersection { + sphere { <0, 0, 0>, 1 + staerke } + cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), 0.4 } + plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 } + plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 } + } +#end + +#macro punkt(p, staerke) + sphere { p, 1.5 * staerke } +#end + +#declare fett = 0.015; +#declare fine = 0.010; + +#declare dreieckfarbe = rgb<0.6,0.6,0.6>; +#declare rot = rgb<0.8,0.2,0.2>; +#declare gruen = rgb<0,0.6,0>; +#declare blau = rgb<0.2,0.2,0.8>; + +sphere { + <0, 0, 0>, 1 + pigment { + color rgb<0.8,0.8,0.8> + } +} + +//union { +// sphere { A, 0.02 } +// sphere { B, 0.02 } +// sphere { C, 0.02 } +// sphere { P, 0.02 } +// pigment { +// color Red +// } +//} + +//union { +// winkel(A, B, C) +// winkel(B, P, C) +// seite(B, C, 0.01) +// seite(B, P, 0.01) +// pigment { +// color rgb<0,0.6,0> +// } +//} diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov new file mode 100644 index 0000000..8afe60e --- /dev/null +++ b/buch/papers/nav/images/dreieck3d1.pov @@ -0,0 +1,58 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fett) + seite(B, C, fett) + seite(A, C, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fine) + seite(B, P, fine) + seite(C, P, fine) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, C, fine) + pigment { + color rot + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, C, A, fine) + pigment { + color gruen + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(C, A, B, fine) + pigment { + color blau + } + finish { + specular 0.95 + metallic + } +} diff --git a/buch/papers/nav/images/dreieck3d1.tex b/buch/papers/nav/images/dreieck3d1.tex new file mode 100644 index 0000000..799b21a --- /dev/null +++ b/buch/papers/nav/images/dreieck3d1.tex @@ -0,0 +1,53 @@ +% +% dreieck3d1.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d1.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +\node at (0.7,3) {$\alpha$}; +\node at (-2.5,-0.5) {$\beta$}; +\node at (2.3,-1.2) {$\gamma$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov new file mode 100644 index 0000000..c23a54c --- /dev/null +++ b/buch/papers/nav/images/dreieck3d2.pov @@ -0,0 +1,26 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fett) + seite(B, C, fett) + seite(A, C, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fine) + seite(B, P, fine) + seite(C, P, fine) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/dreieck3d2.tex b/buch/papers/nav/images/dreieck3d2.tex new file mode 100644 index 0000000..0f6e10c --- /dev/null +++ b/buch/papers/nav/images/dreieck3d2.tex @@ -0,0 +1,53 @@ +% +% dreieck3d2.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d2.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +%\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +%\node at (0.7,3) {$\alpha$}; +%\node at (-2.5,-0.5) {$\beta$}; +%\node at (2.3,-1.2) {$\gamma$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov new file mode 100644 index 0000000..f2496b5 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d3.pov @@ -0,0 +1,37 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fett) + seite(B, C, fett) + seite(A, C, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fine) + seite(B, P, fine) + seite(C, P, fine) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, C, fine) + pigment { + color rot + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/dreieck3d3.tex b/buch/papers/nav/images/dreieck3d3.tex new file mode 100644 index 0000000..a047b1b --- /dev/null +++ b/buch/papers/nav/images/dreieck3d3.tex @@ -0,0 +1,53 @@ +% +% dreieck3d3.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d3.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +%\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +\node at (0.7,3) {$\alpha$}; +%\node at (-2.5,-0.5) {$\beta$}; +%\node at (2.3,-1.2) {$\gamma$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov new file mode 100644 index 0000000..bddcf7c --- /dev/null +++ b/buch/papers/nav/images/dreieck3d4.pov @@ -0,0 +1,37 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fine) + seite(A, C, fine) + punkt(A, fine) + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + seite(B, C, fett) + seite(B, P, fett) + seite(C, P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, C, P, fine) + pigment { + color rgb<0.6,0.4,0.2> + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/dreieck3d4.tex b/buch/papers/nav/images/dreieck3d4.tex new file mode 100644 index 0000000..d49fb66 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d4.tex @@ -0,0 +1,54 @@ +% +% dreieck3d4.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d4.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +%\node at (-1.9,2.1) {$c$}; +\node at (-0.2,-1.2) {$a$}; +%\node at (2.6,1.5) {$b$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +%\node at (0.7,3) {$\alpha$}; +%\node at (-2.5,-0.5) {$\beta$}; +%\node at (2.3,-1.2) {$\gamma$}; +\node at (-2.3,-1.5) {$\beta_1$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov new file mode 100644 index 0000000..32fc9e6 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d5.pov @@ -0,0 +1,26 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fine) + seite(A, C, fine) + punkt(A, fine) + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + seite(B, C, fett) + seite(B, P, fett) + seite(C, P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/dreieck3d5.tex b/buch/papers/nav/images/dreieck3d5.tex new file mode 100644 index 0000000..8011b37 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d5.tex @@ -0,0 +1,53 @@ +% +% dreieck3d5.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d5.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +%\node at (-1.9,2.1) {$c$}; +%\node at (-0.2,-1.2) {$a$}; +%\node at (2.6,1.5) {$b$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +%\node at (0.7,3) {$\alpha$}; +%\node at (-2.5,-0.5) {$\beta$}; +%\node at (2.3,-1.2) {$\gamma$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov new file mode 100644 index 0000000..7611950 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d6.pov @@ -0,0 +1,37 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fett) + seite(A, C, fett) + seite(B, P, fett) + seite(C, P, fett) + seite(A, P, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, A, P, fine) + pigment { + color rgb<0.6,0.2,0.6> + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/dreieck3d6.tex b/buch/papers/nav/images/dreieck3d6.tex new file mode 100644 index 0000000..bbca2ca --- /dev/null +++ b/buch/papers/nav/images/dreieck3d6.tex @@ -0,0 +1,55 @@ +% +% dreieck3d6.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d6.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +%\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; +\node at (-0.7,0.3) {$l$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +%\node at (0.7,3) {$\alpha$}; +%\node at (-2.5,-0.5) {$\beta$}; +%\node at (2.3,-1.2) {$\gamma$}; +\node at (-2.4,-0.6) {$\kappa$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov new file mode 100644 index 0000000..fa48f5b --- /dev/null +++ b/buch/papers/nav/images/dreieck3d7.pov @@ -0,0 +1,39 @@ +// +// dreiecke3d.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, C, fett) + seite(A, P, fett) + seite(C, P, fett) + + seite(A, B, fine) + seite(B, C, fine) + seite(B, P, fine) + punkt(A, fett) + punkt(C, fett) + punkt(P, fett) + punkt(B, fine) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, P, C, fine) + pigment { + color rgb<0.4,0.4,1> + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/dreieck3d7.tex b/buch/papers/nav/images/dreieck3d7.tex new file mode 100644 index 0000000..4027a8b --- /dev/null +++ b/buch/papers/nav/images/dreieck3d7.tex @@ -0,0 +1,55 @@ +% +% dreieck3d7.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d7.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; +\node at (-0.7,0.3) {$l$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +%\node at (0.7,3) {$\alpha$}; +%\node at (-2.5,-0.5) {$\beta$}; +%\node at (2.3,-1.2) {$\gamma$}; +\node at (0.8,3.1) {$\omega$}; + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From fc8bf49548f168fe0a77e1446c73ff7be5d980cf Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 13 May 2022 23:11:38 +0200 Subject: fresnel paper erste Fassung --- buch/papers/fresnel/Makefile | 15 ++- buch/papers/fresnel/eulerspirale.m | 61 +++++++++ buch/papers/fresnel/eulerspirale.pdf | Bin 0 -> 22592 bytes buch/papers/fresnel/eulerspirale.tex | 41 ++++++ buch/papers/fresnel/fresnelgraph.pdf | Bin 0 -> 30018 bytes buch/papers/fresnel/fresnelgraph.tex | 46 +++++++ buch/papers/fresnel/main.tex | 24 +--- buch/papers/fresnel/pfad.pdf | Bin 0 -> 19126 bytes buch/papers/fresnel/pfad.tex | 34 +++++ buch/papers/fresnel/references.bib | 11 ++ buch/papers/fresnel/teil0.tex | 109 +++++++++++++--- buch/papers/fresnel/teil1.tex | 239 ++++++++++++++++++++++++++++------- buch/papers/fresnel/teil2.tex | 48 +++---- buch/papers/fresnel/teil3.tex | 136 +++++++++++++++----- 14 files changed, 617 insertions(+), 147 deletions(-) create mode 100644 buch/papers/fresnel/eulerspirale.m create mode 100644 buch/papers/fresnel/eulerspirale.pdf create mode 100644 buch/papers/fresnel/eulerspirale.tex create mode 100644 buch/papers/fresnel/fresnelgraph.pdf create mode 100644 buch/papers/fresnel/fresnelgraph.tex create mode 100644 buch/papers/fresnel/pfad.pdf create mode 100644 buch/papers/fresnel/pfad.tex diff --git a/buch/papers/fresnel/Makefile b/buch/papers/fresnel/Makefile index c8aa073..11af3a7 100644 --- a/buch/papers/fresnel/Makefile +++ b/buch/papers/fresnel/Makefile @@ -1,9 +1,22 @@ # # Makefile -- make file for the paper fresnel # -# (c) 2020 Prof Dr Andreas Mueller +# (c) 2022 Prof Dr Andreas Mueller # +all: fresnelgraph.pdf eulerspirale.pdf pfad.pdf images: @echo "no images to be created in fresnel" +eulerpath.tex: eulerspirale.m + octave eulerspirale.m + +fresnelgraph.pdf: fresnelgraph.tex eulerpath.tex + pdflatex fresnelgraph.tex + +eulerspirale.pdf: eulerspirale.tex eulerpath.tex + pdflatex eulerspirale.tex + +pfad.pdf: pfad.tex + pdflatex pfad.tex + diff --git a/buch/papers/fresnel/eulerspirale.m b/buch/papers/fresnel/eulerspirale.m new file mode 100644 index 0000000..84e3696 --- /dev/null +++ b/buch/papers/fresnel/eulerspirale.m @@ -0,0 +1,61 @@ +# +# eulerspirale.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +# +global n; +n = 1000; +global tmax; +tmax = 10; +global N; +N = round(n*5/tmax); + +function retval = f(x, t) + x = pi * t^2 / 2; + retval = [ cos(x); sin(x) ]; +endfunction + +x0 = [ 0; 0 ]; +t = tmax * (0:n) / n; + +c = lsode(@f, x0, t); + +fn = fopen("eulerpath.tex", "w"); + +fprintf(fn, "\\def\\fresnela{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", c(i,1), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\fresnelb{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", -c(i,1), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fclose(fn); diff --git a/buch/papers/fresnel/eulerspirale.pdf b/buch/papers/fresnel/eulerspirale.pdf new file mode 100644 index 0000000..4a85a50 Binary files /dev/null and b/buch/papers/fresnel/eulerspirale.pdf differ diff --git a/buch/papers/fresnel/eulerspirale.tex b/buch/papers/fresnel/eulerspirale.tex new file mode 100644 index 0000000..38ef756 --- /dev/null +++ b/buch/papers/fresnel/eulerspirale.tex @@ -0,0 +1,41 @@ +% +% eulerspirale.tex -- Darstellung der Eulerspirale +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{eulerpath.tex} + +\def\s{8} + +\begin{scope}[scale=\s] +\draw[color=blue] (-0.5,-0.5) rectangle (0.5,0.5); +\draw[color=darkgreen,line width=1.4pt] \fresnela; +\draw[color=darkgreen,line width=1.4pt] \fresnelb; +\fill[color=blue] (0.5,0.5) circle[radius={0.1/\s}]; +\fill[color=blue] (-0.5,-0.5) circle[radius={0.1/\s}]; +\draw (-0.5,{-0.05/\s}) -- (-0.5,{0.05/\s}); +\draw (0.5,{-0.05/\s}) -- (0.5,{-0.05/\s}); +\node at (-0.5,0) [above left] {$\frac12$}; +\node at (0.5,0) [below right] {$\frac12$}; +\node at (0,-0.5) [below right] {$\frac12$}; +\node at (0,0.5) [above left] {$\frac12$}; +\end{scope} + +\draw[->] (-6.7,0) -- (6.9,0) coordinate[label={$C(x)$}];; +\draw[->] (0,-5.8) -- (0,6.1) coordinate[label={left:$S(x)$}];; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/fresnelgraph.pdf b/buch/papers/fresnel/fresnelgraph.pdf new file mode 100644 index 0000000..9ccad56 Binary files /dev/null and b/buch/papers/fresnel/fresnelgraph.pdf differ diff --git a/buch/papers/fresnel/fresnelgraph.tex b/buch/papers/fresnel/fresnelgraph.tex new file mode 100644 index 0000000..20df951 --- /dev/null +++ b/buch/papers/fresnel/fresnelgraph.tex @@ -0,0 +1,46 @@ +% +% fresnelgraph.tex -- Graphs of the fresnel functions +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{eulerpath.tex} +\def\dx{1.3} +\def\dy{2.6} + +\draw[color=gray] (0,{0.5*\dy}) -- ({5*\dx},{0.5*\dy}); +\draw[color=gray] (0,{-0.5*\dy}) -- ({-5*\dx},{-0.5*\dy}); + +\draw[color=blue,line width=1.4pt] \Splotright; +\draw[color=blue,line width=1.4pt] \Splotleft; + +\draw[color=red,line width=1.4pt] \Cplotright; +\draw[color=red,line width=1.4pt] \Cplotleft; + +\draw[->] (-6.7,0) -- (6.9,0) coordinate[label={$x$}]; +\draw[->] (0,-2.3) -- (0,2.3) coordinate[label={$y$}]; + +\foreach \x in {1,2,3,4,5}{ + \draw ({\x*\dx},-0.05) -- ({\x*\dx},0.05); + \draw ({-\x*\dx},-0.05) -- ({-\x*\dx},0.05); + \node at ({\x*\dx},-0.05) [below] {$\x$}; + \node at ({-\x*\dx},0.05) [above] {$-\x$}; +} +\draw (-0.05,{0.5*\dy}) -- (0.05,{0.5*\dy}); +\node at (-0.05,{0.5*\dy}) [left] {$\frac12$}; +\draw (-0.05,{-0.5*\dy}) -- (0.05,{-0.5*\dy}); +\node at (0.05,{-0.5*\dy}) [right] {$-\frac12$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/main.tex b/buch/papers/fresnel/main.tex index bbaf7e6..e6ee3b5 100644 --- a/buch/papers/fresnel/main.tex +++ b/buch/papers/fresnel/main.tex @@ -3,29 +3,11 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:fresnel}} -\lhead{Thema} +\chapter{Fresnel-Integrale\label{chapter:fresnel}} +\lhead{Fresnel-Integrale} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Andreas Müller} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} \input{papers/fresnel/teil0.tex} \input{papers/fresnel/teil1.tex} diff --git a/buch/papers/fresnel/pfad.pdf b/buch/papers/fresnel/pfad.pdf new file mode 100644 index 0000000..ff514cc Binary files /dev/null and b/buch/papers/fresnel/pfad.pdf differ diff --git a/buch/papers/fresnel/pfad.tex b/buch/papers/fresnel/pfad.tex new file mode 100644 index 0000000..5439a71 --- /dev/null +++ b/buch/papers/fresnel/pfad.tex @@ -0,0 +1,34 @@ +% +% pfad.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\draw[->] (-1,0) -- (9,0) coordinate[label={$\operatorname{Re}$}]; +\draw[->] (0,-1) -- (0,6) coordinate[label={left:$\operatorname{Im}$}]; + +\draw[->,color=red,line width=1.4pt] (0,0) -- (7,0); +\draw[->,color=blue,line width=1.4pt] (7,0) arc (0:45:7); +\draw[->,color=darkgreen,line width=1.4pt] (45:7) -- (0,0); + +\node[color=red] at (3.5,0) [below] {$\gamma_1(t) = tR$}; +\node[color=blue] at (25:7) [right] {$\gamma_2(t) = Re^{it}$}; +\node[color=darkgreen] at (45:3.5) [above left] {$\gamma_3(t) = te^{i\pi/4}$}; + +\node at (7,0) [below] {$R$}; +\node at (45:7) [above] {$Re^{i\pi/4}$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/references.bib b/buch/papers/fresnel/references.bib index 84cd3bc..58e9242 100644 --- a/buch/papers/fresnel/references.bib +++ b/buch/papers/fresnel/references.bib @@ -33,3 +33,14 @@ url = {https://doi.org/10.1016/j.acha.2017.11.004} } +@online{fresnel:fresnelC, + url = { https://functions.wolfram.com/GammaBetaErf/FresnelC/introductions/FresnelIntegrals/ShowAll.html }, + title = { FresnelC }, + date = { 2022-05-13 } +} + +@online{fresnel:wikipedia, + url = { https://en.wikipedia.org/wiki/Fresnel_integral }, + title = { Fresnel Integral }, + date = { 2022-05-13 } +} diff --git a/buch/papers/fresnel/teil0.tex b/buch/papers/fresnel/teil0.tex index 5e9fdaf..253e2f3 100644 --- a/buch/papers/fresnel/teil0.tex +++ b/buch/papers/fresnel/teil0.tex @@ -1,22 +1,101 @@ % -% einleitung.tex -- Beispiel-File für die Einleitung +% teil0.tex -- Definition % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{fresnel:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fresnel:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. +\section{Definition\label{fresnel:section:teil0}} +\rhead{Definition} +Die Funktion $e^{x^2}$ hat bekanntermassen keine elementare Stammfunktion, +weshalb die Fehlerfunktion als Stammfunktion definiert wurde. +Die Funktionen $\cos x^2$ und $\sin x^2$ sind eng mit $e^{x^2}$ +verwandt, es ist daher nicht überraschend, dass sie ebenfalls +keine elementare Stammfunktionen haben. +Dies rechtfertigt die Definition der Fresnel-Integrale als neue spezielle +Funktionen. -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. +\begin{definition} +Die Funktionen +\begin{align*} +C(x) &= \int_0^x \cos\biggl(\frac{\pi}2 t^2\biggr)\,dt +\\ +S(x) &= \int_0^x \sin\biggl(\frac{\pi}2 t^2\biggr)\,dt +\end{align*} +heissen die Fesnel-Integrale. +\end{definition} +Der Faktor $\frac{\pi}2$ ist einigermassen willkürlich, man könnte +daher noch allgemeiner die Funktionen +\begin{align*} +C_a(x) &= \int_0^x \cos(at^2)\,dt +\\ +S_a(x) &= \int_0^x \sin(at^2)\,dt +\end{align*} +definieren, so dass die Funktionen $C(x)$ und $S(x)$ der Fall +$a=\frac{\pi}2$ werden, also +\[ +\begin{aligned} +C(x) &= C_{\frac{\pi}2}(x), +& +S(x) &= S_{\frac{\pi}2}(x). +\end{aligned} +\] +Durch eine Substution $t=bs$ erhält man +\begin{align*} +C_a(x) +&= +\int_0^x \cos(at^2)\,dt += +b +\int_0^{\frac{x}b} \cos(ab^2s^2)\,ds += +b +C_{ab^2}\biggl(\frac{x}b\biggr) +\\ +S_a(x) +&= +\int_0^x \sin(at^2)\,dt += +b +\int_0^{\frac{x}b} \sin(ab^2s^2)\,ds += +b +S_{ab^2}\biggl(\frac{x}b\biggr). +\end{align*} +Indem man $ab^2=\frac{\pi}2$ setzt, also +\[ +b += +\sqrt{\frac{\pi}{2a}} +, +\] +kann man die Funktionen $C_a(x)$ und $S_a(x)$ durch $C(x)$ und $S(x)$ +ausdrücken: +\begin{align} +C_a(x) +&= +\sqrt{\frac{\pi}{2a}} +C\biggl(x +\sqrt{\frac{2a}{\pi}} +\biggr) +&&\text{und}& +S_a(x) +&= +\sqrt{\frac{\pi}{2a}} +S\biggl(x +\sqrt{\frac{2a}{\pi}} +\biggr). +\label{fresnel:equation:arg} +\end{align} +Im Folgenden werden wir meistens nur den Fall $a=1$, also die Funktionen +$C_1(x)$ und $S_1(x)$ betrachten, da in diesem Fall die Formeln einfacher +werden. +\begin{figure} +\centering +\includegraphics{papers/fresnel/fresnelgraph.pdf} +\caption{Graph der Funktionen $C(x)$ ({\color{red}rot}) +und $S(x)$ ({\color{blue}blau}) +\label{fresnel:figure:plot}} +\end{figure} +Die Abbildung~\ref{fresnel:figure:plot} zeigt die Graphen der +Funktion $C(x)$ und $S(x)$. diff --git a/buch/papers/fresnel/teil1.tex b/buch/papers/fresnel/teil1.tex index a2df138..df84797 100644 --- a/buch/papers/fresnel/teil1.tex +++ b/buch/papers/fresnel/teil1.tex @@ -1,55 +1,202 @@ % -% teil1.tex -- Beispiel-File für das Paper +% teil1.tex -- Euler-Spirale % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 1 -\label{fresnel:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{fresnel:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. +\section{Euler-Spirale +\label{fresnel:section:eulerspirale}} +\rhead{Euler-Spirale} +\begin{figure} +\centering +\includegraphics{papers/fresnel/eulerspirale.pdf} +\caption{Die Eulerspirale ist die Kurve mit der Parameterdarstellung +$x\mapsto (C(x),S(x))$, sie ist rot dargestellt. +Sie windet sich unendlich oft um die beiden Punkte $(\pm\frac12,\pm\frac12)$. +\label{fresnel:figure:eulerspirale}} +\end{figure} +Ein besseres Verständnis für die beiden Funktionen $C(x)$ und $S(x)$ +als die Darstellung~\ref{fresnel:figure:plot} ermöglicht die +Abbildung~\ref{fresnel:figure:eulerspirale}, die die beiden Funktionen +als die $x$- und $y$-Koordinaten der Parameterdarstellung einer Kurve +zeigt. +Sie heisst die {\em Euler-Spirale}. +Die Spirale scheint sich für $x\to\pm\infty$ um die Punkte +$(\pm\frac12,\pm\frac12)$ zu winden. -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? +\begin{figure} +\centering +\includegraphics{papers/fresnel/pfad.pdf} +\caption{Pfad zur Berechnung der Grenzwerte $C_1(\infty)$ und +$S_1(\infty)$ mit Hilfe des Cauchy-Integralsatzes +\label{fresnel:figure:pfad}} +\end{figure} -\subsection{De finibus bonorum et malorum -\label{fresnel:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. -Et harum quidem rerum facilis est et expedita distinctio -\ref{fresnel:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{fresnel:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. +\begin{satz} +Die Grenzwerte der Fresnel-Integrale für $x\to\pm\infty$ sind +\[ +\lim_{x\to\pm\infty} C(x) += +\lim_{x\to\pm\infty} S(x) += +\frac12. +\] +\end{satz} +\begin{proof}[Beweis] +Die komplexe Funktion +\[ +f(z) = e^{-z^2} +\] +ist eine ganze Funktion, das Integral über einen geschlossenen +Pfad in der komplexen Ebene verschwindet daher. +Wir verwenden den Pfad in Abbildung~\ref{fresnel:figure:pfad} +bestehend aus den drei Segmenten $\gamma_1$ entlang der reellen +Achse von $0$ bis $R$, dem Kreisbogen $\gamma_2$ um $0$ mit Radius $R$ +und $\gamma_3$ mit der Parametrisierung $t\mapsto te^{i\pi/4}$. + +Das Teilintegral über $\gamma_1$ ist +\[ +\lim_{R\to\infty} +\int_{\gamma_1} e^{-z^2}\,dz += +\int_0^\infty e^{-t^2}\,dt += +\frac{\sqrt{\pi}}2. +\] +Das Integral über $\gamma_3$ ist +\begin{align*} +\lim_{R\to\infty} +\int_{\gamma_3} +e^{-z^2}\,dz +&= +-\int_0^\infty \exp(-t^2 e^{i\pi/2}) e^{i\pi/4}\,dt += +- +\int_0^\infty e^{-it^2}\,dt\, +e^{i\pi/4} +\\ +&= +-e^{i\pi/4}\int_0^\infty \cos t^2 - i \sin t^2\,dt +\\ +&= +-\frac{1}{\sqrt{2}}(1+i) +\bigl( +C_1(\infty) +-i +S_1(\infty) +\bigr) +\\ +&= +-\frac{1}{\sqrt{2}} +\bigl( +C_1(\infty)+S_1(\infty) ++ +i(C_1(\infty)-S_1(\infty)) +\bigr), +\end{align*} +wobei wir +\[ +C_1(\infty) = \lim_{R\to\infty} C_1(R) +\qquad\text{und}\qquad +S_1(\infty) = \lim_{R\to\infty} S_1(R) +\] +abgekürzt haben. +Das Integral über das Segment $\gamma_2$ lässt sich +mit der Parametrisierung +\( +\gamma_2(t) += +Re^{it} += +R(\cos t + i\sin t) +\) +wie folgt +abschätzen: +\begin{align*} +\biggl|\int_{\gamma_2} e^{-z^2} \,dz\biggr| +&= +\biggl| +\int_0^{\frac{\pi}4} +\exp(-R^2(\cos 2t + i\sin 2t)) iR e^{it}\,dt +\biggr| +\\ +&\le +R +\int_0^{\frac{\pi}4} +e^{-R^2\cos 2t} +\,dt +\le +R +\int_0^{\frac{\pi}4} +e^{-R^2(1-\frac{4}{\pi}t)} +\,dt. +\intertext{Dabei haben wir $\cos 2t\ge 1-\frac{4}\pi t$ verwendet. +Mit dieser Vereinfachung kann das Integral ausgewertet werden und +ergibt} +&= +Re^{-R^2} +\int_0^{\frac{\pi}4} +e^{R^2\frac{\pi}4t} +\,dt += +Re^{-R^2} +\biggl[ +\frac{4}{\pi R^2} +e^{R^2\frac{\pi}4t} +\biggr]_0^{\frac{\pi}4} += +\frac{4}{\pi R} +e^{-R^2}(e^{R^2}-1) += +\frac{4}{\pi R} +(1-e^{-R^2}) +\to 0 +\end{align*} +für $R\to \infty$. +Im Grenzwert $R\to \infty$ kann der Teil $\gamma_2$ des Pfades +vernachlässigt werden. + +Das Integral über den geschlossenen Pfad $\gamma$ verschwindet. +Da der Teil $\gamma_2$ keine Rolle spielt, müssen sich die +Integrale über $\gamma_1$ und $\gamma_3$ wegheben, also +\begin{align*} +0 += +\int_\gamma e^{-z^2}\,dz +&= +\int_{\gamma_1} e^{-z^2}\,dz ++ +\int_{\gamma_2} e^{-z^2}\,dz ++ +\int_{\gamma_3} e^{-z^2}\,dz +\\ +&\to +\frac{\sqrt{\pi}}2 +-\frac{1}{\sqrt{2}}(C_1(\infty)+S_1(\infty)) +-\frac{i}{\sqrt{2}}(C_1(\infty)-S_1(\infty)). +\end{align*} +Der Imaginärteil ist $C_1(\infty)-S_1(\infty)$, da er verschwinden +muss, folgt $C_1(\infty)=S_1(\infty)$. +Nach Multlikation mit $\sqrt{2}$ folgt aus der Tatsache, dass auch +der Realteil verschwinden muss +\[ +\frac{\sqrt{\pi}}{\sqrt{2}} = C_1(\infty)+S_1(\infty) +\qquad +\Rightarrow +\qquad +C_1(\infty) += +S_1(\infty) += +\frac{\sqrt{\pi}}{2\sqrt{2}} +\] +Aus +\eqref{fresnel:equation:arg} +erhält man dann auch die Grenzwerte +\[ +C(\infty)=S(\infty)=\frac12. +\qedhere +\] +\end{proof} diff --git a/buch/papers/fresnel/teil2.tex b/buch/papers/fresnel/teil2.tex index 701c3ee..22d2a89 100644 --- a/buch/papers/fresnel/teil2.tex +++ b/buch/papers/fresnel/teil2.tex @@ -3,38 +3,22 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 -\label{fresnel:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? +\section{Klothoide +\label{fresnel:section:klothoide}} +\rhead{Klothoide} +In diesem Abschnitt soll gezeigt werden, dass die Krümmung der +Euler-Spirale proportional zur vom Nullpunkt aus gemessenen Bogenlänge +ist. -\subsection{De finibus bonorum et malorum -\label{fresnel:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\begin{definition} +Eine ebene Kurve, deren Krümmung proportionale zur Kurvenlänge ist, +heisst {\em Klothoide}. +\end{definition} +Die Klothoide wird zum Beispiel im Strassenbau bei Autobahnkurven +angewendet. +Fährt man mit konstanter Geschwindigkeit mit entlang einer Klothoide, +muss man die Krümmung mit konstaner Geschwindigkeit ändern, +also das Lenkrad mit konstanter Geschwindigkeit drehen. +Dies ermöglicht eine ruhige Fahrweise. diff --git a/buch/papers/fresnel/teil3.tex b/buch/papers/fresnel/teil3.tex index d4f15f6..a5b5878 100644 --- a/buch/papers/fresnel/teil3.tex +++ b/buch/papers/fresnel/teil3.tex @@ -3,38 +3,110 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 3 -\label{fresnel:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? +\section{Numerische Berechnung der Fresnel-Integrale +\label{fresnel:section:numerik}} +\rhead{Numerische Berechnung} +Die Fresnel-Integrale können mit verschiedenen Methoden effizient berechnet +werden. -\subsection{De finibus bonorum et malorum -\label{fresnel:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\subsection{Komplexe Fehlerfunktionen} +Es wurde schon darauf hingewiesen, dass der Integrand der Fresnel-Integrale +mit $e^{t^2}$ verwandt ist. +Tatsächlich kann gezeigt werden dass sich die Fresnel-Integrale mit +Hilfe der komplexen Fehlerfunktion als +\[ +\left. +\begin{matrix} +S_1(z) +\\ +C_1(z) +\end{matrix} +\; +\right\} += +\frac{1\pm i}4\biggl( +\operatorname{erf}\biggl(\frac{1+i}2\sqrt{\pi}z\biggr) +\mp +\operatorname{erf}\biggl(\frac{1-i}2\sqrt{\pi}z\biggr) +\biggr) +\] +ausdrücken lassen. +Diese Darstellung ist jedoch für die numerische Berechnung nur +beschränkt nützlich, weil die meisten Bibliotheken für die Fehlerfunktion +diese nur für reelle Argument auszuwerten gestatten. + +\subsection{Als Lösung einer Differentialgleichung} +Da die Fresnel-Integrale die sehr einfachen Differentialgleichungen +\[ +C'(x) = \cos \biggl(\frac{\pi}2 x^2\biggr) +\qquad\text{und}\qquad +S'(x) = \sin \biggl(\frac{\pi}2 x^2\biggr) +\] +erfüllen, kann man eine Methode zur Lösung von Differentialgleichung +verwenden. +Die Abbildungen~\ref{fresnel:figure:plot} und \ref{fresnel:figure:eulerspirale} +wurden auf diese Weise erzeugt. + +\subsection{Taylor-Reihe integrieren} +Die Taylorreihen +\begin{align*} +\cos x +&= +\sum_{k=0}^\infty \frac{(-1)^k}{(2k)!} x^{2k} +&&\text{und}& +\sin x +&= +\sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)!} x^{2k+1} +\intertext{% +der trigonometrischen Funktionen werden durch Einsetzen von $x=t^2$ +zu} +\cos t^2 +&= +\sum_{k=0}^\infty \frac{(-1)^k}{(2k)!} t^{4k} +&&\text{und}& +\sin t^2 +&= +\sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)!} t^{4k+2}. +\intertext{% +Die Fresnel-Integrale $C_1(x)$ und $S_1(x)$ können daher durch +termweise Integration mit Hilfe der Reihen} +C_1(x) +&= +\sum_{k=0}^\infty \frac{(-1)^k}{(2k)!} \frac{x^{4k+1}}{4k+1} +&&\text{und}& +S_1(x) +&= +\sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)!} \frac{x^{4k+3}}{4k+3} +\end{align*} +berechnet werden. +Diese Reihen sind insbesondere für kleine Werte von $x$ sehr +schnell konvergent. + +\subsection{Hypergeometrische Reihen} +Aus der Reihenentwicklung kann jetzt auch eine Darstellung der +Fresnel-Integrale durch hypergeometrische Reihen gefunden werden +\cite{fresnel:fresnelC}. +Es ergibt sich +\begin{align*} +S(z) +&= +\frac{\pi z^3}{6} +\cdot +\mathstrut_1F_2\biggl( +\begin{matrix}\frac34\\\frac32,\frac74\end{matrix} +; +-\frac{\pi^2z^4}{16} +\biggr) +\\ +C(z) +&= +z +\cdot +\mathstrut_1F_2\biggl( +\begin{matrix}\frac14\\\frac12,\frac54\end{matrix} +; +-\frac{\pi^2z^4}{16} +\biggr). +\end{align*} -- cgit v1.2.1 From 2b1142edd31d88f9c4b050abf4aeb1e885925ad5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 13 May 2022 23:15:21 +0200 Subject: typos --- buch/papers/fresnel/teil1.tex | 6 +++--- buch/papers/fresnel/teil3.tex | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/buch/papers/fresnel/teil1.tex b/buch/papers/fresnel/teil1.tex index df84797..a41ddb7 100644 --- a/buch/papers/fresnel/teil1.tex +++ b/buch/papers/fresnel/teil1.tex @@ -45,9 +45,9 @@ Die Grenzwerte der Fresnel-Integrale für $x\to\pm\infty$ sind \begin{proof}[Beweis] Die komplexe Funktion -\[ +\( f(z) = e^{-z^2} -\] +\) ist eine ganze Funktion, das Integral über einen geschlossenen Pfad in der komplexen Ebene verschwindet daher. Wir verwenden den Pfad in Abbildung~\ref{fresnel:figure:pfad} @@ -190,7 +190,7 @@ C_1(\infty) = S_1(\infty) = -\frac{\sqrt{\pi}}{2\sqrt{2}} +\frac{\sqrt{\pi}}{2\sqrt{2}}. \] Aus \eqref{fresnel:equation:arg} diff --git a/buch/papers/fresnel/teil3.tex b/buch/papers/fresnel/teil3.tex index a5b5878..37e6bee 100644 --- a/buch/papers/fresnel/teil3.tex +++ b/buch/papers/fresnel/teil3.tex @@ -30,7 +30,7 @@ C_1(z) \operatorname{erf}\biggl(\frac{1-i}2\sqrt{\pi}z\biggr) \biggr) \] -ausdrücken lassen. +ausdrücken lassen \cite{fresnel:fresnelC}. Diese Darstellung ist jedoch für die numerische Berechnung nur beschränkt nützlich, weil die meisten Bibliotheken für die Fehlerfunktion diese nur für reelle Argument auszuwerten gestatten. -- cgit v1.2.1 From a28b0e8a16564e78aaecc299526fa8bb96964e0e Mon Sep 17 00:00:00 2001 From: runterer Date: Sat, 14 May 2022 18:21:13 +0200 Subject: corrections to zeta_gamma --- buch/papers/zeta/zeta_gamma.tex | 53 ++++++++++++++++++++++++----------------- 1 file changed, 31 insertions(+), 22 deletions(-) diff --git a/buch/papers/zeta/zeta_gamma.tex b/buch/papers/zeta/zeta_gamma.tex index 59c8744..bed4262 100644 --- a/buch/papers/zeta/zeta_gamma.tex +++ b/buch/papers/zeta/zeta_gamma.tex @@ -1,38 +1,47 @@ -\section{Zusammenhang mit Gammafunktion} \label{zeta:section:zusammenhang_mit_gammafunktion} -\rhead{Zusammenhang mit Gammafunktion} +\section{Zusammenhang mit der Gammafunktion} \label{zeta:section:zusammenhang_mit_gammafunktion} +\rhead{Zusammenhang mit der Gammafunktion} -Dieser Abschnitt stellt die Verbindung zwischen der Gamma- und der Zetafunktion her. +In diesem Abschnitt wird gezeigt, wie sich die Zetafunktion durch die Gammafunktion $\Gamma(s)$ ausdrücken lässt. +Dieser Zusammenhang der Art $\zeta(s) = f(\Gamma(s))$ wird später für die Herleitung der analytischen Fortsetzung gebraucht. %TODO ref Gamma -Wenn in der Gammafunkion die Integrationsvariable $t$ substituieren mit $t = nu$ und $dt = n du$, dann können wir die Gleichung umstellen und erhalten den Zusammenhang mit der Zetafunktion -\begin{align} +Wir erinnern uns an die Definition der Gammafunktion in \ref{buch:rekursion:gamma:integralbeweis} +\begin{equation*} + \Gamma(s) + = + \int_0^{\infty} t^{s-1} e^{-t} \,dt, +\end{equation*} +wobei die Notation an die Zetafunktion angepasst ist. +Durch die Substitution von $t$ mit $t = nu$ und $dt = n\,du$ wird daraus +\begin{align*} \Gamma(s) &= - \int_0^{\infty} t^{s-1} e^{-t} dt - \\ + \int_0^{\infty} n^{s-1}u^{s-1} e^{-nu} n \,du \\ &= - \int_0^{\infty} n^{s\cancel{-1}}u^{s-1} e^{-nu} \cancel{n}du - && - \text{Division durch }n^s - \\ + \int_0^{\infty} n^s u^{s-1} e^{-nu} \,du. +\end{align*} +Durch Division mit durch $n^s$ ergibt sich die Quotienten +\begin{equation*} \frac{\Gamma(s)}{n^s} - &= - \int_0^{\infty} u^{s-1} e^{-nu}du - && - \text{Zeta durch Summenbildung } \sum_{n=1}^{\infty} - \\ + = + \int_0^{\infty} u^{s-1} e^{-nu} \,du, +\end{equation*} +welche sich zur Zetafunktion summieren +\begin{equation} + \sum_{n=1}^{\infty} \frac{\Gamma(s)}{n^s} + = \Gamma(s) \zeta(s) - &= + = \int_0^{\infty} u^{s-1} \sum_{n=1}^{\infty}e^{-nu} - du. + \,du. \label{zeta:equation:zeta_gamma1} -\end{align} +\end{equation} Die Summe über $e^{-nu}$ können wir als geometrische Reihe schreiben und erhalten \begin{align} - \sum_{n=1}^{\infty}e^{-u^n} + \sum_{n=1}^{\infty}\left(e^{-u}\right)^n &= - \sum_{n=0}^{\infty}e^{-u^n} + \sum_{n=0}^{\infty}\left(e^{-u}\right)^n - 1 \\ @@ -42,7 +51,7 @@ Die Summe über $e^{-nu}$ können wir als geometrische Reihe schreiben und erhal &= \frac{1}{e^u - 1}. \end{align} -Wenn wir dieses Resultat einsetzen in \eqref{zeta:equation:zeta_gamma1} und durch $\Gamma(s)$ teilen, erhalten wir +Wenn wir dieses Resultat einsetzen in \eqref{zeta:equation:zeta_gamma1} und durch $\Gamma(s)$ teilen, erhalten wir %TODO formulieren als Satz \begin{equation}\label{zeta:equation:zeta_gamma_final} \zeta(s) = -- cgit v1.2.1 From 8f643765aa134d48da27f161890f07038d2223f3 Mon Sep 17 00:00:00 2001 From: runterer Date: Sat, 14 May 2022 22:17:18 +0200 Subject: Alle einfachen Korrekturen umgesetzt --- buch/papers/zeta/analytic_continuation.tex | 108 ++++++++++++++++++----------- buch/papers/zeta/zeta_gamma.tex | 2 +- 2 files changed, 68 insertions(+), 42 deletions(-) diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex index bb95b92..5e09e42 100644 --- a/buch/papers/zeta/analytic_continuation.tex +++ b/buch/papers/zeta/analytic_continuation.tex @@ -14,8 +14,8 @@ Zuerst definieren die Dirichletsche Etafunktion als wobei die Reihe bis auf die alternierenden Vorzeichen die selbe wie in der Zetafunktion ist. Diese Etafunktion konvergiert gemäss dem Leibnitz-Kriterium im Bereich $\Re(s) > 0$, da dann die einzelnen Glieder monoton fallend sind. -Wenn wir es nun schaffen, die sehr ähnliche Zetafunktion mit der Etafunktion auszudrücken, dann haben die gesuchte Fortsetzung. -Die folgenden Schritte zeigen, wie man dazu kommt: +Wenn wir es nun schaffen, die sehr ähnliche Zetafunktion durch die Etafunktion auszudrücken, dann haben die gesuchte Fortsetzung. +Zuerst wiederholen wir zweimal die Definition der Zetafunktion \eqref{zeta:equation1}, wobei wir sie einmal durch $2^{s-1}$ teilen \begin{align} \zeta(s) &= @@ -26,8 +26,10 @@ Die folgenden Schritte zeigen, wie man dazu kommt: \zeta(s) &= \sum_{n=1}^{\infty} - \frac{2}{(2n)^s} \label{zeta:align2} - \\ + \frac{2}{(2n)^s}. \label{zeta:align2} +\end{align} +Durch Subtraktion der beiden Gleichungen \eqref{zeta:align1} minus \eqref{zeta:align2}, ergibt sich +\begin{align} \left(1 - \frac{1}{2^{s-1}} \right) \zeta(s) &= @@ -36,14 +38,15 @@ Die folgenden Schritte zeigen, wie man dazu kommt: + \frac{1}{3^s} \underbrace{-\frac{2}{4^s} + \frac{1}{4^s}}_{-\frac{1}{4^s}} \ldots - && \text{\eqref{zeta:align1}} - \text{\eqref{zeta:align2}} - \\ - &= \eta(s) \\ + &= \eta(s). +\end{align} +Dies ist die Fortsetzung auf den noch unbekannten Bereich $0 < \Re(s) < 1$ +\begin{equation} \zeta(s) - &= + := \left(1 - \frac{1}{2^{s-1}} \right)^{-1} \eta(s). -\end{align} +\end{equation} \subsection{Fortsetzung auf ganz $\mathbb{C}$} \label{zeta:subsection:auf_ganz} Für die Fortsetzung auf den Rest von $\mathbb{C}$, verwenden wir den Zusammenhang von Gamma- und Zetafunktion aus \ref{zeta:section:zusammenhang_mit_gammafunktion}. @@ -61,7 +64,7 @@ Nun substituieren wir $t$ mit $t = \pi n^2 x$ und $dt=\pi n^2 dx$ und erhalten (\pi n^2)^{\frac{s}{2}} x^{\frac{s}{2}-1} e^{-\pi n^2 x} - dx + \,dx && \text{Division durch } (\pi n^2)^{\frac{s}{2}} \\ \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}} n^s} @@ -69,7 +72,7 @@ Nun substituieren wir $t$ mit $t = \pi n^2 x$ und $dt=\pi n^2 dx$ und erhalten \int_0^{\infty} x^{\frac{s}{2}-1} e^{-\pi n^2 x} - dx + \,dx && \text{Zeta durch Summenbildung } \sum_{n=1}^{\infty} \\ \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}}} @@ -79,7 +82,7 @@ Nun substituieren wir $t$ mit $t = \pi n^2 x$ und $dt=\pi n^2 dx$ und erhalten x^{\frac{s}{2}-1} \sum_{n=1}^{\infty} e^{-\pi n^2 x} - dx. \label{zeta:equation:integral1} + \,dx. \label{zeta:equation:integral1} \end{align} Die Summe kürzen wir ab als $\psi(x) = \sum_{n=1}^{\infty} e^{-\pi n^2 x}$. %TODO Wieso folgendes -> aus Fourier Signal @@ -97,82 +100,103 @@ Zunächst teilen wir nun das Integral aus \eqref{zeta:equation:integral1} auf al \int_0^{\infty} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx = + \underbrace{ \int_0^{1} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx + }_{I_1} + + \underbrace{ \int_1^{\infty} x^{\frac{s}{2}-1} \psi(x) - dx, + \,dx + }_{I_2} + = + I_1 + I_2, \end{equation} -wobei wir uns nun auf den ersten Teil konzentrieren werden. -Dabei setzen wir das Wissen aus \eqref{zeta:equation:psi} ein und erhalten +wobei wir uns nun auf den ersten Teil $I_1$ konzentrieren werden. +Dabei setzen wir die Definition von $\psi(x)$ aus \eqref{zeta:equation:psi} ein und erhalten \begin{align} + I_1 + = \int_0^{1} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx &= \int_0^{1} x^{\frac{s}{2}-1} \left( - \frac{1}{2} + \frac{\psi\left(\frac{1}{x} \right)}{\sqrt{x}} - + \frac{1}{2 \sqrt{x}}. + + \frac{1}{2 \sqrt{x}} \right) - dx + \,dx \\ &= \int_0^{1} x^{\frac{s}{2}-\frac{3}{2}} \psi \left( \frac{1}{x} \right) + \frac{1}{2} - \left( + \biggl( x^{\frac{s}{2}-\frac{3}{2}} - x^{\frac{s}{2}-1} - \right) - dx + \biggl) + \,dx \\ &= + \underbrace{ \int_0^{1} x^{\frac{s}{2}-\frac{3}{2}} \psi \left( \frac{1}{x} \right) - dx - + \frac{1}{2} + \,dx + }_{I_3} + + + \underbrace{ + \frac{1}{2} \int_0^1 x^{\frac{s}{2}-\frac{3}{2}} - x^{\frac{s}{2}-1} - dx. \label{zeta:equation:integral3} + \,dx + }_{I_4}. \label{zeta:equation:integral3} \end{align} -Dabei kann das zweite Integral gelöst werden als +Dabei kann das zweite Integral $I_4$ gelöst werden als \begin{equation} + I_4 + = \frac{1}{2} \int_0^1 x^{\frac{s}{2}-\frac{3}{2}} - x^{\frac{s}{2}-1} - dx + \,dx = \frac{1}{s(s-1)}. \end{equation} -Das erste Integral aus \eqref{zeta:equation:integral3} mit $\psi \left(\frac{1}{x} \right)$ ist nicht lösbar in dieser Form. +Das erste Integral $I_3$ aus \eqref{zeta:equation:integral3} mit $\psi \left(\frac{1}{x} \right)$ ist nicht lösbar in dieser Form. Deshalb substituieren wir $x = \frac{1}{u}$ und $dx = -\frac{1}{u^2}du$. Die untere Integralgrenze wechselt ebenfalls zu $x_0 = 0 \rightarrow u_0 = \infty$. Dies ergibt \begin{align} + I_3 + = \int_{\infty}^{1} - {\frac{1}{u}}^{\frac{s}{2}-\frac{3}{2}} + \left( + \frac{1}{u} + \right)^{\frac{s}{2}-\frac{3}{2}} \psi(u) \frac{-du}{u^2} &= \int_{1}^{\infty} - {\frac{1}{u}}^{\frac{s}{2}-\frac{3}{2}} + \left( + \frac{1}{u} + \right)^{\frac{s}{2}-\frac{3}{2}} \psi(u) \frac{du}{u^2} \\ @@ -180,21 +204,23 @@ Dies ergibt \int_{1}^{\infty} x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} \psi(x) - dx, + \,dx, \end{align} wobei wir durch Multiplikation mit $(-1)$ die Integralgrenzen tauschen dürfen. Es ist zu beachten das diese Grenzen nun identisch mit den Grenzen des zweiten Integrals von \eqref{zeta:equation:integral2} sind. Wir setzen beide Lösungen ein in Gleichung \eqref{zeta:equation:integral3} und erhalten \begin{equation} + I_1 + = \int_0^{1} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx = \int_{1}^{\infty} x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} \psi(x) - dx + \,dx + \frac{1}{s(s-1)}. \end{equation} @@ -206,12 +232,12 @@ Dieses Resultat setzen wir wiederum ein in \eqref{zeta:equation:integral2}, um s \int_0^{1} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx + \int_1^{\infty} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx \nonumber \\ &= @@ -220,12 +246,12 @@ Dieses Resultat setzen wir wiederum ein in \eqref{zeta:equation:integral2}, um s \int_{1}^{\infty} x^{(-1) \left(\frac{s}{2}+\frac{1}{2}\right)} \psi(x) - dx + \,dx + \int_1^{\infty} x^{\frac{s}{2}-1} \psi(x) - dx + \,dx \\ &= \frac{1}{s(s-1)} @@ -237,7 +263,7 @@ Dieses Resultat setzen wir wiederum ein in \eqref{zeta:equation:integral2}, um s x^{\frac{s}{2}-1} \right) \psi(x) - dx + \,dx \\ &= \frac{-1}{s(1-s)} @@ -249,7 +275,7 @@ Dieses Resultat setzen wir wiederum ein in \eqref{zeta:equation:integral2}, um s x^{\frac{s}{2}} \right) \frac{\psi(x)}{x} - dx, + \,dx, \end{align} zu erhalten. Wenn wir dieses Resultat genau anschauen, erkennen wir dass sich nichts verändert wenn $s$ mit $1-s$ ersetzt wird. @@ -261,4 +287,4 @@ Somit haben wir die analytische Fortsetzung gefunden als \frac{\Gamma \left( \frac{1-s}{2} \right)}{\pi^{\frac{1-s}{2}}} \zeta(1-s). \end{equation} - +%TODO Definitionen und Gleichungen klarer unterscheiden diff --git a/buch/papers/zeta/zeta_gamma.tex b/buch/papers/zeta/zeta_gamma.tex index bed4262..49fea74 100644 --- a/buch/papers/zeta/zeta_gamma.tex +++ b/buch/papers/zeta/zeta_gamma.tex @@ -5,7 +5,7 @@ In diesem Abschnitt wird gezeigt, wie sich die Zetafunktion durch die Gammafunkt Dieser Zusammenhang der Art $\zeta(s) = f(\Gamma(s))$ wird später für die Herleitung der analytischen Fortsetzung gebraucht. %TODO ref Gamma -Wir erinnern uns an die Definition der Gammafunktion in \ref{buch:rekursion:gamma:integralbeweis} +Wir erinnern uns an die Definition der Gammafunktion in \eqref{buch:rekursion:gamma:integralbeweis} \begin{equation*} \Gamma(s) = -- cgit v1.2.1 From 2bba3b1d52604c9f671763927ec592a72b09088e Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Sun, 15 May 2022 15:36:08 +0200 Subject: a few animations --- buch/papers/fm/Python animation/Bessel-FM.ipynb | 193 ++++++++++++++++++++++++ buch/papers/fm/Python animation/Bessel-FM.py | 42 ++++++ buch/papers/fm/RS presentation/RS.tex | 162 ++++++++++++++++++++ 3 files changed, 397 insertions(+) create mode 100644 buch/papers/fm/Python animation/Bessel-FM.ipynb create mode 100644 buch/papers/fm/Python animation/Bessel-FM.py create mode 100644 buch/papers/fm/RS presentation/RS.tex diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb new file mode 100644 index 0000000..9d0835a --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -0,0 +1,193 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 74, + "metadata": {}, + "outputs": [ + { + "ename": "ValueError", + "evalue": "operands could not be broadcast together with shapes (3,) (600,) ", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/Python animation/Bessel-FM.ipynb Cell 1'\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 13\u001b[0m x \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.01\u001b[39m, N\u001b[39m*\u001b[39mT, N)\n\u001b[1;32m 14\u001b[0m beta \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.1\u001b[39m,\u001b[39m10\u001b[39m, \u001b[39m3\u001b[39m)\n\u001b[0;32m---> 15\u001b[0m y_old \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39msin(\u001b[39m100.0\u001b[39m \u001b[39m*\u001b[39m \u001b[39m2.0\u001b[39m\u001b[39m*\u001b[39mnp\u001b[39m.\u001b[39mpi\u001b[39m*\u001b[39mx\u001b[39m+\u001b[39mbeta\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49msin(\u001b[39m50.0\u001b[39;49m \u001b[39m*\u001b[39;49m \u001b[39m2.0\u001b[39;49m\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49mpi\u001b[39m*\u001b[39;49mx))\n\u001b[1;32m 16\u001b[0m y \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\u001b[39m*\u001b[39mx;\n\u001b[1;32m 17\u001b[0m xf \u001b[39m=\u001b[39m fftfreq(N, \u001b[39m1\u001b[39m \u001b[39m/\u001b[39m \u001b[39m400\u001b[39m)\n", + "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (600,) " + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy import signal\n", + "from scipy.fft import fft, ifft, fftfreq\n", + "import scipy.special as sc\n", + "import scipy.fftpack\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.widgets import Slider\n", + "\n", + "# Number of samplepoints\n", + "N = 600\n", + "# sample spacing\n", + "T = 1.0 / 800.0\n", + "x = np.linspace(0.01, N*T, N)\n", + "beta = 1.0\n", + "y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x))\n", + "y = 0*x;\n", + "xf = fftfreq(N, 1 / 400)\n", + "for k in range (-5, 5):\n", + " y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x)\n", + " yf = fft(y)\n", + " plt.plot(xf, np.abs(yf))\n", + "\n", + "axamp = plt.axes(np.linspace(0.1, 3, 10))\n", + "beta_slider = Slider(\n", + "ax=axamp,\n", + "label=\"Amplitude\",\n", + "valmin=0,\n", + "valmax=10,\n", + "valinit=beta,\n", + "orientation=\"vertical\"\n", + ")\n", + "plt.show()\n", + "\n", + "yf_old = fft(y_old)\n", + "plt.plot(xf, np.abs(yf_old))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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gNOXrz6ql5+ATVyzkf71xiIFTY7TUp8v960REqtK8H8w+H3fc1MnJ0Tzf69k3e2UREZlWVQfFh5e0cH1nG4//373k9RxtEZFzUtVBAfDljy9n/9FT/OOu9yrdFBGRWKr6oPiNrkUsaa3nb/7prUo3RUQklqo+KFLJBL9746W8tOd9dhzUw4xERM5W1QcFwLrrl5FNJ3j8n/ZWuikiIrFTE0HR2pDhX31kKT967SD9gyOVbo6ISKzURFAAfPmmTkZzBf77lncq3RQRkVipmaBYsaiJX12xkCdfepvRXKHSzRERiY2aCQqA3/vEcg6fGOGv/8+blW6KiEhs1FRQfPLKDm699mK+9pN/ZuvbmgNKRKQUNRUUZsaf/8sPs7gly70bt3F8eKzSTRIRmfdqKigAmrNpvr7uOg4NDPOnP9xOMBu6iIicSc0FBcBHL72Ae29ewY9ePcj/2BbJc5RERGKrJoMC4O5PXcHqzgv40x9u5+3+oUo3R0Rk3qrZoEgmjIfXXUcyYfze469waOBUpZskIjIv1WxQACxprefbX1rFe8dHuO1bL7Knb7DSTRIRmXdqOigAPnZZOxvvuoHhsTy3/7cX2X5AEweKiBSr+aCA4AFH3/vKjWTTSdY/+hJb9vRXukkiIvOGgiJ0WccCvveVG7mwuY4vbXiZDT9/i4KeiicioqAodnFrPd/7yk3cdHk7Dzyzk9/6a41biIgoKKa4oDHDhn9zPf/19mv5f++d4Jav/4xv/3SPnrktIjVLQTENM+Nff3QpP/7DX+NXVyzkwc27+Pw3fsaz2w/pcpSI1BwFxQwWNWf59pdW8ZfrVzKSK/CVv/sFn/vGz9j8hgJDRGqHxWmuo1WrVnlPT09FfncuX+B/vn6Qv/xJL3uODHHlogX89scu5TevW0JLQ7oibRIRmY2ZbXX3Ved1DAXF2ckXnGdeP8ijP93DjoPHyaQSrLnmIr54/TJuvKydRMIq2j4RkWIKigrbfmCATT37+OG2AxwfznFhUx2/3rWIz3Qt4qbL26lLJSvdRBGpcQqKeWJ4LM8/7HyPZ7cf4n/v7uPkaJ7GTJJfu6qDmy5fyA2XtXN5RyNm6m2ISLTmIihSc9WYWpZNJ7n12ou59dqLGR7L8+Kb/fzDzvd44ZeH2fzGuwBc2FTHDZe1c31nG9cua+Xqi5rJpHQvgYjMfwqKOZZNJ/nU1RfyqasvxN3Z23+Sl/b08+Kb/by4p5/u1w4CkEkm+NDFzVy7tIUPLW7m6ouauHJRE411+k8iIvOLPpXKyMxYvrCR5QsbWb/6EtydgwPDvLbvGK/tO8ar+47x/a37GRrNT+xzaXsDl3csoLO9kc6FDcFreyNL2upJaqBcRCpAQREhM2NJaz1LWuv53K8sBqBQcA4cO8WuQ8f55bsn2P3uCd7sG+TFN/s5NTYZIOmksaytgc6FjVza3sDStgYWt2S5qCXL4pYsHQvqSCV1KUtE5p6CosISCWPZBQ0su6CB37jmoolyd+fwiRH2Hhlib/8Qe/tPhsvBpayTRb0QgITBhU1ZFrVkWdwcBEhHUx0LF2Rob6yjfUGGhQuC14aM/rOLSOn0iTFPmRmLmrMsas7yscvaT9vm7gycGuPQwDDvDgyHr6eC1+PD9PYN8vPeIwyO5KY9dn06SfuCDO0L6mitT9My3U/DB8saMknduSVSgxQUMWRmtDZkaG3I8KHFzWesNzyWp39olCMnRugfGuHI4Cj9g6P0D44E5YMjHD05yt7+IQZOjXH81BgzzUySShgt9Wmasika64KfBROvSRozp5c11iWLtqfIppPUZ5LUp4OfulRCX1AUiQEFRRXLppMTYyKlKBScwdEcAyfHJoJjYJqf48M5hkaCn8Mnhhk6kmcwXJ96SWz2NiaCAAl/isPktG1hWV0YMHWpBJlUgkwyfE0lqEslTyurS53+Wlw3k0yodyRSIgWFTEgkjOZsmuZsmmXneIx8wTk5mmNoZDI8hkZyDI7kGM4VGB7Nc2os/BnNM5zLF5UVODWaZyQXbDt6cpRTY5Pbh8cKpw3wn69MKkFdUXikkwlSSSOdCF5TyQSZpJEK19PJBKmETdRLJRKkkzZlOThOOjG+bKROWz7zsVJJI2FB/WQiXJ5SdtqPGYnElG1hmchcKikozGwN8HUgCXzH3f/zlO11wN8CHwX6gS+6+95w2/3AnUAe+H13f66UY0o8JRNGUzZNU7Y8EyW6O6P5AqO58CdfYGSsMFE2kht/zU9sLy6f3CfPSNFxRnIFcvkCYwUPXvPOWL5ALu/kCgVOjQWvufHygp+2PF53fL2SzCBpp4dHMmmnl00Jl1LLzIyEQSLcbuFywoJ/aIwvB9sm607+nF4vEQZb4gzHmbqfWRiG0+xr4e8drz9RN1G0XLwtMb4MMFmeMDCC41m4nEiEr+NlZhjT1x9vy3h9xss4fZslOK0sEfZwbbr6Fe79zhoUZpYEHgE+A+wHXjGzbnffWVTtTuCou19hZuuAh4AvmlkXsA64BrgY+EczuzLcZ7ZjinyAmVGXSs7rebTcfTJIwnCZGkJTQ2csX6BQgFyhQMGDfQvhcfIF/0BZoTC5LV9w8j5ZNrHNnXw+fJ1ynOKy/JTjFK+P5goTZQV3CgWCV3cKHiy7M7G9eLngwXsx3jYP6+eLtxV8xnExmRQEzOnhcXr4hGFjHwyf81VKj2I10Ovue4LG2kZgLVD8ob4W+E/h8tPAX1kQgWuBje4+ArxlZr3h8SjhmCKxZGakk0Y6CfXM30CbTzwMj+LAGQ8VLxQHTNG2ovAZ39eLAiw/JZwmthXG18N9wt8/8epMBFkQYkVlTIach+vF9f20OpPLFIVjcJzp6xfCufcm6o2H8Rnqj7e7MPF3TB5j/L3aNgf/fUoJiiXAvqL1/cDHzlTH3XNmNgC0h+UvTdl3Sbg82zFFpEYEl4bQ7ANl8OdzcIx5/1VeM7vLzHrMrKevr6/SzRERqTmlBMUBOO0mmKVh2bR1zCwFtBAMap9p31KOCYC7P+ruq9x9VUdHRwnNFRGRuVRKULwCrDCz5WaWIRic7p5Spxu4I1y+DXjegwdddAPrzKzOzJYDK4CXSzymiIjMA7OOUYRjDvcAzxHcyrrB3XeY2QNAj7t3A48BT4aD1e8TfPAT1ttEMEidA+529zzAdMec+z9PRETOl55wJyJSxebiCXfzfjBbREQqS0EhIiIzUlCIiMiMFBQiIjKjWA1mm9kJYHel2zFPLASOVLoR84Deh0l6LybpvZh0lbs3nc8B4jbN+O7zHb2vFmbWo/dC70MxvReT9F5MMrPzvlVUl55ERGRGCgoREZlR3ILi0Uo3YB7RexHQ+zBJ78UkvReTzvu9iNVgtoiIRC9uPQoREYmYgkJERGYUi6AwszVmttvMes3svkq3J0pmtszMXjCznWa2w8zuDcsvMLMfm9k/h69tlW5rVMwsaWbbzOyZcH25mW0Jz4+nwqnrq56ZtZrZ02b2SzPbZWY31up5YWb/Pvz/Y7uZfdfMsrVyXpjZBjM7bGbbi8qmPQ8s8I3wPXndzD5Syu+Y90FhZkngEeAWoAtYb2ZdlW1VpHLAH7l7F3ADcHf4998H/MTdVwA/Cddrxb3ArqL1h4CH3f0K4ChwZ0VaFb2vA8+6+9XAtQTvSc2dF2a2BPh9YJW7f5jg0QXrqJ3z4nFgzZSyM50HtxA8F2gFcBfwrVJ+wbwPCmA10Ovue9x9FNgIrK1wmyLj7ofc/Rfh8gmCD4MlBO/BE2G1J4DfrEgDI2ZmS4HPA98J1w34NPB0WKUm3gszawH+BcGzYHD3UXc/Ro2eFwRfHq4Pn7DZAByiRs4Ld/8pwXOAip3pPFgL/K0HXgJazWzxbL8jDkGxBNhXtL4/LKs5ZtYJrAS2AIvc/VC46V1gUaXaFbGvAX8MFML1duCYu+fC9Vo5P5YDfcDfhJfhvmNmjdTgeeHuB4D/ArxDEBADwFZq87wYd6bz4Jw+T+MQFAKY2QLg+8AfuPvx4m3hY2er/j5nM/sCcNjdt1a6LfNACvgI8C13XwkMMeUyUw2dF20E/1JeDlwMNPLBSzE1ay7OgzgExQFgWdH60rCsZphZmiAk/t7dfxAWvzfeZQxfD1eqfRH6OHCrme0luAT5aYLr9K3hJQeonfNjP7Df3beE608TBEctnhe/Drzl7n3uPgb8gOBcqcXzYtyZzoNz+jyNQ1C8AqwI72DIEAxSdVe4TZEJr8E/Buxy978o2tQN3BEu3wH8KOq2Rc3d73f3pe7eSXAePO/uvw28ANwWVquV9+JdYJ+ZXRUW3UzwbPqaOy8ILjndYGYN4f8v4+9FzZ0XRc50HnQDXwrvfroBGCi6RHVGsfhmtpl9juDadBLY4O4PVrZF0TGzTwA/A95g8rr8nxCMU2wCLgHeBn7L3acOaFUtM/sk8B/c/QtmdhlBD+MCYBvwO+4+UsHmRcLMriMY1M8Ae4AvE/zjr+bOCzP7M+CLBHcJbgP+LcG196o/L8zsu8AnCaZWfw/4j8APmeY8CIP0rwguzZ0Evuzus84uG4ugEBGRyonDpScREakgBYWIiMxIQSEiIjNSUIiIyIwUFCIiMiMFhYiIzEhBISIiM/r/lXwoXNBP92cAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Number of samplepoints\n", + "N = 600\n", + "# sample spacing\n", + "T = 1.0 / 800.0\n", + "x = np.linspace(0.0, N*T, N)\n", + "y = sc.jv(3,x)#np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)\n", + "yf = scipy.fftpack.fft(y)\n", + "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(xf, 2.0/N * np.abs(yf[:N//2]))\n", + "ax.set(\n", + " xlim=(0, 100)\n", + ")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "for n in range (5):\n", + " x = np.linspace(0,15,1000)\n", + " y = sc.jv(n,x)\n", + " plt.plot(x, y, '-')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from scipy import special\n", + "\n", + "def drumhead_height(n, k, distance, angle, t):\n", + " kth_zero = special.jn_zeros(n, k)[-1]\n", + " return np.cos(t) * np.cos(n*angle) * special.jn(n, distance*kth_zero)\n", + "\n", + "theta = np.r_[0:2*np.pi:50j]\n", + "radius = np.r_[0:1:50j]\n", + "x = np.array([r * np.cos(theta) for r in radius])\n", + "y = np.array([r * np.sin(theta) for r in radius])\n", + "z = np.array([drumhead_height(1, 1, r, theta, 0.5) for r in radius])\n", + "\n", + "import matplotlib.pyplot as plt\n", + "fig = plt.figure()\n", + "ax = fig.add_axes(rect=(0, 0.05, 0.95, 0.95), projection='3d')\n", + "ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap='RdBu_r', vmin=-0.5, vmax=0.5)\n", + "ax.set_xlabel('X')\n", + "ax.set_ylabel('Y')\n", + "ax.set_xticks(np.arange(-1, 1.1, 0.5))\n", + "ax.set_yticks(np.arange(-1, 1.1, 0.5))\n", + "ax.set_zlabel('Z')\n", + "\n", + "plt.show()" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" + }, + "kernelspec": { + "display_name": "Python 3.8.10 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/buch/papers/fm/Python animation/Bessel-FM.py b/buch/papers/fm/Python animation/Bessel-FM.py new file mode 100644 index 0000000..cf30e16 --- /dev/null +++ b/buch/papers/fm/Python animation/Bessel-FM.py @@ -0,0 +1,42 @@ +import numpy as np +from scipy import signal +from scipy.fft import fft, ifft, fftfreq +import scipy.special as sc +import scipy.fftpack +import matplotlib.pyplot as plt +from matplotlib.widgets import Slider + +# Number of samplepoints +N = 600 +# sample spacing +T = 1.0 / 800.0 +x = np.linspace(0.01, N*T, N) +beta = 1.0 +y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x)) +y = 0*x; +xf = fftfreq(N, 1 / 400) +for k in range (-5, 5): + y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x) + yf = fft(y) + plt.plot(xf, np.abs(yf)) + +axbeta =plt.axes([0.25, 0.1, 0.65, 0.03]) +beta_slider = Slider( +ax=axbeta, +label="Beta", +valmin=0.1, +valmax=3, +valinit=beta, +) + +def update(val): + line.set_ydata(fm(beta_slider.val)) + fig.canvas.draw_idle() + + +beta_slider.on_changed(update) +plt.show() + +yf_old = fft(y_old) +plt.plot(xf, np.abs(yf_old)) +plt.show() \ No newline at end of file diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex new file mode 100644 index 0000000..8e3de17 --- /dev/null +++ b/buch/papers/fm/RS presentation/RS.tex @@ -0,0 +1,162 @@ +\documentclass[11pt,aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage[ngerman]{babel} +\usepackage{tikz} +\usetheme{Hannover} + +\begin{document} + \author{Joshua Bär} + \title{FM - Bessel} + \subtitle{} + \logo{} + \institute{OST Ostschweizer Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar} + %\setbeamercovered{transparent} + \setbeamercovered{invisible} + \setbeamertemplate{navigation symbols}{} + \begin{frame}[plain] + \maketitle + \end{frame} +%------------------------------------------------------------------------------- +\section{Einführung} + \begin{frame} + \frametitle{Frequenzmodulation} + \begin{itemize} + \visible<1->{\item Für Übertragung von Daten} + \visible<2->{\item Amplituden unabhängig} + \end{itemize} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \frametitle{Parameter} + \begin{center} + \begin{tabular}{ c c c } + \hline + Nutzlas & Fehler & Versenden \\ + \hline + 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\ + 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\ +\visible<1->{3}& +\visible<1->{3}& +\visible<1->{9 Werte eines Polynoms vom Grad 2} \\ + &&\\ +\visible<1->{$k$} & +\visible<1->{$t$} & +\visible<1->{$k+2t$ Werte eines Polynoms vom Grad $k-1$} \\ + \hline + &&\\ + &&\\ + \multicolumn{3}{l} { + \visible<1>{Ausserdem können bis zu $2t$ Fehler erkannt werden!} + } + \end{tabular} + \end{center} + \end{frame} + +%------------------------------------------------------------------------------- + +\section{Diskrete Fourier Transformation} + \begin{frame} + \frametitle{Idee} + \begin{itemize} + \item Fourier-transformieren + \item Übertragung + \item Rücktransformieren + \end{itemize} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \begin{figure} + \only<1>{ + \includegraphics[width=0.9\linewidth]{images/fig1.pdf} + } + \only<2>{ + \includegraphics[width=0.9\linewidth]{images/fig2.pdf} + } + \only<3>{ + \includegraphics[width=0.9\linewidth]{images/fig3.pdf} + } + \only<4>{ + \includegraphics[width=0.9\linewidth]{images/fig4.pdf} + } + \only<5>{ + \includegraphics[width=0.9\linewidth]{images/fig5.pdf} + } + \only<6>{ + \includegraphics[width=0.9\linewidth]{images/fig6.pdf} + } + \only<7>{ + \includegraphics[width=0.9\linewidth]{images/fig7.pdf} + } + \end{figure} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \frametitle{Diskrete Fourier Transformation} + \begin{itemize} + \item Diskrete Fourier-Transformation gegeben durch: + \visible<1->{ + \[ + \label{ft_discrete} + \hat{c}_{k} + = \frac{1}{N} \sum_{n=0}^{N-1} + {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn} + \]} + \visible<2->{ + \item Ersetzte + \[ + w = e^{-\frac{2\pi j}{N} k} + \]} + \visible<3->{ + \item Wenn $N$ konstant: + \[ + \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) + \]} + \end{itemize} + \end{frame} + +%------------------------------------------------------------------------------- + +%------------------------------------------------------------------------------- + \begin{frame} + \frametitle{Ein Beispiel} + + \begin{itemize} + + \onslide<1->{\item endlicher Körper $q = 11$} + + \onslide<2->{ist eine Primzahl} + + \onslide<3->{beinhaltet die Zahlen $\mathbb{F}_{11} = \{0,1,2,3,4,5,6,7,8,9,10\}$} + + \vspace{10pt} + + \onslide<4->{\item Nachrichtenblock $=$ Nutzlast $+$ Fehlerkorrekturstellen} + + \onslide<5->{$n = q - 1 = 10$ Zahlen} + + \vspace{10pt} + + \onslide<6->{\item Max.~Fehler $t = 2$} + + \onslide<7->{maximale Anzahl von Fehler, die wir noch korrigieren können} + + \vspace{10pt} + + \onslide<8->{\item Nutzlast $k = n -2t = 6$ Zahlen} + + \onslide<9->{Fehlerkorrkturstellen $2t = 4$ Zahlen} + + \onslide<10->{Nachricht $m = [0,0,0,0,4,7,2,5,8,1]$} + + \onslide<11->{als Polynom $m(X) = 4X^5 + 7X^4 + 2X^3 + 5X^2 + 8X + 1$} + + \end{itemize} + + \end{frame} + + +\end{document} -- cgit v1.2.1 From 4fd4422b52f6377a82696ea67da9beb13d93e581 Mon Sep 17 00:00:00 2001 From: Nicolas Tobler Date: Sun, 15 May 2022 23:15:36 +0200 Subject: draft --- buch/papers/ellfilter/main.tex | 370 ++++++++++++++++++++++++++-- buch/papers/ellfilter/packages.tex | 3 + buch/papers/ellfilter/python/chebychef.py | 65 +++++ buch/papers/ellfilter/python/elliptic.py | 316 ++++++++++++++++++++++++ buch/papers/ellfilter/python/elliptic2.py | 78 ++++++ buch/papers/ellfilter/references.bib | 32 +-- buch/papers/ellfilter/teil0.tex | 28 +-- buch/papers/ellfilter/teil1.tex | 90 +++---- buch/papers/ellfilter/teil2.tex | 64 ++--- buch/papers/ellfilter/teil3.tex | 64 ++--- buch/papers/ellfilter/tikz/arccos.tikz.tex | 97 ++++++++ buch/papers/ellfilter/tikz/arccos2.tikz.tex | 46 ++++ 12 files changed, 1084 insertions(+), 169 deletions(-) create mode 100644 buch/papers/ellfilter/python/chebychef.py create mode 100644 buch/papers/ellfilter/python/elliptic.py create mode 100644 buch/papers/ellfilter/python/elliptic2.py create mode 100644 buch/papers/ellfilter/tikz/arccos.tikz.tex create mode 100644 buch/papers/ellfilter/tikz/arccos2.tikz.tex diff --git a/buch/papers/ellfilter/main.tex b/buch/papers/ellfilter/main.tex index 26aaec1..29ebf7a 100644 --- a/buch/papers/ellfilter/main.tex +++ b/buch/papers/ellfilter/main.tex @@ -8,29 +8,361 @@ \begin{refsection} \chapterauthor{Nicolas Tobler} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} + +\section{Einleitung} + +Lineare filter + +Filter, Signalverarbeitung + + +Der womöglich wichtigste Filtertyp ist das Tiefpassfilter. +Dieses soll im Durchlassbereich unter der Grenzfrequenz $\Omega_p$ unverstärkt durchlassen und alle anderen Frequenzen vollständig auslöschen. + +Bei der Implementierung von Filtern + + +In der Elektrotechnik führen Schaltungen mit linearen Bauelementen wie Kondensatoren, Spulen und Widerständen immer zu linearen zeitinvarianten Systemen (LTI-System von englich \textit{time-invariant system}). +Die Übertragungsfunktion im Frequenzbereich $|H(\Omega)|$ eines solchen Systems ist dabei immer eine rationale Funktion, also eine Division von zwei Polynomen. +Die Polynome habe dabei immer reelle oder komplex-konjugierte Nullstellen. + + +\begin{equation} \label{ellfilter:eq:h_omega} + | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 F_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p} +\end{equation} + +$\Omega = 2 \pi f$ ist die analoge Frequenz + + +% Linear filter +Damit das Filter implementierbar und stabil ist, muss $H(\Omega)^2$ eine rationale Funktion sein, deren Nullstellen und Pole auf der linken Halbebene liegen. + +$N \in \mathbb{N} $ gibt dabei die Ordnung des Filters vor, also die maximale Anzahl Pole oder Nullstellen. + +% In \eqref{ellfilter:eq:h_omega} wird $F_N(w)$ so verzogen, dass $F_N(w) \forall |w| < 1$ + + +Damit ein Filter die Passband Kondition erfüllt muss $|F_N(w)| \leq 1 \forall |w| \leq 1$ und für $|w| \geq 1$ sollte die Funktion möglichst schnell divergieren. +Eine einfaches Polynom, dass das erfüllt, erhalten wir wenn $F_N(w) = w^N$. +Tatsächlich erhalten wir damit das Butterworth Filter, wie in Abbildung \ref{ellfilter:fig:butterworth} ersichtlich. +\begin{figure} + \centering + \includegraphics[scale=1]{papers/ellfilter/python/F_N_butterworth.pdf} + \caption{$F_N$ für Butterworth filter. Der grüne Bereich definiert die erlaubten Werte für alle $F_N$-Funktionen.} + \label{ellfilter:fig:butterworth} +\end{figure} + +wenn $F_N(w)$ eine rationale Funktion ist, ist auch $H(\Omega)$ eine rationale Funktion und daher ein lineares Filter. %proof? + +\begin{align} + F_N(w) & = + \begin{cases} + w^N & \text{Butterworth} \\ + T_N(w) & \text{Tschebyscheff, Typ 1} \\ + [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\ + R_N(w) & \text{Elliptisch (Cauer)} \\ + \end{cases} +\end{align} + +Mit der Ausnahme vom Butterworth filter sind alle Filter nach speziellen Funktionen benannt. +Alle diese Filter sind optimal für unterschiedliche Anwendungsgebiete. +Das Butterworth-Filter, zum Beispiel, ist maximal flach im Durchlassbereich. +Das Tschebyscheff-1 Filter sind maximal steil für eine definierte Welligkeit im Durchlassbereich, währendem es im Sperrbereich monoton abfallend ist. +Es scheint so als sind gewisse Eigenschaften dieser speziellen Funktionen verantwortlich für die Optimalität dieser Filter. + +\section{Tschebyscheff-Filter} + +Als Einstieg betrachent Wir das Tschebyscheff-Filter, welches sehr verwand ist mit dem elliptischen Filter. +Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Fitler ein Spezialfall davon. + +Der Name des Filters deutet schon an, dass die Tschebyschff-Polynome $T_N$ relevant sind für das Filter: +\begin{align} + T_{0}(x)&=1\\ + T_{1}(x)&=x\\ + T_{2}(x)&=2x^{2}-1\\ + T_{3}(x)&=4x^{3}-3x\\ + T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x). +\end{align} +Bemerkenswert ist, dass die Polynome im Intervall $[-1, 1]$ mit der Trigonometrischen Funktion +\begin{equation} \label{ellfilter:eq:chebychef_polynomials} + T_N(w) = \cos \left( N \cos^{-1}(w) \right) +\end{equation} +übereinstimmt. +Abbildung \ref{ellfilter:fig:chebychef_polynomials} zeigt einige Tschebyscheff-Polynome. +\begin{figure} + \centering + \includegraphics[scale=1]{papers/ellfilter/python/F_N_chebychev2.pdf} + \caption{Die Tschebyscheff-Polynome $C_N$.} + \label{ellfilter:fig:chebychef_polynomials} +\end{figure} +Da der Kosinus begrenzt zwischen $-1$ und $1$ ist, sind auch die Tschebyscheff-Polynome begrenzt. +Geht man aber über das Intervall $[-1, 1]$ hinaus, divergieren die Funktionen mit zunehmender Ordnung immer steiler gegen $\pm \infty$. +Diese Eigenschaft ist sehr nützlich für ein Filter. +Wenn wir die Tschebyscheff-Polynome quadrieren, passen sie perfekt in die Voraussetzungen für Filterfunktionen, wie es Abbildung \ref{ellfiter:fig:chebychef} demonstriert. +\begin{figure} + \centering + \includegraphics[scale=1]{papers/ellfilter/python/F_N_chebychev.pdf} + \caption{Die Tschebyscheff-Polynome füllen den erlaubten Bereich besser, und erhalten dadurch eine steilere Flanke im Sperrbereich.} + \label{ellfiter:fig:chebychef} +\end{figure} + + +Die analytische Fortsetzung von \eqref{ellfilter:eq:chebychef_polynomials} über das Intervall $[-1,1]$ hinaus stimmt mit den Polynomen überein, wie es zu erwarten ist. +Die genauere Betrachtung wird uns dann helfen die elliptischen Filter zu verstehen. + +\begin{equation} + \cos^{-1}(x) + = + \int_{0}^{x} + \frac{ + dz + }{ + \sqrt{ + 1-z^2 + } + } +\end{equation} %TOdO is it minus dz? + +\begin{equation} + \frac{ + 1 + }{ + \sqrt{ + 1-z^2 + } + } + \in \mathbb{R} + \quad + \forall + \quad + -1 \leq z \leq 1 +\end{equation} +Wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ. +Durch die Quadratwurzel entstehen zwei Reinkomplexe Lösungen +\begin{equation} + \frac{ + 1 + }{ + \sqrt{ + 1-z^2 + } + } + = i \xi \quad | \quad \xi \in \mathbb{R} + \quad + \forall + \quad + z \leq -1 \cup z \geq 1 +\end{equation} + +\begin{figure} + \centering + \input{papers/ellfilter/tikz/arccos.tikz.tex} + \caption{Die Funktion $z = \cos^{-1}(w)$ dargestellt in der komplexen ebene.} + \label{ellfilter:fig:arccos} +\end{figure} + + + +\begin{figure} + \centering + \input{papers/ellfilter/tikz/arccos2.tikz.tex} + \caption{ + $z$-Ebene der Tschebyscheff-Funktion. + Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden hat das Tschebyscheff-Polynom. + } + % \label{ellfilter:fig:arccos} +\end{figure} + + + + + +% Analytische Fortsetzung + + + +\section{Jacobische elliptische Funktionen} + + +Für das elliptische Filter, wird statt der für das Tschebyscheff-Filter benutzen Kreis-Trigonometrie die elliptischen Funktionen gebraucht. +Der begriff elliptische Funktion wird für sehr viele Funktionen gebraucht, daher ist es hier wichtig zu erwähnen, dass es ausschliesslich um die Jacobischen elliptischen Funktionen geht. + +Im Wesentlichen erweitern die Jacobi elliptischen Funktionen die trigonometrische Funktionen für Ellipsen. + +%TODO $z$ or $u$ for parameter? + +neu zwei parameter +$sn(z, k)$ +$z$ ist das winkelargument +Im Kreis ist der Radius für alle Winkel konstant, bei Ellipsen ändert sich das. +Dies hat zur Folge, dass bei einer Ellipse die Kreisbodenstrecke nicht linear zum Winkel verläuft. +Darum kann hier nicht der gewohnte Winkel verwendet werden. +An deren stelle kommt der parameter $k$ zum Einsatz, welcher durch das elliptische Integral erster Art +\begin{equation} + z + = + F(\phi, k) + = + \int_{0}^{\phi} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + } +\end{equation} +mit dem Winkel $\phi$ in Verbindung liegt. + + + + +Dabei wird das vollständige und unvollständige Elliptische integral unterschieden. +Beim vollständigen Integral +\begin{equation} + K(k) + = + \int_{0}^{\pi / 2} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + } +\end{equation} +wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$. + +Die Jacobischen elliptischen Funktionen können mit der inversen Funktion +\begin{equation} + \phi = F^{-1}(z, k) +\end{equation} +definiert werden. Dabei ist zu beachten dass nur das $z$ Argument der Funktion invertiert wird also +\begin{equation} + z = F(\phi, k) + \Leftrightarrow + \phi = F^{-1}(z, k). +\end{equation} +Mithilfe von $F^{-1}$ kann $sn^{-1}$ mit dem Elliptischen integral dargestellt werden: +\begin{equation} + \sin(\phi) + = + \sin \left( F^{-1}(z, k) \right) + = + \sn(u, k) +\end{equation} + +\begin{align} + \sn^{-1}(w, k) + & = + \int_{0}^{\phi} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + }, + \quad + \phi = \sin^{-1}(w) + \\ + & = + \int_{0}^{w} + \frac{ + dt + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } +\end{align} + +Beim $\cos^{-1}(x)$ haben wir gesehen, dass die analytische Fortsetzung bei $x < -1$ und $x > 1$ rechtwinklig in die Komplexen zahlen wandert. +Wenn man das gleiche mit $\sn^{-1}(w, k)$ macht, erkennt man zwei interessante Stellen. +Die erste ist die gleiche wie beim $\cos^{-1}(x)$ nämlich bei $t = \pm 1$. +Der erste Term unter der Wurzel wird dann negativ, während der zweite noch positiv ist, da $k \leq 1$. +\begin{equation} + \frac{ + 1 + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } + \in \mathbb{R} + \quad \forall \quad + -1 \leq t \leq 1 +\end{equation} +Die zweite stelle passiert wenn beide Faktoren unter der Wurzel negativ werden, was bei $t = 1/k$ der Fall ist. + + + + +Funktion in relle und komplexe Richtung periodisch + +In der reellen Richtung ist sie $4K(k)$-periodisch und in der imaginären Richtung $4K^\prime(k)$-periodisch. + + + +%TODO sn^{-1} grafik + + +\section{Elliptische rationale Funktionen} + + +\begin{equation} + R_N(\xi, w) = \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) +\end{equation} +\begin{equation} + R_N(\xi, w) = \cd (N~u K_1, k_1), \quad w= \cd(uK, k) +\end{equation} + + +sieht ähnlich aus wie die trigonometrische darstellung der Tschebyschef-Polynome + +der Ordnungszahl $N$ kommt auch als Faktor for + +%TODO cd^{-1} grafik mit + + +\subsection{Degree Equation} + +Der $cd^{-1}$ Term muss so verzogen werden, dass die umgebene $cd$ funktion die nullstellen und pole trifft. +Dies trifft ein wenn die Degree Equation erfüllt ist. + +\begin{equation} + N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1} +\end{equation} + + +Leider ist das lösen dieser Gleichung nicht trivial. +Die Rechnung wird in \ref{ellfilter:bib:orfanidis} im Detail angeschaut. + + +\subsection{Polynome?} + +Bei den Tschebyscheff-Polynomen haben wir gesehen, dass die Trigonometrische Formel zu einfachen Polynomen umgewandelt werden kann. +Im gegensatz zum $\cos^{-1}$ hat der $\cd^{-1}$ nicht nur Nullstellen sondern auch Pole. +Somit entstehen bei den elliptischen rationalen Funktionen, wie es der name auch deutet, rationale Funktionen, also ein Bruch von zwei Polynomen. + + + + +\begin{figure} + \centering + \includegraphics[scale=1]{papers/ellfilter/python/F_N_elliptic.pdf} + \caption{$F_N$ für ein elliptischs filter.} + \label{ellfilter:fig:elliptic} +\end{figure} + + + + \input{papers/ellfilter/teil0.tex} \input{papers/ellfilter/teil1.tex} \input{papers/ellfilter/teil2.tex} \input{papers/ellfilter/teil3.tex} -\printbibliography[heading=subbibliography] +% \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/ellfilter/packages.tex b/buch/papers/ellfilter/packages.tex index c94db34..8045a1a 100644 --- a/buch/papers/ellfilter/packages.tex +++ b/buch/papers/ellfilter/packages.tex @@ -8,3 +8,6 @@ % following example %\usepackage{packagename} + +\DeclareMathOperator{\sn}{\text{sn}} +\DeclareMathOperator{\cd}{\text{cd}} diff --git a/buch/papers/ellfilter/python/chebychef.py b/buch/papers/ellfilter/python/chebychef.py new file mode 100644 index 0000000..a278989 --- /dev/null +++ b/buch/papers/ellfilter/python/chebychef.py @@ -0,0 +1,65 @@ +# %% + +import matplotlib.pyplot as plt +import scipy.signal +import numpy as np + + +order = 5 +passband_ripple_db = 1 +omega_c = 1000 + +a, b = scipy.signal.cheby1( + order, + passband_ripple_db, + omega_c, + btype='low', + analog=True, + output='ba', + fs=None, +) + +w, mag, phase = scipy.signal.bode((a, b), w=np.linspace(0,2000,256)) +f, axs = plt.subplots(2,1, sharex=True) +axs[0].plot(w, 10**(mag/20)) +axs[0].set_ylabel("$|H(\omega)| /$ db") +axs[0].grid(True, "both") +axs[1].plot(w, phase) +axs[1].set_ylabel(r"$arg H (\omega) / $ deg") +axs[1].grid(True, "both") +axs[1].set_xlim([0, 2000]) +axs[1].set_xlabel("$\omega$") +plt.show() + + +# %% Cheychev filter F_N plot + +w = np.linspace(-1.1,1.1, 1000) +plt.figure(figsize=(5.5,2)) +for N in [3,6,11]: + # F_N = np.cos(N * np.arccos(w)) + F_N = scipy.special.eval_chebyt(N, w) + plt.plot(w, F_N, label=f"$N={N}$") +plt.xlim([-1.2,1.2]) +plt.ylim([-2,2]) +plt.grid() +plt.xlabel("$w$") +plt.ylabel("$C_N(w)$") +plt.legend() +plt.savefig("F_N_chebychev2.pdf") +plt.show() + +# %% Build Chebychev polynomials + +N = 11 + +zeros = (np.arange(N)+0.5) * np.pi +zeros = np.cos(zeros/N) + +x = np.linspace(-1.2,1.2,1000) +y = np.prod(x[:, None] - zeros[None, :], axis=-1)*2**(N-1) + +plt.plot(x, y) +plt.ylim([-1,1]) +plt.grid() +plt.show() diff --git a/buch/papers/ellfilter/python/elliptic.py b/buch/papers/ellfilter/python/elliptic.py new file mode 100644 index 0000000..9f209e9 --- /dev/null +++ b/buch/papers/ellfilter/python/elliptic.py @@ -0,0 +1,316 @@ + +# %% + +import scipy.special +import scipyx as spx +import numpy as np +import matplotlib.pyplot as plt +import matplotlib +from matplotlib.patches import Rectangle + +matplotlib.rcParams.update({ + "pgf.texsystem": "pdflatex", + 'font.family': 'serif', + 'font.size': 9, + 'text.usetex': True, + 'pgf.rcfonts': False, +}) + +def last_color(): + plt.gca().lines[-1].get_color() + +# %% Buttwerworth filter F_N plot + +w = np.linspace(0,1.5, 100) +plt.figure(figsize=(4,2.5)) + +for N in range(1,5): + F_N = w**N + plt.plot(w, F_N**2, label=f"$N={N}$") +plt.gca().add_patch(Rectangle( + (0, 0), + 1, 1, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.gca().add_patch(Rectangle( + (1, 1), + 0.5, 1, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.xlim([0,1.5]) +plt.ylim([0,2]) +plt.grid() +plt.xlabel("$w$") +plt.ylabel("$F^2_N(w)$") +plt.legend() +plt.savefig("F_N_butterworth.pdf") +plt.show() + +# %% Cheychev filter F_N plot + +w = np.linspace(0,1.5, 100) + +plt.figure(figsize=(4,2.5)) +for N in range(1,5): + # F_N = np.cos(N * np.arccos(w)) + F_N = scipy.special.eval_chebyt(N, w) + plt.plot(w, F_N**2, label=f"$N={N}$") +plt.gca().add_patch(Rectangle( + (0, 0), + 1, 1, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.gca().add_patch(Rectangle( + (1, 1), + 0.5, 1, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.xlim([0,1.5]) +plt.ylim([0,2]) +plt.grid() +plt.xlabel("$w$") +plt.ylabel("$F^2_N(w)$") +plt.legend() +plt.savefig("F_N_chebychev.pdf") +plt.show() + +# %% define elliptic functions + +def ell_int(k): + """ Calculate K(k) """ + m = k**2 + return scipy.special.ellipk(m) + +def sn(z, k): + return spx.ellipj(z, k**2)[0] + +def cn(z, k): + return spx.ellipj(z, k**2)[1] + +def dn(z, k): + return spx.ellipj(z, k**2)[2] + +def cd(z, k): + sn, cn, dn, ph = spx.ellipj(z, k**2) + return cn / dn + +# https://mathworld.wolfram.com/JacobiEllipticFunctions.html eq 3-8 + +def sn_inv(z, k): + m = k**2 + return scipy.special.ellipkinc(np.arcsin(z), m) + +def cn_inv(z, k): + m = k**2 + return scipy.special.ellipkinc(np.arccos(z), m) + +def dn_inv(z, k): + m = k**2 + x = np.sqrt((1-z**2) / k**2) + return scipy.special.ellipkinc(np.arcsin(x), m) + +def cd_inv(z, k): + m = k**2 + x = np.sqrt(((m - 1) * z**2) / (m*z**2 - 1)) + return scipy.special.ellipkinc(np.arccos(x), m) + + +k = 0.8 +z = 0.5 + +assert np.allclose(sn_inv(sn(z ,k), k), z) +assert np.allclose(cn_inv(cn(z ,k), k), z) +assert np.allclose(dn_inv(dn(z ,k), k), z) +assert np.allclose(cd_inv(cd(z ,k), k), z) + +# %% plot arcsin + +def lattice(a1, b1, c1, a2, b2, c2): + r1 = np.logspace(a1, b1, c1) + x1 = np.concatenate((-np.flip(r1), [0], r1), axis=0) + x1 = x1.astype(np.complex128) + r2 = np.logspace(a2, b2, c2) + x2 = np.concatenate((-np.flip(r2), [0], r2), axis=0) + x2 = x2.astype(np.complex128) + x = (x1[:, None] + (x2[None, :] * 1j)) + return x + +plt.figure(figsize=(12,12)) +y = np.arcsin(lattice(-1,6,1000, -1,5,10)) +plt.plot(np.real(y), np.imag(y), "-", color="red", lw=0.5) +y = np.arcsin(lattice(-1,6,10, -1,5,100)).T +plt.plot(np.real(y), np.imag(y), "-", color="red", lw=0.5) +y = np.arcsin(lattice(-1,6,10, -1,5,10)) +plt.plot(np.real(y), np.imag(y), ".", color="red", lw=0.5) +plt.show() + +# %% plot cd^-1 TODO complex cd^-1 missing + + +r = np.logspace(-1,8, 50) + + + +x = np.concatenate((-np.flip(r), [0], r), axis=0) +y = cd_inv(x, 0.99) + +plt.figure(figsize=(12,12)) +plt.plot(np.real(y), np.imag(y), "-") +plt.show() + +# %%plot cd +plt.figure(figsize=(10,6)) +z = np.linspace(-4,4, 500) +for k in [0, 0.9, 0.99, 0.999, 0.99999]: + w = cd(z*ell_int(k), k) + plt.plot(z, w, label=f"$k={k}$") +plt.grid() +plt.legend() +# plt.xlim([-4,4]) +plt.xlabel("$u$") +plt.ylabel("$cd(uK, k)$") +plt.show() + +# %% Test ???? + +N = 5 +k = 0.9 +k1 = k**N + +assert np.allclose(k**(-N), k1**(-1)) + +K = ell_int(k) +Kp = ell_int(np.sqrt(1-k**2)) + +K1 = ell_int(k1) +Kp1 = ell_int(np.sqrt(1-k1**2)) + +print(Kp * (K1 / K) * N, Kp1) + + +# %% + + +k = 0.9 +k_prim = np.sqrt(1 - k**2) +K = ell_int(k) +Kp = ell_int(k_prim) + +print(K, Kp) + +zs = [ + 0 + (K + 0j) * np.linspace(0,1,25), + K + (Kp*1j) * np.linspace(0,1,25), + (K + Kp*1j) + (-K) * np.linspace(0,1,25), +] + + +for z in zs: + plt.plot(np.real(z), np.imag(z)) +plt.show() + + + +for z in zs: + w = cd(z, k) + plt.plot(np.real(w), np.imag(w)) +plt.show() + + + + + +# %% + +for i in range(10): + x = np.linspace(i*1,i*1+1,10, dtype=np.complex64) + w = np.arccos(x) + + x2 = np.cos(w) + x4 = np.cos(w+ 2*np.pi) + x3 = np.cos(np.conj(w)) + + assert np.allclose(x2, x4, rtol=0.001, atol=1e-5) + + assert np.allclose(x2, x3) + assert np.allclose(x2, x, rtol=0.001, atol=1e-5) + + plt.plot(np.real(w), np.imag(w), ".-") + +for i in range(10): + x = -np.linspace(i*1,i*1+1,100, dtype=np.complex64) + w = np.arccos(x) + plt.plot(np.real(w), np.imag(w), ".-") + +plt.grid() +plt.show() + + + + +# %% + +plt.plot(omega, np.abs(G)) +plt.show() + + +def cd_inv(u, m): + return K(1/2) - F(np.arcsin()) + +def K(m): + return scipy.special.ellipk(m) + +def L(n, xi): + return 1 #TODO + +def R(n, xi, x): + cn(n*K(1/L(n, xi))/K(1/xi) * cd_inv(x, 1/xi, 1/L(n, xi))) + +epsilon = 0.1 +n = 3 +omega = np.linspace(0, np.pi, 1000) +omega_0 = 1 +xi = 1.1 + +G = 1 / np.sqrt(1 + epsilon**2 * R(n, xi, omega/omega_0)**2) + + +plt.plot(omega, np.abs(G)) +plt.show() + + + +# %% Chebychef + +epsilon = 0.5 +omega = np.linspace(0, np.pi, 1000) +omega_0 = 1 +n = 4 + +def chebychef_poly(n, x): + x = x.astype(np.complex64) + y = np.cos(n* np.arccos(x)) + return np.real(y) + +F_omega = chebychef_poly + +for n in (1,2,3,4): + plt.plot(omega, F_omega(n, omega/omega_0)**2) +plt.ylim([0,5]) +plt.xlim([0,1.5]) +plt.grid() +plt.show() + +for n in (1,2,3,4): + G = 1 / np.sqrt(1 + epsilon**2 * F_omega(n, omega/omega_0)**2) + plt.plot(omega, np.abs(G)) +plt.grid() +plt.show() diff --git a/buch/papers/ellfilter/python/elliptic2.py b/buch/papers/ellfilter/python/elliptic2.py new file mode 100644 index 0000000..92fefd9 --- /dev/null +++ b/buch/papers/ellfilter/python/elliptic2.py @@ -0,0 +1,78 @@ +# %% + +import matplotlib.pyplot as plt +import scipy.signal +import numpy as np +import matplotlib +from matplotlib.patches import Rectangle + + +def ellip_filter(N): + + order = N + passband_ripple_db = 3 + stopband_attenuation_db = 20 + omega_c = 1000 + + a, b = scipy.signal.ellip( + order, + passband_ripple_db, + stopband_attenuation_db, + omega_c, + btype='low', + analog=True, + output='ba', + fs=None + ) + + w, mag_db, phase = scipy.signal.bode((a, b), w=np.linspace(0*omega_c,2*omega_c, 4000)) + + mag = 10**(mag_db/20) + + passband_ripple = 10**(-passband_ripple_db/20) + epsilon2 = (1/passband_ripple)**2 - 1 + + FN2 = ((1/mag**2) - 1) + + return w/omega_c, FN2 / epsilon2 + + +plt.figure(figsize=(4,2.5)) + +for N in [5]: + w, FN2 = ellip_filter(N) + plt.semilogy(w, FN2, label=f"$N={N}$") + +plt.gca().add_patch(Rectangle( + (0, 0), + 1, 1, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.gca().add_patch(Rectangle( + (1, 1), + 0.01, 1e2-1, + fc ='green', + alpha=0.2, + lw = 10, +)) + +plt.gca().add_patch(Rectangle( + (1.01, 100), + 1, 1e6, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.xlim([0,2]) +plt.ylim([1e-4,1e6]) +plt.grid() +plt.xlabel("$w$") +plt.ylabel("$F^2_N(w)$") +plt.legend() +plt.savefig("F_N_elliptic.pdf") +plt.show() + + + diff --git a/buch/papers/ellfilter/references.bib b/buch/papers/ellfilter/references.bib index 81b3577..2b873af 100644 --- a/buch/papers/ellfilter/references.bib +++ b/buch/papers/ellfilter/references.bib @@ -4,32 +4,10 @@ % (c) 2020 Autor, Hochschule Rapperswil % -@online{ellfilter:bibtex, - title = {BibTeX}, - url = {https://de.wikipedia.org/wiki/BibTeX}, - date = {2020-02-06}, - year = {2020}, - month = {2}, - day = {6} -} - -@book{ellfilter:numerical-analysis, - title = {Numerical Analysis}, - author = {David Kincaid and Ward Cheney}, - publisher = {American Mathematical Society}, - year = {2002}, - isbn = {978-8-8218-4788-6}, - inseries = {Pure and applied undegraduate texts}, - volume = {2} -} - -@article{ellfilter:mendezmueller, - author = { Tabea Méndez and Andreas Müller }, - title = { Noncommutative harmonic analysis and image registration }, - journal = { Appl. Comput. Harmon. Anal.}, - year = 2019, - volume = 47, - pages = {607--627}, - url = {https://doi.org/10.1016/j.acha.2017.11.004} +@online{ellfilter:bib:orfanidis, + author = { Sophocles J. Orfanidis}, + title = { LECTURE NOTES ON ELLIPTIC FILTER DESIGN }, + year = 2006, + url = {https://www.ece.rutgers.edu/~orfanidi/ece521/notes.pdf} } diff --git a/buch/papers/ellfilter/teil0.tex b/buch/papers/ellfilter/teil0.tex index fd04ba9..6204bc0 100644 --- a/buch/papers/ellfilter/teil0.tex +++ b/buch/papers/ellfilter/teil0.tex @@ -3,20 +3,20 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{ellfilter:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{ellfilter:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. +% \section{Teil 0\label{ellfilter:section:teil0}} +% \rhead{Teil 0} +% Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +% nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +% erat, sed diam voluptua \cite{ellfilter:bibtex}. +% At vero eos et accusam et justo duo dolores et ea rebum. +% Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum +% dolor sit amet. -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. +% Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +% nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +% erat, sed diam voluptua. +% At vero eos et accusam et justo duo dolores et ea rebum. Stet clita +% kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit +% amet. diff --git a/buch/papers/ellfilter/teil1.tex b/buch/papers/ellfilter/teil1.tex index 7e62a2f..4760473 100644 --- a/buch/papers/ellfilter/teil1.tex +++ b/buch/papers/ellfilter/teil1.tex @@ -3,53 +3,53 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 1 -\label{ellfilter:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{ellfilter:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. +% \section{Teil 1 +% \label{ellfilter:section:teil1}} +% \rhead{Problemstellung} +% Sed ut perspiciatis unde omnis iste natus error sit voluptatem +% accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +% quae ab illo inventore veritatis et quasi architecto beatae vitae +% dicta sunt explicabo. +% Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +% aut fugit, sed quia consequuntur magni dolores eos qui ratione +% voluptatem sequi nesciunt +% \begin{equation} +% \int_a^b x^2\, dx +% = +% \left[ \frac13 x^3 \right]_a^b +% = +% \frac{b^3-a^3}3. +% \label{ellfilter:equation1} +% \end{equation} +% Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +% consectetur, adipisci velit, sed quia non numquam eius modi tempora +% incidunt ut labore et dolore magnam aliquam quaerat voluptatem. -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? +% Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +% suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +% Quis autem vel eum iure reprehenderit qui in ea voluptate velit +% esse quam nihil molestiae consequatur, vel illum qui dolorem eum +% fugiat quo voluptas nulla pariatur? -\subsection{De finibus bonorum et malorum -\label{ellfilter:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. +% \subsection{De finibus bonorum et malorum +% \label{ellfilter:subsection:finibus}} +% At vero eos et accusamus et iusto odio dignissimos ducimus qui +% blanditiis praesentium voluptatum deleniti atque corrupti quos +% dolores et quas molestias excepturi sint occaecati cupiditate non +% provident, similique sunt in culpa qui officia deserunt mollitia +% animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. -Et harum quidem rerum facilis est et expedita distinctio -\ref{ellfilter:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{ellfilter:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. +% Et harum quidem rerum facilis est et expedita distinctio +% \ref{ellfilter:section:loesung}. +% Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +% impedit quo minus id quod maxime placeat facere possimus, omnis +% voluptas assumenda est, omnis dolor repellendus +% \ref{ellfilter:section:folgerung}. +% Temporibus autem quibusdam et aut officiis debitis aut rerum +% necessitatibus saepe eveniet ut et voluptates repudiandae sint et +% molestiae non recusandae. +% Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +% voluptatibus maiores alias consequatur aut perferendis doloribus +% asperiores repellat. diff --git a/buch/papers/ellfilter/teil2.tex b/buch/papers/ellfilter/teil2.tex index 71fdc6d..39dd5d7 100644 --- a/buch/papers/ellfilter/teil2.tex +++ b/buch/papers/ellfilter/teil2.tex @@ -3,38 +3,38 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 -\label{ellfilter:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? +% \section{Teil 2 +% \label{ellfilter:section:teil2}} +% \rhead{Teil 2} +% Sed ut perspiciatis unde omnis iste natus error sit voluptatem +% accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +% quae ab illo inventore veritatis et quasi architecto beatae vitae +% dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +% aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +% eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +% est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +% velit, sed quia non numquam eius modi tempora incidunt ut labore +% et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +% veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +% nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +% reprehenderit qui in ea voluptate velit esse quam nihil molestiae +% consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +% pariatur? -\subsection{De finibus bonorum et malorum -\label{ellfilter:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +% \subsection{De finibus bonorum et malorum +% \label{ellfilter:subsection:bonorum}} +% At vero eos et accusamus et iusto odio dignissimos ducimus qui +% blanditiis praesentium voluptatum deleniti atque corrupti quos +% dolores et quas molestias excepturi sint occaecati cupiditate non +% provident, similique sunt in culpa qui officia deserunt mollitia +% animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +% est et expedita distinctio. Nam libero tempore, cum soluta nobis +% est eligendi optio cumque nihil impedit quo minus id quod maxime +% placeat facere possimus, omnis voluptas assumenda est, omnis dolor +% repellendus. Temporibus autem quibusdam et aut officiis debitis aut +% rerum necessitatibus saepe eveniet ut et voluptates repudiandae +% sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +% sapiente delectus, ut aut reiciendis voluptatibus maiores alias +% consequatur aut perferendis doloribus asperiores repellat. diff --git a/buch/papers/ellfilter/teil3.tex b/buch/papers/ellfilter/teil3.tex index 79a5f3d..dad96ad 100644 --- a/buch/papers/ellfilter/teil3.tex +++ b/buch/papers/ellfilter/teil3.tex @@ -3,38 +3,38 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 3 -\label{ellfilter:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? +% \section{Teil 3 +% \label{ellfilter:section:teil3}} +% \rhead{Teil 3} +% Sed ut perspiciatis unde omnis iste natus error sit voluptatem +% accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +% quae ab illo inventore veritatis et quasi architecto beatae vitae +% dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +% aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +% eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +% est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +% velit, sed quia non numquam eius modi tempora incidunt ut labore +% et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +% veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +% nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +% reprehenderit qui in ea voluptate velit esse quam nihil molestiae +% consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +% pariatur? -\subsection{De finibus bonorum et malorum -\label{ellfilter:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +% \subsection{De finibus bonorum et malorum +% \label{ellfilter:subsection:malorum}} +% At vero eos et accusamus et iusto odio dignissimos ducimus qui +% blanditiis praesentium voluptatum deleniti atque corrupti quos +% dolores et quas molestias excepturi sint occaecati cupiditate non +% provident, similique sunt in culpa qui officia deserunt mollitia +% animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +% est et expedita distinctio. Nam libero tempore, cum soluta nobis +% est eligendi optio cumque nihil impedit quo minus id quod maxime +% placeat facere possimus, omnis voluptas assumenda est, omnis dolor +% repellendus. Temporibus autem quibusdam et aut officiis debitis aut +% rerum necessitatibus saepe eveniet ut et voluptates repudiandae +% sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +% sapiente delectus, ut aut reiciendis voluptatibus maiores alias +% consequatur aut perferendis doloribus asperiores repellat. diff --git a/buch/papers/ellfilter/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex new file mode 100644 index 0000000..2bdcc2d --- /dev/null +++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex @@ -0,0 +1,97 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + + + \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{Im $z$}; + \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{Re $z$}; + + \begin{scope} + \draw[thick, ->, orange] (-1, 0) -- (0,0); + \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); + \draw[thick, ->, darkgreen] (0, 0) -- (0,-1.5); + \draw[thick, ->, orange] (1, 0) -- (0,0); + \draw[thick, ->, red] (2, 0) -- (1,0); + \draw[thick, ->, blue] (2,1.5) -- (2, 0); + \draw[thick, ->, blue] (2,-1.5) -- (2, 0); + \draw[thick, ->, red] (2, 0) -- (3,0); + + \node[anchor=south west] at (0,1.5) {$\infty$}; + \node[anchor=south west] at (0,-1.5) {$\infty$}; + \node[anchor=south west] at (0,0) {$1$}; + \node[anchor=south] at (1,0) {$0$}; + \node[anchor=south west] at (2,0) {$-1$}; + \node[anchor=south west] at (2,1.5) {$-\infty$}; + \node[anchor=south west] at (2,-1.5) {$-\infty$}; + \node[anchor=south west] at (3,0) {$0$}; + \end{scope} + + \begin{scope}[xshift=4cm] + \draw[thick, ->, orange] (-1, 0) -- (0,0); + \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); + \draw[thick, ->, darkgreen] (0, 0) -- (0,-1.5); + % \draw[thick, ->, orange] (1, 0) -- (0,0); + % \draw[thick, ->, red] (2, 0) -- (1,0); + % \draw[thick, ->, blue] (2,1.5) -- (2, 0); + % \draw[thick, ->, blue] (2,-1.5) -- (2, 0); + % \draw[thick, ->, red] (2, 0) -- (3,0); + + \node[anchor=south west] at (0,1.5) {$\infty$}; + \node[anchor=south west] at (0,-1.5) {$\infty$}; + \node[anchor=south west] at (0,0) {$1$}; + % \node[anchor=south] at (1,0) {$0$}; + % \node[anchor=south west] at (2,0) {$-1$}; + % \node[anchor=south west] at (2,1.5) {$-\infty$}; + % \node[anchor=south west] at (2,-1.5) {$-\infty$}; + % \node[anchor=south west] at (3,0) {$0$}; + \end{scope} + + \begin{scope}[xshift=-4cm] + % \draw[thick, ->, orange] (-1, 0) -- (0,0); + \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); + \draw[thick, ->, darkgreen] (0, 0) -- (0,-1.5); + \draw[thick, ->, orange] (1, 0) -- (0,0); + \draw[thick, ->, red] (2, 0) -- (1,0); + \draw[thick, ->, blue] (2,1.5) -- (2, 0); + \draw[thick, ->, blue] (2,-1.5) -- (2, 0); + \draw[thick, ->, red] (2, 0) -- (3,0); + + \node[anchor=south west] at (0,1.5) {$\infty$}; + \node[anchor=south west] at (0,-1.5) {$\infty$}; + \node[anchor=south west] at (0,0) {$1$}; + \node[anchor=south] at (1,0) {$0$}; + \node[anchor=south west] at (2,0) {$-1$}; + \node[anchor=south west] at (2,1.5) {$-\infty$}; + \node[anchor=south west] at (2,-1.5) {$-\infty$}; + \node[anchor=south west] at (3,0) {$0$}; + \end{scope} + + \node[gray, anchor=north west] at (-4,0) {$-2\pi$}; + \node[gray, anchor=north west] at (-2,0) {$-\pi$}; + \node[gray, anchor=north west] at (0,0) {$0$}; + \node[gray, anchor=north west] at (2,0) {$\pi$}; + \node[gray, anchor=north west] at (4,0) {$2\pi$}; + + + \node[gray, anchor=south east] at (0,-1.5) {$-\infty$}; + \node[gray, anchor=south east] at (0, 0) {$0$}; + \node[gray, anchor=south east] at (0, 1.5) {$\infty$}; + + + + \begin{scope}[yshift=-2.5cm] + + \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$w$}; + + \draw[thick, ->, blue] (-4, 0) -- (-2, 0); + \draw[thick, ->, red] (-2, 0) -- (0, 0); + \draw[thick, ->, orange] (0, 0) -- (2, 0); + \draw[thick, ->, darkgreen] (2, 0) -- (4, 0); + + \node[anchor=south] at (-4,0) {$-\infty$}; + \node[anchor=south] at (-2,0) {$-1$}; + \node[anchor=south] at (0,0) {$0$}; + \node[anchor=south] at (2,0) {$1$}; + \node[anchor=south] at (4,0) {$\infty$}; + + \end{scope} + +\end{tikzpicture} \ No newline at end of file diff --git a/buch/papers/ellfilter/tikz/arccos2.tikz.tex b/buch/papers/ellfilter/tikz/arccos2.tikz.tex new file mode 100644 index 0000000..dcf02fd --- /dev/null +++ b/buch/papers/ellfilter/tikz/arccos2.tikz.tex @@ -0,0 +1,46 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + + \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] + + \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} + + \begin{scope}[xscale=0.5] + + \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{Im $z$}; + \draw[gray, ->] (-10,0) -- (10,0) node[anchor=west]{Re $z$}; + + \begin{scope} + + \draw[>->, line width=0.05, thick, blue] (2, 1.5) -- (2,0.05) -- node[anchor=south, pos=0.5]{$N=1$} (0.1,0.05) -- (0.1,1.5); + \draw[>->, line width=0.05, thick, orange] (4, 1.5) -- (4,0) -- node[anchor=south, pos=0.25]{$N=2$} (0,0) -- (0,1.5); + \draw[>->, line width=0.05, thick, red] (6, 1.5) -- (6,-0.05) -- node[anchor=south, pos=0.1666]{$N=3$} (-0.1,-0.05) -- (-0.1,1.5); + + + \node[zero] at (-7,0) {}; + \node[zero] at (-5,0) {}; + \node[zero] at (-3,0) {}; + \node[zero] at (-1,0) {}; + \node[zero] at (1,0) {}; + \node[zero] at (3,0) {}; + \node[zero] at (5,0) {}; + \node[zero] at (7,0) {}; + + + \end{scope} + + \node[gray, anchor=north] at (-8,0) {$-4\pi$}; + \node[gray, anchor=north] at (-6,0) {$-3\pi$}; + \node[gray, anchor=north] at (-4,0) {$-2\pi$}; + \node[gray, anchor=north] at (-2,0) {$-\pi$}; + \node[gray, anchor=north] at (2,0) {$\pi$}; + \node[gray, anchor=north] at (4,0) {$2\pi$}; + \node[gray, anchor=north] at (6,0) {$3\pi$}; + \node[gray, anchor=north] at (8,0) {$4\pi$}; + + + \node[gray, anchor=east] at (0,-1.5) {$-\infty$}; + \node[gray, anchor=east] at (0, 1.5) {$\infty$}; + + \end{scope} + +\end{tikzpicture} \ No newline at end of file -- cgit v1.2.1 From 5fa246097347d82af591aa186f1b7fe32fbd1cf3 Mon Sep 17 00:00:00 2001 From: Runterer <37069007+Runterer@users.noreply.github.com> Date: Mon, 16 May 2022 15:35:30 +0200 Subject: added tikz -> kudos nic --- buch/papers/zeta/continuation_overview.tikz.tex | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) create mode 100644 buch/papers/zeta/continuation_overview.tikz.tex diff --git a/buch/papers/zeta/continuation_overview.tikz.tex b/buch/papers/zeta/continuation_overview.tikz.tex new file mode 100644 index 0000000..03224ff --- /dev/null +++ b/buch/papers/zeta/continuation_overview.tikz.tex @@ -0,0 +1,17 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=0.9cm, scale=2, + dot/.style={fill, circle, inner sep=0, minimum size=0.1cm}] + + \draw[->] (-2,0) -- (-1,0) node[dot]{} node[anchor=north]{$-1$} -- (0,0) node[anchor=north west]{$0$} -- (1,0) node[anchor=north west]{$1$} -- (2,0) node[anchor=west]{Re$(s)$}; 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charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/nav/bilder/dreieck.png | Bin 0 -> 91703 bytes buch/papers/nav/bilder/kugel1.png | Bin 0 -> 9051 bytes buch/papers/nav/bilder/kugel2.png | Bin 0 -> 9103 bytes buch/papers/nav/bilder/kugel3.png | Bin 0 -> 215188 bytes buch/papers/nav/bilder/projektion.png | Bin 0 -> 41289 bytes buch/papers/nav/einleitung.tex | 17 +++ buch/papers/nav/flatearth.tex | 31 ++++++ buch/papers/nav/geschichte.tex | 22 ++++ buch/papers/nav/main.log | 109 +++++++++++++++++++ buch/papers/nav/main.tex | 29 ++---- buch/papers/nav/nautischesdreieck.tex | 190 ++++++++++++++++++++++++++++++++++ buch/papers/nav/packages.tex | 6 ++ buch/papers/nav/trigo.tex | 51 +++++++++ 13 files changed, 433 insertions(+), 22 deletions(-) create mode 100644 buch/papers/nav/bilder/dreieck.png create mode 100644 buch/papers/nav/bilder/kugel1.png create mode 100644 buch/papers/nav/bilder/kugel2.png create mode 100644 buch/papers/nav/bilder/kugel3.png create mode 100644 buch/papers/nav/bilder/projektion.png create mode 100644 buch/papers/nav/einleitung.tex create mode 100644 buch/papers/nav/flatearth.tex create mode 100644 buch/papers/nav/geschichte.tex create mode 100644 buch/papers/nav/main.log create mode 100644 buch/papers/nav/nautischesdreieck.tex create mode 100644 buch/papers/nav/trigo.tex diff --git a/buch/papers/nav/bilder/dreieck.png b/buch/papers/nav/bilder/dreieck.png new file mode 100644 index 0000000..2b02105 Binary files /dev/null and b/buch/papers/nav/bilder/dreieck.png differ diff --git a/buch/papers/nav/bilder/kugel1.png b/buch/papers/nav/bilder/kugel1.png new file mode 100644 index 0000000..b3188b7 Binary files /dev/null and b/buch/papers/nav/bilder/kugel1.png differ diff --git a/buch/papers/nav/bilder/kugel2.png b/buch/papers/nav/bilder/kugel2.png new file mode 100644 index 0000000..057740f Binary files /dev/null and b/buch/papers/nav/bilder/kugel2.png differ diff --git a/buch/papers/nav/bilder/kugel3.png b/buch/papers/nav/bilder/kugel3.png new file mode 100644 index 0000000..97066a2 Binary files /dev/null and b/buch/papers/nav/bilder/kugel3.png differ diff --git a/buch/papers/nav/bilder/projektion.png b/buch/papers/nav/bilder/projektion.png new file mode 100644 index 0000000..5dcc0c8 Binary files /dev/null and b/buch/papers/nav/bilder/projektion.png differ diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex new file mode 100644 index 0000000..42f4b6c --- /dev/null +++ b/buch/papers/nav/einleitung.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + +\begin{document} +\section{Einleitung} +Heut zu Tage ist die Navigation ein Teil des Lebens. +Man versendet dem Kollegen seinen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein um sich die Sucherei zu schenken. +Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. +Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf kleineren Schiffen benötigt wird im Falle eines Stromausfalls. +Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? +In diesem Kapitel werden genau diese Fragen mithilfe des Nautischen Dreiecks, der Sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. + + +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex new file mode 100644 index 0000000..b14dd4b --- /dev/null +++ b/buch/papers/nav/flatearth.tex @@ -0,0 +1,31 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + +\begin{document} + \section{Warum ist die Erde nicht flach?} + + \begin{figure}[h] + \begin{center} + \includegraphics[width=10cm]{bilder/projektion.png} + \caption{Mercator Projektion} + \end{center} + \end{figure} + +Es gibt heut zu Tage viele Beweise dafür, dass die Erde eine Kugel ist. +Die Fotos von unserem Planeten oder die Berichte der Astronauten. + Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. + Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. + Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. + Mithilfe der Geometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. + Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. +Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. +In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. +Das liegt daran, das man die 3D – Weltkarte nicht einfach auslegen kann. +Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. +Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. + + +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/geschichte.tex b/buch/papers/nav/geschichte.tex new file mode 100644 index 0000000..a20eb6d --- /dev/null +++ b/buch/papers/nav/geschichte.tex @@ -0,0 +1,22 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + +\begin{document} +\section{Geschichte der sphärischen Navigation} +Die Orientierung mit Hilfe der Sterne und der sphärischen Trigonometrie bewegt die Menschheit schon seit mehreren tausend Jahren. +Nach Hinweisen und Schätzungen von Forscher haben schon vor 4000 Jahren die Ägypter und Gelehrten aus Babylon mit Hilfe der Astronomie den Lauf der Gestirne (Himmelskörper) zu berechnen versucht, jedoch ohne Erfolg. +Etwa 350 vor Christus waren es die Griechen, welche den damaligen Astronomen Hilfestellungen mittels Kugel-Geometrien leisten konnten. +Aus diesen Geometrien wurden erste mathematische Sätze aufgestellt und ein paar Jahrhunderte später kamen zu diesem Thema auch Berechnungen dazu. +Ebenso wurden Kartenmaterial mit Sternenbilder angefertigt. +Die Sinusfunktion war noch nicht bekannt, jedoch kamen zu dieser Zeit die ersten Ansätze der Cosinusfunktion aus Indien. +Von diesen Hilfen darauf aufbauend konnte um 900 die Araber der Sinussatz entwickeln. +Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde. +Dies aus dem Grund, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung vermehrt an Wichtigkeit gewann. +Auch die Verwendung der Tangens- und Sinusfunktion sowie der neu entwickelte Seitencosinussatz trugen zu einer Verbesserung der Orientierung herbei. +Im 16. Jahrhundert wurde dann ein weiterer trigonometrischer Satz, der Winkelcosinussatz hergeleitet. Stück für Stück wurden infolge der Entdeckung des Logarithmus im 17. Jahrhundert viele neue Methoden entwickelt. +Auch eine Verbesserung der kartographischen Verwendung der Kugelgeometrie wurde vorgenommen. +Es folgten weitere Entwicklungen in nicht euklidische Geometrien und im 19. Jahrhundert sowie auch im 20. Jahrhundert wurde zudem für die Relativitätstheorie auch die sphärische Trigonometrie beigezogen. +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/main.log b/buch/papers/nav/main.log new file mode 100644 index 0000000..d7aa0a9 --- /dev/null +++ b/buch/papers/nav/main.log @@ -0,0 +1,109 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (MiKTeX 22.3) (preloaded format=pdflatex 2022.4.16) 16 MAY 2022 20:27 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**./main.tex +(main.tex +LaTeX2e <2021-11-15> patch level 1 +L3 programming layer <2022-02-24> +! Undefined control sequence. +l.6 \chapter + {Thema\label{chapter:nav}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.6 \chapter{T + hema\label{chapter:nav}} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +! Undefined control sequence. +l.7 \lhead + {Thema} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no T in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! + +! LaTeX Error: Environment refsection undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.8 \begin{refsection} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.9 \chapterauthor + {Hans Muster} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Emergency stop. + + +l.13 \input{papers/nav/einleitung.tex} + ^^M +*** (cannot \read from terminal in nonstop modes) + + +Here is how much of TeX's memory you used: + 22 strings out of 478582 + 530 string characters out of 2856069 + 288951 words of memory out of 3000000 + 18307 multiletter control sequences out of 15000+600000 + 469259 words of font info for 28 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 16i,0n,26p,84b,28s stack positions out of 10000i,1000n,20000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index e11e2c0..1ad16da 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -8,29 +8,14 @@ \begin{refsection} \chapterauthor{Hans Muster} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} -\input{papers/nav/teil0.tex} -\input{papers/nav/teil1.tex} -\input{papers/nav/teil2.tex} -\input{papers/nav/teil3.tex} + +\input{papers/nav/einleitung.tex} +\input{papers/nav/geschichte.tex} +\input{papers/nav/flatearth.tex} +\input{papers/nav/trigo.tex} +\input{papers/nav/nautischesdreieck.tex} + \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex new file mode 100644 index 0000000..0bb213c --- /dev/null +++ b/buch/papers/nav/nautischesdreieck.tex @@ -0,0 +1,190 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + \usepackage{xcolor, soul} + \sethlcolor{yellow} +\begin{document} + \setlength{\parindent}{0em} +\section{Das Nautische Dreieck} +\subsection{Definition des Nautischen Dreiecks} +Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der \textbf{Himmelskugel}. +Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient.\\ +Das Nautische Dreieck definiert sich durch folgende Ecken: +\begin{itemize} + \item Zenit + \item Gestirn + \item Himmelspol +\end{itemize} +Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. +Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. +Der Himmelspol ist der Nordpol an die Himmelskugel projeziert. +\\ +Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfache Zusammenhänge: +\begin{itemize} + \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ + \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ + \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ + \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ + \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ +\end{itemize} +Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: + +$\alpha \ \widehat{=} \ Rektaszension $ + +$\delta \ \widehat{=} \ Deklination =$ Breitengrad des Gestirns + +$\theta \ \widehat{=} \ Sternzeit$ + +$\phi \ \widehat{=} \ Geographische \ Breite $ + +$\tau = \theta-\alpha \ \widehat{=} \ Stundenwinkel =$ Längengrad des Gestirns + +$a \ \widehat{=} \ Azimut $ + +$h \ \widehat{=} \ Hoehe$ + + + +\subsection{Zusammenhang des Nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} + + \begin{center} + \includegraphics[height=5cm,width=5cm]{Bilder/kugel3.png} + \end{center} +Wie man im oberen Bild sieht und auch am Anfang dieses Kapitels bereits erwähnt wurde, liegt das Nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. +Das selbe Dreieck kann man aber auch auf die Erdkugel projezieren und hat dann die Ecken Standort, Bildpunkt und Nordpol. +Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. + +\subsection{Varianten vom Nautischen Dreieck} +\section{Standortbestimmung ohne elektronische Hilfsmittel} +Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion Nautische Dreieck auf der Erdkugel zur Hilfe genommen. +Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. + + \begin{center} + \includegraphics[width=6cm]{Bilder/dreieck.png} + \end{center} + + + +\subsection{Ecke P - Unser Standort} +Unser eigener Standort ist der gesuchte Punkt A. + +\subsection{Ecke A - Nordpol} +Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol (in der Himmelskugel der Himmelsnordpol) ist. +Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. + +\subsection{Ecke B und C - Bildpunkt XXX und YYY} +Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. +Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. +\\ +Es gibt diverse Gestirne, die man nutzen kann. +\begin{itemize} + \item Sonne + \item Mond + \item Die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn +\end{itemize} + +Zu all diesen Gestirnen gibt es Ephemeriden (Jahrbücher). +Dort findet man unter Anderem die Rektaszension und Deklination, welche für jeden Tag und Stunde beschrieben ist. Für Minuten genaue Angaben muss man dann zwischen den Stunden interpolieren. +Mithilfe dieser beiden Angaben kann man die Längen- und Breitengrade diverser Gestirne berechnen. + +\subsubsection{Sternzeit und Rektaszension} +Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht. +Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. +Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. +Die Lösung ist die Sternzeit. +Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit +$\theta = 0$. + +Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. +Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. +Für die Sternzeit von Greenwich braucht man als erstes das Julianische Datum vom aktuellen Tag, welches sich leicht recherchieren oder berechnen lässt: \hl{$JD=....$} + +Nun berechnet man $T=\frac{JD-2451545}{36525}$ und damit die mittlere Sternzeit von Greenwich + + $T_{Greenwich} = 6^h 41^m 50^s,54841 + 8640184^s,812866 * T + 0^s,093104*T^2 - 0^s,0000062 * T^3$. + + Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit bestimmen. + Dies gilt analog auch für das zweite Gestirn. + + \subsubsection{Deklination} + Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad $\psi = \delta$. + + + +\subsection{Bestimmung des eigenen Standortes P} +Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. +Somit können wir ein erstes Kugeldreieck auf der Erde aufspannen. + + + \begin{center} + \includegraphics[width=5cm]{Bilder/dreieck.png} + \end{center} + + +\subsubsection{Bestimmung des ersten Dreiecks} + Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. + + Die Seitenlänge der Seite "Nordpol zum Bildpunkt XXX" sei $c$. + Dann ist $c = \frac{\pi}{2} - \delta_1$. + + Die Seitenlänge der Seite "Nordpol zum Bildpunkt YYY" sei $b$. + Dann ist $b = \frac{\pi}{2} - \delta_2$. + + Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. + Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. + +mit + + $\delta_1 =$ Deklination Bildpunkt XXX + +$\delta_2 =$ Deklination Bildpunk YYY + +$\lambda_1 =$ Längengrad Bildpunkt XXX + +$\lambda_2 =$ Längengrad Bildpunkt YYY + + Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! + +Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. +Mithilfe des Seiten-Kosinussatzes $cos(a) = cos(b)*cos(c) + sin(b) * sin(c)*cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. +Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. +Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. + +Dieser bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. +Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. Somit ist $sin(\beta) = sin(b) * \frac{sin(\alpha)}{sin(a)} $. + +Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. + +\subsubsection{Bestimmung des zweiten Dreiecks} +Wir bilden nun ein zweites Dreieck, welches die Ecken B und C des ersten Dreiecks besitzt. +Die dritte Ecke ist der eigene Standort P. +Unser Standort definiere sich aus einer geographischen Breite $\delta$ und einer geographischen Länge $\lambda$. + +Die Seite von P zu B sei $pb$ und die Seite von P zu C sei $pc$. +Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache Formel bestimmen, nämlich $pb=\frac{\pi}{2} - h_{B}$ und $pc=\frac{\pi}{2} - h_{C}$ + +mit $h_B=$ Höhe von Gestirn in B und $h_C=$ Höhe von Gestirn in C mit Sextant gemessen. +\\ + +Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$ mit den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes + +$cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$ berechnen. + +Es fehlt uns noch $\beta1$. +Da wir aber $pc$, $pb$ und $a$ kennen, kann man mit dem Seiten-Kosinussatz den Winkel $\beta1$ berechnen +\\ + +Somit ist $\delta = cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$. +\\ + +Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ABP$ în der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. +\\ + +Somit ist $\omega=sin(pb)*\frac{sin(\beta)}{sin(l)}$ und unsere gesuchte geographische Länge schlussendlich +$\lambda=\lambda_1 - \omega$ + + + +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 9faa48d..15c7fdc 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,3 +8,9 @@ % following example %\usepackage{packagename} +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} +\usepackage{xcolor, soul} diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex new file mode 100644 index 0000000..0dbd7a1 --- /dev/null +++ b/buch/papers/nav/trigo.tex @@ -0,0 +1,51 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + + +\begin{document} + \section{Sphärische Trigonometrie} + \subsection{Das Kugeldreieck} + +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck ABC. +A, B und C sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. +Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. +Laut dieser Definition ist die Seite c der Winkel AMB. +Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. +Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. +Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. +Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. +\begin{figure}[h] + \begin{center} + \includegraphics[width=6cm]{Bilder/kugel1.png} + \end{center} + +\end{figure} + +\subsection{Rechtwinkliges Dreieck und Rechtseitiges Dreieck} +Wie auch im uns bekannten Dreieck gibt es beim Kugeldreieck auch ein Rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. +Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. + \newpage +\subsection{Winkelangabe} + + \begin{center} + \includegraphics[width=8cm]{Bilder/kugel2.png} + \end{center} + +Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. +Für die Summe der Innenwinkel gilt $\alpha+\beta+\gamma = \frac{A}{r^2} + \pi$ und +$\alpha+\beta+\gamma > \pi$. +Der sphärische Exzess $\epsilon = \alpha+\beta+\gamma - \pi$ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. + +\subsection{Sphärischer Sinussatz} +In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. +Das bedeutet, dass $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} $ auch beim Kugeldreieck gilt. + +\subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} +Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. +In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. +Es gilt nämlich: $\cos c = \cos a * \cos b$ wenn $\alpha \lor \beta \lor \gamma = \frac{\pi}{2} $. + +\end{document} \ No newline at end of file -- cgit v1.2.1 From e898a9c36fb707474ee869f6ec47119d0592e59f Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Mon, 16 May 2022 20:32:38 +0200 Subject: =?UTF-8?q?Revert=20"Ich=20habe=20nun=20alle=20Kapitel=20als=20Tex?= =?UTF-8?q?tfile=20seperat=20eingef=C3=BCgt,=20einen=20zus=C3=A4tzlichen?= =?UTF-8?q?=20unterordner=20gemacht=20f=C3=BCr=20die=20bilder,=20dann=20im?= =?UTF-8?q?=20main.tex=20die=20input=20befehle=20angepasst=20und=20committ?= =?UTF-8?q?e=20nun."?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This reverts commit d7bff7e403a0e54880cb04b350a91a2f664b2708. --- buch/papers/nav/bilder/dreieck.png | Bin 91703 -> 0 bytes buch/papers/nav/bilder/kugel1.png | Bin 9051 -> 0 bytes buch/papers/nav/bilder/kugel2.png | Bin 9103 -> 0 bytes buch/papers/nav/bilder/kugel3.png | Bin 215188 -> 0 bytes buch/papers/nav/bilder/projektion.png | Bin 41289 -> 0 bytes buch/papers/nav/einleitung.tex | 17 --- buch/papers/nav/flatearth.tex | 31 ------ buch/papers/nav/geschichte.tex | 22 ---- buch/papers/nav/main.log | 109 ------------------- buch/papers/nav/main.tex | 29 ++++-- buch/papers/nav/nautischesdreieck.tex | 190 ---------------------------------- buch/papers/nav/packages.tex | 6 -- buch/papers/nav/trigo.tex | 51 --------- 13 files changed, 22 insertions(+), 433 deletions(-) delete mode 100644 buch/papers/nav/bilder/dreieck.png delete mode 100644 buch/papers/nav/bilder/kugel1.png delete mode 100644 buch/papers/nav/bilder/kugel2.png delete mode 100644 buch/papers/nav/bilder/kugel3.png delete mode 100644 buch/papers/nav/bilder/projektion.png delete mode 100644 buch/papers/nav/einleitung.tex delete mode 100644 buch/papers/nav/flatearth.tex delete mode 100644 buch/papers/nav/geschichte.tex delete mode 100644 buch/papers/nav/main.log delete mode 100644 buch/papers/nav/nautischesdreieck.tex delete mode 100644 buch/papers/nav/trigo.tex diff --git a/buch/papers/nav/bilder/dreieck.png b/buch/papers/nav/bilder/dreieck.png deleted file mode 100644 index 2b02105..0000000 Binary files a/buch/papers/nav/bilder/dreieck.png and /dev/null differ diff --git a/buch/papers/nav/bilder/kugel1.png b/buch/papers/nav/bilder/kugel1.png deleted file mode 100644 index b3188b7..0000000 Binary files a/buch/papers/nav/bilder/kugel1.png and /dev/null differ diff --git a/buch/papers/nav/bilder/kugel2.png b/buch/papers/nav/bilder/kugel2.png deleted file mode 100644 index 057740f..0000000 Binary files a/buch/papers/nav/bilder/kugel2.png and /dev/null differ diff --git a/buch/papers/nav/bilder/kugel3.png b/buch/papers/nav/bilder/kugel3.png deleted file mode 100644 index 97066a2..0000000 Binary files a/buch/papers/nav/bilder/kugel3.png and /dev/null differ diff --git a/buch/papers/nav/bilder/projektion.png b/buch/papers/nav/bilder/projektion.png deleted file mode 100644 index 5dcc0c8..0000000 Binary files a/buch/papers/nav/bilder/projektion.png and /dev/null differ diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex deleted file mode 100644 index 42f4b6c..0000000 --- a/buch/papers/nav/einleitung.tex +++ /dev/null @@ -1,17 +0,0 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - -\begin{document} -\section{Einleitung} -Heut zu Tage ist die Navigation ein Teil des Lebens. -Man versendet dem Kollegen seinen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein um sich die Sucherei zu schenken. -Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. -Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf kleineren Schiffen benötigt wird im Falle eines Stromausfalls. -Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? -In diesem Kapitel werden genau diese Fragen mithilfe des Nautischen Dreiecks, der Sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. - - -\end{document} \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex deleted file mode 100644 index b14dd4b..0000000 --- a/buch/papers/nav/flatearth.tex +++ /dev/null @@ -1,31 +0,0 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - -\begin{document} - \section{Warum ist die Erde nicht flach?} - - \begin{figure}[h] - \begin{center} - \includegraphics[width=10cm]{bilder/projektion.png} - \caption{Mercator Projektion} - \end{center} - \end{figure} - -Es gibt heut zu Tage viele Beweise dafür, dass die Erde eine Kugel ist. -Die Fotos von unserem Planeten oder die Berichte der Astronauten. - Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. - Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. - Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. - Mithilfe der Geometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. - Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. -Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. -In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. -Das liegt daran, das man die 3D – Weltkarte nicht einfach auslegen kann. -Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. -Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. - - -\end{document} \ No newline at end of file diff --git a/buch/papers/nav/geschichte.tex b/buch/papers/nav/geschichte.tex deleted file mode 100644 index a20eb6d..0000000 --- a/buch/papers/nav/geschichte.tex +++ /dev/null @@ -1,22 +0,0 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - -\begin{document} -\section{Geschichte der sphärischen Navigation} -Die Orientierung mit Hilfe der Sterne und der sphärischen Trigonometrie bewegt die Menschheit schon seit mehreren tausend Jahren. -Nach Hinweisen und Schätzungen von Forscher haben schon vor 4000 Jahren die Ägypter und Gelehrten aus Babylon mit Hilfe der Astronomie den Lauf der Gestirne (Himmelskörper) zu berechnen versucht, jedoch ohne Erfolg. -Etwa 350 vor Christus waren es die Griechen, welche den damaligen Astronomen Hilfestellungen mittels Kugel-Geometrien leisten konnten. -Aus diesen Geometrien wurden erste mathematische Sätze aufgestellt und ein paar Jahrhunderte später kamen zu diesem Thema auch Berechnungen dazu. -Ebenso wurden Kartenmaterial mit Sternenbilder angefertigt. -Die Sinusfunktion war noch nicht bekannt, jedoch kamen zu dieser Zeit die ersten Ansätze der Cosinusfunktion aus Indien. -Von diesen Hilfen darauf aufbauend konnte um 900 die Araber der Sinussatz entwickeln. -Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde. -Dies aus dem Grund, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung vermehrt an Wichtigkeit gewann. -Auch die Verwendung der Tangens- und Sinusfunktion sowie der neu entwickelte Seitencosinussatz trugen zu einer Verbesserung der Orientierung herbei. -Im 16. Jahrhundert wurde dann ein weiterer trigonometrischer Satz, der Winkelcosinussatz hergeleitet. Stück für Stück wurden infolge der Entdeckung des Logarithmus im 17. Jahrhundert viele neue Methoden entwickelt. -Auch eine Verbesserung der kartographischen Verwendung der Kugelgeometrie wurde vorgenommen. -Es folgten weitere Entwicklungen in nicht euklidische Geometrien und im 19. Jahrhundert sowie auch im 20. Jahrhundert wurde zudem für die Relativitätstheorie auch die sphärische Trigonometrie beigezogen. -\end{document} \ No newline at end of file diff --git a/buch/papers/nav/main.log b/buch/papers/nav/main.log deleted file mode 100644 index d7aa0a9..0000000 --- a/buch/papers/nav/main.log +++ /dev/null @@ -1,109 +0,0 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (MiKTeX 22.3) (preloaded format=pdflatex 2022.4.16) 16 MAY 2022 20:27 -entering extended mode - restricted \write18 enabled. - %&-line parsing enabled. -**./main.tex -(main.tex -LaTeX2e <2021-11-15> patch level 1 -L3 programming layer <2022-02-24> -! Undefined control sequence. -l.6 \chapter - {Thema\label{chapter:nav}} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - - -! 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Otherwise just continue, -and I'll forget about whatever was undefined. - -Missing character: There is no T in font nullfont! -Missing character: There is no h in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no m in font nullfont! -Missing character: There is no a in font nullfont! - -! LaTeX Error: Environment refsection undefined. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.8 \begin{refsection} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Undefined control sequence. -l.9 \chapterauthor - {Hans Muster} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - -Missing character: There is no H in font nullfont! -Missing character: There is no a in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no M in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no r in font nullfont! - -Overfull \hbox (20.0pt too wide) in paragraph at lines 6--10 -[][] - [] - - -! LaTeX Error: File `papers/nav/einleitung.tex' not found. - -Type X to quit or to proceed, -or enter new name. (Default extension: tex) - -Enter file name: -! Emergency stop. - - -l.13 \input{papers/nav/einleitung.tex} - ^^M -*** (cannot \read from terminal in nonstop modes) - - -Here is how much of TeX's memory you used: - 22 strings out of 478582 - 530 string characters out of 2856069 - 288951 words of memory out of 3000000 - 18307 multiletter control sequences out of 15000+600000 - 469259 words of font info for 28 fonts, out of 8000000 for 9000 - 1141 hyphenation exceptions out of 8191 - 16i,0n,26p,84b,28s stack positions out of 10000i,1000n,20000p,200000b,80000s -! ==> Fatal error occurred, no output PDF file produced! diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 1ad16da..e11e2c0 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -8,14 +8,29 @@ \begin{refsection} \chapterauthor{Hans Muster} +Ein paar Hinweise für die korrekte Formatierung des Textes +\begin{itemize} +\item +Absätze werden gebildet, indem man eine Leerzeile einfügt. +Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. +\item +Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende +Optionen werden gelöscht. +Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. +\item +Beginnen Sie jeden Satz auf einer neuen Zeile. +Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen +in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt +anzuwenden. +\item +Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren +Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. +\end{itemize} - -\input{papers/nav/einleitung.tex} -\input{papers/nav/geschichte.tex} -\input{papers/nav/flatearth.tex} -\input{papers/nav/trigo.tex} -\input{papers/nav/nautischesdreieck.tex} - +\input{papers/nav/teil0.tex} +\input{papers/nav/teil1.tex} +\input{papers/nav/teil2.tex} +\input{papers/nav/teil3.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex deleted file mode 100644 index 0bb213c..0000000 --- a/buch/papers/nav/nautischesdreieck.tex +++ /dev/null @@ -1,190 +0,0 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - \usepackage{xcolor, soul} - \sethlcolor{yellow} -\begin{document} - \setlength{\parindent}{0em} -\section{Das Nautische Dreieck} -\subsection{Definition des Nautischen Dreiecks} -Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der \textbf{Himmelskugel}. -Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient.\\ -Das Nautische Dreieck definiert sich durch folgende Ecken: -\begin{itemize} - \item Zenit - \item Gestirn - \item Himmelspol -\end{itemize} -Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. -Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. -Der Himmelspol ist der Nordpol an die Himmelskugel projeziert. -\\ -Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfache Zusammenhänge: -\begin{itemize} - \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ - \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ - \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ - \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ - \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ -\end{itemize} -Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: - -$\alpha \ \widehat{=} \ Rektaszension $ - -$\delta \ \widehat{=} \ Deklination =$ Breitengrad des Gestirns - -$\theta \ \widehat{=} \ Sternzeit$ - -$\phi \ \widehat{=} \ Geographische \ Breite $ - -$\tau = \theta-\alpha \ \widehat{=} \ Stundenwinkel =$ Längengrad des Gestirns - -$a \ \widehat{=} \ Azimut $ - -$h \ \widehat{=} \ Hoehe$ - - - -\subsection{Zusammenhang des Nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} - - \begin{center} - \includegraphics[height=5cm,width=5cm]{Bilder/kugel3.png} - \end{center} -Wie man im oberen Bild sieht und auch am Anfang dieses Kapitels bereits erwähnt wurde, liegt das Nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. -Das selbe Dreieck kann man aber auch auf die Erdkugel projezieren und hat dann die Ecken Standort, Bildpunkt und Nordpol. -Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. - -\subsection{Varianten vom Nautischen Dreieck} -\section{Standortbestimmung ohne elektronische Hilfsmittel} -Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion Nautische Dreieck auf der Erdkugel zur Hilfe genommen. -Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. - - \begin{center} - \includegraphics[width=6cm]{Bilder/dreieck.png} - \end{center} - - - -\subsection{Ecke P - Unser Standort} -Unser eigener Standort ist der gesuchte Punkt A. - -\subsection{Ecke A - Nordpol} -Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol (in der Himmelskugel der Himmelsnordpol) ist. -Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. - -\subsection{Ecke B und C - Bildpunkt XXX und YYY} -Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. -Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. -\\ -Es gibt diverse Gestirne, die man nutzen kann. -\begin{itemize} - \item Sonne - \item Mond - \item Die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn -\end{itemize} - -Zu all diesen Gestirnen gibt es Ephemeriden (Jahrbücher). -Dort findet man unter Anderem die Rektaszension und Deklination, welche für jeden Tag und Stunde beschrieben ist. Für Minuten genaue Angaben muss man dann zwischen den Stunden interpolieren. -Mithilfe dieser beiden Angaben kann man die Längen- und Breitengrade diverser Gestirne berechnen. - -\subsubsection{Sternzeit und Rektaszension} -Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht. -Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. -Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. -Die Lösung ist die Sternzeit. -Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit -$\theta = 0$. - -Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. -Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. -Für die Sternzeit von Greenwich braucht man als erstes das Julianische Datum vom aktuellen Tag, welches sich leicht recherchieren oder berechnen lässt: \hl{$JD=....$} - -Nun berechnet man $T=\frac{JD-2451545}{36525}$ und damit die mittlere Sternzeit von Greenwich - - $T_{Greenwich} = 6^h 41^m 50^s,54841 + 8640184^s,812866 * T + 0^s,093104*T^2 - 0^s,0000062 * T^3$. - - Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit bestimmen. - Dies gilt analog auch für das zweite Gestirn. - - \subsubsection{Deklination} - Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad $\psi = \delta$. - - - -\subsection{Bestimmung des eigenen Standortes P} -Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. -Somit können wir ein erstes Kugeldreieck auf der Erde aufspannen. - - - \begin{center} - \includegraphics[width=5cm]{Bilder/dreieck.png} - \end{center} - - -\subsubsection{Bestimmung des ersten Dreiecks} - Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. - - Die Seitenlänge der Seite "Nordpol zum Bildpunkt XXX" sei $c$. - Dann ist $c = \frac{\pi}{2} - \delta_1$. - - Die Seitenlänge der Seite "Nordpol zum Bildpunkt YYY" sei $b$. - Dann ist $b = \frac{\pi}{2} - \delta_2$. - - Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. - Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. - -mit - - $\delta_1 =$ Deklination Bildpunkt XXX - -$\delta_2 =$ Deklination Bildpunk YYY - -$\lambda_1 =$ Längengrad Bildpunkt XXX - -$\lambda_2 =$ Längengrad Bildpunkt YYY - - Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! - -Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. -Mithilfe des Seiten-Kosinussatzes $cos(a) = cos(b)*cos(c) + sin(b) * sin(c)*cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. -Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. -Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. - -Dieser bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. -Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. Somit ist $sin(\beta) = sin(b) * \frac{sin(\alpha)}{sin(a)} $. - -Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. - -\subsubsection{Bestimmung des zweiten Dreiecks} -Wir bilden nun ein zweites Dreieck, welches die Ecken B und C des ersten Dreiecks besitzt. -Die dritte Ecke ist der eigene Standort P. -Unser Standort definiere sich aus einer geographischen Breite $\delta$ und einer geographischen Länge $\lambda$. - -Die Seite von P zu B sei $pb$ und die Seite von P zu C sei $pc$. -Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache Formel bestimmen, nämlich $pb=\frac{\pi}{2} - h_{B}$ und $pc=\frac{\pi}{2} - h_{C}$ - -mit $h_B=$ Höhe von Gestirn in B und $h_C=$ Höhe von Gestirn in C mit Sextant gemessen. -\\ - -Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$ mit den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes - -$cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$ berechnen. - -Es fehlt uns noch $\beta1$. -Da wir aber $pc$, $pb$ und $a$ kennen, kann man mit dem Seiten-Kosinussatz den Winkel $\beta1$ berechnen -\\ - -Somit ist $\delta = cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$. -\\ - -Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ABP$ în der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. -\\ - -Somit ist $\omega=sin(pb)*\frac{sin(\beta)}{sin(l)}$ und unsere gesuchte geographische Länge schlussendlich -$\lambda=\lambda_1 - \omega$ - - - -\end{document} \ No newline at end of file diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 15c7fdc..9faa48d 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,9 +8,3 @@ % following example %\usepackage{packagename} -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} -\usepackage{xcolor, soul} diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex deleted file mode 100644 index 0dbd7a1..0000000 --- a/buch/papers/nav/trigo.tex +++ /dev/null @@ -1,51 +0,0 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - - -\begin{document} - \section{Sphärische Trigonometrie} - \subsection{Das Kugeldreieck} - -Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck ABC. -A, B und C sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. -Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. -Laut dieser Definition ist die Seite c der Winkel AMB. -Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. -Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. -Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. -Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. -\begin{figure}[h] - \begin{center} - \includegraphics[width=6cm]{Bilder/kugel1.png} - \end{center} - -\end{figure} - -\subsection{Rechtwinkliges Dreieck und Rechtseitiges Dreieck} -Wie auch im uns bekannten Dreieck gibt es beim Kugeldreieck auch ein Rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. -Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. - \newpage -\subsection{Winkelangabe} - - \begin{center} - \includegraphics[width=8cm]{Bilder/kugel2.png} - \end{center} - -Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. -Für die Summe der Innenwinkel gilt $\alpha+\beta+\gamma = \frac{A}{r^2} + \pi$ und -$\alpha+\beta+\gamma > \pi$. -Der sphärische Exzess $\epsilon = \alpha+\beta+\gamma - \pi$ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. - -\subsection{Sphärischer Sinussatz} -In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. -Das bedeutet, dass $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} $ auch beim Kugeldreieck gilt. - -\subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} -Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. -In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. -Es gilt nämlich: $\cos c = \cos a * \cos b$ wenn $\alpha \lor \beta \lor \gamma = \frac{\pi}{2} $. - -\end{document} \ No newline at end of file -- cgit v1.2.1 From 309284c1f79df5b8553b0b8875db188ff7d930af Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Mon, 16 May 2022 20:43:09 +0200 Subject: no message --- buch/papers/nav/bilder/dreieck.png | Bin 0 -> 91703 bytes buch/papers/nav/bilder/kugel1.png | Bin 0 -> 9051 bytes buch/papers/nav/bilder/kugel2.png | Bin 0 -> 9103 bytes buch/papers/nav/bilder/kugel3.png | Bin 0 -> 215188 bytes buch/papers/nav/bilder/projektion.png | Bin 0 -> 41289 bytes buch/papers/nav/einleitung.tex | 17 +++ buch/papers/nav/flatearth.tex | 31 ++++++ buch/papers/nav/geschichte.tex | 22 ++++ buch/papers/nav/main.tex | 28 ++--- buch/papers/nav/nautischesdreieck.tex | 190 ++++++++++++++++++++++++++++++++++ buch/papers/nav/packages.tex | 5 + buch/papers/nav/teil0.tex | 22 ---- buch/papers/nav/teil1.tex | 55 ---------- buch/papers/nav/teil2.tex | 40 ------- buch/papers/nav/teil3.tex | 40 ------- buch/papers/nav/trigo.tex | 51 +++++++++ 16 files changed, 322 insertions(+), 179 deletions(-) create mode 100644 buch/papers/nav/bilder/dreieck.png create mode 100644 buch/papers/nav/bilder/kugel1.png create mode 100644 buch/papers/nav/bilder/kugel2.png create mode 100644 buch/papers/nav/bilder/kugel3.png create mode 100644 buch/papers/nav/bilder/projektion.png create mode 100644 buch/papers/nav/einleitung.tex create mode 100644 buch/papers/nav/flatearth.tex create mode 100644 buch/papers/nav/geschichte.tex create mode 100644 buch/papers/nav/nautischesdreieck.tex delete mode 100644 buch/papers/nav/teil0.tex delete mode 100644 buch/papers/nav/teil1.tex delete mode 100644 buch/papers/nav/teil2.tex delete mode 100644 buch/papers/nav/teil3.tex create mode 100644 buch/papers/nav/trigo.tex diff --git a/buch/papers/nav/bilder/dreieck.png b/buch/papers/nav/bilder/dreieck.png new file mode 100644 index 0000000..2b02105 Binary files /dev/null and b/buch/papers/nav/bilder/dreieck.png differ diff --git a/buch/papers/nav/bilder/kugel1.png b/buch/papers/nav/bilder/kugel1.png new file mode 100644 index 0000000..b3188b7 Binary files /dev/null and b/buch/papers/nav/bilder/kugel1.png differ diff --git a/buch/papers/nav/bilder/kugel2.png b/buch/papers/nav/bilder/kugel2.png new file mode 100644 index 0000000..057740f Binary files /dev/null and b/buch/papers/nav/bilder/kugel2.png differ diff --git a/buch/papers/nav/bilder/kugel3.png b/buch/papers/nav/bilder/kugel3.png new file mode 100644 index 0000000..97066a2 Binary files /dev/null and b/buch/papers/nav/bilder/kugel3.png differ diff --git a/buch/papers/nav/bilder/projektion.png b/buch/papers/nav/bilder/projektion.png new file mode 100644 index 0000000..5dcc0c8 Binary files /dev/null and b/buch/papers/nav/bilder/projektion.png differ diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex new file mode 100644 index 0000000..42f4b6c --- /dev/null +++ b/buch/papers/nav/einleitung.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + +\begin{document} +\section{Einleitung} +Heut zu Tage ist die Navigation ein Teil des Lebens. +Man versendet dem Kollegen seinen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein um sich die Sucherei zu schenken. +Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. +Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf kleineren Schiffen benötigt wird im Falle eines Stromausfalls. +Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? +In diesem Kapitel werden genau diese Fragen mithilfe des Nautischen Dreiecks, der Sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. + + +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex new file mode 100644 index 0000000..b14dd4b --- /dev/null +++ b/buch/papers/nav/flatearth.tex @@ -0,0 +1,31 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + +\begin{document} + \section{Warum ist die Erde nicht flach?} + + \begin{figure}[h] + \begin{center} + \includegraphics[width=10cm]{bilder/projektion.png} + \caption{Mercator Projektion} + \end{center} + \end{figure} + +Es gibt heut zu Tage viele Beweise dafür, dass die Erde eine Kugel ist. +Die Fotos von unserem Planeten oder die Berichte der Astronauten. + Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. + Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. + Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. + Mithilfe der Geometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. + Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. +Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. +In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. +Das liegt daran, das man die 3D – Weltkarte nicht einfach auslegen kann. +Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. +Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. + + +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/geschichte.tex b/buch/papers/nav/geschichte.tex new file mode 100644 index 0000000..a20eb6d --- /dev/null +++ b/buch/papers/nav/geschichte.tex @@ -0,0 +1,22 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + +\begin{document} +\section{Geschichte der sphärischen Navigation} +Die Orientierung mit Hilfe der Sterne und der sphärischen Trigonometrie bewegt die Menschheit schon seit mehreren tausend Jahren. +Nach Hinweisen und Schätzungen von Forscher haben schon vor 4000 Jahren die Ägypter und Gelehrten aus Babylon mit Hilfe der Astronomie den Lauf der Gestirne (Himmelskörper) zu berechnen versucht, jedoch ohne Erfolg. +Etwa 350 vor Christus waren es die Griechen, welche den damaligen Astronomen Hilfestellungen mittels Kugel-Geometrien leisten konnten. +Aus diesen Geometrien wurden erste mathematische Sätze aufgestellt und ein paar Jahrhunderte später kamen zu diesem Thema auch Berechnungen dazu. +Ebenso wurden Kartenmaterial mit Sternenbilder angefertigt. +Die Sinusfunktion war noch nicht bekannt, jedoch kamen zu dieser Zeit die ersten Ansätze der Cosinusfunktion aus Indien. +Von diesen Hilfen darauf aufbauend konnte um 900 die Araber der Sinussatz entwickeln. +Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde. +Dies aus dem Grund, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung vermehrt an Wichtigkeit gewann. +Auch die Verwendung der Tangens- und Sinusfunktion sowie der neu entwickelte Seitencosinussatz trugen zu einer Verbesserung der Orientierung herbei. +Im 16. Jahrhundert wurde dann ein weiterer trigonometrischer Satz, der Winkelcosinussatz hergeleitet. Stück für Stück wurden infolge der Entdeckung des Logarithmus im 17. Jahrhundert viele neue Methoden entwickelt. +Auch eine Verbesserung der kartographischen Verwendung der Kugelgeometrie wurde vorgenommen. +Es folgten weitere Entwicklungen in nicht euklidische Geometrien und im 19. Jahrhundert sowie auch im 20. Jahrhundert wurde zudem für die Relativitätstheorie auch die sphärische Trigonometrie beigezogen. +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index e11e2c0..9758de9 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -8,29 +8,13 @@ \begin{refsection} \chapterauthor{Hans Muster} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} -\input{papers/nav/teil0.tex} -\input{papers/nav/teil1.tex} -\input{papers/nav/teil2.tex} -\input{papers/nav/teil3.tex} + +\input{papers/nav/einleitung.tex} +\input{papers/nav/geschichte.tex} +\input{papers/nav/flatearth.tex} +\input{papers/nav/trigo.tex} +\input{papers/nav/nautischesdreieck.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex new file mode 100644 index 0000000..0bb213c --- /dev/null +++ b/buch/papers/nav/nautischesdreieck.tex @@ -0,0 +1,190 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + \usepackage{xcolor, soul} + \sethlcolor{yellow} +\begin{document} + \setlength{\parindent}{0em} +\section{Das Nautische Dreieck} +\subsection{Definition des Nautischen Dreiecks} +Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der \textbf{Himmelskugel}. +Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient.\\ +Das Nautische Dreieck definiert sich durch folgende Ecken: +\begin{itemize} + \item Zenit + \item Gestirn + \item Himmelspol +\end{itemize} +Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. +Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. +Der Himmelspol ist der Nordpol an die Himmelskugel projeziert. +\\ +Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfache Zusammenhänge: +\begin{itemize} + \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ + \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ + \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ + \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ + \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ +\end{itemize} +Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: + +$\alpha \ \widehat{=} \ Rektaszension $ + +$\delta \ \widehat{=} \ Deklination =$ Breitengrad des Gestirns + +$\theta \ \widehat{=} \ Sternzeit$ + +$\phi \ \widehat{=} \ Geographische \ Breite $ + +$\tau = \theta-\alpha \ \widehat{=} \ Stundenwinkel =$ Längengrad des Gestirns + +$a \ \widehat{=} \ Azimut $ + +$h \ \widehat{=} \ Hoehe$ + + + +\subsection{Zusammenhang des Nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} + + \begin{center} + \includegraphics[height=5cm,width=5cm]{Bilder/kugel3.png} + \end{center} +Wie man im oberen Bild sieht und auch am Anfang dieses Kapitels bereits erwähnt wurde, liegt das Nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. +Das selbe Dreieck kann man aber auch auf die Erdkugel projezieren und hat dann die Ecken Standort, Bildpunkt und Nordpol. +Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. + +\subsection{Varianten vom Nautischen Dreieck} +\section{Standortbestimmung ohne elektronische Hilfsmittel} +Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion Nautische Dreieck auf der Erdkugel zur Hilfe genommen. +Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. + + \begin{center} + \includegraphics[width=6cm]{Bilder/dreieck.png} + \end{center} + + + +\subsection{Ecke P - Unser Standort} +Unser eigener Standort ist der gesuchte Punkt A. + +\subsection{Ecke A - Nordpol} +Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol (in der Himmelskugel der Himmelsnordpol) ist. +Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. + +\subsection{Ecke B und C - Bildpunkt XXX und YYY} +Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. +Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. +\\ +Es gibt diverse Gestirne, die man nutzen kann. +\begin{itemize} + \item Sonne + \item Mond + \item Die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn +\end{itemize} + +Zu all diesen Gestirnen gibt es Ephemeriden (Jahrbücher). +Dort findet man unter Anderem die Rektaszension und Deklination, welche für jeden Tag und Stunde beschrieben ist. Für Minuten genaue Angaben muss man dann zwischen den Stunden interpolieren. +Mithilfe dieser beiden Angaben kann man die Längen- und Breitengrade diverser Gestirne berechnen. + +\subsubsection{Sternzeit und Rektaszension} +Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht. +Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. +Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. +Die Lösung ist die Sternzeit. +Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit +$\theta = 0$. + +Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. +Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. +Für die Sternzeit von Greenwich braucht man als erstes das Julianische Datum vom aktuellen Tag, welches sich leicht recherchieren oder berechnen lässt: \hl{$JD=....$} + +Nun berechnet man $T=\frac{JD-2451545}{36525}$ und damit die mittlere Sternzeit von Greenwich + + $T_{Greenwich} = 6^h 41^m 50^s,54841 + 8640184^s,812866 * T + 0^s,093104*T^2 - 0^s,0000062 * T^3$. + + Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit bestimmen. + Dies gilt analog auch für das zweite Gestirn. + + \subsubsection{Deklination} + Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad $\psi = \delta$. + + + +\subsection{Bestimmung des eigenen Standortes P} +Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. +Somit können wir ein erstes Kugeldreieck auf der Erde aufspannen. + + + \begin{center} + \includegraphics[width=5cm]{Bilder/dreieck.png} + \end{center} + + +\subsubsection{Bestimmung des ersten Dreiecks} + Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. + + Die Seitenlänge der Seite "Nordpol zum Bildpunkt XXX" sei $c$. + Dann ist $c = \frac{\pi}{2} - \delta_1$. + + Die Seitenlänge der Seite "Nordpol zum Bildpunkt YYY" sei $b$. + Dann ist $b = \frac{\pi}{2} - \delta_2$. + + Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. + Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. + +mit + + $\delta_1 =$ Deklination Bildpunkt XXX + +$\delta_2 =$ Deklination Bildpunk YYY + +$\lambda_1 =$ Längengrad Bildpunkt XXX + +$\lambda_2 =$ Längengrad Bildpunkt YYY + + Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! + +Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. +Mithilfe des Seiten-Kosinussatzes $cos(a) = cos(b)*cos(c) + sin(b) * sin(c)*cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. +Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. +Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. + +Dieser bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. +Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. Somit ist $sin(\beta) = sin(b) * \frac{sin(\alpha)}{sin(a)} $. + +Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. + +\subsubsection{Bestimmung des zweiten Dreiecks} +Wir bilden nun ein zweites Dreieck, welches die Ecken B und C des ersten Dreiecks besitzt. +Die dritte Ecke ist der eigene Standort P. +Unser Standort definiere sich aus einer geographischen Breite $\delta$ und einer geographischen Länge $\lambda$. + +Die Seite von P zu B sei $pb$ und die Seite von P zu C sei $pc$. +Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache Formel bestimmen, nämlich $pb=\frac{\pi}{2} - h_{B}$ und $pc=\frac{\pi}{2} - h_{C}$ + +mit $h_B=$ Höhe von Gestirn in B und $h_C=$ Höhe von Gestirn in C mit Sextant gemessen. +\\ + +Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$ mit den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes + +$cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$ berechnen. + +Es fehlt uns noch $\beta1$. +Da wir aber $pc$, $pb$ und $a$ kennen, kann man mit dem Seiten-Kosinussatz den Winkel $\beta1$ berechnen +\\ + +Somit ist $\delta = cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$. +\\ + +Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ABP$ în der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. +\\ + +Somit ist $\omega=sin(pb)*\frac{sin(\beta)}{sin(l)}$ und unsere gesuchte geographische Länge schlussendlich +$\lambda=\lambda_1 - \omega$ + + + +\end{document} \ No newline at end of file diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 9faa48d..16d3a3c 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,3 +8,8 @@ % following example %\usepackage{packagename} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} +\usepackage{xcolor, soul} \ No newline at end of file diff --git a/buch/papers/nav/teil0.tex b/buch/papers/nav/teil0.tex deleted file mode 100644 index f3323a9..0000000 --- a/buch/papers/nav/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{nav:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{nav:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/nav/teil1.tex b/buch/papers/nav/teil1.tex deleted file mode 100644 index 996202f..0000000 --- a/buch/papers/nav/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{nav:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{nav:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{nav:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{nav:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{nav:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/nav/teil2.tex b/buch/papers/nav/teil2.tex deleted file mode 100644 index 5a52e03..0000000 --- a/buch/papers/nav/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{nav:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{nav:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/nav/teil3.tex b/buch/papers/nav/teil3.tex deleted file mode 100644 index 2b5d2d5..0000000 --- a/buch/papers/nav/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{nav:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{nav:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex new file mode 100644 index 0000000..0dbd7a1 --- /dev/null +++ b/buch/papers/nav/trigo.tex @@ -0,0 +1,51 @@ +\documentclass[12pt]{scrartcl} +\usepackage{ucs} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{graphicx} + + +\begin{document} + \section{Sphärische Trigonometrie} + \subsection{Das Kugeldreieck} + +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck ABC. +A, B und C sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. +Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. +Laut dieser Definition ist die Seite c der Winkel AMB. +Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. +Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. +Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. +Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. +\begin{figure}[h] + \begin{center} + \includegraphics[width=6cm]{Bilder/kugel1.png} + \end{center} + +\end{figure} + +\subsection{Rechtwinkliges Dreieck und Rechtseitiges Dreieck} +Wie auch im uns bekannten Dreieck gibt es beim Kugeldreieck auch ein Rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. +Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. + \newpage +\subsection{Winkelangabe} + + \begin{center} + \includegraphics[width=8cm]{Bilder/kugel2.png} + \end{center} + +Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. +Für die Summe der Innenwinkel gilt $\alpha+\beta+\gamma = \frac{A}{r^2} + \pi$ und +$\alpha+\beta+\gamma > \pi$. +Der sphärische Exzess $\epsilon = \alpha+\beta+\gamma - \pi$ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. + +\subsection{Sphärischer Sinussatz} +In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. +Das bedeutet, dass $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} $ auch beim Kugeldreieck gilt. + +\subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} +Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. +In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. +Es gilt nämlich: $\cos c = \cos a * \cos b$ wenn $\alpha \lor \beta \lor \gamma = \frac{\pi}{2} $. + +\end{document} \ No newline at end of file -- cgit v1.2.1 From 800ca10daf88dd073c239b6478bb34f81e48410f Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 17 May 2022 13:34:13 +0200 Subject: first commit nav --- buch/buch.aux | 22 + buch/buch.bbl | 0 buch/buch.blg | 48 + buch/buch.idx | 0 buch/buch.log | 2106 +++++++++++++++++++++++++++++++++ buch/papers/nav/einleitung.tex | 12 +- buch/papers/nav/flatearth.tex | 38 +- buch/papers/nav/main.tex | 5 +- buch/papers/nav/nautischesdreieck.tex | 139 ++- buch/papers/nav/packages.tex | 5 - 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Man versendet dem Kollegen seinen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein um sich die Sucherei zu schenken. Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf kleineren Schiffen benötigt wird im Falle eines Stromausfalls. Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? -In diesem Kapitel werden genau diese Fragen mithilfe des Nautischen Dreiecks, der Sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. - - -\end{document} \ No newline at end of file +In diesem Kapitel werden genau diese Fragen mithilfe des Nautischen Dreiecks, der Sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index b14dd4b..fbabbde 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -1,31 +1,23 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} -\begin{document} - \section{Warum ist die Erde nicht flach?} - - \begin{figure}[h] - \begin{center} - \includegraphics[width=10cm]{bilder/projektion.png} - \caption{Mercator Projektion} - \end{center} - \end{figure} + +\section{Warum ist die Erde nicht flach?} + +\begin{figure}[h] + \begin{center} + \includegraphics[width=10cm]{papers/nav/bilder/projektion.png} + \caption[Mercator Projektion]{Mercator Projektion} + \end{center} +\end{figure} Es gibt heut zu Tage viele Beweise dafür, dass die Erde eine Kugel ist. Die Fotos von unserem Planeten oder die Berichte der Astronauten. - Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. - Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. - Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. - Mithilfe der Geometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. - Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. +Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. +Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. +Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. +Mithilfe der Geometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. +Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. Das liegt daran, das man die 3D – Weltkarte nicht einfach auslegen kann. Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. -Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. - - -\end{document} \ No newline at end of file +Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. \ No newline at end of file diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 9758de9..8688421 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -4,9 +4,9 @@ % (c) 2020 Hochschule Rapperswil % \chapter{Thema\label{chapter:nav}} -\lhead{Thema} +\lhead{Sphärische Navigation} \begin{refsection} -\chapterauthor{Hans Muster} +\chapterauthor{Enez Erdem, Marc Kühne} @@ -15,6 +15,7 @@ \input{papers/nav/flatearth.tex} \input{papers/nav/trigo.tex} \input{papers/nav/nautischesdreieck.tex} +\input{papers/nav/sincos.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index 0bb213c..d6e1388 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -1,12 +1,3 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - \usepackage{xcolor, soul} - \sethlcolor{yellow} -\begin{document} - \setlength{\parindent}{0em} \section{Das Nautische Dreieck} \subsection{Definition des Nautischen Dreiecks} Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der \textbf{Himmelskugel}. @@ -19,7 +10,7 @@ Das Nautische Dreieck definiert sich durch folgende Ecken: \end{itemize} Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. -Der Himmelspol ist der Nordpol an die Himmelskugel projeziert. +Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. \\ Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfache Zusammenhänge: \begin{itemize} @@ -35,7 +26,7 @@ $\alpha \ \widehat{=} \ Rektaszension $ $\delta \ \widehat{=} \ Deklination =$ Breitengrad des Gestirns -$\theta \ \widehat{=} \ Sternzeit$ +$\theta \ \widehat{=} \ Sternzeit\ von\ Greenwich$ $\phi \ \widehat{=} \ Geographische \ Breite $ @@ -46,24 +37,31 @@ $a \ \widehat{=} \ Azimut $ $h \ \widehat{=} \ Hoehe$ - +\newpage \subsection{Zusammenhang des Nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} - +\begin{figure}[h] \begin{center} - \includegraphics[height=5cm,width=5cm]{Bilder/kugel3.png} + \includegraphics[height=5cm,width=5cm]{papers/nav/bilder/kugel3.png} + \caption[Nautisches Dreieck]{Nautisches Dreieck} \end{center} +\end{figure} + Wie man im oberen Bild sieht und auch am Anfang dieses Kapitels bereits erwähnt wurde, liegt das Nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. Das selbe Dreieck kann man aber auch auf die Erdkugel projezieren und hat dann die Ecken Standort, Bildpunkt und Nordpol. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. -\subsection{Varianten vom Nautischen Dreieck} + \section{Standortbestimmung ohne elektronische Hilfsmittel} Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion Nautische Dreieck auf der Erdkugel zur Hilfe genommen. Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. +\begin{figure}[h] \begin{center} - \includegraphics[width=6cm]{Bilder/dreieck.png} - \end{center} + \includegraphics[width=6cm]{papers/nav/bilder/dreieck.png} + \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} + \end{center} +\end{figure} + @@ -73,8 +71,8 @@ Unser eigener Standort ist der gesuchte Punkt A. \subsection{Ecke A - Nordpol} Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol (in der Himmelskugel der Himmelsnordpol) ist. Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. - -\subsection{Ecke B und C - Bildpunkt XXX und YYY} +\newpage +\subsection{Ecke B und C - Bildpunkt X und Y} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. \\ @@ -96,64 +94,80 @@ Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eige Die Lösung ist die Sternzeit. Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit $\theta = 0$. - + Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. -Für die Sternzeit von Greenwich braucht man als erstes das Julianische Datum vom aktuellen Tag, welches sich leicht recherchieren oder berechnen lässt: \hl{$JD=....$} - -Nun berechnet man $T=\frac{JD-2451545}{36525}$ und damit die mittlere Sternzeit von Greenwich +Für die Sternzeit von Greenwich braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. +Im Anschluss berechnet man die Sternzeit von Greenwich +\\ +\\ +$T_{Greenwich} = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3$. +\\ +\\ +Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit bestimmen. +Dies gilt analog auch für das zweite Gestirn. - $T_{Greenwich} = 6^h 41^m 50^s,54841 + 8640184^s,812866 * T + 0^s,093104*T^2 - 0^s,0000062 * T^3$. - - Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit bestimmen. - Dies gilt analog auch für das zweite Gestirn. - - \subsubsection{Deklination} - Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad $\psi = \delta$. - +\subsubsection{Deklination} +Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad. +\newpage \subsection{Bestimmung des eigenen Standortes P} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Somit können wir ein erstes Kugeldreieck auf der Erde aufspannen. +\begin{figure}[h] \begin{center} - \includegraphics[width=5cm]{Bilder/dreieck.png} - \end{center} + \includegraphics[width=4.5cm]{papers/nav/bilder/dreieck.png} + \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} + \end{center} +\end{figure} \subsubsection{Bestimmung des ersten Dreiecks} - Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. - - Die Seitenlänge der Seite "Nordpol zum Bildpunkt XXX" sei $c$. - Dann ist $c = \frac{\pi}{2} - \delta_1$. - - Die Seitenlänge der Seite "Nordpol zum Bildpunkt YYY" sei $b$. - Dann ist $b = \frac{\pi}{2} - \delta_2$. - - Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. - Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. - + +$A=$ Nordpol + +$B=$ Bildpunkt des Gestirns XXX + +$C=$ Bildpunkt des Gestirns YYY +\\ +\\ +Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. + +Die Seitenlänge der Seite "Nordpol zum Bildpunkt XXX" sei $c$. +Dann ist $c = \frac{\pi}{2} - \delta_1$. + +Die Seitenlänge der Seite "Nordpol zum Bildpunkt YYY" sei $b$. +Dann ist $b = \frac{\pi}{2} - \delta_2$. + +Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. +Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. + mit - - $\delta_1 =$ Deklination Bildpunkt XXX - + +$\delta_1 =$ Deklination Bildpunkt XXX + $\delta_2 =$ Deklination Bildpunk YYY $\lambda_1 =$ Längengrad Bildpunkt XXX $\lambda_2 =$ Längengrad Bildpunkt YYY - Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! + +Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. -Mithilfe des Seiten-Kosinussatzes $cos(a) = cos(b)*cos(c) + sin(b) * sin(c)*cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. +Mithilfe des Seiten-Kosinussatzes + +$cos(a) = \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. + Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. Dieser bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. -Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. Somit ist $sin(\beta) = sin(b) * \frac{sin(\alpha)}{sin(a)} $. +Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. Somit ist $\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}] $. Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. @@ -168,23 +182,22 @@ Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache mit $h_B=$ Höhe von Gestirn in B und $h_C=$ Höhe von Gestirn in C mit Sextant gemessen. \\ -Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$ mit den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes +Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$, den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes berechnen. -$cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$ berechnen. +Für den Seiten-Kosinussatz benötigt es noch $\kappa$. +Da wir aber $pc$, $pb$ und $a$ kennen, kann man mit dem Seiten-Kosinussatz den Winkel $\beta1$ berechnen und anschliessend $\beta + \beta1 =\kappa$. -Es fehlt uns noch $\beta1$. -Da wir aber $pc$, $pb$ und $a$ kennen, kann man mit dem Seiten-Kosinussatz den Winkel $\beta1$ berechnen -\\ +Somit ist $cos(l) = \cos(c)\cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)$ -Somit ist $\delta = cos(l) = cos(c)*cos(pb) + sin(c) * sin(pb)*cos(\beta)$. -\\ +und -Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ABP$ în der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. +$\delta =\cos^{-1} [\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)]$. \\ -Somit ist $\omega=sin(pb)*\frac{sin(\beta)}{sin(l)}$ und unsere gesuchte geographische Länge schlussendlich -$\lambda=\lambda_1 - \omega$ - - +Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. +\\ -\end{document} \ No newline at end of file +Somit ist $\omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}]$ und unsere gesuchte geographische Länge schlussendlich +$\lambda=\lambda_1 - \omega$ mit $\lambda_1$=Längengrad Bildpunkt XXX. +\newpage +\listoffigures \ No newline at end of file diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 16d3a3c..9faa48d 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,8 +8,3 @@ % following example %\usepackage{packagename} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} -\usepackage{xcolor, soul} \ No newline at end of file diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex new file mode 100644 index 0000000..23e3303 --- /dev/null +++ b/buch/papers/nav/sincos.tex @@ -0,0 +1,16 @@ + + + +\section{Warum sind die Sinus- und Kosinusfunktionen spezielle Funktionen?} +Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren sich mit Problemen der sphärischen Trigonometrie beschäftigt haben um den Lauf von Gestirnen (Himmelskörper) zu berechnen. +Jedoch konnten sie sie nicht lösen. +Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und wurde zu einer Hilfswissenschaft der Astronomen. +In Folge werden auch die ersten Sätze aufgestellt und wenige Jahrhunderte später wurden Berechnungen zu diesem Thema angestellt. +In dieser Zeit wurden auch die ersten Sternenkarten angefertigt, jedoch kannte man damals die Sinusfunktion noch nicht. +Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. +Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um 900 den Sinussatz. +Zur Zeit der großen Entdeckungsreisen im 15. Jahrhundert wurden die Forschungen in sphärischer Trigonometrie wieder forciert. +Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet. +Im nächsten Jahrhundert folgte der Winkelkosinussatz. +Durch weitere mathematische Entwicklungen wie den Logarithmus wurden im Laufe des nächsten Jahrhunderts viele neue Methoden und kartographische Anwendungen der Kugelgeometrie entdeckt. +Im 19. und 20. Jahrhundert wurden weitere nicht-euklidische Geometrien entwickelt und die sphärische Trigonometrie fand auch ihre Anwendung in der Relativitätstheorie. \ No newline at end of file diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index 0dbd7a1..2edd651 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,14 +1,6 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} +\section{Sphärische Trigonometrie} +\subsection{Das Kugeldreieck} - -\begin{document} - \section{Sphärische Trigonometrie} - \subsection{Das Kugeldreieck} - Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck ABC. A, B und C sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. @@ -19,7 +11,8 @@ Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiec Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. \begin{figure}[h] \begin{center} - \includegraphics[width=6cm]{Bilder/kugel1.png} + \includegraphics[width=6cm]{papers/nav/bilder/kugel1.png} + \caption[Das Kugeldreieck]{Das Kugeldreieck} \end{center} \end{figure} @@ -27,12 +20,15 @@ Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha \subsection{Rechtwinkliges Dreieck und Rechtseitiges Dreieck} Wie auch im uns bekannten Dreieck gibt es beim Kugeldreieck auch ein Rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. - \newpage +\newpage \subsection{Winkelangabe} - +\begin{figure}[h] + \begin{center} - \includegraphics[width=8cm]{Bilder/kugel2.png} + \includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} + \caption[Winkelangabe im Kugeldreieck]{Winkelangabe im Kugeldreieck} \end{center} +\end{figure} Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. Für die Summe der Innenwinkel gilt $\alpha+\beta+\gamma = \frac{A}{r^2} + \pi$ und @@ -46,6 +42,4 @@ Das bedeutet, dass $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta) \subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. -Es gilt nämlich: $\cos c = \cos a * \cos b$ wenn $\alpha \lor \beta \lor \gamma = \frac{\pi}{2} $. - -\end{document} \ No newline at end of file +Es gilt nämlich: $\cos c = \cos a \cdot \cos b$ wenn $\alpha= \frac{\pi}{2} \lor \beta=\frac{\pi}{2} \lor \gamma = \frac{\pi}{2} $. \ No newline at end of file -- cgit v1.2.1 From c0f7b4bd46fa66526f8ddfb20ce9edbcfbb03d81 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 17 May 2022 16:02:53 +0200 Subject: no message --- buch/papers/nav/main.tex | 5 +++-- buch/papers/nav/nautischesdreieck.tex | 37 +++++++++++++++++++---------------- buch/papers/nav/packages.tex | 1 + buch/papers/nav/trigo.tex | 36 +++++++++++++++++++++++++++------- 4 files changed, 53 insertions(+), 26 deletions(-) diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 8688421..de8d1d6 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -3,7 +3,7 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:nav}} +\chapter{Spährische Navigation\label{chapter:nav}} \lhead{Sphärische Navigation} \begin{refsection} \chapterauthor{Enez Erdem, Marc Kühne} @@ -11,11 +11,12 @@ \input{papers/nav/einleitung.tex} +\input{papers/nav/sincos.tex} \input{papers/nav/geschichte.tex} \input{papers/nav/flatearth.tex} \input{papers/nav/trigo.tex} \input{papers/nav/nautischesdreieck.tex} -\input{papers/nav/sincos.tex} + \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index d6e1388..b61e908 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -37,6 +37,7 @@ $a \ \widehat{=} \ Azimut $ $h \ \widehat{=} \ Hoehe$ + \newpage \subsection{Zusammenhang des Nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} \begin{figure}[h] @@ -129,45 +130,47 @@ Somit können wir ein erstes Kugeldreieck auf der Erde aufspannen. $A=$ Nordpol -$B=$ Bildpunkt des Gestirns XXX +$B=$ Bildpunkt des Gestirns X -$C=$ Bildpunkt des Gestirns YYY +$C=$ Bildpunkt des Gestirns Y \\ \\ Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. -Die Seitenlänge der Seite "Nordpol zum Bildpunkt XXX" sei $c$. +Die Seitenlänge der Seite "Nordpol zum Bildpunkt X" sei $c$. Dann ist $c = \frac{\pi}{2} - \delta_1$. -Die Seitenlänge der Seite "Nordpol zum Bildpunkt YYY" sei $b$. +Die Seitenlänge der Seite "Nordpol zum Bildpunkt Y" sei $b$. Dann ist $b = \frac{\pi}{2} - \delta_2$. Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. - +\\ +\\ mit -$\delta_1 =$ Deklination Bildpunkt XXX - -$\delta_2 =$ Deklination Bildpunk YYY +$\delta_1 =$ Deklination Bildpunkt X -$\lambda_1 =$ Längengrad Bildpunkt XXX +$\delta_2 =$ Deklination Bildpunk Y -$\lambda_2 =$ Längengrad Bildpunkt YYY +$\lambda_1 =$ Längengrad Bildpunkt X +$\lambda_2 =$ Längengrad Bildpunkt Y Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! - +\\ +\\ Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. Mithilfe des Seiten-Kosinussatzes - -$cos(a) = \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. - +$cos(a) = \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha)$ +können wir nun die dritte Seitenlänge bestimmen. Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. -Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. -Dieser bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. -Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. Somit ist $\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}] $. +Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. +Diese bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. +Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. +Im Zähler sind die Seiten, im Nenner die Winkel. +Somit ist $\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}] $. Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 9faa48d..5b87303 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,3 +8,4 @@ % following example %\usepackage{packagename} +\usepackage{amsmath} \ No newline at end of file diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index 2edd651..8b4634f 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,3 +1,4 @@ +\setlength{\parindent}{0em} \section{Sphärische Trigonometrie} \subsection{Das Kugeldreieck} @@ -11,7 +12,7 @@ Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiec Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. \begin{figure}[h] \begin{center} - \includegraphics[width=6cm]{papers/nav/bilder/kugel1.png} + %\includegraphics[width=6cm]{papers/nav/bilder/kugel1.png} \caption[Das Kugeldreieck]{Das Kugeldreieck} \end{center} @@ -25,21 +26,42 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S \begin{figure}[h] \begin{center} - \includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} + %\includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} \caption[Winkelangabe im Kugeldreieck]{Winkelangabe im Kugeldreieck} \end{center} \end{figure} + Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. -Für die Summe der Innenwinkel gilt $\alpha+\beta+\gamma = \frac{A}{r^2} + \pi$ und -$\alpha+\beta+\gamma > \pi$. -Der sphärische Exzess $\epsilon = \alpha+\beta+\gamma - \pi$ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. +Für die Summe der Innenwinkel gilt +\begin{align} + \alpha+\beta+\gamma &= \frac{A}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi. \nonumber +\end{align} + +Der sphärische Exzess +\begin{align} + \epsilon = \alpha+\beta+\gamma - \pi \nonumber +\end{align} +beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. \subsection{Sphärischer Sinussatz} In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. -Das bedeutet, dass $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} $ auch beim Kugeldreieck gilt. + +Das bedeutet, dass + +\begin{align} + \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \ \text{auch beim Kugeldreieck gilt.} +\end{align} + + \subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. -Es gilt nämlich: $\cos c = \cos a \cdot \cos b$ wenn $\alpha= \frac{\pi}{2} \lor \beta=\frac{\pi}{2} \lor \gamma = \frac{\pi}{2} $. \ No newline at end of file + +Es gilt nämlich: +\begin{align} + \cos c = \cos a \cdot \cos b \ \text{wenn} \nonumber & + \alpha = \frac{\pi}{2} \lor \beta =\frac{\pi}{2} \lor \gamma = \frac{\pi}{2}.\nonumber +\end{align} + \ No newline at end of file -- cgit v1.2.1 From 955047b8a63a3b08b27d9203030e2b5193e21dab Mon Sep 17 00:00:00 2001 From: Andrea Mozzini Vellen Date: Wed, 18 May 2022 13:55:56 +0200 Subject: Ersten Entwurf --- buch/papers/kreismembran/main.tex | 10 -- buch/papers/kreismembran/teil1.tex | 181 ++++++++++++++++++------------------- buch/papers/kreismembran/teil2.tex | 128 +++++++++++++++++++------- buch/papers/kreismembran/teil3.tex | 102 ++++++++++++++------- 4 files changed, 255 insertions(+), 166 deletions(-) diff --git a/buch/papers/kreismembran/main.tex b/buch/papers/kreismembran/main.tex index eafec18..e63a118 100644 --- a/buch/papers/kreismembran/main.tex +++ b/buch/papers/kreismembran/main.tex @@ -7,16 +7,6 @@ \lhead{Schwingungen einer kreisförmligen Membran} \begin{refsection} \chapterauthor{Andrea Mozzini Vellen und Tim Tönz} -\begin{itemize} -\item -Tim ist ein snitch -\item -ich dachte wir sind gute Freunden -\item -du schuldest mir ein bier -\item -auch ein gin tonic -\end{itemize} \input{papers/kreismembran/teil0.tex} \input{papers/kreismembran/teil1.tex} diff --git a/buch/papers/kreismembran/teil1.tex b/buch/papers/kreismembran/teil1.tex index 29a47a6..aef5b79 100644 --- a/buch/papers/kreismembran/teil1.tex +++ b/buch/papers/kreismembran/teil1.tex @@ -3,101 +3,98 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -\section{Die Hankel Transformation \label{kreismembran:section:teil1}} -\rhead{Die Hankel Transformation} - -Hermann Hankel (1839-1873) war ein deutscher Mathematiker, der für seinen Beitrag zur mathematischen Analyse und insbesondere für seine namensgebende Transformation bekannt ist. -Diese Transformation tritt bei der Untersuchung von funktionen auf, die nur von der Enternung des Ursprungs abhängen. -Er studierte auch funktionen, jetzt Hankel- oder Bessel- Funktionen genannt, der dritten Art. -Die Hankel Transformation mit Bessel Funktionen al Kern taucht natürlich bei achsensymmetrischen Problemen auf, die in Zylindrischen Polarkoordinaten formuliert sind. -In diesem Kapitel werden die Theorie der Transformation und einige Eigenschaften der Grundoperationen erläutert. - -Wir führen die Definition der Hankel Transformation aus der zweidimensionalen Fourier Transformation und ihrer Umkehrung ein, die durch: -\begin{align} - \mathscr{F}\{f(x,y)\} & = F(k,l)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-i( \bm{\kappa}\cdot \mathbf{r})}f(x,y) dx dy,\label{equation:fourier_transform}\\ - \mathscr{F}^{-1}\{F(x,y)\} & = f(x,y)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{i(\bm{\kappa}\cdot \mathbf{r}))}F(k,l) dx dy \label{equation:inv_fourier_transform} -\end{align} -wo $\mathbf{r}=(x,y)$ und $\bm{\kappa}=(k,l)$. Wie bereits erwähnt, sind Polarkoordinaten für diese Art von Problemen am besten geeignet, also mit, $(x,y)=r(\cos\theta,\sin\theta)$ und $(k,l)=\kappa(\cos\phi,\sin\phi)$, findet man $\bm{\kappa}\cdot\mathbf{r}=\kappa r(\cos(\theta-\phi))$ und danach: -\begin{align} - F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}r dr \int_{0}^{2\pi}e^{-ikr\cos(\theta-\phi)}f(r,\theta) d\phi. - \label{equation:F_ohne_variable_wechsel} -\end{align} -Dann wird angenommen dass, $f(r,\theta)=e^{in\theta}f(r)$, was keine strenge Einschränkung ist, und es wird eine Änderung der Variabeln vorgenommen $\theta-\phi=\alpha-\frac{\pi}{2}$, um \ref{equation:F_ohne_variable_wechsel} zu reduzieren: -\begin{align} - F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}rf(r) dr \int_{\phi_{0}}^{2\pi+\phi_{0}}e^{in(\phi-\frac{\pi}{2})+i(n\alpha-kr\sin\alpha)} d\alpha, - \label{equation:F_ohne_bessel} -\end{align} -wo $\phi_{0}=(\frac{\pi}{2}-\phi)$. - -Unter Verwendung der Integral Darstellung der Besselfunktion vom Ordnung n -\begin{align} - J_n(\kappa r)=\frac{1}{2\pi}\int_{\phi_{0}}^{2\pi + \phi_{0}}e^{i(n\alpha-\kappa r \sin \alpha)} d\alpha - \label{equation:bessel_n_ordnung} -\end{align} -\eqref{equation:F_ohne_bessel} wird sie zu: -\begin{align} - F(k,\phi)&=e^{in(\phi-\frac{\pi}{2})}\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr \label{equation:F_mit_bessel_step_1} \\ - &=e^{in(\phi-\frac{\pi}{2})}\tilde{f}_n(\kappa), - \label{equation:F_mit_bessel_step_2} -\end{align} -wo $\tilde{f}_n(\kappa)$ ist die \textit{Hankel Transformation} von $f(r)$ und ist formell definiert durch: -\begin{align} - \mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)=\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr. - \label{equation:hankel} -\end{align} - -Ähnlich verhält es sich mit der inversen Fourier Transformation in Form von polaren Koordinaten unter der Annahme $f(r,\theta)=e^{in\theta}f(r)$ mit \ref{equation:F_mit_bessel_step_2}, wird die inverse Fourier Transformation \ref{equation:inv_fourier_transform}: +\section{Lösungsmethode 1: Separationsmethode  + \label{kreismembran:section:teil1}} +\rhead{Lösungsmethode 1: Separationsmethode} +An diesem Punkt bleibt also nur noch die Lösung der partiellen Differentialgleichung. In diesem Kapitel wird sie mit Hilfe der Separationsmetode gelöst. + +Wie im vorherigen Kapitel gezeigt, lautet die partielle Differentialgleichung, die die Schwingungen einer Membran beschreibt: +\begin{equation*} + \frac{1}{c^2}\frac{\partial^2u}{\partial t^2} = \Delta u +\end{equation*} +Da es sich um eine Kreisscheibe handelt, werden Polarkoordinaten verwendet, so dass sich der Laplaceoperator ergibt: +\begin{equation*} + \Delta + = + \frac{\partial^2}{\partial r^2} + + + \frac1r + \frac{\partial}{\partial r} + + + \frac{1}{r 2} + \frac{\partial^2}{\partial\varphi^2}. + \label{buch:pde:kreis:laplace} +\end{equation*} + +Es wird eine runde elastische Membran berücksichtigt, die den Gebietbereich $\Omega$ abdeckt und am Rand $\Gamma$ befestigt ist. +Es wird daher davon ausgegangen, dass die Membran aus einem homogenen Material von vernachlässigbarer Dicke gefertigt ist. +Die Membran kann verformt werden, aber innere elastische Kräfte wirken den Verformungen entgegen. Es wirken keine äusseren Kräfte. Es handelt sich somit von einer kreisförmligen eigespannten homogenen schwingenden Membran. + +Daher ist die Membranabweichung im Punkt $(r,\varphi)$ $\in$ $\overline{\rm \Omega}$ zum Zeitpunkt $t$: \begin{align*} - e^{in\theta}f(r)&=\frac{1}{2\pi}\int_{0}^{\infty}\kappa d\kappa \int_{0}^{2\pi}e^{i\kappa r \cos (\theta - \phi)}F(\kappa,\phi) d\phi\\ - &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{0}^{2\pi}e^{in(\phi - \frac{\pi}{2})- i\kappa r \cos (\theta - \phi)} d\phi, + u: \overline{\rm \Omega} \times \mathbb{R}_{\geq 0} &\longrightarrow \mathbb{R}\\ + (r,\varphi,t) &\longmapsto u(r,\varphi,t) \end{align*} -was durch den Wechsel der Variablen $\theta-\phi=-(\alpha+\frac{\pi}{2})$ und $\theta_0=-(\theta+\frac{\pi}{2})$, - -\begin{align} - &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{\theta_0}^{2\pi+\theta_0}e^{in(\theta + \alpha - i\kappa r \sin\alpha)} d\alpha \nonumber \\ - &= e^{in\theta}\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa,\quad \text{von \eqref{equation:bessel_n_ordnung}} -\end{align} - -Also, die inverse \textit{Hankel Transformation} ist so definiert: -\begin{align} - \mathscr{H}^{-1}_n\{\tilde{f}_n(\kappa)\}=f(r)=\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa. - \label{equation:inv_hankel} -\end{align} - -Anstelle von $\tilde{f}_n(\kappa)$, wird häufig für die Hankel Transformation verwendet, indem die Ordnung angegeben wird. -\eqref{equation:hankel} und \eqref{equation:inv_hankel} Integralen existieren für eine grosse Klasse von Funktionen, die normalerweise in physikalischen Anwendungen benötigt werden. -Alternativ kann auch die berühmte Hankel Transformationsformel verwendet werden, - -\begin{align} - f(r) = \int_{0}^{\infty}\kappa J_n(\kappa r) d\kappa \int_{0}^{\infty} p J_n(\kappa p)f(p) dp, - \label{equation:hankel_integral_formula} -\end{align} -um die Hankel Transformation \eqref{equation:hankel} und ihre Inverse \eqref{equation:inv_hankel} zu definieren. -Insbesondere die Hankel Transformation der nullten Ordnung ($n=0$) und der ersten Ordnung ($n=1$) sind häufig nützlich, um Lösungen für Probleme mit der Laplace Gleichung in einer achsensymmetrischen zylindrischen Geometrie zu finden. - -\subsection{Operative Eigenschaften der Hankel Transformation\label{sub:op_properties_hankel}} -In diesem Kapitel werden die operativen Eigenschaften der Hankel Transformation aufgeführt. Der Beweis für ihre Gültigkeit wird jedoch nicht analysiert. - -\subsubsection{Skalierung \label{subsub:skalierung}} -Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: - -\begin{equation} - \mathscr{H}_n\{f(ar)\}=\frac{1}{a^{2}}\tilde{f}_n \left(\frac{\kappa}{a}\right), \quad a>0. -\end{equation} - -\subsubsection{Persevalsche Relation \label{subsub:perseval}} -Wenn $\tilde{f}(\kappa)=\mathscr{H}_n\{f(r)\}$ und $\tilde{g}(\kappa)=\mathscr{H}_n\{g(r)\}$, dann: - +Da die Membran am Rand befestigt ist, kann es keine Schwingungen geben, so dass die \textit{Dirichlet-Randbedingung} gilt: +\begin{equation*} + u\big|_{\Gamma} = 0 +\end{equation*} +Um eine eindeutige Lösung bestimmen zu können, werden die folgenden Anfangsbedingungen festgelegt: +\begin{align*} + u(r,\varphi, 0) &= f(r,\varphi)\\ + \frac{\partial}{\partial t} u(r,\varphi, 0) &= g(r,\varphi) +\end{align*} +Daher muss an dieser Stelle von einer Separation der Variablen ausgegangen werden: +\begin{equation*} + u(r,\varphi, t) = F(r)G(\varphi)T(t) +\end{equation*} +Dank der Randbedingungen kann also gefordert werden, dass $F(R)=0$ ist, und natürlich, dass $G(\varphi)$ $2\pi$ periodisch ist. Eingesetz in der Differenzialgleichung ergibt: +\begin{equation*} + \frac{1}{c^2}\frac{T''(t)}{T(t)}=\frac{F''(r)}{F(r)}+\frac{1}{r}\frac{F'(r)}{F(r)}+\frac{1}{r^2}\frac{G''(\varphi)}{G(\varphi)} +\end{equation*} +Da die linke Seite nur von $t$ und die rechte Seite nur von $r$ und $\varphi$ abhängt, müssen sie gleich einer reellen Zahl sein. Aus physikalischen Grunden suchen wir nach Lösungen, die weder exponentiell in der Zeit wachsen noch exponentiell abklingen. Dies bedeutet, dass die Konstante negativ sein muss, also schreibt man $k=-k^2$. Daraus ergeben sich die folgenden zwei Gleichungen: +\begin{gather*} + T''(t) + c^2\kappa^2T(t) = 0\\ + r^2\frac{F''(r)}{F(r)} + r \frac{F'(r)}{F(r)} +\kappa^2 r^2 = - \frac{G''(\varphi)}{G(\varphi)} +\end{gather*} +In der zweiten Gleichung hängt die linke Seite nur von $r$ ab, während die rechte Seite nur von $\varphi$ abhängt. Sie müssen also wiederum gleich einer reellen Zahl $\nu$ sein. Also das: +\begin{gather*} + r^2F''(r) + rF'(r) + (\kappa^2 r^2 - \nu)F(r) = 0 \\ + G''(\varphi) = \nu G(\varphi) +\end{gather*} +$G$ kann in einer Fourierreihe entwickelt werden, so dass man sieht, dass $\nu$ die Form $n^2$ mit einer positiven ganzen Zahl sein muss, also: +\begin{equation*} + G(\varphi) = C_n \cos(\varphi) + D_n \sin(\varphi) +\end{equation*} +Die Gleichung $F$ hat die Gestalt +\begin{equation*} + r^2F''(r) + rF'(r) + (\kappa^2 r^2 - n^2)F(r) = 0 \quad (*) +\end{equation*} +Wir bereits in der Vorlesung von Prof. Müller gezeigt, sind die Besselfunktionen +\begin{equation*} + J_{\nu}(x) = r^\nu \displaystyle\sum_{m=0}^{\infty} \frac{(-1)^m x^{2m}}{2^{2m+\nu}m! \Gamma (\nu + m+1)} +\end{equation*} +Lösungen der "Besselschen Differenzialgleichung" +\begin{equation*} + x^2 y'' + xy' + (x^2 - \nu^2)y = 0 +\end{equation*} +Die Funktionen $F(r) = J_n(\kappa r)$ lösen also die Differentialgleichung $(*)$. Die +Randbedingung $F(R)=0$ impliziert, dass $\kappa R$ eine Nullstelle der Besselfunktion +$J_n$ sein muss. Man kann zeigen, dass die Besselfunktionen $J_n, n \geq 0$, alle unendlich +viele Nullstellen +\begin{equation*} + \alpha_{1n} < \alpha_{2n} < ... +\end{equation*} +haben, und dass $\underset{\substack{m\to\infty}}{\text{lim}} \alpha_{mn}=\infty$. Somit ergit sich, dass $\kappa = \frac{\alpha_{mn}}{R}$ für ein $m\geq 1$, und dass +\begin{equation*} + F(r) = J_n (\kappa_{mn}r) \quad mit \quad \kappa_{mn}=\frac{\alpha_{mn}}{R} +\end{equation*} +Die Differenzialgleichung $T''(t) + c^2\kappa^2T(t) = 0$, wird auf ähnliche Weise gelöst wie $G(\varphi)$. Durch Überlagerung aller Ergebnisse erhält man die Lösung \begin{equation} - \int_{0}^{\infty}rf(r) dr = \int_{0}^{\infty}\kappa\tilde{f}(\kappa)\tilde{g}(\kappa) d\kappa. + u(r, \varphi, t) = \displaystyle\sum_{m=1}^{\infty}\displaystyle\sum_{n=0}^{\infty} J_n (k_{mn}r)\cos(n\varphi)[a_{mn}\cos(c \kappa_{mn} t)+b_{mn}\sin(c \kappa_{mn} t)] \end{equation} +Dabei sind m und n ganze Zahlen, wobei m für die Anzahl der Knotenkreise und n +für die Anzahl der Knotenlinien steht. Es gibt bestimmte Bereiche auf der Membran, in denen es keine Bewegung oder Vibration gibt. Wenn der nicht schwingende Bereich ein Kreis ist, nennt man ihn einen Knotenkreis, und wenn er eine Linie ist, nennt man ihn ebenfalls eine Knotenlinie. $Jn(\kappa_{mn}r)$ ist die Besselfunktion $n$-ter Ordnung, wobei kmn die Wellenzahl und $r$ der Radius ist. $a_{mn}$ und $b_{mn}$ sind die zu bestimmenden Konstanten. -\subsubsection{Hankel Transformationen von Ableitungen \label{subsub:ableitungen}} -Wenn $\tilde{f}_n(\kappa)=\mathscr{H}_n\{f(r)\}$, dann: - -\begin{align} - &\mathscr{H}_n\{f'(r)\}=\frac{\kappa}{2n}\left[(n-1)\tilde{f}_{n+1}(\kappa)-(n+1)\tilde{f}_{n-1}(\kappa)\right], \quad n\geq1, \\ - &\mathscr{H}_1\{f'(r)\}=-\kappa \tilde{f}_0(\kappa), -\end{align} -bereitgestellt dass $[rf(r)]$ verschwindet als $r\to0$ und $r\to\infty=0$. \ No newline at end of file +An diesem Punkt stellte sich die Frage, ob es möglich wäre, die partielle Differentialgleichung mit einer anderen Methode als der der Trennung der Variablen zu lösen. Nach einer kurzen Recherche und Diskussion mit Prof. Müller wurde festgestellt, dass die beste Methode die Transformationsmethode ist, genauer gesagt die Anwendung der Hankel-Transformation. Im nächsten Kapitel wird daher diese Integraltransformation vorgestellt und entwickelt, und es wird erläutert, warum sie für diese Art von Problem geeignet ist. diff --git a/buch/papers/kreismembran/teil2.tex b/buch/papers/kreismembran/teil2.tex index 45357f2..8afe817 100644 --- a/buch/papers/kreismembran/teil2.tex +++ b/buch/papers/kreismembran/teil2.tex @@ -2,48 +2,112 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Lösung der partiellen Differentialgleichung - \label{kreismembran:section:teil2}} -\rhead{Lösung der partiellen Differentialgleichung} +\section{Die Hankel Transformation \label{kreismembran:section:teil2}} +\rhead{Die Hankel Transformation} + +Hermann Hankel (1839-1873) war ein deutscher Mathematiker, der für seinen Beitrag zur mathematischen Analyse und insbesondere für seine namensgebende Transformation bekannt ist. +Diese Transformation tritt bei der Untersuchung von funktionen auf, die nur von der Enternung des Ursprungs abhängen. +Er studierte auch funktionen, jetzt Hankel- oder Bessel- Funktionen genannt, der dritten Art. +Die Hankel Transformation mit Bessel Funktionen al Kern taucht natürlich bei achsensymmetrischen Problemen auf, die in Zylindrischen Polarkoordinaten formuliert sind. +In diesem Kapitel werden die Theorie der Transformation und einige Eigenschaften der Grundoperationen erläutert. + + +Wir führen die Definition der Hankel Transformation aus der zweidimensionalen Fourier Transformation und ihrer Umkehrung ein, die durch: +\begin{align} + \mathscr{F}\{f(x,y)\} & = F(k,l)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-i( \bm{\kappa}\cdot \mathbf{r})}f(x,y) dx dy,\label{equation:fourier_transform}\\ + \mathscr{F}^{-1}\{F(x,y)\} & = f(x,y)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{i(\bm{\kappa}\cdot \mathbf{r}))}F(k,l) dx dy \label{equation:inv_fourier_transform} +\end{align} +wo $\mathbf{r}=(x,y)$ und $\bm{\kappa}=(k,l)$. Wie bereits erwähnt, sind Polarkoordinaten für diese Art von Problemen am besten geeignet, also mit, $(x,y)=r(\cos\theta,\sin\theta)$ und $(k,l)=\kappa(\cos\phi,\sin\phi)$, findet man $\bm{\kappa}\cdot\mathbf{r}=\kappa r(\cos(\theta-\phi))$ und danach: +\begin{align} + F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}r dr \int_{0}^{2\pi}e^{-ikr\cos(\theta-\phi)}f(r,\theta) d\phi. + \label{equation:F_ohne_variable_wechsel} +\end{align} +Dann wird angenommen dass, $f(r,\theta)=e^{in\theta}f(r)$, was keine strenge Einschränkung ist, und es wird eine Änderung der Variabeln vorgenommen $\theta-\phi=\alpha-\frac{\pi}{2}$, um \eqref{equation:F_ohne_variable_wechsel} zu reduzieren: +\begin{align} + F(k,\phi)=\frac{1}{2\pi}\int_{0}^{\infty}rf(r) dr \int_{\phi_{0}}^{2\pi+\phi_{0}}e^{in(\phi-\frac{\pi}{2})+i(n\alpha-kr\sin\alpha)} d\alpha, + \label{equation:F_ohne_bessel} +\end{align} +wo $\phi_{0}=(\frac{\pi}{2}-\phi)$. + +Unter Verwendung der Integral Darstellung der Besselfunktion vom Ordnung n +\begin{align} + J_n(\kappa r)=\frac{1}{2\pi}\int_{\phi_{0}}^{2\pi + \phi_{0}}e^{i(n\alpha-\kappa r \sin \alpha)} d\alpha + \label{equation:bessel_n_ordnung} +\end{align} +\eqref{equation:F_ohne_bessel} wird sie zu: +\begin{align} + F(k,\phi)&=e^{in(\phi-\frac{\pi}{2})}\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr \label{equation:F_mit_bessel_step_1} \\ + &=e^{in(\phi-\frac{\pi}{2})}\tilde{f}_n(\kappa), + \label{equation:F_mit_bessel_step_2} +\end{align} +wo $\tilde{f}_n(\kappa)$ ist die \textit{Hankel Transformation} von $f(r)$ und ist formell definiert durch: +\begin{align} + \mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)=\int_{0}^{\infty}rJ_n(\kappa r) f(r) dr. + \label{equation:hankel} +\end{align} + +Ähnlich verhält es sich mit der inversen Fourier Transformation in Form von polaren Koordinaten unter der Annahme $f(r,\theta)=e^{in\theta}f(r)$ mit \eqref{equation:F_mit_bessel_step_2}, wird die inverse Fourier Transformation \eqref{equation:inv_fourier_transform}: + +\begin{align} + e^{in\theta}f(r)&=\frac{1}{2\pi}\int_{0}^{\infty}\kappa d\kappa \int_{0}^{2\pi}e^{i\kappa r \cos (\theta - \phi)}F(\kappa,\phi) d\phi\\ + &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{0}^{2\pi}e^{in(\phi - \frac{\pi}{2})- i\kappa r \cos (\theta - \phi)} d\phi, +\end{align} +was durch den Wechsel der Variablen $\theta-\phi=-(\alpha+\frac{\pi}{2})$ und $\theta_0=-(\theta+\frac{\pi}{2})$, + +\begin{align} + &= \frac{1}{2\pi}\int_{0}^{\infty}\kappa \tilde{f}_n(\kappa) d\kappa \int_{\theta_0}^{2\pi+\theta_0}e^{in(\theta + \alpha - i\kappa r \sin\alpha)} d\alpha \nonumber \\ + &= e^{in\theta}\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa,\quad \text{von \eqref{equation:bessel_n_ordnung}} +\end{align} + +Also, die inverse \textit{Hankel Transformation} ist so definiert: +\begin{align} + \mathscr{H}^{-1}_n\{\tilde{f}_n(\kappa)\}=f(r)=\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) d\kappa. + \label{equation:inv_hankel} +\end{align} + +Anstelle von $\tilde{f}_n(\kappa)$, wird häufig für die Hankel Transformation verwendet, indem die Ordnung angegeben wird. +\eqref{equation:hankel} und \eqref{equation:inv_hankel} Integralen existieren für eine grosse Klasse von Funktionen, die normalerweise in physikalischen Anwendungen benötigt werden. +Alternativ kann auch die berühmte Hankel Transformationsformel verwendet werden, + +\begin{align} + f(r) = \int_{0}^{\infty}\kappa J_n(\kappa r) d\kappa \int_{0}^{\infty} p J_n(\kappa p)f(p) dp, + \label{equation:hankel_integral_formula} +\end{align} +um die Hankel Transformation \eqref{equation:hankel} und ihre Inverse \eqref{equation:inv_hankel} zu definieren. +Insbesondere die Hankel Transformation der nullten Ordnung ($n=0$) und der ersten Ordnung ($n=1$) sind häufig nützlich, um Lösungen für Probleme mit der Laplace Gleichung in einer achsensymmetrischen zylindrischen Geometrie zu finden. + +\subsection{Operative Eigenschaften der Hankel Transformation\label{sub:op_properties_hankel}} +In diesem Kapitel werden die operativen Eigenschaften der Hankel Transformation aufgeführt. Der Beweis für ihre Gültigkeit wird jedoch nicht analysiert. + +\subsubsection{Theorem 1: Skalierung \label{subsub:skalierung}} +Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: -Wie im vorherigen Kapitel gezeigt, lautet die partielle Differentialgleichung, die die Schwingungen einer Membran beschreibt: \begin{equation*} - \frac{1}{c^2}\frac{\partial^2u}{\partial t^2} = \Delta u + \mathscr{H}_n\{f(ar)\}=\frac{1}{a^{2}}\tilde{f}_n \left(\frac{\kappa}{a}\right), \quad a>0. \end{equation*} -Da es sich um eine Kreisscheibe handelt, werden Polarkoordinaten verwendet, so dass sich der Laplaceoperator ergibt: + +\subsubsection{Theorem 2: Persevalsche Relation \label{subsub:perseval}} +Wenn $\tilde{f}(\kappa)=\mathscr{H}_n\{f(r)\}$ und $\tilde{g}(\kappa)=\mathscr{H}_n\{g(r)\}$, dann: + \begin{equation*} - \Delta - = - \frac{\partial^2}{\partial r^2} - + - \frac1r - \frac{\partial}{\partial r} - + - \frac{1}{r 2} - \frac{\partial^2}{\partial\varphi^2}. - \label{buch:pde:kreis:laplace} + \int_{0}^{\infty}rf(r) dr = \int_{0}^{\infty}\kappa\tilde{f}(\kappa)\tilde{g}(\kappa) d\kappa. \end{equation*} -Es wird eine runde elastische Membran berücksichtigt, die den Gebietbereich $\Omega$ abdeckt und am Rand $\Gamma$ befestigt ist. -Es wird daher davon ausgegangen, dass die Membran aus einem homogenen Material von vernachlässigbarer Dicke gefertigt ist. -Die Membran kann verformt werden, aber innere elastische Kräfte wirken den Verformungen entgegen. Es wirken keine äusseren Kräfte. Es handelt sich somit von einer kreisförmligen eigespannten homogenen schwingenden Membran. +\subsubsection{Theorem 3: Hankel Transformationen von Ableitungen \label{subsub:ableitungen}} +Wenn $\tilde{f}_n(\kappa)=\mathscr{H}_n\{f(r)\}$, dann: -Daher ist die Membranabweichung im Punkt $(r,\theta)$ $\in$ $\overline{\rm \Omega}$ zum Zeitpunkt $t$: \begin{align*} - u: \overline{\rm \Omega} \times \mathbb{R}_{\geq 0} &\longrightarrow \mathbb{R}\\ - (r,\theta,t) &\longmapsto u(r,\theta,t) + &\mathscr{H}_n\{f'(r)\}=\frac{\kappa}{2n}\left[(n-1)\tilde{f}_{n+1}(\kappa)-(n+1)\tilde{f}_{n-1}(\kappa)\right], \quad n\geq1, \\ + &\mathscr{H}_1\{f'(r)\}=-\kappa \tilde{f}_0(\kappa), \end{align*} -Da die Membran am Rand befestigt ist, kann es keine Schwingungen geben, so dass die \textit{Dirichlet-Randbedingung} gilt: -\begin{equation*} - u\big|_{\Gamma} = 0 -\end{equation*} +bereitgestellt dass $[rf(r)]$ verschwindet als $r\to0$ und $r\to\infty$. +\subsubsection{Theorem 4 \label{subsub:thorem4}} +Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: -Um eine eindeutige Lösung bestimmen zu können, werden die folgenden Anfangsbedingungen festgelegt: +\begin{equation*} + \mathscr{H}_n \left\{ \left( \nabla^2 - \frac{n^2}{r^2} f(r)\right)\right\}= \mathscr{H}_n\left\{\frac{1}{r}\frac{d}{dr}\left(r\frac{df}{dr}\right) - \frac{n^2}{r^2}f(r)\right\}=-\kappa^2\tilde{f}_{n}(\kappa), +\end{equation*} +bereitgestellt dass $rf'(r)$ und $rf(r)$ verschwinden als $r\to0$ und $r\to\infty$. -\begin{align*} - u(r,\theta, 0) &:= f(x,y)\\ - \frac{\partial}{\partial t} u(r,\theta, 0) &:= g(x,y) -\end{align*} -An dieser Stelle könnte man zum Beispiel die bereits in Kapitel (TODO:refKAPITEL) vorgestellte Methode der Separation anwenden. Da es sich in diesem Fall jedoch um einem achsensymmetrischen Problem handelt, das in Polarkoordinaten formuliert ist, wird man die Transformationsmethode verwenden, insbesondere die Hankel Transformation. diff --git a/buch/papers/kreismembran/teil3.tex b/buch/papers/kreismembran/teil3.tex index 73dee0f..bef8b5f 100644 --- a/buch/papers/kreismembran/teil3.tex +++ b/buch/papers/kreismembran/teil3.tex @@ -3,38 +3,76 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 3 +\section{Lösungsmethode 2: Transformationsmethode \label{kreismembran:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{kreismembran:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\rhead{Lösungsmethode 2: Transformationsmethode} +Die Hankel-Transformation wird dann zur Lösung der Differentialgleichung verwendet. Es müssen jedoch einige Änderungen an dem Problem vorgenommen werden, damit es mit den Annahmen übereinstimmt, die für die Verwendung der Hankel-Transformation erforderlich sind. Das heisst, dass die Funktion u nur von der Entfernung zum Ausgangspunkt abhängt. Wir führen also das Konzept einer unendlichen und achsensymmetrischen Membran ein: +\begin{equation*} + \frac{\partial^2u}{\partial t^2} + = + c^2 \left(\frac{\partial^2 u}{\partial r^2} + + + \frac{1}{r} + \frac{\partial u}{\partial r} \right), \quad 00 + \label{eq:PDE_inf_membane} +\end{equation*} + +\begin{align} + u(r,0)=f(r), \quad \frac{\partial}{\partial t} u(r,0) = g(r), \quad \text{für} \quad 0 Date: Wed, 18 May 2022 14:20:41 +0200 Subject: =?UTF-8?q?Dreiecke=20f=C3=BCr=20Nav?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../050-differential/uebungsaufgaben/airy.cpp | 4 +- buch/chapters/110-elliptisch/ellintegral.tex | 2 +- buch/papers/nav/images/Makefile | 10 ++- buch/papers/nav/images/common.inc | 28 +++++- buch/papers/nav/images/dreieck3d1.pdf | Bin 0 -> 90451 bytes buch/papers/nav/images/dreieck3d1.pov | 12 +-- buch/papers/nav/images/dreieck3d2.pdf | Bin 0 -> 69523 bytes buch/papers/nav/images/dreieck3d2.pov | 6 +- buch/papers/nav/images/dreieck3d3.pdf | Bin 0 -> 82512 bytes buch/papers/nav/images/dreieck3d3.pov | 8 +- buch/papers/nav/images/dreieck3d4.pdf | Bin 0 -> 85037 bytes buch/papers/nav/images/dreieck3d4.pov | 8 +- buch/papers/nav/images/dreieck3d5.pdf | Bin 0 -> 70054 bytes buch/papers/nav/images/dreieck3d5.pov | 6 +- buch/papers/nav/images/dreieck3d6.pov | 2 +- buch/papers/nav/images/dreieck3d7.pov | 10 +-- buch/papers/nav/images/dreieck3d8.jpg | Bin 0 -> 93432 bytes buch/papers/nav/images/dreieck3d8.pdf | Bin 0 -> 107370 bytes buch/papers/nav/images/dreieck3d8.pov | 96 +++++++++++++++++++++ buch/papers/nav/images/dreieck3d8.tex | 57 ++++++++++++ vorlesungen/stream/countdown.html | 2 +- 21 files changed, 217 insertions(+), 34 deletions(-) create mode 100644 buch/papers/nav/images/dreieck3d1.pdf create mode 100644 buch/papers/nav/images/dreieck3d2.pdf create mode 100644 buch/papers/nav/images/dreieck3d3.pdf create mode 100644 buch/papers/nav/images/dreieck3d4.pdf create mode 100644 buch/papers/nav/images/dreieck3d5.pdf create mode 100644 buch/papers/nav/images/dreieck3d8.jpg create mode 100644 buch/papers/nav/images/dreieck3d8.pdf create mode 100644 buch/papers/nav/images/dreieck3d8.pov create mode 100644 buch/papers/nav/images/dreieck3d8.tex diff --git a/buch/chapters/050-differential/uebungsaufgaben/airy.cpp b/buch/chapters/050-differential/uebungsaufgaben/airy.cpp index e4df8e1..eb5c6be 100644 --- a/buch/chapters/050-differential/uebungsaufgaben/airy.cpp +++ b/buch/chapters/050-differential/uebungsaufgaben/airy.cpp @@ -44,8 +44,8 @@ double h0f1(double c, double x) { double f1(double x) { // unfortunately, gsl_sf_hyperg_0F1 does not work if c<1, because // it uses a relation to the bessel functions - //return gsl_sf_hyperg_0F1(2/3, x*x*x/9.); - return h0f1(2./3., x*x*x/9.); + return gsl_sf_hyperg_0F1(2/3, x*x*x/9.); + //return h0f1(2./3., x*x*x/9.); } double f2(double x) { diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 4cb2ba3..3acce2f 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -651,7 +651,7 @@ werden, dass $1-k'^2=k^2$ ist. \begin{definition} Ist $0\le k\le 1$ der Modul eines elliptischen Integrals, dann heisst -$k' = \sqrt{1-k^2}$ er {\em Komplementärmodul} oder {\em Komplement +$k' = \sqrt{1-k^2}$ der {\em Komplementärmodul} oder {\em Komplement des Moduls}. Es ist $k^2+k'^2=1$. \end{definition} diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile index c9dcacc..bbdea2f 100644 --- a/buch/papers/nav/images/Makefile +++ b/buch/papers/nav/images/Makefile @@ -50,7 +50,8 @@ DREIECKE3D = \ dreieck3d4.pdf \ dreieck3d5.pdf \ dreieck3d6.pdf \ - dreieck3d7.pdf + dreieck3d7.pdf \ + dreieck3d8.pdf dreiecke3d: $(DREIECKE3D) @@ -106,3 +107,10 @@ dreieck3d7.jpg: dreieck3d7.png dreieck3d7.pdf: dreieck3d7.tex dreieck3d7.jpg pdflatex dreieck3d7.tex +dreieck3d8.png: dreieck3d8.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d8.png dreieck3d8.pov +dreieck3d8.jpg: dreieck3d8.png + convert dreieck3d8.png -density 300 -units PixelsPerInch dreieck3d8.jpg +dreieck3d8.pdf: dreieck3d8.tex dreieck3d8.jpg + pdflatex dreieck3d8.tex + diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc index 33d9384..e2a1ed0 100644 --- a/buch/papers/nav/images/common.inc +++ b/buch/papers/nav/images/common.inc @@ -97,13 +97,13 @@ union { } #end -#macro winkel(w, p, q, staerke) +#macro winkel(w, p, q, staerke, r) #declare n = vnormalize(w); #declare pp = vnormalize(p - vdot(n, p) * n); #declare qq = vnormalize(q - vdot(n, q) * n); intersection { sphere { <0, 0, 0>, 1 + staerke } - cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), 0.4 } + cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), r } plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 } plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 } } @@ -113,8 +113,30 @@ union { sphere { p, 1.5 * staerke } #end +#macro dreieck(p, q, r, farbe) + #declare n1 = vnormalize(vcross(p, q)); + #declare n2 = vnormalize(vcross(q, r)); + #declare n3 = vnormalize(vcross(r, p)); + intersection { + plane { n1, 0 } + plane { n2, 0 } + plane { n3, 0 } + sphere { <0, 0, 0>, 1 + 0.001 } + pigment { + color farbe + } + finish { + metallic + specular 0.4 + } + } +#end + #declare fett = 0.015; -#declare fine = 0.010; +#declare fein = 0.010; + +#declare klein = 0.3; +#declare gross = 0.4; #declare dreieckfarbe = rgb<0.6,0.6,0.6>; #declare rot = rgb<0.8,0.2,0.2>; diff --git a/buch/papers/nav/images/dreieck3d1.pdf b/buch/papers/nav/images/dreieck3d1.pdf new file mode 100644 index 0000000..015bce7 Binary files /dev/null and b/buch/papers/nav/images/dreieck3d1.pdf differ diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov index 8afe60e..e491075 100644 --- a/buch/papers/nav/images/dreieck3d1.pov +++ b/buch/papers/nav/images/dreieck3d1.pov @@ -12,9 +12,9 @@ union { punkt(A, fett) punkt(B, fett) punkt(C, fett) - punkt(P, fine) - seite(B, P, fine) - seite(C, P, fine) + punkt(P, fein) + seite(B, P, fein) + seite(C, P, fein) pigment { color dreieckfarbe } @@ -25,7 +25,7 @@ union { } object { - winkel(A, B, C, fine) + winkel(A, B, C, fein, gross) pigment { color rot } @@ -36,7 +36,7 @@ object { } object { - winkel(B, C, A, fine) + winkel(B, C, A, fein, gross) pigment { color gruen } @@ -47,7 +47,7 @@ object { } object { - winkel(C, A, B, fine) + winkel(C, A, B, fein, gross) pigment { color blau } diff --git a/buch/papers/nav/images/dreieck3d2.pdf b/buch/papers/nav/images/dreieck3d2.pdf new file mode 100644 index 0000000..6b3f09d Binary files /dev/null and b/buch/papers/nav/images/dreieck3d2.pdf differ diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov index c23a54c..c0625ce 100644 --- a/buch/papers/nav/images/dreieck3d2.pov +++ b/buch/papers/nav/images/dreieck3d2.pov @@ -12,9 +12,9 @@ union { punkt(A, fett) punkt(B, fett) punkt(C, fett) - punkt(P, fine) - seite(B, P, fine) - seite(C, P, fine) + punkt(P, fein) + seite(B, P, fein) + seite(C, P, fein) pigment { color dreieckfarbe } diff --git a/buch/papers/nav/images/dreieck3d3.pdf b/buch/papers/nav/images/dreieck3d3.pdf new file mode 100644 index 0000000..7d79455 Binary files /dev/null and b/buch/papers/nav/images/dreieck3d3.pdf differ diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov index f2496b5..b6f64d5 100644 --- a/buch/papers/nav/images/dreieck3d3.pov +++ b/buch/papers/nav/images/dreieck3d3.pov @@ -12,9 +12,9 @@ union { punkt(A, fett) punkt(B, fett) punkt(C, fett) - punkt(P, fine) - seite(B, P, fine) - seite(C, P, fine) + punkt(P, fein) + seite(B, P, fein) + seite(C, P, fein) pigment { color dreieckfarbe } @@ -25,7 +25,7 @@ union { } object { - winkel(A, B, C, fine) + winkel(A, B, C, fein, gross) pigment { color rot } diff --git a/buch/papers/nav/images/dreieck3d4.pdf b/buch/papers/nav/images/dreieck3d4.pdf new file mode 100644 index 0000000..e1ea757 Binary files /dev/null and b/buch/papers/nav/images/dreieck3d4.pdf differ diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov index bddcf7c..b6f17e3 100644 --- a/buch/papers/nav/images/dreieck3d4.pov +++ b/buch/papers/nav/images/dreieck3d4.pov @@ -6,9 +6,9 @@ #include "common.inc" union { - seite(A, B, fine) - seite(A, C, fine) - punkt(A, fine) + seite(A, B, fein) + seite(A, C, fein) + punkt(A, fein) punkt(B, fett) punkt(C, fett) punkt(P, fett) @@ -25,7 +25,7 @@ union { } object { - winkel(B, C, P, fine) + winkel(B, C, P, fein, gross) pigment { color rgb<0.6,0.4,0.2> } diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf new file mode 100644 index 0000000..6848331 Binary files /dev/null and b/buch/papers/nav/images/dreieck3d5.pdf differ diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov index 32fc9e6..188f181 100644 --- a/buch/papers/nav/images/dreieck3d5.pov +++ b/buch/papers/nav/images/dreieck3d5.pov @@ -6,9 +6,9 @@ #include "common.inc" union { - seite(A, B, fine) - seite(A, C, fine) - punkt(A, fine) + seite(A, B, fein) + seite(A, C, fein) + punkt(A, fein) punkt(B, fett) punkt(C, fett) punkt(P, fett) diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov index 7611950..191a1e7 100644 --- a/buch/papers/nav/images/dreieck3d6.pov +++ b/buch/papers/nav/images/dreieck3d6.pov @@ -25,7 +25,7 @@ union { } object { - winkel(B, A, P, fine) + winkel(B, A, P, fein, gross) pigment { color rgb<0.6,0.2,0.6> } diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov index fa48f5b..aae5c6c 100644 --- a/buch/papers/nav/images/dreieck3d7.pov +++ b/buch/papers/nav/images/dreieck3d7.pov @@ -10,13 +10,13 @@ union { seite(A, P, fett) seite(C, P, fett) - seite(A, B, fine) - seite(B, C, fine) - seite(B, P, fine) + seite(A, B, fein) + seite(B, C, fein) + seite(B, P, fein) punkt(A, fett) punkt(C, fett) punkt(P, fett) - punkt(B, fine) + punkt(B, fein) pigment { color dreieckfarbe } @@ -27,7 +27,7 @@ union { } object { - winkel(A, P, C, fine) + winkel(A, P, C, fein, gross) pigment { color rgb<0.4,0.4,1> } diff --git a/buch/papers/nav/images/dreieck3d8.jpg b/buch/papers/nav/images/dreieck3d8.jpg new file mode 100644 index 0000000..52bd25e Binary files /dev/null and b/buch/papers/nav/images/dreieck3d8.jpg differ diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf new file mode 100644 index 0000000..9d630aa Binary files /dev/null and b/buch/papers/nav/images/dreieck3d8.pdf differ diff --git a/buch/papers/nav/images/dreieck3d8.pov b/buch/papers/nav/images/dreieck3d8.pov new file mode 100644 index 0000000..9e9921a --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.pov @@ -0,0 +1,96 @@ +// +// dreiecke3d8.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +union { + seite(A, B, fett) + seite(B, C, fett) + seite(A, C, fett) + seite(A, P, fein) + seite(B, P, fett) + seite(C, P, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, C, fein, klein) + pigment { + color rot + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, C, A, fein, klein) + pigment { + color gruen + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(C, A, B, fein, gross) + pigment { + color blau + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, P, C, fein/2, gross) + pigment { + color rgb<0.8,0,0.8> + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, P, C, fein, klein) + pigment { + color rgb<1,0.8,0> + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, P, A, fein/2, gross) + pigment { + color rgb<0.4,0.6,0.8> + } + finish { + specular 0.95 + metallic + } +} + +dreieck(A, B, C, White) + + diff --git a/buch/papers/nav/images/dreieck3d8.tex b/buch/papers/nav/images/dreieck3d8.tex new file mode 100644 index 0000000..c59c7b0 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d8.tex @@ -0,0 +1,57 @@ +% +% dreieck3d8.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{dreieck3d8.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (0.7,3.8) {$A$}; +\node at (-3.4,-0.8) {$B$}; +\node at (3.3,-2.1) {$C$}; +\node at (-1.4,-3.5) {$P$}; + +\node at (-1.9,2.1) {$c$}; +\node at (-0.2,-1.2) {$a$}; +\node at (2.6,1.5) {$b$}; +\node at (-0.8,0) {$l$}; + +\node at (-2.6,-2.2) {$p_b$}; +\node at (1,-2.9) {$p_c$}; + +\node at (0.7,3.3) {$\alpha$}; +\node at (0.8,2.85) {$\omega$}; +\node at (-2.6,-0.6) {$\beta$}; +\node at (2.3,-1.2) {$\gamma$}; +\node at (-2.6,-1.3) {$\beta_1$}; +\node at (-2.1,-0.8) {$\kappa$}; + +\end{tikzpicture} + +\end{document} + diff --git a/vorlesungen/stream/countdown.html b/vorlesungen/stream/countdown.html index d8ec82e..e9d7d6e 100644 --- a/vorlesungen/stream/countdown.html +++ b/vorlesungen/stream/countdown.html @@ -25,7 +25,7 @@ function checkfor(d) { console.log("time string: " + ds); let start = new Date(ds).getTime(); console.log("now: " + now); - if ((start > now) && ((start-now) < 3600*1000)) { + if ((start > now) && ((start-now) < 3300*1000)) { deadline = start; console.log("set deadline to: " + ds); } else { -- cgit v1.2.1 From 525ff82400b685dc6dd0d6376253545720471be0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 18 May 2022 14:25:26 +0200 Subject: remove bad files --- buch/buch.aux | 22 - buch/buch.bbl | 0 buch/buch.blg | 48 - buch/buch.idx | 0 buch/buch.log | 2106 --------------------------------- buch/papers/nav/images/dreieck3d5.pdf | Bin 70054 -> 70045 bytes 6 files changed, 2176 deletions(-) delete mode 100644 buch/buch.aux delete mode 100644 buch/buch.bbl delete mode 100644 buch/buch.blg delete mode 100644 buch/buch.idx delete mode 100644 buch/buch.log diff --git a/buch/buch.aux b/buch/buch.aux deleted file mode 100644 index 6730af9..0000000 --- a/buch/buch.aux +++ /dev/null @@ -1,22 +0,0 @@ -\relax -\providecommand\hyper@newdestlabel[2]{} -\providecommand\babel@aux[2]{} -\@nameuse{bbl@beforestart} -\catcode `"\active -\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} -\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined -\global\let\oldcontentsline\contentsline -\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} -\global\let\oldnewlabel\newlabel -\gdef\newlabel#1#2{\newlabelxx{#1}#2} -\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} -\AtEndDocument{\ifx\hyper@anchor\@undefined -\let\contentsline\oldcontentsline -\let\newlabel\oldnewlabel -\fi} -\fi} -\global\let\hyper@last\relax -\gdef\HyperFirstAtBeginDocument#1{#1} -\providecommand\HyField@AuxAddToFields[1]{} -\providecommand\HyField@AuxAddToCoFields[2]{} -\providecommand\BKM@entry[2]{} diff --git a/buch/buch.bbl b/buch/buch.bbl deleted file mode 100644 index e69de29..0000000 diff --git a/buch/buch.blg b/buch/buch.blg deleted file mode 100644 index 706b1d8..0000000 --- a/buch/buch.blg +++ /dev/null @@ -1,48 +0,0 @@ -This is BibTeX, Version 0.99d -Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 -The top-level auxiliary file: buch.aux -I found no \citation commands---while reading file buch.aux -I found no \bibdata command---while reading file buch.aux -I found no \bibstyle command---while reading file buch.aux -You've used 0 entries, - 0 wiz_defined-function locations, - 83 strings with 482 characters, -and the built_in function-call counts, 0 in all, are: -= -- 0 -> -- 0 -< -- 0 -+ -- 0 -- -- 0 -* -- 0 -:= -- 0 -add.period$ -- 0 -call.type$ -- 0 -change.case$ -- 0 -chr.to.int$ -- 0 -cite$ -- 0 -duplicate$ -- 0 -empty$ -- 0 -format.name$ -- 0 -if$ -- 0 -int.to.chr$ -- 0 -int.to.str$ -- 0 -missing$ -- 0 -newline$ -- 0 -num.names$ -- 0 -pop$ -- 0 -preamble$ -- 0 -purify$ -- 0 -quote$ -- 0 -skip$ -- 0 -stack$ -- 0 -substring$ -- 0 -swap$ -- 0 -text.length$ -- 0 -text.prefix$ -- 0 -top$ -- 0 -type$ -- 0 -warning$ -- 0 -while$ -- 0 -width$ -- 0 -write$ -- 0 -(There were 3 error messages) diff --git a/buch/buch.idx b/buch/buch.idx deleted file mode 100644 index e69de29..0000000 diff --git a/buch/buch.log b/buch/buch.log deleted file mode 100644 index 4175a27..0000000 --- a/buch/buch.log +++ /dev/null @@ -1,2106 +0,0 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (MiKTeX 22.3) (preloaded format=pdflatex 2022.4.16) 17 MAY 2022 13:22 -entering extended mode - 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TeX capacity exceeded, sorry [main memory size=3000000]. - \XKV@resb - -l.575 } - -If you really absolutely need more capacity, -you can ask a wizard to enlarge me. - - -Here is how much of TeX's memory you used: - 81845 strings out of 478582 - 2061696 string characters out of 2856069 - 3000001 words of memory out of 3000000 - 98832 multiletter control sequences out of 15000+600000 - 484206 words of font info for 75 fonts, out of 8000000 for 9000 - 1143 hyphenation exceptions out of 8191 - 105i,3n,99p,3369b,2422s stack positions out of 10000i,1000n,20000p,200000b,80000s -! ==> Fatal error occurred, no output PDF file produced! diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf index 6848331..0c86d36 100644 Binary files a/buch/papers/nav/images/dreieck3d5.pdf and b/buch/papers/nav/images/dreieck3d5.pdf differ -- cgit v1.2.1 From 93bdfca3b41397e43537ee334e57883a9ef79279 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 18 May 2022 14:30:12 +0200 Subject: fix nav/makefile.inc --- buch/papers/nav/Makefile.inc | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/buch/papers/nav/Makefile.inc b/buch/papers/nav/Makefile.inc index b30377e..24ab4ee 100644 --- a/buch/papers/nav/Makefile.inc +++ b/buch/papers/nav/Makefile.inc @@ -6,9 +6,11 @@ dependencies-nav = \ papers/nav/packages.tex \ papers/nav/main.tex \ - papers/nav/references.bib \ - papers/nav/teil0.tex \ - papers/nav/teil1.tex \ - papers/nav/teil2.tex \ - papers/nav/teil3.tex + papers/nav/einleitung.tex \ + papers/nav/flatearth.tex \ + papers/nav/geschichte.tex \ + papers/nav/nautischesdreieck.tex \ + papers/nav/sincos.tex \ + papers/nav/trigo.tex \ + papers/nav/references.bib -- cgit v1.2.1 From 88cc6d9775114c70d8723a52a869179ce806d2f7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 18 May 2022 14:43:23 +0200 Subject: fix paper offset --- buch/splitpapers | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/splitpapers b/buch/splitpapers index 9ae5aae..e1b6834 100755 --- a/buch/splitpapers +++ b/buch/splitpapers @@ -16,7 +16,7 @@ then fi awk 'BEGIN { - offsetpage = 10 + offsetpage = 12 startpage = 0 identifier = "" chapterno = 0 -- cgit v1.2.1 From b37f9519bbfd57b3a7d25cca887ff44ff2253921 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Thu, 19 May 2022 14:40:25 +0200 Subject: Korrektur von Feedback --- buch/papers/nav/bilder/dreieck.pdf | Bin 0 -> 107370 bytes buch/papers/nav/bilder/ephe.png | Bin 0 -> 184799 bytes buch/papers/nav/einleitung.tex | 6 +- buch/papers/nav/flatearth.tex | 12 ++- buch/papers/nav/geschichte.tex | 22 ---- buch/papers/nav/nautischesdreieck.tex | 190 ++++++++++++++++------------------ buch/papers/nav/sincos.tex | 21 ++-- buch/papers/nav/trigo.tex | 57 +++++++--- 8 files changed, 158 insertions(+), 150 deletions(-) create mode 100644 buch/papers/nav/bilder/dreieck.pdf create mode 100644 buch/papers/nav/bilder/ephe.png delete mode 100644 buch/papers/nav/geschichte.tex diff --git a/buch/papers/nav/bilder/dreieck.pdf b/buch/papers/nav/bilder/dreieck.pdf new file mode 100644 index 0000000..9d630aa Binary files /dev/null and b/buch/papers/nav/bilder/dreieck.pdf differ diff --git a/buch/papers/nav/bilder/ephe.png b/buch/papers/nav/bilder/ephe.png new file mode 100644 index 0000000..0aeef6f Binary files /dev/null and b/buch/papers/nav/bilder/ephe.png differ diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex index e24f294..8d8c5c1 100644 --- a/buch/papers/nav/einleitung.tex +++ b/buch/papers/nav/einleitung.tex @@ -1,9 +1,9 @@ \section{Einleitung} -Heut zu Tage ist die Navigation ein Teil des Lebens. -Man versendet dem Kollegen seinen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein um sich die Sucherei zu schenken. +Heutzutage ist die Navigation ein Teil des Lebens. +Man sendet dem Kollegen seinen eigenen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein, damit man seinen Aufenthaltsort zum Beispiel auf einer riesigen Wiese am See findet. Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf kleineren Schiffen benötigt wird im Falle eines Stromausfalls. Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? -In diesem Kapitel werden genau diese Fragen mithilfe des Nautischen Dreiecks, der Sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file +In diesem Kapitel werden genau diese Fragen mithilfe des nautischen Dreiecks, der sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index fbabbde..bec242e 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -2,7 +2,7 @@ \section{Warum ist die Erde nicht flach?} -\begin{figure}[h] +\begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/projektion.png} \caption[Mercator Projektion]{Mercator Projektion} @@ -14,10 +14,14 @@ Die Fotos von unserem Planeten oder die Berichte der Astronauten. Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. -Mithilfe der Geometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. +Mithilfe der Trigonometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. + Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. -Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. +Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. +Grönland ist auf der Weltkarte so gross wie Afrika. In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. Das liegt daran, das man die 3D – Weltkarte nicht einfach auslegen kann. -Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. + +Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. +Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. \ No newline at end of file diff --git a/buch/papers/nav/geschichte.tex b/buch/papers/nav/geschichte.tex deleted file mode 100644 index a20eb6d..0000000 --- a/buch/papers/nav/geschichte.tex +++ /dev/null @@ -1,22 +0,0 @@ -\documentclass[12pt]{scrartcl} -\usepackage{ucs} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{graphicx} - -\begin{document} -\section{Geschichte der sphärischen Navigation} -Die Orientierung mit Hilfe der Sterne und der sphärischen Trigonometrie bewegt die Menschheit schon seit mehreren tausend Jahren. -Nach Hinweisen und Schätzungen von Forscher haben schon vor 4000 Jahren die Ägypter und Gelehrten aus Babylon mit Hilfe der Astronomie den Lauf der Gestirne (Himmelskörper) zu berechnen versucht, jedoch ohne Erfolg. -Etwa 350 vor Christus waren es die Griechen, welche den damaligen Astronomen Hilfestellungen mittels Kugel-Geometrien leisten konnten. -Aus diesen Geometrien wurden erste mathematische Sätze aufgestellt und ein paar Jahrhunderte später kamen zu diesem Thema auch Berechnungen dazu. -Ebenso wurden Kartenmaterial mit Sternenbilder angefertigt. -Die Sinusfunktion war noch nicht bekannt, jedoch kamen zu dieser Zeit die ersten Ansätze der Cosinusfunktion aus Indien. -Von diesen Hilfen darauf aufbauend konnte um 900 die Araber der Sinussatz entwickeln. -Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde. -Dies aus dem Grund, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung vermehrt an Wichtigkeit gewann. -Auch die Verwendung der Tangens- und Sinusfunktion sowie der neu entwickelte Seitencosinussatz trugen zu einer Verbesserung der Orientierung herbei. -Im 16. Jahrhundert wurde dann ein weiterer trigonometrischer Satz, der Winkelcosinussatz hergeleitet. Stück für Stück wurden infolge der Entdeckung des Logarithmus im 17. Jahrhundert viele neue Methoden entwickelt. -Auch eine Verbesserung der kartographischen Verwendung der Kugelgeometrie wurde vorgenommen. -Es folgten weitere Entwicklungen in nicht euklidische Geometrien und im 19. Jahrhundert sowie auch im 20. Jahrhundert wurde zudem für die Relativitätstheorie auch die sphärische Trigonometrie beigezogen. -\end{document} \ No newline at end of file diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index b61e908..a85b119 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -1,17 +1,13 @@ \section{Das Nautische Dreieck} \subsection{Definition des Nautischen Dreiecks} -Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der \textbf{Himmelskugel}. -Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient.\\ -Das Nautische Dreieck definiert sich durch folgende Ecken: -\begin{itemize} - \item Zenit - \item Gestirn - \item Himmelspol -\end{itemize} +Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel}. +Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient. +Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. + Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. -\\ + Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfache Zusammenhänge: \begin{itemize} \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ @@ -21,34 +17,30 @@ Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfach \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ \end{itemize} Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: - -$\alpha \ \widehat{=} \ Rektaszension $ - -$\delta \ \widehat{=} \ Deklination =$ Breitengrad des Gestirns - -$\theta \ \widehat{=} \ Sternzeit\ von\ Greenwich$ - -$\phi \ \widehat{=} \ Geographische \ Breite $ - -$\tau = \theta-\alpha \ \widehat{=} \ Stundenwinkel =$ Längengrad des Gestirns - -$a \ \widehat{=} \ Azimut $ - -$h \ \widehat{=} \ Hoehe$ - - - -\newpage -\subsection{Zusammenhang des Nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} -\begin{figure}[h] +\begin{center} + \begin{tabular}{ c c c } + Winkel && Name / Beziehung \\ + \hline + $\alpha$ && Rektaszension \\ + $\delta$ && Deklination \\ + $\theta$ && Sternzeit von Greenwich\\ + $\phi$ && Geographische Breite\\ + $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ + $a$ && Azimut\\ + $h$ && Höhe + \end{tabular} +\end{center} + +\subsection{Zusammenhang des nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} +\begin{figure} \begin{center} - \includegraphics[height=5cm,width=5cm]{papers/nav/bilder/kugel3.png} + \includegraphics[height=5cm,width=8cm]{papers/nav/bilder/kugel3.png} \caption[Nautisches Dreieck]{Nautisches Dreieck} \end{center} \end{figure} -Wie man im oberen Bild sieht und auch am Anfang dieses Kapitels bereits erwähnt wurde, liegt das Nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. -Das selbe Dreieck kann man aber auch auf die Erdkugel projezieren und hat dann die Ecken Standort, Bildpunkt und Nordpol. +Wie man im oberen Bild sieht, liegt das nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. +Das selbe Dreieck kann man aber auch auf die Erdkugel projizieren und es hat dann die Ecken Standort, Bildpunkt und Nordpol. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. @@ -56,9 +48,9 @@ Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion Nautische Dreieck auf der Erdkugel zur Hilfe genommen. Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. -\begin{figure}[h] +\begin{figure} \begin{center} - \includegraphics[width=6cm]{papers/nav/bilder/dreieck.png} + \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} \end{center} \end{figure} @@ -66,75 +58,76 @@ Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann di -\subsection{Ecke P - Unser Standort} -Unser eigener Standort ist der gesuchte Punkt A. - -\subsection{Ecke A - Nordpol} -Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol (in der Himmelskugel der Himmelsnordpol) ist. +\subsection{Ecke $P$ und $A$} +Unser eigener Standort ist der gesuchte Ecke $P$ und die Ecke $A$ ist in unserem Fall der Nordpol. +Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. -\newpage -\subsection{Ecke B und C - Bildpunkt X und Y} + +\subsection{Ecke $B$ und $C$ - Bildpunkt X und Y} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. -\\ -Es gibt diverse Gestirne, die man nutzen kann. -\begin{itemize} - \item Sonne - \item Mond - \item Die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn -\end{itemize} +Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mond oder die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn. + +\subsection{Ephemeriden} +Zu all diesen Gestirnen gibt es Ephemeriden, die man auch Jahrbücher nennt. +In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. +Da diese Angaben in Stundenabständen gegeben sind, muss man für die minutengenaue Bestimmung zwischen den Stunden interpolieren. +Was diese Begriffe bedeuten, wird in den kommenden beiden Abschnitten erklärt. -Zu all diesen Gestirnen gibt es Ephemeriden (Jahrbücher). -Dort findet man unter Anderem die Rektaszension und Deklination, welche für jeden Tag und Stunde beschrieben ist. Für Minuten genaue Angaben muss man dann zwischen den Stunden interpolieren. -Mithilfe dieser beiden Angaben kann man die Längen- und Breitengrade diverser Gestirne berechnen. +\begin{figure} + \begin{center} + \includegraphics[width=18cm]{papers/nav/bilder/ephe.png} + \caption[Astrodienst - Ephemeriden Januar 2022]{Astrodienst - Ephemeriden Januar 2022} + \end{center} +\end{figure} + +\subsubsection{Deklination} +Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad. \subsubsection{Sternzeit und Rektaszension} -Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht. +Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht und geht vom Koordinatensystem der Himmelskugel aus. Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. Die Lösung ist die Sternzeit. +Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit $\theta = 0$. Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. -Für die Sternzeit von Greenwich braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. +Für die Sternzeit von Greenwich $\theta $braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. Im Anschluss berechnet man die Sternzeit von Greenwich -\\ -\\ -$T_{Greenwich} = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3$. -\\ -\\ -Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit bestimmen. -Dies gilt analog auch für das zweite Gestirn. -\subsubsection{Deklination} -Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad. +$\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3$. +Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit von Greenwich bestimmen. +Dies gilt analog auch für das zweite Gestirn. -\newpage \subsection{Bestimmung des eigenen Standortes P} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. -Somit können wir ein erstes Kugeldreieck auf der Erde aufspannen. - +Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. +Mithilfe dieser Dreiecken können wir die einfachen Sätze der sphärischen Trigonometrie anwenden und benötigen lediglich ein Ephemeride zu den Gestirnen und einen Sextant. -\begin{figure}[h] +\begin{figure} \begin{center} - \includegraphics[width=4.5cm]{papers/nav/bilder/dreieck.png} + \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} \end{center} \end{figure} -\subsubsection{Bestimmung des ersten Dreiecks} - -$A=$ Nordpol +\subsubsection{Dreieck $ABC$} -$B=$ Bildpunkt des Gestirns X +\begin{center} + \begin{tabular}{ c c c } + Ecke && Name \\ + \hline + $A$ && Nordpol \\ + $B$ && Bildpunkt des Gestirns $X$ \\ + $C$&& Bildpunkt des Gestirns $Y$ + \end{tabular} +\end{center} -$C=$ Bildpunkt des Gestirns Y -\\ -\\ Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. Die Seitenlänge der Seite "Nordpol zum Bildpunkt X" sei $c$. @@ -145,24 +138,24 @@ Dann ist $b = \frac{\pi}{2} - \delta_2$. Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. -\\ -\\ -mit - -$\delta_1 =$ Deklination Bildpunkt X -$\delta_2 =$ Deklination Bildpunk Y - -$\lambda_1 =$ Längengrad Bildpunkt X - -$\lambda_2 =$ Längengrad Bildpunkt Y +mit +\begin{center} + \begin{tabular}{ c c c } + Ecke && Name \\ + \hline + $\delta_1$ && Deklination Bildpunkt $X$ \\ + $\delta_2$ && Deklination Bildpunk $Y$ \\ + $\lambda_1 $&& Längengrad Bildpunkt $X$\\ + $\lambda_2$ && Längengrad Bildpunkt $Y$ + \end{tabular} +\end{center} Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! -\\ -\\ + Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. Mithilfe des Seiten-Kosinussatzes -$cos(a) = \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha)$ +$\cos(a) = \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. @@ -174,7 +167,7 @@ Somit ist $\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}] $. Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. -\subsubsection{Bestimmung des zweiten Dreiecks} +\subsubsection{Dreieck $BPC$} Wir bilden nun ein zweites Dreieck, welches die Ecken B und C des ersten Dreiecks besitzt. Die dritte Ecke ist der eigene Standort P. Unser Standort definiere sich aus einer geographischen Breite $\delta$ und einer geographischen Länge $\lambda$. @@ -183,24 +176,23 @@ Die Seite von P zu B sei $pb$ und die Seite von P zu C sei $pc$. Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache Formel bestimmen, nämlich $pb=\frac{\pi}{2} - h_{B}$ und $pc=\frac{\pi}{2} - h_{C}$ mit $h_B=$ Höhe von Gestirn in B und $h_C=$ Höhe von Gestirn in C mit Sextant gemessen. -\\ +Zum Schluss müssen wir noch den Winkel $\beta1$ mithilfe des Seiten-Kosinussatzes mit den bekannten Seiten $pc$, $pb$ und $a$ bestimmen. +\subsubsection{Dreieck $ABP$} Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$, den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes berechnen. -Für den Seiten-Kosinussatz benötigt es noch $\kappa$. -Da wir aber $pc$, $pb$ und $a$ kennen, kann man mit dem Seiten-Kosinussatz den Winkel $\beta1$ berechnen und anschliessend $\beta + \beta1 =\kappa$. +Für den Seiten-Kosinussatz benötigt es noch $\kappa=\beta + \beta1$. -Somit ist $cos(l) = \cos(c)\cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)$ +Somit ist $\cos(l) = \cos(c)\cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)$ und -$\delta =\cos^{-1} [\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)]$. -\\ +\[ +\delta =\cos^{-1} [\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)]. +\] Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. -\\ -Somit ist $\omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}]$ und unsere gesuchte geographische Länge schlussendlich -$\lambda=\lambda_1 - \omega$ mit $\lambda_1$=Längengrad Bildpunkt XXX. -\newpage -\listoffigures \ No newline at end of file +Somit ist \[ \omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}] \]und unsere gesuchte geographische Länge schlussendlich +\[\lambda=\lambda_1 - \omega\] +mit $\lambda_1$=Längengrad Bildpunkt XXX. diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index 23e3303..bb7f1e4 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -1,16 +1,19 @@ -\section{Warum sind die Sinus- und Kosinusfunktionen spezielle Funktionen?} -Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren sich mit Problemen der sphärischen Trigonometrie beschäftigt haben um den Lauf von Gestirnen (Himmelskörper) zu berechnen. -Jedoch konnten sie sie nicht lösen. -Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und wurde zu einer Hilfswissenschaft der Astronomen. -In Folge werden auch die ersten Sätze aufgestellt und wenige Jahrhunderte später wurden Berechnungen zu diesem Thema angestellt. +\section{Sphärische Navigation und Winkelfunktionen} +Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren sich mit Problemen der sphärischen Trigonometrie beschäftigt haben um den Lauf von Gestirnen zu berechnen. +Jedoch konnten sie dieses Problem nicht lösen. + +Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und sie wurde zu einer Hilfswissenschaft der Astronomen. +In Folge werden auch die ersten Sätze aufgestellt und wenige Jahrhunderte später wurden Berechnungen mithilfe des Sternkataloges von Hipparchos angestellt und darauffolgend Kartenmaterial erstellt. In dieser Zeit wurden auch die ersten Sternenkarten angefertigt, jedoch kannte man damals die Sinusfunktion noch nicht. Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. -Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um 900 den Sinussatz. -Zur Zeit der großen Entdeckungsreisen im 15. Jahrhundert wurden die Forschungen in sphärischer Trigonometrie wieder forciert. -Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet. -Im nächsten Jahrhundert folgte der Winkelkosinussatz. +Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. +Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung mit Sternen vermehrt an Wichtigkeit gewann. +Man nutzte für die Kartographie nun die Kugelgeometrie, um die Genauigkeit zu erhöhen. +Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet und im darauffolgenden Jahrhundert folgte der Winkelkosinussatz. + + Durch weitere mathematische Entwicklungen wie den Logarithmus wurden im Laufe des nächsten Jahrhunderts viele neue Methoden und kartographische Anwendungen der Kugelgeometrie entdeckt. Im 19. und 20. Jahrhundert wurden weitere nicht-euklidische Geometrien entwickelt und die sphärische Trigonometrie fand auch ihre Anwendung in der Relativitätstheorie. \ No newline at end of file diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index 8b4634f..cf2f242 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,18 +1,38 @@ -\setlength{\parindent}{0em} + \section{Sphärische Trigonometrie} +In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. +Dabei gibt es folgenden Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie: +\begin{center} + + +\begin{tabular}{ccc} + Eben & $\leftrightarrow$ & sphärisch \\ + \hline + $a$ & $\leftrightarrow$ & $\sin \ a$ \\ + + $a^2$ & $\leftrightarrow$ & $-\cos \ a$ \\ +\end{tabular} +\end{center} + \subsection{Das Kugeldreieck} -Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck ABC. -A, B und C sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck $ABC$. +Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. +$A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. +Ein Grosskreis ist ein größtmöglicher Kreis auf einer Kugeloberfläche. +Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Schnitt auf dem Großkreis teilt die Kugel in jedem Fall in zwei gleich grosse Hälften. + +Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. -Laut dieser Definition ist die Seite c der Winkel AMB. -Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. +Laut dieser Definition ist die Seite $c$ der Winkel $AMB$. + Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. -\begin{figure}[h] + +\begin{figure} \begin{center} - %\includegraphics[width=6cm]{papers/nav/bilder/kugel1.png} + \includegraphics[width=6cm]{papers/nav/bilder/kugel1.png} \caption[Das Kugeldreieck]{Das Kugeldreieck} \end{center} @@ -21,12 +41,12 @@ Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha \subsection{Rechtwinkliges Dreieck und Rechtseitiges Dreieck} Wie auch im uns bekannten Dreieck gibt es beim Kugeldreieck auch ein Rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. -\newpage -\subsection{Winkelangabe} -\begin{figure}[h] + +\subsection{Winkelsumme} +\begin{figure} \begin{center} - %\includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} + \includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} \caption[Winkelangabe im Kugeldreieck]{Winkelangabe im Kugeldreieck} \end{center} \end{figure} @@ -37,13 +57,15 @@ Für die Summe der Innenwinkel gilt \begin{align} \alpha+\beta+\gamma &= \frac{A}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi. \nonumber \end{align} - +\subsubsection{Sphärischer Exzess} Der sphärische Exzess \begin{align} \epsilon = \alpha+\beta+\gamma - \pi \nonumber \end{align} beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. +\subsubsection{Flächeninnhalt} +Der Flächeninhalt $A$ lässt sich aus den Winkeln $\alpha,\ \beta, \ \gamma$ und dem Kugelradius $r$ berechnen. \subsection{Sphärischer Sinussatz} In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. @@ -53,7 +75,16 @@ Das bedeutet, dass \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \ \text{auch beim Kugeldreieck gilt.} \end{align} +\subsection{Sphärischer Kosinussätze} +Auch in der sphärischen Trigonometrie gibt es den Seitenkosinussatz +\begin{align} + cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber +\end{align} %Seitenkosinussatz +und den Winkelkosinussatz +\begin{align} + \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c \nonumber +\end{align} \subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. @@ -62,6 +93,6 @@ In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Se Es gilt nämlich: \begin{align} \cos c = \cos a \cdot \cos b \ \text{wenn} \nonumber & - \alpha = \frac{\pi}{2} \lor \beta =\frac{\pi}{2} \lor \gamma = \frac{\pi}{2}.\nonumber + \alpha = \frac{\pi}{2} \nonumber \end{align} \ No newline at end of file -- cgit v1.2.1 From b3283eb05091a88841668c39d422da53d66e1cdd Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Thu, 19 May 2022 14:51:50 +0200 Subject: update korrektur --- buch/papers/nav/main.tex | 5 ++--- buch/papers/nav/nautischesdreieck.tex | 4 ++-- 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index de8d1d6..47764e8 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -6,14 +6,13 @@ \chapter{Spährische Navigation\label{chapter:nav}} \lhead{Sphärische Navigation} \begin{refsection} -\chapterauthor{Enez Erdem, Marc Kühne} +\chapterauthor{Enez Erdem und Marc Kühne} \input{papers/nav/einleitung.tex} -\input{papers/nav/sincos.tex} -\input{papers/nav/geschichte.tex} \input{papers/nav/flatearth.tex} +\input{papers/nav/sincos.tex} \input{papers/nav/trigo.tex} \input{papers/nav/nautischesdreieck.tex} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index a85b119..0a498f0 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -1,6 +1,6 @@ \section{Das Nautische Dreieck} \subsection{Definition des Nautischen Dreiecks} -Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel}. +Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel. Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient. Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. @@ -195,4 +195,4 @@ Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Wink Somit ist \[ \omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}] \]und unsere gesuchte geographische Länge schlussendlich \[\lambda=\lambda_1 - \omega\] -mit $\lambda_1$=Längengrad Bildpunkt XXX. +mit $\lambda_1$=Längengrad Bildpunkt $X -- cgit v1.2.1 From 56cc6c1fbae271c16c78935384b52e047cdd6f27 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 19 May 2022 16:11:27 +0200 Subject: Error correction & add gamma integrand plot --- buch/papers/laguerre/eigenschaften.tex | 11 ++++++++-- buch/papers/laguerre/gamma.tex | 4 ++-- buch/papers/laguerre/quadratur.tex | 6 +++--- buch/papers/laguerre/scripts/integrand.py | 34 +++++++++++++++++++++++++++++++ 4 files changed, 48 insertions(+), 7 deletions(-) create mode 100644 buch/papers/laguerre/scripts/integrand.py diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index b0cc3a3..93d19a3 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -25,13 +25,20 @@ Sturm\--Liouville\--Problem umwandeln können, haben wir bewiesen, dass es sich bei den Laguerre\--Polynomen um orthogonale Polynome handelt (siehe Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem}). -Der Sturm-Liouville-Operator hat die Form +Der Sturm-Liouville-Operator \begin{align} S = \frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right). \label{laguerre:slop} \end{align} +und der Laguerre-Operator +\begin{align} +\Lambda += +x \frac{d}{dx^2} + (\nu + 1 -x) \frac{d}{dx} +\end{align} +sind einander gleichzusetzen. Aus der Beziehung \begin{align} S @@ -56,7 +63,7 @@ Durch Separation erhalten wir dann \begin{align*} \int \frac{dp}{p} & = --\int \frac{\nu + 1 - x}{x}dx +-\int \frac{\nu + 1 - x}{x} \, dx \\ \log p & = diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index e3838b0..b15523b 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -30,12 +30,12 @@ welches alle Eigenschaften erfüllt, um mit der Gauss-Laguerre-Quadratur berechnet zu werden. \subsubsection{Funktionalgleichung} -Die Funktionalgleichung besagt +Die Funktionalgleichung der Gamma-Funktion besagt \begin{align} z \Gamma(z) = \Gamma(z+1). \label{laguerre:gamma_funktional} \end{align} -Mittels dieser Gleichung kann der Wert an einer bestimmten, +Mittels dieser Gleichung kann der Wert von $\Gamma(z)$ an einer bestimmten, geeigneten Stelle evaluiert werden und dann zurückverschoben werden, um das gewünschte Resultat zu erhalten. diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 60fad7f..be69dee 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -7,7 +7,7 @@ \label{laguerre:section:quadratur}} {\large \color{red} TODO: Einleitung und kurze Beschreibung Gauss-Quadratur} \begin{align} -\int_a^b f(x) w(x) +\int_a^b f(x) w(x) \, dx \approx \sum_{i=1}^N f(x_i) A_i \label{laguerre:gaussquadratur} @@ -33,7 +33,7 @@ Gleichung~\eqref{laguerre:laguerrequadratur} lässt sich wiefolgt umformulieren: Nach der Definition der Gauss-Quadratur müssen als Stützstellen die Nullstellen des verwendeten Polynoms genommen werden. Das heisst für das Laguerre-Polynom $L_n$ müssen dessen Nullstellen $x_i$ und -als Gewichte $A_i$ werden die Integrale $l_i(x)e^{-x}$ verwendet werden. +als Gewichte $A_i$ die Integrale $l_i(x)e^{-x}$ verwendet werden. Dabei sind \begin{align*} l_i(x_j) @@ -57,7 +57,7 @@ A_i \subsubsection{Fehlerterm} Der Fehlerterm $R_n$ folgt direkt aus der Approximation \begin{align*} -\int_0^{\infty} f(x) e^{-x} dx +\int_0^{\infty} f(x) e^{-x} \, dx = \sum_{i=1}^n f(x_i) A_i + R_n \end{align*} diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py new file mode 100644 index 0000000..89b9256 --- /dev/null +++ b/buch/papers/laguerre/scripts/integrand.py @@ -0,0 +1,34 @@ +#!/usr/bin/env python3 +# -*- coding:utf-8 -*- +"""Plot for integrand of gamma function with shifting terms.""" + +import os +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np + +EPSILON = 1e-12 +xlims = np.array([-3, 3]) + +root = str(Path(__file__).parent) +img_path = f"{root}/../images" +os.makedirs(img_path, exist_ok=True) + +t = np.logspace(*xlims, 1001)[:, None] +z = np.arange(-5, 5)[None] + 0.5 + + +r = t ** z + +fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) +ax.semilogx(t, r) +ax.set_xlim(*(10.**xlims)) +ax.set_ylim(1e-3, 40) +ax.set_xlabel(r"$t$") +ax.set_ylabel(r"$t^z$") +ax.grid(1, "both") +labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z)] +ax.legend(labels, ncol=2, loc="upper left") +fig.savefig(f"{img_path}/integrands.pdf") +# plt.show() -- cgit v1.2.1 From 32f1a1d818f0fe28b2ae97071e31a773ee2d028a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 19 May 2022 17:28:33 +0200 Subject: some local changes --- buch/papers/fresnel/Makefile | 14 -- buch/papers/fresnel/eulerspirale.m | 61 --------- buch/papers/fresnel/eulerspirale.pdf | Bin 22592 -> 0 bytes buch/papers/fresnel/eulerspirale.tex | 41 ------ buch/papers/fresnel/fresnelgraph.pdf | Bin 30018 -> 0 bytes buch/papers/fresnel/fresnelgraph.tex | 46 ------- buch/papers/fresnel/images/Makefile | 38 ++++++ buch/papers/fresnel/images/apfel.jpg | Bin 0 -> 139884 bytes buch/papers/fresnel/images/apfel.pdf | Bin 0 -> 157895 bytes buch/papers/fresnel/images/apfel.tex | 49 +++++++ buch/papers/fresnel/images/eulerspirale.m | 61 +++++++++ buch/papers/fresnel/images/eulerspirale.pdf | Bin 0 -> 22592 bytes buch/papers/fresnel/images/eulerspirale.tex | 41 ++++++ buch/papers/fresnel/images/fresnelgraph.pdf | Bin 0 -> 30018 bytes buch/papers/fresnel/images/fresnelgraph.tex | 46 +++++++ buch/papers/fresnel/images/kruemmung.pdf | Bin 0 -> 10179 bytes buch/papers/fresnel/images/kruemmung.tex | 51 ++++++++ buch/papers/fresnel/images/pfad.pdf | Bin 0 -> 19264 bytes buch/papers/fresnel/images/pfad.tex | 37 ++++++ buch/papers/fresnel/images/schale.pdf | Bin 0 -> 352570 bytes buch/papers/fresnel/images/schale.pov | 191 ++++++++++++++++++++++++++++ buch/papers/fresnel/images/schale.tex | 77 +++++++++++ buch/papers/fresnel/main.tex | 5 + buch/papers/fresnel/pfad.pdf | Bin 19126 -> 0 bytes buch/papers/fresnel/pfad.tex | 34 ----- buch/papers/fresnel/references.bib | 6 + buch/papers/fresnel/teil0.tex | 6 +- buch/papers/fresnel/teil1.tex | 11 +- buch/papers/fresnel/teil2.tex | 161 ++++++++++++++++++++++- buch/papers/fresnel/teil3.tex | 4 +- 30 files changed, 772 insertions(+), 208 deletions(-) delete mode 100644 buch/papers/fresnel/eulerspirale.m delete mode 100644 buch/papers/fresnel/eulerspirale.pdf delete mode 100644 buch/papers/fresnel/eulerspirale.tex delete mode 100644 buch/papers/fresnel/fresnelgraph.pdf delete mode 100644 buch/papers/fresnel/fresnelgraph.tex create mode 100644 buch/papers/fresnel/images/Makefile create mode 100644 buch/papers/fresnel/images/apfel.jpg create mode 100644 buch/papers/fresnel/images/apfel.pdf create mode 100644 buch/papers/fresnel/images/apfel.tex create mode 100644 buch/papers/fresnel/images/eulerspirale.m create mode 100644 buch/papers/fresnel/images/eulerspirale.pdf create mode 100644 buch/papers/fresnel/images/eulerspirale.tex create mode 100644 buch/papers/fresnel/images/fresnelgraph.pdf create mode 100644 buch/papers/fresnel/images/fresnelgraph.tex create mode 100644 buch/papers/fresnel/images/kruemmung.pdf create mode 100644 buch/papers/fresnel/images/kruemmung.tex create mode 100644 buch/papers/fresnel/images/pfad.pdf create mode 100644 buch/papers/fresnel/images/pfad.tex create mode 100644 buch/papers/fresnel/images/schale.pdf create mode 100644 buch/papers/fresnel/images/schale.pov create mode 100644 buch/papers/fresnel/images/schale.tex delete mode 100644 buch/papers/fresnel/pfad.pdf delete mode 100644 buch/papers/fresnel/pfad.tex diff --git a/buch/papers/fresnel/Makefile b/buch/papers/fresnel/Makefile index 11af3a7..ed74861 100644 --- a/buch/papers/fresnel/Makefile +++ b/buch/papers/fresnel/Makefile @@ -3,20 +3,6 @@ # # (c) 2022 Prof Dr Andreas Mueller # -all: fresnelgraph.pdf eulerspirale.pdf pfad.pdf - images: @echo "no images to be created in fresnel" -eulerpath.tex: eulerspirale.m - octave eulerspirale.m - -fresnelgraph.pdf: fresnelgraph.tex eulerpath.tex - pdflatex fresnelgraph.tex - -eulerspirale.pdf: eulerspirale.tex eulerpath.tex - pdflatex eulerspirale.tex - -pfad.pdf: pfad.tex - pdflatex pfad.tex - diff --git a/buch/papers/fresnel/eulerspirale.m b/buch/papers/fresnel/eulerspirale.m deleted file mode 100644 index 84e3696..0000000 --- a/buch/papers/fresnel/eulerspirale.m +++ /dev/null @@ -1,61 +0,0 @@ -# -# eulerspirale.m -# -# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue -# -global n; -n = 1000; -global tmax; -tmax = 10; -global N; -N = round(n*5/tmax); - -function retval = f(x, t) - x = pi * t^2 / 2; - retval = [ cos(x); sin(x) ]; -endfunction - -x0 = [ 0; 0 ]; -t = tmax * (0:n) / n; - -c = lsode(@f, x0, t); - -fn = fopen("eulerpath.tex", "w"); - -fprintf(fn, "\\def\\fresnela{ (0,0)"); -for i = (2:n) - fprintf(fn, "\n\t-- (%.4f,%.4f)", c(i,1), c(i,2)); -end -fprintf(fn, "\n}\n\n"); - -fprintf(fn, "\\def\\fresnelb{ (0,0)"); -for i = (2:n) - fprintf(fn, "\n\t-- (%.4f,%.4f)", -c(i,1), -c(i,2)); -end -fprintf(fn, "\n}\n\n"); - -fprintf(fn, "\\def\\Cplotright{ (0,0)"); -for i = (2:N) - fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,1)); -end -fprintf(fn, "\n}\n\n"); - -fprintf(fn, "\\def\\Cplotleft{ (0,0)"); -for i = (2:N) - fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,1)); -end -fprintf(fn, "\n}\n\n"); - -fprintf(fn, "\\def\\Splotright{ (0,0)"); -for i = (2:N) - fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,2)); -end -fprintf(fn, "\n}\n\n"); - -fprintf(fn, "\\def\\Splotleft{ (0,0)"); -for i = (2:N) - fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,2)); -end -fprintf(fn, "\n}\n\n"); - -fclose(fn); diff --git a/buch/papers/fresnel/eulerspirale.pdf b/buch/papers/fresnel/eulerspirale.pdf deleted file mode 100644 index 4a85a50..0000000 Binary files a/buch/papers/fresnel/eulerspirale.pdf and /dev/null differ diff --git a/buch/papers/fresnel/eulerspirale.tex b/buch/papers/fresnel/eulerspirale.tex deleted file mode 100644 index 38ef756..0000000 --- a/buch/papers/fresnel/eulerspirale.tex +++ /dev/null @@ -1,41 +0,0 @@ -% -% eulerspirale.tex -- Darstellung der Eulerspirale -% -% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -% -\documentclass[tikz]{standalone} -\usepackage{amsmath} -\usepackage{times} -\usepackage{txfonts} -\usepackage{pgfplots} -\usepackage{csvsimple} -\usetikzlibrary{arrows,intersections,math} -\begin{document} -\def\skala{1} -\definecolor{darkgreen}{rgb}{0,0.6,0} -\begin{tikzpicture}[>=latex,thick,scale=\skala] - -\input{eulerpath.tex} - -\def\s{8} - -\begin{scope}[scale=\s] -\draw[color=blue] (-0.5,-0.5) rectangle (0.5,0.5); -\draw[color=darkgreen,line width=1.4pt] \fresnela; -\draw[color=darkgreen,line width=1.4pt] \fresnelb; -\fill[color=blue] (0.5,0.5) circle[radius={0.1/\s}]; -\fill[color=blue] (-0.5,-0.5) circle[radius={0.1/\s}]; -\draw (-0.5,{-0.05/\s}) -- (-0.5,{0.05/\s}); -\draw (0.5,{-0.05/\s}) -- (0.5,{-0.05/\s}); -\node at (-0.5,0) [above left] {$\frac12$}; -\node at (0.5,0) [below right] {$\frac12$}; -\node at (0,-0.5) [below right] {$\frac12$}; -\node at (0,0.5) [above left] {$\frac12$}; -\end{scope} - -\draw[->] (-6.7,0) -- (6.9,0) coordinate[label={$C(x)$}];; -\draw[->] (0,-5.8) -- (0,6.1) coordinate[label={left:$S(x)$}];; - -\end{tikzpicture} -\end{document} - diff --git a/buch/papers/fresnel/fresnelgraph.pdf b/buch/papers/fresnel/fresnelgraph.pdf deleted file mode 100644 index 9ccad56..0000000 Binary files a/buch/papers/fresnel/fresnelgraph.pdf and /dev/null differ diff --git a/buch/papers/fresnel/fresnelgraph.tex b/buch/papers/fresnel/fresnelgraph.tex deleted file mode 100644 index 20df951..0000000 --- a/buch/papers/fresnel/fresnelgraph.tex +++ /dev/null @@ -1,46 +0,0 @@ -% -% fresnelgraph.tex -- Graphs of the fresnel functions -% -% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -% -\documentclass[tikz]{standalone} -\usepackage{amsmath} -\usepackage{times} -\usepackage{txfonts} -\usepackage{pgfplots} -\usepackage{csvsimple} -\usetikzlibrary{arrows,intersections,math} -\begin{document} -\def\skala{1} -\begin{tikzpicture}[>=latex,thick,scale=\skala] - -\input{eulerpath.tex} -\def\dx{1.3} -\def\dy{2.6} - -\draw[color=gray] (0,{0.5*\dy}) -- ({5*\dx},{0.5*\dy}); -\draw[color=gray] (0,{-0.5*\dy}) -- ({-5*\dx},{-0.5*\dy}); - -\draw[color=blue,line width=1.4pt] \Splotright; -\draw[color=blue,line width=1.4pt] \Splotleft; - -\draw[color=red,line width=1.4pt] \Cplotright; -\draw[color=red,line width=1.4pt] \Cplotleft; - -\draw[->] (-6.7,0) -- (6.9,0) coordinate[label={$x$}]; -\draw[->] (0,-2.3) -- (0,2.3) coordinate[label={$y$}]; - -\foreach \x in {1,2,3,4,5}{ - \draw ({\x*\dx},-0.05) -- ({\x*\dx},0.05); - \draw ({-\x*\dx},-0.05) -- ({-\x*\dx},0.05); - \node at ({\x*\dx},-0.05) [below] {$\x$}; - \node at ({-\x*\dx},0.05) [above] {$-\x$}; -} -\draw (-0.05,{0.5*\dy}) -- (0.05,{0.5*\dy}); -\node at (-0.05,{0.5*\dy}) [left] {$\frac12$}; -\draw (-0.05,{-0.5*\dy}) -- (0.05,{-0.5*\dy}); -\node at (0.05,{-0.5*\dy}) [right] {$-\frac12$}; - -\end{tikzpicture} -\end{document} - diff --git a/buch/papers/fresnel/images/Makefile b/buch/papers/fresnel/images/Makefile new file mode 100644 index 0000000..eb7dc57 --- /dev/null +++ b/buch/papers/fresnel/images/Makefile @@ -0,0 +1,38 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +all: schale.pdf \ + fresnelgraph.pdf \ + eulerspirale.pdf \ + pfad.pdf \ + apfel.pdf \ + kruemmung.pdf + +schale.png: schale.pov + povray +A0.1 -W1920 -H1080 -Oschale.png schale.pov + +schale.jpg: schale.png Makefile + convert -extract 1240x1080+340 schale.png -density 300 -units PixelsPerInch schale.jpg + +schale.pdf: schale.tex schale.jpg + pdflatex schale.tex + +eulerpath.tex: eulerspirale.m + octave eulerspirale.m + +fresnelgraph.pdf: fresnelgraph.tex eulerpath.tex + pdflatex fresnelgraph.tex + +eulerspirale.pdf: eulerspirale.tex eulerpath.tex + pdflatex eulerspirale.tex + +pfad.pdf: pfad.tex + pdflatex pfad.tex + +apfel.pdf: apfel.tex apfel.jpg eulerpath.tex + pdflatex apfel.tex + +kruemmung.pdf: kruemmung.tex + pdflatex kruemmung.tex diff --git a/buch/papers/fresnel/images/apfel.jpg b/buch/papers/fresnel/images/apfel.jpg new file mode 100644 index 0000000..76e48e7 Binary files /dev/null and b/buch/papers/fresnel/images/apfel.jpg differ diff --git a/buch/papers/fresnel/images/apfel.pdf b/buch/papers/fresnel/images/apfel.pdf new file mode 100644 index 0000000..69e5092 Binary files /dev/null and b/buch/papers/fresnel/images/apfel.pdf differ diff --git a/buch/papers/fresnel/images/apfel.tex b/buch/papers/fresnel/images/apfel.tex new file mode 100644 index 0000000..754886b --- /dev/null +++ b/buch/papers/fresnel/images/apfel.tex @@ -0,0 +1,49 @@ +% +% apfel.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{7} +\def\hoehe{4} + +\input{eulerpath.tex} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\begin{scope} +\clip(-0.6,-0.6) rectangle (7,6); +\node at (3.1,2.2) [rotate=-3] {\includegraphics[width=9.4cm]{apfel.jpg}}; +\end{scope} + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\draw[color=gray!50] (0,0) rectangle (4,4); +\draw[->] (-0.5,0) -- (7.5,0) coordinate[label={$C(t)$}]; +\draw[->] (0,-0.5) -- (0,6.0) coordinate[label={left:$S(t)$}]; +\begin{scope}[scale=8] +\draw[color=red,opacity=0.5,line width=1.4pt] \fresnela; +\end{scope} + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/fresnel/images/eulerspirale.m b/buch/papers/fresnel/images/eulerspirale.m new file mode 100644 index 0000000..84e3696 --- /dev/null +++ b/buch/papers/fresnel/images/eulerspirale.m @@ -0,0 +1,61 @@ +# +# eulerspirale.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +# +global n; +n = 1000; +global tmax; +tmax = 10; +global N; +N = round(n*5/tmax); + +function retval = f(x, t) + x = pi * t^2 / 2; + retval = [ cos(x); sin(x) ]; +endfunction + +x0 = [ 0; 0 ]; +t = tmax * (0:n) / n; + +c = lsode(@f, x0, t); + +fn = fopen("eulerpath.tex", "w"); + +fprintf(fn, "\\def\\fresnela{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", c(i,1), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\fresnelb{ (0,0)"); +for i = (2:n) + fprintf(fn, "\n\t-- (%.4f,%.4f)", -c(i,1), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Cplotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,1)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotright{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", t(i), c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fprintf(fn, "\\def\\Splotleft{ (0,0)"); +for i = (2:N) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", -t(i), -c(i,2)); +end +fprintf(fn, "\n}\n\n"); + +fclose(fn); diff --git a/buch/papers/fresnel/images/eulerspirale.pdf b/buch/papers/fresnel/images/eulerspirale.pdf new file mode 100644 index 0000000..db74e4b Binary files /dev/null and b/buch/papers/fresnel/images/eulerspirale.pdf differ diff --git a/buch/papers/fresnel/images/eulerspirale.tex b/buch/papers/fresnel/images/eulerspirale.tex new file mode 100644 index 0000000..38ef756 --- /dev/null +++ b/buch/papers/fresnel/images/eulerspirale.tex @@ -0,0 +1,41 @@ +% +% eulerspirale.tex -- Darstellung der Eulerspirale +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{eulerpath.tex} + +\def\s{8} + +\begin{scope}[scale=\s] +\draw[color=blue] (-0.5,-0.5) rectangle (0.5,0.5); +\draw[color=darkgreen,line width=1.4pt] \fresnela; +\draw[color=darkgreen,line width=1.4pt] \fresnelb; +\fill[color=blue] (0.5,0.5) circle[radius={0.1/\s}]; +\fill[color=blue] (-0.5,-0.5) circle[radius={0.1/\s}]; +\draw (-0.5,{-0.05/\s}) -- (-0.5,{0.05/\s}); +\draw (0.5,{-0.05/\s}) -- (0.5,{-0.05/\s}); +\node at (-0.5,0) [above left] {$\frac12$}; +\node at (0.5,0) [below right] {$\frac12$}; +\node at (0,-0.5) [below right] {$\frac12$}; +\node at (0,0.5) [above left] {$\frac12$}; +\end{scope} + +\draw[->] (-6.7,0) -- (6.9,0) coordinate[label={$C(x)$}];; +\draw[->] (0,-5.8) -- (0,6.1) coordinate[label={left:$S(x)$}];; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/images/fresnelgraph.pdf b/buch/papers/fresnel/images/fresnelgraph.pdf new file mode 100644 index 0000000..c658901 Binary files /dev/null and b/buch/papers/fresnel/images/fresnelgraph.pdf differ diff --git a/buch/papers/fresnel/images/fresnelgraph.tex b/buch/papers/fresnel/images/fresnelgraph.tex new file mode 100644 index 0000000..20df951 --- /dev/null +++ b/buch/papers/fresnel/images/fresnelgraph.tex @@ -0,0 +1,46 @@ +% +% fresnelgraph.tex -- Graphs of the fresnel functions +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\input{eulerpath.tex} +\def\dx{1.3} +\def\dy{2.6} + +\draw[color=gray] (0,{0.5*\dy}) -- ({5*\dx},{0.5*\dy}); +\draw[color=gray] (0,{-0.5*\dy}) -- ({-5*\dx},{-0.5*\dy}); + +\draw[color=blue,line width=1.4pt] \Splotright; +\draw[color=blue,line width=1.4pt] \Splotleft; + +\draw[color=red,line width=1.4pt] \Cplotright; +\draw[color=red,line width=1.4pt] \Cplotleft; + +\draw[->] (-6.7,0) -- (6.9,0) coordinate[label={$x$}]; +\draw[->] (0,-2.3) -- (0,2.3) coordinate[label={$y$}]; + +\foreach \x in {1,2,3,4,5}{ + \draw ({\x*\dx},-0.05) -- ({\x*\dx},0.05); + \draw ({-\x*\dx},-0.05) -- ({-\x*\dx},0.05); + \node at ({\x*\dx},-0.05) [below] {$\x$}; + \node at ({-\x*\dx},0.05) [above] {$-\x$}; +} +\draw (-0.05,{0.5*\dy}) -- (0.05,{0.5*\dy}); +\node at (-0.05,{0.5*\dy}) [left] {$\frac12$}; +\draw (-0.05,{-0.5*\dy}) -- (0.05,{-0.5*\dy}); +\node at (0.05,{-0.5*\dy}) [right] {$-\frac12$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/images/kruemmung.pdf b/buch/papers/fresnel/images/kruemmung.pdf new file mode 100644 index 0000000..1180116 Binary files /dev/null and b/buch/papers/fresnel/images/kruemmung.pdf differ diff --git a/buch/papers/fresnel/images/kruemmung.tex b/buch/papers/fresnel/images/kruemmung.tex new file mode 100644 index 0000000..af0a1a9 --- /dev/null +++ b/buch/papers/fresnel/images/kruemmung.tex @@ -0,0 +1,51 @@ +% +% kruemmung.tex -- Krümmung einer ebenen Kurve +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\begin{scope} +\clip (-1,-1) rectangle (4,4); + +\def\r{3} +\def\winkel{30} + +\fill[color=blue!20] (0,0) -- (0:{0.6*\r}) arc (0:\winkel:{0.6*\r}) -- cycle; +\fill[color=blue!20] (\winkel:\r) + -- ($(\winkel:\r)+(0,{0.6*\r})$) arc (90:{90+\winkel}:{0.6*\r}) -- cycle; +\node[color=blue] at ({0.5*\winkel}:{0.45*\r}) {$\Delta\varphi$}; + +\node[color=blue] at ($(\winkel:\r)+({90+0.5*\winkel}:{0.45*\r})$) + {$\Delta\varphi$}; + +\draw[line width=0.3pt] (0,0) circle[radius=\r]; + +\draw[->] (0,0) -- (0:\r); +\draw[->] (0,0) -- (\winkel:\r); + +\draw[->] (0:\r) -- ($(0:\r)+(90:0.7*\r)$); +\draw[->] (\winkel:\r) -- ($(\winkel:\r)+({90+\winkel}:0.7*\r)$); +\draw[->,color=gray] (\winkel:\r) -- ($(\winkel:\r)+(0,0.7*\r)$); + +\draw[color=red,line width=1.4pt] (0:\r) arc (0:\winkel:\r); +\node[color=red] at ({0.5*\winkel}:\r) [left] {$\Delta s$}; +\fill[color=red] (0:\r) circle[radius=0.05]; +\fill[color=red] (\winkel:\r) circle[radius=0.05]; + +\node at (\winkel:{0.5*\r}) [above] {$r$}; +\node at (0:{0.5*\r}) [below] {$r$}; +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/images/pfad.pdf b/buch/papers/fresnel/images/pfad.pdf new file mode 100644 index 0000000..df3c7af Binary files /dev/null and b/buch/papers/fresnel/images/pfad.pdf differ diff --git a/buch/papers/fresnel/images/pfad.tex b/buch/papers/fresnel/images/pfad.tex new file mode 100644 index 0000000..680cd78 --- /dev/null +++ b/buch/papers/fresnel/images/pfad.tex @@ -0,0 +1,37 @@ +% +% pfad.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\fill[color=gray!40] (0,0) -- (2,0) arc (0:45:2) -- cycle; +\node at (22.5:1.4) {$\displaystyle\frac{\pi}4$}; + +\draw[->] (-1,0) -- (9,0) coordinate[label={$\operatorname{Re}$}]; +\draw[->] (0,-1) -- (0,6) coordinate[label={left:$\operatorname{Im}$}]; + +\draw[->,color=red,line width=1.4pt] (0,0) -- (7,0); +\draw[->,color=blue,line width=1.4pt] (7,0) arc (0:45:7); +\draw[->,color=darkgreen,line width=1.4pt] (45:7) -- (0,0); + +\node[color=red] at (3.5,0) [below] {$\gamma_1(t) = tR$}; +\node[color=blue] at (25:7) [right] {$\gamma_2(t) = Re^{it}$}; +\node[color=darkgreen] at (45:3.5) [above left] {$\gamma_3(t) = te^{i\pi/4}$}; + +\node at (7,0) [below] {$R$}; +\node at (45:7) [above] {$Re^{i\pi/4}$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/fresnel/images/schale.pdf b/buch/papers/fresnel/images/schale.pdf new file mode 100644 index 0000000..9c21951 Binary files /dev/null and b/buch/papers/fresnel/images/schale.pdf differ diff --git a/buch/papers/fresnel/images/schale.pov b/buch/papers/fresnel/images/schale.pov new file mode 100644 index 0000000..085a6a4 --- /dev/null +++ b/buch/papers/fresnel/images/schale.pov @@ -0,0 +1,191 @@ +// +// schale.pov -- +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +#declare O = <0,0,0>; + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.036; + +camera { + location <40, 20, -20> + look_at <0, 0.5, 0> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <10, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +sphere { + <0, 0, 0>, 1 + pigment { + color rgb<0.8,0.8,0.8> + } + finish { + specular 0.95 + metallic + } +} + +#declare stripcolor = rgb<0.2,0.2,0.8>; + +#declare R = 1.002; + +#macro punkt(phi,theta) +R * < cos(phi) * cos(theta), sin(theta), sin(phi) * cos(theta) > +#end + +#declare N = 24; +#declare thetaphi = 0.01; +#declare thetawidth = pi * 0.008; +#declare theta = function(phi) { phi * thetaphi } + +#declare axisdiameter = 0.007; + +cylinder { + < 0, -2, 0>, < 0, 2, 0>, axisdiameter + pigment { + color White + } + finish { + specular 0.95 + metallic + } +} + +#declare curvaturecircle = 0.008; +#declare curvaturecirclecolor = rgb<0.4,0.8,0.4>; + +#declare phit = 12.8 * 2 * pi; +#declare P = punkt(phit, theta(phit)); +#declare Q = <0, R / sin(theta(phit)), 0>; + +#declare e1 = vnormalize(P - Q) / tan(theta(phit)); +#declare e2 = vnormalize(vcross(e1, <0,1,0>)) / tan(theta(phit)); +#declare psimin = -0.1 * pi; +#declare psimax = 0.1 * pi; +#declare psistep = (psimax - psimin) / 30; + +union { + #declare psi = psimin; + #declare K = Q + cos(psi) * e1 + sin(psi) * e2; + #while (psi < psimax - psistep/2) + sphere { K, curvaturecircle } + #declare psi = psi + psistep; + #declare K2 = Q + cos(psi) * e1 + sin(psi) * e2; + cylinder { K, K2, curvaturecircle } + #declare K = K2; + #end + sphere { K, curvaturecircle } + pigment { + color curvaturecirclecolor + } + finish { + specular 0.95 + metallic + } +} + +object { + mesh { + #declare psi = psimin; + #declare K = Q + cos(psi) * e1 + sin(psi) * e2; + #while (psi < psimax - psistep/2) + #declare psi = psi + psistep; + #declare K2 = Q + cos(psi) * e1 + sin(psi) * e2; + triangle { K, K2, Q } + #declare K = K2; + #end + } + pigment { + color rgbt<0.4,0.8,0.4,0.5> + } + finish { + specular 0.95 + metallic + } +} + +union { + sphere { P, 0.02 } + sphere { Q, 0.02 } + cylinder { P, Q, 0.01 } + pigment { + color Red + } + finish { + specular 0.95 + metallic + } +} + +#declare phisteps = 300; +#declare phistep = 2 * pi / phisteps; +#declare phimin = 0; +#declare phimax = N * 2 * pi; + +object { + mesh { + #declare phi = phimin; + #declare Poben = punkt(phi, theta(phi) + thetawidth); + #declare Punten = punkt(phi, theta(phi) - thetawidth); + triangle { O, Punten, Poben } + #while (phi < phimax - phistep/2) + #declare phi = phi + phistep; + #declare Poben2 = punkt(phi, theta(phi) + thetawidth); + #declare Punten2 = punkt(phi, theta(phi) - thetawidth); + triangle { O, Punten, Punten2 } + triangle { O, Poben, Poben2 } + triangle { Punten, Punten2, Poben } + triangle { Punten2, Poben2, Poben } + #declare Poben = Poben2; + #declare Punten = Punten2; + #end + triangle { O, Punten, Poben } + } + pigment { + color stripcolor + } + finish { + specular 0.8 + metallic + } +} + +union { + #declare phi = phimin; + #declare P = punkt(phi, theta(phi)); + #while (phi < phimax - phistep/2) + sphere { P, 0.003 } + #declare phi = phi + phistep; + #declare P2 = punkt(phi, theta(phi)); + cylinder { P, P2, 0.003 } + #declare P = P2; + #end + sphere { P, 0.003 } + pigment { + color stripcolor + } + finish { + specular 0.8 + metallic + } +} diff --git a/buch/papers/fresnel/images/schale.tex b/buch/papers/fresnel/images/schale.tex new file mode 100644 index 0000000..577ede4 --- /dev/null +++ b/buch/papers/fresnel/images/schale.tex @@ -0,0 +1,77 @@ +% +% schlange.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math,calc} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} +\def\a{47} +\def\r{3.3} +\def\skala{0.95} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\begin{scope}[xshift=-7.4cm,yshift=-1.2cm] + \clip (-3.6,-2.2) rectangle (3.6,5.1); + + \fill[color=blue!20] (0,0) + -- ({180-\a}:{0.4*\r}) arc ({180-\a}:180:{0.4*\r}) + -- cycle; + \node[color=blue] at ({180-\a/2}:{0.3*\r}) {$\vartheta$}; + + \fill[color=blue!20] (0,{\r/sin(\a)}) + -- ($(0,{\r/sin(\a)})+({270-\a}:{0.3*\r})$) + arc ({270-\a}:270:{0.3*\r}) + -- cycle; + \node[color=blue] at ($(0,{\r/sin(\a)})+({270-\a/2}:{0.2*\r})$) + {$\vartheta$}; + + + \draw (0,0) circle[radius=\r]; + \draw[->] (0,-3.0) -- (0,5); + \draw ({-\r-0.2},0) -- ({\r+0.2},0); + \fill (0,0) circle[radius=0.06]; + + \draw (0,0) -- ({180-\a}:\r); + \node at ({180-\a+3}:{0.65*\r}) [above right] {$1$}; + + \draw[color=red,line width=1.4pt] + ({180-\a}:\r) -- (0,{\r/cos(90-\a)}); + \fill[color=red] ({180-\a}:\r) circle[radius=0.08]; + \fill[color=red] (0,{\r/cos(90-\a)}) circle[radius=0.08]; + \node[color=red] at (-1.0,3.7) [left] {$r=\cot\vartheta$}; + \node[color=red] at ({180-\a}:\r) [above left] {$P$}; + \node[color=red] at (0,{\r/sin(\a)}) [right] {$Q$}; +\end{scope} + +% Povray Bild +\node at (0,0) {\includegraphics[width=7.6cm]{schale.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node[color=red] at (-1.4,1.4) {$r$}; +\node[color=red] at (-2.2,-0.2) {$P$}; +\node[color=red] at (0,3.3) [right] {$Q$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/fresnel/main.tex b/buch/papers/fresnel/main.tex index e6ee3b5..2050fd4 100644 --- a/buch/papers/fresnel/main.tex +++ b/buch/papers/fresnel/main.tex @@ -8,6 +8,11 @@ \begin{refsection} \chapterauthor{Andreas Müller} +{\parindent0pt Die} Fresnel-Integrale tauchen in der Untersuchung der Beugung +in paraxialer Näherung auf, auch bekannt als die Fresnel-Approximation. +In diesem Kapitel betrachen wir jedoch nur die geometrische +Anwendung der Fresnel-Integrale als Parametrisierung der Euler-Spirale +und zeigen, dass letztere eine Klothoide ist. \input{papers/fresnel/teil0.tex} \input{papers/fresnel/teil1.tex} diff --git a/buch/papers/fresnel/pfad.pdf b/buch/papers/fresnel/pfad.pdf deleted file mode 100644 index ff514cc..0000000 Binary files a/buch/papers/fresnel/pfad.pdf and /dev/null differ diff --git a/buch/papers/fresnel/pfad.tex b/buch/papers/fresnel/pfad.tex deleted file mode 100644 index 5439a71..0000000 --- a/buch/papers/fresnel/pfad.tex +++ /dev/null @@ -1,34 +0,0 @@ -% -% pfad.tex -- template for standalon tikz images -% -% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -% -\documentclass[tikz]{standalone} -\usepackage{amsmath} -\usepackage{times} -\usepackage{txfonts} -\usepackage{pgfplots} -\usepackage{csvsimple} -\usetikzlibrary{arrows,intersections,math} -\begin{document} -\def\skala{1} -\definecolor{darkgreen}{rgb}{0,0.6,0} -\begin{tikzpicture}[>=latex,thick,scale=\skala] - -\draw[->] (-1,0) -- (9,0) coordinate[label={$\operatorname{Re}$}]; -\draw[->] (0,-1) -- (0,6) coordinate[label={left:$\operatorname{Im}$}]; - -\draw[->,color=red,line width=1.4pt] (0,0) -- (7,0); -\draw[->,color=blue,line width=1.4pt] (7,0) arc (0:45:7); -\draw[->,color=darkgreen,line width=1.4pt] (45:7) -- (0,0); - -\node[color=red] at (3.5,0) [below] {$\gamma_1(t) = tR$}; -\node[color=blue] at (25:7) [right] {$\gamma_2(t) = Re^{it}$}; -\node[color=darkgreen] at (45:3.5) [above left] {$\gamma_3(t) = te^{i\pi/4}$}; - -\node at (7,0) [below] {$R$}; -\node at (45:7) [above] {$Re^{i\pi/4}$}; - -\end{tikzpicture} -\end{document} - diff --git a/buch/papers/fresnel/references.bib b/buch/papers/fresnel/references.bib index 58e9242..cf8fb21 100644 --- a/buch/papers/fresnel/references.bib +++ b/buch/papers/fresnel/references.bib @@ -44,3 +44,9 @@ title = { Fresnel Integral }, date = { 2022-05-13 } } + +@online{fresnel:schale, + url = { https://www.youtube.com/watch?v=D3tdW9l1690 }, + title = { A Strange Map Projection (Euler Spiral) - Numberphile }, + date = { 2022-05-14 } +} diff --git a/buch/papers/fresnel/teil0.tex b/buch/papers/fresnel/teil0.tex index 253e2f3..85b8bf7 100644 --- a/buch/papers/fresnel/teil0.tex +++ b/buch/papers/fresnel/teil0.tex @@ -20,7 +20,7 @@ C(x) &= \int_0^x \cos\biggl(\frac{\pi}2 t^2\biggr)\,dt \\ S(x) &= \int_0^x \sin\biggl(\frac{\pi}2 t^2\biggr)\,dt \end{align*} -heissen die Fesnel-Integrale. +heissen die Fresnel-Integrale. \end{definition} Der Faktor $\frac{\pi}2$ ist einigermassen willkürlich, man könnte @@ -39,7 +39,7 @@ C(x) &= C_{\frac{\pi}2}(x), S(x) &= S_{\frac{\pi}2}(x). \end{aligned} \] -Durch eine Substution $t=bs$ erhält man +Durch eine Substitution $t=bs$ erhält man \begin{align*} C_a(x) &= @@ -91,7 +91,7 @@ $C_1(x)$ und $S_1(x)$ betrachten, da in diesem Fall die Formeln einfacher werden. \begin{figure} \centering -\includegraphics{papers/fresnel/fresnelgraph.pdf} +\includegraphics{papers/fresnel/images/fresnelgraph.pdf} \caption{Graph der Funktionen $C(x)$ ({\color{red}rot}) und $S(x)$ ({\color{blue}blau}) \label{fresnel:figure:plot}} diff --git a/buch/papers/fresnel/teil1.tex b/buch/papers/fresnel/teil1.tex index a41ddb7..c716cd7 100644 --- a/buch/papers/fresnel/teil1.tex +++ b/buch/papers/fresnel/teil1.tex @@ -8,7 +8,7 @@ \rhead{Euler-Spirale} \begin{figure} \centering -\includegraphics{papers/fresnel/eulerspirale.pdf} +\includegraphics{papers/fresnel/images/eulerspirale.pdf} \caption{Die Eulerspirale ist die Kurve mit der Parameterdarstellung $x\mapsto (C(x),S(x))$, sie ist rot dargestellt. Sie windet sich unendlich oft um die beiden Punkte $(\pm\frac12,\pm\frac12)$. @@ -25,7 +25,7 @@ $(\pm\frac12,\pm\frac12)$ zu winden. \begin{figure} \centering -\includegraphics{papers/fresnel/pfad.pdf} +\includegraphics{papers/fresnel/images/pfad.pdf} \caption{Pfad zur Berechnung der Grenzwerte $C_1(\infty)$ und $S_1(\infty)$ mit Hilfe des Cauchy-Integralsatzes \label{fresnel:figure:pfad}} @@ -182,7 +182,7 @@ muss, folgt $C_1(\infty)=S_1(\infty)$. Nach Multlikation mit $\sqrt{2}$ folgt aus der Tatsache, dass auch der Realteil verschwinden muss \[ -\frac{\sqrt{\pi}}{\sqrt{2}} = C_1(\infty)+S_1(\infty) +\sqrt{\frac{\pi}{2}} = C_1(\infty)+S_1(\infty) \qquad \Rightarrow \qquad @@ -190,7 +190,10 @@ C_1(\infty) = S_1(\infty) = -\frac{\sqrt{\pi}}{2\sqrt{2}}. +\frac12 +\sqrt{ +\frac{\pi}{2} +}. \] Aus \eqref{fresnel:equation:arg} diff --git a/buch/papers/fresnel/teil2.tex b/buch/papers/fresnel/teil2.tex index 22d2a89..ec8c896 100644 --- a/buch/papers/fresnel/teil2.tex +++ b/buch/papers/fresnel/teil2.tex @@ -15,10 +15,165 @@ Eine ebene Kurve, deren Krümmung proportionale zur Kurvenlänge ist, heisst {\em Klothoide}. \end{definition} -Die Klothoide wird zum Beispiel im Strassenbau bei Autobahnkurven -angewendet. -Fährt man mit konstanter Geschwindigkeit mit entlang einer Klothoide, +Die Klothoide wird zum Beispiel im Strassenbau für Autobahnkurven +verwendet. +Fährt man mit konstanter Geschwindigkeit entlang einer Klothoide, muss man die Krümmung mit konstaner Geschwindigkeit ändern, also das Lenkrad mit konstanter Geschwindigkeit drehen. Dies ermöglicht eine ruhige Fahrweise. +\subsection{Krümmung einer ebenen Kurve} +\begin{figure} +\centering +\includegraphics{papers/fresnel/images/kruemmung.pdf} +\caption{Berechnung der Krümmung einer ebenen Kurve. +\label{fresnel:figure:kruemmung}} +\end{figure} +Abbildung~\ref{fresnel:figure:kruemmung} erinnert daran, dass der +Bogen eines Kreises vom Radius $r$, entlang dem sich die Richtung +der Tangente um $\Delta\varphi$ ändert, die Länge +$\Delta s = r\Delta\varphi$. +Die Krümmung ist der Kehrwert des Krümmungsradius, daraus kann +man ablesen, dass +\[ +\kappa = \frac{1}{r} = \frac{\Delta \varphi}{\Delta s}. +\] +Für eine beliebige ebene Kurve ist daher die Krümmung +\[ +\kappa = \frac{d\varphi}{ds}. +\] + +\subsection{Krümmung der Euler-Spirale} +Wir betrachten jetzt die Euler-Spirale mit der Parametrisierung +$\gamma(s) = (C_1(s),S_1(s))$. +Zunächst stellen wir fest, dass die Länge der Tangente +\[ +\dot{\gamma}(s) += +\frac{d\gamma}{ds} += +\begin{pmatrix} +\dot{C}_1(s)\\ +\dot{S}_1(s) +\end{pmatrix} += +\begin{pmatrix} +\cos s^2\\ +\sin s^2 +\end{pmatrix} +\qquad\Rightarrow\qquad +|\dot{\gamma}(s)| += +\sqrt{\cos^2s^2+\sin^2s^2} += +1. +\] +Insbesondere ist der Parameter $s$ der Kurve $\gamma(s)$ die +Bogenlänge. + +Der zu $\dot{\gamma}(s)$ gehörige Polarwinkel kann aus dem Vergleich +mit einem Vektor mit bekanntem Polarwinkel $\varphi$ abgelesen werden: +\[ +\begin{pmatrix} +\cos \varphi\\ +\sin \varphi +\end{pmatrix} += +\dot{\gamma}(s) += +\begin{pmatrix} +\cos s^2\\\sin s^2 +\end{pmatrix}, +\] +der Polarwinkel +ist daher $\varphi = s^2$. +Die Krümmung ist die Ableitung des Polarwinkels nach $s$, also +\[ +\kappa += +\frac{d\varphi}{ds} += +\frac{ds^2}{ds} += +2s, +\] +sie ist somit proportional zur Bogenlänge $s$. +Damit folgt, dass die Euler-Spirale eine Klothoide ist. + +\subsection{Eine Kugel schälen} +\begin{figure} +\centering +\includegraphics[width=\textwidth]{papers/fresnel/images/schale.pdf} +\caption{Schält man eine einen Streifen konstanter Breite beginnend am +Äquator von einer Kugel ab und breitet ihn in der Ebene aus, entsteht +eine Klothoide. +\label{fresnel:figure:schale}} +\end{figure} +\begin{figure} +\centering +\includegraphics{papers/fresnel/images/apfel.pdf} +\caption{Klothoide erhalten durch Abschälen eines Streifens von einem +Apfel (vgl.~Abbildung~\ref{fresnel:figure:schale}) +\label{fresnel:figure:apfel}} +\end{figure} +Schält man einen Streifen konstanter Breite beginnend parallel zum Äquator +von einer Kugel ab und breitet ihn in die Ebene aus, entsteht eine +Approximation einer Klothoide. +Abbildung~\ref{fresnel:figure:schale} zeigt blau den abgeschälten Streifen, +Abbildung~\ref{fresnel:figure:apfel} zeigt das Resultat dieses Versuches +an einem Apfel, das Youtube-Video \cite{fresnel:schale} des +Numberphile-Kanals illustriert das Problem anhand eines aufblasbaren +Globus. + +Windet sich die Kurve in Abbildung~\ref{fresnel:figure:schale} $n$ +mal um die vertikale Achse, bevor sie den Nordpol erreicht, dann kann +die Kurve mit der Funktion +\[ +\gamma(t) += +\begin{pmatrix} +\cos(t) \cos(t/n) \\ +\sin(t) \cos(t/n) \\ +\sin(t/n) +\end{pmatrix} +\] +parametrisiert werden. +Der Tangentialvektor +\[ +\dot{\gamma}(t) += +\begin{pmatrix} +-\sin(t)\cos(t/n) - \cos(t)\sin(t/n)/n \\ +\cos(t)\cos(t/n) - \sin(t)\sin(t/n)/n \\ +\cos(t/n)/n +\end{pmatrix} +\] +hat die Länge +\[ +| \dot{\gamma}(t) |^2 += +\frac{1}{n^2} ++ +\cos^2\frac{t}{n}. +\] +Die Ableitung der Bogenlänge ist daher +\[ +\dot{s}(t) += +\sqrt{ +\frac{1}{n^2} ++ +\cos^2\frac{t}{n} +}. +\] + + +Der Krümmungsradius des blauen Streifens, der die Kugel im Punkt $P$ bei +geographischer $\vartheta$ berührt, hat die Länge der Tangente, die +die Kugel im Punkt $P$ berührt und im Punkt $Q$ durch die Achse der +Kugel geht (Abbildung~\ref{fresnel:figure:schale}). +Die Krümmung in Abhängigkeit von $\vartheta$ ist daher $\tan\vartheta$. + + + + diff --git a/buch/papers/fresnel/teil3.tex b/buch/papers/fresnel/teil3.tex index 37e6bee..ceddbe0 100644 --- a/buch/papers/fresnel/teil3.tex +++ b/buch/papers/fresnel/teil3.tex @@ -42,8 +42,8 @@ C'(x) = \cos \biggl(\frac{\pi}2 x^2\biggr) \qquad\text{und}\qquad S'(x) = \sin \biggl(\frac{\pi}2 x^2\biggr) \] -erfüllen, kann man eine Methode zur Lösung von Differentialgleichung -verwenden. +erfüllen, kann man eine Methode zur numerischen Lösung von +Differentialgleichung verwenden. Die Abbildungen~\ref{fresnel:figure:plot} und \ref{fresnel:figure:eulerspirale} wurden auf diese Weise erzeugt. -- cgit v1.2.1 From 0fe9bb56da147bf7986852e6f657149206d967a4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 19 May 2022 17:31:23 +0200 Subject: fixes --- buch/papers/nav/Makefile.inc | 1 - buch/papers/nav/nautischesdreieck.tex | 2 +- 2 files changed, 1 insertion(+), 2 deletions(-) diff --git a/buch/papers/nav/Makefile.inc b/buch/papers/nav/Makefile.inc index 24ab4ee..5e86543 100644 --- a/buch/papers/nav/Makefile.inc +++ b/buch/papers/nav/Makefile.inc @@ -8,7 +8,6 @@ dependencies-nav = \ papers/nav/main.tex \ papers/nav/einleitung.tex \ papers/nav/flatearth.tex \ - papers/nav/geschichte.tex \ papers/nav/nautischesdreieck.tex \ papers/nav/sincos.tex \ papers/nav/trigo.tex \ diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index 0a498f0..c1ad38a 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -195,4 +195,4 @@ Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Wink Somit ist \[ \omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}] \]und unsere gesuchte geographische Länge schlussendlich \[\lambda=\lambda_1 - \omega\] -mit $\lambda_1$=Längengrad Bildpunkt $X +mit $\lambda_1$=Längengrad Bildpunkt $X$ -- cgit v1.2.1 From f0a6f930187eb0226ddd4735feba1d93667b8a58 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 19 May 2022 22:12:27 +0200 Subject: add dreieck3d9.pov --- buch/papers/nav/images/Makefile | 7 ++++ buch/papers/nav/images/common.inc | 60 +++++++++++++++++++------------ buch/papers/nav/images/dreieck3d9.pov | 66 +++++++++++++++++++++++++++++++++++ 3 files changed, 111 insertions(+), 22 deletions(-) create mode 100644 buch/papers/nav/images/dreieck3d9.pov diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile index bbdea2f..da4defa 100644 --- a/buch/papers/nav/images/Makefile +++ b/buch/papers/nav/images/Makefile @@ -114,3 +114,10 @@ dreieck3d8.jpg: dreieck3d8.png dreieck3d8.pdf: dreieck3d8.tex dreieck3d8.jpg pdflatex dreieck3d8.tex +dreieck3d9.png: dreieck3d9.pov common.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d9.png dreieck3d9.pov +dreieck3d9.jpg: dreieck3d9.png + convert dreieck3d9.png -density 300 -units PixelsPerInch dreieck3d9.jpg +dreieck3d9.pdf: dreieck3d9.tex dreieck3d9.jpg + pdflatex dreieck3d9.tex + diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc index e2a1ed0..2c0ae6e 100644 --- a/buch/papers/nav/images/common.inc +++ b/buch/papers/nav/images/common.inc @@ -12,6 +12,7 @@ global_settings { #declare imagescale = 0.034; +#declare O = <0, 0, 0>; #declare A = vnormalize(< 0, 1, 0>); #declare B = vnormalize(< 1, 2, -8>); #declare C = vnormalize(< 5, 1, 0>); @@ -102,8 +103,8 @@ union { #declare pp = vnormalize(p - vdot(n, p) * n); #declare qq = vnormalize(q - vdot(n, q) * n); intersection { - sphere { <0, 0, 0>, 1 + staerke } - cone { <0, 0, 0>, 0, 1.2 * vnormalize(w), r } + sphere { O, 1 + staerke } + cone { O, 0, 1.2 * vnormalize(w), r } plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 } plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 } } @@ -132,6 +133,35 @@ union { } #end +#macro ebenerwinkel(a, p, q, s, r, farbe) + #declare n = vnormalize(-vcross(p, q)); + #declare np = vnormalize(-vcross(p, n)); + #declare nq = -vnormalize(-vcross(q, n)); +// arrow(a, a + n, 0.02, White) +// arrow(a, a + np, 0.01, Red) +// arrow(a, a + nq, 0.01, Blue) + intersection { + cylinder { a - (s/2) * n, a + (s/2) * n, r } + plane { np, vdot(np, a) } + plane { nq, vdot(nq, a) } + pigment { + farbe + } + finish { + metallic + specular 0.5 + } + } +#end + +#macro komplement(a, p, q, s, r, farbe) + #declare n = vnormalize(-vcross(p, q)); +// arrow(a, a + n, 0.015, Orange) + #declare m = vnormalize(-vcross(q, n)); +// arrow(a, a + m, 0.015, Pink) + ebenerwinkel(a, p, m, s, r, farbe) +#end + #declare fett = 0.015; #declare fein = 0.010; @@ -143,29 +173,15 @@ union { #declare gruen = rgb<0,0.6,0>; #declare blau = rgb<0.2,0.2,0.8>; +#declare kugelfarbe = rgb<0.8,0.8,0.8>; +#declare kugeltransparent = rgbt<0.8,0.8,0.8,0.5>; + +#macro kugel(farbe) sphere { <0, 0, 0>, 1 pigment { - color rgb<0.8,0.8,0.8> + color farbe } } +#end -//union { -// sphere { A, 0.02 } -// sphere { B, 0.02 } -// sphere { C, 0.02 } -// sphere { P, 0.02 } -// pigment { -// color Red -// } -//} - -//union { -// winkel(A, B, C) -// winkel(B, P, C) -// seite(B, C, 0.01) -// seite(B, P, 0.01) -// pigment { -// color rgb<0,0.6,0> -// } -//} diff --git a/buch/papers/nav/images/dreieck3d9.pov b/buch/papers/nav/images/dreieck3d9.pov new file mode 100644 index 0000000..24d3843 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d9.pov @@ -0,0 +1,66 @@ +// +// dreiecke3d8.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +//union { +// seite(A, B, fein) +// seite(B, C, fein) +// seite(A, C, fein) +// seite(A, P, fein) +// seite(B, P, fett) +// seite(C, P, fett) +// punkt(A, fein) +// punkt(B, fett) +// punkt(C, fett) +// punkt(P, fett) +// pigment { +// color dreieckfarbe +// } +// finish { +// specular 0.95 +// metallic +// } +//} + +//dreieck(A, B, C, White) + +kugel(kugeltransparent) + +ebenerwinkel(O, C, P, 0.01, 1.001, rot) +ebenerwinkel(P, C, P, 0.01, 0.3, rot) +komplement(P, C, P, 0.01, 0.3, Yellow) + +ebenerwinkel(O, B, P, 0.01, 1.001, blau) +ebenerwinkel(P, B, P, 0.01, 0.3, blau) +komplement(P, B, P, 0.01, 0.3, Green) + +arrow(B, 1.5 * B, 0.015, White) +arrow(C, 1.5 * C, 0.015, White) +arrow(P, 1.5 * P, 0.015, White) + +union { + cylinder { O, P, 0.7 * fein } + + cylinder { P, P + 3 * B, 0.7 * fein } + cylinder { O, B + 3 * B, 0.7 * fein } + + cylinder { P, P + 3 * C, 0.7 * fein } + cylinder { O, C + 3 * C, 0.7 * fein } + + pigment { + color White + } +} + +#declare imagescale = 0.044; + +camera { + location <40, 20, -20> + look_at <0, 0.24, -0.20> + right x * imagescale + up y * imagescale +} + -- cgit v1.2.1 From 5187a5a947c0283e9f3d7fbc2acef96278109939 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Fri, 20 May 2022 18:14:40 +0200 Subject: presentation FM-Bessel --- buch/papers/fm/.vscode/settings.json | 3 + buch/papers/fm/Python animation/Bessel-FM.ipynb | 164 ++++++++++------ buch/papers/fm/RS presentation/FM_presentation.pdf | Bin 0 -> 357597 bytes buch/papers/fm/RS presentation/FM_presentation.tex | 125 ++++++++++++ ...quency modulation (FM) and Bessel functions.pdf | Bin 0 -> 159598 bytes buch/papers/fm/RS presentation/README.txt | 1 + buch/papers/fm/RS presentation/RS.tex | 209 +++++++++------------ buch/papers/fm/RS presentation/images/100HZ.png | Bin 0 -> 8601 bytes buch/papers/fm/RS presentation/images/200HZ.png | Bin 0 -> 8502 bytes buch/papers/fm/RS presentation/images/300HZ.png | Bin 0 -> 9059 bytes buch/papers/fm/RS presentation/images/400HZ.png | Bin 0 -> 9949 bytes 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create mode 100644 buch/papers/fm/RS presentation/images/400HZ.png create mode 100644 buch/papers/fm/RS presentation/images/bessel.png create mode 100644 buch/papers/fm/RS presentation/images/bessel2.png create mode 100644 buch/papers/fm/RS presentation/images/bessel_beta1.png create mode 100644 buch/papers/fm/RS presentation/images/bessel_frequenz.png create mode 100644 buch/papers/fm/RS presentation/images/beta_0.001.png create mode 100644 buch/papers/fm/RS presentation/images/beta_0.1.png create mode 100644 buch/papers/fm/RS presentation/images/beta_0.5.png create mode 100644 buch/papers/fm/RS presentation/images/beta_1.png create mode 100644 buch/papers/fm/RS presentation/images/beta_2.png create mode 100644 buch/papers/fm/RS presentation/images/beta_3.png create mode 100644 buch/papers/fm/RS presentation/images/fm_10Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_20hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_30Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_3Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_40Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_5Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_7Hz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_frequenz.png create mode 100644 buch/papers/fm/RS presentation/images/fm_in_time.png diff --git a/buch/papers/fm/.vscode/settings.json b/buch/papers/fm/.vscode/settings.json new file mode 100644 index 0000000..5125289 --- /dev/null +++ b/buch/papers/fm/.vscode/settings.json @@ -0,0 +1,3 @@ +{ + "notebook.cellFocusIndicator": "border" +} \ No newline at end of file diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb index 9d0835a..bfbb83d 100644 --- a/buch/papers/fm/Python animation/Bessel-FM.ipynb +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -2,21 +2,9 @@ "cells": [ { "cell_type": "code", - "execution_count": 74, + "execution_count": 117, "metadata": {}, - "outputs": [ - { - "ename": "ValueError", - "evalue": "operands could not be broadcast together with shapes (3,) (600,) ", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/Python animation/Bessel-FM.ipynb Cell 1'\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 13\u001b[0m x \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.01\u001b[39m, N\u001b[39m*\u001b[39mT, N)\n\u001b[1;32m 14\u001b[0m beta \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39mlinspace(\u001b[39m0.1\u001b[39m,\u001b[39m10\u001b[39m, \u001b[39m3\u001b[39m)\n\u001b[0;32m---> 15\u001b[0m y_old \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39msin(\u001b[39m100.0\u001b[39m \u001b[39m*\u001b[39m \u001b[39m2.0\u001b[39m\u001b[39m*\u001b[39mnp\u001b[39m.\u001b[39mpi\u001b[39m*\u001b[39mx\u001b[39m+\u001b[39mbeta\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49msin(\u001b[39m50.0\u001b[39;49m \u001b[39m*\u001b[39;49m \u001b[39m2.0\u001b[39;49m\u001b[39m*\u001b[39;49mnp\u001b[39m.\u001b[39;49mpi\u001b[39m*\u001b[39;49mx))\n\u001b[1;32m 16\u001b[0m y \u001b[39m=\u001b[39m \u001b[39m0\u001b[39m\u001b[39m*\u001b[39mx;\n\u001b[1;32m 17\u001b[0m xf \u001b[39m=\u001b[39m fftfreq(N, \u001b[39m1\u001b[39m \u001b[39m/\u001b[39m \u001b[39m400\u001b[39m)\n", - "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (600,) " - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from scipy import signal\n", @@ -25,45 +13,71 @@ "import scipy.fftpack\n", "import matplotlib.pyplot as plt\n", "from matplotlib.widgets import Slider\n", - "\n", + "def fm(beta):\n", + " # Number of samplepoints\n", + " N = 600\n", + " # sample spacing\n", + " T = 1.0 / 1000.0\n", + " fc = 100.0\n", + " fm = 30.0\n", + " x = np.linspace(0.01, N*T, N)\n", + " #beta = 1.0\n", + " y_old = np.sin(fc * 2.0*np.pi*x+beta*np.sin(fm * 2.0*np.pi*x))\n", + " y = 0*x;\n", + " xf = fftfreq(N, 1 / 400)\n", + " for k in range (-4, 4):\n", + " y = sc.jv(k,beta)*np.sin((fc+k*fm) * 2.0*np.pi*x)\n", + " yf = fft(y)/(fc*np.pi)\n", + " plt.plot(xf, np.abs(yf))\n", + " plt.xlim(-150, 150)\n", + " plt.show()\n", + " #yf_old = fft(y_old)\n", + " #plt.plot(xf, np.abs(yf_old))\n", + " #plt.show()\n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ "# Number of samplepoints\n", - "N = 600\n", + "N = 800\n", "# sample spacing\n", - "T = 1.0 / 800.0\n", + "T = 1.0 / 1000.0\n", "x = np.linspace(0.01, N*T, N)\n", - "beta = 1.0\n", - "y_old = np.sin(100.0 * 2.0*np.pi*x+beta*np.sin(50.0 * 2.0*np.pi*x))\n", - "y = 0*x;\n", - "xf = fftfreq(N, 1 / 400)\n", - "for k in range (-5, 5):\n", - " y = sc.jv(k,beta)*np.sin((100.0+k*50) * 2.0*np.pi*x)\n", - " yf = fft(y)\n", - " plt.plot(xf, np.abs(yf))\n", "\n", - "axamp = plt.axes(np.linspace(0.1, 3, 10))\n", - "beta_slider = Slider(\n", - "ax=axamp,\n", - "label=\"Amplitude\",\n", - "valmin=0,\n", - "valmax=10,\n", - "valinit=beta,\n", - "orientation=\"vertical\"\n", - ")\n", - "plt.show()\n", - "\n", - "yf_old = fft(y_old)\n", + "y_old = np.sin(100* 2.0*np.pi*x+1*np.sin(15* 2.0*np.pi*x))\n", + "yf_old = fft(y_old)/(100*np.pi)\n", + "xf = fftfreq(N, 1 / 1000)\n", "plt.plot(xf, np.abs(yf_old))\n", - "plt.show()\n" + "#plt.xlim(-150, 150)\n", + "plt.show()" ] }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 118, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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"text/plain": [ "
" ] @@ -75,32 +89,17 @@ } ], "source": [ - "\n", - "# Number of samplepoints\n", - "N = 600\n", - "# sample spacing\n", - "T = 1.0 / 800.0\n", - "x = np.linspace(0.0, N*T, N)\n", - "y = sc.jv(3,x)#np.sin(50.0 * 2.0*np.pi*x) + 0.5*np.sin(80.0 * 2.0*np.pi*x)\n", - "yf = scipy.fftpack.fft(y)\n", - "xf = np.linspace(0.0, 1.0/(2.0*T), N//2)\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.plot(xf, 2.0/N * np.abs(yf[:N//2]))\n", - "ax.set(\n", - " xlim=(0, 100)\n", - ")\n", - "plt.show()\n" + "fm(1)" ] }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 122, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -109,20 +108,35 @@ "needs_background": "light" }, "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7651976865579666\n" + ] } ], "source": [ "\n", - "for n in range (5):\n", - " x = np.linspace(0,15,1000)\n", + "for n in range (-4,4):\n", + " x = np.linspace(0,11,1000)\n", " y = sc.jv(n,x)\n", " plt.plot(x, y, '-')\n", - "plt.show()" + "plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", + "plt.xlim(0,10)\n", + "plt.grid(True)\n", + "plt.ylabel('Bessel J_n(b)')\n", + "plt.xlabel('b')\n", + "plt.plot(x, y)\n", + "plt.show()\n", + "\n", + "print(sc.jv(0,1))" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 85, "metadata": {}, "outputs": [ { @@ -163,6 +177,32 @@ "\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "x = np.linspace(0,0.1,1000)\n", + "y = np.sin(100 * 2.0*np.pi*x+1.5*np.sin(30 * 2.0*np.pi*x))\n", + "plt.plot(x, y, '-')\n", + "plt.show()" + ] } ], "metadata": { diff --git a/buch/papers/fm/RS presentation/FM_presentation.pdf b/buch/papers/fm/RS presentation/FM_presentation.pdf new file mode 100644 index 0000000..496e35e Binary files /dev/null and b/buch/papers/fm/RS presentation/FM_presentation.pdf differ diff --git a/buch/papers/fm/RS presentation/FM_presentation.tex b/buch/papers/fm/RS presentation/FM_presentation.tex new file mode 100644 index 0000000..92cb501 --- /dev/null +++ b/buch/papers/fm/RS presentation/FM_presentation.tex @@ -0,0 +1,125 @@ +%% !TeX root = RS.tex + +\documentclass[11pt,aspectratio=169]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{lmodern} +\usepackage[ngerman]{babel} +\usepackage{tikz} +\usetheme{Hannover} + +\begin{document} + \author{Joshua Bär} + \title{FM - Bessel} + \subtitle{} + \logo{} + \institute{OST Ostschweizer Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar} + %\setbeamercovered{transparent} + \setbeamercovered{invisible} + \setbeamertemplate{navigation symbols}{} + \begin{frame}[plain] + \maketitle + \end{frame} +%------------------------------------------------------------------------------- +\section{Einführung} + \begin{frame} + \frametitle{Frequenzmodulation} + + \visible<1->{ + \begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt)) + \end{equation}} + + \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} + \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} + \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} + + + \end{frame} +%------------------------------------------------------------------------------- +\section{Proof} +\begin{frame} + \frametitle{Bessel} + + \visible<1->{\begin{align} + \cos(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + \sin(\beta\sin\varphi) + &= + J_0(\beta) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \end{align}} + \visible<2->{\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \end{align}} +\end{frame} + +%------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Prof->Done} + \begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \end{align} + \end{frame} +%------------------------------------------------------------------------------- + \begin{frame} + \begin{figure} + \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} + \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} + \end{figure} + \end{frame} +%------------------------------------------------------------------------------- +\section{Input Parameter} + \begin{frame} + \frametitle{Träger-Frequenz Parameter} + \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} + \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} + \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} + \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} + \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} + \end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Modulations-Frequenz Parameter} +\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} +\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} +\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} +\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} +\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} +\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} +\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Beta Parameter} + \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t)\end{equation}} + \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} + \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} + \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} + \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} + \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} + \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} + \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} + \includegraphics[scale=0.5]{images/beta_1.png} + \includegraphics[scale=0.5]{images/bessel.png} +\end{frame} +\end{document} diff --git a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf new file mode 100644 index 0000000..a6e701c Binary files /dev/null and b/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf differ diff --git a/buch/papers/fm/RS presentation/README.txt b/buch/papers/fm/RS presentation/README.txt new file mode 100644 index 0000000..4d0620f --- /dev/null +++ b/buch/papers/fm/RS presentation/README.txt @@ -0,0 +1 @@ +Dies ist die Presentation des Reed-Solomon-Code \ No newline at end of file diff --git a/buch/papers/fm/RS presentation/RS.tex b/buch/papers/fm/RS presentation/RS.tex index 8e3de17..8a67619 100644 --- a/buch/papers/fm/RS presentation/RS.tex +++ b/buch/papers/fm/RS presentation/RS.tex @@ -1,3 +1,5 @@ +%% !TeX root = RS.tex + \documentclass[11pt,aspectratio=169]{beamer} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} @@ -13,7 +15,7 @@ \logo{} \institute{OST Ostschweizer Fachhochschule} \date{16.5.2022} - \subject{Mathematisches Seminar} + \subject{Mathematisches Seminar- Spezielle Funktionen} %\setbeamercovered{transparent} \setbeamercovered{invisible} \setbeamertemplate{navigation symbols}{} @@ -24,139 +26,98 @@ \section{Einführung} \begin{frame} \frametitle{Frequenzmodulation} - \begin{itemize} - \visible<1->{\item Für Übertragung von Daten} - \visible<2->{\item Amplituden unabhängig} - \end{itemize} + + \visible<1->{\begin{equation} \cos(\omega_c t+\beta\sin(\omega_mt))\end{equation}} + + \only<2>{\includegraphics[scale= 0.7]{images/fm_in_time.png}} + \only<3>{\includegraphics[scale= 0.7]{images/fm_frequenz.png}} + \only<4>{\includegraphics[scale= 0.7]{images/bessel_frequenz.png}} + + \end{frame} %------------------------------------------------------------------------------- - \begin{frame} - \frametitle{Parameter} - \begin{center} - \begin{tabular}{ c c c } - \hline - Nutzlas & Fehler & Versenden \\ - \hline - 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\ - 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\ -\visible<1->{3}& -\visible<1->{3}& -\visible<1->{9 Werte eines Polynoms vom Grad 2} \\ - &&\\ -\visible<1->{$k$} & -\visible<1->{$t$} & -\visible<1->{$k+2t$ Werte eines Polynoms vom Grad $k-1$} \\ - \hline - &&\\ - &&\\ - \multicolumn{3}{l} { - \visible<1>{Ausserdem können bis zu $2t$ Fehler erkannt werden!} - } - \end{tabular} - \end{center} - \end{frame} +\section{Proof} +\begin{frame} + \frametitle{Bessel} -%------------------------------------------------------------------------------- + \visible<1->{\begin{align} + \cos(\beta\sin\varphi) + &= + J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + \sin(\beta\sin\varphi) + &= + J_0(\beat) + 2\sum_{m=1}^\infty J_{2m}(\beta) \cos(2m\varphi) + \\ + J_{-n}(\beat) &= (-1)^n J_n(\beta) + \end{align}} + \visible<2->{\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \end{align}} +\end{frame} -\section{Diskrete Fourier Transformation} - \begin{frame} - \frametitle{Idee} - \begin{itemize} - \item Fourier-transformieren - \item Übertragung - \item Rücktransformieren - \end{itemize} +%------------------------------------------------------------------------------- +\begin{frame} + \frametitle{Prof->Done} + \begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t) + \end{align} \end{frame} %------------------------------------------------------------------------------- \begin{frame} - \begin{figure} - \only<1>{ - \includegraphics[width=0.9\linewidth]{images/fig1.pdf} - } - \only<2>{ - \includegraphics[width=0.9\linewidth]{images/fig2.pdf} - } - \only<3>{ - \includegraphics[width=0.9\linewidth]{images/fig3.pdf} - } - \only<4>{ - \includegraphics[width=0.9\linewidth]{images/fig4.pdf} - } - \only<5>{ - \includegraphics[width=0.9\linewidth]{images/fig5.pdf} - } - \only<6>{ - \includegraphics[width=0.9\linewidth]{images/fig6.pdf} - } - \only<7>{ - \includegraphics[width=0.9\linewidth]{images/fig7.pdf} - } + \begin{figure} + \only<1>{\includegraphics[scale = 0.75]{images/fm_frequenz.png}} + \only<2>{\includegraphics[scale = 0.75]{images/bessel_frequenz.png}} \end{figure} \end{frame} %------------------------------------------------------------------------------- +\section{Input Parameter} \begin{frame} - \frametitle{Diskrete Fourier Transformation} - \begin{itemize} - \item Diskrete Fourier-Transformation gegeben durch: - \visible<1->{ - \[ - \label{ft_discrete} - \hat{c}_{k} - = \frac{1}{N} \sum_{n=0}^{N-1} - {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn} - \]} - \visible<2->{ - \item Ersetzte - \[ - w = e^{-\frac{2\pi j}{N} k} - \]} - \visible<3->{ - \item Wenn $N$ konstant: - \[ - \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N) - \]} - \end{itemize} - \end{frame} - -%------------------------------------------------------------------------------- - -%------------------------------------------------------------------------------- - \begin{frame} - \frametitle{Ein Beispiel} - - \begin{itemize} - - \onslide<1->{\item endlicher Körper $q = 11$} - - \onslide<2->{ist eine Primzahl} - - \onslide<3->{beinhaltet die Zahlen $\mathbb{F}_{11} = \{0,1,2,3,4,5,6,7,8,9,10\}$} - - \vspace{10pt} - - \onslide<4->{\item Nachrichtenblock $=$ Nutzlast $+$ Fehlerkorrekturstellen} - - \onslide<5->{$n = q - 1 = 10$ Zahlen} - - \vspace{10pt} - - \onslide<6->{\item Max.~Fehler $t = 2$} - - \onslide<7->{maximale Anzahl von Fehler, die wir noch korrigieren können} - - \vspace{10pt} - - \onslide<8->{\item Nutzlast $k = n -2t = 6$ Zahlen} - - \onslide<9->{Fehlerkorrkturstellen $2t = 4$ Zahlen} - - \onslide<10->{Nachricht $m = [0,0,0,0,4,7,2,5,8,1]$} - - \onslide<11->{als Polynom $m(X) = 4X^5 + 7X^4 + 2X^3 + 5X^2 + 8X + 1$} - - \end{itemize} - + \frametitle{Träger-Frequenz Parameter} + \onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} + \only<1>{\includegraphics[scale=0.75]{images/100HZ.png}} + \only<2>{\includegraphics[scale=0.75]{images/200HZ.png}} + \only<3>{\includegraphics[scale=0.75]{images/300HZ.png}} + \only<4>{\includegraphics[scale=0.75]{images/400HZ.png}} \end{frame} - - +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Modulations-Frequenz Parameter} +\onslide<1->{\begin{equation}\cos(\omega_ct+\beta\sin(\omega_mt))\end{equation}} +\only<1>{\includegraphics[scale=0.75]{images/fm_3Hz.png}} +\only<2>{\includegraphics[scale=0.75]{images/fm_5Hz.png}} +\only<3>{\includegraphics[scale=0.75]{images/fm_7Hz.png}} +\only<4>{\includegraphics[scale=0.75]{images/fm_10Hz.png}} +\only<5>{\includegraphics[scale=0.75]{images/fm_20Hz.png}} +\only<6>{\includegraphics[scale=0.75]{images/fm_30Hz.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} +\frametitle{Beta Parameter} + \onslide<1->{\begin{equation}\sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omgea_m)t)\end{equation}} + \only<1>{\includegraphics[scale=0.7]{images/beta_0.001.png}} + \only<2>{\includegraphics[scale=0.7]{images/beta_0.1.png}} + \only<3>{\includegraphics[scale=0.7]{images/beta_0.5.png}} + \only<4>{\includegraphics[scale=0.7]{images/beta_1.png}} + \only<5>{\includegraphics[scale=0.7]{images/beta_2.png}} + \only<6>{\includegraphics[scale=0.7]{images/beta_3.png}} + \only<7>{\includegraphics[scale=0.7]{images/bessel.png}} +\end{frame} +%------------------------------------------------------------------------------- +\begin{frame} + \includegraphics[scale=0.5]{images/beta_1.png} + \includegraphics[scale=0.5]{images/bessel.png} +\end{frame} \end{document} diff --git a/buch/papers/fm/RS presentation/images/100HZ.png b/buch/papers/fm/RS 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presentation/images/fm_7Hz.png new file mode 100644 index 0000000..b3dd7e3 Binary files /dev/null and b/buch/papers/fm/RS presentation/images/fm_7Hz.png differ diff --git a/buch/papers/fm/RS presentation/images/fm_frequenz.png b/buch/papers/fm/RS presentation/images/fm_frequenz.png new file mode 100644 index 0000000..26bfd86 Binary files /dev/null and b/buch/papers/fm/RS presentation/images/fm_frequenz.png differ diff --git a/buch/papers/fm/RS presentation/images/fm_in_time.png b/buch/papers/fm/RS presentation/images/fm_in_time.png new file mode 100644 index 0000000..068eafc Binary files /dev/null and b/buch/papers/fm/RS presentation/images/fm_in_time.png differ diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index de3e10a..00fb34b 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -2,8 +2,8 @@ % main.tex -- Paper zum Thema % % (c) 2020 Hochschule Rapperswil -% -% !TeX root = /.../...buch.tex +% +% !TeX root = buch.tex %\begin {document} \chapter{Thema\label{chapter:fm}} \lhead{Thema} -- cgit v1.2.1 From 5d1cd4306966a5433bcc8375d627989aade53a3c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 21 May 2022 07:21:47 +0200 Subject: add new script for risch part --- buch/chapters/060-integral/experiments/rxy.maxima | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100644 buch/chapters/060-integral/experiments/rxy.maxima diff --git a/buch/chapters/060-integral/experiments/rxy.maxima b/buch/chapters/060-integral/experiments/rxy.maxima new file mode 100644 index 0000000..0d5a56d --- /dev/null +++ b/buch/chapters/060-integral/experiments/rxy.maxima @@ -0,0 +1,9 @@ +y: sqrt(a*x^2+b*x+c); + +F: log(x + b/(2 * a) + y/sqrt(a))/sqrt(a); + +f: diff(F, x); + +ratsimp(f); + +ratsimp(y*f); -- cgit v1.2.1 From eceae67b3a13bc28acc446288429a90be2efa99d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 21 May 2022 12:45:42 +0200 Subject: curvature graph --- buch/papers/kugel/images/Makefile | 13 ++++++ buch/papers/kugel/images/curvature.pov | 72 +++++++++++++++++++++++++++++ buch/papers/kugel/images/curvgraph.m | 83 ++++++++++++++++++++++++++++++++++ 3 files changed, 168 insertions(+) create mode 100644 buch/papers/kugel/images/Makefile create mode 100644 buch/papers/kugel/images/curvature.pov create mode 100644 buch/papers/kugel/images/curvgraph.m diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile new file mode 100644 index 0000000..8efa228 --- /dev/null +++ b/buch/papers/kugel/images/Makefile @@ -0,0 +1,13 @@ +# +# Makefile -- build images +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +all: curvature.png + +curvature.inc: curvgraph.m + octave curvgraph.m + +curvature.png: curvature.pov curvature.inc + povray +A0.1 +W1920 +H1080 +Ocurvature.png curvature.pov + diff --git a/buch/papers/kugel/images/curvature.pov b/buch/papers/kugel/images/curvature.pov new file mode 100644 index 0000000..3535488 --- /dev/null +++ b/buch/papers/kugel/images/curvature.pov @@ -0,0 +1,72 @@ +// +// curvature.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// + +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.1; + +camera { + location <40, 10, -20> + look_at <0, 0, 0> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <10, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +// +// draw an arrow from to with thickness with +// color +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +arrow(<-3.1,0,0>, <3.1,0,0>, 0.01, White) +arrow(<0,-1,0>, <0,1,0>, 0.01, White) +arrow(<0,0,-2.1>, <0,0,2.1>, 0.01, White) + +#include "curvature.inc" diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m new file mode 100644 index 0000000..96ca4b1 --- /dev/null +++ b/buch/papers/kugel/images/curvgraph.m @@ -0,0 +1,83 @@ +# +# curvature.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# + +global N; +N = 10; + +global sigma2; +sigma2 = 1; + +global s; +s = 1; + +xmin = -3; +xmax = 3; +xsteps = 1000; +hx = (xmax - xmin) / xsteps; + +ymin = -2; +ymax = 2; +ysteps = 1000; +hy = (ymax - ymin) / ysteps; + +function retval = f0(r) + global sigma2; + retval = exp(-r^2/sigma2)/sigma2 - exp(-r^2/(2*sigma2))/(sqrt(2)*sigma2); +end + +global N0; +N0 = f0(0); + +function retval = f1(x,y) + global N0; + retval = f0(hypot(x, y)) / N0; +endfunction + +function retval = f(x, y) + global s; + retval = f1(x+s, y) - f1(x-s, y); +endfunction + +function retval = curvature0(r) + global sigma2; + retval = ( + (2*sigma2-r^2)*exp(-r^2/(2*sigma2)) + + + 4*(r^2-sigma2)*exp(-r^2/sigma2) + ) / (sigma2^2); +endfunction + +function retval = curvature1(x, y) + retval = curvature0(hypot(x, y)); +endfunction + +function retval = curvature(x, y) + global s; + retval = curvature1(x+s, y) + curvature1(x-s, y); +endfunction + +function retval = farbe(x, y) + c = curvature(x, y); + retval = c * ones(1,3); +endfunction + +fn = fopen("curvature.inc", "w"); + +for ix = (0:xsteps) + x = xmin + ix * hx; + for iy = (0:ysteps) + y = ymin + iy * hy; + fprintf(fn, "sphere { <%.4f, %.4f, %.4f>, 0.01\n", + x, f(x, y), y); + color = farbe(x, y); + fprintf(fn, "pigment { color rgb<%.4f,%.4f,%.4f> }\n", + color(1,1), color(1,2), color(1,3)); + fprintf(fn, "finish { metallic specular 0.5 }\n"); + fprintf(fn, "}\n"); + end +end + +fclose(fn); -- cgit v1.2.1 From 411fb410f790fcc1bb3da381c17119ebb5130032 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Sat, 21 May 2022 18:56:21 +0200 Subject: Korrektur 21.05 --- buch/papers/nav/bilder/ephe.png | Bin 184799 -> 543515 bytes buch/papers/nav/bilder/recht.jpg | Bin 0 -> 42889 bytes buch/papers/nav/bilder/sextant.jpg | Bin 0 -> 8280 bytes buch/papers/nav/einleitung.tex | 2 +- buch/papers/nav/flatearth.tex | 15 +++-- buch/papers/nav/main.tex | 2 +- buch/papers/nav/nautischesdreieck.tex | 123 +++++++++++++++++----------------- buch/papers/nav/sincos.tex | 6 +- buch/papers/nav/trigo.tex | 66 ++++++++++-------- 9 files changed, 114 insertions(+), 100 deletions(-) create mode 100644 buch/papers/nav/bilder/recht.jpg create mode 100644 buch/papers/nav/bilder/sextant.jpg diff --git a/buch/papers/nav/bilder/ephe.png b/buch/papers/nav/bilder/ephe.png index 0aeef6f..3f99a36 100644 Binary files a/buch/papers/nav/bilder/ephe.png and b/buch/papers/nav/bilder/ephe.png differ diff --git a/buch/papers/nav/bilder/recht.jpg b/buch/papers/nav/bilder/recht.jpg new file mode 100644 index 0000000..3f60370 Binary files /dev/null and b/buch/papers/nav/bilder/recht.jpg differ diff --git a/buch/papers/nav/bilder/sextant.jpg b/buch/papers/nav/bilder/sextant.jpg new file mode 100644 index 0000000..53dd784 Binary files /dev/null and b/buch/papers/nav/bilder/sextant.jpg differ diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex index 8d8c5c1..aafa107 100644 --- a/buch/papers/nav/einleitung.tex +++ b/buch/papers/nav/einleitung.tex @@ -4,6 +4,6 @@ Heutzutage ist die Navigation ein Teil des Lebens. Man sendet dem Kollegen seinen eigenen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein, damit man seinen Aufenthaltsort zum Beispiel auf einer riesigen Wiese am See findet. Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. -Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf kleineren Schiffen benötigt wird im Falle eines Stromausfalls. +Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf Schiffen verwendet wird im Falle eines Stromausfalls. Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? In diesem Kapitel werden genau diese Fragen mithilfe des nautischen Dreiecks, der sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index bec242e..5bfc1b7 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -9,19 +9,20 @@ \end{center} \end{figure} -Es gibt heut zu Tage viele Beweise dafür, dass die Erde eine Kugel ist. +Es gibt heutzutage viele Beweise dafür, dass die Erde eine Kugel ist. Die Fotos von unserem Planeten oder die Berichte der Astronauten. -Aber schon vor ca. 2300 Jahren hat Aristotoles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist oder der Erdschatten bei einer Mondfinsternis immer rund ist. +Aber schon vor ca. 2300 Jahren hat Aristoteles bemerkt, dass Schiffe im Horizont verschwinden und die einzige Erklärung dafür die Kugelgestalt der Erde ist. +Auch der Erdschatten bei einer Mondfinsternis ist immer rund. Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. Mithilfe der Trigonometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. -Auch in der Navigation würden grobe Fehler passieren, wenn man davon ausgeht, dass die Erde eine Scheibe ist. -Man sieht es zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. +Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. +Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. +Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. + +Dies sieht man zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. Das liegt daran, das man die 3D – Weltkarte nicht einfach auslegen kann. -Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. -Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. -Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. \ No newline at end of file diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 47764e8..e16dc2a 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -3,7 +3,7 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Spährische Navigation\label{chapter:nav}} +\chapter{Sphärische Navigation\label{chapter:nav}} \lhead{Sphärische Navigation} \begin{refsection} \chapterauthor{Enez Erdem und Marc Kühne} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index c1ad38a..c239d64 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -1,22 +1,14 @@ \section{Das Nautische Dreieck} \subsection{Definition des Nautischen Dreiecks} -Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel. Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient. -Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. - Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. +Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. -Zur Anwendung der Formeln der sphärischen Trigonometrie gelten folgende einfache Zusammenhänge: -\begin{itemize} - \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ - \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ - \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ - \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ - \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ -\end{itemize} -Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: +Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel zu bestimmen. + +Für die Definition gilt: \begin{center} \begin{tabular}{ c c c } Winkel && Name / Beziehung \\ @@ -31,6 +23,15 @@ Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: \end{tabular} \end{center} +\begin{itemize} + \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ + \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ + \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ + \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ + \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ +\end{itemize} + + \subsection{Zusammenhang des nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} \begin{figure} \begin{center} @@ -39,15 +40,13 @@ Um mit diesen Zusammenhängen zu rechnen benötigt man folgende Legende: \end{center} \end{figure} -Wie man im oberen Bild sieht, liegt das nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. -Das selbe Dreieck kann man aber auch auf die Erdkugel projizieren und es hat dann die Ecken Standort, Bildpunkt und Nordpol. -Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. - +Wie man in der Abbildung 21.4 sieht, liegt das nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. +Das selbe Dreieck kann man aber auch auf die Erdkugel projizieren. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. \section{Standortbestimmung ohne elektronische Hilfsmittel} -Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion Nautische Dreieck auf der Erdkugel zur Hilfe genommen. -Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. - +Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion des nautische Dreiecks auf die Erdkugel zur Hilfe genommen. +Mithilfe eines Sextanten, einem Jahrbuch und der sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. +Was ein Sextant und ein Jahrbuch ist, wird im Kapitel 21.6 erklärt. \begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} @@ -60,31 +59,30 @@ Mithilfe einiger Hilfsmittel und der Sphärischen Trigonometrie kann man dann di \subsection{Ecke $P$ und $A$} Unser eigener Standort ist der gesuchte Ecke $P$ und die Ecke $A$ ist in unserem Fall der Nordpol. -Der Vorteil ander Idee des Nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. +Der Vorteil ander Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. -\subsection{Ecke $B$ und $C$ - Bildpunkt X und Y} +\subsection{Ecke $B$ und $C$ - Bildpunkt $X$ und $Y$} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mond oder die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn. +Die Bildpunkte von den beiden Gestirnen $X$ und $Y$ bilden die beiden Ecken $B$ und $C$ im Dreieck der Abbildung 21.5. \subsection{Ephemeriden} Zu all diesen Gestirnen gibt es Ephemeriden, die man auch Jahrbücher nennt. In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. -Da diese Angaben in Stundenabständen gegeben sind, muss man für die minutengenaue Bestimmung zwischen den Stunden interpolieren. -Was diese Begriffe bedeuten, wird in den kommenden beiden Abschnitten erklärt. \begin{figure} \begin{center} - \includegraphics[width=18cm]{papers/nav/bilder/ephe.png} - \caption[Astrodienst - Ephemeriden Januar 2022]{Astrodienst - Ephemeriden Januar 2022} + \includegraphics[width=\textwidth]{papers/nav/bilder/ephe.png} + \caption[Nautical Almanac Mai 2002]{Nautical Almanac Mai 2002} \end{center} \end{figure} \subsubsection{Deklination} -Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und ergibt schlussendlich den Breitengrad. +Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und entspricht dem Breitengrad des Gestirns. -\subsubsection{Sternzeit und Rektaszension} +\subsubsection{Rektaszension und Sternzeit} Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht und geht vom Koordinatensystem der Himmelskugel aus. Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. @@ -98,19 +96,28 @@ Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Für die Sternzeit von Greenwich $\theta $braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. Im Anschluss berechnet man die Sternzeit von Greenwich -$\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3$. +\[\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3.\] -Wenn mann die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit von Greenwich bestimmen. +Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit von Greenwich bestimmen. Dies gilt analog auch für das zweite Gestirn. +\subsubsection{Sextant} +Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann, insbesondere den Winkelabstand zu einem Gestirn vom Horizont. Man nutze ihn vor allem für die astronomische Navigation auf See. -\subsection{Bestimmung des eigenen Standortes P} +\begin{figure} + \begin{center} + \includegraphics[width=10cm]{papers/nav/bilder/sextant.jpg} + \caption[Sextant]{Sextant} + \end{center} +\end{figure} + +\subsection{Bestimmung des eigenen Standortes $P$} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. Mithilfe dieser Dreiecken können wir die einfachen Sätze der sphärischen Trigonometrie anwenden und benötigen lediglich ein Ephemeride zu den Gestirnen und einen Sextant. \begin{figure} \begin{center} - \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} + \includegraphics[width=8cm]{papers/nav/bilder/dreieck.pdf} \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} \end{center} \end{figure} @@ -128,15 +135,15 @@ Mithilfe dieser Dreiecken können wir die einfachen Sätze der sphärischen Trig \end{tabular} \end{center} -Mithilfe des sphärischen Trigonometrie und den darausfolgenden Zusammenhängen des Nautischen Dreiecks können wir nun alle Seiten des Dreiecks $ABC$ berechnen. +Mit unserem erlangten Wissen können wir nun alle Seiten des Dreiecks $ABC$ berechnen. -Die Seitenlänge der Seite "Nordpol zum Bildpunkt X" sei $c$. +Die Seite vom Nordpol zum Bildpunkt $X$ sei $c$. Dann ist $c = \frac{\pi}{2} - \delta_1$. -Die Seitenlänge der Seite "Nordpol zum Bildpunkt Y" sei $b$. +Die Seite vom Nordpol zum Bildpunkt $Y$ sei $b$. Dann ist $b = \frac{\pi}{2} - \delta_2$. -Der Innenwinkel beim der Ecke "Nordpol" sei $\alpha$. +Der Innenwinkel bei der Ecke, wo der Nordpol ist sei $\alpha$. Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. mit @@ -144,55 +151,49 @@ mit \begin{tabular}{ c c c } Ecke && Name \\ \hline - $\delta_1$ && Deklination Bildpunkt $X$ \\ - $\delta_2$ && Deklination Bildpunk $Y$ \\ - $\lambda_1 $&& Längengrad Bildpunkt $X$\\ - $\lambda_2$ && Längengrad Bildpunkt $Y$ + $\delta_1$ && Deklination vom Bildpunkt $X$ \\ + $\delta_2$ && Deklination vom Bildpunk $Y$ \\ + $\lambda_1 $&& Längengrad vom Bildpunkt $X$\\ + $\lambda_2$ && Längengrad vom Bildpunkt $Y$ \end{tabular} \end{center} -Wichtig ist: Die Differenz der Längengrade ist gleich der Innenwinkel Alpha, deswegen der Betrag! - -Nun haben wir die beiden Seiten $c\ und\ b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. +Nun haben wir die beiden Seiten $c$ und $b$ und den Winkel $\alpha$, der sich zwischen diesen Seiten befindet. Mithilfe des Seiten-Kosinussatzes $\cos(a) = \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha)$ können wir nun die dritte Seitenlänge bestimmen. Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. -Jetzt fehlen noch die beiden anderen Innenwinkel $\beta \ und\ \gamma$. -Diese bestimmen wir mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$. +Jetzt fehlen noch die beiden anderen Innenwinkel $\beta$ und\ $\gamma$. +Diese bestimmen wir mithilfe des Sinussatzes \[\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}.\] Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. Im Zähler sind die Seiten, im Nenner die Winkel. -Somit ist $\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}] $. +Somit ist \[\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}].\] -Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha, \beta \ und \ \gamma$ bestimmt und somit das ganze erste Kugeldreieck berechnet. +Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha$, $\beta$ und $\gamma$ bestimmt und somit das ganze Kugeldreieck $ABC$ berechnet. \subsubsection{Dreieck $BPC$} -Wir bilden nun ein zweites Dreieck, welches die Ecken B und C des ersten Dreiecks besitzt. -Die dritte Ecke ist der eigene Standort P. +Wir bilden nun ein zweites Dreieck, welches die Ecken $B$ und $C$ des ersten Dreiecks besitzt. +Die dritte Ecke ist der eigene Standort $P$. Unser Standort definiere sich aus einer geographischen Breite $\delta$ und einer geographischen Länge $\lambda$. -Die Seite von P zu B sei $pb$ und die Seite von P zu C sei $pc$. +Die Seite von $P$ zu $B$ sei $pb$ und die Seite von $P$ zu $C$ sei $pc$. Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache Formel bestimmen, nämlich $pb=\frac{\pi}{2} - h_{B}$ und $pc=\frac{\pi}{2} - h_{C}$ -mit $h_B=$ Höhe von Gestirn in B und $h_C=$ Höhe von Gestirn in C mit Sextant gemessen. +mit $h_B=$ Höhe von Gestirn in $B$ und $h_C=$ Höhe von Gestirn in $C$ mit Sextant gemessen. -Zum Schluss müssen wir noch den Winkel $\beta1$ mithilfe des Seiten-Kosinussatzes mit den bekannten Seiten $pc$, $pb$ und $a$ bestimmen. +Zum Schluss müssen wir noch den Winkel $\beta_1$ mithilfe des Seiten-Kosinussatzes \[\cos(pb)=\cos(pc)\cdot\cos(a)+\sin(pc)\cdot\sin(a)\cdot\cos(\beta_1)\] mit den bekannten Seiten $pc$, $pb$ und $a$ bestimmen. \subsubsection{Dreieck $ABP$} -Nun muss man eine Verbindungslinie ziehen zwischen P und A. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$, den bekannten Seiten $c\ und \ pb$ und des Seiten-Kosinussatzes berechnen. - -Für den Seiten-Kosinussatz benötigt es noch $\kappa=\beta + \beta1$. - -Somit ist $\cos(l) = \cos(c)\cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)$ - +Nun muss man eine Verbindungslinie ziehen zwischen $P$ und $A$. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$, den bekannten Seiten $c$ und $pb$ und des Seiten-Kosinussatzes berechnen. +Für den Seiten-Kosinussatz benötigt es noch $\kappa=\beta + \beta_1$. +Somit ist \[\cos(l) = \cos(c)\cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)\] und - \[ \delta =\cos^{-1} [\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)]. \] -Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet mithilfe des Sinussatzes $\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}$ bestimmen. - +Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet. +Mithilfe des Sinussatzes \[\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}\] können wir das bestimmen. Somit ist \[ \omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}] \]und unsere gesuchte geographische Länge schlussendlich \[\lambda=\lambda_1 - \omega\] -mit $\lambda_1$=Längengrad Bildpunkt $X$ +wobei $\lambda_1$ die Länge des Bildpunktes $X$ von $C$ ist. diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index bb7f1e4..d56d482 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -6,14 +6,16 @@ Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren si Jedoch konnten sie dieses Problem nicht lösen. Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und sie wurde zu einer Hilfswissenschaft der Astronomen. -In Folge werden auch die ersten Sätze aufgestellt und wenige Jahrhunderte später wurden Berechnungen mithilfe des Sternkataloges von Hipparchos angestellt und darauffolgend Kartenmaterial erstellt. +Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom names Hipparchos. +Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten. +Chord ist der Vorgänger der Sinusfunktion und galt damals als wichtigste Grundlage der Trigonometrie. In dieser Zeit wurden auch die ersten Sternenkarten angefertigt, jedoch kannte man damals die Sinusfunktion noch nicht. + Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung mit Sternen vermehrt an Wichtigkeit gewann. Man nutzte für die Kartographie nun die Kugelgeometrie, um die Genauigkeit zu erhöhen. Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet und im darauffolgenden Jahrhundert folgte der Winkelkosinussatz. - Durch weitere mathematische Entwicklungen wie den Logarithmus wurden im Laufe des nächsten Jahrhunderts viele neue Methoden und kartographische Anwendungen der Kugelgeometrie entdeckt. Im 19. und 20. Jahrhundert wurden weitere nicht-euklidische Geometrien entwickelt und die sphärische Trigonometrie fand auch ihre Anwendung in der Relativitätstheorie. \ No newline at end of file diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index cf2f242..ce367f6 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -2,33 +2,35 @@ \section{Sphärische Trigonometrie} In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. Dabei gibt es folgenden Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie: -\begin{center} - - -\begin{tabular}{ccc} - Eben & $\leftrightarrow$ & sphärisch \\ - \hline - $a$ & $\leftrightarrow$ & $\sin \ a$ \\ - - $a^2$ & $\leftrightarrow$ & $-\cos \ a$ \\ -\end{tabular} -\end{center} \subsection{Das Kugeldreieck} +Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie "Grosskreisebene" und "Grosskreisbögen" verstehen. +Ein Grosskreis ist ein größtmöglicher Kreis auf einer Kugeloberfläche. +Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Schnitt auf dem Großkreis teilt die Kugel in jedem Fall in zwei gleich grosse Hälften. +Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. +Grosskreisbögen sind die Verbindungslinien zwischen zwei Punkten auf der Kugel, welche auch "Seiten" eines Kugeldreiecks gennant werden. Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck $ABC$. Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. -$A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten. -Ein Grosskreis ist ein größtmöglicher Kreis auf einer Kugeloberfläche. -Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Schnitt auf dem Großkreis teilt die Kugel in jedem Fall in zwei gleich grosse Hälften. +$A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung 21.2). -Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. -Laut dieser Definition ist die Seite $c$ der Winkel $AMB$. +Laut dieser Definition ist die Seite $c$ der Winkel $AMB$, wobei der Punkt $M$ die Erdmitte ist. Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. -Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersche Dreiecke. +Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersches Dreieck. + +Es gibt einen Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie, wobei folgend $a$ eine Seite beschreibt: +\begin{center} + \begin{tabular}{ccc} + Eben & $\leftrightarrow$ & sphärisch \\ + \hline + $a$ & $\leftrightarrow$ & $\sin \ a$ \\ + + $a^2$ & $\leftrightarrow$ & $-\cos \ a$ \\ + \end{tabular} +\end{center} \begin{figure} \begin{center} @@ -38,9 +40,16 @@ Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha \end{figure} -\subsection{Rechtwinkliges Dreieck und Rechtseitiges Dreieck} -Wie auch im uns bekannten Dreieck gibt es beim Kugeldreieck auch ein Rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. +\subsection{Rechtwinkliges Dreieck und rechtseitiges Dreieck} +Wie auch im ebenen Dreieck gibt es beim Kugeldreieck auch ein rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. +\begin{figure} + + \begin{center} + \includegraphics[width=10cm]{papers/nav/bilder/recht.jpg} + \caption[Rechtseitiges Kugeldreieck]{Rechtseitiges Kugeldreieck} + \end{center} +\end{figure} \subsection{Winkelsumme} \begin{figure} @@ -55,8 +64,9 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. Für die Summe der Innenwinkel gilt \begin{align} - \alpha+\beta+\gamma &= \frac{A}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi. \nonumber + \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi, \nonumber \end{align} +wobei F der Flächeninhalt des Kugeldreiecks ist. \subsubsection{Sphärischer Exzess} Der sphärische Exzess \begin{align} @@ -65,31 +75,31 @@ Der sphärische Exzess beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zum Flächeninhalt des Kugeldreiecks. \subsubsection{Flächeninnhalt} -Der Flächeninhalt $A$ lässt sich aus den Winkeln $\alpha,\ \beta, \ \gamma$ und dem Kugelradius $r$ berechnen. +Mithilfe des Radius $r$ und dem sphärischen Exzess $\epsilon$ gilt für den Flächeninhalt +\[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon\]. \subsection{Sphärischer Sinussatz} In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. - Das bedeutet, dass \begin{align} - \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \ \text{auch beim Kugeldreieck gilt.} + \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \end{align} +auch beim Kugeldreieck gilt. -\subsection{Sphärischer Kosinussätze} +\subsection{Sphärische Kosinussätze} Auch in der sphärischen Trigonometrie gibt es den Seitenkosinussatz \begin{align} - cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber + \cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber \end{align} %Seitenkosinussatz und den Winkelkosinussatz \begin{align} - \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c \nonumber + \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c. \nonumber \end{align} \subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. -In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. - +In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt. Es gilt nämlich: \begin{align} \cos c = \cos a \cdot \cos b \ \text{wenn} \nonumber & -- cgit v1.2.1 From ab62c3937cc111ce1d61d76f0bdf396a4a5a9297 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 21 May 2022 20:36:01 +0200 Subject: add image code --- buch/papers/kugel/images/Makefile | 4 +- buch/papers/kugel/images/curvature.maxima | 6 ++ buch/papers/kugel/images/curvature.pov | 72 +++++++++++++++++++++++- buch/papers/kugel/images/curvgraph.m | 93 +++++++++++++++++++++++++------ 4 files changed, 153 insertions(+), 22 deletions(-) create mode 100644 buch/papers/kugel/images/curvature.maxima diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile index 8efa228..e8bf919 100644 --- a/buch/papers/kugel/images/Makefile +++ b/buch/papers/kugel/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: curvature.png +all: curvature.jpg curvature.inc: curvgraph.m octave curvgraph.m @@ -11,3 +11,5 @@ curvature.inc: curvgraph.m curvature.png: curvature.pov curvature.inc povray +A0.1 +W1920 +H1080 +Ocurvature.png curvature.pov +curvature.jpg: curvature.png + convert curvature.png -density 300 -units PixelsPerInch curvature.jpg diff --git a/buch/papers/kugel/images/curvature.maxima b/buch/papers/kugel/images/curvature.maxima new file mode 100644 index 0000000..6313642 --- /dev/null +++ b/buch/papers/kugel/images/curvature.maxima @@ -0,0 +1,6 @@ + +f: exp(-r^2/sigma^2)/sigma; +laplacef: ratsimp(diff(r * diff(f,r), r) / r); +f: exp(-r^2/(2*sigma^2))/(sqrt(2)*sigma); +laplacef: ratsimp(diff(r * diff(f,r), r) / r); + diff --git a/buch/papers/kugel/images/curvature.pov b/buch/papers/kugel/images/curvature.pov index 3535488..9dbaa86 100644 --- a/buch/papers/kugel/images/curvature.pov +++ b/buch/papers/kugel/images/curvature.pov @@ -11,17 +11,17 @@ global_settings { assumed_gamma 1 } -#declare imagescale = 0.1; +#declare imagescale = 0.09; camera { - location <40, 10, -20> + location <10, 10, -40> look_at <0, 0, 0> right 16/9 * x * imagescale up y * imagescale } light_source { - <10, 10, -40> color White + <-10, 10, -40> color White area_light <1,0,0> <0,0,1>, 10, 10 adaptive 1 jitter @@ -70,3 +70,69 @@ arrow(<0,-1,0>, <0,1,0>, 0.01, White) arrow(<0,0,-2.1>, <0,0,2.1>, 0.01, White) #include "curvature.inc" + +#declare sigma = 1; +#declare N0 = 0.5; +#declare funktion = function(r) { + (exp(-r*r/(sigma*sigma)) / sigma + - + exp(-r*r/(2*sigma*sigma)) / (sqrt(2)*sigma)) / N0 +}; +#declare hypot = function(xx, yy) { sqrt(xx*xx+yy*yy) }; + +#declare Funktion = function(x,y) { funktion(hypot(x+1,y)) - funktion(hypot(x-1,y)) }; +#macro punkt(xx,yy) + +#end + +#declare griddiameter = 0.006; +union { + #declare xmin = -3; + #declare xmax = 3; + #declare ymin = -2; + #declare ymax = 2; + + + #declare xstep = 0.2; + #declare ystep = 0.02; + #declare xx = xmin; + #while (xx < xmax + xstep/2) + #declare yy = ymin; + #declare P = punkt(xx, yy); + #while (yy < ymax - ystep/2) + #declare yy = yy + ystep; + #declare Q = punkt(xx, yy); + sphere { P, griddiameter } + cylinder { P, Q, griddiameter } + #declare P = Q; + #end + sphere { P, griddiameter } + #declare xx = xx + xstep; + #end + + #declare xstep = 0.02; + #declare ystep = 0.2; + #declare yy = ymin; + #while (yy < ymax + ystep/2) + #declare xx = xmin; + #declare P = punkt(xx, yy); + #while (xx < xmax - xstep/2) + #declare xx = xx + xstep; + #declare Q = punkt(xx, yy); + sphere { P, griddiameter } + cylinder { P, Q, griddiameter } + #declare P = Q; + #end + sphere { P, griddiameter } + #declare yy = yy + ystep; + #end + + pigment { + color rgb<0.8,0.8,0.8> + } + finish { + metallic + specular 0.8 + } +} + diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m index 96ca4b1..b83c877 100644 --- a/buch/papers/kugel/images/curvgraph.m +++ b/buch/papers/kugel/images/curvgraph.m @@ -13,23 +13,34 @@ sigma2 = 1; global s; s = 1; +global cmax; +cmax = 0.9; +global cmin; +cmin = -0.9; + +global Cmax; +global Cmin; +Cmax = 0; +Cmin = 0; + xmin = -3; xmax = 3; -xsteps = 1000; +xsteps = 200; hx = (xmax - xmin) / xsteps; ymin = -2; ymax = 2; -ysteps = 1000; +ysteps = 200; hy = (ymax - ymin) / ysteps; function retval = f0(r) global sigma2; - retval = exp(-r^2/sigma2)/sigma2 - exp(-r^2/(2*sigma2))/(sqrt(2)*sigma2); + retval = exp(-r^2/sigma2)/sqrt(sigma2) - exp(-r^2/(2*sigma2))/(sqrt(2*sigma2)); end global N0; -N0 = f0(0); +N0 = f0(0) +N0 = 0.5; function retval = f1(x,y) global N0; @@ -44,10 +55,10 @@ endfunction function retval = curvature0(r) global sigma2; retval = ( - (2*sigma2-r^2)*exp(-r^2/(2*sigma2)) + -4*(sigma2-r^2)*exp(-r^2/sigma2) + - 4*(r^2-sigma2)*exp(-r^2/sigma2) - ) / (sigma2^2); + (2*sigma2-r^2)*exp(-r^2/(2*sigma2)) + ) / (sigma2^(5/2)); endfunction function retval = curvature1(x, y) @@ -56,28 +67,74 @@ endfunction function retval = curvature(x, y) global s; - retval = curvature1(x+s, y) + curvature1(x-s, y); + retval = curvature1(x+s, y) - curvature1(x-s, y); endfunction function retval = farbe(x, y) + global Cmax; + global Cmin; + global cmax; + global cmin; c = curvature(x, y); - retval = c * ones(1,3); + if (c < Cmin) + Cmin = c + endif + if (c > Cmax) + Cmax = c + endif + u = (c - cmin) / (cmax - cmin); + if (u > 1) + u = 1; + endif + if (u < 0) + u = 0; + endif + color = [ u, 0.5, 1-u ]; + color = color/max(color); + color(1,4) = c/2; + retval = color; endfunction -fn = fopen("curvature.inc", "w"); +function dreieck(fn, A, B, C) + fprintf(fn, "\ttriangle {\n"); + fprintf(fn, "\t <%.4f,%.4f,%.4f>,\n", A(1,1), A(1,3), A(1,2)); + fprintf(fn, "\t <%.4f,%.4f,%.4f>,\n", B(1,1), B(1,3), B(1,2)); + fprintf(fn, "\t <%.4f,%.4f,%.4f>\n", C(1,1), C(1,3), C(1,2)); + fprintf(fn, "\t}\n"); +endfunction +function viereck(fn, punkte) + color = farbe(mean(punkte(:,1)), mean(punkte(:,2))); + fprintf(fn, " mesh {\n"); + dreieck(fn, punkte(1,:), punkte(2,:), punkte(3,:)); + dreieck(fn, punkte(2,:), punkte(3,:), punkte(4,:)); + fprintf(fn, "\tpigment { color rgb<%.4f,%.4f,%.4f> } // %.4f\n", + color(1,1), color(1,2), color(1,3), color(1,4)); + fprintf(fn, " }\n"); +endfunction + +fn = fopen("curvature.inc", "w"); +punkte = zeros(4,3); for ix = (0:xsteps) x = xmin + ix * hx; + punkte(1,1) = x; + punkte(2,1) = x; + punkte(3,1) = x + hx; + punkte(4,1) = x + hx; for iy = (0:ysteps) y = ymin + iy * hy; - fprintf(fn, "sphere { <%.4f, %.4f, %.4f>, 0.01\n", - x, f(x, y), y); - color = farbe(x, y); - fprintf(fn, "pigment { color rgb<%.4f,%.4f,%.4f> }\n", - color(1,1), color(1,2), color(1,3)); - fprintf(fn, "finish { metallic specular 0.5 }\n"); - fprintf(fn, "}\n"); + punkte(1,2) = y; + punkte(2,2) = y + hy; + punkte(3,2) = y; + punkte(4,2) = y + hy; + for i = (1:4) + punkte(i,3) = f(punkte(i,1), punkte(i,2)); + endfor + viereck(fn, punkte); end end - +#fprintf(fn, " finish { metallic specular 0.5 }\n"); fclose(fn); + +printf("Cmax = %.4f\n", Cmax); +printf("Cmin = %.4f\n", Cmin); -- cgit v1.2.1 From d8d6a61a2ab45d9171a93e4a72d254a3ed5ef87f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 21 May 2022 20:42:47 +0200 Subject: fix some bugs --- buch/papers/kugel/images/curvature.pov | 5 +++-- buch/papers/kugel/images/curvgraph.m | 8 ++++---- 2 files changed, 7 insertions(+), 6 deletions(-) diff --git a/buch/papers/kugel/images/curvature.pov b/buch/papers/kugel/images/curvature.pov index 9dbaa86..3b15d77 100644 --- a/buch/papers/kugel/images/curvature.pov +++ b/buch/papers/kugel/images/curvature.pov @@ -72,7 +72,8 @@ arrow(<0,0,-2.1>, <0,0,2.1>, 0.01, White) #include "curvature.inc" #declare sigma = 1; -#declare N0 = 0.5; +#declare s = 1.4; +#declare N0 = 0.4; #declare funktion = function(r) { (exp(-r*r/(sigma*sigma)) / sigma - @@ -80,7 +81,7 @@ arrow(<0,0,-2.1>, <0,0,2.1>, 0.01, White) }; #declare hypot = function(xx, yy) { sqrt(xx*xx+yy*yy) }; -#declare Funktion = function(x,y) { funktion(hypot(x+1,y)) - funktion(hypot(x-1,y)) }; +#declare Funktion = function(x,y) { funktion(hypot(x+s,y)) - funktion(hypot(x-s,y)) }; #macro punkt(xx,yy) #end diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m index b83c877..75effd6 100644 --- a/buch/papers/kugel/images/curvgraph.m +++ b/buch/papers/kugel/images/curvgraph.m @@ -11,7 +11,7 @@ global sigma2; sigma2 = 1; global s; -s = 1; +s = 1.4; global cmax; cmax = 0.9; @@ -40,7 +40,7 @@ end global N0; N0 = f0(0) -N0 = 0.5; +N0 = 0.4; function retval = f1(x,y) global N0; @@ -115,13 +115,13 @@ endfunction fn = fopen("curvature.inc", "w"); punkte = zeros(4,3); -for ix = (0:xsteps) +for ix = (0:xsteps-1) x = xmin + ix * hx; punkte(1,1) = x; punkte(2,1) = x; punkte(3,1) = x + hx; punkte(4,1) = x + hx; - for iy = (0:ysteps) + for iy = (0:ysteps-1) y = ymin + iy * hy; punkte(1,2) = y; punkte(2,2) = y + hy; -- cgit v1.2.1 From f144be56b0c7ec03f74c46928b1354a959a59246 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 22 May 2022 13:36:59 +0200 Subject: add hermite application presentation --- vorlesungen/18_hermiteintegrierbar/Makefile | 33 ++++++++ .../MathSem-18-hermiteintegrierbar.tex | 14 ++++ vorlesungen/18_hermiteintegrierbar/common.tex | 17 +++++ .../hermiteintegrierbar-handout.tex | 11 +++ vorlesungen/18_hermiteintegrierbar/slides.tex | 11 +++ vorlesungen/slides/hermite/Makefile.inc | 5 ++ vorlesungen/slides/hermite/hermiteentwicklung.tex | 69 +++++++++++++++++ vorlesungen/slides/hermite/loesung.tex | 56 ++++++++++++++ vorlesungen/slides/hermite/normalhermite.tex | 88 ++++++++++++++++++++++ vorlesungen/slides/hermite/normalintegrale.tex | 54 +++++++++++++ vorlesungen/slides/hermite/skalarprodukt.tex | 72 ++++++++++++++++++ vorlesungen/slides/test.tex | 6 +- 12 files changed, 435 insertions(+), 1 deletion(-) create mode 100644 vorlesungen/18_hermiteintegrierbar/Makefile create mode 100644 vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex create mode 100644 vorlesungen/18_hermiteintegrierbar/common.tex create mode 100644 vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex create mode 100644 vorlesungen/18_hermiteintegrierbar/slides.tex create mode 100644 vorlesungen/slides/hermite/hermiteentwicklung.tex create mode 100644 vorlesungen/slides/hermite/loesung.tex create mode 100644 vorlesungen/slides/hermite/normalhermite.tex create mode 100644 vorlesungen/slides/hermite/normalintegrale.tex create mode 100644 vorlesungen/slides/hermite/skalarprodukt.tex diff --git a/vorlesungen/18_hermiteintegrierbar/Makefile b/vorlesungen/18_hermiteintegrierbar/Makefile new file mode 100644 index 0000000..a2dfb87 --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/Makefile @@ -0,0 +1,33 @@ +# +# Makefile -- hermiteintegrierbar +# +# (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +# +all: hermiteintegrierbar-handout.pdf MathSem-18-hermiteintegrierbar.pdf + +include ../slides/Makefile.inc + +SOURCES = common.tex slides.tex $(slides) + +MathSem-18-hermiteintegrierbar.pdf: MathSem-18-hermiteintegrierbar.tex $(SOURCES) + pdflatex MathSem-18-hermiteintegrierbar.tex + +hermiteintegrierbar-handout.pdf: hermiteintegrierbar-handout.tex $(SOURCES) + pdflatex hermiteintegrierbar-handout.tex + +thumbnail: thumbnail.jpg # fix1.jpg + +thumbnail.pdf: MathSem-18-hermiteintegrierbar.pdf + pdfjam --outfile thumbnail.pdf --papersize '{16cm,9cm}' \ + MathSem-18-hermiteintegrierbar.pdf 1 +thumbnail.jpg: thumbnail.pdf + convert -density 300 thumbnail.pdf \ + -resize 1920x1080 -units PixelsPerInch thumbnail.jpg + +fix1.pdf: MathSem-18-hermiteintegrierbar.pdf + pdfjam --outfile fix1.pdf --papersize '{16cm,9cm}' \ + MathSem-18-hermiteintegrierbar.pdf 1 +fix1.jpg: fix1.pdf + convert -density 300 fix1.pdf \ + -resize 1920x1080 -units PixelsPerInch fix1.jpg + diff --git a/vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex b/vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex new file mode 100644 index 0000000..7a3a647 --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/MathSem-18-hermiteintegrierbar.tex @@ -0,0 +1,14 @@ +% +% MathSem-18-hermiteintegrierbar.tex -- Präsentation +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{true} +\begin{document} +\begin{frame} +\titlepage +\end{frame} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/18_hermiteintegrierbar/common.tex b/vorlesungen/18_hermiteintegrierbar/common.tex new file mode 100644 index 0000000..8b1c71f --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/common.tex @@ -0,0 +1,17 @@ +% +% common.tex -- gemeinsame definition +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\input{../common/packages.tex} +\input{../common/common.tex} +\mode{% +\usetheme[hideothersubsections,hidetitle]{Hannover} +} +\beamertemplatenavigationsymbolsempty +\title[$\int P(t)e^{-t^2}\,dt$]{Elementare Stammfunktion für +$\displaystyle\int P(t)e^{-t^2}\,dt$?} +\author[A.~Müller]{Prof. Dr. Andreas Müller} +\date[]{} +\newboolean{presentation} + diff --git a/vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex b/vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex new file mode 100644 index 0000000..a466024 --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/hermiteintegrierbar-handout.tex @@ -0,0 +1,11 @@ +% +% hermiteintegrierbar-handout.tex -- Handout XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\documentclass[handout,aspectratio=169]{beamer} +\input{common.tex} +\setboolean{presentation}{false} +\begin{document} +\input{slides.tex} +\end{document} diff --git a/vorlesungen/18_hermiteintegrierbar/slides.tex b/vorlesungen/18_hermiteintegrierbar/slides.tex new file mode 100644 index 0000000..cb3bbea --- /dev/null +++ b/vorlesungen/18_hermiteintegrierbar/slides.tex @@ -0,0 +1,11 @@ +% +% slides.tex -- XXX +% +% (c) 2017 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\folie{hermite/normalintegrale.tex} +\folie{hermite/normalhermite.tex} +\folie{hermite/hermiteentwicklung.tex} +\folie{hermite/loesung.tex} +\folie{hermite/skalarprodukt.tex} + diff --git a/vorlesungen/slides/hermite/Makefile.inc b/vorlesungen/slides/hermite/Makefile.inc index 5c55467..58c21f2 100644 --- a/vorlesungen/slides/hermite/Makefile.inc +++ b/vorlesungen/slides/hermite/Makefile.inc @@ -4,4 +4,9 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # chapterhermite = \ + ../slides/hermite/normalintegrale.tex \ + ../slides/hermite/normalhermite.tex \ + ../slides/hermite/hermiteentwicklung.tex \ + ../slides/hermite/loesung.tex \ + ../slides/hermite/skalarprodukt.tex \ ../slides/hermite/test.tex diff --git a/vorlesungen/slides/hermite/hermiteentwicklung.tex b/vorlesungen/slides/hermite/hermiteentwicklung.tex new file mode 100644 index 0000000..e1ced30 --- /dev/null +++ b/vorlesungen/slides/hermite/hermiteentwicklung.tex @@ -0,0 +1,69 @@ +% +% hermiteentwicklung.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Beliebige Polynome} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Polynom} +\[ +P(x) += +p_0 + p_1x + p_2x^2 + \dots + p_nx^n +\] +als Linearkombination von Hermite-Polynome schreiben: +\begin{align*} +P(x) +&= +a_0H_0(x)% + a_1H_1(x) ++ \dots + a_nH_n(x) +\\ +&= +a_0\cdot 1 +\\ +&\quad + a_1\cdot 2x +\\ +&\quad + a_2\cdot(4x^2-2) +\\ +&\quad + a_3\cdot(8x^3-12x) +\\ +&\quad + a_4\cdot(16x^4-48x^2+12) +\\ +&\quad\;\;\vdots +\\ +&\quad + a_n(2^nx^n + \dots) +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Koeffizientenvergleich} +führt auf ein Gleichungssystem +\begin{center} +\begin{tabular}{|>{$}r<{$}>{$}r<{$}>{$}r<{$}>{$}r<{$}>{$}r<{$}>{$}c<{$}|>{$}c<{$}|} +\hline +a_0&a_1&a_2&a_3&a_4&\dots&\\ +\hline + 1& 0& 0& 0& 0&\dots&p_0\\ + 0& 2& 0& 0& 0&\dots&p_1\\ +-2& 0& 4& 0& 0&\dots&p_2\\ + 0&-12& 0& 8& 0&\dots&p_3\\ +12& 0&-48& 0& 16&\dots&p_4\\ +\vdots&\vdots&\vdots&\vdots&\vdots&\ddots&\vdots\\ +\hline +\end{tabular} +\end{center} +Dreiecksmatrix, Diagonalelement +$\ne 0$ +$\Rightarrow$ +$\exists$ eindeutige Lösung +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/loesung.tex b/vorlesungen/slides/hermite/loesung.tex new file mode 100644 index 0000000..7d4741f --- /dev/null +++ b/vorlesungen/slides/hermite/loesung.tex @@ -0,0 +1,56 @@ +% +% loesung.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Lösung} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Frage} +Für welche Polynome $P(t)$ kann man eine Stammfunktion +\[ +\int +P(t)e^{-\frac{t^2}2} +\,dt +\] +in geschlossener Form angeben? +\end{block} +\begin{block}{``Hermite-Antwort''} +\[ +\int H_n(x)e^{-x^2}\,dx +\] +kann genau für $n>0$ in geschlossener Form angegeben werden. +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Allgemein} +\begin{align*} +\int P(x)e^{-x^2}\,dx +&= +\int \sum_{k=0}^n a_kH_k(x)e^{-x^2}\,dx +\\ +&= +\sum_{k=0}^n +a_k +\int +H_k(x)e^{-x^2}\,dx +\\ +&= +a_0\operatorname{erf}(x) + C +\\ +&\hspace*{2mm} + \sum_{k=1}^n a_k\int H_k(x)e^{-x^2}\,dx +\end{align*} +\end{block} +\begin{theorem} +Das Integral von $P(x)e^{-x^2}$ ist genau dann elementar darstellbar, wenn +$a_0=0$ +\end{theorem} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/normalhermite.tex b/vorlesungen/slides/hermite/normalhermite.tex new file mode 100644 index 0000000..bcd30f2 --- /dev/null +++ b/vorlesungen/slides/hermite/normalhermite.tex @@ -0,0 +1,88 @@ +% +% normalhermite.tex -- integrability of hermite polynomials +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Hermite-Polynome} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Definition (Rodrigues-Formel)} +\[ +H_n(x) += +(-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2} +\] +\end{block} +\vspace{-10pt} +\begin{block}{Orthogonalität} +$H_n(x)$ sind orthogonale Polynome bezüglich $w(x)=e^{-x^2}$, d.~h. +\begin{align*} +\langle H_n,H_m\rangle_w +&= +\int H_n(x)H_m(x)e^{-x^2}\,dx +\\ +&= +\biggl\{ +\renewcommand{\arraycolsep}{1pt} +\begin{array}{l@{\quad}l} +1&\text{falls $n=m$}\\ +0&\text{sonst} +\end{array} +\biggr\} += +\delta_{mn} +\end{align*} +\end{block} +\vspace{-10pt} +\begin{block}{Rekursion: Auf-/Absteigeoperatoren} +Rekursionsformel: +\[ +H_n(x) += +2x\cdot H_{n-1}(x) - H_{n-1}'(x) +\] +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Stammfunktion} +\begin{align*} +\int H_n(x) e^{-x^2}\,dx +&= +\int \bigl({\color{red}2x}H_{n-1}(x) +\\ +&\qquad -H_{n-1}'(x)\bigr) e^{-x^2}\,dx +\\ +{\color{gray}(e^{-x^2}=-2x)} +&= +{\color{red}-}\int {\color{red}(e^{-x^2})'} H_{n-1}(x)\,dx +\\ +&\qquad +- +\int H_{n-1}'(x) e^{-x^2}\,dx +\\ +\text{\color{gray}(Produktregel)} +&= +\int (e^{-x^2}H_{n-1}(x))'\,dx +\\ +\text{\color{gray}(Ableitung)} +&= +e^{-x^2}H_{n-1}(x) +\end{align*} +ausser für $n=0$: +\[ +\int +H_0(x)e^{-x^2}\,dx += +\int +e^{-x^2}\,dx +\] +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/normalintegrale.tex b/vorlesungen/slides/hermite/normalintegrale.tex new file mode 100644 index 0000000..88abbe8 --- /dev/null +++ b/vorlesungen/slides/hermite/normalintegrale.tex @@ -0,0 +1,54 @@ +% +% normalintegrale.tex -- +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Integranden $P(t)e^{-t^2}$} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Frage} +Für welche Polynome $P(t)$ kann man eine Stammfunktion +\[ +\int +P(t)e^{-t^2} +\,dt +\] +in geschlossener Form angeben? +\end{block} +\begin{block}{Allgemeine Antwort} +Satz von Liouville und +Risch- Algorithmus können entscheiden, ob es eine elementare Stammfunktion gibt +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Negativbeispiel} +$P(t) = 1$, das Normalverteilungsintegral +\[ +F(x) += +\frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-t^2}\,dt +\] +ist nicht elementar darstellbar. +\end{block} +\begin{block}{Positivbeispiel} +$P(t)=t$. Wegen +\begin{align*} +\frac{d}{dx}e^{-x^2} +&= +-xe^{-x^2} +\intertext{ist} +\int te^{-t^2}\,dt +&= +-e^{-x^2}+C +\end{align*} +elementar darstellbar. +\end{block} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/hermite/skalarprodukt.tex b/vorlesungen/slides/hermite/skalarprodukt.tex new file mode 100644 index 0000000..32b933f --- /dev/null +++ b/vorlesungen/slides/hermite/skalarprodukt.tex @@ -0,0 +1,72 @@ +% +% skalarprodukt.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Skalarprodukt} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Orthogonale Zerlegung} +Orthogonale $H_k$ normalisieren: +\[ +\tilde{H}_k(x) = \frac{1}{\|H_k\|_w} H_k(x) +\] +mit Gewichtsfunktion $w(x)=e^{-x^2}$ +\end{block} +\begin{block}{``Hermite''-Analyse} +\begin{align*} +P(x) +&= +\sum_{k=1}^\infty a_k H_k(x) += +\sum_{k=1}^\infty \tilde{a}_k \tilde{H}_k(x) +\\ +\tilde{a}_k +&= +\| H_k\|_w\, a_k +\\ +a_k +&= +\frac{1}{\|H_k\|} +\langle \tilde{H}_k, P\rangle_w += +\frac{1}{\|H_k\|^2} +\langle H_k, P\rangle_w +\end{align*} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{Integrationsproblem} +Bedingung: +\begin{align*} +a_0=0 +\qquad\Leftrightarrow\qquad +\langle H_0,P\rangle_w +&= +0 +\\ +\int_{-\infty}^\infty +P(t) w(t) \,dt += +\int_{-\infty}^\infty +P(t) e^{-t^2} \,dt +&= +0 +\end{align*} +\end{block} +\begin{theorem} +Das Integral von $P(t)e^{-t^2}$ ist in geschlossener Form darstellbar +genau dann, wenn +\[ +\int_{-\infty}^\infty P(t)e^{-t^2}\,dt = 0 +\] +\end{theorem} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex index 6aa09f8..ca4ccc9 100644 --- a/vorlesungen/slides/test.tex +++ b/vorlesungen/slides/test.tex @@ -3,4 +3,8 @@ % % (c) 2019 Prof Dr Andreas Müller, Hochschule Rapperswil % -\folie{0/intro.tex} +\folie{hermite/normalintegrale.tex} +\folie{hermite/normalhermite.tex} +\folie{hermite/hermiteentwicklung.tex} +\folie{hermite/loesung.tex} +\folie{hermite/skalarprodukt.tex} -- cgit v1.2.1 From 1b887f44b5ec310f00184c916623d59abcf6e14d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 22 May 2022 15:21:28 +0200 Subject: typo --- vorlesungen/slides/hermite/normalhermite.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/vorlesungen/slides/hermite/normalhermite.tex b/vorlesungen/slides/hermite/normalhermite.tex index bcd30f2..16a314c 100644 --- a/vorlesungen/slides/hermite/normalhermite.tex +++ b/vorlesungen/slides/hermite/normalhermite.tex @@ -57,7 +57,7 @@ H_n(x) \\ &\qquad -H_{n-1}'(x)\bigr) e^{-x^2}\,dx \\ -{\color{gray}(e^{-x^2}=-2x)} +{\color{gray}((e^{-x^2})'=-2x)} &= {\color{red}-}\int {\color{red}(e^{-x^2})'} H_{n-1}(x)\,dx \\ -- cgit v1.2.1 From 53aea87685ea9f37f982f1ec90a82ce168d6d7cb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 23 May 2022 11:34:57 +0200 Subject: rewriting the risch algorithm stuff --- buch/chapters/060-integral/Makefile.inc | 7 + buch/chapters/060-integral/differentialkoerper.tex | 1957 +------------------- .../chapters/060-integral/differentialkoerper2.tex | 1953 +++++++++++++++++++ buch/chapters/060-integral/diffke.tex | 20 + buch/chapters/060-integral/elementar.tex | 7 + buch/chapters/060-integral/erweiterungen.tex | 12 + buch/chapters/060-integral/iproblem.tex | 93 + buch/chapters/060-integral/irat.tex | 140 ++ buch/chapters/060-integral/logexp.tex | 27 + buch/chapters/060-integral/rational.tex | 8 + buch/chapters/060-integral/risch.tex | 3 +- buch/chapters/060-integral/sqrat.tex | 8 + 12 files changed, 2286 insertions(+), 1949 deletions(-) create mode 100644 buch/chapters/060-integral/differentialkoerper2.tex create mode 100644 buch/chapters/060-integral/diffke.tex create mode 100644 buch/chapters/060-integral/elementar.tex create mode 100644 buch/chapters/060-integral/erweiterungen.tex create mode 100644 buch/chapters/060-integral/iproblem.tex create mode 100644 buch/chapters/060-integral/irat.tex create mode 100644 buch/chapters/060-integral/logexp.tex create mode 100644 buch/chapters/060-integral/rational.tex create mode 100644 buch/chapters/060-integral/sqrat.tex diff --git a/buch/chapters/060-integral/Makefile.inc b/buch/chapters/060-integral/Makefile.inc index d85caad..e0dfc21 100644 --- a/buch/chapters/060-integral/Makefile.inc +++ b/buch/chapters/060-integral/Makefile.inc @@ -8,5 +8,12 @@ CHAPTERFILES += \ chapters/060-integral/fehlerfunktion.tex \ chapters/060-integral/eulertransformation.tex \ chapters/060-integral/differentialkoerper.tex \ + chapters/060-integral/rational.tex \ + chapters/060-integral/erweiterungen.tex \ + chapters/060-integral/diffke.tex \ + chapters/060-integral/irat.tex \ + chapters/060-integral/sqratrat.tex \ chapters/060-integral/risch.tex \ + chapters/060-integral/logexp.tex \ + chapters/060-integral/elementar.tex \ chapters/060-integral/chapter.tex diff --git a/buch/chapters/060-integral/differentialkoerper.tex b/buch/chapters/060-integral/differentialkoerper.tex index f41d3ba..66bb0c1 100644 --- a/buch/chapters/060-integral/differentialkoerper.tex +++ b/buch/chapters/060-integral/differentialkoerper.tex @@ -1,1953 +1,14 @@ % -% differentialalgebren.tex +% differentialkoerper.tex % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % -\section{Differentialkörper und der Satz von Liouville +\section{Differentialkörper \label{buch:integrale:section:dkoerper}} -\rhead{Differentialkörper und der Satz von Liouville} -Das Problem der Darstellbarkeit eines Integrals in geschlossener -Form verlangt zunächst einmal nach einer Definition dessen, was man -als ``geschlossene Form'' akzeptieren will. -Die sogenannten {\em elementaren Funktionen} von -Abschnitt~\ref{buch:integrale:section:elementar} -bilden dafür den theoretischen Rahmen. -Das Problem ist dann die Frage zu beantworten, ob ein Integral eine -Stammfunktion hat, die eine elementare Funktion ist. -Der Satz von Liouville von Abschnitt~\ref{buch:integrale:section:liouville} -löst das Problem. - -\subsection{Eine Analogie -\label{buch:integrale:section:analogie}} -% XXX Analogie: Formel für Polynom-Nullstellen -% XXX Stammfunktion als elementare Funktion -Das Analysis-Problem, eine Stammfunktion zu finden, ist analog zum -wohlbekannten algebraischen Problem, Nullstellen von Polynomen zu finden. -Wir entwickeln diese Analogie in etwas mehr Detail, um zu sehen, ob man -aus dem algebraischen Problem etwas über das Problem der Analysis -lernen kann. - -Für ein Polynom $p(X) = a_nX^n+a_{n-1}X^{n-1}+\dots+a_1X+a_0\in\mathbb{C}[X]$ -mit Koeffizienten $a_k\in\mathbb{C}$ ist es sehr einfach, für jede beliebige -komplexe Zahl $z\in\mathbb{C}$ den Wert $p(z)$ des Polynoms auszurechnen. -Ein paar wenige Rechenregeln genügen dazu, man kann leicht einem Kind -beibringen, mit einem Taschenrechner so einen Wert auszurechnen. - -Ähnlich sieht es mit der Ableitungsoperation aus. -Einige wenige Ableitungsregeln, die man in der Analysis~I lernt, -erlauben, auf mehr oder weniger mechanische Art und Weise, jede -beliebige Funktion abzuleiten. -Man kann auch leicht einen Computer dazu programmieren, solche Ableitungen -symbolisch zu berechnen. - -Aus dem Fundamentalsatz der Algebra, der von Gauss vollständig bewiesen -wurde, ist bekannt, dass jedes Polynom mit Koeffizienten in $\mathbb{C}$ -genau so viele Lösungen in $\mathbb{C}$, wie der Grad des Polynoms angibt. -Dies ist aber ein Existenzsatz, er sagt nichts darüber aus, wie man diese -Lösungen finden kann. -In Spezialfällen, wie zum Beispiel für quadratische Polynome, gibt -es spezialsierte Lösungsverfahren, mit denen man Lösungen angeben kann. -Natürlich existieren numerische Methoden wie zum Beispiel das -Newton-Verfahren, mit dem man Nullstellen von Polynomen beliebig genau -bestimmen kann. - -Der Fundamentalsatz der Integralrechnung besagt, dass jede stetige -Funktion eine Stammfunktion hat, die bis auf eine Konstante eindeutig -bestimmt ist. -Auch dieser Existenzsatz gibt keinerlei Hinweise darauf, wie man die -Stammfunktion finden kann. -In der Analysis-Vorlesung lernt man viele Tricks, die in einer -beindruckenden Zahl von Spezialfällen ermöglichen, ein passende -Funktion anzugeben. -Man lernt auch numerische Verfahren kennen, mit denen sich Werte der -Stammfunktion, also bestimmte Integrale, mit beliebiger Genauigkeit -finden kann. - -Die numerische Lösung des Nullstellenproblems ist insofern unbefriedigend, -als sie nur schwer eine Diskussion der Abhängigkeit der Nullstellen von -den Koeffizienten des Polynoms ermöglichen. -Eine Formel wie die Lösungsformel für die quadratische Gleichung -stellt genau für solche Fälle ein ideales Werkzeug bereit. -Was man sich also wünscht ist nicht nur einfach eine Lösung, sondern eine -einfache Formel zur Bestimmung aller Lösungen. -Im Zusammenhang mit algebraischen Gleichungen erwartet man eine Formel, -in der nur arithmetische Operationen und Wurzeln vorkommen. -Für quadratische Gleichungen ist so eine Formel seit dem Altertum bekannt, -Formeln für die kubische Gleichung und die Gleichung vierten Grades wurden -im 16.~Jahrhundert von Cardano bzw.~Ferrari gefunden. -Erst viel später haben Abel und Ruffini gezeigt, dass so eine allgemeine -Formel für Polynome höheren Grades als 4 nicht existiert. -Die Galois-Theorie, die auf den Ideen von Évariste Galois beruht, -stellt eine vollständige Theorie unter anderem für die Lösbarkeit -von Gleichungen durch Wurzelausdrücke dar. - -Numerische Integralwerte haben ebenfalls den Nachteil, dass damit -Diskussionen wie die Abhängigkeit von Parametern eines Integranden -nur schwer möglich sind. -Was man sich daher wünscht ist eine Formel für die Stammfunktion, -die Werte als Zusammensetzung gut bekannter Funktionen wie der Exponential- -und Logarithmus-Funktionen oder der trigonometrischen Funktionen -sowie Wurzeln, Potenzen und den arithmetischen Operationen. -Man sagt, man möchte die Stammfunktion in ``geschlossener Form'' -dargestellt haben. -Tatsächlich ist dieses Problem auch zu Beginn des 19.~Jahrhunderts -von Joseph Liouville genauer untersucht worden. -Er hat zunächst eine Klasse von ``elementaren Funktionen'' definiert, -die als Darstellungen einer Stammfunktion in Frage kommen. -Der Satz von Liouville besagt dann, dass nur Funktionen mit einer -ganz speziellen Form eine elementare Stammfunktion haben. -Damit wird es möglich, zu entscheiden, ob ein Integrand wie $e^{-x^2}$ -eine elementare Stammfunktion hat. -Seit dieser Zeit weiss man zum Beispiel, dass die Fehlerfunktion nicht -mit den bekannten Funktionen dargestellt werden kann. - -Mit dem Aufkommen der Computer und vor allem der Computer-Algebra-System (CAS) -wurde die Frage nach der Bestimmung einer Stammfunktion erneut aktuell. -Die ebenfalls weiter entwickelte abstrakte Algebra hat ermöglicht, die -Ideen von Liouville in eine erweiterte, sogenannte differentielle -Galois-Theorie zu verpacken, die eine vollständige Lösung des Problems -darstellt. -Robert Henry Risch hat in den Sechzigerjahren auf dieser Basis -einen Algorithmus entwickelt, mit dem es möglich wird, zu entscheiden, -ob eine Funktion eine elementare Stammfunktion hat und diese -gegebenenfalls auch zu finden. -Moderne CAS implementieren diesen Algorithmus -in Teilen, besonders weit zu gehen scheint das quelloffene System -Axiom. - -Der Risch-Algorithmus hat allerdings eine Achillesferse: er benötigt -eine Method zu entscheiden, ob zwei Ausdrücke übereinstimmen. -Dies ist jedoch ein im Allgemeinen nicht entscheidbares Problem. -Moderne CAS treiben einigen Aufwand, um die -Gleichheit von Ausdrücken zu entscheiden, sie können das Problem -aber grundsätzlich nicht vollständig lösen. -Damit kann der Risch-Algorithmus in praktischen Anwendungen das -Stammfunktionsproblem ebenfalls nur mit Einschränkungen lösen, -die durch die Fähigkeiten des Ausdrucksvergleichs in einem CAS -gesetzt werden. - -Im Folgenden sollen elementare Funktionen definiert werden, es sollen -die Grundideen der differentiellen Galois-Theorie zusammengetragen werden -und der Satz von Liouvill vorgestellt werden. -An Hand der Fehler-Funktion soll dann gezeigt werden, wie man jetzt -einsehen kann, dass die Fehlerfunktion nicht elementar darstellbar ist. -Im nächsten Abschnitt dann soll der Risch-Algorithmus skizziert werden. - -\subsection{Elementare Funktionen -\label{buch:integrale:section:elementar}} -Es soll die Frage beantwortet werden, welche Stammfunktionen sich -in ``geschlossener Form'' oder durch ``wohlbekannte Funktionen'' -ausdrücken lassen. -Welche Funktionen dabei als ``wohlbekannt'' gelten dürfen ist -ziemlich willkürlich. -Sicher möchte man Potenzen und Wurzeln, Logarithmus und Exponentialfunktion, -aber auch die trigonometrischen Funktionen dazu zählen dürfen. -Ausserdem will man beliebig mit den arithmetischen Operationen -rechnen. -So entsteht die Menge der Funktionen, die man ``elementar'' nennen -will. - -In der Menge der elementaren Funktionen möchte man jetzt -Stammfunktionen ausgewählter Funktionen suchen. -Dazu muss man von jeder Funktion ihre Ableitung kennen. -Die Ableitungsoperation macht aus der Funktionenmenge eine -differentielle Algebra. -Der Satz von Liouville (Satz~\ref{buch:integrale:satz:liouville1}) -liefert Bedingungen, die erfüllt sein müssen, wenn eine Funktion -eine elementare Stammfunktion hat. -Sind diese Bedingungen nicht erfüllbar, ist auch keine -elementare Stammfunktion möglich. - -In den folgenden Abschnitten soll die differentielle Algebra -der elementaren Funktionen konstruiert werden. - -\subsubsection{Körper} -Die einfachsten Funktionen sind die die Konstanten, für die wir -für die nachfolgenden Betrachtungen fast immer die komplexen Zahlen -$\mathbb{C}$ -zu Grunde legen wollen. -Dabei ist vor allem wichtig, dass sich darin alle arithmetischen -Operationen durchführen lassen mit der einzigen Ausnahme, dass -nicht durch $0$ dividiert werden darf. -Man nennt $\mathbb{C}$ daher ein {\em Körper}. -\index{Körper}% -\label{buch:integrale:def:koerper} - -\subsubsection{Polynome und rationale Funktionen} -Die Polynome einer Variablen beschreiben eine Menge von -Funktionen, in der Addition, Subtraktion, Multiplikation -von Funktionen und Multiplikation mit komplexen Zahlen -uneingeschränkt möglich ist. -Wir bezeichen wie früher die Menge der Polynome in $z$ mit -$\mathbb{C}[z]$. - -Die Division ist erst möglich, wenn man beliebige Brüche -zulässt, deren Zähler und Nenner Polynome sind. -Die Menge -\[ -\mathbb{C}(z) -= -\biggl\{ -\frac{p(z)}{q(z)} -\;\bigg|\; -p,q\in \mathbb{C}[z] -\biggr\} -\] -heisst die Menge der {\em rationalen Funktionen}. -\label{buch:integrale:def:rationalefunktion} -\index{Funktion, rationale}% -\index{rationale Funktion}% -In ihr sind jetzt alle arithmetischen Operationen ausführbar -ausser natürlich die Division durch die Nullfunktion. -Die rationalen Funktionen bilden also wieder eine Körper. - -Die Tatsache, dass die rationalen Funktionen einen Körper -bilden bedeutet auch, dass die Konstruktion erneut durchgeführt -werden kann. -Ausgehend von einem beliebigen Körper $K$ können wieder zunächst -die Polynome $K[X]$ und anschliesen die rationalen Funktionen $K[X]$ -in der neuen Variablen, jetzt aber mit Koeffizienten in $K$ -gebildet werden. -So entstehen Funktionen von mehreren Variablen und, indem -wir für die neue Variable $X$ zum Beispiel die im übernächsten -Abschnitt betrachtete Wurzel $X=\sqrt{z}$ -einsetzen, rationale Funktionen in $z$ und $\sqrt{z}$. - -Solche Funktionenkörper werden im folgenden mit geschweiften -Buchstaben $\mathscr{D}$ bezeichnet. -\index{Funktionenkörper}% - -\subsubsection{Ableitungsoperation} -In allen Untersuchungen soll immer die Ableitungsoperation -mit berücksichtigt werden. -In unserer Betrachtungsweise spielt es keine Rolle, dass die -Ableitung aus einem Grenzwert entsteht, es sind nur die algebraischen -Eigenschaften wichtig. -Diese sind in der folgenden Definition zusammengefasst. - -\begin{definition} -\label{buch:integrale:def:derivation} -Ein {\em Ableitungsoperator} oder eine {\em Derivation} einer Algebra -$\mathscr{D}$ von Funktionen ist eine lineare Abbildung -\[ -\frac{d}{dz} -\colon \mathscr{D} \to \mathscr{D} -: -f \mapsto \frac{df}{dz} = f', -\] -die zusätzlich die Produktregel -\begin{equation} -\frac{d}{dz} (fg) -= -\frac{df}{dz} \cdot g + f \cdot \frac{dg}{dz} -\qquad\Leftrightarrow\qquad -(fg)' = f' g + fg' -\label{buch:integrale:eqn:produktregel} -\end{equation} -\index{Produktregel}% -erfüllt. -Die Funktion $f'\in \mathscr{D}$ heisst auch die {\em Ableitung} -von $f\in\mathscr{D}$. -\index{Derivation}% -\index{Ableitungsoperator}% -\index{Ableitung}% -\end{definition} - -Die Produktregel hat zum Beispiel auch die bekannten Quotientenregel -zur Folge. -Dazu betrachten wir das Produkt $f= (f/g)\cdot g$ und leiten es mit -Hilfe der Produktregel ab: -\[ -\frac{d}{dz}f -= -\frac{d}{dz} -\biggl( -\frac{f}{g}\cdot g -\biggr) -= -{\color{darkred} -\frac{d}{dz} -\biggl( -\frac{f}{g} -\biggr)} -\cdot g -+ -\frac{f}{g}\cdot \frac{d}{dz}g. -\] -Jetzt lösen wir nach der {\color{darkred}roten} Ableitung des Quotienten -auf und erhalten -\begin{equation} -\biggl(\frac{f}{g}\biggr)' -= -\frac{d}{dz}\biggl(\frac{f}{g}\biggr) -= -\frac1g\biggl( -\frac{d}{dz}f - \frac{f}{g}\cdot \frac{d}{dz}g -\biggr) -= -\frac{1}{g} -\biggl( -f'-\frac{fg'}{g} -\biggr) -= -\frac{f'g-fg'}{g^2}. -\label{buch:integrale:eqn:quotientenregel} -\end{equation} -Dies ist die Quotientenregel. - -Aus der Produktregel folgt natürlich sofort auch die Potenzregel -für die Ableitung der $n$ten Potenz einer Funktion $f\in\mathscr{D}$, -sie lautet: -\begin{equation} -\frac{d}{dz} f^n -= -\underbrace{ -f'f^{n-1} + ff'f^{n-2} + f^2f'f^{n-3}+\dots f^{n-1}f' -}_{\displaystyle \text{$n$ Terme}} -= -nf^{n-1}f'. -\label{buch:integrale:eqn:potenzregel} -\end{equation} -In dieser Form versteckt sich natürlich auch die Kettenregel, die -Potenzfunktion ist die äussere Funktion, $f$ die innere, $f'$ ist also -die Ableitung er inneren Funktion, wie in der Kettenregel verlangt. -Falls $f$ ein Element von $\mathscr{D}$ ist mit der Eigenschaft -$df/dz=1$, dann entsteht die übliche Produktregel. - -\begin{definition} -Eine Algebra $\mathscr{D}$ von Funktionen mit einem Ableitungsoperator -$d/dz$ heisst eine {\em differentielle Algebra}. -\index{differentielle Algebra}% -\index{Algebra, differentielle}% -In einer differentiellen Algebra gelten die üblichen -Ableitungsregeln. -\end{definition} - -Die Potenzregel war in der Form~\eqref{buch:integrale:eqn:potenzregel} -geschrieben worden, nicht als die Ableitung von $z$. -Der Grund dafür ist, dass wir gar nicht voraussetzen wollen, dass in -unserer differentiellen Algebra eine Funktion existiert, die die -Rolle von $z$ hat. -Dies ist gar nicht nötig, wie das folgende Beispiel zeigt. - -\begin{beispiel} -Als Funktionenmenge $\mathscr{D}$ nehmen wir rationale Funktionen -in zwei Variablen, die wir $\cos x $ und $\sin x$ nennen. -Diese Menge bezeichnen wir mit -$\mathscr{D}=\mathbb{Q}(\cos x,\sin x)$ -Der Ableitungsoperator ist -\begin{align*} -\frac{d}{dx} \cos x &= -\sin x -\\ -\frac{d}{dx} \sin x &= \phantom{-}\cos x. -\end{align*} -Die Funktionen von $\mathbb{Q}(\cos x,\sin x)$ sind also Brüche, -deren Zähler und Nenner Polynome in $\cos x$ und $\sin x$ sind. -Aus den Produkt- und Quotientenregeln und den Ableitungsregeln für -$\cos x$ und $\sin x$ folgt, dass die Ableitung einer Funktion in -$\mathscr{D}$ wieder in $\mathscr{D}$ ist, $\mathscr{D}$ ist eine -differentielle Algebra. -\end{beispiel} - -Die konstanten Funktionen spielen eine besondere Rolle. -Da wir bei der Ableitung nicht von der Vorstellung einer -Funktion mit einem variablen Argument ausgehen wollten und -die Ableitung nicht als Grenzwert definieren wollten, müssen -wir auch bei der Definition der ``Konstanten'' einen neuen -Weg gehen. -In der Analysis sind die Konstanten genau die Funktionen, -deren Ableitung $0$ ist. - -\begin{definition} -\label{buch:integrale:def:konstante} -Ein Element $f\in \mathscr{D}$ mit $df/dz=f'=0$ heissen -{\em Konstante} in $\mathscr{D}$. -\index{Konstante}% -\end{definition} - -Die in der Potenzregel~\eqref{buch:integrale:eqn:potenzregel} -vermisste Funktion $z$ kann man ähnlich zu den Konstanten -zu definieren versuchen. -$z$ müsste ein Element von $\mathscr{D}$ mit $z' = 1$ sein. -Allerdings gibt es viele solche Elemente, ist $c$ eine Konstanten -und $z'=1$, dann ist auch $(z+c)'=1$, $(z+c)$ hat also für -die Zwecke unserer Untersuchung die gleichen Eigenschaften wie -$z$. -Dies deckt sich natürlich auch mit der Erwartung, dass Stammfunktionen -nur bis auf eine Konstante bestimmt sind. -Eine differentielle Algebra muss allerdings kein Element $z$ mit der -Eigenschaft $z'=1$ enthalten. - -\begin{beispiel} -In $\mathscr{D}=\mathbb{Q}(\cos x,\sin x)$ gibt es kein Element $x$. -Ein solches wäre von der Form -\[ -x = \frac{p(\cos x,\sin x)}{q(\cos x,\sin x)}. -\] -Eine solche goniometrische Beziehung würde für $x=\frac{\pi}4$ bedeuten, -dass -\[ -\frac{\pi}4 -= -\frac{p(\sqrt{2}/2,\sqrt{2}/2)}{q(\sqrt{2}/2,\sqrt{2}/2)}. -\] -Auf der rechten Seite steht ein Quotient von Polynome, in dessen -Argument nur rationale Zahlen und $\sqrt{2}$ steht. -So ein Ausdruck kann immer in die Form -\[ -\pi -= -4\frac{a\sqrt{2}+b}{c\sqrt{2}+d} -= -\frac{4(a\sqrt{2}+b)(c\sqrt{2}-d)}{2c^2+d^2} -= -r\sqrt{2}+s -\] -gebracht werden. -Die Zahl auf der rechten Seite ist zwar irrational, aber sie ist Nullstelle -des quadratischen Polynoms -\[ -p(x) -= -(x-r\sqrt{2}-s)(x+r\sqrt{2}-s) -= -x^2 --2sx --2r^2+s^2 -\] -mit rationalen Koeffizienten, wie man mit der Lösungsformel für die -quadratische Gleichung nachprüfen kann. -Es ist bekannt, dass $\pi$ als transzendente Zahl nicht Nullstelle -eines Polynoms mit rationalen Koeffizienten ist. -Dieser Widerspruch zeigt, dass $x$ nicht in $\mathbb{Q}(\cos x, \sin x)$ -vorkommen kann. -\end{beispiel} - -In einer differentiellen Algebra kann jetzt die Frage nach der -Existenz einer Stammfunktion gestellt werden. - -\begin{aufgabe} -\label{buch:integrale:aufgabe:existenz-stammfunktion} -Gegeben eine differentielle Algebra $\mathscr{D}$ und ein Element -$f\in\mathscr{D}$, entscheide, ob es ein Element $F\in\mathscr{D}$ -gibt mit der Eigenschaft $F'=f$. -Ein solches $F\in\mathscr{D}$ heisst {\em Stammfunktion} von $f$. -\end{aufgabe} - -\begin{satz} -In einer differentiellen Algebra $\mathscr{D}$ mit $z\in\mathscr{D}$ -hat die Potenzfunktion $f=z^n$ für $n\in\mathbb{N}\setminus\{-1\}$ -ein Stammfunktion, nämlich -\[ -F = \frac{1}{n+1} z^{n+1}. -\] -\label{buch:integrale:satz:potenzstammfunktion} -\end{satz} - -\begin{proof}[Beweis] -Tatsächlich kann man dies sofort nachrechnen, muss allerdings die -Fälle $n+1 >0$ und $n+1<0$ unterscheiden, da die Potenzregel -\eqref{buch:integrale:eqn:potenzregel} nur für natürliche Exponenten -gilt. -Man erhält -\begin{align*} -n+1&>0\colon -& -\frac{d}{dz}\frac{1}{n+1}z^{n+1} -&= -\frac{1}{n+1}(n+1)z^{n+1-1} -= -z^n, -\\ -n+1&<0\colon -& -\frac{d}{dz}\frac{1}{n+1}\frac{1}{z^{-(n+1)}} -&= -\frac{1}{n+1}\frac{1'z^{-(n+1)}-1(-(n+1))z^{-n-1-1}}{z^{-2n-2}} -\\ -&& -&= -\frac{1}{n+1} -\frac{(n+1)z^n{-n-2}}{z^{-2n-2}} -\\ -&& -&= -\frac{1}{z^{-n}}=z^n. -\end{align*} -Man beachte, dass in dieser Rechnung nichts anderes als die -algebraischen Eigenschaften der Produkt- und Quotientenregel -verwendet wurden. -\end{proof} - -\subsubsection{Wurzeln} -Die Wurzelfunktionen sollen natürlich als elementare Funktionen -erlaubt sein. -Es ist bekannt, dass $\sqrt{z}\not\in \mathscr{D}=\mathbb{C}(z)$ -ist, ein solches Element müsste also erst noch hinzugefügt werden. -Dabei muss auch seine Ableitung definiert werden. -Auch dabei dürfen wir nicht auf eine Grenzwertüberlegung zurückgreifen, -vielmehr müssen wir die Ableitung auf vollständig algebraische -Weise bestimmen. - -Wir schreiben $f=\sqrt{z}$ und leiten die Gleichung $f^2=z$ nach $z$ ab. -Dabei ergibt sich nach der Potenzregel -\[ -\frac{d}{dz}f^2 = 2f'f = \frac{d}{dz}z=1 -\qquad\Rightarrow\qquad f' = \frac{1}{2f}. -\] -Diese Rechnung lässt sich auch auf $n$-Wurzeln $g=\root{n}\of{z}$ mit -der Gleichung $g^n = z$ verallgemeinern. -Die Ableitung der $n$-ten Wurzel ist -\begin{equation} -\frac{d}{dz}g^n -= -ng^{n-1} = \frac{d}{dz}z=1 -\qquad\Rightarrow\qquad -\frac{d}{dz}g = \frac{1}{ng^{n-1}}. -\end{equation} -Es ist also möglich, eine differentielle Algebra $\mathscr{D}$ mit einer -$n$-ten Wurzel $g$ zu einer grösseren differentiellen Algebra $\mathscr{D}(g)$ -zu erweitern, in der wieder alle Regeln für das Rechnen mit Ableitungen -erfüllt sind. - -\subsubsection{Algebraische Elemente} -Die Charakterisierung der Wurzelfunktionen passt zwar zum verlangten -algebraischen Vorgehen, ist aber zu spezielle und nicht gut für die -nachfolgenden Untersuchengen geeignet. -Etwas allgemeiner ist der Begriff der algebraischen Elemente. - -\begin{definition} -\label{buch:integrale:def:algebraisches-element} -Seien $K\subset L$ zwei Körper. -Ein Element $\alpha \in L$ heisst {\em algebraisch} über $K$, -wenn $\alpha$ Nullstelle eines Polynoms $p\in K[X]$ mit Koeffizienten -in $K$ ist. -\index{algebraisch}% -\end{definition} - -Jedes Element $\alpha\in K$ ist algebraisch, da $\alpha$ Nullstelle -von $X-\alpha\in K[X]$ ist. -Die $n$tem Wurzeln eines Elemente $\alpha\in K$ sind ebenfalls algebraisch, -da sie Nullstellen des Polynoms $p(X) = X^n - \alpha$ sind. -Allerdings ist nicht klar, dass diese Wurzeln überhaupt existieren. -Nach dem Satz von Abel~\ref{buch:potenzen:satz:abel} gibt es aber -Nullstellen von Polynomen, die sich nicht als Wurzelausdrücke schreiben -lassen. -Der Begriff der algebraischen Elemente ist also allgemeiner als der -Begriff der Wurzel. - -\begin{definition} -\label{buch:integrale:def:algebraisch-abgeschlossen} -Ein Körper $K$ heisst {\em algebraisch abgeschlossen}, wenn jedes Polynom mit -Koeffizienten in $K$ eine Nullstelle in $K$ hat. -\end{definition} - -Der Körper $\mathbb{C}$ ist nach dem -Fundamentalsatz~\label{buch:potenzen:satz:fundamentalsatz} -der Algebra algebraisch abgeschlossen. -Da wir aber mit Funktionen arbeiten, müssen wir auch Wurzeln -von Funktionen finden können. -Dies ist nicht selbstverständlich, wie das folgende Beispiel zeigt. - -\begin{beispiel} -Es gibt keine stetige Funktion $f\colon \mathbb{C}\to\mathbb{C}$, die -die Gleichung $f(z)^2 = z$ und $f(1)=1$ erfüllt. -Für die Argumente $z(t)= e^{it}$ folgt, dass $f(z(t)) = e^{it/2}$ sein -muss. -Setzt man aber $t=\pm \pi$ ein, ergeben sich die Werte -$f(z(\pm\pi))=e^{\pm i\pi/2}=\pm 1$, die beiden Grenzwerte -für $t\to\pm\pi$ sind also verschieden. -\end{beispiel} - -Die Mathematik hat verschiedene ``Tricks'' entwickelt, wie mit diesem -Problem umgegangen werden kann: Funktionskeime, Garben, Riemannsche -Flächen. -Sie sind alle gleichermassen gut geeignet, das Problem zu lösen. -Für die vorliegende Aufgabe genügt es aber, dass es tatsächlich -immer ein wie auch immer geartetes Element gibt, welches Nullstelle -des Polynoms ist. - -Ist $f$ eine Nullstelle des Polynoms $p(X)$ mit Koeffizienten in -$\mathscr{D}$, dann kann man die Ableitung wie folgt berechnen. -Zunächst leitet man $p(f)$ ab: -\begin{align} -0&= -\frac{d}{dz}(a_nf^n + a_{n-1}f^{n-1}+\ldots+a_1f+a_0) -\notag -\\ -&= -a_n'f^n + a_{n-1}'f^{n-1}+\ldots+a_1'f+a_0' -+ -na_nf^{n-1}f' -+ -(n-1)a_nf^{n-2}f' -+ -\ldots -+ -a_2ff' -+ -a_1f' -\notag -\\ -&= -a_n'f^n + a_{n-1}'f^{n-1}+\ldots+a_1'f+a_0' -+ -( -na_nf^{n-1} -+ -(n-1)a_nf^{n-2} -+ -\ldots -+ -a_2f -+ -a_1 -)f' -\notag -\\ -\Rightarrow -\qquad -f'&=\frac{ -a_n'f^n + a_{n-1}'f^{n-1}+\dots+a_1'f+a_0' -}{ -na_nf^{n-1} -+ -(n-1)a_nf^{n-2} -+ -\dots -+ -a_1 -}. -\label{buch:integrale:eqn:algabl} -\end{align} -Das einzige, was dabei schief gehen könnte ist, dass der Nenner ebenfalls -verschwindet. -Dieses Problem kann man dadurch lösen, dass man als Polynom das -sogenannte Minimalpolynom verwendet. - -\begin{definition} -Das {\em Minimalpolynome} $m(X)$ eines algebraischen Elementes $\alpha$ ist -das Polynom kleinsten Grades, welches $m(\alpha)=0$ erfüllt. -\end{definition} - -Da das Minimalpolynom den kleinstmöglichen Grad hat, kann der Nenner -von~\eqref{buch:integrale:eqn:algabl}, -der noch kleineren Grad hat, unmöglich verschwinden. -Das Minimalpolynom ist auch im wesentlichen eindeutig. -Gäbe es nämlich zwei verschiedene Minimalpolynome $m_1$ und $m_2$, -dann müsste $\alpha$ auch eine Nullstelle des grössten gemeinsamen -Teilers $m_3=\operatorname{ggT}(m_1,m_2)$ sein. -Wären die beiden Polynome wesentlich verschieden, dann hätte $m_3$ -kleineren Grad, im Widerspruch zur Definition des Minimalpolynoms. -Also unterscheiden sich die beiden Polynome $m_1$ und $m_2$ nur um -einen skalaren Faktor. - -\subsubsection{Konjugation, Spur und Norm} -% Konjugation, Spur und Norm -Das Minimalpolynom eines algebraischen Elementes ist nicht -eindeutig bestimmt. -Zum Beispiel ist $\sqrt{2}$ algebraisch über $\mathbb{Q}$, das -Minimalpolynom ist $m(X)=X^2-2\in\mathbb{Q}[X]$. -Es hat aber noch eine zweite Nullstelle $-\sqrt{2}$. -Mit rein algebraischen Mitteln sind die beiden Nullstellen $\pm\sqrt{2}$ -nicht zu unterscheiden, erst die Verwendung der Vergleichsrelation -ermöglicht, sie zu unterscheiden. - -Dasselbe gilt für die imaginäre Einheit $i$, die das Minimalpolynom -$m(X)=X^2+1\in\mathbb{R}[X]$ hat. -Hier gibt es nicht einmal mehr eine Vergleichsrelation, mit der man -die beiden Nullstellen unterscheiden könnte. -In der Tat ändert sich aus algebraischer Sicht nichts, wenn man in -allen Formeln $i$ durch $-i$ ersetzt. - -Etwas komplizierter wird es bei $\root{3}\of{2}$. -Das Polynom $m=x^3-2\in\mathbb{Q}[X]$ hat $\root{3}\of{2}$ als -Nullstelle und dies ist auch tatsächlich das Minimalpolynom. -Das Polynom hat noch zwei weitere Nullstellen -\[ -\alpha_+ = \frac{-1+i\sqrt{3}}{2}\root{3}\of{2} -\qquad\text{und}\qquad -\alpha_- = \frac{-1-i\sqrt{3}}{2}\root{3}\of{2}. -\] -Die beiden Lösungen gehen durch die Vertauschung von $i$ und $-i$ -auseinander hervor. -Betrachtet man dasselbe Polynom aber als Polynom in $\mathbb{R}[X]$, -dann ist es nicht mehr das Minimalpolynom von $\root{3}\of{2}$, da -$X-\root{3}\of{2}\in\mathbb{R}[X]$ kleineren Grad und $\root{3}\of{2}$ -als Nullstelle hat. -Indem man -\[ -m(X)/(X-\root{3}\of{2})=X^2+\root{3}\of{2}X+\root{3}\of{2}^2=m_2(X) -\] -rechnet, bekommt man das Minimalpolynom der beiden Nullstellen $\alpha_+$ -und $\alpha_-$. -Wir lernen aus diesen Beispielen, dass das Minimalpolynom vom Grundkörper -abhängig ist (Die Faktorisierung $(X-\root{3}\of{2})\cdot m_2(X)$ von -$m(X)$ ist in $\mathbb{Q}[X]$ nicht möglich) und dass wir keine -algebraische Möglichkeit haben, die verschiedenen Nullstellen des -Minimalpolynoms zu unterscheiden. - -Die beiden Nullstellen $\alpha_+$ und $\alpha_-$ des Polynoms $m_2(X)$ -erlauben, $m_2(X)=(X-\alpha_+)(X-\alpha_-)$ zu faktorisieren. -Durch Ausmultiplizieren -\[ -(X-\alpha_+)(X-\alpha_-) -= -X^2 -(\alpha_++\alpha_-)X+\alpha_+\alpha_- -\] -und Koeffizientenvergleich mit $m_2(X)$ findet man die symmetrischen -Formeln -\[ -\alpha_+ + \alpha_- = \root{3}\of{2} -\qquad\text{und}\qquad -\alpha_+ \alpha_ = \root{3}\of{2}. -\] -Diese Ausdrücke sind nicht mehr abhängig von einer speziellen Wahl -der Nullstellen. - -Das Problem verschärft sich nocheinmal, wenn wir Funktionen betrachten. -Das Polynom $m(X)=X^3-z$ ist das Minimalpolynom der Funktion $\root{3}\of{z}$. -Die komplexe Zahl $z=re^{i\varphi}$ hat aber drei die algebraisch nicht -unterscheidbaren Nullstellen -\[ -\alpha_0(z)=\root{3}\of{r}e^{i\varphi/3}, -\quad -\alpha_1(z)=\root{3}\of{r}e^{i\varphi/3+2\pi/3} -\qquad\text{und}\qquad -\alpha_2(z)=\root{3}\of{r}e^{i\varphi/3+4\pi/3}. -\] -Aus der Faktorisierung $ (X-\alpha_0(z)) (X-\alpha_1(z)) (X-\alpha_2(z))$ -und dem Koeffizientenvergleich mit dem Minimalpolynom kann man wieder -schliessen, dass die Relationen -\[ -\alpha_0(z) + \alpha_1(z) + \alpha_2(z)=0 -\qquad\text{und}\qquad -\alpha_0(z) \alpha_1(z) \alpha_2(z) = z -\] -gelten. - -Wir können also oft keine Aussagen über individuelle Nullstellen -eines Minimalpolynoms machen, sondern nur über deren Summe oder -Produkt. - -\begin{definition} -\index{buch:integrale:def:spur-und-norm} -Sie $m(X)\in K[X]$ das Minimalpolynom eines über $K$ algebraischen -Elements und -\[ -m(X) = a_nX^n + a_{n-1}X^{n-1} + \ldots + a_1X + a_0. -\] -Dann heissen -\[ -\operatorname{Tr}(\alpha) = -a_{n-1} -\qquad\text{und}\qquad -\operatorname{Norm}(\alpha) = (-1)^n a_0 -\] -die {\em Spur} und die {\em Norm} des Elementes $\alpha$. -\index{Spur eines algebraischen Elementes}% -\index{Norm eines algebraischen Elementes}% -\end{definition} - -Die Spur und die Norm können als Spur und Determinante einer Matrix -verstanden werden, diese allgemeineren Definitionen, die man in der -Fachliteratur, z.~B.~in~\cite{buch:lang} nachlesen kann, führen aber -für unsere Zwecke zu weit. - -\begin{hilfssatz} -Die Ableitungen von Spur und Norm sind -\[ -\operatorname{Tr}(\alpha)' -= -\operatorname{Tr}(\alpha') -\qquad\text{und}\qquad -\operatorname{Norm}(\alpha)' -= -\operatorname{Tr}(\alpha)' -\] -XXX Wirklich? -\end{hilfssatz} - -\subsubsection{Logarithmen und Exponentialfunktionen} -Die Funktion $z^{-1}$ musste im -Satz~\ref{buch:integrale:satz:potenzstammfunktion} -ausgeschlossen werden, sie hat keine Stammfunktion in $\mathbb{C}(z)$. -Aus der Analysis ist bekannt, dass die Logarithmusfunktion $\log z$ -eine Stammfunktion ist. -Der Logarithmus von $z$ aber auch der Logarithmus $\log f(z)$ -einer beliebigen Funktion $f(z)$ oder die Exponentialfunktion $e^{f(z)}$ -sollen ebenfalls elementare Funktionen sein. -Da wir aber auch hier nicht auf die analytischen Eigenschaften zurückgreifen -wollen, brauchen wir ein rein algebraische Definition. - -\begin{definition} -\label{buch:integrale:def:logexp} -Sei $\mathscr{D}$ ein differentielle Algebra und $f\in\mathscr{D}$. -Ein Element $\vartheta\in\mathscr{D}$ heisst ein {\em Logarithmus} -von $f$, geschrieben $\vartheta = \log f$, wenn $f\vartheta' = f'$ gilt. -$\vartheta$ heisst eine Exponentialfunktion von $f$ wenn -$\vartheta'=\vartheta f'$ gilt. -\end{definition} - -Die Formel für die Exponentialfunktion ist etwas vertrauter, sie ist -die bekannte Kettenregel -\begin{equation} -\vartheta' -= -\frac{d}{dz} e^f -= -e^f \cdot \frac{d}{dz} f -= -\vartheta \cdot f'. -\label{buch:integrale:eqn:exponentialableitung} -\end{equation} -Da wir uns vorstellen, dass Logarithmen Umkehrfunktionen von -Exponentialfunktionen sein sollen, -muss die definierende Gleichung genau wie -\eqref{buch:integrale:eqn:exponentialableitung} -aussehen, allerdings mit vertauschten Plätzen von $f$ und $\vartheta$, -also -\begin{equation} -\vartheta' = \vartheta\cdot f' -\qquad -\rightarrow -\qquad -f' = f\cdot \vartheta' -\;\Leftrightarrow\; -\vartheta' = (\log f)' = \frac{f'}{f}. -\label{buch:integrale:eqn:logarithmischeableitung} -\end{equation} -Dies ist die aus der Analysis bekannte Formel für die logarithmische -Ableitung. - -Der Logarithmus von $f$ und die Exponentialfunktion von $f$ sollen -also ebenfalls als elementare Funktionen betrachtet werden. - -\subsubsection{Die trigonometrischen Funktionen} -Die bekannten trigonometrischen Funktionen und ihre Umkehrfunktionen -sollten natürlich auch elementare Funktionen sein. -Dabei kommt uns zur Hilfe, dass sie sich mit Hilfe der Exponentialfunktion -als -\[ -\cos f = \frac{e^{if}+e^{-if}}2 -\qquad\text{und}\qquad -\sin f = \frac{e^{if}-e^{-if}}{2i} -\] -schreiben lassen. -Eine differentielle Algebra, die die Exponentialfunktionen von $if$ und -$-if$ enthält, enthält also automatisch auch die trigonometrischen -Funktionen. -Im Folgenden ist es daher nicht mehr nötig, die trigonometrischen -Funktionen speziell zu untersuchen. - -\subsubsection{Elementare Funktionen} -Damit sind wir nun in der Lage, den Begriff der elementaren Funktion -genau zu fassen. - -\begin{definition} -\label{buch:integrale:def:einfache-elementare-funktion} -Sie $\mathscr{D}$ eine differentielle Algebra über $\mathbb{C}$ und -$\mathscr{D}(\vartheta)$ eine Erweiterung von $\mathscr{D}$ um eine -neue Funktion $\vartheta$, dann heissen $\vartheta$ und die Elemente -von $\mathscr{D}(\vartheta)$ einfach elementar, wenn eine der folgenden -Bedingungen erfüllt ist: -\begin{enumerate} -\item $\vartheta$ ist algebraisch über $\mathscr{D}$, d.~h.~$\vartheta$ -ist eine ``Wurzel''. -\item $\vartheta$ ist ein Logarithmus einer Funktion in $\mathscr{D}$, -d.~h.~es gibt $f\in \mathscr{D}$ mit $f'=f\vartheta'$ -(Definition~\ref{buch:integrale:def:logexp}). -\item $\vartheta$ ist eine Exponentialfunktion einer Funktion in $\mathscr{D}$, -d.~h.~es bit $f\in\mathscr{D}$ mit $\vartheta'=\vartheta f'$ -(Definition~\ref{buch:integrale:def:logexp}). -\end{enumerate} -\end{definition} - -Einfache elementare Funktionen entstehen also ausgehend von einer -differentiellen Algebra, indem man genau einmal eine Wurzel, einen -Logarithmus oder eine Exponentialfunktion hinzufügt. -So etwas wie die zusammengesetzte Funktion $e^{\sqrt{z}}$ ist -damit noch nicht möglich. -Daher erlauben wir, dass man die gesuchten Funktionen in mehreren -Schritten aufbauen kann. - -\begin{definition} -Sei $\mathscr{F}$ eine differentielle Algebra, die die differentielle -Algebra $\mathscr{D}$ enthält, also $\mathscr{D}\subset\mathscr{F}$. -$\mathscr{F}$ und die Elemente von $\mathscr{F}$ heissen einfach, -wenn es endlich viele Elemente $\vartheta_1,\dots,\vartheta_n$ gibt -derart, dass -\[ -\renewcommand{\arraycolsep}{2pt} -\begin{array}{ccccccccccccc} -\mathscr{D} -&\subset& -\mathscr{D}(\vartheta_1) -&\subset& -\mathscr{D}(\vartheta_1,\vartheta_2) -&\subset& -\; -\cdots -\; -&\subset& -\mathscr{D}(\vartheta_1,\vartheta_2,\dots,\vartheta_{n-1}) -&\subset& -\mathscr{D}(\vartheta_1,\vartheta_2,\dots,\vartheta_{n-1},\vartheta_n) -&=& -\mathscr{F} -\\ -\| -&& -\| -&& -\| -&& -&& -\| -&& -\| -&& -\\ -\mathscr{F}_0 -&\subset& -\mathscr{F}_1 -&\subset& -\mathscr{F}_2 -&\subset& -\cdots -&\subset& -\mathscr{F}_{n-1} -&\subset& -\mathscr{F}_{n\mathstrut} -&& -\end{array} -\] -gilt so, dass jedes $\vartheta_{i+1}$ einfach ist über -$\mathscr{F}_i=\mathscr{D}(\vartheta_1,\dots,\vartheta_i)$. -\end{definition} - -In Worten bedeutet dies, dass man den Funktionen von $\mathscr{D}$ -nacheinander Wurzeln, Logarithmen oder Exponentialfunktionen einzelner -Funktionen hinzufügt. -Die Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion} kann -jetzt so formuliert werden. - -\begin{aufgabe} -\label{buch:integrale:aufgabe:existenz-stammfunktion-dalg} -Gegeben ist eine Differentielle Algebra $\mathscr{D}$ und eine -Funktion $f\in \mathscr{D}$. -Gibt es eine Folge $\vartheta_1,\dots,\vartheta_n$ und eine Funktion -$F\in\mathscr{D}(\vartheta_1,\dots,\vartheta_n)$ derart, dass -$F'=f$. -\end{aufgabe} - -Das folgende Beispiel zeigt, wie man möglicherweise mehrere -Erweiterungsschritte vornehmen muss, um zu einer Stammfunktion -zu kommen. -Es illustriert auch die zentrale Rolle, die der Partialbruchzerlegung -in der weiteren Entwicklung zukommen wird. - -\begin{beispiel} -\label{buch:integrale:beispiel:nichteinfacheelementarefunktion} -Es soll eine Stammfunktion der Funktion -\[ -f(z) -= -\frac{z}{(az+b)(cz+d)} -\in -\mathbb{C}(z) -\] -gefunden werden. -In der Analysis lernt man, dass solche Integrale mit der -Partialbruchzerlegung -\[ -\frac{z}{(az+b)(cz+d)} -= -\frac{A_1}{az+b}+\frac{A_2}{cz+d} -= -\frac{A_1cz+A_1d+A_2az+A_2b}{(az+b)(cz+d)} -\quad\Rightarrow\quad -\left\{ -\renewcommand{\arraycolsep}{2pt} -\begin{array}{rcrcr} -cA_1&+&aA_2&=&1\\ -dA_1&+&bA_2&=&0 -\end{array} -\right. -\] -bestimmt werden. -Die Lösung des Gleichungssystems ergibt -$A_1=b/(bc-ad)$ und $A_2=d/(ad-bc)$. -Die Stammfunktion kann dann aus -\begin{align*} -\int f(z)\,dz -&= -\int\frac{A_1}{az+b}\,dz -+ -\int\frac{A_2}{cz+d}\,dz -= -\frac{A_1}{a}\int\frac{a}{az+b}\,dz -+ -\frac{A_2}{c}\int\frac{c}{cz+d}\,dz -\end{align*} -bestimmt werden. -In den Integralen auf der rechten Seite ist der Zähler jeweils die -Ableitung des Nenners, der Integrand hat also die Form $g'/g$. -Genau diese Form tritt in der Definition eines Logarithmus auf. -Die Stammfunktion ist jetzt -\[ -F(z) -= -\int f(z)\,dz -= -\frac{A_1}{a}\log(az+b) -+ -\frac{A_2}{c}\log(cz+d) -= -\frac{b\log(az+b)}{a(bc-ad)} -+ -\frac{d\log(cz+d)}{c(ad-bc)}. -\] -Die beiden Logarithmen kann man nicht durch rein rationale Operationen -ineinander überführen. -Sie müssen daher beide der Algebra $\mathscr{D}$ hinzugefügt werden. -\[ -\left. -\begin{aligned} -\vartheta_1&=\log(az+b)\\ -\vartheta_2&=\log(cz+d) -\end{aligned} -\quad -\right\} -\qquad\Rightarrow\qquad -F(z) \in \mathscr{F}=\mathscr{D}(\vartheta_1,\vartheta_2). -\] -Die Stammfunktion $F(z)$ ist also keine einfache elementare Funktion, -aber $F$ ist immer noch eine elementare Funktion. -\end{beispiel} - -\subsection{Partialbruchzerlegung -\label{buch:integrale:section:partialbruchzerlegung}} -Die Konstruktionen des letzten Abschnitts haben gezeigt, -wie man die Funktionen, die man als Stammfunktionen einer Funktion -zulassen möchte, schrittweise konstruieren kann. -Die Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion-dalg} -ist eine rein algebraische Formulierung der ursprünglichen -Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion}. -Schliesslich hat das Beispiel auf -Seite~\pageref{buch:integrale:beispiel:nichteinfacheelementarefunktion} -gezeigt, dass es im allgemeinen mehrere Schritte braucht, um zu einer -elementaren Stammfunktion zu gelangen. -Die Lösung setzt sich aus den Termen der Partialbruchzerlegung. -In diesem Abschnitt soll diese genauer studiert werden. - -In diesem Abschnitt gehen wir immer von einer differentiellen -Algebra über den komplexen Zahlen aus und verlangen, dass die -Konstanten in allen betrachteten differentiellen Algebren -$\mathbb{C}$ sind. - -\subsubsection{Monome} -Die beiden Funktionen $\vartheta-1=\log(az+b)$ und $\vartheta_2=(cz+d)$, -die im Beispiel hinzugefügt werden mussten, verhalten sich ich algebraischer -Hinsicht wie ein Monom: man kann es nicht faktorisieren oder bereits -bekannte Summanden aufspalten. -Solchen Funktionen kommt eine besondere Bedeutung zu. - -\begin{definition} -\label{buch:integrale:def:monom} -Die Funktion $\vartheta$ heisst ein Monom, wenn $\vartheta$ nicht -algebraisch ist über $\mathscr{D}$ und $\mathscr{D}(\vartheta)$ die -gleichen Konstanten enthält wie $\mathscr{D}$. -\end{definition} - -\begin{beispiel} -Als Beispiel beginnen wir mit den komplexen Zahlen $\mathbb{C}$ -und fügen die Funktion $\vartheta_1=z$ hinzu und erhalten -$\mathscr{D}=\mathbb{C}(z)$. -Die Funktionen $z^k$ sind für alle $k$ linear unabhängig, d.~h.~es -gibt keinen Ausdruck -\[ -a_nz^n + a_{n-1}z^{n-1}+\cdots+a_1z+a_0=0. -\] -Dies ist gleichbedeutend damit, dass $z$ nicht algebraisch ist. -Das Monom $z$ ist also auch ein Monom im Sinne der -Definition~\ref{buch:integrale:def:monom}. -\end{beispiel} - -\begin{beispiel} -Wir beginnen wieder mit $\mathbb{C}$ und fügen die Funktion -$e^z$ hinzu. -Gäbe es eine Beziehung -\[ -b_m(e^z)^m + b_{m-1}(e^z)^{m-1}+\dots+b_1e^z + b_0=0 -\] -mit komplexen Koeffizienten $b_i\in\mathbb{C}$, -dann würde daraus durch Einsetzen von $z=1$ die Relation -\[ -b_me^m + b_{m-1}e^{m-1} + \dots + b_1e + b_0=0, -\] -die zeigen würde, dass $e$ eine algebraische Zahl ist. -Es ist aber bekannt, dass $e$ transzendent ist. -Dieser Widersprich zeigt, dass $e^z$ ein Monom ist. -\end{beispiel} - -\begin{beispiel} -Jetzt fügen wir die Exponentialfunktion $\vartheta_2=e^z$ -der differentiellen Algebra $\mathscr{D}=\mathbb{C}(z)$ hinzu -und erhalten $\mathscr{F}_1=\mathscr{D}(e^z) = \mathbb{C}(z,e^z)$. -Gäbe es das Minimalpolynom -\begin{equation} -b_m(z)(e^z)^m + b_{m-1}(z)(e^z)^{m-1}+\dots+b_1(z)e^z + b_0(z)=0 -\label{buch:integrale:beweis:exp-analytisch} -\end{equation} -mit Koeffizienten $b_i\in\mathbb{C}(z)$, dann könnte man mit dem -gemeinsamen Nenner der Koeffizienten durchmultiplizieren und erhielte -eine Relation~\eqref{buch:integrale:beweis:exp-analytisch} mit -Koeffizienten in $\mathbb{C}[z]$. -Dividiert man durch $e^{mz}$ erhält man -\[ -b_m(z) + b_{m-1}(z)\frac{1}{e^z} + \dots + b_1(z)\frac{1}{(e^z)^{m-1}} + b_0(z)\frac{1}{(e^z)^m}=0. -\] -Aus der Analysis weiss man, dass die Exponentialfunktion schneller -anwächst als jedes Polynom, alle Terme auf der rechten Seite -konvergieren daher gegen 0 für $z\to\infty$. -Das bedeutet, dass $b_m(z)\to0$ für $z\to \infty$. -Das Polynom~\eqref{buch:integrale:beweis:exp-analytisch} wäre also gar -nicht das Minimalpolynom. -Dieser Widerspruch zeigt, dass $e^z$ nicht algebraisch ist über -$\mathbb{C}(z)$ und damit ein Monom ist\footnote{Etwas unbefriedigend -an diesem Argument ist, dass man hier wieder rein analytische statt -algebraische Eigenschaften von $e^z$ verwendet. -Gäbe es aber eine minimale Relation wie -\eqref{buch:integrale:beweis:exp-analytisch} -mit Polynomkoeffizienten, dann wäre sie von der Form -\[ -P(z,e^z)=p(z)(e^z)^m + q(z,e^z)=0, -\] -wobei Grad von $e^z$ in $q$ höchstens $m-1$ ist. -Die Ableitung wäre dann -\[ -Q(z,e^z) -= -mp(z)(e^z)^m + p'(z)(e^z)^m + r(z,e^z) -= -(mp(z) + p'(z))(e^z)^m + r(z,e^z) -=0, -\] -wobei der Grad von $e^z$ in $r$ wieder höchstens $m-1$ ist. -Bildet man $mP(z,e^z) - Q(z,e^z) = 0$ ensteht eine Relation, -in der der Grad des Koeffizienten von $(e^z)^m$ um eins abgenommen hat. -Wiederholt man dies $m$ mal, verschwindet der Term $(e^z)^m$, die -Relation~\eqref{buch:integrale:beweis:exp-analytisch} -war also gar nicht minimal. -Dieser Widerspruch zeigt wieder, dass $e^z$ nicht algebraisch ist, -verwendet aber nur die algebraischen Eigenschaften der differentiellen -Algebra. -}. -\end{beispiel} - -\begin{beispiel} -Wir hätten auch in $\mathbb{Q}$ arbeiten können und $\mathbb{Q}$ -erst die Exponentialfunktion $e^z$ und dann den Logarithmus $z$ von $e^z$ -hinzufügen können. -Es gibt aber noch weitere Logarithmen von $e^z$ zum Beispiel $z+2\pi i$. -Offenbar ist $\psi=z+2\pi i\not\in \mathbb{Q}(z,e^z)$, wir könnten also -auch noch $\psi$ hinzufügen. -Zwar ist $\psi$ auch nicht algebraisch, aber wenn wir $\psi$ hinzufügen, -dann wird aber die Menge der Konstanten grösser, sie umfasst jetzt -$\mathbb{Q}(2\pi i)$. -Die Bedingung in der Definition~\ref{buch:integrale:def:monom}, -dass die Menge der Konstanten nicht grösser werden darf, ist also -verletzt. - -Hätte man mit $\mathbb{Q}(e^z, z+2\pi i)$ begonnen, wäre $z$ aus -dem gleichen Grund kein Monom, aber $z+2\pi i$ wäre eines im Sinne -der Definition~\ref{buch:integrale:def:monom}. -In allen Rechnungen könnte man $\psi=z+2\pi i$ nicht weiter aufteilen, -da $\pi$ oder seine Potenzen keine Elemente von $\mathbb{Q}(e^z)$ sind. -\end{beispiel} - -Da wir im Folgenden davon ausgehen, dass die Konstanten unserer -differentiellen Körper immer $\mathbb{C}$ sind, wird es jeweils -genügen zu untersuchen, ob eine neu hinzuzufügende Funktion algebraisch -ist oder nicht. - -\subsubsection{Ableitungen von Polynomen und rationalen Funktionen von Monomen} -Fügt man einer differentiellen Algebra ein Monom hinzu, dann lässt -sich etwas mehr über Ableitungen von Polynomen oder Brüchen in diesen -Monomen sagen. -Diese Eigenschaften werden später bei der Auflösung der Partialbruchzerlegung -nützlich sein. - -\begin{satz} -\label{buch:integrale:satz:polynom-ableitung-grad} -Sei -\[ -P -= -A_nX^n + A_{n-1}X^{n-1} + \dots A_1X+A_0 -\in\mathscr{D}[X] -\] -ein Polynom mit Koeffizienten in einer differentiellen Algebra $\mathscr{D}$ -und $\vartheta$ ein Monom über $\mathscr{D}$. -Dann gilt -\begin{enumerate} -\item -\label{buch:integrale:satz:polynom-ableitung-grad-log} -Falls $\vartheta=\log f$ ist, ist $P(\vartheta)'$ ein -Polynom vom Grad $n$ in $\vartheta$, wenn der Leitkoeffizient $A_n$ -nicht konstant ist, andernfalls ein Polynom vom Grad $n-1$. -\item -\label{buch:integrale:satz:polynom-ableitung-grad-exp} -Falls $\vartheta = \exp f$ ist, dann ist $P(\vartheta)'$ ein Polynom -in $\vartheta$ vom Grad $n$. -\end{enumerate} -\end{satz} - -Der Satz macht also genaue Aussagen darüber, wie sich der Grad eines -Polynoms in $\vartheta$ beim Ableiten ändert. - -\begin{proof}[Beweis] -Für Exponentialfunktion ist $\vartheta'=\vartheta f'$, die Ableitung -fügt also einfach einen Faktor $f'$ hinzu. -Terme der Form $A_k\vartheta^k$ haben die Ableitung -\[ -(A_k\vartheta^k) -= -A'_k\vartheta^k + A_kk\vartheta^{k-1}\vartheta' -= -A'_k\vartheta^k + A_kk\vartheta^{k-1}\vartheta f' -= -(A'_k + kA_k f)\vartheta^k. -\] -Damit wird die Ableitung des Polynoms -\begin{equation} -P(\vartheta)' -= -\underbrace{(A'_n+nA_nf')\vartheta^n}_{\displaystyle=(A_n\vartheta^n)'} -+ -(A'_{n-1}+(n-1)A_{n-1}f')\vartheta^{n-1} -+ \dots + -(A'_1+A_1f')\vartheta + A_0'. -\label{buch:integrale:ableitung:polynom} -\end{equation} -Der Grad der Ableitung kann sich also nur ändern, wenn $A_n'+nA_nf'=0$ ist. -Dies bedeutet aber wegen -\( -(A_n\vartheta^n)' -= -0 -\), dass $A_n\vartheta^n=c$ eine Konstante ist. -Da alle Konstanten bereits in $\mathscr{D}$ sind, folgt, dass -\[ -\vartheta^n=\frac{c}{A_n} -\qquad\Rightarrow\qquad -\vartheta^n - \frac{c}{A_n}=0, -\] -also wäre $\vartheta$ algebraisch über $\mathscr{D}$, also auch kein Monom. -Dieser Widerspruch zeigt, dass der Leitkoeffizient nicht verschwinden kann. - -Für die erste Aussage ist die Ableitung der einzelnen Terme des Polynoms -\[ -(A_k\vartheta^k)' -= -A_k'\vartheta^k + A_kk\vartheta^{k-1}\vartheta' -= -A_k'\vartheta^k + A_kk\vartheta^{k-1}\frac{f'}{f} -= -\biggl(A_k'\vartheta + kA_k\frac{f'}{f}\biggr)\vartheta^{k-1}. -\] -Die Ableitung des Polynoms ist daher -\[ -P(\vartheta)' -= -A_n'\vartheta^n + \biggl(nA_n\frac{f'}{f}+ A'_{n-1}\biggr)\vartheta^{n-1}+\dots -\] -Wenn $A_n$ keine Konstante ist, ist $A_n'\ne 0$ und der Grad von -$P(\vartheta)'$ ist $n$. -Wenn $A_n$ eine Konstante ist, müssen wir noch zeigen, dass der nächste -Koeffizient nicht verschwinden kann. -Wäre der zweite Koeffizient $=0$, dann wäre die Ableitung -\[ -(nA_n\vartheta+A_{n-1})' -= -nA_n\vartheta'+A'_{n-1} -= -nA_n\frac{f'}{f}+A'_{n-1} -= -0, -\] -d.h. $nA_n\vartheta+A_{n-1}=c$ wäre eine Konstante. -Da alle Konstanten schon in $\mathscr{D}$ sind, müsste auch -\[ -\vartheta = \frac{c-A_{n-1}}{nA_n} \in \mathscr{D} -\] -sein, wieder wäre $\vartheta$ kein Monom. -\end{proof} - -Der nächste Satz gibt Auskunft über den führenden Term in -$(\log P(\vartheta))' = P(\vartheta)'/P(\vartheta)$. - -\begin{satz} -\label{buch:integrale:satz:log-polynom-ableitung-grad} -Sei $P$ ein Polynom vom Grad $n$ wie in -\label{buch:integrale:satz:log-polynom-ableitung} -welches zusätzlich normiert ist, also $A_n=1$. -\begin{enumerate} -\item -\label{buch:integrale:satz:log-polynom-ableitung-log} -Ist $\vartheta=\log f$, dann ist -$(\log P(\vartheta))' = P(\vartheta)'/P(\vartheta)$ und $P(\vartheta)'$ -hat Grad $n-1$. -\item -\label{buch:integrale:satz:log-polynom-ableitung-exp} -Ist $\vartheta=\exp f$, dann gibt es ein Polynom $N(\vartheta)$ so, dass -$(\log P(\vartheta))' -= -P(\vartheta)'/P(\vartheta) -= -N(\vartheta)/P(\vartheta)+nf'$ -ist. -Falls $P(\vartheta)=\vartheta$ ist $N=0$, andernfalls ist $N(\vartheta)$ -ein Polynom vom Grad $0$ das kleinste $k$ so, dass $p<(k+1)q$. -Insbesondere ist dann $kq\le p$. -Nach dem euklidischen Satz für die Division von $P(X)$ durch $Q(X)^k$ -gibt es ein Polynom $P_k(X)$ vom Grad $\le p-qk$ derart, dass -\[ -P(X) = P_k(X)Q(X)^k + R_k(X) -\] -mit einem Rest $R_k(X)$ vom Grad $1$ können mit der Potenzregel -integriert werden, aber für eine Stammfunktion $1/(z-1)$ muss -der Logarithmus $\log(z-1)$ hinzugefügt werden. -Die Stammfunktion -\[ -\int f(z)\,dz -= -\int -\frac{1}{z-1} -\,dz -+ -\int -\frac{4}{(z-1)^2} -\,dz -+ -\int -\frac{4}{(z-1)^3} -\,dz -= -\log(z-1) -- -\underbrace{\frac{4z-2}{(z-1)^2}}_{\displaystyle\in\mathscr{D}} -\in \mathscr{D}(\log(z-1)) = \mathscr{F} -\] -hat eine sehr spezielle Form. -Sie besteht aus einem Term in $\mathscr{D}$ und einem Logarithmus -einer Funktion von $\mathscr{D}$, also einem Monom über $\mathscr{D}$. - -\subsubsection{Einfach elementare Stammfunktionen} -Der in diesem Abschnitt zu beweisende Satz von Liouville zeigt, -dass die im einführenden Beispiel konstruierte Form der Stammfunktion -eine allgemeine Eigenschaft elementar integrierbarer -Funktionen ist. -Zunächst aber soll dieses Bespiel etwas verallgemeinert werden. - -\begin{satz}[Liouville-Vorstufe für Monome] -\label{buch:integrale:satz:liouville-vorstufe-1} -Sei $\vartheta$ ein Monom über $\mathscr{D}$ und $g\in\mathscr{D}(\vartheta)$ -mit $g'\in\mathscr{D}$. -Dann hat $g$ die Form $v_0 + c_1\vartheta$ mit $v_0\in\mathscr{D}$ und -$c_1\in\mathbb{C}$. -\end{satz} - -\begin{proof}[Beweis] -In Anlehnung an das einführende Beispiel nehmen wir an, dass die -Stammfunktion $g\in\mathscr{D}[\vartheta]$ für ein Monom $\vartheta$ -über $\mathscr{D}$ ist. -Dann hat $g$ die Partialbruchzerlegung -\[ -g -= -H(\vartheta) -+ -\sum_{j\le r(i)} \frac{P_{ij}(\vartheta)}{Q_i(\vartheta)^j} -\] -mit irreduziblen normierten Polynomen $Q_i(\vartheta)$ und -Polynomen $P_{ij}(\vartheta)$ vom Grad kleiner als $\deg Q_i(\vartheta)$. -Ausserdem ist $H(\vartheta)$ ein Polynom. -Die Ableitung von $g$ muss jetzt aber wieder in $\mathscr{D}$ sein. -Zu ihrer Berechnung können die Sätze -\ref{buch:integrale:satz:polynom-ableitung-grad}, -\ref{buch:integrale:satz:log-polynom-ableitung-grad} -und -\ref{buch:integrale:satz:partialbruch-monom} -verwendet werden. -Diese besagen, dass in der Partialbruchzerlegung die Exponenten der -Nenner die Quotienten in der Summe nicht kleiner werden. -Die Ableitung $g'\in\mathscr{D}$ darf aber gar keine Nenner mit -$\vartheta$ enthalten, also dürfen die Quotienten gar nicht erst -vorkommen. -$g=H(\vartheta)$ muss also ein Polynom in $\vartheta$ sein. -Die Ableitung des Polynoms darf wegen $g'\in\mathscr{d}$ das Monom -$\vartheta$ ebenfalls nicht mehr enthalten, daher kann es höchstens vom -Grad $1$ sein. -Nach Satz~\ref{buch:integrale:satz:log-polynom-ableitung-grad} -muss ausserdem der Leitkoeffizient von $g$ eine Konstante sein, -das Polynom hat also genau die behauptete Form. -\end{proof} - -\begin{satz}[Liouville-Vorstufe für algebraische Elemente] -\label{buch:integrale:satz:liouville-vorstufe-2} -Sei $\vartheta$ algebraische über $\mathscr{D}$ und -$g\in\mathscr{D}(\vartheta)$ mit $g'\in\mathscr{D}$. -\end{satz} - -\subsubsection{Elementare Stammfunktionen} -Nach den Vorbereitungen über einfach elementare Stammfunktionen -in den Sätzen~\label{buch:integrale:satz:liouville-vorstufe-1} -und -\label{buch:integrale:satz:liouville-vorstufe-2} sind wir jetzt -in der Lage, den allgemeinen Satz von Liouville zu formulieren -und zu beweisen. - -\begin{satz}[Liouville] -Sei $\mathscr{D}$ ein Differentialkörper, $\mathscr{F}$ einfach über -$\mathscr{D}$ mit gleichem Konstantenkörper $\mathbb{C}$. -Wenn $g\in \mathscr{F}$ eine Stammfunktion von $f\in\mathscr{D}$ ist, -also $g'=f$, dann gibt es Zahlen $c_i\in\mathbb{C}$ und -$v_0,v_i\in\mathscr{D}$ derart, dass -\begin{equation} -g = v_0 + \sum_{i=1}^k c_i \log v_i -\qquad\Rightarrow\qquad -g' = v_0' + \sum_{i=1}^k c_i \frac{v_i'}{v_i} = f -\label{buch:integrale:satz:liouville-fform} -\end{equation} -gilt. -\end{satz} - -Der Satz hat zur Folge, dass eine elementare Stammfunktion für $f$ -nur dann existieren kann, wenn sich $f$ in der speziellen Form -\eqref{buch:integrale:satz:liouville-fform} -schreiben lässt. -Die Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion-dalg} -lässt sich damit jetzt lösen. - - -\begin{proof}[Beweis] -Wenn die Stammfunktion $g\in\mathscr{D}$ ist, dann hat $g$ die Form -\eqref{buch:integrale:satz:liouville-fform} mit $v_0=g$, die Summe -wird nicht benötigt. - -Wir verwenden Induktion nach der Anzahl der Elemente, die zu $\mathscr{D}$ -hinzugefügt werden müssen, um einen Differentialkörper -$\mathscr{F}=\mathscr{D}(\vartheta_1,\dots,\vartheta_n)$ zu konstruieren, -der $g$ enthält. -Da $f\in\mathscr{D}\subset\mathscr{D}(\vartheta_1)$ ist, können wir die -Induktionsannahme auf die Erweiterung -\[ -\mathscr{D}(\vartheta_1)\subset\mathscr{D}(\vartheta_1,\vartheta_2) -\subset\cdots\subset \mathscr{D}(\vartheta_1,\cdots,\vartheta_n)=\mathscr{F} -\] -anwenden, die durch Hinzufügen von nur $n-1$ Elemente -$\vartheta_2,\dots,\vartheta_n$ aus $\mathscr{D}(\vartheta_1)$ den -Differentialkörper $\mathscr{F}$ erreicht, der $g$ enthält. -Sie besagt, dass sich $g$ schreiben lässt als -\[ -g = w_0 + \sum_{i=1}^{k_1} c_i\log w_i -\qquad\text{mit $c_i\in\mathbb{C}$ und $w_0,w_i\in\mathscr{D}(\vartheta_1)$.} -\] -Wir müssen jetzt zeigen, dass sich dieser Ausdruck umformen lässt -in den Ausdruck der Form~\eqref{buch:integrale:satz:liouville-fform}. - -Der Term $w_0\in\mathscr{D}(\vartheta_1)$ hat eine Partialbruchzerlegung -\[ -H(\vartheta_1) -+ -\sum_{j\le r(l)} \frac{P_{lj}(\vartheta_1)}{Q_l(\vartheta_1)^j} -\] -in der Variablen $\vartheta_1$. - -Da $w_i\in\mathscr{D}(\vartheta_1)$ ist, kann man Zähler und Nenner -von $w_i$ als Produkt irreduzibler normierter Polynome schreiben: -\[ -w_i -= -\frac{h_i Z_{i1}(\vartheta_1)^{s_{i1}}\cdots Z_{im(i)}^{s_{im(i)}} -}{ -N_{i1}(\vartheta_1)^{t_{i1}}\cdots N_{in(i)}(\vartheta_1)^{t_{in(i)}} -} -\] -Der Logarithmus hat die Form -\begin{align*} -\log w_i -&= \log h_i + -s_{i1} -\log Z_{i1}(\vartheta_1) -+ -\cdots -+ -s_{im(i)} -\log Z_{im(i)} -- -t_{i1} -\log -N_{i1}(\vartheta_1) -- -\cdots -- -t_{in(i)} -\log -N_{in(i)}(\vartheta_1). -\end{align*} -$g$ kann also geschrieben werden als eine Summe von Polynomen, Brüchen, -wie sie in der Partialbruchzerlegung vorkommen, Logarithmen von irreduziblen -normierten Polynomen und Logarithmen von Elementen von $\mathscr{D}$. - -Die Ableitung $g'$ muss jetzt aber wieder in $\mathscr{D}$ sein, beim -Ableiten müssen also alle Terme verschwinden, die $\vartheta_1$ enthalten. -Dabei spielt es eine Rolle, ob $\vartheta_1$ ein Monom oder algebraisch ist. -\begin{enumerate} -\item -Wenn $\vartheta_1$ ein Monom ist, dann kann man wie im Beweis des -Satzes~\ref{buch:integrale:satz:liouville-vorstufe-1} argumentieren, -dass die Brüchterme gar nicht vorkommen und -$H(\vartheta_1)=v_0+c_1\vartheta_1$ sein muss. -Die Ableitung Termen der Form $\log Z(\vartheta_1)$ ist ein Bruchterm -mit dem irreduziblen Nenner $Z(\vartheta_1)$, die ebenfalls verschwinden -müssen. -Ist $\vartheta_1$ eine Exponentialfunktion, dann ist -$\vartheta_1' \in \mathscr{D}(\vartheta_1)\setminus\mathscr{D}$, also muss -$c_1=0$ sein. -Ist $\vartheta_1$ ein Logarithmus, also $\vartheta_1=\log v_1$, dann -kommen nur noch Terme der in -\eqref{buch:integrale:satz:liouville-fform} -erlaubten Form vor. - -\item -Wenn $\vartheta_1$ algebraisch vom Grad $m$ ist, dann ist -\[ -g' = w_0' + \sum_{i=1}^{k_1} d_i\frac{w_i'}{w_i} = f. -\] -Weder $w_0$ noch $\log w_i$ sind in $\mathscr{D}(\vartheta_1)$. -Aber wenn man $\vartheta_1$ durch die $m$ konjugierten Elemente -ersetzt und alle summiert, dann ist -\[ -mf -= -\operatorname{Tr}(w_0) + \sum_{i=1}^{k_1} d_i \log\operatorname{Norm}(w_i). -\] -Da die Spur und die Norm in $\mathscr{D}$ sind, folgt, dass -\[ -f -= -\underbrace{\frac{1}{m} -\operatorname{Tr}(w_0)}_{\displaystyle= v_0} -+ -\sum_{i=1}^{k_1} \underbrace{\frac{d_i}{m}}_{\displaystyle=c_i} -\log -\underbrace{ \operatorname{Norm}(w_i)}_{\displaystyle=v_i} -= -v_0 + \sum_{i=1}^{k_1} c_i\log v_i -\] -die verlangte Form hat. -\qedhere -\end{enumerate} -\end{proof} - -\subsection{Die Fehlerfunktion ist keine elementare Funktion -\label{buch:integrale:section:fehlernichtelementar}} -% \url{https://youtu.be/bIdPQTVF5n4} -Mit Hilfe des Satzes von Liouville kann man jetzt beweisen, dass -die Fehlerfunktion keine elementare Funktion ist. -Dazu braucht man die folgende spezielle Form des Satzes. - -\begin{satz} -\label{buch:integrale:satz:elementarestammfunktion} -Wenn $f(x)$ und $g(x)$ rationale Funktionen von $x$ sind, dann -ist die Stammfunktion von $f(x)e^{g(x)}$ genau dann eine -elementare Funktion, wenn es eine rationale Funktion gibt, die -Lösung der Differentialgleichung -\[ -r'(x) + g'(x)r(x)=f(x) -\] -ist. -\end{satz} - -\begin{satz} -Die Funktion $x\mapsto e^{-x^2}$ hat keine elementare Stammfunktion. -\label{buch:iintegrale:satz:expx2} -\end{satz} - -\begin{proof}[Beweis] -Unter Anwendung des Satzes~\ref{buch:integrale:satz:elementarestammfunktion} -auf $f(x)=1$ und $g(x)=-x^2$ folgt, $e^{-x^2}$ genau dann eine rationale -Stammfunktion hat, wenn es eine rationale Funktion $r(x)$ gibt, die -Lösung der Differentialgleichung -\begin{equation} -r'(x) -2xr(x)=1 -\label{buch:integrale:expx2dgl} -\end{equation} -ist. - -Zunächst halten wir fest, dass $r(x)$ kein Polynom sein kann. -Wäre nämlich -\[ -r(x) -= -a_0 + a_1x + \dots + a_nx^n -= -\sum_{k=0}^n a_kx^k -\quad\Rightarrow\quad -r'(x) -= -a_1 + 2a_2x + \dots + na_nx^{n-1} -= -\sum_{k=1}^n -ka_kx^{k-1} -\] -ein Polynom, dann ergäbe sich beim Einsetzen in die Differentialgleichung -\begin{align*} -1 -&= -r'(x)-2xr(x) -\\ -&= -a_1 + 2a_2x + 3a_3x^2 + \dots + (n-1)a_{n-1}x^{n-2} + na_nx^{n-1} -\\ -&\qquad -- -2a_0x -2a_1x^2 -2a_2x^3 - \dots - 2a_{n-1}x^n - 2a_nx^{n+1} -\\ -& -\hspace{0.7pt} -\renewcommand{\arraycolsep}{1.8pt} -\begin{array}{crcrcrcrcrcrcrcr} -=&a_1&+&2a_2x&+&3a_3x^2&+&\dots&+&(n-1)a_{n-1}x^{n-2}&+&na_{n }x^{n-1}& & & & \\ - & &-&2a_0x&-&2a_1x^2&-&\dots&-& 2a_{n-3}x^{n-2}&-&2a_{n-2}x^{n-1}&-&2a_{n-1}x^n&-&2a_nx^{n+1} -\end{array} -\\ -&= -a_1 -+ -(2a_2-2a_0)x -+ -(3a_3-2a_1)x^2 -%+ -%(4a_4-2a_2)x^3 -+ -\dots -+ -(na_n-2a_{n-2})x^{n-1} -- -2a_{n-1}x^n -- -2a_nx^{n+1}. -\end{align*} -Koeffizientenvergleich zeigt, dass $a_1=1$ sein muss. -Aus den letzten zwei Termen liest man ebenfalls mittels Koeffizientenvergleich -ab, dass $a_n=0$ und $a_{n-1}=0$ sein müssen. -Aus den Koeffizienten $(ka_k-2a_{k-2})=0$ folgt, dass -$a_{k-2}=\frac{k}{2}a_k$ für alle $k>1$ sein muss, diese Koeffizienten -verschwinden also auch, inklusive $a_1=0$. -Dies ist allerdings im Widerspruch zu $a_1=1$. -Es folgt, dass $r(x)$ kein Polynom sein kann. - -Der Nenner der rationalen Funktion $r(x)$ hat also mindestens eine Nullstelle -$\alpha$, man kann daher $r(x)$ auch schreiben als -\[ -r(x) = \frac{s(x)}{(x-\alpha)^n}, -\] -wobei die rationale Funktion $s(x)$ keine Nullstellen und keine Pole hat. -Einsetzen in die Differentialgleichung ergibt: -\[ -1 -= -r'(x) -2xr(x) -= -\frac{s'(x)}{(x-\alpha)^n} --n -\frac{s(x)}{(x-\alpha)^{n+1}} -- -\frac{2xs(x)}{(x-\alpha)^n}. -\] -Multiplizieren mit $(x-\alpha)^{n+1}$ gibt -\[ -(x-\alpha)^{n+1} -= -s'(x)(x-\alpha) -- -ns(x) -- -2xs(x)(x-\alpha) -\] -Setzt man $x=\alpha$ ein, verschwinden alle Terme ausser dem mittleren -auf der rechten Seite, es bleibt -\[ -ns(\alpha) = 0. -\] -Dies widerspricht aber der Wahl der rationalen Funktion $s(x)$, für die -$\alpha$ keine Nullstelle ist. - -Somit kann es keine rationale Funktion $r(x)$ geben, die eine Lösung der -Differentialgleichung~\eqref{buch:integrale:expx2dgl} ist und -die Funktion $e^{-x^2}$ hat keine elementare Stammfunktion. -\end{proof} - -Der Satz~\ref{buch:iintegrale:satz:expx2} rechtfertigt die Einführung -der Fehlerfunktion $\operatorname{erf}(x)$ als neue spezielle Funktion, -mit deren Hilfe die Funktion $e^{-x^2}$ integriert werden kann. - - - +\rhead{Differentialkörper} +\input{chapters/060-integral/rational.tex} +\input{chapters/060-integral/erweiterungen.tex} +\input{chapters/060-integral/diffke.tex} +\input{chapters/060-integral/iproblem.tex} +\input{chapters/060-integral/irat.tex} +\input{chapters/060-integral/sqrat.tex} diff --git a/buch/chapters/060-integral/differentialkoerper2.tex b/buch/chapters/060-integral/differentialkoerper2.tex new file mode 100644 index 0000000..f41d3ba --- /dev/null +++ b/buch/chapters/060-integral/differentialkoerper2.tex @@ -0,0 +1,1953 @@ +% +% differentialalgebren.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\section{Differentialkörper und der Satz von Liouville +\label{buch:integrale:section:dkoerper}} +\rhead{Differentialkörper und der Satz von Liouville} +Das Problem der Darstellbarkeit eines Integrals in geschlossener +Form verlangt zunächst einmal nach einer Definition dessen, was man +als ``geschlossene Form'' akzeptieren will. +Die sogenannten {\em elementaren Funktionen} von +Abschnitt~\ref{buch:integrale:section:elementar} +bilden dafür den theoretischen Rahmen. +Das Problem ist dann die Frage zu beantworten, ob ein Integral eine +Stammfunktion hat, die eine elementare Funktion ist. +Der Satz von Liouville von Abschnitt~\ref{buch:integrale:section:liouville} +löst das Problem. + +\subsection{Eine Analogie +\label{buch:integrale:section:analogie}} +% XXX Analogie: Formel für Polynom-Nullstellen +% XXX Stammfunktion als elementare Funktion +Das Analysis-Problem, eine Stammfunktion zu finden, ist analog zum +wohlbekannten algebraischen Problem, Nullstellen von Polynomen zu finden. +Wir entwickeln diese Analogie in etwas mehr Detail, um zu sehen, ob man +aus dem algebraischen Problem etwas über das Problem der Analysis +lernen kann. + +Für ein Polynom $p(X) = a_nX^n+a_{n-1}X^{n-1}+\dots+a_1X+a_0\in\mathbb{C}[X]$ +mit Koeffizienten $a_k\in\mathbb{C}$ ist es sehr einfach, für jede beliebige +komplexe Zahl $z\in\mathbb{C}$ den Wert $p(z)$ des Polynoms auszurechnen. +Ein paar wenige Rechenregeln genügen dazu, man kann leicht einem Kind +beibringen, mit einem Taschenrechner so einen Wert auszurechnen. + +Ähnlich sieht es mit der Ableitungsoperation aus. +Einige wenige Ableitungsregeln, die man in der Analysis~I lernt, +erlauben, auf mehr oder weniger mechanische Art und Weise, jede +beliebige Funktion abzuleiten. +Man kann auch leicht einen Computer dazu programmieren, solche Ableitungen +symbolisch zu berechnen. + +Aus dem Fundamentalsatz der Algebra, der von Gauss vollständig bewiesen +wurde, ist bekannt, dass jedes Polynom mit Koeffizienten in $\mathbb{C}$ +genau so viele Lösungen in $\mathbb{C}$, wie der Grad des Polynoms angibt. +Dies ist aber ein Existenzsatz, er sagt nichts darüber aus, wie man diese +Lösungen finden kann. +In Spezialfällen, wie zum Beispiel für quadratische Polynome, gibt +es spezialsierte Lösungsverfahren, mit denen man Lösungen angeben kann. +Natürlich existieren numerische Methoden wie zum Beispiel das +Newton-Verfahren, mit dem man Nullstellen von Polynomen beliebig genau +bestimmen kann. + +Der Fundamentalsatz der Integralrechnung besagt, dass jede stetige +Funktion eine Stammfunktion hat, die bis auf eine Konstante eindeutig +bestimmt ist. +Auch dieser Existenzsatz gibt keinerlei Hinweise darauf, wie man die +Stammfunktion finden kann. +In der Analysis-Vorlesung lernt man viele Tricks, die in einer +beindruckenden Zahl von Spezialfällen ermöglichen, ein passende +Funktion anzugeben. +Man lernt auch numerische Verfahren kennen, mit denen sich Werte der +Stammfunktion, also bestimmte Integrale, mit beliebiger Genauigkeit +finden kann. + +Die numerische Lösung des Nullstellenproblems ist insofern unbefriedigend, +als sie nur schwer eine Diskussion der Abhängigkeit der Nullstellen von +den Koeffizienten des Polynoms ermöglichen. +Eine Formel wie die Lösungsformel für die quadratische Gleichung +stellt genau für solche Fälle ein ideales Werkzeug bereit. +Was man sich also wünscht ist nicht nur einfach eine Lösung, sondern eine +einfache Formel zur Bestimmung aller Lösungen. +Im Zusammenhang mit algebraischen Gleichungen erwartet man eine Formel, +in der nur arithmetische Operationen und Wurzeln vorkommen. +Für quadratische Gleichungen ist so eine Formel seit dem Altertum bekannt, +Formeln für die kubische Gleichung und die Gleichung vierten Grades wurden +im 16.~Jahrhundert von Cardano bzw.~Ferrari gefunden. +Erst viel später haben Abel und Ruffini gezeigt, dass so eine allgemeine +Formel für Polynome höheren Grades als 4 nicht existiert. +Die Galois-Theorie, die auf den Ideen von Évariste Galois beruht, +stellt eine vollständige Theorie unter anderem für die Lösbarkeit +von Gleichungen durch Wurzelausdrücke dar. + +Numerische Integralwerte haben ebenfalls den Nachteil, dass damit +Diskussionen wie die Abhängigkeit von Parametern eines Integranden +nur schwer möglich sind. +Was man sich daher wünscht ist eine Formel für die Stammfunktion, +die Werte als Zusammensetzung gut bekannter Funktionen wie der Exponential- +und Logarithmus-Funktionen oder der trigonometrischen Funktionen +sowie Wurzeln, Potenzen und den arithmetischen Operationen. +Man sagt, man möchte die Stammfunktion in ``geschlossener Form'' +dargestellt haben. +Tatsächlich ist dieses Problem auch zu Beginn des 19.~Jahrhunderts +von Joseph Liouville genauer untersucht worden. +Er hat zunächst eine Klasse von ``elementaren Funktionen'' definiert, +die als Darstellungen einer Stammfunktion in Frage kommen. +Der Satz von Liouville besagt dann, dass nur Funktionen mit einer +ganz speziellen Form eine elementare Stammfunktion haben. +Damit wird es möglich, zu entscheiden, ob ein Integrand wie $e^{-x^2}$ +eine elementare Stammfunktion hat. +Seit dieser Zeit weiss man zum Beispiel, dass die Fehlerfunktion nicht +mit den bekannten Funktionen dargestellt werden kann. + +Mit dem Aufkommen der Computer und vor allem der Computer-Algebra-System (CAS) +wurde die Frage nach der Bestimmung einer Stammfunktion erneut aktuell. +Die ebenfalls weiter entwickelte abstrakte Algebra hat ermöglicht, die +Ideen von Liouville in eine erweiterte, sogenannte differentielle +Galois-Theorie zu verpacken, die eine vollständige Lösung des Problems +darstellt. +Robert Henry Risch hat in den Sechzigerjahren auf dieser Basis +einen Algorithmus entwickelt, mit dem es möglich wird, zu entscheiden, +ob eine Funktion eine elementare Stammfunktion hat und diese +gegebenenfalls auch zu finden. +Moderne CAS implementieren diesen Algorithmus +in Teilen, besonders weit zu gehen scheint das quelloffene System +Axiom. + +Der Risch-Algorithmus hat allerdings eine Achillesferse: er benötigt +eine Method zu entscheiden, ob zwei Ausdrücke übereinstimmen. +Dies ist jedoch ein im Allgemeinen nicht entscheidbares Problem. +Moderne CAS treiben einigen Aufwand, um die +Gleichheit von Ausdrücken zu entscheiden, sie können das Problem +aber grundsätzlich nicht vollständig lösen. +Damit kann der Risch-Algorithmus in praktischen Anwendungen das +Stammfunktionsproblem ebenfalls nur mit Einschränkungen lösen, +die durch die Fähigkeiten des Ausdrucksvergleichs in einem CAS +gesetzt werden. + +Im Folgenden sollen elementare Funktionen definiert werden, es sollen +die Grundideen der differentiellen Galois-Theorie zusammengetragen werden +und der Satz von Liouvill vorgestellt werden. +An Hand der Fehler-Funktion soll dann gezeigt werden, wie man jetzt +einsehen kann, dass die Fehlerfunktion nicht elementar darstellbar ist. +Im nächsten Abschnitt dann soll der Risch-Algorithmus skizziert werden. + +\subsection{Elementare Funktionen +\label{buch:integrale:section:elementar}} +Es soll die Frage beantwortet werden, welche Stammfunktionen sich +in ``geschlossener Form'' oder durch ``wohlbekannte Funktionen'' +ausdrücken lassen. +Welche Funktionen dabei als ``wohlbekannt'' gelten dürfen ist +ziemlich willkürlich. +Sicher möchte man Potenzen und Wurzeln, Logarithmus und Exponentialfunktion, +aber auch die trigonometrischen Funktionen dazu zählen dürfen. +Ausserdem will man beliebig mit den arithmetischen Operationen +rechnen. +So entsteht die Menge der Funktionen, die man ``elementar'' nennen +will. + +In der Menge der elementaren Funktionen möchte man jetzt +Stammfunktionen ausgewählter Funktionen suchen. +Dazu muss man von jeder Funktion ihre Ableitung kennen. +Die Ableitungsoperation macht aus der Funktionenmenge eine +differentielle Algebra. +Der Satz von Liouville (Satz~\ref{buch:integrale:satz:liouville1}) +liefert Bedingungen, die erfüllt sein müssen, wenn eine Funktion +eine elementare Stammfunktion hat. +Sind diese Bedingungen nicht erfüllbar, ist auch keine +elementare Stammfunktion möglich. + +In den folgenden Abschnitten soll die differentielle Algebra +der elementaren Funktionen konstruiert werden. + +\subsubsection{Körper} +Die einfachsten Funktionen sind die die Konstanten, für die wir +für die nachfolgenden Betrachtungen fast immer die komplexen Zahlen +$\mathbb{C}$ +zu Grunde legen wollen. +Dabei ist vor allem wichtig, dass sich darin alle arithmetischen +Operationen durchführen lassen mit der einzigen Ausnahme, dass +nicht durch $0$ dividiert werden darf. +Man nennt $\mathbb{C}$ daher ein {\em Körper}. +\index{Körper}% +\label{buch:integrale:def:koerper} + +\subsubsection{Polynome und rationale Funktionen} +Die Polynome einer Variablen beschreiben eine Menge von +Funktionen, in der Addition, Subtraktion, Multiplikation +von Funktionen und Multiplikation mit komplexen Zahlen +uneingeschränkt möglich ist. +Wir bezeichen wie früher die Menge der Polynome in $z$ mit +$\mathbb{C}[z]$. + +Die Division ist erst möglich, wenn man beliebige Brüche +zulässt, deren Zähler und Nenner Polynome sind. +Die Menge +\[ +\mathbb{C}(z) += +\biggl\{ +\frac{p(z)}{q(z)} +\;\bigg|\; +p,q\in \mathbb{C}[z] +\biggr\} +\] +heisst die Menge der {\em rationalen Funktionen}. +\label{buch:integrale:def:rationalefunktion} +\index{Funktion, rationale}% +\index{rationale Funktion}% +In ihr sind jetzt alle arithmetischen Operationen ausführbar +ausser natürlich die Division durch die Nullfunktion. +Die rationalen Funktionen bilden also wieder eine Körper. + +Die Tatsache, dass die rationalen Funktionen einen Körper +bilden bedeutet auch, dass die Konstruktion erneut durchgeführt +werden kann. +Ausgehend von einem beliebigen Körper $K$ können wieder zunächst +die Polynome $K[X]$ und anschliesen die rationalen Funktionen $K[X]$ +in der neuen Variablen, jetzt aber mit Koeffizienten in $K$ +gebildet werden. +So entstehen Funktionen von mehreren Variablen und, indem +wir für die neue Variable $X$ zum Beispiel die im übernächsten +Abschnitt betrachtete Wurzel $X=\sqrt{z}$ +einsetzen, rationale Funktionen in $z$ und $\sqrt{z}$. + +Solche Funktionenkörper werden im folgenden mit geschweiften +Buchstaben $\mathscr{D}$ bezeichnet. +\index{Funktionenkörper}% + +\subsubsection{Ableitungsoperation} +In allen Untersuchungen soll immer die Ableitungsoperation +mit berücksichtigt werden. +In unserer Betrachtungsweise spielt es keine Rolle, dass die +Ableitung aus einem Grenzwert entsteht, es sind nur die algebraischen +Eigenschaften wichtig. +Diese sind in der folgenden Definition zusammengefasst. + +\begin{definition} +\label{buch:integrale:def:derivation} +Ein {\em Ableitungsoperator} oder eine {\em Derivation} einer Algebra +$\mathscr{D}$ von Funktionen ist eine lineare Abbildung +\[ +\frac{d}{dz} +\colon \mathscr{D} \to \mathscr{D} +: +f \mapsto \frac{df}{dz} = f', +\] +die zusätzlich die Produktregel +\begin{equation} +\frac{d}{dz} (fg) += +\frac{df}{dz} \cdot g + f \cdot \frac{dg}{dz} +\qquad\Leftrightarrow\qquad +(fg)' = f' g + fg' +\label{buch:integrale:eqn:produktregel} +\end{equation} +\index{Produktregel}% +erfüllt. +Die Funktion $f'\in \mathscr{D}$ heisst auch die {\em Ableitung} +von $f\in\mathscr{D}$. +\index{Derivation}% +\index{Ableitungsoperator}% +\index{Ableitung}% +\end{definition} + +Die Produktregel hat zum Beispiel auch die bekannten Quotientenregel +zur Folge. +Dazu betrachten wir das Produkt $f= (f/g)\cdot g$ und leiten es mit +Hilfe der Produktregel ab: +\[ +\frac{d}{dz}f += +\frac{d}{dz} +\biggl( +\frac{f}{g}\cdot g +\biggr) += +{\color{darkred} +\frac{d}{dz} +\biggl( +\frac{f}{g} +\biggr)} +\cdot g ++ +\frac{f}{g}\cdot \frac{d}{dz}g. +\] +Jetzt lösen wir nach der {\color{darkred}roten} Ableitung des Quotienten +auf und erhalten +\begin{equation} +\biggl(\frac{f}{g}\biggr)' += +\frac{d}{dz}\biggl(\frac{f}{g}\biggr) += +\frac1g\biggl( +\frac{d}{dz}f - \frac{f}{g}\cdot \frac{d}{dz}g +\biggr) += +\frac{1}{g} +\biggl( +f'-\frac{fg'}{g} +\biggr) += +\frac{f'g-fg'}{g^2}. +\label{buch:integrale:eqn:quotientenregel} +\end{equation} +Dies ist die Quotientenregel. + +Aus der Produktregel folgt natürlich sofort auch die Potenzregel +für die Ableitung der $n$ten Potenz einer Funktion $f\in\mathscr{D}$, +sie lautet: +\begin{equation} +\frac{d}{dz} f^n += +\underbrace{ +f'f^{n-1} + ff'f^{n-2} + f^2f'f^{n-3}+\dots f^{n-1}f' +}_{\displaystyle \text{$n$ Terme}} += +nf^{n-1}f'. +\label{buch:integrale:eqn:potenzregel} +\end{equation} +In dieser Form versteckt sich natürlich auch die Kettenregel, die +Potenzfunktion ist die äussere Funktion, $f$ die innere, $f'$ ist also +die Ableitung er inneren Funktion, wie in der Kettenregel verlangt. +Falls $f$ ein Element von $\mathscr{D}$ ist mit der Eigenschaft +$df/dz=1$, dann entsteht die übliche Produktregel. + +\begin{definition} +Eine Algebra $\mathscr{D}$ von Funktionen mit einem Ableitungsoperator +$d/dz$ heisst eine {\em differentielle Algebra}. +\index{differentielle Algebra}% +\index{Algebra, differentielle}% +In einer differentiellen Algebra gelten die üblichen +Ableitungsregeln. +\end{definition} + +Die Potenzregel war in der Form~\eqref{buch:integrale:eqn:potenzregel} +geschrieben worden, nicht als die Ableitung von $z$. +Der Grund dafür ist, dass wir gar nicht voraussetzen wollen, dass in +unserer differentiellen Algebra eine Funktion existiert, die die +Rolle von $z$ hat. +Dies ist gar nicht nötig, wie das folgende Beispiel zeigt. + +\begin{beispiel} +Als Funktionenmenge $\mathscr{D}$ nehmen wir rationale Funktionen +in zwei Variablen, die wir $\cos x $ und $\sin x$ nennen. +Diese Menge bezeichnen wir mit +$\mathscr{D}=\mathbb{Q}(\cos x,\sin x)$ +Der Ableitungsoperator ist +\begin{align*} +\frac{d}{dx} \cos x &= -\sin x +\\ +\frac{d}{dx} \sin x &= \phantom{-}\cos x. +\end{align*} +Die Funktionen von $\mathbb{Q}(\cos x,\sin x)$ sind also Brüche, +deren Zähler und Nenner Polynome in $\cos x$ und $\sin x$ sind. +Aus den Produkt- und Quotientenregeln und den Ableitungsregeln für +$\cos x$ und $\sin x$ folgt, dass die Ableitung einer Funktion in +$\mathscr{D}$ wieder in $\mathscr{D}$ ist, $\mathscr{D}$ ist eine +differentielle Algebra. +\end{beispiel} + +Die konstanten Funktionen spielen eine besondere Rolle. +Da wir bei der Ableitung nicht von der Vorstellung einer +Funktion mit einem variablen Argument ausgehen wollten und +die Ableitung nicht als Grenzwert definieren wollten, müssen +wir auch bei der Definition der ``Konstanten'' einen neuen +Weg gehen. +In der Analysis sind die Konstanten genau die Funktionen, +deren Ableitung $0$ ist. + +\begin{definition} +\label{buch:integrale:def:konstante} +Ein Element $f\in \mathscr{D}$ mit $df/dz=f'=0$ heissen +{\em Konstante} in $\mathscr{D}$. +\index{Konstante}% +\end{definition} + +Die in der Potenzregel~\eqref{buch:integrale:eqn:potenzregel} +vermisste Funktion $z$ kann man ähnlich zu den Konstanten +zu definieren versuchen. +$z$ müsste ein Element von $\mathscr{D}$ mit $z' = 1$ sein. +Allerdings gibt es viele solche Elemente, ist $c$ eine Konstanten +und $z'=1$, dann ist auch $(z+c)'=1$, $(z+c)$ hat also für +die Zwecke unserer Untersuchung die gleichen Eigenschaften wie +$z$. +Dies deckt sich natürlich auch mit der Erwartung, dass Stammfunktionen +nur bis auf eine Konstante bestimmt sind. +Eine differentielle Algebra muss allerdings kein Element $z$ mit der +Eigenschaft $z'=1$ enthalten. + +\begin{beispiel} +In $\mathscr{D}=\mathbb{Q}(\cos x,\sin x)$ gibt es kein Element $x$. +Ein solches wäre von der Form +\[ +x = \frac{p(\cos x,\sin x)}{q(\cos x,\sin x)}. +\] +Eine solche goniometrische Beziehung würde für $x=\frac{\pi}4$ bedeuten, +dass +\[ +\frac{\pi}4 += +\frac{p(\sqrt{2}/2,\sqrt{2}/2)}{q(\sqrt{2}/2,\sqrt{2}/2)}. +\] +Auf der rechten Seite steht ein Quotient von Polynome, in dessen +Argument nur rationale Zahlen und $\sqrt{2}$ steht. +So ein Ausdruck kann immer in die Form +\[ +\pi += +4\frac{a\sqrt{2}+b}{c\sqrt{2}+d} += +\frac{4(a\sqrt{2}+b)(c\sqrt{2}-d)}{2c^2+d^2} += +r\sqrt{2}+s +\] +gebracht werden. +Die Zahl auf der rechten Seite ist zwar irrational, aber sie ist Nullstelle +des quadratischen Polynoms +\[ +p(x) += +(x-r\sqrt{2}-s)(x+r\sqrt{2}-s) += +x^2 +-2sx +-2r^2+s^2 +\] +mit rationalen Koeffizienten, wie man mit der Lösungsformel für die +quadratische Gleichung nachprüfen kann. +Es ist bekannt, dass $\pi$ als transzendente Zahl nicht Nullstelle +eines Polynoms mit rationalen Koeffizienten ist. +Dieser Widerspruch zeigt, dass $x$ nicht in $\mathbb{Q}(\cos x, \sin x)$ +vorkommen kann. +\end{beispiel} + +In einer differentiellen Algebra kann jetzt die Frage nach der +Existenz einer Stammfunktion gestellt werden. + +\begin{aufgabe} +\label{buch:integrale:aufgabe:existenz-stammfunktion} +Gegeben eine differentielle Algebra $\mathscr{D}$ und ein Element +$f\in\mathscr{D}$, entscheide, ob es ein Element $F\in\mathscr{D}$ +gibt mit der Eigenschaft $F'=f$. +Ein solches $F\in\mathscr{D}$ heisst {\em Stammfunktion} von $f$. +\end{aufgabe} + +\begin{satz} +In einer differentiellen Algebra $\mathscr{D}$ mit $z\in\mathscr{D}$ +hat die Potenzfunktion $f=z^n$ für $n\in\mathbb{N}\setminus\{-1\}$ +ein Stammfunktion, nämlich +\[ +F = \frac{1}{n+1} z^{n+1}. +\] +\label{buch:integrale:satz:potenzstammfunktion} +\end{satz} + +\begin{proof}[Beweis] +Tatsächlich kann man dies sofort nachrechnen, muss allerdings die +Fälle $n+1 >0$ und $n+1<0$ unterscheiden, da die Potenzregel +\eqref{buch:integrale:eqn:potenzregel} nur für natürliche Exponenten +gilt. +Man erhält +\begin{align*} +n+1&>0\colon +& +\frac{d}{dz}\frac{1}{n+1}z^{n+1} +&= +\frac{1}{n+1}(n+1)z^{n+1-1} += +z^n, +\\ +n+1&<0\colon +& +\frac{d}{dz}\frac{1}{n+1}\frac{1}{z^{-(n+1)}} +&= +\frac{1}{n+1}\frac{1'z^{-(n+1)}-1(-(n+1))z^{-n-1-1}}{z^{-2n-2}} +\\ +&& +&= +\frac{1}{n+1} +\frac{(n+1)z^n{-n-2}}{z^{-2n-2}} +\\ +&& +&= +\frac{1}{z^{-n}}=z^n. +\end{align*} +Man beachte, dass in dieser Rechnung nichts anderes als die +algebraischen Eigenschaften der Produkt- und Quotientenregel +verwendet wurden. +\end{proof} + +\subsubsection{Wurzeln} +Die Wurzelfunktionen sollen natürlich als elementare Funktionen +erlaubt sein. +Es ist bekannt, dass $\sqrt{z}\not\in \mathscr{D}=\mathbb{C}(z)$ +ist, ein solches Element müsste also erst noch hinzugefügt werden. +Dabei muss auch seine Ableitung definiert werden. +Auch dabei dürfen wir nicht auf eine Grenzwertüberlegung zurückgreifen, +vielmehr müssen wir die Ableitung auf vollständig algebraische +Weise bestimmen. + +Wir schreiben $f=\sqrt{z}$ und leiten die Gleichung $f^2=z$ nach $z$ ab. +Dabei ergibt sich nach der Potenzregel +\[ +\frac{d}{dz}f^2 = 2f'f = \frac{d}{dz}z=1 +\qquad\Rightarrow\qquad f' = \frac{1}{2f}. +\] +Diese Rechnung lässt sich auch auf $n$-Wurzeln $g=\root{n}\of{z}$ mit +der Gleichung $g^n = z$ verallgemeinern. +Die Ableitung der $n$-ten Wurzel ist +\begin{equation} +\frac{d}{dz}g^n += +ng^{n-1} = \frac{d}{dz}z=1 +\qquad\Rightarrow\qquad +\frac{d}{dz}g = \frac{1}{ng^{n-1}}. +\end{equation} +Es ist also möglich, eine differentielle Algebra $\mathscr{D}$ mit einer +$n$-ten Wurzel $g$ zu einer grösseren differentiellen Algebra $\mathscr{D}(g)$ +zu erweitern, in der wieder alle Regeln für das Rechnen mit Ableitungen +erfüllt sind. + +\subsubsection{Algebraische Elemente} +Die Charakterisierung der Wurzelfunktionen passt zwar zum verlangten +algebraischen Vorgehen, ist aber zu spezielle und nicht gut für die +nachfolgenden Untersuchengen geeignet. +Etwas allgemeiner ist der Begriff der algebraischen Elemente. + +\begin{definition} +\label{buch:integrale:def:algebraisches-element} +Seien $K\subset L$ zwei Körper. +Ein Element $\alpha \in L$ heisst {\em algebraisch} über $K$, +wenn $\alpha$ Nullstelle eines Polynoms $p\in K[X]$ mit Koeffizienten +in $K$ ist. +\index{algebraisch}% +\end{definition} + +Jedes Element $\alpha\in K$ ist algebraisch, da $\alpha$ Nullstelle +von $X-\alpha\in K[X]$ ist. +Die $n$tem Wurzeln eines Elemente $\alpha\in K$ sind ebenfalls algebraisch, +da sie Nullstellen des Polynoms $p(X) = X^n - \alpha$ sind. +Allerdings ist nicht klar, dass diese Wurzeln überhaupt existieren. +Nach dem Satz von Abel~\ref{buch:potenzen:satz:abel} gibt es aber +Nullstellen von Polynomen, die sich nicht als Wurzelausdrücke schreiben +lassen. +Der Begriff der algebraischen Elemente ist also allgemeiner als der +Begriff der Wurzel. + +\begin{definition} +\label{buch:integrale:def:algebraisch-abgeschlossen} +Ein Körper $K$ heisst {\em algebraisch abgeschlossen}, wenn jedes Polynom mit +Koeffizienten in $K$ eine Nullstelle in $K$ hat. +\end{definition} + +Der Körper $\mathbb{C}$ ist nach dem +Fundamentalsatz~\label{buch:potenzen:satz:fundamentalsatz} +der Algebra algebraisch abgeschlossen. +Da wir aber mit Funktionen arbeiten, müssen wir auch Wurzeln +von Funktionen finden können. +Dies ist nicht selbstverständlich, wie das folgende Beispiel zeigt. + +\begin{beispiel} +Es gibt keine stetige Funktion $f\colon \mathbb{C}\to\mathbb{C}$, die +die Gleichung $f(z)^2 = z$ und $f(1)=1$ erfüllt. +Für die Argumente $z(t)= e^{it}$ folgt, dass $f(z(t)) = e^{it/2}$ sein +muss. +Setzt man aber $t=\pm \pi$ ein, ergeben sich die Werte +$f(z(\pm\pi))=e^{\pm i\pi/2}=\pm 1$, die beiden Grenzwerte +für $t\to\pm\pi$ sind also verschieden. +\end{beispiel} + +Die Mathematik hat verschiedene ``Tricks'' entwickelt, wie mit diesem +Problem umgegangen werden kann: Funktionskeime, Garben, Riemannsche +Flächen. +Sie sind alle gleichermassen gut geeignet, das Problem zu lösen. +Für die vorliegende Aufgabe genügt es aber, dass es tatsächlich +immer ein wie auch immer geartetes Element gibt, welches Nullstelle +des Polynoms ist. + +Ist $f$ eine Nullstelle des Polynoms $p(X)$ mit Koeffizienten in +$\mathscr{D}$, dann kann man die Ableitung wie folgt berechnen. +Zunächst leitet man $p(f)$ ab: +\begin{align} +0&= +\frac{d}{dz}(a_nf^n + a_{n-1}f^{n-1}+\ldots+a_1f+a_0) +\notag +\\ +&= +a_n'f^n + a_{n-1}'f^{n-1}+\ldots+a_1'f+a_0' ++ +na_nf^{n-1}f' ++ +(n-1)a_nf^{n-2}f' ++ +\ldots ++ +a_2ff' ++ +a_1f' +\notag +\\ +&= +a_n'f^n + a_{n-1}'f^{n-1}+\ldots+a_1'f+a_0' ++ +( +na_nf^{n-1} ++ +(n-1)a_nf^{n-2} ++ +\ldots ++ +a_2f ++ +a_1 +)f' +\notag +\\ +\Rightarrow +\qquad +f'&=\frac{ +a_n'f^n + a_{n-1}'f^{n-1}+\dots+a_1'f+a_0' +}{ +na_nf^{n-1} ++ +(n-1)a_nf^{n-2} ++ +\dots ++ +a_1 +}. +\label{buch:integrale:eqn:algabl} +\end{align} +Das einzige, was dabei schief gehen könnte ist, dass der Nenner ebenfalls +verschwindet. +Dieses Problem kann man dadurch lösen, dass man als Polynom das +sogenannte Minimalpolynom verwendet. + +\begin{definition} +Das {\em Minimalpolynome} $m(X)$ eines algebraischen Elementes $\alpha$ ist +das Polynom kleinsten Grades, welches $m(\alpha)=0$ erfüllt. +\end{definition} + +Da das Minimalpolynom den kleinstmöglichen Grad hat, kann der Nenner +von~\eqref{buch:integrale:eqn:algabl}, +der noch kleineren Grad hat, unmöglich verschwinden. +Das Minimalpolynom ist auch im wesentlichen eindeutig. +Gäbe es nämlich zwei verschiedene Minimalpolynome $m_1$ und $m_2$, +dann müsste $\alpha$ auch eine Nullstelle des grössten gemeinsamen +Teilers $m_3=\operatorname{ggT}(m_1,m_2)$ sein. +Wären die beiden Polynome wesentlich verschieden, dann hätte $m_3$ +kleineren Grad, im Widerspruch zur Definition des Minimalpolynoms. +Also unterscheiden sich die beiden Polynome $m_1$ und $m_2$ nur um +einen skalaren Faktor. + +\subsubsection{Konjugation, Spur und Norm} +% Konjugation, Spur und Norm +Das Minimalpolynom eines algebraischen Elementes ist nicht +eindeutig bestimmt. +Zum Beispiel ist $\sqrt{2}$ algebraisch über $\mathbb{Q}$, das +Minimalpolynom ist $m(X)=X^2-2\in\mathbb{Q}[X]$. +Es hat aber noch eine zweite Nullstelle $-\sqrt{2}$. +Mit rein algebraischen Mitteln sind die beiden Nullstellen $\pm\sqrt{2}$ +nicht zu unterscheiden, erst die Verwendung der Vergleichsrelation +ermöglicht, sie zu unterscheiden. + +Dasselbe gilt für die imaginäre Einheit $i$, die das Minimalpolynom +$m(X)=X^2+1\in\mathbb{R}[X]$ hat. +Hier gibt es nicht einmal mehr eine Vergleichsrelation, mit der man +die beiden Nullstellen unterscheiden könnte. +In der Tat ändert sich aus algebraischer Sicht nichts, wenn man in +allen Formeln $i$ durch $-i$ ersetzt. + +Etwas komplizierter wird es bei $\root{3}\of{2}$. +Das Polynom $m=x^3-2\in\mathbb{Q}[X]$ hat $\root{3}\of{2}$ als +Nullstelle und dies ist auch tatsächlich das Minimalpolynom. +Das Polynom hat noch zwei weitere Nullstellen +\[ +\alpha_+ = \frac{-1+i\sqrt{3}}{2}\root{3}\of{2} +\qquad\text{und}\qquad +\alpha_- = \frac{-1-i\sqrt{3}}{2}\root{3}\of{2}. +\] +Die beiden Lösungen gehen durch die Vertauschung von $i$ und $-i$ +auseinander hervor. +Betrachtet man dasselbe Polynom aber als Polynom in $\mathbb{R}[X]$, +dann ist es nicht mehr das Minimalpolynom von $\root{3}\of{2}$, da +$X-\root{3}\of{2}\in\mathbb{R}[X]$ kleineren Grad und $\root{3}\of{2}$ +als Nullstelle hat. +Indem man +\[ +m(X)/(X-\root{3}\of{2})=X^2+\root{3}\of{2}X+\root{3}\of{2}^2=m_2(X) +\] +rechnet, bekommt man das Minimalpolynom der beiden Nullstellen $\alpha_+$ +und $\alpha_-$. +Wir lernen aus diesen Beispielen, dass das Minimalpolynom vom Grundkörper +abhängig ist (Die Faktorisierung $(X-\root{3}\of{2})\cdot m_2(X)$ von +$m(X)$ ist in $\mathbb{Q}[X]$ nicht möglich) und dass wir keine +algebraische Möglichkeit haben, die verschiedenen Nullstellen des +Minimalpolynoms zu unterscheiden. + +Die beiden Nullstellen $\alpha_+$ und $\alpha_-$ des Polynoms $m_2(X)$ +erlauben, $m_2(X)=(X-\alpha_+)(X-\alpha_-)$ zu faktorisieren. +Durch Ausmultiplizieren +\[ +(X-\alpha_+)(X-\alpha_-) += +X^2 -(\alpha_++\alpha_-)X+\alpha_+\alpha_- +\] +und Koeffizientenvergleich mit $m_2(X)$ findet man die symmetrischen +Formeln +\[ +\alpha_+ + \alpha_- = \root{3}\of{2} +\qquad\text{und}\qquad +\alpha_+ \alpha_ = \root{3}\of{2}. +\] +Diese Ausdrücke sind nicht mehr abhängig von einer speziellen Wahl +der Nullstellen. + +Das Problem verschärft sich nocheinmal, wenn wir Funktionen betrachten. +Das Polynom $m(X)=X^3-z$ ist das Minimalpolynom der Funktion $\root{3}\of{z}$. +Die komplexe Zahl $z=re^{i\varphi}$ hat aber drei die algebraisch nicht +unterscheidbaren Nullstellen +\[ +\alpha_0(z)=\root{3}\of{r}e^{i\varphi/3}, +\quad +\alpha_1(z)=\root{3}\of{r}e^{i\varphi/3+2\pi/3} +\qquad\text{und}\qquad +\alpha_2(z)=\root{3}\of{r}e^{i\varphi/3+4\pi/3}. +\] +Aus der Faktorisierung $ (X-\alpha_0(z)) (X-\alpha_1(z)) (X-\alpha_2(z))$ +und dem Koeffizientenvergleich mit dem Minimalpolynom kann man wieder +schliessen, dass die Relationen +\[ +\alpha_0(z) + \alpha_1(z) + \alpha_2(z)=0 +\qquad\text{und}\qquad +\alpha_0(z) \alpha_1(z) \alpha_2(z) = z +\] +gelten. + +Wir können also oft keine Aussagen über individuelle Nullstellen +eines Minimalpolynoms machen, sondern nur über deren Summe oder +Produkt. + +\begin{definition} +\index{buch:integrale:def:spur-und-norm} +Sie $m(X)\in K[X]$ das Minimalpolynom eines über $K$ algebraischen +Elements und +\[ +m(X) = a_nX^n + a_{n-1}X^{n-1} + \ldots + a_1X + a_0. +\] +Dann heissen +\[ +\operatorname{Tr}(\alpha) = -a_{n-1} +\qquad\text{und}\qquad +\operatorname{Norm}(\alpha) = (-1)^n a_0 +\] +die {\em Spur} und die {\em Norm} des Elementes $\alpha$. +\index{Spur eines algebraischen Elementes}% +\index{Norm eines algebraischen Elementes}% +\end{definition} + +Die Spur und die Norm können als Spur und Determinante einer Matrix +verstanden werden, diese allgemeineren Definitionen, die man in der +Fachliteratur, z.~B.~in~\cite{buch:lang} nachlesen kann, führen aber +für unsere Zwecke zu weit. + +\begin{hilfssatz} +Die Ableitungen von Spur und Norm sind +\[ +\operatorname{Tr}(\alpha)' += +\operatorname{Tr}(\alpha') +\qquad\text{und}\qquad +\operatorname{Norm}(\alpha)' += +\operatorname{Tr}(\alpha)' +\] +XXX Wirklich? +\end{hilfssatz} + +\subsubsection{Logarithmen und Exponentialfunktionen} +Die Funktion $z^{-1}$ musste im +Satz~\ref{buch:integrale:satz:potenzstammfunktion} +ausgeschlossen werden, sie hat keine Stammfunktion in $\mathbb{C}(z)$. +Aus der Analysis ist bekannt, dass die Logarithmusfunktion $\log z$ +eine Stammfunktion ist. +Der Logarithmus von $z$ aber auch der Logarithmus $\log f(z)$ +einer beliebigen Funktion $f(z)$ oder die Exponentialfunktion $e^{f(z)}$ +sollen ebenfalls elementare Funktionen sein. +Da wir aber auch hier nicht auf die analytischen Eigenschaften zurückgreifen +wollen, brauchen wir ein rein algebraische Definition. + +\begin{definition} +\label{buch:integrale:def:logexp} +Sei $\mathscr{D}$ ein differentielle Algebra und $f\in\mathscr{D}$. +Ein Element $\vartheta\in\mathscr{D}$ heisst ein {\em Logarithmus} +von $f$, geschrieben $\vartheta = \log f$, wenn $f\vartheta' = f'$ gilt. +$\vartheta$ heisst eine Exponentialfunktion von $f$ wenn +$\vartheta'=\vartheta f'$ gilt. +\end{definition} + +Die Formel für die Exponentialfunktion ist etwas vertrauter, sie ist +die bekannte Kettenregel +\begin{equation} +\vartheta' += +\frac{d}{dz} e^f += +e^f \cdot \frac{d}{dz} f += +\vartheta \cdot f'. +\label{buch:integrale:eqn:exponentialableitung} +\end{equation} +Da wir uns vorstellen, dass Logarithmen Umkehrfunktionen von +Exponentialfunktionen sein sollen, +muss die definierende Gleichung genau wie +\eqref{buch:integrale:eqn:exponentialableitung} +aussehen, allerdings mit vertauschten Plätzen von $f$ und $\vartheta$, +also +\begin{equation} +\vartheta' = \vartheta\cdot f' +\qquad +\rightarrow +\qquad +f' = f\cdot \vartheta' +\;\Leftrightarrow\; +\vartheta' = (\log f)' = \frac{f'}{f}. +\label{buch:integrale:eqn:logarithmischeableitung} +\end{equation} +Dies ist die aus der Analysis bekannte Formel für die logarithmische +Ableitung. + +Der Logarithmus von $f$ und die Exponentialfunktion von $f$ sollen +also ebenfalls als elementare Funktionen betrachtet werden. + +\subsubsection{Die trigonometrischen Funktionen} +Die bekannten trigonometrischen Funktionen und ihre Umkehrfunktionen +sollten natürlich auch elementare Funktionen sein. +Dabei kommt uns zur Hilfe, dass sie sich mit Hilfe der Exponentialfunktion +als +\[ +\cos f = \frac{e^{if}+e^{-if}}2 +\qquad\text{und}\qquad +\sin f = \frac{e^{if}-e^{-if}}{2i} +\] +schreiben lassen. +Eine differentielle Algebra, die die Exponentialfunktionen von $if$ und +$-if$ enthält, enthält also automatisch auch die trigonometrischen +Funktionen. +Im Folgenden ist es daher nicht mehr nötig, die trigonometrischen +Funktionen speziell zu untersuchen. + +\subsubsection{Elementare Funktionen} +Damit sind wir nun in der Lage, den Begriff der elementaren Funktion +genau zu fassen. + +\begin{definition} +\label{buch:integrale:def:einfache-elementare-funktion} +Sie $\mathscr{D}$ eine differentielle Algebra über $\mathbb{C}$ und +$\mathscr{D}(\vartheta)$ eine Erweiterung von $\mathscr{D}$ um eine +neue Funktion $\vartheta$, dann heissen $\vartheta$ und die Elemente +von $\mathscr{D}(\vartheta)$ einfach elementar, wenn eine der folgenden +Bedingungen erfüllt ist: +\begin{enumerate} +\item $\vartheta$ ist algebraisch über $\mathscr{D}$, d.~h.~$\vartheta$ +ist eine ``Wurzel''. +\item $\vartheta$ ist ein Logarithmus einer Funktion in $\mathscr{D}$, +d.~h.~es gibt $f\in \mathscr{D}$ mit $f'=f\vartheta'$ +(Definition~\ref{buch:integrale:def:logexp}). +\item $\vartheta$ ist eine Exponentialfunktion einer Funktion in $\mathscr{D}$, +d.~h.~es bit $f\in\mathscr{D}$ mit $\vartheta'=\vartheta f'$ +(Definition~\ref{buch:integrale:def:logexp}). +\end{enumerate} +\end{definition} + +Einfache elementare Funktionen entstehen also ausgehend von einer +differentiellen Algebra, indem man genau einmal eine Wurzel, einen +Logarithmus oder eine Exponentialfunktion hinzufügt. +So etwas wie die zusammengesetzte Funktion $e^{\sqrt{z}}$ ist +damit noch nicht möglich. +Daher erlauben wir, dass man die gesuchten Funktionen in mehreren +Schritten aufbauen kann. + +\begin{definition} +Sei $\mathscr{F}$ eine differentielle Algebra, die die differentielle +Algebra $\mathscr{D}$ enthält, also $\mathscr{D}\subset\mathscr{F}$. +$\mathscr{F}$ und die Elemente von $\mathscr{F}$ heissen einfach, +wenn es endlich viele Elemente $\vartheta_1,\dots,\vartheta_n$ gibt +derart, dass +\[ +\renewcommand{\arraycolsep}{2pt} +\begin{array}{ccccccccccccc} +\mathscr{D} +&\subset& +\mathscr{D}(\vartheta_1) +&\subset& +\mathscr{D}(\vartheta_1,\vartheta_2) +&\subset& +\; +\cdots +\; +&\subset& +\mathscr{D}(\vartheta_1,\vartheta_2,\dots,\vartheta_{n-1}) +&\subset& +\mathscr{D}(\vartheta_1,\vartheta_2,\dots,\vartheta_{n-1},\vartheta_n) +&=& +\mathscr{F} +\\ +\| +&& +\| +&& +\| +&& +&& +\| +&& +\| +&& +\\ +\mathscr{F}_0 +&\subset& +\mathscr{F}_1 +&\subset& +\mathscr{F}_2 +&\subset& +\cdots +&\subset& +\mathscr{F}_{n-1} +&\subset& +\mathscr{F}_{n\mathstrut} +&& +\end{array} +\] +gilt so, dass jedes $\vartheta_{i+1}$ einfach ist über +$\mathscr{F}_i=\mathscr{D}(\vartheta_1,\dots,\vartheta_i)$. +\end{definition} + +In Worten bedeutet dies, dass man den Funktionen von $\mathscr{D}$ +nacheinander Wurzeln, Logarithmen oder Exponentialfunktionen einzelner +Funktionen hinzufügt. +Die Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion} kann +jetzt so formuliert werden. + +\begin{aufgabe} +\label{buch:integrale:aufgabe:existenz-stammfunktion-dalg} +Gegeben ist eine Differentielle Algebra $\mathscr{D}$ und eine +Funktion $f\in \mathscr{D}$. +Gibt es eine Folge $\vartheta_1,\dots,\vartheta_n$ und eine Funktion +$F\in\mathscr{D}(\vartheta_1,\dots,\vartheta_n)$ derart, dass +$F'=f$. +\end{aufgabe} + +Das folgende Beispiel zeigt, wie man möglicherweise mehrere +Erweiterungsschritte vornehmen muss, um zu einer Stammfunktion +zu kommen. +Es illustriert auch die zentrale Rolle, die der Partialbruchzerlegung +in der weiteren Entwicklung zukommen wird. + +\begin{beispiel} +\label{buch:integrale:beispiel:nichteinfacheelementarefunktion} +Es soll eine Stammfunktion der Funktion +\[ +f(z) += +\frac{z}{(az+b)(cz+d)} +\in +\mathbb{C}(z) +\] +gefunden werden. +In der Analysis lernt man, dass solche Integrale mit der +Partialbruchzerlegung +\[ +\frac{z}{(az+b)(cz+d)} += +\frac{A_1}{az+b}+\frac{A_2}{cz+d} += +\frac{A_1cz+A_1d+A_2az+A_2b}{(az+b)(cz+d)} +\quad\Rightarrow\quad +\left\{ +\renewcommand{\arraycolsep}{2pt} +\begin{array}{rcrcr} +cA_1&+&aA_2&=&1\\ +dA_1&+&bA_2&=&0 +\end{array} +\right. +\] +bestimmt werden. +Die Lösung des Gleichungssystems ergibt +$A_1=b/(bc-ad)$ und $A_2=d/(ad-bc)$. +Die Stammfunktion kann dann aus +\begin{align*} +\int f(z)\,dz +&= +\int\frac{A_1}{az+b}\,dz ++ +\int\frac{A_2}{cz+d}\,dz += +\frac{A_1}{a}\int\frac{a}{az+b}\,dz ++ +\frac{A_2}{c}\int\frac{c}{cz+d}\,dz +\end{align*} +bestimmt werden. +In den Integralen auf der rechten Seite ist der Zähler jeweils die +Ableitung des Nenners, der Integrand hat also die Form $g'/g$. +Genau diese Form tritt in der Definition eines Logarithmus auf. +Die Stammfunktion ist jetzt +\[ +F(z) += +\int f(z)\,dz += +\frac{A_1}{a}\log(az+b) ++ +\frac{A_2}{c}\log(cz+d) += +\frac{b\log(az+b)}{a(bc-ad)} ++ +\frac{d\log(cz+d)}{c(ad-bc)}. +\] +Die beiden Logarithmen kann man nicht durch rein rationale Operationen +ineinander überführen. +Sie müssen daher beide der Algebra $\mathscr{D}$ hinzugefügt werden. +\[ +\left. +\begin{aligned} +\vartheta_1&=\log(az+b)\\ +\vartheta_2&=\log(cz+d) +\end{aligned} +\quad +\right\} +\qquad\Rightarrow\qquad +F(z) \in \mathscr{F}=\mathscr{D}(\vartheta_1,\vartheta_2). +\] +Die Stammfunktion $F(z)$ ist also keine einfache elementare Funktion, +aber $F$ ist immer noch eine elementare Funktion. +\end{beispiel} + +\subsection{Partialbruchzerlegung +\label{buch:integrale:section:partialbruchzerlegung}} +Die Konstruktionen des letzten Abschnitts haben gezeigt, +wie man die Funktionen, die man als Stammfunktionen einer Funktion +zulassen möchte, schrittweise konstruieren kann. +Die Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion-dalg} +ist eine rein algebraische Formulierung der ursprünglichen +Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion}. +Schliesslich hat das Beispiel auf +Seite~\pageref{buch:integrale:beispiel:nichteinfacheelementarefunktion} +gezeigt, dass es im allgemeinen mehrere Schritte braucht, um zu einer +elementaren Stammfunktion zu gelangen. +Die Lösung setzt sich aus den Termen der Partialbruchzerlegung. +In diesem Abschnitt soll diese genauer studiert werden. + +In diesem Abschnitt gehen wir immer von einer differentiellen +Algebra über den komplexen Zahlen aus und verlangen, dass die +Konstanten in allen betrachteten differentiellen Algebren +$\mathbb{C}$ sind. + +\subsubsection{Monome} +Die beiden Funktionen $\vartheta-1=\log(az+b)$ und $\vartheta_2=(cz+d)$, +die im Beispiel hinzugefügt werden mussten, verhalten sich ich algebraischer +Hinsicht wie ein Monom: man kann es nicht faktorisieren oder bereits +bekannte Summanden aufspalten. +Solchen Funktionen kommt eine besondere Bedeutung zu. + +\begin{definition} +\label{buch:integrale:def:monom} +Die Funktion $\vartheta$ heisst ein Monom, wenn $\vartheta$ nicht +algebraisch ist über $\mathscr{D}$ und $\mathscr{D}(\vartheta)$ die +gleichen Konstanten enthält wie $\mathscr{D}$. +\end{definition} + +\begin{beispiel} +Als Beispiel beginnen wir mit den komplexen Zahlen $\mathbb{C}$ +und fügen die Funktion $\vartheta_1=z$ hinzu und erhalten +$\mathscr{D}=\mathbb{C}(z)$. +Die Funktionen $z^k$ sind für alle $k$ linear unabhängig, d.~h.~es +gibt keinen Ausdruck +\[ +a_nz^n + a_{n-1}z^{n-1}+\cdots+a_1z+a_0=0. +\] +Dies ist gleichbedeutend damit, dass $z$ nicht algebraisch ist. +Das Monom $z$ ist also auch ein Monom im Sinne der +Definition~\ref{buch:integrale:def:monom}. +\end{beispiel} + +\begin{beispiel} +Wir beginnen wieder mit $\mathbb{C}$ und fügen die Funktion +$e^z$ hinzu. +Gäbe es eine Beziehung +\[ +b_m(e^z)^m + b_{m-1}(e^z)^{m-1}+\dots+b_1e^z + b_0=0 +\] +mit komplexen Koeffizienten $b_i\in\mathbb{C}$, +dann würde daraus durch Einsetzen von $z=1$ die Relation +\[ +b_me^m + b_{m-1}e^{m-1} + \dots + b_1e + b_0=0, +\] +die zeigen würde, dass $e$ eine algebraische Zahl ist. +Es ist aber bekannt, dass $e$ transzendent ist. +Dieser Widersprich zeigt, dass $e^z$ ein Monom ist. +\end{beispiel} + +\begin{beispiel} +Jetzt fügen wir die Exponentialfunktion $\vartheta_2=e^z$ +der differentiellen Algebra $\mathscr{D}=\mathbb{C}(z)$ hinzu +und erhalten $\mathscr{F}_1=\mathscr{D}(e^z) = \mathbb{C}(z,e^z)$. +Gäbe es das Minimalpolynom +\begin{equation} +b_m(z)(e^z)^m + b_{m-1}(z)(e^z)^{m-1}+\dots+b_1(z)e^z + b_0(z)=0 +\label{buch:integrale:beweis:exp-analytisch} +\end{equation} +mit Koeffizienten $b_i\in\mathbb{C}(z)$, dann könnte man mit dem +gemeinsamen Nenner der Koeffizienten durchmultiplizieren und erhielte +eine Relation~\eqref{buch:integrale:beweis:exp-analytisch} mit +Koeffizienten in $\mathbb{C}[z]$. +Dividiert man durch $e^{mz}$ erhält man +\[ +b_m(z) + b_{m-1}(z)\frac{1}{e^z} + \dots + b_1(z)\frac{1}{(e^z)^{m-1}} + b_0(z)\frac{1}{(e^z)^m}=0. +\] +Aus der Analysis weiss man, dass die Exponentialfunktion schneller +anwächst als jedes Polynom, alle Terme auf der rechten Seite +konvergieren daher gegen 0 für $z\to\infty$. +Das bedeutet, dass $b_m(z)\to0$ für $z\to \infty$. +Das Polynom~\eqref{buch:integrale:beweis:exp-analytisch} wäre also gar +nicht das Minimalpolynom. +Dieser Widerspruch zeigt, dass $e^z$ nicht algebraisch ist über +$\mathbb{C}(z)$ und damit ein Monom ist\footnote{Etwas unbefriedigend +an diesem Argument ist, dass man hier wieder rein analytische statt +algebraische Eigenschaften von $e^z$ verwendet. +Gäbe es aber eine minimale Relation wie +\eqref{buch:integrale:beweis:exp-analytisch} +mit Polynomkoeffizienten, dann wäre sie von der Form +\[ +P(z,e^z)=p(z)(e^z)^m + q(z,e^z)=0, +\] +wobei Grad von $e^z$ in $q$ höchstens $m-1$ ist. +Die Ableitung wäre dann +\[ +Q(z,e^z) += +mp(z)(e^z)^m + p'(z)(e^z)^m + r(z,e^z) += +(mp(z) + p'(z))(e^z)^m + r(z,e^z) +=0, +\] +wobei der Grad von $e^z$ in $r$ wieder höchstens $m-1$ ist. +Bildet man $mP(z,e^z) - Q(z,e^z) = 0$ ensteht eine Relation, +in der der Grad des Koeffizienten von $(e^z)^m$ um eins abgenommen hat. +Wiederholt man dies $m$ mal, verschwindet der Term $(e^z)^m$, die +Relation~\eqref{buch:integrale:beweis:exp-analytisch} +war also gar nicht minimal. +Dieser Widerspruch zeigt wieder, dass $e^z$ nicht algebraisch ist, +verwendet aber nur die algebraischen Eigenschaften der differentiellen +Algebra. +}. +\end{beispiel} + +\begin{beispiel} +Wir hätten auch in $\mathbb{Q}$ arbeiten können und $\mathbb{Q}$ +erst die Exponentialfunktion $e^z$ und dann den Logarithmus $z$ von $e^z$ +hinzufügen können. +Es gibt aber noch weitere Logarithmen von $e^z$ zum Beispiel $z+2\pi i$. +Offenbar ist $\psi=z+2\pi i\not\in \mathbb{Q}(z,e^z)$, wir könnten also +auch noch $\psi$ hinzufügen. +Zwar ist $\psi$ auch nicht algebraisch, aber wenn wir $\psi$ hinzufügen, +dann wird aber die Menge der Konstanten grösser, sie umfasst jetzt +$\mathbb{Q}(2\pi i)$. +Die Bedingung in der Definition~\ref{buch:integrale:def:monom}, +dass die Menge der Konstanten nicht grösser werden darf, ist also +verletzt. + +Hätte man mit $\mathbb{Q}(e^z, z+2\pi i)$ begonnen, wäre $z$ aus +dem gleichen Grund kein Monom, aber $z+2\pi i$ wäre eines im Sinne +der Definition~\ref{buch:integrale:def:monom}. +In allen Rechnungen könnte man $\psi=z+2\pi i$ nicht weiter aufteilen, +da $\pi$ oder seine Potenzen keine Elemente von $\mathbb{Q}(e^z)$ sind. +\end{beispiel} + +Da wir im Folgenden davon ausgehen, dass die Konstanten unserer +differentiellen Körper immer $\mathbb{C}$ sind, wird es jeweils +genügen zu untersuchen, ob eine neu hinzuzufügende Funktion algebraisch +ist oder nicht. + +\subsubsection{Ableitungen von Polynomen und rationalen Funktionen von Monomen} +Fügt man einer differentiellen Algebra ein Monom hinzu, dann lässt +sich etwas mehr über Ableitungen von Polynomen oder Brüchen in diesen +Monomen sagen. +Diese Eigenschaften werden später bei der Auflösung der Partialbruchzerlegung +nützlich sein. + +\begin{satz} +\label{buch:integrale:satz:polynom-ableitung-grad} +Sei +\[ +P += +A_nX^n + A_{n-1}X^{n-1} + \dots A_1X+A_0 +\in\mathscr{D}[X] +\] +ein Polynom mit Koeffizienten in einer differentiellen Algebra $\mathscr{D}$ +und $\vartheta$ ein Monom über $\mathscr{D}$. +Dann gilt +\begin{enumerate} +\item +\label{buch:integrale:satz:polynom-ableitung-grad-log} +Falls $\vartheta=\log f$ ist, ist $P(\vartheta)'$ ein +Polynom vom Grad $n$ in $\vartheta$, wenn der Leitkoeffizient $A_n$ +nicht konstant ist, andernfalls ein Polynom vom Grad $n-1$. +\item +\label{buch:integrale:satz:polynom-ableitung-grad-exp} +Falls $\vartheta = \exp f$ ist, dann ist $P(\vartheta)'$ ein Polynom +in $\vartheta$ vom Grad $n$. +\end{enumerate} +\end{satz} + +Der Satz macht also genaue Aussagen darüber, wie sich der Grad eines +Polynoms in $\vartheta$ beim Ableiten ändert. + +\begin{proof}[Beweis] +Für Exponentialfunktion ist $\vartheta'=\vartheta f'$, die Ableitung +fügt also einfach einen Faktor $f'$ hinzu. +Terme der Form $A_k\vartheta^k$ haben die Ableitung +\[ +(A_k\vartheta^k) += +A'_k\vartheta^k + A_kk\vartheta^{k-1}\vartheta' += +A'_k\vartheta^k + A_kk\vartheta^{k-1}\vartheta f' += +(A'_k + kA_k f)\vartheta^k. +\] +Damit wird die Ableitung des Polynoms +\begin{equation} +P(\vartheta)' += +\underbrace{(A'_n+nA_nf')\vartheta^n}_{\displaystyle=(A_n\vartheta^n)'} ++ +(A'_{n-1}+(n-1)A_{n-1}f')\vartheta^{n-1} ++ \dots + +(A'_1+A_1f')\vartheta + A_0'. +\label{buch:integrale:ableitung:polynom} +\end{equation} +Der Grad der Ableitung kann sich also nur ändern, wenn $A_n'+nA_nf'=0$ ist. +Dies bedeutet aber wegen +\( +(A_n\vartheta^n)' += +0 +\), dass $A_n\vartheta^n=c$ eine Konstante ist. +Da alle Konstanten bereits in $\mathscr{D}$ sind, folgt, dass +\[ +\vartheta^n=\frac{c}{A_n} +\qquad\Rightarrow\qquad +\vartheta^n - \frac{c}{A_n}=0, +\] +also wäre $\vartheta$ algebraisch über $\mathscr{D}$, also auch kein Monom. +Dieser Widerspruch zeigt, dass der Leitkoeffizient nicht verschwinden kann. + +Für die erste Aussage ist die Ableitung der einzelnen Terme des Polynoms +\[ +(A_k\vartheta^k)' += +A_k'\vartheta^k + A_kk\vartheta^{k-1}\vartheta' += +A_k'\vartheta^k + A_kk\vartheta^{k-1}\frac{f'}{f} += +\biggl(A_k'\vartheta + kA_k\frac{f'}{f}\biggr)\vartheta^{k-1}. +\] +Die Ableitung des Polynoms ist daher +\[ +P(\vartheta)' += +A_n'\vartheta^n + \biggl(nA_n\frac{f'}{f}+ A'_{n-1}\biggr)\vartheta^{n-1}+\dots +\] +Wenn $A_n$ keine Konstante ist, ist $A_n'\ne 0$ und der Grad von +$P(\vartheta)'$ ist $n$. +Wenn $A_n$ eine Konstante ist, müssen wir noch zeigen, dass der nächste +Koeffizient nicht verschwinden kann. +Wäre der zweite Koeffizient $=0$, dann wäre die Ableitung +\[ +(nA_n\vartheta+A_{n-1})' += +nA_n\vartheta'+A'_{n-1} += +nA_n\frac{f'}{f}+A'_{n-1} += +0, +\] +d.h. $nA_n\vartheta+A_{n-1}=c$ wäre eine Konstante. +Da alle Konstanten schon in $\mathscr{D}$ sind, müsste auch +\[ +\vartheta = \frac{c-A_{n-1}}{nA_n} \in \mathscr{D} +\] +sein, wieder wäre $\vartheta$ kein Monom. +\end{proof} + +Der nächste Satz gibt Auskunft über den führenden Term in +$(\log P(\vartheta))' = P(\vartheta)'/P(\vartheta)$. + +\begin{satz} +\label{buch:integrale:satz:log-polynom-ableitung-grad} +Sei $P$ ein Polynom vom Grad $n$ wie in +\label{buch:integrale:satz:log-polynom-ableitung} +welches zusätzlich normiert ist, also $A_n=1$. +\begin{enumerate} +\item +\label{buch:integrale:satz:log-polynom-ableitung-log} +Ist $\vartheta=\log f$, dann ist +$(\log P(\vartheta))' = P(\vartheta)'/P(\vartheta)$ und $P(\vartheta)'$ +hat Grad $n-1$. +\item +\label{buch:integrale:satz:log-polynom-ableitung-exp} +Ist $\vartheta=\exp f$, dann gibt es ein Polynom $N(\vartheta)$ so, dass +$(\log P(\vartheta))' += +P(\vartheta)'/P(\vartheta) += +N(\vartheta)/P(\vartheta)+nf'$ +ist. +Falls $P(\vartheta)=\vartheta$ ist $N=0$, andernfalls ist $N(\vartheta)$ +ein Polynom vom Grad $0$ das kleinste $k$ so, dass $p<(k+1)q$. +Insbesondere ist dann $kq\le p$. +Nach dem euklidischen Satz für die Division von $P(X)$ durch $Q(X)^k$ +gibt es ein Polynom $P_k(X)$ vom Grad $\le p-qk$ derart, dass +\[ +P(X) = P_k(X)Q(X)^k + R_k(X) +\] +mit einem Rest $R_k(X)$ vom Grad $1$ können mit der Potenzregel +integriert werden, aber für eine Stammfunktion $1/(z-1)$ muss +der Logarithmus $\log(z-1)$ hinzugefügt werden. +Die Stammfunktion +\[ +\int f(z)\,dz += +\int +\frac{1}{z-1} +\,dz ++ +\int +\frac{4}{(z-1)^2} +\,dz ++ +\int +\frac{4}{(z-1)^3} +\,dz += +\log(z-1) +- +\underbrace{\frac{4z-2}{(z-1)^2}}_{\displaystyle\in\mathscr{D}} +\in \mathscr{D}(\log(z-1)) = \mathscr{F} +\] +hat eine sehr spezielle Form. +Sie besteht aus einem Term in $\mathscr{D}$ und einem Logarithmus +einer Funktion von $\mathscr{D}$, also einem Monom über $\mathscr{D}$. + +\subsubsection{Einfach elementare Stammfunktionen} +Der in diesem Abschnitt zu beweisende Satz von Liouville zeigt, +dass die im einführenden Beispiel konstruierte Form der Stammfunktion +eine allgemeine Eigenschaft elementar integrierbarer +Funktionen ist. +Zunächst aber soll dieses Bespiel etwas verallgemeinert werden. + +\begin{satz}[Liouville-Vorstufe für Monome] +\label{buch:integrale:satz:liouville-vorstufe-1} +Sei $\vartheta$ ein Monom über $\mathscr{D}$ und $g\in\mathscr{D}(\vartheta)$ +mit $g'\in\mathscr{D}$. +Dann hat $g$ die Form $v_0 + c_1\vartheta$ mit $v_0\in\mathscr{D}$ und +$c_1\in\mathbb{C}$. +\end{satz} + +\begin{proof}[Beweis] +In Anlehnung an das einführende Beispiel nehmen wir an, dass die +Stammfunktion $g\in\mathscr{D}[\vartheta]$ für ein Monom $\vartheta$ +über $\mathscr{D}$ ist. +Dann hat $g$ die Partialbruchzerlegung +\[ +g += +H(\vartheta) ++ +\sum_{j\le r(i)} \frac{P_{ij}(\vartheta)}{Q_i(\vartheta)^j} +\] +mit irreduziblen normierten Polynomen $Q_i(\vartheta)$ und +Polynomen $P_{ij}(\vartheta)$ vom Grad kleiner als $\deg Q_i(\vartheta)$. +Ausserdem ist $H(\vartheta)$ ein Polynom. +Die Ableitung von $g$ muss jetzt aber wieder in $\mathscr{D}$ sein. +Zu ihrer Berechnung können die Sätze +\ref{buch:integrale:satz:polynom-ableitung-grad}, +\ref{buch:integrale:satz:log-polynom-ableitung-grad} +und +\ref{buch:integrale:satz:partialbruch-monom} +verwendet werden. +Diese besagen, dass in der Partialbruchzerlegung die Exponenten der +Nenner die Quotienten in der Summe nicht kleiner werden. +Die Ableitung $g'\in\mathscr{D}$ darf aber gar keine Nenner mit +$\vartheta$ enthalten, also dürfen die Quotienten gar nicht erst +vorkommen. +$g=H(\vartheta)$ muss also ein Polynom in $\vartheta$ sein. +Die Ableitung des Polynoms darf wegen $g'\in\mathscr{d}$ das Monom +$\vartheta$ ebenfalls nicht mehr enthalten, daher kann es höchstens vom +Grad $1$ sein. +Nach Satz~\ref{buch:integrale:satz:log-polynom-ableitung-grad} +muss ausserdem der Leitkoeffizient von $g$ eine Konstante sein, +das Polynom hat also genau die behauptete Form. +\end{proof} + +\begin{satz}[Liouville-Vorstufe für algebraische Elemente] +\label{buch:integrale:satz:liouville-vorstufe-2} +Sei $\vartheta$ algebraische über $\mathscr{D}$ und +$g\in\mathscr{D}(\vartheta)$ mit $g'\in\mathscr{D}$. +\end{satz} + +\subsubsection{Elementare Stammfunktionen} +Nach den Vorbereitungen über einfach elementare Stammfunktionen +in den Sätzen~\label{buch:integrale:satz:liouville-vorstufe-1} +und +\label{buch:integrale:satz:liouville-vorstufe-2} sind wir jetzt +in der Lage, den allgemeinen Satz von Liouville zu formulieren +und zu beweisen. + +\begin{satz}[Liouville] +Sei $\mathscr{D}$ ein Differentialkörper, $\mathscr{F}$ einfach über +$\mathscr{D}$ mit gleichem Konstantenkörper $\mathbb{C}$. +Wenn $g\in \mathscr{F}$ eine Stammfunktion von $f\in\mathscr{D}$ ist, +also $g'=f$, dann gibt es Zahlen $c_i\in\mathbb{C}$ und +$v_0,v_i\in\mathscr{D}$ derart, dass +\begin{equation} +g = v_0 + \sum_{i=1}^k c_i \log v_i +\qquad\Rightarrow\qquad +g' = v_0' + \sum_{i=1}^k c_i \frac{v_i'}{v_i} = f +\label{buch:integrale:satz:liouville-fform} +\end{equation} +gilt. +\end{satz} + +Der Satz hat zur Folge, dass eine elementare Stammfunktion für $f$ +nur dann existieren kann, wenn sich $f$ in der speziellen Form +\eqref{buch:integrale:satz:liouville-fform} +schreiben lässt. +Die Aufgabe~\ref{buch:integrale:aufgabe:existenz-stammfunktion-dalg} +lässt sich damit jetzt lösen. + + +\begin{proof}[Beweis] +Wenn die Stammfunktion $g\in\mathscr{D}$ ist, dann hat $g$ die Form +\eqref{buch:integrale:satz:liouville-fform} mit $v_0=g$, die Summe +wird nicht benötigt. + +Wir verwenden Induktion nach der Anzahl der Elemente, die zu $\mathscr{D}$ +hinzugefügt werden müssen, um einen Differentialkörper +$\mathscr{F}=\mathscr{D}(\vartheta_1,\dots,\vartheta_n)$ zu konstruieren, +der $g$ enthält. +Da $f\in\mathscr{D}\subset\mathscr{D}(\vartheta_1)$ ist, können wir die +Induktionsannahme auf die Erweiterung +\[ +\mathscr{D}(\vartheta_1)\subset\mathscr{D}(\vartheta_1,\vartheta_2) +\subset\cdots\subset \mathscr{D}(\vartheta_1,\cdots,\vartheta_n)=\mathscr{F} +\] +anwenden, die durch Hinzufügen von nur $n-1$ Elemente +$\vartheta_2,\dots,\vartheta_n$ aus $\mathscr{D}(\vartheta_1)$ den +Differentialkörper $\mathscr{F}$ erreicht, der $g$ enthält. +Sie besagt, dass sich $g$ schreiben lässt als +\[ +g = w_0 + \sum_{i=1}^{k_1} c_i\log w_i +\qquad\text{mit $c_i\in\mathbb{C}$ und $w_0,w_i\in\mathscr{D}(\vartheta_1)$.} +\] +Wir müssen jetzt zeigen, dass sich dieser Ausdruck umformen lässt +in den Ausdruck der Form~\eqref{buch:integrale:satz:liouville-fform}. + +Der Term $w_0\in\mathscr{D}(\vartheta_1)$ hat eine Partialbruchzerlegung +\[ +H(\vartheta_1) ++ +\sum_{j\le r(l)} \frac{P_{lj}(\vartheta_1)}{Q_l(\vartheta_1)^j} +\] +in der Variablen $\vartheta_1$. + +Da $w_i\in\mathscr{D}(\vartheta_1)$ ist, kann man Zähler und Nenner +von $w_i$ als Produkt irreduzibler normierter Polynome schreiben: +\[ +w_i += +\frac{h_i Z_{i1}(\vartheta_1)^{s_{i1}}\cdots Z_{im(i)}^{s_{im(i)}} +}{ +N_{i1}(\vartheta_1)^{t_{i1}}\cdots N_{in(i)}(\vartheta_1)^{t_{in(i)}} +} +\] +Der Logarithmus hat die Form +\begin{align*} +\log w_i +&= \log h_i + +s_{i1} +\log Z_{i1}(\vartheta_1) ++ +\cdots ++ +s_{im(i)} +\log Z_{im(i)} +- +t_{i1} +\log +N_{i1}(\vartheta_1) +- +\cdots +- +t_{in(i)} +\log +N_{in(i)}(\vartheta_1). +\end{align*} +$g$ kann also geschrieben werden als eine Summe von Polynomen, Brüchen, +wie sie in der Partialbruchzerlegung vorkommen, Logarithmen von irreduziblen +normierten Polynomen und Logarithmen von Elementen von $\mathscr{D}$. + +Die Ableitung $g'$ muss jetzt aber wieder in $\mathscr{D}$ sein, beim +Ableiten müssen also alle Terme verschwinden, die $\vartheta_1$ enthalten. +Dabei spielt es eine Rolle, ob $\vartheta_1$ ein Monom oder algebraisch ist. +\begin{enumerate} +\item +Wenn $\vartheta_1$ ein Monom ist, dann kann man wie im Beweis des +Satzes~\ref{buch:integrale:satz:liouville-vorstufe-1} argumentieren, +dass die Brüchterme gar nicht vorkommen und +$H(\vartheta_1)=v_0+c_1\vartheta_1$ sein muss. +Die Ableitung Termen der Form $\log Z(\vartheta_1)$ ist ein Bruchterm +mit dem irreduziblen Nenner $Z(\vartheta_1)$, die ebenfalls verschwinden +müssen. +Ist $\vartheta_1$ eine Exponentialfunktion, dann ist +$\vartheta_1' \in \mathscr{D}(\vartheta_1)\setminus\mathscr{D}$, also muss +$c_1=0$ sein. +Ist $\vartheta_1$ ein Logarithmus, also $\vartheta_1=\log v_1$, dann +kommen nur noch Terme der in +\eqref{buch:integrale:satz:liouville-fform} +erlaubten Form vor. + +\item +Wenn $\vartheta_1$ algebraisch vom Grad $m$ ist, dann ist +\[ +g' = w_0' + \sum_{i=1}^{k_1} d_i\frac{w_i'}{w_i} = f. +\] +Weder $w_0$ noch $\log w_i$ sind in $\mathscr{D}(\vartheta_1)$. +Aber wenn man $\vartheta_1$ durch die $m$ konjugierten Elemente +ersetzt und alle summiert, dann ist +\[ +mf += +\operatorname{Tr}(w_0) + \sum_{i=1}^{k_1} d_i \log\operatorname{Norm}(w_i). +\] +Da die Spur und die Norm in $\mathscr{D}$ sind, folgt, dass +\[ +f += +\underbrace{\frac{1}{m} +\operatorname{Tr}(w_0)}_{\displaystyle= v_0} ++ +\sum_{i=1}^{k_1} \underbrace{\frac{d_i}{m}}_{\displaystyle=c_i} +\log +\underbrace{ \operatorname{Norm}(w_i)}_{\displaystyle=v_i} += +v_0 + \sum_{i=1}^{k_1} c_i\log v_i +\] +die verlangte Form hat. +\qedhere +\end{enumerate} +\end{proof} + +\subsection{Die Fehlerfunktion ist keine elementare Funktion +\label{buch:integrale:section:fehlernichtelementar}} +% \url{https://youtu.be/bIdPQTVF5n4} +Mit Hilfe des Satzes von Liouville kann man jetzt beweisen, dass +die Fehlerfunktion keine elementare Funktion ist. +Dazu braucht man die folgende spezielle Form des Satzes. + +\begin{satz} +\label{buch:integrale:satz:elementarestammfunktion} +Wenn $f(x)$ und $g(x)$ rationale Funktionen von $x$ sind, dann +ist die Stammfunktion von $f(x)e^{g(x)}$ genau dann eine +elementare Funktion, wenn es eine rationale Funktion gibt, die +Lösung der Differentialgleichung +\[ +r'(x) + g'(x)r(x)=f(x) +\] +ist. +\end{satz} + +\begin{satz} +Die Funktion $x\mapsto e^{-x^2}$ hat keine elementare Stammfunktion. +\label{buch:iintegrale:satz:expx2} +\end{satz} + +\begin{proof}[Beweis] +Unter Anwendung des Satzes~\ref{buch:integrale:satz:elementarestammfunktion} +auf $f(x)=1$ und $g(x)=-x^2$ folgt, $e^{-x^2}$ genau dann eine rationale +Stammfunktion hat, wenn es eine rationale Funktion $r(x)$ gibt, die +Lösung der Differentialgleichung +\begin{equation} +r'(x) -2xr(x)=1 +\label{buch:integrale:expx2dgl} +\end{equation} +ist. + +Zunächst halten wir fest, dass $r(x)$ kein Polynom sein kann. +Wäre nämlich +\[ +r(x) += +a_0 + a_1x + \dots + a_nx^n += +\sum_{k=0}^n a_kx^k +\quad\Rightarrow\quad +r'(x) += +a_1 + 2a_2x + \dots + na_nx^{n-1} += +\sum_{k=1}^n +ka_kx^{k-1} +\] +ein Polynom, dann ergäbe sich beim Einsetzen in die Differentialgleichung +\begin{align*} +1 +&= +r'(x)-2xr(x) +\\ +&= +a_1 + 2a_2x + 3a_3x^2 + \dots + (n-1)a_{n-1}x^{n-2} + na_nx^{n-1} +\\ +&\qquad +- +2a_0x -2a_1x^2 -2a_2x^3 - \dots - 2a_{n-1}x^n - 2a_nx^{n+1} +\\ +& +\hspace{0.7pt} +\renewcommand{\arraycolsep}{1.8pt} +\begin{array}{crcrcrcrcrcrcrcr} +=&a_1&+&2a_2x&+&3a_3x^2&+&\dots&+&(n-1)a_{n-1}x^{n-2}&+&na_{n }x^{n-1}& & & & \\ + & &-&2a_0x&-&2a_1x^2&-&\dots&-& 2a_{n-3}x^{n-2}&-&2a_{n-2}x^{n-1}&-&2a_{n-1}x^n&-&2a_nx^{n+1} +\end{array} +\\ +&= +a_1 ++ +(2a_2-2a_0)x ++ +(3a_3-2a_1)x^2 +%+ +%(4a_4-2a_2)x^3 ++ +\dots ++ +(na_n-2a_{n-2})x^{n-1} +- +2a_{n-1}x^n +- +2a_nx^{n+1}. +\end{align*} +Koeffizientenvergleich zeigt, dass $a_1=1$ sein muss. +Aus den letzten zwei Termen liest man ebenfalls mittels Koeffizientenvergleich +ab, dass $a_n=0$ und $a_{n-1}=0$ sein müssen. +Aus den Koeffizienten $(ka_k-2a_{k-2})=0$ folgt, dass +$a_{k-2}=\frac{k}{2}a_k$ für alle $k>1$ sein muss, diese Koeffizienten +verschwinden also auch, inklusive $a_1=0$. +Dies ist allerdings im Widerspruch zu $a_1=1$. +Es folgt, dass $r(x)$ kein Polynom sein kann. + +Der Nenner der rationalen Funktion $r(x)$ hat also mindestens eine Nullstelle +$\alpha$, man kann daher $r(x)$ auch schreiben als +\[ +r(x) = \frac{s(x)}{(x-\alpha)^n}, +\] +wobei die rationale Funktion $s(x)$ keine Nullstellen und keine Pole hat. +Einsetzen in die Differentialgleichung ergibt: +\[ +1 += +r'(x) -2xr(x) += +\frac{s'(x)}{(x-\alpha)^n} +-n +\frac{s(x)}{(x-\alpha)^{n+1}} +- +\frac{2xs(x)}{(x-\alpha)^n}. +\] +Multiplizieren mit $(x-\alpha)^{n+1}$ gibt +\[ +(x-\alpha)^{n+1} += +s'(x)(x-\alpha) +- +ns(x) +- +2xs(x)(x-\alpha) +\] +Setzt man $x=\alpha$ ein, verschwinden alle Terme ausser dem mittleren +auf der rechten Seite, es bleibt +\[ +ns(\alpha) = 0. +\] +Dies widerspricht aber der Wahl der rationalen Funktion $s(x)$, für die +$\alpha$ keine Nullstelle ist. + +Somit kann es keine rationale Funktion $r(x)$ geben, die eine Lösung der +Differentialgleichung~\eqref{buch:integrale:expx2dgl} ist und +die Funktion $e^{-x^2}$ hat keine elementare Stammfunktion. +\end{proof} + +Der Satz~\ref{buch:iintegrale:satz:expx2} rechtfertigt die Einführung +der Fehlerfunktion $\operatorname{erf}(x)$ als neue spezielle Funktion, +mit deren Hilfe die Funktion $e^{-x^2}$ integriert werden kann. + + + diff --git a/buch/chapters/060-integral/diffke.tex b/buch/chapters/060-integral/diffke.tex new file mode 100644 index 0000000..53b46ad --- /dev/null +++ b/buch/chapters/060-integral/diffke.tex @@ -0,0 +1,20 @@ +% +% diffke.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Differentialkörper und ihre Erweiterungen +\label{buch:integral:subsection:diffke}} +% +\subsubsection{Derivation} +% Ableitungsaxiome + +\subsubsection{Ableitungsregeln} +% Ableitungsregeln + +\subsubsection{Konstantenkörper} +% Konstantenkörper + +\subsubsection{Logarithmus und Exponentialfunktion} +% Logarithmus und Exponentialfunktion + diff --git a/buch/chapters/060-integral/elementar.tex b/buch/chapters/060-integral/elementar.tex new file mode 100644 index 0000000..2962178 --- /dev/null +++ b/buch/chapters/060-integral/elementar.tex @@ -0,0 +1,7 @@ +% +% elementar.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Elementare Funktionen +\label{buch:integral:subsection:elementar}} diff --git a/buch/chapters/060-integral/erweiterungen.tex b/buch/chapters/060-integral/erweiterungen.tex new file mode 100644 index 0000000..f88f6e3 --- /dev/null +++ b/buch/chapters/060-integral/erweiterungen.tex @@ -0,0 +1,12 @@ +% +% erweiterungen.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Körpererweiterungen +\label{buch:integral:subsection:koerpererweiterungen}} +% +% algebraische Zahl-Erweiterungen +% rationale Funktionen als Körpererweiterungen +% Erweiterungen mit algebraischen Funktionen +% diff --git a/buch/chapters/060-integral/iproblem.tex b/buch/chapters/060-integral/iproblem.tex new file mode 100644 index 0000000..85db464 --- /dev/null +++ b/buch/chapters/060-integral/iproblem.tex @@ -0,0 +1,93 @@ +% +% iproblem.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Das Integrationsproblem +\label{buch:integral:subsection:integrationsproblem}} +\index{Integrationsproblem}% +Die Ableitung ist ein einem Differentialkörper mit Hilfe der Ableitungsregeln +immer ausführbar, ganz ähnlich wie die Berechnung von Potenzen in einem Körper +immer ausführbar ist. +Die Umkehrung, also eine sogenannte Stammfunktion zu finden, ist dagegen +deutlich schwieriger. + +\begin{definition} +\index{Stammfunktion} +Eine {\em Stammfunktion} einer Funktion $f\in\mathscr{K}$ im Funktionenkörper +$\mathscr{K}$ ist eine Funktion $F\in\mathscr{K}$ derart, dass $F'=f$. +Wir schreiben auch $F=\int f$. +\end{definition} + +Zwei Stammfunktionen $F_1$ und $F_2$ einer Funktion $f\in\mathscr{K}$ +haben die Eigenschaft +\[ +\left.\begin{aligned} +F_1' &= f \\ +F_2' &= f +\end{aligned}\quad\right\} +\qquad +\Rightarrow +\qquad +(F_1-F_2)' = 0 +\qquad\Rightarrow\qquad +F_1-F_2\in\mathscr{C}, +\] +die beiden Stammfunktionen unterscheiden sich daher nur durch eine +Konstante. + +\subsubsection{Stammfunktion von Polynomen} +Für Polynome ist das Problem leicht lösbar. +Aus der Ableitungsregel +\[ +\frac{d}{dx} x^n = nx^{n-1} +\] +folgt, dass +\[ +\int x^n = \frac{1}{n+1} x^{n+1} +\] +eine Stammfunktion von $x^n$ ist. +Da $\int$ linear ist, ergibt sich damit auch eine Stammfunktion für +ein beliebiges Polynom +\[ +g(x) += +g_0 + g_1x + g_2x^2 + \dots g_nx^n += +\sum_{k=0}^n g_kx^k +\in\mathbb{Q}(x) +\] +angeben: +\begin{equation} +\int g(x) += +g_0x + \frac12g_1x^2 + \frac13g_2x^3 + \dots \frac{1}{n+1}g_nx^{n+1} += +\sum_{k=0}^n +\frac{g_k}{k+1}x^{k+1}. +\label{buch:integral:iproblem:eqn:polyintegral} +\end{equation} + +\subsubsection{Körpererweiterungen} +Obwohl die Ableitung in einem Differentialkörper immer ausgeführt werden +kann, gibt es keine Garantie, dass es eine Stammfunktion im gleichen +Körper gibt. +Im kleinsten denkbaren Funktionenkörper $\mathbb{Q}(x)$ +haben die negativen Potenzen linearer Funktionen die Stammfunktionen +\[ +\int +\frac{1}{(x-\alpha)^k} += +\frac{1}{(-k+1)(x-\alpha)^{k-1}} +\] +für $k\ne 1$, sind also wieder in $\mathbb{Q}(x)$. +Für $k=1$ ist aber +\[ +\int \frac{1}{x-\alpha} += +\log(x-\alpha), +\] +es braucht also eine Körpererweiterung um $\log(x-\alpha)$, damit +$(x-\alpha)^{-1}$ eine Stammfunktion in $\mathbb{Q}(x,\log(x-\alpha))$ +hat. + diff --git a/buch/chapters/060-integral/irat.tex b/buch/chapters/060-integral/irat.tex new file mode 100644 index 0000000..2d03b7b --- /dev/null +++ b/buch/chapters/060-integral/irat.tex @@ -0,0 +1,140 @@ +% +% irat.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Integration rationaler Funktionen +\label{buch:integral:subsection:rationalefunktionen}} +Für die Integration der rationalen Funktionen lernt man in einem +Analysis-Kurs üblicherweise ein Lösungsverfahren. +Dies zeigt zunächst, dass rationale Funktionen immer eine Stammfunktion +in einem geeigneten Erweiterungskörper haben. +Es deutet aber auch an, dass Stammfunktionen eine ziemlich spezielle +Form haben, die später als +Satz von Liouville~\ref{buch:integral:satz:liouville} +ein besondere Rolle spielen wird. + +% +% Aufgabenstellung +% +\subsubsection{Aufgabenstellung} +In diesem Abschnitt ist eine rationale Funktion $f(x)\in\mathbb{Q}(x)$ +gegeben, deren Stammfunktion bestimmt werden soll. +Als rationale Funktion kann sie als Bruch +\begin{equation} +f(x) = \frac{p(x)}{q(x)} +\label{buch:integral:irat:eqn:quotient} +\end{equation} +mit Polynomen $p(x),q(x)\in\mathbb{Q}[x]$ geschrieben werden. +Gesucht ist ein Erweiterungskörper $\mathscr{K}\supset \mathbb{Q}(x)$ +derart und eine Stammfunktion $F\in\mathscr{K}$ von $f$, also $F'=f$. + +% +% Polynomdivision +% +\subsubsection{Polynomdivision} +Der Quotient~\eqref{buch:integral:irat:eqn:quotient} kann durch Polynomdivision +mit Rest vereinfacht werden in einen polynomialen Teil und einen echten +Bruch: +\begin{equation} +f(x) += +g(x) ++ +\frac{a(x)}{b(x)} +\label{buch:integral:irat:eqn:polydiv} +\end{equation} +mit Polynomen $g(x),a(x),b(x)\in\mathbb[Q](x)$ und $\deg a(x) < \deg b(x)$. +Für den ersten Summanden liefert +\eqref{buch:integral:iproblem:eqn:polyintegral} eine Stammfunktion. +Im Folgenden bleibt also nur noch der zweite Term zu behandeln. + +% +% Partialbruchzerlegung +% +\subsubsection{Partialbruchzerlegung} +Zur Berechnung des Integral des Bruchs +in~\eqref{buch:integral:irat:eqn:polydiv} wird die Partialbruchzerlegung +benötigt. +Der Einfachheit halber nehmen wir an, dass wir den Körper $\mathbb{Q}(x)$ +mit alle Nullstellen $\beta_i$ des Nenner-Polynoms $b(x)$ zu einem Körper +$\mathscr{K}$ erweitert haben, in dem Nenner in Linearfaktoren zerfällt. +Unter diesen Voraussetzungen hat die Partialbruchzerlegung die Form +\begin{equation} +\frac{a(x)}{b(x)} += +\sum_{i=1}^m +\sum_{k=1}^{k_i} +\frac{A_{ik}}{(x-\beta_i)^k}, +\label{buch:integral:irat:eqn:partialbruch} +\end{equation} +wobei $k_i$ die Vielfachheit der Nullstelle $\beta_i$ ist. +Die Koeffizienten $A_{ik}$ können zum Beispiel mit Hilfe eines linearen +Gleichungssystems bestimmt werden. + +Um eine Stammfunktion zu finden, muss man also Stammfunktionen für +jeden einzelnen Summanden bestimmen. +Für Exponenten $k>1$ im Nenner eines Terms der +Partialbruchzerlegung~\eqref{buch:integral:irat:eqn:partialbruch} +kann dazu die Regel +\[ +\int \frac{A_{ik}}{(x-\beta_i)^k} += +\frac{A_{ik}}{(-k+1)(x-\beta_i)^{k-1}} +\] +verwendet werden. +Diese Stammfunktion liegt wieder in $\mathbb{Q}(x)$ liegt. + +% +% Körpererweiterungen +% +\subsubsection{Körpererweiterung} +Für $k=1$ ist eine logarithmische Erweiterung um die Funktion +\begin{equation} +\int \frac{A_{i1}}{x-\alpha_i} += +A_{i1} +\log(x-\alpha_i) +\label{buch:integral:irat:eqn:logs} +\end{equation} +nötig. +Es gibt also eine Stammfunktion in einem Erweiterungskörper, sofern +er zusätzlich alle logarithmischen Funktionen +in~\ref{buch:integral:irat:eqn:logs} enthält. +Sie hat die Form +\[ +\sum_{i=1}^m A_{i1} \log(x-\beta_i), +\] +wobei $A_{i1}\in\mathbb{Q}$ ist. + +Setzt man alle vorher schon gefundenen Teile der Stammfunktion zusammen, +kann man sehen, dass die Stammfunktion die Form +\begin{equation} +F(x) = v_0(x) + \sum_{i=1}^m c_i \log v_i(x) +\label{buch:integral:irat:eqn:liouvillstammfunktion} +\end{equation} +haben muss. +Dabei ist $v_0(x)\in\mathbb{Q}(x)$ und besteht aus der Stammfunktion +des polynomiellen Teils und den Stammfunktionen der Terme der Partialbruchzerlegung mit Exponenten $k>1$. +Die logarithmischen Terme bestehen aus den Konstanten $c_i=A_{i1}$ +und den Logarithmusfunktionen $v_i(x)=x-\beta_i\in\mathbb{Q}(x)$. +Die Funktion $f(x)$ muss daher die Form +\[ +f(x) += +v_0'(x) ++ +\sum_{i=1}^m c_i\frac{v'_i(x)}{v_i(x)} +\] +gehabt haben. +Die Form~\eqref{buch:integral:irat:eqn:liouvillstammfunktion} +der Stammfunktion ist nicht eine Spezialität der rationalen Funktionen. +Sie wird auch bei grösseren Funktionenkörpern immer wieder auftreten +und ist als Satz von Liouville bekannt. + +% +% Minimale algebraische Erweiterung +% +\subsubsection{Minimale algebraische Erweiterung} +XXX Rothstein-Trager + diff --git a/buch/chapters/060-integral/logexp.tex b/buch/chapters/060-integral/logexp.tex new file mode 100644 index 0000000..7cbb906 --- /dev/null +++ b/buch/chapters/060-integral/logexp.tex @@ -0,0 +1,27 @@ +% +% logexp.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Log-Exp-Notation für elementare Funktionen +\label{buch:integral:subsection:logexp}} +Die Integration rationaler Funktionen hat bereits gezeigt, dass +eine Stammfunktion nicht immer im Körper der rationalen Funktionen +existiert. +Es kann notwendig sein, dem Körper logarithmische Erweiterungen der Form +$\log(x-\alpha)$ hinzuzufügen. + +Es können jedoch noch ganz andere neue Funktionen auftreten, wie die +folgende Zusammenstellung einiger Stammfunktionen zeigt: +\begin{align*} +\int\frac{dx}{1+x^2} +&= +\arctan x +\\ +\end{align*} + + + + + + diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex new file mode 100644 index 0000000..19f2ad9 --- /dev/null +++ b/buch/chapters/060-integral/rational.tex @@ -0,0 +1,8 @@ +% +% rational.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Rationale Funktionen und Funktionenkörper +\label{buch:integral:subsection:rational}} + diff --git a/buch/chapters/060-integral/risch.tex b/buch/chapters/060-integral/risch.tex index 6c8ff96..1ba746a 100644 --- a/buch/chapters/060-integral/risch.tex +++ b/buch/chapters/060-integral/risch.tex @@ -6,7 +6,8 @@ \section{Der Risch-Algorithmus \label{buch:integral:section:risch}} \rhead{Risch-Algorithmus} - +\input{chapters/060-integral/logexp.tex} +\input{chapters/060-integral/elementar.tex} diff --git a/buch/chapters/060-integral/sqrat.tex b/buch/chapters/060-integral/sqrat.tex new file mode 100644 index 0000000..71eb39b --- /dev/null +++ b/buch/chapters/060-integral/sqrat.tex @@ -0,0 +1,8 @@ +% +% sqrat.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +% +\subsection{Integranden der Form $R(x,\sqrt{ax^2+bx+c})$ +\label{buch:integral:subsection:rxy}} + -- cgit v1.2.1 From a5b447ef1ab21d9dcb88d696862c75b81e994a32 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 23 May 2022 12:36:40 +0200 Subject: more rational integration stuff --- buch/chapters/060-integral/irat.tex | 8 +-- buch/chapters/060-integral/sqrat.tex | 110 +++++++++++++++++++++++++++++++++++ 2 files changed, 114 insertions(+), 4 deletions(-) diff --git a/buch/chapters/060-integral/irat.tex b/buch/chapters/060-integral/irat.tex index 2d03b7b..4c472ea 100644 --- a/buch/chapters/060-integral/irat.tex +++ b/buch/chapters/060-integral/irat.tex @@ -83,7 +83,7 @@ kann dazu die Regel \frac{A_{ik}}{(-k+1)(x-\beta_i)^{k-1}} \] verwendet werden. -Diese Stammfunktion liegt wieder in $\mathbb{Q}(x)$ liegt. +Diese Stammfunktion liegt wieder in $\mathscr{K}(x)$ liegt. % % Körpererweiterungen @@ -105,7 +105,7 @@ Sie hat die Form \[ \sum_{i=1}^m A_{i1} \log(x-\beta_i), \] -wobei $A_{i1}\in\mathbb{Q}$ ist. +wobei $A_{i1}\in\mathscr{K}$ ist. Setzt man alle vorher schon gefundenen Teile der Stammfunktion zusammen, kann man sehen, dass die Stammfunktion die Form @@ -114,10 +114,10 @@ F(x) = v_0(x) + \sum_{i=1}^m c_i \log v_i(x) \label{buch:integral:irat:eqn:liouvillstammfunktion} \end{equation} haben muss. -Dabei ist $v_0(x)\in\mathbb{Q}(x)$ und besteht aus der Stammfunktion +Dabei ist $v_0(x)\in\mathscr{K}(x)$ und besteht aus der Stammfunktion des polynomiellen Teils und den Stammfunktionen der Terme der Partialbruchzerlegung mit Exponenten $k>1$. Die logarithmischen Terme bestehen aus den Konstanten $c_i=A_{i1}$ -und den Logarithmusfunktionen $v_i(x)=x-\beta_i\in\mathbb{Q}(x)$. +und den Logarithmusfunktionen $v_i(x)=x-\beta_i\in\mathscr{K}(x)$. Die Funktion $f(x)$ muss daher die Form \[ f(x) diff --git a/buch/chapters/060-integral/sqrat.tex b/buch/chapters/060-integral/sqrat.tex index 71eb39b..38b1504 100644 --- a/buch/chapters/060-integral/sqrat.tex +++ b/buch/chapters/060-integral/sqrat.tex @@ -5,4 +5,114 @@ % \subsection{Integranden der Form $R(x,\sqrt{ax^2+bx+c})$ \label{buch:integral:subsection:rxy}} +Für rationale Funktionen lässt sich immer eine Stammfunktion in einem +Erweiterungskörper angeben, der durch hinzufügen einzelner logarithmischer +Funktionen entsteht. +Die dabei verwendeten Techniken lassen sich verallgemeinern. +Zur Illustration und Motivation des später beschriebenen Risch-Algorithmus +stellen wir uns in diesem Abschnitt der Aufgabe, Integrale +mit einem Integranden zu berechnen, der eine rationale Funktion von $x$ +und $\sqrt{ax^2+bx+c}$ ist. + +% +% Aufgabenstellung +% +\subsubsection{Aufgabenstellung} +Eine rationale Funktion von $x$ und $\sqrt{ax^2+bx+c}$ ist ein +Element des Differentialkörpers, den man aus $\mathbb{Q}(x)$ durch +hinzufügen des Elementes +\[ +y=\sqrt{ax^2+bx+c} +\] +erhält. +Eine Funktion $f\in\mathbb{Q}(x,y)$ kann geschrieben werden als Bruch +\begin{equation} +f += +\frac{ +\tilde{p}_0 + \tilde{p}_1y + \dots + \tilde{p}_n y^n +}{ +\tilde{q}_0 + \tilde{q}_1y + \dots + \tilde{q}_m y^m +} +\label{buch:integral:sqrat:eqn:ftilde} +\end{equation} +mit rationalen Koeffizienten $\tilde{p}_i,\tilde{q}_i\in\mathbb{Q}(x)$. +Gesucht ist eine Stammfunktion von $f$. + +% +% Algebraische Vereinfachungen +% +\subsubsection{Algebraische Vereinfachungen} +Da $x^2=ax^2+bx+c$ ein Polynom ist, sind auch alle geraden Potenzen +von $y$ Polynome in $\mathbb{Q}(x)$, +und die ungeraden Potenzen von $y$ lassen sich als Produkt aus einem +Polynom und dem Faktor $y$ schreiben. +Der Integrand~\eqref{buch:integral:sqrat:eqn:ftilde} +lässt sich daher vereinfachen zu einem Bruch der Form +\begin{equation} +f(x) += +\frac{p_0+p_1y}{q_0+q_1y}, +\label{buch:integral:sqrat:eqn:moebius} +\end{equation} +wobei $p_i$ und $q_i$ rationale Funktionen in $\mathbb{Q}(x)$ sind. + +% +% Rationalisieren +% +\subsubsection{Rationalisieren} +Unschön an der Form~\eqref{buch:integral:sqrat:eqn:moebius} ist die +Tatsache, dass $y$ sowohl im Nenner wie auch im Zähler auftreten kann. +Da aber $y$ die quadratische Identität $y^2=ax^2+bx+c$ erfüllt, +kann das $y$ im Nenner durch Erweitern mit $q_0-q_1y$ zum verschwinden +gebracht werden. +Die Rechnung ergibt +\begin{align*} +\frac{p_0+p_1y}{q_0+q_1y} +&= +\frac{p_0+p_1y}{q_0+q_1y} +\cdot +\frac{q_0-q_1y}{q_0-q_1y} += +\frac{(p_0+p_1y)(q_0-q_1y)}{q_0^2-q_1^2y^2} +\\ +&= +\frac{p_0q_0-p_1q_1(ax^2+bx+c)}{q_0^2-q_1^2(ax^2+bx+c)} ++ +\frac{q_0p_1-q_1p_0}{q_0^2-q_1^2(ax^2+bx+c)} y. +\end{align*} +Die Quotienten enthalten $y$ nicht mehr, sind also in $\mathbb{Q}(x)$. +In der späteren Rechnung stellt sich heraus, dass es praktischer ist, +das $y$ im Nenner zu haben, was man durch erweitern mit $y$ wieder +unter Ausnützung von $y^2=ax^2+bx+c$ erreichen kann. +Die zu integrierende Funktion kann also in der Form +\begin{equation} +f(x) += +W_1 + W_2\frac{1}{y} +\end{equation} +geschrieben werden mit rationalen Funktionen +$W_1,W_2\in\mathbb{Q}(x)$. +Eine Stammfunktion von $W_1$ kann mit der Methode von +Abschnitt~\ref{buch:integral:subsection:rationalefunktionen} +gefunden werden. +Im Folgenden kümmern wir uns daher nur noch um $W_1$. + +\subsubsection{Polynomdivision} + +\subsubsection{Integranden der Form $p(x)/y$} + +\subsubsection{Partialbruchzerlegung} + +\begin{equation} +\int +\frac{1}{(x-\alpha)^k \sqrt{ax^2+bx+c}} +\label{buch:integral:sqrat:eqn:2teart} +\end{equation} + +\subsubsection{Integrale der Form \eqref{buch:integral:sqrat:eqn:2teart}} + + + + -- cgit v1.2.1 From e8bb3fd399f2261c9b430ffa319626950499d4c1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 23 May 2022 23:06:11 +0200 Subject: new spherical graph --- buch/papers/kugel/images/Makefile | 12 ++- buch/papers/kugel/images/spherecurve.m | 160 ++++++++++++++++++++++++++++ buch/papers/kugel/images/spherecurve.maxima | 13 +++ buch/papers/kugel/images/spherecurve.pov | 73 +++++++++++++ 4 files changed, 257 insertions(+), 1 deletion(-) create mode 100644 buch/papers/kugel/images/spherecurve.m create mode 100644 buch/papers/kugel/images/spherecurve.maxima create mode 100644 buch/papers/kugel/images/spherecurve.pov diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile index e8bf919..6187fed 100644 --- a/buch/papers/kugel/images/Makefile +++ b/buch/papers/kugel/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: curvature.jpg +all: curvature.jpg spherecurve.jpg curvature.inc: curvgraph.m octave curvgraph.m @@ -13,3 +13,13 @@ curvature.png: curvature.pov curvature.inc curvature.jpg: curvature.png convert curvature.png -density 300 -units PixelsPerInch curvature.jpg + +spherecurve.inc: spherecurve.m + octave spherecurve.m + +spherecurve.png: spherecurve.pov spherecurve.inc + povray +A0.1 +W1920 +H1080 +Ospherecurve.png spherecurve.pov + +spherecurve.jpg: spherecurve.png + convert spherecurve.png -density 300 -units PixelsPerInch spherecurve.jpg + diff --git a/buch/papers/kugel/images/spherecurve.m b/buch/papers/kugel/images/spherecurve.m new file mode 100644 index 0000000..ea9c901 --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.m @@ -0,0 +1,160 @@ +# +# spherecurv.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global a; +a = 5; +global A; +A = 10; + +phisteps = 400; +hphi = 2 * pi / phisteps; +thetasteps = 200; +htheta = pi / thetasteps; + +function retval = f(z) + global a; + global A; + retval = A * exp(a * (z^2 - 1)); +endfunction + +function retval = g(z) + global a; + retval = -f(z) * 2 * a * (2 * a * z^4 + (3 - 2*a) * z^2 - 1); + # 2 + # - a 2 4 2 2 a z + #(%o6) - %e (4 a z + (6 a - 4 a ) z - 2 a) %e +endfunction + +phi = (1 + sqrt(5)) / 2; + +global axes; +axes = [ + 0, 0, 1, -1, phi, -phi; + 1, -1, phi, phi, 0, 0; + phi, phi, 0, 0, 1, 1; +]; +axes = axes / (sqrt(phi^2+1)); + +function retval = kugel(theta, phi) + retval = [ + cos(phi) * sin(theta); + sin(phi) * sin(theta); + cos(theta) + ]; +endfunction + +function retval = F(v) + global axes; + s = 0; + for i = (1:6) + z = axes(:,i)' * v; + s = s + f(z); + endfor + retval = s / 6; +endfunction + +function retval = F2(theta, phi) + v = kugel(theta, phi); + retval = F(v); +endfunction + +function retval = G(v) + global axes; + s = 0; + for i = (1:6) + s = s + g(axes(:,i)' * v); + endfor + retval = s / 6; +endfunction + +function retval = G2(theta, phi) + v = kugel(theta, phi); + retval = G(v); +endfunction + +function retval = cnormalize(u) + utop = 11; + ubottom = -30; + retval = (u - ubottom) / (utop - ubottom); + if (retval > 1) + retval = 1; + endif + if (retval < 0) + retval = 0; + endif +endfunction + +global umin; +umin = 0; +global umax; +umax = 0; + +function color = farbe(v) + global umin; + global umax; + u = G(v); + if (u < umin) + umin = u; + endif + if (u > umax) + umax = u; + endif + u = cnormalize(u); + color = [ u, 0.5, 1-u ]; + color = color/max(color); +endfunction + +function dreieck(fn, v0, v1, v2) + fprintf(fn, " mesh {\n"); + c = (v0 + v1 + v2) / 3; + c = c / norm(c); + color = farbe(c); + v0 = v0 * (1 + F(v0)); + v1 = v1 * (1 + F(v1)); + v2 = v2 * (1 + F(v2)); + fprintf(fn, "\ttriangle {\n"); + fprintf(fn, "\t <%.6f,%.6f,%.6f>,\n", v0(1,1), v0(3,1), v0(2,1)); + fprintf(fn, "\t <%.6f,%.6f,%.6f>,\n", v1(1,1), v1(3,1), v1(2,1)); + fprintf(fn, "\t <%.6f,%.6f,%.6f>\n", v2(1,1), v2(3,1), v2(2,1)); + fprintf(fn, "\t}\n"); + fprintf(fn, "\tpigment { color rgb<%.4f,%.4f,%.4f> }\n", + color(1,1), color(1,2), color(1,3)); + fprintf(fn, "\tfinish { metallic specular 0.5 }\n"); + fprintf(fn, " }\n"); +endfunction + +fn = fopen("spherecurve.inc", "w"); + + for i = (1:phisteps) + # Polkappe nord + v0 = [ 0; 0; 1 ]; + v1 = kugel(htheta, (i-1) * hphi); + v2 = kugel(htheta, i * hphi); + fprintf(fn, " // i = %d\n", i); + dreieck(fn, v0, v1, v2); + + # Polkappe sued + v0 = [ 0; 0; -1 ]; + v1 = kugel(pi-htheta, (i-1) * hphi); + v2 = kugel(pi-htheta, i * hphi); + dreieck(fn, v0, v1, v2); + endfor + + for j = (1:thetasteps-2) + for i = (1:phisteps) + v0 = kugel( j * htheta, (i-1) * hphi); + v1 = kugel((j+1) * htheta, (i-1) * hphi); + v2 = kugel( j * htheta, i * hphi); + v3 = kugel((j+1) * htheta, i * hphi); + fprintf(fn, " // i = %d, j = %d\n", i, j); + dreieck(fn, v0, v1, v2); + dreieck(fn, v1, v2, v3); + endfor + endfor + +fclose(fn); + +umin +umax diff --git a/buch/papers/kugel/images/spherecurve.maxima b/buch/papers/kugel/images/spherecurve.maxima new file mode 100644 index 0000000..1e9077c --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.maxima @@ -0,0 +1,13 @@ +/* + * spherecurv.maxima + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +f: exp(-a * sin(theta)^2); + +g: ratsimp(diff(sin(theta) * diff(f, theta), theta)/sin(theta)); +g: subst(z, cos(theta), g); +g: subst(sqrt(1-z^2), sin(theta), g); +ratsimp(g); + +f: ratsimp(subst(sqrt(1-z^2), sin(theta), f)); diff --git a/buch/papers/kugel/images/spherecurve.pov b/buch/papers/kugel/images/spherecurve.pov new file mode 100644 index 0000000..86c3745 --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.pov @@ -0,0 +1,73 @@ +// +// curvature.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// + +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.14; + +camera { + location <10, 10, -40> + look_at <0, 0, 0> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <-10, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +// +// draw an arrow from to with thickness with +// color +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +arrow(<-2.7,0,0>, <2.7,0,0>, 0.03, White) +arrow(<0,-2.7,0>, <0,2.7,0>, 0.03, White) +arrow(<0,0,-2.7>, <0,0,2.7>, 0.03, White) + +#include "spherecurve.inc" + -- cgit v1.2.1 From 6ee6a7b0cf91469c7a79827293b8e3b880a6a0aa Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 24 May 2022 11:45:50 +0200 Subject: add C++ program to compute the surface --- buch/papers/kugel/images/Makefile | 9 +- buch/papers/kugel/images/spherecurve.cpp | 292 +++++++++++++++++++++++++++++++ buch/papers/kugel/images/spherecurve.m | 4 +- buch/papers/kugel/images/spherecurve.pov | 4 +- 4 files changed, 303 insertions(+), 6 deletions(-) create mode 100644 buch/papers/kugel/images/spherecurve.cpp diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile index 6187fed..4226dab 100644 --- a/buch/papers/kugel/images/Makefile +++ b/buch/papers/kugel/images/Makefile @@ -14,12 +14,17 @@ curvature.png: curvature.pov curvature.inc curvature.jpg: curvature.png convert curvature.png -density 300 -units PixelsPerInch curvature.jpg -spherecurve.inc: spherecurve.m +spherecurve2.inc: spherecurve.m octave spherecurve.m spherecurve.png: spherecurve.pov spherecurve.inc - povray +A0.1 +W1920 +H1080 +Ospherecurve.png spherecurve.pov + povray +A0.1 +W1080 +H1080 +Ospherecurve.png spherecurve.pov spherecurve.jpg: spherecurve.png convert spherecurve.png -density 300 -units PixelsPerInch spherecurve.jpg +spherecurve: spherecurve.cpp + g++ -o spherecurve -g -Wall -O spherecurve.cpp + +spherecurve.inc: spherecurve + ./spherecurve diff --git a/buch/papers/kugel/images/spherecurve.cpp b/buch/papers/kugel/images/spherecurve.cpp new file mode 100644 index 0000000..eff8c33 --- /dev/null +++ b/buch/papers/kugel/images/spherecurve.cpp @@ -0,0 +1,292 @@ +/* + * spherecurve.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include + +inline double sqr(double x) { return x * x; } + +/** + * \brief Class for 3d vectors (also used as colors) + */ +class vector { + double X[3]; +public: + vector() { X[0] = X[1] = X[2] = 0; } + vector(double a) { X[0] = X[1] = X[2] = a; } + vector(double x, double y, double z) { + X[0] = x; X[1] = y; X[2] = z; + } + vector(double theta, double phi) { + double s = sin(theta); + X[0] = cos(phi) * s; + X[1] = sin(phi) * s; + X[2] = cos(theta); + } + vector(const vector& other) { + for (int i = 0; i < 3; i++) { + X[i] = other.X[i]; + } + } + vector operator+(const vector& other) const { + return vector(X[0] + other.X[0], + X[1] + other.X[1], + X[2] + other.X[2]); + } + vector operator*(double l) const { + return vector(X[0] * l, X[1] * l, X[2] * l); + } + double operator*(const vector& other) const { + double s = 0; + for (int i = 0; i < 3; i++) { + s += X[i] * other.X[i]; + } + return s; + } + double norm() const { + double s = 0; + for (int i = 0; i < 3; i++) { + s += sqr(X[i]); + } + return sqrt(s); + } + vector normalize() const { + double l = norm(); + return vector(X[0]/l, X[1]/l, X[2]/l); + } + double max() const { + return std::max(X[0], std::max(X[1], X[2])); + } + double l0norm() const { + double l = 0; + for (int i = 0; i < 3; i++) { + if (fabs(X[i]) > l) { + l = fabs(X[i]); + } + } + return l; + } + vector l0normalize() const { + double l = l0norm(); + vector result(X[0]/l, X[1]/l, X[2]/l); + return result; + } + const double& operator[](int i) const { return X[i]; } + double& operator[](int i) { return X[i]; } +}; + +/** + * \brief Derived 3d vector class implementing color + * + * The constructor in this class converts a single value into a + * color on a suitable gradient. + */ +class color : public vector { +public: + static double utop; + static double ubottom; + static double green; +public: + color(double u) { + u = (u - ubottom) / (utop - ubottom); + if (u > 1) { + u = 1; + } + if (u < 0) { + u = 0; + } + u = pow(u,2); + (*this)[0] = u; + (*this)[1] = green; + (*this)[2] = 1-u; + double l = l0norm(); + for (int i = 0; i < 3; i++) { + (*this)[i] /= l; + } + } +}; + +double color::utop = 12; +double color::ubottom = -31; +double color::green = 0.5; + +/** + * \brief Surface model + * + * This class contains the definitions of the functions to plot + * and the parameters to + */ +class surfacefunction { + static vector axes[6]; + + double _a; + double _A; + + double _umin; + double _umax; +public: + double a() const { return _a; } + double A() const { return _A; } + + double umin() const { return _umin; } + double umax() const { return _umax; } + + surfacefunction(double a, double A) : _a(a), _A(A), _umin(0), _umax(0) { + } + + double f(double z) { + return A() * exp(a() * (sqr(z) - 1)); + } + + double g(double z) { + return -f(z) * 2*a() * ((2*a()*sqr(z) + (3-2*a()))*sqr(z) - 1); + } + + double F(const vector& v) { + double s = 0; + for (int i = 0; i < 6; i++) { + s += f(axes[i] * v); + } + return s / 6; + } + + double G(const vector& v) { + double s = 0; + for (int i = 0; i < 6; i++) { + s += g(axes[i] * v); + } + return s / 6; + } +protected: + color farbe(const vector& v) { + double u = G(v); + if (u < _umin) { + _umin = u; + } + if (u > _umax) { + _umax = u; + } + return color(u); + } +}; + +static double phi = (1 + sqrt(5)) / 2; +static double sl = sqrt(sqr(phi) + 1); +vector surfacefunction::axes[6] = { + vector( 0. , -1./sl, phi/sl ), + vector( 0. , 1./sl, phi/sl ), + vector( 1./sl, phi/sl, 0. ), + vector( -1./sl, phi/sl, 0. ), + vector( phi/sl, 0. , 1./sl ), + vector( -phi/sl, 0. , 1./sl ) +}; + +/** + * \brief Class to construct the plot + */ +class surface : public surfacefunction { + FILE *outfile; + + int _phisteps; + int _thetasteps; + double _hphi; + double _htheta; +public: + int phisteps() const { return _phisteps; } + int thetasteps() const { return _thetasteps; } + double hphi() const { return _hphi; } + double htheta() const { return _htheta; } + void phisteps(int s) { _phisteps = s; _hphi = 2 * M_PI / s; } + void thetasteps(int s) { _thetasteps = s; _htheta = M_PI / s; } + + surface(const std::string& filename, double a, double A) + : surfacefunction(a, A) { + outfile = fopen(filename.c_str(), "w"); + phisteps(400); + thetasteps(200); + } + + ~surface() { + fclose(outfile); + } + +private: + void triangle(const vector& v0, const vector& v1, const vector& v2) { + fprintf(outfile, " mesh {\n"); + vector c = (v0 + v1 + v2) * (1./3.); + vector color = farbe(c.normalize()); + vector V0 = v0 * (1 + F(v0)); + vector V1 = v1 * (1 + F(v1)); + vector V2 = v2 * (1 + F(v2)); + fprintf(outfile, "\ttriangle {\n"); + fprintf(outfile, "\t <%.6f,%.6f,%.6f>,\n", + V0[0], V0[2], V0[1]); + fprintf(outfile, "\t <%.6f,%.6f,%.6f>,\n", + V1[0], V1[2], V1[1]); + fprintf(outfile, "\t <%.6f,%.6f,%.6f>\n", + V2[0], V2[2], V2[1]); + fprintf(outfile, "\t}\n"); + fprintf(outfile, "\tpigment { color rgb<%.4f,%.4f,%.4f> }\n", + color[0], color[1], color[2]); + fprintf(outfile, "\tfinish { metallic specular 0.5 }\n"); + fprintf(outfile, " }\n"); + } + + void northcap() { + vector v0(0, 0, 1); + for (int i = 1; i <= phisteps(); i++) { + fprintf(outfile, " // northcap i = %d\n", i); + vector v1(htheta(), (i - 1) * hphi()); + vector v2(htheta(), i * hphi()); + triangle(v0, v1, v2); + } + } + + void southcap() { + vector v0(0, 0, -1); + for (int i = 1; i <= phisteps(); i++) { + fprintf(outfile, " // southcap i = %d\n", i); + vector v1(M_PI - htheta(), (i - 1) * hphi()); + vector v2(M_PI - htheta(), i * hphi()); + triangle(v0, v1, v2); + } + } + + void zone() { + for (int j = 1; j < thetasteps() - 1; j++) { + for (int i = 1; i <= phisteps(); i++) { + fprintf(outfile, " // zone j = %d, i = %d\n", + j, i); + vector v0( j * htheta(), (i-1) * hphi()); + vector v1((j+1) * htheta(), (i-1) * hphi()); + vector v2( j * htheta(), i * hphi()); + vector v3((j+1) * htheta(), i * hphi()); + triangle(v0, v1, v2); + triangle(v1, v2, v3); + } + } + } +public: + void draw() { + northcap(); + southcap(); + zone(); + } +}; + +/** + * \brief main function + */ +int main(int argc, char *argv[]) { + surface S("spherecurve.inc", 5, 10); + color::green = 0.3; + S.draw(); + std::cout << "umin: " << S.umin() << std::endl; + std::cout << "umax: " << S.umax() << std::endl; + return EXIT_SUCCESS; +} diff --git a/buch/papers/kugel/images/spherecurve.m b/buch/papers/kugel/images/spherecurve.m index ea9c901..99d5c9a 100644 --- a/buch/papers/kugel/images/spherecurve.m +++ b/buch/papers/kugel/images/spherecurve.m @@ -1,5 +1,5 @@ # -# spherecurv.m +# spherecurve.m # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # @@ -125,7 +125,7 @@ function dreieck(fn, v0, v1, v2) fprintf(fn, " }\n"); endfunction -fn = fopen("spherecurve.inc", "w"); +fn = fopen("spherecurve2.inc", "w"); for i = (1:phisteps) # Polkappe nord diff --git a/buch/papers/kugel/images/spherecurve.pov b/buch/papers/kugel/images/spherecurve.pov index 86c3745..b1bf4b8 100644 --- a/buch/papers/kugel/images/spherecurve.pov +++ b/buch/papers/kugel/images/spherecurve.pov @@ -11,12 +11,12 @@ global_settings { assumed_gamma 1 } -#declare imagescale = 0.14; +#declare imagescale = 0.13; camera { location <10, 10, -40> look_at <0, 0, 0> - right 16/9 * x * imagescale + right x * imagescale up y * imagescale } -- cgit v1.2.1 From d08813723e1cab4bca4a527218610023775a4634 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 24 May 2022 11:53:56 +0200 Subject: better color coding --- buch/papers/kugel/images/spherecurve.cpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/papers/kugel/images/spherecurve.cpp b/buch/papers/kugel/images/spherecurve.cpp index eff8c33..8ddf5e5 100644 --- a/buch/papers/kugel/images/spherecurve.cpp +++ b/buch/papers/kugel/images/spherecurve.cpp @@ -102,7 +102,7 @@ public: } u = pow(u,2); (*this)[0] = u; - (*this)[1] = green; + (*this)[1] = green * u * (1 - u); (*this)[2] = 1-u; double l = l0norm(); for (int i = 0; i < 3; i++) { @@ -284,7 +284,7 @@ public: */ int main(int argc, char *argv[]) { surface S("spherecurve.inc", 5, 10); - color::green = 0.3; + color::green = 1.0; S.draw(); std::cout << "umin: " << S.umin() << std::endl; std::cout << "umax: " << S.umax() << std::endl; -- cgit v1.2.1 From c9c9f97f5cf1bbe669acfdb8aae1e6c81f8faed9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 24 May 2022 16:23:27 +0200 Subject: Integrale von R(x,y) --- buch/chapters/060-integral/differentialkoerper.tex | 12 +- buch/chapters/060-integral/sqrat.tex | 365 ++++++++++++++++++++- 2 files changed, 374 insertions(+), 3 deletions(-) diff --git a/buch/chapters/060-integral/differentialkoerper.tex b/buch/chapters/060-integral/differentialkoerper.tex index 66bb0c1..a071ae2 100644 --- a/buch/chapters/060-integral/differentialkoerper.tex +++ b/buch/chapters/060-integral/differentialkoerper.tex @@ -3,9 +3,19 @@ % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % -\section{Differentialkörper +\section{Differentialkörper und das Integrationsproblem \label{buch:integrale:section:dkoerper}} \rhead{Differentialkörper} +Die Einführung einer neuen Funktion $\operatorname{erf}(x)$ wurde +durch die Behauptung gerechtfertigt, dass es für den Integranden +$e^{-x^2}$ keine Stammfunktion in geschlossener Form gäbe. +Die Fehlerfunktion ist bei weitem nicht die einzige mit dieser +Eigenschaft. +Doch woher weiss man, dass es keine solche Funktion gibt, und +was heisst überhaupt ``Stammfunktion in geschlossener Form''? +In diesem Abschnitt wird daher ein algebraischer Rahmen entwickelt, +in dem diese Frage sinnvoll gestellt werden kann. + \input{chapters/060-integral/rational.tex} \input{chapters/060-integral/erweiterungen.tex} \input{chapters/060-integral/diffke.tex} diff --git a/buch/chapters/060-integral/sqrat.tex b/buch/chapters/060-integral/sqrat.tex index 38b1504..20f1ef7 100644 --- a/buch/chapters/060-integral/sqrat.tex +++ b/buch/chapters/060-integral/sqrat.tex @@ -90,6 +90,7 @@ Die zu integrierende Funktion kann also in der Form f(x) = W_1 + W_2\frac{1}{y} +\label{buch:integral:sqint:eqn:w1w2y} \end{equation} geschrieben werden mit rationalen Funktionen $W_1,W_2\in\mathbb{Q}(x)$. @@ -98,20 +99,380 @@ Abschnitt~\ref{buch:integral:subsection:rationalefunktionen} gefunden werden. Im Folgenden kümmern wir uns daher nur noch um $W_1$. +% +% Polynomdivision +% \subsubsection{Polynomdivision} +Die Funktion $W_2$ in \eqref{buch:integral:sqint:eqn:w1w2y} ist eine +rationale Funktion $W_2\in \mathbb{K}(x)$, also ein Bruch mit Polynomen +in $x$ als Zähler und Nenner. +Durch Polynomdivision mit Rest können wir $W_2$ schreiben als +\[ +W_1 = \varphi + W_3, +\] +wobei $\varphi$ ein Polynom in $x$ ist und $W_3$ eine rationale +Funktion, deren Zählergrad kleiner ist als der Nennergrad. +Zur Bestimmung der Stammfunktion bleibt jetzt nur noch +\begin{equation} +\int W_2\frac{1}{y} += +\int \frac{\varphi}{y} ++ +\int W_3\frac1{y} +\label{buch:integral:sqint:eqn:Wy} +\end{equation} +zu berechnen. -\subsubsection{Integranden der Form $p(x)/y$} +% +% Integranden der Form $\varphi(x)/y$ +% +\subsubsection{Integranden der Form $\varphi(x)/y$} +Der erste Term in~\eqref{buch:integral:sqint:eqn:Wy} ist ein Integral eines +Quotienten eines Polynoms geteilt durch $y$. +Solche Integrale können, wie im Folgenden gezeigt werden soll, reduziert +werden auf das Integral von $1/y$. +Genauer gilt der folgende Satz. -\subsubsection{Partialbruchzerlegung} +\begin{satz} +\label{buch:integral:sqint:satz:polyy} +Sei $\varphi\in\mathcal{K}(x)$ ein Polynom in $x$, dann gibt +es ein Polynom $\psi\in\mathcal{K}(x)$ vom Grad $\deg\psi < \deg\varphi$, +und $A\in\mathcal{K}$ derart, dass +\begin{equation} +\int \frac{\varphi}{y} += +\psi y + A\int\frac{1}{y}. +\label{buch:integral:sqint:eqn:phipsi} +\end{equation} +\end{satz} + +\begin{proof}[Beweis] +Wir schreiben die Polynome in der Form +\begin{align*} +\varphi +&= +\varphi_mx^m + \varphi_{m-1}x^{m-1} + \dots + \varphi_2x^2 + \varphi_1x + \varphi_0 +\\ +\psi +&= +\phantom{\varphi_mx^m+\mathstrut} +\psi_{m-1}x^{m-1} + \dots + \psi_2x^2 + \psi_1x + \psi_0 +\intertext{mit der Ableitung} +\psi' +&= +\phantom{\varphi_mx^m+\mathstrut} +\psi_{m-1}(m-1)x^{m-2} + \dots + 2\psi_2x + \psi_1. +\end{align*} +Wir leiten die Gleichung~\eqref{buch:integral:sqint:eqn:phipsi} +nach $x$ ab und erhalten +\begin{align*} +\frac{\varphi}{y} +&= +\psi'y + \psi y' + \frac{A}{y} += +\psi'y + \psi \frac{ax+b/2}{y} + \frac{A}{y}. +\intertext{Durch Multiplikation mit $y$ wird die Gleichung wesentlich +vereinfacht zu} +\varphi +&= +\psi' y^2 + \psi y' y + A += +\psi' \cdot(ax^2+bx+c) + \psi\cdot (ax+b/2) + A. +\end{align*} +Auf beiden Seiten stehen Polynome, man kann daher versuchen, die +Koeffizienten von $\psi$ mit Hilfe eines Koeffizientenvergleichs zu +bestimmen. +Dazu müssen die Produkte auf der rechten Seite ausmultipliziert werden. +So ergeben sich die Gleichungen +\begin{equation} +\renewcommand{\arraycolsep}{2pt} +\begin{array}{lcrcrcrcrcrcrcr} +\varphi_m +&=& +(m-1)\psi_{m-1} a &+& & & +&+& +\psi_{m-1} a & & & & +\\ +\varphi_{m-1} +&=& +(m-2)\psi_{m-2}a +&+& +(m-1)\psi_{m-1}b +& & +&+& +\psi_{m-2}a +&+& +\psi_{m-1}\frac{b}2 +& & +\\ +\varphi_{m-2} +&=& +(m-3)\psi_{m-3}a +&+& +(m-2)\psi_{m-2}b +&+& +(m-1)\psi_{m-1}c +&+& +\psi_{m-3}a +&+& +\psi_{m-2}\frac{b}2 +& & +\\ +&\vdots&&&&&&&&&&& +\\ +\varphi_2 +&=& +\psi_{1\phantom{-m}}a +&+& +2\psi_{2\phantom{-m}}b +&+& +3\psi_{3\phantom{-m}}c +&+& +\psi_{1\phantom{-m}}a +&+& +\psi_{2\phantom{-m}}\frac{b}2 +& & +\\ +\varphi_1 +&=& +& & +\psi_{1\phantom{-m}}b +& & +2\psi_{2\phantom{-m}}c +&+& +\psi_{0\phantom{-m}}a +&+& +\psi_{1\phantom{-m}}\frac{b}2 +\\ +\varphi_0 +&=& +& & +& & +\psi_{1\phantom{-m}}c +& & +&+& +\psi_{0\phantom{-m}}\frac{b}2 +&+&A +\end{array} +\end{equation} +In jeder Gleichung kommen hächstens drei der Koeffizienten von $\psi$ vor. +Fasst man sie zusammen und stellt die Terme etwas um, +erhält man die einfacheren Gleichungen +\begin{equation} +\renewcommand{\arraycolsep}{2pt} +\renewcommand{\arraystretch}{1.3} +\begin{array}{lcrcrcrcrcrcrcr} +\varphi_m +&=& +(m-0){\color{red}\psi_{m-1}}a & & & & +& & +\\ +\varphi_{m-1} +&=& +(m-1+\frac12)\psi_{m-1}b +&+& +(m-1){\color{red}\psi_{m-2}}a +& & +& & +\\ +\varphi_{m-2} +&=& +(m-1)\psi_{m-1}c +&+& +(m-2+\frac12)\psi_{m-2}b +&+& +(m-2){\color{red}\psi_{m-3}}a +& & +\\ +&\vdots&&&&&&&&&&& +\\ +\varphi_2 +&=& +3\psi_{3\phantom{-m}}c +&+& +(2+\frac12)\psi_{2\phantom{-m}}b +&+& +2{\color{red}\psi_{1\phantom{-m}}}a +& & +\\ +\varphi_1 +&=& +2\psi_{2\phantom{-m}}c +&+& +(1+\frac12)\psi_{1\phantom{-m}}b +&+& +{\color{red}\psi_{0\phantom{-m}}}a +& & +\\ +\varphi_0 +&=& +\psi_{1\phantom{-m}}c +& & +&+& +(0+\frac12) \psi_{0\phantom{-m}}b +&+&{\color{red}A} +\end{array} +\end{equation} +Die erste Gleichung kann wegen $a\ne 0$ nach $\psi_{m-1}$ aufgelöst werden, +dadurch ist $\psi_{m-1}$ bestimmt. +In allen folgenden Gleichungen taucht jeweils ein neuer Koeffizient +von $\psi$ auf, der rot hervorgehoben ist. +Wieder wegen $a\ne 0$ kann die Gleichung immer nach dieser Variablen +aufgelöst werden. +Die Gleichungen zeigen daher, dass die Koeffizienten des Polynoms $\psi$ +in absteigender Folge und die Konstanten $A$ eindeutig bestimmt werden. +\end{proof} + +Mit diesem Satz ist das Integral über den Teil $\varphi/y$ auf den +Fall des Integrals von $1/y$ reduziert. +Letzteres wird im nächsten Abschnitt berechnet. +% +% Das Integral von $1/y$ +% +\subsubsection{Das Integral von $1/y$} +Eine Stammfunktion von $1/y$ kann mit etwas Geschick bekannten +Interationstechnikgen gefunden werden. +Durch Ableitung der Funktion +\[ +F += +\frac{1}{\sqrt{a}}\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{y}}\biggr) +\] +kann man nachprüfen, dass $F$ eine Stammfunktion von $1/y$ ist, +also +\begin{equation} +\int +\frac{1}{y} += +\frac{1}{\sqrt{a}}\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{y}}\biggr). +\end{equation} + +% +% Partialbruchzerlegung +% +\subsubsection{Partialbruchzerlegung} +In der rationalen Funktion $W_3$ in \eqref{buch:integral:sqint:eqn:Wy} +hat der Zähler kleineren Grad als der Nenner, sie kann daher wieder +in Partialbrüche +\[ +W_3 += +\sum_{i=1}^n +\sum_{k=1}^{k_i} +\frac{A_{ik}}{(x-\alpha_i)^k} +\] +mit den Nullstellen $\alpha_i$ des Nenners von $W_3$ mit Vielfachheiten +$k_i$ zerlegt werden. +Die Stammfunktion von $W_3/y$ wird damit zu +\begin{equation} +\int W_3\frac{1}{y} += +\sum_{i=1}^n +\sum_{k=1}^{k_i} +A_{ik} +\int +\frac{1}{(x-\alpha_i)^ky} += +\sum_{i=1}^n +\sum_{k=1}^{k_i} +A_{ik} +\int +\frac{1}{(x-\alpha_i)^k \sqrt{ax^2+bx+c}}. +\end{equation} +Die Stammfunktion ist damit reduziert auf Integrale der Form \begin{equation} \int \frac{1}{(x-\alpha)^k \sqrt{ax^2+bx+c}} \label{buch:integral:sqrat:eqn:2teart} \end{equation} +mit $k>0$. +% +% Integrale der Form \eqref{buch:integral:sqrat:eqn:2teart} +% \subsubsection{Integrale der Form \eqref{buch:integral:sqrat:eqn:2teart}} +Die Integrale~\eqref{buch:integral:sqrat:eqn:2teart} +können mit Hilfe der Substution +\[ +t=\frac{1}{x-\alpha} +\qquad\text{oder}\qquad +x=\frac1t+\alpha +\] +In ein Integral verwandelt werden, für welches bereits eine +Berechnungsmethode entwickelt wurde. +Dazu berechnet man +\begin{align*} +y^2 +&= a\biggl(\frac1t+\alpha\biggr)^2 + b\biggl(\frac1t+\alpha\biggr) + c +\\ +&= +a\biggl(\frac{1}{t^2}+2\frac{\alpha}{t}+\alpha^2\biggr) ++\frac{b}{t}+b\alpha+c += +\frac{1}{t^2}\bigl( +\underbrace{a+(2a\alpha+b)t+(a\alpha^2+c)t^2}_{\displaystyle=Y^2} +\bigr) +\intertext{und damit} +y&=\frac{Y}{t}. +\end{align*} +Führt man die Substition +$dx = -dt/t^2$ im Integral aus, erhält man +\begin{align*} +\int\frac{dx}{(x-\alpha)^ky} +&= +- +\int +t^k\cdot\frac{t}{Y}\frac{dt}{t^2} += +-\int\frac{t^{k-1}}{Y}\,dt. +\end{align*} +Das letzte Integral ist wieder von der Form, die in +Satz~\ref{buch:integral:sqint:satz:polyy} behandelt wurde. +Insbesondere gibt es ein Polynom $\psi$ vom Grad $k-2$ und +eine Konstante $A$ derart, dass +\[ +\int\frac{1}{(x-\alpha)^ky} += +\psi Y + A\int\frac{1}{Y} +\] +ist. +Damit ist das Integral von $R(x,y)$ vollständig bestimmt. +\subsubsection{Beobachtungen} +Die eben dargestellte Berechnung des Integrals von $R(x,y)$ zeigt einige +Gemeinsamkeiten mit der entsprechenden Rechnung für rationale +Integranden, aber auch einige wesentliche Unterschiede. +Wieder zeigt sich, dass Polynomdivision und Partialbruchzerlegung +die zentralen Werkzeuge sind, mit denen der Integrand zerlegt und +leichter integrierbare Funktionen umgeformt werden kann. +Andererseits ist der in +Satz~\ref{buch:integral:sqint:satz:polyy} +zusammengefasste Schritt eine wesentliche zusätzliche Vereinfachung, +die keine Entsprechung bei rationalen Integranden hat. + +Die gefunden Form der Stammfunktion hat jedoch die allgemeine +Form +\[ +\int R(x,y) += +v_0 + +C +\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{y}}\biggr) ++ +\sum_{i=1}^n c_i +\log v_i, +\] +die ganz der bei rationalen Integranden gefunden Form entspricht. +Darin ist $v_0$ die Summe der angefallenen rationalen Teilintegrale, +also $v_0\in\mathcal{K}(x,y)$. +Die $v_i\in\mathcal{K}(x,y)$ sind die entsprechenden Logarithmusfunktionen, +die bei der Berechnung der Integrale \eqref{buch:integral:sqrat:eqn:2teart} +auftreten. +Insbesondere liefert die Rechnung eine Körpererweiterung von +$\mathcal{K}(x,y)$ um die logarithmische Funktionen +$\log(x+b/2a+y/\sqrt{y})$ und $\log v_i$, in der $R(x,y)$ eine +Stammfunktion hat. -- cgit v1.2.1 From 2dd23cdeef2889a5b3210e324c159ab462bb267c Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 24 May 2022 16:20:10 +0200 Subject: Korrektur (noch nicht fertig) --- buch/papers/nav/einleitung.tex | 2 +- buch/papers/nav/flatearth.tex | 3 +- buch/papers/nav/main.tex | 1 + buch/papers/nav/nautischesdreieck.tex | 89 +++++++++++++++---------------- buch/papers/nav/packages.tex | 3 +- buch/papers/nav/sincos.tex | 6 ++- buch/papers/nav/trigo.tex | 99 ++++++++++++++++++++++------------- 7 files changed, 116 insertions(+), 87 deletions(-) diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex index aafa107..8eb4481 100644 --- a/buch/papers/nav/einleitung.tex +++ b/buch/papers/nav/einleitung.tex @@ -3,7 +3,7 @@ \section{Einleitung} Heutzutage ist die Navigation ein Teil des Lebens. Man sendet dem Kollegen seinen eigenen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein, damit man seinen Aufenthaltsort zum Beispiel auf einer riesigen Wiese am See findet. -Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. +Dies wird durch Technologien wie Funknavigation, welches ein auf Laufzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist, oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf Schiffen verwendet wird im Falle eines Stromausfalls. Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? In diesem Kapitel werden genau diese Fragen mithilfe des nautischen Dreiecks, der sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index 5bfc1b7..3b08e8d 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -17,10 +17,9 @@ Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. Mithilfe der Trigonometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. -Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. +Der Kartograph Gerhard Mercator projizierte die Erdkugel wie in Abbildung 21.1 dargestellt auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. - Dies sieht man zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index e16dc2a..4c52547 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -19,3 +19,4 @@ \printbibliography[heading=subbibliography] \end{refsection} + diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index c239d64..36e9c99 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -4,49 +4,26 @@ Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. -Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. +Das nautische Dreieck hat die Ecken Zenit, Gestirn und Himmelspol, wie man in der Abbildung 21.5 sehen kann. Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel zu bestimmen. -Für die Definition gilt: -\begin{center} - \begin{tabular}{ c c c } - Winkel && Name / Beziehung \\ - \hline - $\alpha$ && Rektaszension \\ - $\delta$ && Deklination \\ - $\theta$ && Sternzeit von Greenwich\\ - $\phi$ && Geographische Breite\\ - $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ - $a$ && Azimut\\ - $h$ && Höhe - \end{tabular} -\end{center} - -\begin{itemize} - \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ - \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ - \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ - \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ - \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ -\end{itemize} - - -\subsection{Zusammenhang des nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} +\subsection{Das Bilddreieck} \begin{figure} \begin{center} - \includegraphics[height=5cm,width=8cm]{papers/nav/bilder/kugel3.png} + \includegraphics[width=8cm]{papers/nav/bilder/kugel3.png} \caption[Nautisches Dreieck]{Nautisches Dreieck} \end{center} \end{figure} - -Wie man in der Abbildung 21.4 sieht, liegt das nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. -Das selbe Dreieck kann man aber auch auf die Erdkugel projizieren. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. + Man kann das nautische Dreieck auf die Erdkugel projizieren. +Dieses Dreieck nennt man dann Bilddreieck. +Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. +Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. \section{Standortbestimmung ohne elektronische Hilfsmittel} Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion des nautische Dreiecks auf die Erdkugel zur Hilfe genommen. Mithilfe eines Sextanten, einem Jahrbuch und der sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. -Was ein Sextant und ein Jahrbuch ist, wird im Kapitel 21.6 erklärt. +Was ein Sextant und ein Jahrbuch ist, wird im Abschnitt 21.6.3 erklärt. \begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} @@ -59,8 +36,8 @@ Was ein Sextant und ein Jahrbuch ist, wird im Kapitel 21.6 erklärt. \subsection{Ecke $P$ und $A$} Unser eigener Standort ist der gesuchte Ecke $P$ und die Ecke $A$ ist in unserem Fall der Nordpol. -Der Vorteil ander Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. -Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. +Der Vorteil an der Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. +Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so einfach. \subsection{Ecke $B$ und $C$ - Bildpunkt $X$ und $Y$} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. @@ -69,8 +46,8 @@ Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mo Die Bildpunkte von den beiden Gestirnen $X$ und $Y$ bilden die beiden Ecken $B$ und $C$ im Dreieck der Abbildung 21.5. \subsection{Ephemeriden} -Zu all diesen Gestirnen gibt es Ephemeriden, die man auch Jahrbücher nennt. -In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. +Zu all diesen Gestirnen gibt es Ephemeriden. +Diese enthalten die Rektaszensionen und Deklinationen in Abhängigkeit von der Zeit. \begin{figure} \begin{center} @@ -83,25 +60,24 @@ In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und entspricht dem Breitengrad des Gestirns. \subsubsection{Rektaszension und Sternzeit} -Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht und geht vom Koordinatensystem der Himmelskugel aus. -Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. +Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt, welcher der Nullpunkt auf dem Himmelsäquator ist, steht und geht vom Koordinatensystem der Himmelskugel aus. + Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. Die Lösung ist die Sternzeit. -Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die -Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit -$\theta = 0$. +Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit $\theta = 0$. Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. -Für die Sternzeit von Greenwich $\theta $braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. +Für die Sternzeit von Greenwich $\theta$ braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht nachschlagen lässt. Im Anschluss berechnet man die Sternzeit von Greenwich \[\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3.\] -Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit von Greenwich bestimmen. +Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ bestimmen, wobei $\alpha$ die Rektaszension und $\theta$ die Sternzeit von Greenwich ist. Dies gilt analog auch für das zweite Gestirn. \subsubsection{Sextant} -Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann, insbesondere den Winkelabstand zu einem Gestirn vom Horizont. Man nutze ihn vor allem für die astronomische Navigation auf See. +Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann. Es wird vor allem der Winkelabstand zu Gestirnen gemessen. +Man benutzt ihn vor allem für die astronomische Navigation auf See. \begin{figure} \begin{center} @@ -109,7 +85,32 @@ Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen d \caption[Sextant]{Sextant} \end{center} \end{figure} - +\subsubsection{Eingeschaften} +Für das nautische Dreieck gibt es folgende Eigenschaften: +\begin{center} + \begin{tabular}{ l c l } + Legende && Name / Beziehung \\ + \hline + $\alpha$ && Rektaszension \\ + $\delta$ && Deklination \\ + $\theta$ && Sternzeit von Greenwich\\ + $\phi$ && Geographische Breite\\ + $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ + $a$ && Azimut\\ + $h$ && Höhe + \end{tabular} +\end{center} +\begin{center} + \begin{tabular}{ l c l } + Eigenschaften \\ + \hline + Seitenlänge Zenit zu Himmelspol= && $\frac{\pi}{2} - \phi$ \\ + Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - \delta$ \\ + Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - h$ \\ + Winkel von Zenit zu Himmelsnordpol zu Gestirn= && $\pi-\alpha$\\ + Winkel von Himmelsnordpol zu Zenit zu Gestirn= && $\tau$\\ + \end{tabular} +\end{center} \subsection{Bestimmung des eigenen Standortes $P$} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 5b87303..f2e6132 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,4 +8,5 @@ % following example %\usepackage{packagename} -\usepackage{amsmath} \ No newline at end of file +\usepackage{amsmath} +\usepackage{cancel} \ No newline at end of file diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index d56d482..a1653e8 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -7,12 +7,14 @@ Jedoch konnten sie dieses Problem nicht lösen. Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und sie wurde zu einer Hilfswissenschaft der Astronomen. Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom names Hipparchos. -Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten. +Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten und im Abschnitt 3.1.1 beschrieben sind. Chord ist der Vorgänger der Sinusfunktion und galt damals als wichtigste Grundlage der Trigonometrie. -In dieser Zeit wurden auch die ersten Sternenkarten angefertigt, jedoch kannte man damals die Sinusfunktion noch nicht. +In dieser Zeit wurden auch die ersten Sternenkarten angefertigt. Damals kannte man die Sinusfunktionen noch nicht. Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. +Die Definition der trigonometrischen Funktionen ermöglicht nur, rechtwinklige Dreiecke zu berechnen. +Die Beziehung zwischen Seiten und Winkeln sind komplizierter und als Sinus- und Kosinussätze bekannt. Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung mit Sternen vermehrt an Wichtigkeit gewann. Man nutzte für die Kartographie nun die Kugelgeometrie, um die Genauigkeit zu erhöhen. Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet und im darauffolgenden Jahrhundert folgte der Winkelkosinussatz. diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index ce367f6..aca8bd2 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,16 +1,13 @@ \section{Sphärische Trigonometrie} -In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. -Dabei gibt es folgenden Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie: - \subsection{Das Kugeldreieck} -Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie "Grosskreisebene" und "Grosskreisbögen" verstehen. -Ein Grosskreis ist ein größtmöglicher Kreis auf einer Kugeloberfläche. +Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie Grosskreisebene und Grosskreisbögen verstehen. +Ein Grosskreis ist ein grösstmöglicher Kreis auf einer Kugeloberfläche. Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Schnitt auf dem Großkreis teilt die Kugel in jedem Fall in zwei gleich grosse Hälften. Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. -Grosskreisbögen sind die Verbindungslinien zwischen zwei Punkten auf der Kugel, welche auch "Seiten" eines Kugeldreiecks gennant werden. +Grosskreisbögen sind die kürzesten Verbindungslinien zwischen zwei Punkten auf der Kugel. -Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck $ABC$. +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden werden, so entsteht ein Kugeldreieck $ABC$. Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. $A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung 21.2). @@ -19,18 +16,6 @@ Laut dieser Definition ist die Seite $c$ der Winkel $AMB$, wobei der Punkt $M$ d Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. -Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersches Dreieck. - -Es gibt einen Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie, wobei folgend $a$ eine Seite beschreibt: -\begin{center} - \begin{tabular}{ccc} - Eben & $\leftrightarrow$ & sphärisch \\ - \hline - $a$ & $\leftrightarrow$ & $\sin \ a$ \\ - - $a^2$ & $\leftrightarrow$ & $-\cos \ a$ \\ - \end{tabular} -\end{center} \begin{figure} \begin{center} @@ -41,8 +26,11 @@ Es gibt einen Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie, \end{figure} \subsection{Rechtwinkliges Dreieck und rechtseitiges Dreieck} +In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. + Wie auch im ebenen Dreieck gibt es beim Kugeldreieck auch ein rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. -Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. +Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss, wie man in der Abbildung 21.3 sehen kann. + \begin{figure} \begin{center} @@ -51,7 +39,7 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S \end{center} \end{figure} -\subsection{Winkelsumme} +\subsection{Winkelsumme und Flächeninhalt} \begin{figure} \begin{center} @@ -64,9 +52,9 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. Für die Summe der Innenwinkel gilt \begin{align} - \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi, \nonumber + \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \quad \text{und} \quad \alpha+\beta+\gamma > \pi, \nonumber \end{align} -wobei F der Flächeninhalt des Kugeldreiecks ist. +wobei $F$ der Flächeninhalt des Kugeldreiecks ist. \subsubsection{Sphärischer Exzess} Der sphärische Exzess \begin{align} @@ -77,32 +65,69 @@ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zu \subsubsection{Flächeninnhalt} Mithilfe des Radius $r$ und dem sphärischen Exzess $\epsilon$ gilt für den Flächeninhalt \[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon\]. -\subsection{Sphärischer Sinussatz} -In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. -Das bedeutet, dass +\subsection{Seiten und Winkelberechnung} +Es gibt in der sphärischen Trigonometrie eigentlich gar keinen Satz des Pythagoras, wie man ihn aus der zweidimensionalen Geometrie kennt. +Es gibt aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt und zum jetzigen Punkt noch unklar ist, weshalb dieser Satz so aussieht. +Die Approximation folgt noch. +Es gilt nämlich: +\begin{align} + \cos c = \cos a \cdot \cos b \quad \text{wenn} \nonumber & + \quad \alpha = \frac{\pi}{2} \nonumber +\end{align} + +\subsubsection{Approximation von kleinen Dreiecken} +Die Sätze in der ebenen Trigonometrie sind eigentlich Approximationen der sphärischen Trigonometrie. +So ist der Sinussatz in der Ebene nur eine Annäherung des sphärischen Sinussatzes. Das Gleiche gilt für den Kosinussatz und dem Satz des Pythagoras. +So kann mit dem Taylorpolynom 2. Grades den Sinus und den Kosinus vom Sphärischen in die Ebene approximieren: +\begin{align} + \sin(a) &\approx a \nonumber \intertext{und} + \cos(a)&\approx 1-\frac{a^2}{2}.\nonumber +\end{align} +Es gibt ebenfalls folgende Approximierung der Seiten von der Sphäre in die Ebene: +\begin{align} + a &\approx \sin(a) \nonumber \intertext{und} + a^2 &\approx 1-\cos(a). \nonumber +\end{align} +Die Korrespondenzen zwischen der ebenen- und sphärischen Trigonometrie werden in den kommenden Abschnitten erläutert. + +\subsubsection{Sphärischer Satz des Pythagoras} +Die Korrespondenz \[ a^2 \approx 1-cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich + +\begin{align} + \cos(a)\cdot \cos(b) &= \cos(c) \\ + \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \\ + \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} + -a^2-b^2 &=-c^2\\ + a^2+b^2&=c^2 +\end{align} + +\subsubsection{Sphärischer Sinussatz} +Den sphärischen Sinussatz \begin{align} \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \end{align} -auch beim Kugeldreieck gilt. +kann man ebenfalls mit der Korrespondenz \[a \approx \sin(a) \] zum entsprechenden ebenen Sinussatz \[\frac{a}{\sin (\alpha)} =\frac{b}{\sin (\beta)} = \frac{c}{\sin (\gamma)}\] approximieren. -\subsection{Sphärische Kosinussätze} -Auch in der sphärischen Trigonometrie gibt es den Seitenkosinussatz + +\subsubsection{Sphärische Kosinussätze} +In der sphärischen Trigonometrie gibt es den Seitenkosinussatz \begin{align} \cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber \end{align} %Seitenkosinussatz und den Winkelkosinussatz \begin{align} - \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c. \nonumber -\end{align} + \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c, \nonumber +\end{align} der nur in der sphärischen Trigonometrie vorhanden ist. -\subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} -Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. -In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt. -Es gilt nämlich: +Analog gibt es auch beim Seitenkosinussatz eine Korrespondenz zu \[ a^2 \leftrightarrow 1-\cos(a),\] die den ebenen Kosinussatz herleiten lässt, nämlich \begin{align} - \cos c = \cos a \cdot \cos b \ \text{wenn} \nonumber & - \alpha = \frac{\pi}{2} \nonumber + \cos(a)&= \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha) \\ + 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha) \\ + \xcancel{1}-\frac{a^2}{2} &= \xcancel{1}-\frac{b^2}{2}-\frac{c^2}{2} \xcancel{+\frac{b^2c^2}{4}}+bc \cdot \cos(\alpha)\intertext{Höhere Potenzen vernachlässigen} + a^2&=b^2+c^2-2bc \cdot \cos(\alpha) \end{align} + + \ No newline at end of file -- cgit v1.2.1 From 537a80724031881b7ca7e84873d8f189fe70db45 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 24 May 2022 16:23:00 +0200 Subject: Revert "Korrektur (noch nicht fertig)" This reverts commit ebe0085df81f3190423e14e6a48fc9d17550e417. --- buch/papers/nav/einleitung.tex | 2 +- buch/papers/nav/flatearth.tex | 3 +- buch/papers/nav/main.tex | 1 - buch/papers/nav/nautischesdreieck.tex | 89 ++++++++++++++++--------------- buch/papers/nav/packages.tex | 3 +- buch/papers/nav/sincos.tex | 6 +-- buch/papers/nav/trigo.tex | 99 +++++++++++++---------------------- 7 files changed, 87 insertions(+), 116 deletions(-) diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex index 8eb4481..aafa107 100644 --- a/buch/papers/nav/einleitung.tex +++ b/buch/papers/nav/einleitung.tex @@ -3,7 +3,7 @@ \section{Einleitung} Heutzutage ist die Navigation ein Teil des Lebens. Man sendet dem Kollegen seinen eigenen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein, damit man seinen Aufenthaltsort zum Beispiel auf einer riesigen Wiese am See findet. -Dies wird durch Technologien wie Funknavigation, welches ein auf Laufzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist, oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. +Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf Schiffen verwendet wird im Falle eines Stromausfalls. Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? In diesem Kapitel werden genau diese Fragen mithilfe des nautischen Dreiecks, der sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index 3b08e8d..5bfc1b7 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -17,9 +17,10 @@ Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. Mithilfe der Trigonometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. -Der Kartograph Gerhard Mercator projizierte die Erdkugel wie in Abbildung 21.1 dargestellt auf ein Papier und erstellte so eine winkeltreue Karte. +Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. + Dies sieht man zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 4c52547..e16dc2a 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -19,4 +19,3 @@ \printbibliography[heading=subbibliography] \end{refsection} - diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index 36e9c99..c239d64 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -4,26 +4,49 @@ Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. -Das nautische Dreieck hat die Ecken Zenit, Gestirn und Himmelspol, wie man in der Abbildung 21.5 sehen kann. +Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel zu bestimmen. -\subsection{Das Bilddreieck} +Für die Definition gilt: +\begin{center} + \begin{tabular}{ c c c } + Winkel && Name / Beziehung \\ + \hline + $\alpha$ && Rektaszension \\ + $\delta$ && Deklination \\ + $\theta$ && Sternzeit von Greenwich\\ + $\phi$ && Geographische Breite\\ + $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ + $a$ && Azimut\\ + $h$ && Höhe + \end{tabular} +\end{center} + +\begin{itemize} + \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ + \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ + \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ + \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ + \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ +\end{itemize} + + +\subsection{Zusammenhang des nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} \begin{figure} \begin{center} - \includegraphics[width=8cm]{papers/nav/bilder/kugel3.png} + \includegraphics[height=5cm,width=8cm]{papers/nav/bilder/kugel3.png} \caption[Nautisches Dreieck]{Nautisches Dreieck} \end{center} \end{figure} - Man kann das nautische Dreieck auf die Erdkugel projizieren. -Dieses Dreieck nennt man dann Bilddreieck. -Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. -Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. + +Wie man in der Abbildung 21.4 sieht, liegt das nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. +Das selbe Dreieck kann man aber auch auf die Erdkugel projizieren. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. \section{Standortbestimmung ohne elektronische Hilfsmittel} Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion des nautische Dreiecks auf die Erdkugel zur Hilfe genommen. Mithilfe eines Sextanten, einem Jahrbuch und der sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. -Was ein Sextant und ein Jahrbuch ist, wird im Abschnitt 21.6.3 erklärt. +Was ein Sextant und ein Jahrbuch ist, wird im Kapitel 21.6 erklärt. \begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} @@ -36,8 +59,8 @@ Was ein Sextant und ein Jahrbuch ist, wird im Abschnitt 21.6.3 erklärt. \subsection{Ecke $P$ und $A$} Unser eigener Standort ist der gesuchte Ecke $P$ und die Ecke $A$ ist in unserem Fall der Nordpol. -Der Vorteil an der Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. -Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so einfach. +Der Vorteil ander Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. +Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. \subsection{Ecke $B$ und $C$ - Bildpunkt $X$ und $Y$} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. @@ -46,8 +69,8 @@ Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mo Die Bildpunkte von den beiden Gestirnen $X$ und $Y$ bilden die beiden Ecken $B$ und $C$ im Dreieck der Abbildung 21.5. \subsection{Ephemeriden} -Zu all diesen Gestirnen gibt es Ephemeriden. -Diese enthalten die Rektaszensionen und Deklinationen in Abhängigkeit von der Zeit. +Zu all diesen Gestirnen gibt es Ephemeriden, die man auch Jahrbücher nennt. +In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. \begin{figure} \begin{center} @@ -60,24 +83,25 @@ Diese enthalten die Rektaszensionen und Deklinationen in Abhängigkeit von der Z Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und entspricht dem Breitengrad des Gestirns. \subsubsection{Rektaszension und Sternzeit} -Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt, welcher der Nullpunkt auf dem Himmelsäquator ist, steht und geht vom Koordinatensystem der Himmelskugel aus. - +Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht und geht vom Koordinatensystem der Himmelskugel aus. +Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. Die Lösung ist die Sternzeit. -Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit $\theta = 0$. +Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die +Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit +$\theta = 0$. Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. -Für die Sternzeit von Greenwich $\theta$ braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht nachschlagen lässt. +Für die Sternzeit von Greenwich $\theta $braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. Im Anschluss berechnet man die Sternzeit von Greenwich \[\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3.\] -Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ bestimmen, wobei $\alpha$ die Rektaszension und $\theta$ die Sternzeit von Greenwich ist. +Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit von Greenwich bestimmen. Dies gilt analog auch für das zweite Gestirn. \subsubsection{Sextant} -Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann. Es wird vor allem der Winkelabstand zu Gestirnen gemessen. -Man benutzt ihn vor allem für die astronomische Navigation auf See. +Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann, insbesondere den Winkelabstand zu einem Gestirn vom Horizont. Man nutze ihn vor allem für die astronomische Navigation auf See. \begin{figure} \begin{center} @@ -85,32 +109,7 @@ Man benutzt ihn vor allem für die astronomische Navigation auf See. \caption[Sextant]{Sextant} \end{center} \end{figure} -\subsubsection{Eingeschaften} -Für das nautische Dreieck gibt es folgende Eigenschaften: -\begin{center} - \begin{tabular}{ l c l } - Legende && Name / Beziehung \\ - \hline - $\alpha$ && Rektaszension \\ - $\delta$ && Deklination \\ - $\theta$ && Sternzeit von Greenwich\\ - $\phi$ && Geographische Breite\\ - $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ - $a$ && Azimut\\ - $h$ && Höhe - \end{tabular} -\end{center} -\begin{center} - \begin{tabular}{ l c l } - Eigenschaften \\ - \hline - Seitenlänge Zenit zu Himmelspol= && $\frac{\pi}{2} - \phi$ \\ - Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - \delta$ \\ - Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - h$ \\ - Winkel von Zenit zu Himmelsnordpol zu Gestirn= && $\pi-\alpha$\\ - Winkel von Himmelsnordpol zu Zenit zu Gestirn= && $\tau$\\ - \end{tabular} -\end{center} + \subsection{Bestimmung des eigenen Standortes $P$} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index f2e6132..5b87303 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,5 +8,4 @@ % following example %\usepackage{packagename} -\usepackage{amsmath} -\usepackage{cancel} \ No newline at end of file +\usepackage{amsmath} \ No newline at end of file diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index a1653e8..d56d482 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -7,14 +7,12 @@ Jedoch konnten sie dieses Problem nicht lösen. Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und sie wurde zu einer Hilfswissenschaft der Astronomen. Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom names Hipparchos. -Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten und im Abschnitt 3.1.1 beschrieben sind. +Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten. Chord ist der Vorgänger der Sinusfunktion und galt damals als wichtigste Grundlage der Trigonometrie. -In dieser Zeit wurden auch die ersten Sternenkarten angefertigt. Damals kannte man die Sinusfunktionen noch nicht. +In dieser Zeit wurden auch die ersten Sternenkarten angefertigt, jedoch kannte man damals die Sinusfunktion noch nicht. Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. -Die Definition der trigonometrischen Funktionen ermöglicht nur, rechtwinklige Dreiecke zu berechnen. -Die Beziehung zwischen Seiten und Winkeln sind komplizierter und als Sinus- und Kosinussätze bekannt. Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung mit Sternen vermehrt an Wichtigkeit gewann. Man nutzte für die Kartographie nun die Kugelgeometrie, um die Genauigkeit zu erhöhen. Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet und im darauffolgenden Jahrhundert folgte der Winkelkosinussatz. diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index aca8bd2..ce367f6 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,13 +1,16 @@ \section{Sphärische Trigonometrie} +In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. +Dabei gibt es folgenden Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie: + \subsection{Das Kugeldreieck} -Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie Grosskreisebene und Grosskreisbögen verstehen. -Ein Grosskreis ist ein grösstmöglicher Kreis auf einer Kugeloberfläche. +Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie "Grosskreisebene" und "Grosskreisbögen" verstehen. +Ein Grosskreis ist ein größtmöglicher Kreis auf einer Kugeloberfläche. Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Schnitt auf dem Großkreis teilt die Kugel in jedem Fall in zwei gleich grosse Hälften. Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. -Grosskreisbögen sind die kürzesten Verbindungslinien zwischen zwei Punkten auf der Kugel. +Grosskreisbögen sind die Verbindungslinien zwischen zwei Punkten auf der Kugel, welche auch "Seiten" eines Kugeldreiecks gennant werden. -Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden werden, so entsteht ein Kugeldreieck $ABC$. +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck $ABC$. Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. $A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung 21.2). @@ -16,6 +19,18 @@ Laut dieser Definition ist die Seite $c$ der Winkel $AMB$, wobei der Punkt $M$ d Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. +Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersches Dreieck. + +Es gibt einen Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie, wobei folgend $a$ eine Seite beschreibt: +\begin{center} + \begin{tabular}{ccc} + Eben & $\leftrightarrow$ & sphärisch \\ + \hline + $a$ & $\leftrightarrow$ & $\sin \ a$ \\ + + $a^2$ & $\leftrightarrow$ & $-\cos \ a$ \\ + \end{tabular} +\end{center} \begin{figure} \begin{center} @@ -26,11 +41,8 @@ Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiec \end{figure} \subsection{Rechtwinkliges Dreieck und rechtseitiges Dreieck} -In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. - Wie auch im ebenen Dreieck gibt es beim Kugeldreieck auch ein rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. -Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss, wie man in der Abbildung 21.3 sehen kann. - +Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. \begin{figure} \begin{center} @@ -39,7 +51,7 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S \end{center} \end{figure} -\subsection{Winkelsumme und Flächeninhalt} +\subsection{Winkelsumme} \begin{figure} \begin{center} @@ -52,9 +64,9 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. Für die Summe der Innenwinkel gilt \begin{align} - \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \quad \text{und} \quad \alpha+\beta+\gamma > \pi, \nonumber + \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi, \nonumber \end{align} -wobei $F$ der Flächeninhalt des Kugeldreiecks ist. +wobei F der Flächeninhalt des Kugeldreiecks ist. \subsubsection{Sphärischer Exzess} Der sphärische Exzess \begin{align} @@ -65,69 +77,32 @@ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zu \subsubsection{Flächeninnhalt} Mithilfe des Radius $r$ und dem sphärischen Exzess $\epsilon$ gilt für den Flächeninhalt \[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon\]. +\subsection{Sphärischer Sinussatz} +In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. +Das bedeutet, dass -\subsection{Seiten und Winkelberechnung} -Es gibt in der sphärischen Trigonometrie eigentlich gar keinen Satz des Pythagoras, wie man ihn aus der zweidimensionalen Geometrie kennt. -Es gibt aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt und zum jetzigen Punkt noch unklar ist, weshalb dieser Satz so aussieht. -Die Approximation folgt noch. -Es gilt nämlich: -\begin{align} - \cos c = \cos a \cdot \cos b \quad \text{wenn} \nonumber & - \quad \alpha = \frac{\pi}{2} \nonumber -\end{align} - -\subsubsection{Approximation von kleinen Dreiecken} -Die Sätze in der ebenen Trigonometrie sind eigentlich Approximationen der sphärischen Trigonometrie. -So ist der Sinussatz in der Ebene nur eine Annäherung des sphärischen Sinussatzes. Das Gleiche gilt für den Kosinussatz und dem Satz des Pythagoras. -So kann mit dem Taylorpolynom 2. Grades den Sinus und den Kosinus vom Sphärischen in die Ebene approximieren: -\begin{align} - \sin(a) &\approx a \nonumber \intertext{und} - \cos(a)&\approx 1-\frac{a^2}{2}.\nonumber -\end{align} -Es gibt ebenfalls folgende Approximierung der Seiten von der Sphäre in die Ebene: -\begin{align} - a &\approx \sin(a) \nonumber \intertext{und} - a^2 &\approx 1-\cos(a). \nonumber -\end{align} -Die Korrespondenzen zwischen der ebenen- und sphärischen Trigonometrie werden in den kommenden Abschnitten erläutert. - -\subsubsection{Sphärischer Satz des Pythagoras} -Die Korrespondenz \[ a^2 \approx 1-cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich - -\begin{align} - \cos(a)\cdot \cos(b) &= \cos(c) \\ - \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \\ - \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} - -a^2-b^2 &=-c^2\\ - a^2+b^2&=c^2 -\end{align} - -\subsubsection{Sphärischer Sinussatz} -Den sphärischen Sinussatz \begin{align} \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \end{align} -kann man ebenfalls mit der Korrespondenz \[a \approx \sin(a) \] zum entsprechenden ebenen Sinussatz \[\frac{a}{\sin (\alpha)} =\frac{b}{\sin (\beta)} = \frac{c}{\sin (\gamma)}\] approximieren. +auch beim Kugeldreieck gilt. - -\subsubsection{Sphärische Kosinussätze} -In der sphärischen Trigonometrie gibt es den Seitenkosinussatz +\subsection{Sphärische Kosinussätze} +Auch in der sphärischen Trigonometrie gibt es den Seitenkosinussatz \begin{align} \cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber \end{align} %Seitenkosinussatz und den Winkelkosinussatz \begin{align} - \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c, \nonumber -\end{align} der nur in der sphärischen Trigonometrie vorhanden ist. + \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c. \nonumber +\end{align} -Analog gibt es auch beim Seitenkosinussatz eine Korrespondenz zu \[ a^2 \leftrightarrow 1-\cos(a),\] die den ebenen Kosinussatz herleiten lässt, nämlich +\subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} +Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. +In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt. +Es gilt nämlich: \begin{align} - \cos(a)&= \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha) \\ - 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha) \\ - \xcancel{1}-\frac{a^2}{2} &= \xcancel{1}-\frac{b^2}{2}-\frac{c^2}{2} \xcancel{+\frac{b^2c^2}{4}}+bc \cdot \cos(\alpha)\intertext{Höhere Potenzen vernachlässigen} - a^2&=b^2+c^2-2bc \cdot \cos(\alpha) + \cos c = \cos a \cdot \cos b \ \text{wenn} \nonumber & + \alpha = \frac{\pi}{2} \nonumber \end{align} - - \ No newline at end of file -- cgit v1.2.1 From 7776e5829bf5da82b6b3fc5478ed05c6c9a66d29 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 24 May 2022 16:23:21 +0200 Subject: Revert "Revert "Korrektur (noch nicht fertig)"" This reverts commit 2fd00f1b2f0d123fdb1fb1a93b5e4d361587329c. --- buch/papers/nav/einleitung.tex | 2 +- buch/papers/nav/flatearth.tex | 3 +- buch/papers/nav/main.tex | 1 + buch/papers/nav/nautischesdreieck.tex | 89 +++++++++++++++---------------- buch/papers/nav/packages.tex | 3 +- buch/papers/nav/sincos.tex | 6 ++- buch/papers/nav/trigo.tex | 99 ++++++++++++++++++++++------------- 7 files changed, 116 insertions(+), 87 deletions(-) diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex index aafa107..8eb4481 100644 --- a/buch/papers/nav/einleitung.tex +++ b/buch/papers/nav/einleitung.tex @@ -3,7 +3,7 @@ \section{Einleitung} Heutzutage ist die Navigation ein Teil des Lebens. Man sendet dem Kollegen seinen eigenen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein, damit man seinen Aufenthaltsort zum Beispiel auf einer riesigen Wiese am See findet. -Dies wird durch Technologien wie Funknavigation, welches ein auf Langzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. +Dies wird durch Technologien wie Funknavigation, welches ein auf Laufzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist, oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. Vor all diesen technologischen Fortschritten gab es lediglich die Astronavigation, welche heute noch auf Schiffen verwendet wird im Falle eines Stromausfalls. Aber wie funktioniert die Navigation mit den Sternen? Welche Hilfsmittel benötigt man, welche Rolle spielt die Mathematik und weshalb kann die Erde nicht flach sein? In diesem Kapitel werden genau diese Fragen mithilfe des nautischen Dreiecks, der sphärischen Trigonometrie und einigen Hilfsmitteln und Messgeräten beantwortet. \ No newline at end of file diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index 5bfc1b7..3b08e8d 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -17,10 +17,9 @@ Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. Mithilfe der Trigonometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. -Der Kartograph Gerhard Mercator projizierte die Erdkugel auf ein Papier und erstellte so eine winkeltreue Karte. +Der Kartograph Gerhard Mercator projizierte die Erdkugel wie in Abbildung 21.1 dargestellt auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. - Dies sieht man zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. Grönland ist auf der Weltkarte so gross wie Afrika. In der Anwendung Google Earth jedoch ist Grönland etwa so gross wie Algerien. diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index e16dc2a..4c52547 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -19,3 +19,4 @@ \printbibliography[heading=subbibliography] \end{refsection} + diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index c239d64..36e9c99 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -4,49 +4,26 @@ Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. -Das nautische Dreieck definiert sich durch folgende Ecken: Zenit, Gestirn und Himmelspol. +Das nautische Dreieck hat die Ecken Zenit, Gestirn und Himmelspol, wie man in der Abbildung 21.5 sehen kann. Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel zu bestimmen. -Für die Definition gilt: -\begin{center} - \begin{tabular}{ c c c } - Winkel && Name / Beziehung \\ - \hline - $\alpha$ && Rektaszension \\ - $\delta$ && Deklination \\ - $\theta$ && Sternzeit von Greenwich\\ - $\phi$ && Geographische Breite\\ - $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ - $a$ && Azimut\\ - $h$ && Höhe - \end{tabular} -\end{center} - -\begin{itemize} - \item Seitenlänge Zenit zu Himmelspol $= \frac{\pi}{2} - \phi $ - \item Seitenlänge Himmelspol zu Gestirn $= \frac{\pi}{2} - \delta$ - \item Seitenlänge Zenit zu Gestirn $= \frac{\pi}{2} - h$ - \item Winkel von Zenit zu Himmelsnordpol zu Gestirn$=\pi - \alpha$ - \item Winkel von Himmelsnordpol zu Zenit und Gestirn$= \tau$ -\end{itemize} - - -\subsection{Zusammenhang des nautischen Dreiecks und des Kugeldreiecks auf der Erdkugel} +\subsection{Das Bilddreieck} \begin{figure} \begin{center} - \includegraphics[height=5cm,width=8cm]{papers/nav/bilder/kugel3.png} + \includegraphics[width=8cm]{papers/nav/bilder/kugel3.png} \caption[Nautisches Dreieck]{Nautisches Dreieck} \end{center} \end{figure} - -Wie man in der Abbildung 21.4 sieht, liegt das nautische Dreieck auf der Himmelskugel mit den Ecken Zenit, Gestirn und Himmelsnordpol. -Das selbe Dreieck kann man aber auch auf die Erdkugel projizieren. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. + Man kann das nautische Dreieck auf die Erdkugel projizieren. +Dieses Dreieck nennt man dann Bilddreieck. +Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. +Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. \section{Standortbestimmung ohne elektronische Hilfsmittel} Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion des nautische Dreiecks auf die Erdkugel zur Hilfe genommen. Mithilfe eines Sextanten, einem Jahrbuch und der sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. -Was ein Sextant und ein Jahrbuch ist, wird im Kapitel 21.6 erklärt. +Was ein Sextant und ein Jahrbuch ist, wird im Abschnitt 21.6.3 erklärt. \begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} @@ -59,8 +36,8 @@ Was ein Sextant und ein Jahrbuch ist, wird im Kapitel 21.6 erklärt. \subsection{Ecke $P$ und $A$} Unser eigener Standort ist der gesuchte Ecke $P$ und die Ecke $A$ ist in unserem Fall der Nordpol. -Der Vorteil ander Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. -Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so simpel. +Der Vorteil an der Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. +Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so einfach. \subsection{Ecke $B$ und $C$ - Bildpunkt $X$ und $Y$} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. @@ -69,8 +46,8 @@ Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mo Die Bildpunkte von den beiden Gestirnen $X$ und $Y$ bilden die beiden Ecken $B$ und $C$ im Dreieck der Abbildung 21.5. \subsection{Ephemeriden} -Zu all diesen Gestirnen gibt es Ephemeriden, die man auch Jahrbücher nennt. -In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. +Zu all diesen Gestirnen gibt es Ephemeriden. +Diese enthalten die Rektaszensionen und Deklinationen in Abhängigkeit von der Zeit. \begin{figure} \begin{center} @@ -83,25 +60,24 @@ In diesen findet man Begriffe wie Rektaszension, Deklination und Sternzeit. Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Gestirn und entspricht dem Breitengrad des Gestirns. \subsubsection{Rektaszension und Sternzeit} -Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt steht und geht vom Koordinatensystem der Himmelskugel aus. -Der Frühlungspunkt ist der Nullpunkt auf dem Himmelsäquator. +Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt, welcher der Nullpunkt auf dem Himmelsäquator ist, steht und geht vom Koordinatensystem der Himmelskugel aus. + Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. Die Lösung ist die Sternzeit. -Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die -Am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit -$\theta = 0$. +Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit $\theta = 0$. Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. -Für die Sternzeit von Greenwich $\theta $braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht recherchieren lässt. +Für die Sternzeit von Greenwich $\theta$ braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht nachschlagen lässt. Im Anschluss berechnet man die Sternzeit von Greenwich \[\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3.\] -Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ mithilfe der Rektaszension und Sternzeit von Greenwich bestimmen. +Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ bestimmen, wobei $\alpha$ die Rektaszension und $\theta$ die Sternzeit von Greenwich ist. Dies gilt analog auch für das zweite Gestirn. \subsubsection{Sextant} -Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann, insbesondere den Winkelabstand zu einem Gestirn vom Horizont. Man nutze ihn vor allem für die astronomische Navigation auf See. +Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann. Es wird vor allem der Winkelabstand zu Gestirnen gemessen. +Man benutzt ihn vor allem für die astronomische Navigation auf See. \begin{figure} \begin{center} @@ -109,7 +85,32 @@ Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen d \caption[Sextant]{Sextant} \end{center} \end{figure} - +\subsubsection{Eingeschaften} +Für das nautische Dreieck gibt es folgende Eigenschaften: +\begin{center} + \begin{tabular}{ l c l } + Legende && Name / Beziehung \\ + \hline + $\alpha$ && Rektaszension \\ + $\delta$ && Deklination \\ + $\theta$ && Sternzeit von Greenwich\\ + $\phi$ && Geographische Breite\\ + $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ + $a$ && Azimut\\ + $h$ && Höhe + \end{tabular} +\end{center} +\begin{center} + \begin{tabular}{ l c l } + Eigenschaften \\ + \hline + Seitenlänge Zenit zu Himmelspol= && $\frac{\pi}{2} - \phi$ \\ + Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - \delta$ \\ + Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - h$ \\ + Winkel von Zenit zu Himmelsnordpol zu Gestirn= && $\pi-\alpha$\\ + Winkel von Himmelsnordpol zu Zenit zu Gestirn= && $\tau$\\ + \end{tabular} +\end{center} \subsection{Bestimmung des eigenen Standortes $P$} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index 5b87303..f2e6132 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -8,4 +8,5 @@ % following example %\usepackage{packagename} -\usepackage{amsmath} \ No newline at end of file +\usepackage{amsmath} +\usepackage{cancel} \ No newline at end of file diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index d56d482..a1653e8 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -7,12 +7,14 @@ Jedoch konnten sie dieses Problem nicht lösen. Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und sie wurde zu einer Hilfswissenschaft der Astronomen. Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom names Hipparchos. -Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten. +Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten und im Abschnitt 3.1.1 beschrieben sind. Chord ist der Vorgänger der Sinusfunktion und galt damals als wichtigste Grundlage der Trigonometrie. -In dieser Zeit wurden auch die ersten Sternenkarten angefertigt, jedoch kannte man damals die Sinusfunktion noch nicht. +In dieser Zeit wurden auch die ersten Sternenkarten angefertigt. Damals kannte man die Sinusfunktionen noch nicht. Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. +Die Definition der trigonometrischen Funktionen ermöglicht nur, rechtwinklige Dreiecke zu berechnen. +Die Beziehung zwischen Seiten und Winkeln sind komplizierter und als Sinus- und Kosinussätze bekannt. Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung mit Sternen vermehrt an Wichtigkeit gewann. Man nutzte für die Kartographie nun die Kugelgeometrie, um die Genauigkeit zu erhöhen. Der Sinussatz, die Tangensfunktion und der neu entwickelte Seitenkosinussatz wurden in dieser Zeit bereits verwendet und im darauffolgenden Jahrhundert folgte der Winkelkosinussatz. diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index ce367f6..aca8bd2 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,16 +1,13 @@ \section{Sphärische Trigonometrie} -In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. -Dabei gibt es folgenden Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie: - \subsection{Das Kugeldreieck} -Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie "Grosskreisebene" und "Grosskreisbögen" verstehen. -Ein Grosskreis ist ein größtmöglicher Kreis auf einer Kugeloberfläche. +Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie Grosskreisebene und Grosskreisbögen verstehen. +Ein Grosskreis ist ein grösstmöglicher Kreis auf einer Kugeloberfläche. Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Schnitt auf dem Großkreis teilt die Kugel in jedem Fall in zwei gleich grosse Hälften. Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. -Grosskreisbögen sind die Verbindungslinien zwischen zwei Punkten auf der Kugel, welche auch "Seiten" eines Kugeldreiecks gennant werden. +Grosskreisbögen sind die kürzesten Verbindungslinien zwischen zwei Punkten auf der Kugel. -Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden, so entsteht ein Kugeldreieck $ABC$. +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden werden, so entsteht ein Kugeldreieck $ABC$. Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. $A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung 21.2). @@ -19,18 +16,6 @@ Laut dieser Definition ist die Seite $c$ der Winkel $AMB$, wobei der Punkt $M$ d Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. -Jenes Kugeldreieck mit den Seitenlängen $a, b, c < \pi$ und den Winkeln $\alpha, \beta, \gamma < \pi$ nennt man Eulersches Dreieck. - -Es gibt einen Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie, wobei folgend $a$ eine Seite beschreibt: -\begin{center} - \begin{tabular}{ccc} - Eben & $\leftrightarrow$ & sphärisch \\ - \hline - $a$ & $\leftrightarrow$ & $\sin \ a$ \\ - - $a^2$ & $\leftrightarrow$ & $-\cos \ a$ \\ - \end{tabular} -\end{center} \begin{figure} \begin{center} @@ -41,8 +26,11 @@ Es gibt einen Zusammenhang zwischen der ebenen- und sphärischen Trigonometrie, \end{figure} \subsection{Rechtwinkliges Dreieck und rechtseitiges Dreieck} +In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. + Wie auch im ebenen Dreieck gibt es beim Kugeldreieck auch ein rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. -Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss. +Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss, wie man in der Abbildung 21.3 sehen kann. + \begin{figure} \begin{center} @@ -51,7 +39,7 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S \end{center} \end{figure} -\subsection{Winkelsumme} +\subsection{Winkelsumme und Flächeninhalt} \begin{figure} \begin{center} @@ -64,9 +52,9 @@ Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. Für die Summe der Innenwinkel gilt \begin{align} - \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \ \text{und} \ \alpha+\beta+\gamma > \pi, \nonumber + \alpha+\beta+\gamma &= \frac{F}{r^2} + \pi \quad \text{und} \quad \alpha+\beta+\gamma > \pi, \nonumber \end{align} -wobei F der Flächeninhalt des Kugeldreiecks ist. +wobei $F$ der Flächeninhalt des Kugeldreiecks ist. \subsubsection{Sphärischer Exzess} Der sphärische Exzess \begin{align} @@ -77,32 +65,69 @@ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zu \subsubsection{Flächeninnhalt} Mithilfe des Radius $r$ und dem sphärischen Exzess $\epsilon$ gilt für den Flächeninhalt \[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon\]. -\subsection{Sphärischer Sinussatz} -In jedem Dreieck ist das Verhältnis des Sinus einer Seite zum Sinus des Gegenwinkels konstant. -Das bedeutet, dass +\subsection{Seiten und Winkelberechnung} +Es gibt in der sphärischen Trigonometrie eigentlich gar keinen Satz des Pythagoras, wie man ihn aus der zweidimensionalen Geometrie kennt. +Es gibt aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt und zum jetzigen Punkt noch unklar ist, weshalb dieser Satz so aussieht. +Die Approximation folgt noch. +Es gilt nämlich: +\begin{align} + \cos c = \cos a \cdot \cos b \quad \text{wenn} \nonumber & + \quad \alpha = \frac{\pi}{2} \nonumber +\end{align} + +\subsubsection{Approximation von kleinen Dreiecken} +Die Sätze in der ebenen Trigonometrie sind eigentlich Approximationen der sphärischen Trigonometrie. +So ist der Sinussatz in der Ebene nur eine Annäherung des sphärischen Sinussatzes. Das Gleiche gilt für den Kosinussatz und dem Satz des Pythagoras. +So kann mit dem Taylorpolynom 2. Grades den Sinus und den Kosinus vom Sphärischen in die Ebene approximieren: +\begin{align} + \sin(a) &\approx a \nonumber \intertext{und} + \cos(a)&\approx 1-\frac{a^2}{2}.\nonumber +\end{align} +Es gibt ebenfalls folgende Approximierung der Seiten von der Sphäre in die Ebene: +\begin{align} + a &\approx \sin(a) \nonumber \intertext{und} + a^2 &\approx 1-\cos(a). \nonumber +\end{align} +Die Korrespondenzen zwischen der ebenen- und sphärischen Trigonometrie werden in den kommenden Abschnitten erläutert. + +\subsubsection{Sphärischer Satz des Pythagoras} +Die Korrespondenz \[ a^2 \approx 1-cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich + +\begin{align} + \cos(a)\cdot \cos(b) &= \cos(c) \\ + \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \\ + \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} + -a^2-b^2 &=-c^2\\ + a^2+b^2&=c^2 +\end{align} + +\subsubsection{Sphärischer Sinussatz} +Den sphärischen Sinussatz \begin{align} \frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)} \nonumber \end{align} -auch beim Kugeldreieck gilt. +kann man ebenfalls mit der Korrespondenz \[a \approx \sin(a) \] zum entsprechenden ebenen Sinussatz \[\frac{a}{\sin (\alpha)} =\frac{b}{\sin (\beta)} = \frac{c}{\sin (\gamma)}\] approximieren. -\subsection{Sphärische Kosinussätze} -Auch in der sphärischen Trigonometrie gibt es den Seitenkosinussatz + +\subsubsection{Sphärische Kosinussätze} +In der sphärischen Trigonometrie gibt es den Seitenkosinussatz \begin{align} \cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber \end{align} %Seitenkosinussatz und den Winkelkosinussatz \begin{align} - \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c. \nonumber -\end{align} + \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c, \nonumber +\end{align} der nur in der sphärischen Trigonometrie vorhanden ist. -\subsection{Sphärischer Satz des Pythagoras für das rechtwinklige Kugeldreieck} -Es gibt in der sphärischen Trigonometrie eigentlich garkeinen "Satz des Pythagoras", wie man ihn aus der zweidimensionalen Geometrie kennt. -In der sphärischen Trigonometrie gibt es aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt. -Es gilt nämlich: +Analog gibt es auch beim Seitenkosinussatz eine Korrespondenz zu \[ a^2 \leftrightarrow 1-\cos(a),\] die den ebenen Kosinussatz herleiten lässt, nämlich \begin{align} - \cos c = \cos a \cdot \cos b \ \text{wenn} \nonumber & - \alpha = \frac{\pi}{2} \nonumber + \cos(a)&= \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha) \\ + 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha) \\ + \xcancel{1}-\frac{a^2}{2} &= \xcancel{1}-\frac{b^2}{2}-\frac{c^2}{2} \xcancel{+\frac{b^2c^2}{4}}+bc \cdot \cos(\alpha)\intertext{Höhere Potenzen vernachlässigen} + a^2&=b^2+c^2-2bc \cdot \cos(\alpha) \end{align} + + \ No newline at end of file -- cgit v1.2.1 From 76a5de291c288aa6e439fb97b0172dcfb5c9f1fe Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 25 May 2022 10:30:01 +0200 Subject: rationale Funktionen --- buch/chapters/060-integral/rational.tex | 169 ++++++++++++++++++++++++++++++++ 1 file changed, 169 insertions(+) diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex index 19f2ad9..989e65b 100644 --- a/buch/chapters/060-integral/rational.tex +++ b/buch/chapters/060-integral/rational.tex @@ -5,4 +5,173 @@ % \subsection{Rationale Funktionen und Funktionenkörper \label{buch:integral:subsection:rational}} +Welche Funktionen sollen als Antwort auf die Frage nach einer Stammfunktion +akzeptiert werden? +Polynome in der unabhängigen Variablen $x$ sollten sicher dazu gehören, +also alles, was man mit Hilfe der Multiplikation, Addition und Subtraktion +aus Koeffizienten zum Beispiel in den rationalen Zahlen $\mathbb{Q}$ und +der unabhängigen Variablen aufbauen kann. +Doch welche weiteren Operationen sollen zugelassen werden und was lässt +sich über die entstehende Funktionenmenge aussagen? + +\subsubsection{Körper} +Die kleinste Zahlenmenge, in der alle arithmetischen Operationen soweit +sinnvoll durchgeführt werden können, ist die Menge $\mathbb{Q}$ der +rationalen Zahlen. +Etwas formaler ist eine solche Menge, in der die Arithmetik uneingeschränkt +ausgeführt werden kann, ein Körper gemäss der folgenden Definition. +\index{Korper@Körper}% + +\begin{definition} +\label{buch:integral:definition:koerper} +Eine {\em Körper} ist eine Menge $K$ mit zwei Verknüpfungen $+$, die Addition, +und $\cdot$, die Multiplikation, +welche die folgenden Eigenschaften haben. +\begin{center} +\renewcommand{\tabcolsep}{0pt} +\begin{tabular}{p{68mm}p{4mm}p{68mm}} +%Eigenschaften der +Addition: +\begin{enumerate}[{\bf A}.1)] +\item assoziativ: $(a+b)+c=a+(b+c)$ +für alle $a,b,c\in K$ +\item kommutativ: $a+b=b+a$ +für alle $a,b\in K$ +\item Neutrales Element der Addition: es gibt ein Element $0\in K$ mit +der Eigenschaft $a+0=a$ für alle $a\in K$ +\item Additiv inverses Element: zu jedem Element $a\in K$ gibt es das Element +$-a$ mit der Eigenschaft $a+(-a)=0$. +\end{enumerate} +&&% +%Eigenschaften der +Multiplikation: +\begin{enumerate}[{\bf M}.1)] +\item assoziativ: $(a\cdot b)\cdot c=a\cdot (b\cdot c)$ +für alle $a,b,c\in K$ +\index{Assoziativgesetz}% +\index{assoziativ}% +\item kommutativ: $a\cdot b=b\cdot a$ +für alle $a,b\in K$ +\index{Kommutativgesetz}% +\index{kommutativ}% +\item Neutrales Element der Multiplikation: es gibt ein Element $1\in K$ mit +der Eigenschaft $a\cdot 1 =a$ für alle $a\in K$ +\index{neutrales Element}% +\item Multiplikativ inverses Element: zu jedem Element +\index{inverses Element}% +$a\in K^*=K\setminus\{0\}$ +gibt es das Element $a^{-1}$ mit der Eigenschaft $a\cdot a^{-1}=1$. +Die Menge $K^*$ heisst auch die {\em Einheitengruppe} oder die +{\em Gruppe der invertierbaren Elemente} des Körpers. +\index{Einheitengruppe}% +\index{Gruppe der invertierbaren Elemente}% +\end{enumerate} +\end{tabular} +\end{center} +\vspace{-10pt} +Ausserdem gilt das Distributivgesetz: für alle $a,b,c\in K$ gilt +$a\cdot(b+c)=a\cdot b + a\cdot c$. +\index{Disitributivgesetz}% +\end{definition} + +Das Assoziativgesetz {\bf A}.1 besagt, dass Summen mit beliebig +vielen Termen ohne Klammern geschrieben werden kann, weil es nicht +darauf ankommt, in welcher Reihenfolge die Additionen ausgeführt werden. +Ebenso für das Assoziativgesetz {\bf M}.1 der Multiplikation. +Die Kommutativgesetze {\bf A}.2 und {\bf M}.2 implizieren, dass man +nicht auf die Reihenfolge der Summanden oder Faktoren achten muss. +Das Distributivgesetz schliesslich besagt, dass man Produkte ausmultiplizieren +oder gemeinsame Faktoren ausklammern kann, wie man es in der Schule +gelernt hat. + +Die rellen Zahlen $\mathbb{R}$ und die komplexen Zahlen $\mathbb{C}$ +bilden ebenfalls einen Körper, die von den rationalen Zahlen geerbten +Eigenschaften der Verknüpfungen setzen sich auf $\mathbb{R}$ und +$\mathbb{C}$ fort. +Es lassen sich allerdings auch Zahlkörper zwischen $\mathbb{Q}$ und +$\mathbb{R}$ konstruieren, wie das folgende Beispiel zeigt. + +\begin{beispiel} +Die Menge +\[ +\mathbb{Q}(\!\sqrt{2}) += +\{ +a+b\sqrt{2} +\;|\; +a,b\in \mathbb{Q} +\} +\] +ist eine Teilmenge von $\mathbb{R}$. +Die Rechenoperationen haben alle verlangten Eigenschaften, wenn gezeigt +werden kann, dass Produkte und Quotienten von Zahlen in $\mathbb{Q}(\!\sqrt{2})$ +wieder in $\mathbb{Q}(\!\sqrt{2})$ sind. +Dazu rechnet man +\begin{align*} +(a+b\sqrt{2}) +(c+d\sqrt{2}) +&= +ac + 2bd + (ad+bc)\sqrt{2} \in \mathbb{Q}(\!\sqrt{2}) +\intertext{und} +\frac{a+b\sqrt{2}}{c+d\sqrt{2}} +&= +\frac{a+b\sqrt{2}}{c+d\sqrt{2}} +\cdot +\frac{c-d\sqrt{2}}{c-d\sqrt{2}} += +\frac{ac-2bd +(-ad+bc)\sqrt{2}}{c^2-2d^2} +\\ +&= +\underbrace{\frac{ac-2bd}{c^2-2d^2}}_{\displaystyle\in\mathbb{Q}} ++ +\underbrace{\frac{-ad+bc}{c^2-2d^2}}_{\displaystyle\in\mathbb{Q}} +\sqrt{2} +\in \mathbb{Q}(\!\sqrt{2}). +\qedhere +\end{align*} +\end{beispiel} + + +\subsubsection{Rationalen Funktionen} +Die als Antworten auf die Frage nach einer Stammfunktion akzeptablen +Funktionen sollten alle rationalen Zahlen sowie die unabhängige +Variable $x$ enthalten. +Ausserdem sollte man beliebige arithmetische Operationen mit +diesen Ausdrücken durchführen können. +Mit Addition, Subtraktion und Multiplikation entstehen aus den +rationalen Zahlen und der unabhängigen Variablen die Polynome $\mathbb{Q}[x]$ +(siehe auch Abschnitt~\ref{buch:potenzen:section:polynome}). + + +\begin{definition} +Die Menge +\[ +\mathbb{Q}(x) += +\biggl\{ +\frac{p(x)}{q(x)} +\;\bigg|\; +p(x),q(x)\in\mathbb{Q}[x] +\wedge +q(x)\ne 0 +\biggr\}, +\] +bestehenden aus allen Quotienten von Polynome, deren Nenner nicht +das Nullpolynom ist, heisst der Körper der {\em rationalen Funktionen} +\index{rationale Funktion}% +mit Koeffizienten in $\mathbb{Q}$. +\end{definition} + +Die Definition erlaubt, dass der Nenner Nullstellen hat, die sich in +Polen der Funktion äussern. +Die Eigenschaften eines Körpers sind sicher erfüllt, wenn wir uns +nur davon überzeugen können, +dass die arithmetischen Operationen nicht aus dieser Funktionenmenge +herausführen. +Dazu muss man nur verstehen, dass die Operation des gleichnamig Machens +zweier Brüche auch für Nenner funktioniert, die Polynome sind, und die +Summe wzeier Brüche von Polynomen wieder in einen Bruch von Polynomen +umwandelt. + + -- cgit v1.2.1 From 8453542b493fe8396a406c5a195dc0a4125f638d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 25 May 2022 11:59:00 +0200 Subject: Koerpererweiterungen --- buch/chapters/060-integral/erweiterungen.tex | 128 ++++++++++++++++++++++++++- buch/chapters/060-integral/rational.tex | 1 + 2 files changed, 128 insertions(+), 1 deletion(-) diff --git a/buch/chapters/060-integral/erweiterungen.tex b/buch/chapters/060-integral/erweiterungen.tex index f88f6e3..d5c7c72 100644 --- a/buch/chapters/060-integral/erweiterungen.tex +++ b/buch/chapters/060-integral/erweiterungen.tex @@ -5,8 +5,134 @@ % \subsection{Körpererweiterungen \label{buch:integral:subsection:koerpererweiterungen}} +Das Beispiel des Körpers $\mathbb{Q}(\!\sqrt{2})$ auf Seite +\pageref{buch:integral:beispiel:Qsqrt2} illustriert eine Möglichkeit, +einen kleinen Körper zu vergrössern. +Das Prinzip ist verallgemeinerungsfähig und soll in diesem Abschnitt +erarbeitet werden. + % % algebraische Zahl-Erweiterungen +\subsubsection{Algebraische Erweiterungen} +Der Körper $\mathbb{Q}(\!\sqrt{2})$ entsteht aus dem Körper $\mathbb{Q}$ +dadurch, dass man die Zahl $\sqrt{2}$ hinzufügt und alle erlaubten +arithmetischen Operationen zulässt. +Die Darstellung von Elementen von $\mathbb{Q}(\!\sqrt{2})$ als +$a+b\sqrt{2}$ ist möglich, weil die Zahl $\alpha=\sqrt{2}$ die +algebraische Relation +\[ +\alpha^2-2 = \sqrt{2}^2 -2 = 0 +\] +erfüllt. +Voraussetzung für diese Aussage ist, dass es die Zahl $\sqrt{2}$ in einem +geeigneten grösseren Körper gibt. +Die reellen oder komplexen Zahlen bilden einen solchen Körper. +Wir verallemeinern diese Situation wie folgt. + +\begin{definition} +Ist $K$ ein Körper, dann heisst ein Körper $L$ mit $K\subset L$ ein +{\em Erweiterungskörper} von $K$. +\index{Erweiterungskoerper@Erweiterungskörper} +\end{definition} + +\begin{definition} +\label{buch:integral:definition:algebraisch} +Sei $K\subset L$ eine Körpererweiterung. +Das Element $\alpha\in L$ heisst {\em algebraisch} über $K$, wenn es +ein Polynom $p(x)\in K[x]$ gibt derart, dass $\alpha$ eine Nullstelle +von $p(x)$ ist, also gibt mit $p(\alpha)=0$. +Das normierte Polynom $m(x)$ geringsten Grades, welches $m(\alpha)=0$ +erfüllt, heisst das {\em Minimalpolynom} von $\alpha$. +\index{Minimalpolynom}% +\end{definition} + +Man sagt auch $\alpha$ ist algebraisch vom Grad $n$, wenn das Minimalpolynom +den Grad $n$ hat. +Wenn $\alpha\ne 0$ algebraisch ist, dann ist auch $1/\alpha$ algebraisch, +wie das folgende Argument zeigt. +Für das Minimalpolynom $m(x)$ von $\alpha$, ist $m(\alpha)=0$. +Teilt man diese Gleichung durch $\alpha^n$ teilt, erhält man +\[ +m_0\frac{1}{\alpha^n} ++ +m_1\frac{1}{\alpha^{n-1}} ++ +\ldots ++ +m_{n-1}\frac{1}{\alpha} ++ +1 += +0, +\] +das Polynom +\[ +\hat{m}(x) += +m_0x^n + m_1x^{n-1} + \ldots m_{n-1} x + 1 +\in +K[x] +\] +hat also $\alpha^{-1}$ als Nullstelle. +Das Polynom $\hat{m}(x)$ beweist daher, dass $\alpha^{-1}$ algebraisch ist. + +Die Zahl $\sqrt{2}\in\mathbb{R}$ ist also algebraisch über $\mathbb{Q}$ +und jede andere Quadratwurzel von Elementen von $\mathbb{Q}$ ist +ebenfalls algebraisch über $\mathbb{Q}$. +Auch der Körper $\mathbb{Q}(\alpha)$ kann für jede andere Quadratwurzel +auf die genau gleiche Art wie für $\sqrt{2}$ konstruiert werden. + +\begin{definition} +\label{buch:integral:definition:algebraischeerweiterung} +Sei $K\subset L$ eine Körpererweiterung und $\alpha\in L$ ein algebraisches +Element mit Minimalpolynom $m(x)\in K[x]$. +Dann heisst die Menge +\begin{equation} +K(\alpha) += +\{ +a_0 + a_1\alpha + \ldots +a_n\alpha^n +\;|\; +a_i\in K +\} +\label{buch:integral:eqn:algelement} +\end{equation} +mit $n=\deg m(x) - 1$ der durch Adjunktion von $\alpha$ erhaltene +Erweiterungsköper. +\end{definition} + +Wieder muss nur überprüft werden, dass jedes Produkt oder jeder +Quotient von Ausdrücken der Form~\eqref{buch:integral:eqn:algelement} +wieder in diese Form gebracht werden kann. +Dazu sei +\[ +m(x) += +m_0+m_1x + m_2x^2 ++\ldots +m_{n-1}x^{n-1} + x^n +\] +das Minimalpolynom von $\alpha$. +Die Gleichung $m(\alpha)=0$ kann nach $\alpha^n$ aufgelöst werden und +liefert +\[ +\alpha^n = -m_0 - m_1\alpha - m_2\alpha^2 -\ldots -m_{n-1}\alpha^{n-1}. +\] +Damit kann jede Potenz von $\alpha$ mit einem Exponenten grösser als $n$ +in eine Linearkombination von Potenzen mit kleineren Exponenten +reduziert werden. +Ein Polynom in $\alpha$ kann also immer auf die +Form~\eqref{buch:integral:eqn:algelement} +gebracht werden. + +XXX Quotienten + % rationale Funktionen als Körpererweiterungen +\subsubsection{Rationale Funktionen als Körpererweiterung} + % Erweiterungen mit algebraischen Funktionen -% +\subsubsection{Algebraische Funktionen} + +% Transzendente Körpererweiterungen +\subsubsection{Transzendente Erweiterungen} + + diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex index 989e65b..9cef3a7 100644 --- a/buch/chapters/060-integral/rational.tex +++ b/buch/chapters/060-integral/rational.tex @@ -92,6 +92,7 @@ Es lassen sich allerdings auch Zahlkörper zwischen $\mathbb{Q}$ und $\mathbb{R}$ konstruieren, wie das folgende Beispiel zeigt. \begin{beispiel} +\label{buch:integral:beispiel:Qsqrt2} Die Menge \[ \mathbb{Q}(\!\sqrt{2}) -- cgit v1.2.1 From 6e9f45ad084ca9341c2893bdfe1ddcb07ee8a45b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 25 May 2022 12:07:43 +0200 Subject: typo --- buch/chapters/060-integral/rational.tex | 6 +++--- buch/chapters/060-integral/sqrat.tex | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex index 9cef3a7..4cd7d7f 100644 --- a/buch/chapters/060-integral/rational.tex +++ b/buch/chapters/060-integral/rational.tex @@ -61,17 +61,17 @@ der Eigenschaft $a\cdot 1 =a$ für alle $a\in K$ \index{inverses Element}% $a\in K^*=K\setminus\{0\}$ gibt es das Element $a^{-1}$ mit der Eigenschaft $a\cdot a^{-1}=1$. -Die Menge $K^*$ heisst auch die {\em Einheitengruppe} oder die -{\em Gruppe der invertierbaren Elemente} des Körpers. \index{Einheitengruppe}% \index{Gruppe der invertierbaren Elemente}% \end{enumerate} \end{tabular} \end{center} -\vspace{-10pt} +\vspace{-22pt} Ausserdem gilt das Distributivgesetz: für alle $a,b,c\in K$ gilt $a\cdot(b+c)=a\cdot b + a\cdot c$. \index{Disitributivgesetz}% +Die Menge $K^*$ heisst auch die {\em Einheitengruppe} oder die +{\em Gruppe der invertierbaren Elemente} des Körpers. \end{definition} Das Assoziativgesetz {\bf A}.1 besagt, dass Summen mit beliebig diff --git a/buch/chapters/060-integral/sqrat.tex b/buch/chapters/060-integral/sqrat.tex index 20f1ef7..f6838e5 100644 --- a/buch/chapters/060-integral/sqrat.tex +++ b/buch/chapters/060-integral/sqrat.tex @@ -332,7 +332,7 @@ Letzteres wird im nächsten Abschnitt berechnet. % \subsubsection{Das Integral von $1/y$} Eine Stammfunktion von $1/y$ kann mit etwas Geschick bekannten -Interationstechnikgen gefunden werden. +Interationstechniken gefunden werden. Durch Ableitung der Funktion \[ F -- cgit v1.2.1 From 4197abc20216c15f11660d63549eb8b765f1c892 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 25 May 2022 12:08:44 +0200 Subject: typos --- buch/chapters/060-integral/sqrat.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/buch/chapters/060-integral/sqrat.tex b/buch/chapters/060-integral/sqrat.tex index f6838e5..ceb8650 100644 --- a/buch/chapters/060-integral/sqrat.tex +++ b/buch/chapters/060-integral/sqrat.tex @@ -337,7 +337,7 @@ Durch Ableitung der Funktion \[ F = -\frac{1}{\sqrt{a}}\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{y}}\biggr) +\frac{1}{\sqrt{a}}\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{a}}\biggr) \] kann man nachprüfen, dass $F$ eine Stammfunktion von $1/y$ ist, also @@ -345,7 +345,7 @@ also \int \frac{1}{y} = -\frac{1}{\sqrt{a}}\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{y}}\biggr). +\frac{1}{\sqrt{a}}\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{a}}\biggr). \end{equation} % @@ -458,7 +458,7 @@ Form = v_0 + C -\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{y}}\biggr) +\log\biggl(x+\frac{b}{2a}+\frac{y}{\sqrt{a}}\biggr) + \sum_{i=1}^n c_i \log v_i, -- cgit v1.2.1 From 03881a82e1a30cfaea1709f4f3f50c5cd9dfd0ea Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 25 May 2022 17:40:27 +0200 Subject: algebraische Erweiterungen --- buch/chapters/060-integral/erweiterungen.tex | 109 ++++++++++++++++++++++++++- buch/chapters/060-integral/rational.tex | 2 +- 2 files changed, 106 insertions(+), 5 deletions(-) diff --git a/buch/chapters/060-integral/erweiterungen.tex b/buch/chapters/060-integral/erweiterungen.tex index d5c7c72..7039cc0 100644 --- a/buch/chapters/060-integral/erweiterungen.tex +++ b/buch/chapters/060-integral/erweiterungen.tex @@ -27,7 +27,7 @@ erfüllt. Voraussetzung für diese Aussage ist, dass es die Zahl $\sqrt{2}$ in einem geeigneten grösseren Körper gibt. Die reellen oder komplexen Zahlen bilden einen solchen Körper. -Wir verallemeinern diese Situation wie folgt. +Wir verallgemeinern diese Situation wie folgt. \begin{definition} Ist $K$ ein Körper, dann heisst ein Körper $L$ mit $K\subset L$ ein @@ -124,15 +124,116 @@ Ein Polynom in $\alpha$ kann also immer auf die Form~\eqref{buch:integral:eqn:algelement} gebracht werden. -XXX Quotienten +Es muss aber noch gezeigt werden, dass auch der Kehrwert eines Elements +der Form~\eqref{buch:integral:eqn:algelement} in dieser Form geschrieben +werden kann. +Sei also $a(\alpha)$ so ein Element, dann sind die beiden Polynome +$a(x)$ und $m(x)$ teilerfremd, der grösste gemeinsame Teiler ist $1$. +Mit dem erweiterten euklidischen Algorithmus kann man zwei Polynome +$s(x)$ und $t(x)$ finden derart, dass $s(x)a(x)+t(x)m(x)=1$. +Setzt man $\alpha$ für $x$ ein, verschwindet das Minimalpolynom und +es bleibt +\[ +s(\alpha)a(\alpha) = 1 +\qquad\Rightarrow\qquad +s(\alpha) = \frac{1}{a(\alpha)}. +\] +Damit ist $s(\alpha)$ eine Darstellung von $1/a(\alpha)$ in der +Form~\eqref{buch:integral:eqn:algelement}. + +% Transzendente Körpererweiterungen +\subsubsection{Transzendente Erweiterungen} +Nicht alle Zahlen in $\mathbb{R}$ sind algebraisch. +Lindemann bewies 1882 einen allgemeinen Satz, aus dem folgt, +dass $\pi$ und $e$ nicht algebraisch sind, es gibt also +kein Polynom mit rationalen Koeffizienten, welches $\pi$ +oder $e$ als Nullstelle hat. + +\begin{definition} +Eine Zahl $\alpha\in L$ in einer Körpererweiterung $K\subset L$ +heisst {\em transzendent}, wenn $\alpha$ nicht algebraisch ist, +wenn es also kein Polynom in $K[x]$ gibt, welches $\alpha$ als +Nullstelle hat. +\end{definition} + +Die Zahlen $\pi$ und $e$ sind also transzendent. +Eine andere Art, diese Eigenschaft zu beschreiben ist zu sagen, +dass die Potenzen +\[ +1=\pi^0, \pi, \pi^2,\pi^3,\dots +\] +linear unabhängig sind. +Gäbe es nämlich eine lineare Abhängigkeit, dann gäbe es Koeffizienten +$l_i$ derart, dass +\[ +l_0 + l_1\pi^1 + l_2\pi^2 + \ldots + l_{n-1}\pi^{n-1} + l_{n}\pi^n = l(\pi)=0, +\] +und damit wäre dann ein Polynom gefunden, welches $\pi$ als Nullstelle hat. + +Selbstverstländlich kann man zu einem transzendenten Element $\alpha$ +immer noch einen Körper konstruieren, der alle Zahlen enthält, welche man +mit den arithmetischen Operationen aus $\alpha$ bilden kann. +Man kann ihn schreiben als +\[ +K(\alpha) += +\biggl\{ +\frac{p(\alpha)}{q(\alpha)} +\;\bigg|\; +p(x),q(x)\in K[x] \wedge p(x)\ne 0 +\biggr\}, +\] +aber die Vereinfachungen zur +Form~\eqref{buch:integral:eqn:algelement}, die bei einem algebraischen +Element $\alpha$ möglich waren, können jetzt nicht mehr durchgeführt +werden. +$K\subset K(\alpha)$ ist zwar immer noch eine Körpererweiterung, aber +$K(\alpha)$ ist nicht mehr ein endlichdimensionaler Vektorraum. +Die Körpererweiterung $K\subset K(\alpha)$ heisst {\em transzendent}. % rationale Funktionen als Körpererweiterungen \subsubsection{Rationale Funktionen als Körpererweiterung} +Die unabhängige Variable wird bei Rechnen so behandelt, dass die +Potenzen alle linear unabhängig sind. +Dies ist die Grundlage für den Koeffizientenvergleich. +Der Körper der rationalen Funktion $K(x)$ +ist also eine transzendente Körpererweiterung von $K$. % Erweiterungen mit algebraischen Funktionen \subsubsection{Algebraische Funktionen} +Für das Integrationsproblem möchten wir nicht nur rationale Funktionen +verwenden können, sondern auch Wurzelfunktionen. +Wir möchten also zum Beispiel auch mit der Funktion $\sqrt{ax^2+bx+c}$ +und allem, was man mit arithmetischen Operationen daraus machen kann, +arbeiten können. +Eine Körpererweiterung, die $\sqrt{ax^2+bx+c}$ enthält, enthält auch +alles, was man daraus bilden kann. +Doch wie bekommen wir die Funktion $\sqrt{ax^2+bx+c}$ in den Körper? -% Transzendente Körpererweiterungen -\subsubsection{Transzendente Erweiterungen} +Die Art und Weise, wie man Wurzeln in der Schule kennenlernt ist als +eine neue Operation, die zu einer Zahl die Quadratwurzel liefert. +Diese Idee, den Körper mit einer weiteren Funktion anzureichern, +führt über nicht auf eine nützliche neue algebraische Struktur. +Wir dürfen daher $\sqrt{ax^2+bx+c}$ nicht als die Zusammensetzung +einer einzelnen neuen Funktion $\sqrt{\phantom{A}}$ mit +einem Polynom betrachten. + +Die Wurzel $\sqrt{ax^2+bx+c}$ ist aber auch die Nullstelle des Polynoms +\[ +p(z) += +z^2 - [ax^2+bx+c] +\in +K(x)[z] +\] +mit Koeffizienten in $K(x)$. +Die eckigen Klammern sollen helfen, die Koeffizienten in $K(x)$ +zu erkennen. +Die Funktion $\sqrt{ax^2+bx+c}$ ist also algebraisch über $K(x)$. +Einen Funktionenkörper, der die Funktion enthält, kann man also erhalten, +indem man den Körper $K(x)$ um das über $K(x)$ algebraische Element +$y=\sqrt{ax^2+bx+c}$ zu $K(x,y)=K(x,\sqrt{ax^2+bx+c}$ erweitert. +Wurzelfunktion werden daher nicht als Zusammensetzungen, sondern als +algebraische Erweiterungen eines Funktionenkörpers betrachtet. diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex index 4cd7d7f..ae64c34 100644 --- a/buch/chapters/060-integral/rational.tex +++ b/buch/chapters/060-integral/rational.tex @@ -157,7 +157,7 @@ p(x),q(x)\in\mathbb{Q}[x] q(x)\ne 0 \biggr\}, \] -bestehenden aus allen Quotienten von Polynome, deren Nenner nicht +bestehend aus allen Quotienten von Polynome, deren Nenner nicht das Nullpolynom ist, heisst der Körper der {\em rationalen Funktionen} \index{rationale Funktion}% mit Koeffizienten in $\mathbb{Q}$. -- cgit v1.2.1 From 9a90404d081513254925c76b2fbaabb1a1c62982 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 25 May 2022 20:15:57 +0200 Subject: differenialkoerper --- buch/chapters/060-integral/diffke.tex | 33 ++++++++++++++++++++++++++++++++- 1 file changed, 32 insertions(+), 1 deletion(-) diff --git a/buch/chapters/060-integral/diffke.tex b/buch/chapters/060-integral/diffke.tex index 53b46ad..a943fa3 100644 --- a/buch/chapters/060-integral/diffke.tex +++ b/buch/chapters/060-integral/diffke.tex @@ -5,16 +5,47 @@ % \subsection{Differentialkörper und ihre Erweiterungen \label{buch:integral:subsection:diffke}} +Die Ableitung wird in den Grundvorlesungen der Analysis jeweils +als ein Grenzprozess eingeführt. +Die praktische Berechnung von Ableitungen verwendet aber praktisch +nie diese Definition, sondern fast ausschliesslich die rein algebraischen +Ableitungsregeln. +So wie die Wurzelfunktionen im letzten Abschnitt als algebraische +Körpererweiterungen erkannt wurden, muss jetzt auch für die Ableitung +eine rein algebraische Definition gefunden werden. +Die entstehende Struktur ist der Differentialkörper, der in diesem +Abschnitt definiert werden soll. + +% +% Derivation % \subsubsection{Derivation} -% Ableitungsaxiome +\begin{definition} +Sei $\mathscr{F}$ ein Funktionenkörper. +Eine {\em Derivation} ist eine lineare Abbildung +$D\colon \mathscr{F}\to\mathscr{F}$ +mit der Eigenschaft +\[ +D(fg) = (Df)g+f(Dg). +\] +\end{definition} + +% +% Ableitungsregeln +% \subsubsection{Ableitungsregeln} % Ableitungsregeln +% +% Konstantenkörper +% \subsubsection{Konstantenkörper} % Konstantenkörper +% +% Logarithmus und Exponantialfunktion +% \subsubsection{Logarithmus und Exponentialfunktion} % Logarithmus und Exponentialfunktion -- cgit v1.2.1 From f24e5bd9fda39e2f8bbfb0946aac2ee7dcda547d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 26 May 2022 08:35:55 +0200 Subject: new stuff --- buch/chapters/060-integral/diffke.tex | 96 +++++++++++++++++++- buch/chapters/060-integral/elementar.tex | 8 ++ buch/chapters/060-integral/erweiterungen.tex | 10 +++ buch/chapters/060-integral/logexp.tex | 127 +++++++++++++++++++++++++-- buch/chapters/060-integral/rational.tex | 2 +- buch/chapters/060-integral/sqrat.tex | 7 +- 6 files changed, 237 insertions(+), 13 deletions(-) diff --git a/buch/chapters/060-integral/diffke.tex b/buch/chapters/060-integral/diffke.tex index a943fa3..02e90f6 100644 --- a/buch/chapters/060-integral/diffke.tex +++ b/buch/chapters/060-integral/diffke.tex @@ -20,32 +20,120 @@ Abschnitt definiert werden soll. % Derivation % \subsubsection{Derivation} +Für die praktische Berechnung der Ableitung einer Funktion verwendet +man in erster Linie die bekannten Rechenregeln. +Dazu gehören für zwei Funktionen $f$ und $g$ +\begin{itemize} +\item Linearität: $(\alpha f+\beta g)' = \alpha f' + \beta g'$ für +Konstanten $\alpha$, $\beta$. +\item Produktregel: $(fg)'=f'g+fg'$. +\index{Produktregel}% +\item Quotientenregel: $(f/g)' = (f'g-fg')/g^2$. +\index{Quotientenregel}% +\end{itemize} +Die ebenfalls häufig verwendete Kettenregel $(f\circ g)' = (f'\circ g) g'$ +\index{Kettenregel}% +für zusammengesetzte Funktionen wird später kaum benötigt, da wir +Verkettungen durch Körpererweiterungen ersetzen wollen. +Die Ableitung hat somit die rein algebraischen Eigenschaften +einer Derivation gemäss folgender Definition. \begin{definition} -Sei $\mathscr{F}$ ein Funktionenkörper. +Sei $\mathscr{F}$ ein Körper. Eine {\em Derivation} ist eine lineare Abbildung +\index{Derivation}% $D\colon \mathscr{F}\to\mathscr{F}$ mit der Eigenschaft \[ D(fg) = (Df)g+f(Dg). \] +Ein {\em Differentialkörper} ist ein Körper mit einer Derivation. +\index{Differentialkoerper@Differentialkörper}% \end{definition} +Die Ableitung in einem Funktionenkörper ist eine Derivation, +die sich zusätzlich dadurch auszeichnet, dass $Dx=x'=1$. +Sie wird weiterhin mit dem Strich bezeichnet. + % % Ableitungsregeln % \subsubsection{Ableitungsregeln} -% Ableitungsregeln +Die Definition einer Derivation macht keine Aussagen über Quotienten, +diese kann man aber aus den Eigenschaften einer Derivation sofort +ableiten. +Wir schreiben $q=f/g$ für $f,g\in\mathscr{F}$, dann ist $f=qg$. +Nach der Kettenregel gilt +\( +f'=q'g+qg' +\). +Substituiert man darin $q=f/g$ und löst nach $q'$ auf, erhält man +\[ +f'=q'g+\frac{fg'}{g} +\qquad\Rightarrow\qquad +q'=\frac1{g}\biggl(f'-\frac{fg'}{g}\biggr) += +\frac{f'g-fg'}{g^2}. +\] + % % Konstantenkörper % \subsubsection{Konstantenkörper} -% Konstantenkörper +Die Ableitung einer Konstanten verschwindet. +Beim Hinzufügen von Funktionen zu einem Funktionenkörper können weitere +Konstanten hinzukommen, ohne dass dies auf den ersten Blick sichtbar wird. +Zum Beispiel enthält $\mathbb{Q}(x,\!\sqrt{x+\pi})$ wegen +$(\!\sqrt{x+\pi})^2-x=\pi$ auch die Konstante $\pi$. +Eine Derivation ermöglicht dank des nachfolgenden Satzes auch, +solche Konstanten zu erkennen. + +\begin{satz} +Sei $\mathscr{F}$ ein Körper und $D$ eine Derivation in $\mathscr{F}$. +Dann ist die Menge $C=\{a\in\mathscr{F}\;|\;Da=0\}$ ein Körper. +\end{satz} + +\begin{proof}[Beweis] +Es muss gezeigt werden, dass Summe und Produkt von Element von $C$ +wieder in $C$ liegen. +Wenn $Da=Db=0$, dann ist $D(a+b)=Da+Db=0$, also ist $a+b\in C$. +Für das Produkt gilt $D(ab)=(Da)b+a(Db)=0b+a0=0$, also ist auch +$ab\in C$. +\end{proof} + +Die Menge $C$ heisst der {\em Konstantenkörper} von $\mathscr{F}$. +\index{Konstantenkörper}% % % Logarithmus und Exponantialfunktion % \subsubsection{Logarithmus und Exponentialfunktion} -% Logarithmus und Exponentialfunktion +Die Exponentialfunktion und der Logarithmus sind nicht algebraisch +über $\mathbb{Q}(x)$, sie lassen sich nicht durch eine algebraische +Gleichung charakterisieren. +Sie zeichnen sich aber durch besondere Ableitungseigenschaften aus. +Die Theorie der gewöhnlichen Differentialgleichungen garantiert, +dass eine Funktion durch eine Differentialgleichung und Anfangsbedingungen +festgelegt ist. +Für die Exponentialfunktion und der Logarithmus haben die +Ableitungseigenschaften +\[ +\exp'(x) = \exp(x) +\qquad\text{und}\qquad +x \log'(x) = 1. +\] +\index{Exponentialfunktion}% +\index{Logarithmus}% +In der algebraischen Beschreibung eines Funktionenkörpers gibt es +das Konzept des Wertes einer Funktion an einer bestimmten Stelle nicht. +Somit können keine Anfangsbedingungen vorgegeben werden. +Da die Gleichungen linear sind, sind Vielfache einer Lösung wieder +Lösungen. +Insbesondere ist mit $\exp(x)$ auch $a\exp(x)$ eine Lösung und mit +$\log(x)$ auch $a\log(x)$ für alle Konstanten $a$. + +Die Eigenschaft, dass die Exponentialfunktion die Umkehrfunktion +des Logarithmus ist, lässt sich mit den Mitteln eines Differentialkörpers +nicht ausdrücken. diff --git a/buch/chapters/060-integral/elementar.tex b/buch/chapters/060-integral/elementar.tex index 2962178..854a875 100644 --- a/buch/chapters/060-integral/elementar.tex +++ b/buch/chapters/060-integral/elementar.tex @@ -5,3 +5,11 @@ % \subsection{Elementare Funktionen \label{buch:integral:subsection:elementar}} +Etwas allgemeiner kann man sagen, dass in den +Beispielen~\eqref{buch:integration:risch:eqn:integralbeispiel2} +algebraische Erweiterungen von $\mathbb{Q}(x)$ und Erweiterungen +um Logarithmen oder Exponentialfunktionen vorgekommen sind. +Die Stammfunktionen verwenden dieselben Funktionen oder höchstens +Erweiterungen um Logarithmen von Funktionen, die man schon im +Integranden gesehen hat. + diff --git a/buch/chapters/060-integral/erweiterungen.tex b/buch/chapters/060-integral/erweiterungen.tex index 7039cc0..a999ebb 100644 --- a/buch/chapters/060-integral/erweiterungen.tex +++ b/buch/chapters/060-integral/erweiterungen.tex @@ -141,6 +141,16 @@ s(\alpha) = \frac{1}{a(\alpha)}. Damit ist $s(\alpha)$ eine Darstellung von $1/a(\alpha)$ in der Form~\eqref{buch:integral:eqn:algelement}. +% +% Komplexe Zahlen +% +\subsubsection{Komplexe Zahlen} +Die imaginäre Einheit $i$ hat die Eigenschaft, dass $i^2=-1$, insbesondere +ist sie Nullstelle des Polynoms $m(x)=x^2+1\in\mathbb{Q}[x]$. +Die Menge $\mathbb{Q}(i)$ ist daher eine algebraische Körpererweiterung +von $\mathbb{Q}$ bestehend aus den komplexen Zahlen mit rationalem +Real- und Imaginärteil. + % Transzendente Körpererweiterungen \subsubsection{Transzendente Erweiterungen} Nicht alle Zahlen in $\mathbb{R}$ sind algebraisch. diff --git a/buch/chapters/060-integral/logexp.tex b/buch/chapters/060-integral/logexp.tex index 7cbb906..2bfe0e1 100644 --- a/buch/chapters/060-integral/logexp.tex +++ b/buch/chapters/060-integral/logexp.tex @@ -13,15 +13,132 @@ $\log(x-\alpha)$ hinzuzufügen. Es können jedoch noch ganz andere neue Funktionen auftreten, wie die folgende Zusammenstellung einiger Stammfunktionen zeigt: -\begin{align*} +\begin{equation} +\begin{aligned} \int\frac{dx}{1+x^2} &= -\arctan x +\arctan x, \\ -\end{align*} - - +\int \cos x\,dx +&= +\sin x, +\\ +\int\frac{dx}{\sqrt{1-x^2}} +&= +\arcsin x, +\\ +\int +\operatorname{arcosh} x\,dx +&= +x \operatorname{arcosh} x - \sqrt{x^2-1}. +\end{aligned} +\label{buch:integration:risch:allgform} +\end{equation} +In der Stammfunktion treten Funktionen auf, die auf den ersten +Blick nichts mit den Funktionen im Integranden zu tun haben. +Die trigonometrischen und hyperbolichen Funktionen +in~\eqref{buch:integration:risch:allgform} +lassen sich alle durch Exponentialfunktionen ausdrücken. +So gilt +\begin{equation} +\begin{aligned} +\sin x &= \frac{1}{2i}\bigl( e^{ix} - e^{-ix}\bigr), +& +&\qquad& +\cos x &= \frac{1}{2}\bigl( e^{ix} + e^{-ix}\bigr), +\\ +\sinh x &= \frac12\bigl( e^x - e^{-x} \bigr), +& +&\qquad& +\cosh x &= \frac12\bigl( e^x + e^{-x} \bigr). +\end{aligned} +\label{buch:integral:risch:trighypinv} +\end{equation} +Nach Multiplikation mit $e^{ix}$ bzw.~$e^{x}$ entsteht eine +quadratische Gleichung in $e^{ix}$ bzw.~$e^{x}$. +Die Lösungsformel für quadratische Gleichungen erlaubt daher, $e^{ix}$ +bzw.~$e^{x}$ zu finden und damit auch die Umkehrfunktionen. +Die Rechnung ergibt +\begin{equation} +\begin{aligned} +\arcsin y +&= +\frac{1}{i}\log\bigl( +iy\pm\sqrt{1-y^2} +\bigr) +& +&\qquad& +\arccos y +&= +\log\bigl( +y\pm \sqrt{y^2-1} +\bigr) +\\ +\operatorname{arsinh}y +&= +\log\bigl( +y \pm \sqrt{1+y^2} +\bigr) +& +&\qquad& +\operatorname{arcosh} y +&= +\log\bigl( +y\pm \sqrt{y^2-1} +\bigr) +\end{aligned} +\label{buch:integral:risch:trighypinv} +\end{equation} +Alle Funktionen, die man aus dem elementaren Analysisunterricht +kennt, können also mit Hilfe von Exponentialfunktionen und Logarithmen +geschrieben werden. +Man nennt dies die $\log$-$\exp$-Notation der trigonometrischen +und hyperbolischen Funktionen. +\index{logexpnotation@$\log$-$\exp$-Notation}% +Wendet man die Substitutionen +\eqref{buch:integral:risch:trighyp} +und +\eqref{buch:integral:risch:trighypinv} +auf die Integrale +\eqref{buch:integration:risch:allgform} +an, entstehen die Beziehungen +\begin{equation} +\begin{aligned} +\int\frac{1}{1+x^2} +&= +\frac12i\bigl( +\log(1-ix) - \log(1+ix) +\bigr) +\\ +\int\bigl( +{\textstyle\frac12} +e^{ix} ++ +{\textstyle\frac12} +e^{-ix} +\bigr) +&= +-{\textstyle\frac12}ie^{ix} ++{\textstyle\frac12}ie^{-ix} +\\ +\int +\frac{1}{\sqrt{1-x^2}} +&= +-i\log\bigl(ix+\sqrt{1-x^2}) +\\ +\int \log\bigl(x+\sqrt{x^2-1}\bigr) +&= +x\log\bigl(x+\sqrt{x^2-1}\bigr) - \sqrt{x^2-1}. +\end{aligned} +\label{buch:integration:risch:eqn:integralbeispiel2} +\end{equation} +Die in den Stammfuntionen auftretenden Funktionen treten entweder +schon im Integranden auf oder sind Logarithmen von solchen +Funktionen. +Zum Beispiel hat der Nenner im ersten Integral die Faktorisierung +$1+x^2=(1+ix)(1-ix)$, in der Stammfunktion findet man die Logarithmen +der Faktoren. diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex index ae64c34..7b24e9f 100644 --- a/buch/chapters/060-integral/rational.tex +++ b/buch/chapters/060-integral/rational.tex @@ -157,7 +157,7 @@ p(x),q(x)\in\mathbb{Q}[x] q(x)\ne 0 \biggr\}, \] -bestehend aus allen Quotienten von Polynome, deren Nenner nicht +bestehend aus allen Quotienten von Polynomen, deren Nenner nicht das Nullpolynom ist, heisst der Körper der {\em rationalen Funktionen} \index{rationale Funktion}% mit Koeffizienten in $\mathbb{Q}$. diff --git a/buch/chapters/060-integral/sqrat.tex b/buch/chapters/060-integral/sqrat.tex index ceb8650..787cfc9 100644 --- a/buch/chapters/060-integral/sqrat.tex +++ b/buch/chapters/060-integral/sqrat.tex @@ -331,8 +331,9 @@ Letzteres wird im nächsten Abschnitt berechnet. % Das Integral von $1/y$ % \subsubsection{Das Integral von $1/y$} -Eine Stammfunktion von $1/y$ kann mit etwas Geschick bekannten -Interationstechniken gefunden werden. +Eine Stammfunktion von $1/y$ kann mit etwas Geschick mit den +Interationstechniken gefunden werden, die man in einem Analysis-Kurs +lernt. Durch Ableitung der Funktion \[ F @@ -471,7 +472,7 @@ die bei der Berechnung der Integrale \eqref{buch:integral:sqrat:eqn:2teart} auftreten. Insbesondere liefert die Rechnung eine Körpererweiterung von $\mathcal{K}(x,y)$ um die logarithmische Funktionen -$\log(x+b/2a+y/\sqrt{y})$ und $\log v_i$, in der $R(x,y)$ eine +$\log(x+b/2a+y/\!\sqrt{y})$ und $\log v_i$, in der $R(x,y)$ eine Stammfunktion hat. -- cgit v1.2.1 From 50ecdafd467b0ec21be5b3bffce1d4c5acbb4fe6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 26 May 2022 08:36:59 +0200 Subject: add missing file --- buch/SeminarSpezielleFunktionen.tex | 7 +++++++ 1 file changed, 7 insertions(+) create mode 100644 buch/SeminarSpezielleFunktionen.tex diff --git a/buch/SeminarSpezielleFunktionen.tex b/buch/SeminarSpezielleFunktionen.tex new file mode 100644 index 0000000..4ee1900 --- /dev/null +++ b/buch/SeminarSpezielleFunktionen.tex @@ -0,0 +1,7 @@ +% +% buch.tex -- Buch zum mathematischen Seminar Spezielle Funktionen +% +% (c) 2022 Prof. Dr. Andreas Mueller, OST Ostschweizer Fachhochschule +% +\def\IncludeBookCover{1} +\input{common/content.tex} -- cgit v1.2.1 From 14b48dfeb636fe25b0745a2ab617cc5d307c06e6 Mon Sep 17 00:00:00 2001 From: runterer Date: Thu, 26 May 2022 20:38:30 +0200 Subject: =?UTF-8?q?tikz=20und=20eulerprodukt=20hinzugef=C3=BCgt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/zeta/analytic_continuation.tex | 23 ++++++- buch/papers/zeta/continuation_overview.tikz.tex | 7 +- buch/papers/zeta/euler_product.tex | 85 +++++++++++++++++++++++++ buch/papers/zeta/main.tex | 1 + buch/papers/zeta/zeta_gamma.tex | 7 +- 5 files changed, 114 insertions(+), 9 deletions(-) create mode 100644 buch/papers/zeta/euler_product.tex diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex index 5e09e42..408a1f7 100644 --- a/buch/papers/zeta/analytic_continuation.tex +++ b/buch/papers/zeta/analytic_continuation.tex @@ -1,7 +1,26 @@ \section{Analytische Fortsetzung} \label{zeta:section:analytische_fortsetzung} \rhead{Analytische Fortsetzung} -%TODO missing Text +Die analytische Fortsetzung der Riemannschen Zetafunktion ist äusserst interessant. +Sie ermöglicht die Berechnung von $\zeta(-1)$ und weiterer spannender Werte. +So liegen zum Beispiel unendlich viele Nullstellen der Zetafunktion bei $\Re(s) = 0.5$. +Diese sind relevant für die Primzahlverteilung und sind Gegenstand der Riemannschen Vermutung. + +Es werden zwei verschiedene Fortsetzungen benötigt. +Die erste erweitert die Zetafunktion auf $\Re(s) > 0$. +Die zweite verwendet eine Spiegelung an der $\Re(s) = 0.5$ Linie und erschliesst damit die ganze komplexe Ebene. +Eine grafische Darstellung dieses Plans ist in Abbildung \ref{zeta:fig:continuation_overview} zu sehen. +\begin{figure} + \centering + \input{papers/zeta/continuation_overview.tikz.tex} + \caption{ + Die verschiedenen Abschnitte der Riemannschen Zetafunktion. + Die originale Definition von \eqref{zeta:equation1} ist im grünen Bereich gültig. + Für den blauen Bereich gilt \eqref{zeta:equation:fortsetzung1}. + Um den roten Bereich zu bekommen verwendet die Funktionalgleichung \eqref{zeta:equation:functional} eine Spiegelung an $\Re(s) = 0.5$. + } + \label{zeta:fig:continuation_overview} +\end{figure} \subsection{Fortsetzung auf $\Re(s) > 0$} \label{zeta:subsection:auf_bereich_ge_0} Zuerst definieren die Dirichletsche Etafunktion als @@ -42,7 +61,7 @@ Durch Subtraktion der beiden Gleichungen \eqref{zeta:align1} minus \eqref{zeta:a &= \eta(s). \end{align} Dies ist die Fortsetzung auf den noch unbekannten Bereich $0 < \Re(s) < 1$ -\begin{equation} +\begin{equation} \label{zeta:equation:fortsetzung1} \zeta(s) := \left(1 - \frac{1}{2^{s-1}} \right)^{-1} \eta(s). diff --git a/buch/papers/zeta/continuation_overview.tikz.tex b/buch/papers/zeta/continuation_overview.tikz.tex index 03224ff..836ab1d 100644 --- a/buch/papers/zeta/continuation_overview.tikz.tex +++ b/buch/papers/zeta/continuation_overview.tikz.tex @@ -1,12 +1,13 @@ \begin{tikzpicture}[>=stealth', auto, node distance=0.9cm, scale=2, dot/.style={fill, circle, inner sep=0, minimum size=0.1cm}] - \draw[->] (-2,0) -- (-1,0) node[dot]{} node[anchor=north]{$-1$} -- (0,0) node[anchor=north west]{$0$} -- (1,0) node[anchor=north west]{$1$} -- (2,0) node[anchor=west]{Re$(s)$}; + \draw[->] (-2,0) -- (-1,0) node[dot]{} node[anchor=north]{$-1$} -- (0,0) node[anchor=north west]{$0$} -- (0.5,0) node[anchor=north west]{$0.5$}-- (1,0) node[anchor=north west]{$1$} -- (2,0) node[anchor=west]{$\Re(s)$}; - \draw[->] (0,-1.2) -- (0,1.2) node[anchor=south]{Im$(s)$}; + \draw[->] (0,-1.2) -- (0,1.2) node[anchor=south]{$\Im(s)$}; \begin{scope}[yscale=0.1] \draw[] (1,-1) -- (1,1); \end{scope} + \draw[dotted] (0.5,-1) -- (0.5,1); \begin{scope}[] \fill[opacity=0.2, red] (-1.8,1) rectangle (0, -1); @@ -14,4 +15,4 @@ \fill[opacity=0.2, green] (1,1) rectangle (1.8, -1); \end{scope} -\end{tikzpicture} \ No newline at end of file +\end{tikzpicture} diff --git a/buch/papers/zeta/euler_product.tex b/buch/papers/zeta/euler_product.tex new file mode 100644 index 0000000..a6ed512 --- /dev/null +++ b/buch/papers/zeta/euler_product.tex @@ -0,0 +1,85 @@ +\section{Eulerprodukt} \label{zeta:section:eulerprodukt} +\rhead{Eulerprodukt} + +Das Eulerprodukt stellt die Verbindung der Zetafunktion und der Primzahlen her. +Diese Verbindung ist sehr wichtig, da durch sie eine Aussage zur Primzahlverteilung gemacht werden kann. +Die Verteilung der Primzahlen ist Gegenstand der Riemannschen Vermutung, welche eines der grössten ungelösten Probleme der Mathematik ist. + +\begin{satz} + Für alle Zahlen $s$ mit $\Re(s) > 1$ ist die Zetafunktion identisch mit dem unendlichen Eulerprodukt + \begin{equation}\label{zeta:eq:eulerprodukt} + \zeta(s) + = + \sum_{n=1}^\infty + \frac{1}{n^s} + = + \prod_{p \in P} + \frac{1}{1-p^{-s}} + \end{equation} + wobei $P$ die Menge aller Primzahlen darstellt. +\end{satz} + +\begin{proof}[Beweis] + Der Beweis startet mit dem Eulerprodukt und stellt dieses so um, dass die Zetafunktion erscheint. + Als erstes ersetzen wir die Faktoren durch geometrische Reihen + \begin{equation} + \prod_{i=1}^{\infty} + \frac{1}{1-p^{-s}} + = + \prod_{p \in P} + \sum_{k_i=0}^{\infty} + \left( + \frac{1}{p_i^s} + \right)^{k_i} + = + \prod_{p \in P} + \sum_{k_i=0}^{\infty} + \frac{1}{p_i^{s k_i}}, + \end{equation} + dabei iteriert der Index $i$ über alle Primzahlen $p_i$. + Durch Ausschreiben der Multiplikation und Ausklammern der Summen erhalten wir + \begin{align} + \prod_{p \in P} + \sum_{k_i=0}^{\infty} + \frac{1}{p_i^{s k_i}} + &= + \sum_{k_1=0}^{\infty} + \frac{1}{p_1^{s k_1}} + \sum_{k_2=0}^{\infty} + \frac{1}{p_2^{s k_2}} + \ldots + \nonumber \\ + &= + \sum_{k_1=0}^{\infty} + \sum_{k_2=0}^{\infty} + \ldots + \left( + \frac{1}{p_1^{k_1}} + \frac{1}{p_2^{k_2}} + \ldots + \right)^s. + \label{zeta:equation:eulerprodukt2} + \end{align} + Der Fundamentalsatz der Arithmetik (Primfaktorzerlegung) besagt, dass jede beliebige Zahl $n \in \mathbb{N}$ durch eine eindeutige Primfaktorzerlegung beschrieben werden kann + \begin{equation} + n = \prod_i p_i^{k_i} \quad \forall \quad n \in \mathbb{N}. + \end{equation} + Jeder Summand der Summen in \eqref{zeta:equation:eulerprodukt2} ist somit eine Zahl $n$. + Da die Summen alle möglichen Kombinationen von Exponenten und Primzahlen in \eqref{zeta:equation:eulerprodukt2} enthält haben wir + \begin{equation} + \sum_{k_1=0}^{\infty} + \sum_{k_2=0}^{\infty} + \ldots + \left( + \frac{1}{p_1^{k_1}} + \frac{1}{p_2^{k_2}} + \ldots + \right)^s + = + \sum_{n=1}^\infty + \frac{1}{n^s} + = + \zeta(s) + \end{equation} +\end{proof} + diff --git a/buch/papers/zeta/main.tex b/buch/papers/zeta/main.tex index e0ea8e1..caddace 100644 --- a/buch/papers/zeta/main.tex +++ b/buch/papers/zeta/main.tex @@ -11,6 +11,7 @@ %TODO Einleitung \input{papers/zeta/einleitung.tex} +\input{papers/zeta/euler_product.tex} \input{papers/zeta/zeta_gamma.tex} \input{papers/zeta/analytic_continuation.tex} diff --git a/buch/papers/zeta/zeta_gamma.tex b/buch/papers/zeta/zeta_gamma.tex index 49fea74..db41676 100644 --- a/buch/papers/zeta/zeta_gamma.tex +++ b/buch/papers/zeta/zeta_gamma.tex @@ -2,9 +2,8 @@ \rhead{Zusammenhang mit der Gammafunktion} In diesem Abschnitt wird gezeigt, wie sich die Zetafunktion durch die Gammafunktion $\Gamma(s)$ ausdrücken lässt. -Dieser Zusammenhang der Art $\zeta(s) = f(\Gamma(s))$ wird später für die Herleitung der analytischen Fortsetzung gebraucht. +Dieser Zusammenhang der Art $\zeta(s) = f(\Gamma(s))$ ist nicht nur interessant, er wird später auch für die Herleitung der analytischen Fortsetzung gebraucht. -%TODO ref Gamma Wir erinnern uns an die Definition der Gammafunktion in \eqref{buch:rekursion:gamma:integralbeweis} \begin{equation*} \Gamma(s) @@ -51,12 +50,12 @@ Die Summe über $e^{-nu}$ können wir als geometrische Reihe schreiben und erhal &= \frac{1}{e^u - 1}. \end{align} -Wenn wir dieses Resultat einsetzen in \eqref{zeta:equation:zeta_gamma1} und durch $\Gamma(s)$ teilen, erhalten wir %TODO formulieren als Satz +Wenn wir dieses Resultat einsetzen in \eqref{zeta:equation:zeta_gamma1} und durch $\Gamma(s)$ teilen, erhalten wir den gewünschten Zusammenhang \begin{equation}\label{zeta:equation:zeta_gamma_final} \zeta(s) = \frac{1}{\Gamma(s)} \int_0^{\infty} \frac{u^{s-1}}{e^u -1} - du. + du \qed \end{equation} -- cgit v1.2.1 From 7459c95431d89576126a6a0007238592a4f5f033 Mon Sep 17 00:00:00 2001 From: runterer Date: Fri, 27 May 2022 20:10:13 +0200 Subject: Minor improvements --- buch/papers/zeta/analytic_continuation.tex | 26 ++++++++++++++------------ 1 file changed, 14 insertions(+), 12 deletions(-) diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex index 408a1f7..40424e0 100644 --- a/buch/papers/zeta/analytic_continuation.tex +++ b/buch/papers/zeta/analytic_continuation.tex @@ -14,7 +14,7 @@ Eine grafische Darstellung dieses Plans ist in Abbildung \ref{zeta:fig:continuat \centering \input{papers/zeta/continuation_overview.tikz.tex} \caption{ - Die verschiedenen Abschnitte der Riemannschen Zetafunktion. + Die verschiedenen Abschnitte der Riemannschen Zetafunktion. Die originale Definition von \eqref{zeta:equation1} ist im grünen Bereich gültig. Für den blauen Bereich gilt \eqref{zeta:equation:fortsetzung1}. Um den roten Bereich zu bekommen verwendet die Funktionalgleichung \eqref{zeta:equation:functional} eine Spiegelung an $\Re(s) = 0.5$. @@ -76,33 +76,35 @@ Wir beginnen damit, die Gammafunktion für den halben Funktionswert zu berechnen \int_0^{\infty} t^{\frac{s}{2}-1} e^{-t} dt. \end{equation} Nun substituieren wir $t$ mit $t = \pi n^2 x$ und $dt=\pi n^2 dx$ und erhalten -\begin{align} +\begin{equation} \Gamma \left( \frac{s}{2} \right) - &= + = \int_0^{\infty} (\pi n^2)^{\frac{s}{2}} x^{\frac{s}{2}-1} e^{-\pi n^2 x} - \,dx - && \text{Division durch } (\pi n^2)^{\frac{s}{2}} - \\ + \,dx. +\end{equation} +Analog zum Abschnitt \ref{zeta:section:zusammenhang_mit_gammafunktion} teilen wir durch $(\pi n^2)^{\frac{s}{2}}$ +\begin{equation} \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}} n^s} - &= + = \int_0^{\infty} x^{\frac{s}{2}-1} e^{-\pi n^2 x} - \,dx - && \text{Zeta durch Summenbildung } \sum_{n=1}^{\infty} - \\ + \,dx, +\end{equation} +und finden Zeta durch die Summenbildung $\sum_{n=1}^{\infty}$ +\begin{equation} \frac{\Gamma \left( \frac{s}{2} \right)}{\pi^{\frac{s}{2}}} \zeta(s) - &= + = \int_0^{\infty} x^{\frac{s}{2}-1} \sum_{n=1}^{\infty} e^{-\pi n^2 x} \,dx. \label{zeta:equation:integral1} -\end{align} +\end{equation} Die Summe kürzen wir ab als $\psi(x) = \sum_{n=1}^{\infty} e^{-\pi n^2 x}$. %TODO Wieso folgendes -> aus Fourier Signal Es gilt -- cgit v1.2.1 From 42a5955183a1bc0678158c61fd6189c39d305697 Mon Sep 17 00:00:00 2001 From: runterer Date: Fri, 27 May 2022 23:29:56 +0200 Subject: added poissonsche summenformel --- buch/papers/zeta/analytic_continuation.tex | 176 ++++++++++++++++++++++++++++- 1 file changed, 171 insertions(+), 5 deletions(-) diff --git a/buch/papers/zeta/analytic_continuation.tex b/buch/papers/zeta/analytic_continuation.tex index 40424e0..0ccc116 100644 --- a/buch/papers/zeta/analytic_continuation.tex +++ b/buch/papers/zeta/analytic_continuation.tex @@ -106,15 +106,65 @@ und finden Zeta durch die Summenbildung $\sum_{n=1}^{\infty}$ \,dx. \label{zeta:equation:integral1} \end{equation} Die Summe kürzen wir ab als $\psi(x) = \sum_{n=1}^{\infty} e^{-\pi n^2 x}$. -%TODO Wieso folgendes -> aus Fourier Signal -Es gilt +Im Abschnitt \ref{zeta:subsec:poisson_summation} wird die poissonsche Summenformel $\sum f(n) = \sum F(n)$ bewiesen. +In unserem Problem ist $f(n) = e^{-\pi n^2 x}$ und die zugehörige Fouriertransformation $F(n)$ ist +\begin{equation} + F(n) + = + \mathcal{F} + ( + e^{-\pi n^2 x} + ) + = + \frac{1}{\sqrt{x}} + e^{\frac{-n^2 \pi}{x}}. +\end{equation} +Dadurch ergibt sich \begin{equation}\label{zeta:equation:psi} - \psi(x) + \sum_{n=-\infty}^{\infty} + e^{-\pi n^2 x} = + \frac{1}{\sqrt{x}} + \sum_{n=-\infty}^{\infty} + e^{\frac{-n^2 \pi}{x}}, +\end{equation} +wobei wir die Summen so verändern müssen, dass sie bei $n=1$ beginnen und wir $\psi(x)$ erhalten als +\begin{align} + 2 + \sum_{n=1}^{\infty} + e^{-\pi n^2 x} + + + 1 + &= + \frac{1}{\sqrt{x}} + \left( + 2 + \sum_{n=1}^{\infty} + e^{\frac{-n^2 \pi}{x}} + + + 1 + \right) + \\ + 2 + \psi(x) + + + 1 + &= + \frac{1}{\sqrt{x}} + \left( + 2 + \psi\left(\frac{1}{x}\right) + + + 1 + \right) + \\ + \psi(x) + &= - \frac{1}{2} + \frac{\psi\left(\frac{1}{x} \right)}{\sqrt{x}} - + \frac{1}{2 \sqrt{x}}. -\end{equation} + + \frac{1}{2 \sqrt{x}}.\label{zeta:equation:psi} +\end{align} +Diese Gleichung wird später wichtig werden. Zunächst teilen wir nun das Integral aus \eqref{zeta:equation:integral1} auf als \begin{equation}\label{zeta:equation:integral2} @@ -309,3 +359,119 @@ Somit haben wir die analytische Fortsetzung gefunden als \zeta(1-s). \end{equation} %TODO Definitionen und Gleichungen klarer unterscheiden + +\subsection{Poissonsche Summenformel} \label{zeta:subsec:poisson_summation} + +Der Beweis für Gleichung \ref{zeta:equation:psi} folgt direkt durch die poissonsche Summenformel. +Um diese zu beweisen, berechnen wir zunächst die Fourierreihe der Dirac Delta Funktion. + +\begin{lemma} + Die Fourierreihe der periodischen Dirac Delta Funktion $\sum \delta(x - 2\pi k)$ ist + \begin{equation} \label{zeta:equation:fourier_dirac} + \sum_{k=-\infty}^{\infty} + \delta(x - 2\pi k) + = + \frac{1}{2\pi} + \sum_{n=-\infty}^{\infty} + e^{i n x}. + \end{equation} +\end{lemma} + +\begin{proof}[Beweis] + Eine Fourierreihe einer beliebigen periodischen Funktion $f(x)$ berechnet sich als + \begin{align} + f(x) + &= + \sum_{n=-\infty}^{\infty} + c_n + e^{i n x} \\ + c_n + &= + \frac{1}{2\pi} + \int_{-\pi}^{\pi} + f(x) + e^{-i n x} + \, dx. + \end{align} + Wenn $f(x)=\delta(x)$ eingesetz wird ergeben sich konstante Koeffizienten + \begin{equation} + c_n + = + \frac{1}{2\pi} + \int_{-\pi}^{\pi} + \delta(x) + e^{-i n x} + \, dx + = + \frac{1}{2\pi}, + \end{equation} + womit die sehr einfache Fourierreihe der Dirac Delta Funktion berechnet wäre. +\end{proof} + +\begin{satz}[Poissonsche Summernformel] + Die Summe einer Funktion $f(n)$ über alle ganzen Zahlen $n$ ist äquivalent zur Summe ihrer Fouriertransformation $F(k)$ über alle ganzen Zahlen $k$ + \begin{equation} + \sum_{n=-\infty}^{\infty} + f(n) + = + \sum_{k=-\infty}^{\infty} + F(k). + \end{equation} +\end{satz} + +\begin{proof}[Beweis] + Wir schreiben die Summe über die Fouriertransformation aus + \begin{align} + \sum_{k=-\infty}^{\infty} + F(k) + &= + \sum_{k=-\infty}^{\infty} + \int_{-\infty}^{\infty} + f(x) + e^{-i 2\pi x k} + \, dx + \\ + &= + \int_{-\infty}^{\infty} + f(x) + \underbrace{ + \sum_{k=-\infty}^{\infty} + e^{-i 2\pi x k} + }_{\text{\eqref{zeta:equation:fourier_dirac}}} + \, dx, + \end{align} + und verwenden die Fouriertransformation der Dirac Funktion aus \eqref{zeta:equation:fourier_dirac} + \begin{align} + \sum_{k=-\infty}^{\infty} + e^{-i 2\pi x k} + &= + 2 \pi + \sum_{k=-\infty}^{\infty} + \delta(-2\pi x - 2\pi k) + \\ + &= + \frac{2 \pi}{2 \pi} + \sum_{k=-\infty}^{\infty} + \delta(x + k). + \end{align} + Wenn wir dies einsetzen und erhalten wir den gesuchten Beweis für die poissonsche Summenformel + \begin{equation} + \sum_{k=-\infty}^{\infty} + F(k) + = + \int_{-\infty}^{\infty} + f(x) + \sum_{k=-\infty}^{\infty} + \delta(x + k) + \, dx + = + \sum_{k=-\infty}^{\infty} + \int_{-\infty}^{\infty} + f(x) + \delta(x + k) + \, dx + = + \sum_{k=-\infty}^{\infty} + f(k). + \end{equation} +\end{proof} -- cgit v1.2.1 From df8e535423f408f789f0cb624df7a4980572bc4d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 28 May 2022 14:57:18 +0200 Subject: more onm integration and lemniscate --- buch/chapters/060-integral/differentialkoerper.tex | 5 + buch/chapters/060-integral/diffke.tex | 106 ++++++++++- buch/chapters/060-integral/elementar.tex | 199 +++++++++++++++++++++ buch/chapters/060-integral/erweiterungen.tex | 98 +++++++++- buch/chapters/060-integral/logexp.tex | 20 ++- buch/chapters/060-integral/rational.tex | 27 ++- buch/chapters/060-integral/risch.tex | 12 ++ buch/chapters/110-elliptisch/lemniskate.tex | 24 ++- buch/chapters/references.bib | 7 + 9 files changed, 475 insertions(+), 23 deletions(-) diff --git a/buch/chapters/060-integral/differentialkoerper.tex b/buch/chapters/060-integral/differentialkoerper.tex index a071ae2..a112e33 100644 --- a/buch/chapters/060-integral/differentialkoerper.tex +++ b/buch/chapters/060-integral/differentialkoerper.tex @@ -15,6 +15,11 @@ Doch woher weiss man, dass es keine solche Funktion gibt, und was heisst überhaupt ``Stammfunktion in geschlossener Form''? In diesem Abschnitt wird daher ein algebraischer Rahmen entwickelt, in dem diese Frage sinnvoll gestellt werden kann. +Das ultimative Ziel, welches aber erst in +Abschnitt~\ref{buch:integral:section:risch} in Angriff genommen +wird, ist ein Computer-Algorithmus, der Integrale in geschlossener +Form findet oder beweist, dass dies für einen gegebenen Integranden +nicht möglich ist. \input{chapters/060-integral/rational.tex} \input{chapters/060-integral/erweiterungen.tex} diff --git a/buch/chapters/060-integral/diffke.tex b/buch/chapters/060-integral/diffke.tex index 02e90f6..61badc8 100644 --- a/buch/chapters/060-integral/diffke.tex +++ b/buch/chapters/060-integral/diffke.tex @@ -105,6 +105,94 @@ $ab\in C$. Die Menge $C$ heisst der {\em Konstantenkörper} von $\mathscr{F}$. \index{Konstantenkörper}% +% +% Ableitung algebraischer Elemente +% +\subsubsection{Ableitung und algebraische Körpererweiterungen} +Die Rechenregeln in einem Differentialkörper $\mathscr{F}$ legen auch die +Ableitung eines algebraischen Elements fest. +Sei $m(z)=m_0+m_1z+\ldots+m_{n-1}z^{n-1}+z^n$ das Minimalpolynom eines +über $\mathscr{F}$ algebraischen Elements $f$. +Aus $m(f)=0$ folgt durch Ableiten +\[ +0 += +m(f)' += +m_0' ++ +(m_1'f+m_1f') ++ +(m_2'f + m_12f'f) ++ +\ldots ++ +(m_{n-1}'f^{n-1} + m_{n-1} (n-1)f'f^{n-2}) ++ +nf'f^{n-1}. +\] +Zusammenfassen der Ableitung $f'$ auf der linken Seite liefert die +Gleichung +\[ +f'( +m_1+2m_2f+\ldots+(n-1)m_{n-1}f^{n-2}+nf^{n-1} +) += +m_0' + m_1'f + m_2'f^2 + \ldots + m_{n-1}'f^{n-1} + f^n, +\] +aus der +\[ +f' += +\frac{ +m_0' + m_1'f + m_2'f^2 + \ldots + m_{n-1}'f^{n-1} + f^n +}{ +m_1+2m_2f+\ldots+(n-1)m_{n-1}f^{n-2}+nf^{n-1} +} +\] +als Element von $\mathscr{F}(g)$ berechnet werden kann. +Die Ableitungsoperation lässt sich somit auf die Körpererweiterung +$\mathscr{F}(f)$ fortsetzen. + +\begin{beispiel} +Das über $\mathbb{Q}(x)$ algebraische Element $y=\sqrt{ax^2+bx+c}$ +hat das Minimalpolynom +\[ +m(z) += +z^2 - [ax^2+bx+c] +\in +\mathbb{Q}(x)[z] +\] +mit Koeffizienten $m_0 = ax^2+bx+c,$ $m_1=0$ und $m_2=1$. +Es hat die Ableitung +\[ +y' += +\frac{m_0'}{2m_2y} += +\frac{ +2ax+b +}{ +2y +} +\in +\mathbb{Q}(x,y) +\] +wegen $m_0'=2ax+b$. +\end{beispiel} + +\begin{definition} +Eine differentielle Körpererweiterung ist eine Körpererweiterung +$\mathscr{K}\subset\mathscr{F}$ von Differentialkörpern derart, dass +die Ableitungen $D_{\mathscr{K}}$ in $\mathscr{K}$ +und $D_{\mathscr{F}}$ in $\mathscr{F}$ übereinstimmen: +\( +D_{\mathscr{K}}g= D_{\mathscr{F}} g +\) +für alle $g\in\mathscr{K}$. +\end{definition} + % % Logarithmus und Exponantialfunktion % @@ -116,6 +204,7 @@ Sie zeichnen sich aber durch besondere Ableitungseigenschaften aus. Die Theorie der gewöhnlichen Differentialgleichungen garantiert, dass eine Funktion durch eine Differentialgleichung und Anfangsbedingungen festgelegt ist. +\label{buch:integral:expundlog} Für die Exponentialfunktion und der Logarithmus haben die Ableitungseigenschaften \[ @@ -128,10 +217,19 @@ x \log'(x) = 1. In der algebraischen Beschreibung eines Funktionenkörpers gibt es das Konzept des Wertes einer Funktion an einer bestimmten Stelle nicht. Somit können keine Anfangsbedingungen vorgegeben werden. -Da die Gleichungen linear sind, sind Vielfache einer Lösung wieder -Lösungen. -Insbesondere ist mit $\exp(x)$ auch $a\exp(x)$ eine Lösung und mit -$\log(x)$ auch $a\log(x)$ für alle Konstanten $a$. +Da die Gleichung für $\exp$ linear sind, sind Vielfache einer Lösung wieder +Lösungen, +insbesondere ist mit $\exp(x)$ auch $a\exp(x)$ eine Lösung. +Die Gleichung für $\log$ ist nicht linear, aber es ist +$\log'(x) = 1/x$, $\log$ ist eine Stammfunktion von $1/x$, die +nur bis auf eine Konstante bestimmt ist. +Tatsächlich gilt +\[ +x(\log(x)+a)' += +x\log(x) + xa' = x\log(x)=1, +\] +die Funktion $\log(x)+a$ ist also auch eine Lösung für den Logarithmus. Die Eigenschaft, dass die Exponentialfunktion die Umkehrfunktion des Logarithmus ist, lässt sich mit den Mitteln eines Differentialkörpers diff --git a/buch/chapters/060-integral/elementar.tex b/buch/chapters/060-integral/elementar.tex index 854a875..fd5f051 100644 --- a/buch/chapters/060-integral/elementar.tex +++ b/buch/chapters/060-integral/elementar.tex @@ -13,3 +13,202 @@ Die Stammfunktionen verwenden dieselben Funktionen oder höchstens Erweiterungen um Logarithmen von Funktionen, die man schon im Integranden gesehen hat. +% +% Exponentielle und logarithmische Funktione +% +\subsubsection{Exponentielle und logarithmische Funktionen} +In Abschnitt~\ref{buch:integral:subsection:diffke} haben wir +bereits die Exponentialfunktion $e^x$ und die Logarithmusfunktion +$\log x$ charakterisiert als eine Körpererweiterung durch +Elemente, die der Differentialgleichung +\[ +\exp' = \exp +\qquad\text{und}\qquad +\log' = \frac{1}{x} +\] +genügen. +Für die Stammfunktionen, die in +Abschnitt~\ref{buch:integral:subsection:logexp} +gefunden wurden, sind aber Logarithmusfunktionen nicht von +$x$ sondern von beliebigen über $\mathbb{Q}$ algebraischen Elementen +nötig. +Um zu verstehen, wie wir diese Funktion als Körpererweiterung erhalten +könnten, betrachten wir die Ableitung einer Exponentialfunktion +$\vartheta(x) = \exp(f(x))$ und eines +Logarithmus +$\psi(x) = \log(f(x))$, wie man sie mit der Kettenregel +berechnet hätte: +\begin{align*} +\vartheta'(x) +&=\exp(f(x)) \cdot f'(x) +& +\psi'(x) +&= +\frac{f'(x)}{f(x)} +\quad\Leftrightarrow\quad +f(x)\psi'(x) += +f'(x). +\end{align*} +Dies motiviert die folgende Definition + +\begin{definition} +\label{buch:integral:def:explog} +Sei $\mathscr{F}$ ein Differentialklörper und $f\in\mathscr{F}$. +Ein Exponentialfunktion von $f$ ist ein $\vartheta\in \mathscr{F}$mit +$\vartheta' = \vartheta f'$. +Ein Logarithmus von $f$ ist ein $\vartheta\in\mathscr{F}$ mit +$f\vartheta'=f'$. +\end{definition} + +Für $f=x$ mit $f'=1$ reduziert sich die +Definition~\ref{buch:integral:def:explog} +auf die Definition der Exponentialfunktion $\exp(x)$ und +Logarithmusfunktion $\log(x)$ auf Seite~\pageref{buch:integral:expundlog}. + + +% +% +% +\subsubsection{Transzendente Körpererweiterungen} +Die Wurzelfunktionen haben wir früher als algebraische Erweiterungen +eines Differentialkörpers erkannt. +Die logarithmischen und exponentiellen Elemente gemäss +Definition~\ref{buch:integral:def:explog} sind nicht algebraisch. + +\begin{definition} +\label{buch:integral:def:transzendent} +Sei $\mathscr{F}\subset\mathscr{G}$ eine Körpererweiterung und +$\vartheta\in\mathscr{G}$. +$\vartheta$ heisst {\em transzendent}, wenn $\vartheta$ nicht +algebraisch ist. +\end{definition} + +\begin{beispiel} +Die Funktion $f = e^x + e^{2x} + e^{x/2}$ ist sicher transzendent, +in diesem Beispiel zeigen wir, dass es mindestens drei verschiedene +Möglichkeiten gibt, eine Körpererweiterung von $\mathbb{Q}(x)$ zu +konstruieren, die $f$ enthält. + +Erste Möglichkeit: $f=\vartheta_1 + \vartheta_2 + \vartheta_3$ mit +$\vartheta_1=e^x$, +$\vartheta_2=e^{2x}$ +und +$\vartheta_3=e^{x/2}$. +Jedes der Elemente $\vartheta_i$ ist exponentiell über $\mathbb{Q}(x)$ und +$f$ ist in +\[ +\mathbb{Q}(x) +\subset +\mathbb{Q}(x,\vartheta_1) +\subset +\mathbb{Q}(x,\vartheta_1,\vartheta_2) +\subset +\mathbb{Q}(x,\vartheta_1,\vartheta_2,\vartheta_3) +\ni +f. +\] +Jede dieser Körpererweiterungen ist transzendent. + +Zweite Möglichkeit: $\vartheta_1=e^x$ ist exponentiell über +$\mathbb{Q}(x)$ und $\mathbb{Q}(x,\vartheta_1)$ enthält wegen +\[ +(\vartheta_1^2)' += +2\vartheta_1\vartheta_1' += +2\vartheta_1^2, +\] +somit ist $\vartheta_1^2=\vartheta_2$ eine Exponentialfunktion von $2x$ +über $\mathbb{Q}(x)$. +Das Element $\vartheta_3=e^{x/2}$ ist zwar auch exponentiell über +$\mathbb{Q}(x)$, es ist aber auch eine Nullstelle des Polynoms +$m(z)=z^2-[\vartheta_1]$. +Die Erweiterung +$\mathbb{Q}(x,\vartheta_1)\subset\mathbb{Q}(x,\vartheta_1,\vartheta_3)$ +ist eine algebraische Erweiterung, die +$f=\vartheta_1 + \vartheta_1^2+\vartheta_3$ enthält. + +Dritte Möglichkeit: $\vartheta_3=e^{x/2}$ ist exponentiell über +$\mathbb{Q}(x)$. +Die transzendente Körpererweiterung +\[ +\mathbb{Q}(x) \subset \mathbb{Q}(x,\vartheta_3) +\] +enthält das Element +$f=\vartheta_3^4+\vartheta_3^2 + \vartheta_3 $. +\end{beispiel} + +Das Beispiel zeigt, dass man nicht sagen kann, dass eine Funktion +ausschliesslich in einer algebraischen oder transzendenten Körpererweiterung +zu finden ist. +Vielmehr gibt es für die gleiche Funktion möglicherweise verschiedene +Körpererweiterungen, die alle die Funktion enthalten können. + +% +% Elementare Funktionen +% +\subsubsection{Elementare Funktionen} +Die Stammfunktionen~\eqref{buch:integration:risch:eqn:integralbeispiel2} +können aufgebaut werden, indem man dem Körper $\mathbb{Q}(x)$ schrittweise +sowohl algebraische wie auch transzendente Elemente hinzufügt, +wie in der folgenden Definition, die dies für abstrakte +Differentialkörpererweiterungen formuliert. + +\begin{definition} +Eine Körpererweiterung $\mathscr{F}\subset\mathscr{G}$ heisst +{\em transzendente elementare Erweiterung}, wenn +$\mathscr{G} = \mathscr{F}(\vartheta_1,\dots,\vartheta_n)$ und +jedes der Element $\vartheta_i$ transzendent und logarithmisch oder +exponentiell ist über +$\mathscr{F}_{i-1}=\mathscr{F}(\vartheta_1,\dots,\vartheta_{i-1})$. +Die Körpererweiterung $\mathscr{F}\subset\mathscr{G}$ heisst +{\em elementare Erweiterung}, wenn +$\mathscr{G} = \mathscr{F}(\vartheta_1,\dots,\vartheta_n)$ und +jedes Element $\vartheta_i$ ist entweder logarithmisch, exponentiell +oder algebraisch über $\mathscr{F}_{i-1}$. +\end{definition} + +Die Funktionen, die als akzeptable Stammfunktionen für das Integrationsproblem +in Betracht kommen, sind also jene, die in einer geeigneten elementaren +Erweiterung des von $\mathbb{Q}(x)$ liegen. +Ausserdem können auch noch weitere Konstanten nötig sein, sowohl +algebraische Zahlen wie auch Konstanten wie $\pi$ oder $e$. + +\begin{definition} +Sei $\mathscr{K}(x)$ der Differentialklörper der rationalen Funktionen +über dem Konstantenkörper $\mathscr{K}\supset\mathbb{Q}$, der in $\mathbb{C}$ +enthalten ist. +Ist $\mathscr{F}\supset \mathscr{K}(x)$ eine transzendente elementare +Erweiterung von $\mathscr{K}(x)$, dann heisst $\mathscr{F}$ +ein Körper von {\em transzendenten elementaren Funktionen}. +Ist $\mathscr{F}$ eine elementare Erweiterung von $\mathscr{K}(x)$, dann +heisst $\mathscr{F}$ ein Körper von {\em elementaren Funktionen}. +\end{definition} + +\subsubsection{Das Integrationsproblem} +Die elementaren Funktionen enthalten alle Funktionen, die sich mit +arithmetischen Operationen, Wurzeln, Exponentialfunktionen, Logarithmen und +damit auch mit trigonometrischen und hyperbolischen Funktionen und ihren +Umkehrfunktionen aus den rationalen Zahlen, der unabhängigen Variablen $x$ +und möglicherweise einigen zusätzlichen Konstanten aufbauen lassen. +Sei also $f$ eine Funktion in einem Körper von elementaren +Funktionen +\[ +\mathscr(F) += +\mathbb{Q}(\alpha_1,\dots,\alpha_l)(x,\vartheta_1,\dots,\vartheta_n). +\] +Eine elementare Stammfunktion ist eine Funktion $F=\int f$ in einer +elementaren Körpererweiterung +\[ +\mathscr{G} += +\mathbb{Q}(\alpha_1,\dots,\alpha_l,\dots,\alpha_{l+k}) +(x,\vartheta_1,\dots,\vartheta_n,\dots,\vartheta_{n+m}) +\] +mit $F'=f$. +Das Ziel ist, $F$ mit Hilfe eines Algorithmus zu bestimmen. + + + diff --git a/buch/chapters/060-integral/erweiterungen.tex b/buch/chapters/060-integral/erweiterungen.tex index a999ebb..9138f3e 100644 --- a/buch/chapters/060-integral/erweiterungen.tex +++ b/buch/chapters/060-integral/erweiterungen.tex @@ -97,8 +97,8 @@ a_i\in K \} \label{buch:integral:eqn:algelement} \end{equation} -mit $n=\deg m(x) - 1$ der durch Adjunktion von $\alpha$ erhaltene -Erweiterungsköper. +mit $n=\deg m(x) - 1$ der durch {\em Adjunktion} oder Hinzufügen +von $\alpha$ erhaltene Erweiterungsköper. \end{definition} Wieder muss nur überprüft werden, dass jedes Produkt oder jeder @@ -151,7 +151,9 @@ Die Menge $\mathbb{Q}(i)$ ist daher eine algebraische Körpererweiterung von $\mathbb{Q}$ bestehend aus den komplexen Zahlen mit rationalem Real- und Imaginärteil. +% % Transzendente Körpererweiterungen +% \subsubsection{Transzendente Erweiterungen} Nicht alle Zahlen in $\mathbb{R}$ sind algebraisch. Lindemann bewies 1882 einen allgemeinen Satz, aus dem folgt, @@ -201,7 +203,9 @@ $K\subset K(\alpha)$ ist zwar immer noch eine Körpererweiterung, aber $K(\alpha)$ ist nicht mehr ein endlichdimensionaler Vektorraum. Die Körpererweiterung $K\subset K(\alpha)$ heisst {\em transzendent}. +% % rationale Funktionen als Körpererweiterungen +% \subsubsection{Rationale Funktionen als Körpererweiterung} Die unabhängige Variable wird bei Rechnen so behandelt, dass die Potenzen alle linear unabhängig sind. @@ -209,7 +213,9 @@ Dies ist die Grundlage für den Koeffizientenvergleich. Der Körper der rationalen Funktion $K(x)$ ist also eine transzendente Körpererweiterung von $K$. +% % Erweiterungen mit algebraischen Funktionen +% \subsubsection{Algebraische Funktionen} Für das Integrationsproblem möchten wir nicht nur rationale Funktionen verwenden können, sondern auch Wurzelfunktionen. @@ -246,4 +252,92 @@ $y=\sqrt{ax^2+bx+c}$ zu $K(x,y)=K(x,\sqrt{ax^2+bx+c}$ erweitert. Wurzelfunktion werden daher nicht als Zusammensetzungen, sondern als algebraische Erweiterungen eines Funktionenkörpers betrachtet. +% +% Konjugation +% +\subsubsection{Konjugation} +Die komplexen Zahlen sind die algebraische Erweiterung der reellen Zahlen +um die Nullstelle $i$ des Polynoms $m(x)=x^2+1$. +Die Zahl $-i$ ist aber auch eine Nullstelle von $m(x)$, die mit algebraischen +Mitteln nicht von $i$ unterscheidbar ist. +Die komplexe Konjugation $a+bi\mapsto a-bi$ vertauscht die beiden +\index{Konjugation, komplexe}% +\index{komplexe Konjugation}% +Nullstellen des Minimalpolynoms. + +Ähnliches gilt für die Körpererweiterung $\mathbb{Q}(\!\sqrt{2})$. +$\sqrt{2}$ und $\sqrt{2}$ sind beide Nullstellen des Minimalpolynoms +$m(x)=x^2-2$, die mit algebraischen Mitteln nicht unterschiedbar sind. +Sie haben zwar verschiedene Vorzeichen, doch ohne eine Ordnungsrelation +können diese nicht unterschieden werden. +\index{Ordnungsrelation}% +Eine Ordnungsrelation zwischen rationalen Zahlen lässt sich zwar +definieren, aber die Zahl $\sqrt{2}$ ist nicht rational, es braucht +also eine zusätzliche Annahme, zum Beispiel die Identifikation von +$\sqrt{2}$ mit einer reellen Zahl in $\mathbb{R}$, wo der Vergleich +möglich ist. + +Auch in $\mathbb{Q}(\!\sqrt{2})$ ist die Konjugation +$a+b\sqrt{2}\mapsto a-b\sqrt{2}$ eine Selbstabbildung, die +die Körperoperationen respektiert. + +Das Polynom $m(x)=x^2-x-1$ hat die Nullstellen +\[ +\frac12 \pm\sqrt{\biggl(\frac12\biggr)^2+1} += +\frac{1\pm\sqrt{5}}{2} += +\left\{ +\bgroup +\renewcommand{\arraystretch}{2.20} +\renewcommand{\arraycolsep}{2pt} +\begin{array}{lcl} +\displaystyle +\frac{1+\sqrt{5}}{2} &=& \phantom{-}\varphi \\ +\displaystyle +\frac{1-\sqrt{5}}{2} &=& \displaystyle-\frac{1}{\varphi}. +\end{array} +\egroup +\right. +\] +Sie erfüllen die gleiche algebraische Relation $x^2=x+1$. +Sie sind sowohl im Vorzeichen wie auch im absoluten Betrag +verschieden, beides verlangt jedoch eine Ordnungsrelation als +Voraussetzung, die uns fehlt. +Aus beiden kann man mit rationalen Operationen $\sqrt{5}$ gewinnen, +denn +\[ +\sqrt{5} += +4\varphi-1 += +-4\biggl(-\frac{1}{\varphi}\biggr)^2-1 +\qquad\Rightarrow\qquad +\mathbb{Q}(\!\sqrt{5}) += +\mathbb{Q}(\varphi) += +\mathbb{Q}(-1/\varphi). +\] +Die Abbildung $a+b\varphi\mapsto a-b/\varphi$ ist eine Selbstabbildung +des Körpers $\mathbb{Q}(\!\sqrt{5})$, welche die beiden Nullstellen +vertauscht. + +Dieses Phänomen gilt für jede algebraische Erweiterung. +Die Nullstellen des Minimalpolynoms, welches die Erweiterung +definiert, sind grundsätzlich nicht unterscheidbar. +Mit der Adjunktion einer Nullstelle enthält der Erweiterungskörper +auch alle anderen. +Sind $\alpha_1$ und $\alpha_2$ zwei Nullstellen des Minimalpolynoms, +dann definiert die Abbildung $\alpha_1\mapsto\alpha_2$ eine Selbstabbildung, +die die Nullstellen permutiert. + +Die algebraische Körpererweiterung +$\mathbb{Q}(x)\subset \mathbb{Q}(x,\sqrt{ax^2+bx+c})$ +ist nicht unterscheidbar von +$\mathbb{Q}(x)\subset \mathbb{Q}(x,-\!\sqrt{ax^2+bx+c})$. +Für das Integrationsproblem bedeutet dies, dass alle Methoden so +formuliert werden müssen, dass die Wahl der Nullstellen auf die +Lösung keinen Einfluss haben. + diff --git a/buch/chapters/060-integral/logexp.tex b/buch/chapters/060-integral/logexp.tex index 2bfe0e1..e0efab2 100644 --- a/buch/chapters/060-integral/logexp.tex +++ b/buch/chapters/060-integral/logexp.tex @@ -3,7 +3,7 @@ % % (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue % -\subsection{Log-Exp-Notation für elementare Funktionen +\subsection{Log-Exp-Notation für trigonometrische und hyperbolische Funktionen \label{buch:integral:subsection:logexp}} Die Integration rationaler Funktionen hat bereits gezeigt, dass eine Stammfunktion nicht immer im Körper der rationalen Funktionen @@ -37,6 +37,7 @@ x \operatorname{arcosh} x - \sqrt{x^2-1}. In der Stammfunktion treten Funktionen auf, die auf den ersten Blick nichts mit den Funktionen im Integranden zu tun haben. +\subsubsection{Trigonometrische und hyperbolische Funktionen} Die trigonometrischen und hyperbolichen Funktionen in~\eqref{buch:integration:risch:allgform} lassen sich alle durch Exponentialfunktionen ausdrücken. @@ -53,7 +54,7 @@ So gilt &\qquad& \cosh x &= \frac12\bigl( e^x + e^{-x} \bigr). \end{aligned} -\label{buch:integral:risch:trighypinv} +\label{buch:integral:risch:trighyp} \end{equation} Nach Multiplikation mit $e^{ix}$ bzw.~$e^{x}$ entsteht eine quadratische Gleichung in $e^{ix}$ bzw.~$e^{x}$. @@ -66,27 +67,27 @@ Die Rechnung ergibt &= \frac{1}{i}\log\bigl( iy\pm\sqrt{1-y^2} -\bigr) +\bigr), & &\qquad& \arccos y &= \log\bigl( y\pm \sqrt{y^2-1} -\bigr) +\bigr), \\ \operatorname{arsinh}y &= \log\bigl( y \pm \sqrt{1+y^2} -\bigr) +\bigr), & &\qquad& \operatorname{arcosh} y &= \log\bigl( y\pm \sqrt{y^2-1} -\bigr) +\bigr). \end{aligned} \label{buch:integral:risch:trighypinv} \end{equation} @@ -97,6 +98,7 @@ Man nennt dies die $\log$-$\exp$-Notation der trigonometrischen und hyperbolischen Funktionen. \index{logexpnotation@$\log$-$\exp$-Notation}% +\subsubsection{$\log$-$\exp$-Notation} Wendet man die Substitutionen \eqref{buch:integral:risch:trighyp} und @@ -110,7 +112,7 @@ an, entstehen die Beziehungen &= \frac12i\bigl( \log(1-ix) - \log(1+ix) -\bigr) +\bigr), \\ \int\bigl( {\textstyle\frac12} @@ -121,12 +123,12 @@ e^{-ix} \bigr) &= -{\textstyle\frac12}ie^{ix} -+{\textstyle\frac12}ie^{-ix} ++{\textstyle\frac12}ie^{-ix}, \\ \int \frac{1}{\sqrt{1-x^2}} &= --i\log\bigl(ix+\sqrt{1-x^2}) +-i\log\bigl(ix+\sqrt{1-x^2}), \\ \int \log\bigl(x+\sqrt{x^2-1}\bigr) &= diff --git a/buch/chapters/060-integral/rational.tex b/buch/chapters/060-integral/rational.tex index 7b24e9f..0ca164d 100644 --- a/buch/chapters/060-integral/rational.tex +++ b/buch/chapters/060-integral/rational.tex @@ -132,7 +132,9 @@ ac + 2bd + (ad+bc)\sqrt{2} \in \mathbb{Q}(\!\sqrt{2}) \end{align*} \end{beispiel} - +% +% Rationale Funktionen +% \subsubsection{Rationalen Funktionen} Die als Antworten auf die Frage nach einer Stammfunktion akzeptablen Funktionen sollten alle rationalen Zahlen sowie die unabhängige @@ -174,5 +176,28 @@ zweier Brüche auch für Nenner funktioniert, die Polynome sind, und die Summe wzeier Brüche von Polynomen wieder in einen Bruch von Polynomen umwandelt. +% +% Warum rationale Zahlen? +% +\subsubsection{Warum die Beschränkung auf rationale Zahlen?} +Aus mathematischer Sicht gibt es gute Gründe, Analysis im Körper $\mathbb{R}$ +oder $\mathbb{C}$ zu betreiben. +Da Ableitung und Integral als Grenzwerte definiert sind, stellt diese +Wahl des Körpers sicher, dass die Grenzwerte auch tatsächlich existieren. +Der Fundamentalsatz der Algebra garantiert, dass über $\mathbb{C}$ +jedes Polynome in Linearfaktoren zerlegt werden kann. + +Der Einfachheit der Analyse in $\mathbb{R}$ oder $\mathbb{C}$ steht +die Schwierigkeit gegenüber, beliebige Elemente von $\mathbb{R}$ in +einem Computer exakt darzustellen. +Für Brüche in $\mathbb{Q}$ gibt es eine solche Darstellung durch +Paare von Ganzzahlen, wie sie die GNU Multiprecision Arithmetic Library +\cite{buch:gmp} realisiert. +Irrationale Zahlen dagegen können nur exakt gehandhabt werden, wenn +man im wesentlichen symbolisch mit ihnen rechnet. +Die Grundlage dafür wird in +Abschnitt~\ref{buch:integral:subsection:koerpererweiterungen} +gelegt. + diff --git a/buch/chapters/060-integral/risch.tex b/buch/chapters/060-integral/risch.tex index 1ba746a..2080ce8 100644 --- a/buch/chapters/060-integral/risch.tex +++ b/buch/chapters/060-integral/risch.tex @@ -6,6 +6,18 @@ \section{Der Risch-Algorithmus \label{buch:integral:section:risch}} \rhead{Risch-Algorithmus} +Die Lösung des Integrationsproblem für $\mathbb{Q}(x)$ und für +$\mathbb{Q}(x,y)$ mit $y=\!\sqrt{ax^2+bx+c}$ hat gezeigt, dass +ein Differentialkörper genau die richtige Bühne für dieses Unterfangen +sein dürfte. +Die Stammfunktionen konnten in einem Erweiterungskörper gefunden +werden, der ein paar Logarithmen hinzugefügt worden sind. +Tatsächlich lässt sich in diesem Rahmen sogar ein Algorithmus +formulieren, der in einem noch zu definierenden Sinn ``elementare'' +Funktionen als Stammfunktionen finden kann oder beweisen kann, dass +eine solche nicht existiert. +Dieser Abschnitt soll einen Überblick darüber geben. + \input{chapters/060-integral/logexp.tex} \input{chapters/060-integral/elementar.tex} diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index 0df27a7..f750a82 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -20,7 +20,9 @@ elliptischen Funktionen hergestellt werden. \caption{Bogenlänge und Radius der Lemniskate von Bernoulli. \label{buch:elliptisch:fig:lemniskate}} \end{figure} -Die Lemniskate von Bernoulli ist die Kurve vierten Grades mit der Gleichung +Die {\em Lemniskate von Bernoulli} ist die Kurve vierten Grades +mit der Gleichung +\index{Lemniskate von Bernoulli}% \begin{equation} (X^2+Y^2)^2 = 2a^2(X^2-Y^2). \label{buch:elliptisch:eqn:lemniskate} @@ -161,13 +163,14 @@ Parameters $k$. Die Länge des rechten Blattes der Lemniskate wird mit $\varpi$ bezeichnet und hat den numerischen Wert -\[ +\begin{equation} \varpi = 2\int_0^1\sqrt{\frac{1}{1-t^4}}\,dt = 2.6220575542. -\] +\label{buch:elliptisch:eqn:varpi} +\end{equation} $\varpi$ ist auch als die {\em lemniskatische Konstante} bekannt. \index{lemniskatische Konstante}% Der Lemniskatenbogen zwischen dem Nullpunkt und $(1,0)$ hat die Länge @@ -179,7 +182,7 @@ $\varpi/2$. \subsection{Bogenlängenparametrisierung} Die Lemniskate mit der Gleichung \[ -(X^2+X^2)^2=2(X^2-X^2) +(X^2+Y^2)^2=2(X^2-Y^2) \] (der Fall $a=1$ in \eqref{buch:elliptisch:eqn:lemniskate}) kann mit Jacobischen elliptischen Funktionen @@ -332,7 +335,8 @@ Dies bedeutet, dass die Bogenlänge zwischen den Parameterwerten $0$ und $s$ = s, \] -der Parameter $t$ ist also ein Bogenlängenparameter. +der Parameter $t$ ist also ein Bogenlängenparameter, man darf also +$s=t$ schreiben. Die mit dem Faktor $1/\sqrt{2}$ skalierte Standard-Lemniskate mit der Gleichung @@ -355,10 +359,9 @@ y(t) \end{equation} \subsection{Der lemniskatische Sinus und Kosinus} -Der Sinus Berechnet die Gegenkathete zu einer gegebenen Bogenlänge des +Der Sinus berechnet die Gegenkathete zu einer gegebenen Bogenlänge des Kreises, er ist die Umkehrfunktion der Funktion, die der Gegenkathete die Bogenlänge zuordnet. - Daher ist es naheliegend, die Umkehrfunktion von $s(r)$ in \eqref{buch:elliptisch:eqn:lemniskatebogenlaenge} den {\em lemniskatischen Sinus} zu nennen mit der Bezeichnung @@ -368,6 +371,13 @@ Der Kosinus ist der Sinus des komplementären Winkels. Auch für die lemniskatische Bogenlänge $s(r)$ lässt sich eine komplementäre Bogenlänge definieren, nämlich die Bogenlänge zwischen dem Punkt $(x(r), y(r))$ und $(1,0)$. +Da die Bogenlänge zwischen $(0,0)$ und $(1,0)$ in +in \eqref{buch:elliptisch:eqn:varpi} bereits bereichnet wurde. +ist sie $\varpi/2-s$. +Der {\em lemniskatische Kosinus} ist daher +$\operatorname{cl}(s) = \operatorname{sl}(\varpi/2-s)$ +Graphen des lemniskatische Sinus und Kosinus sind in +Abbildung~\label{buch:elliptisch:figure:slcl} dargestellt. Da die Parametrisierung~\eqref{buch:elliptisch:lemniskate:bogenlaenge} eine Bogenlängenparametrisierung ist, darf man $t=s$ schreiben. diff --git a/buch/chapters/references.bib b/buch/chapters/references.bib index 17ef273..32a86ec 100644 --- a/buch/chapters/references.bib +++ b/buch/chapters/references.bib @@ -111,3 +111,10 @@ publisher = { Addison-Wesley } } +@online{buch:gmp, + title = {GNU Multiprecision Arithmetic Library}, + DAY = 26, + MONTH = 5, + YEAR = 2022, + url = {https://de.wikipedia.org/wiki/GNU_Multiple_Precision_Arithmetic_Library} +} -- cgit v1.2.1 From 161adb15af8d10ccf6090a43a4c89b0d05c6ecda Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Sat, 28 May 2022 16:16:52 +0200 Subject: Add introduction, integrand plot and reason why shifting evalutaion of gamma-func --- buch/papers/laguerre/definition.tex | 22 +- buch/papers/laguerre/eigenschaften.tex | 42 +- buch/papers/laguerre/gamma.tex | 21 +- buch/papers/laguerre/images/integrands.pgf | 2907 ++++++++++++++++++++ buch/papers/laguerre/images/integrands_exp.pgf | 2035 ++++++++++++++ buch/papers/laguerre/images/laguerre_polynomes.pdf | Bin 16239 -> 0 bytes buch/papers/laguerre/images/laguerre_polynomes.pgf | 1838 +++++++++++++ buch/papers/laguerre/main.tex | 16 +- buch/papers/laguerre/quadratur.tex | 2 +- buch/papers/laguerre/scripts/gamma_approx.ipynb | 98 +- buch/papers/laguerre/scripts/integrand.py | 24 +- buch/papers/laguerre/scripts/laguerre_plot.py | 5 +- 12 files changed, 6955 insertions(+), 55 deletions(-) create mode 100644 buch/papers/laguerre/images/integrands.pgf create mode 100644 buch/papers/laguerre/images/integrands_exp.pgf delete mode 100644 buch/papers/laguerre/images/laguerre_polynomes.pdf create mode 100644 buch/papers/laguerre/images/laguerre_polynomes.pgf diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index d111f6f..f1f0d00 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -118,6 +118,17 @@ L_n^\nu(x) \sum_{k=0}^{n} \frac{(-1)^k}{(\nu + 1)_k} \binom{n}{k} x^k. \label{laguerre:allg_polynom} \end{align} +Die Laguerre-Polynome von Grad $0$ bis $7$ sind in +Abbildung~\ref{laguerre:fig:polyeval} dargestellt. +\begin{figure} +\centering +\scalebox{0.8}{\input{papers/laguerre/images/laguerre_polynomes.pgf}} +% \includegraphics[width=0.7\textwidth]{% +% papers/laguerre/images/laguerre_polynomes.eps% +% } +\caption{Laguerre-Polynome vom Grad $0$ bis $7$} +\label{laguerre:fig:polyeval} +\end{figure} \subsection{Analytische Fortsetzung} Durch die analytische Fortsetzung erhalten wir zudem noch die zweite Lösung der @@ -142,16 +153,5 @@ L_n(x) \ln(x) \end{align*} wobei $\alpha_0 = 0$ und $\alpha_k =\sum_{i=1}^k i^{-1}$, $\forall k \in \mathbb{N}$. -Die Laguerre-Polynome von Grad $0$ bis $7$ sind in -Abbildung~\ref{laguerre:fig:polyeval} dargestellt. -\begin{figure} -\centering -\includegraphics[width=0.7\textwidth]{% - papers/laguerre/images/laguerre_polynomes.pdf% -} -\caption{Laguerre-Polynome vom Grad $0$ bis $7$} -\label{laguerre:fig:polyeval} -\end{figure} - % https://www.math.kit.edu/iana1/lehre/hm3phys2012w/media/laguerre.pdf % http://www.physics.okayama-u.ac.jp/jeschke_homepage/E4/kapitel4.pdf diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 93d19a3..77b2a2c 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -3,20 +3,22 @@ % % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % -\section{Eigenschaften - \label{laguerre:section:eigenschaften}} -{ -\large \color{red} -TODO: -Evtl. nur Orthogonalität hier behandeln, da nur diese für die Gauss-Quadratur -benötigt wird. -} +% \section{Eigenschaften +% \label{laguerre:section:eigenschaften}} +% { +% \large \color{red} +% TODO: +% Evtl. nur Orthogonalität hier behandeln, da nur diese für die Gauss-Quadratur +% benötigt wird. +% } -Die Laguerre-Polynome besitzen einige interessante Eigenschaften -\rhead{Eigenschaften} +% Die Laguerre-Polynome besitzen einige interessante Eigenschaften +% \rhead{Eigenschaften} -\subsection{Orthogonalität - \label{laguerre:subsection:orthogonal}} +% \subsection{Orthogonalität +% \label{laguerre:subsection:orthogonal}} +\section{Orthogonalität + \label{laguerre:section:orthogonal}} Im Abschnitt~\ref{laguerre:section:definition} haben wir behauptet, dass die Laguerre-Polynome orthogonale Polynome sind. Zu dieser Behauptung möchten wir nun einen Beweis liefern. @@ -113,14 +115,14 @@ Für den rechten Rand ist die Bedingung (Gleichung~\eqref{laguerre:sllag_randb}) 0 \end{align*} für beliebige Polynomlösungen erfüllt für $k_\infty=0$ und $h_\infty=1$. -Damit können wir schlussfolgern, dass die Laguerre-Polynome orthogonal -bezüglich des Skalarproduktes auf dem Intervall $(0, \infty)$ mit der Laguerre\--Gewichtsfunktion -$w(x)=x^\nu e^{-x}$ sind. +Damit können wir schlussfolgern, dass die verallgemeinerten Laguerre-Polynome +orthogonal bezüglich des Skalarproduktes auf dem Intervall $(0, \infty)$ +mit der verallgemeinerten Laguerre\--Gewichtsfunktion $w(x)=x^\nu e^{-x}$ sind. +Die Laguerre-Polynome ($\nu=0$) sind somit orthognal im Intervall $(0, \infty)$ +mit der Gewichtsfunktion $w(x)=e^{-x}$. +% \subsection{Rodrigues-Formel} -\subsection{Rodrigues-Formel} - -\subsection{Drei-Terme Rekursion} - -\subsection{Beziehung mit der Hypergeometrischen Funktion} +% \subsection{Drei-Terme Rekursion} +% \subsection{Beziehung mit der Hypergeometrischen Funktion} diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index b15523b..59c0b81 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -26,8 +26,10 @@ Integral der Form , \label{laguerre:gamma} \end{align} -welches alle Eigenschaften erfüllt, um mit der Gauss-Laguerre-Quadratur -berechnet zu werden. +Der Term $e^{-t}$ ist genau die Gewichtsfunktion der Laguerre-Integration und +der Definitionsbereich passt ebenfalls genau für dieses Verfahren. +Zu erwähnen ist auch, dass für die verallgemeinerte Laguerre-Integration die +Gewichtsfunktion $t^\nu e^{-t}$ genau dem Integranden für $\nu=z-1$ entspricht. \subsubsection{Funktionalgleichung} Die Funktionalgleichung der Gamma-Funktion besagt @@ -39,6 +41,19 @@ Mittels dieser Gleichung kann der Wert von $\Gamma(z)$ an einer bestimmten, geeigneten Stelle evaluiert werden und dann zurückverschoben werden, um das gewünschte Resultat zu erhalten. +In Abbildung~\ref{laguerre:fig:integrand} ist der Integrand $t^z$ für +unterschiedliche Werte von $z$ dargestellt. +Man erkennt, dass für kleine $z$ sich ein singulärer Integrand ergibt, +was dazu führt, dass die Genauigkeit sich verschlechtert. +Die Genauigkeit verschlechtert sich aber auch zunehmends für grosse $z$, +da in diesem Fall der Integrand sehr schnell anwächst. +\begin{figure} +\centering +\scalebox{0.8}{\input{papers/laguerre/images/integrands.pgf}} +\caption{Integrand $t^z$ mit unterschiedlichen Werten für $z$} +\label{laguerre:fig:integrand} +\end{figure} + \subsection{Berechnung mittels Gauss-Laguerre-Quadratur} Fehlerterm: @@ -52,7 +67,7 @@ R_n Nun stellt sich die Frage, ob die Approximation mittels Gauss-Laguerre-Quadratur verbessert werden kann, wenn man das Problem an einer geeigneten Stelle evaluiert und -dann zurückverschiebt mit der Funktionalgleichung. +dann mit der Funktionalgleichung zurückverschiebt. Dazu wollen wir den Fehlerterm in Gleichung~\eqref{laguerre:lagurre:lag_error} anpassen und dann minimieren. Zunächst wollen wir dies nur für $z\in \mathbb{R}$ und $0.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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b/buch/papers/laguerre/images/integrands_exp.pgf @@ -0,0 +1,2035 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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+für das Integral $\int_0^\infty exp(-x)\, dx$ suchte. +Darum möchten wir in diesem Kapitel uns, +ganz im Sinne des Entdeckers, +den Laguerre-Polynomen für Approximationen von Integralen mit +exponentiell-abfallenden Funktionen widmen. +Namentlich werden wir versuchen, +eine geeignete Approximation für die Gamma-Funktion zu finden +mittels Laguerre-Polynomen und der Gauss-Quadratur. + +Laguerre-Polynome tauchen zudem auch in der Quantenmechanik im radialen Anteil +der Lösung für die Schrödinger-Gleichung eines Wasserstoffatoms auf. \input{papers/laguerre/definition} \input{papers/laguerre/eigenschaften} diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index be69dee..f4e2955 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -21,7 +21,7 @@ In unserem Falle möchten wir die Gauss Quadratur auf die Laguerre-Polynome $L_n$ ausweiten. Diese sind orthogonal im Intervall $(0, \infty)$ bezüglich der Gewichtsfunktion $e^{-x}$. -Gleichung~\eqref{laguerre:laguerrequadratur} lässt sich wiefolgt umformulieren: +Gleichung~\eqref{laguerre:laguerrequadratur} lässt sich wie folgt umformulieren: \begin{align} \int_{0}^{\infty} f(x) e^{-x} dx \approx diff --git a/buch/papers/laguerre/scripts/gamma_approx.ipynb b/buch/papers/laguerre/scripts/gamma_approx.ipynb index 44f3abd..337b307 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.ipynb +++ b/buch/papers/laguerre/scripts/gamma_approx.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 112, "metadata": {}, "outputs": [], "source": [ @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 113, "metadata": {}, "outputs": [], "source": [ @@ -86,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 114, "metadata": {}, "outputs": [], "source": [ @@ -150,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 115, "metadata": {}, "outputs": [], "source": [ @@ -203,9 +203,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 116, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "zeros, weights = np.polynomial.laguerre.laggauss(12)\n", "targets = np.arange(16, 21)\n", @@ -241,9 +254,44 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 117, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "(-7.5, 25.0)" + ] + }, + "execution_count": 117, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "z = 0.5\n", "ns = [4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12] # np.arange(4, 13)\n", diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py index 89b9256..43fc1bf 100644 --- a/buch/papers/laguerre/scripts/integrand.py +++ b/buch/papers/laguerre/scripts/integrand.py @@ -16,19 +16,33 @@ img_path = f"{root}/../images" os.makedirs(img_path, exist_ok=True) t = np.logspace(*xlims, 1001)[:, None] -z = np.arange(-5, 5)[None] + 0.5 - +z = np.array([-4.5, -2, -1, -0.5, 0.0, 0.5, 1, 2, 4.5]) r = t ** z fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) ax.semilogx(t, r) -ax.set_xlim(*(10.**xlims)) +ax.set_xlim(*(10.0 ** xlims)) ax.set_ylim(1e-3, 40) ax.set_xlabel(r"$t$") ax.set_ylabel(r"$t^z$") ax.grid(1, "both") labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z)] ax.legend(labels, ncol=2, loc="upper left") -fig.savefig(f"{img_path}/integrands.pdf") -# plt.show() +fig.savefig(f"{img_path}/integrands.pgf") + +z2 = np.array([-1, -0.5, 0.0, 0.5, 1, 2, 3, 4, 4.5]) +r2 = t**z2 * np.exp(-t) + +fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(6, 4)) +ax2.semilogx(t, r2) +# ax2.plot(t,np.exp(-t)) +ax2.set_xlim(10**(-2), 20) +ax2.set_ylim(1e-3, 10) +ax2.set_xlabel(r"$t$") +ax2.set_ylabel(r"$t^z e^{-t}$") +ax2.grid(1, "both") +labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z2)] +ax2.legend(labels, ncol=2, loc="upper left") +fig2.savefig(f"{img_path}/integrands_exp.pgf") +plt.show() diff --git a/buch/papers/laguerre/scripts/laguerre_plot.py b/buch/papers/laguerre/scripts/laguerre_plot.py index b9088d0..1be3552 100644 --- a/buch/papers/laguerre/scripts/laguerre_plot.py +++ b/buch/papers/laguerre/scripts/laguerre_plot.py @@ -29,7 +29,7 @@ fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4 for n in np.arange(0, 8): k = np.arange(0, n + 1)[None] L = np.sum((-1) ** k * ss.binom(n, k) / ss.factorial(k) * t ** k, -1) - ax.plot(t, L, label=f"n={n}") + ax.plot(t, L, label=f"$n={n}$") ax.set_xticks(get_ticks(int(t[0]), t[-1]), minor=True) ax.set_xticks(get_ticks(0, t[-1], step)) @@ -97,4 +97,5 @@ ax.arrow( clip_on=False, ) -fig.savefig(f"{img_path}/laguerre_polynomes.pdf") +fig.savefig(f"{img_path}/laguerre_polynomes.pgf") +# plt.show() -- cgit v1.2.1 From 2fad6877aa1883714a060e1204e6d4d3566541d9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 28 May 2022 19:02:25 +0200 Subject: add example --- buch/papers/nav/beispiel.txt | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 buch/papers/nav/beispiel.txt diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt new file mode 100644 index 0000000..c63525b --- /dev/null +++ b/buch/papers/nav/beispiel.txt @@ -0,0 +1,24 @@ +Datum: 28. 5. 2022 +Zeit: 15:29:49 UTC +Sternzeit: 7h 54m 26.593s + +Deneb + +RA 20h 42m 12.14s 10.703372h +DEC 45 21' 40.3" 45.361194 + +H 50g 15' 17.1" 50.254750h +Azi 59g 36' 02.0" 59.600555 + +Spica + +RA 13h 26m 23.44s 13.439844h +DEC -11g 16' 46.8" 11.279666 + +H 18g 27' 30.0" 18.458333 +Azi 240g 23' 52.5" 240.397916 + +Position: + +l = 140.228920 E +b = 35.734946 N -- cgit v1.2.1 From 082afe0e8250519008c73b947922be22afda3fd5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 28 May 2022 19:14:50 +0200 Subject: beispiel korrektur --- buch/papers/nav/beispiel.txt | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt index c63525b..853ae4e 100644 --- a/buch/papers/nav/beispiel.txt +++ b/buch/papers/nav/beispiel.txt @@ -20,5 +20,5 @@ Azi 240g 23' 52.5" 240.397916 Position: -l = 140.228920 E -b = 35.734946 N +l = 140 14' 00.01" E 140.233336 E +b = 35 43' 00.02" N 35.716672 N -- cgit v1.2.1 From f4e1f6e84837c77dd49e6ec055efb1b110f7d573 Mon Sep 17 00:00:00 2001 From: Nicolas Tobler Date: Mon, 30 May 2022 00:05:03 +0200 Subject: Added content, presentation --- buch/papers/ellfilter/main.tex | 316 ++++-- buch/papers/ellfilter/packages.tex | 18 +- .../papers/ellfilter/presentation/presentation.tex | 413 +++++++ buch/papers/ellfilter/python/F_N_butterworth.pgf | 1083 ++++++++++++++++++ buch/papers/ellfilter/python/F_N_chebychev.pgf | 1066 ++++++++++++++++++ buch/papers/ellfilter/python/F_N_chebychev2.pgf | 1023 +++++++++++++++++ buch/papers/ellfilter/python/F_N_elliptic.pgf | 847 ++++++++++++++ buch/papers/ellfilter/python/chebychef.py | 7 +- buch/papers/ellfilter/python/elliptic.pgf | 709 ++++++++++++ buch/papers/ellfilter/python/elliptic.py | 162 +-- buch/papers/ellfilter/python/elliptic2.py | 85 +- buch/papers/ellfilter/python/k.pgf | 1157 ++++++++++++++++++++ buch/papers/ellfilter/python/plot_params.py | 9 + buch/papers/ellfilter/references.bib | 9 + buch/papers/ellfilter/tikz/arccos.tikz.tex | 101 +- buch/papers/ellfilter/tikz/arccos2.tikz.tex | 7 +- buch/papers/ellfilter/tikz/cd.tikz.tex | 87 ++ buch/papers/ellfilter/tikz/cd2.tikz.tex | 84 ++ .../ellfilter/tikz/fundamental_rectangle.tikz.tex | 26 + buch/papers/ellfilter/tikz/sn.tikz.tex | 86 ++ 20 files changed, 7056 insertions(+), 239 deletions(-) create mode 100644 buch/papers/ellfilter/presentation/presentation.tex create mode 100644 buch/papers/ellfilter/python/F_N_butterworth.pgf create mode 100644 buch/papers/ellfilter/python/F_N_chebychev.pgf create mode 100644 buch/papers/ellfilter/python/F_N_chebychev2.pgf create mode 100644 buch/papers/ellfilter/python/F_N_elliptic.pgf create mode 100644 buch/papers/ellfilter/python/elliptic.pgf create mode 100644 buch/papers/ellfilter/python/k.pgf create mode 100644 buch/papers/ellfilter/python/plot_params.py create mode 100644 buch/papers/ellfilter/tikz/cd.tikz.tex create mode 100644 buch/papers/ellfilter/tikz/cd2.tikz.tex create mode 100644 buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex create mode 100644 buch/papers/ellfilter/tikz/sn.tikz.tex diff --git a/buch/papers/ellfilter/main.tex b/buch/papers/ellfilter/main.tex index 29ebf7a..e9d6aba 100644 --- a/buch/papers/ellfilter/main.tex +++ b/buch/papers/ellfilter/main.tex @@ -11,16 +11,15 @@ \section{Einleitung} -Lineare filter +% Lineare filter -Filter, Signalverarbeitung +% Filter, Signalverarbeitung Der womöglich wichtigste Filtertyp ist das Tiefpassfilter. Dieses soll im Durchlassbereich unter der Grenzfrequenz $\Omega_p$ unverstärkt durchlassen und alle anderen Frequenzen vollständig auslöschen. -Bei der Implementierung von Filtern - +% Bei der Implementierung von Filtern In der Elektrotechnik führen Schaltungen mit linearen Bauelementen wie Kondensatoren, Spulen und Widerständen immer zu linearen zeitinvarianten Systemen (LTI-System von englich \textit{time-invariant system}). Die Übertragungsfunktion im Frequenzbereich $|H(\Omega)|$ eines solchen Systems ist dabei immer eine rationale Funktion, also eine Division von zwei Polynomen. @@ -39,15 +38,12 @@ Damit das Filter implementierbar und stabil ist, muss $H(\Omega)^2$ eine rationa $N \in \mathbb{N} $ gibt dabei die Ordnung des Filters vor, also die maximale Anzahl Pole oder Nullstellen. -% In \eqref{ellfilter:eq:h_omega} wird $F_N(w)$ so verzogen, dass $F_N(w) \forall |w| < 1$ - - Damit ein Filter die Passband Kondition erfüllt muss $|F_N(w)| \leq 1 \forall |w| \leq 1$ und für $|w| \geq 1$ sollte die Funktion möglichst schnell divergieren. Eine einfaches Polynom, dass das erfüllt, erhalten wir wenn $F_N(w) = w^N$. Tatsächlich erhalten wir damit das Butterworth Filter, wie in Abbildung \ref{ellfilter:fig:butterworth} ersichtlich. \begin{figure} \centering - \includegraphics[scale=1]{papers/ellfilter/python/F_N_butterworth.pdf} + \input{papers/ellfilter/python/F_N_butterworth.pgf} \caption{$F_N$ für Butterworth filter. Der grüne Bereich definiert die erlaubten Werte für alle $F_N$-Funktionen.} \label{ellfilter:fig:butterworth} \end{figure} @@ -60,7 +56,7 @@ wenn $F_N(w)$ eine rationale Funktion ist, ist auch $H(\Omega)$ eine rationale F w^N & \text{Butterworth} \\ T_N(w) & \text{Tschebyscheff, Typ 1} \\ [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\ - R_N(w) & \text{Elliptisch (Cauer)} \\ + R_N(w, \xi) & \text{Elliptisch (Cauer)} \\ \end{cases} \end{align} @@ -73,9 +69,9 @@ Es scheint so als sind gewisse Eigenschaften dieser speziellen Funktionen verant \section{Tschebyscheff-Filter} Als Einstieg betrachent Wir das Tschebyscheff-Filter, welches sehr verwand ist mit dem elliptischen Filter. -Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Fitler ein Spezialfall davon. +Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Filter Spezialfälle davon. -Der Name des Filters deutet schon an, dass die Tschebyschff-Polynome $T_N$ relevant sind für das Filter: +Der Name des Filters deutet schon an, dass die Tschebyscheff-Polynome $T_N$ für das Filter relevant sind: \begin{align} T_{0}(x)&=1\\ T_{1}(x)&=x\\ @@ -83,15 +79,17 @@ Der Name des Filters deutet schon an, dass die Tschebyschff-Polynome $T_N$ relev T_{3}(x)&=4x^{3}-3x\\ T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x). \end{align} -Bemerkenswert ist, dass die Polynome im Intervall $[-1, 1]$ mit der Trigonometrischen Funktion -\begin{equation} \label{ellfilter:eq:chebychef_polynomials} - T_N(w) = \cos \left( N \cos^{-1}(w) \right) -\end{equation} +Bemerkenswert ist, dass die Polynome im Intervall $[-1, 1]$ mit der trigonometrischen Funktion +\begin{align} \label{ellfilter:eq:chebychef_polynomials} + T_N(w) &= \cos \left( N \cos^{-1}(w) \right) \\ + &= \cos \left(N~z \right), \quad w= \cos(z) +\end{align} übereinstimmt. +Der Zusammenhang lässt sich mit den Doppel- und Mehrfachwinkelfunktionen der trigonometrischen Funktionen erklären. Abbildung \ref{ellfilter:fig:chebychef_polynomials} zeigt einige Tschebyscheff-Polynome. \begin{figure} \centering - \includegraphics[scale=1]{papers/ellfilter/python/F_N_chebychev2.pdf} + \input{papers/ellfilter/python/F_N_chebychev2.pgf} \caption{Die Tschebyscheff-Polynome $C_N$.} \label{ellfilter:fig:chebychef_polynomials} \end{figure} @@ -101,103 +99,123 @@ Diese Eigenschaft ist sehr nützlich für ein Filter. Wenn wir die Tschebyscheff-Polynome quadrieren, passen sie perfekt in die Voraussetzungen für Filterfunktionen, wie es Abbildung \ref{ellfiter:fig:chebychef} demonstriert. \begin{figure} \centering - \includegraphics[scale=1]{papers/ellfilter/python/F_N_chebychev.pdf} + \input{papers/ellfilter/python/F_N_chebychev.pgf} \caption{Die Tschebyscheff-Polynome füllen den erlaubten Bereich besser, und erhalten dadurch eine steilere Flanke im Sperrbereich.} \label{ellfiter:fig:chebychef} \end{figure} Die analytische Fortsetzung von \eqref{ellfilter:eq:chebychef_polynomials} über das Intervall $[-1,1]$ hinaus stimmt mit den Polynomen überein, wie es zu erwarten ist. -Die genauere Betrachtung wird uns dann helfen die elliptischen Filter zu verstehen. +Die genauere Betrachtung wird uns dann helfen die elliptischen Filter besser zu verstehen. -\begin{equation} +Starten wir mit der Funktion, die als erstes auf $w$ angewendet wird, dem Arcuscosinus. +Die invertierte Funktion des Kosinus kann als definites Integral dargestellt werden: +\begin{align} \cos^{-1}(x) - = - \int_{0}^{x} + &= + \int_{x}^{1} \frac{ dz }{ \sqrt{ 1-z^2 } - } -\end{equation} %TOdO is it minus dz? - -\begin{equation} + }\\ + &= + \int_{0}^{x} \frac{ - 1 + -1 }{ \sqrt{ 1-z^2 } } - \in \mathbb{R} - \quad - \forall - \quad - -1 \leq z \leq 1 -\end{equation} -Wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ. -Durch die Quadratwurzel entstehen zwei Reinkomplexe Lösungen + ~dz + + \frac{\pi}{2} +\end{align} +Der Integrand oder auch die Ableitung \begin{equation} \frac{ - 1 + -1 }{ \sqrt{ 1-z^2 } } - = i \xi \quad | \quad \xi \in \mathbb{R} - \quad - \forall - \quad - z \leq -1 \cup z \geq 1 \end{equation} - +bestimmt dabei die Richtung, in der die Funktion verläuft. +Der reelle Arcuscosinus is bekanntlich nur für $|z| \leq 1$ definiert. +Hier bleibt der Wert unter der Wurzel positiv und das Integral liefert reelle Werte. +Doch wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ. +Durch die Quadratwurzel entstehen für den Integranden zwei rein komplexe Lösungen. +Der Wert des Arcuscosinus verlässt also bei $z= \pm 1$ den reellen Zahlenstrahl und knickt in die komplexe Ebene ab. +Abbildung \ref{ellfilter:fig:arccos} zeigt den $\arccos$ in der komplexen Ebene. \begin{figure} \centering \input{papers/ellfilter/tikz/arccos.tikz.tex} \caption{Die Funktion $z = \cos^{-1}(w)$ dargestellt in der komplexen ebene.} \label{ellfilter:fig:arccos} \end{figure} - - - +Wegen der Periodizität des Kosinus ist auch der Arcuscosinus $2\pi$-periodisch und es entstehen periodische Nullstellen. +% \begin{equation} +% \frac{ +% 1 +% }{ +% \sqrt{ +% 1-z^2 +% } +% } +% \in \mathbb{R} +% \quad +% \forall +% \quad +% -1 \leq z \leq 1 +% \end{equation} +% \begin{equation} +% \frac{ +% 1 +% }{ +% \sqrt{ +% 1-z^2 +% } +% } +% = i \xi \quad | \quad \xi \in \mathbb{R} +% \quad +% \forall +% \quad +% z \leq -1 \cup z \geq 1 +% \end{equation} + +Die Tschebyscheff-Polynome skalieren diese Nullstellen mit dem Ordnungsfaktor $N$, wie dargestellt in Abbildung \ref{ellfilter:fig:arccos2}. \begin{figure} \centering \input{papers/ellfilter/tikz/arccos2.tikz.tex} \caption{ - $z$-Ebene der Tschebyscheff-Funktion. - Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden hat das Tschebyscheff-Polynom. + $z_1=N \cos^{-1}(w)$-Ebene der Tschebyscheff-Funktion. + Die eingefärbten Pfade sind Verläufe von $w~\forall~[-\infty, \infty]$ für verschiedene Ordnungen $N$. + Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden passiert. } - % \label{ellfilter:fig:arccos} + \label{ellfilter:fig:arccos2} \end{figure} - - - - - -% Analytische Fortsetzung - - +Somit passert $\cos( N~\cos^{-1}(w))$ im Intervall $[-1, 1]$ $N$ Nullstellen. +Durch die spezielle Anordnung der Nullstellen hat die Funktion Equirippel-Verhalten und ist dennoch ein Polynom, was sich perfekt für linear Filter eignet. \section{Jacobische elliptische Funktionen} +%TODO $z$ or $u$ for parameter? -Für das elliptische Filter, wird statt der für das Tschebyscheff-Filter benutzen Kreis-Trigonometrie die elliptischen Funktionen gebraucht. -Der begriff elliptische Funktion wird für sehr viele Funktionen gebraucht, daher ist es hier wichtig zu erwähnen, dass es ausschliesslich um die Jacobischen elliptischen Funktionen geht. +Für das elliptische Filter wird statt der, für das Tschebyscheff-Filter benutzen Kreis-Trigonometrie die elliptischen Funktionen gebraucht. +Der Begriff elliptische Funktion wird für sehr viele Funktionen gebraucht, daher ist es hier wichtig zu erwähnen, dass es ausschliesslich um die Jacobischen elliptischen Funktionen geht. Im Wesentlichen erweitern die Jacobi elliptischen Funktionen die trigonometrische Funktionen für Ellipsen. - -%TODO $z$ or $u$ for parameter? - -neu zwei parameter -$sn(z, k)$ -$z$ ist das winkelargument +Zum Beispiel gibt es analog zum Sinus den elliptischen $\sn(z, k)$. +Im Gegensatz zum den trigonometrischen Funktionen haben die elliptischen Funktionen zwei parameter. +Zum einen gibt es den \textit{elliptische Modul} $k$, der die Exzentrizität der Ellipse parametrisiert. +Zum andern das Winkelargument $z$. Im Kreis ist der Radius für alle Winkel konstant, bei Ellipsen ändert sich das. Dies hat zur Folge, dass bei einer Ellipse die Kreisbodenstrecke nicht linear zum Winkel verläuft. Darum kann hier nicht der gewohnte Winkel verwendet werden. -An deren stelle kommt der parameter $k$ zum Einsatz, welcher durch das elliptische Integral erster Art +Das Winkelargument $z$ kann durch das elliptische Integral erster Art \begin{equation} z = @@ -211,12 +229,18 @@ An deren stelle kommt der parameter $k$ zum Einsatz, welcher durch das elliptisc 1-k^2 \sin^2 \theta } } + = + \int_{0}^{\phi} + \frac{ + dt + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } %TODO which is right? are both functions from phi? \end{equation} mit dem Winkel $\phi$ in Verbindung liegt. - - - Dabei wird das vollständige und unvollständige Elliptische integral unterschieden. Beim vollständigen Integral \begin{equation} @@ -231,25 +255,75 @@ Beim vollständigen Integral } } \end{equation} -wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$. - -Die Jacobischen elliptischen Funktionen können mit der inversen Funktion +wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$ und liefert das Winkelargument für eine Vierteldrehung. +Die Zahl wird oft auch abgekürzt mit $K = K(k)$ und ist für das elliptische Filter sehr relevant. +Alle elliptishen Funktionen sind somit $4K$-periodisch. + +Neben dem $\sn$ gibt es zwei weitere basis-elliptische Funktionen $\cn$ und $\dn$. +Dazu kommen noch weitere abgeleitete Funktionen, die durch Quotienten und Kehrwerte dieser Funktionen zustande kommen. +Insgesamt sind es die zwölf Funktionen +\begin{equation*} + \sn \quad + \ns \quad + \scelliptic \quad + \sd \quad + \cn \quad + \nc \quad + \cs \quad + \cd \quad + \dn \quad + \nd \quad + \ds \quad + \dc. +\end{equation*} + +Die Jacobischen elliptischen Funktionen können mit der inversen Funktion des kompletten elliptischen Integrals erster Art \begin{equation} \phi = F^{-1}(z, k) \end{equation} -definiert werden. Dabei ist zu beachten dass nur das $z$ Argument der Funktion invertiert wird also +definiert werden. Dabei ist zu beachten dass nur das $z$ Argument der Funktion invertiert wird, also \begin{equation} z = F(\phi, k) \Leftrightarrow \phi = F^{-1}(z, k). \end{equation} -Mithilfe von $F^{-1}$ kann $sn^{-1}$ mit dem Elliptischen integral dargestellt werden: +Mithilfe von $F^{-1}$ kann zum Beispiel $sn^{-1}$ mit dem Elliptischen integral dargestellt werden: \begin{equation} \sin(\phi) = \sin \left( F^{-1}(z, k) \right) = - \sn(u, k) + \sn(z, k) + = + w +\end{equation} + +\begin{equation} + \phi + = + F^{-1}(z, k) + = + \sin^{-1} \big( \sn (z, k ) \big) + = + \sin^{-1} ( w ) +\end{equation} + +\begin{equation} + F(\phi, k) + = + z + = + F( \sin^{-1} \big( \sn (z, k ) \big) , k) + = + F( \sin^{-1} ( w ), k) +\end{equation} + +\begin{equation} + \sn^{-1}(w, k) + = + F(\phi, k), + \quad + \phi = \sin^{-1}(w) \end{equation} \begin{align} @@ -306,28 +380,90 @@ In der reellen Richtung ist sie $4K(k)$-periodisch und in der imaginären Richtu %TODO sn^{-1} grafik +\begin{figure} + \centering + \input{papers/ellfilter/tikz/sn.tikz.tex} + \caption{ + $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$. + Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch. + } + % \label{ellfilter:fig:cd2} +\end{figure} \section{Elliptische rationale Funktionen} +Kommen wir nun zum eigentlichen Teil dieses Papers, den elliptischen rationalen Funktionen +\begin{align} + R_N(\xi, w) &= \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) \\ + &= \cd \left(N~\frac{K_1}{K}~\cd^{-1}(w, k), k_1)\right) , \quad k= 1/\xi, k_1 = 1/f(\xi) \\ + &= \cd \left(N~K_1~z , k_1 \right), \quad w= \cd(z K, k) +\end{align} + -\begin{equation} - R_N(\xi, w) = \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) -\end{equation} -\begin{equation} - R_N(\xi, w) = \cd (N~u K_1, k_1), \quad w= \cd(uK, k) -\end{equation} +sieht ähnlich aus wie die trigonometrische Darstellung der Tschebyschef-Polynome \eqref{ellfilter:eq:chebychef_polynomials} +Anstelle vom Kosinus kommt hier die $\cd$-Funktion zum Einsatz. +Die Ordnungszahl $N$ kommt auch als Faktor for. +Zusätzlich werden noch zwei verschiedene elliptische Module $k$ und $k_1$ gebraucht. + + + +Sinus entspricht $\sn$ + +Damit die Nullstellen an ähnlichen Positionen zu liegen kommen wie bei den Tschebyscheff-Polynomen, muss die $\cd$-Funktion gewählt werden. + +Die $\cd^{-1}(w, k)$-Funktion ist um $K$ verschoben zur $\sn^{-1}(w, k)$-Funktion, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd}. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/cd.tikz.tex} + \caption{ + $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$. + Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch. + } + \label{ellfilter:fig:cd} +\end{figure} +Auffallend ist, dass sich alle Nullstellen und Polstellen um $K$ verschoben haben. +Durch das Konzept vom fundamentalen Rechteck, siehe Abbildung \ref{ellfilter:fig:fundamental_rectangle} können für alle inversen Jaccobi elliptischen Funktionen die Positionen der Null- und Polstellen anhand eines Diagramms ermittelt werden. +Der erste Buchstabe bestimmt die Position der Nullstelle und der zweite Buchstabe die Polstelle. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/fundamental_rectangle.tikz.tex} + \caption{ + Fundamentales Rechteck der inversen Jaccobi elliptischen Funktionen. + } + \label{ellfilter:fig:fundamental_rectangle} +\end{figure} -sieht ähnlich aus wie die trigonometrische darstellung der Tschebyschef-Polynome +Auffallend an der $w = \sn(z, k)$-Funktion ist, dass sich $w$ auf der reellen Achse wie der Kosinus immer zwischen $-1$ und $1$ bewegt, während bei $\mathrm{Im(z) = K^\prime}$ die Werte zwischen $\pm 1/k$ und $\pm \infty$ verlaufen. +Die Funktion hat also Equirippel-Verhalten um $w=0$ und um $w=\pm \infty$. +Falls es möglich ist diese Werte abzufahren im Sti der Tschebyscheff-Polynome, kann ein Filter gebaut werden, dass Equirippel-Verhalten im Durchlass- und Sperrbereich aufweist. -der Ordnungszahl $N$ kommt auch als Faktor for -%TODO cd^{-1} grafik mit +Analog zu Abbildung \ref{ellfilter:fig:arccos2} können wir auch bei den elliptisch rationalen Funktionen die komplexe $z$-Ebene betrachten, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd2}, um die besser zu verstehen. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/cd2.tikz.tex} + \caption{ + $z_1$-Ebene der elliptischen rationalen Funktionen. + Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen passiert. + } + \label{ellfilter:fig:cd2} +\end{figure} +% Da die $\cd^{-1}$-Funktion + + + +\begin{figure} + \centering + \input{papers/ellfilter/python/F_N_elliptic.pgf} + \caption{$F_N$ für ein elliptischs filter.} + \label{ellfilter:fig:elliptic} +\end{figure} \subsection{Degree Equation} -Der $cd^{-1}$ Term muss so verzogen werden, dass die umgebene $cd$ funktion die nullstellen und pole trifft. +Der $\cd^{-1}$ Term muss so verzogen werden, dass die umgebene $\cd$-Funktion die Nullstellen und Pole trifft. Dies trifft ein wenn die Degree Equation erfüllt ist. \begin{equation} @@ -345,19 +481,7 @@ Bei den Tschebyscheff-Polynomen haben wir gesehen, dass die Trigonometrische For Im gegensatz zum $\cos^{-1}$ hat der $\cd^{-1}$ nicht nur Nullstellen sondern auch Pole. Somit entstehen bei den elliptischen rationalen Funktionen, wie es der name auch deutet, rationale Funktionen, also ein Bruch von zwei Polynomen. - - - -\begin{figure} - \centering - \includegraphics[scale=1]{papers/ellfilter/python/F_N_elliptic.pdf} - \caption{$F_N$ für ein elliptischs filter.} - \label{ellfilter:fig:elliptic} -\end{figure} - - - - +Da Transformationen einer rationalen Funktionen mit Grundrechenarten, wie es in \eqref{ellfilter:eq:h_omega} der Fall ist, immer noch rationale Funktionen ergeben, stellt dies kein Problem für die Implementierung dar. \input{papers/ellfilter/teil0.tex} \input{papers/ellfilter/teil1.tex} diff --git a/buch/papers/ellfilter/packages.tex b/buch/papers/ellfilter/packages.tex index 8045a1a..9a550e2 100644 --- a/buch/papers/ellfilter/packages.tex +++ b/buch/papers/ellfilter/packages.tex @@ -8,6 +8,20 @@ % following example %\usepackage{packagename} +% \usepackage[dvipsnames]{xcolor} + +\usetikzlibrary{trees,shapes,decorations} + +\DeclareMathOperator{\sn}{\mathrm{sn}} +\DeclareMathOperator{\ns}{\mathrm{ns}} +\DeclareMathOperator{\scelliptic}{\mathrm{sc}} +\DeclareMathOperator{\sd}{\mathrm{sd}} +\DeclareMathOperator{\cn}{\mathrm{cn}} +\DeclareMathOperator{\nc}{\mathrm{nc}} +\DeclareMathOperator{\cs}{\mathrm{cs}} +\DeclareMathOperator{\cd}{\mathrm{cd}} +\DeclareMathOperator{\dn}{\mathrm{dn}} +\DeclareMathOperator{\nd}{\mathrm{nd}} +\DeclareMathOperator{\ds}{\mathrm{ds}} +\DeclareMathOperator{\dc}{\mathrm{dc}} -\DeclareMathOperator{\sn}{\text{sn}} -\DeclareMathOperator{\cd}{\text{cd}} diff --git a/buch/papers/ellfilter/presentation/presentation.tex b/buch/papers/ellfilter/presentation/presentation.tex new file mode 100644 index 0000000..7fdb864 --- /dev/null +++ b/buch/papers/ellfilter/presentation/presentation.tex @@ -0,0 +1,413 @@ +\documentclass[ngerman, aspectratio=169, xcolor={rgb}]{beamer} + +% style +\mode{ + \usetheme{Frankfurt} +} +%packages +\usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +\usepackage[english]{babel} +\usepackage{graphicx} +\usepackage{array} + +\newcolumntype{L}[1]{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{#1}} +\usepackage{ragged2e} + +\usepackage{bm} % bold math +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{mathtools} +\usepackage{amsmath} +\usepackage{multirow} % multi row in tables +\usepackage{booktabs} %toprule midrule bottomrue in tables +\usepackage{scrextend} +\usepackage{textgreek} +\usepackage[rgb]{xcolor} + +\usepackage{ marvosym } % \Lightning + +\usepackage{multimedia} % embedded videos + +\usepackage{tikz} +\usepackage{pgf} +\usepackage{pgfplots} + +\usepackage{algorithmic} + +%citations +\usepackage[style=verbose,backend=biber]{biblatex} +\addbibresource{references.bib} + + +%math font +\usefonttheme[onlymath]{serif} + +%Beamer Template modifications +%\definecolor{mainColor}{HTML}{0065A3} % HSR blue +\definecolor{mainColor}{HTML}{D72864} % OST pink +\definecolor{invColor}{HTML}{28d79b} % OST pink +\definecolor{dgreen}{HTML}{38ad36} % Dark green + +%\definecolor{mainColor}{HTML}{000000} % HSR blue +\setbeamercolor{palette primary}{bg=white,fg=mainColor} +\setbeamercolor{palette secondary}{bg=orange,fg=mainColor} +\setbeamercolor{palette tertiary}{bg=yellow,fg=red} +\setbeamercolor{palette quaternary}{bg=mainColor,fg=white} %bg = Top bar, fg = active top bar topic +\setbeamercolor{structure}{fg=black} % itemize, enumerate, etc (bullet points) +\setbeamercolor{section in toc}{fg=black} % TOC sections +\setbeamertemplate{section in toc}[sections numbered] +\setbeamertemplate{subsection in toc}{% + \hspace{1.2em}{$\bullet$}~\inserttocsubsection\par} + +\setbeamertemplate{itemize items}[circle] +\setbeamertemplate{description item}[circle] +\setbeamertemplate{title page}[default][colsep=-4bp,rounded=true] +\beamertemplatenavigationsymbolsempty + +\setbeamercolor{footline}{fg=gray} +\setbeamertemplate{footline}{% + \hfill\usebeamertemplate***{navigation symbols} + \hspace{0.5cm} + \insertframenumber{}\hspace{0.2cm}\vspace{0.2cm} +} + +\usepackage{caption} +\captionsetup{labelformat=empty} + +%Title Page +\title{Elliptische Filter} +\subtitle{Eine Anwendung der Jaccobi elliptischen Funktionen} +\author{Nicolas Tobler} +% \institute{OST Ostschweizer Fachhochschule} +% \institute{\includegraphics[scale=0.3]{../img/ost_logo.png}} +\date{\today} + +\input{../packages.tex} + +\newcommand*{\QED}{\hfill\ensuremath{\blacksquare}}% + +\newcommand*{\HL}{\textcolor{mainColor}} +\newcommand*{\RD}{\textcolor{red}} +\newcommand*{\BL}{\textcolor{blue}} +\newcommand*{\GN}{\textcolor{dgreen}} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + + +\makeatletter +\newcount\my@repeat@count +\newcommand{\myrepeat}[2]{% + \begingroup + \my@repeat@count=\z@ + \@whilenum\my@repeat@count<#1\do{#2\advance\my@repeat@count\@ne}% + \endgroup +} +\makeatother + +\usetikzlibrary{automata,arrows,positioning,calc,shapes.geometric, fadings} + +\begin{document} + + \begin{frame} + \titlepage + \end{frame} + + \begin{frame} + \frametitle{Content} + \tableofcontents + \end{frame} + + \section{Linear Filter} + + \begin{frame} + \frametitle{Lineare Filter} + + + \begin{equation} + | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 F_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p} + \end{equation} + + \pause + + \begin{equation} + F_N(w) = w^N + \end{equation} + + \end{frame} + + \begin{frame} + \frametitle{Beispiel: Butterworth Filter} + + \begin{equation} + F_N(w) = w^N + \end{equation} + + \begin{center} + \input{../python/F_N_butterworth.pgf} + \end{center} + + \end{frame} + + + \begin{frame} + \frametitle{Arten von linearen filtern} + + \begin{align*} + F_N(w) & = + \begin{cases} + w^N & \text{Butterworth} \\ + T_N(w) & \text{Tschebyscheff, Typ 1} \\ + [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\ + R_N(w,\xi) & \text{Elliptisch (Cauer)} \\ + \end{cases} + \end{align*} + + \end{frame} + + \section{Tschebycheff Filter} + + \begin{frame} + \frametitle{Tschebyscheff-Polynome} + + + \begin{columns} + \begin{column}[T]{0.35\textwidth} + + \begin{align*} + T_{0}(x)&=1\\ + T_{1}(x)&=x\\ + T_{2}(x)&=2x^{2}-1\\ + T_{3}(x)&=4x^{3}-3x\\ + T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x) + \end{align*} + + \end{column} + \begin{column}[T]{0.65\textwidth} + + \begin{center} + \resizebox{\textwidth}{!}{ + \input{../python/F_N_chebychev2.pgf} + } + \end{center} + + \end{column} + \end{columns} + + + + \end{frame} + + \begin{frame} + \frametitle{Tschebyscheff-Filter} + + \begin{equation*} + | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 T_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p} + \end{equation*} + + \begin{center} + \scalebox{0.9}{ + \input{../python/F_N_chebychev.pgf} + } + \end{center} + + \end{frame} + + + \begin{frame} + \frametitle{Tschebyscheff-Filter} + + Darstellung mit trigonometrischen Funktionen: + + \begin{align} \label{ellfilter:eq:chebychef_polynomials} + T_N(w) &= \cos \left( N \cos^{-1}(w) \right) \\ + &= \cos \left(N~z \right), \quad w= \cos(z) + \end{align} + + + \end{frame} + + \begin{frame} + \frametitle{Tschebyscheff-Filter} + + \begin{equation*} + z = \cos^{-1}(w) + \end{equation*} + + \begin{center} + \scalebox{0.85}{ + \input{../tikz/arccos.tikz.tex} + } + \end{center} + + \end{frame} + + \begin{frame} + \frametitle{Tschebyscheff-Filter} + + \begin{equation*} + z_1 = N~\cos^{-1}(w) + \end{equation*} + + \begin{center} + \scalebox{0.85}{ + \input{../tikz/arccos2.tikz.tex} + } + \end{center} + + \end{frame} + + + \section{Jaccobi elliptische Funktionen} + + \begin{frame} + \frametitle{Jaccobi elliptische Funktionen} + + + \begin{equation} + z + = + F(\phi, k) + = + \int_{0}^{\phi} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + } + = + \int_{0}^{\phi} + \frac{ + dt + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } + \end{equation} + + \begin{equation} + K(k) + = + \int_{0}^{\pi / 2} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + } + \end{equation} + + + + \end{frame} + + \begin{frame} + \frametitle{Jaccobi elliptische Funktionen} + + \begin{equation*} + z = \sn^{-1}(w, k) + \end{equation*} + + \begin{center} + \scalebox{0.7}{ + \input{../tikz/sn.tikz.tex} + } + \end{center} + + \end{frame} + + \begin{frame} + \frametitle{Fundamentales Rechteck} + + Nullstelle beim ersten Buchstabe, Polstelle beim zweiten Buchstabe + + \begin{center} + \scalebox{0.8}{ + \input{../tikz/fundamental_rectangle.tikz.tex} + } + \end{center} + + \end{frame} + + + \begin{frame} + \frametitle{Jaccobi elliptische Funktionen} + + \begin{equation*} + z = \cd^{-1}(w, k) + \end{equation*} + + \begin{center} + \scalebox{0.7}{ + \input{../tikz/cd.tikz.tex} + + } + \end{center} + + \end{frame} + + \begin{frame} + \frametitle{Periodizität in realer und imaginärer Richtung} + + \begin{center} + \input{../python/k.pgf} + \end{center} + + + \end{frame} + + \begin{frame} + \frametitle{Elliptisches Filter} + + \begin{equation*} + z_1 = N~\frac{K_1}{K}~\cd^{-1}(w, k) + \end{equation*} + + \begin{center} + \scalebox{0.8}{ + \input{../tikz/cd2.tikz.tex} + } + \end{center} + + \end{frame} + + \begin{frame} + \frametitle{Elliptisches Filter} + + \begin{columns} + + \begin{column}[T]{0.5\textwidth} + + \begin{center} + \resizebox{\textwidth}{!}{ + \input{../python/F_N_elliptic.pgf} + } + \end{center} + + \end{column} + \begin{column}[T]{0.5\textwidth} + + \begin{center} + \resizebox{\textwidth}{!}{ + \input{../python/elliptic.pgf} + } + \end{center} + + \end{column} + \end{columns} + + \end{frame} + + \begin{frame} + \frametitle{Gradgleichung} + + \begin{equation} + N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1} + \end{equation} + + \end{frame} + + \end{document} diff --git a/buch/papers/ellfilter/python/F_N_butterworth.pgf b/buch/papers/ellfilter/python/F_N_butterworth.pgf new file mode 100644 index 0000000..857e363 --- /dev/null +++ b/buch/papers/ellfilter/python/F_N_butterworth.pgf @@ -0,0 +1,1083 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% 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your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% 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in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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a/buch/papers/ellfilter/python/F_N_elliptic.pgf b/buch/papers/ellfilter/python/F_N_elliptic.pgf new file mode 100644 index 0000000..03084c6 --- /dev/null +++ b/buch/papers/ellfilter/python/F_N_elliptic.pgf @@ -0,0 +1,847 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% 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+\makeatother% +\endgroup% diff --git a/buch/papers/ellfilter/python/chebychef.py b/buch/papers/ellfilter/python/chebychef.py index a278989..254ad4b 100644 --- a/buch/papers/ellfilter/python/chebychef.py +++ b/buch/papers/ellfilter/python/chebychef.py @@ -35,7 +35,7 @@ plt.show() # %% Cheychev filter F_N plot w = np.linspace(-1.1,1.1, 1000) -plt.figure(figsize=(5.5,2)) +plt.figure(figsize=(5.5,2.5)) for N in [3,6,11]: # F_N = np.cos(N * np.arccos(w)) F_N = scipy.special.eval_chebyt(N, w) @@ -44,9 +44,10 @@ plt.xlim([-1.2,1.2]) plt.ylim([-2,2]) plt.grid() plt.xlabel("$w$") -plt.ylabel("$C_N(w)$") +plt.ylabel("$T_N(w)$") plt.legend() -plt.savefig("F_N_chebychev2.pdf") +plt.tight_layout() +plt.savefig("F_N_chebychev2.pgf") plt.show() # %% Build Chebychev polynomials diff --git a/buch/papers/ellfilter/python/elliptic.pgf b/buch/papers/ellfilter/python/elliptic.pgf new file mode 100644 index 0000000..31b77d4 --- /dev/null +++ b/buch/papers/ellfilter/python/elliptic.pgf @@ -0,0 +1,709 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.500000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% 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spx.ellipj(z, k**2)[0] + +def cn(z, k): + return spx.ellipj(z, k**2)[1] + +def dn(z, k): + return spx.ellipj(z, k**2)[2] + +def cd(z, k): + sn, cn, dn, ph = spx.ellipj(z, k**2) + return cn / dn + +# https://mathworld.wolfram.com/JacobiEllipticFunctions.html eq 3-8 + +def sn_inv(z, k): + m = k**2 + return scipy.special.ellipkinc(np.arcsin(z), m) + +def cn_inv(z, k): + m = k**2 + return scipy.special.ellipkinc(np.arccos(z), m) + +def dn_inv(z, k): + m = k**2 + x = np.sqrt((1-z**2) / k**2) + return scipy.special.ellipkinc(np.arcsin(x), m) + +def cd_inv(z, k): + m = k**2 + x = np.sqrt(((m - 1) * z**2) / (m*z**2 - 1)) + return scipy.special.ellipkinc(np.arccos(x), m) + + +k = 0.8 +z = 0.5 + +assert np.allclose(sn_inv(sn(z ,k), k), z) +assert np.allclose(cn_inv(cn(z ,k), k), z) +assert np.allclose(dn_inv(dn(z ,k), k), z) +assert np.allclose(cd_inv(cd(z ,k), k), z) + # %% Buttwerworth filter F_N plot @@ -37,7 +80,7 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1, 1), 0.5, 1, - fc ='green', + fc ='orange', alpha=0.2, lw = 10, )) @@ -47,7 +90,8 @@ plt.grid() plt.xlabel("$w$") plt.ylabel("$F^2_N(w)$") plt.legend() -plt.savefig("F_N_butterworth.pdf") +plt.tight_layout() +plt.savefig("F_N_butterworth.pgf") plt.show() # %% Cheychev filter F_N plot @@ -69,7 +113,7 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1, 1), 0.5, 1, - fc ='green', + fc ='orange', alpha=0.2, lw = 10, )) @@ -79,57 +123,10 @@ plt.grid() plt.xlabel("$w$") plt.ylabel("$F^2_N(w)$") plt.legend() -plt.savefig("F_N_chebychev.pdf") +plt.tight_layout() +plt.savefig("F_N_chebychev.pgf") plt.show() -# %% define elliptic functions - -def ell_int(k): - """ Calculate K(k) """ - m = k**2 - return scipy.special.ellipk(m) - -def sn(z, k): - return spx.ellipj(z, k**2)[0] - -def cn(z, k): - return spx.ellipj(z, k**2)[1] - -def dn(z, k): - return spx.ellipj(z, k**2)[2] - -def cd(z, k): - sn, cn, dn, ph = spx.ellipj(z, k**2) - return cn / dn - -# https://mathworld.wolfram.com/JacobiEllipticFunctions.html eq 3-8 - -def sn_inv(z, k): - m = k**2 - return scipy.special.ellipkinc(np.arcsin(z), m) - -def cn_inv(z, k): - m = k**2 - return scipy.special.ellipkinc(np.arccos(z), m) - -def dn_inv(z, k): - m = k**2 - x = np.sqrt((1-z**2) / k**2) - return scipy.special.ellipkinc(np.arcsin(x), m) - -def cd_inv(z, k): - m = k**2 - x = np.sqrt(((m - 1) * z**2) / (m*z**2 - 1)) - return scipy.special.ellipkinc(np.arccos(x), m) - - -k = 0.8 -z = 0.5 - -assert np.allclose(sn_inv(sn(z ,k), k), z) -assert np.allclose(cn_inv(cn(z ,k), k), z) -assert np.allclose(dn_inv(dn(z ,k), k), z) -assert np.allclose(cd_inv(cd(z ,k), k), z) # %% plot arcsin @@ -314,3 +311,46 @@ for n in (1,2,3,4): plt.plot(omega, np.abs(G)) plt.grid() plt.show() + + + + +# %% + + +k = np.concatenate(([0.00001,0.0001,0.001], np.linspace(0,1,101)[1:-1], [0.999,0.9999, 0.99999]), axis=0) +K = ell_int(k) +K_prime = ell_int(np.sqrt(1-k**2)) + + +f, axs = plt.subplots(1,2, figsize=(5,2.5)) +axs[0].plot(k, K, linewidth=0.1) +axs[0].text(k[30], K[30]+0.1, f"$K$") +axs[0].plot(k, K_prime, linewidth=0.1) +axs[0].text(k[30], K_prime[30]+0.1, f"$K^\prime$") +axs[0].set_xlim([0,1]) +axs[0].set_ylim([0,4]) +axs[0].set_xlabel("$k$") + +axs[1].axvline(x=np.pi/2, color="gray", linewidth=0.5) +axs[1].axhline(y=np.pi/2, color="gray", linewidth=0.5) +axs[1].text(0.1, np.pi/2 + 0.1, "$\pi/2$") +axs[1].text(np.pi/2+0.1, 0.1, "$\pi/2$") +axs[1].plot(K, K_prime, linewidth=1) + +k = np.array([0.1,0.2,0.4,0.6,0.9,0.99]) +K = ell_int(k) +K_prime = ell_int(np.sqrt(1-k**2)) + +axs[1].plot(K, K_prime, '.', color=last_color(), markersize=2) +for x, y, n in zip(K, K_prime, k): + axs[1].text(x+0.1, y+0.1, f"$k={n:.2f}$", rotation_mode="anchor") +axs[1].set_ylabel("$K^\prime$") +axs[1].set_xlabel("$K$") +axs[1].set_xlim([0,6]) +axs[1].set_ylim([0,5]) +plt.tight_layout() +plt.savefig("k.pgf") +plt.show() + +print(K[0], K[-1]) diff --git a/buch/papers/ellfilter/python/elliptic2.py b/buch/papers/ellfilter/python/elliptic2.py index 92fefd9..29c6f47 100644 --- a/buch/papers/ellfilter/python/elliptic2.py +++ b/buch/papers/ellfilter/python/elliptic2.py @@ -6,13 +6,14 @@ import numpy as np import matplotlib from matplotlib.patches import Rectangle +import plot_params def ellip_filter(N): order = N passband_ripple_db = 3 stopband_attenuation_db = 20 - omega_c = 1000 + omega_c = 1 a, b = scipy.signal.ellip( order, @@ -34,14 +35,14 @@ def ellip_filter(N): FN2 = ((1/mag**2) - 1) - return w/omega_c, FN2 / epsilon2 + return w/omega_c, FN2 / epsilon2, mag, a, b plt.figure(figsize=(4,2.5)) for N in [5]: - w, FN2 = ellip_filter(N) - plt.semilogy(w, FN2, label=f"$N={N}$") + w, FN2, mag, a, b = ellip_filter(N) + plt.semilogy(w, FN2, label=f"$N={N}, k=0.1$", linewidth=1) plt.gca().add_patch(Rectangle( (0, 0), @@ -53,7 +54,7 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1, 1), 0.01, 1e2-1, - fc ='green', + fc ='orange', alpha=0.2, lw = 10, )) @@ -61,18 +62,88 @@ plt.gca().add_patch(Rectangle( plt.gca().add_patch(Rectangle( (1.01, 100), 1, 1e6, - fc ='green', + fc ='red', alpha=0.2, lw = 10, )) + +zeros = [0,0.87,1] +poles = [1.01,1.155] + +import matplotlib.transforms +plt.plot( # mark errors as vertical bars + zeros, + np.zeros_like(zeros), + "o", + mfc='none', + color='black', + transform=matplotlib.transforms.blended_transform_factory( + plt.gca().transData, + plt.gca().transAxes, + ), +) +plt.plot( # mark errors as vertical bars + poles, + np.ones_like(poles), + "x", + mfc='none', + color='black', + transform=matplotlib.transforms.blended_transform_factory( + plt.gca().transData, + plt.gca().transAxes, + ), +) + plt.xlim([0,2]) plt.ylim([1e-4,1e6]) plt.grid() plt.xlabel("$w$") plt.ylabel("$F^2_N(w)$") plt.legend() -plt.savefig("F_N_elliptic.pdf") +plt.tight_layout() +plt.savefig("F_N_elliptic.pgf") plt.show() +plt.figure(figsize=(4,2.5)) +plt.plot(w, mag, linewidth=1) + +plt.gca().add_patch(Rectangle( + (0, np.sqrt(2)/2), + 1, 1, + fc ='green', + alpha=0.2, + lw = 10, +)) +plt.gca().add_patch(Rectangle( + (1, 0.1), + 0.01, np.sqrt(2)/2 - 0.1, + fc ='orange', + alpha=0.2, + lw = 10, +)) + +plt.gca().add_patch(Rectangle( + (1.01, 0), + 1, 0.1, + fc ='red', + alpha=0.2, + lw = 10, +)) + +plt.grid() +plt.xlim([0,2]) +plt.ylim([0,1]) +plt.xlabel("$w$") +plt.ylabel("$|H(w)|$") +plt.tight_layout() +plt.savefig("elliptic.pgf") +plt.show() + +print("zeros", a) +print("poles", b) + + + + diff --git a/buch/papers/ellfilter/python/k.pgf b/buch/papers/ellfilter/python/k.pgf new file mode 100644 index 0000000..95d61d4 --- /dev/null +++ b/buch/papers/ellfilter/python/k.pgf @@ -0,0 +1,1157 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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+\pgftext[x=3.644803in,y=1.164003in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.90\)}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.992820in,y=1.137383in,left,base]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle k=0.99\)}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/buch/papers/ellfilter/python/plot_params.py b/buch/papers/ellfilter/python/plot_params.py new file mode 100644 index 0000000..4ddd1d8 --- /dev/null +++ b/buch/papers/ellfilter/python/plot_params.py @@ -0,0 +1,9 @@ +import matplotlib + +matplotlib.rcParams.update({ + "pgf.texsystem": "pdflatex", + 'font.family': 'serif', + 'font.size': 9, + 'text.usetex': True, + 'pgf.rcfonts': False, +}) diff --git a/buch/papers/ellfilter/references.bib b/buch/papers/ellfilter/references.bib index 2b873af..8f21971 100644 --- a/buch/papers/ellfilter/references.bib +++ b/buch/papers/ellfilter/references.bib @@ -11,3 +11,12 @@ url = {https://www.ece.rutgers.edu/~orfanidi/ece521/notes.pdf} } +% Schwalm +% https://en.wikipedia.org/wiki/Elliptic_rational_functions +% https://en.wikipedia.org/wiki/Rational_function +% https://en.wikipedia.org/wiki/Jacobi_elliptic_functions +% https://de.wikipedia.org/wiki/Elliptisches_Integral +% https://de.wikipedia.org/wiki/Tschebyschow-Polynom +% https://en.wikipedia.org/wiki/Chebyshev_filter +% https://mathworld.wolfram.com/JacobiEllipticFunctions.html +% https://mathworld.wolfram.com/EllipticIntegraloftheFirstKind.html diff --git a/buch/papers/ellfilter/tikz/arccos.tikz.tex b/buch/papers/ellfilter/tikz/arccos.tikz.tex index 2bdcc2d..2772620 100644 --- a/buch/papers/ellfilter/tikz/arccos.tikz.tex +++ b/buch/papers/ellfilter/tikz/arccos.tikz.tex @@ -1,81 +1,49 @@ \begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] + \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} - \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{Im $z$}; - \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{Re $z$}; + \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{$\mathrm{Im}~z$}; + \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$}; - \begin{scope} - \draw[thick, ->, orange] (-1, 0) -- (0,0); - \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); - \draw[thick, ->, darkgreen] (0, 0) -- (0,-1.5); - \draw[thick, ->, orange] (1, 0) -- (0,0); - \draw[thick, ->, red] (2, 0) -- (1,0); - \draw[thick, ->, blue] (2,1.5) -- (2, 0); - \draw[thick, ->, blue] (2,-1.5) -- (2, 0); - \draw[thick, ->, red] (2, 0) -- (3,0); - - \node[anchor=south west] at (0,1.5) {$\infty$}; - \node[anchor=south west] at (0,-1.5) {$\infty$}; - \node[anchor=south west] at (0,0) {$1$}; - \node[anchor=south] at (1,0) {$0$}; - \node[anchor=south west] at (2,0) {$-1$}; - \node[anchor=south west] at (2,1.5) {$-\infty$}; - \node[anchor=south west] at (2,-1.5) {$-\infty$}; - \node[anchor=south west] at (3,0) {$0$}; - \end{scope} + \begin{scope}[xscale=0.6] - \begin{scope}[xshift=4cm] - \draw[thick, ->, orange] (-1, 0) -- (0,0); - \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); - \draw[thick, ->, darkgreen] (0, 0) -- (0,-1.5); - % \draw[thick, ->, orange] (1, 0) -- (0,0); - % \draw[thick, ->, red] (2, 0) -- (1,0); - % \draw[thick, ->, blue] (2,1.5) -- (2, 0); - % \draw[thick, ->, blue] (2,-1.5) -- (2, 0); - % \draw[thick, ->, red] (2, 0) -- (3,0); - - \node[anchor=south west] at (0,1.5) {$\infty$}; - \node[anchor=south west] at (0,-1.5) {$\infty$}; - \node[anchor=south west] at (0,0) {$1$}; - % \node[anchor=south] at (1,0) {$0$}; - % \node[anchor=south west] at (2,0) {$-1$}; - % \node[anchor=south west] at (2,1.5) {$-\infty$}; - % \node[anchor=south west] at (2,-1.5) {$-\infty$}; - % \node[anchor=south west] at (3,0) {$0$}; - \end{scope} + \clip(-7.5,-2) rectangle (7.5,2); - \begin{scope}[xshift=-4cm] - % \draw[thick, ->, orange] (-1, 0) -- (0,0); \draw[thick, ->, darkgreen] (0, 0) -- (0,1.5); - \draw[thick, ->, darkgreen] (0, 0) -- (0,-1.5); \draw[thick, ->, orange] (1, 0) -- (0,0); \draw[thick, ->, red] (2, 0) -- (1,0); \draw[thick, ->, blue] (2,1.5) -- (2, 0); - \draw[thick, ->, blue] (2,-1.5) -- (2, 0); - \draw[thick, ->, red] (2, 0) -- (3,0); - - \node[anchor=south west] at (0,1.5) {$\infty$}; - \node[anchor=south west] at (0,-1.5) {$\infty$}; - \node[anchor=south west] at (0,0) {$1$}; - \node[anchor=south] at (1,0) {$0$}; - \node[anchor=south west] at (2,0) {$-1$}; - \node[anchor=south west] at (2,1.5) {$-\infty$}; - \node[anchor=south west] at (2,-1.5) {$-\infty$}; - \node[anchor=south west] at (3,0) {$0$}; - \end{scope} - - \node[gray, anchor=north west] at (-4,0) {$-2\pi$}; - \node[gray, anchor=north west] at (-2,0) {$-\pi$}; - \node[gray, anchor=north west] at (0,0) {$0$}; - \node[gray, anchor=north west] at (2,0) {$\pi$}; - \node[gray, anchor=north west] at (4,0) {$2\pi$}; - - - \node[gray, anchor=south east] at (0,-1.5) {$-\infty$}; - \node[gray, anchor=south east] at (0, 0) {$0$}; - \node[gray, anchor=south east] at (0, 1.5) {$\infty$}; + \foreach \i in {-2,...,1} { + \begin{scope}[opacity=0.5, xshift=\i*4cm] + \draw[->, orange] (-1, 0) -- (0,0); + \draw[->, darkgreen] (0, 0) -- (0,1.5); + \draw[->, darkgreen] (0, 0) -- (0,-1.5); + \draw[->, orange] (1, 0) -- (0,0); + \draw[->, red] (2, 0) -- (1,0); + \draw[->, blue] (2,1.5) -- (2, 0); + \draw[->, blue] (2,-1.5) -- (2, 0); + \draw[->, red] (2, 0) -- (3,0); + + \node[zero] at (1,0) {}; + \node[zero] at (3,0) {}; + \end{scope} + } + + \node[gray, anchor=north] at (-6,0) {$-3\pi$}; + \node[gray, anchor=north] at (-4,0) {$-2\pi$}; + \node[gray, anchor=north] at (-2,0) {$-\pi$}; + % \node[gray, anchor=north] at (0,0) {$0$}; + \node[gray, anchor=north] at (2,0) {$\pi$}; + \node[gray, anchor=north] at (4,0) {$2\pi$}; + \node[gray, anchor=north] at (6,0) {$3\pi$}; + + \node[gray, anchor=east] at (0,-1.5) {$-\infty$}; + % \node[gray, anchor=south east] at (0, 0) {$0$}; + \node[gray, anchor=east] at (0, 1.5) {$\infty$}; + \end{scope} \begin{scope}[yshift=-2.5cm] @@ -94,4 +62,5 @@ \end{scope} + \end{tikzpicture} \ No newline at end of file diff --git a/buch/papers/ellfilter/tikz/arccos2.tikz.tex b/buch/papers/ellfilter/tikz/arccos2.tikz.tex index dcf02fd..3fc3cc6 100644 --- a/buch/papers/ellfilter/tikz/arccos2.tikz.tex +++ b/buch/papers/ellfilter/tikz/arccos2.tikz.tex @@ -1,19 +1,18 @@ \begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] - \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} \begin{scope}[xscale=0.5] - \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{Im $z$}; - \draw[gray, ->] (-10,0) -- (10,0) node[anchor=west]{Re $z$}; + \draw[gray, ->] (0,-2) -- (0,2) node[anchor=south]{$\mathrm{Im}~z_1$}; + \draw[gray, ->] (-10,0) -- (10,0) node[anchor=west]{$\mathrm{Re}~z_1$}; \begin{scope} \draw[>->, line width=0.05, thick, blue] (2, 1.5) -- (2,0.05) -- node[anchor=south, pos=0.5]{$N=1$} (0.1,0.05) -- (0.1,1.5); \draw[>->, line width=0.05, thick, orange] (4, 1.5) -- (4,0) -- node[anchor=south, pos=0.25]{$N=2$} (0,0) -- (0,1.5); - \draw[>->, line width=0.05, thick, red] (6, 1.5) -- (6,-0.05) -- node[anchor=south, pos=0.1666]{$N=3$} (-0.1,-0.05) -- (-0.1,1.5); + \draw[>->, line width=0.05, thick, red] (6, 1.5) node[anchor=north west]{$-\infty$} -- (6,-0.05) node[anchor=west]{$-1$} -- node[anchor=north]{$0$} node[anchor=south, pos=0.1666]{$N=3$} (-0.1,-0.05) node[anchor=east]{$1$} -- (-0.1,1.5) node[anchor=north east]{$\infty$}; \node[zero] at (-7,0) {}; diff --git a/buch/papers/ellfilter/tikz/cd.tikz.tex b/buch/papers/ellfilter/tikz/cd.tikz.tex new file mode 100644 index 0000000..7155a85 --- /dev/null +++ b/buch/papers/ellfilter/tikz/cd.tikz.tex @@ -0,0 +1,87 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + + \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] + + \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} + + \begin{scope}[xscale=1, yscale=2] + + \draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$}; + \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$}; + + \draw[gray] ( 1,0) +(0,0.1) -- +(0, -0.1) node[inner sep=0, anchor=north] {\small $K$}; + + \draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$}; + + + \begin{scope} + + \begin{scope}[xshift=0cm] + + \clip(-4.5,-1.25) rectangle (4.5,1.25); + + \fill[yellow!30] (0,0) rectangle (1, 0.5); + + + \draw[thick, ->, darkgreen] (0, 0) -- (0,0.5); + \draw[thick, ->, orange] (1, 0) -- (0,0); + \draw[thick, ->, red] (2, 0) -- (1,0); + \draw[thick, ->, blue] (2,0.5) -- (2, 0); + \draw[thick, ->, purple] (1, 0.5) -- (2,0.5); + \draw[thick, ->, cyan] (0, 0.5) -- (1,0.5); + + + + \foreach \i in {-2,...,1} { + \foreach \j in {-2,...,1} { + \begin{scope}[xshift=\i*4cm, yshift=\j*1cm] + \draw[opacity=0.5, ->, darkgreen] (0, 0) -- (0,0.5); + \draw[opacity=0.5, ->, orange] (1, 0) -- (0,0); + \draw[opacity=0.5, ->, red] (2, 0) -- (1,0); + \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 0); + \draw[opacity=0.5, ->, purple] (1, 0.5) -- (2,0.5); + \draw[opacity=0.5, ->, cyan] (0, 0.5) -- (1,0.5); + \draw[opacity=0.5, ->, darkgreen] (0,1) -- (0,0.5); + \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 1); + \draw[opacity=0.5, ->, purple] (3, 0.5) -- (2,0.5); + \draw[opacity=0.5, ->, cyan] (4, 0.5) -- (3,0.5); + \draw[opacity=0.5, ->, red] (2, 0) -- (3,0); + \draw[opacity=0.5, ->, orange] (3, 0) -- (4,0); + + \node[zero] at ( 1, 0) {}; + \node[zero] at ( 3, 0) {}; + \node[pole] at ( 1,0.5) {}; + \node[pole] at ( 3,0.5) {}; + + \end{scope} + } + } + + \end{scope} + + \end{scope} + + \end{scope} + + \begin{scope}[yshift=-3.5cm, xscale=0.75] + + \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$}; + + \draw[thick, ->, purple] (-5, 0) -- (-3, 0); + \draw[thick, ->, blue] (-3, 0) -- (-2, 0); + \draw[thick, ->, red] (-2, 0) -- (0, 0); + \draw[thick, ->, orange] (0, 0) -- (2, 0); + \draw[thick, ->, darkgreen] (2, 0) -- (3, 0); + \draw[thick, ->, cyan] (3, 0) -- (5, 0); + + \node[anchor=south] at (-5,0) {$-\infty$}; + \node[anchor=south] at (-3,0) {$-1/k$}; + \node[anchor=south] at (-2,0) {$-1$}; + \node[anchor=south] at (0,0) {$0$}; + \node[anchor=south] at (2,0) {$1$}; + \node[anchor=south] at (3,0) {$1/k$}; + \node[anchor=south] at (5,0) {$\infty$}; + + \end{scope} + +\end{tikzpicture} \ No newline at end of file diff --git a/buch/papers/ellfilter/tikz/cd2.tikz.tex b/buch/papers/ellfilter/tikz/cd2.tikz.tex new file mode 100644 index 0000000..0743f7d --- /dev/null +++ b/buch/papers/ellfilter/tikz/cd2.tikz.tex @@ -0,0 +1,84 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + + \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] + \tikzstyle{dot} = [fill, circle, inner sep =0, minimum height=0.1cm] + + \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} + + \begin{scope}[xscale=1.25, yscale=2.5] + + \draw[gray, ->] (0,-0.75) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z_1$}; + \draw[gray, ->] (-1.5,0) -- (6,0) node[anchor=west]{$\mathrm{Re}~z_1$}; + + \draw[gray] ( 1,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K_1$}; + \draw[gray] ( 5,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $5K_1$}; + \draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=east]{\small $jK^\prime_1$}; + + \begin{scope} + + \clip(-1.5,-0.75) rectangle (6.8,1.25); + + % \draw[>->, line width=0.05, thick, blue] (1, 0.45) -- (2, 0.45) -- (2, 0.05) -- ( 0.1, 0.05) -- ( 0.1,0.45) -- (1, 0.45); + % \draw[>->, line width=0.05, thick, orange] (2, 0.5 ) -- (4, 0.5 ) -- (4, 0 ) -- ( 0 , 0 ) -- ( 0 ,0.5 ) -- (2, 0.5 ); + % \draw[>->, line width=0.05, thick, red] (3, 0.55) -- (6, 0.55) -- (6,-0.05) -- (-0.1,-0.05) -- (-0.1,0.55) -- (3, 0.55); + % \node[blue] at (1, 0.25) {$N=1$}; + % \node[orange] at (3, 0.25) {$N=2$}; + % \node[red] at (5, 0.25) {$N=3$}; + + + + % \draw[line width=0.1cm, fill, red!50] (0,0) rectangle (3, 0.5); + % \draw[line width=0.05cm, fill, orange!50] (0,0) rectangle (2, 0.5); + % \fill[yellow!50] (0,0) rectangle (1, 0.5); + % \node[] at (0.5, 0.25) {\small $N=1$}; + % \node[] at (1.5, 0.25) {\small $N=2$}; + % \node[] at (2.5, 0.25) {\small $N=3$}; + + \fill[orange!30] (0,0) rectangle (5, 0.5); + \fill[yellow!30] (0,0) rectangle (1, 0.5); + \node[] at (2.5, 0.25) {\small $N=5$}; + + + \draw[decorate,decoration={brace,amplitude=3pt,mirror}, yshift=0.05cm] + (5,0.5) node(t_k_unten){} -- node[above, yshift=0.1cm]{$NK$} + (0,0.5) node(t_k_opt_unten){}; + + \draw[decorate,decoration={brace,amplitude=3pt,mirror}, xshift=0.1cm] + (5,0) node(t_k_unten){} -- node[right, xshift=0.1cm]{$K^\prime \frac{K_1N}{K} = K^\prime_1$} + (5,0.5) node(t_k_opt_unten){}; + + \foreach \i in {-2,...,1} { + \foreach \j in {-2,...,1} { + \begin{scope}[xshift=\i*4cm, yshift=\j*1cm] + + \node[zero] at ( 1, 0) {}; + \node[zero] at ( 3, 0) {}; + \node[pole] at ( 1,0.5) {}; + \node[pole] at ( 3,0.5) {}; + + \end{scope} + } + } + + + + + \draw[thick, ->, darkgreen] (5, 0) -- node[yshift=-0.5cm]{Durchlassbereich} (0,0); + \draw[thick, ->, orange] (-0, 0) -- node[align=center]{Übergangs-\\berech} (0,0.5); + \draw[thick, ->, red] (0,0.5) -- node[align=center, yshift=0.5cm]{Sperrbereich} (5, 0.5); + + \draw (4,0 ) node[dot]{} node[anchor=south] {\small $1$}; + \draw (2,0 ) node[dot]{} node[anchor=south] {\small $-1$}; + \draw (0,0 ) node[dot]{} node[anchor=south west] {\small $1$}; + \draw (0,0.5) node[dot]{} node[anchor=north west] {\small $1/k$}; + \draw (2,0.5) node[dot]{} node[anchor=north] {\small $-1/k$}; + \draw (4,0.5) node[dot]{} node[anchor=north] {\small $1/k$}; + + + + \end{scope} + + + \end{scope} + +\end{tikzpicture} \ No newline at end of file diff --git a/buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex b/buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex new file mode 100644 index 0000000..921dbfa --- /dev/null +++ b/buch/papers/ellfilter/tikz/fundamental_rectangle.tikz.tex @@ -0,0 +1,26 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + + \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] + + \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} + + \begin{scope}[xscale=2, yscale=2] + + \draw[gray, ->] (0,-0.25) -- (0,1.25) node[anchor=south]{$\mathrm{Im}~z$}; + \draw[gray, ->] (-0.25,0) -- (1.5,0) node[anchor=west]{$\mathrm{Re}~z$}; + + \draw[gray] ( 1,0) +(0,0.05) -- +(0, -0.05) node[inner sep=0, anchor=north] {\small $K$}; + + \draw[gray] (0, 1) +(0.05, 0) -- +(-0.05, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$}; + + \fill[yellow!50] (0,0) rectangle (1, 1); + + \node[anchor=south east] at ( 1,0) {$c$}; + \node[anchor=north east] at ( 1,1) {$d$}; + \node[anchor=north west] at ( 0,1) {$n$}; + \node[anchor=south west] at ( 0,0) {$s$}; + + \end{scope} + + +\end{tikzpicture} \ No newline at end of file diff --git a/buch/papers/ellfilter/tikz/sn.tikz.tex b/buch/papers/ellfilter/tikz/sn.tikz.tex new file mode 100644 index 0000000..87c63c0 --- /dev/null +++ b/buch/papers/ellfilter/tikz/sn.tikz.tex @@ -0,0 +1,86 @@ +\begin{tikzpicture}[>=stealth', auto, node distance=2cm, scale=1.2] + + \tikzstyle{zero} = [draw, circle, inner sep =0, minimum height=0.15cm] + + \tikzset{pole/.style={cross out, draw=black, minimum size=(0.15cm-\pgflinewidth), inner sep=0pt, outer sep=0pt}} + + \begin{scope}[xscale=1, yscale=2] + + \draw[gray, ->] (0,-1.5) -- (0,1.5) node[anchor=south]{$\mathrm{Im}~z$}; + \draw[gray, ->] (-5,0) -- (5,0) node[anchor=west]{$\mathrm{Re}~z$}; + + \begin{scope} + + \clip(-4.5,-1.25) rectangle (4.5,1.25); + + \fill[yellow!30] (0,0) rectangle (1, 0.5); + + \begin{scope}[xshift=-1cm] + + \draw[thick, ->, darkgreen] (0, 0) -- (0,0.5); + \draw[thick, ->, orange] (1, 0) -- (0,0); + \draw[thick, ->, red] (2, 0) -- (1,0); + \draw[thick, ->, blue] (2,0.5) -- (2, 0); + \draw[thick, ->, purple] (1, 0.5) -- (2,0.5); + \draw[thick, ->, cyan] (0, 0.5) -- (1,0.5); + + + \foreach \i in {-2,...,2} { + \foreach \j in {-2,...,1} { + \begin{scope}[xshift=\i*4cm, yshift=\j*1cm] + \draw[opacity=0.5, ->, darkgreen] (0, 0) -- (0,0.5); + \draw[opacity=0.5, ->, orange] (1, 0) -- (0,0); + \draw[opacity=0.5, ->, red] (2, 0) -- (1,0); + \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 0); + \draw[opacity=0.5, ->, purple] (1, 0.5) -- (2,0.5); + \draw[opacity=0.5, ->, cyan] (0, 0.5) -- (1,0.5); + \draw[opacity=0.5, ->, darkgreen] (0,1) -- (0,0.5); + \draw[opacity=0.5, ->, blue] (2,0.5) -- (2, 1); + \draw[opacity=0.5, ->, purple] (3, 0.5) -- (2,0.5); + \draw[opacity=0.5, ->, cyan] (4, 0.5) -- (3,0.5); + \draw[opacity=0.5, ->, red] (2, 0) -- (3,0); + \draw[opacity=0.5, ->, orange] (3, 0) -- (4,0); + + \node[zero] at ( 1, 0) {}; + \node[zero] at ( 3, 0) {}; + \node[pole] at ( 1,0.5) {}; + \node[pole] at ( 3,0.5) {}; + + \end{scope} + } + } + + \end{scope} + + \end{scope} + + \draw[gray] ( 1,0) +(0,0.1) -- +(0, -0.1) node[inner sep=0, anchor=north] {\small $K$}; + \draw[gray] (0, 0.5) +(0.1, 0) -- +(-0.1, 0) node[inner sep=0, anchor=east]{\small $jK^\prime$}; + + + + \end{scope} + + \begin{scope}[yshift=-3.5cm, xscale=0.75] + + \draw[gray, ->] (-6,0) -- (6,0) node[anchor=west]{$w$}; + + \draw[thick, ->, purple] (-5, 0) -- (-3, 0); + \draw[thick, ->, blue] (-3, 0) -- (-2, 0); + \draw[thick, ->, red] (-2, 0) -- (0, 0); + \draw[thick, ->, orange] (0, 0) -- (2, 0); + \draw[thick, ->, darkgreen] (2, 0) -- (3, 0); + \draw[thick, ->, cyan] (3, 0) -- (5, 0); + + \node[anchor=south] at (-5,0) {$-\infty$}; + \node[anchor=south] at (-3,0) {$-1/k$}; + \node[anchor=south] at (-2,0) {$-1$}; + \node[anchor=south] at (0,0) {$0$}; + \node[anchor=south] at (2,0) {$1$}; + \node[anchor=south] at (3,0) {$1/k$}; + \node[anchor=south] at (5,0) {$\infty$}; + + \end{scope} + + +\end{tikzpicture} \ No newline at end of file -- cgit v1.2.1 From 2cbc79a82e39702dd78919ac704fae01f50efb12 Mon Sep 17 00:00:00 2001 From: Nicolas Tobler Date: Mon, 30 May 2022 00:33:47 +0200 Subject: split main into section files --- buch/papers/ellfilter/Makefile.inc | 17 +- buch/papers/ellfilter/einleitung.tex | 56 ++++ buch/papers/ellfilter/elliptic.tex | 92 ++++++ buch/papers/ellfilter/jacobi.tex | 189 +++++++++++++ buch/papers/ellfilter/main.tex | 485 +------------------------------- buch/papers/ellfilter/teil0.tex | 22 -- buch/papers/ellfilter/teil1.tex | 55 ---- buch/papers/ellfilter/teil2.tex | 40 --- buch/papers/ellfilter/teil3.tex | 40 --- buch/papers/ellfilter/tschebyscheff.tex | 133 +++++++++ 10 files changed, 483 insertions(+), 646 deletions(-) create mode 100644 buch/papers/ellfilter/einleitung.tex create mode 100644 buch/papers/ellfilter/elliptic.tex create mode 100644 buch/papers/ellfilter/jacobi.tex delete mode 100644 buch/papers/ellfilter/teil0.tex delete mode 100644 buch/papers/ellfilter/teil1.tex delete mode 100644 buch/papers/ellfilter/teil2.tex delete mode 100644 buch/papers/ellfilter/teil3.tex create mode 100644 buch/papers/ellfilter/tschebyscheff.tex diff --git a/buch/papers/ellfilter/Makefile.inc b/buch/papers/ellfilter/Makefile.inc index 8f20278..97e4089 100644 --- a/buch/papers/ellfilter/Makefile.inc +++ b/buch/papers/ellfilter/Makefile.inc @@ -3,12 +3,11 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -dependencies-ellfilter = \ - papers/ellfilter/packages.tex \ - papers/ellfilter/main.tex \ - papers/ellfilter/references.bib \ - papers/ellfilter/teil0.tex \ - papers/ellfilter/teil1.tex \ - papers/ellfilter/teil2.tex \ - papers/ellfilter/teil3.tex - +dependencies-ellfilter = \ + papers/ellfilter/packages.tex \ + papers/ellfilter/main.tex \ + papers/ellfilter/references.bib \ + papers/ellfilter/einleitung.tex \ + papers/ellfilter/tschebyscheff.tex \ + papers/ellfilter/jacobi.tex \ + papers/ellfilter/elliptic.tex diff --git a/buch/papers/ellfilter/einleitung.tex b/buch/papers/ellfilter/einleitung.tex new file mode 100644 index 0000000..37fd89f --- /dev/null +++ b/buch/papers/ellfilter/einleitung.tex @@ -0,0 +1,56 @@ +\section{Einleitung} + +% Lineare filter + +% Filter, Signalverarbeitung + + +Der womöglich wichtigste Filtertyp ist das Tiefpassfilter. +Dieses soll im Durchlassbereich unter der Grenzfrequenz $\Omega_p$ unverstärkt durchlassen und alle anderen Frequenzen vollständig auslöschen. + +% Bei der Implementierung von Filtern + +In der Elektrotechnik führen Schaltungen mit linearen Bauelementen wie Kondensatoren, Spulen und Widerständen immer zu linearen zeitinvarianten Systemen (LTI-System von englich \textit{time-invariant system}). +Die Übertragungsfunktion im Frequenzbereich $|H(\Omega)|$ eines solchen Systems ist dabei immer eine rationale Funktion, also eine Division von zwei Polynomen. +Die Polynome habe dabei immer reelle oder komplex-konjugierte Nullstellen. + + +\begin{equation} \label{ellfilter:eq:h_omega} + | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 F_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p} +\end{equation} + +$\Omega = 2 \pi f$ ist die analoge Frequenz + + +% Linear filter +Damit das Filter implementierbar und stabil ist, muss $H(\Omega)^2$ eine rationale Funktion sein, deren Nullstellen und Pole auf der linken Halbebene liegen. + +$N \in \mathbb{N} $ gibt dabei die Ordnung des Filters vor, also die maximale Anzahl Pole oder Nullstellen. + +Damit ein Filter die Passband Kondition erfüllt muss $|F_N(w)| \leq 1 \forall |w| \leq 1$ und für $|w| \geq 1$ sollte die Funktion möglichst schnell divergieren. +Eine einfaches Polynom, dass das erfüllt, erhalten wir wenn $F_N(w) = w^N$. +Tatsächlich erhalten wir damit das Butterworth Filter, wie in Abbildung \ref{ellfilter:fig:butterworth} ersichtlich. +\begin{figure} + \centering + \input{papers/ellfilter/python/F_N_butterworth.pgf} + \caption{$F_N$ für Butterworth filter. Der grüne Bereich definiert die erlaubten Werte für alle $F_N$-Funktionen.} + \label{ellfilter:fig:butterworth} +\end{figure} + +wenn $F_N(w)$ eine rationale Funktion ist, ist auch $H(\Omega)$ eine rationale Funktion und daher ein lineares Filter. %proof? + +\begin{align} + F_N(w) & = + \begin{cases} + w^N & \text{Butterworth} \\ + T_N(w) & \text{Tschebyscheff, Typ 1} \\ + [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\ + R_N(w, \xi) & \text{Elliptisch (Cauer)} \\ + \end{cases} +\end{align} + +Mit der Ausnahme vom Butterworth filter sind alle Filter nach speziellen Funktionen benannt. +Alle diese Filter sind optimal für unterschiedliche Anwendungsgebiete. +Das Butterworth-Filter, zum Beispiel, ist maximal flach im Durchlassbereich. +Das Tschebyscheff-1 Filter sind maximal steil für eine definierte Welligkeit im Durchlassbereich, währendem es im Sperrbereich monoton abfallend ist. +Es scheint so als sind gewisse Eigenschaften dieser speziellen Funktionen verantwortlich für die Optimalität dieser Filter. diff --git a/buch/papers/ellfilter/elliptic.tex b/buch/papers/ellfilter/elliptic.tex new file mode 100644 index 0000000..88bfbfe --- /dev/null +++ b/buch/papers/ellfilter/elliptic.tex @@ -0,0 +1,92 @@ +\section{Elliptische rationale Funktionen} + +Kommen wir nun zum eigentlichen Teil dieses Papers, den elliptischen rationalen Funktionen +\begin{align} + R_N(\xi, w) &= \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) \\ + &= \cd \left(N~\frac{K_1}{K}~\cd^{-1}(w, k), k_1)\right) , \quad k= 1/\xi, k_1 = 1/f(\xi) \\ + &= \cd \left(N~K_1~z , k_1 \right), \quad w= \cd(z K, k) +\end{align} + + +sieht ähnlich aus wie die trigonometrische Darstellung der Tschebyschef-Polynome \eqref{ellfilter:eq:chebychef_polynomials} +Anstelle vom Kosinus kommt hier die $\cd$-Funktion zum Einsatz. +Die Ordnungszahl $N$ kommt auch als Faktor for. +Zusätzlich werden noch zwei verschiedene elliptische Module $k$ und $k_1$ gebraucht. + + + +Sinus entspricht $\sn$ + +Damit die Nullstellen an ähnlichen Positionen zu liegen kommen wie bei den Tschebyscheff-Polynomen, muss die $\cd$-Funktion gewählt werden. + +Die $\cd^{-1}(w, k)$-Funktion ist um $K$ verschoben zur $\sn^{-1}(w, k)$-Funktion, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd}. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/cd.tikz.tex} + \caption{ + $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$. + Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch. + } + \label{ellfilter:fig:cd} +\end{figure} +Auffallend ist, dass sich alle Nullstellen und Polstellen um $K$ verschoben haben. + +Durch das Konzept vom fundamentalen Rechteck, siehe Abbildung \ref{ellfilter:fig:fundamental_rectangle} können für alle inversen Jaccobi elliptischen Funktionen die Positionen der Null- und Polstellen anhand eines Diagramms ermittelt werden. +Der erste Buchstabe bestimmt die Position der Nullstelle und der zweite Buchstabe die Polstelle. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/fundamental_rectangle.tikz.tex} + \caption{ + Fundamentales Rechteck der inversen Jaccobi elliptischen Funktionen. + } + \label{ellfilter:fig:fundamental_rectangle} +\end{figure} + +Auffallend an der $w = \sn(z, k)$-Funktion ist, dass sich $w$ auf der reellen Achse wie der Kosinus immer zwischen $-1$ und $1$ bewegt, während bei $\mathrm{Im(z) = K^\prime}$ die Werte zwischen $\pm 1/k$ und $\pm \infty$ verlaufen. +Die Funktion hat also Equirippel-Verhalten um $w=0$ und um $w=\pm \infty$. +Falls es möglich ist diese Werte abzufahren im Sti der Tschebyscheff-Polynome, kann ein Filter gebaut werden, dass Equirippel-Verhalten im Durchlass- und Sperrbereich aufweist. + + + +Analog zu Abbildung \ref{ellfilter:fig:arccos2} können wir auch bei den elliptisch rationalen Funktionen die komplexe $z$-Ebene betrachten, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd2}, um die besser zu verstehen. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/cd2.tikz.tex} + \caption{ + $z_1$-Ebene der elliptischen rationalen Funktionen. + Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen passiert. + } + \label{ellfilter:fig:cd2} +\end{figure} +% Da die $\cd^{-1}$-Funktion + + + +\begin{figure} + \centering + \input{papers/ellfilter/python/F_N_elliptic.pgf} + \caption{$F_N$ für ein elliptischs filter.} + \label{ellfilter:fig:elliptic} +\end{figure} + +\subsection{Degree Equation} + +Der $\cd^{-1}$ Term muss so verzogen werden, dass die umgebene $\cd$-Funktion die Nullstellen und Pole trifft. +Dies trifft ein wenn die Degree Equation erfüllt ist. + +\begin{equation} + N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1} +\end{equation} + + +Leider ist das lösen dieser Gleichung nicht trivial. +Die Rechnung wird in \ref{ellfilter:bib:orfanidis} im Detail angeschaut. + + +\subsection{Polynome?} + +Bei den Tschebyscheff-Polynomen haben wir gesehen, dass die Trigonometrische Formel zu einfachen Polynomen umgewandelt werden kann. +Im gegensatz zum $\cos^{-1}$ hat der $\cd^{-1}$ nicht nur Nullstellen sondern auch Pole. +Somit entstehen bei den elliptischen rationalen Funktionen, wie es der name auch deutet, rationale Funktionen, also ein Bruch von zwei Polynomen. + +Da Transformationen einer rationalen Funktionen mit Grundrechenarten, wie es in \eqref{ellfilter:eq:h_omega} der Fall ist, immer noch rationale Funktionen ergeben, stellt dies kein Problem für die Implementierung dar. diff --git a/buch/papers/ellfilter/jacobi.tex b/buch/papers/ellfilter/jacobi.tex new file mode 100644 index 0000000..6a208fa --- /dev/null +++ b/buch/papers/ellfilter/jacobi.tex @@ -0,0 +1,189 @@ +\section{Jacobische elliptische Funktionen} + +%TODO $z$ or $u$ for parameter? + +Für das elliptische Filter wird statt der, für das Tschebyscheff-Filter benutzen Kreis-Trigonometrie die elliptischen Funktionen gebraucht. +Der Begriff elliptische Funktion wird für sehr viele Funktionen gebraucht, daher ist es hier wichtig zu erwähnen, dass es ausschliesslich um die Jacobischen elliptischen Funktionen geht. + +Im Wesentlichen erweitern die Jacobi elliptischen Funktionen die trigonometrische Funktionen für Ellipsen. +Zum Beispiel gibt es analog zum Sinus den elliptischen $\sn(z, k)$. +Im Gegensatz zum den trigonometrischen Funktionen haben die elliptischen Funktionen zwei parameter. +Zum einen gibt es den \textit{elliptische Modul} $k$, der die Exzentrizität der Ellipse parametrisiert. +Zum andern das Winkelargument $z$. +Im Kreis ist der Radius für alle Winkel konstant, bei Ellipsen ändert sich das. +Dies hat zur Folge, dass bei einer Ellipse die Kreisbodenstrecke nicht linear zum Winkel verläuft. +Darum kann hier nicht der gewohnte Winkel verwendet werden. +Das Winkelargument $z$ kann durch das elliptische Integral erster Art +\begin{equation} + z + = + F(\phi, k) + = + \int_{0}^{\phi} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + } + = + \int_{0}^{\phi} + \frac{ + dt + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } %TODO which is right? are both functions from phi? +\end{equation} +mit dem Winkel $\phi$ in Verbindung liegt. + +Dabei wird das vollständige und unvollständige Elliptische integral unterschieden. +Beim vollständigen Integral +\begin{equation} + K(k) + = + \int_{0}^{\pi / 2} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + } +\end{equation} +wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$ und liefert das Winkelargument für eine Vierteldrehung. +Die Zahl wird oft auch abgekürzt mit $K = K(k)$ und ist für das elliptische Filter sehr relevant. +Alle elliptishen Funktionen sind somit $4K$-periodisch. + +Neben dem $\sn$ gibt es zwei weitere basis-elliptische Funktionen $\cn$ und $\dn$. +Dazu kommen noch weitere abgeleitete Funktionen, die durch Quotienten und Kehrwerte dieser Funktionen zustande kommen. +Insgesamt sind es die zwölf Funktionen +\begin{equation*} + \sn \quad + \ns \quad + \scelliptic \quad + \sd \quad + \cn \quad + \nc \quad + \cs \quad + \cd \quad + \dn \quad + \nd \quad + \ds \quad + \dc. +\end{equation*} + +Die Jacobischen elliptischen Funktionen können mit der inversen Funktion des kompletten elliptischen Integrals erster Art +\begin{equation} + \phi = F^{-1}(z, k) +\end{equation} +definiert werden. Dabei ist zu beachten dass nur das $z$ Argument der Funktion invertiert wird, also +\begin{equation} + z = F(\phi, k) + \Leftrightarrow + \phi = F^{-1}(z, k). +\end{equation} +Mithilfe von $F^{-1}$ kann zum Beispiel $sn^{-1}$ mit dem Elliptischen integral dargestellt werden: +\begin{equation} + \sin(\phi) + = + \sin \left( F^{-1}(z, k) \right) + = + \sn(z, k) + = + w +\end{equation} + +\begin{equation} + \phi + = + F^{-1}(z, k) + = + \sin^{-1} \big( \sn (z, k ) \big) + = + \sin^{-1} ( w ) +\end{equation} + +\begin{equation} + F(\phi, k) + = + z + = + F( \sin^{-1} \big( \sn (z, k ) \big) , k) + = + F( \sin^{-1} ( w ), k) +\end{equation} + +\begin{equation} + \sn^{-1}(w, k) + = + F(\phi, k), + \quad + \phi = \sin^{-1}(w) +\end{equation} + +\begin{align} + \sn^{-1}(w, k) + & = + \int_{0}^{\phi} + \frac{ + d\theta + }{ + \sqrt{ + 1-k^2 \sin^2 \theta + } + }, + \quad + \phi = \sin^{-1}(w) + \\ + & = + \int_{0}^{w} + \frac{ + dt + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } +\end{align} + +Beim $\cos^{-1}(x)$ haben wir gesehen, dass die analytische Fortsetzung bei $x < -1$ und $x > 1$ rechtwinklig in die Komplexen zahlen wandert. +Wenn man das gleiche mit $\sn^{-1}(w, k)$ macht, erkennt man zwei interessante Stellen. +Die erste ist die gleiche wie beim $\cos^{-1}(x)$ nämlich bei $t = \pm 1$. +Der erste Term unter der Wurzel wird dann negativ, während der zweite noch positiv ist, da $k \leq 1$. +\begin{equation} + \frac{ + 1 + }{ + \sqrt{ + (1-t^2)(1-k^2 t^2) + } + } + \in \mathbb{R} + \quad \forall \quad + -1 \leq t \leq 1 +\end{equation} +Die zweite stelle passiert wenn beide Faktoren unter der Wurzel negativ werden, was bei $t = 1/k$ der Fall ist. + + + + +Funktion in relle und komplexe Richtung periodisch + +In der reellen Richtung ist sie $4K(k)$-periodisch und in der imaginären Richtung $4K^\prime(k)$-periodisch. + + + +%TODO sn^{-1} grafik + +\begin{figure} + \centering + \input{papers/ellfilter/tikz/sn.tikz.tex} + \caption{ + $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$. + Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch. + } + % \label{ellfilter:fig:cd2} +\end{figure} diff --git a/buch/papers/ellfilter/main.tex b/buch/papers/ellfilter/main.tex index e9d6aba..c58dfa7 100644 --- a/buch/papers/ellfilter/main.tex +++ b/buch/papers/ellfilter/main.tex @@ -8,485 +8,10 @@ \begin{refsection} \chapterauthor{Nicolas Tobler} +\input{papers/ellfilter/einleitung.tex} +\input{papers/ellfilter/tschebyscheff.tex} +\input{papers/ellfilter/jacobi.tex} +\input{papers/ellfilter/elliptic.tex} -\section{Einleitung} - -% Lineare filter - -% Filter, Signalverarbeitung - - -Der womöglich wichtigste Filtertyp ist das Tiefpassfilter. -Dieses soll im Durchlassbereich unter der Grenzfrequenz $\Omega_p$ unverstärkt durchlassen und alle anderen Frequenzen vollständig auslöschen. - -% Bei der Implementierung von Filtern - -In der Elektrotechnik führen Schaltungen mit linearen Bauelementen wie Kondensatoren, Spulen und Widerständen immer zu linearen zeitinvarianten Systemen (LTI-System von englich \textit{time-invariant system}). -Die Übertragungsfunktion im Frequenzbereich $|H(\Omega)|$ eines solchen Systems ist dabei immer eine rationale Funktion, also eine Division von zwei Polynomen. -Die Polynome habe dabei immer reelle oder komplex-konjugierte Nullstellen. - - -\begin{equation} \label{ellfilter:eq:h_omega} - | H(\Omega)|^2 = \frac{1}{1 + \varepsilon_p^2 F_N^2(w)}, \quad w=\frac{\Omega}{\Omega_p} -\end{equation} - -$\Omega = 2 \pi f$ ist die analoge Frequenz - - -% Linear filter -Damit das Filter implementierbar und stabil ist, muss $H(\Omega)^2$ eine rationale Funktion sein, deren Nullstellen und Pole auf der linken Halbebene liegen. - -$N \in \mathbb{N} $ gibt dabei die Ordnung des Filters vor, also die maximale Anzahl Pole oder Nullstellen. - -Damit ein Filter die Passband Kondition erfüllt muss $|F_N(w)| \leq 1 \forall |w| \leq 1$ und für $|w| \geq 1$ sollte die Funktion möglichst schnell divergieren. -Eine einfaches Polynom, dass das erfüllt, erhalten wir wenn $F_N(w) = w^N$. -Tatsächlich erhalten wir damit das Butterworth Filter, wie in Abbildung \ref{ellfilter:fig:butterworth} ersichtlich. -\begin{figure} - \centering - \input{papers/ellfilter/python/F_N_butterworth.pgf} - \caption{$F_N$ für Butterworth filter. Der grüne Bereich definiert die erlaubten Werte für alle $F_N$-Funktionen.} - \label{ellfilter:fig:butterworth} -\end{figure} - -wenn $F_N(w)$ eine rationale Funktion ist, ist auch $H(\Omega)$ eine rationale Funktion und daher ein lineares Filter. %proof? - -\begin{align} - F_N(w) & = - \begin{cases} - w^N & \text{Butterworth} \\ - T_N(w) & \text{Tschebyscheff, Typ 1} \\ - [k_1 T_N (k^{-1} w^{-1})]^{-1} & \text{Tschebyscheff, Typ 2} \\ - R_N(w, \xi) & \text{Elliptisch (Cauer)} \\ - \end{cases} -\end{align} - -Mit der Ausnahme vom Butterworth filter sind alle Filter nach speziellen Funktionen benannt. -Alle diese Filter sind optimal für unterschiedliche Anwendungsgebiete. -Das Butterworth-Filter, zum Beispiel, ist maximal flach im Durchlassbereich. -Das Tschebyscheff-1 Filter sind maximal steil für eine definierte Welligkeit im Durchlassbereich, währendem es im Sperrbereich monoton abfallend ist. -Es scheint so als sind gewisse Eigenschaften dieser speziellen Funktionen verantwortlich für die Optimalität dieser Filter. - -\section{Tschebyscheff-Filter} - -Als Einstieg betrachent Wir das Tschebyscheff-Filter, welches sehr verwand ist mit dem elliptischen Filter. -Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Filter Spezialfälle davon. - -Der Name des Filters deutet schon an, dass die Tschebyscheff-Polynome $T_N$ für das Filter relevant sind: -\begin{align} - T_{0}(x)&=1\\ - T_{1}(x)&=x\\ - T_{2}(x)&=2x^{2}-1\\ - T_{3}(x)&=4x^{3}-3x\\ - T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x). -\end{align} -Bemerkenswert ist, dass die Polynome im Intervall $[-1, 1]$ mit der trigonometrischen Funktion -\begin{align} \label{ellfilter:eq:chebychef_polynomials} - T_N(w) &= \cos \left( N \cos^{-1}(w) \right) \\ - &= \cos \left(N~z \right), \quad w= \cos(z) -\end{align} -übereinstimmt. -Der Zusammenhang lässt sich mit den Doppel- und Mehrfachwinkelfunktionen der trigonometrischen Funktionen erklären. -Abbildung \ref{ellfilter:fig:chebychef_polynomials} zeigt einige Tschebyscheff-Polynome. -\begin{figure} - \centering - \input{papers/ellfilter/python/F_N_chebychev2.pgf} - \caption{Die Tschebyscheff-Polynome $C_N$.} - \label{ellfilter:fig:chebychef_polynomials} -\end{figure} -Da der Kosinus begrenzt zwischen $-1$ und $1$ ist, sind auch die Tschebyscheff-Polynome begrenzt. -Geht man aber über das Intervall $[-1, 1]$ hinaus, divergieren die Funktionen mit zunehmender Ordnung immer steiler gegen $\pm \infty$. -Diese Eigenschaft ist sehr nützlich für ein Filter. -Wenn wir die Tschebyscheff-Polynome quadrieren, passen sie perfekt in die Voraussetzungen für Filterfunktionen, wie es Abbildung \ref{ellfiter:fig:chebychef} demonstriert. -\begin{figure} - \centering - \input{papers/ellfilter/python/F_N_chebychev.pgf} - \caption{Die Tschebyscheff-Polynome füllen den erlaubten Bereich besser, und erhalten dadurch eine steilere Flanke im Sperrbereich.} - \label{ellfiter:fig:chebychef} -\end{figure} - - -Die analytische Fortsetzung von \eqref{ellfilter:eq:chebychef_polynomials} über das Intervall $[-1,1]$ hinaus stimmt mit den Polynomen überein, wie es zu erwarten ist. -Die genauere Betrachtung wird uns dann helfen die elliptischen Filter besser zu verstehen. - -Starten wir mit der Funktion, die als erstes auf $w$ angewendet wird, dem Arcuscosinus. -Die invertierte Funktion des Kosinus kann als definites Integral dargestellt werden: -\begin{align} - \cos^{-1}(x) - &= - \int_{x}^{1} - \frac{ - dz - }{ - \sqrt{ - 1-z^2 - } - }\\ - &= - \int_{0}^{x} - \frac{ - -1 - }{ - \sqrt{ - 1-z^2 - } - } - ~dz - + \frac{\pi}{2} -\end{align} -Der Integrand oder auch die Ableitung -\begin{equation} - \frac{ - -1 - }{ - \sqrt{ - 1-z^2 - } - } -\end{equation} -bestimmt dabei die Richtung, in der die Funktion verläuft. -Der reelle Arcuscosinus is bekanntlich nur für $|z| \leq 1$ definiert. -Hier bleibt der Wert unter der Wurzel positiv und das Integral liefert reelle Werte. -Doch wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ. -Durch die Quadratwurzel entstehen für den Integranden zwei rein komplexe Lösungen. -Der Wert des Arcuscosinus verlässt also bei $z= \pm 1$ den reellen Zahlenstrahl und knickt in die komplexe Ebene ab. -Abbildung \ref{ellfilter:fig:arccos} zeigt den $\arccos$ in der komplexen Ebene. -\begin{figure} - \centering - \input{papers/ellfilter/tikz/arccos.tikz.tex} - \caption{Die Funktion $z = \cos^{-1}(w)$ dargestellt in der komplexen ebene.} - \label{ellfilter:fig:arccos} -\end{figure} -Wegen der Periodizität des Kosinus ist auch der Arcuscosinus $2\pi$-periodisch und es entstehen periodische Nullstellen. -% \begin{equation} -% \frac{ -% 1 -% }{ -% \sqrt{ -% 1-z^2 -% } -% } -% \in \mathbb{R} -% \quad -% \forall -% \quad -% -1 \leq z \leq 1 -% \end{equation} -% \begin{equation} -% \frac{ -% 1 -% }{ -% \sqrt{ -% 1-z^2 -% } -% } -% = i \xi \quad | \quad \xi \in \mathbb{R} -% \quad -% \forall -% \quad -% z \leq -1 \cup z \geq 1 -% \end{equation} - -Die Tschebyscheff-Polynome skalieren diese Nullstellen mit dem Ordnungsfaktor $N$, wie dargestellt in Abbildung \ref{ellfilter:fig:arccos2}. -\begin{figure} - \centering - \input{papers/ellfilter/tikz/arccos2.tikz.tex} - \caption{ - $z_1=N \cos^{-1}(w)$-Ebene der Tschebyscheff-Funktion. - Die eingefärbten Pfade sind Verläufe von $w~\forall~[-\infty, \infty]$ für verschiedene Ordnungen $N$. - Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden passiert. - } - \label{ellfilter:fig:arccos2} -\end{figure} -Somit passert $\cos( N~\cos^{-1}(w))$ im Intervall $[-1, 1]$ $N$ Nullstellen. -Durch die spezielle Anordnung der Nullstellen hat die Funktion Equirippel-Verhalten und ist dennoch ein Polynom, was sich perfekt für linear Filter eignet. - -\section{Jacobische elliptische Funktionen} - -%TODO $z$ or $u$ for parameter? - -Für das elliptische Filter wird statt der, für das Tschebyscheff-Filter benutzen Kreis-Trigonometrie die elliptischen Funktionen gebraucht. -Der Begriff elliptische Funktion wird für sehr viele Funktionen gebraucht, daher ist es hier wichtig zu erwähnen, dass es ausschliesslich um die Jacobischen elliptischen Funktionen geht. - -Im Wesentlichen erweitern die Jacobi elliptischen Funktionen die trigonometrische Funktionen für Ellipsen. -Zum Beispiel gibt es analog zum Sinus den elliptischen $\sn(z, k)$. -Im Gegensatz zum den trigonometrischen Funktionen haben die elliptischen Funktionen zwei parameter. -Zum einen gibt es den \textit{elliptische Modul} $k$, der die Exzentrizität der Ellipse parametrisiert. -Zum andern das Winkelargument $z$. -Im Kreis ist der Radius für alle Winkel konstant, bei Ellipsen ändert sich das. -Dies hat zur Folge, dass bei einer Ellipse die Kreisbodenstrecke nicht linear zum Winkel verläuft. -Darum kann hier nicht der gewohnte Winkel verwendet werden. -Das Winkelargument $z$ kann durch das elliptische Integral erster Art -\begin{equation} - z - = - F(\phi, k) - = - \int_{0}^{\phi} - \frac{ - d\theta - }{ - \sqrt{ - 1-k^2 \sin^2 \theta - } - } - = - \int_{0}^{\phi} - \frac{ - dt - }{ - \sqrt{ - (1-t^2)(1-k^2 t^2) - } - } %TODO which is right? are both functions from phi? -\end{equation} -mit dem Winkel $\phi$ in Verbindung liegt. - -Dabei wird das vollständige und unvollständige Elliptische integral unterschieden. -Beim vollständigen Integral -\begin{equation} - K(k) - = - \int_{0}^{\pi / 2} - \frac{ - d\theta - }{ - \sqrt{ - 1-k^2 \sin^2 \theta - } - } -\end{equation} -wird über ein viertel Ellipsenbogen integriert also bis $\phi=\pi/2$ und liefert das Winkelargument für eine Vierteldrehung. -Die Zahl wird oft auch abgekürzt mit $K = K(k)$ und ist für das elliptische Filter sehr relevant. -Alle elliptishen Funktionen sind somit $4K$-periodisch. - -Neben dem $\sn$ gibt es zwei weitere basis-elliptische Funktionen $\cn$ und $\dn$. -Dazu kommen noch weitere abgeleitete Funktionen, die durch Quotienten und Kehrwerte dieser Funktionen zustande kommen. -Insgesamt sind es die zwölf Funktionen -\begin{equation*} - \sn \quad - \ns \quad - \scelliptic \quad - \sd \quad - \cn \quad - \nc \quad - \cs \quad - \cd \quad - \dn \quad - \nd \quad - \ds \quad - \dc. -\end{equation*} - -Die Jacobischen elliptischen Funktionen können mit der inversen Funktion des kompletten elliptischen Integrals erster Art -\begin{equation} - \phi = F^{-1}(z, k) -\end{equation} -definiert werden. Dabei ist zu beachten dass nur das $z$ Argument der Funktion invertiert wird, also -\begin{equation} - z = F(\phi, k) - \Leftrightarrow - \phi = F^{-1}(z, k). -\end{equation} -Mithilfe von $F^{-1}$ kann zum Beispiel $sn^{-1}$ mit dem Elliptischen integral dargestellt werden: -\begin{equation} - \sin(\phi) - = - \sin \left( F^{-1}(z, k) \right) - = - \sn(z, k) - = - w -\end{equation} - -\begin{equation} - \phi - = - F^{-1}(z, k) - = - \sin^{-1} \big( \sn (z, k ) \big) - = - \sin^{-1} ( w ) -\end{equation} - -\begin{equation} - F(\phi, k) - = - z - = - F( \sin^{-1} \big( \sn (z, k ) \big) , k) - = - F( \sin^{-1} ( w ), k) -\end{equation} - -\begin{equation} - \sn^{-1}(w, k) - = - F(\phi, k), - \quad - \phi = \sin^{-1}(w) -\end{equation} - -\begin{align} - \sn^{-1}(w, k) - & = - \int_{0}^{\phi} - \frac{ - d\theta - }{ - \sqrt{ - 1-k^2 \sin^2 \theta - } - }, - \quad - \phi = \sin^{-1}(w) - \\ - & = - \int_{0}^{w} - \frac{ - dt - }{ - \sqrt{ - (1-t^2)(1-k^2 t^2) - } - } -\end{align} - -Beim $\cos^{-1}(x)$ haben wir gesehen, dass die analytische Fortsetzung bei $x < -1$ und $x > 1$ rechtwinklig in die Komplexen zahlen wandert. -Wenn man das gleiche mit $\sn^{-1}(w, k)$ macht, erkennt man zwei interessante Stellen. -Die erste ist die gleiche wie beim $\cos^{-1}(x)$ nämlich bei $t = \pm 1$. -Der erste Term unter der Wurzel wird dann negativ, während der zweite noch positiv ist, da $k \leq 1$. -\begin{equation} - \frac{ - 1 - }{ - \sqrt{ - (1-t^2)(1-k^2 t^2) - } - } - \in \mathbb{R} - \quad \forall \quad - -1 \leq t \leq 1 -\end{equation} -Die zweite stelle passiert wenn beide Faktoren unter der Wurzel negativ werden, was bei $t = 1/k$ der Fall ist. - - - - -Funktion in relle und komplexe Richtung periodisch - -In der reellen Richtung ist sie $4K(k)$-periodisch und in der imaginären Richtung $4K^\prime(k)$-periodisch. - - - -%TODO sn^{-1} grafik - -\begin{figure} - \centering - \input{papers/ellfilter/tikz/sn.tikz.tex} - \caption{ - $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$. - Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch. - } - % \label{ellfilter:fig:cd2} -\end{figure} - -\section{Elliptische rationale Funktionen} - -Kommen wir nun zum eigentlichen Teil dieses Papers, den elliptischen rationalen Funktionen -\begin{align} - R_N(\xi, w) &= \cd \left(N~f_1(\xi)~\cd^{-1}(w, 1/\xi), f_2(\xi)\right) \\ - &= \cd \left(N~\frac{K_1}{K}~\cd^{-1}(w, k), k_1)\right) , \quad k= 1/\xi, k_1 = 1/f(\xi) \\ - &= \cd \left(N~K_1~z , k_1 \right), \quad w= \cd(z K, k) -\end{align} - - -sieht ähnlich aus wie die trigonometrische Darstellung der Tschebyschef-Polynome \eqref{ellfilter:eq:chebychef_polynomials} -Anstelle vom Kosinus kommt hier die $\cd$-Funktion zum Einsatz. -Die Ordnungszahl $N$ kommt auch als Faktor for. -Zusätzlich werden noch zwei verschiedene elliptische Module $k$ und $k_1$ gebraucht. - - - -Sinus entspricht $\sn$ - -Damit die Nullstellen an ähnlichen Positionen zu liegen kommen wie bei den Tschebyscheff-Polynomen, muss die $\cd$-Funktion gewählt werden. - -Die $\cd^{-1}(w, k)$-Funktion ist um $K$ verschoben zur $\sn^{-1}(w, k)$-Funktion, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd}. -\begin{figure} - \centering - \input{papers/ellfilter/tikz/cd.tikz.tex} - \caption{ - $z$-Ebene der Funktion $z = \sn^{-1}(w, k)$. - Die Funktion ist in der realen Achse $4K$-periodisch und in der imaginären Achse $2jK^\prime$-periodisch. - } - \label{ellfilter:fig:cd} -\end{figure} -Auffallend ist, dass sich alle Nullstellen und Polstellen um $K$ verschoben haben. - -Durch das Konzept vom fundamentalen Rechteck, siehe Abbildung \ref{ellfilter:fig:fundamental_rectangle} können für alle inversen Jaccobi elliptischen Funktionen die Positionen der Null- und Polstellen anhand eines Diagramms ermittelt werden. -Der erste Buchstabe bestimmt die Position der Nullstelle und der zweite Buchstabe die Polstelle. -\begin{figure} - \centering - \input{papers/ellfilter/tikz/fundamental_rectangle.tikz.tex} - \caption{ - Fundamentales Rechteck der inversen Jaccobi elliptischen Funktionen. - } - \label{ellfilter:fig:fundamental_rectangle} -\end{figure} - -Auffallend an der $w = \sn(z, k)$-Funktion ist, dass sich $w$ auf der reellen Achse wie der Kosinus immer zwischen $-1$ und $1$ bewegt, während bei $\mathrm{Im(z) = K^\prime}$ die Werte zwischen $\pm 1/k$ und $\pm \infty$ verlaufen. -Die Funktion hat also Equirippel-Verhalten um $w=0$ und um $w=\pm \infty$. -Falls es möglich ist diese Werte abzufahren im Sti der Tschebyscheff-Polynome, kann ein Filter gebaut werden, dass Equirippel-Verhalten im Durchlass- und Sperrbereich aufweist. - - - -Analog zu Abbildung \ref{ellfilter:fig:arccos2} können wir auch bei den elliptisch rationalen Funktionen die komplexe $z$-Ebene betrachten, wie ersichtlich in Abbildung \ref{ellfilter:fig:cd2}, um die besser zu verstehen. -\begin{figure} - \centering - \input{papers/ellfilter/tikz/cd2.tikz.tex} - \caption{ - $z_1$-Ebene der elliptischen rationalen Funktionen. - Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen passiert. - } - \label{ellfilter:fig:cd2} -\end{figure} -% Da die $\cd^{-1}$-Funktion - - - -\begin{figure} - \centering - \input{papers/ellfilter/python/F_N_elliptic.pgf} - \caption{$F_N$ für ein elliptischs filter.} - \label{ellfilter:fig:elliptic} -\end{figure} - -\subsection{Degree Equation} - -Der $\cd^{-1}$ Term muss so verzogen werden, dass die umgebene $\cd$-Funktion die Nullstellen und Pole trifft. -Dies trifft ein wenn die Degree Equation erfüllt ist. - -\begin{equation} - N \frac{K^\prime}{K} = \frac{K^\prime_1}{K_1} -\end{equation} - - -Leider ist das lösen dieser Gleichung nicht trivial. -Die Rechnung wird in \ref{ellfilter:bib:orfanidis} im Detail angeschaut. - - -\subsection{Polynome?} - -Bei den Tschebyscheff-Polynomen haben wir gesehen, dass die Trigonometrische Formel zu einfachen Polynomen umgewandelt werden kann. -Im gegensatz zum $\cos^{-1}$ hat der $\cd^{-1}$ nicht nur Nullstellen sondern auch Pole. -Somit entstehen bei den elliptischen rationalen Funktionen, wie es der name auch deutet, rationale Funktionen, also ein Bruch von zwei Polynomen. - -Da Transformationen einer rationalen Funktionen mit Grundrechenarten, wie es in \eqref{ellfilter:eq:h_omega} der Fall ist, immer noch rationale Funktionen ergeben, stellt dies kein Problem für die Implementierung dar. - -\input{papers/ellfilter/teil0.tex} -\input{papers/ellfilter/teil1.tex} -\input{papers/ellfilter/teil2.tex} -\input{papers/ellfilter/teil3.tex} - -% \printbibliography[heading=subbibliography] +\printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/ellfilter/teil0.tex b/buch/papers/ellfilter/teil0.tex deleted file mode 100644 index 6204bc0..0000000 --- a/buch/papers/ellfilter/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -% \section{Teil 0\label{ellfilter:section:teil0}} -% \rhead{Teil 0} -% Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -% nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -% erat, sed diam voluptua \cite{ellfilter:bibtex}. -% At vero eos et accusam et justo duo dolores et ea rebum. -% Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -% dolor sit amet. - -% Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -% nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -% erat, sed diam voluptua. -% At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -% kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -% amet. - - diff --git a/buch/papers/ellfilter/teil1.tex b/buch/papers/ellfilter/teil1.tex deleted file mode 100644 index 4760473..0000000 --- a/buch/papers/ellfilter/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -% \section{Teil 1 -% \label{ellfilter:section:teil1}} -% \rhead{Problemstellung} -% Sed ut perspiciatis unde omnis iste natus error sit voluptatem -% accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -% quae ab illo inventore veritatis et quasi architecto beatae vitae -% dicta sunt explicabo. -% Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -% aut fugit, sed quia consequuntur magni dolores eos qui ratione -% voluptatem sequi nesciunt -% \begin{equation} -% \int_a^b x^2\, dx -% = -% \left[ \frac13 x^3 \right]_a^b -% = -% \frac{b^3-a^3}3. -% \label{ellfilter:equation1} -% \end{equation} -% Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -% consectetur, adipisci velit, sed quia non numquam eius modi tempora -% incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -% Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -% suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -% Quis autem vel eum iure reprehenderit qui in ea voluptate velit -% esse quam nihil molestiae consequatur, vel illum qui dolorem eum -% fugiat quo voluptas nulla pariatur? - -% \subsection{De finibus bonorum et malorum -% \label{ellfilter:subsection:finibus}} -% At vero eos et accusamus et iusto odio dignissimos ducimus qui -% blanditiis praesentium voluptatum deleniti atque corrupti quos -% dolores et quas molestias excepturi sint occaecati cupiditate non -% provident, similique sunt in culpa qui officia deserunt mollitia -% animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -% Et harum quidem rerum facilis est et expedita distinctio -% \ref{ellfilter:section:loesung}. -% Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -% impedit quo minus id quod maxime placeat facere possimus, omnis -% voluptas assumenda est, omnis dolor repellendus -% \ref{ellfilter:section:folgerung}. -% Temporibus autem quibusdam et aut officiis debitis aut rerum -% necessitatibus saepe eveniet ut et voluptates repudiandae sint et -% molestiae non recusandae. -% Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -% voluptatibus maiores alias consequatur aut perferendis doloribus -% asperiores repellat. - - diff --git a/buch/papers/ellfilter/teil2.tex b/buch/papers/ellfilter/teil2.tex deleted file mode 100644 index 39dd5d7..0000000 --- a/buch/papers/ellfilter/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -% \section{Teil 2 -% \label{ellfilter:section:teil2}} -% \rhead{Teil 2} -% Sed ut perspiciatis unde omnis iste natus error sit voluptatem -% accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -% quae ab illo inventore veritatis et quasi architecto beatae vitae -% dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -% aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -% eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -% est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -% velit, sed quia non numquam eius modi tempora incidunt ut labore -% et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -% veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -% nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -% reprehenderit qui in ea voluptate velit esse quam nihil molestiae -% consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -% pariatur? - -% \subsection{De finibus bonorum et malorum -% \label{ellfilter:subsection:bonorum}} -% At vero eos et accusamus et iusto odio dignissimos ducimus qui -% blanditiis praesentium voluptatum deleniti atque corrupti quos -% dolores et quas molestias excepturi sint occaecati cupiditate non -% provident, similique sunt in culpa qui officia deserunt mollitia -% animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -% est et expedita distinctio. Nam libero tempore, cum soluta nobis -% est eligendi optio cumque nihil impedit quo minus id quod maxime -% placeat facere possimus, omnis voluptas assumenda est, omnis dolor -% repellendus. Temporibus autem quibusdam et aut officiis debitis aut -% rerum necessitatibus saepe eveniet ut et voluptates repudiandae -% sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -% sapiente delectus, ut aut reiciendis voluptatibus maiores alias -% consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/ellfilter/teil3.tex b/buch/papers/ellfilter/teil3.tex deleted file mode 100644 index dad96ad..0000000 --- a/buch/papers/ellfilter/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -% \section{Teil 3 -% \label{ellfilter:section:teil3}} -% \rhead{Teil 3} -% Sed ut perspiciatis unde omnis iste natus error sit voluptatem -% accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -% quae ab illo inventore veritatis et quasi architecto beatae vitae -% dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -% aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -% eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -% est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -% velit, sed quia non numquam eius modi tempora incidunt ut labore -% et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -% veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -% nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -% reprehenderit qui in ea voluptate velit esse quam nihil molestiae -% consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -% pariatur? - -% \subsection{De finibus bonorum et malorum -% \label{ellfilter:subsection:malorum}} -% At vero eos et accusamus et iusto odio dignissimos ducimus qui -% blanditiis praesentium voluptatum deleniti atque corrupti quos -% dolores et quas molestias excepturi sint occaecati cupiditate non -% provident, similique sunt in culpa qui officia deserunt mollitia -% animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -% est et expedita distinctio. Nam libero tempore, cum soluta nobis -% est eligendi optio cumque nihil impedit quo minus id quod maxime -% placeat facere possimus, omnis voluptas assumenda est, omnis dolor -% repellendus. Temporibus autem quibusdam et aut officiis debitis aut -% rerum necessitatibus saepe eveniet ut et voluptates repudiandae -% sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -% sapiente delectus, ut aut reiciendis voluptatibus maiores alias -% consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/ellfilter/tschebyscheff.tex b/buch/papers/ellfilter/tschebyscheff.tex new file mode 100644 index 0000000..7d426b6 --- /dev/null +++ b/buch/papers/ellfilter/tschebyscheff.tex @@ -0,0 +1,133 @@ +\section{Tschebyscheff-Filter} + +Als Einstieg betrachent Wir das Tschebyscheff-Filter, welches sehr verwand ist mit dem elliptischen Filter. +Genauer ausgedrückt sind die Tschebyscheff-1 und -2 Filter Spezialfälle davon. + +Der Name des Filters deutet schon an, dass die Tschebyscheff-Polynome $T_N$ für das Filter relevant sind: +\begin{align} + T_{0}(x)&=1\\ + T_{1}(x)&=x\\ + T_{2}(x)&=2x^{2}-1\\ + T_{3}(x)&=4x^{3}-3x\\ + T_{n+1}(x)&=2x~T_{n}(x)-T_{n-1}(x). +\end{align} +Bemerkenswert ist, dass die Polynome im Intervall $[-1, 1]$ mit der trigonometrischen Funktion +\begin{align} \label{ellfilter:eq:chebychef_polynomials} + T_N(w) &= \cos \left( N \cos^{-1}(w) \right) \\ + &= \cos \left(N~z \right), \quad w= \cos(z) +\end{align} +übereinstimmt. +Der Zusammenhang lässt sich mit den Doppel- und Mehrfachwinkelfunktionen der trigonometrischen Funktionen erklären. +Abbildung \ref{ellfilter:fig:chebychef_polynomials} zeigt einige Tschebyscheff-Polynome. +\begin{figure} + \centering + \input{papers/ellfilter/python/F_N_chebychev2.pgf} + \caption{Die Tschebyscheff-Polynome $C_N$.} + \label{ellfilter:fig:chebychef_polynomials} +\end{figure} +Da der Kosinus begrenzt zwischen $-1$ und $1$ ist, sind auch die Tschebyscheff-Polynome begrenzt. +Geht man aber über das Intervall $[-1, 1]$ hinaus, divergieren die Funktionen mit zunehmender Ordnung immer steiler gegen $\pm \infty$. +Diese Eigenschaft ist sehr nützlich für ein Filter. +Wenn wir die Tschebyscheff-Polynome quadrieren, passen sie perfekt in die Voraussetzungen für Filterfunktionen, wie es Abbildung \ref{ellfiter:fig:chebychef} demonstriert. +\begin{figure} + \centering + \input{papers/ellfilter/python/F_N_chebychev.pgf} + \caption{Die Tschebyscheff-Polynome füllen den erlaubten Bereich besser, und erhalten dadurch eine steilere Flanke im Sperrbereich.} + \label{ellfiter:fig:chebychef} +\end{figure} + + +Die analytische Fortsetzung von \eqref{ellfilter:eq:chebychef_polynomials} über das Intervall $[-1,1]$ hinaus stimmt mit den Polynomen überein, wie es zu erwarten ist. +Die genauere Betrachtung wird uns dann helfen die elliptischen Filter besser zu verstehen. + +Starten wir mit der Funktion, die als erstes auf $w$ angewendet wird, dem Arcuscosinus. +Die invertierte Funktion des Kosinus kann als definites Integral dargestellt werden: +\begin{align} + \cos^{-1}(x) + &= + \int_{x}^{1} + \frac{ + dz + }{ + \sqrt{ + 1-z^2 + } + }\\ + &= + \int_{0}^{x} + \frac{ + -1 + }{ + \sqrt{ + 1-z^2 + } + } + ~dz + + \frac{\pi}{2} +\end{align} +Der Integrand oder auch die Ableitung +\begin{equation} + \frac{ + -1 + }{ + \sqrt{ + 1-z^2 + } + } +\end{equation} +bestimmt dabei die Richtung, in der die Funktion verläuft. +Der reelle Arcuscosinus is bekanntlich nur für $|z| \leq 1$ definiert. +Hier bleibt der Wert unter der Wurzel positiv und das Integral liefert reelle Werte. +Doch wenn $|z|$ über 1 hinausgeht, wird der Term unter der Wurzel negativ. +Durch die Quadratwurzel entstehen für den Integranden zwei rein komplexe Lösungen. +Der Wert des Arcuscosinus verlässt also bei $z= \pm 1$ den reellen Zahlenstrahl und knickt in die komplexe Ebene ab. +Abbildung \ref{ellfilter:fig:arccos} zeigt den $\arccos$ in der komplexen Ebene. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/arccos.tikz.tex} + \caption{Die Funktion $z = \cos^{-1}(w)$ dargestellt in der komplexen ebene.} + \label{ellfilter:fig:arccos} +\end{figure} +Wegen der Periodizität des Kosinus ist auch der Arcuscosinus $2\pi$-periodisch und es entstehen periodische Nullstellen. +% \begin{equation} +% \frac{ +% 1 +% }{ +% \sqrt{ +% 1-z^2 +% } +% } +% \in \mathbb{R} +% \quad +% \forall +% \quad +% -1 \leq z \leq 1 +% \end{equation} +% \begin{equation} +% \frac{ +% 1 +% }{ +% \sqrt{ +% 1-z^2 +% } +% } +% = i \xi \quad | \quad \xi \in \mathbb{R} +% \quad +% \forall +% \quad +% z \leq -1 \cup z \geq 1 +% \end{equation} + +Die Tschebyscheff-Polynome skalieren diese Nullstellen mit dem Ordnungsfaktor $N$, wie dargestellt in Abbildung \ref{ellfilter:fig:arccos2}. +\begin{figure} + \centering + \input{papers/ellfilter/tikz/arccos2.tikz.tex} + \caption{ + $z_1=N \cos^{-1}(w)$-Ebene der Tschebyscheff-Funktion. + Die eingefärbten Pfade sind Verläufe von $w~\forall~[-\infty, \infty]$ für verschiedene Ordnungen $N$. + Je grösser die Ordnung $N$ gewählt wird, desto mehr Nullstellen werden passiert. + } + \label{ellfilter:fig:arccos2} +\end{figure} +Somit passert $\cos( N~\cos^{-1}(w))$ im Intervall $[-1, 1]$ $N$ Nullstellen. +Durch die spezielle Anordnung der Nullstellen hat die Funktion Equirippel-Verhalten und ist dennoch ein Polynom, was sich perfekt für linear Filter eignet. -- cgit v1.2.1 From c49717a11a534d1621f819c7a114924047046a04 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 30 May 2022 11:38:12 +0200 Subject: new slides --- buch/chapters/040-rekursion/betaverteilung.tex | 2 +- buch/chapters/040-rekursion/images/order.pdf | Bin 32692 -> 32688 bytes buch/chapters/040-rekursion/images/order.tex | 2 +- vorlesungen/12_dreieck/common.tex | 2 +- vorlesungen/12_dreieck/slides.tex | 4 ++ vorlesungen/slides/dreieck/Makefile.inc | 5 ++ vorlesungen/slides/dreieck/beta.tex | 70 +++++++++++++++++++++++ vorlesungen/slides/dreieck/betaplot.tex | 38 ++++++++++++ vorlesungen/slides/dreieck/chapter.tex | 3 + vorlesungen/slides/dreieck/dichte.tex | 67 ++++++++++++++++++++++ vorlesungen/slides/dreieck/minmax.tex | 22 ++++++- vorlesungen/slides/dreieck/orderplot.tex | 16 ++++++ vorlesungen/slides/dreieck/ordnungsstatistik.tex | 69 +++++++++++++++++++++- vorlesungen/slides/dreieck/stichprobe.tex | 20 ++++--- 14 files changed, 305 insertions(+), 15 deletions(-) create mode 100644 vorlesungen/slides/dreieck/beta.tex create mode 100644 vorlesungen/slides/dreieck/betaplot.tex create mode 100644 vorlesungen/slides/dreieck/dichte.tex create mode 100644 vorlesungen/slides/dreieck/orderplot.tex diff --git a/buch/chapters/040-rekursion/betaverteilung.tex b/buch/chapters/040-rekursion/betaverteilung.tex index 979d04c..77715ca 100644 --- a/buch/chapters/040-rekursion/betaverteilung.tex +++ b/buch/chapters/040-rekursion/betaverteilung.tex @@ -280,7 +280,7 @@ folgt jetzt \begin{align*} \varphi_{X_{k:n}}(x) &= -\varphi_X(x)k\binom{n}{k} F_X(x)^{k-1}(1-F_X(x))^{n-k}(x). +\varphi_X(x)k\binom{n}{k} F_X(x)^{k-1}(1-F_X(x))^{n-k}. \intertext{Im Speziellen für gleichverteilte Zufallsvariablen $X_i$ ist } \varphi_{X_{k:n}}(x) diff --git a/buch/chapters/040-rekursion/images/order.pdf b/buch/chapters/040-rekursion/images/order.pdf index cc175a9..88b2b08 100644 Binary files a/buch/chapters/040-rekursion/images/order.pdf and b/buch/chapters/040-rekursion/images/order.pdf differ diff --git a/buch/chapters/040-rekursion/images/order.tex b/buch/chapters/040-rekursion/images/order.tex index 9a2511c..0284735 100644 --- a/buch/chapters/040-rekursion/images/order.tex +++ b/buch/chapters/040-rekursion/images/order.tex @@ -65,7 +65,7 @@ \node at ({-0.1/\skala},{\y*\dy}) [left] {$\y$}; } -\node[color=darkgreen] at (0.65,{0.5*\dy}) [above,rotate=55] {$k=7$}; +\node[color=darkgreen] at ({0.64*\dx},{0.56*\dy}) [rotate=42] {$k=7$}; \begin{scope}[yshift=-0.7cm] \def\dy{0.125} diff --git a/vorlesungen/12_dreieck/common.tex b/vorlesungen/12_dreieck/common.tex index 9414e42..1be1b4f 100644 --- a/vorlesungen/12_dreieck/common.tex +++ b/vorlesungen/12_dreieck/common.tex @@ -9,7 +9,7 @@ \usetheme[hideothersubsections,hidetitle]{Hannover} } \beamertemplatenavigationsymbolsempty -\title[Dreieckstest]{Dreieckstest} +\title[Ordnungsstatistik]{Ordnungsstatistik und Beta-Funktion} \author[A.~Müller]{Prof. Dr. Andreas Müller} \date[]{30.~Mai 2022} \newboolean{presentation} diff --git a/vorlesungen/12_dreieck/slides.tex b/vorlesungen/12_dreieck/slides.tex index 211a105..19b7417 100644 --- a/vorlesungen/12_dreieck/slides.tex +++ b/vorlesungen/12_dreieck/slides.tex @@ -6,3 +6,7 @@ \folie{dreieck/stichprobe.tex} \folie{dreieck/minmax.tex} \folie{dreieck/ordnungsstatistik.tex} +\folie{dreieck/dichte.tex} +\folie{dreieck/orderplot.tex} +\folie{dreieck/beta.tex} +\folie{dreieck/betaplot.tex} diff --git a/vorlesungen/slides/dreieck/Makefile.inc b/vorlesungen/slides/dreieck/Makefile.inc index 0575397..bbc19b6 100644 --- a/vorlesungen/slides/dreieck/Makefile.inc +++ b/vorlesungen/slides/dreieck/Makefile.inc @@ -4,6 +4,11 @@ # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # chapterdreieck = \ + ../slides/dreieck/stichprobe.tex \ ../slides/dreieck/minmax.tex \ ../slides/dreieck/ordnungsstatistik.tex \ + ../slides/dreieck/orderplot.tex \ + ../slides/dreieck/dichte.tex \ + ../slides/dreieck/beta.tex \ + ../slides/dreieck/betaplot.tex \ ../slides/dreieck/test.tex diff --git a/vorlesungen/slides/dreieck/beta.tex b/vorlesungen/slides/dreieck/beta.tex new file mode 100644 index 0000000..fc3606a --- /dev/null +++ b/vorlesungen/slides/dreieck/beta.tex @@ -0,0 +1,70 @@ +% +% beta.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Beta-Verteilung} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.40\textwidth} +\begin{block}{Ordnungsstatistik} +\begin{align*} +\varphi(x) +&= +{\color{blue}N} x^{k-1} (1-x)^{n-k} +\\ +&\uncover<8->{ += +\beta_{k,n-k+1}(x) +} +\end{align*} +\end{block} +\uncover<8->{% +\begin{block}{Risch-Algorithmus} +Die Beta-Verteilungen haben ausser in Spezialfällen +keine Stammfunktion in geschlossener Form. +\end{block}} +\end{column} +\begin{column}{0.56\textwidth} +\uncover<2->{% +\begin{definition} +Beta-Verteilung +\[ +\beta_{a,b}(x) += +\begin{cases} +\displaystyle +\uncover<7->{ +{\color{blue} +\frac{1}{B(a,b)} +} +} +x^{a-1}(1-x)^{b-1} +&0\le x\le 1 +\\ +0&\text{sonst} +\end{cases} +\] +\end{definition}} +\uncover<3->{% +\begin{block}{Normierung} +\begin{align*} +{\color{blue}\frac{1}{{N}}} +&\uncover<4->{= +\int_{-\infty}^\infty \beta_{a,b}(x)\,dx} +\\ +&\uncover<5->{= +\int_{0}^1 x^{a-1}(1-x)^{b-1}\,dx} +\\ +&\uncover<6->{= +B(a,b)} +\end{align*} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/betaplot.tex b/vorlesungen/slides/dreieck/betaplot.tex new file mode 100644 index 0000000..ee932e8 --- /dev/null +++ b/vorlesungen/slides/dreieck/betaplot.tex @@ -0,0 +1,38 @@ +% +% betaplot.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Beta-Verteilungen} +\begin{center} +\begin{tikzpicture}[>=latex] + +\only<1>{ +\begin{scope} + \clip (-7,-3.2) rectangle (7,3.2); + \node at (0,-6.5) {\includegraphics[width=13.5cm]{../../buch/chapters/040-rekursion/images/beta.pdf}}; +\end{scope} +} + +\only<2>{ +\begin{scope} + \clip (-7,-3.2) rectangle (7,3.2); + \node at (0,-0) {\includegraphics[width=13.5cm]{../../buch/chapters/040-rekursion/images/beta.pdf}}; +\end{scope} +} + +\only<3>{ +\begin{scope} + \clip (-7,-3.2) rectangle (7,3.2); + \node at (0,6.5) {\includegraphics[width=13.5cm]{../../buch/chapters/040-rekursion/images/beta.pdf}}; +\end{scope} +} + +\end{tikzpicture} +\end{center} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/chapter.tex b/vorlesungen/slides/dreieck/chapter.tex index 2c91eb5..0f58c4c 100644 --- a/vorlesungen/slides/dreieck/chapter.tex +++ b/vorlesungen/slides/dreieck/chapter.tex @@ -6,3 +6,6 @@ \folie{dreieck/test.tex} \folie{dreieck/minmax.tex} \folie{dreieck/ordnungsstatistik.tex} +\folie{dreieck/dichte.tex} +\folie{dreieck/beta.tex} +\folie{dreieck/betaplot.tex} diff --git a/vorlesungen/slides/dreieck/dichte.tex b/vorlesungen/slides/dreieck/dichte.tex new file mode 100644 index 0000000..168523a --- /dev/null +++ b/vorlesungen/slides/dreieck/dichte.tex @@ -0,0 +1,67 @@ +% +% dichte.tex -- Wahrscheinlichkeitsdichte +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Wahrscheinlichkeitsdichte} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.40\textwidth} +\begin{block}{Definition} +\[ +\varphi_{X_{k:n}}(x) += +\frac{d}{dx} F_{X_{k:n}}(x) +\] +\end{block} +\end{column} +\begin{column}{0.60\textwidth} +\uncover<4->{% +\begin{block}{Gleichverteilung} +\[ +{\color{darkgreen}F(x)}=\begin{cases} +0&x \le 0\\ +x&0\le x \le 1,\\ +1&x\ge 1 +\end{cases} +\quad +\uncover<5->{ +{\color{red}\varphi(x)} += +\begin{cases} +1&0\le x \le 1\\ +0&\text{sonst} +\end{cases}} +\] +\end{block}} +\end{column} +\end{columns} +\uncover<2->{% +\begin{block}{Ordnungsstatistik} +nach einiger Rechnung: +\begin{align*} +\varphi_{X_{k:n}}(x) +&= +{\color<3->{red}\varphi_X(x)}\,k\binom{n}{k}{\color<3->{darkgreen}F_X(x)}^{k-1} +(1-{\color<3->{darkgreen}F_X(x)})^{n-k} +\intertext{\uncover<4->{für Gleichverteilung}} +\uncover<6->{ +\varphi_{X_{k:n}}(x) +&= +\begin{cases} +\displaystyle +{\color<7->{blue}k\binom{n}{k}}{\color{darkgreen}x}^{k-1}(1-{\color{darkgreen}x})^{n-k} +&0\le x \le 1\\ +0&\text{sonst} +\end{cases} +\qquad\uncover<7->{\text{({\color{blue}Normierung})}} +} +\end{align*} +\end{block}} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/minmax.tex b/vorlesungen/slides/dreieck/minmax.tex index 9ef8d1a..ff3a231 100644 --- a/vorlesungen/slides/dreieck/minmax.tex +++ b/vorlesungen/slides/dreieck/minmax.tex @@ -17,48 +17,66 @@ Verteilungsfunktion von Z=\operatorname{max}(X_1,\dots,X_n) \] \begin{align*} +\uncover<3->{ F_Z(x) &= -P(Z\le x) +P(Z\le x)} \\ +\uncover<4->{ &= P(X_1\le x\wedge\dots\wedge X_n\le x) +} \\ +\uncover<5->{ &= P(X_1\le x)\cdot \ldots\cdot P(X_n\le x) +} \\ +\uncover<6->{ &= F_X(x)^n +} \end{align*} \end{block} \end{column} \begin{column}{0.48\textwidth} +\uncover<2->{% \begin{block}{Minimum} Verteilungsfunktion von \[ Z=\operatorname{min}(X_1,\dots,X_n) \] \begin{align*} +\uncover<7->{ F_Z(x) &= P(Z\le x) +} \\ +\uncover<8->{ &=P(\overline{ X_1\le x\wedge\dots\wedge X_n \le x }) +} \\ +\uncover<9->{ &= 1-P( X_1> x\wedge\dots\wedge X_n > x ) +} \\ +\uncover<10->{ &= 1-(P(X_1>x)\cdot\ldots\cdot P(X_n>x)) +} \\ +\uncover<11->{ &= 1-(1-F_X(x))^n +} \end{align*} -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/dreieck/orderplot.tex b/vorlesungen/slides/dreieck/orderplot.tex new file mode 100644 index 0000000..7cf10c6 --- /dev/null +++ b/vorlesungen/slides/dreieck/orderplot.tex @@ -0,0 +1,16 @@ +% +% orderplot.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Ordnungstatistik} +\vspace*{-18pt} +\begin{center} +\includegraphics[width=10cm]{../../buch/chapters/040-rekursion/images/order.pdf} +\end{center} +\end{frame} +\egroup diff --git a/vorlesungen/slides/dreieck/ordnungsstatistik.tex b/vorlesungen/slides/dreieck/ordnungsstatistik.tex index 6346953..c968e79 100644 --- a/vorlesungen/slides/dreieck/ordnungsstatistik.tex +++ b/vorlesungen/slides/dreieck/ordnungsstatistik.tex @@ -8,11 +8,76 @@ \setlength{\abovedisplayskip}{5pt} \setlength{\belowdisplayskip}{5pt} \frametitle{Ordnungstatistik} +\vspace{-10pt} +\begin{block}{Angeordnete Stichprobe} +\[ +X_{1:n} +\le +X_{2:n} +\le +\dots +\le +X_{(n-1):n} +\le +X_{n:n} +\] +$X_{k:n} = \mathstrut$der $k$-te von $n$ Werten +\end{block} \vspace{-20pt} \begin{columns}[t,onlytextwidth] -\begin{column}{0.48\textwidth} +\begin{column}{0.44\textwidth} +\uncover<2->{% +\begin{block}{Verteilungsfunktion} +\begin{align*} +F_{X_{k:n}}(x) +&= +P(X_{k:n} \le x) +\\ +&\uncover<3->{= +P\bigl( +|\{i\;|\; {\color<4>{red}X_i\le x}\}| \ge k +\bigr)} +\\ +&\uncover<5->{= +P(\text{Anzahl $A_i$}\ge k)} +\\ +&\uncover<9->{= +P(K\ge k)} +\\ +\uncover<6->{ +F_{X_i}(x)&= P(X_i\le x)}\uncover<7->{ = P(A_i)}\uncover<10->{ = p} +} +\end{align*} +\uncover<4->{$A_i=\{X_i\le x\}$}\uncover<7->{ ist ein Beroulli- Experiment +\uncover<10->{mit Eintretens- wahrscheinlichkeit $p$} +\end{block}} \end{column} -\begin{column}{0.48\textwidth} +\begin{column}{0.52\textwidth} +\uncover<8->{% +\begin{block}{Wiederholtes Bernoulli-Experiment} +$K=\mathstrut$Anzahl $k$, für die $A$ eingetreten +ist\only<11->{, ist binomialverteilt:} +\begin{align*} +\uncover<12->{P(K=k) +&= +\phantom{\sum_{i=k}^n\mathstrut} +\binom{n}{k} p^k (1-p)^{n-k} +} +\\ +\uncover<13->{ +P(K\ge k) +&= +\sum_{i=k}^n +\binom{n}{i} p^i (1-p)^{n-i} +} +\\ +\uncover<14->{ +&= +\sum_{i=k}^n +\binom{n}{i} F_X(x)^i (1-F_X(x))^{n-i} +} +\end{align*} +\end{block}} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/dreieck/stichprobe.tex b/vorlesungen/slides/dreieck/stichprobe.tex index da3a20e..4b2eff0 100644 --- a/vorlesungen/slides/dreieck/stichprobe.tex +++ b/vorlesungen/slides/dreieck/stichprobe.tex @@ -12,21 +12,22 @@ \begin{columns}[t,onlytextwidth] \begin{column}{0.48\textwidth} \begin{block}{Zufallsvariable} -Gegeben eine Zufallsvariable $X$ mit +Gegeben eine Zufallsvariable $X$ \uncover<5->{mit Verteilungsfunktion \[ F_X(x) = P(X\le x) -\] -und +\]} +\uncover<6->{und Wahrscheinlichkeitsdichte \[ \varphi_X(x) = \frac{d}{dx} F_X(x) -\] +\]} \end{block} +\uncover<7->{% \begin{block}{Gleichverteilung} \[ F(x) = \begin{cases} @@ -34,6 +35,7 @@ F(x) = \begin{cases} x&\qquad 0\le x \le 1\\ 1&\qquad 1{ \qquad\Rightarrow\qquad \varphi(x) = @@ -41,19 +43,21 @@ x&\qquad 0\le x \le 1\\ 1&\qquad 0\le x \le 1\\ 0&\qquad\text{sonst}. \end{cases} +} \] -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<2->{% \begin{block}{Stichprobe} $n$ Zufallsvariablen $X_1,\dots,X_n$ \begin{itemize} -\item +\item<3-> alle $X_i$ haben die gleiche Verteilung wie $X$ -\item +\item<4-> die $X_i$ sind unabhängig \end{itemize} -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} -- cgit v1.2.1 From 0b6917dcba521381f259dbaeed718ac1407eeefd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 31 May 2022 07:48:27 +0200 Subject: =?UTF-8?q?Sternzeit=20dezimal=20erg=C3=A4nzt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/nav/beispiel.txt | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt index 853ae4e..94466ce 100644 --- a/buch/papers/nav/beispiel.txt +++ b/buch/papers/nav/beispiel.txt @@ -1,6 +1,6 @@ Datum: 28. 5. 2022 Zeit: 15:29:49 UTC -Sternzeit: 7h 54m 26.593s +Sternzeit: 7h 54m 26.593s 7.90738694h Deneb -- cgit v1.2.1 From 8eb7793b2100ff83caa1ab8898dcab572d0d995f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 31 May 2022 07:55:04 +0200 Subject: ra korrigiert --- buch/papers/nav/beispiel.txt | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt index 94466ce..70e3ce2 100644 --- a/buch/papers/nav/beispiel.txt +++ b/buch/papers/nav/beispiel.txt @@ -4,7 +4,7 @@ Sternzeit: 7h 54m 26.593s 7.90738694h Deneb -RA 20h 42m 12.14s 10.703372h +RA 20h 42m 12.14s 20.703372h DEC 45 21' 40.3" 45.361194 H 50g 15' 17.1" 50.254750h -- cgit v1.2.1 From 7d33fc05ecaf5196bfb57420ca823222c6c53b50 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 31 May 2022 11:11:49 +0200 Subject: fix besselgrid labeling --- .../chapters/050-differential/images/besselgrid.pdf | Bin 28324 -> 28297 bytes .../chapters/050-differential/images/besselgrid.tex | 3 ++- 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/buch/chapters/050-differential/images/besselgrid.pdf b/buch/chapters/050-differential/images/besselgrid.pdf index 6c551f4..5f074f8 100644 Binary files a/buch/chapters/050-differential/images/besselgrid.pdf and b/buch/chapters/050-differential/images/besselgrid.pdf differ diff --git a/buch/chapters/050-differential/images/besselgrid.tex b/buch/chapters/050-differential/images/besselgrid.tex index 01021e3..a5dc3bd 100644 --- a/buch/chapters/050-differential/images/besselgrid.tex +++ b/buch/chapters/050-differential/images/besselgrid.tex @@ -65,7 +65,6 @@ } \end{scope} - \node at (-4.5,1.5) {$\Gamma(n+k+1)=\infty$}; } \begin{tikzpicture}[>=latex,thick,scale=\skala] @@ -75,6 +74,7 @@ \punkte \nachse{black} \kachse + \node at (-4.5,1.5) {$\Gamma(n+k+1)=\infty$}; \end{scope} \begin{scope}[yshift=-7.8cm] @@ -83,6 +83,7 @@ \punkte \draw[->] (0.3,-0.3) -- (-6.4,6.4) coordinate[label={above right:$k$}]; \draw[->] (-3.3,3) -- (6.6,3) coordinate[label={right:$m$}]; + \node at (-4.5,1.5) {$\Gamma(m)=\infty$}; \end{scope} \end{tikzpicture} -- cgit v1.2.1 From c2e23011c6a569277d3806818991fd9c1dfbfe51 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 31 May 2022 11:24:37 +0200 Subject: besselgrid fix --- .../chapters/050-differential/images/besselgrid.pdf | Bin 28297 -> 28306 bytes .../chapters/050-differential/images/besselgrid.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/chapters/050-differential/images/besselgrid.pdf b/buch/chapters/050-differential/images/besselgrid.pdf index 5f074f8..a0fa332 100644 Binary files a/buch/chapters/050-differential/images/besselgrid.pdf and b/buch/chapters/050-differential/images/besselgrid.pdf differ diff --git a/buch/chapters/050-differential/images/besselgrid.tex b/buch/chapters/050-differential/images/besselgrid.tex index a5dc3bd..1c19363 100644 --- a/buch/chapters/050-differential/images/besselgrid.tex +++ b/buch/chapters/050-differential/images/besselgrid.tex @@ -83,7 +83,7 @@ \punkte \draw[->] (0.3,-0.3) -- (-6.4,6.4) coordinate[label={above right:$k$}]; \draw[->] (-3.3,3) -- (6.6,3) coordinate[label={right:$m$}]; - \node at (-4.5,1.5) {$\Gamma(m)=\infty$}; + \node at (-4.5,1.5) {$\Gamma(m+1)=\infty$}; \end{scope} \end{tikzpicture} -- cgit v1.2.1 From 19daddc56c44894ebc49dd2698fb6ca19dd7359e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 31 May 2022 11:38:41 +0200 Subject: fix participant lists --- buch/common/teilnehmer.tex | 18 +++++++++--------- cover/backcover.jpg | Bin 903962 -> 905731 bytes cover/backcover.png | Bin 858440 -> 858542 bytes cover/buchcover.jpg | Bin 1160870 -> 1144514 bytes cover/buchcover.png | Bin 1604134 -> 1601326 bytes cover/buchcover.tex | 20 ++++++++++---------- 6 files changed, 19 insertions(+), 19 deletions(-) diff --git a/buch/common/teilnehmer.tex b/buch/common/teilnehmer.tex index c14790a..c1408cb 100644 --- a/buch/common/teilnehmer.tex +++ b/buch/common/teilnehmer.tex @@ -11,20 +11,20 @@ Fabian Dünki%, % E \\ %Robin Eberle, % E Enez Erdem, % B -Nilakshan Eswararajah, % B -Réda Haddouche%, % E -\\ +%Nilakshan Eswararajah, % B +Réda Haddouche, % E David Hugentobler, % E -Alain Keller, % E -Yanik Kuster, % E -Marc Kühne%, % B +Alain Keller%, % E \\ +Yanik Kuster, % E +Marc Kühne, % B Erik Löffler, % E -Kevin Meili, % M-I -Andrea Mozzini Vellen%, % E +Kevin Meili%, % M-I \\ +Andrea Mozzini Vellen, % E Patrik Müller, % MSE -Naoki Pross, % E +Naoki Pross%, % E +\\ Thierry Schwaller, % E Tim Tönz % E diff --git a/cover/backcover.jpg b/cover/backcover.jpg index fbde01f..b1736d1 100644 Binary files a/cover/backcover.jpg and b/cover/backcover.jpg differ diff --git a/cover/backcover.png b/cover/backcover.png index 6425910..c604266 100644 Binary files a/cover/backcover.png and b/cover/backcover.png differ diff --git a/cover/buchcover.jpg b/cover/buchcover.jpg index 52d17d1..158c6a4 100644 Binary files a/cover/buchcover.jpg and b/cover/buchcover.jpg differ diff --git a/cover/buchcover.png b/cover/buchcover.png index 02590e0..96f5123 100644 Binary files a/cover/buchcover.png and b/cover/buchcover.png differ diff --git a/cover/buchcover.tex b/cover/buchcover.tex index 49519af..d6ad7ec 100644 --- a/cover/buchcover.tex +++ b/cover/buchcover.tex @@ -88,35 +88,35 @@ \sf \fontsize{13}{5}\selectfont %Robin Eberle, % E Enez Erdem, % B - Nilakshan Eswararajah, % B - Réda Haddouche%, % E + %Nilakshan Eswararajah, % B + Réda Haddouche, % E + David Hugentobler, % E + Alain Keller%, % E }}; \node at ({\einschlag+2*\gelenk+\ruecken+1.5*\breite},17.1) [color=white,scale=1] {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont - David Hugentobler, % E - Alain Keller, % E Yanik Kuster, % E - Marc Kühne%, % B + Marc Kühne, % B + Erik Löffler, % E + Kevin Meili%, % M-I }}; \node at ({\einschlag+2*\gelenk+\ruecken+1.5*\breite},16.45) [color=white,scale=1] {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont - Erik Löffler, % E - Kevin Meili, % M-I - Andrea Mozzini Vellen%, % E + Andrea Mozzini Vellen, % E + Patrick Müller, % MSE + Naoki Pross%, % E }}; \node at ({\einschlag+2*\gelenk+\ruecken+1.5*\breite},15.8) [color=white,scale=1] {\hbox to\hsize{\hfill% \sf \fontsize{13}{5}\selectfont - Patrick Müller, % MSE - Naoki Pross, % E Thierry Schwaller, % E Tim Tönz% % E % -- cgit v1.2.1 From 6149839224755c21225d2decddeae12207c2cbab Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Tue, 31 May 2022 16:31:25 +0200 Subject: Add rule of thumb, analyse integrand, correct mistake in integration SLP<->LP --- buch/papers/laguerre/definition.tex | 2 +- buch/papers/laguerre/eigenschaften.tex | 20 +- buch/papers/laguerre/gamma.tex | 294 ++- buch/papers/laguerre/images/integrands.pgf | 1448 +++++----- buch/papers/laguerre/images/integrands_exp.pgf | 1323 +++++----- buch/papers/laguerre/images/rel_error_mirror.pgf | 3054 ++++++++++++++++++++++ buch/papers/laguerre/images/rel_error_simple.pgf | 2940 +++++++++++++++++++++ buch/papers/laguerre/images/rel_error_simple.png | Bin 0 -> 61966 bytes buch/papers/laguerre/images/schaetzung.pgf | 1160 ++++++++ buch/papers/laguerre/images/targets.pdf | Bin 0 -> 12940 bytes buch/papers/laguerre/quadratur.tex | 4 +- buch/papers/laguerre/references.bib | 9 + buch/papers/laguerre/scripts/gamma_approx.ipynb | 178 +- buch/papers/laguerre/scripts/gamma_approx.py | 197 ++ buch/papers/laguerre/scripts/integrand.py | 27 +- 15 files changed, 9063 insertions(+), 1593 deletions(-) create mode 100644 buch/papers/laguerre/images/rel_error_mirror.pgf create mode 100644 buch/papers/laguerre/images/rel_error_simple.pgf create mode 100644 buch/papers/laguerre/images/rel_error_simple.png create mode 100644 buch/papers/laguerre/images/schaetzung.pgf create mode 100644 buch/papers/laguerre/images/targets.pdf create mode 100644 buch/papers/laguerre/scripts/gamma_approx.py diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index f1f0d00..3e5d423 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -22,7 +22,7 @@ Die klassische Laguerre-Diffentialgleichung erhält man, wenn $\nu = 0$. Hier wird die verallgemeinerte Laguerre-Differentialgleichung verwendet, weil die Lösung mit der selben Methode berechnet werden kann, aber man zusätzlich die Lösung für den allgmeinen Fall erhält. -Zur Lösung der Gleichung \eqref{laguerre:dgl} verwenden wir einen +Zur Lösung von \eqref{laguerre:dgl} verwenden wir einen Potenzreihenansatz. Da wir bereits wissen, dass die Lösung orthogonale Polynome sind, erscheint dieser Ansatz sinnvoll. diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 77b2a2c..9b901ae 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -22,25 +22,25 @@ Im Abschnitt~\ref{laguerre:section:definition} haben wir behauptet, dass die Laguerre-Polynome orthogonale Polynome sind. Zu dieser Behauptung möchten wir nun einen Beweis liefern. -Wenn wir die Laguerre\--Differentialgleichung in ein -Sturm\--Liouville\--Problem umwandeln können, haben wir bewiesen, dass es sich -bei -den Laguerre\--Polynomen um orthogonale Polynome handelt (siehe +Wenn wir \eqref{laguerre:dgl} in ein +Sturm-Liouville-Problem umwandeln können, haben wir bewiesen, dass es sich +bei den Laguerre-Polynomen um orthogonale Polynome handelt (siehe Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem}). -Der Sturm-Liouville-Operator +Der Beweis kann äquivalent auch über den Sturm-Liouville-Operator \begin{align} S = \frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right). \label{laguerre:slop} \end{align} -und der Laguerre-Operator +und den Laguerre-Operator \begin{align} \Lambda = x \frac{d}{dx^2} + (\nu + 1 -x) \frac{d}{dx} \end{align} -sind einander gleichzusetzen. +erhalten werden, +in dem wir diese Operatoren einander gleichsetzen. Aus der Beziehung \begin{align} S @@ -66,16 +66,18 @@ Durch Separation erhalten wir dann \int \frac{dp}{p} & = -\int \frac{\nu + 1 - x}{x} \, dx += +-\int \frac{\nu + 1}{x} \, dx - \int 1\, dx \\ \log p & = --\log \nu + 1 - x + C +-(\nu + 1)\log x - x + c \\ p(x) & = -C x^{\nu + 1} e^{-x} \end{align*} -Eingefügt in Gleichung~\eqref{laguerre:sl-lag} erhalten wir +Eingefügt in Gleichung~\eqref{laguerre:sl-lag} ergibt sich \begin{align*} \frac{C}{w(x)} \left( diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index 59c0b81..da2fa93 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -19,7 +19,7 @@ Integral der Form \begin{align} \Gamma(z) & = -\int_0^\infty t^{z-1} e^{-t} dt +\int_0^\infty x^{z-1} e^{-x} \, dx , \quad \text{wobei Realteil von $z$ grösser als $0$} @@ -32,54 +32,290 @@ Zu erwähnen ist auch, dass für die verallgemeinerte Laguerre-Integration die Gewichtsfunktion $t^\nu e^{-t}$ genau dem Integranden für $\nu=z-1$ entspricht. \subsubsection{Funktionalgleichung} -Die Funktionalgleichung der Gamma-Funktion besagt +Die Gamma-Funktion besitzt die gleiche Rekursionsbeziehung wie die Fakultät, +nämlich \begin{align} -z \Gamma(z) = \Gamma(z+1). +z \Gamma(z) += +\Gamma(z+1) +. \label{laguerre:gamma_funktional} \end{align} -Mittels dieser Gleichung kann der Wert von $\Gamma(z)$ an einer bestimmten, -geeigneten Stelle evaluiert werden und dann zurückverschoben werden, -um das gewünschte Resultat zu erhalten. -In Abbildung~\ref{laguerre:fig:integrand} ist der Integrand $t^z$ für -unterschiedliche Werte von $z$ dargestellt. -Man erkennt, dass für kleine $z$ sich ein singulärer Integrand ergibt, -was dazu führt, dass die Genauigkeit sich verschlechtert. -Die Genauigkeit verschlechtert sich aber auch zunehmends für grosse $z$, -da in diesem Fall der Integrand sehr schnell anwächst. +\subsubsection{Reflektionsformel} +Die Reflektionsformel +\begin{align} +\Gamma(z) \Gamma(1 - z) += +\frac{\pi}{\sin \pi z} +,\quad +\text{für } +z \notin \mathbb{Z} +\label{laguerre:gamma_refform} +\end{align} +stellt eine Beziehung zwischen den zwei Punkten, +die aus der Spiegelung an der Geraden $\operatorname{Re} z = 1/2$ hervorgehen, +her. +Dadurch lassen Werte der Gamma-Funktion sich für $z$ in der rechten Halbebene +leicht in die linke Halbebene übersetzen und umgekehrt. + +\subsection{Berechnung mittels Gauss-Laguerre-Quadratur} +In den vorherigen Abschnitten haben wir gesehen, +dass sich die Gamma-Funktion bestens für die Gauss-Laguerre-Quadratur eignet. +Nun bieten sich uns zwei Optionen diese zu berechnen: +\begin{enumerate} +\item Wir verwenden die verallgemeinerten Laguerre-Polynome, dann $f(x)=1$. +\item Wir verwenden die Laguerre-Polynome, dann $f(x)=x^{z-1}$. +\end{enumerate} +Die erste Variante wäre optimal auf das Problem angepasst, +allerdings müssten die Gewichte und Nullstellen für jedes $z$ +neu berechnet werden, +da sie per Definition von $z$ abhängen. +Dazu kommt, +dass die Berechnung der Gewichte $A_i$ nach \cite{Cassity1965AbcissasCA} +\begin{align*} +A_i += +\frac{ +\Gamma(n) \Gamma(n+\nu) +} +{ +(n+\nu) +\left[L_{n-1}^{\nu}(x_i)\right]^2 +} +\end{align*} +Evaluationen der Gamma-Funktion benötigen. +Somit scheint diese Methode nicht geeignet für unser Vorhaben. + +Bei der zweiten Variante benötigen wir keine Neuberechung der Gewichte +und Nullstellen für unterschiedliche $z$. +In \eqref{laguerre:quadratur_gewichte} ist ersichtlich, +dass die Gewichte einfach zu berechnen sind. +Auch die Nullstellen können vorgängig, +mittels eines geeigneten Verfahrens aus den Polynomen bestimmt werden. +Als problematisch könnte sich höchstens +die zu integrierende Funktion $f(x)=x^{z-1}$ für $|z| \gg 0$ erweisen. +Somit entscheiden wir uns auf Grund der vorherigen Punkte, +die zweite Variante weiterzuverfolgen. + +\subsubsection{Naiver Ansatz} + \begin{figure} \centering -\scalebox{0.8}{\input{papers/laguerre/images/integrands.pgf}} -\caption{Integrand $t^z$ mit unterschiedlichen Werten für $z$} -\label{laguerre:fig:integrand} +\input{papers/laguerre/images/rel_error_simple.pgf} +\caption{Relativer Fehler des naiven Ansatzes +für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} +\label{laguerre:fig:rel_error_simple} \end{figure} -\subsection{Berechnung mittels Gauss-Laguerre-Quadratur} - -Fehlerterm: +Bevor wir die Gauss-Laguerre-Quadratur anwenden, +möchten wir als erstes eine Fehlerabschätzung durchführen. +Für den Fehlerterm \eqref{laguerre:lag_error} wird die $2n$-te Ableitung +der zu integrierenden Funktion $f(\xi)$ benötigt. +Für das Integral der Gamma-Funktion ergibt sich also +\begin{align*} +\frac{d^{2n}}{d\xi^{2n}} f(\xi) + & = +\frac{d^{2n}}{d\xi^{2n}} \xi^{z-1} +\\ + & = +(z - 2n)_{2n} \xi^{z - 2n - 1} +\end{align*} +Eingesetzt im Fehlerterm \eqref{laguerre:lag_error} resultiert \begin{align*} R_n = (z - 2n)_{2n} \frac{(n!)^2}{(2n)!} \xi^{z-2n-1} +, +\label{laguerre:gamma_err_simple} \end{align*} +wobei $\xi$ ein geeigneter Wert im Interval $(0, \infty)$ ist +und $n$ der Grad des verwendeten Laguerre-Polynoms. +Eine Fehlerabschätzung mit dem Fehlerterm stellt sich als unnütz heraus, +da $R_n$ für $z < 2n - 1$ bei $\xi \rightarrow 0$ eine Singularität aufweist +und für $z > 2n - 1$ bei $\xi \rightarrow \infty$ divergiert. +Nur für den unwahrscheinlichen Fall $ z = 2n - 1$ +wäre eine Fehlerabschätzung plausibel. + +Wenden wir nun also naiv die Gauss-Laguerre-Quadratur auf die Gammafunktion an. +Dazu benötigen wir die Gewichte nach +\eqref{laguerre:quadratur_gewichte} +und als Stützstellen die Nullstellen des Laguerre-Polynomes $L_n$. +Evaluieren wir den relativen Fehler unserer Approximation zeigt sich ein +Bild wie in Abbildung~\ref{laguerre:fig:rel_error_simple}. +Man kann sehen, +wie der relative Fehler Nullstellen aufweist für ganzzahlige $z < 2n$, +was laut der Theorie der Gauss-Quadratur auch zu erwarten ist, +denn die Approximation via Gauss-Quadratur +ist exakt für zu integrierende Polynome mit Grad $< 2n-1$. +Es ist ersichtlich, +dass sich für den Polynomgrad $n$ ein Interval gibt, +in dem der relative Fehler minimal ist. +Links steigt der relative Fehler besonders stark an, +während er auf der rechten Seite zu konvergieren scheint. +Um die linke Hälfte in den Griff zu bekommen, +könnten wir die Reflektionsformel der Gamma-Funktion ausnutzen. + +\begin{figure} +\centering +\input{papers/laguerre/images/rel_error_mirror.pgf} +\caption{Relativer Fehler des naiven Ansatz mit Spiegelung negativer Realwerte +für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} +\label{laguerre:fig:rel_error_mirror} +\end{figure} + +Spiegelt man nun $z$ mit negativem Realteil mittels der Reflektionsformel, +ergibt sich ein stabilerer Fehler in der linken Hälfte, +wie in Abbildung~\ref{laguerre:fig:rel_error_mirror}. +Die Spiegelung bringt nur für wenige Werte einen, +für praktische Anwendungen geeigneten, +relativen Fehler. +Wie wir aber in Abbildung~\ref{laguerre:fig:rel_error_simple} sehen konnten, +gibt es für jeden Polynomgrad $n$ ein Intervall $[a, a+1]$, $a \in \mathbb{Z}$, +in welchem der relative Fehler minimal ist. +Die Funktionalgleichung der Gamma-Funktion \eqref{laguerre:gamma_funktional} +könnte uns hier helfen, +das Problem in den Griff zu bekommen. + +\subsubsection{Analyse des Integranden} +Wie wir im vorherigen Abschnitt gesehen haben, +scheint der Integrand problematisch. +Darum möchten wir jetzt den Integranden analysieren, +um ihn besser verstehen zu können +und dadurch geeignete Gegenmassnahmen zu entwickeln. + +% Dieser Abschnitt soll eine grafisches Verständnis dafür schaffen, +% wieso der Integrand so problematisch ist. +% Was das heisst sollte in Abbildung~\ref{laguerre:fig:integrand} +% und Abbildung~\ref{laguerre:fig:integrand_exp} grafisch dargestellt werden. + +\begin{figure} +\centering +\input{papers/laguerre/images/integrands.pgf} +\caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} +\label{laguerre:fig:integrand} +\end{figure} + +In Abbildung~\ref{laguerre:fig:integrand} ist der Integrand $x^z$ für +unterschiedliche Werte von $z$ dargestellt. +Dies entspricht der zu integrierenden Funktion $f(x)$ +der Gauss-Laguerre-Quadratur für die Gamma-Funktion- +Man erkennt, +dass für kleine $z$ sich ein singulärer Integrand ergibt +und auch für grosse $z$ wächst der Integrand sehr schnell an. +Das heisst, +die Ableitungen im Fehlerterm divergieren noch schneller +und das wirkt sich negativ auf die Genauigkeit der Approximation aus. +Somit lässt sich hier sagen, +dass kleine Exponenten um $0$ genauere Resultate liefern sollten. + +\begin{figure} +\centering +\input{papers/laguerre/images/integrands_exp.pgf} +\caption{Integrand $x^z e^{-x}$ mit unterschiedlichen Werten für $z$} +\label{laguerre:fig:integrand_exp} +\end{figure} + +In Abbildung~\ref{laguerre:fig:integrand_exp} fügen wir +die Dämpfung der Gewichtsfunktion $w(x)$ +der Gauss-Laguerre-Quadratur wieder hinzu +und erhalten so wieder den kompletten Integranden $x^{z-1} e^{-x}$ +der Gamma-Funktion. +Für negative $z$ ergeben sich immer noch Singularitäten, +wenn $x \rightarrow 0$. +Um $1$ wächst der Term $x^z$ schneller als die Dämpfung $e^{-x}$, +aber für $x \rightarrow \infty$ geht der Integrand gegen $0$. +Das führt zu Glockenförmigen Kurven, +die für grosse Exponenten $z$ nach der Stelle $x=1$ schnell anwachsen. +Zu grosse Exponenten $z$ sind also immer noch problematisch. +Kleine positive $z$ scheinen nun also auch zulässig zu sein. +Damit formulieren wir die Vermutung, +dass $a$, +welches das Intervall $[a,a+1]$ definiert, +in dem der relative Fehler minimal ist, +grösser als $0$ und abhängig von $n$ ist. \subsubsection{Finden der optimalen Berechnungsstelle} +% Mittels der Funktionalgleichung \eqref{laguerre:gamma_funktional} +% kann der Wert von $\Gamma(z)$ im Interval $z \in [a,a+1]$, +% in dem der relative Fehler minimal ist, +% evaluiert werden und dann mit der Funktionalgleichung zurückverschoben werden. Nun stellt sich die Frage, ob die Approximation mittels Gauss-Laguerre-Quadratur verbessert werden kann, -wenn man das Problem an einer geeigneten Stelle evaluiert und -dann mit der Funktionalgleichung zurückverschiebt. -Dazu wollen wir den Fehlerterm in -Gleichung~\eqref{laguerre:lagurre:lag_error} anpassen und dann minimieren. -Zunächst wollen wir dies nur für $z\in \mathbb{R}$ und $0.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.000000in}{2.500000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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differ diff --git a/buch/papers/laguerre/images/schaetzung.pgf b/buch/papers/laguerre/images/schaetzung.pgf new file mode 100644 index 0000000..873a10c --- /dev/null +++ b/buch/papers/laguerre/images/schaetzung.pgf @@ -0,0 +1,1160 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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+\pgfpathlineto{\pgfqpoint{0.556162in}{2.276777in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.556162in}{2.276777in}}{\pgfqpoint{4.402168in}{1.681553in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.756261in}{2.276777in}}% +\pgfpathlineto{\pgfqpoint{0.756261in}{3.958330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% 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files /dev/null and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index f4e2955..b5ad316 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -61,14 +61,14 @@ Der Fehlerterm $R_n$ folgt direkt aus der Approximation = \sum_{i=1}^n f(x_i) A_i + R_n \end{align*} -un \cite{abramowitz+stegun} gibt in als +und \cite{abramowitz+stegun} gibt ihn als \begin{align} R_n = \frac{(n!)^2}{(2n)!} f^{(2n)}(\xi) ,\quad 0 < \xi < \infty -\label{lagurre:lag_error} +\label{laguerre:lag_error} \end{align} an. diff --git a/buch/papers/laguerre/references.bib b/buch/papers/laguerre/references.bib index 6956ade..e12e218 100644 --- a/buch/papers/laguerre/references.bib +++ b/buch/papers/laguerre/references.bib @@ -19,4 +19,13 @@ timestamp = {2008-06-25T06:25:58.000+0200}, title = {Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables}, year = 1972 +} + +@article{Cassity1965AbcissasCA, + title={Abcissas, coefficients, and error term for the generalized Gauss-Laguerre quadrature formula using the zero ordinate}, + author={C. Ronald Cassity}, + journal={Mathematics of Computation}, + year={1965}, + volume={19}, + pages={287-296} } \ No newline at end of file diff --git a/buch/papers/laguerre/scripts/gamma_approx.ipynb b/buch/papers/laguerre/scripts/gamma_approx.ipynb index 337b307..a8280aa 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.ipynb +++ b/buch/papers/laguerre/scripts/gamma_approx.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 113, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -86,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -136,21 +136,24 @@ "def laguerre_gamma(z, x, w, target=11):\n", " # res = 0.0\n", " z = complex(z)\n", - " if z.real < 1e-3:\n", - " res = pi / (\n", - " sin(pi * z) * laguerre_gamma(1 - z, x, w, target)\n", - " ) # Reflection formula\n", - " else:\n", - " z_shifted, correction_factor = find_shift(z, target)\n", - " res = np.sum(x ** (z_shifted - 1) * w)\n", - " res *= correction_factor\n", + " # if z.real < 1e-3:\n", + " # res = pi / (\n", + " # sin(pi * z) * laguerre_gamma(1 - z, x, w, target)\n", + " # ) # Reflection formula\n", + " # else:\n", + " # z_shifted, correction_factor = find_shift(z, target)\n", + " # res = np.sum(x ** (z_shifted - 1) * w)\n", + " # res *= correction_factor\n", + " z_shifted, correction_factor = find_shift(z, target)\n", + " res = np.sum(x ** (z_shifted - 1) * w)\n", + " res *= correction_factor\n", " res = drop_imag(res)\n", " return res\n" ] }, { "cell_type": "code", - "execution_count": 115, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -203,26 +206,13 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "zeros, weights = np.polynomial.laguerre.laggauss(12)\n", - "targets = np.arange(16, 21)\n", - "mean_targets = ((16, 17),)\n", + "zeros, weights = np.polynomial.laguerre.laggauss(8)\n", + "targets = np.arange(9, 14)\n", + "mean_targets = ((9, 10),)\n", "x = np.linspace(EPSILON, 1 - EPSILON, 101)\n", "_, axs = plt.subplots(\n", " 2, sharex=True, clear=True, constrained_layout=True, figsize=(12, 12)\n", @@ -239,7 +229,7 @@ "maxs = []\n", "for target in targets:\n", " rel_error = evaluate(x, target)\n", - " mins.append(np.min(np.abs(rel_error[(0.1 <= x) & (x <= 0.9)])))\n", + " mins.append(np.min(np.abs(rel_error[(0.05 <= x) & (x <= 0.95)])))\n", " maxs.append(np.max(np.abs(rel_error)))\n", " axs[0].plot(x, rel_error, label=target)\n", " axs[1].semilogy(x, np.abs(rel_error), label=target)\n", @@ -254,44 +244,9 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(-7.5, 25.0)" - ] - }, - "execution_count": 117, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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4J/onEdUk1rKCRJReZulBimoSVgWPGmEFiUhth3vGAQBrq1lBIkors1Qh4keN6D2K7LJwo0gi5R3pHYfDZsHyUk/aHlOxl1JaDBVuPcIkFaSYghUkG3uQiJR3pHcCqyvzYUvjT4hqvZISnYFZjhpRchWbxYKYJk3RZE9Ei3O4ZyKtDdoAAxKlQIUbjxDm+D6jmgarUCsg2ROBMMoqEpGSBiZCGPSF0rrEH2BAIgJgth4ktQJSsqTOaTYiNR3pTX+DNsCARATAPKvYYpqEzapYQEoEwkhM03kkRKSHIz3xM9jWVLGCRFlm/NgwP1aQjCsZCFlBIlLT4Z5xVBY4UeJxpPVxGZBoXiYorMzPND1IUrkepOkKkvGfPyJauMO9E2ndIDKJAYkIiVVseg8iDdSsILEHiUhVkZiGlv6JtE+vAQxIRADYg2RkVvYgESnrxIAPkZhMe4M2wIBEBCDRg2SCCkRMk7AoNsVmt3KZP5GqDnbFV7Ctr2EFiSgjzHJYbVTRjSIBIKaxgkSkmubuMbjtVqwo86b9sRmQiGCuKTbVjhqxs0mbSFkHu8axrqYgI72Xar2SEp2BRZjjwFMVjxphkzaRmjRN4mD3GDZkYHoNYEAiApCsIOk9iqWLahIW1QISm7SJlNQ2NInJcAzrawsz8vgMSEQALBZzNGlrUsUKEjeKJFJRc3e8QXtDDQMSUcZYTTLFFolpyu2DZGUPEpGSmrvG4LBZsKoy/Q3aAAMSEQDAao2vYjN6FSkak1PL3lVhT/QgRbmKjUgpzV1jWFuVP/UakG4MSETA1PEcRq8iRTUtYy8WuSpZQeI+SETqkFKiuWssY/1HAAMSEYDpm6yR+1iklIjE5NSqLlXYE9saRDnFRqSMzpEAxoPRjPUfAQxIRAAwtfu0kfdCSlZQ7Ir1IE03aXOKjUgVzV1jAIANtZlZ4g8sICAJIX4ihOgXQjSf9rEvCiG6hBB7E7+uzcwwiTLLDBWkZAXFblPr5x4bm7SJlNPcPQabReCsyvSfwZa0kFfSewFcM8vHvyml3Jz49Wh6hkWUXcmAZOQiRDixD5B6y/y5USSRapq7xrGqMh8uuzVj10g5IEkpnwUwnLGREOnIYoIm7WgiIKnWpM2NIonUMtWgnaEdtJPS8Ur6cSHE/sQUXPGZvkgIcbsQYpcQYtfAwEAaLkuUPslMYeQqxFQPkmoBiRtFEimlazSAockwNtUXZfQ6S30l/T6AJgCbAfQA+O8zfaGU8m4p5VYp5dby8vIlXpYovczQpB2OJqbYFNsHaWqjSAYkIiXs7RgFAGyuK8rodZYUkKSUfVLKmJRSA/BDAOenZ1hE2WUzQ5P2VAVJrYA0vcyfU2xEKtjXMQqHzYLVVZlr0AaWGJCEENWn/fYmAM1n+lqiXGaOVWxq9iBZOcVGpJR9HWPYUFMAR4ZX7NpS/UIhxC8BXAagTAjRCeALAC4TQmwGIAG0AfhI+odIlHkWEwSk6VVsagWkZAWJy/yJzC8a03CgawzvPr8+49dKOSBJKW+d5cM/TuNYiHRjhqNGpvZBUmyKjRtFEqnjWJ8PgUgMmzPcoA1wJ20iANMVJCMfVps8rFW1KTZuFEmkjn2dowCATRlu0AYYkIgAmKOCFI7Gx67aKjYhBKwWYejpUSJKzb6OURTl2bGsNC/j12JAIoJJmrQVrSAB8ecvwik2ItPb2zGKTXVFECLzPwiq90pKNAuLCY4ame5BUu+/td0ipr5/IjKnyVAUx/omMr5BZJJ6r6REszDFFJuiZ7EB4BQbkQKau8agSeAcBiSi7DHFFJvKFSSrhWexEZlccgfts+sKs3I99V5JiWZhioA01YOkXgXJZmUFicjs9naMor7EjVKvMyvXY0AigjkOq02exaZiBclmsXCZP5GJSSmxu30EWxqKs3ZN9V5JiWZhhsNqk2exqbbMH0hWkDjFRmRWnSMB9E+EsHUZAxJRVpliik3Rs9iA5DJ/4z53RDS3Xe3DAIBzl5Vk7ZrqvZISzcIcq9gSTdqKncUGAA6rBZEoK0hEZrW7fQT5ThtWV+Vn7ZrqvZISzcIUR40kl/krOMXmsFmmtjkgIvPZ1TaCzQ1FU9X+bGBAIoJJptg0LvMnIvMZD0ZwtG8CW7M4vQYwIBEBMEeT9vQqNgUrSFbL1PdPROay59QopATOzWKDNsCARARgevfpqKErSBqsFpGVM4pyjd1mmerBIiJz2d02DIsANjcUZfW6DEhEMMkUW0wqWT0CWEEiMrNd7SNYW10Ar9OW1esyIBHBJFNsMU3JFWwA4LAJ9iARmVA0pmFvx2hW9z9KUvPVlGiG6QqSzgNZgmhMKrmCDWAFicisjvROwB+O4dzl2W3QBhiQiABMHzVi6GX+mqbkCjYgvsyfFSQi83m1Lb5BJCtIRDqxmGGjyKhUNiDZWUEiMqWdrcOoK3ajpsid9Wur+WpKNIMZmrRD0RicNjX/S3OjSCLz0TSJV9qGsb2xVJfrq/lqSjSDKZq0oxocqgYkVpCITOd4vw/Dk2FsW5H9/iOAAYkIgFkqSJrSFST2IBGZy8utQwDAChKRnmwmCEgqV5DsVgs0OX0eHREZ386TQ6gtcqO+JE+X66v5ako0g8UEASneg2TVexi6SAbDCHfTJjIFKSVebh3GtkZ9ptcABiQiAIDVDKvYYmpXkACwD4nIJJL9R3pNrwEMSEQApitIRt4HKRRRuwcJAFeyEZnEzmT/0QoGJCJdmWEnbZUrSI7EDuIMSETm8HLrMGoKXagvyf7+R0lqvpoSzZDIR4hpxr3BhhVfxQYAEU6xERmelBI7Tw5he2MphNDv+CQ1X02JZhAQsFkEokaeYlN8FRvAChKRGbT0+zDoC+vaoA0wIBFNsVmNHZDCUQ0Oq6Kr2NikTWQazx0fBABc2FSm6zgYkIgS7BZjbzYYisbgtKv5X9rOJm0i03i+ZRDLS/N02/8oSc1XU6JZ2KwCUYPuo6NpEpGYnKqkqMbJChKRKURiGl5uHcLFq/StHgEMSERTbFbjVpCSlRPVK0hGff6IKG7PqVH4wzFcvLJc76EwIBElOawWw+7EHEpUTlStILEHicgcnj8+AIsALmjSb/+jJDVfTYlmEW/SNuYNNhkMnHY1m7STq9hYQSIytudaBnF2XREK3Xa9h8KARJRksxi3BykUjQGY7sVRTXJ7gxArSESGNRaIYF/HKN6UA/1HAAMS0RS7kXuQklNsiu6D5Er0XoUixnz+iAh46cQQNAlcvJIBiSinGHkfpGTlRNWdtF2JqcVgopJGRMbzfMsA8hxWnNNQrPdQADAgEU2xGXgfJFaQEgEpwoBEZFTPHx/E9sbSnHkdy41REOUAu4H3QZquIKnZpO1KvKAGOcVGZEgnByfRNuTHJTnSfwQwIBFNsVkshl/Flis/eWWbzWqBzSJYQSIyqB1H+gEAb15TqfNIpqn5ako0C5tVGHgfpHgwUDUgAfFpNlaQiIxpx9F+NJV70FCq7/Eip1P31ZRoBrvVuBWkZDBwK7oPEhAPSAFWkIgMZzIUxc7WYVy+ukLvobwOAxJRgpH3QUoGA7UDkgUhBiQiw3mhZRDhmIY3r2FAIspJRt4HKRmQXA51/0u77FYu8ycyoB1H++F12rB1eYneQ3kddV9NiWYw8j5IwTArSC67hT1IRAYjpcSOIwO4eGVZzvVQ5tZoiHRks1gQMehRFVMVJJUDks3KVWxEBnO4ZwK948Gcm14DGJBoHlIas6KyGA6bQMSgFaRAJAa7VUwd2qqi+Co2BiQiI9lxNL68/7LV5TqP5I3UfTWllCiUj+L7IBm1BykcU7p6BHCKjciI/nKkHxtqC1BR4NJ7KG/AgERz0hRKSDYD76QdjMSU7j8CACebtIkMZWAihNdOjeDKtbmzOeTpGJBoTgadcVoUu9WCiEH3QQpEYnA71A5IbrsVIVaQiAzjiUN9kBK4en2V3kOZFQMSzUmpCpKB90FiBSk5xcYKEpFRPH6wFw0leVhTla/3UGaVckASQvxECNEvhGg+7WMlQognhBDHE2+LMzNM0otC+Qg2qwVRTRqyMT0Q0diDZONO2kRGMR6M4MUTg7h6fSWEEHoPZ1YLqSDdC+CaGR/7DICnpJSrADyV+D2ZiEoVJLsl/p/UiHshBcOsICVXsRkx4BKpZseRfkRiMmen14AFBCQp5bMAhmd8+EYAP028/1MAb0/PsChXqBSQbIkl8kacZmMPUnyKTZMw7IHDRCr588E+lHmd2NKQuxNPS+1BqpRS9iTe7wWQm63otGgGLKYsmt0aryCFDbjUP8AepKkpRq5kI8ptwUgMTx/tx1XrKmGx5Ob0GpDGJm0Zr2uf8XYqhLhdCLFLCLFrYGAgXZelDFNpusKZuMGGDbibNvdBmn7+2KhNlNteaBnEZDiGq9fndk1lqQGpTwhRDQCJt/1n+kIp5d1Syq1Syq3l5bm3YybNTqUKkjMxxRYyYAUiGInBrfBBtcD0OXRc6k+U2x4/2It8pw0XNpXpPZQ5LfUV9SEA70+8/34ADy7x8SjHqNSD5LQnA5LxbrCcYov3IAHgSjaiHBaOanj8YB+uWFuRc4fTzrSQZf6/BPASgNVCiE4hxIcAfBXAVUKI4wCuTPyeTESpgJT4z2q0KTYpJQMSAI/DBgDwhxmQiHLV8y0DGAtE8LbNNXoPZV62VL9QSnnrGT51RZrGQjlIoXwEpy0xRWOwgOQPxyAl4HWl/N/ZlPISq/gmQ1GdR0JEZ/Lwvh4Uuu24eGXut9rkdn2LdKdSBSlZ7g0ZbIrGlwgEHqfaASn5/TMgEeWmYCSGPx/sxVs3VOX89BrAgETzUKpJ22bMHqRkQPIyIAEAJsMMSES5aMeRfkyGY7hhU+5PrwEMSDQPTaGElJxiM1oPUrJikuzBUZXHmZxiM1YFkEgVj+zvQZnXie2NpXoPJSUMSDQnhWbYpqfYDBaQOMUWlwyInGIjyj2+UBRPHenDdRurYM3hzSFPx4BEc1KpB2l6is1YFYhkxUT1KbbkKr5JrmIjyjlPHe5DMKIZZnoNYECieSgVkAy6D5IvFAEwPcWkKotFwOOwsoJElIMe2NOFmkJXTp+9NhMDEs1JoRYkw/Yg+VhBmpLntMHPJm2inNI/HsSzxwZw05banD57bSYGJJqTSmexOQw7xZZYxab4PkhAPCT62KRNlFMe2NMFTQLv2FKn91AWhAGJ5qRWBSm5D5KxKkiToSgsAsrvpA3EN4v0c4qNKGdIKfG71zqxpaEIjeVevYezIAxINCeVepBsFgGLAMIxYwUkXygKj8MGIYxTus4Uj9M2taqPiPR3oGsMx/p8eMe5xqoeAQxINA+VApIQAk6b1XhN2sGo8kv8kzwOK89iI8ohv9vdCYfNguvPNs7qtSQGJJqTQvkIQLwPyWhHjUyGo8qvYEvKc9q4io0oR4SiMTy4rxtXratEoduu93AWjAGJ5qRSBQmI9yEZroIUinEFW4LXYeNRI0Q5YseRfoz6I/grgzVnJzEg0ZxUatIG4nshGW2Z/2SIU2xJeU4rjxohyhG/fKUDlQVOvGlVmd5DWRQGJJqTahUkh9V4FaSJYIQVpASvM15BUukMQaJc1DHsx7PHB3DLeQ2wWY0ZNYw5asoalfZBApBo0jZWBWIsEDHk/H4mFLjskBLwcZqNSFf3v3oKAsC7z6vXeyiLxoBEc1LtB3Gn3XgVpLFABEV5DEgAUOCOV9LGAxGdR0KkrkhMw69e7cTlqytQU+TWeziLxoBEc1JtqsJlsyJgoGXioWgMwYjGClJC8u9hPMAKEpFenjjUh0FfCO/Z1qD3UJaEAYnmFFNsis3jNNY+OmOJSgkDUlyBK/73MMYKEpFu/nfnKdQUunDZ6gq9h7IkDEg0p5hiFSS3w1iHnSankgoYkABM/z2MBxmQiPTQPjSJ51sG8e7zG2A10MG0s2FAojlFFQtIRtuJmRWk15ueYmNAItLDz15qh80icIuBm7OTGJBoTrGYWgHJ7TBWD9KoPx4EivIcOo8kN3CKjUg/E8EIfvVqB647uxqVBS69h7NkDEg0J+V6kBI7MRtlewNWkF7P60qsYgsaZ5qUyCx+u7sTvlAUH7hohd5DSQsGJJqTej1IVmgShlnqz4D0elaLQL7Lxik2oiyLaRL3vtiGLQ1F2FxfpPdw0oIBieakYg8SAMP0ISUDUoGLO2knFbjsDEhEWfaXI/1oH/Ljgxebo3oEMCDRPFTbBynPEQ8aRlnJNhaIHzNi1K38M6HQbecqNqIsu+eFk6gpdOGa9VV6DyVt+KpKc1KtgpTnNFgFyc9jRmYqcNu4USRRFh3sHsOLJ4bwvguXm+qHNfN8J5QRMc0YvTjpkmewKbahyTBKvVzBdrpCtx2jgbDewyBSxvefPgGv04ZbzzP2ztkzMSDRnJSrICWn2ELGqEAMTYZQ6mFAOl2Jx4nhSQYkomxoG5zEowd68N7tDSg02ZmQDEg0J/V6kAxWQfKFUep16j2MnFLqcWDEH1Hu3y6RHu569gRsVgs+ZKLm7CQGJJqTshWkSO4HJCklp9hmUeJxIKZJbhZJlGF940H8bncX3rW1DhX5xt8YciYGJJqTavsgTVWQDDDF5gtFEY5qKPOwgnS6ZGAc4jQbUUb96LlWxKTERy5p0nsoGcGARHNSLSB5nPEKks8AAWnIFw8AJexBep3k3wf7kIgyZ9Qfxn07T+GGs6tRX5Kn93AyggGJ5qTaFFu+0wYhgAkDHFUxNBkCAE6xzTAdkEI6j4TIvO5+thWBSAwfvXyl3kPJGAYkmpNqFSSLRcDrtBlio8FkBamMTdqvU5qYcuQUG1FmDPpCuOeFNtxwdg3OqszXezgZw4BEc1KtggQkj6owQgUpHgBYQXq9Yk98qfGwjwGJKBO+//QJhKIxfOLKVXoPJaMYkGhOKi6VLjDIURUDE/EpJPYgvZ7TZkW+y8YKElEG9I4F8YuX2/GOLXVoLPfqPZyMYkCiOalZQTLGafA9Y0GUehxw2qx6DyXnlHocDEhEGfDdHS2IaRL/cIW5q0cAAxLNQ7WjRgAg32XHuAGatPvGg6gqNN/eI+lQ4nGwSZsozTqG/bj/1VO45bx6065cOx0DEs0ppl4+Shx2mvsVpN6xIKoKGJBmU+Z1Tk1BElF6/NfjR2G1CPz9m81fPQIYkGgeKlaQClzG6EHqHQ+ikhWkWVUVutA7FtR7GESmsefUCB7e143b39SoTOWaAYnmpGQPktsOXyia0w3qwUgMw5NhVLOCNKvKAhfGg1H4w7k/VUqU66SU+I8/HkaZ14nbLzXnrtmzYUCiOam2DxIQb9KWEpjI4d20+8fj00esIM0uOfXIKhLR0j3W3Ivd7SP45FvOgjdx2oAKGJBoTioGpEJ3fB+dUX/uroLqHY/f+NmDNLvkFEDy74mIFicUjeGrjx3B6sp8vGtrvd7DySoGJJqTigEpuTN1Li8TT974q1lBmlVlIjj2MSARLcmPnz+JU8N+fPa6tbBahN7DySoGJJqTij1IyZ2pc3kn5q6RAAAo0yy5UFMVpDGuZCNarK7RAP7nqRa8ZV0lLj2rXO/hZB0DEs1JxQpScmfqoRzeR+fUsB8lHgfyXXa9h5KTvE4b8p02VpCIluBLDx+EhMTnb1in91B0wYBEcwpF1VvmnzzsdDCHK0gdw340KLBR21JUcqk/0aLtONqPxw/24R+uWIW6YjVfaxiQaE4RBXeKdDus8DisGMrhgNQ+PMmANI/qQhe6RgN6D4PIcIKRGL740EE0lXvw4Ysb9R6ObhiQaE5hBStIAFDqdebsFFskpqF7NMiANI+Gkjx0jPj1HgaR4Xz7qeNoH/LjSzdugMOmbkxQ9zunlKhYQQLifUi5WkHqGQ0ipkk0lDIgzWVZaR5G/RGMGeDYGKJccaBzDHc924pbttbjopVleg9HVwxINKewogGpzOvAoC83K0jtw5MAwArSPJJ/Px3DrCIRpSIc1fDPv92HMq8Dn71urd7D0R0DEs0pHNXgsKr3z6TU48zZfZDaBuMBaRkrSHOqZ0AiWpDv7mjBkd4JfOWmjVMb5qosLXuGCyHaAEwAiAGISim3puNxSX/hmAa7VSAc03sk2VVR4MSQL4RoTIMtxwJiS78PXqeNu2jPI1lBOsWARDSvQ93j+O6OFtx0Ti2uWFup93ByQjoPVblcSjmYxsejHBCOanDYLJhULCHVFLmhSaBvIoTaIrfew3mdY30+rKzwQgi1drVdqHyXHSUeB9oZkIjmFIzEcOf9e1DsceDz16u559FscutHY8o5kZim5CqG5BEe3Tm4TPx4vw+rKrx6D8MQ6kvyOMVGNI+vPHoYx/t9+O93bkJxYqNcSl9AkgD+LITYLYS4PU2PaViaiXafDkc12HNsiikbahJVo1wLSCOTYQz6QlhVyYCUimUleTiZ6Nkiojd68lAffvZSOz508QpcouBxInNJ153vYinlFgBvBfAxIcQlM79ACHG7EGKXEGLXwMBAmi6bmzRpnoAUiUmlK0g9ObYTc8uADwCwqjJf55EYw6oKLzpHAvCHo3oPhSjn9I8H8enf7cfa6gJ8+prVeg8n56Tlziel7Eq87QfwAIDzZ/mau6WUW6WUW8vLzZ1SYyYKSKquYst32ZHvsqEnxypIh3vGAQCrGZBSkgySLf0+nUdClFuiMQ133r8Xk6Eo/ufWzXDarHoPKecs+c4nhPAIIfKT7wN4C4DmpT6ukWkm2TpISomwoj1IAFBT6EZ3jlWQ9neOodTjmKpw0dzOSkxFHutjQCI63df+fBQvtQ7hyzdtxMoK/sA1m3SsYqsE8EBiRY0NwP9KKf+Uhsc1LLNMsUVi8e9DxR4kAKgvcedcg29z1xg21BZyBVuKGkry4LBacLxvQu+hEOWMPzX34K5nWvHebQ34q3Pr9B5OzlpyQJJStgLYlIaxmIZZptiSu2irOMUGACvKPHju+CA0TcJi0T+QBMIxHO/34ap13KMkVTarBY3lHhxjQCICAJwY8OFTv9mPTfVF+PwNXNI/FzXvfBkmTTLFljyo1q7oFFtjuRehqIbusdzoQzrUM46YJrGhtlDvoRjKWZX5nGIjAjAejOCOn++Gw2bB9967hX1H81DzzpdhZqkgBSPxzSHz7Gr+J1pR5gEAtA7kxjLx/Z2jAICNDEgLsq6mAF2jAYzk6NExRNkQiWn42H2v4eTgJL7znnNybgPcXMSAlAFm6UEKJAKS26FmQGosTwak3Kg+vHJyGLVF7qk9mig1Z9fFA+X+rjGdR0KkDyklvvDQQTx3fBBfuXkjLmwq03tIhsCAlAFm2SgykDhexKVoBanc64TXaUNrDmw0KKXEKyeHsW1Fid5DMZyNtYUQAtjfMar3UIh08ePnT+J/d57CHZc24V1b6/UejmEwIGWASfLRdAVJ0YAkhEBTuScn9tBp6fdhaDKMbY0MSAuV77KjscyDfZ2sIJF6HtnfjS8/ehjXrK/Cp6/mZpALwYCUAWbpQUpWkNwOdf+ZrKspwMHucUidn9OdJ4cBANtWlOo6DqPaVFc01cNFpIpnjg3gH3+1F1uXFeObt2zOidW4RqLunS+DTDPFpngFCQA21BZiLBBBx7C+K9mePTaAmkIXlpXm6ToOozq7rhD9EyH05MiKRKJM290+gjt+vhsrK/Lxo/efp2wv6VIwIGWAWZq0k6vYVO1BAqZXjB3QscE3FI3h+ZZBXL6mghtELtLW5fGpyVcSlTgiMzvSO44P3PMKKguc+NkHz0eh2673kAyJASkDTFJAOm2KTd2AtLoqHzaLQHO3fgFpZ+sw/OEY3rymQrcxGN3a6gIUuGx4sWVI76EQZdThnnG854c7keew4ecf2obyfKfeQzIsBqQMiJkkIXGKDXDarFhbXYDX2kd0G8NTh/vgtFm4NHcJrBaBbY2leKmVAYnM62D3GG794ctw2iy4//btqC/hlPxSMCBlgN4NvekS4BQbAGDbihLs6RidmnLMpmhMwx8P9OKy1eVKV/LS4YLGUpwa9qNzJLfO1yNKh+auMbznhzvhcdjwq9svwPLERre0eAxIGWCWVWy+YBRWi4DLrvY/k+2NpQhHNew5NZr1a794YgiDvhDevrk269c2mwtXxlcAcpqNzGZn6xBu/eHLyHfZcP/t29HAxRxpofadL0M0k5zFNhGMIt9lg4DajcHnrSiBRUCX6Zk/7O1CvsuGy9l/tGSrK/NRXejCk4f79B4KUdr8qbkXt/3kFVTkO/Grj1zAabU0YkDKALOsYpsIRpDvsuk9DN0Vuu04u64IO470Z/W6Y/4IHjvQi+s2Vis/zZkOQghcubYSzx0f1GW6lCjdfvFyOz56325sqCnAb++4kOerpRkDUgaYpUl7IhhFvpPLQwHgmg1VONA1ltX+ld/s7kAgEsNtFyzL2jXN7qp1lQhEYnihZVDvoRAtmqZJ/NefjuBzf2jG5asrcN+Ht6PY49B7WKbDgJQBURMFpAI3K0gAcPX6KgDA4wezMz0T0yR++lIbzltejPU1hVm5pgq2N5Yi32nDn5p79R4K0aJMBCO4/ee78L2nT+DW8xtw123ncgFHhjAgZUA4ao4mpPFgBPkuVpAAYEWZB2uq8vHwvu6sXO+hfV3oGA7ggxetyMr1VOGwWXD1hio81tw7tc8XkVG0D03i5u+9iB1HB/ClG9fjKzdtgM3K23im8G82A8IxcwSkZJM2xb1zaz32doziYIY3jYzENHzryeNYW10wVbmi9Ll5Sy18oSj+fIhVJDKOHUf6ceN3X8CAL4Sff/B8vO+C5dxZP8MYkDLATBWkAlaQprxjSy2cNgvu23kqo9f59a4OtA358U9XncXDJTNg+4pS1Ba58bvXuvQeCtG8IjEN//noYXzg3ldRVeDCgx+7CBeu5Kax2cCAlAERE1SQNE3CF2IF6XRFeQ68bVMNfre7E/3jwYxcY2AihP/z2BGcv6IEV67l0v5MsFgEbt5Si+ePD6BjmJtGUu7qGg3glrtewl3PtuK92xrwh49dhGWl3AAyWxiQMsAMFaSJYBRSgocczvCxy1ciqkl87+kTaX9sKSW+9MghBCIxfOWmjSyfZ9B7tjXAIgTufbFN76EQvYGUEg/u7cK133oOx/p8+J9bz8GXb9rI7T6yjAEpA8wQkAYnQwCAMi8POjzd8jIP3nluHe7b2Y5jfRNpfezf7OrEw/u68fdvXoWVFd60Pja9XnWhG9durMavXu3ARDCi93CIpgz6Qvjofa/hzvv3orHcg0f+/mLcsKlG72EpiQEpA0ImmGIb8oUBMCDN5p+vXg2v04b/73f707bn1b6OUfzbg824aGUpPnb5yrQ8Js3tw29aAV8oip+/3K73UIgAAI8d6MHV33wWTx3ux2feuga/veNCnqmmIwakDIiYoYLki1eQSr3cfGymUq8TX7hhPfacGsXXHj+65Mdr6Z/A39zzCioKnPi/t5wDKxuzs+LsuiJcvrocdz3TirEAq0ikn45hPz7801fxd/e9hpoiNx75h4txx6VNfC3QGQNSBphhmf8QA9Kc3n5OLd67rQE/eOYE7tu5+ArEa6dGcMtdL8NqseAXH9qG8nxW7LLpU1evxlgggh8+26r3UEhBoWgM393Rgqu++QxePDGEf712LX7/0QtxVmW+3kMjAFyilAGm6EHyhSEEUJLHgHQmX7hhPbpHA/jXB5ox6o/g7y5tSnlZvpQSv3i5Hf/xx8OoLHDh3g+cx9UpOlhfU4gbNtXgR8+34l1b63kKOmWFlBJ/OdKPLz96GK0Dk7h2YxX+7fp1qC7kWWq5hBWkDDBDQBrwhVCS5+AurXNw2Cz4wW3n4oZNNfja40fxvp+8gqO98zdu72obxi13vYx/e/AgtjWW4oGPXojGcjZl6+Wz166BVQh87sFmSJMcNE25a3/nKN5998v40E93ARK45wPn4XvvPZfhKAexgpQBZtgHqWskgBqeDD0vp82Kb797M7atKMH/+dMRXPOtZ3HxyjK8ZX0V1tcUoNTjQCQm0TMWwGvto3isuQdHeidQ5nXiqzdvxC3n1XM5v86qC9341NWr8f8/fAgP7evGjZtr9R4SmVDb4CT++4ljeHhfN0o9Dvz7jevx7vMbYOcPoTmLASkDQiaoIHWNBtBUzimfVAgh8Nfbl+G6jdW458U2/P61TvzbH5pn+bp4Y/C/37ge7zi3DnkO/vfLFe+7YDke3teNzz3QjM31RZzupLQ5MeDDd//Sgj/s7YLDZsHHL1+Jj1zayHMuDYCv0Blg9CZtKSW6RgK4ZFW53kMxlGKPA/901Vn4xytXoXMkgCO9ExgLRGC3CpTnO7G+ppAbb+Yoq0Xg27eeg2u/9Rw+/r978Js7LuCmfLQkx/om8J2/tODh/d1w2az40MUr8LeXNKIi36X30ChFDEgZEIoYOyCN+CMIRGKoLeYU22IIIVBfkof6Ejb8GkldcR6+/s5NuP3nu/Gp3+zDt999Ds/CowWRUuLZ44P48fMn8eyxAeQ5rPjIJU348JtWcE85A2JAyoDJUFTvISzJycFJAMAy3uBJMW9ZX4V/eesa/OdjR1BT5Ma/vHUNe8RoXoFwDA/s6cJPXjiJln4fyvOd+ORVZ+G925ehxMOVwEbFgJQBEyFjbzrX0h9ficW9OEhFt1/SiK7RAO5+thVCAJ+5hiGJZtfcNYZfvdqBP+ztwkQwivU1BfjGuzbh+rNr4LCx+droGJAyYCJo7ArS8T4fXHYLp9hISUIIfPGG9dCkxF3PtCIQjuHz16/jlhcEABgLRPDQvm786tVTaO4ah8NmwbUbqnDr+Q04f0UJw7SJMCBlgNED0rF+H5rKvdzmnpRlsQj8+40bkOew4e5nW3FycBLfuXULCvPYZK8ifziKJw/34+F93Xjm6ADCMQ3rqgvwpRvX48ZNtfx3YVIMSGlmtQhDnw4upcTBrjFctrpC76EQ6UoIgc9euxZN5R587g/NuP47z+Eb79qM85aX6D00ygJ/OIpnjw3g4f09eOpwH4IRDVUFLtx2wTK8fXMtNtYV6j1EyjAGpDTLd9kwbuAK0qlhP4YmwzinoUjvoRDlhFvOa8DKinx84ld78K67XsLtlzTizitWcR8rE+oc8WPHkX48ebgfL7UOIRzVUOZ14J3n1uOGTTXYuqyYKxsVwv/haVbgsmPUH0EwEjPkPiqvnRoBAGxpKNZ5JES549xlxXjszkvwH48cwl3PtOKhvd34zFvX4G2bathzYmCBcAy72ofxQssQnj7ajyOJo4JWlHnwvu3L8Oa1FTh/eQn7zxTFgJRmFflOnBr2Y2AiZMh9cF46MYR8lw2rq7iCjeh0XqcNX33H2bh5Sx2+9MhB3Hn/XvzwuVZ87LKVuHp9FSsLBhCOatjXOYoXW4bw4olB7Dk1inBMg80isGVZMT577RpcsbYSTTwbkcCAlHZVhfFdUnvGgoYLSJom8ZcjA7j0rHI2aBOdwfkrSvDgxy7GA3u68N0dLfi7+15DU7kH77tgOd6+mQ27uaRvPIjX2kewp2MUr7WP4EDXGEJRDUIAG2oK8YGLluOCplKct7wEHidvh/R6/BeRZtVTASmg80gW7kDXGAZ9IVyxlg3aRHOxWgT+6tw63HROLR490IO7n23FFx46iK88ehjXbazGDZtqcOHKUjhtxptmN6r+iSAOdY/jcM8EmrvHsPfUKLpG46/DDqsFG2oLcNv2Zdi6vAQXNJYyyNK8GJDSrKowvndQ71hQ55Es3AN74ocpXs4VbEQpsVoEbthUgxs21aC5awy/fOUUHtrbjd/v6UK+04Yr1lbg8jUVuLCpDOX5PGoiHSZDUZwcnMSJAR8O9YxPhaJBX2jqa2qL3NjcUIQPXrwC5zQUYX1NAcMqLRgDUpp5nVbkO21TP7kYRTAS3yr/6vVVKMrj1vhEC7WhthBfvmkjPn/DOrzQMog/NffiiUN9+MPebgDAWZVeXNhUhnMainB2XRGWleSxb+kMwlENPWMBnBr2o3UgHoaSb3tO++HTbhVYVZGPy1aXY111AdZWF2BddQGrQ5QWDEgZsKrSO7Uawijuf+UUxgIRvHdbg95DITI0p82KN6+pxJvXVCIa03Cwexwvnog3Bd//6inc+2IbgPiWIBtrC7GmqgCN5R40lXvRVOFBuddp6pVxUkqM+iPonwihfyKIrpEAOkcC6Bzxo3MkgK7RAHrHg5By+s94nTY0lXuwvbEUTeUeNJZ70VjuQWOZl0d6UMYwIGXAupoCPLinG1JKQ7zQ+cNRfO/pE9i2ogTbG0v1Hg6RadisFmyqL8Km+iL83WVNiMQ0HO/z4UDXKPZ3juFAYlouEIlN/Zl8pw21xW5UF7pQXeRGTaEL1YVuVBQ4UZznQLHHgeI8O9x2a068voSjGsYCEYwFwhgLRDDqj0y9HQ1EMDARwsBEEAMTIfRPhDDoCyESk697DKtFoLrQhdoiNy5sKkNdsRu1xW7UFbuxstyL8nxzh0bKTQxIGbC+phC/ePkUWgcnDbFc9GuPH0X/RAjf/+steg+FyNTsVgvW1RRgXU0Bbjkv/jFNk+gdD+LEgA8n+n1oHZxE92gAPWNB7Oscw/BkeNbHctgsKM6zo8jtgNthRV7il8uefN8Gp80Ci0XAKsTUW6sFU+9rEohpGmJa/G1Uk4hpcuptMBKDPxz/FYhEEZh6P/52MhSFPxybdXwAIARQ6nGgzOtERYELqyrzUZ7vREW+M/HWhdpiNyrzndxriHIOA1IGXNRUBgB45uhAzgekJw/14d4X2/C+C5bh3GU8QoEo2ywWgZoiN2qK3HjTqvI3fD4YiaF3LIj+iRBG/GGMTIYx4o9g1B/G8GS8ahOIxBAIxzDqjyTCSzzMhKIaNBkPO5qc5eKnj0MANosFFkv8rdUi4LJbkOewTYUuj9OGMq9zKpB5HDYU5dlR6LajwG1HUZ4DhW47itzTH+OWIWRUDEgZ0FCah1UVXvzxQA8+ePEKvYdzRrvbh3Hn/XuwsbYQn712rd7DIaJZuOxWLC/zYHmZZ0mPI6VMVIzkVGiyWkT8V6LCRETTWNPMkHef34Dd7SPY2zGq91Bm9afmXvz1j15BRYELd9+21ZDHohBR6oSIhyGHzQKXPV4NctmtsFstDEdEs2BAypB3bq1DmdeBzz/YjGhM03s4U4Z8IfzL7/fjjl/sxqpKL379kQumdv8mIiKiOAakDClw2fHFt63H/s4xfPp3+xHROST1jQfx9ceP4rKvP41f7+rE375pBX5zxwXcvI6IiGgW7EHKoOvPrkHrwCS+8cQxtA5M4vM3rMOWhuKsXb97NICnjw7gTwd78WLLIGJS4sq1lfj01auxqpKH0RIREZ0JA1KG/cMVq9BY7sEXHjyIm7/3IjbWFuKaDVU4f0UJ1tcUIM+x9KcgGImhfciPk4M+nBiYxOGecexuH5nacXZZaR4+/KZG3Hp+PZaVLq3Rk4iISAUMSFlw/dk1uHx1Be5/tQN/2NOFrz1+dOpzFflOLCvNQ4nHgQJXfGmsy26FRUzvVRKTcmoZb3IfkqHJEAYmQhj0xZf5nq62yI2ty0twbkMRtjeVYnVlPjdZIyIiWoC0BCQhxDUAvgXACuBHUsqvpuNxzcTjtOFDF6/Ahy5egeHJMHa3j+Bo7zjah/w4NexH26A/sRttBOGYhtiMTUucNgvcDivcdivcDitKPQ6srsrHRV4nyrzxkNVU7sWKMg88TuZeIiKipVjynVQIYQXwXQBXAegE8KoQ4iEp5aGlPrZZlXgcuGpdJa5aVznn12mJ/Uos3KOEiIgoq9Kxiu18AC1SylYpZRjA/QBuTMPjKs9iEbBxjxIiIqKsS8dcTC2AjtN+3wlg28wvEkLcDuB2AGhoeP2J8dGYhpODkzgxMIkBXwiDEyGMByMIRjSEIjEEozEEI/FpJ4n4jrBSAhLxt1ri2GebxQKbVcBmEVPv263xLfPtiffdDiu8Dhs8Thu8zvhbj9OKEo8DlQUulHocPBOIiIhIcVlrVpFS3g3gbgDYunWrBIDjfRP4n7+04MnDfa878FAIwOuwwWm3wmWP7/rqsltgFQIQAhYBCMR3ho2/H6+w+KNRRDWJaEwiqmmIxiQimoZYTCKiSURiGvyhGMJz7ElkEUCp14m6YjfWVOXjrMp8nNNQjI21hTxTiIiISBHpCEhdAOpP+31d4mNzevpoP27/2W447RbcuLkG5y0vwVmV+ajId6Ikw1WccFTDZCgKXyiKyXAUk6Eohicj6BsPon88iL7xENqHJ/Gn5l788pV4caw4z463rKvC+y5chvU1hRkbGxEREekvHQHpVQCrhBArEA9G7wbwnrn+gCYlPvnrfWiq8OLnHzofZd7s7ubssFngsDlQ7HHM+XVSSgxMhPDyyWE8faQfD+3rxq92deDmLbX4/PXrUJQ3958nIiIiY1pyQJJSRoUQHwfwOOLL/H8ipTw4158Z80cQmwzj7vedm/VwtBBCCFQUuPC2TTV426YafOGGCO5+7gTueqYV+zpG8YsPb0N1oVvvYRIREVGapWUeS0r5qJTyLCllk5Tyy/N9/UQoiqoCV1aP3UiHwjw7/vnqNbjvw9vQNx7CHT/fjVA0Nv8fJCIiIkPRZblWKKJhQ22BYXd33tZYiq+/82zs6xzDvS+06T0cIiIiSjNdAlI4pqGuOE+PS6fNNRuqcelZ5fj+MycQjLCKREREZCa6BCRNStSXGDsgAcDtlzRi1B/B4wd79R4KERERpZFuOyKWeY2/AuyCxlKUeZ146nC/3kMhIiKiNNLtVFOPw/gHqlosAhetLMULLUOQ83+58qSUGPFHcGrYj1F/GMGIBk1K5LtsKHDZUVvsRqnHYdjeNCIiMg/dUkqe06rXpdNq24pSPLi3G53Dfr2HkpPGgxE8ur8HzxwbwCsnhzE0GZ7z6wvddqyuysf2FSXY3lSK85eX8OgXIiLKOt0Cktdp/AoSAKytzgcAHOmd0HkkuWVgIoTv7mjBL185hVBUQ22RG5euLse66gIsK/Wg1OuA02aBRQj4QlGM+iPoGPbjxIAPzV1j+M6OFnz7Ly0o8zpww6YavHfbMqys8Or9bRERkSL0m2IzSUA6qzIekI71MSAlPbyvG5994AD84RjesaUW7922DGfXFS5o6mwiGMELLYN4cG837tt5Cve+2Ia3bqjCP111FlZW5Gdw9ERERDoGJLfdHFNsHqcNpR4HukYDeg9Fd1JKfPOJY/j2X1pwTkMRvv7OTWgqX1zVJ99lxzUbqnHNhmoM+UK454U2/PTFNvz5YB/+9pJG3HnFKrhM8m+IiIhyj27NHTaLeRpxa4rc6BphQPr2U/FpsVu21uPXH7lg0eFoplKvE5+6ejWe/ufL8PZzavH9p0/gr37wIjrY90VERBmiW0CymCgg1Ra5la8g/eVIH7755DHcvKUW/3nzRtgz0Fhd6nXi6+/chB+9bytODflxw3eex/7O0bRfh4iISL+AZKKl3OX5TvjD6u6mPRGM4DO/O4C11QX4yk0bMx5+r1xXiYf//mLku2x4zw934rVTIxm9HhERqUe3gGQ1UUAqyrPrPQRdfXfHCQz4QvjqzRuz1he0rNSD33zkQpR5HfjwT3ehbXAyK9clIiI16BaQhIm2tinKM/6u4Is1FojgFy+344aza7Cpviir164qdOGeD5wPKSU+/LNdCChcxSMiovRiBSkNitzqVpDuf+UUfKEoPnJpoy7XX1Hmwf/cugUt/T589bHDuoyBiIjMhz1IaaDyFNvvX+vCucuKsb6mULcxXLyqDB+6eAV++lI7Xm4d0m0cRERkHjquYtPryumnakA62juBo30TuHFzjd5DwT9fvRo1hS586eFDiGk8GY+IiJaGFaQ0MMuu4Av15OE+AMA1G6p0HgngslvxmWvX4lDPOB7Y06X3cIiIyODYg5QGZtkVfKFeOjGENVX5qMh36T0UAMANZ1djXXUBvvd0CzRWkYiIaAn0W8VmnnwEt0O9gBSKxvBq2zAuaCrVeyhThBD4u8ua0DowiT8f6tV7OEREZGA6BiTzJKQ8h3pTbAc6xxCKatjemDsBCQCu3ViNumI37tt5Su+hEBGRgekSkMwTjeJUnGI71DMOANhUV6TvQGawWgTeeW49nm8ZROcIz2ojIqLFMdFaMv1YTXSuXKoOdY+jxONAZYFT76G8wV9trQMA/HZ3p84jISIio9InIKmXJ0znUM841lUX5ORUaW2RG9tWlOCxA+xDIiKixdFpii33bqqUOikljvf5sKrSq/dQzugt66pwtG+CZ7QREdGicIqNFmzAF0IgEsPyUo/eQzmjq9ZVAgCeONSn80iIiMiI2KSdJg6rOlmzYzje/NxQkqfzSM6sviQPZ1V68ezxAb2HQkREBsQepDSxWU34TZ1B+1AiIJXmbkACgAsaS7GrbQThqKb3UIiIyGBYQUoTu0IVpFPDfggB1BW79R7KnC5oKkUgEsP+zlG9h0JERAajzl09w1QKSF0jAZR7nXDacnv/p20rSiFE/EgUIiKiheAqtjRxKDTFNugLoSIH9z+aqdjjQGOZB/tYQSIiogViD1Ka2G3qVJAGfCGUeXM/IAHAxtpCHOga03sYRERkMOrc1TNMpSm2wYmwcQJSXRH6xkPoHw/qPRQiIjIQNmmniSoBSUqJockQyvMNEpBqCwGAVSQiIloQTrGliSo9SGOBCCIxaZgK0vqaAggBNHeN6z0UIiIyEFaQ0kSVA2sHJkIAgDKvQ+eRpMbjtKGu2I2WAZ/eQyEiIgNRY14oC1QJSIO+MACg3CAVJABoKveipZ8BiYiIUmfTewBmkYun2mfCWCAekArz7DqPJHUry7146cQQYppUJshmUziqoW1oEhPBKIrz7KgvyVOmJ4+IzIsBKU2sigSk8WAUAFDgMk5AaqrwIhTV0D0aQH0Onx9nJFJKvNAyhHtfPInnjg8idNpxLl6nDZetLscHL16BLQ3FOo6SiGjxGJDSxKLID8wTBgxIKyu8AICWfh8DUhr0jQfxrw8048nDfSjzOnHr+Q04p6EIBW47hn1h7GofwR/3d+OR/T246ZxafPGG9YaqOBIRAQxIaWNRpII0EYwAALwu4/zTWZYIRR0jfp1HYnyHusfxwXtfxWggjM9euwbvv3D5G46cece5dfjcdWvxg2dO4AfPnMDejlH8+P1b0Vju1WnUREQLp0jdI/NUCUjjgSg8DquhennKvE44bBZ0jgT0HoqhHe2dwC13vwQAeOCjF+H2S5rOeB6fx2nDJ9+yGr/82+0YD0Tw7rtfRtvgZDaHS0S0JAxIaWKkwLAUE8EI8g00vQYAFotAbZEbXQxIi9Y/HsTf3PMK3HYrfnPHBVhbXZDSn9u6vAS/vH07IjEN77/nFYwFIhkeKRFRejAgpYki+QgTwSjyDTS9llRX7EYnp9gWRdMkPvmbfRjxh3HPB85bcB/XWZX5+NH7t6JrJIBP/nofpJQZGikRUfowIKWJKlNsE6GIYQNS1ygrSItx3852PHd8EJ+7bh3W1xQu6jHOXVaCz7x1DZ483IcH9nSleYREROnHgJQmygSkYBQFbmNNsQFAXXEeBn1hBMIxvYdiKMOTYXzt8aO4aGUp3rutYUmP9cGLVmBLQxH+/ZFDGJ4Mp2mERESZwYCUJqr0IPlCUXgcxqsg1RS5AIBVpAX61pPH4AtF8fnr1y95M1SLReArN2/EWCCC7z/dkqYREhFlBgNSmlgUCUihiAaXffaVS7msIj8ekAZ9IZ1HYhz940H88pUO3HJePVZX5aflMddUFeCmc+rws5fa0TceTMtjEhFlAgNSmiiSjxCMxOCyG++fTXl+/Oy45GG7NL8fv3ASUU3DHZc2pfVxP3HlKsQ0ibueaU3r4xIRpZPx7nQ5SpWjRgKRmCErSMnDdRmQUjMZiuK+l0/h2o3VWFbqSetj15fk4dqN1fjNrg5MhqJpfWwionRhQEoTFQ6rlVIiGInBbcCAVOi2w24VGOAUW0r+eKAHvlAUf3Ph8ow8/vsvXI6JUBS/54o2IspRDEhpkjy83MxbvEQ1CU3CkFNsFotAmdfJClKKfrurE41lHpy7LDOHzW5pKMLG2kL8785TGXl8IqKlMt6dLkcll/lrJg5IySXyRpxiA+J9SAxI82sbnMQrbcN459b6jFVGhRC4eUstDveMo6V/IiPXICJaiiUFJCHEF4UQXUKIvYlf16ZrYEaTXMWmmbiEFIwYPCCxgpSSx5p7AQA3bq7J6HWuO7saFgE8tLc7o9chIlqMdFSQviml3Jz49WgaHs+QkqvYTB2QohoAAwekfCd7kFLwxKFebKwtRE2RO6PXqch34YKmUjy0r5vHjxBRzuEUW5okV7FpJp5jC05NsRnzn02p14EhX8jUz9FS9U8EsadjFFetq8zK9a7dWI22IT9ODPiycj0iolSl4073cSHEfiHET4QQmenoNIBkr0bMxPfeYDQekIy4ig0AitwOaBLwhbm0/EyeOtwPKYG3rM9OQLpsdQUA4OmjA1m5HhFRquYNSEKIJ4UQzbP8uhHA9wE0AdgMoAfAf8/xOLcLIXYJIXbFYuY7Dyt51IiZpwqM3oNUmBc/Q27MH9F5JLnr+ZZBVBW4sLoyPTtnz6e2yI1VFV7sONqflesREaVq3kO1pJRXpvJAQogfAnhkjse5G8DdAFBQv9p0KSLZgxQz8fRNIJzsQTLmFFtR4pDdUX8E9SU6DyYHSSmxs3UIb1pVntV9vS5fU4F7XjiJyVAUHqfxzvkjInNa6iq26tN+exOA5qUNx7imV7HpPJAMSk6xGbWCVJTnAACMBVhBmk1Lvw+DvjC2N2Y3PV7YVIpITGJvx2hWr0tENJellgL+SwhxQAixH8DlAP4xDWMypOl9kMybkIw+xVaUmGIbDYR1Hklueql1CABwQWNZVq+7ZVkxhABebRvO6nWJiOaypHq2lPK2dA3E6FRYxRZKLPN3WI0/xUZvtKttBFUFLtSXZHZ5/0wFLjvWVhVgV9tIVq9LRDQXY97pctBUD5KJK0jRWCIg2Yz5z6YgEZA4xTa7/Z2j2FRfqMu5guctL8Zrp0am/o0REenNmHe6HJS8qZg4HyGS2MPAbtAKkstuhctuwaifU2wzjfkjaBvy4+y6Il2uv3V5CfzhGI708tgRIsoNxrzT5TAT5yNEEj/d26zZrzCkS5HbgRFOsb3Bga4xAMDZdYW6XH9jbfy6B7vHdLk+EdFMDEhpMjUrYeISUjIgGbUHCQAK3DZMBBmQZtrfNQpgOqhkW0NJHrxOGw52j+tyfSKimYx7p8sxAokpNp3HkUlRg0+xAYDHacNkyHwblS5Vc9cYGkryprZCyDaLRWBddQGau1hBIqLcYNw7XY5JVpBMXEBCOKZBiOldw43I67TBF+JRIzMd6/NhdVV2ds8+k3U1BTjcM2HqzVaJyDgYkNLEuJEhddGYNHT1CAA8DhsmGZBeJxzV0DY4ibMqvbqOY31NAQKRGE4OTuo6DiIigAEp7aSJJ9kiMQ12A1ePgOQUGwPS6dqHJhHVJFZV6FtBWltdAAA40ss+JCLSHwNSmqgwxRbRJOwG3QMpyeu0copthuP9PgDAygp9K0hN5fHrtw6wgkRE+jP23S6HTO2DpPM4MikS1WCzGPufjMdpw2Q4BmnmJLtAx/omIMR0QNGL22FFbZEbJwZ8uo6DiAhgQEo7M993o5oGh4H3QAIAr8uGmCanjk2heAWpvjgPbof+Z+w1VXhZQSKinMCAlCY6nM6QdZGYhM3gTdpeZ/z4wYkgp9mSWgcm0VTu0XsYAICmcg9ODPhY4SMi3Rn7bpeDzNykHY5qsBu8guRxxAMSG7XjpJToHPZjWWluBKTGci/84Rh6x4N6D4WIFMeAlCbJjSJNnI8Q1TTjL/NPVJDYqB036o9gIhRFXbFb76EAAJrK4kHtJKfZiEhnxr7b5RBh/nyEiAn2QUpOsbGCFHdq2A8gftRHLqhPjKNzJKDzSIhIdca+2+WQ6aPYzBuRIjETTLE5443Ik2EGJADoGEkEpNLcCEhVhS5YBNCZGBcRkV4YkNJEjSZtzTRN2j6exwZguoJUX5wbAclutaC60M0KEhHpzth3uxxk4gISojEJh8EDksseryAFIwxIANAxHECpxzHVm5UL6ordU5UtIiK9GPtul0OSTdomzkeIatLQB9UC0wEpxIAEID6VVZcj/UdJdcV5rCARke4YkNJEhaNGABg+ICU3QwwwIAEAesaCqC5w6T2M16krdqN3PIgwN/MkIh0xIKWZmfdBAgCLwZutXImz5IIR3nwBoG88iKrC3ApI9SV5kBLoHmUViYj0w4CUJsLgwSFVBm9Bgs1qgd0qWEEC4A9HMRGMoqLAqfdQXqcmEdi4WSQR6cngt7vcwym23OeyW9mkDaB3LB5AqnJsii0Z2PoYkIhIRwxIaWL82JAao0+xAQxISX3jIQC5GJDi4+lPjI+ISA8MSGky3aRt7hKSGSpIbruVPUiYrtBU5FhAynfa4LJb0D/BChIR6YcBKU2mdtLWdRSZZzVBBclttyIQZgUpGZByrUlbCIHKAtdUhYuISA9Cj4qHEGIAQHvWL5wdZQAG9R4ELQifM2Pi82ZMfN6Mx8zP2TIpZflsn9AlIJmZEGKXlHKr3uOg1PE5MyY+b8bE5814VH3OOMVGRERENAMDEhEREdEMDEjpd7feA6AF43NmTHzejInPm/Eo+ZyxB4mIiIhoBlaQiIiIiGZgQMogIcQnhRBSCFGm91hobkKIrwkhjggh9gshHhBCFOk9JjozIcQ1QoijQogWIcRn9B4PzU0IUS+E2CGEOCSEOCiEuFPvMVHqhBBWIcQeIcQjeo8lmxiQMkQIUQ/gLQBO6T0WSskTADZIKc8GcAzAv+g8HjoDIYQVwHcBvBXAOgC3CiHW6TsqmkcUwCellOsAbAfwMT5nhnIngMN6DyLbGJAy55sAPg3zb65tClLKP0spo4nfvgygTs/x0JzOB9AipWyVUoYB3A/gRp3HRHOQUvZIKV9LvD+B+M22Vt9RUSqEEHUArgPwI73Hkm0MSBkghLgRQJeUcp/eY6FF+SCAx/QeBJ1RLYCO037fCd5sDUMIsRzAOQB26jwUSs3/RfyHfeUOsLTpPQCjEkI8CaBqlk/9K4DPIj69RjlkrudMSvlg4mv+FfHpgPuyOTYiFQghvAB+B+ATUspxvcdDcxNCXA+gX0q5Wwhxmc7DyToGpEWSUl4528eFEBsBrACwT8QPdq0D8JoQ4nwpZW8Wh0gznOk5SxJC/A2A6wFcIbn/RS7rAlB/2u/rEh+jHCaEsCMeju6TUv5e7/FQSi4C8DYhxLUAXAAKhBC/kFL+tc7jygrug5RhQog2AFullGY96M8UhBDXAPgGgEullAN6j4fOTAhhQ7yR/grEg9GrAN4jpTyo68DojET8p8WfAhiWUn5C5+HQIiQqSJ+SUl6v81Cyhj1IRHHfAZAP4AkhxF4hxA/0HhDNLtFM/3EAjyPe7PtrhqOcdxGA2wC8OfH/a2+iKkGUs1hBIiIiIpqBFSQiIiKiGRiQiIiIiGZgQCIiIiKagQGJiIiIaAYGJCIiIqIZGJCIiIiIZmBAIiIiIpqBAYmIiIhohv8He2jICechzzMAAAAASUVORK5CYII=", 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "z = 0.5\n", "ns = [4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12] # np.arange(4, 13)\n", @@ -439,6 +368,59 @@ "# _ = ax.legend([f\"z={zi}\" for zi in z[0]])\n", "# _ = [ax.axvline(x) for x in zeros]\n" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "bests = []\n", + "N = 200\n", + "step = 1 / (N - 1)\n", + "a = 11 / 8\n", + "b = 1 / 2\n", + "x = np.linspace(step, 1 - step, N + 1)\n", + "ns = np.arange(2, 13)\n", + "for n in ns:\n", + " zeros, weights = np.polynomial.laguerre.laggauss(n)\n", + " est = np.ceil(b + a * n)\n", + " targets = np.arange(max(est - 2, 0), est + 3)\n", + " rel_errors = np.stack([np.abs(evaluate(x, target)) for target in targets], -1)\n", + " best = np.argmin(rel_errors, -1) + targets[0]\n", + " bests.append(best)\n", + "bests = np.stack(bests, 0)\n", + "\n", + "fig, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(5, 3))\n", + "v = ax.imshow(bests, cmap=\"inferno\", aspect=\"auto\")\n", + "plt.colorbar(v, ax=ax, label=r'$m$')\n", + "ticks = np.arange(0, N + 1, 10)\n", + "ax.set_xlim(0, 1)\n", + "ax.set_xticks(ticks, [f\"{v:.2f}\" for v in ticks / N])\n", + "ax.set_xticks(np.arange(N + 1), minor=True)\n", + "ax.set_yticks(np.arange(len(ns)), ns)\n", + "ax.set_xlabel(r\"$z$\")\n", + "ax.set_ylabel(r\"$n$\")\n", + "# for best in bests:\n", + "# print(\", \".join([f\"{int(b):2d}\" for b in best]))\n", + "# print(np.unique(bests, return_counts=True))\n", + "\n", + "targets = np.mean(bests, -1)\n", + "intercept, bias = np.polyfit(ns, targets, 1)\n", + "_, axs2 = plt.subplots(2, sharex=True, clear=True, constrained_layout=True)\n", + "xl = np.array([1, ns[-1] + 1])\n", + "axs2[0].plot(ns, intercept * ns + bias)\n", + "axs2[0].plot(ns, targets, \"x\")\n", + "axs2[1].plot(ns, ((intercept * ns + bias) - targets), \"-x\")\n", + "print(np.mean(bests, -1))\n", + "print(f\"Intercept={intercept:.6g}, Bias={bias:.6g}\")\n", + "\n", + "\n", + "predicts = np.ceil(intercept * ns[:, None] + bias - x)\n", + "print(np.sum(np.abs(bests-predicts)))\n", + "# for best in predicts:\n", + "# print(\", \".join([f\"{int(b):2d}\" for b in best]))\n" + ] } ], "metadata": { diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py new file mode 100644 index 0000000..90843b1 --- /dev/null +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -0,0 +1,197 @@ +from pathlib import Path + +import matplotlib as mpl +import matplotlib.pyplot as plt +import numpy as np +import scipy.special + +EPSILON = 1e-7 +root = str(Path(__file__).parent) +img_path = f"{root}/../images" + + +def _prep_zeros_and_weights(x, w, n): + if x is None or w is None: + return np.polynomial.laguerre.laggauss(n) + return x, w + + +def drop_imag(z): + if abs(z.imag) <= EPSILON: + z = z.real + return z + + +def pochhammer(z, n): + return np.prod(z + np.arange(n)) + + +def find_shift(z, target): + factor = 1.0 + steps = int(np.floor(target - np.real(z))) + zs = z + steps + if steps > 0: + factor = 1 / pochhammer(z, steps) + elif steps < 0: + factor = pochhammer(zs, -steps) + return zs, factor + + +def laguerre_gamma_shift(z, x=None, w=None, n=8, target=11): + x, w = _prep_zeros_and_weights(x, w, n) + + z += 0j + z_shifted, correction_factor = find_shift(z, target) + res = np.sum(x ** (z_shifted - 1) * w) + res *= correction_factor + res = drop_imag(res) + return res + + +def laguerre_gamma_simple(z, x=None, w=None, n=8): + x, w = _prep_zeros_and_weights(x, w, n) + z += 0j + res = np.sum(x ** (z - 1) * w) + res = drop_imag(res) + return res + + +def laguerre_gamma_mirror(z, x=None, w=None, n=8): + x, w = _prep_zeros_and_weights(x, w, n) + z += 0j + if z.real < 1e-3: + return np.pi / ( + np.sin(np.pi * z) * laguerre_gamma_simple(1 - z, x, w) + ) # Reflection formula + return laguerre_gamma_simple(z, x, w) + + +def eval_laguerre_gamma(z, x=None, w=None, n=8, func="simple", **kwargs): + x, w = _prep_zeros_and_weights(x, w, n) + if func == "simple": + f = laguerre_gamma_simple + elif func == "mirror": + f = laguerre_gamma_mirror + else: + f = laguerre_gamma_shift + return np.array([f(zi, x, w, n, **kwargs) for zi in z]) + + +def calc_rel_error(x, y): + return (y - x) / x + + +ns = np.arange(2, 12, 2) + +# Simple / naive +xmin = -5 +xmax = 30 +ylim = np.array([-11, 6]) +x = np.linspace(xmin + EPSILON, xmax - EPSILON, 400) +gamma = scipy.special.gamma(x) +fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) +for n in ns: + gamma_lag = eval_laguerre_gamma(x, n=n) + rel_err = calc_rel_error(gamma, gamma_lag) + ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$") +ax.set_xlim(x[0], x[-1]) +ax.set_ylim(*(10.0 ** ylim)) +ax.set_xticks(np.arange(xmin, xmax + EPSILON, 5)) +ax.set_xticks(np.arange(xmin, xmax), minor=True) +ax.set_yticks(10.0 ** np.arange(*ylim, 2)) +ax.set_yticks(10.0 ** np.arange(*ylim, 2)) +ax.set_xlabel(r"$z$") +ax.set_ylabel("Relativer Fehler") +ax.legend(ncol=3, fontsize="small") +ax.grid(1, "both") +fig.savefig(f"{img_path}/rel_error_simple.pgf") + + +# Mirrored +xmin = -15 +xmax = 15 +ylim = np.array([-11, 1]) +x = np.linspace(xmin + EPSILON, xmax - EPSILON, 400) +gamma = scipy.special.gamma(x) +fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(5, 2.5)) +for n in ns: + gamma_lag = eval_laguerre_gamma(x, n=n, func="mirror") + rel_err = calc_rel_error(gamma, gamma_lag) + ax2.semilogy(x, np.abs(rel_err), label=f"$n={n}$") +ax2.set_xlim(x[0], x[-1]) +ax2.set_ylim(*(10.0 ** ylim)) +ax2.set_xticks(np.arange(xmin, xmax + EPSILON, 5)) +ax2.set_xticks(np.arange(xmin, xmax), minor=True) +ax2.set_yticks(10.0 ** np.arange(*ylim, 2)) +# locmin = mpl.ticker.LogLocator(base=10.0,subs=0.1*np.arange(1,10),numticks=100) +# ax2.yaxis.set_minor_locator(locmin) +# ax2.yaxis.set_minor_formatter(mpl.ticker.NullFormatter()) +ax2.set_xlabel(r"$z$") +ax2.set_ylabel("Relativer Fehler") +ax2.legend(ncol=1, loc="upper left", fontsize="small") +ax2.grid(1, "both") +fig2.savefig(f"{img_path}/rel_error_mirror.pgf") + + +# Move to target +bests = [] +N = 200 +step = 1 / (N - 1) +a = 11 / 8 +b = 1 / 2 +x = np.linspace(step, 1 - step, N + 1) +gamma = scipy.special.gamma(x)[:, None] +ns = np.arange(2, 13) +for n in ns: + zeros, weights = np.polynomial.laguerre.laggauss(n) + est = np.ceil(b + a * n) + targets = np.arange(max(est - 2, 0), est + 3) + gamma_lag = np.stack( + [ + eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted") + for target in targets + ], + -1, + ) + rel_error = np.abs(calc_rel_error(gamma, gamma_lag)) + best = np.argmin(rel_error, -1) + targets[0] + bests.append(best) +bests = np.stack(bests, 0) + +fig3, ax3 = plt.subplots(num=3, clear=True, constrained_layout=True, figsize=(5, 3)) +v = ax3.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest") +plt.colorbar(v, ax=ax3, label=r"$m$") +ticks = np.arange(0, N + 1, N // 5) +ax3.set_xlim(0, 1) +ax3.set_xticks(ticks, [f"{v:.2f}" for v in ticks / N]) +ax3.set_xticks(np.arange(0, N + 1, N // 20), minor=True) +ax3.set_yticks(np.arange(len(ns)), ns) +ax3.set_xlabel(r"$z$") +ax3.set_ylabel(r"$n$") +fig3.savefig(f"{img_path}/targets.pdf") + +targets = np.mean(bests, -1) +intercept, bias = np.polyfit(ns, targets, 1) +fig4, axs4 = plt.subplots( + 2, num=4, sharex=True, clear=True, constrained_layout=True, figsize=(5, 4) +) +xl = np.array([ns[0] - 0.5, ns[-1] + 0.5]) +axs4[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$") +axs4[0].plot(ns, targets, "x", label=r"$\bar{m}$") +axs4[1].plot( + ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \bar{m}$" +) +axs4[0].set_xlim(*xl) +# axs4[0].set_title("Schätzung von Mittelwert") +# axs4[1].set_title("Fehler") +axs4[-1].set_xlabel(r"$z$") +for ax in axs4: + ax.grid(1) + ax.legend() +fig4.savefig(f"{img_path}/schaetzung.pgf") + +print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") +predicts = np.ceil(intercept * ns[:, None] + bias - x) +print(f"Error: {int(np.sum(np.abs(bests-predicts)))}") + +# plt.show() diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py index 43fc1bf..0cf43d1 100644 --- a/buch/papers/laguerre/scripts/integrand.py +++ b/buch/papers/laguerre/scripts/integrand.py @@ -20,29 +20,30 @@ t = np.logspace(*xlims, 1001)[:, None] z = np.array([-4.5, -2, -1, -0.5, 0.0, 0.5, 1, 2, 4.5]) r = t ** z -fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) +fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 3)) ax.semilogx(t, r) ax.set_xlim(*(10.0 ** xlims)) ax.set_ylim(1e-3, 40) -ax.set_xlabel(r"$t$") -ax.set_ylabel(r"$t^z$") +ax.set_xlabel(r"$x$") +ax.set_ylabel(r"$x^z$") ax.grid(1, "both") -labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z)] -ax.legend(labels, ncol=2, loc="upper left") +labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)] +ax.legend(labels, ncol=2, loc="upper left", fontsize="small") fig.savefig(f"{img_path}/integrands.pgf") z2 = np.array([-1, -0.5, 0.0, 0.5, 1, 2, 3, 4, 4.5]) -r2 = t**z2 * np.exp(-t) +e = np.exp(-t) +r2 = t ** z2 * e -fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(6, 4)) +fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(5, 3)) ax2.semilogx(t, r2) # ax2.plot(t,np.exp(-t)) -ax2.set_xlim(10**(-2), 20) +ax2.set_xlim(10 ** (-2), 20) ax2.set_ylim(1e-3, 10) -ax2.set_xlabel(r"$t$") -ax2.set_ylabel(r"$t^z e^{-t}$") +ax2.set_xlabel(r"$x$") +ax2.set_ylabel(r"$x^z e^{-x}$") ax2.grid(1, "both") -labels = [f"$z={zi:.1f}$" for zi in np.squeeze(z2)] -ax2.legend(labels, ncol=2, loc="upper left") +labels =[f"$z={zi: 3.1f}$" for zi in np.squeeze(z2)] +ax2.legend(labels, ncol=2, loc="upper left", fontsize="small") fig2.savefig(f"{img_path}/integrands_exp.pgf") -plt.show() +# plt.show() -- cgit v1.2.1 From 251b4b1bd1c4a0194be650d73f685ffdec60bdd7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 1 Jun 2022 16:23:29 +0200 Subject: typo im beispiel.txt --- buch/papers/nav/beispiel.txt | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt index 70e3ce2..b8716fc 100644 --- a/buch/papers/nav/beispiel.txt +++ b/buch/papers/nav/beispiel.txt @@ -7,7 +7,7 @@ Deneb RA 20h 42m 12.14s 20.703372h DEC 45 21' 40.3" 45.361194 -H 50g 15' 17.1" 50.254750h +H 50g 15' 17.1" 50.254750 Azi 59g 36' 02.0" 59.600555 Spica -- cgit v1.2.1 From b2f6c58490cd3517d1a813e1b51b4e2aafc945a0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 2 Jun 2022 08:09:02 +0200 Subject: Add relative error plots with shift --- buch/papers/laguerre/scripts/gamma_approx.ipynb | 205 +++++++++++++++++++++--- buch/papers/laguerre/scripts/gamma_approx.py | 97 +++++++++-- 2 files changed, 269 insertions(+), 33 deletions(-) diff --git a/buch/papers/laguerre/scripts/gamma_approx.ipynb b/buch/papers/laguerre/scripts/gamma_approx.ipynb index a8280aa..82adca6 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.ipynb +++ b/buch/papers/laguerre/scripts/gamma_approx.ipynb @@ -34,7 +34,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 73, "metadata": {}, "outputs": [], "source": [ @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 74, "metadata": {}, "outputs": [], "source": [ @@ -86,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 75, "metadata": {}, "outputs": [], "source": [ @@ -132,10 +132,42 @@ " factor = pochhammer(zs, -steps)\n", " return zs, factor\n", "\n", + "def find_optimal_shift(z, n):\n", + " mhat = 1.34093 * n + 0.854093\n", + " steps = int(np.ceil(mhat - np.real(z)))-1\n", + " return steps\n", + "\n", + "\n", + "def get_shifting_factor(z, steps):\n", + " zs = z + steps\n", + " factor = 1.0\n", + " if steps > 0:\n", + " factor = 1 / pochhammer(z, steps)\n", + " elif steps < 0:\n", + " factor = pochhammer(zs, -steps)\n", + " return factor\n", + "\n", + "\n", + "def laguerre_gamma_shift(z, x, w):\n", + " z = complex(z)\n", + " n = len(x)\n", + "\n", + " z += 0j\n", + " # z_shifted, correction_factor = find_shift(z, target)\n", + " opt_shift = find_optimal_shift(z, n)\n", + " correction_factor = get_shifting_factor(z, opt_shift)\n", + " z_shifted = z + opt_shift\n", + "\n", + " res = np.sum(x ** (z_shifted - 1) * w)\n", + " res *= correction_factor\n", + " res = drop_imag(res)\n", + " return res\n", + "\n", "\n", "def laguerre_gamma(z, x, w, target=11):\n", " # res = 0.0\n", " z = complex(z)\n", + " n = len(x)\n", " # if z.real < 1e-3:\n", " # res = pi / (\n", " # sin(pi * z) * laguerre_gamma(1 - z, x, w, target)\n", @@ -144,7 +176,13 @@ " # z_shifted, correction_factor = find_shift(z, target)\n", " # res = np.sum(x ** (z_shifted - 1) * w)\n", " # res *= correction_factor\n", + " \n", " z_shifted, correction_factor = find_shift(z, target)\n", + " \n", + " # opt_shift = find_optimal_shift(z, n)\n", + " # correction_factor = get_shifting_factor(z, opt_shift)\n", + " # z_shifted = z + opt_shift\n", + " \n", " res = np.sum(x ** (z_shifted - 1) * w)\n", " res *= correction_factor\n", " res = drop_imag(res)\n", @@ -153,7 +191,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 76, "metadata": {}, "outputs": [], "source": [ @@ -161,6 +199,10 @@ " return np.array([laguerre_gamma(xi, zeros, weights, target) for xi in x])\n", "\n", "\n", + "def eval_laguerre2(x):\n", + " return np.array([laguerre_gamma_shift(xi, zeros, weights) for xi in x])\n", + "\n", + "\n", "def eval_lanczos(x):\n", " return np.array([lanczos_gamma(xi) for xi in x])\n", "\n", @@ -177,6 +219,12 @@ " lanczos_gammas = eval_lanczos(x)\n", " laguerre_gammas = eval_laguerre(x, target)\n", " rel_error = calc_rel_error(lanczos_gammas, laguerre_gammas)\n", + " return rel_error\n", + "\n", + "def evaluate2(x):\n", + " lanczos_gammas = eval_lanczos(x)\n", + " laguerre_gammas = eval_laguerre2(x)\n", + " rel_error = calc_rel_error(lanczos_gammas, laguerre_gammas)\n", " return rel_error\n" ] }, @@ -206,9 +254,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 87, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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4t04hROug00Fgonb0u19br3r+ZEM31y1wahMc/kq7rXtQw2j8YO1UpkcLIVoxCWhCiGvjcMC5A5C2Bo6vgqw9gApWP+g4DqJHaq243fycXakQoi1QFPCN0Y5ed323wVD6ejjU0LLbFqZNm+4wDDoM1aZTCiFEKyEBTQhx5WrKtGmLx1dpwawiD1C0DaGHPQmxo7V9yWTaohCiqSmKNrXRJxp6392wRccxrfHQqQ1wdCns/0S7rX/Cxf3bIpLA7ObMyoVoF+655x6WLl2Kv78/KSkpAMyfP59nn32W1NRUdu7cSe/evZ1cZcskAU0I8eNKs+HYCu04tQHstdp+ZDGjIHYMxIyUlthCCOdTFPDvrB1972tYC3sA0pO1Y9f/YPsboDNAaF9tHWz0SG0fNp3eycUL0fbMmjWLhx56iDvvvPPCZYmJiSxYsIBf/OIXTqys5ZOAJoS4nKpCbkpDKFuudVUD8IqCvvdDp/Ha5rJ6+fUhhGjBdHoI6akdg38LdVVwZntDYFsP61/QDhdvbWQtZpS2VtYjyNmVC9EmDBkyhIyMjMsui4uLc04xrYx8whJCaOvJMndB6mLtKD4DKBDaB0b+GTpNAL9OsuheCNF6GV0aRs2GA89pjY1OrteaGp1cB4cXaLfzT4CYEdroWkQSGMxOLVuI6/Xyzpc5Wni0UR+zs3dn/tD3D436mOIiCWhCtFf2eji9GVKXQOpSKD8HehN0GA6DH9NGymRhvRCirbL6QtebteObmQMn1mqBbcfbsPU/YLRqo2uxo7XDFursqoUQ7YAENCHak/pabWrPkcVwbJnWCt/oqn3wiJuirSmzeDi7SiGEaF6KAoFdtGPQI1BboXWGTFujHceWabfzT2gIa2MgrC/ojU4tW4grISNdrY8ENCHaOnsdpG/Qpu8cXQrVJWC2aSNkcZO1NRcmV2dXKYQQLYfJqv2O7DReG10rOK7t8Zi2Gra9Dlv+pf0ejRkBHcdroc3V29lVCyHaCAloQrRF9nrI2Kht4pq6RBspM9ug80RImKZN2TGYnF2lEEK0fIqircH16wRJD0N1qdbR9vgq7Tj8FSg6COsHHcdqgU3W7ArBzJkzSU5OpqCggNDQUJ577jm8vb15+OGHyc/PZ+LEiXTv3p1Vq1Y5u9QWRwKaEG2FwwFntsGh+Vqjj8rzYHLTGnwkTtdGymSxuxBCXB+Lhzb7IG6y9ns3Zx8cWwnHV8LXz2qHVyR0HKeNwEUMlKmQol2aM2fO914+bdq0Zq6k9ZGAJkRrdy4FDs2DQ19Caaa2pqzjOC2UxYzSOpcJIYRofDodhPTSjhFPQ0mWFtSOr4TdH8COt8Big9ix0HmC9jvZ7O7sqoUQLZwENCFao+Iz2kjZoS8g74i28Wr0SBj1rPYhwGR1doVCCNH+2EKgz73aUVuhtfE/tlzbV/LQPK1TbtRQ7fd0pwngHujsioUQLZAENCFai6pirdHHgc/h7HbtsrD+MOHv2royq69TyxNCCHEJkxXiJmmHvR7O7tDC2tFlsPRR7QjpfXG6pE+0sysWQrQQEtCEaMns9dqePPs/076BtdeAX2cY8UfocpO2zkEIIUTLpjdA5EDtGPM85KVqrfuPLoOv/6wd/gkXw1pAgjQZEaIdk4AmREt0LgUOzIGD86AiD1y8odcs6D4TgrrLf9xCCNFaKQoExGvHkMe1KetHl2kddze8DBteAq+ohtG3Kdoom07n7KqFEM1IApoQLUXFeTj4uTZalnsIdEatZXP32yBmtLTFF6KJORwOVHs9ar0dh8MB9npUux17vXaKQ9VuqNO+IFEUHegUFLQPz4pOQWcyoTeZUIxGdPKhWlwJz3Do/yvtKM/TpkGmLoHtb8HW/4BHiBbU4qdqrfzlfSVEmycBTQhncti1ReT7ZsPR5eCog+AeMP5VSLwRrD7OrlAIp7DX1VJ9/jw15wuoKiykpqiY2ooy6irKqa2spLaykrqqSuqqq6mrqaG+tob6+jrs9fXY7faLh2rH7lCxqw4cqooDcKCignZeARUFh0Kjj0wrqoqigsI3p6C7cCjoFQVdw6FXdOh0evR6HQa9EYPRgMFgxGgyYTCZMZrNGCwWjBYXTFY3TO7umD08MNs8MXt6Yfb0xOLtg8FqlWDYmrn5a7Mles2C6hKtff+RRbD7fdjxX3ALhPgpEH8DhPcHnd7JBQvxw+655x6WLl2Kv78/KSkpADz++OMsWbIEk8lEdHQ0H3zwAZ6ens4ttAWSgCaEMxSegv2faqNlpVnaFMa+90GPn2nTXoRo5RwOB3UlxZRnZlJ+LoeqgnyqigqpLimhuqyUmopyqqsqqa2poaa2hjq7nTqHnTpU6hWwX0XIUFQVvUNFD9qh6BpCj4Jep8ds1KHX69Hr9Oh0WhDS6RvO6/Xo9XoUvb7hch2KorswOqZTFNDptNCjKKBqo2iqqoJKQ9RDu1xVcTgcOOx27XDYUR0OHHYHqmrHYXdgt9fj+CY8OrRTh8OBQ3VQW1+Hvc6BXa3EjoodsCsKDt2VB0dFVTE4VEwoGHU6THoDJqMRk8mC2eKC2eqK2c0DV08vXLy8cfXzxzUwEGtwMBYfXwl3LYnFBt1u0Y6aMm1T7CMLYe9s2PkOWP219WoJ0yAiScKaaHFmzZrFQw89xJ133nnhstGjR/Piiy9iMBj4wx/+wIsvvsjLL7/sxCpbJgloQjSXumptA+m9syFjE6BAzEgY+zet3bJMYRQtmMPhoOZ8IeVnT1OWmUlZbjaVBflUFBVSVVZGdVUl1TXV1NTXUaM6qP2JYKGoKsaGIGHS6zEZjLgZXTGZzJjMFkwuLphcXTG7uWF288Dk7o7JzQ2Tmzsmdw9MNg/MHp6YPW0YXNv2thL2ulrqSsuoLS+jpriY2pJiakpLqCktpbasjJryMm1EsbKS2upKaqqqqK2p1oJvfT0lVZXUVZZT9xPBV1FVTA6VAFVHX6sPeh9vDN6XnHp7YfDxQe/tjcHPD53ViiLrYZuH2V1rDNXlJqgph7TV2sjagTmw+z1wC9BG1RKmyTRI0WIMGTKEjIyMyy4bM2bMhfP9+/fniy++aOaqWgcJaEI0tfzjsOdDOPAZVBWBZwQMf0Zr+GELdXZ1op1zOBxUZGVSeiqd0jNnKMvNoTw/n4qSIioryqisqabaXk+1Ao4f+NBntDswo2DWG7CaXfC2WHBxteLiYcPV5omLtw8uPj64+Pji6h+Aa0AgRg8PGa25QnqjCb2PDxYfH4i4vseqr6ykMi+XipxsKvNyqSwooKqokKqSYqrLysg8n8e5uhpUu52a1KNUFBbiKC393sdSXFww+Plh8PXVTi85b8o9R01oKIaAAHRubhLkGpPZDRKna0dthTaydngB7P0Idr6trVmLv0G7PqSXNJUSnPvb36hJPdqoj2mO60zgU09d12O8//773HLLLY1UUdsiAU2IplBXrS3y3vMBnN6ibSTdeZK2riBqqHy7KZqFw+Gg/Mxpik+kUXI6g9KcLMoK8ikvKaGiqoLK+rqG4PXdD3BGuwOLosPFYMTP6o6r1R2rzYartw9W/wDcg4JxCw3DPSyszY9gtSUGV1c8IqPwiIz63us3fvoBe5cvIvLTTy5cptbWUl9UjL3wPPWFhdjPn6c+v4D6/HztKCigJi2Niq1bcZSVAeAFpL/2HwB0rq4YAgMxBPhjDAjEEBiAMTAIY3AQxuBgjEFB6KzyHromJuvFsFZTpq1ZO7wAdr0L298AWzgkToPEmyCwi4Q10WK88MILGAwGbr/9dmeX0iJJQBOiMRWkaaNl+z+DqkJtn7JRz0L327XF30I0Ikd9PfVZmZxctIDi0xmUZGdTVlhAWXkpFbU1VCrqd0a9FFXFxQGuBgO+bjbcbTas3j64+wfiHhKCR3gEtg7RmDxsTnpVwpmMZgv2em2dnE6vrWlSTCaMAf4YA376d5ijupr6/Hx2rVxJYnAw9edyqcs9R/25XOpzc6nYvp36vDxwOC67n95mwxASjDEoWAttwcGYwkIxhmqH3s2tSV5vm2J2h643a0dVsbZ3ZsqXsO0N2PJv8O2oBbUuN8mm2O3M9Y50NbYPP/yQpUuXsnbtWhld/wES0IS4XvZ6bcPRXf+DUxsbRssmNoyWDZPRMnFdKvPzOH/oIIUnjlOceZaSvFzKSksor62msmH068AltzfZHbjq9Hi6uhFm88LDzx9bcDAeYZF4xsbiHh6BziC/+sX3M5rNANTV1GB2db3q++ssFkxhYdTFxmIbNux7b6PW11NfUEBddjZ1WdnU5eRQl52lnZ45TeW2bTgqKy+7j97LC2NoqBbaQkIxhoViCo/AFBmBwd8fRX7PXs7FU5tG332mtoVL6iI49CUkvwjJf9P20+xyEyRMB1uIs6sV7cjKlSt55ZVX2LBhA67X8DumvZD/pYW4VmXnYM9H2ohZWTbYwmDEH7VOjO4Bzq5OtCKVubnkH9zP+WOpFJ09TXF+PqUVpZTb66nVX/7B02h3YNXp8bK6E+HlTTU6OvXui1dMLF6d4zBLu2JxHQxmCwB1NdXXFNCuhGIwYAwMxBgYCD17fud6VVVxlJRQm5lFXeZZas+epS4zi7qzZ6k6fJjS1Wugvv7i45nNmMLDMEZEaKEtIgJTRDimyEgMAQHyDb3VB3rfox2l2ZCyAFK+gNXPwOo/ah0gu9wMCTeAi5ezqxVtyMyZM0lOTqagoIDQ0FCee+45XnzxRWpqahg9ejSgNQp56623nFxpyyMBTYiroaqQsUWb35+6BBz1ED0CJv5D21Ra2hyLH1BfVUXBgf3kHz7E+VMnKTyXTWlZKWX2uu+EMIvdgbvRTJjNC0//QLzCIvCOicU7IRFrYNBlt01OTibuB0YqhLhaF0fQqp1Wg6Io6D09cfH0xCUx4TvXq3Y79efOUXvmDLWnT1N7uuE0I4OKjZtQa2sv3Fbn6oopMhJThw6YoiIxR0Vp5yMi0Lm4NOfLahk8giHpIe04f1KbAnlwHix9BFb8HmLHaGGt4zgwWpxdrWjl5syZ853L7r33XidU0vpIQBPiStRWwIG59N79b9hwWtufpu8voM+9MpdfXKYyP4+83bvIO5LC+dOnKC48T2l1JRU6UC/5Jt9sd+BuMBHm7YeXfyDekVF4d4rDr1t3Wf8lnMZoaRhBq3ZeQPspil6PMSQEY0gI1gEDLrtOdTi08NYQ2GrST1F76hRVe/dSumzZhX3sAIwhIZhiojFHx2COjsYcE40pOrr9rHfziYahv4chj0POfjg4XxtZO7oUzB7ahthdZkDkIPnyUYhmJgFNiB9TdFobLds7G6pLUN06wJT/aAutTTJ3uj2ryM7m3O4d5Kce5vzZ0xQVnqektprqS0bDdA4VNxQ8Xd2I9PXDJzwS305x+PfsjWuATIMVLY/xwhTHGidXcm0Une5Ck5FvhzdHdbUW3NLTqTl1itqT6dScPEnltu2XjboZAgMbAlsM5o6xmDt2xBwT03ZH3BQFgntox5i/amupD82Hw4tg3yfgHqytV+t2KwR8d0RTCNH4JKAJ8W2qChmbYcdbcGw5oGjfJPb7JXtOVjGs53BnVyiaUW1pCbm7dnLu4H4KTp2ksCCf4tqqy4KY3uHAXdET6OGFd0AwvjGxBHTrjk+XbugbpowJ0Rp8M8WxvpUGtB+js1iwdOqEpVOnyy5X7XbqMjOpOXGCmhMnqTl5gtoTJymaOxf1m5+DomAMD8PSsSPm2I5aaOvYEVNEOIq+DY0u6fQQPVw7Jv5D6wR5cB5sfxO2vgYBXbSg1uVmWWstRBOSgCbEN+qqtG8Nd7wNuSng4g0DH9GmMX6zoXR6sjMrFE3I4XBQfDSV7O3byD12hIKcLIoryynXcWHvIJ1DxR0dAR5e+ASF4N+xEwE9euMdnyCdEUWbYLykSUh7oej1DY1FInAfOfLC5ardTu2ZM9QcT6Pm+HFq0rTTsrXrLmwToLi4aKEtrjOWznFY4jpj7tixbYy2GV0u7rFWUaA1FzkwB1Y/DWv+CB2GQ7eZWtdimVEiRKOSTxRClOVqLfJ3/U/bu8w/QZvG2OVm7T8o0ebUV1aQs20rOfv2kHfqJIXn8ymur6XuklExV7uKl6uVDv5B+EXHEtijF349esqImGjTDC2gSUhLoej1mKOiMEdFwdgxFy53VFdrI23HjlF97Cg1qUcpXbac4rmfazfQ6TBFRGhhLS4Ol4QELPHx6Ftzh1WrL/S7Xzvyj8PBudrI2oKfg8kN4qdC99sgPEm2lhGiEUhAE+1X7mHY9iYcmgf2Oug0Hvr/CiIHXxgxEa1fTVEhWVs2kbN/L3mnT3G+pIhSHBcadugdDjx0BiK8/fGNiCSwSzeCBgzE1U82FhftT3scQbtaOosFl8SEyzpMqqpKXVY2NceOUp16lOqjqVTtP0Dp8hUXbmMMCcHSENYsCQlYEuIxeHs74yVcH7+OMPJPMPwZOLNVG1U7vAj2fwqe4dqoWrdbwbuDsysVotWSgCbaF1WFk2th6+uQvh4MLtDzTuj3K/CNcXZ14jpVnz9P1uYNZO/bQ+7pDArLSyhT1AuB22R34GWyEOofSEBsJ4L69MevRw/0RpOTKxeiZbjYxbHtrUFrSoqiYAoNwRQactk0SXtxMdVHjlB95AhVhw9TfeQIZatXX7jeEBSES5cuWLokaqcJCejd3Z3xEq6eTqd1eIwcBONf1bo/7v8UNrwCG17WRtO6z4T4G8Di4exqhRPcc889LF26FH9/f1JSUgD44x//yKJFi9DpdPj7+/Phhx8SHBzs5EpbHgloon2oq9ZGyra9AflHwS1Q+waw193g2gq/wRTUlpaQtWkjWXt3k5dxkoLS4svCmMXuwNtiJSowmMD4REKSBuLZsTM6mX4jxA+SEbTGpff0xJqUhDUp6cJl9tJSbZTt8GGqU1KoSkm5LLSZoqJw6doFS2IXXLp2wRwXh87Uwr9EMrlC1xnaUZIJBz+H/XNg8cOw/PcQNxl63A6RQ2QKZDsya9YsHnroIe68884Llz3++OP89a9/BeC1117jL3/5i2xU/T0koIm2raoYdr+vdWQsz4XALjDtbUiYDoYW/h+euMBeV8u57dvI2r6VnBPHyS8soFS5OE3RbHfgbXGlQ1AoQYldCB00FFu0jIgKcbX0BgOKTkd9rYygNRW9hwfWfn2x9ut74bL6oiKqUw5TnXKIqoOHKN+6lZJFiwFQjEYs8fG4dO+GpWtXXLp1xxgSjNJSp+LbQmHw72DQbyFrjzaqduhL7UtSW7i2Vq37TPCKdHalookNGTKEjIyMyy7z8Lg4mlpRUdFy38dOJgFNtE0lmbD9v7DnQ6gth+gRWjDrMEzWl7UCRcePcSZ5LTlHUsg7l02hvRZ7w7euBrsDH6OFsMBgghMSCR08DFtsRxkZE6IRKIqC0Wxu0RtVt0UGLy/cBg/CbfAgQFvTVp+bS9WBg1QdPEDVgQMUfT4P9aPZAOh9fXHp1g2Xbt1w7dEdS5cu6Bqmp7YYigKhvbVj7N/g6DJtX7UNL8OGl7T13j3ugLgp0gWyiW2ad5yCs+WN+pi+YW4MntHxmu779NNPM3v2bGw2G+vXr2/UutoKCWiibck9DFv/o7XLV1VIvBGSHoagrs6uTPyA2ooKspLXkblrOzmnTlJQUUpVQzdFRVWxoSPaN4jAjp0JSxqMf6/e0tJeiCZkNFtkiqOTKYqCMTAQY2AgHg0dJNW6OqqPH6fqwAGqDxygav8Byteu1e5gMGCJj8e1Rw9cevTApWcPjP4tqNGR0UXb7LrLTVB8Fg7Mhf2fwFe/gGWPaa38e/xMC3PyJWqb98ILL/DCCy/w4osv8vrrr/Pcc885u6QWRz7liNZPVeH0Vtj8f3BiDRhdoc99MOABraOUaFGK045zet3XZB06QG5+DsUOOw6d9h+yi92Br9WDoKhoQvv0J2TIMEytZcG8EG2EFtBkimNLoxiNuCQk4JKQALfdBmhTI6v27adq3z4q9+2laO5cCj/6CNC6Rrr07Ilrr5649uqFKToapSXMNPAMg6GPa9Mgz2yFfZ9qX6ru/Qj8OmtBrdutWmt/0SiudaSrqd1+++1MmDBBAtr3kIAmWi9VheOrYPM/4ewOcPWFEc9A73ul8UcL4aivJ2fbFs5s3kh22lHySoup1F/c9NlLZ6BTYBghiV0JHzYCr06dnVyxEMJoNssIWith8PLCfcRw3EcMB0CtraU6NZXKffuo2ruPiu3bKF2yBAC9zYZLr1649uqFa5/eWOLiUIxG5xV/WRfIl+HwAtj7sbYR9tfPalvf9LxTW6Kg0zuvTtGo0tLSiI2NBWDRokV07iz/738fCWii9bHXw5GF2ohZbgrYwmDC37W57LKxtFPVlpVxZs0qzuzcTs7ZU5yvqbqw+bPJ7sDP1Y34yGjC+yURNnwEBlerkysWQnybwSIjaK2VYjJdWJvGrFna/mxnz1K5ew+Vu3dTuWc35evWabd1ccGlezdce/fG2rcvlq5d0TVsVN7sLB7Qa5Z25KVqQe3gXEhdDB4hWmORHndIY5FWZubMmSQnJ1NQUEBoaCjPPfccy5cv59ixY+h0OiIiIqSD4w+QgCZaj/oa2P8ZbPkXFGWAbye44S1tTrveid8CtmOV+XlkrFrB2T07ycnOpMhRf2G6orsDwr39COmcQMTQ4fj26CWNPIRoBWQNWtuhKAqm8HBM4eF4Tp8GQF1eHlV7914IbQWvv0GB+roW7rp3x7VvX1z79sGlWzfnBDb/OBj3Nxj1LBxbDvs+ho1/144Ow6DXXdBponRibgXmzJnzncvuvfdeJ1TS+khAEy1fbQXs/kBr/lF+DoJ7wpjntV/Q8oG/WZWdPUP6iqWcPbCPc/nnKMEBioKiqniip1NQGGHdexE5eizuYbL+T4jWyGg2U1VS7OwyRBMx+vtjHDcOj3HjALCXlFC5Zw+VO3dRuXMnBW+8Aa+rF0bjXPv2xdq/H5Zu3Zp3PzaDCRJu0I6STK0D5N6PYf4scPWBbjOh513g1zLXVwlxPSSgiZaruhR2vattLl15XmvJO+0taZXfjEozTpG+cjlnD+zlXEEupQ15WOdw4GMw0zUknPA+/YgcMw6zl6z7E6ItkCYh7YveZsN9xAjcR4wAtI20K3fvoXLnTip37aLgzTcpeOMNFIsF1549cR3QH2v//lji41H0zbQ2zBYKw56AIY/DyfWw90Ntf9Ntr0P4AC2oxU+Vdv2izZCAJlqeqiLY8ba2j1l1McSMgiG/h/B+zq6szSs9nUH68qWcObCXc+fzKGsIZHqHA1+jhejwDkQmDSZ81ChZPyZEGyVNQto3vYfHZY1H7CUlVO7aRcX2HVTu2E7+P/5JPqBzd8e1Tx+s/fthHTAAU0xM0286rNND7CjtKM/Tlj3snQ0Lfwkr/wBdb9XWsQXEN20dQjQxCWii5ag4D9vfgJ3vQk2pNoVxyO8gpJezK2uzKs7lkL58Kaf37CQnL+fCCJkWyFyIjexARNIgwkeOweAiDViEaA9kDZq4lN5mw33UKNxHjQKgPj+fip07qdy+nYrtOy40HTH4+2MdMABr0gBcBwxo+n3Y3Pxh0CMw8DeQsVlr07/nA9j5NoT21YJawjQZVROtkgQ04Xzl+bD1Ndj1HtRVatMUhjwGgV2cXVmbU1NUSPqypZzetY2snEyKG9aQ6RwqvgYT0RHRRA0eStiIURLIhGinjA1dHFVVbfoREdHqGPz8sE2ciG3iRABqM7Oo2LaViq1bKd+wgZJFiwAwx8ZiTRqANSkJ1z590Lk2UVBSFIgarB3jXoYDc2DPh7DoAVj5JHS7RQtrQrQiEtCE81wIZv+D+mpIvEnbuNJf9sRoLPaaGk6vWcmpTRvIPJ3OeUcdakNTDx+dga6hHYgcMJCIcRMxWWXKohBCG0FTHQ7s9fUYnLlPlmgVTKEhmG6+Ga+bb0Z1OKhOTaViqxbYiubMpfCj2dom27164TZoINZBgzB36tQ04d/qA0kPwYAH4fRWLajt+Qh2vkMPj07g+Yg2qiZb8ogWTgKaaH4VBVow2/muFsy63Kwt/PWNdXZlrZ7D4SB3+1ZOfr2as8dTyauuoF6vA1XFEx1xgWFE9k2iw8RJ0tRDCPG9DCattXpdTbUENHFVFJ0Ol4QEXBIS8L3vPhzV1VTu2UPF5i1UbN5M3t//AX//B3o/X9yStLBmHZiEwbuR/z9SFIgcqB3jtVE148Y3YOGvtFG17rdBr7ulA2QTy8zM5MEHH+TIkSM4HA4mTZrEq6++iulHuoEWFxfz2Wef8cADDwCQnZ3Nr3/9a7744ovrrufZZ5/Fzc2Nxx577Cdv++GHH7J7925ef/3171w3YcIEPvvsMzw9PXnttdf473//S8+ePbn55pvp2LEj8fHXvwZSAppoPhUFWqv8ne9CfZU2YjbkcfkFeZ1KT2dwYvFCMvbvIafkPNUNG0Nb7SqR3v5E9OhN9KQp0vZeCHFFjJaGgFZdjYubu5OrEa2ZzmLBbeBA3AYOhD/8nrrcXC2sbdlMeXKyNh1SUbAkJOA2ZAhuQwZj6dKlcbtDunrDgAfZWR3PsEhDwzq1d2H7mxAxCHrfDXGTweCkTbrbKFVVmT59Or/61a9YtGgRdrud+++/n6effppXX331B+9XXFzMm2++eSGgBQcHN0o4a0zLly+/cP7NN9/k66+/JjQ0lFmzZjFp0iQJaKKVqCyELf/WfiHWVWobSw/5vQSza1RbUUHGssWkb91EVvZZihUVAKPdQaDVg/D4RKLHTcKvW3fnFiqEaJWMZguANAoRjc4YEIDnjdPxvHE6qt1O9eHDlG/eTMXGTRS89RYFb76J3tMT66BBuA0dgnXQIAxeXo3z5JeuVSvPh/2faFMgv7xX21etxx3aqJp3VOM8Xzu3bt06LBYLd999NwB6vZ7/+7//Iyoqiueee4558+bx1VdfUVJSQlZWFnfccQd//vOfeeKJJzh58iTdu3dn9OjRPPjgg0yaNImUlBQ+/PBDFi5cSEVFBWlpaTz22GPU1tby8ccfYzabWb58Od7e3rz77ru888471NbWEhMTw8cff4zrj6yBnD9/Ps899xx6vR6bzcbGjRsBbfRu3LhxnDx5kmnTpvHKK68AEBkZye7du3nmmWdIT09n/Pjx3HrrrSxevJgNGzbw/PPP8+WXXxIdHX3NP79mC2iKooQBs4EAQAXeUVX13831/MIJqoq1b6i2vQm15ZB4Iwz9Pfh1cnZlrYrD4SBv9y5OrFjK6eNHyK+twq7TNawjM9IjMpoOw0cSNmIUemMzbiIqhGiTvglo9bIXmmhCil6PS9euuHTtit8DD1BfVKStXdu4kfJNmyldulQbXevaRRtdGzoMS3wcik53/U/u5geDHoWk30D6etj9Pmx9Hba8BjEjofe90HGs1ta/DVj/4TvknU5v1Mf0j+jA8Fn3/+D1hw8fplevy7twe3h4EB4ezokTJwDYuXMnKSkpuLq60qdPHyZOnMhLL71ESkoK+/fvByAjI+Oyx0hJSWHfvn1UV1cTExPDyy+/zL59+3j00UeZPXs2jzzyCNOnT+e+++4D4JlnnuG9997j4Ycf/sFa//KXv7Bq1SpCQkIoLi6+cPn+/fvZt28fZrOZTp068fDDDxMWFnbh+rfeeouVK1eyfv16fH19SUtLY9KkSdx0001X8iP8Uc05glYP/E5V1b2KorgDexRFWaOq6pFmrEE0h5pybQPJrf/R9jGLnwrDngT/OGdX1mpU5RdwYvEC0nduI/t8LpWXTFuM9gsiqt8AoifegIufr5MrFUK0NTKCJpzB4OV1oTuk6nBoo2sbN2qja6+/QcF/Xsfg54d16BDchw3DOmAAuuttbqXTaYEsZiSUZmt7qu35EObOBI9QrftjzzvBPaAxXqL4ltGjR+Pj4wPA9OnT2bx5MzfccMOP3mf48OG4u7vj7u6OzWZj8uTJAHTp0oWDBw8CWoh75plnKC4upry8nLFjx/7oYw4cOJBZs2YxY8YMpk+ffuHykSNHYrPZAIiPj+f06dOXBbSm1GwBTVXVHCCn4XyZoiipQAggAa2tqKvSWuVv/j+oLICO42D4UxDUzdmVtXgOh4PsjcmkrV7BmfS0C90W9Q4HAS5WusUlEjthMn7dezq7VCFEG2cwf9MkREbQhHMoOh0uXbrg0qULfg8+SH1hIRWbNlGWnEzZylWUfPElitGIa9++uA0bhtuwoZiu94OzRzAMe0LrJn1sBex+D9Y/Dxtegs6ToM+9EDlYmyrZyvzYSFdTiY+P/87asdLSUs6cOUNMTAx79+79TifPK+nsaTZfXCuo0+ku/Fmn01FfXw/ArFmzWLhwId26dePDDz8kOTn5Rx/zrbfeYseOHSxbtoxevXqxZ8+e7zyXXq+/8PjNwSlr0BRFiQR6ADu+57r7gfsBAgICfvKHKpxPcdQRlLOaiNPzMdcWUejVnYxOv6fU1gmOFcGxZGeX2GjKy8sb7T3pKCmhcvd2StPTKKyuoMagTaVwr3cQavPGvVM85u690JnN1AKHi0tB/j2Ib2nM96QQAJUFeQDs37OH08Vl1/QY8r4Ujc5mg6lTYdIkjCdOYj50iLpDh6jYsoXcF16gPjiImq5dqenalbrISG107BJX9570gPBHcfG9heDslQQe/xrjkYVUuIaSHTyBc4HDsBta9tY0NpuNsrJr+/fbGPr27Ut5eTlvv/02t912G3a7nUceeeTC+erqalavXs3p06dxcXFhwYIFvPHGG4AW5L6pvby8HIfDQVlZGdXV1dTW1l64TlVVysvLMZvNl11XWlqKu7s7hYWFzJ49m6CgIMrKyqipqcFoNH7n55Kenk58fDzx8fEsXbqUo0ePfue56uvrqayspKys7LLnvfS82WwmPz//e3/u1dXVV/U7sdkDmqIobsCXwCOqqpZ++3pVVd8B3gHo3bu3OmzYsOYtUFw5hx0Ofg7rX4SSMxCeBCOexjtyEG21gXtycjLX+p50OBzkbNnEiVXLOX3iGAUNo2SGhuYeUV170HHqdDxjpXmKuHLX854U4vsUncsmdf5sOsZEkzB02DU9hrwvRZMaOfLC2dqMDMqSkylfn0zlmq+xrlyF3tcXt2FDcR8xQpsK6eJyHe/J27QZQoe/wrrrf8SeeIfY059C1xnQ5+cQmNhoL6sxpaam4u7u3C6sixYt4oEHHuDvf/87DoeDCRMm8Pe//x2z2YzFYqFfv37MmjWLzMxM7rjjDoYOHQrAoEGDGDBgAOPHj+fBBx9Ep9Ph7u6OxWLBZDJdeF2KouDm5vad655//nlGjhyJn58f/fr1o6ysDHd39wsh6ts/l+eee460tDRUVWXkyJEkJSWRlpZ22XMZDAZcXV1xd3e/7HkvPX/nnXdy33338c477/DFF19c1iTEYrHQo0ePK/7ZKaqqXu/P/8qfTFGMwFJglaqq//yp2/fu3VvdvXt30xcmro6qwtGlsO55yD+qTWEc+SeIHtkqh/6vxtX+gq8tLeHEwgWc2LqJzIJzVDWsJfNwQFhIBDFDhhM5fiIGF9k0U1wb+SAsGlt5USFv//JORt77AN3HTLimx5D3pXAGe0kJ5Zs2U75uHeUbN+IoL0cxm7EmJZEVGkLvX/4SQ8Oap2uWtVdbzpHyhbaXa1h/6Htfi2vVn5qaSlxcy137/2P7jLVF3/f3oSjKHlVVe3/f7Zuzi6MCvAekXkk4Ey1U+gZY+xxk7QGfWLj5I60JSBsPZlej8Mhhji36klOHD5JbU4lDp9PWklms9EjsRqcbpuPd+fr3yBBCiKZwsYujNAkRrYveZsM2aSK2SRNRa2up3LOHsnXrKV+3Dtv69aR98ikuPXviPnIk7qNGYgq/hv1BQ3pqx5i/wv5PtbD25b1g9dMaivS+B2yhjf/iRLvSnFMcBwI/Aw4pirK/4bKnVFVd/sN3ES1G1h5Y+xdIT9Y6G015HbrNBL1speeor+f0qhUc/3oVZzIzKG2Y9u5qV4n1DyY6aQjRU6dhcvJUAyGEuBJGaRIi2gDFZMI6YADWAQNQn3qSLZ9+SqfiEsrWriXvlVfIe+UVzLGxuI0aifvIUVgS4q+oScUFrt6Q9DD0fxDS18HO/8Gmf2qN0jpNgL73Q9QQ+QL7B8yaNYtZs2Y5u4wWqzm7OG4G5F3a2hSkacEsdbG2kePYF7Vvh4wWZ1fmVNXnz3NswTxO7thKVvF5avUN+5LpjfSO7UzHCZMJ6DcAXWPs1yKEEM1Ip9ejNxikzb5oMxRFoT40FL877sDvoQepzcyifN1ayr5ey/m33+H8f9/CEBSE+6hReIwZjUvPnij6K9wDTaeDmFHaUXRa21Nt72xtKYhvJ236Y9dbwOLRtC9StCky/CG+X9k5SH5J+yVjdNH2MRvwIJjb7yhQ4dEjFH81n0/f/Q95tdU4dFqDj2A3Gx169qXzjTdjDZFpDUKI1s9otkhAE22WKTQE7zvvxPvOO6kvKqJ8fTJlX39N8eefU/Txx+i9vbVpkGPGYO3XF8VkurIH9oqA0c9pn5kOL4Cd78Dyx+DrZ6HbrdDnPvDv3KSv7VKqql7dqKBoEtfS70MCmrhcdQlseQ22vwn2Oq1D0ZDHwc3P2ZU1u2/2Jju6fDGnM05SrGj/wKx2lY6BIcQOHUmHSVOkwYcQos0xWCzUVcsUR9H2Gby88Jw+Dc/p03BUVFC+aRNlq1dTumwZxfPno3N3x234MNxHj8Zt8GB0liuYQWS0QPfbtCNzD+x6V/vCe9f/IGqoNv2x03jQXeEo3TWwWCycP38eHx8fCWlOpKoq58+fx3Il75tLSEATmvoabaHrxlehqhASb4IRT4N3B2dX1qzqq6o4ufgr0jas40xettZ1UVXxUQz0jOlEXUQHRv38fpm6KIRo02QETbRHOqsVj3Hj8Bg3DkdNDRVbt1K25mvK166ldPESFFdX3IcNxX3MWNyGDEbn6vrTDxraSzvGPA97P4Jd78Pnt4MtHPrcAz3v0tazNbLQ0FAyMzPJz89v9McWV8disRAaenUzrCSgtXcOh9Yqdt1fofgMdBgGo56D4O7OrqzZVOUXcOyLuZzYuZXssmLq9Dp0DgeBFiu9u/Wk040zsHXQ9rJITk6WcCaEaPOMZjP1tTKCJtovndmM+/DhuA8fjlr/HJU7d1K6ajVla9ZQunwFiosLbkOG4DF2DG5Dh6Kz/sTG1VZfGPw7SPoNHFuuTX/8+lltOUniTdDvfm3bokZiNBqJiopqtMcTzUsCWnuWvgHW/BFyDkBgV/jZvyF6hLOrahalGac4Mu8z0g/sI7e2CodOwWR3EOrpQ+yAwXS8cQZmT09nlymEEE5hNFuoq5YRNCEAFIMBa1IS1qQkAv/0Ryp376Fs1SpK16ymbNUqba+1wYPwGDcet2HD0Lv9SFjTGyB+inbkHtGmPx6YC/s/gbB+2vTH+KmgNzbfCxQtjgS09ijvKKz5E6StAlsYTH9X+/amjY8M5e/dw5GFX3Dq2BHOq/WgKLjaHXQMDKXTqLFETZyM3niFC4GFEKINM5rNVJeXObsMIVocRa/H2q8v1n59CXj6Kar27dNG1latovzrtShmszayNn4cbsOG/fg0yIB4mPR/MPLPsP8zbVTty3th9TNax+xes8DNv9lem2g5JKC1J2XnYP3fYN/HYHLXpjL2+2WbbZnvcDjI2byR1CULOZVx4sL+ZDaHQrfIWDpPnELwkGEyZVEIIb7FaLZQdr7A2WUI0aIpej2uvXvj2rs3AU8+oYW1FSspXbWSsjVrUCwW3IYNw2PcONyGDkH3Q03FXDxhwAPaZ7ITa2DH27D+Ba0vQMJ0bfpjSK9mfW3CuSSgtQc15bDtda07o70G+v5C68xo9XF2ZY3um02jj65axunss1ToFa3Jh85An04JxN04A79u3Z1dphBCtGhGs1mahAhxFRSdDtdevXDt1YuAJ5+gcs8eylau1EbXVq5EcXHBffhwPCZOwDp4MLrva92v00HHsdpRkKaNqO3/DA7OhdA+2ue3+KlgkNk+bZ0EtLbMYdf+Ya/7K5Tnav+oR/4ZfKKdXVmjstfUcHLRAo6t/5oz+TlUN2wa7W+y0K1rD+JnzLzQ5EMIIcRPM1os1NVIkxAhroWi12Pt2xdr374EPP00lbt2Ubp8hda+f/lydO7uuI8ejceECVj790MxfM/Hcd9YmPAqjPjjxemPC36uTX/sc69Mf2zjJKC1VekbYNXTkHtI+9ZlxscQ3s/ZVTWa+soKji/4guMb1nG2KJ/ahs6LQa5uxPTqR9wtt2ENDHJ2mUII0SoZpM2+EI1C0eux9u+PtX9/Av/4DBXbt1O6bDllq1dTsmCBtin22DHYJkzApVcvlG8vu7B4QP9fas1DTq6FHW9dnP6YeKM2LbIddd5uLySgtTUFabD6j3B8hbbHxk3va/OX28AmhbVlZRybP5fjmzeQVVpInV6H3uEgxM2TjgMG0XnGrZi9Gn8vESGEaG+MZgv1NTWoDsd3PzAKIa6JYjTiNngwboMH46h5lvKNGyldvpySrxZSPGcuhoAAPCZOxDZpIua4uMs3mNbpIHa0dlw6/fHAHAjrD/1+AXGTpftjGyEBra2oLNT20tj9HhhcYNSz0O9Xrb4BSG1pCalzP+X41s1kVRRj1+kw2h2E2rzpOHAYHW++BZO7u7PLFEKINsVoNgNQX1uL0dK6/x8RoiXSmc14jB6Nx+jROCoqKFufTOnSpRTOnk3h++9j6tABj4kTsE2ciCky8vI7X5j++Azs+xR2vg1f3A0eIQ3TH+9uks2vRfORgNba1ddqe2hseBlqyrQd6Yc/1arnJdcUFZL6+RyOb9tEdmUpdp0Ok91BpJcfnYaOJHb6jRhcf2JDSCGEENfsm4BWV1MtAU2IJqazWrFN0kbO6ouKKFu9htKlSyn4z+sU/Od1LF26YJs0Effx4zH6X/L5zmJr6P74C0hbAzv+C2v/Ahtega4ztOmPAQnOe2HimklAa61UFY6v1NaZFZ7UNpge84K2p0YrVH3+PKlzP+H4jq3kVJVdCGVRPgF0HjGamBtuRN/wgUEIIUTTMpq1UCbr0IRoXgYvL7xumYHXLTOoy8mhdPkKSpYtJffFl8h9+RWs/fvjMXky7qNHX9wQW6eHTuO0Iy9VW6d24HPYOxuihmgzqjqO1W4nWgUJaK1RXiqsfBLS14NPLNw2HzqOcXZVV62mqJAjcz7h+PYtZFeV49ApmO0OOvgG0HnkOKJvmCYbRwshhBN8M2omnRyFcB5jUBA+996Dz733UHPyJCVLl1K6ZCk5Tz7Jueeew33ECDymTMZt4EAUY8PaM/84mPxvrWv33o9g5/9g7kzwitTa9Pe4XRt5Ey2aBLTWpLJQ22h69/tgdoNxL0Gfn7eqBaE1xcXamrJtm8iqLMWh02G2O4jxC6LzqLF0mHKDhDIhhHAyGUETomUxR0fj/5vf4PfrX1O1bz8lSxZTtnwFpcuXo/fywmP8eGxTJmPp1k1rLuLqDYMehQEPw9ElsP0tWPWk1gGyxx1aV8g2tu1SWyIBrTWw12mhbP3foKZUW/w5/OlWs9H0xUYfm8iqKLkwfTHaN5DOo8YRPVVCmRBCtCQGU8MatGoZQROiJVEUBdeePXDt2YPAJ5+kfPMWSpYspvjLLyn67DOMEeHYpkzBNmUKprAw0BsgYZp2ZO2FHW/Drve0047jtBb+UUPbRLfvtkQCWkt3Yq02nbHgmPYPaNyLrWLBZ21FBcc/n8PRTevJLC+6bE1Z3CiZviiEEC2Z0XKxSYgQomVSTCbcRwzHfcRw7GVllK1eQ8nixReai7j06oVtyhQ8xo9D7+EBIT1h+tsw+jktpO1+H2avAP94raFI1xlgdHH2yxJIQGu5CtO1BiDHloNXFNz6GXSa0KK/4aivquL4l/M4uv5rzpacp16vtcSP9PIjbuQYYqbdJI0+hBCiFZApjkK0Lnp3dzxvnI7njdOpy86mZMlSShYt4tyf/0zuCy/gNnw4tqlTcBs8GMU9EEY8DYN/BylfwPb/wpJfw9fPQu97tOUzHkHOfkntmgS0lqamHDb/E7b+B3RGbZHngAfB0DKDjb2ulpMLvyJ1zQpOF+ZRp9dhsDsIs3nTedgoOt50CwYX+TZGCCFaEwloQrRexuBgfH9xPz7330d1ymFKFi+mdOlSylat0tarTZqE7YapWOLjUXrcAd1vh4zNWlDb9A/Y8i9ImA79f6WNuolmJwGtpVBVSPkSVv8RyrKh6y0w6rkW+Q2Gw+EgY/kSjixfSkZeFjV6HXqHgxA3TzoPHkanGTNl82ghhGjFvuniWC9dHIVotRRFwaVLIi5dEgn4/eOUb9pMyaJFFM+dS9HHH2OOjcV2ww14TJ6EMWowRA3WZnDtfBf2fgyH5kFYfy2odZ6krWcTzUJ+0i1BzgFY8Qc4sw2CusHNH0B4f2dXdRmHw0FW8joOL15AemYGVXodOodKsKsbnQYMIW7mHZg9PZ1dphBCiEZwcaNqCWhCtAWK0XhxvVpxMaUrVlC8cCF5r75K3j/+gXXQQDynTcNtxAh0416EYU/Cvk+0PdXm3wW2MK3zY887wcXT2S+nzZOA5kyVhbDur7D7A60d6uTXtNanLWgjwXM7d5Ayfw4nT6VRrldQVJUAswt9evcn4Y67cPXz/+kHEUII0aoYGpo4yRRHIdoevacnXjNn4jVzJjXp6ZQsXETJokVkPfpbdB4eeEwYj+f06Vj6/wql3y/g2Apt+uOaP0LyS9D9Nm1UTdr0NxkJaM7gsGubB679C1SXQr9fwLAnwMXL2ZUBUHj0CIc++5gTR1MoVlRQVfwMRrp2703i7XfiHhbu7BKFEEI0IUWnw2A2U1ctAU2ItszcoQP+v30Uv9/8msodOyj+aiElXy2keO7nmGKi8Zw2DduUKRjungQ5B7Wgtvcj2PU/6DgW+j8AUUNadBO71kgCWnM7uwuWPwY5+yFiEEx4pUW0zS87e4aUTz7i+IE9FDjqQFHwQkefzl3octudeHXq7OwShRBCNCOj2SIjaEK0E4pejzUpCWtSEvY//ZHSFSsoWfAVea/+nbx//h9ugwdjmzYN94n/Rhn1LOx+T2vVP3sKBCRqI2qJN4HR4uyX0iZIQGsu5fla+9L9n4B7ENz4HiTe6NRvHKrPn+fwp7M5tmML5+qqUBUFN7tK9+iOdLl5Jv69+zqtNiGEEM5lNFukSYgQ7ZDe3R2vGTPwmjGDmvRTlHz1FSWLFlGenIze0xOPKZPxvPFGLI/+Fg7Nh+1vwqIHG9r03wt97gU3WQJzPSSgNTV7vbYR4PrnobYCkn4NQ38PZud0OayvquLYvM84sn4tWRXF2HU6XOwO4oLDSbzhJkKGjUCn0zmlNiGEEC2H0WyWJiFCtHPmDlH4/+63+D3yGyq2bqV4wQKK58ylaPbHWBISsN04HdttK9AX7odtb8KGl7TtorrcrE1/DEx09ktolSSgNaUz22HZY5B7CDoMg/Gvgl/HZi/DUV9P+tJFHF6xlNPnc6lr2EA6yieAhPGT6DBpKjqDvBWEEEJcZLTIFEchhEbR63EbPBi3wYOxFxdTsnQZxV9+Se5f/kreSy/jPno0njc+guvov6Lsegf2fwb7P9XWp/V/EGLHgAwAXDH5VN4UyvPh6z9rb0yPELj5I4if2uzTGbM2beDQl/NIzzzV0BbfQaibJ3HDRtB5xkwMrtZmrUcIIUTrYTSZJaAJIb5D7+mJ9x23433H7VQfOULxgq8oWbKE0mXLMAQH4TltOp63rMV4bhXseAfm3ALe0do6te63gUk+f/4UCWiNyWGHPR9o3RlrK2DgI9p0xmZ8IxYeOczBz2aTduwwpToutMXv128gCbffhcXHp9lqEUII0XoZLRbKCwudXYYQogWzxMcTGB+P/+OPUb5uHcVffEnBm29S8OabWJOS8Lzx77gFlqHb847WJG/dX6HXLG1PNVuos8tvsSSgNZasPbDsd5C9DyIHw8R/gF+nZnnqinM5HJr9Psf37iK/oQOjt05Hv8QedP3ZLDwio5qlDiGEEG2HQbo4CiGukM5sxmP8eDzGj6cuK4viBV9R/NUCsn77GHpPT2xTpmAb/iCW3EWw9T+w9XVIuEGb/hjay9nltzgS0K5XZaE2YrbnQ61jzfT/QZebmnw6Y21FBamfzebopvVkV1Xg0GkdGLt1iKXrLbfj36tPkz6/EEKIts1oNlNXK01ChBBXxxgSgt/DD+H7wK+o2Lad4i++oHDOHApn12Hp1hXPCS/i4ZmO/sgcSPkSwvppDUU6TwK9RBOQgHbtVFVbY7bmT1BVrM2rHfYkWDya7CkvNPtYvoTThXnU6XWY7Q5iA0LoMuVGwkaPkQ6MQgghGoXRbKFeNqoWQlwjRa/HbdBA3AYNpL6wkJLFiyn58kvOvfhv8lxd8Rh3O56JZiy5C1Dm3wW2cOj3C+j5M7DYnF2+U0lAuxZ5qbD0t3Bmq5b6J/4DArs02dPlbNvCwXlzOHk2nSq9Dr3DQaiHFwkjxtLx5lvQm81N9txCCCHaJ63NvgQ0IcT1M3h74zNrFt533UX1gQMUzZ9PyfIVFC+owtwxFs8hE7GZ96Jf/TQkvwQ97tDCmnf7XKYjAe1q1FbAhldg2+vaPmZT/gPd72iStqElJ09w8OMPOH7kIMWKCqpKoMmFfv2l2YcQQoimZzRbsNfX47Db0en1zi5HCNEGKIqCS/fuuHTvTsCTT1K6bDnF8+eT+79F5JlMuA+5Gc/IUlx3vouy823oNAEGPAjhA5q9G7ozSUC7UkeXw4o/QMkZLZSN/gtYGzck1RQVkvLxhxzdvoVz9dWgKHii0DeuG13vvAdbh+hGfT4hhBDihxgbZmfU1VRjlm1ZhBCNTO/mhtctM/C6ZQbVqakUz59PyZKllH5dhim8J569fLEd24Lh6FII6q4FtfgbwGBydulNTgLaTyk+qwWzY8vALw7uXgERSY328Pa6WtK+mMfhNSs5W1aIXafDxe4gMawDXWfMJGjAwEZ7LiGEEOJKGS0WAOqqJaAJIZqWJS6OwD/9Cf/HH6d05SqK588n76u95Bs9cO/VA8+qDFyz70NZ8yfoex/0uhtcvZ1ddpORgPZD7HWw/b+Q/KLWEGTUs1or0EZK7Vkbkzn4xVzSs89QrddhsDuI9PIjcfxkOky5AZ1B/mqEEEI4j9HcENCkk6MQopnoXFzwnHYDntNuoCYtTVurtmgxpdurMQZ1xauzii3/eQwbXtU2ve7/K/CNdXbZjU5SwPc5uwuWPgK5KdBxHIx/BbwirvthS06e4MBH73M89SAlDZtIB1msxA0cSvwdd2Fyd7/+2oUQQohGcCGgSSdHIYQTmGNjCXzqKfx/+1vKVq+maN488tbvIc8QgnucD145c3Hd9R5Kx7Ew4AGIGtpm1qlJQLtUdYm2p9mu98A9CG75RNuT4Tr+smuKi0mZ/QGp2zeT27CuzEtp2ET6zrvxiIhsvPqFEEKIRmK4sAZNRtCEEM6js1i0ja6nTKHm5EmK582nZOFCyg7ZMPqF4pW+D9uhaRgi4rURtS43g6F1dziXgAbaFMYjC7W1ZhX50O+XMOJprVPjNXDU13Piqy9JWbmUM6XnL64rC+9Atxm3E9h/QOPWL4QQQjSyS5uECCFES2COjibgySfw++2jlK1aRdHn88jbtYf8fSG4dyjD8+CjuEY9i9L3Puh9D7j5ObvkayIBrSgDlj0GJ9ZAUDeYORdCel7TQ53bsZ0Dcz+5sF+ZweEgwuZL4vhJRE+dLuvKhBBCtBoXpjhKQBNCtDA6s/niqFpaGkXz5lOyaBGlx30xHTThufffeMb8E32fm6H/AxAQ7+ySr0r7TQz2Otj2hrYZnk4P416CPveB/up+JGVnz3Dwo/c4dnAfRYpD26/M7EL/AYNJuGMWZk/PpqlfCCGEaELfdHGslymOQogWzBwbS+DTT+H/20e1DpCff07e/v3kp+jw2LsczzVzcemThDLgIYgZ1ST7Fze29hnQMvfAkl9rTUA6TYQJr4At9IrvXl9ZweFPZ5O6cT3ZNRWoioJNhT6du9LtrnuwRcc0YfFCCCFE05MRNCFEa3JpB8jqY8co/vxzShYtoiTdjHnvcbxW34VHrxD0g38F3WaCydXZJf+g9hXQaspg3fOw4+2GJiCfQtykK7qrw+HgzKoVHFq8gFP5OdTpdZjtDjoHhtH15lsJHTq8iYsXQgghms/FLo4ygiaEaF0snTpp+6r97neULF1G0dw5nNtzlNyDldjWPodXwvNYxszS9lTzCHZ2ud/RfgLasRWw7HdQmg19fg4j/wQWj5+8W+GRwxz4+EOOpx2hXK+gc6iEutlIGDWOTjffit7curvECCGEEN/HIE1ChBCtnM5qxeuWGXjOuJnqQ4comjuXkmXLKD5Zi2XLbLxi38Fj3Fh0gx+65h4UTaHtB7Syc7Di93BkEfjHw80fQVifH71LTVEhhz56n9QdW8iz14Ki4Gsw0K1nX7re9XNcAwKaqXghhBDCOfQGA4pOJwFNCNHqKYqCS9euuHTtSsAf/kDJokUUffoJOdvPkrt3K55Ra/Aa3BHThN9A54lafwonarsBzeGAvR/CmmehvlobMUv6NeiN33/zC63xl3CmtBC7ToerXaVrZAzd77gLv+4tJ1ULIYQQTU1RFIxmiwQ0IUSborfZ8L7zTrx+9jMqd+yk6NOPKVy3nsJj2ViXPIJntydxn/FLlN53XdFsu6bQNgNa/nFY/DCc3Q5RQ2DSv8An+ntvem7nDg7M/ZiTZxpa49sdRHr5kThxCh2mTEPXCjq9CCGEEE3BaLFIF0chRJukKArW/v2w9u9HXV4eJV98QdFns8laXYJh03/w7Ph/eE6bjHHMI+Ad1ay1ta2AVl8LW/4FG18FoytMfRO63waKctnNKs7lcPCD/3F0/y4K0VrjB5i01viJd92NycPmnPqFEEKIFsRoNlMnAU0I0cYZ/f3xfeABfH7xC8o3bKTow7cp2HWAgoOrcP/fIrxGdMV15uMokYO+kyuaQtsJaGd3aaNm+amQeKO2r5mb/4Wr7TU1HPv8M1LWriKrsgyHTsHdAb07JdD1znvw6tjJicULIYQQLY9McRRCtCeKXo/7iOG4jxhO7ZkzFM1+n5KvvqJsdhqmr+7Gq6cntjsfRN/vNjA0XaPA1h/Qasph3V+11vkewTDzc+g07sLVmRvWc/CLz0nPOUONXofR7iDWP5gu024mbORomcIohBBC/ACD2UxdtQQ0IUT7YwoPJ+CZZ/F77AlKly6m+MO3yd2QTd7ml7DFvITXTTdgmfYYuPk1+nO37oCWtgaWPgolmdo+BiP/BGZ3Sk9ncODD/3Hs8AFKFBVFVQl2cSNh6AjibvsZBlersysXQgghWjyj2UJddZWzyxBCCKfRWSx43jQDz5tmUJVymOJ3/knJum0Uv7AYl7e/xGtkN9zvfQZdeI9Ge87WGdAqzsPKJ+DQPPDrDPeupt4ngcMffcSRjevJqa1EVRQ8UeiX0JNud/8c97BwZ1cthBBCtCpGs4XKkmJnlyGEEC2CS2ICLq+9h39pKSWfvEvRnDlkf34E/cJb8Ozhg9c9D2IcNPO62/S3roCmqpDypbavWXUpjsG/52xtVw7+7W1O5edQp9dhtjvoHBxOt5tnEjJ4qLMrFkIIIVoto9ksXRyFEOJb9B4eeD/wO7x++SiVG9ZQ+M6/OL8jg/M7nsct/EW8bpqC9Y4nUFyurfFg6wloJVmw7LdwfCXFLj05UB7Psbe2Uabbhs6hEupmI2HkWDrNmIne3HSL9oQQQoj2wmiRJiFCCPFDFJ0O6/CxWIePpe7sGYreepHiFRsp/8dCjO8swGtkVzx/+Uf0kV2v6nGbNaApijIO+DegB/6nqupLP3knhwP2fEDt8mc5fMqTI5UDOYcCymm8dTqSuveh690/xxoY1NTlCyGEEO2K0WSWgCaEEFfAGBaO/wv/xffPtZTNeZuizz4mb2EK+UtmYOvmi9e9D2AZMfOK2vQ3W0BTFEUPvAGMBjKBXYqiLFZV9cgP3qm+hvSnx3DoWAUZukTq9XpcHA4Sw6PoduvPCOzbr5mqF0IIIdofo8VCXXUNqqqiNMPeP0II0drpTCZsdz2M7a6Hqd69kaI3X6FkxwmKH/wrLkEv4nXTJDzufupHH6M5R9D6AidUVU0HUBRlLjAV+MGAlnf6LF+lR6DTmwhz86LLuInE3jgDnaH1zMwUQgghWiuj2YKqOrDX1WEwmZxdjhBCtCqW3kMIen8I/gW5FL/1V4qWrOfMG4tIW3z4R+/XnEknBDh7yZ8zge8MgSmKcj9wP0Coty9616FUR1lRuoWSY/MgZ/Pm5qlWiO9RXl5OcnKys8sQ4gJ5T4qmlHtW+287ed1aDBaXK76fvC9FSyPvSeFMdoed46EhZA9OxJZZjaLaf/T2LW4oSlXVd4B3AGwhkWpmgBcR2RHkZCukh5yj76hYhvTriaKTqRai+SUnJzNs2DBnlyHEBfKeFE3poL2GzC3r6du7Nx6+V74Zq7wvRUsj70nhDKnpe1m9bDal+9JwrVCwKUZ0xs5URcUAy37wfs0Z0LKAsEv+HNpw2Q8K8fFkkT6Yft1q6EkxyhEPUj4qYdcXCwntb2XyhMFYrVf+jZ4QQgghrpzRYgGQRiFCCHGFikoLWLL8PTK2bcd6rg4VFaMlAKNrT0rcYxh5VzeSegXxzF/v/8HHaM6AtguIVRQlCi2Y3Qrc9mN3cDUZeGxqIk8sOETc4J48fFcYX65aTdGOKs6vtfG/5A2YOlcxblJfoqJCmuM1CCGEEO2G0aRtWyN7oQkhxA+z2+tZs3k+e9Yuw3CiCINdQXGD2shELEX90Os8oJsnj9/bHYvppzexbraApqpqvaIoDwGr0Nrsv6+q6o+vkANu7RvOkZxS3t10ioRgG3dPuxHHDQ7W7N7Ezq+z8DgSyvLDx6gJ2E6vkVEMHtgdnV7X5K9HCCGEaOuM5oYRtGoZQRNCiG87dHwHXy//hIr96bhUKegMDtS4ACK7TCB9ky+uJSp5HgpT702kZ9yVTxNv1jVoqqouB5Zf7f3+OCmeY+fK+MOXB4n2c6NLqI2xfYYyts9QjmansXTZZuwpHqR8Vsyer5YS1NeFiROS8LBZm+BVCCGEEO2D0aKNoMkURyGE0OQX5bB0+fuc2bYTt3w7DlQcoRZCBw9jzNDbWfT5abJXFoLiQBngxzO3J2A0/PSo2aVaXJOQ72PU63jz9p5MeX0L93+8m8UPDcLPXftPo3NwLJ3vi6W4uoQvV68if3sF5g0RfLhxC8aOVYye2JuYjjL9UQghhLhaF0bQamWKoxCi/aqtq2FV8hwOJK/GlF6C3qGgeIDLyEQmTLybyJBOHNh1jg+ePYC5RuWcl4E7ftmVuAiva3q+VhHQAHzczLz9s17c9NZWHvh0D5/+vD8mw8WpjJ4WG/dOmYF9kp01+zey/et0PNMiWPXPYyzx3Un34REMGdodvUGmPwohhBBXQqY4CiHas72HN7F+xRyqD2VgqdahNzqgazADxtxM/x6j0el0VJbW8L+/76LmRBmVegduo4L5y/Q49NfRcb7VBDSAxBAbL9/Yld/M3c9zSw7zwrQu37mNXqdnXM/hjOs5nKPn0liyfAN1h9w5Mr+Y/YtXENDLxIRJA/D0dnPCKxBCCCFaj4tdHGUETQjRPpwrOMuSpf8jZ8c+rIUOHIqKI9yNiCEjmDjqZ7hYtCVUqqqy7evT7PjqJDq7SmaAkV/8sgfRQe7XXUOrCmgAU7uHcCSnlLc3pJMQbOO2fuE/eNvOgbF0vieWkuoSvly3ktytJRi3duDjbdvQR1cyYnx3OsWHoyiyp5oQQgjxbQaTrEETQrR91TWVLFv7MUc2rMN8uhy9qoCXgtvY7kyceC+hAVGX3b7oXAXz3j5IfU4V+QYHMVPCeWlcLLpG2qe51QU0gN+P7czRnDL+vDiFGH83+kZ5/+jtbRYb90y4Bfs4O2tTNrF1TSoe6WGs/c9JVnjtJ3FoEMNH9MJwBW0vhRBCiPbiQpMQmeIohGhjHA4HOw58zaZV86k/nIW5VofO7EDXM5wh426hT9fh37mPvc5B8qITHFmbSa2qcjbczKP39SDCr3EbE7bKgKbXKbw2swfT3tjCrz7Zw6KHBhLq5XoF99MzpuswxnQdxvH8Eyxavp6aA1aOLyzn8LJV+PTQMWFSEj7+Hs3wKoQQQoiWTafTozcaZQRNCNFmnM5OY/my98nfdQhrCaBTcUTZiB02hnHDb8NkNH/v/TKPFbLk/cM4Suo4abbTY2oHHh3WodFGzS7VKgMagM3FyLt39eaGN7bw84928+WvkrCar/zldPSL4fG7YiirKWPBxlWc2HQe/c5oPtu5EyWyjCHjutKlWweZ/iiEEKJdM5ot1EsXRyFEK1ZeWcLS1R9xfPNGXM5WoUNB9dPjNbk3kybci7938A/et6q8ljWfHeXs3gKKdQ6yYlx48p4ehHn/9ODQtWq1AQ0g2s+N12/ryd0f7OR38w7w5u09rzrFupvduWv0TThGOdh4dBsbVx3E9UQIm946zVrbIToO8mP06H6YLK36RyWEEEJcE6PZQl21BDQhROvicDjYsHMx29cshKN5mOp16FxUDAM6MHL87XTt1P9H76+qKqlbc0ied5z6Gjv7XR0Mnx7DUwMjm3wAp9WnjqEd/XhqQhzPL0vlX2vT+O3ojtf0ODpFx7C4gQyLG8jpwjN8tXId5XuNZCzz4M1Vq3Hv6mDS5CQCgn58vZsQQgjRlhjMZpniKIRoNY5lHGDV0o8o2XcM13IFRe/AEetD4oiJjBp0E3r9T8efwpwKVs8+wvlTZWTq7eTFW3nuju5NOmp2qVYf0ADuHRTF0XNlvLY2jU4B7kzsGnRdjxfhHc4jt82i6uYqFm1eQ+rGc+j3RjF/717qw0oYMKYzfXvHy/RHIYQQbZ5RApoQooUrLMljyfL3ydi2HbfcelRU1CAzAeOSmDzuHmzuVzbAUldrZ/fyDPauPk21qrLN3c7U6R35W/+IZv3c3yYCmqIovDAtkfT8cn43fz8RPq4khtiu+3FdjC7cOnwK6jCVXen7+HrFHkzH/Nn9Xi6b5x0nYoAHE8YNxNXV0givQgghhGh5jGaLBDQhRItTW1fD6g2fsz95JcaTJRgcCjp3MA+LY+z4O4mN/O5+yT8m42AB6+cco7KohhRjPRVx7vzfrd2abdTsUm0ioAGYDXre+lkvpr6+hftn72bRQ4Pwc//+LixXS1EU+kb3pO9DPckty+OrlWup3GUnd7WNd9auxxxfxbjJ/YgKD2mU5xNCCCFaCqPFQnVZqbPLEEIIAHanJLNh5edUHzqNpVqH3uiALkH0HT2dgb3Go9Pprurxygqr2fT5cU4dKKBQr5LsWc+sGzpzRz/n7ZXcZgIagL+7hXfv7M1Nb23ll5/s4bP7+mE2NO7eZgHu/vzy5pnU31jPiu3J7F+fjS4ljOWHjlEVtJmeI6MYNqA3Ov3VvTmEEEKIlshoNlNWIE1ChBDOc/bcSZYte5+8XQexFqk4FBVHhBsRg0cwcdTPcLFc/T5kdruDA2vPsnPJKWrtDjZb6tB3dufDGc231uyHtKmABpAYYuPvN3fjoc/28cxXKbxyU9cmSb8GnYHJSaOYnASpmcdZsWw7HLaR+kk5exYsxK+PgRsmDsPTQ/ZUE0II0XrJFEchhDOUV5awbPVsjm3egEtmFTpVAR8d7uN6MGniPQT7R17zY2enFbPhs2MU5lRwyuxgo3s9D07qzM/6RzTJvmZXq80FNIBJXYM5fq6M19adoFOgOz8f3KFJny8utCNxv+hIWVU5C9eso2RrNRUbAvlw8xbU2GJGTuhB146dm7QGIYQQoikYzWbqqiWgCSGant1eT/KOxez8ejHKsTyMDa3x9f2iGDHuNrrHJV3X41eW1rLtqxMc3XaOGpPCMmsN3rE25t3UjUjfqx+FayptMqABPDKqI2l55bywPJUOflZGdA5o8ud0d3HjZ1OmoE5W2bx/D9tWH8VyzJ9NR7NZ6rebTkP8mDRsOGajqclrEUIIIRqDwWyhrkamOAohms6h4zv4esWnVBw4iUvFtbXG/zEOh8rhjVnsWJROTU09+6x2tlnq+e34ztydFNkiRs0u1WYDmk6n8I8Z3Tj7diUPf7aPBQ8MpFOge7M8t6IoDO7Rm8E9epOdn8uSpZsw7Xfn3JdG/rVsMa7da5g8cQiRfmHNUo8QQghxrYxmC/W1NagOB8pVLr4XQogfkpN/hmXL3yd75z6sBXYcqDhCLAROSGLS2LuvuDX+Tzl3qoSNc46Tf6aMMpueeYZqIqNsLLm5Gx383BrlORpbmw1oAK4mA+/e2Zupr2/h3o92sfDBgfi6NU5nxysV7BfAL+6+ibr6elau28LRjQ5024NYuDOF8shV9B0dy6jug9Ep8p+eEEKIlsdo1v7frK+txWiRbWWEENeuqrqCZV9/ROrGZCxnKrR1ZZ4KrqO7Mn78XUSGdGq85yqvZftXJzmyJQe91cA6LweHlBp+N6ETPx/cAX0LGzW7VJsOaABBNhfevbM3M97exi8/3sOnTdDZ8UoYDQYmjxnK5DGQeuwUXy/fi0daGGlv29nm9RGB/c1MGzUaf6tfs9cmhBBC/JBvQlldTbUENCHEVbuwrmztYjiWh6lOh87iQNc7giFjZtCn6/BGfT7VoXJkSzbbFp6ktsrO+VAzH5cV0znYxtIZ/egY0Dwz6q5Hmw9oAN3CPPnHDK2z45MLDvGPm7s5bV8DgLhOUcR1iqKspJKlyzdTu9OX+hVW3l+7gbq4PEaO6cWADn2dWqMQQggB2hRHQDo5CiGuysFj21m74lMqDqbjUqGg06vUx3gTN2wco4fMwGho/J4MuRmlbJx7nLyMUlxCXPnKvZxTlSX8ekxHfjUsGmMr2QarXQQ00Do7nsgr519fp9ExwJ1fDo12dkm421yZOXMMjhkOdmw/wq6vy9Af6Myug0UsDn6NjoP9mN5/Ap4WT2eXKoQQop36ZoqjdHIUQvyUzNxTLF/xIed27sN63tFk68q+raqslu0LT3Jkaw4u7kbyEtz4KDOfzkHuLJrRh4RgW5M8b1NpNwEN4DcjYzmRV87LK4/SwdfKmIRAZ5cEgE6vY8DARAYMTCT79HnWLNuNcjiOqrkG/rH8C4xdyxg/YjC9g3rJqJoQQohmdXEETTo5CiG+q7SimGWrPiJt66aL+5V5KVhHd2P8hFlEBMc22XM77A4Ob8pmx+J06qrt+PXy5fXcfDKzS3lwRDS/HhnrlKVN16tdBTRFUfj7zd04W1jJI5/vZ/4vB7S4RB0c4cNdD4yluqKOjWsPYt8YjH6zhXU7z/BpxEp6DI3ihi6TsJlbVt1CCCHapgsjaDLFUQjRoK6+ljWb5rM/eSW6tPMY7Q37lfWNYuiYGfRKHNLkNWSnFbNx7nHOZ5UT3MmTA346Xk45Swc/K1/+LIke4V5NXkNTaVcBDcBi1PNOQ2fH+z7azcKHBuLv3vIWPVusRsZM6cWoSSrH92ezeVUKbmlJlJyo51nfd3DvVc8NA8bSw7+HjKoJIYRoMjKCJoQAcDgc7DjwNVvWLKDm8Bks1ToUgwO1sz9dR0xkxIBp171f2ZWoKK5h64ITHN+Zi5uXmdgbInnhYAZnDldx76AoHh/bCYux9Y2aXardBTSAAA8L/7urNze/tY37Zu/h8/v7t9i/SJ1OoXPPEDr3DKHoXAUbV6ag290dZaWehZv383aHuQwc3IUpsZNlrZoQQohGd2kXRyFE+5OavpevV3xK0f5jWEvBoag4ItyJGDyU8SN/htWleboi2uscHFh3lt3LM3DYVbqPDWejvpZnN6QS6uXCnPv607+DT7PU0tTaZUADSAyx8a9bu/PLT/bw23n7eX1mzxa3i/i3eQVamTqrH7W31HNw82l2r7MTcDCS3NRSHgt8Gb9eBqZ1m0yfwD4yqiaEEKJRSBdHIdqf7LwMlq/4kKxd+3DLtwOgBhjwGtqbiePvJsAnpNlqUVWV04fOs3l+GiX5VUR29cVvUCBPf51KWl45t/UL56kJcbiZ206saTuv5BqMTQjkyfGd+dvyo/zd5xi/H9fZ2SVdEZOLgd6jo+k1sgNnUwvZtvooLsdGoWY6mLNpI691eJdhffpzQ+xUfF18nV2uEEKIVsxwoYujTHEUoi0rKStk2ZqPOLF1y4VmH4oNzMPjGTvuZ8RGdmn2morOVbB5fhpnDhfiFejK+Ae7sji3kN/M3Y2Pm4kP7+7DsE7+zV5XU2vXAQ3gvsEdOFVQyZvJJ4n0tTKjd5izS7piik4hPMGH8ISBlORXsn/9afRbdMTs6knW4UweDHqakO5uTI+fxoCgAeh1LXMapxBCiJZLmoQI0XZV11axesNcDm34GkN6MQa7gs5FRdcngiGjb270TaSvVE1VPbuWneLQukwMJh0Db4rBJd7Gb748xKGsEm7oHsxzUxKxuRqdUl9Ta/cBTVEU/jI1gbOFlTy14BChXi4kRbe+USebnytDZ8SRNLUjx3eeY/daI74nQ6k5XcmH25bzatS/GNtlBDfE3ECwW7CzyxVCCNFKGExmUBTqa2UETYi2wG6vZ+OupexctwR7ag7mWh06owM1LoCuwyc0W7OP76M6VFK35bB94UmqyuuISwqi75QOzDmQxatvbsXNbOCtO3oyLjHIKfU1l3Yf0ACMeh1v3N6TG/+7lV99spcFDyQR7efm7LKuidGsJ2FwCPGDgslOK+bAujOYD4xEzR5B+pHD3Bv4a8I6ezO903RGhI3ApG/8XdyFEEK0HYqiYDSZZaNqIVq5PSkb2bBmHpUHT+FSqYBORe3gSfTgkYwbPhOL2dWp9WWfKGbzvDTyz5QR2MGDSQ91o9rNwD1z97LzVCGj4wP427Qu+LmbnVpnc5CA1sDmYuSDWX244Y0t3PPhLr56YCDe1tYbXhRFIaSjFyEdvSgrrObwxizMm4xEpXah7HQBH+5fxMshrzKu4ximxU6jo1dHZ5cshBCihTJaLDLFUYhWKDV9L2tXzaFwXyrWkoYOjKEuBE4cwIQxd+Hl4fxZY6UFVWz76iQn9uRh9TQz6u54Yvv4M3dXJs8vO4K+YR/jG3uGtJsmeBLQLhHm7co7d/Zm5rvb+eXHe/j4531b5e7j3+bubaH/DdH0nhjJyT15HFififspXxxn60g9uYN79/6KsLAAboi5gXFR4/AweTi7ZCGEEC2IwWSWfdCEaCVOZ6exauVszu05iLVA68CIvwHbxB6MG3snoQFRzi2wQW11PXtXnWb/mrMoCvSZGEmPMREU1tRxz0e7ST6Wz8AYH165qRshni7OLrdZSUD7ll4RXvzj5m48PGcfT355iH/M6NZm0rrBqKdT/yA69Q8i91Qph5IzMew2kZAziPNnz/Dx8a941fdVRkaOZFrMNPoE9kGn6JxdthBCCCczmmWKoxAtWe75LFasms2ZnbtwyalBhwJeCi4jExkz9g5iIhKdXeIFqkPl2I5zbFt4ksqSWmL7BDBgWjTu3haWHMjmmYUp1NTbeXZyPHcOiGzx22A1BQlo32Nyt2AyCir4x5rjRPpa+fXIWGeX1OgCojwIiIon6cYYjmzOJmWTGZ9j4dgzaziYvYGHjv0GHy9PpkZPZWrMVGksIoQQ7ZhMcRSi5SkqLWDFmtmc3L4N89lK9KqC4g7GgbEMH3ML3ToPcHaJ35FzopjN89PIO12Gf6QH43/RhcAONoora3nos70sPZhD9zBP/jmjGx1aaT+IxiAB7Qc8NCKGU+cr+Oea44R5uzCtR6izS2oSrh4mek+IpOfYcE4dLOBQchb6Y2PoeWY050My+CLnK/574L/0DerL1OipjIoYhYuhfQ0zCyFEe2c0W6SLoxAtQHllCSvXfcrRLRsxZpRhcCgoLir63uEMGHkD/buNRqdrebOfSvKr2PbVCU7uzb+wzqxjnwAUnULysTx+/8VBCitqeWxMR345NBqDvuW9huYkAe0HKIrCS9O7klNcze+/OEighwsDon2cXVaT0el1RPfwJ7qHP4XZFaRsyOTodgPTz/wW/KvYV7qOP2b9iRfMLzAuchxTY6bS3a97m5n+KYQQ4ocZzWbKCyucXYYQ7VJ1TSWrkueSsmUd+hOFGO06dGYHStdgeg6fxJA+k5zWFv+n1FTWsXt5BgeTM9HpFPpOjqL7qHCMZj0VNfW8sDyVz3acoWOAG+/P6kNiiM3ZJbcILfNvs4UwGXS8dUcvbnxrK7/4eDcLHkgixt/d2WU1Oe9gK0NmdqL/DdEc23GOQ8mZ9Dg8kT4ukyjukMHKqrl8mfYl4e7hTI2ZypToKQRaA51dthBCiCZiNMsURyGaU3VtFWs3fcGBzWtQ0gow1TXsVdbZj/jBYxk56EZMxpbbbt5ud3B4Yza7lp6iurKOuAFB9JvSAaunVvPujEJ+O+8AZ4sq+cWQDjw6uiMWY+tvzNdYJKD9BJur1n5/2ptbmfWB1n6/Pey/AGByMdBlWCiJQ0PIOlbEoQ1Z2A/ATeofsHSo55Cykf/sfZ3X971Ov6B+TImewsjwkbganbuPhhBCiMZlMJsloAnRxOrqa1m/9Sv2blyJ41iutoG0wYEj2pvYQSMZM/QWp+9V9lNUVSXj0Hm2fnmC4txKQjt7kXRjDH5h2gBHTb2df32dxtsbThLi5cLn9w+gb5S3k6tueSSgXYEwb1fen9WbW97ezr0f7WLu/f1xNbWfH52iKIR29ia0szflRdUc3pTN4U1ZxJ4cQXffsVR2zGJF4RyeynkKF4MLoyNGMyV6inSBFEKINkJG0IRoGnX1tWzYvpi9m1ZSdzQbS7UORa+iRnkSOXAo44bfhtWldczeyjtdytYFJ8g6VoxXoCsTH+xKRKLPheUwqTmlPPr5fo6eK2Nm3zCenhiPm7n9fJ6+GvJTuUJdQz35z8we3P/xbn49Zz9v/6wX+nbY9tPNy0K/KR3oPSGSk/vyOLQ+i4qt/kwyPop3FwPHvLex7MwCFp9cTKA1kMkdJjMpehIdbB2cXboQQohrZLRYqKuWJiFCNAa7vZ4NO5awe8Ny6o5mYanWoepU1EgPwgYMYtzIO/Cwejq7zCtWWlDF9kXppO3KxeJmZMitHYkfHIy+odGH3aHyzsZ0/rnmGDYXE+/P6s2IzgFOrrplk4B2FUbFB/DnyQn8efFh/rr0CM9OSXB2SU6jN+jo2CeQjn0CyT9bRkpyJsd35eK1txePRg5FSSxmvXER76W8x7uH3qWLbxcmdZjEuKhxeFtkKFsIIVoTo9mMw16Pvb4evUE+Oghxtez2ejbuWsqu5GXUpWZjqVZQdSqOCHdC+w9i3Mjbsbm3rs9H1RV17Fl5moPrz6IoCr3GRdBzbAQml4u/I06fr+B38w6w+3QRE7oE8vwNXfC2mpxYdesgv2Wv0l1JkZwprOS9zacI93blnkEtYzd2Z/ILc2f4z+JIujGGo9vOkbIxi+KlBnq53cpN/X7J6dADLM3/ihd3vsiru15lYMhAJnWYxLCwYVgMFmeXL4QQ4icYzdrv6vraGgloQlwhu72e5B2L2bNxBbVHs3GpUkCn4gh3I7hfEuNG3Y6Xh6+zy7xq9joHhzZksnt5BjVV9XQeEES/yVG4eV38TKeqKnN2nuX5ZUfQ6xT+dUt3pnYPlu7fV0h+y16DpyfEkVVUxV+XHSHY04VxidLBEMDsaqTbyDC6jggl82gRKRuyOLouH5Vg7kn8E169YLthLctOLWND5gasRiujI0YzqcMkWa8mhBAt2DcBra66GrOr1cnVCNFy1dXXkrx9EXs3rqT+WA6Wah3oVNRwN4L69mPcqDvwtvk7u8xrojpU0vbksn1hOmXnqwlP8GbAtBh8Qy/fUDqvtJrff3mQ5GP5DIzx4dWbuhHsKXvoXg0JaNdAp1P4v1u6M/Pd7fxm7j4+u68/vSK8nF1Wi6EoCmFx3oTFeVNWWM2Rzdkc3pxNxqFa/Hz78/KgaVT3zGXVuWWsOb2GhScWEuAawISoCUzsMJGOXh3lGxYhhGhBjGate7E0ChHiu2rrali/9Sv2bVqN4/g5zDUNoSzSg5B+SYwdcVurHCm71NnUQrZ9dZL8M2X4hrkx/I7uhMV9d0rmsoM5PL3wEFW1dp6dHM+dAyLRtcOeDddLAto1cjHpee+u3tz43638/KNdfPmrJDr4uf30HdsZd++LTUXS9+eTsiGLHQtPoTMoDOl1K/cOfJhUw16WnlrCx0c+5oPDHxBti2Zih4mMjxpPqHuos1+CEEK0exdG0GqkUYgQoG0evWbjPFK2rUdNy8dcq3VfdETaCOs/kLHDb2t1a8q+T97pUrZ9dZLMo0W4e1sYNSuOjn0DUb4Vukoq6/jT4hQW7c+mW6iNf8zoToy/fC6+VhLQroOPm5kP7+7Ljf/dyl0f7OTLXyXh7y5rqr6P3qAjtncAsb0DOJ9dzuGN2RzdnsPxHbn4hHrzqyFP8eepZtbnrGX5qeW8tu81Xtv3Gt39ujOxw0TGRI6R5iJCCOEkF0fQJKCJ9qu8soRVyXM5un0TupOFmOp1KAYHjigvIvoPZszwW1tV98UfU5xXyY7F6ZzYnYfFamTQzbEkDglBb/zucpTNaQU8Nv8A+eU1PDIqlgeHx2DUy7KV6yEB7TpF+lp5b1YfZr6znXs/3M3c+/tjlT0dfpRPsBtDbu1I/xs6kLYrl0Mbstjw2TGMC/R06tedfw6ZSLWthBWnVrAsfRkv7HiBl3e+TP/g/kyImsDwsOG4meRbGSGEaC4GyzcjaDLFUbQvhSV5rF4/lxM7t2HIKMFo16EzOlBjfYkZMIwxQ2/BxdJ21mVWlNSwe3kGRzZlozMo9J4QSY/R4Zd1ZvxGVa2dl1ce5cOtGUT7WXnnziS6hno2f9FtkCSJRtA9zJPXb+vBfbN388Cne/nfXb3lm4MrYLIYSBgcQvygYHJPlZKyIYvULTmkbMgiKNrG4CGTuHvCPZwsP8Gy9GWsPLWSpzY/hVlvZkjoEMZFjmNI6BDpBCmEEE3s4hRHCWii7cvOy2DN2rmc3rMbS1YVeoeCzuyA+ADiBo5ixMDpWExtq+lFTVU9+9ecYf/aszjqHMQPCqb3xEisNvP33v7A2WIenbef9PwKZiVF8sT4zliM+mauuu2SgNZIRsYF8MK0Ljy54BBPLTjEKzd1lUYXV0hRFAI72AjsYGPQzbGkbsvh8MYsvv7gCJvnpxE3IIh7hvyCR3o+woH8A6w4tYJVGatYc3oNrgZXRoSPYHzUeAYEDcCoNzr75QghRJtzoc1+tQQ00TadPHuEtV/P5dz+Q7icq0WHgs6qovQIpcegcQzuOxGjoe3t31VXa+fQ+kz2rjpNTWU9Mb386TelA54Brt9/e7uD19ed4PX1J/B3N/Ppz/sxMKZ1N0BpiSSgNaKZfcPJKanmtbVpBHm68NvRHZ1dUqtjcTPSY3Q43UeGaa36N2Wxf+1Z9q05Q1i8N4mDQ/h97z/weJ/H2Z27mxWnVrDm9BqWpi/FZrYxMnwkYyPH0jewLwadvL2FEKIxyBo00dY4HA72p25hy4ZFFKUcx3reoV1hA0NSNAOGTqFv1xHodG1zRpS93kHqlmx2Lc+gsqSW8AQf+k/tgF+4+w/e50ReOb+bt58DmSVM6xHCs1MSsLnIF+NNQT7BNrJHR8VyrqRKC2k2CzP7hju7pFZJ0SmExXsTFu9NeVENR7Zkk7olmxVvH8LVZiJ+YDAJg7rTP6k/z/R7hq3ZW1l+ajkrT61kQdoCvMxejIoYxdjIsfQO6I1eJ8PuQghxrWSKo2gL6upr2bx7OXs3r6Iy9Qyu5Q0znXz1mIfHM2T4dLp26u/cIpuYw6GStiuXnUvSKS2oJijGxtifJxIc6/mj95m9LYMXVxzFxaTnzdt7MqFLUPMV3Q5JQGtkiqLwwrQu5JbW8MzCFAI8zIzoHODsslo1Ny8zfSdF0Xt8BKdTznN4Uza7V2SwZ0UGEYk+JAwJYXDCEIaGDaW6vpotWVtYlbGKpelLmX98Pt4Wb0ZHjGZs5Fh6+veUsCaEEFfJaJERNNE6VVSVsXbTF+xat4Kt77+CuUaHXVFRQyx4De/OiOEziAzp5Owym5yqqpw6UMCOxekUZlfgG+bGpIe6EZ7g/aNLcnJKqnh8/kE2nyhgeCc/Xr6xK/4esva/qUlAawJGvY43b+/Jre9s58FP9zHn/v50D/N0dlmtnk6vI6qbH1Hd/CgtqOLI5myObM0h442DuHmbSRgUTFxSMCMjRjIyYiRV9VVsytzEqoxVLDqxiM+PfY6PxYdREaMYHTGaXgG9ZBqkEEJcAb3BiE6vlxE00Srk5J9hzfq5nN67B9OZcgx2BavBQX2kJyF9+jN62C34eLaPL89VVeV0ynl2LjlF/pkyPANcGfPzBGJ6+n9nL7Nv32/xgWz+uDCFeofK36Z1YWbfMOmv0Ezk02kTsZoNvD+rDzf+dyt3f7CTL36VRLRsZN1oPHxd6H9DNH0mR3FqfwGHN2WxY/Epdi7NILKLNqoWFufNmMgxjIkcQ2VdJRszN7L69OoLYc3b4s2I8BGMjhhNn8A+GHUyj1oIIX6I0WyRgCZarEPHd7B5w0LyD6bikleHDgXFRYWEQDr3H4ZB9WXsqPHOLrPZqKpK5tEidi5J51x6KR6+FkbcGUenfgHofqLTeHFlLU8vTGHZwRx6hnvyzxndifRtO1sJtAYS0JqQn7uZ2ff05aa3tnLne9pG1oE2GRZuTHq9jphe/sT08qc4t5IjW7I5ui2HUwcKcPe2ED8omLiBQVhtroyLGse4qHFU1lWyJXsLazLWsCx9GV8c/wJPsycjwkcwKnwU/YL6YdK3vU5NQghxPQxmM3XVMsVRtAy1dTVs3LGEA9vXUXHsDNbShiu8FIwDY+k7eDz9u42+0OQjOTnZabU2t+y0YnYsTic7rRg3LzPDbu9E5wFB6A0/3fAk+Vgev//iIIUVtTw+thO/GNIBg2wd1eyaJaApivIqMBmoBU4Cd6uqWtwcz+1skb5WPry7L7e8vY273t/JvF8OkI43TcQzwJWk6TH0m9yB9AP5HN6UzY7F6exceoqorr4kDA4mLM4bV6MroyNGMzpitLZmLXsLa06vYVXGKhakLcDN6MaQ0CGMihjFwOCBuBq/v9WsEEK0J0azWUbQhFPlF+WwdsN8Tu7Zge5UEaY6bT0ZQRY8BiYybNhNxEZ2cXaZTnPuVAk7F6dzNrUIVw8Tg2+JJX5QMIYr2J+ssraevy1P5ZPtZ4j1d+P9WX1IDLE1Q9Xi+zTXCNoa4ElVVesVRXkZeBL4QzM9t9Mlhth4587ezPpgJ/d9tJvZ9/aVzfyakN6oI7Z3ALG9A7RRtc3ZpG7LIX1/Pu7eFuIGBhGXFIyblxmLwcLI8JGMDB9Jrb2W7TnbWXtmLevOrGP5qeWY9WYGBg9kVMQohoQOcfZLE0IIp5EpjsIZDh3fwZZNi8k7dETbn0xVUEwO1Ggfwnv1Z+TQm/G2+Tu7TKc6d6qEXUszOHP4PBY3I0k3xpA4NASj6co+a+47U8Rv5x0g43wFPx8UxWNjO8nnVCdrloCmqurqS/64HbipOZ63JRkY48v/3dKdh+fs49dz9vHm7T1lyLgZeAa4knRjDP2maKNqRzZns3PJKXYtPUVEF1/iBwUTkeCNTq/DpDcxJHQIQ0KH8Mf+f2Rv7l6+PvO1FtjOrsOgGIgxx5B7NJdhYcMIsLaPBcZCCAFaQKuXLo6iiVVVV7B+20IO79xA9fGsi63wbaDvG0XPpDEM7D2uTW4afbXOpZewa9kpzhwuxGI1MmBaNIlDQzBZruzjfZ3dwX/WpvFG8kkCPSx89vP+DIj2aeKqxZVwxhq0e4DPnfC8TjepazAFZTU8u+QIf1yUwt+mdZFuOM3k0lG1kvxKjmzOIXVbDhkHC7B6molLCiIuKQgPXxcADDoDfYP60jeoL0/0fYKUghS+PvM1S48u5fkdz/P8judJ9ElkRPgIRoSPoIOtw/+zd9/hbZVnH8e/R9uyhqe893bsTGcPEnaAMNKy9yy0dC9eaEvpAlraAi2Ussree4adkL2Xndjx3ntva5z3DzmGQIAAjiXb9+e6dB3pWLZvJ8fy+el5zv3I/6UQYkLTm0wM9ff5ugwxAVXUFrF6zUtU796FvrobvVuDqlFRYwKwL8lh0eIzyUye7usy/ca3DWYAJU3d/PTZ3eyt7eQ7M2O5+fRsbCa5BMdfKKqqjs4XUpT3gcjDfOgmVVVfHX7OTUAesFL9gm+sKMo1wDUAERERs5555plRqc+fvHhgiNfLnJyeomdlmrwD5CuqR6W7DtpLVXrqvfsskRCUomCNBo3284Gru7ubXlMve/r2sKdvD5VDlQCE68KZap7K1ICpJBoT0SgyOirGRk9PDxaLdIgVR1/pqlcY7Owg+9zLvvK5clyKL+NyOymt2UF9RQHUtmLt9P697TN5cMZYCU3IICNxLibj6HUOnAjHZF+LSnOB95xFa4DQLIWQVNDqj/wNYo+q8n6li+cPDGHUwmVTjORFSs9AX1i2bNl2VVXzDvexUQtoX0VRlMuA7wHHqap6RG/B5eXlqdu2bTuqdfmCqqrc8OJent1WzR/OmMIl8xN9XdKk19Xaz/4N9RRuqKenfRCTRU/mvEiyFkYTEvXJH4jVq1ezdOnSkcdNfU2srl7Nh1UfsrlhMy6Pi2BjMItjF7M0bikLohcQqJfWtOLo+ewxKcTR8ubdf6O+pIir7n7wK58rx6X4rOr6Ej5a+xJVu3airerE4NTgUVT6HHpCs9OZt+gUZmYvGem6ONrG8zFZV9zBtrfKqd7fjilQz4wT47/2iBlAXUc/v3xhN+tLWjk208Ft38nFYZXu4r6iKMoXBrSx6uJ4MvAr4JgjDWcTmaIo/PmsHFp7h7j5tQJCAg2cNjXa12VNarbQAOauSGb2qUlU72tj3/o69nxYw673q4lKsZO1MJrUWZ+/CNlhdnBOxjmck3EO3UPdrK9dz+qa1ayuXs1rpa+h1+iZEzmHY+KOYWnsUqIsUWP/wwkhxCjQm0w4B6RJiDgyA0P9rNvyJnu3raG7sILAdu+AgGLyQFo48TPmsHTxSsKD5e/i4Rxcx2zbWxXUFXcQYP1mUxkPfq1XdtXyu1cLcHtUbl2Zy3mzZdFpfzZWY5r/BozAe8MHwyZVVa8do+/tl3RaDf++YAYXP7SZnz67C6tJzzHp4b4ua9LTaBQSckJJyAmlr2uIwk317F9fz4eP7WftcwewxHhoTOjCkWj93Aub1WAdWWvN5XGxs2knq6u9Ye0vm//CXzb/hYzgjJFGJLlhuWg10iVJCDE+6I0mXEPSJER8scKyXWzY8Dq1e/PR13Sjd3lHyVSHHuOydOYuWM6snGOO2ijZRKCqKpX5rWx7q4LG8i4Cg4wsOsfbLv9IuzJ+WnvvEL95JZ8399YzKyGYf5wzjYRQmdnj78aqi2PqWHyf8cak1/LgpbM57/5NXPv4dp64ai6zEoJ9XZYYZrYZmHliAjNOiKe+tJN96+o4sLWBF27fRkh0IFkLosiYG0mA9fPXEeo0OmZHzmZ25Gx+kfcLyrvKWVO9htXVq3k4/2Ee2PsAwcZgFsYsZEnsEhZEL8BulPVGhBD+S2804RwYRFVVeeddANDZ3caaja9SuH0Dg6X1mLu9+xWzClkRJM6Yx9KFZxIaJF2Pv4rqUSnb3cy2typoqe7BGmLimAsyyJofhVb/zQLtR8OLTnf0DfGrkzP43pIUtBr53R0P5KpAH7MH6Hnsijmcfd8GrnhkK89+bx6ZkTZflyU+RVEUolODiE4NQoluJDIgnX3r61n/QgkbXy4laWoYWQujicsOQXOYFz5FUUi2J5NsT+bynMvpHOxkQ90GPq75mHW163ij7A20ipZp4dNYEruExbGLSQtKkxMgIYRf0RuNqKoHt9OJziANriYjp2uIzTvfZ+fWD2kvKsXUOIRWVUY6LloXZDFv4ankpM2RUbIj5HZ7KN7ayI53qmiv78XuCODYS7JInxuB9hsux9Q76OLPb+3nqc1VZERYeeTy2UyJljeBxxMJaH4g3Grk8Svn8t37NnDxQ1t48doFxIeafV2WOAytQWHK4himLI6htbaH/RvqKdrcQOnOZgKDjGTOjyRzfhRBji/+/7Mb7SxPWs7ypOW4PW72tuzl45qPWVu7ljt33MmdO+4kwhzBophFLIxZyLyoeVgN1jH8KYUQ4vP0Jm8zAefggAS0SaSoYjcbNrxJ7d49aKu7MDiHQ0OwgnZ2AtkzF7Fk3goCA+Tv1NfhHHKzf309u96rorttgNAYCydcmU3qrIjDvtl7pLZXtvOz53ZR1dbHNUuS+dkJ6bLo9DgkAc1PxIWYeeLKuZz9341c9NBmXrh2Pg6bdNbxZ6ExFhadncb8s1Ko2NPC/g317FhVyfa3K4lKtZO1IIqUmY4vvZhXq9Ey3TGd6Y7p/Gjmj2jsbWR93XrW1a7j3Yp3ebH4xZHRtUUxi1gUs4iMkAxp4y+EGHM6gxHwBrQAq8z0mKjqm6v4eMOrlO/ZgbOi6ZOFogNU1NQwoqfOYvHC04mNSPJtoePUYJ+TvWtq2fNhNf3dTqJS7Cw5P52EnNBvNXNmyOXhrg8O8J/VpUTZA3j66nnMS5ZFp8crCWh+JC3CyiOXz+GCBzZxycNbePaa+djNsmigv9PqNKTMdJAy00FP+yBFm+vZv6GeDx8r5ONni0mdGU7WgiiiUoO+8sU3IjCClWkrWZm2EqfHyd7mvayrXce62nXcvfNu7t55N6GmUOZHz2dB9ALmR88nLCBsjH5SIcRkNjKCNiCNQiaSzu42Pt70GkW7NtFXWjvSbRGdB6ItWBdmMGf+cqZmzJNpi99Cb+cgez6sJn9NLUMDbuKnhDLr5ASi04K+9dc+0NjNT5/dRUFdF2fPiuV3K7KxyqLT45oEND8zPS6I+y/O44pHtnL5I1t44qq5mA3y3zReWIKNzDo5kZknJdBQ2sn+jfWUbGuicGMDtvAAsuZHkjEvCmvIV4+O6jV6ZkbMZGbETH4080e09LewoW4D62rXsaFuA2+UvQFAenD6SFib6ZiJSScjr0KI0ac3el9bpJPj+Nbb3836rW+xb+cGukoqMTU70aoKHo0KDgOGY1KYlncM82aciEFv9HW54157Qy+73q+maFMDHreHlFkOZp6UQHjct58S6vGoPLSunL+9W4TVqOP+i2dx4pTIUaha+Jqc+fuhRWlh3H3+dL7/5A6ufWIHD16Sh0En71qNJ4qiEJUaRFRqEIvPSad0ZxOFG+rZ/Fo5m18vJzYjmMx5kSTPcKA3Htnc8LCAME5POZ3TU07Ho3ooaitiQ90GNtZt5Mn9T/JIwSMYtUZmRcxiXtQ85kbNJTMkU6ZDCiFGhd44PMVR1kIbVwYG+9iw/R3yd6ylo7gcU9MQWo+CBxVCtWhnJ5A1cyGL5pyKLTDI1+VOGPWlnex8t5LyPS1otRoy50cy/fh4giJGp8dATXsfP39uN5vL2zghO4JbV+YSZpFAPVFIQPNTJ+dEcevKXH794l5++twu7j5vhrRGHaf0Ri2Z86LInBdFV0s/hZsaKNpUz/uP7Ef/9AFSZjnInBfp7RJ5hP/HGkVDVmgWWaFZXJl7JX3OPrY3bh8JbP/Y/g8AgoxBzI6czbyoecyLmkecVRamFEJ8MwdH0JyDEtD8Wf9ALxt3vEvBrvW0F5djbBxA51ZQUSFYgzIjltRpc1k091Rpfz/KVI9K+Z4Wdr1XRX1pJ0azjrzlieQujcVsG53GOqqq8sL2Gm55fR8Af/3uVM6eFSt/2ycYCWh+7NzZ8XT1e1ulBhq03LZy6rfq7CN8zxYWwJzTkph9SiL1pR3s39hA6Xbv6JotzETGXO8USHt4wNf6uma9mcWxi1kcuxiApr4mNtdvZnP9ZjbVb+K9yvcAiAqMYl7UPOZEzWF2xGwiAuWPsxDiyIyMoElA8yu9/d1s2LaK/bs20FFagbFxCJ1n+FwhSEHJjSJx6mwWzTuNiNAY3xY7Qbmcbg5sbmTne1V0NPZhDTGx+Nw0shZEH/EsmSPR0jPIjS/t5d19jcxJCuHvZ08jLkS6fk9EEtD83NVLkukedHH3B8WYDTpuXpEt75JMAIpGITotmOi0YJacm07ZziYKNzWw9a0Ktr5ZQVSqnYy5kaTOcmD8Bo1iHGYHK1JWsCJlBaqqUtlVyab6TWyu38z7Ve/zcsnLACTYEpgdOZs5kXOYHTlbGo4IIb7QJyNocg2aL7V1NrFh6yqK87fSVVZNQLMTreeTETLN9BgSc2excM4pRIbF+brcCa2va4j8j2vJX1NDf7eTsDgLJ145hZSZ4Wi+4RpmX+S9fY3830t76Op3cdMpWVy5KEnetJ/AJKCNAz89Po3eQRcPrSvHYtTxi5MyfF2SGEV6o5aMeVFkzIuiu22AA1saKNrUwOoni1j7bDGJU8PInBdJ3JSQb7RopaIoJNoTSbQncl7mebg9borai9jasJWtDVtZVb6KFw68AECyPZnZkbPJi8wjLyJPApsQYsQnXRxlBG0sVdeXsHHrKioKdjNQ2UBAuwcNCh5FRQnRop0VT2rubBbMWU54cJSvy50UWut62PNBNUWbG3G7PCTmhjLt+Hhi0r+6W/PX1T3g5I9v7OO5bTVkR9l48qrpZETKmnMTnQS0cUBRFH5zahZ9Qy7+/VEJgUYd1y1N8XVZ4iiwhphGukA2V3VTuKmB4q2NlO5oIsCqJy0vgox5kYTHW7/xHwGtRkt2aDbZodlcOuVSXB4XhW2FbGnYwpaGLbxW+hrPFj0LQKItkVkRs0Zu0Zbo0fxxhRDjyMgUR+nieNS43S52F25k9+611Bftx13TNrIOmapVwWHEsCiejKlzmT/zJOzWEB9XPHmoqkr1/jZ2v19N1b42dHoNmQuimHZsLMGRgUfle24qa+Xnz+2mvrOf65el8qPj0qRp3CQhAW2cUBSFP52ZS9+Qm9tXFRJo1HLJ/ERflyWOEkVRcCTYcCTYWPjdVKoK2ijaVE/+2lr2fFRDcKSZ9DmRpM+JwBb29a5X+yydRkdOWA45YTlckXMFTo+TwtZCtjduZ1vjtpEFs8F7DVteRJ63/b9jJkn2JJlyK8QkoZMujqOus7uNzTvfoyh/K+1lFegb+jA4h0/AjR6IsmCen0rutEXkTVuGyfDtXu/F1+ccclO8pZHdH1bTVteL2WZg7unJTFkSTYBldBp/fNaA080d7xTx0PpyEkLMPH/tAmYlBB+V7yX8kwS0cUSrUbjj7Gn0Dbn53asFmA06vjsr1tdliaNMq9WQNDWMpKlhDPQ6Kd3RxIEtjWx+rYzNr5URlWInfW4kqTMdmCzffmFKvUZPbnguueG5XJZzGW6Pm5KOErY1bmN743bW163n9bLXAbAb7cwIn8F0x3RmRswkOzQbo1ba/AoxEWk0WnR6gzQJ+YY8Hg+FZTvYuWsNNQf2MVjdTEC7G406/CaXHZSMCBwZ2cyauYzM5JmyMLQPdbcNkL+mhoJ1dQz2ugiNtXDcpVmk5UWg1R+9/5f82k5++uwuipt6uGhePDeekiXr4U5C8j8+zui1Gv51/gyuenQbv3phN2aDllNyZc75ZGEK1DNlcQxTFsfQ1dpP8dZGijY1sOapItY+e4CEnFDS50SSmBuKzjA6naO0Gi0ZIRlkhGRwYdaFqKpKRVcFu5p2sbNpJzubdrK6ZjXgDXc5YTlMd0xnWvg0poVPk+vYhJhAdEajNAk5Qm2dTWze8T4l+7bTXlGFrqEX45D3xF7VeiDChG5eAqlTZjF31ok4QmQKua+pqkp9SSd7PqymbFczAMnTw5l6bCxRqaN/fdmnudwe/rO6lLs+KCbUYuDRK+ZwTHr4Uft+wr9JQBuHTHot918yi0se2sKPn9lJgF7LskyHr8sSY8wWGjByvVpLdQ9FWxoo3tJI+e4WDCYtyTPCSZ8dSUxG0Kh2k1IUhSR7Ekn2JM5KOwuAtoG2QwLb4/se53+e/wEQY4lhavjUkcCWEZyBXvvtR/qEEGNPbzThkhG0z+kf6GVHwcfsz99MU1kprrp2zF0qCsMn9DZQUsMJScsgd+oCpmUuQK87OtPjxNfncrop3trIno9qaKnuwWjWMf2EeHKOicEWevSnlZY29/Cz53azu7qDFdOi+eMZUwgyy/ExmUlAG6fMBh0PXz6bCx7YxLVPbOfhy2azMFVGKiYjRVEIj7cSHm9lwcpUagvbObCtkbIdTRRubCDAZiBtloO0ORFEJNqOyjuAIaYQjo0/lmPjjwVg0D3I/tb97G7eze7m3Wxv3M7b5W8DYNQayQ7NJjcsl9ywXHLCcoixxMi1bEKMA3oZQcPpGiL/wFYKCjZSW7yfwdpmTG1utAfXHjN6UCICMUyLIzV7JrNnHCfdFf1UV0s/+Wtq2b+hnoFeJyHRgSy9MIP0uZHoR2kWypfxeFQe21jBbasKMeq03H3+DE6fJiOpQgLauGYz6Xnsirmcf/8mrnp0G49eMYc5SdLRaTLTaBTiskOIyw7hmPPTqcxvpXhLIwVr69jzUQ22MBPpcyJJy4sgJProdJ0Cbwib7pjOdMf0kX0NvQ0jgW13826eKXyGxzyPARBsDCYnLGcksOWE5RBskguihfA3epNpUl2DdjCM7du3ibrSIvprmjC0DqF3f2qqYrgR7axY4tOnMGPaMSTHZcu1Y37M41GpKmglf00tlQWtKIpC8rQwco6JISYjeMzeLKzr6OeXL+xmfUkrSzPCuf07U4mwmcbkewv/JwFtnAsJNPDEVXM57/6NXP6/LTx25Vzp9CMA0Om1pMxwkDLDwWC/i7KdzRRvbWD72xVse6uC0JhAUvMiSMtzYA83H/V6IgMjiQyM5KTEkwBwup0UdxST35LP3pa95Lfks652nXexVbxTIw8uB5Adms2U0CnYjfajXqcQ4ovpjRM3oA0M9rG7cCNFRdtpKCtmoLb5kDDm0aoQqkczNYaIlAyys+eSmzFXpiqOE65BlR3vVlLwcS1dLQOYbQbyTklkyqJoLMFjF4xUVeXlnbXc/FoBbo/KX87K5fw5cTKLRBxCAtoEEG418tTV8zj3vxu57OEtPHn1XKbGBvm6LOFHjAE6shZEkbUgit7OQUp3NFOyrZHNr5ax+dUyHAlW0mZHkDrLMWZ/qPRa/Uj4OifjHAB6nb3sa93H3pa9FLQUsK91H+9VvjfyOYeEtpBsMkMzCTHJqLEQY0VvNNLX1eXrMr61ts4mdhWsp+TALloqy3HVt2Pq8KAd7qjo0XpQQySMjXeqqtJQ1kXB2loObFFRPaVEpwUx78wUkmeEox3F67OPRGvPIDe+vJd3ChqZnRjMHWdPIyH06M1mEeOXBLQJIsJm8oa0+zdy0YObefqaeUyJltEG8XmBdiNTl8UydVks3W0DlGxronhbI+tfKGH9CyVEpdpJy4sgeUY4gfaxbZkfqA9kduRsZkfOHtnXOdjJ/rb97Gvdd9jQ5ghwkBGSQWZI5sg2zhqHRpEpRkKMNm8Xx/EzguZ2u9hftpPCoq3UlB2gu7YOmnsx935qtMLogbAAtOmRxCZnkpU1m6yUmRLGxrHBPidFmxsoWFtHW10vepOWoGQ46fw5hMZYfFLTuwUN3PjyXrr6Xfzf8kyuWpyMViOjZuLwJKBNINFBATx1lXck7aIHN/PMNfPJiLT6uizhx6whJmacGM+ME+PpaOyjZHsjB7Y28fEzB/j42QPEpAWROstB8gwHZptvTlbsRjvzouYxL2reyL7OwU4K2wopbCukqK2IwvZCNtRtwK26ATDrzKQHp5MenE5acBrpwemkBqdiM9h88jMIMVH46xRHj8dDbWMZBQe2UlW6j9baapwN7RjbXejcw6NiqKg2BU2kDUNsDPEp2UydsoCE6HS5ZmwCUFWVxvIuCj6upWR7Ey6nB0eClWUXZZKa52DDpnU+CWddA05ueW0fL+6oITvKxhNXTSMzUv4WiS8nAW2CiQsxj4ykXfjgJp65Zj6pDt+8WyTGl6AIM3mnJJF3ShKtdT2Ubm+iZHsTa54+wMfPHCA6PZjUWQ5SZoQTYPXtO8t2o525UXOZGzV3ZN+ge5DSjlJvYBsOb2+Xv81zB54beU5kYKQ3tAWlkRacRmpQKon2RFlcW4gj5G2z79sujvXNVRQUbaGybB8tNZUMNrahaxscWWMMQDV4INSIZloMYQkppGVMZ2rGPCxmmVky0Qz0OjmwpZF962ppre1Fb9SSMS+SKYtjCI/37ZvU60ta+OXzu2noGuCHx6byw2PTMOjkzQDx1SSgTUCJYYE8edU8zrt/Exc8sInnvjefxDCZ4yyOXGi0hdBoC7NPS6KtrpeSg2HtqSI+fuYAMelBpMx0kDw93Gcja591sH1/dmj2yD5VVWnsa+RA+wGK24u9245iNtRtwOVxAaBRNMRb40m2J5MSlDJyS7InSXAT4jO8XRyPfkDzeDyUVe+jqGQnNZVFtNfWMtjcjr596NAgpvOgButR0h1YY+OJT85iSsYcYhxJMio2gakelZoD7exfX0/ZzmbcLg/h8VaWXphB2uwIDCbfnt72D7m57e39PLqxkuTwQF68bgEz4qWBmzhyEtAmqFSHhSevmsv5D3hD2rPfm09cyNHv1CcmFkVRCI2xEBpjYc6KJFpreynZ3kjpjmbWPFXEmqeLiE4NImVmOMnTHViC/SvQKIoy0j1ySeySkf1Ot5PyrnLKOsoo6SihrNO7XVOzZmSapEbREGOJIcmeRKItkUR7Ikm2JBLtiYSaQqXjlpiU9EYjrqFBVI8HZRQCUFtnE4UlO6mo3EdTTSW9jU2427oxdLpHuicCqHoPSrABJc1BYHQMMQlpZGfOISkmU4LYJNLdNkDhxnr2b6inu3UAo1lH9sIoshZG+3y07KDtle384vndlLf0cvnCRH51UiYBY7CmmphYJKBNYBmRVp640hvSzrt/E89cM09CmvjGFEUhLNZCWKyFuacn01bXS+mOJkp3NrP22WLWPltMZLLdG9ZmhGMLDfB1yV9Ir9WPXKP2aU63k8quSko6SyjtKKW8s5yKzgo2129m0P3JqIHVYB0Ja/HWeOJt8SNbq8E/ThKEOBr0Rm+XV+fQIAbTkf2Ot3U2UVS2i+rqAzTVVdHd1MhQSye6jiFMg5+EKw8qnkAg2IQmIYTg2HjiEjPJSssjOjxBgtgk5XZ6KN/Twv71dVTtbwMVYjODmXdGMsnTw9H5SfgZdLm56/1i7ltTSpQ9gKeunsuClDBflyXGKQloE1x2tI0nr5rLhQ9ulpAmRs2hI2vJtNX3UrbTG9YOdoMMj7eSPCOc5OnhhESNjym2eq2e1OBUUoNTD9nvUT009DZQ0VlBeVe5N7h1eYPba6WvHfLcYGMwcbY4EqwJxNniiLXEEmuNJdYSS1hAmIy8iXFNZ/SOkjsHBkYCmtM1RGXtAcqr91NfV057Yx0tVdWseeGf6Dudh0xJBPAYPSh2A5qUcEyRkUTGJZOcmENm8nQCTOPjtUIcXaqq0ljRRdHGBoq3NTLY58ISbCRveSJZC6KwhfnXG4D76rr42XO7KGzo5ty8OH5zWhZWk97XZYlxTALaJJATY5eQJo6qkKhAQqK8DUY6mvoo29lM2a7mkXXWgiPNJE0PJ2VGOOHx1nEXUjSKhmhLNNGWaBbELDjkYwOuAaq7q6nqrqKqq2pku7VxK6+XvX7Ic41aIzGWGGIsMcRaY0fuRwVGEWWJItgYPO7+bcTE5/Q4ae5rpr63nsKuQgD+dcePGOrtRekcxNQHGvWT41ZFxRCgogaZUNKDCYiIxBEdT0J8FqmJuQTbZFRBHF5P+wBFmxso2tRAe0MfWr2G5OnhZM6LJDYrBI2ftaV3uT3ct6aUuz4oJshs4KFL8zguK8LXZYkJQALaJCEhTYyVIIeZmSclMPOkBHraBynf7Q1rO9+tYseqSizBRpKnh5M0PZzoVDuaMV4odLSZdCbSgr1dIT9rwDVAXW8dNd011PbUUttdS02P9/7Opp30OHsO/VpaE5GBkSOBLSowisjASCLMEUSYI3CYHVgM0pVVjB6Xx0VLfwtNfU009TXR2NdIY18jDT0N1PfWU99bT3N/Mx7VA0B4u4GTlUg8Va1g1aNE2dGGhhAcEUVEdCLxsemkxGWzedNWli5d6tsfTowLzkE3ZbuaKdpUT3VhO6gQlWpn2UWZpMxyYAzwz1PVkqYefv7cLnbXdLJiWjR/OH0KwYH+0TRLjH/+edSLo0JCmhhrlmAjuUtjyV0ay0CPk4q9LZTubKZgXR17PqrBaNaRkBtK0tRw4qeE+Lzz1mgz6Uwk25NJtid/7mOqqtI11EVdT93IiXB9T/3I/Y9rPqalv+Vzn2fWmYkI9Ia1CHME/e391O6vJSwgjPCAcMICwggLCMOsl9/tyczpdtI60Eprfyst/S009zfT0t9ySBhr6muidaB1JHwdpNfoR94omBs11/uGwfAt0hKJ4zoHFqO8USC+OY/bQ3VhOwe2NFC2qwXXoBtrqIm8UxLJnBeJPdx/X788HpWH15fzt3eKMBu0/PuCGZw2NdrXZYkJZmKdDYmvJCFN+IrJoidzfhSZ86NwDrqp3tdG+e5mKva2cmBzIxqdQmxGCEnTwkiaFkag3b86Qo42RVGwG+3YjXayQrMO+5wh9xCNvd4RjYOjG58e5djSsIWm3ibe2/Le5z7XrDOPhLUQUwjBpmCCTcGEmEI+eWwMJjQgFLvRjl4j10v4M6fHSddgF52DnbQNtNE20Eb7QDttg2209bfRPtjufTzQRmt/K+2D7Yf9OjaDbSTcpwen4zA7Rh4fvB9sCkajjO+RbeF/Dl5XdmBLIyXbGunvdmI060ifHUH6nAiiU4NQ/GwK42dVtfbxixd2s6W8jeOzHPxlZS4Oq8nXZYkJSALaJCQhTfia3qj1NhCZEY7H7aGhrJOyXS2U725mzVOtrHmqCEeijaSpoSTkhhEWa5mU12YZtAbibHHE2eK+8DkffvQh0+dPHxkdOeTW10LLQAvlneXsaNpBx2DH50ZLDgrUB2I3eAOjzWjDbrATZAzyPjbYsBgsWAwWrHrrIVuL3kKALmBS/v98Haqq0u/qp8fZQ89QD93ObrqHuukZ6qFrqGtkf9eQN4R1DnbSMdgx8viz02E/zWawjQTvBFsCsyJmERoQ6g3opjDCzeEjQd2glSlYYmy1N/RyYGsjB7Y00tXcj1anIXFqKOlzIkmYEopW7/9vBqiqylNbqvjzm/vRKgp3nD2N78yMkdc9cdRIQJukJKQJf6HRaohOCyY6LZiF302lra6X8t0tVOxtYfPr5Wx+rRxLsJGE3DASc0OJzQxGp/ePtsr+QKNoRk7OP7tswGe5PW46hzpHRloObjsGO+gc7DwkHBT3FY/cP7g23BfRKlrMOjNm/fBN96nt8H2TzoRBa8CkNWHUGjHpvNuD9w0aA3qNHr1Wj16jR6fReR9rPnmsUTQjN62iRaPRoGH4sebQY0JV1UMfo6KqKi7Vhcfjwa26catuPKoHl8c1snV6nDg9TobcQyP3nW4nQ54hhtxDDLoHGXANMOAeYMA18LnHfa4++px99Dp76Xf10+vsHdmncmhNh/t3tBqsI8E43BxOalDqyEir3egNzTL6KfxdZ3M/JdsbKd7WRGtNDygQmxFM3vIEkmf473Vlh1PX0c+vX9zD2uIWFqWG8dfvTiU6yL+6SIqJZ/z8hohR9+mQdu5/N/LU1fNIDJMWx8J3Pt2+P++URPq6hqjMb6FiTytFmxso+LgWnUFDbGYIibmhJOSE+d3i2P5Mq9GOhLkUUo7oc1RVpc/VNzLa0+McHvEZvt891E2Ps4d+Vz99zr6RMNLn6qOpr2kkpAy4Bxh0DTLkGTrKP+XYMmlNI2HTpDONBNKwgDAC9YGfC6xWgxWL3oLVYB25HXwsI5FiPOtuG6BkWxMl2xtpquwGICLJxqKz00iZ6Rh3r9WqqvL89hr++Po+3KrKH8+YwoVzE/yuk6SYmCSgTXI5MXaeunouFz+0hXOGQ1qqQy7+Fv7BbDOQtSCarAXRuJxuag90ULmnhfK9LVTsaQGKCI21kJATSkJOKJFJtnHfFdLfKIpCoD6QQH0gjML7Nx7Vw6B7kEHXoDe0DY9AOT3OT0aw3M6R0atPj2p5VA8e1TMy8uX2uFFRRx5/rnYOPZHSKtqR0baD9w+OzGkVLTqNzjuSp9Ufcv/g6J5BaxgJYgdH/SRQicmsp32A0h3NlGxvpKGsC4DweCvzV6aQOsuBLXR8jjQ1dg1w40t7+aCwiTlJIdzx3WnEh8osIzF2JKAJpkTbefrqecPTHTfy5FXzyIi0+rosIQ6h02tJmBJKwpRQFp+XTltdL5X5rVTmt4608DeadcRnh5CQE0pcdihmm1xv4280ioYAXQABuvF54ibEZNfZ3EfpjmZKdzbTVOENZaExFuaekUzqLAdBjvEbZFRV5dVdddz8WgEDTje/PS2byxckyqiZGHMS0AQAGZFWnrlmHhc8sInz7t/IE1fNZUq03ddlCXFYn54KOfOkBAb7nFTvb6eywBvYirc1gQKOeCtx2SHET5HRNSGE+Kba6nop3dlE6c5m7zVleEfK5p6RTMqMcIIjx//lES09g9z08l7eKWhkRnwQfz97GsnhMqNI+IYENDEi1WHhue/N54IHNnHBA5t5/Mo5TI0N8nVZQnwlo1lP6iwHqbMcqB6VlpoeKvNbqNrXxo53qtj+diUGk5bYrBDis0OIyw4Zt1NvhBDiaFM9Ko2VXZTvbqF8VzPtDX0ARCbbWfjdVJKnh2MLmzivoW/uqee3r+bTM+DihuWZXL04Ga2MmgkfkoAmDpEYFsiz35vP+Q9s4sIHNvPIFXOYlRDs67KEOGKKRiE83kp4vJW8U5IY7HNSU9ROVUEbVftaKdvZDEBwpJm4rBDiskKITg+acItkCyHE1+FyuqkpbKd8j/ca377OIRSNQnSandylsSRPDycwaHw1+vgqrT2D/O7VAt7cW09ujJ2/nzON9Ai5xEP4npyRiM+JCzGPjKRd8tBmHr5sNnOTQ31dlhDfiNGsJ2WGg5QZDlRVpb2hj+p9bVQVtLJvXR17PqpBo1GISLaNBDZHglWmQwohJryBHieV+S2U726hcl8brkE3eqOW+CkhJE0LJyEnFFPgxFzG4e299fzmlXy6Bpz88qQMvrckGZ287gs/IQFNHFZ0UADPDoe0y/63lQcvzWNhapivyxLiW1EUhZCoQEKiApl2XBwup5uG0k6q97dTvb+NLW+Us+X1cgwmLTEZwcRmhhCbEUxwlFm69Qkhxj1VVWmt7aFibyuVe1tpLO9EVcFsN5AxJ4KkaeHEZgSPi8Wjv6n23iF+91oBr++uIyfGxpNnzyUz0ubrsoQ4hAQ08YUibCaeuWY+Fz24mcsf2cp9F83k2MwIX5clxKjR6bXeEJYZwvyzUhjo8U6HrN7fRvX+Nsp3twAQYDMQmxFMbEYwMRnB2MMnzrUXQoiJzTnopqawjYr8VqryW+lpHwS8TT5mLU8kMTcMR4IVZRJcc/VOQQM3vZxPR98QPzshneuWpqCXUTPhhySgiS8VbjXyzDXzuPR/W7jmse3889zprJgW7euyhDgqTJZPNRtRVbpaBqg90E5NYTu1Re0Ub20EwBpiIibTG9ii04Kwhph8XLkQQnipqkpbfa93Kve+NuoOdOB2edCbtMRlhTD7NO+6kYH2iXU92Zdp7x3ivt0DbKrfTnaUjceumEN2tIyaCf8lAU18peBAA09eNZcrH9nGj57ZSd+Qi3Nnx/u6LCGOKkVRsIcHYA8PIHth9Mj1a7VF7dQUtVO+q5nCDfUA2MJMRKcFEZ0WTEx6ENZQk0yJFEKMmYEeJ9WF3kBWva+N3g7vKFlwpJmcY2JIyA0lOjUIrW7yjRa9W9DATa/k09bj5ifHp/GDZakyaib8ngQ0cUSsJj2PXjGHa5/Yzq9f3EvPoJsrFyX5uiwhxsynr1/LXRrrbedf20PdgQ7qijuo2NNK4cYGACzBRqLTg4hJCyYq1U5QhFzDJoQYPW6nh4ayzuEOta00VXWDCkazjtjMT5YTmcyj++29Q/z+9QJe3VVHVpSN63MVLj0+3ddlCXFEJKCJIxZg0PLAJXn8+Jmd/PGNffQMuPjRcaly4ikmJUWjEB5nJTzOyrTj4lA93mlFdcUd1B7ooHpfGwc2e6dEBlj1RKUEEZVqJyoliLB4C1p5B1cIcYQ8HpXmqm5qCtuoLWqnvqQTl9ODokBEko3ZpyYRnx2CI9GGZhJcS/ZVVuU38JtX9tLR5+Qnx6fx/aWpbFj3sa/LEuKISUATX4tBp+Ff58/ghpf28s/3D9A75OL/lmdKSBOTnqJRCI2xEBpj8Y6wqSodjX3Ul3RSX9JBXWknZbu8a7Dp9Boikm1EpQQRmWInMsmG0TwxW1kLIb6+g2/4jFwDe6CDoX4XACHRgWQvjvZeA5sejDFATuUOausd4ubhDo3ea83myrVmYlyS32rxtem0Gv76nalYjDru/7iM7gEXfzozB628ayfECEVRCI4MJDgykOxF3sY6vZ2D3sBW2kF9SSfb365AVb3PD440e8Nasp3IJDvBkeZJ0VVNCAEet4eWmh7qir1TputKOhjs9QYyW5iJ1JnhxGaGEJMRjNlm8HG1/umtvfX8dnhdM+nQKMY7CWjiG9FoFG5ekU2gUcs9H5XSO+ji7+dMkxdDIb5EoN040iUSYGjARVNFFw1lXTSUe0fY9q/3Nh4xmnVEJNqISLIRkWTHkWglwCInZkJMBC6nm+bKbupKOqgr9r5p4xxwA2ALDyB5Wvhw46EgbGGyrMeXaekZ5ObXCnhzTz05MTae+O5csqJk1EyMbxLQxDemKAq/PCkTi1HP7asK6Rpwcu+FMzEb5LAS4kgYTLqRddiAkWmRBwNbY1knW9+qgOFRNluYCUeijYhEG45EG+HxVt8VL4Q4Yn1dQzSUeoNYQ1knTVXdeFzeX+zgSDPpcyKJTrMTnRqMJXjytL//NlRV5fU99fz+tQK6B5z84sR0vneMjJqJiUHOpMW3dt3SFILMem56eS8XPbiZhy+bTZBZ3ukX4uv69LTIrAVRgHeUrbmqm8aKruHRtk5KtjV5n69RMNhUPFX7CY+3Eh5vJSzWgs6g9eWPIcSk5nZ7aKvtpbG8k4ayLupLO+hqGQBAq9PgSLAybVncyJRmmbL49TV1DXDTK/m8t6+RabF2/nb2PNIj5A0rMXFIQBOj4vw58QSb9fzo6V2c89+NPHbFXCLtk7e9rxCjxWDSEZMeTEx68Mi+vq4hmiq6aKzoonBHBeV7Wtg/vCabolEIiTJ7O0wmWAmPtxEaE4jBJC/3Qow2VVXpbO4f+X1squiiuboHt9MDQIDNQFSynZxjYolKsRMeZ0WrlxGeb0pVVV7YXsMf39jHoMvDjadkcsXCJHQyaiYmGPmLLUbNyTlRPHK5nqsf28Z3/rOBx6+cQ3K4xddlCTHhmG0GEqeGkTg1jH5bFcccs4ie9kGaq7ppruqmqbKbyoJWCjd512VDAXt4AGGx3hG2sDgLYbEWAoOM0oFViCOkqirdrQMjv2fNVd00VnaNNPPQ6TWEJ1jJOSbGe/1ook0WrR9FtR393PjSXtYcaGZ2YjC3f2eqnGOICUsCmhhVC1LDeOaa+Vz2vy2cfd9GHrl8Drmxdl+XJcSEpigK1hAT1hATydPDAe/JZG/HEM1VXbTU9NBS00NzdTelO5pGPs8UqCc01kJYjIWQmEBCor0Lcctom5jsPB6VzqY+mqu7aa7qobmqm5bqbgb7vGHs4Eh18vTwkWY+IVGBaGQkZ9SpqspTW6q49a1C3B6V36/I5pL5ibLem5jQ5K+wGHW5sXaev3Y+Fz+0hfMf2MT9l8xiQUqYr8sSYlJRFAVLsBFLcDhJ08JH9g/1u2it7RkJbS3V3RSsrcU1PCULvM1IQqIthEQHEhrtDW5BDrNc2yYmpIEeJy21PbQevNX00FbXO/I7odVpCI0JJGWWwzt1ON5KaEwgOr38Phxtla293PDiXjaWtbIgJZTbVk4lPtTs67KEOOokoImjIjncwovXLeCShzdz2cNbufv86ZycE+XrsoSY9AwBOqJSg4hKDRrZp3pUulr7aa3tpa2ul7a6HlrreqnKb8XjGW4hqYAt1DTcxMRMcFQgwRHerSlQFtkW/m+w30V7fS9t9b20N/TRNhzIejuHRp5jsugJi7UwZXEMobGBhMfbCI4yo5WRsTHl9qj8b305d7xbhF6j4S9n5XL+nDiZLiomDQlo4qiJtJt47nvzueKRrXz/yR388cwcLpyb4OuyhBCfoWgU7OFm7OHmkSmSAG6Xh47GPu8JbX0v7Y19tNf3UVPYjtv1yYhbgFVPkMOMPcJMkCMAe7iZoAgzdkcAehl1E2NIVVX6uobobOqjrb7vk0BW33tIENPqNARFmonNCiE0xkJoTCChMRbMNoOEAB8raujmVy/uYXd1B8dnOfjTmbnSdExMOmMa0BRF+TlwBxCuqmrLWH5v4RtBZgNPXDWXHzy5g5tezqe+Y4Cfn5gufwCFGAe8U7sshMYceiG+x6PS3dpPe4M3sLU39tLZ1E9VfiuFXUOHPDcwyEhQRAD2sABs4QHYQgOwhQVgCzdhCtTLa4H42lRVZaDXSWdTPx2NfXQ09XnvD2+dg+6R5+qNWoKHg1hIVKB35DfSjC0sQK5h8jNDLg/3ri7hno9KsJr03H3+DFZMjZLXCDEpjVlAUxQlDjgRqBqr7yn8g9mg44FL8vjNK/n8+6MS6jsHuO07ubKYpBDjlOZTI26JuYd+bGjA9amT5T46mvrpbOqjfG8r/Z8Jb3qT1hvWQk3YwgKwhpiwhBhHGp6YLBLgJivnoJuu1n66Wwboau2nq3l4O/zYOfBJCFM0CrZQE3aHmejUoJHR2+DIQCzB0ql0PNhd3cGvXthDUWM3Z0yP5uYVUwgJlPXhxOQ1liNo/wR+Bbw6ht9T+AmdVsOtK73TFO58v5jmnkHuvXAmFqPMshViIjGYdCOLZn+Wc9BNV0v/8G1g5H5HYx/V+9twDXkOeb5Wr/GGtmAjlhATliAjgXYDgUHGkVuA1SAjIeOM2+2ht2OQnrZBetoH6GkfpKdtgO72Tx4P9DgP+RydXoM1LABbmIno9CBsoSaCHN6ptNZQE1qdvOE3HvUNufjnewd4aF05DquJhy7N47isCF+XJYTPjcnZsaIoZwC1qqrulneyJi9FUfjJ8elE2U3c+HI+592/kYcvm43DKnPLhZgM9EbtYadMgnfa2mCvi+62AbrbBuhpH6C7bfjEvW2A6oJW+rqGUNVDP09RvOvCBQYZMdsMBNgMmK2f35ptBoxmHYqEuaNC9agM9Dnp73Yy0DNEZ5XK7g+q6esapLdziL6uIfo6vfc/G77A27zG23XUhCPRhjXYhC3MO7JqCwsgwCqjqRPNuuIW/u/lPVS39XPB3HhuWJ6JzSQNh4QAUNTP/rX7pl9IUd4HIg/zoZuAG4ETVVXtVBSlAsj7omvQFEW5BrgGICIiYtYzzzwzKvUJ/7KrycW9uwexGRR+PstElGV8vPvZ09ODxSILYwr/MZmOSdWj4hoEVz84+4a3/erwFtwD4BoA1yBwuD9tCmgNwzcj6Ia33seKd6sHjd67T6P/5LFGx6QICKpHxeMC99Cnbk7wjDxWcTuH/60HwT04vB3isP/migZ0puFbwMGtgj4A9GbQmb1brX7i/9sKr54hlWeKhlhX6yLSrHB5jpGMkKPfTGgyvVaK8WHZsmXbVVXNO9zHRi2gfRFFUXKBD4C+4V2xQB0wR1XVhi/73Ly8PHXbtm1HtT7hO7urO7jika14VJUHL53NrIRgX5f0lVavXs3SpUt9XYYQI+SY/LyDozl9XUP0dzvp7/KO4Az0OhnocXq3B2/Djz87vfKzFI2CwaRFb/TedIbP3Ddp0Ru0aPUadHoNWp2CVqdFq1fQ6jRo9RrvVqtB0Xi/nkareLeaT22HQ6B6MO185k+0qoLH7cHjUVHdKh63isdzcOvB41ZxOz24nJ7PbN0jj12DbpyDboYGvFvnoGvksdv51f8ORrOOAIsek0VPgNVAwPDWFKgnwKonwGKg4MBujjl+ISazXkYtBeAdJX9jTz23vF5AR5+Ta49J4fpjUzGN0Xpy8lop/I2iKF8Y0I76FEdVVfcCjk8VU8GXjKCJyWNaXBAvXreAS/+3hQse2MTd58/gpCmHG4QVQogjp2gUAiwGAixH3mTANeRmsM/FYL+LoeHb4Ge2Q/1unEPukYDjHHTT1zWEa+iTx26nB5fLc/gRPB/RaBVvaBy+6Y069EYtBpOWAKveGy6NOgxGb9A0mHQYzToMATpMgTqMZj2GAO8+vVF7RCOJpU3K1/r3FxNbfWc/v30ln/f3NzE11s5jV8wlO9rm67KE8FvSoUH4VGJYIC9et4ArH93GtU9s56ZTsrhyUdKkmEokhPAfOoN3JCwwyPitv5aqeke13E4PbpcHt1PF7XLjcnq8UwjdKqrHu1yB6vHg8eAdDfOofHpWy8jr4KEbNFoFjVbzyQic1jv65t3vHbn7dCCTJirCVzwelSc3V3L7qiJcHg+/OTWLyxYkopMuzkJ8qTEPaKqqJo719xT+Lcxi5Jmr5/GTZ3fypzf3U9nax80rsuUFXAgxLimKglaroJXXMDGJHWjs5v9e2sv2ynYWpYbxl7NyiQ81+7osIcYFGUETfiHAoOU/F87itlWF3P9xGTXtffzrAmnDL4QQQownA04393xUwn1rSrEYdfzjnGmcNSNGZsYI8TXI2a/wGxqNwo2nZBEfYubm1wo4+76NPHxZHlH2AF+XJoQQQoivsLG0lRtf3kt5Sy8rZ8Rw06lZhFq+/bRhISYbmX8h/M5F8xJ4+LLZVLf1ceY968mv7fR1SUIIIYT4Ah19Q/z6hT2c/8Am3B6Vx6+cwz/OnS7hTIhvSAKa8EvHpIfzwnXz0SoK5/x3Ix/sb/R1SUIIIYT4FFVVeW13Hcf/Yw0v7Kjh2mNSeOcnS1icFu7r0oQY1ySgCb+VGWnjlR8sJCXcwtWPbeOR9eUc7XX7hBBCCPHVqlr7uPR/W/nR0zuJDgrgtesXcsPyTAIMY7OumRATmVyDJvyaw2bi2e/N48fP7OL3r++juKmH358+Bb10RxNCCCHGnNPt4YG1Zdz1fjE6jcLNK7K5ZH4iWlnOQYhRIwFN+D2zQcd9F83ijneL+M/qUsqae7n3wpkEB8oiqEIIIcRY2V7Zxo0v5VPU2M3JUyK5+fRsaeQlxFEgAU2MC1qNwq9PziTNYeGGF/dy5r3reejSPFIdVl+XJoQQQkxonX1ObltVyNNbqogJCuDBS/I4PjvC12UJMWHJPDExrqycGcvT18yjd9DNWfdsYHVRk69LEkIIISYkVVV5dVctx/1jNc9tq+bqxUm8+9MlEs6EOMokoIlxZ1ZCMK9ev5C4EDNXPLKVh9ZJ8xAhhBBiNJU193DxQ1v48TO7iAk289r1C7np1GwCjTL5SoijTX7LxLgUExTAC9fN52fP7uaPb+zjQEM3fzwzB4NO3nMQQgghvqkBp5t7V5dy3+pSjDoNfzhjChfOTZAmIEKMIQloYtwyG3Tce+FM7nz/AHd/WEJ5Sy/3XjSTMFkYUwghhPja1hxo5nev5lPZ2scZ06O56dQsHFaTr8sSYtKR4QYxrmk0Cj87MYO7z5/BntoOVvxrHXtqOnxdlhBCCDFuNHQO8IMnd3Dpw1vQKgpPXjWXu86bIeFMCB+RgCYmhNOnRfPCtQvQKArfvW8jL2yv8XVJQgghhF9zuT08tK6c4/+xhvf2N/KzE9J5+yeLWZga5uvShJjUZIqjmDByYuy8/sNFXP/UDn7x/G7yazu56dQsWdRaCCGE+IztlW385pUC9td3cUx6OH84YwoJoYG+LksIgQQ0McGEBBp47Io53PZ2IQ+uK2dffRf3XijXpQkhhBAALT2D3P52Ic9vryHKbuLeC2eyPCcSRZEmIEL4CwloYsLRaTX85rRscmPt/PrFPaz41zruu2gW0+KCfF2aEEII4RNuj8pTW6r426pC+obcXHtMCj88NlXa5gvhh+S3UkxYZ0yPISXcwvce387Z/93In8/M4ey8OF+XJYQQQoypnVXt/PbVfPJru5ifHMofz5xCqsPq67KEEF9AApqY0D59XdovX9jD7poOfntaNkad1telCSGEEEdVW+8Qf3unkGe2VhNuMXL3+TNYMTVKpjMK4eckoIkJ7+B1aX99p4j7Py5jb00n91w4k9hgs69LE0IIIUad26Py9JYq7ni3iO4BF1ctSuLHx6djkemMQowL8psqJgWdVsONp2QxMz6YXz6/m9P+tY5/njudZRkOX5cmhBBCjJptFW3c/FoBBXVdzE0K4Q9n5JARKdMZhRhPJKCJSeXknEgyIq1c98R2rnhkKz9clsqPj09Hq5HpHkIIIcavpq4Bbnu7kJd21hJlN/Gv82dwmkxnFGJckoAmJp2ksEBe/v5CfvtqPnd/WMLO6g7uPHc6odKKXwghxDgz5PLwyIZy7v6ghCGXhx8sS+EHy1IxG+QUT4jxSn57xaQUYNDyt+9OJS8hmN+9VsBp/1rHvy+YyayEYF+XJoQQQhyRtcXN/P61Akqbezk208HvTssmMUwWmxZivNP4ugAhfEVRFM6bE89L1y1Ap1U4978beXhdOaqq+ro0IYQQ4gtVtvZy9WPbuPihLbg8Kg9dmsfDl82WcCbEBCEjaGLSy4mx88b1i/n587v5wxv72FDayh1nTyXIbPB1aUIIIcSInkEX93xUwkNry9FpFX55UgZXLkrCpJelY4SYSCSgCQHYzXoeuGQWD6+v4La393PKXWu5+/wZ5CWG+Lo0IYQQk5zHo/LyzlpuX1VIU/cgK2fG8OuTM4mwmXxdmhDiKJApjkIMUxSFKxcl8eJ1C9BpNZx7/ybu+agEj0emPAohhPCNnVXtrPzPBn7+/G6iggJ46fsL+Mc50yWcCTGByQiaEJ8xNTaIN360iBtf2svf3iliU1kr/zhnOuFW6fIohBBibDR2DXD7qkJe2lFLuNXI38+exlkzYtDIsjBCTHgS0IQ4DJtJz7/On8Gi1DBufq2A5Xet5c5zp/u6LCGEEBNc/5Cb+z8u4741pbg9Ktct9bbNtxjllE2IyUJ+24X4Age7PM6ID+b6p3Zw8cObOTVJz8LFHvRamR0shBBi9Hg8Kq/uruWvq4qo7xxgeU4k/7c8i/hQs69LE0KMMTnLFOIrZERaefX6hZwzK443ypx89z8bKG/p9XVZQgghJohtFW2c9Z8N/PTZ3YRZjDx7zTz+c9EsCWdCTFIygibEETAbdNz+3amEuZp4oqiPU+9ey+9Oy+bc2XEoilwPIIQQ4uurbuvjtlWFvLmnngibkTvOnsZKuc5MiElPApoQX8PsSB0XLZ/Lz5/bzQ0v7eWjoiZuWzmV4EBZM00IIcSR6Rpw8p/VpTy0rhyNAj86Lo1rj0nGbJDTMiGEBDQhvrYoewBPXDmXh9aV87d3ijjpzo/5+znTWJwW7uvShBBC+DGn28OTmyq5+8MS2nqHOGtGDL86OYMoe4CvSxNC+BEJaEJ8AxqNwtVLklmQGsqPn9nFxQ9t4YqFSfzq5AxMeq2vyxNCCOFHVFXlnYIGbl9VRHlLL/OTQ7nxlCxyY+2+Lk0I4YckoAnxLUyJtvPGDxdx61v7eXh9ORtKW/jHOdPJjrb5ujQhhBB+YEdVO395cz/bKttJc1h4+LI8lmU45PplIcQXkoAmxLdk0mu55YwclmY6+NULezjjnnX86Ng0rluagk7a8QshxKRU1drH7e94G4CEWYzcujKXs2fFyt8FIcRXkoAmxChZluHg3Z8s4ebXCvj7ewd4b38jfz97GmkRVl+XJoQQYoy09Azy7w9LeHJzJTqNhh8fl8Y1S5IJlIWmhRBHSF4thBhFwYEG7j5/BifnRPKbV/I59V/r+MWJ6Vy5KBmttE0WQogJq3fQxYNry7n/41IGXB7OyYvjJ8enEWEz+bo0IcQ4IwFNiKPglNwoZieGcNPLe/nLW4W8W9DIHWdPIzEs0NelCSGEGEVOt4dntlRx1wfFtPQMsTwnkl+clEFKuMXXpQkhxikJaEIcJeFWI/+9eBav7Krl5lcLWH7XWm5YnsnF8xJkEVIhhBjnPB6VN/fW8/d3i6ho7WNOUgj3X5LJzPhgX5cmhBjnJKAJcRQpisJZM2KZnxzGr1/cw82vFfDW3npu+85UkmQ0TQghxh1VVVlb3MLf3ilib20nmZFW/nfZbJZmhEtnRiHEqJCAJsQYiLSbeOTy2Ty/rYY/vbmPk+/8mJ+ekM5Vi5Kko5cQQowT2yvb+OuqIjaXtxETFMDfz57GmTNi5BpjIcSokoAmxBhRFIVzZsexNCOc371awG1vF/LGnjpu/85UpkTLYqVCCOGvCuo6+fu7B/iwsIkwi5FbTp/CeXPiMOq0vi5NCDEBSUATYow5bCbuu3gWb++t57evFnD6v9dzzZJkfnxcGia9/LEXQgh/Udbcwz/eO8Abe+qxmXT86uQMLluQiNkgp09CiKNHXmGE8JHluVEsSAnjz2/t4z+rS3knv4FbV+YyNznU16UJIcSkVtvRz93vF/PCjhqMOg0/PDaVqxYnYw/Q+7o0IcQkIAFNCB+ym/X89bvTOH1aDP/38h7OvX8TF8yN59cnZWI3y4mAEEKMpfrOfu75qIRnt1ajoHDp/ES+vyyFMIvR16UJISYRCWhC+IFFaWG885Ml/OPdA/xvQwXv5Ddw06lZnDUjRrqCCSHEUdbYNcC9H5Xw9JZqVFTOyYvjB8tSiQ4K8HVpQohJSAKaEH7CbNDxm9OyWTkzlpte2cvPntvNc9uq+dOZOaQ6rL4uTwghJpym7gHuW13Gk5srcXlUzp4Vyw+WpRIXYvZ1aUKISUwCmhB+JjvaxovXLuCZrdXcvqqQ5Xet5erFyfzw2DQCDNJERAghvq2WnkHu/7iMxzZW4HSrrJwRww+PTSM+VIKZEML3JKAJ4Yc0GoUL5sZz4pQIbn2rkHtXl/La7jr+cMYUjs2M8HV5QggxLjV1D3D/mjKe3FzFoMvNmdNj+OFxaSSFBfq6NCGEGCEBTQg/FmYx8vdzpnF2Xiy/eSWfKx7ZxklTIvjNqdkyBUcIIY5QQ+cA960p5ektVTjdHs6YHsMPlqWS6rD4ujQhhPgcCWhCjAPzkkN560eLeXBdGf/6oITji9bwvSXJXLc0VaY9CiHEF6jt6Oe+1aU8u7Uaj6py1gxvMEuUETMhhB+TgCbEOGHQafj+0lTOmhHDbW8XcveHJbywvYb/OyWL06ZGSbdHIYQYVt3Wx72rva+RAN+dFcf3l6bIzAMhxLggAU2IcSbKHsBd583gonkJ/P61An749E4e31TJzSuymRJt93V5QgjhMwcau7lvdSmv7q5Dq1E4f0481x6TIu3yhRDjypgFNEVRfgj8AHADb6qq+qux+t5CTESzE0N47fpFPLetmr+9U8SKf63j/Dnx/PzEDEICDb4uTwghxszOqnbuXV3Ke/saMRu0XL4gkauXJBNhM/m6NCGE+NrGJKApirIMOAOYpqrqoKIojrH4vkJMdAffIT4lJ4o7PzjAYxsreX13HT88No1LFiRg1Mn1aUKIiUlVVdaXtHLv6hI2lLZiD9Dz4+PSuGxBIsHyJpUQYhwbqxG064DbVFUdBFBVtWmMvq8Qk4LdrOfmFVO4YE48f3pzP39+az+PbqzglydlsGJqNBqNXJ8mhJgYPB6Vd/c1cu/qEvbUdBJhM/KbU7M4f048gUa5ckMIMf6N1StZOrBYUZQ/AwPAL1RV3TpG31uISSMtwsqjV8xhbXEzf3mrkB8/s4uH15Vz4ylZzE0O9XV5QgjxjQ043by0o5YH15ZR1tJLQqiZW1fmsnJmjMwWEEJMKIqqqqPzhRTlfSDyMB+6Cfgz8BHwI2A28CyQrB7mmyuKcg1wDUBERMSsZ555ZlTqE2I09PT0YLGMj3VzPKrKhjoXLxU7aRtQmeHQcna6gWiLxteliVE0no5JMXmM5nHZM6TyQZWT96ucdA9Bok3D8iQ9eRFatDI7QBwhea0U/mbZsmXbVVXNO9zHRi2gfRlFUVYBt6uq+tHw41JgnqqqzV/2eXl5eeq2bduOen1CHKnVq1ezdOlSX5fxtQw43Ty0rpz/rC6l3+nmvNlx/Pj4NBxWuXh+IhiPx6SY+EbjuKxq7eOhdWU8t62GfqebZRnhXLMkhXnJIbKsiPja5LVS+BtFUb4woI3VFMdXgGXAR4qipAMGoGWMvrcQk5pJr+UHy1I5b3Ycd39QzJObq3hpRy2XLkjk2mOSCTLLxfRCCP+xs6qdB9eW83Z+PVqNwpnTY7h6STLpEVZflyaEEGNirALaw8DDiqLkA0PApYeb3iiEOHpCLUZuOSOHyxcmcef7B/jvx6U8uamSqxYnc8WiRKwmva9LFEJMUk63h1X5DTy8vpydVR1YTTquWZLC5QsTpVW+EGLSGZOApqrqEHDRWHwvIcSXSwwL5M7zZnDd0lT+8V4R/3z/AI9sKOe6pSlcMj8Rk14uthdCjI2OviGe3lLNYxsrqO8cIDHUzC2nT+E7s2KxSEdGIcQkJa9+QkxSGZFW/ntxHrurO7jj3SL+8lYhD64t54fHpnLu7HgMOmkmIoQ4Okqauvnf+gpe3FHDgNPDwtRQ/nRmDssyHLIsiBBi0pOAJsQkNy0uiMevnMvmslbueLeI375awH1ryrh2aQpnz4qVETUhxKhwe1Q+Kmzi0Y0VrC1uwaDTcNb0GC5flEhmpM3X5QkhhN+QgCaEAGBucijPfW8+aw40c/cHxfz2lXz+/WEx1yxJ4YI58QQYJKgJIb6+tt4hnt1azRObKqnt6CfCZuRnJ6Rz4dx4Qi1GX5cnhBB+RwKaEGKEoigszXBwTHo4G0pbufuDYv74xj7+s7qEqxYnc/G8BALluhAhxBHYVd3BYxsreGNPPUMuD/OSQ7jp1CxOyI5Ar5Up1EII8UXkTEsI8TmKorAwNYyFqWFsKW/jXx8Wc9vbhdy3ppQrFyZx6cJEbNL1UQjxGf1Dbt7cW889G/spX7WeQIOWc/PiuHh+grTJF0KIIyQBTQjxpeYkhfD4lXPZWdXOvz8s4e/vHeD+j8u4YG48ly9MItIuLbCFmOwKG7p4Zks1L+2ooWvARVSgwi2nT2HlzBhZwkMIIb4mCWhCiCMyIz6Yhy6bTX5tJ/etKeWBtWU8vL6c06fFcM2SZDIi5d1xISaT/iE3b+yp4+ktVeyo6sCg1bA8N5LzZsczULWHZQsSfV2iEEKMSxLQhBBfS06MnX9fMJPqtj4eWlfOs1ureXFHDcekh/O9JcnMTwlFUaRNthAT1f76Lp7eUsXLO2vpHnCREh7Ib07NYuXMWEICDQCsrpbXACGE+KYkoAkhvpG4EDO/P30KPz4ujSc2VfLoxgoueHAzOTE2rl6czCm5UdIIQIgJoqNviNd21/H8thr21nZi0Gk4NTeK8+fEMzsxWN6UEUKIUSQBTQjxrQQHGvjhcWlcvSSZl3fW8sDaMn78zC5ufauQC+fGc96ceMKt0kpbiPHG7VFZW9zM89treK+gkSG3h6woG787LZuzZsQQPDxaJoQQYnRJQBNCjAqTXsv5c+I5Ny+Oj4qaeGRDBX9/7wD/+rCEU6dGccn8BGbEB/u6TCHEVyhr7uH57TW8tKOGxq5Bgs16Lpgbz9l5sUyJtvu6PCGEmPAkoAkhRpVGo3BcVgTHZUVQ2tzD4xsreWF7DS/vrGVarJ1LFyRy6tQojDpZ+FoIf9HaM8ibe+t5eWctO6s60GoUjkkP5/crYjk2yyG/r0IIMYYkoAkhjpqUcAu/P30Kvzgpg5d21PDohgp+9txu/vzmfs7Oi+O82XEkhgX6ukwhJqW+IRfv7WvklZ21fFzcgtujkhlp5f+WZ3LWjBgcNllCQwghfEECmhDiqLMYdVwyP5GL5yWwvqSVRzdW8MDaMu5bU8r85FDOmxPHSVMiMenlXXohjiaX28P60lZe2VnLOwUN9A25ibabuHpxMmfOiCYz0ubrEoUQYtKTgCaEGDOKorAoLYxFaWE0dg3wwvYant1azY+f2YU9QM9ZM2I4b06cnCQKMYrcHpUt5W28ubeOVfkNtPQMYTPpOGN6NGdMj2FOYggajXRhFEIIfyEBTQjhExE2Ez9Ylsp1x6SwsayVZ7ZW89TmKh7ZUMH0uCDOyYvj1Nwo7Ga9r0sVYtxxe1S2VrTx5p563s5voKVnkAC9lmOzHKyYGsWyTLmuTAgh/JUENCGET2k0CgtTw1iYGkZ77xAv7azlmS1V3PjyXn7/WgHHZTk4c0YMSzPC5YRSiC/h9qhsr2znzT11vJXfQHP3ICa9huMyIzh1ahRLM8IxG+TPvhBC+Dt5pRZC+I3gQANXLkriioWJ5Nd28fLOWl7bXcvb+Q3YA/ScNjWKs2bEMCtBFsYVAmDA6WZ9SQvvFjTy/v5GWnuHMOo0HJvp4NSpURyb6ZBQJoQQ44y8agsh/I6iKOTG2smNtXPjKZmsK2nh5Z21vLijhic3VxEXEsCZ02M4dWoUGRFWCWtiUunsc/JRURPv7mtgdVEzfUNurEYdyzIdnJAdwbGZDgKN8uddCCHGK3kFF0L4NZ1Ww9IMB0szHPQMungnv4FXdtVyz0cl/OvDEpLDAlmeG8nynCimRNskrIkJqbyll48Km/iwsIlNZa24PCoOq5GzZsRw4pRI5ieHYtBpfF2mEEKIUSABTQgxbliMOr4zK5bvzIqluXuQdwoaeDu/nv+sLuWej0pJCDWzPCeKU3IjyY2xS1gT49agy83msjY+KmpidVEz5S29AKSEB3LV4mROmhLBtNgg6b4ohBATkAQ0IcS4FG41ctG8BC6al0BrzyDv7Wvkzb31I+urxQYHcHxWBMdlOZiTFCINRoTfq2nv4+MDLXxY2MSG0hb6htwYdRrmp4Ry2YJElmU4iA81+7pMIYQQR5kENCHEuBdqMXLenHjOmxNPe+8Q7+1vZFV+A09v8bbtDzRoWZIezrGZDpZlOgizGH1dshB09jvZWNrKupJm1pe0joySxQQF8J2ZsSzLDGd+chgBBnlzQQghJhMJaEKICSU40MA5eXGckxdH/5CbDaUtvL+/iQ8LG3k7vwFFgelxQRyX6b2uLTvKJtPExJgYdLnZUdnB+pIW1pa0sLemA48KZoOWecmhXDwvgcVpYaQ6LDI9VwghJjEJaEKICSvAoOW4rAiOy4pAVXMoqOviw8ImPihs4o53D3DHuwcINutZkOJdh21RaphMIROjpn/Izc6qdjaXt7GlvI0dVe0MujxoNQrT44K4/tg0FqeFMS02SBp8CCGEGCEBTQgxKSiKQk6MnZwYOz86Lo3m7kHWl7SwrqSFdcUtvLm3HoD4EPNIWJufEkpIoMHHlYvxonvAybbKdrYMB7I9NR043SoaBbKjbVw4N4F5ySHMSwnFZtL7ulwhhBB+SgKaEGJSCrcaOXNGDGfOiEFVVUqbe71Tz4pbeH13HU9vqQIg1WFhdmIweQkhzEkKITY4QKafCTweldLmHnZWdbCzup2dVR0UNXajqqDTKEyNtXPlomTmJoUwKzFYApkQQogjJgFNCDHpKYpCqsNCqsPCpQsScbk97K7pYFNZG9sq2nhjTz1Pb6kGIMJmJC8xhNkJweQlhpARaUWvlelpE11z9yB7azvYVdXBzmrvtnvQBYA9QM/0uCBOmhLJ3KQQpscHYTbIn1chhBDfjPwFEUKIz9BpNcxKCGFWQgjgHS0pauxmW0UbWyva2VrRxpt7vFMijToN2dE2psbYyY0NYlqsneRwC1ppPDIuqapKTXs/BXVdFNR1UlDXRX5tJ03dgwBoNQqZkVbOmBHN9LhgZsQHkRQaKI1mhBBCjBoJaEII8RU0GoWsKBtZUTYunp8IQG1HP9sq2thb08me2k6e317DoxsrAW9XvpxoO7mxdrKibGREWEmLsGDSS7t0f9I14KS4sYeSpm4ONPawv76LgrouOvudgDeMpYZbWJQaxpQYOznRNnJj7TI6JoQQ4qiSvzJCCPENxAQFEDM9hjOmxwDg9qiUNfewp6aTPTUd7Knt5IlNlQy6PABoFEgMDSQ9wkpG5Ce3hBAzOpkiedSoqkp7n5Pyll5KmropbuzhQFMPxY3d1HcOjDzPpNeQEWHllNwocmJsTIm2kxlplVAthBBizElAE0KIUaDVKKRFWEmLsPKdWbEAuNweKlr7ONDYTWFDN0UNXRQ1dvPOvgZU1ft5Oo1CXIiZxFAziWGBJIYGkhgWSFJoINFBJglvR0BVVVp6hqhs7aWitW9kW9HSS0VrL90DrpHnGnUaUh0W5iWHkhZhId1hJT3CSmxwgExTFEII4RckoAkhxFGi02pGmo+ckhs1sr9/yE1JUw+FDV2UtfRS2dpLeUsfm8vb6BtyjzxPr1WICQogyh5AVJCJ6M9so+wBqAeT3gSlqipd/S6augeo7einvnOAuo5+6jq82/rOfuo6BxgaHqkE72hlbLCZhFAzZ8XHkBAaSEKImVSHhbgQs1wfKIQQwq9JQBNCiDEWYNCSG+u9Ru3TVFWluXuQ8uGRn4rWPqra+qjv6GdjaSuNXQN4PpPHTFpwbP2IkEADoYEGQi0GQgKNhFkMhAR6b7YAPVajDotJh8WoI9Cg88lokdPtoXvARfeAk67+4e2Ak64BFx19Q7T0DNHSM0hLzxCtPYO09gzR2juI033oD61RIMJmIspuIifGzolTIom2m0gYHn2MCQqQhZ+FEEKMWxLQhBDCTyiKgsNmwmEzMTc59HMfd7k9NHUPekeNOgao7+xnW0EJAcFBtPUOUd85QH5dJ229Q58LNZ8VaNCOBLYAgxa9VoNeq8Go0wzfVzDotOi1CjqNgqqCCsNb7wPvYxWPCkMuD4MuNwNO73bQ5WHQ5WHA6d3XO+ii3+n+0poMOg3hFm+4jLCZmBJtI9RiJGx4X0xQAFFBAURYjTL1UwghxIQlAU0IIcYJnVZDdFAA0UEBzErw7kv3VLN06YxDnqeqKt2DLlp7hmjrHaRrwEXPgIveQRc9gy66B7zbngEX3YNOBp0ehtwehlzeIOV0qwy5PDjd3v0ut4qigAIji3QryvANBY0CRp0Wo94b8MwGHSGBGu8+nQajXoPFqMNq0mM16bAd3AZ88jjIrMdi1Mki4EIIISY9CWhCCDHBKIqCzaTHZtKTFBbo63KEEEII8TXIHBEhhBBCCCGE8BMS0IQQQgghhBDCT0hAE0IIIYQQQgg/IQFNCCGEEEIIIfyEBDQhhBBCCCGE8BMS0IQQQgghhBDCT0hAE0IIIYQQQgg/IQFNCCGEEEIIIfyEBDQhhBBCCCGE8BMS0IQQQgghhBDCT0hAE0IIIYQQQgg/IQFNCCGEEEIIIfyEBDQhhBBCCCGE8BMS0IQQQgghhBDCT0hAE0IIIYQQQgg/IQFNCCGEEEIIIfyEBDQhhBBCCCGE8BOKqqq+ruELKYrSDFT6ug4hPiUMaPF1EUJ8ihyTwh/JcSn8jRyTwt8kqKoafrgP+HVAE8LfKIqyTVXVPF/XIcRBckwKfyTHpfA3ckyK8USmOAohhBBCCCGEn5CAJoQQQgghhBB+QgKaEF/P/b4uQIjPkGNS+CM5LoW/kWNSjBtyDZoQQgghhBBC+AkZQRNCCCGEEEIIPyEBTQghhBBCCCH8hAQ0IYQQQgghhPATEtCEEEIIIYQQwk9IQBNCCCGEEEIIPyEBTQghhBBCCCH8hM7XBXyZsLAwNTEx0ddlCDGit7eXwMBAX5chxAg5JoU/kuNS+Bs5JoW/2b59e4uqquGH+5hfB7TExES2bdvm6zKEGLF69WqWLl3q6zKEGCHHpPBHclwKfyPHpPA3iqJUftHHZIqjEEIIIYQQQvgJCWhCCCGEEEII4Sf8eoqjEEKIsaOqKm6Pistz6NajqgAow89TFGXksaKAgoJWq6DXKug1GjQa5fDfQAghhBBfSQKaEEKMI6qqMuD00NE/RHuvk/2tbpz7GukddNE96KJ30EXPgIueg/cHXQw43Qw4PQy43Ax+ajvo8u4fcntwD4ex0aBRQKfVoNco6HUadBoNJr0Gk15LwPDNqNd47xu0mHRazEYtVqMOq0mPxaTDYtRhMemwmXRYjHqsJh1BZj0Beu1IQBRCCHF4TqeTmpoaBgYGfF3KpGcymYiNjUWv1x/x50hAE0IIH+sddNHcPUhLz+An254hmrsHaesdpL3PSWef0xvK+pwMuTyHfoGthzZT0igQaNRhNeoINOpGQpDFqCM00BuOTDotJr0Go06LQadBp1HQahTvVju81Xj3axQ4GN2GB9NQVXVkn0cFt8eD063idHtwuVWcnuGt27vfGwbd9A95Q2H3gPdnHnC66Rvy7u8Zco18/S9i0GkINusJCjAQZNYTZNYTbDYQZDYQZjEQZjF6b1YD4RYjwWaDjOgJISadmpoarFYriYmJ8qaWD6mqSmtrKzU1NSQlJR3x50lAE0KIo0RVVdr7nNR19NPQOUB9Zz/1nQPDN+/9pq5B+p3uz32uokCI2UCoxRs+EkLNTDPbCTYbsA8HlGCznvID+1g0d9bIiJPFqBu3o0wej0rvkHfUr2fAOyLYM+Cie8BF14CTjj4nHX1DdPQ5aR/elrf0sqOvg46+IZzuz6c7rUYhJNAb3CJsRiJtJiLtpk+2w/ftAfpx+W8mhBCHMzAwIOHMDyiKQmhoKM3NzV/r8ySgCSHEt9A76KK6vY+q1j6q2vqoae+nqu3g/T4GnIeOduk0ChE2E9FBJnJj7ERmmQizGgm3GAmzGgmzGAi3GgkxG9Bpv7qP0+rWIqbGBh2ln25saTQKVpMeq0kP9q/3uaqq0tXvornHOwLZ0jNIS/cgLT1DI48buwbJr+2ipWfwc59v0muItgcQExxAbLCZ2OCA4ZuZuOAAwixGGYkTQowrEs78wzf5f5CAJoQQX8Hp9lDZ2kdZcw9lLb3ebXMv5S29tPYOHfJci1FHfIiZlPBAlqaHExMcQJTdRJTdu5UT/aNDURTsZj12s55Uh+VLnzvk8tDUPUBD5wANXQPDo5veUc2a9n4K6hpo+8z/q0GrITY4gIRQMwmhgSSFBZIQaiYxNJDY4IAjCtNCCDGZ3HXXXTzwwAOoqsrVV1/NT37yE1+XNG5IQBNCiGGDLjelTb0UNXZR1NBDSVM3Zc29VLb1HdJAI8xiJDk8kBOyI4gPNRMf4r3FBZsJMstUOX9n0GmGR8nMX/icviEXte3ewFbT/snIaEVrH5vL2+gb+mRaqk6jEBscQGJYIMlhFlIdn9xCAg1j8SMJIYRfyc/P54EHHmDLli0YDAZOPvlkTjvtNFJTU31d2rigqF91RbYPKIqyAlgRExNz9RNPPOHrcoQY0dPTg8Xy5e/OC/+nqiot/SpV3R5qezzUdHtvDX0qB3OYVoGoQIXIQA2RgRqiAhWiAjVEBGoI1PtPAJNjcuypqkrnkEpjr0pTn4fGPpXGPg+NvSoNvR6GPjWr1aKHaIuGqEDvLdaqEGvRYDcqEzrIy3Ep/M1kOybtdrtPw9DLL7/M+++/zz333APA7bffjtFonLSjaCUlJXR2dh6yb9myZdtVVc073PP9cgRNVdXXgdfz8vKuXrp0qa/LEWLE6tWrkWNyfPF4VCrb+thb20lBbSd7azvJr+2ka8A18py4kACy422sjLSSHmklM9JKUlgg+nEwbU2OSf/i8ajUdvRT2txDSVMPpc29lDb1sLe5hzU1n0ybDDbryYi0khlpIzPSSkaklfQIK4FGv/yz/LXJcSn8zWQ7Jvfv34/VagXgltcL2FfXNapfPzvaxs0rpnzhx2fPns2f/vQnhoaGCAgI4IMPPiAvL2+kpsnGZDIxY8aMI37+xPhLIIQQeEc26jsH2FHVzq6qDvbWdrKvrovuQW8YM2g1ZERaOXVqNDkxNrKjbKRFWLFMkJNi4XsajUJciJm4EDNLMxyHfKytd4iihm6KGrooauymsKGb57ZVHzJdMiHUTE60nexoGzkxdqZE2wizGMf6xxBCiG8lKyuLX//615x44okEBgYyffp0tFqtr8saN+SsRAgxbg043eTXdrKjqp2dVR3sqGqnscvboc+o05AVZePMGTHkxHhPdtMcVgw6/x8VExNTSKCB+SmhzE8JHdnn8ajUtPdT2NBFUUM3+xu62FvbyZt760eeE2kzed9QiLaTE21jelwQDpvJFz+CEGIc+rKRrqPpyiuv5MorrwTgxhtvJDY21id1jEcS0IQQ40ZH3xBbytvYXN7Gtoo29tV3jax9FRcSwLzkUGbEBTEzIZjMSJuEMeH3NBrF22gm1MyJUyJH9nf2O9lX10VBnXdKbn5dFx8WNo1cIxllNzE9LohpcUFMiw0iN9YuI8FCCL/S1NSEw+GgqqqKl156iU2bNvm6pHFDXs2FEH6ruXuQrRVtbC5rZXN5G4UN3YC3C9/0uCCuWpzMjLggZsQHE26VaWBi4rAH6D832tY35GJfXRe7azrZXd3BruoO3s5vAECjQJrDyrQ4OzPjg8lLDCY5zCJLOgghfOY73/kOra2t6PV67rnnHoKCgnxd0rghAU0I4Tc6+51sLG1lXUkzG0tbKW3uBSBAryUvMZhTc6OYmxzKtDg7Rp3MZReTi9mgIy8xhLzEkJF9bb1D7K7pYHe19/bevkae21YDQJBZz8z4YGYlBJOXEMy0uCBMevm9EUKMjbVr1/q6hHFLApoQwmecbg+7qjtYW9zCuuJmdtd04vaomA1a5iSF8N1ZccxNDiE3xj4uOioKMdZCAg0sy3CwbLghiaqqlLX0sr2yne0V7WyrbOPDwibAu17blBg7cxKDmZsUyuykEOwBel+WL4QQ4jAkoAkhxlR1Wx8fFTXx8YEWNpW10jPoQqNAbmwQ31+awqLUMGbEB8v1Y0J8A4qikBJuISXcwjl5cQC09w6xo6qdbcOh7dGNlTywthxFgewoG3OTQpmXHMKcpBCCzLKwthBC+JoENCHEUeVye9hZ3cEH+5v4qLCJokbvdWRxIQGcPj2axalhLEgJw26Wd/KFOBqCAw0clxXBcVkRgLf76a7qDjaVtbK5rI0nN1fy8HpvYMuIsDI/JZRFqWHMTQ6VxiNCCOED8sorhBh1nX1O1hQ38+H+RlYfaKajz4lOozA7MYTfnJrFskwHKeEWX5cpxKRk0muZlxzKvGRvA5JBl5vd1Z1sLmtlU3krT22u4n/rK9BpFKbHBbEwNYxFaWFMjwuSqcZCCDEGJKAJIUZFc/cg7+5rYFV+AxtLW3F5VEICDRyb6eDYTAeL08Llehch/JBR573mc05SCD8kjQGnmx1V7awvaWFdcQt3f1jMXR8UE2jwBruFqWEckxFOclggiiJdIoUQYrRJQBNCfGP1nf2sym/g7fwGtla0oaqQFBbIVYuTOSE7gulxQWilzbcQ44pJr2VBinfq8S9P8o6IbyxrYV1JC+tLWvmgsAne8E5TXpru4Jj0cBakhmI2yCmFEEKMBnk1FUJ8LbUd/by5p4638xvYWdUBQHqEhR8dm8by3EgyIqzyrroQE4jdrOfknChOzokCvI1+Vh9oZk1REy/uqOHxTZUYtBrmJIWwNCOcpRnhqKrq46qFEL52xRVX8MYbb+BwOMjPzwegra2Nc889l4qKChITE3nuuecIDg72caX+RwKaEOIrtfcO8ebeel7bVceWijYAcmJs/PKkDE7OiZTryYSYROJCzFw8L4GL5yUw6HKzraKd1UVNrC5q5k9v7udPb+4nPEBhRc8+js9yMDspRK5dE2ISuuyyy7j++uu55JJLRvbddtttHHfccdxwww3cdttt3Hbbbdx+++0+rNI/SUATQhxW/5Cb9/Y38urOWtYcaMblUUl1WPjFiemcPi2G+FCzr0sUQviYUadlYWoYC1PDuOlUqGnvY3VRM8+v388Tw90hrSYdyzIcHJflYGmGQ65FFWKSWLJkCRUVFYfse/XVV1m9ejUAl156KUuXLpWAdhgS0IQQI9welfUlLby8s5Z3ChroG3ITaTNxxaIkzpgeTXaUTaYvCiG+UGywmYvmJRA7UM6cBYtYW9zCB/sb+WB/E6/trkOnUZiTFMIJ2RGcnBNJlD3A1yULMfG9fQM07B3drxmZC8tv+9qf1tjYSFSUd7p0ZGQkjY2No1vXBCEBTQhBdVsfz2+v4YVt1dR1DmAz6Th9WjRnTI9hblIIGmn0IYT4mswGHSdNieSkKZG4PSq7qjv4YH8j7+1r5JbX93HL6/uYHhfEyTmRLM+JJCE00NclCyHGkKIo8qbvF5CAJsQkNeB0805BA89urWZDaSuKAotSw7jx1CyOz4rApNf6ukQhxASh1SjMSghmVkIwvzo5k7LmHt7O9y7Lcdvbhdz2diFZUTaW50Ryck4kaQ6LnLgJMVq+wUjX0RIREUF9fT1RUVHU19fjcDh8XZJfkoAmxCSTX9vJs1ureXVXLV0DLmKDA/jp8el8Ny+WmCCZbiSEOPqSwy38YFkqP1iWSk17H6uGw9o/3z/AP947QEp4ICumRXPa1GhSHdKESIiJ4vTTT+fRRx/lhhtu4NFHH+WMM87wdUl+SQKaEJPAgNPNW3vreWxjJbuqOzDoNCzPieScvDjmJ4fKFEYhhM/EBpu5anEyVy1OpqlrgHcKGnhzbz13fVDMne8XkxVlY8W0KFZMjSYuRJoTCTFenH/++axevZqWlhZiY2O55ZZbuOGGGzjnnHN46KGHSEhI4LnnnvN1mX5JApoQE1hNex9Pbq7i2a3VtPUOkRweyM0rslk5Ixa7WTqpCSH8i8Nm4uL5iVw8P5HGrgHe2lvP67vr+OuqIv66qojpcUGsmBbNqblRRNpNvi5XCPElnn766cPu/+CDD8a4kvFHApoQE4zHo7KupIXHNlbyYaG3O9LxWRFcMj+Rhamhcl2HEGJciLCZuHxhEpcvTKK6rY83h8PaH9/Yx5/e3Mf85FDOmhHD8twoLEY5nRFCTByKqqq+ruFzFEVZAayIiYm5+oknnvB1OUKM6OnpwWLxz+shBt0q62pdvFvhpLFPxWqAY2L1LIvTERogi8ROVP58TIrJ62gelw29HjbVu9hQ56KpT8WggZkRWhZE65gSqkUrU7bFYUy210q73U5qaqqvyxDDSkpK6OzsPGTfsmXLtquqmne45/tlQDsoLy9P3bZtm6/LEGLE6tWrWbp0qa/LOERz9yCPb6zg8U2VtPc5mRYXxOULElmeG4lRJ50YJzp/PCaFGIvjUlVVdlR18NKOGt7YU09nv5Mwi5HTp0WzcmYMU6Jl3Ubxicn2Wrl//36ysrJ8XYYYdrj/D0VRvjCgyZwAIcapkqYeHlpXxos7anG6PZyQFcE1S5KZlRAsJyVCiAlPUT5p3f+7Fdl8VNjMyztreHxTBQ+vLycz0so5eXGcOSOGkECDr8sVQogjJgFNiHFEVVU2l7fxwMdlfFDYhFGn4exZsVy5KInk8MkzdUMIIT7NqNNy8vAaah19Q7y+p57nt1Xzhzf2cdvbhZyQHcHZebEsTguXKZBCCL8nAU2IcUBVVVYXNXP3h8XsrOogNNDAT45P4+J5CYRajL4uTwgh/EaQ2cDF8xK4eF4C++u7eG5bNa/srOXNvfVE2U18d1YsZ8+KIz5UWvYLIfyTdA4Qwo+pqsq7BQ2c/u/1XP7IVpq6BvnjmTmsv+FYfnJ8uoQzIYT4EllRNm5eMYVNNx7HPRfMJD3Cyr8/KmHJ3z7iwgc38dbeepxuj6/LFGJCuuKKK3A4HOTk5Izse/7555kyZQoajQbpM/HFZARNCD/k8aisKmjg7g+KKWzoJiHUzF+/M5WzZsag18r7KkII8XUYdVpOnRrFqVOjqOvo54XtNTy7tZrvP7mDcKuRc/PiOG9OHLHBMqomxGi57LLLuP7667nkkktG9uXk5PDSSy/xve99z4eV+T8JaEL4EbdH5Y09dfz7wxKKm3pIDg/kH+dM4/Rp0egkmAkhxLcWHRTAj45L4wfLUllzoIknN1Vxz+oS7lldwrIMBxfNi+eYdIdcqybEt7RkyRIqKioO2SedJY+MBDQh/ICqqqzKb+COd4sobe4lPcLC3efP4NTcKDlJEEKIo0CrUTg2M4JjMyOoae/j2a3VPLO1mise2UZMUADnz4njvDnxhMlUcjHO3b7ldgrbCkf1a2aGZPLrOb8e1a8pPiEBTQgfW1fcwl/fKWRPTSepDgv3XjiTk6dEopFgJoQQYyI22MzPT8zgR8el8f6+Rp7YXMkd7x7g7g9LWDE1mssXJpITY/d1mUKISUICmhA+squ6g7+uKmRDaSsxQQH87btTWTkzVkbMhBDCR/RaDctzo1ieG0VJUzePbqjkxR01vLijhryEYC5bmMhJUyLlWmAxrshI1/gjAU2IMVbS1M0d7xxgVUEDoYEGbl6RzQVz4zHqtL4uTQghxLBUh5U/npnDL07K4IXtNTy6oYLrn9pJpM3ExfMTOG92nHTSFUIcFRLQhBgjjV0D3PFOES/uqMFs0PHT49O5cnESFqP8GgohhL+yB+i5clESly1IZHVRE49sqOBv7xRx1wfFrJwRw1WLk0h1WH1dphB+5/zzz2f16tW0tLQQGxvLLbfcQkhICD/84Q9pbm7m1FNPZfr06bzzzju+LtXvyJmhEEfZgNPNg2vLuHd1KS63yhULk/j+slRCAg2+Lk0IIcQR0moUjsuK4LisCIobu3l4fQUv7ajhma3VHJfp4OolycxNCkFRZJq6EABPP/30YfefddZZY1zJ+CMBTYijRFVV3txbz61vFVLb0c/JUyK58ZQs4kNlnR0hhBjP0iKs3Loyl1+cmM7jmyp5bGMl592/iamxdq5enMzynEhZGkUI8Y1JQBPiKMiv7eQPr+9jS0UbWVE27jh7GvNTQn1dlhBCiFEUajHyk+PTufaYFF7cUcODa8v54dM7iQkK4IpFSZw3O45AmcYuhPia5FVDiFHU1D3A31YV8cKOGkLMBm5dmcs5eXHSmVEIISYwk17LhXMTOH92PB8UNvHAx2X88Y193P1BMZcvTOSyBYkEmWVauxDiyEhAE2IUuNweHtlQwT/fO8CQ28PVi5O5/thUbCa9r0sTQggxRjQahROyIzghO4KdVe3cu7qUO98v5v6Py7hoXgJXLUrCYTP5ukwhhJ+TgCbEt7Szqp0bX85nf30XyzLC+d2KKSSFBfq6LCGEED40Iz6YBy7Jo6ihm/+sLuHBtWU8sr6Cs/Ni+d6SFLkeWQjxhSSgCfENdfY7+ds7hTy5uYoIq4n7LprJSVMipYOXEEKIERmRVu48bwY/PSGd+9aU8fw2b+fH06dF8/2lKaRFSIt+IcShpMWQEF+Tqqq8uquW4/6+hqc2V3H5giTe//kxnJwTJeFMCCHEYSWEBnLrylw+/tUyLl+QyKr8Bk6882Ouf2oHxY3dvi5PiFF3xRVX4HA4yMnJGdn3y1/+kszMTKZOncpZZ51FR0eH7wr0YxLQhPgaGns9XPLwFn78zC5igky8dv0ifrciWxabFkIIcUQi7SZ+c1o26284luuOSeHDwiZOvPNjfvj0TkqaJKiJieOyyy5j1apVh+w74YQTyM/PZ8+ePaSnp3Prrbf6qDr/JmeVQhwBl9vDfz8u45/r+wnQO/njGVO4YG6CdGcUQgjxjYQEGvjVyZlctTiZB9aW8eiGCt7YU8eKqdH86Lg0Uh0WX5coxLeyZMkSKioqDtl34oknjtyfN28eL7zwwhhXNT5IQBPiKxQ3dvPz53ezp6aT2ZFa7rniGOnCJYQQYlSEBBr49cmZXLUoiQfWlvPYxgpe31PH6dO8QS0lXIKa+HYa/vIXBvcXjurXNGZlEnnjjd/qazz88MOce+65o1TRxCIBTYgv4HJ7uH9tGXe+V4zFpOPeC2dibi2ScCaEEGLUhVqM3LA8k6sXJ3H/x2U8trGS13fX8Z2ZsfzkhHRiggJ8XaIQo+bPf/4zOp2OCy+80Nel+CUJaEIcRklTNz9/fg+7qzs4JTeSP5yRQ5jFyOrVRb4uTQghxAQWajHyf6dkcfWSZP6zupTHN1by6q46LpqXwA+WpRBqMfq6RDHOfNuRrtH2yCOP8MYbb/DBBx9Ic7UvIAFNiE9xe1QeXFvG3987QKBBy78vmMFpU6N9XZYQQohJJsxi5LenZXPFoiTuev8Aj2wo59mtVVy1OJmrFidhNel9XaIQX9uqVav461//ypo1azCbZS3AL6KoqurrGj5HUZQVwIqYmJirn3jiCV+XIyaJ+h4PD+4dpLTTw6wILZdkG7EbD31np6enB4tFrgcQ/kOOSeGP5LgcfXU9Hl4qHmJboxurHk5LMbAsTodBKyMQR2KyHZN2u53U1FSf1nD55Zezbt06WltbcTgc3Hjjjfz9739naGiIkJAQAGbPns2dd97p0zrHQklJCZ2dnYfsW7Zs2XZVVfMO93y/DGgH5eXlqdu2bfN1GWKCU1WVZ7ZWc8vrBZj0Wm45fQqnT4s+7LD76tWrWbp06dgXKcQXkGNS+CM5Lo+ePTUd/O2dItYWtxBtN/HzEzM4a0YMGukq/KUm2zG5f/9+srKyfF2GGHa4/w9FUb4woMk6aGJS6+xz8oOndvB/L+0lLyGEd3+yhDOmx8icaCGEEH5pamwQj185l6eunku41cjPn9/Nin+vY0Npi69LE0KMEgloYtLaVtHGKXev5d2CRv5veSaPXTFHOjQKIYQYFxakhPHy9xdy13nT6ehzcsEDm7nyka2y2LUQE4A0CRGTjtuj8u8PS7jrgwPEhZh58boFTIsL8nVZQgghxNei0SicMT2Gk6ZE8r/1Fdz7UQkn3bmW8+fE8ZPj0wmTjo9CjEsS0MSkUtfRz0+e3cWW8jbOmhHDH8/MwWKUXwMhhBDjl0mv5bqlKZyTF8tdHxTz5OYqXtlZx3VLU7hyURImvdbXJQohvgaZ4igmjVX5DSy/ay0FtZ3845xp/PPc6RLOhBBCTBihFiN/OCOHd3+6hHnJofztnSKO+/saVuXX489N4YQQh5KAJiY8l9vDn97Yx7VPbCch1MybP1rMypmxvi5LCCGEOCpSwi08eGkeT109F6tJx7VP7OCihzZzoFGuTxNiPJCAJia05u5BLnxwMw+uK+fS+Qm8cO0CEsMCfV2WEEIIcdQtSAnjjR8u4g9nTCG/tovld63lltcL6Ox3+ro0MQlcccUVOBwOcnJyRvb99re/ZerUqUyfPp0TTzyRuro6H1bovySgiQlrR1U7K/61jt01Hfzz3GncckYOBp0c8kIIISYPnVbDJfMT+egXSzlvdhyPbKhg2R2reWZLFW6PTHsUR89ll13GqlWrDtn3y1/+kj179rBr1y5OO+00/vCHP/ioOv8mZ6tiwlFVlSc2VXLufzei1ym8eN0CzpohUxqFEEJMXiGBBv58Vi6vX7+IlPBAbnhpL2fes57tle2+Lk1MUEuWLCEkJOSQfTabbeR+b2+vrDv7BaRDgphQBpxufvNKPi9sr+GY9HDuOm86QWaDr8sSQggh/EJOjJ3nvjef13bXcetbhXznPxs4f04cvz45U/5eTlBrnztAS3XPqH7NsDgLi89J/0afe9NNN/HYY49ht9v56KOPRrWuiUJG0MSEUd3Wx3fv28AL22v40bGpPHzZbPljI4QQQnyGonjXT/vg58dwzZJknttWw7F/X8OL22uk26M46v785z9TXV3NhRdeyL///W9fl+OXZARNTAgbSlv4/pM7cHtUHrwkj+OzI3xdkhBCCOHXAo06bjwli7NmxHDTy3v5+fO7eW5bNX8+K4dUh9XX5YlR8k1Huo62Cy+8kFNOOYVbbrnF16X4HRlBE+Pec9uqueShLYRZjLx2/SIJZ0IIIcTXkBVl44VrF3DrylwKG7pZftda/vZOIf1Dbl+XJiaY4uLikfuvvvoqmZmZPqzGf8kImhi3PB6VO94t4t7VpSxOC+PfF8zEHqD3dVlCCCHEuKPRKJw/J54TsiP4y1v7ueejUl7bXccfzshhWYbD1+WJcej8889n9erVtLS0EBsbyy233MJbb71FUVERGo2GhIQE7rvvPl+X6ZckoIlxacDp5ufP7ebNvfWcPyeeP5wxBb1WBoSFEEKIbyPMYuQf50zn7Flx/OaVvVz+v62cOT2a362YQkigXNctjtzTTz/9uX1XXnmlDyoZf+SMVow7zd2DnHf/Jt7Kr+emU7L4y1k5Es6EEEKIUTQ/JZS3f7yEnxyfxpt76zn+H2t4bXedNBERYgzIWa0YV4obuznr3vUUNnTxnwtncfWSZFlDQwghhDgKDDoNPzk+nTd+uJi4EDM/enonVz+2jYbOAV+XJsSEJgFNjBtri5tZee8GBl0envvefE7OifR1SUIIIcSElxFp5aXrFvCbU7NYV9LCCf9Yw9NbqmQ0TYijRAKaGBee21rNZf/bSkxwAK/+YCFTY4N8XZIQQggxaWg1ClctTuadnywhJ8bO/720lwse2Exla6+vSxNiwpGAJvzef9eU8qsX97AwNYwXrltAdFCAr0sSQgghJqWE0ECeunout67MJb+2k5Pu/Jj/rS/H45HRNCFGiwQ04bdUVeX2VYXc+nYhK6ZF8+AleViM0nhUCCGE8CVF8bbkf+9nxzA/OZRbXt/HhQ9upqa9z9elCTEhSEATfsntUbnplXz+s7qUC+fGc+e50zHo5HAVwm+pKrhdMNQH/R3Q2wJdddBeAS3F0FQITfuhsQAa8qFhL9TvhrpdULfTu23YC437oLkIWkqgrQzaK6GzBroboL/d+/U9sniuEP4g0m7i4ctmc9vKXPbUdHDynWt5blu1XJsmAKipqeGMM84gLS2NlJQUfvzjHzM0NPSln9PR0cG999478riuro7vfve7o1LP73//e+64444jeu4jjzzC9ddff9iPnXLKKXR0dABw9913k5WVxYUXXsgrr7zCvn37RqVWGY4QfmfI5eGnz+3izT31/GBZCr84MUM6NQpxNDj7oa/VG6gGu2Cga3jb6b0d3DfU4w1Gzj7v5zh7h7f9MDR83z0EjOFJmUYHOhPojKA1ercGCxgCP3WzHHrfaIWAIDDZh2+fum8IBHmdEeJrUxSF8+bEszA1jJ8/v5tfvbCHdwsauXVlLuFWo6/LEz6iqiorV67kuuuu49VXX8XtdnPNNddw00038be//e0LP+9gQPv+978PQHR0NC+88MJYlX1E3nrrrZH79957L++//z6xsbFcdtllnHbaaWRnZ3/r7yEBTfiV/iE31z6xnTUHmrnxlEyuWZLi65KEGD/cTuht9o429TQO35q8o1l9rZ/c+tu9W+dXTEfSGsBoA6MF9IFgMIM+AAKCvVuDGfTmTwUlA2j1w9tP3dfoQaMBRQMo3iD06fsogOodGVPdw1vPoY89Lm8IdA2Aa3g78njQux3q84bJgU7v6N1Q73C47AX34Jf/rBqdN7AFhoE5DAJDvVtz6PC+UAgMB0sEWCO8z5VAJ8SIuBAzz1w9j4fXl/PXd4o46c6P+fOZOSzPjfJ1acIHPvzwQ0wmE5dffjkAWq2Wf/7znyQlJXHLLbfw3HPP8fLLL9PZ2UltbS0XXXQRN998MzfccAOlpaVMnz6dE044gR/84Aecdtpp5Ofn88gjj/DKK6/Q29tLcXExv/jFLxgaGuLxxx/HaDTy1ltvERISwgMPPMD999/P0NAQqampPP7445jN5i+s9fnnn+eWW25Bq9Vit9v5+OOPAe/o3cknn0xpaSlnnXUWf/3rXwFITExk27Zt/OY3v6GsrIzly5dz3nnn8dprr7FmzRr+9Kc/8eKLL5KS8s3PYSWgCb/R2efkike3srOqndu/k8u5s+N9XZIQ/mOoD7pqvdP9Dm47a5hasRf2u7yhrK+Vw45iGe1gDvGGDGsUROR88tgc4g1cRhuYbN7nmmzex3rTmP+YR43bCYPdMNDhHTEc6PTePzha2N8xHFxboLfVOx2zrxX62jjsv6nONBzWIj/ZWiPBFgP2WO/NGg06w5j+mEL4kma40+Mx6eH87LndXPfkDs6cHs0tp+dgN+t9Xd6k9dEj99NUWTaqX9ORkMyyy675wo8XFBQwa9asQ/bZbDbi4+MpKSkBYMuWLeTn52M2m5k9ezannnoqt912G/n5+ezatQuAioqKQ75Gfn4+O3fuZGBggNTUVG6//XZ2/j979x0eVbU1cPg3NZNMeu8JISEEAoQaeu9SpAgIUizYxe71qveq12vvXUGUKtJEEARFpPdeEkghpPfeJ1PO98dBvH4CQtqk7Pd55pmUmXPWwMnMWWfvvdbJkzz++OMsW7aMxx57jMmTJzN//nwAXnjhBRYvXswjjzxyzVj/85//8PPPP+Pn53dl6iLAqVOnOHnyJDY2NoSHh/PII48QEBBw5fdffPEF27ZtY+fOnbi7u5OQkMC4cePqZUqmSNCEJiG3rJo5i4+QlFfBpzO7iStuQutjNkJxKhRdktdtFV6+L06BkgyoKvx/T1CAvRdqhQN4tgP/npeTBU+w9/5jpEfvKZIEkEfz7Fzl282wmP8YcSzPlUcly7KhPBvKcuT7vAuQtBsMJf/vyfL/EU6/J20B4BwILsHyzTlQHokUhBYmzMuB7x/sy6c7E/n4t0SOXCrkgxld6dXmJv/+hBZtxIgRuLm5ATB58mT27dvHrbfeet3nDBkyBAcHBxwcHHBycmL8+PEAdOrUiTNnzgByEvfCCy9QXFxMeXk5o0aNuu42+/Xrx7x585g2bRqTJ0++8vNhw4bh5OQEQIcOHUhJSflTgtaQRIImWF1OaTUzFh4ip7SaxfN6MCDMw9ohCULDsJjlJCw/AQoSID/+ciJ2SR4Rkyx/PFZl88dJvF+PP07wfz/Zvzw6c2LXLgYPHmytV9TyKVXyFEe9O3iEX/+xl0c5peI0zIUZmIqyMRdnYyrJw5RSgLksAYvJhAUVkqTEggqLrQeS3geL3guL3htJ73k5ufZBof3rlByFApQqBUqVUr5XKv78vVqBWqNErVVduVeqFGIdr9DoNColjw1vx5BwTx797iQzFh7k4aFhLBgailolin41puuNdDWUDh06/GXtWGlpKampqYSGhnLixIm/vC/dyPuUjc0f6xqVSuWV75VKJSaTCYB58+bxww8/0KVLF5YsWcKuXbuuu80vvviCw4cPs2XLFrp3787x48f/si+VSnVl+41BJGiCVeWWVnP7wkPkllaz/O5edA8SV9eEFsBkkCsR5p6Xk7D8eChIhIKLf14LZesCbqEQEA2dZ/wxsuLaRh4FU4qTmMZksUjUVJqorjRiqDRh+P2+wkh1pYmaShM1BjPGahNGg5ma6v/3tcGMyWjGYgLwu3z7G0VX+2EVUH/TkRQKUGlVaLRKVBolWp0arU6FVqdGo1OjtVX98TNbNVpbNTq95o+bvQYbvRqVOKkWaqFLgDObFwzgxY0xfLQjgf2J+XwwPYoA12uvCRKav2HDhvHss8+ybNky5syZg9ls5sknn2TevHlX1oNt376dwsJCbG1t+eGHH/j6669xcHCgrKysTvsuKyvDx8cHo9HIypUr8fO7/nvxxYsXiY6OJjo6mq1bt5KWllar/dZH7L8TCZpgNXllBm5fdIjs0mqW3SWSM6EZsligOFkuDZ8bK5eQzz0vJ2PS5VLwCpWccLmFQehwcA8D93by93o3q4bfGtRUm6goNlBRUkNVaQ1V5TVUlRmpKrt8/z/fGyqvf3VUpVaitVWhsVGhsZETGp29Bgc3HRqdWv65VolKLY9cqdRyQqT+/WcaJUq1Uh71UipQ/M8ImEKpQGmpQVGeBUUpSMWp8vTW4jR51LWqGAAJBRalDotTm8u3YCyOgVgcArDYemK2gNlkwVRjwVRjlu+Nv9/LPzMazNRUmaiuNFFWWE1NlelKgnk9Gp3qStJm56jFzlGL7eV7O0ctdg5a7Jzkr0WZdeF/2duoeXdaFwa2c+eFDecY+9FeXpvUifFdfK0dmtBAFAoFGzZs4MEHH+SVV17BYrEwduxYXnvttSuP6dWrF1OmTCE9PZ077riDHj16APKUw8jISMaMGcNDDz100/t+5ZVXiI6OxsPDg+jo6L9Nmp5++mkSEhKQJIlhw4bRpUuXK2vgbsaMGTOYP38+H330EevWratTkRBFU34T7dGjh3Ts2DFrhyE0gPxyA7cvPER6URVL7uxJdEjzOFHdJaaTtV5mozwqlnVK7t+VdVru52Ws+OMxLsHg2UG+eV2+d23boGvAWusxKVkkKstqKC80UFZYTXlR9ZVETL6XvzZdJelQKEBnr8HWQYvt/9zr7DXY2MmjRTo7DTZ26ivf29ipUWtUVnill1UVySOw+fHyRYC8C3JvuZLUPx6j1skXALw6gXckeHf6oyDMKE7SbwAA3X5JREFUDbBYJIwGM4YKeeSwutxIdaVRvq8wYqgwUV1hpKpcTmgrS+Wk12L563mEQgVO7nbonW2wd/n9psPe2Qa9iw0Orjp0elE0ojVKK6xkwXcnOZlazNTu/rw8oSN6m4YfL2ht75Xnz58nIiLC2mFc05IlSzh27BiffPKJtUNpFFf7/1AoFMclSepxtcc3yQRNoVCMB8b7+fnNX7FihbXDEepZWY3Em0eqyK2UeLy7jgg3K5703KTy8nLs7e2tHYbQwBQWM/qKFBzKEnEoS8S+PAn78mSUkhEAs1JHmUMI5fZtqNAHU24fRKVdIGZ14xd8aKnHpCRJcuX8cjCWQ025JLdhq7jcjq3yz0v2QE4KNLagvnzT2IJap7jyvVon31QaUChbxposlakSu8p09BWp6CvS0FekoK9Ixqbmj7mT1TbulNu3+Z9bW6p1nvXSJkCSpD+6HVSDqUq+ryytQWHUYKwC0+X2ef+/GKZSI7ef09j/fq+40rZOYy+vtRNaJpNFYuNFI5svGvG0U3B/FxvaODXsuUBLfa+8FicnJ0JDQ60dxjWtXLmSEydO8O6771o7lEaRmJhIScmfC0kNGTKkeSVovxMjaC1PcWUNty86TFJeOV/P60m/UHdrh3RTWtsVuFajNAsyjkH6UUg/Bpkn/+gRZuMEPp3Bpwv4dpXvXUPk4hFNQHM+Ji0WifLCaopyKinJraI0r4qS/CpK8+WvTcb/ycAUoHfU4uCmw95Vh4PL5Xs3HQ6u8uiMjZ1aFMP4XXkuZJ+FnHPyffZZuTjN71NvbV3k49m32+X7ruDoW2+93f7/cWmxSFSV1lBeZKC8qJqywmpK86ooLaiW/78LqjH/v/9vBxcdzl62OHvp5XtPO5y97LB31aFsIQl2a3coqYDHV58iv9zAC7d0YE6foAb7G27O75W10dRH0Fqbmx1BE2vQhEZTUmnkjsWHuZhXzldzejS75ExoIcwmyD4DqQch7YickJWmy79TauQErNtc8O8Bft3ApY1oSFxHNVUmirIrKc6poCinkuIrtyrMpj9OytVaJY7utjh52BLQwRUnd1scPWxxcrfFwU2HSi2KVNwwe08IHSbffmesktdKZp2WL0JknIR97/+RtOk95UTNr5vctsG/B+ic6iUcpVKB3tkGvbMNXm0c//J7SZKoLK2hNF9O2EryqijJlY+TuENZ1FT/MVVVpVbi5GmLq48eV1/55uZrj6OHrUjcmpneIW78tGAAT6w5xYubYjiaXMgbUzpj3whTHgWhKRN/AUKjKKkyMvvrw8Rnl/Pl7O4MbCdK6QuNxFgNmScgZT+kHJCTsppy+XdOgRAYDf4Py6XsvTu1rObMjcxoMFOUXUFBRgWFWRUUZpZTmFlBedEflSsVSgWO7jpcvOwIiHDF2csOF289Tp622DlqxQhYQ9LYgl93+fY7Y5W8ljLz5OXbCUj4BXk+ogI82kNAT/DvBQG95OI2DVBdVKFQoHeyQe9kg0/bPyeFkiRRVWakOKeC4pwqinMqKcqpJDellMQTuVemTqrUSpy97XD7PWnzs8cj0AG9k81V9ig0FS56LYvn9uTz3Rd595c4YjNL+eyObrT3/msiL9wcSZLEe2oTUJvZiiJBExpcucHE3K+PcD6rlM9ndWdIe09rhyS0ZMZqSDsMl/bICVnGMTDXyL/z7ABdZkBQXwjsC46iIXptSJJEaX41+ell5KeVk59eTmFmOaUF1X86WXbxscM3zBlXXz0u3npcvO1wdLcVI2FNicZWTsACev7xs+oSyDgOaUch/QjEboQTy+Tf6Zzl0bWgPhDUTx5xUzdsAqRQKK5UivQNc/nT736/KFCYWUFBpnyfmVBM/JGcK4+xddTiEWCPe4ADHgEOuAfY4+Ru22LWIbYESqWCh4aE0j3IhUdWneTWT/fz31s7MbW7v7VDa7Z0Oh0FBQW4ubmJJM2KJEmioKAAne7mLv6KBE1oUDUmCw+sOM7ZjBI+m9WN4R28rB2S0NJYzPKUrUu7IWkXpB6SqxQoVOAbBdH3yclYYO8brmYn/MFsslCYWfGnZCw/rezKlDOFApy99XgGOdK+j88f083cdShF36zmSecEbYfKN5DbSRQkXJ4SfFS+ALJju/w7tU4efQ7qI1/48O8FNo1XiEFjo8IzyBHPoD+PthiqTBSkl5GXKh+veWnlpJ9PvVJxUqNT4RHggFewI15tHPEMdsTexUacyFpZ7xA3tizoz4JVJ3lq7WmOXirk5Ykd0Vmzgmoz5e/vT3p6Onl5edYOpdXT6XT4+9/cxQaRoAkNxmKReGbdafYm5PPW1M6M6uht7ZCElqLwElzcAUm75ZGy6mL5554doMddEDJYPlm0cbBmlM2OxSJRlFVBbkoZuSml5CaXkp9RjsUkn9SqtUrc/e1pF+2Nu788IuHmq0etFSdPLZpSCR7h8q3bbPlnFQXyOs6UA5B6APa+C3veli+M+HQhRBUM/mb5wohW3+gh29iq8Q1z+dOIm8loli82pJWTl1ZGbkoZp3emYdkuH992Tto/JWxeQY5obcVpUmPzdNCx4u5o3v81nk93XuTM5Qu8bdwb/zhqzjQaDW3atLF2GEItiXceocG8ue0CP5zK5OlR4UzrEWDtcITmzGSQTwQTtsvrYwoS5J87BUDEOGgzGNoMBAcxQnujJEmivMhAdlIJOZdKyU0pJS+t/ErfMI1OhWegA52HBOAZJE8NE0UYhCv0bvLfXsQ4+XtDmTyylnIQUvbjn7YJVnwvF94J6AVtBsl/o/495D4HVqDW/HW0zWy0kJ9eTk5yKTnJJeQml3HpdD4gjw67+dvj09YZn1AnfNo6Y+8i1rM1BrVKydOj2tMjyJXH15xiwsf7eG96FCPELByhlRAJmtAgvtqbxJd7kpjTJ4gHB9e+k7rQihWnQeJ2OSlL2i03wFLZQHB/6HkPhA4Ht7aiwuINMhst5KWVkZ1UIt8ullBRIq/NU6mVuAfYE9HXB88gBzyDHHHxshNrdIQbZ+Mg/02GDgdg345tDAxS/zHKvet12PUaaPTy6HbIYPmxHuFW/RtWaZR4tXG8XFlSnoJUXWEkL6WMrKQSsi8Wc+FgFmd3yZVeHdx0V5I1n1AnXH30YlpkAxrS3pMtCwZw//LjzF92jCdGtOPhIaHiQpHQ4okETah3G09l8N8t5xnbyZsXx3cUH17CjZEkufz9hS3yLeec/HPnQIi6HcJGysmZFaZLNUfVFUayEovJTCgmO6mE3NSyK1MVHdx0+LZzwTvEEe8QJ9z87VGJ9WJCPbKodBA6+ErCRmWhXEk1abe8XvSX5+Wbo9/ldgDD5VE2W2drhg2ATq8hoIMrAR3kNasWszzKlpVYQtbFYtLOFxF/WC5CYuugwT/cBb9wF/zbu+Dobis+8+qZn7Mta+/vw3Pfn+W97fHEZJbw7rQoUYpfaNHE0S3Uq30J+Ty19jTRbVx5b1oUKnGVS7ges0lex/J7UlaSCgolBPaBkf+VkzL3dmKU7AZUlBjISiwhM76IzMRiCjIqAFCqFXgGOtJ5SMCVhEyUHRcanZ0rRIyXbwAl6ZC4AxJ/hZjLVSIVKnkKZOhwOWnz6dogJf1vllKlvDI1ssuwgMtVTKvITCgmI66Y9AuFJBzLBcDe1Qb/cJfLSZurmBJZT3QaFe9O60KknxOv/nSeSZ/uZ+GcHmJdmtBiiQRNqDfnMkq4b/kx2nrYs3BOD1F1Sbg6YzVc/A0ubIa4rVBVKE9dbDsUBj0D4WNAL5qY/52KEgMZcUVkHLGwcuchinMqAVDbqPAJcSS0uye+Yc54BjuiFn+LQlPj5A/d58o3s0luh5H4q3zb+RrsfBXsveSLNOFj5CmRTWT0XKFQ4ORhh5OHHRF9fZEkieKcSjLiikiPKyL5TAEXDmYD4OJtR2BHN4I6uuET5iT+FutAoVBwV/82tPd24KFvTzDhk318dHtXhoSL1j1CyyMSNKFepBZUMu+bozjbaVlyZy+cbK2zCFxookw1cgn8mO/lkTJDqVzKu91oaD9OTs4asTR3c2SoMpEZX0T6BfkksDDz8giZBgLb29Khny++Yc64B4rpikIzo1LL1R4De8PQF6AiX07U4rfJPdhOLpcv4oQMgnaj5PcNp6bTH0uhUFzu86cncpA/kkUiP6Oc9AtFpMUWcHZ3Oqd3pKHWKPELdyGwoyuBHd1w9rSzdujNUt9QdzY93J97lx/nriVHeXpUOA8MaiumlgotikjQhDorKDcw5+vDmCwWvrsrGm+nm2vGJ7RQZhMk74Fz38P5H+VS+DoniJgAkZPk9SZWqubWHJjNFrIvlpB2vpD0C0XkppQhWSRUGiU+bZ1o18sL//auxCYdZ8jQLtYOVxDqj95dbijfZYZ8cSf1AMRtg/itchXXLU+Cdydof3nKpGdEk5oGrVAq8LjcFLvriECMBjMZ8UWkxhSSGlNAyrkCIAFHD1uCIt1o09kd33bO4sLKTQhwteP7B/ryzPozvLUtjpjMUt6e2hk7rTitFVoGcSQLdVJjsnD/iuNklVTz7fzehHqKvlOtmiTJzWzPrJavfFfmg9YB2o+FjpPlkTK11tpRNlml+VWkxsoncelxRRirzSiUCjyDHOg2KhD/9q54h/x5yuL55KZzYioI9U6tlac3hgyG0a9Dfrw8NTpu6x+VIV3bXl7fNgF8m8a6tf+lsVER3Mmd4E7y1O3i3ErSYgtJiSkgdl8mZ3emo7VVX0nWAiPdsBH91/6WrVbFRzOiiPR15M1tF0gpqGDx3J54OYqLxELzJ94BhFqTJIkXN8VwNLmIj2/vSvcgl79/ktAyFSXD6dVwehUUXQK1LYSPlpOysBGgsbV2hE2SqcZMRkIxqTEFpMUWUpQtryOzd7UhrKcXQR3c8GvvIk7WBAHkUbLfG2b3fwzKciBuizxCf/AT2P+BXBWy/S1ywhbYV54+2cQ4e9rh7GlHp8H+GA1m0s4XculMPsln8kk4moNSpcCvnTPBnT1o08UdB1eRcFyLQqHgvkFtCfOy55FvTzLxk/0snteDjr5O1g5NEOqk6b1zCc3GikMprDqSyoOD2zK+i6+1wxEaW3WJPEp2+ju5fDZA8AC50EfEeLkvkvAXFSUGks/kk3y2gPTzhZiMFlRqJX7tnOk4wI/Ajq44e9mJ9RSC8HccvKDHXfKtqgjif5aTtRPL4MhC0HtAh4kQOQUCeje5kTWQR9dCojwIifLAYpHISSrh0ul8Lp3JZ+/qePaujserjVz0p203T5GsXcPQ9l6svb8vdy89ym1fHOSjGV0ZLppaC82YSNCEWjlwMZ+XfoxlWHtPnhoZbu1whMZiscClXXBypVyF0VQNbqEw9F/QeZrcs0z4E0mSyE8rJ/msfIU8N6UMAAdXHRH9fAmKdMO3nTMarajuJgi1Zuvyx7q1mgq5wX3M9/J71dGvwMEXOk6CyMng171JrVn7nVKpwCfUGZ9QZ/pOCaUou4KkU3kkHs9l/7pE9q9LFMnadXTwdWTjQ/24Z9kx5i8/xgu3dOCufsHiYpfQLIkETbhpaYWVPLTyBG3c9XwwIwql6HXW8pVlw6mVcHwpFKeAzhm63gFdbm+yJzvWZDZbyIwvJulUHsln8ikvMoACvIIdiZ4YQpvO7rj66sWJgyA0BK0eOt4q3wzlcjXIc+vh6CI49Kl8IanjJIicKhcbaaJ/hy7eerqP1tN9dDDFuZVcPJH7p2TNO8SRtt08CevpJXobXubpqGP1vX14fPUpXtkcy6X8cl4a3xG1KMAiNDMiQRNuSoXBxPxlxzBbJBbN6YGDTlTha7EsZrlf2fEl8oJ8ySxPYRz2b7k0vkZcvf1fphp5LUnSyTwuncnHUGlCrVUS2MGNXuPdCIp0x85RFEgRhEZlYw+dpsq3qmKI+0lO1g5+Cvs/BM8O0Hk6dLoNnPysHe01OXva0X108FWTtQPrE/Fv70J4tDdtojzQ6lr3qZ2tVsVns7rx1s9xfLH7IikFlXw6q5u1wxKEm9K6/4qFm2KxSDyx5hTxOWUsubMXbdybRtNQoZ6VZsl9h04sg5I0sHOHPg9Bt7ngHmrt6JqUmmoTKecKuHgij5SYAkwGMzZ2aoI7uxMS5UFgB1fUYuqiIDQNts4QNVO+VRRA7AZ5De2vL8KvL0GbgfIUySa+hvZPyVpOJXGHs4k/ks2vS86j1sYREuVBu2hvAtq7oGylI0dKpYJnx7Snjbsdz284x5TPDnBve4u1wxKEGyYSNOGGfbAjgZ9jcvjXuA4MbOdh7XCE+vR7efzDX8D5TWAxyWWtR74C4beI0vj/w2gwy9XWjuWQGlOI2WTB1kFDeC8vQrp64BfuIvoZCUJTp3eDnvfIt4KLcmuQM6vhhwdg8xNyJcgut0PbIaBsuhdZnL3siJ4QQq/xbci+WELc4WwSj+cSfyQHW0ct7Xp40b6vN+7+TTfhbEjTewYS4GLH/SuO89/DZjpElYgKj0KzIBI04YZsPZvFRzsSmNrdn7v6BVs7HKG+GKvlhfSHv4Cs02DjBNH3Q8+7wTXE2tE1GSajmdRzhSQcyyH5bD6mGgt2Tlo6DvClbTdPvNs6ibWYgtBcubWFIc/B4H9e7uP4HZz7Hs6tk8v2R82EqFng2sbakV6TQvFHgZEB09qRcq6AuMPZnN2dzunf0vAMciCiny/tenqhbWVtO/qGurP+gb5M/3wv0788xMI53enb1t3aYQnCdbWuv1KhVmIzS3lizWm6Bjrz6qRIUdigJSjNhKOL4fg3UFkAHu1h3PvyWgytmLoKcqGPtNhCEo/nknQqD2O1GZ29hva9fQjt4YlPqLNIygShJVEoIDBavo1+Q157e3I57HkH9rwtr8HtNkeeAtmEezuqNEpCunoQ0tWD6goj8Ueyid2Xye5v49i/LoHQ7p506OeLd1unVvN5HublwAu9dXxxXsW8r4/y/vQobunsY+2wBOGaRIImXFdZtZEHVh7H0VbNl3d0x0bddKd6CDcg4wQc+PjyNEYzhI+B6PugzaAmW8msMUmSRG5yGXGHs0k4lkN1uREbOzWh3TwJ7eGJf3jrXdMhCK2K2uaPSpAl6XBqlZysfT9fnmnQaSp0mw2+Xa0d6XXp9Bo6Dwmg02B/clPKiN2fScKRHC4czMbF246Ifr607+2NrUPLn8buqlOy9r6+3LPsKA+vOkF+eUfm9g22dliCcFUiQROuSZIknttwjvSiKr67tzeejqJqX7MkSXBxh1yx7NIesHG8PI3xniY9ZacxleZXEX8km7jDORTnVKJSK2nTxZ120d4EdnBFpRZJmSC0Wk7+MOhpGPAkpOyDE8vltiPHFoNPlDwlPHJKk559oFAo8Ap2xCvYkX5TQrl4IpfYfVkcWJ/IoY0XCevuRafB/ni1cbR2qA3KyU7D8rujeWTVSV7cFENuWTVPjQxvNSOJQvMhEjThmlYfTePH05k8NbIdPYNdrR2OcLPMRojZICdmOefkRq0jXoHu80DXsj+Eb4ShysTF47nEHc4mM6EYAN8wZ7qODKRtN09sWtk6DUEQ/oZSKVd6bDMQqt6GM2vg2New6RH4+QW5AmSPu8CzvbUjvS6tTk1EX18i+vpSmFnBuT0ZXDiYRdzhbDyDHOg02J/QHp6oNS1zxoxOo+LzWd3418YYPt15kbwyA69N6iR6pQlNijgDEa4qPqeMl36MoV+oGw8MFqXVmxVDuTwV5+Cncpl8j/Zw6+dyU9ZWXo1RskhkJBRzfn8mF0/mYTZarlRBa9fLC0f3pruuRBCEJsTWGaLvhV7zIfWQPJp2/Bs48iUE9Yced0LEhCb/nuvqq2fgjHb0nhgiFxXZlc6OpefZvz6RDv186TjQF0e3lve+qFYpeW1SJJ4ONny4I4GC8ho+mdkNW9EWRWgiRIIm/EVVjZmHVp7A3kbN+9OjUIlCCM1DVTEc/hIOfQbVxRDUD255F0JHyFd+W7HyIgMXDmZx/kAmpfnVaG3VRPT1oX0fHzyDHMT0FkEQakehgKA+8m30G/LFsWPfwPq7Qe8h94/seQ84Nu2CFFpbNZ0G+xM5yI/0uCLO7kzn5C8pnPwlheDO7kSNCMSnhRUVUSgUPD6iHR4ONvxr4zlmfXWIb+7shZOtxtqhCYJI0IS/evnHGBLzyll2Vy88HcS6syavqggOfQGHPgdDCYSPhf5PQEBPa0dmVWaTheQz+cTuzyIttgBJAr9wZ3qND6FtVw/RQFoQhPqld4f+j0PfR+Hib3D0K9j7Luz/ADrcCr0fAP8e1o7yuhQKBQHtXQlo70pZYTXn9mQQszeDS6fz8WrjSNcRgbSJ8mhRFWzv6B2Eu72WR1adZOaiQyy/OxpXfdMe+RRaPpGgCX+y6XQm3x1N48HBbRkQJppRN2mVhXJSdvgLMJRC+3Ew6B/g09nakVlVSV4VsfsyOH8gi6oyI3pnG7qNDiKirw9OHnbWDk8QhJZOqYSw4fKtMAmOLIKTK+S+an495EStw0RQNe2RGgdXHX1ubUuPMcFcOJjFqR1pbFt4Dkd3HVHDA2nfxweNTcu40DU60odFc1Tct/w40788yMp7okVhNMGqRIImXJGcX8Fz35+le5ALT4xoZ+1whGupLISDn8DhhVBTJq9zGPQMeHeydmRWY7FIpJzN59yeDFJjC1EAwZ3d6dDfl8CObi3qaq8gCM2IawiMfl1uhH3qW/mC2vq74ZcX5OqP3e+UR96aMI2Nik6D/ek40I9Lp/I4uT2VPd/Fc/jHJDoN8qfTYH/sHJv/iNPgcE+W3NmLu5ceZdqXB1k5vzd+zi1v/Z3QPIgETQDAYDLzyKqTqJQKPrq9q6hm1BRVl8g9zA59DjUV8hXYQc+AV0drR2Y1FSUGzu/PJGZvJuVFBuyctPQYG0zH/r7Yu4irn4IgNBE2DnLPyZ7zIXG7/D7+23/lJthRs6DPQ+DW1tpRXpdSqaBtN09CunqQfbGEk9tTObY1mZO/pBLR14euowKbfUGRPm3dWHFPNHO/PsK0L+SRtGD3pts+QWi5RIImAPDm1jjOZpTw5ezu4opRU2Os/mMtQ1WhvJZh8LPgGWHtyKxCkiSyEos5szODS6fysFgk/Nu70H9aGMGd3VGJiwuCIDRVSiW0GyXfci/IsyFOLpcrQEaMl9ev+Xe3dpTXpVAo8Al1xifUmeKcSk5uTyV2fyax+zIJ7+NN99FBzXo6ebdAF1bN782cr4/II2n3RBPm5WDtsIRWRiRoAr/G5vD1/kvM6xvMqI7e1g5H+J3ZBGe+g52vQ2k6tB0Kw/4Nvl2tHZlVmIxmEo7mcmZnGvlp5djYqek01J/IAX44ezXfk4HWyGgxUmmspMJYceVWba6mxlxDtakag9kgf/37z8zVGM1GTJIJs8WMWTJjspgwS+Y/ff+73yvNKfjzvUqpQqVQoVaq0Sg1qJXqKzeVQoVWpcVGZYNOpUOn1qFT6bBR2/zpZ/Yae/RaPXq1HpWyZay/EazEsz1M/ASGviBPfTz6NcRulMv091vQLCrwOnvZMeSO9vQYG8zJn1OI3Z/FhYPZtOvpRfcxQbh4N8/Rp0g/J1bf25uZXx1m+sJDLLurF5F+TtYOS2hFRILWyuWVGXh63Wk6+jryz7FNu7lmqyFJcGEz7HgF8uPArzvc+hmEDLJ2ZFZRUWLg3G65klhVmRFXXz2DZ4XTLtobjajEaDVGi5Gi6iKKqosoqC6g1FBKaU0pJYYSSmv+39eGUsqN5VeSshpLzU3v7/fESqVQoVKqUCvUf0q4lAolChRISIA80gpc+R64ksj95SaZrrrPv2OrtkWv0V+52WvscdQ64mTjhKONI05aJ5xsLt8uf+2ic8FF54JG2bQLRAiNyMEbhr8EA56E40vlVinfTgOPCDlR63RbsygoMvD2cLqPCebk9lRi9mQQdySb0O6e9BgTjJufvbVDvGlhXg6sva8Ps746zO2LDrH0rl50C3SxdlhCKyEStFZMkiRe+OEsFTVmPpwRhY1anOxaXfJ+2P5vyDgGbmEwbbk87aUF9Z65UTnJpZz5LY3E47lYLBLBkW50HhqAf3uXFtWLpymRJIkSQwm5VbnkVuaSV5lHTmUO+VX5FFYXUlBVQGF1IYXVhZTWlF5zOzqVDketI442jjhqHfGx95FHnjR67DR26NV/JDW2Glv0aj22alt0ah1alRad6s/3NiqbBh2tkiQJs2SmxlyDwWyg2lRNtbn6z1+bDFSZq6g0VlJeU06FqYKKmooriWe5sZwKYwXJpcmUGEooNhRjtBivuU8nGydcda646dzke1v53t3WHU87T7zsvPC088TZxlkc762FjQP0fVheq3bue9j/IfzwgDyLov9j0PUOUNtYO8rr0jvb0P+2MLqNCuL0jlTO7sog8Vgubbt5ED0hpNmNqAW761l9X29mfXWY2V8dZsldvegZ7GrtsIRWQCRordjmM1n8HJPDs2PaE+op5ldbVeEl2P4vOP8jOPjChI+hy0xQta4/UckicelMPqe2p5J1sQSNTkXkQD86DfHH2VNMY6yrSmMlWRVZZJZnXrnPLM8kpzJHTsiq8jCYDX95npON05VEop1LO1x1rrja/pFcuOhcrowQOdo4YqOyzkmkxWLBVFWFobCAmuJiDCXF1JSWYigrpaa8HGNVJSaDAXNNDaYaA2aj8fK9CbPRiMVixmIxI1kkLJLlT/eSZEGSJBQKBTrAVqFArr2nkBMohTyVUql0QKlyRqUKAaUSSQkWpYRFAWaFBZPKgkFtoVplolJppExZQIkynURFBYXKSip1EmW2FipsJSSlAq1Si4edB152Xlfufe198dX7yvf2vjhoxft3i6LSQJfp0HkaJGyHPW/Blidgz9vQdwF0nwfapv1+aOeopc+kULqOCOL0b2mc2pFG0sk82vfxoee4Nji4Np8iTv4udqy9rw8zFh1i3tdHWH5PtBhJExpc6zr7E67ILzfw743n6BLgzD3921g7nNbLUCYX/zj4KSjVMOQF+QqqpnUVajEZzcQfzuHk9lSKcypxcNXR/7YwIvr6oLUVb1M3yiJZyKvMI7UslbSyNFJLU0ktSyWjPIOs8iyKDEV/erxaocZb742X3otOHp2ujNr8ngh42nniYeuBVtW4JbRNlRWUpaVRkZVJRXYWFXl5VBYXYSgvxVBRiaG6CkNNNTVGIzVmE0aLGSNgUiqQajHapJAklJKEUgIF//+m+OPry9v+Y/rkHyTk6ZQSYLn8vUUBFsX1Y9IDemzwxQb4nyvzkoTaIqGSJJRIKMhCUmRgUpjJUZlIU1uo0lqo0pkx2mlQuTlh6+GBk18gXgFhBDkHE+gQiJ+9H5omPj1OuAaFAtqNhLARcGm3XPHx53/Knxl9H4ae98ijbk2Yzl5D9IQQOg3258S2FM7uSSfuSDaRA/3oPjq42ZTn93TUsWp+b6Z/eZC5i4+w4p5ougQ4WzssoQVT/P5B0xT16NFDOnbsmLXDaJEeWnmC7bE5bFnQX1Qnugm7du1i8ODBdd+QxQKnVsKO/0BFLnS5XS4A4uhb9203I9UVRmL2ZnD6t3SqSmtwD7Cn28gg2nbzQCmqMV5TiaGESyWXSCpJYs+5PUhOEqllqaSXpVNtrr7yOLVSjZ+9H/72/vjY+/xp1MVH74OHrUejFbowG2soS06mNCWZsow0ynKyKc/Po6KkhMrKcqprDBjMZgxImK7zf6+yWNBIoFUo0ShV2Gi0aLVatDY6tDpbtDpbNLa2aO3s0Ort0drbo3VwQGvvgEavR22nR21ri1avR623R623Q6Vp2JNEi8WCxWDAVFmJsbICY1kZNWVlGMvLqKkox1hRgbGyEmNlJYaKcmoqyqmprMRQVUWNoZoaowHjlWTUQg0SRqXimlOfFRYJjcWEQjIjKcygUaCys0HraI+tuwdu/sEEduhG2469sdE3zNqgenuvFP4s5SDsfQcSfwWds9z0Ovp+sHW2dmQ3pKywmqNbLnHhQBYqrYqoYQFEjQjEphEuxNXHMZlZXMX0hQcpqTTy7fzeonCIUCcKheK4JEk9rvo7kaC1PlvOZPHQtyd4elQ4Dw0JtXY4zUq9nHSkHIBtz0LWafDvBaPfaPJlletbWWE1p3ekEbMvE5PBTEAHV7qODMQ/XKwv+50kSRRUF5BQlEBSSdKVhCypOImC6oIrj1OjJsgpiADHAAIdAgl0CLzytbfeG7Wy4U98LBYL5WmpFMXHUZycRFlmJqX5eZSXFlNRXUml2UT1NRIKrdmCTqFEp9ags7HF1k6PrYMDds4u2Lm6offwRO/jg97XDztPL9S2rWt0+VrMxhoqs7OpyMqiMjebyvw8qgoLqSwuorQon/KyEqqqKqkxyaOLNSrlX//9JQmt2YwaCa1Gja29Hic3T7wD2hLQuSsuER1Ru7vX6m9SJGgNLOOEPKIWtwV0TtD3ETlRa+Ijar8ryq7gyI+XSDyei42dmm6jg+gyJACVpuEuzNXXMZleVMn0Lw9RbjCxan5vOvg61j04oVUSCZpwRUG5gZHv78HX2ZYND/YVDalvUp3e4Esy4JfnIWYDOPrB8Jeh09RWVQCkOLeSE9tSiDuUjQSE9fCk68hA3P2bx0lFQ6k2VXOx5CLxhfHEF8WTUJRAfFH8n6YkOmgcaOPchhCnkD/dEo4nMHTI0AaPsaa0hIJzZymIv0BRSjIlOTmUlhZRbqimAgmL8s/HsdIiYSeBnUaL3s4ee2dn9K5u2Ht64eQXgGNQEI5tQlDbNa+iAc2V2VhDRUYG2QkxpCWdoyDtEhV5+dSUV2A2mLBYlJiUKsyqP0ZUbYwmnKprcFSr8XBxxz84DH1QMBp/P7RBwWiDAlHqrr6WSCRojSTrDOx6HeJ+AltXuZhIz/lNfo3a7/JSyzi0MYnUmAIc3XX0mRRK224eDXKhrj6PybTCSqZ/eZBqk4VV83sT7t26P8OE2hEJmnDFI6tOsu1cFpsfGSDeUGqhVm/wZhMc+RJ2vgYWE/R/XF7o3Uw+QOtDYWYFx7clk3A0B6VKSYf+vkSNCMDRrfWNhpTWlHK+4DyxBbHEFsQSVxRHSmkKFskCyBUQQ51DaefajnYu7Qh1DiXEKQR326uPZNTnSYfZYKDg3Blyz56mIOkiRdmZlJSWUG6qofr/XcxRWSzoUeJga4ejowuOHp44+fnhFByCc1g77AMCUTbxHk7CHwxmAymlKVy8dJr000cpjUvCnFOKslKBgstr2CQJ++oanCsNOFUZcKwy4OLkgl1wMNrgYLRBQVfuDyYlMXjYMOu+qNYk/TjsfBUu7gC9p1yyv/s80DSPYhxpsYXsX59AQUYFPqFO9L8tDM+g+h2Zqu+LBsn5FUxfeBCTWeK7e3uL5SLCTWt2CZpCoRgPjPfz85u/YsUKa4fTYhzLNvHJKQOTwzRMaNs8FuY2NeXl5djb3/iaDYfSOMLjPse+4hIFrt1JCLuXatvW0wy8qkgiP0aiNF2ugeISCm7hCjS2rWPUsNJSSZohjbSaNFJrUkmrSSPflH/l964qV/y0fvJN44ev1hd3tTtKxY0nNjd7TAJYqqowJiViSE2mOi+HqooyqkxGKpUKpP8ZCdOYLdihwFarw8beERtXNzSe3qj9A1C5e6AQCViLZ7AYyChLJjfrIhW5mShyirErsqAxX/6/lyRszEZcKmpwKa++kripFEpM3t6Yfbwx+fhi8vHG5OOD2dMTVKKlS0NxLDlPm0srcSk+S7WNG6mBt5HlMxypGfTdkywSRUmQe1bCbACnYPDqrEBjVz+fF7V5r/w72RUWXj9SjSTBP3vp8LEX74nCjRsyZEjzStB+J0bQ6k9RRQ0j3t+Nl6OOHx7qh0ZMbayVG74CV1UkFwA59o3chHTMmxAxodVMZ8y+VMLxn5JJPluAVqei89AAOg/1x9a+5V4YMFvMJBYncib/DKdzT3Mm/wyXSi5d+b2fvR8d3DrIN9cORLhF4KKre6nm6x2TZmMNuceOknPqJHkXEyjMzaK4soJyJVeORYUkYS8pcNTZ4ezmjqt/IO7tIvDo2hWHgMA6xye0PBaLhaS0WE6f209aYiylaRmocivRGeTPFQkJhcKMi0XCq7QGt5xCHKpqUAJoNNgEB2ET1g6b9u3RRbTHJjwctUfDTGtrtZJ2yyNqaYfBpQ0M+xd0mATN4KJKTZWJ49tSOL0jDYUCokYG0m1kEBqbuiX2DTXtNjG3nBkLD6JUKFhzXx+C3cW0beHGNLsRtN+JBK3+PPbdSTafyeLHR/oT4SMWtNbW377BSxKcWSOvNasskBdtD3mu2SzcrqvclFIOb7pEakwBNno1UcMC6DTYHxu7pn/19mYVVxdzKu8UZ/LOcDrvNOfyz1FpqgTAVedKZ/fOdPboTEf3jnRw7YCzzrlB4vj9mDQUF5O5fy/ZZ06Sm3yJgqICSiQTFuUfIx32FnCy0+Pm4Y1721C8Okfh2a27WAcm1IuUzAROn9tHcvxZ8hIuYltoxKZGPv7MSgtKnQJXlQbfagXeWcXYZGRfea7KzQ1deDg2Ee3RtW+PLiICbZs2KMRoW+1Jklzt8deXIOcc+HaFEf+BNgOtHdkNKc2v4uCGiyQez0XvpKXfbWGEdvesdSLfkOsi43PKmLHwEHZaFesf6IuXY/OYWipYl0jQWrlfYrK5d/lxHhsexmPD21k7nGbtum/wBRdh82NwaQ/4dYdx74NPl8YMz2ry08s58mMSl07nY6NX021kEJGD/NDqWk4Ps5yKHE7knuB4znGO5xwnsTgRkHuJtXNtRxePLnT26EwXjy742/s36GhAdUEB6bt3knHqOKnxF6g01fxpVExjtuCs1uLm7oln2zC8O0fh1bMXWkdRElpoHLt27WLgwIHEJZ/i1Km9pCfEUJmWg22BCZVFPk6rbSV0Trb42zgQUq3FNS0XY+JFJKMRAIWdHboOEdhGdkIXGYltZEc0QUFipO1mWczyhcPf/gul6RA6XC5S5R1p7chuSFZiMXtWx5OfVo5/excG3R6Os9fNr+Fu6MI1Z9NLmLHwIP4udqy+rzfOdi13xohQP0SC1oqVVBoZ/v5u3O1t2PhQP7Tqpj+9oSm76hu8xQyHv4Adr4BKC8NflBdnN1J/KWsqzKrg6Ga5VLJWpyJqRCBdhga0iObSaWVpHMs+diUhSy9PB8BObUdXz6509+pOV8+udHTviK264YqdmCoryNi/j4yjh8hOSqSgpIhShXQlGdOZzLja2ePu5Yt3+wh8o/vi0jFSFOgQrOpaJ8PVhkqOn9tNzOkD5CYkoMgsRVctH6s1Ggsmbzu8PLwJt/EgpATMseepvnAByWAAQOnoiK5jB2wjO2HbNQrbqCjUrq5/2Y9wFcZqOLJQbnRdXQJdZsCQ58E5wNqR/S2LReLc7gwOb0rCZDTTbWQQ3UYHodHe+OdsY1QWPZCYz7xvjhLp58iKe6Kx0zb/z0Kh4YgErRV7ceM5lh9KYdPD/UVDxXrwlzf4/AT44UFIPwLtRsujZq2g2XRJXiVHNycTfyQblVZFl6H+RA0PRKdvvlMZC6oKOJJ9hMNZhzmUdYiM8gwAnG2c6ebZje5e3enu3Z1wl/AG7S1WcjGR5B2/kHH2DDm5mRRbzFdK2GvNFlxtbPH08ccnshMBA4dwMjVNlDMXmpwbPRm2WCzEJZ3i2IkdpF+IwZiWj75U/p1JJWHw1uEW2obO3u1pX6PHFHuB6nPnqI6PB5MJAE1QIHZRXbHtKt9sQtuKqZHXU1UEe9+Dw1/K30ffBwOfkvupNXEVJQYOfJ9I/OEcHNx0DJzejuDO7jf03MZq/bDtXBYPrjzBgDAPFs3pIS6MC9ckErRW6nxWKbd8tJc7egfxn4nNYypDU3flDd5ihoOfyouw1ToY8xZ0ntbii4BUlBg4uvkSsfuzUKoUdBrsT7eRgdg6NL+pHBXGCo7nHOdQ1iEOZx0mvigekPuN9fDuQbRPNNHe0YQ4h9xUVcWbYTbWkHVgP6n795CZGE9eaTGVKvkYUlokXJRqPD198InoQED/QbhGdvrLyJjoNyU0RXU5LjNzkzlwZBtJZ49RfSkbfYn8c6PaQo2PHR7hYXTp3I9OCk9qzpyh8uQpqk6exFxYCIBSr8e2Sxdse3RH37Mnui5dUGqb33tUgytJh99ehdOrwM4Nhr4A3eY0i9kfGXFF7P4unqKsCtp0caf/tLC/bdvSmO+Vq4+m8o/1Z5nQxZcPpkehVLbscwOhdkSC1gpJksT0hYdIyClj51ODxVzoerJr1y4Gd/SRR80yjkH4LTDuPblSYwtWU2Xi5PZUTv2aisUk0XGAL93HBqN3srF2aDdMkiQSixPZl7GPfRn7OJF7ApPFhFappatXV3r79CbaO5oIt4gGGyEzGwyk7dpByt7dZFy6SJ6hEtPliqo2ZgsedvZ4B7cloFdv/IcMR6v/++IdIkETmqL6PC7Tcy6x/9BmLp09iTE5F7sy+ecGrQUp0JmATl3o328C/pKeqpMnqTx5kqqTpzDEx4MkodBqsY2Kwq5nT+x69sQ2qss1G2y3SpknYds/IfUgeHWC0a9DmwHWjupvmU0WTu9I4+iWSyBBrwkhdBkWcM1kqLHfKz/fdZE3t11gbp8gXprQUaydFP7iegmamBzbQm06ncmRS4W8NqmTSM7qi9lEQOp62LtabjI9ZTFETmnRo2Zmk4WYvRkc+ymZqjIjod09iZ4YgrNn82iyXV5TzuGsw+zN2Mv+zP1kV8hV48JcwpjdYTZ9ffsS5RGFTt0wJ2umqirSfvuV5AN7ybx0kXxjFabLI2D2ZolgV0/8OkQSNHgobp2jxLoxQbgKf682TJ/4CEyUv0/OiGP/wc2knDkJyYXkJe5lw4a9VDiBbagfHQb0Z8DTj6E3QuXx41QeOUrl0aPkf/45fPopCo0GXefO6KN7oe/bF9vOnVG05hE2365w51aI/QF++TcsHQftx8HI/4JrG2tHd00qtZJuo4II6+nFnu/iObA+kcTjuQyd0x433/rtd1Yb9w8KoaiyhoV7knDRa0WRNuGmiBG0FqjCYGLou7vwcLBh40P9UYmh9borvATfz4f0oxAxHm55D+w9rR1Vg5EsEokncjm0MYnSvCr8wp3pMykUr+Cm36IhrSyNnak72Z2+mxM5JzBJJvQaPX18+tDfrz/9/PrhrW+YEU+LxUL2gX1c/PVn0hLiyK2pxHw56XKwgLebBwGdomgzcgzOYfXzYS1G0ISmqLGOS4vFwvFzuzl66Gfyz8ejyzagsigwKyWqfXX4dIpk4ODJhAd3wVxWJidsR49SefQY1efOgcWC0s4Ou5490ffri75PH7Shoa13tMNYBQc/gb3vg8UIvR+AAU+Brmm/90uSROLxXPZ8F09NlYmetwTTdVQQqv/p+WqN90pJknhm3RnWHk/n5Qkdmds3uFH3LzRtYgStlflkZyI5pQY+m9VdJGd1JUlw+jv46SlQqIiNeJIO0/7VokfNMuKKOPB9IrkpZbj56Rn3cBcCO7o22RMWi2QhtiCW31J/Y2fazivl70OdQ5ndcTYD/AYQ5RGFRtUwBUyK4uO4+NOPpJw5SVZpEYbLJwR6s0SIuxeBUT0IGT0Wx+CmeyVaEJorpVJJz85D6Nl5CAClFcXsObiJ88f3oUjIpHTrcTZvPc5qJ9C3DyKq9zAGPLYAL40N5tJSKo8coeLAASr2H6B8924A1J6e6Pv0kRO2/v1bV5VIjS0MfBqi7oAd/4H9H8KpVTDyFeg8vcl+9ikUCsJ6eOEf7sLe1fEc3nSJxBN5DJsTgUeg9fqQKhQKXp/cieIqIy/9GIOznYaJUX5Wi0doPsQIWgtzKb+Cke/vZkIXP96d1jp6cDWYqmLY8gScWw+BfWHyl+w6ldRiRytK8qo4sD6RpFN52LvYED0hhHbR3k1ycbPRbORw9mF2pu5kV9oucqtyUSqUdPPsxpCAIQwJGEKAY8OUjjZVVpC0eROJ+3aTnpVO2eULtFqzBW97JwI7diJ09DjcOnVukP3/f2IETWiKmspxeTb+MPv3biL37Hlssw0oJQU1GguWYBfa9ohm5JAZuDrJsyGMGRlUHDwoJ2wHDmIuLgaFAtvOndEPGoj9wEHoOkSgaE1TkTOOw09Py/dB/WDsO+DVwdpR/a2kU3ns/jaOqnIjXUcG0vOWYPbt32u1Y7LaaGbO10c4lVrM8rt7ER3iZpU4hKZFFAlpJSRJ4s4lRzmWXMRvTw3C00Esgq61lAPw/b1QmglD/gn9nwClqsmcdNSnmioTx7Ymc/q3NJQqJd1HBRE1PAD1TfSXaQxGs5GDWQf5OflndqbtpKymDFu1Lf18+zEkcAgD/QbirHNukH0XxV0gbuN6ks+dJruqHLNSidIi4a7WEtC2HW2HDMdv0BCU6saflNASj0mh+WuKx2VBcQ6/7VlHwonDkJSPjUEpT4X0syWwW3eGD5uBv5c80i1ZLFTHxFK+Zzflu/dQffYsSBIqD3fsBwzEfuBA9P36onKw3uhMo7FY4OQy+PUlqC6Vpz0OfhZsmvZrr64wsn99IhcOZOHibYdzZBVjpw6xWjwllUYmfb6fwooavn+gLyEe1l8nJ1iXSNBaiV9jc7hn2TFeuCWCewaEWDuc5slshN1vyo08nYNgylfg/8ffTlM86agti0XiwsEsDm1Moqq0hva9vel9a1v0zk2nMuPVkjIHjQNDAocwImgEfXz7YKOq/3jNxhpStm4lYecvpKWnUHL5grmt2YKfmxch0X0JmzgZnZv1r4K2pGNSaDma+nFpNNWw79hPHN+7jarzadhVKLAgUemlwTsqkqFDpxMW3OnK400FBZTv3UvFnj2U79uPpbQU1Gr0vXphP3wYDsOGofHysuIragQVBbDjJTixDBx8YdSr0HFSk532+LvUmAJ2rrxAeZGBnmOD6TE2GKXKOqOgqQWVTPpsP/Y6NRse7IervhUXpxFEgtYaVBvNjHx/D1q1kq2PDkBjpTefZq0wCdbPl8vnR82CMW/+5QphUz/puFGZCUXsXZNAflo53iFO9J8W1mQKgJgsJg5mHmRb8ra/JGWjgkfR26c3WlX9f6jVlJURv341ifv3klaUR41KiUKScFNqCAoNJ2zUWHz6DWhylRZbyjEptCzN6bj8vdDIgd0bKTl3EX2xfF5U4arALaoDw0bcTvuQqCuPl0wmqk6domznTsp/3UFNSgoAus6dcRg2DIcRw7EJacEXSdOOytP/s89AyBB52qN7qLWjui5DlYm1H+6hJBm82jgy/M4OVqtGfDyliNsXHaKznxMr7olGp2las1WExiMStFbgk98SeOeXeFbcHU3/MHdrh9P8xG6EHx4CpRLGfQCRk6/6sOZ00nE1ZYXV7F+XyMUTudi72NB3ciihPTytXgBEkiTO5Z9jc9JmtiVvo7C6sFGSsoqMdM6v/Y6LJ46QdXnqotpiwVfvRNvu0YTfNh29t0+977c+NfdjUmiZmvNxeT7xBLt2riXvVCz6fDMAFe5KPLt2YsSoWbQN+GMNliRJ1CQlUbb9V8p27JCnQgLaNm1wGD4Mh5Ej0UVGWv09tt5ZzHB0Mfz2Cpiq5WUAA54AddOZgfH/7dq1Cz/7CHZ/G4fZLDFgWhgRfX2s8n+z5UwWD317gvFdfPlQNLJutUQVxxYus7iKT3deZEykt0jObpbZCNtfhEOfgl93uG0JOAdaO6p6d6Wh50/JYJHoNb4NXUcEWn2dWWppKluStrDl0hZSSlPQKrUMChjEuJBx9Pfr3yBJWWnyJWJWLSfhzEnyzTVICgU6s4U2bl60GzCEtpOm3FCDaEEQWqaI0G5EhHYDIC75NDt+WUXFyRgqtp/mh+2nqfBU4929C6NG3kGQbxg2bdti07Yt7vffhzEri7LffqN8xw4KvllCwaKv0AQE4Dh6NI5jRmMTEdEykjWlCqLvhQ4T4efnYPcbch+18R9BYLS1o7umsB5eeIc4sWNpLDuXXyDlbAGD7wjH1r5xpxre0tmH1ML2vLntAkGudjw1KrxR9y80fSJBawFe/ek8EhLP3xJh7VCal9JMWHsnpB2CnvPl+fRN+OpfbaXHFbFnVRxF2ZW06eJO/9vCcHS3tVo8JYYSfrr0E5uTNnMm7wwKFPT07sndkXczPGg4Dtr6X3j+v0lZnrkGFArszRIdA4IJHzmWwBGjrFLgQxCEpi08uAvh98oVkc8lHGXn9tVUnI6jbOtx1m49RqWvDSF9+zJ+9F04Obii8fHBddYsXGfNwlxcTNmOHZT+tJWCr7+mYNEitEFBOIwZjeOYsdi0C2v+yZqDF0xdLJfg3/w4fD0Ket4Dw19sskVEHFx1THy0K6d+TePQxot890oJw+ZGENihcdcU3z8ohJSCCj7ZmUigmx3TejRM5WGheRJnJM3cgYv5bDmTxePD2+HvYp351M1S0m5YfzfUVMKUxdBpqrUjqncVJQb2r0sk4WgOju46bnmoM8GdrDPCapEsHM46zIaEDexI3UGNpYYwlzCe6P4EY9qMaZDG0ddKyjoFhdBx4hR8+g9scuvJBEFouiLDehIZ1hOAU+cPsOuX1ShOJ5KzbhdfbNiJqa0zUYNHM3LQdDRqLSpnZ5ynTMF5yhRMRUWU/bKd0m1bKVi4iIIvvkTbti2OY8fgNGEC2oBmfnLebiQ8dAh++y8c/hLifoJb3oPw0daO7KoUSgVdRwbiH+HC9q9j+fGj03Qe6k/fSaGoNI3zuaBQKHjl1kgyiqt47vuz+Dnb0i9UzIISZGINWjMmSRK3frqf/PIadjw5SCw0vREWC+x7D3a+Cm5hMH05eNz41ILmsK7CYrZwdlcGR35MwmSy0G1UEN1HBVllOmNWeRY/JP7AD4k/kFmRiaPWkVtCbmFS6CQi3Op/xLcqL59zK74h7uhBckyGK0lZSFBbOkyc3CKTsuZwTAqtT2s5Li0WC7sObeTIjk1IcTlojUqqdRZsOgYyaPT0Kw20/5cpP5/SX36h7KetVF4+x7Ht1g2nCRNwHDMalZNTY7+M+pV2FDY9AnnnoeNkueCWvae1o7rmMWmqMXNgw0XO7kzHM8iBUfdG4ujWeLNMSquNTP38AFkl1Xz/QF/CvJrmyKNQ/0SRkBbq55hs7lt+nLemdGZaz2Z+9a0xVBbChvsh4WeInArjPwSbm+tD0tRPOrIvlbBrZRwF6eUEdnRlwPR2jV6pymg2siN1B98nfM+hrEMA9PbpzaSwSQwNHFrvZfFNVVVcWL2S87t2kF5RgkWpxM5sISQwhMhbp7bIpOx/NfVjUmidWuNxWVFVxtYdyzm/dxc2KRWoJAUVLgq8e3dj4vh78XLz+8tzjJmZlPy4mZJNm6i5eBGFRoP94ME4TZyA/cCBKLTNtAy7qQb2fwB73gaNHYx+A7rMsGpJ/r87Ji+ezOW3pedRKBUMn9eB4M6NN5qVXlTJpM8OYKNWsunh/qL8fishErQWyGyRGPvhXoxmC788PhC1KKt/fdnn4LvboTQLRr8uz5GvxQdFUz3pqKk2cXhTEmd2pqN3smHA9DBCojwadX1DZnkm6+LXsT5hPYXVhfjqfbk19FYmhk7E1963XvdlsVhI3vwj5376geT8HIwqJRqzhWB3byLHTiR43PgWnZT9r6Z6TAqtW2s/LrPz09i8ZTGZh46jL5QwKyVq2jrRY8R4RvS/DZXqzytMJEmiOiaWkk0bKd3yE+aCAlROTjjeMhanKVOw7djRSq+kjvLi5NG0tMMQfguM/8Bqo2k3ckyW5FWybeE58tPK6TYqkOgJIY3WM+10WjG3fXmQHkEuLLurlzivawVEgtYCbTyVwaPfneKj27syoUv9nvy2OBe2yP3NdI4wfcWfGk/frKZ40pESU8CulRcoLzTQaZAfvW9ti9a2cZaXWiQL+zP2syZuDXsy9gAwyH8Q08On08e3D0pF/X7AFF6I5dSSxcQnXqBCpUBpseCvdyJi8DDaT5+F2tZ6xU+spSkek4Igjss/HDr1K7t/WoUlNgutUUmlXsKpezjjJtxDyP+U7P+dZDJRsX8/JRs3UbZjB5LBgE2HCJynTMFp3LjmNwXSYoaDn8rr07R6GPee3OC6kd3oMWkymtm3JoGYvZn4hDox6p5I9M6NU0Bs7bE0nl53hrv7t+Ff4/56bAgti0jQWhij2cKI93aj06j4acEA0T/jWiRJXm+24xXw7QozvgXHuvW0akonHVVlNexbm0D8kRxcvO0Yckd7fEKdG2XfRdVFbEjcwNq4taSXp+Omc2NKuylMDZuKj3399g2rqaggZuliYvbtJsdUDQoFHgo1Eb36Ejn7Lmw9Wvei6qZ0TArC78Rx+VfllSVs2vY1iXv2os+qwYJEVYAtUSNvYczQWWjUf53WZi4tpWTzZorXrsNw/jwKGxscRo3EeepU7Hr2bF5VIHMvwA/3Q+ZJiJwiN7i2c2203d/sMRl3OJtdKy+gsVEx4u6OBLRvnFhf2hTDkgPJvD+9C5O6+jfKPgXrEH3QWph1x9NJLqjkqzk9RHJ2LcZqeVrF2TXyerOJn4CmZYyuSJJE/JEc9q1JoKbaRM9bguk+OrhRKk/FFcaxPHY5Wy9tpcZSQw+vHjza/VGGBQxDo9LU234sFgvpv/3K6fWruZSXhVGlxNZsoXNQKFGz5+ER1a3e9iUIgtAY7O2cmDn5cZj8OOeTTrBt0zeoTl4kYfF6zny3DpfoSCZNegBfz+Arz1E5OuI6cyauM2dSFRND8bp1lG7eQummH9EGBeE0ZQrOUyajdmvcEvG14tke7v4V9r0v901L3ievBQ8fY+3Irio82huPAAe2LTzLpg9P0WtcG3qMCUbRwOddz98SwfmsUp5df5YwTwci/ZrZiKlQL8QIWjNTbTQz5J1deDnq2PBg3+Z19ayxlGXDdzMh4zgMfQEGPFVvC5OtfVW4tKCK3SvjSI0txKuNI0Nmt8fN9+YKndwsi2Rhb/pelscu53D2YWzVtkxoO4EZ4TMIdQmt131V5eVzavEXxJw4TIlCQmmR8Nc70WnUWMKmTkOlEQun/z9rH5OCcDXiuLwx1TVVbNq2mAs7dqDPNmJWShhDnel3y3QG9hp31bW0lqoqyn75heK16+QqkBoNjqNG4TJzJrZdo5rHeUHWGfjhAcg5B1Gz5LXhuoZNRGp7TNZUm9j9bRzxR3Jo08Wd4Xd2QKtr2PGN/HIDEz7eh0KhYNPD/XCzb3k9WgUxxbFF+XrfJf6zOZaV90SLfhlXk3lKTs6qimDyQogYX6+bt9ZJhyRJnN+fxb61CQD0vrUtkYP8GnQEtdJYyaaLm1h5fiXJpcl42XkxM2ImU8Km4GRTvx+k6bt+4/iq5VwqzMGsVOJogQ5RPYi68170vmKN5fWIE2GhKRLH5c07Gbuf7RuXYDmXgcakpMJFQcCA3ky59SEc9c5XfY4hKYmib1dR8sMPWMrLsYmIwGXm7TiNG4eyqa/JNRlg95vyiJqDL0xZBEF9G2x3dTkmJUni7K509q1NxMXbjlse7Iyje8P++55NL2HqFwfoGujM8ruj0YiiIS2OSNBaiAqDiYFv7STc24Fv5/e2djhNT8wPchl9Oze4fRX4dK73XVjjpKO8yMDOFRdIjSnAL9yZobMjGvSDIacih1UXVrE2fi2lNaVEukUyp+MchgcNR6Osv2mMNaUlnP7qS84d3kchFpQWiSBHF7pOnk7QmFtaTRXGuhInwkJTJI7L2ispK+T7TZ+TtvcQ+iKJGo0Fm+4hTLrtYdr4t7/qcywVFZT8+CNFK7/FkJCA0tER50mTcLl9Btrg4MZ9ATcr/RisvweKU+QZL4P+Aar6H6Gqj2My7XwhPy86h0KhYPS9kfiFu9RPcNfw/Yl0nlhzmjv7BfPi+GZayVO4JrEGrYVYciCZgooanhp1442VWwVJkq/A7XgZ/HvBjJVNoilmXf2+1mzv6njMRgsDprej0yC/Bpv/nlySzDcx37Dp4iYskoVhgcOY3WE2UR71O2Um78Rxjnz9JRez0zGqlNibJXpFRtFt/gPo/cSCaEEQWjcnB1funPU8ltst7Dz0Awc2rUZ96BLrDj9JTagzgyfdQb/uf163pdTrcZkxA+fp06k6fpzClSvl29Kl6AcOwO3OO7Hr3btpTn/07wH374WfnoE9b0HSLnk0zSXY2pH9RUCEK1P/0YOfPj/Dpg9PMWB6GJGDGu5za3I3f85mlPDN/mQifZ2Y0l18RrYWIkFrJkqqjHy5+yLD2nvSLbBhr9g0KxYzbPsnHPlSrgo18TPQ6KwdVZ1Vltawa+UFLp3OxzvEiWFzI3D2apiG0+cLzvPV2a/YnrIdrUrLlLApzOs4D3+H+vsgsFgsJKz9jhM/biCzphIFEGDvRNT4SbSdNFWMlgmCIPw/SqWSYX0nM6zvZC4kneLHdZ+jOp3Gobc+ZYfnl0SMGMHEMfeg1fyxPkmhUGDXowd2PXpgzM2leM1ailatIvXOu7Bp3x7XeXNxGju26TXAtnGASZ9D6DDY/Dh83h/GvQ+db7N2ZH/h7GXHlH/0YPviGHaviqcgo4L+08NQNdAUxOfGykVD/rnhLGFe9nT2d26Q/QhNi5ji2Ey883Mcn+xMZMuC/nT0FRV9ALlS44b7IPYH6PMwjHgFGvhEvzGm7SQez2X3qjiM1WaiJ4TQZXhAva81kySJ4znH+ersV+zP3I+9xp7p4dO5o8MduNvW39pGQ3ExJ774hLPHD1GmBK3ZQvugUHrc9xAu7cRIcH0QU8mEpkgclw2jsCSXdes/JmffCewqFFTZSXgO7M70qY/h5HD1MvAWg4HSzZspXLIEQ0Iiag8PXO64A5fp01A5OzfuC7gRRSnw/b2Qdgg6T5fL8esc67zZ+j4mLRaJQz9c5OQvqfi1c2bUvZHY2jdM4ltQbmDCJ/uxSBKbH+kvioa0EGINWjOXX25g4Fs7Gdrek09mivLiAFSXwHezIHkvjPwv9H2kUXbbkCcdhiq5UlTC0Rw8Ah0YPq8Drr76et2HJEnszdjLojOLOJV3CledK7M7zGZ6+HQctA71tp/CmLMcWfgZ8RkpGFVKnCQFXXoPoMv8B9A61N9+BHEiLDRN4rhsWEZTDZt++YaYrVvR55owaC3Y9wpn2u1P4O0ecNXnSJJExb79FH7zDRUHDqCwtcV50iRc581FGxjYyK/gb5hNsPcduYiIUwBMWQwBPeu0yYY6JuMOZ7Nz+QXsnLTc8lDnBqusfC6jhMmfH6B3iBtL5vUUbZZaALEGrZn7bOdFqo1mHh/RztqhNA2lmbBiKuTHw+RF0HmatSOqs6yLJWxfHEN5sYFe49vQbXRQvU6X+D0x++zUZ8QUxOCr9+W56OeYFDoJnbr+poSm7djOoeXfkFZZggT42znQffI0QiZMEtMYBUEQ6olGrWXK2PuYMvY+dh76gX3rv8W4L4GlB+9H2cWPSTMWEBoU+afnKBQK7Af0x35Af6rj4ilcupTitWsp+u47HMeMwe3ee9GFN5HzDJUaBj8LIYNh/Xz4ehQMfxH6Lqi3tjn1JTzaG2dPO3764gwb3jnBmPs74deu/peiRPo58e9xHXjhh3N8uSeJBwa3rfd9CE2HSNCauMziKlYcTmFKN3/aejRsv6tmIS8OVkyRy+jPWgtth1g7ojqxmC0c25rCsS2XcHDTMfmpbniH1N8UVkmS2J+5n89OfcbZ/LP42fvxn77/YVzbcfVWkdFisRC/+luOblpPrsWI2mKhvXcgve9/CNeOneplH4IgCMLVDel9K0N638qJmL1sW7MQ5ckMNpz8B8ZwV0ZPu5duHQf85Tm68Hb4vvYqHo89StGyZRR9u4rSLVuwHzIE9/vuxTYqqvFfyNUE9pYLiGx6BLb/G1IPwa2fgW3TWovv1caRKc90Z/PHp9n00SmGz+tAWA+vet/PrOhADl4s4J1f4ugZ7EKP4KtPaxWaPzHFsYn75/dnWXc8jd+eHEyAa8MUiWg20o7At9NAqZGTM9+oRg+hPqdIlOZX8es3sWRdLCE82puBM9qhta2fayaSJHEw6yCfnvqUM3ln8NH7cF/n+5gQOqHeEjOzwcDphZ9zYs8OSpQSNmYLHcMj6fXI4+i9feplH8LfE1PJhKZIHJfWk5hyjg3ffYTldAZqs4LKYDtG3H4vvaOGX/M55pISClesoGjZcswlJdj17o37ffc2ncqPkgSHv4BfXgBHP5i2FHy73tQmGuOYrK4w8tNnZ8hKKqH/1DC6DLv6dNO6KK02Mu6jfZjMFrYsGICLvokVfBFumFiD1kzlllXT/42dTO3hz2uTWvlIRNw2WDsPHH3gju/BtY1VwqivN/iEoznsWnkBCRh0ezjh0d513ubvDmcd5tNTn3Iy9yTeem/md5rPpNBJaFT1k5gZios5+tF7nD1zjMrLZfKjovvR9cFH0errd82c8PfEibDQFInj0vqy89NYvepdKg/FozUpqQyyY9jtd9O366hrPsdSUUHRmrUUfv01prw8dJ07437fvdgPHdo0ErW0o/K5QEUujH4detx9w1MeG+uYNNWY2f5NLEkn84gaHkDfyaH13h7nTHoxUz4/wKB2Hiya06Np/N8IN02sQWumlh1IwWixMH9AiLVDsa7YjbDuLvDuBDPXgr2HtSOqtZpqE3u+iyfuUDZebRwZeXfHems6HVMQwwfHP+BQ1iE8bT15Pvp5JodNRquqn6trVXn5HPrgLc7FnaNGpcRNpaH/qHF0nHMnSrV4KxEEQWhKvN0DePSRD8i7I4tVK99GfegCB9/4mB2BXzFsxj307f7XRE2p1+N25zxcZt5OyYYfKPjqK9Ifehhdhw64L3gE+0GDrJsMBPSUpzx+fy9seRJSDsL4D8Gm6SwBUWtVjJofyb41CZz6NY2KYgPD5nZApam/ddid/Z15bmwEL/8Yy+J9l7intZ8ntkDirKqJqqwxsfxQCiM7eNHGvRWPSpxdJ78R+/eQpzXqmm+LgbzUMrYtOkdZfhU9xgbT85ZglPVQCCStLI2PT3zM1uStONs483SPp5nefjo2qvopw1uRncWh998i5mIcRpUSL60tfabPou3EyfWyfUEQBKHheLj4sODh9yi4I4dvV75FzcHzHHzrY34NWMTQ6XfRv+fYvzxHaWODy4zpOE+dQsmmH8n/7DPS738AXZfOeDyyAH2/vtZL1OxcYeYa2Pce7HwVss/AbUvBq4N14rkKpVLBgOlh2LvYcHDDRSpLaxhzfyds7OpnJgvAvL7BHLhYwJvbLtAj2JWoAOd627ZgfWKKYxO19EAyL26KYd39fVrvItBT38LGhyCwL8xc3SSukNVmioQkScTszWTfmgR09hpG3t0R3zDnOsdSUFXAwjMLWRO/BrVCzewOs7kz8s56K5dfkZHOgffeIjYlEZNKiY9GR99ZdxI85pZ62b5QP8RUMqEpEsdl01VYksu3375N2f4YtEYlFQE6Rt5x/3XXqElGI8UbNpD/+ReYsrKw7d4dj0ceQd87uhEjv4pLe2Dd3WAogwkfX7extbWOybjD2fy27DzOXnaMf6QL9i71Vzm5uLKGWz7ah0IBWxYMwMm2/hJAoeGJNWjNjNkiMfidnbjb2/D9A1a8SmVNx5fCj49CyCCYsQq0TaNAys2+wddUy73N4o/kENjBleF3dsDWoW5TDiuNlSyLXcY3577BYDYwOWwy93e5H087zzpt93elKckceP9tLmRcwqxU4m9jR9+58wkYNqJeti/UL3EiLDRF4rhs+opK81n57VuU7TuH1qikKtSRW+c9TmTYtfuNWWpqKF63joIvvsSUm4tddDQejy7ArpsVe7SWZcPaOyH1gNwTdfjLoFT95WHWPCbTzhey9cuz2NipufXxrjh51N85zYnUIqZ9cZARHbz4bFa31nnO2ExdL0ETjYmaoJ9jskkrrOLeASGt8w/tyCL4cQGEDofbVzeZ5OxmFWZWsO6NY8QfzaHX+DaMe7hLnZIzs8XMuvh1jP1+LJ+e+pS+vn35fuL3/LvPv+slOavIzuKXJx/h66ceJCYzGT+9EzMeeorpy9aI5EwQBKGFcXF05+H73+Kejxej7NMG9aVitv7rJV5/ZR5JabFXfY5Sq8V15kza/vIzXs/9E8PFi6TMnEXaffdjSEho5FdwmYM3zN0EPefDgY9h5VSoLLROLNcQEOHKpCe6YTJY2PDOCYqyK+pt290CXXh6VDhbz2Wz/FBKvW1XsC6xBq2JkSSJhXuSCHS1Y2TH+qvs12wc/BR+fg7Cb4HbvgF1/ayjamxxh7PZtfICGhsVEx6NIqB93aapHss+xptH3+RC4QW6enblgyEfEOUZVS+xGooKOfDW65xNiMGoUhJg58iA+x/Bp0+/etm+IAiC0HR5uPjw+GMfk5Z9kVXfvIHqdCbrnnkaZbcAZs17Dh+PwL88R6nT4TpnDs5Tp1K4ciUFCxeRNPFWnCbdiseCBWi86r8H2HWpNHDLO3IxsS1PwqKhMOPbJrUuzSPQgVuf6MrGD06y4d0TTHysK25+9bN0Y/6AEA4lFfDfzefpFuhCpF/zXa8vyMQIWhNzPKWIU2nF3DOgDap6Lsva5O19T07OOkyUe5w0w+TMZDSzc+UFfv0mFs8gR6Y/36tOyVlmeSZP7nqSO3++kxJDCW8Pepulo5fWS3JWU1bG3pdfYOH8OziRdB53nR3T7nuMaUu/E8mZIAhCKxPg3ZZn/rmIiW+8hqmdK9KxNJY+dj8fffIEJWVXH5FS2tnhPn8+bX/5GdfZsynd9CMXR40m9/0PMJeVNfIrALrPhTt/AmMlfDUczv/Y+DFch5ufPZOe7IZSpWTDeyfITSmtl+0qlQrenRaFi17DY6tPUW0018t2BesRCVoTs3BPEs52GqZ297d2KI1r15uw42XodBtM+Vq+GtbMlORVsf6t48TuzaTbqCAmPhaF3rl2SWalsZJPTn7ChB8msCd9Dw9GPcjGWzcyOnh0nae9mqqqOPTWq3x153SOxJ7CSWPDpNnzmbliHQFDr71IXBAEQWj5woO78NzLyxn+4nMYAxww7o3nk4fvYNl3b2I01Vz1OWoXF7z++SwhW3/CYfhwCr78kosjRlK4bDlSzdWf02ACesG9u8CzPay+A3a+BhZL48ZwHS7eeiY92Q2tjZqNH5wiO6mkXrbrqtfy9tQuJOaW887PcfWyTcF6RILWhCTllbP9fA6zewdhp21Fs0/3fwi7XoMuM2HSl6Bqfq897Xwha984SllBNbc82Jk+k9rWqoS+JElsTtrM+B/G8+WZLxkWOIwfJ/3IA10ewFZdt35pFouF019+xlezp7L/+EF0KjXjJs9kzqoNhIybWKdtC4IgCC1L1w79+Ncbq+n++L2YHDTkbdjL6w9PYdvuVdd8jtbfH7933iZ43Tps2rcn57XXuHjLOEq3baNRi9I5+sK8nyBqFux+E76bicpU2Xj7/xtOHrZMeqobtvYaNn14ioz4onrZ7sB2HszuHcTi/Zc4lFRQL9sUrEMkaE3I4n2X0CiVzOkTbO1QGs+xr2H7v6HjZJj4yVUrLzVlkiRx6tdUfvzoFHonG277Zw+CO7vXalvxRfHM2TqHf+79J+627iwbs4w3B76Jt77uaxEvbfmRZbdP4tfffkKpUDBy1ETmrfqB8Okz67xtQRAEoeUa3HsC//poA/63j0JpsBDz2Upeefo2Tl84eM3n2EZ2JPCbrwlYtBClrS0Zjz1O6tx5VMc14siORgcTP4XRb0LCL3Q78QwUNZ0iGg6uOiY91Q17Fxs2f3ya1Nj6Saj+ObY9Qa52PLX2NGXVxnrZptD4RILWRBSUG1h3PJ3J3fzwcGh+a69q5cwa2PwEtBsNkxc2u+TMVGPm1yWx7F+XSJsoD6Y8071WpXMrjZW8e+xdpv04jZTSFP7T9z+sumUVXT271jnGvBPHWTN3Bt8v+5Jys5F+3ftw94r1dLprPkql+PMXBEEQ/p5SqWT6rY/w+GffYTssEk1mBb+89F/efO1uMnOTr/ochUKB/YABtNnwPd4vvYghLo5LkyaT9fLLmIrqZ8TobykU0Pt+mP09NoZCeV1a+vHG2fcN0DvZcOsT3XDysmPLZ2e4dCa/ztu006p5d1oXMour+O/m8/UQpWAN4gytiVh+KAWDycI9A9pYO5TGcWELbLgfgvvDbUua3ZqzssJqvn/nBPGHc4ie0IbR8yPR6m5+aubO1J3cuvFWlsQs4dbQW9l06yYmhU1Cqajbn2ZZWipbHp7P8jf+TWZlKV0CQ7nny+X0fuZ5VDat5AKAIAiCUK/0tg48eO8bzHn/MyydvVGeyWbZ4w/yxeLnqa6puupzFCoVLjNm0PbnbbjcfjvFa9ZycfQYCleuRDKZGifwkMGc6PaGPKq25BaI3dg4+70Bdo5abn28K+5+9mz78izJZ+uepHUPcuX+QW1ZfSyNX2Nz6iFKobGJBK0JqDaaWXYwhWHtPQn1dLB2OA3v4k5YOw98u8Ltq0BTt7VVjS0zoZi1rx+lOLeSsQ92psfYNihusuJmVnkWC35bwIKdC9Br9Cwbs4yX+r6Es865TrHVVFSw+1/P8s3j93MhN5MQJ3fmvfYBw9/+AJ2bW522LQiCIAgAvp7B/OO5xYx48XlqvG2p+OU0bz18G7/sWX3N56icnfH+1wu02fA9uogIcl75L5cmTabi0OFGiblSHwj3/AbekbBmrrz+vTHXxV2HTq9hwuWy+9sWniMjru4jjI8Nb0eEjyPPfn+GgnJDPUQpNCaRoDUB60+kU1hRw/yBIdYOpeGlHobvZoJbGMxaCzbNJyGVJInCBImN75/Exk7Dbc/2oM1NrjczWowsObeEiRsncijrEE90f4I149fUy3TGmKWL+XruNI7Fn8PNxpYZjzzDrYuW4hzWrs7bFgRBEIT/LyqiLy+8vZaQeRNRmiTOfrqc/z4/85qNrgF07doR+M3X+H30IZbKSlLnzSP90ccw5jTCSI+9B8z9UW7ns/3fsPkxMDeNdVo2tmrGL+iCo7stmz87U+fqjlq1kvemdaG0ysQLP5xr3CItQp2JBM3KLBaJr/ZeorO/E9Ft6tbMuMnLOgMrbwMHH5i9Aeyaz+s1my3sXhVP1nGJgA6uTP1Hd1y89Te1jZj8GGZsnsG7x98l2juaHyb+wJ2Rd6JR1m16Z+6xI3w7ayrbftqAAhg7fhqzVq7Hb8CgOm1XEARBEP6OUqlk0pj5PPbJt2j6h6FJKmHNP57i0y//QVV1xVWfo1AocBw5kpAtm3Ff8Ajlu3aRNPYWuSy/uYF7eGlsYeo30P8JOL4Evp0G1fVT6r6ubO21THwsCjtHLZs/OU1eWt16yUX4OPLEyHZsPZfNxlOZ9RSl0BhEgmZlv57P4VJ+BfMHhNS5v1WTlhcPyyfJI2ZzNoKDl7UjumGGKhNbPj1DzJ4M3CNg7IOdsbG78aTKYDbw4YkPmfXTLIqri/lg8Ad8NPQjfO196xRXdUEB2x57iJVvvkxeTSU9wjtx97I1RNwxp07bFQRBEISbZW/nxIJH3mfiq69iDHCg+rcY3nl4Olt2LL/mc5Q6HR4PPkjIj5uw7dqVnNdeI3n6DKpiYho2WKUShr8IEz6GS3tg8SgoTm3Yfd4gvZMNEx+LQmOj4sePTlGYdfUk90bNHxBCjyAX/rXxHFklV18nKDQ9IkGzskV7k/BztmVMZN1LqTdZJemwbCIolDB3EzgHWDuiG1ZaUMX3bx8n40IRQ2a3x6uLEuVNrDc7k3eGaT9O46uzXzG+7Xg23LqBYUHD6pSMWywWjn/0Povvm01MVgpBji7Mfe0DBv3nddR2NzeqJwiCIAj1qX1IFP96czXh86cBcGHhal55djrJGdcusa8NDCRg0UL83nsXY042ybdNI/u11zCX1y05+Vvd5sCsdVCaKVd4zD7bsPu7QY5utkx8rCsoFGz64CQlebVPrFRKBe9O64LZIvH02jNYLGKqY3MgEjQrOp9VytHkIu7sF4y6Fk2Nm4XqEnlaY025PK3Rra21I7phOcmlrHvzOOVFBsYt6EKHfjc+4lVtqubdY+8ye+tsKowVfD78c17p9wqOWsc6xZS+eyfLbp/Erv070ClVTJo9n8mLV4h1ZoIgCEKTMm74HJ76ZDU2gyPQppTz3TOPs3jZfzCbr165UaFQ4Dh2LG23bMF5+jSKlq8g6ZZbKN2+vWHXT7UdAnf/DEo1fDMWkvc33L5ugrOXHRMfjcJksrDxg5OUF1XXeltBbnpeuKUD+xLzWXG46fSCE66thWYFzcPqo2loVUqmdPO3digNw2yUKyXlx8O0ZXLlpGbi4slcfnj3BGqNkilPdyeg/Y2vlzuZe5LbfryNJTFLmBw2mR8m/kB/v/51isdQVMjWBfez5tN3KLvcz+zObzcQMm5inbYrCIIgCA3FVqfn4QfeZvwrL1PjqaN4yxH+++gUTsTsveZzVI6O+Lz4IsHfrULl7EzGIwtIf/Chhi0i4hkBd/0M9l7ycowLWxpuXzfBzc+eCQuiqK4wsvGDU1SW1tR6W7f3CmBQOw/e2HqBjGIx1bGpEwmalRhMZn44lcGIjl646LXWDqf+SRJseQKSdsL4D+UrVM2AJEmc/CWVbQvP4eZvz9R/9MDV98amDVaZqnjzyJvM3TqXGnMNC0cs5MU+L2Kvta9TTLHLvuHr+XcQm5NOiJM7d324kN7PPI9SffN91wRBEAShsXUI7cEL767Da+pgNCVGfn3lDd7/cAEVVdcugmHbpQtt1q/D85lnqDh0iKRx4yle/33DjaY5B8hJmnckrL4DTlx77Vxj8gxyZNzDXSgvrGbTh6eorqhd1UmFQsGrkyKRJPi3qOrY5IkEzUp+icmhuNLI9B7NZz3WTdn3HpxYBgOfhq53WDuaG2I2W9j1bRwHvk+kbVdPbn28K3aON5Y8ny84z/TN01lxfgXTwqfx/cTv6ePbp07xFCfEs2buDLZuWY9KoWTi7Xdy66Kl6P1a6IirIAiC0GIplUruuO0p5r37GaZ2LlgOJPHeI7dft3eaQq3G7a47Cdn4A7rwcLKef560e+/DmJ3dMEHq3WDOJggZDJsehn3vN4leab6hzox9oDNF2RVs/eIsZqOlVtvxd7HjyZHt2HEhl63nGujfUKgXIkGzkjXH0vBztqV/6M310WoWzq6DHf+BTrfBkOetHc0Nqak28dOnZ4jdm0m3UUGMuqcjaq3qb59ntphZfHYxM3+aSUVNBQtHLOSF3i+g19S+WIfFZOLAay+z9J+PkVFZRtc24dy1dDWht06p9TYFQRAEoSnw9Qzmuf+sIOL+28Ei9057/eW55BVlXfM52sBAApctxev556k8duzyaNr6hhkFsrGH21dD5BT49SX45QWw1C4hqk8BHVwZOieCzIRiflt+vtavfV7fYCL9HHlxUwwlVU2jB5zwVyJBs4K0wkr2JeYztbv/TVUEbBZSDsIPD0BgX5j4KTSD1gFV5TVs/OAUaecLGTwrnD6T2qK4gf+XrPIs7vnlHj448QFDAoawfsL6Oo+ape/eyZJZkzl4+iiuGhtmPfsSQ994V1RnFARBEFqUsUNm8ejHKyE6CHVsPl8+fs91S/IrlEpcZ98hj6ZFRJD1/Aukzb8XY9a1E7taU2th8lfQ6z44+Il8XtMEGlqHR3sTPTGE+CM5HN6UVKttqFVK3pjcmYJyA29tu1DPEQr1RSRoVrD2eDoAt/VoYVPVCi7Cd7eDcyDMWAlqG2tH9LfkMvonKMgoZ/R9neg4wO+Gnrf10lambJpCbEEs/+n7H94d9C7OOudax2GqrODXpx9jzafvUGE2MbjfUGatXI9n95613qYgCIIgNGWOemeefOJT+jz1EBaNggsLV/P6K/MoLMm95nO0gYEELl2C179eoPL4cZLGjado7dr6H01TKmHMmzD0BTjzHXw3E2oq63cftdB9dBAd+vlwfGsKsftq13w60s+Ju/q1YeXhVI4lF9ZzhEJ9UDTFRYIKhWI8MN7Pz2/+ihUrrB1OvbJIEk/trsJXr+Spnjprh1NvNDWldD35DGpTBSe6vUW1rY+1Q/pb1SUSKbskLCYIHKBA7/n3o2b5pfn8VPMTRyuOEqwNZo77HDw0HnWKw3DuDMk7t1GuVuKl1OIzdSYqtxY49VVoEOXl5djb160QjSDUN3FcCjfLYKzi4L5v0V8opNpWwnVAXzq2vX4FZFVeHo7LlqNNSMAQGUnJnNlIjldvZ1OXY9In82faxX9OsXMkZzu9gEVl3fM3ySKRukeiPAcCBypw8Ln52UrVJonn91Vho4b/9LVF3dJmdDUDQ4YMOS5JUo+r/a5JJmi/69Gjh3Ts2DFrh1GvdsfnMffrI3wysyvjOt94X60mzVgNyyZA5imYtxkCelk7or+VdbGELZ+eRqVWMn5BFO7+f/+mfSr3FI/+8igllhLu63wf8zvPR62sfSVFU2UFO//9HGdTE9FaJAaNnUSnu+bXentC67Rr1y4GDx5s7TAE4U/EcSnU1u7Dm9izaCF2ZWDq7MX9C97GyeHarW4ki4WiFSvJfecdlA4O+L7+GvYDB/7lcXU+Js+sgQ33QUA0zFwDurr1Na2rmmoT379zgtK8KiY91Q2PAIeb3sZvF3K4a8kxnhzRjkeGhTVAlML1KBSKayZoYopjI1tzNA0XOw0jOnhZO5T6IUmw+TFIOwyTv2wWyVny2Xw2fXASnV7DlGe6/21yJkkSS84tYd62eSgUCpaMXsIDUQ/UKTlL27Gdb+ZO50zaRYLsnbnzw4UiORMEQRBavUHRE3j8o5VI3f1Rncnmo0dns33v2ms+XqFU4jpnNsFr16J2dSXt3vvI/u+rWKpr39j5qjpPgymLIe0IrJgMVcX1u/2bpNWpGfdQF2zs1Gz55DRlhTf/eoe29+KWzj58vDORpLzyBohSqC2RoDWiwooafonN5tauftio/75CYLNw9Cs4vQoG/xM6TrJ2NH8r7lAWP31+FhcfPZOf7o6ju+11H19iKGHBbwt49/i7DA0cyj98/kGUZ1St92+qrGD7kwtY++UHGCQLo0bdypSvV4rS+YIgCIJwmb2dE0898wXdHr0HFHDmk6W8+84DVBuuvQZMF96O4HVrcZkzm6IVK0i+bRrVcfH1G1jkZJi2TJ4xtGwiVFp3/Za9iw3jHu6C0WBmy6enMVSZbnobL47vgI1ayfMbRG+0pkQkaI1ow8kMjGaJ6T1bSO+z1EOw7VloNxoGPmPtaP7WqV9T+XXJeXzDnG+ox9m5/HNM3zydfZn7eLbXs7w76F1slddP6K4nY88uedQsPYkgexfu/OgrIu+6p9bbEwRBEISWbGjfSSz4YDnGTp5wNI23Hp3O6QsHr/l4pY0N3s89R8CihZiKiki+7TYKly1Dqs8y+RHj5EJoubGwdAJU5NfftmvBzc+e0fd1oiirkm1fnsVsvrnX6umg459jIjiYVMC6y0XsBOsTCVojkSSJNUfT6BLgTHtv685brhdl2bBmDjgFwKQv5WpHTZQkSRzZfIn96xJp282D8Q93QWt77emJkiTx7flvmb11NhbJwtLRS5kVMQtFLVsGWEwm9rz4HGs+fvt/Rs1WoPdtIWsQBUEQBKGBODm48uwLXxM8dzzqCjPbXv4v36x8Fct1ki77AQMI2bQRfb9+5Lz2Omn33oeypKT+gmo3Cm7/DgoSYMk4KMupv23XQkCEK4PvaE/6hSL2fHfzo4YzegbQI8iFV386T0G5oQEiFG5W0z2rbmFOp5cQl1PG9B4tYPTMVANr5oKhTL6KZOts7YiuSZIkDm1M4ujmS7Tv7c3IeyJRaa592JfXlPPU7qd4/cjr9PPtx9rxa+ns0bnW+y+Kj+Pb2dM4euEM3jZ2zHn3MzFqJgiCIAg3acrY+5j5xvsYvG0o3HSQV5+7nez8tGs+Xu3qiv9nn+L90otUHjuG639fpeLQofoLKHSYXCykOAWW3AKlDdCP7SZE9PWh26ggYvdmErM346aeq1QqeH1yJyoMJv675XwDRSjcDJGgNZLVR1Ox1agY36Xpl5//W788D2mHYMLH4NXR2tFckyRJ7F+fyIltKXTo78vQORHXbQweVxjH9M3T2ZG6g8e7P85HQz/Cycap1vs/vehzlj/3OHmmavpGRTN92Wocg4JrvT1BEARBaM2C/cJ5/p012A3vhE1yOYufvJ9tu1dd8/EKhQKXGTNos3YNkl5P6l13k//55/U35TFkENyxHsqy4JsxUGLdKYLRE0MI6ODKntXxZF+6uRHDMC8H7h/Ulg0nMzicVNBAEQo3SiRojaCyxsSPp7MY28kHB53G2uHUzalVcGQh9HkYOk21djTXJEkSe1cncPrXNDoN8mPwzHAU10nOtl7ayh0/3UG1qZqvR33NXZF3oVTU7s+juqCADfPn8OuvW9ArVdz+1L/p889/oWzC00AFQRAEoTlQqdQ8MP91BvzjUSwaBec+W8G77zx43QIiNmFhFD77DxzHjiXvw49Iu+9+TEVF9RNQUF+YvQEqC2DpeHkJiJUolQpG3t0Re2cbtn15joqSm5uu+ODgUHyddPxncyxmiygYYk3ijLERbDmTRbnB1PyLg2SdlkvqBw+A4S9bO5prkiwSu76N4+yudLoMD2DAjHbXTM7MFjMfHP+AZ/Y8Qwe3Dqwev5puXt1qve/krVtYct8ckkoKiPQNYu6S7/CO7l3r7QmCIAiC8Fd9uo5kwfvLMHXyhKOpvPXE7SSmnLvm4yWdDt+335KnPB46xKXJU6g6dap+ggnoBbPWyWvRlk2ECuuNQOn0Gsbc3wlDhZGfF527qaIhtloVz46NICazlHXHrz19VGh4IkFrBGuOpRHirqdnsIu1Q6m9ykJYfQfYusLUb0BV+x5gDclikfht+Xli92bSbXQQ/aaEXrO4R1lNGY/89giLzy3mtna38dXIr3C3da/dfk0mdr3wD77/5jMsSEyYPpdR73+K2k5fl5cjCIIgCMI1yAVEviFw1hi0xUbWPv8MP25fcs3H/z7lMWjVKhQqFcl3zJarPNZHefnAaJj5HRQlw/Jbrdonzd3fgSFz2pOVWML+dYk39dzxnX3oEeTC2z/HUVZtbKAIhb8jErQGdjGvnKPJRUzrGVDrKoBWZzHD+rvlYfvpy8Hew9oRXZXFbOHXb2K5cDCbnuPa0HtiyDX/zS+VXGLmlpkczDzIv3r/i3/3+TcaVe2mn5alpfLd3BkcT4jBT2fP3E8WEzZlWl1eiiAIgiAIN+i2CQ8x7qWXMdqriP9qHe9/8Ag1xmtP77ON7Eib9euwHzSInNdeJ+PRxzCXldU9kDYDYfoKyD0PK6fKxdSspF1Pb7oMD+DsznQuHLrxAiYKhYJ/j+9AfnkNn+y8ueROqD8iQWtga46loVIqmNzNz9qh1N6u1+HibzD2bfDvYe1orspstvDL4lgSjubQ+9YQeo1rc83kbG/6XmZtmUVpTSmLRi5iWnjtk6lLW35k+eP3k22sIjqyO7ctWYXeuwUUghEEQRCEZiQyrCdPvLeCmo7uWA5e4o2nZpCWde0EQ+XkhP8nH+P59NOU7dhB8tTbMFy8WPdAwkbAbd9Axgn4dgbUXHttXEPrO6ktfuHO7FoZR25K6Q0/r7O/M1O7+/P1vksk51c0YITCtYgErQEZzRbWH89gaHtPPB101g6ndi7thT3vQNQd0H2etaO5KovZwvbFsVw8kUu/qaF0Hx181cdJksTX577moR0P4efgx6pbVtHDu3YJp8ViYc+/n2PD0i9QoGDK3Y/Q/18vi0IggiAIgmAl9nZO/PPfS/CcMgib3BqWPbuA7XvXXvPxCoUCt7vvImjZUswVFSRPm07Zrl11DyRivNwjNmW/vDzEZJ3eYkqVklH3RGJrr2Hrl2epKqu54ec+MyocrUrJqz+JsvvWIM4mG9DehDzyyw3Nt/dZZSFsuA9cQ2DMm9aO5qoki8Rvyy9w8UQufaeEEjU88KqPM5gNPLv3Wd4//j4jg0eydPRSfO1r1yi6IjOT1XOnczTuDL42euZ88hVBo0bX5WUIgiAIglBPZk97muHP/wOLRsmpT5bwyRfPYLaYr/l4u+7dabN2DdqgINIfeJD8RYvqvi6t821yO6KLO2DtnWC2znouWwctY+7vRFWpkZ+/isFyg0VDPB11PDgklO2xOexPzG/gKIX/TyRoDeins9k46NQMbNc012xdlyTJFRvLc2DKV2Bjb+2I/kKSJHaviiPuUDbRE9rQdcTVk7Pi6mLm/zKfny79xIKuC3h74NvYaexqtc/qUydYtuAesgyV9IrowrSl34kpjYIgCILQxHSPHMjD7y2hJtQJw85Ydm38iILinGs+XuPjQ9DKFTiOGUPeu++R+fQzWKqr6xZEt9kw5m2I2yJf8L5OktiQPIMcGTQznIy4Ig7+kHTDz7u7fxsCXG35z4+xmG6iGqRQdyJBayBGs4XtsTmMiPBCq26G/8wnl0PsRhj6AvjVvux8Q5Ekif1rE4m5XK2x+5jgqz4urTSN2VtnE5MfwzuD3mF+5/m1KtZisVjY/+pLxO7fgQRMnvcAA156VUxpFARBEIQmysXRnX++sgLHMd1xzDHx6dN3czb+8DUfr7S1xffdd/B4/HFKt2whZdYdGLPr2Ncs+l65NdG59fDjo/IFcCuI6OtD5EA/Tm1PJSXmxtoA6DQqnhsTQVxOGauOirL7jUmcXTaQQ0kFlFQZGR3pbe1Qbl5+Imz9h9zvrO+j1o7mqg5vSuL0b2l0Hup/zWqNZ/LOcMfWOygyFPHVqK8YFTyqVvuqqahg473zOHTmGK4KFXM/XEjw2HF1fQmCIAiCIDQwpVLJ/HkvYz+qP+pqC5tffpnNvy675uMVCgXu992L/6efUpOczKWpt1F58mTdguj/GAx8Wr74vfPVum2rDvpNDcXVV8+OJbFUlt7YerTRkd5Et3HlvV/iKKkUZfcbi0jQGsjWc9nYaVXNb3qjqUYuqa+2kRe4NsERomM/JXN8awodBvjS/7awqyZnv6X+xt0/342d2o4VY1bQ1bNrrfZVFB/HirtuJ6mskM7+IQTd9yh6P/+6vgRBEARBEBpRRJs+THnldYwOKs4vWs1nC5/FYrn2tD2HoUMIXv0dSjs7UufMpXj993ULYMjz0HU27Hkbji6u27ZqSa1VMfLujtRUm9mxNBbJ8vejeb+X3S+uMvLhjoRGiFIAkaA1CLNF4peYbIaEe6LTqKwdzs3Z+SpknZIXtjo1vdYAp35N5fCmJMKjvRl8e/hVk7OV51fy2M7HCHMJY8XYFQQ7BddqX0mbN7LyuccptZgYPmwsI979CIWqmf1/CoIgCIIAQHhwFx59eymGto5U7TjH6/+eTXllyTUfbxMaSps1q7Hr2YOs558n9933kK6T1F2XQgHjPoCwUfDTU3B+c+22U0dufvb0mxJKakwhZ3am39BzOvo6MaNnIMsOJpOYW97AEQogErQGcSy5kPzymuY3vfHSHtj/IXSbK5eIbWLO7clg/7pE2nbzYOic9iiUf07OLJKFt4++zRtH3mBwwGAWj1qMm61brfZ16K1X+WHZQtQouG3BP+hy74P18RIEQRAEQbAiJwdXnvvvSmyGdMAmoZj3nryDi2mx13y8ytmZgIULcZ4+nYJFi8h85h9Yam68XP2fN6aWe6T5dpVnK6UequWrqJvIQX4Ed3bnwIZE8tJurJn2kyPbYatR8eqWa/9bCfVHJGgNYFtMNlq1kiHtPa0dyo2rLITv7wO3UBj9urWj+Yu4w9nsXhVHcCc3RtzVEaXqz4dutamap3Y/xbLYZcxsP5P3B7+Prdr2pvdjqqxg4313sv/4QTzVOmZ/tAi/AYPq62UIgiAIgmBlSqWSh+9/i7C7pqAtNbP6+af47cCGaz5eoVbj/dKLcvGQzZtJu2c+5tIbb/z8J1o9zFwDjn7w7XTIi6vlq6g9hULB0Dnt0ek1bF8cg9Hw99Ul3e1tWDAsjJ1xeeyJz2uEKFs3kaDVM0mS+PlcNgPDPLC3UVs7nBsjSbDpEajIk0vqa/XWjuhPUmIK2LH0PH7tXBh1bySq/1cVs8JYwYM7HuTXlF95qsdTPNvrWVTKm5+KWHIxkRV3ziSxOI+OPoHcvnQVet/a9UoTBEEQBKFpmzjqLka/8AJmrZJjH33Ft+vfu+Zjfy8e4vv2W1SePEnyzJkYMzNrt2O9O8z+HlRaWDEFSrNq+Qpqz9Zey/A7O1CUU8m+dTe2tmxu32D8nG1555e4uveJE65LJGj17HR6CZkl1YxpTtMbTyyFC5th2L/AN8ra0fxJTnIp2xaew81Pz9j7O6H+f2v6iquLuefneziRc4LXB7zO3I5za1VGP333Tlb+YwFFFiNDB45g9AefodJo6+tlCIIgCILQBEVF9OW+txZS7aUla81vfPzpk9ctHuI0fjyBixZhysklefoMqs+fr92OXYLhjnVQVQQrp0L1tdfCNZSA9q50GxlI7N5MLp7M/dvHa9VKHh0expn0En6OuXZPOaHuRIJWz7aey0KtVDA8wsvaodyYomTY9k9oMwj6PGLtaP6kOLeSLZ+extZew7iHu6C1/fOIZF5lHnf+fCfxRfG8P/h9bgm5pVb7iV2xlPWfvI0ETL3/cbo+1DRbCwiCIAiCUP88XX15+s0VVIc7U7MnjjdfuZPqmqprPl7fO5qglStArSZl1h2U791Xux37dIHpyyHvAnw3C0yGWr6C2us1PgTPIAd2Lr9AWeHfN+ae3NWPEA89722Pw3wDVSCF2hEJWj2SJIlt57Lp09YNJzuNtcP5e5IEPz4GCiVM/LRJldSvLK3hx49OIUkwYUEUeiebP/0+ozyDudvmklGewafDP2VI4JBa7efg66+wbdMa9KiY+ep7BAwbUR/hC4IgCILQjNjq9PzzpWWo+oWijS3grX/MoqD42qNEunbtCP5uFZrAQNLuv5/i9etrt+O2Q+HWzyF5L2y4H2pbJbKWVGolI+7uiNks8es3sVj+JulSq5Q8Prwd8Tnl/Hi6llM8hb/VdM7IW4DzWWWkFFQyJtLH2qHcmNOrIGknDH8JnAOsHc0VNdUmNn9ymsrSGm55qDPOXnZ/+n1SSRJzt86l2FDMopGL6O3T+6b3YTGZ+GnB/Rw4dRhvjS2zPvsGl/D29fUSBEEQBEFoZpRKJY8t+ACPKQOxzTLw6TN3k5hy7pqP13h5EbRiOfroaLKef4H8zz+v3dqsztNgxH8g5nvY/UYdXkHtOHvaMWhGOzITijmxLeVvH39LJx8ifBx5/9d4jObGTShbC5Gg1aNtMdkoFTCyYzOY3lieK09tDOgNPe62djRXmM0Wfl54jvz0ckbNj8S7jdOffn++4Dx3brsTk8XEN6O+oYtHl5veh6G4mLV3zeR8TjrtXL2Y/vVKbD3c6+slCIIgCILQjM2Z9gydHrgDTYWF1f9+hoMnf7nmY1X29gR8+QVOEyeQ9+FH5L37bu2StL4LoOsdsPtNOFfL0bg6CO/tTVhPL45svkRe6vVL7yuVCp4c0Y6UgkrWHb+xXmrCzREJWj3adi6LnsGuuNvb/P2DrW3rM2CslBtSN5GpjZIksXPZBVJjCxk8K5zgTn9Omk7mnuTun+/GRmXD0jFL/6+9+w6Pq7gePv69u6u66r1YxXLvFVeM5YJtDMZ0MISO6QQCgRAgoYTQEyD86C10QgfT3LDce5VtualYva36rqRt9/fHGhkhyd6VdiVZOp/neR+/zJ07c2TuS3TemTnDoLBBLs9RnZXJRzdeRX6DkQlDR3P2y2+i9TkF/n0JIYQQotPMm76IuQ/8FVWjsPrZF/hu2btt9lW8vIh98klCFl2G4a23KX70UdcvtFYUOPvfkDgZvrkVCrZ38CdwdXqFMy4biF+AF798kIHtJCtjs4ZEMTohhP+sPEyD5eRl+oVrusdv5j1AZlkdh0rqTo3qjQd+hH1fwxn3QeTAro6myaZvMjm4uZgJC/oydGrz8vYbCzdy0/KbCPML471575EUlOTy+EUb1vHRfXdQo1qZM3ch0x5+HE03SU6FEEII0b2MHTaNK//5AuZgLQff/oL3Pn26zb6KRkPM3/9O+OIbqPr0fxTefz+q1erahDofuPRDCIiCTy6Hms494+Wr9+KMRQMpz6tj1/LcE/ZVFIV75w6iqLqBjzefuK9wnfx26iY/7y0GYG53T9AaquGHuyFqGEztPtUK96zKY8fSXIadEc/4+cnNnm0q2sQdv9xBQmAC/533X2IDXD/jd+SbL/ns309gB86/4Y+MuP5G9wQuhBBCiB4rKW4Adz7zHvV9fCn/ei2vvvVAm30VRSHqnnuIvOsuar5bQsGf/oTdbHZtQn0ELPoUzHXw6eVgNnXwJ3BNvzFR9BsTydbvc6gsNp6w79T+EUxOCeeVtCOYzC4mo+KEJEFzk5/2FjE6IYTYYL+uDuXElj8MdSWw8CXQdY97vnLSy1n72WH6jorgjMsGNrvHbGvxVu5YeQeJQYm8NectIvxcPyu29523WPLRO/iisOjhp0iaO8+d4QshhBCiBwsODOO+Jz6gvl8gpuV7eP6FO054V1rEzTcR/cAD1C5fQf7Nt2A3uZhkRQ+DC9+Cwl3w7W2OqtudaNplA9F5a1j14QHUk1R1/PPcQZTXmXl3fU7nBNdLSILmBnkVJvYW1HT/7Y0562D7uzDpVogf19XRAGAorGPZ2/uI6BPAmdcNQ6M5npxtL9nObStvIz4gnjfPfJNQ31CXx9/6/LMs+/lrghUtlz//KuEjRrozfCGEEEL0Ar4+/vzlsfewDI/EvjGbZ564Hou17dWxsKuuJPaf/8S4aRO5NyzGVnviwhstDDrLUWV731ew+pmOBe8ifbAPp188gKIj1exdU3DCvuOSQpk5OIrXV2dSXW/ppAh7PknQ3GDpPsf2xm5dXt9SD9/d4bi5fkbby/Odqb7OzI+v7MHLW8vZt47Ey0fb9GxX6S5uXXEr0f7RvDX3LcL9wl0ef+0jD7Jm02oitd4sevkdAhMS3Rm+EEIIIXoRL5039z34NsrEZLzSy3j64WtoaGx7dSzkwguI//e/qN+zh9yrr8FaWenahFPvhFGLIO0J2PdNx4J30aBJMSQMDWPj15knvcD6njkDqWmw8vbarE6KrueTBM0NftpbzNDYIBLD/U/euaukPQUVWbDgRfDWd3U02Kx2fn59L8YqM2fdMoKAUN+mZ3vK9nDzipuJ9I/k7blvu7yt0W63s/Tu29mSsZs+PnoufetDKaMvhBBCiA7TaDTcfff/4TdrOH5HanjmgSupMVa12T9o3jwSXv4/GjMzyb3qaqwVFc5PpihwzgvQZ4LjEuvCXR0N34WpFVIvH4QKpH108IRXBwyLC+bsEbG8vS4bQ11jp8XYk0mC1kElNQ1sP1rJvO68vbFwF2x4yXG/RkpqV0eDqqqs/uQghYermHnV4GZ3ne0r38fNy28m1CeUt+a8RZR/lEtj2yxmltxyPXsLcugXHM5Fb3+At77rE1IhhBBC9By33vgU4Qun4pffwAv3X0NZZVGbfQOmTyfh9dcw5+aSe9312KqqnJ/Iyxcu+8hRPOSTRVBb0vHgnRQU4cfk81LI3Wfg0JYTz/unMwdSb7Hx2urMToquZ5MErYOOb2/spgmazerY2qiPgDmPd3U0AOxemUfG+iLGnZXEwAnH/94yDBksXr6YIJ8g3pn7DjF61/5OzUYjX1x/JUeqyhgel8S5r72L1qt7FEIRQgghRM9yzeV/JfmK+fiWWXj1/hvJKzrSZl/9pEn0efllzFlZ5F5/A7aaGucnCoiCRZ9AfSV8cZ3jd7tOMnx6H2JSgln72SFMNW2fuesfFcD5Y/rw/sajlNSceEukODlJ0Drop/Ri+kXqGRAd2NWhtG7b21C8B856BvxcL7Lhbkf3Gtjw5RFSRkcycUFKU/vBioMsXr6YAK8A3p77tsul9BsMBv53wx/IbzQyftAI5j7/stxxJoQQQgiPuvjc2xh+0+X41Np59+93cbTwcJt9A06fSp+X/kPDoUOOwiF1dc5PFDMCFrwAR9fBL//oeOBO0mgUZlw5GEujjbWfHTph37tmD8Cuqryyqu1EVThHfoPtAENdI5uzDd23OIipAlY94djWOHRhV0dDRaGRZW/tJbxPALOvHYpyrGLj0Zqj3Lj8Rny1vrw9923iA+JdGre+rJxPb72OMpuZaROmMf2xJz0RvhBCCCFEC/NnXMH426/H22jn/b//6cRJ2vTp9HnxBRr27ydv8Y3Y6k5811gzoy6DcdfA+hfgwI8djttZYbF6TpvflyPbSsnaVdZmv4Qwfy4Y04f/bcuTs2gdJAlaB6zIKMGu0n3Pn616AhprYO6TjoOmXai+zswPr+xG661l/i3HKzaWmcq4aflNqKrKW3PeIiEwwaVxTWWlfHr7dVSoVmbOOIsJ9/zFE+ELIYQQQrRp1pQLOO32G/AynTxJC5w5k/h/Oao75t98s2v3pM17GmJHOYqGVHRe1cQxcxMJjw9g9ScHaTS1XU5/8RkpNFrtvLchp9Ni64kkQeuAVQfKiAv2ZVhcUFeH0lLJftj2Doy/DqKHdmkoNtvxio3zbx5BYJijYmOtuZZbVtxCRUMFr8x+heTgZJfGNZWU8L/bb6BStTFr1tmMvuV2D0QvhBBCCHFys6ZcwITbFzclaTkFB9vsGzR3DvHPPoNpxw7ybr0Ne329c5N4+cIl7zv+P94/u8pxjVIn0Go1zLxqMPU1ZrZ8n91mv/5RAZw5JJr3Nh7F2Nh5Z+V6GknQ2slmV9mYZWBK/wiULl6dakFVYelfwScQZjzY1dGw8atMCg9XMePKwcSkOCo2Ntoa+eMvfySzKpMXUl9geMRwl8Y0Fhfx6R2LHcnZmecw6qZbPRG6EEIIIYTTZk45vylJ++Dhe06cpM2fT9xTT2LavJn8227H3ujktsDQZLjgDShOh5/uc0/gTohKCmLo6XGkpxVQUdj21sybU/tRXW/h0615nRZbTyMJWjvtL6yhut7C1P6uX6DscQd/gqw0SP0r+Id1aShHtpeye2UeI2b0YdBEx1ZQm93G/WvuZ1vJNh4//XGmxE9xaUxjYSGf/vFGqrBx5rzzGLX4Fk+ELoQQQgjhsplTzmfiH290KkkLPvdcYh9/HOOGDeT/8Y+o5rYrJTYzcC5Muwd2vA87P3JT5Cc38dwUvHy0rPvicJt3o41NDGVC3zDeXpuFxWbvtNh6EknQ2mlDZjkAU/p1swuQrY2w9AGIGASnXd+loVSVmPjlgwyi+wYx9cL+gOMOtH9u/icrcldw32n3cXbK2S6NaSzI59O7bqJGtTNn/vmMuG6xJ0IXQgghhGi3GZPOa5akZecfaLNvyIUXEPPooxhXr6HwoYdQ7U4mNTMehL5nwA93O1bTOoFfoDcTzulL3v4KctINbfa7ZXo/CqsbWLK7sFPi6mkkQWun9ZkG+kcFEB3k29WhNLf5NajMhnlPgNary8KwNNr46fV0tDoNcxcPR6tzfGqv7X6Nzw99zvXDr+fKoVe6NGZtXi6f3HULNaqduQsuYvg1N3gidCGEEEKIDpsx6Twm/fFmvOrtfPjIn0+YpIVeegmRd91JzXdLKH3uX85NoNHChe84rlH67CpoqHZT5Cc2PDWe0Bh/1n9+GJul9WQydVAkg2MCeX11VpsrbaJtkqC1g9lqZ2t2BVP7dbPtjXWlsPpZGDAX+s/usjBUVSXt4wNUFBmZc92wpqIgnx38jFd2v8J5/c/jzrF3ujRmbV4u/7v7VmqxM3fhJQy96lpPhC6EEEII4Tapk85l8m+StPyStgtshN90E6GXX07FO+9geOdd5yYIiISL/wuVR+GbWx11CDxMq9Vw+sUDqC6rZ/eq1s+ZKYrCTdNTOFhSy6qDpR6PqaeRBK0dduZWUm+xMaV/N9veuPIxsNbD3Ce6NIx9aws5tLmECef0JWGo4wzc8qPLeXzT40zvM52HJz/sUmEVY3ER/7v7NmpRmXf+ZQz9w9WeCl0IIYQQwq2mTzyXiXfciLdR5Z2H/4ihqqTVfoqiEP3gAwTOnUvpM89Q/d13zk2QOAnOfAwOfA+bXnFj5CeYclg4ySPC2fZjDsbq1oubnDMyjvgQP15L67zrAHoKSdDaYX2mAY0Ck1K60Qpa4S7Y+SFMvBki+ndZGKVHa1j72SESh4Ux/qxkAHaW7uT+NfczMnIkz05/Fp1G5/R4jZUVfH7nzdQojpWzIZe7ti1SCCGEEKKrzZh0HsOuvxTfKjsv/+0maoxVrfZTtFrinnka/wkTKHzgQerWrnNugsm3waCzYcUjnXYebepFA7BZ7Gz6tvUEzEur4frT+7Ilp4LtRys7JaaeQhK0dthwpJwR8cEE+3XdGa9mVBV+vh/8w+GMe7ssjIY6Cz+/vhf/IG/OvHYYikahoK6Au1bdRYw+hv+b+X/46fycHs9sNPL5bTdgUK3MnDlfVs6EEEIIcco6Z/ZVJC2ah3+phRcevoGGxtYvqNb4+NDn5f/Dp39/8u+8k/p0JxIuRYFzX3KcR/vyhk65Hy0k2p9RMxM4sKGIkpyaVvtcNiGBEH8vXlud6fF4ehJJ0FxkbLSyK6+qe21v3Pc15G6EmQ+BX0iXhKDaVZa/ux9jdSPzFo/AN8ALo8XIHb/cgcVm4aVZLxHi63xstsZGvr7lOkpsZqaddjqjb77Nc8ELIYQQQnSCSxfeQfjCqejzGnjusRuwWFsvq68NDCThjdfRhYaSd+NNNGa3fXatiT4cznsVyg7A8ofdHHnrxs9Pxi/Qi3WfHWq1GIi/t46rJiezfH8JR0prOyWmnkASNBdtya7AaleZ0l0KhFjqYfnfIXoEjL2qy8LY/nMOufsMnH7xAKL7BjnuOlt7P1lVWTw3/TlSglOcHstutfLtrTeQ32hkwpBRTLj3rx6MXAghhBCi81x7+QP4zRqO35Ea/vXUTdjbKKvvFRVFwltvApB3w2IspU4U2+g/CybeAlteh8PL3Rl2q7z9dEw6rx/FWTUc2tL62bprpiTj66Xh9dVyFs1ZkqC5aP2Rcry1GsYnde0F0E02vgzVeTDvSUe51S6Qf6CCzUuyGTghmuHT4wF4ceeLpOWlcd9p97l0EbXdbufHO28hu66SkQn9mPbIPz0UtRBCCCFE17j1xqdQJibjlV7GCy/8sc1+Pn37kvDG61grK8m78SZsdXUnH3z2IxA11FHVsa7MfUG3YcjkWCITA9n41RHMDdYWz8P03lw6PoFvdhVQVO35rZc9gSRoLlqfaWBsUgh+3l2TDDXTUA0b/uMoq993WteEUGdhxbv7CY32J/WKwSiKwrdHvuXdve9yycBLWDR4kUvjrbzvTxwsL2JwZCyznnneQ1ELIYQQQnStu+76D5YRUaibc3jljfvb7Oc3YgR9XnyRxsOHKbjnHlSb7cQDe/nChW85fk/87g6Pl95XNArTLh2IsdrMzmW5rfa5YVoKdhXeWefEVk0hCZorDHWNZBTVMLVfNzl/tulVx//jm/FAl0yvqiqrPjpAfZ2FM68bhpePlp2lO3l046NMjJnI/RPvd6mc/pqHH2BPXiZ9A0M564VX0Wjk8xRCCCFEz6TRaLjn/tdo6B9E/cq9vPtR27uGAqadTsxDD2Jcvca5i6yjhzlW0g79BNudvFOtA2L7BTPgtGh2LsulprzlKllCmD/njIzl4825VJssHo/nVCe/AbtgU1YFQPcoEGKqcGxvHHwOxI3ukhAyNhSRtbOMiQtTiEwMbKrYGKuP5V+p/8JL43yVy83PPsHWA3vo46Nn4atvo9E5X4pfCCGEEOJU5KXz5p6H38aY4Ev5dxv45ue32+wbumiR4yLrd9+l6suvTj74xJshZQb8/ACUHXJj1K2bckE/FA1s+qb1io03ndEPo9nGh5uPejyWU50kaC5Yn1lOgI+OUX2CuzoUR3LWWAOpXVNAo6rExNrPDhM/KIQxsxNbVGwM9nH+72jfe2+zbut6orU+nP/qO2i9vD0YuRBCCCFE9+Hr7cedD79BfbiWg+9/xYadS9vsG/3AX9FPmUzRI49g2r79xANrNI6qjl5+8NUN0EbFSHcJCPVl5IwEDm8vxVDQ8qzc0LggzhgYyX835GCxtV4YRThIguaCDUfKmdg3DJ22i//ajAbY/BoMPQ9ihnf69DabneXv7kerVZh19VDs2NtdsTF3xTKWf/8lIWi46KU38NbrPRi5EEIIIUT3ExwYxrV/+zcWH1j1woscObq31X6KTkf888/jHRdH/u13YM4vOPHAQbGO+9GKdkPaEx6IvLkxZybi5aNly/etnzW7ZkoSZbWNLNvXesVH4SAJmpMKqurJMZi6x/bGDS+C2dhlq2fbfsihNKeG1CsGExjmyyu7X2lXxcaKfel899oLeKtw4T//hW94N7m6QAghhBCikyXE9mf+n+9HY4WP/3k/hqrWkxhtcDB9Xn0V1WYj/9ZbsdUZTzzwkHMcVzGtewGy17o/8N/wDfBi1KwEsnaWUZbb8t6z6QOjiA/x48NNss3xRCRBc9L6I+UATO3fxUlEXSlseRNGXARRgzt9+sIjVWz/KYfBk2PoPy6KdQXreGPPG5zX/zyXKjYai4v44pG/YgMW3vkXQgYM9FzQQgghhBCngLHDpjHmxivxq1F5+dFbaDC3XpbeJ6Uv8c//m8bMTArvuw+1jbvUmsx9EsJS4JtboNGzF0aPnpWAj7+OLUta3num1ShcPjGRjVkGjpQ6cWVALyUJmpM2HCknXO/NoOjArg1k/YtgbYDpf+n0qRvrrax4Zz+B4b5Mu3QgRXVF/HXtXxkYOpAHJj7gdMVGq8nIl3+6lTpFZd7FfyB+2nQPRy6EEEIIcWqYN30R0RdMR19o5vmnbm7zIuuAqVOJvv9+6n75hbLnT3I1kU8AnPcKVOfDyn94IOrfTOXvxejZieSkGyjOrm7x/NLTEvDSKny8ufWS/EISNKeoqsr6TAOT+4W7VDbe7WqKYOtbMPIyiBjQ6dOv+fQgdVWNnHndMBQvlT+v/jMWu4V/p/4bP52fU2PY7Xa+u+MmyuwWpk2azqBLL/dw1EIIIYQQp5arLrkP7ZR+eO8znPCOtNA/XEHIpZdiePMtqr/99sSDJk6CCTfCljcgd5ObI25u5Mw++Oq92LKk5Vm0iAAf5g2P5YvtedSbT3KnWy8lCZoTjpTWUVbbyNSuPn+27nmwWWD6vZ0+9aGtxRzaXMJpZycTkxLMv7f/mz3le3hsymMkBSU5Pc4vf7mb7LoqRib047S77/NgxEIIIYQQp64/3vE8DQODaVy1n0+/+U+rfRRFIeahB/GfMIGih/6GaefOEw866+8Q3MdxgbWlwQNRO3j76hgzN5G8/RUUHqlq8fwPExOpabCyZE+hx2I4lUmC5oSm82ddeUF1dYHjosExVzj2EHeiGkM9qz8+RExKMOPmJbEsZxkfZnzIFUOuYE7yHKfH2frvZ9ide4S+ASHMeuYkS/FCCCGEEL2YRqPh7gffoC5aR+7/lvLLhq9b7ad4eRH/4gvoYmIouOtPWCsq2h7UJwAWvADlh2DNs54J/JgRqX3wC/Jmy3ctz6JN6BvGgKgAPpJiIa2SBM0J6zMN9An1IzHcv+uCWPscqCpM+3OnTquqKr+8n4Gqqsy+dih5xjz+vuHvjIwYyT3j7nF6nIP/+5i1m1YTqfHi3JdeR6ORT08IIYQQ4kT8fPXc/PDLNOoVNr/yJhlHdrTaTxcaSvwLz2OrrKTwvr+cuGhI/9kwahGsfwGK0z0TOODlrWXc3CQKDlWRf6B50qgoCldMTGR3fjXp+S3PqfV28lvySdjsKpuyDF27elZ5FHZ8AGOvhFDntxO6w/51hRQcrGLqhf3xCVW4O+1udBodz01/Di+tl1NjFG/ayM+ff0iAqnDh86+g85e7zoQQQgghnBEdHs9F9z8GwOfP/J3q2tZXyPyGDSP6gQcwrluH4fXXTzzo3CfALxS+vR1sVneH3GTYGXHoQ3zY/F02qqo2e3bBuD74eWml5H4rJEE7ib0F1dQ2WJnSleX11z4HitLpq2d1lQ1s+PII8YNCGHp6HE9ueZJDlYd48vQniQ2IdWoMU0kJ3z73OBrgwr8/gT7GufeEEEIIIYTDkP5jGXX9FfhVq7z05G1tVnYMufQSghYsoOyl/8O46QSFQPzDYP6zULQLNr3smaABnZeW8WclUZxVTe7+5ollkK8XC0fH8e3uAqrrLR6L4VQkCdpJrM90nD+b0lUraBVZsPMjGHctBMd32rSqqrL644PYbSoz/jCYbzO/5avDX7F4xGKm9Znm1Bh2q5Vv77kdowbmLbqG8BEjPRy1EEIIIUTPNH/GFehnjcAvs5bX3nqg1T6KohD7yMN49+1LwT1/xlJa2vaAQ8+DwefAqifAkOmZoIEhU+MIDPNly3dZLVbR/jApiQaLna925Hts/lORJGgnseGIgUHRgUQG+nRNAGueA60XTLu7U6c9sq2UnHQDExemUKLL55+b/smEmAncNvo2p8dYef89FFrqmTB8HAMuvMSD0QohhBBC9Hw33/AE9f0CMa5M58dVH7XaR6PX0+fFF7CbTBTefQ+qtY0tjIoC858DrQ9890c42WXX7aTVaRh/djKlR2vJ2VPe7Nnw+GBGJYTw0ebcFslbbyYJ2gk0WGxszanouu2NNUWw5zMYezUExnTatPV1Ztb87xBRyUEMPCOS+1bfR4B3AE+f8TRajdapMdLfeo09eZn0DQhhykOPeDZgIYQQQoheQKPRcMdfX6Y+RMPutz/iQNauVvv59O9P7KOPYNq2jbL/vNT2gEGxMPdxOLoOdvzXIzEDDJoUQ1CkH5uXZKPaf7eKNjGRI6V1bMo6QfXJXkYStBPYkVtJo9Xeddsbt74JditMuqVTp1332WHM9VZmXjmYl3b9h8zqTP55+j+J8HPu76FowzpWLv2OUFXDOS+8KhUbhRBCCCHcJDgwjIvvfRSAz575GzXGqtb7nXsuIZdcguGNN6hNS2t7wDFXQt8zYNnfHdc6eYBWq2HC2ckY8uvI3FnW7NmCUXEE+3nx4WYpFvIr+c35BDYcMaBRYGJKWOdPbjbCtndg8NkQ1rfTps1JL+fQlhLGnZXMYc1ePsz4kMsHX86UuClOvW8sLuLbfz+JVoXzHnsK78BAD0cshBBCCNG7DOk/lhHXXIZ/pf2ERUOiH3wAnyFDKPzL/VgK2ki+FAUW/MexKPD9nxzXOnnAgAkxhMb4s/WH5hUdfb20XDSuD0v3FlNa67nLs08lkqCdwMYsAyP7hBDk61w5ebfa/QnUV8Lk2zttSnO9ldUfHyQsTs+AmaE8tO4hkoOSuWvcXU697ygKcgcmDZz1h+sJGzzUswELIYQQQvRS58y+Ct8Zw/A9XM0b7/6t1T4aHx/6vPgC2Gzk3303qtnc+mBhfWHmQ3B4KRz4wSPxajQKY+clUVFoJO93FR2vmJiI1a7y2dY8j8x9qpEErQ1Wm529BdWMSwrt/Mntdtj0KsSNhcRJnTbthq8zMVY1MvPKITy9/SkM9QaemvYUfjo/p95f8Zc/UWRtYOKo0+h/3oUejlYIIYQQone79canqE8JoHb5Lpau/rTVPt6JicQ+8U8adu+h5Lnn2h5s4k0QOQSW/hUs9R6Jd8D4aPyDvdm1snkilhIZwNT+4XyyJQ+bXYqFSILWhsOldTRa7YyID+6CyZeB4QhMvs2x7NwJCg5Vsm9NASNnJbBT2cAPWT9w46gbGRYxzKn3d7/xCun52aQEhjH5r3/3cLRCCCGEEEKj0XDbX/+P+kCF7W+9z+Gc9Fb7Bc2ZQ+iVV1L5/gfUrV/f+mBaL5j/DFTlwvr/eCRerU7DiNQ+5O2vwFBQ1+zZHyYmUVBVz6oDJ7gaoJeQBK0N6QXVgKP8Z6fb+H8QFA9DF3bKdFazjVUfHCAowpe+swL4x8Z/MCJiBItHLHbq/aIN61i1/HtCVQ1nP/+yFAURQgghhOgkoUERXHDfw2js8MmzD9Fgbn31K+qeu/Hu14+iBx7EVl3d+mB9z3Dcj7bu345EzQOGT4tH56Vh9+9W0WYPjSYq0EeKhSAJWpvS86vRe2tJidB37sRFeyBnrWOZWds5Z9+2fJ9NdVk9M/4wmH9sexSzzcwTpz+BTqM76buNVVUsef4ptCqc/49npCiIEEIIIUQnGz7gNFIunY++3MbL//fnVvtofH2Je+ZprAYDxY/9o+3B5jwOKLD0QY/E6hvgxeApsRzcUoyp5viZOC+thstOS2D1oTIKqjyzxfJUIQlaG9ILqhkWH4xG0zlbDJtsegW89I67zzqBoaCOXSvyGDo1lnUsY33hev48/s8kByc79f5P991JrQZmX7CI0EGDPRusEEIIIYRo1SXn3o5leCRsPtrmJdZ+w4YRedut1PzwAzU//tj6QCEJMO0eyPgOstI8EuuomQnYbSrpafnN2i8al4Cqwre7PFPu/1QhCVorLDY7GUU1jOzs7Y21xZD+BYz5A/iFeHw6VVVZ+79DePtpiZvlxb+2/Yup8VO5ZNAlTr2/8+UXyaw2MCw2iSGXX+nhaIUQQgghxIncevfzGINh57sfkVec2Wqf8MWL8Rs1iqJHH8NSUtL6QFPugNBk+PE+sFncHmdItD/JIyLYu7oAq9nW1J4Y7s/YxBC+3Vno9jlPJZKgteJwybECIX06OUHb8uvF1Dd3ynRHtpdScKiK0xYk88iOv+Gj8+GxKY+hOFGYpGzXDtasWkoYGmY/eYKKQEIIIYQQolME6UM4+4/3obMovPvMfdhs1hZ9FJ2OuKefQjWbKXrgwWZ3kjXx8oW5T0L5QdjyhkdiHT07gQajhYObi5u1nzcmnoMltWQU1Xhk3lOBJGit2NsVBULMJtj29rGLqVM8Pp2l0caGL48QkRDA+qAf2GvYy98m/Y0o/6iTvms1GVnyxCMowIIH/4HOz7ky/EIIIYQQwrPGDT+DyLMnoy9o5PW3H2q1j3dyMtH33Ytx/XoqP/649YEGnQX9Z0PaU1Dn/sqKcQNCiEwMZPfKPNTflNY/e0QsWo3CN714m6MkaK1IL6gmwEdH3/BOLBDSdDH1bZ0y3fafc6irbKTvfD/e3PsGZ6eczdzkuU69u+z+e6hU7Ew/8xwiRo7ycKRCCCGEEMIV11z+APUpARh/SWft1tYvng657DL006ZR+uxzNGZlt+ygKDDvKcedaCsedXuMiqIwenYClcUmju4zNLWHB/hwxoAIluwqxN5L70STBK0VewqqGRYX1HkFQux2R3GQuDGQONnj01WVmti5PJeBE6J5segpAr0Duf+0+516d/8H/yWjJJ8BoZGMuulWD0cqhBBCCCFcpdFouOm+52n0g7RXX8FQ1fKsmaIoxD7+OBofHwrvvx/V2nI7JBEDYNItsOtDyN/m9jj7jYtCH+LDrhXNS+6fNyaewuoGtuRUuH3OU4EkaL/za4GQTr2g+sjyYxdT394pF1Ov//wwWq2G8lH72VO2h3tPu5cQ35CTvld56CArv/2MIDvMe9YzFxgKIYQQQoiOiwyNZdrNN+Frglef/RN2u71FH6/oKGIeeZiGPXsof/311geafh8ExMCP9zoWFdxIq9UwckYfCg5WUpZX29R+5tBo/L21vbaaoyRov3OopBZzZxcI6cSLqXPSy8lJNzDkzEj+c/DfTIydyDkp55z0PZvFzJKH78emwIJ7HpT7zoQQQgghurnpE8/FL3UYfkdq+OB/z7TaJ+isswhasIDyV16lPn1vyw4+gXDmY1C4w7GS5mZDT49D56NtdnG1v7eOOUOj+WFPEY1W2wne7pkkQfudXwuEdNoKWtEeyF4DE270+MXUNouddZ8dJiTan2/83sFsM/O3SX9zqmpj2kN/ocxuYcqk6cRM8vw2TCGEEEII0XG3LH4CY5w3xd+tZVfGhlb7xPztIXSRkRT+5S/YGxtbdhh5CSRMcpxFq69ya3y+ei+GTonl8NYSjFXH5144Jp6aBitpB8vcOt+pQBK030kvqCbQR0dyZxUI2fSq42LqcZ6/mHrXylyqy+oJmdnAsvyl3DjyRpKCkk763pFvvmRX9iGS/IMZ/6d7PR6nEEIIIYRwD61Wx9X3Po3NS+W7F5+kodHUsk9QELH/fBxzVhaG11spq68oMP8ZMBlg3fNuj3HkzATsdpU9v7m4elr/CML13r1ym6MkaL+Tnl/NsPhOKhBiLIf0z2HMFeAX6tGp6iob2fbTURJHhvKfsidJCU7huuHXnfQ9U1kpyz58G70dzn7mRTQa+WSEEEIIIU4lSXEDGHr5hegrVV57/YFW+wRMnUrQuQsof/NNGrOyWnaIHeVYSdv8GtS49yLp4Eg/UkZHsm9NAZZGx5ZGnVbDOSNjWZFRSk2D+y/L7s7kt+3fsNjsZBTXdt72xj2fgd0C4671+FQbvjqCalc5PGQdhcZCHp78MF5ObKlc/uB91GsU5lxzI36RER6PUwghhBBCuN95866ncVAIlg2H2bRrRat9ov/yFzT+/hT//WHU1gqCpP4V7DZY3fp5to4YPSuBRpOVAxuLmtoWjonHbLXz897iE7zZ80iC9hvHC4SEeH4yVYWdH0LcWIge6tGpCg9XcnhrCYnT/Hk/720uHHAhY6PHnvS9jI8/4Eh1OUNjEkg5x/MFTIQQQgghhOfccNczmH1Ulr36YqtbHXXh4UTf+2dM27ZR/fXXLQcI6wvjr4Ud74Mh062xxfQLJrpvELtX5jXdfzYmIYSkcP9et81RErTfSM/vxAIhRbugdJ9je6MH2W121nx6iIAwHz7y+Q/BPsH8adyfTvqeqaSEVV99QoBNZdY/n/VojEIIIYQQwvOiwuIYfvlF6KtUXnvtr632Cb7gAvzGj6PkmWexGgwtO5xxL+h84ZfH3RqboiiMmplAdVk9BQcqm9oWjopjQ6aBkpoGt87XnUmC9hu/FghJCvP3/GQ7P3J83MMv8ug0BzYWYygwYp9UzJ6q3fzltL8Q7HPyBHTpQ/dSr1GYe/2tUlJfCCGEEKKHWDj3OhoHh2LZeISNO5e1eK5oNMQ+8gh2k4nSZ1rZyhgQBZNvhX1fQeEut8aWMjoSH72OjA3Hz7gtHBOPqsKS3e4999adSYL2G3sLqhkeH+z5AiGWBkj/DAafA34hHpvGarax5ftswpL8eL32WabETeGsvmed9L39H/yXrJoKhscnk3zW2R6LTwghhBBCdL4b7nwasw8sf+2lVrc6+vTvT/gN11P97XcYN25sOcCUOxwF7lY+6ta4tF4aBk6IIWtXOQ1GR2GQfpEBjIgP5ptetM1RErRjzFY7GUW1nXNB9cEfoKEaxvzBo9OkpxVgrGpkT8oKrKqVhyY+dNI7z4yFhaz69jMC7TDjcfcfABVCCCGEEF0rKiyOEVc4tjq++tr9rfaJuOkmvJISKXrkkZZ3o/kGw7R7IPMXyFrt1tiGTInFZrVzeGtJU9vC0XHsLajhSGmdW+fqriRBO+ZQSS1mm71zzp/t/BCCE6DvdI9N0WiysP3nHAL7KXzf8Bk3j7qZhKCEk7639G/30ahRmHvjHXjrO+kuOCGEEEII0anOnXMtjYNDsW7MZMP2pS2ea3x9iX34YSxHczG8/nrLAU67AYLiHatoquq2uCITAolICCBjw/FqjueOikOj0GuKhUiCdszegk4qEFKdD5mrYPTl4ME7xXYuy6XRZGVZ9IckBiZy9dCTX4S99523yK6rYnhCCklnzvVYbEIIIYQQoustvusZzD6w4vWXqG8wtniunzLl2N1ob9GY+buqjV5+kHo/FGyHA9+7Na4hU2Ipy62lLK8WgKggX6b0i+DbXYWobkwGuytJ0I7ZU1BNoK+OpHAPFwjZ9QmgOhI0DzFWN7L7lzx8BjWwW93C3ePuPumdZ8aCfNJ+/IogO8z8x1Mei00IIYQQQnQPkaGxjPjDReir4bU2tjr+ejda0cOt3I026nIIHwAr/wE2q9viGnhaDBqdwoHfrKItHB1HboWJHblVbpunu5IE7Zi9BdWMiA8+6RmtDrHbYdeHkDwNQpM9Ns22H3OwWVW+DnmDcdHjmJk486Tv/PTQXzBrFObdfCc6f9naKIQQQgjRG5x75rU0DgnDuimr1a2Ov96NVr9te8u70bQ6mPU3KD8Iez51W0y+AV6kjIrk0JYSbBZHUjhveAw+Ok2v2OYoCRqOAiEHimo9v70xdwNU5sCYKz02RXWZif1rC7EOKiNXk8m9p9170qRz95uvctRUzcikASTMOtNjsQkhhBBCiO5n8Z1P0+gLK9qo6tjsbrSKiuYPh5wLcWNg1ZOOSuVuMmRKLA1GC9l7ygEI9PVi9pBovt9ThMVmP8nbpzZJ0DheIGS4pxO0nR+BTxAMWeCxKTZ/l42ihf8FvMy5/c5lWPiwE/Y3FhaydukSgu0KqY896bG4hBBCCCFE9xQZGsvIyy9CXwNvvftIi+dNd6MZjZT95z+/e6jA7EegJh+2ve22mPoMCSMg1KdZsZCFo+OoMJpZd6TcbfN0R52WoCmKkqgoyjeKoryjKErrm1y7SPqxAiEjPVliv7EW9n8Dwy8Ab8+ccyvLq+Xw1hIMAw5j9jFxx5g7TvrOysceclRtvPmP6Pz8PBKXEEIIIYTo3s6dcy2mZD3GNfs4nJPe4rlP//6EXnopVZ99TuPhw80fpqRCygxY85zjKik30GgUBk+OJW+/gbpKx8rc9EGR6L21LN9fcpK3T21OJWjHkqpSRVH2/q59nqIoBxVFOeJE0jUC+EJV1euAMe2M1yPSC6oJ8tWRGObBAiH7vgaLCUZ77u6zTd9kofNT+Er/FlcPu5oYfcwJ+x9d+jOHK0oYFBErWxuFEEIIIXq5y255CFT49NXHW30ecfttaPR6Sp59tuXDWX+H+grY+Irb4hk8OQZVhQObigHw0WmZNiCSlRklPbqao7MraP8F5v22QVEULfAycBYwFFikKMpQRVFGKIry/e/+TxSwCbheUZRfgJ/d9yN0XHp+NSP6eLhAyM4PIWIQ9BnvkeELDlWSu8/Akb6bCQrUc93w607Y32Yxs/LtV/Cxq8x8+J8eiUkIIYQQQpw6BiSPQD99GP45Rr5b/m6L57rQUCJuvhnjmrXUrVvf/GH8WBh8Dmx+1bFzzA2CI/2JHxhCxoaipoRs1pAoSmoa2VtQ45Y5uiPF2exTUZRk4HtVVYcf++fJwCOqqs499s9/BVBVtdWDTIqi/BnYoqrqGkVRvlBV9aI2+t0I3AgQHR097tNP3VcRpjVWu8rNy03MSfbikkHeHpnDz5TPxC23kZlyNXmJF7h9fFVVyV6hYjKaeWvkA1wadTGTAyaf8J2qb74gsyiHgX0HEzjvHLfH1FPV1dUREBDQ1WEI0US+SdEdyXcpuhv5Jp1ntjay8ZMXUewwYdHt+P7+aI7FQvijj6L6+FLx4APN7vUNrDnEuB33uvV33qpslYLNKskzFfRRCjWNKneuMnFuPy/OH+CZ3907w4wZM7arqtrqyo2uA+PGA3m/+ed8YOIJ+v8MPKIoyuVATludVFV9A3gDYPz48WpqamoHQjy5vQXVWJetY/7k4aSOjPPMJMsfBkVLv/MfpF9gtNuHz95dxn5DOruH/EL/iBTum38fWo22zf41Odn8Nz+LSC8fzn7iGTQevDC7p0lLS8PT36QQrpBvUnRH8l2K7ka+SdeoXpXsfeVDDh5cxp13vNDieY3NRsFdf2KUwUDoxRf/5kkqVC6hX+nP9Fv0DHj5djgWyxQb7+5eh68pktTUoQC8l7WBzAYbqanTOjx+d9Rpv5mrqrpXVdWLVFW9WVXVP3fWvCezJ/9YgZD4EM9MYLPC7k9hwBzwQHJmt6ts+jYLJcTM5uCl/Pm0P58wOQNY8Y+/YdUonPnHP0tyJoQQQgghmpk7/TIa+gfRuOEwGUd2tHgeOHcufmPGUPbif7DVGZs/nHYP1JXA7o/dEouXt5YBp0VzZEcp5nrHZdizhkSxt6CG4mr3lfXvTjry23kBkPCbf+5zrO2Ukl5QTbCfFwlhHqpgmLkS6ophjGeKgxzeUkxFoZHVsV9wRsI0JsVOOmH/I199QXZdFcPik4mdPNUjMQkhhBBCiFPbFbc+jF2j8vmr/8Rub37vmKIoRN//F2zl5Rjefqv5i32nQ9xYWPeCY6HCDYZMicVqtnNkeykAs4c4Fj1WHuiZ1Rw7kqBtBQYoitJXURRv4DLgO/eE1Xn2FlQzPD7IcwVCdn4I/hEwcK7bh7bbVbb9dBRrqJGDIdu4e/zdJ+xvra/nl0/+i5/NTqoUBhFCCCGEEG1Ijh9E6Kyx6PMb+erHN1o89xs1iqD586l4510sRcfvKkNRHKtoVUcdVczdIDo5iNBYfdOdaAOiAkgI82NlRqlbxu9unC2z/wmwERikKEq+oijXq6pqBW4HlgIZwGeqqu7zXKju12i1caC4hhGe2t5oNMDBn2DUZaD1cvvw2bvKqCoxkRb5BZcMvoSU4JQT9l//xKPUamDa/PPxCQlxezxCCCGEEKLnuPbKv2EMUTjwxRKqaytaPI+8+25QVcpeeKH5g0HzIXIwrPs3/G71rT0URWHIlFiKs6qpLDaiKAqzBkez/kg59WZbh8fvbpxK0FRVXaSqaqyqql6qqvZRVfXtY+0/qqo6UFXVfqqqnnJLMoeK67DYVEbEe+iC6oxvwW6BUYvcPrSqqmz/+SjmgDpKog9zy6hbTti/4sB+dh7YQ6yXLyOuW+z2eIQQQgghRM/i7eXDtGuvx69e4a03/9byeZ94wq6+iupvv6M+/TfXJWs0MPUuKN0Ph5e6JZZBE2PQaJSmVbTZQ6JptNpZd6TcLeN3J726QkR6wbECIX08laAtgbB+ED3M7UPnZVRQllvLhqglXD70ckJ9Q0/Yf/kTj6KicOa9D7k9FiGEEEII0TPNmHQejUPCsG/JYVfGhhbPw2+8EW1YGKVPP9388ugRF0FwIqz9F7jhUmn/IG+SRoRzYFMxNpudCX3DCPTRsTKj551D6+UJWhXBfl70CfVAgZD6KsheA0MWOPbiutn2n45i9aunMC6DK4deecK++z98j/xGI6P6DSZy1Gi3xyKEEEIIIXquq255FKtO5bvXn21RMEQbGEjkHbdj2raN2hUrfvPAC6b+EfK3Qs46t8QxZEos9TVm8vZV4K3TcMbASFYeKMVu73gC2J308gStmhHxwZ4pEHJoKditjgTNzYoyqyk8XMXm6J+4bNilBPu0vQJorq1lzTefEWBTOf1vj7k9FiGEEEII0bP1ie5L9LzJ6IssfPH9Ky2eh1x8Md79+lH63HOoZvPxB2P+APpIx1k0N0gcHo6Pv47MHY7iILOGRFFW29i0K66n6LUJmtlq52BxLSM8tr3xOwiMc5QZdbMdP+dg8zaTG7+bq4ZedcK+G59+HKNWYfqFi/DW690eixBCCCGE6PmuvOwvGEMUDn77Ew2NpmbPFJ2O6PvuxXI0l8pPPz3+wMsPJt0Kmb9A4c4Ox6DVakgeGUH2nnJsNjszBkWhUehx2xx7bYKWW2HCYlMZGB3g/sHNJjiyEoac4zgk6Ubl+XXkpBvYHr2cS4ZdfMLVs9q8XHYdSCdG58PgRZ65h00IIYQQQvR8Xjpvxlx0If51Cu9/8nSL5/ozzsB/4kTK33gTe3398QenXQ8+wbDWPatoKaMjaTRZKTxURajem3FJoazoYeX2e22CllPuuPU8OdwDq0qZK8FaD4PPcfvQO5Yexa6zkt1n+0lXz9Y8/ThWjULqzX90exxCCCGEEKJ3OXvWVRhjvSlfuZWK6uZJkaIoRNx2K7bycqo+++z4A99gmHCDo3he2aEOx5A4NAydt4asnWUAzBoSzf6iGgqr6k/y5qmj9yZoBg8maBlLwC8Ukqa6ddjqMhOHt5WwJ2o1F424gBDfkDb7lu3excHSAlKCwomfNt2tcQghhBBCiN5Ho9Ew++qb8DFreO/df7R4rp8wAf8JEyh/6y3sDQ3HH0y8BXQ+sP6FDseg89aSNDycrF1lqHaV2UOiAFh5oOesovXaBO2owUSQr44QfzdfIG01w8GfYdDZoNW5degdy3JRFRuHEzafdPUs7flnUFSV1HsfcGsMQgghhBCi95oyZi71A4Iwb84ip+Bgi+cRt92Graycqs8+P94YEAljr4Y9/4OqvA7HkDImElONmeLsGvpFBpAU7t+jzqH12gQtx2AkOULv/gqOOWuhsdpx/syNjFWNZGwoZH/kJs4fteCEq2dHl/5Mbn0NQxNSCB002K1xCCGEEEKI3u2i6+5DUeGTt59s8Uw/cQL+48djePNN7I2Nxx9MucPx54aXOjx/8vAINDqFrJ2lKIrCrMHRbMg0YDJbOzx2d+DeJR43URRlAbAgPj6etLQ0j8xxIN9EvxCN28cfePB1ojW+rM/XYi9y39jFO+3YbXb2x69hfuWdbcat2u1kv/l/eGHHa/qZHvv7663q6urk71R0K/JNiu5IvkvR3cg36X51A4IJ3FfG+/97jcTo5gsCXtNOJ2zbNrY+8QT1M2Y0tQ+OnEbktvfY4D0dm65jx4z8I1X2bczDHJ5PhNmO2Wrn1a/TGBfdLdMbl3TLn0BV1SXAkvHjxy9OTU11+/hmqx3D0p9YNKQvqamD3Dew3QZbF8OQszhj1hy3DdtQZ+G/X63jSMQOzht3NueMa3t1bv/777JDCxOHn8bpCxe6LQbhkJaWhie+SSHaS75J0R3Jdym6G/km3W/QsBTeu+tmjm77hauevbnZM3X6dI6uXYtuVRr9HngAjY+P48GAIHhzBtMC8mDSza2M6rz9XoWs+uAAw/uP5/Q4Pa+mL6dEG0lq6qgOjdsd9MotjgVV9dhVSHJ3gZD8rWAsdXv1xj1p+djMKvsT13L1sKvb7GezmFm35Ev0NpVJ99zn1hiEEEIIIYT4VWxkIgHThuOfa2LFui+aPVMUhcjbbsNaWkrVF795Fj8W4sfB1rdAVTs0f9+RESgKZO0sw0urYfrASH45UIbd3rFxu4NemaA1VXCM8HfvwBlLQOsNA9y3emZusLJr5VFyQtM5a9xMQn1D2+y7/YV/UauBSbPno/OXS6mFEEIIIYTnXHPVg9T7qWz45APsdnuzZ/6TJuE3diyGN9/CbjYff3DaYjAchuzVHZrbL9CbuAEhZO1ylNufPSSa8rpGdudXdWjc7qBXJmhHj92B5tYVNFWFjO8gZQb4Brlt2P3rCrHU29mXuOaEq2eNVVVs3byWUDSMvPEWt80vhBBCCCFEawL8g0mcdwb6chtffv9qs2eKohB5+21Yi4up/vLL4w+GnQ/+4bDlzQ7PnzImkopCI5XFRlIHRaLVKKzsAZdW98oELcdgIsBHR7je232DFu+BqlwYssBtQ9ptdrYvz6Yw6DCzJ0wlzDeszb7rn3qcBq2GMxZdjUbTK/+1CiGEEEKITrbooj9hDIYD3/5Ig7n5ZdH+kyfjN2YM5a+/cXwVzcsXxlwJB3+E6vwOzd13VCQAWbvKCPH3ZlxSKCt6QLn9Xvmb/FGDkaRwf/eW2M/4HhQNDDrLbUPmpBtoqLZxMH4T1wy7ps1+NUdzSM/cT5y3H/3Pu9Bt8wshhBBCCHEiXjpvRl98If51Ch9+8nSzZ4qiEHHbsVW0r746/mD8dY7dZ9ve7dDcgWG+RCUHkbXz122OURworiW/0tShcbtaL03QTCS7u0BIxhJImgr6CLcNuX1lFnXelZw2cfAJV89WP/UPbIrCjNvudtvcQgghhBBCOOOcWVdjjPGidOUWKqqbbzHUT52C36hRlL/xBuqvq2ihSTBwLux4D6yNrYzovH5jIik9WkttRQOzhkQDnPLbHHtdgma12cmtMJEU7sYCIeVHoCzDrdsbK4uNlB42sj96A5cPu7zNfqXbtnDYUEy/0ChiJk122/xCCCGEEEI4Q6PRMOuqG/Fp1PD+e080e6YoChG33461sIiqr785/uC0xWAsg/3fdWjulNHHtzn2iwwgOdyfNYfKOjRmV+t1CVphVQNWu+reFbQDSxx/Dj7bbUPuSsvFplgJG6MhITChzX5rXn4Rjaoy/c9/ddvcQgghhBBCuGLquLMw9dVTv/kQhqrm58D0p0/Fd9RIDK+/fnwVrd9MCEtxlNzvgJBof8Li9E3bHCf3C2dLTgW2U7jcfq9L0H4tse/WFbSMJRA3FoL7uGU4c4OVjA2FZIXt5vKxl7TZr3T7Vo4aqxgYk0jIgIFumVsIIYQQQoj2mH3p9XhbNXzyyXPN2n+9F81SWEjVN984GjUaGH895G2C4vQOzZsyJpKiI1WYasxM7BtObYOVjKKaDo3ZlXpdgna06Q40N62gVRdAwXa3bm88tKUY1axQO+Ao46PHt9lv/asvoVFh6l1/dtvcQgghhBBCtMfkMXMwJvhSs2Ef1bUVzZ7pp03Dd+RIDG++hWqzORrHXAE6vw6X3O83JhJVhZw95UxMcdRt2JRl6NCYXanXJWg5BhO+XhqiAn3cM+CBHxx/uilBU1WVLSsOU+6fz9lTZrVZadKQvofsGgP9I2II7tffLXMLIYQQQgjREdMvvgofs4ZP/vevZu2KohB+3XVY8vKoS0tzNPqFwoiLIP1zqK9q95zh8QEERfiSubOM2GA/EsP82ZxdcfIXu6lel6AdNRhJDte7r8R+xncQORgiBrhluKIj1dSXquQk7OTsfvPb7Lf+5ecBmHqHVG4UQgghhBDdw/SJ52KM88awdid1pupmzwJnz0IXF0vFe+8fb5ywGCwm2PVxu+dUFIWU0ZHkH6igsd7KxL5hbM2pwH6KnkPrdQlajsGNFRyNBji63q3bGzevOESjtp5xU/vjo219la/y0EEyDaWkhEQQNnSY2+YWQgghhBCioyZfsAjfBg2ffv58s3ZFpyPsiiswbdlCw8GDjsbYUdBngqNYiN3e7jlTxkRht6kcTS9nYko4VSYLB0tqO/JjdJlelaDZ7Cq5BpP7zp8d/BFUOww+xy3DGasbKdhTw6GoLVw6vO3iIBv+8xyqAlNvvdMt8wohhBBCCOEus6ZeiDFKR/GqrTQ0Nr80OuSii1D8/Kh4/zeraKfdABWZkJ3W7jlj+gbhH+RN1s4yJvZ1nEPbfIqeQ+tVCVpxTQNmm919JfaPrICgeEfm7wY707JRVA2R43VE+ke22qcmJ5tDJQUkBYQSOXqsW+YVQgghhBDCXTQaDWMXXoBfvcL/vvpPs2fa4GCCz1tIzZLvsVYcOyc27Dzwj4At7S+5r2gc2xyP7jMQE+BDfIjfKXsOTdfVAbRGUZQFwIL4+HjSfj1E6Ab7DY6KMVV5h0kzZXVsMNXOlMO/UBE2ngOrV3c4NtWukv5LA4XBWQzVJbX5c5e+/xZ2RSFw8jS3/t0I59TV1cnfu+hW5JsU3ZF8l6K7kW+y8/lr+lATomJctoYVUePQab2anmkHDSLCbGbnU09hnO+oudA3IpXEg1+x6efPafRtfaHiZOo0Klazyk+frSHJ38K6Q8WsWrXKfbUnOkm3TNBUVV0CLBk/fvzi1NRUt41buDkXtqazcNYU4kL8OjZY8V5YXUPM5EuIGZ3a4dgObStmf+N+6kcVcdXc21rtYyzI583aChL1wcxZfFOH5xSuS0tLw53fpBAdJd+k6I7kuxTdjXyTXaOy4TA57y2htCqdyy9sXtgud+UvaDduZPzjj6N4e8PofvDiV0zW7YfUh9s1n81m590t69BbI1g4OYANX6bTZ+h4BkQHuuPH6TS9aovjUYMRb52GmCDfjg+WfWzVrO+0jo8FrF+2n1ofA/NTz2izz4bnn8Wm0TDlOknOhBBCCCFE93be3Osxhigc+fkXbDZrs2dhV12JraycmqVLHQ0hCTDwLNjxPlgb2zWfVquhz+Aw8g9WMiH52H1op+A2x16VoGWXG0kK80ejccMyZ/YaCOsHwX06PFRFoRFTLuQlpDMreWarfUwlJWTkHCbe25/4M1I7PKcQQgghhBCepNXqGHTWHPQ18PVPbzR7pp86Fe++fal4731U9Vg5/PHXgakcDi9r95x9BodSV9lIiF0hJsj3lCwU0qsStKMGE0nuKBBis0LOeujb9mqXK9Yu24tNsTJuej90mtZ3nW56/lksWg2Tr7reLXMKIYQQQgjhaReccxOmQNj//U/Yf1NGX9FoCLvqShr27qV+5y5HY0oq6KNg96ftnq/PoFAACg5WMTEljM3ZFccTwFNEr0nQ7HaVoxVGkt1xB1rRLjDXuiVBMzdYyd1eTU7kHi4ceV6rfRoMBvYe2U+MzoekM+d2eE4hhBBCCCE6g5fOm+Q509FXqny/4r1mz4IXLkQTFETFB8dK7mt1MOIixwqaqX1bE4Oj/AgI9SH/QCUT+4ZTVttIdrmxoz9Gp+o1CVppbSMNFjtJ7rgDren8WccTtB1rM9FYdESepiPYJ7jVPptffM6xerboqg7PJ4QQQgghRGe6+Lzbqder7Pr2m2araBp/f0IuuojaZcuxFBU5GkdeCjYz7P+2XXMpikL8oFAKDlUyIdmxmnaqldvvNQlajsGRObtlBS17DUQPB31Eh4ZRVZXtv2RRqs/lkmkLWu1jrqkmff9uIjVepJyzsEPzCSGEEEII0dl8vf2ImzkZfbmNpaubb18Mu+JyUFUqP/7Y0RA7CiIGwZ7/tXu+PoNCaaizEGyGiACfU+4cWq9J0I42JWgdXEGzNEDuJresnhVmV0KlD5bBpfQL6ddqny0v/ptGrYZJFy7q8HxCCCGEEEJ0hUUX/Yl6P5Wt33zerN0rPp7A2bOp/Oxz7PX1oCgw6lLI3QiVOe2aK77pHFolE1PC2JR1ap1D6zUJWo7BhJdWITa4gyX287eCtcEtCdrqlbuwKhZmpZ7W6nObxUz67q2Eo6X/BRd1eD4hhBBCCCG6gp+vnvCpI9EXW9i6Z1WzZ2FXX4W9uprqb79zNIy42PHnns9pj8AwX4Kj/Cg4WMmkvmEU1zSQW2HqSPidqtckaEcNRhJC/dFpO/gjZ68BRQNJUzo0jM1mp2xvI0URhzij3+mt9tn//n8xaTWMnjEHjabX/KsSQgghhBA90AUX3I5Vo7Lim+bFQvzGjsV36FAqPvjAsdIVkghJUx3bHNu58tVnUCgFh6s4LclxH9rmrFPnHFqv+a0/p9xEkrvOn8WNAd/WC3o4K2NXLrpGH6JG++Kl8Wq1z64VP+FrszPi2hs6NJcQQgghhBBdLTo8HvvQSDQZZZQYCpraFUUh9KorMWdmYly/wdE48lIwHIbCne2aq8/gMCwNNoLr7YTpvdmUfeqcQ+sVCZqqqhw1GDt+B1pjHRRsc8v2xg2r91Gvq2P+Ga2PVbhuDaV2C0MHDEPr49Ph+YQQQgghhOhqZ55/DTq7wpdfvtSsPWj+fLQREcdL7g9dCFqfdhcLiR8YAkDBoSomJIfJClp3U15nxmi20bejJfZzN4HdCn2nd2iYxnorDUe8qIjPYXDkoFb7bP3gXTR2lfG33tGhuYQQQgghhOguxg9PxRjjRcWmdCxWc1O7xtub0Msuw7h6DebcXPALgUHzIP0LsFlcnscv0Jvw+ADHfWgpYRRU1ZNfeWqcQ+sVCdqvFRw7vMUxOw203pAwsUPDbFi3B61dx6CJMa0+NxYXkV1RQlJQGIEJiR2aSwghhBBCiO5k6Jln4mdUWLLsv83aQy66EBSF6m+O3YE28lIwlUPmqpaDOKHP4FCKM6sZn3DsPrRTZBWtVyRov94e3uES+9lroM8E8O5Yope+IZdq3zIWTJ7d6vPtr7yETaNh/KIrOzSPEEIIIYQQ3c25c6+n3k9l7/Kfm7V7xcSgnzyZ6m++QbXbof+Z4Bfa7m2OfQaFYrPaCTHaCfbzYvMpcg6tVyRoRw0mtBqF+FC/9g9iqoCiPR0+f1ZpqENTFIi1XwVhfmEtntssZvbt3004WhJnz+nQXEIIIYQQQnQ33l4+hEwahr7QzM7965s9Cz7/fCyFhZi2bgOdNwy7AA78AI21Ls8TNyAERaNQcKiSCX3D2JwtK2jdRo7BSJ9QP7w6UmL/6HpA7XCCtnLlVhQUJk0f3OrzjI/ex6RVGDV9VofmEUIIIYQQoru68MLbsWlUln39TrP2wNmz0AQEUP31146GkZeCtR4ylrg8h7efjqikQMeF1X3DOGowUVzd4I7wPapXJGhHDaaOV3DMXgNe/hA/rt1DqKpK7vZqyoPymDG89bvPdi398Vhp/cXtnkcIIYQQQojuLDYyEeugcNR9RRiqSpraNX5+BJ11FjXLlmE3GiFhAoQmd2ibY0lOLePjQwBOiW2OPT5BU1WVHIOR5A4XCFkDiZMdS63tlJNVhE91EIHD7a3efVa8aSMldjOD+w1G59eB7ZhCCCGEEEJ0czMW/gEvm4Yvv/q/Zu3B55+HajJRs3QZKIpjFS1rNdQUujxH/OBQVLtKUK2NQF8dm06BQiG6rg6gNYqiLAAWxMfHk5aW1qGxas0qtQ1WLJVFpKWVt2sM78YKppQdIDNwInkdiGfr5lx8lBgiQ31a/bmK3n4Vxa6ijpvY4Z9beEZdXZ38uxHdinyTojuS71J0N/JNdlfeVIeBcd12ViavRKvROppVlfDISI7+97/sCgvFrz6ZiahkfvM0eYnnuzSD3aqiaGDLL+mkBKqs2pdHWlj3XkXrlgmaqqpLgCXjx49fnJqa2qGxduRWwi8bmD1xJKlDots3yJ7PAeg3+1r6xY1p1xB2u8qOr7+nMiqPPy64vsVzU0kJbzTUkhQYxuxLLm1fnMLj0tLS6Og3KYQ7yTcpuiP5LkV3I99k91VctYeCT5ZhsuWxYOY1Te3lVxyk7IUXmdK/P959UqHgbfoZt9Mv9UWX56hJ30Gjycr808N58qcDDB03iahAX/f9EG7W47c4Hr8DrQNn0LJXg28wxIxs9xCbt6Xj06gncVxIq8+3v3astP6lf2j3HEIIIYQQQpxKzjvrBhp87exc+n2z9uBzz21+J9qoy6AkHUr2uTxHn0GhlOfVMTYmGOj+96H1+AQtp9yEokBCWAfOdGWvgeRp8OuyaztsWXOQRm09C2aktnhmt1rZl76TMDQkzZ3X/jiFEEIIIYQ4hfj6+BM4fhD6vAb2Ht7a1O4VF4f/pInH70Qbdj5odO0qFtJnsONqq+AaK3pvbbcvFNLjE7SjBiNxwX746NqZXFXmQNXRDpXXN9U3QHYgDUmlRASGt3h+4JMPMWoVRp0+s91zCCGEEEIIcSo6/6LbsCkqP331ZrP2kPPPx5Kfj2nbNtBHQP/ZjqNHdptL40cmBeLlo6XocDXjksPY0s3vQ+vxCVqOwURyRAcqOGavdfzZgQRtedpGdDZvRk5JavX5zp+W4GOzM/J6Ka0vhBBCCCF6l4TY/lj6h2Dbk0917fHkKXD2bDR6/fFtjiMvhdpCyFnn0vharYa4ASHkH6xkbGIIh0vrMJmt7vwR3KrHJ2hHDcYOnj9bA/ooiGz9YmlnHNpSgtGnijmTWt59VrxlM8W2RganDETn38G72oQQQgghhDgFTTv3MrysGj7/+qWmNo2/P4FnzaPm558dd6INOgt0fnDg+xOM1Lo+g0OpKjExMNAfVYWMohp3hu9WPTpBqzZZqDRZ2n8Hmqo6CoT0PcNxB0M7FJWV4VsUgdcgE96t3KG27b9voagqp910e/tiFEIIIYQQ4hR3+vizMYZrKFy7Fbvd3tQect6xO9GWLwcvP+g3Ew7+5Pg93QXxg0IBCDM6xt5XKAlal8g5VsExub0raOWHoK6kQ9sbf16xHg0aps8c3eJZY2UFmWUFJOpDCO7Xv91zCCGEEEIIcSrTaDT0TZ2GvgZWbfqmqd1v3Di8EhKo/vpY26CzoDoPSva6NH5EfAC+ei/qcusI9fdiX4EkaF2iKUGLaGeClr3G8WcHErSSXY3UBpcydvDwFs/S338Xq0bD6AWuXbgnhBBCCCFET3PuWddj0drZsvK7pjZFUQg+/zxMmzdjKSiAgXMBxbGK5gJFoxA/KISCg5UMiw1iX1G1m6N3nx6doB01mABIDGvnFsfs1RCcCKHJ7Xp918EMAqsjiRzp0+rzA5vW42+zk3Luee2LTwghhBBCiB4iODAM+4BwOFBKnel4AhWycCEAVd9+CwFR0Oc0OPijy+P3GRRKXWUjI4L1HCquw2Kzn/ylLtCjE7Qcg5HYYF98vdpZYj9vCyRNbvf5sw3r9wAwZ9akFs8qDx6gxNZI/6T+aHS69sUnhBBCCCFEDzJ25ny8rRp+WP5+U5tXfDz+EydS/fU3qKrq2OZYuBNqCl0a+9dzaH2sGsw2O4dL6twau7v06ATtqMFEUnsLhNQUOc6fxY1p9/zVh+zUhZSREBPb4tnuD94FRWHU5Ve2e3whhBBCCCF6kllTL6TeT+XgujXN2oPPPw9LXh7127fDoPmOxkM/uzR2SLQ/+hAffCssAOwr7J7bHHt4gmZsf4GQol2OP2NHt+v1IwU5BFVFEzbYq8Uzu93OoYP7CEdL1LjT2hefEEIIIYQQPYyXzhv/kX3xyzORV5zZ1B40Zw4af3+qvv4aIgdBaF/Xz6EpjnNo1Udr8dNpu20lxx6boNU2WCivM7f/DrTCXYACMSPa9frq9dsBmDJ5ZItneSuXU6uBQaPHty82IYQQQggheqgZ8xahURV+/PHdpjaNvz+B8+ZR+/NS7PX1jlW0rNXQ6No2xejkIOprLYyOCGC/JGid69cCIe2+A61oF0QMBJ+A9r2+v456vxqGDuzX4ln611+gsauMvPr69sUmhBBCCCFEDzVm6FSM4RpKtuxu1h583kLsRiO1K39xnEOzNULWKpfGjkwMAmCYnx/7i2qw2127T60z9NgELa/CkaAltLeCY+EuiBvdrldLa8oJLI3Gt58F5XcFRqz19WSXFhDvH4g+Lq59sQkhhBBCCNGDxUwYg75SZdvetKY2//Hj0UVGUrtiBSROAt8Ql7c5RiQEoCgQp2qoa7SSeyxn6E56bIJWXtcIQFRg6yXuT6i2GOqK233+bOX6jejs3oyZMKDFs4xPPsSs1TB0xux2jS2EEEIIIURPd878a7ErKqt//qypTdFoCJg1k7q1a7FbbDBgjqNQiN3m9Lhe3lpCY/X41Tne6Y7n0HpsgmYwmgEI1Xu7/nLRseXUdq6gZe0uw6JrYOLYlufX9qetwNtmZ/ClV7RrbCGEEEIIIXq6uKhkGhL1NKTnYLGam9oDZ81GNZkwbtzo2OZoMjiuxnJBZGIg9SX16BSFvd2wkmOPTdAqjGaCfHV4advxIzYVCGlZ4ONk6hqN+BREQKIRna75/WvGgnwK6+tIiYlH5+fnelxCCCGEEEL0EkPOSMW3QcPyNcdX0fQTJ6AJCHBsc+w/GzReLl9aHZUUSH2thRHhAbKC1pkMRjPhAe3Y3gjHCoQMaFeBkJXb1uNnCWDwmPgWz/a8/w52jcLI8y9pX1xCCCGEEEL0EmfPvhqzl52dq46fM1O8vQmYPp26X1aheumh7zSXz6H9WihkhL8f+wurHZdfdyM9NkGrqDMT1p7tjeBYQYsd1a5X92/Pxa7YmDZ5bItnB3ZtI8gO8TNmtS8uIYQQQgghegk/Xz3K4Bh0R6qorClvag+cPQtbZSX1O3Y4yu0bDkP5YafH/bVQSDxayuvMlNY2eiL8duuxCVqlqZ0JWl0p1Ba2q0CIxWbBnqPHEl2NPsC32bPiLZupwM7AQcPQaHrsX7sQQgghhBBuM/nM89DZFZb8/E5Tm37aGSheXtSuWAkD5zkaXVhF+7VQiL7ODsC+bnYOTdfVAbRGUZQFwIL4+HjS0tLaNUZRpYkoXb3L74cZtjES2FkK1S6+m1GWSYipL/aUohbzln34DqgqlqEj2/0zia5XV1cn//5EtyLfpOiO5LsU3Y18k6cuuz0Ao95O1eq1pEVNaGoPGTSIsu+/J2PSRMYF9MW25RN2WZyvH2HztlNXAPjC9+t3oylu5847D+iWCZqqqkuAJePHj1+cmpranvcxLvuJ4f2TSE0d7NrLqx1VYMbMuwp8g1x6devbmfgDl110NpExIU3tdquV1/7vGaK9/Zh9uVRvPJWlpaXRnm9SCE+Rb1J0R/Jdiu5GvslT296M77GsOUR8cjgDkh1V0ivLyij+29+ZFBuL77hLYM2zpJ42AvThTo25257Hus8OMzjGD5N3MKmp4zz5I7ikR+61q6m3YrWr7dviWLgLwvu7nJzZVTt1hxUag2uaJWcAR775inqthiGTTnc9HiGEEEIIIXqxOWddBcDSn95vagucMQMUxbHNcdBZoNrh8DKnx4xKDARglF7PvqLutcWxRyZoBqPjoF94QHvuQNvVrvNnO3P3EFGVQOQQ3xbP9v68BJ3dzvCrrnU9HiGEEEIIIXqxwSmjqYvWUbk9A7vdcW5MFxGB39ixjnL7saMhMNalcvsRCYEoCiQqWvIq6qmut3goetf1yASt4tgl1WF6F8vs15VBTUG7Lqhet3EnGrRMmdJ872tjVRW51QYSgyPwCQlxeVwhhBBCCCF6u+TJk/CvhQ3bf25qC5w1i8YDBzAXFDhW0Y6sBEuDU+N5+WgJidETaHKU2N/fje5D65EJmuFYghbu6hbHot2OP9uxglaW0YjF10RK/9hm7XvffxebRsPws85xeUwhhBBCCCEEnHPWtVg1KuuXf9nUFjjbcXVV7YoVjnL7FiPkrHN6zKjEQCzljoSuO1Vy7JEJ2vEVNFcTtJ2OP2OdrwADcLg8k/DyRAL6g6JRmj3L2LQWP5udfgsvcC0WIYQQQgghBADhIdFYU4Kx7y+iodEEgHdiIj4DB1K3YiUkTwMvvUvbHCMTA2motZDs78M+WUHzrHYnaIW7IKwf+Aa79NqqzZvwtvkybuKgZu2Vhw5SYm2kf1I/NLpuWTBTCCGEEEKIU8LI1Dl4WzT8sPKDprbA2bMx7diBtdYE/Wc67kNTVafGi0xyFAoZE6iXFTRPM9SZ8ffW4uulde3Fot3tOn92dE8FNq2FEaNSmrXv+/QjUBRGXny5y2MKIYQQQgghjpubugizl52Dm49vYwycPQvsdupWrXJsc6wtdBT9c0JEnwBQIFnRkVlmpMFi81DkrumRCVqFsdH11TOjAarzXD5/VlRXRGBRHF6JZnTezRPC7Ix0AmwqMZMmuxaLEEIIIYQQohlvLx/sKWEomQbMFkfVdp8hQ/CKi6N2+QoYMAcUjWMVzZnxfHWERvsT1KBis6scKK71ZPhO65EJmsFobkeBkGPnz1xcQVuxYx2B5lCGjUts1m4sLKTMZiapT7JrcQghhBBCCCFaNXD8ZLwtGlZv/g4ARVEImD0L44YN2PGD+HGQleb0eJFJgdgMjmSvu2xz7JEJWqXJ3L7zZwAxrhUIObizABWV8ROGNGs/8MWnqIrCoDPnuRaHEEIIIYQQolWzUy/FplHZtWFFU1vg7NmoZjN169ZD8ulQsB3MRqfGi0oMorHWQoyXrtsUCumRCVpFndn1O9CKdkFoX/ALcfqV6sZqdLmhqNEm/IOaJ4SZ27fgY7OTNPcs1+IQQgghhBBCtCo0KIKGeD8aDuQ3XVrtP3Ys2pAQR7n95NPBboW8zU6NF5noKBQyNkgvCZqnqKrq2OIY4OoKmusFQn7JWEukMYGUUZHN2s1GI4WmGhLCoqR6oxBCCCGEEG6UMGYM/kaFHfvXAKDodATMnEldWhpqzHhQtE7fhxaR4CgU0lfrzYGiGqw2uydDd0qPS9BMZhuNVrtrWxxNFVCd63KBkPTt2QBMmjysWfuRrz7HptEw4PTpLo0nhBBCCCGEOLGZMy4BYOPqJU1tgbNnYa+txbh7H8SPhZz1To31a6GQ0AaVRqudrHLntkZ6Uo9L0Np1B9qvpThdWEFTVZWGHC1WvYmwmIBmzw6vW43Wbqf/+Rc5H4MQQgghhBDipJLiBmCM0FK573BTm37KFBQ/P+pWroSkqS6dQ4tMDIRKRw7RHQqF9LgEzXAsQXOpiuOvBUJiRzn9SlZVFuGVCQQka1EUpandbrWSZygh1i8Q78BA52MQQgghhBBCOCVsxCD0BjvZ+QcA0Pj6EnD66dSuWImaOBXsFsjb4tRYkYmBNNZaCNVo2FfQ9efQelyCVmF0lMl0eQUtNBn8Qp1+ZeO+Hfha9QwentCsPXfZzzRqNfQbN8H5+YUQQgghhBBOm3rGQgB++eWzprbAM2djLS2loTbIpXNoUUnHCoUEdo9CIT0uQTPU/bqC5kIVx8JdLp8/O7K/CIARI/o1az+4/CcUVWXIxYtcGk8IIYQQQgjhnFGDJ2MKhILdu5vaAqZPB52O2tUbIG6MC4VCAkGB/jpv9hVWo6qqp8J2So9L0JrOoDlbxdFUAVVHXTp/ZlftNORqsOrrCYrwa/bsaP5RIrTe6OPinB5PCCGEEEII4TyNRoP/4AR8CxowVJUAoA0Oxn/0aIwbNvzmPjTTScf6tVBImBlqGqzkV9Z7OvwT6pEJmrdOg95b69wLRceybhdW0A4ZDhFRlUhQcvMS+qXbtlCrgZTBw50eSwghhBBCCOG6MVPmoFUVVqQd3+boP2kSDRkZ2CLGOs6h5Tt/Dk1TZQG6vlBIj0vQDEYz4XrvZoU7TujXCo4uFAjZtH8nftYAhgxPbNae8e1XAAy54GKnxxJCCCGEEEK4btqEs2n0sXN428amNv3ECWC3YyrWuHQOLTIxEHOthUCULj+H1uMStAqjmVB/Fys4hiSBf5jTr2RlFAMwdERys/bsQxkE2xXCR4x0fn4hhBBCCCGEy7x03tAvAm12FQ1mx7ZE31GjUHx8MO5MdxxhcrFQyCi9vyRo7lZhNBPu7PkzcKyguXD+zGa30ZinxRbQ0Oz8WU1ONgbVSlJSivNzCyGEEEIIIdptyIRpeFs1rFr/NQAab2/8x43FtHmL4xxa/janzqH9WihkoLePbHF0twqj2fkS+/WVUJnj0vmzjPIMIquSW5w/O/D5p6AoDJ6/wPlghRBCCCGEEO0264yLsWpU9mxc2dTmP2EijQcPYg0d7fQ5NG9fHSFR/kRaoKSmkfK6Rg9GfWK9O0H7tUCICytomzN24WcNYOjw5Gbtmbt34GezE5860+mxhBBCCCGEEO0XpA/BnKjHcqgYu90OgP9Ex33EpiIFFA3krHdqLEehECsAmaV1ngnYCT0qQWu02qhrtBLuaoLmwgrar+fPfntBdWNlBcWNJhKj4tFoetRfqRBCCCGEEN1a0phx+NUrbN69AgC/4cPR+Ptj2pnu+D3fhXNo1joL/nY4WnHybZGeojt5l86nKMoCYEF8fDxpaWlOv1fR4MiaywtySEsrOGn/ofuWEeQTxaYte5wa36baaMzVYfY1smPv5qb2upXLsGsUNAlJLsUrTj11dXXy71h0K/JNiu5IvkvR3cg32bMFBvSlhDUs+/5jGqsdCzUhffti/mUV5iuT6JO3hHUrl2LX+pxwHGOF44LqGLuGtTsyiKrL9HjsremWCZqqqkuAJePHj1+cmprq9Ht7C6ohbR2TxowgdXjMyV/Y8ydImYizc+ws2UnMlymED/Zr9s5XH7yFl83OnLvuQefn1/YA4pSXlpbm9PciRGeQb1J0R/Jdiu5Gvsme79FlH6MUGJr+PRsyMyl99jlih92KJu9rzujrCynTTziGud7Km7+sYYCXDwSGkpo6phMib6lH7cerMJoBnKvi2FADFVkubW/ckrHbcf7sN+X1bY2N5FdXEBcUKsmZEEIIIYQQXSBq5FD0lSoHcxxHmPwnTgLAVMSxc2gn3+bo7acjJNqfPqqWXIPRk+GeUI9M0JwqElKR5fgzYqDT42dnlAAwcFh8U1vW999i0WroP2GK84EKIYQQQggh3GZ66gUArP7lCwB8hwxGExSEacceiB0FR50vFBLUoHbpGbQelaAZfl1BcyVBC3Pu3jKzzYw13we7vpHAcN+m9kOrVqCxqwy68FKX4xVCCCGEEEJ03ND+4zEGQfGevQAoWi3+48djbLoPbStY6k86TmRiILoGO411FqrrLZ4Ou1U9KkGrMDai1SgE+Xo50fnXBK2vU2PvKt1FTHUKoSk+KIoCgN1uJ7e4gChvX/wiI9obthBCCCGEEKKDAoYm41dspsTgKBaonzQRS24uFv1wsJkdSdpJhMfrHX/aNeQaumYVrYclaGZC/b3RaBQnOmdDQAx4650ae2sr58+K1q3BpFVIGdE1BwiFEEIIIYQQDqedfhYaVWHFqk8B8J84EQBjgd3pc2jBkf4AhNgUjlZ0zTm0HpegOX0HWkWW06tnADkZZQD0GxLb1HbwxyUADLnwEueDFEIIIYQQQrjdlLFzafC1k71zOwA+AwagDQ3FtCPdcQ7NiQQtMMwHRaMQalc42kUraIqqql0ysTMURSkDjnZ1HEL8RgRQ3tVBCPEb8k2K7ki+S9HdyDcpupskVVUjW3vQrRM0IbobRVG2qao6vqvjEOJX8k2K7ki+S9HdyDcpTiU9aoujEEIIIYQQQpzKJEETQgghhBBCiG5CEjQhXPNGVwcgxO/INym6I/kuRXcj36Q4ZcgZNCGEEEIIIYToJmQFTQghhBBCCCG6CUnQhGiFoijzFEU5qCjKEUVR7m/l+d2KouxXFGWPoigrFUVJ6oo4Re9xsm/yN/0uVBRFVRRFqpUJj3Lmm1QU5ZJj/63cpyjKx50do+h9nPjf70RFUVYpirLz2P+Gz++KOIU4EdniKMTvKIqiBQ4BZwL5wFZgkaqq+3/TZwawWVVVk6IotwCpqqpe2iUBix7PmW/yWL9A4AfAG7hdVdVtnR2r6B2c/O/kAOAzYKaqqpWKokSpqlraJQGLXsHJ7/INYKeqqq8qijIU+FFV1eSuiFeItsgKmhAtTQCOqKqapaqqGfgUWPjbDqqqrlJV9dfr5TcBfTo5RtG7nPSbPOYfwNNAQ2cGJ3olZ77JxcDLqqpWAkhyJjqBM9+lCgQd+78HA4WdGJ8QTpEETYiW4oG83/xz/rG2tlwP/OTRiERvd9JvUlGUsUCCqqo/dGZgotdy5r+TA4GBiqKsVxRlk6Io8zotOtFbOfNdPgL8QVGUfOBH4I7OCU0I5+m6OgAhTmWKovwBGA9M7+pYRO+lKIoG+DdwTReHIsRv6YABQCqOXQZrFEUZoapqVVcGJXq9RcB/VVX9l6Iok4EPFEUZrqqqvasDE+JXsoImREsFQMJv/rnPsbZmFEWZDTwInKuqamMnxSZ6p5N9k4HAcCBNUZQcYBLwnRQKER7kzH8n84HvVFW1qKqajeNs0IBOik/0Ts58l9fjOBuJqqobAV8golOiE8JJkqAJ0dJWYICiKH0VRfEGLgO++20HRVHGAK/jSM7kXIXwtBN+k6qqVquqGqGqavKxw+6bcHybUiREeMpJ/zsJfINj9QxFUSJwbHnM6sQYRe/jzHeZC8wCUBRlCI4EraxToxTiJCRBE+J3VFW1ArcDS4EM4DNVVfcpivKYoijnHuv2LBAAfK4oyi5FUX7/PwBCuI2T36QQncbJb3IpYFAUZT+wCrhXVVVD10QsegMnv8t7gMWKouwGPgGuUaWkuehmpMy+EEIIIYQQQnQTsoImhBBCCCGEEN2EJGhCCCGEEEII0U1IgiaEEEIIIYQQ3YQkaEIIIYQQQgjRTUiCJoQQQgghhBDdhCRoQgghhBBCCNFNSIImhBBCCCGEEN2EJGhCCCGEEEII0U38P6cU2w+0/a30AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "zeros, weights = np.polynomial.laguerre.laggauss(8)\n", "targets = np.arange(9, 14)\n", @@ -219,11 +280,11 @@ ")\n", "\n", "lanczos = eval_lanczos(x)\n", - "for mean_target in mean_targets:\n", - " vals = eval_mean_laguerre(x, mean_target)\n", - " rel_error_mean = calc_rel_error(lanczos, vals)\n", - " axs[0].plot(x, rel_error_mean, label=mean_target)\n", - " axs[1].semilogy(x, np.abs(rel_error_mean), label=mean_target)\n", + "# for mean_target in mean_targets:\n", + "# vals = eval_mean_laguerre(x, mean_target)\n", + "# rel_error_mean = calc_rel_error(lanczos, vals)\n", + "# axs[0].plot(x, rel_error_mean, label=mean_target)\n", + "# axs[1].semilogy(x, np.abs(rel_error_mean), label=mean_target)\n", "\n", "mins = []\n", "maxs = []\n", @@ -233,6 +294,11 @@ " maxs.append(np.max(np.abs(rel_error)))\n", " axs[0].plot(x, rel_error, label=target)\n", " axs[1].semilogy(x, np.abs(rel_error), label=target)\n", + " \n", + "rel_error = evaluate2(x)\n", + "axs[0].plot(x, rel_error, label=\"Optimal shift\")\n", + "axs[1].semilogy(x, np.abs(rel_error), label=\"Optimal shift\")\n", + "\n", "# axs[0].set_ylim(*(np.array([-1, 1]) * 3.5e-8))\n", "\n", "axs[0].set_xlim(x[0], x[-1])\n", @@ -244,9 +310,44 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 82, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "(-7.5, 25.0)" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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SBDQAacOKXRwBAIC7EdAApB2mOAIAALcioAEAAACASxDQAKSN4BRHRtAAAIBbEdAAAAAAwCUIaADSRu19qtkkBAAAuBQBDQAAAABcgoAGIH0Y/x9ssw8AANyKgAYgbQSnNrJJCAAAcCsCGgAAAAC4BAENQNphBA0AALgVAQ0AAAAAXIKABiBt1G6zLzYJAQAA7kRAAwAAAACXIKABSCPBXRwZQQMAAO5EQAOQNmqnOLJJCAAAcCkCGgAAAAC4BAENQNphiiMAAHCrpAc0Y0wbY8yLxpiNxpgNxpjxyT4nAAAAAEiGjGSfgKRHJf3LWnuDMaaZpJxknxCAs5M1gU1CxBo0AADgTkkNaMaYXEmTJN0iSdbaKklVyTwnAAAAAEiWZE9x7CXpgKSZxpgVxpi/G2NaJPmcAJytAkvPHIcRNAAA4E7JDmgZkkZIesxae66kU5LuqXuAMeY2Y8xSY8zSAwcOJOMcAQAAAOAzkeyAViqp1Fq7KPDvF+UPbLWstY9ba0dZa0d17NjxMz9BAGcPawJ/il0cAQCAOyU1oFlr90raaYwZEPjSZEnrk3hKAM5qgU1C2GYfAAC4lBt2cfyupKcCOzhul/TVJJ8PAAAAACRF0gOatXalpFHJPg8AZ7/acTPLJiEAAMCdkr0GDQAAAAAQQEADkHZYgwYAANyKgAYAAAAALkFAA5A2bO2fjKABAAB3IqABSBvBYOawSQgAAHApAhoAAAAAuAQBDUDaYZMQAADgVgQ0AAAAAHAJAhqAtFG7SQgjaAAAwKUIaAAAAADgEgQ0AGnHsosjAABwKQIagLQR3GbfioAGAADciYAGAAAAAC5BQAOQdtgkBAAAuBUBDQAAAABcgoAGIG3YEH8DAABwEwIaAAAAALgEAQ1A2nFYgwYAAFyKgAYgbdjaqY1ssw8AANyJgAYAAAAALkFAA5B22GYfAAC4FQENAAAAAFyCgAYgbQTHzRhBAwAAbkVAAwAAAACXIKABSBvWBP5kBA0AALgUAQ0AAAAAXIKABiB92OAf3AcNAAC4EwENQNqwxp/QmOIIAADcioAGAAAAAC5BQAOQdpjiCAAA3IqABgAAAAAuQUADkDZO36g6qacBAAAQFgENAAAAAFyCgAYgbZweQWMIDQAAuBMBDUAaIqABAAB3IqABAAAAgEsQ0ACkjeC4mWPZZh8AALgTAQ0AAAAAXIKABiANsQYNAAC4EwENAAAAAFyCgAYgbZxeg8YIGgAAcCcCGoC0YU9HtKSeBwAAQDgENAAAAABwCQIagLRjmeIIAABcioAGAAAAAC5BQAOQNqwJ/oURNAAA4E4ENAAAAABwCQIagLTDHo4AAMCtCGgAAAAA4BIENABpo3blmWUMDQAAuBMBDUDasLV/skkIAABwJwIaAAAAALgEAQ1A2mEEDQAAuBUBDQAAAABcgoAGIG3UrkHjRtUAAMClCGgAAAAA4BIENABpx7LNPgAAcCkCGoC0cfo+aExxBAAA7kRAAwAAAACXIKABSBvB7fXZZh8AALgVAQ0AAAAAXIKABiDtMIIGAADcioAGAAAAAC5BQAOQNqwJ/MkujgAAwKUIaADShg3xNwAAADchoAEAAACASxDQAKQdhymOAADApQhoAAAAAOASBDQAaYM1aAAAwO0IaAAAAADgEgQ0AGmDETQAAOB2BDQAaYf7oAEAALcioAEAAACASxDQAKQNW/snI2gAAMCdCGgAAAAA4BIENABpo3YEjTVoAADApQhoAAAAAOASBDQA6cP4/2ANGgAAcCsCGgAAAAC4BAENQNqoHTdjDRoAAHApAhqAtME2+wAAwO0IaAAAAADgEkkPaMYYrzFmhTHmjWSfC4D0wAgaAABwq6QHNEl3SNqQ7JMAAAAAgGRLakAzxuRJukrS35N5HgDSA5uEAAAAt0v2CNrvJP1AkpPk8wAAAACApEtaQDPGTJG031q7rInjbjPGLDXGLD1w4MBndHYAzkbs4ggAANwumSNoEyRdY4wplvSspIuNMf9seJC19nFr7Shr7aiOHTt+1ucI4KxEQAMAAO6UtIBmrf2RtTbPWpsv6SZJc621X0rW+QAAAABAsiV7DRoAfGaC42YOA2gAAMClMpJ9ApJkrZ0vaX6STwMAAAAAkooRNABpw5ravyXzNAAAAMIioAEAAACASxDQAKSN2m32uVE1AABwKQIagDREQAMAAO5EQAMAAAAAlyCgAUgbtVMcGUEDAAAuRUADAAAAAJcgoAFIG1Ym8CcjaAAAwJ0IaAAAAADgEgQ0AGmjdtyMbfYBAIBLEdAApB2mOAIAALcioAEAAACASxDQAKQNG+JvAAAAbkJAAwAAAACXIKABSBvWBP5kAA0AALgUAQ0AAAAAXIKABiBt2No/GUIDAADuREADAAAAAJcgoAFIO4ygAQAAtyKgAUgbbLMPAADcjoAGAAAAAC5BQAOQNmo3CWEADQAAuBQBDQAAAABcgoAGIG2c3mbfSep5AAAAhENAAwAAAACXIKABSBvWmMBfknseAAAA4RDQAKQd7oMGAADcioAGAAAAAC5BQAOQFhyfr86/GEEDAADuREADAAAAAJcgoAFIC449vbU+42cAAMCtCGgAAAAA4BIENABpwXHqjqAxhgYAANyJgAYgLTiWTUIAAID7EdAAAAAAwCUIaADSgmPrjJpZRtAAAIA7EdAAAAAAwCUIaADSgnXYZh8AALgfAQ0AAAAAXIKABiAt1N3FkW32AQCAWxHQAKQFh41BAABACiCgAUgTts7fCGsAAMCdCGgA0oK1Tt1/JO9EAAAAGkFAAwAAAACXIKABSAvWqTvFEQAAwJ0IaAAAAADgEgQ0AGmh7jb7jKEBAAC3IqABAAAAgEsQ0ACkBafOLo5ssw8AANyKgAYgLTh1NgkhnwEAALcioAEAAACASxDQAKQFyxRHAACQAghoAAAAAOASBDQAaaHuJiEsQgMAAG5FQAMAAAAAlyCgAUgLjj09asb4GQAAcCsCGoC0YB02CQEAAO5HQAMAAAAAlyCgAUgP1pfsMwAAAGgSAQ0AAAAAXIKABiAt1N8khDVoAADAnQhoAAAAAOASBDQAaaHejaotI2gAAMCdCGgA0oJ1Tm8SQjwDAABuRUADAAAAAJcgoAFIC069aY2MoQEAAHcioAEAAACASxDQAKSFupuEsM0+AABwKwIaAAAAALgEAQ1AmnCaPgQAACDJCGgAAAAA4BIENABpwTqn152xBg0AALgVAQ1AWqi/SQgAAIA7EdAAAAAAwCUIaADSAjeqBgAAqYCABgAAAAAuQUADkBas9dX5exJPBAAAoBEENAAAAABwCQIagLRQbw2aYQgNAAC4EwENQHqou80++QwAALgUAQ0AAAAAXIKABiAt1L1RNdvsAwAAt0pqQDPGdDfGzDPGrDfGrDPG3JHM8wEAAACAZMpIcvk1kr5vrV1ujGklaZkx5l1r7foknxeAs0zdTUIsI2gAAMClkjqCZq3dY61dHvj7CUkbJHVL5jkBAAAAQLK4Zg2aMSZf0rmSFjX4+m3GmKXGmKUHDhxIyrkBOAs4dXZxTOJpAAAANMYVAc0Y01LSS5K+Z609Xvd71trHrbWjrLWjOnbsmJwTBJDyHPbWBwAAKSDpAc0Ykyl/OHvKWvtyss8HAAAAAJIl2bs4GknTJW2w1v42mecC4Oxm5av3LwAAADdK9gjaBElflnSxMWZl4L/PJfmcAAAAACApkrrNvrV2oSSTzHMAkB6sU3ebfQAAAHdK9ggaAAAAACCAgAYgLTiqu80+Y2gAAMCdCGgA0oK1TtMHAQAAJBkBDQAAAABcgoAGIC1YW3eTEKY4AgAAd0qpgLb14DpVVJYl+zQAAAAA4N8ipQJapZF8Pl/TBwJAA45l1AwAALhfSgU0Sar2VSb7FAAAAADg3yL1AlpNVbJPAUAqqrOLo2U0DQAAuFTKBTSmOAIAAAA4W6VcQKuuqU72KQBIQfXug2aSdx4AAACNSbmAVuNjiiOA6Dn1ttkHAABwp5QLaD5fTbJPAQAAAAD+LVIwoDHFEUD06k1xZJMQAADgUikX0KqZ4ggAAADgLJVyAc1x2MURQPTqjqAxfgYAANwq5QJaDbs4AgAAADhLpV5AYw0agBjUuzm1YQwNAAC4U8oFNJ9lF0cA0au3zT75DAAAuFTqBTS22QcAAABwlkq5gMYURwCxqLfNPgAAgEulXEBjF0cAAAAAZ6uUC2iMoAGIRf1t9lmEBgAA3CnlAprPYQ0aAAAAgLNTygU0xzLFEUD0GDUDAACpIOUCWg27OAKIQd37oBHWAACAW6VcQHOY4ggAAADgLJVyAc3HLo4AYlB/kxAAAAB3SsGAxi6OAAAAAM5OKRjQGEEDEL26a9BkknceAAAAjUm5gGbZxREAAADAWSrlAhr3QQMQC6s6a9Asq9AAAIA7pWBAYwQNQPQcQhkAAEgBKRfQ6u7EBgARI6ABAIAUkHIBrYYpjgBiUPfm1EQ1AADgVikX0CwBDQAAAMBZKuUCmsMURwAxqL8xCGNoAADAnVIuoPnYZh8AAADAWSrlAprDFEcAsagz+s74GQAAcKvUC2hMcQQAAABwlkrBgMYURwDR4+bUAAAgFRDQAKSFetvsG8IaAABwpxQMaExxBAAAAHB2SsGAxggagOjV69xhAA0AALhUygU0S0ADAAAAcJZKuYDmOHR9A4he3U1CrEniiQAAADQi9QKaGEEDAAAAcHZKvYDGFEcAMai/zT4j8QAAwJ1SMKBxYQUgerbOJiG0IgAAwK1SLqBZpjgCAAAAOEulXEBzHO6DBiB6VrQdAADA/VIvoHGRBQAAAOAslXIBjV5wALGot81+Es8DAACgMSkV0IwkxxLQAMTOsNEQAABwsZQKaBIBDUCs/MHMSLKMoQEAAJdKqYBmLFMcAcQmeIsOk+TzAAAAaExKBTSp/r2MACBaBDQAAOBmKRfQHKYmAYgJN6oGAADul1IBzYgRNADxYQQNAAC4WUoFNIn7oAGITXCbfcPwGQAAcLGUCmhGTHEEEB9G0AAAgJulVECT6t9sFgAiVf9G1bQjAADAnVIvoDHFEUAMHLHNPgAAcL+UCmhMcQQQq+DaM0MbAgAAXCylAprE1CQAsQmOvhuxzT4AAHCvlAto7OIIIB5McQQAAG6WUgHN3/NN3zeA6LHNPgAASAUpFdAkdnEEEB9G0AAAgJulXEBjkxAAsai7Aywj8QAAwK1SKqAxxRFAvBhBAwAAbpZSAU1iBA1AbGztNvsAAADulXIBjRE0ALGou36VVgQAALhVSgU0Yw0jaADiklKNHgAASDspd61i2SMbQExs7R+WeY4AAMClUi+gMYIGIA5kMwAA4GYpFdCMVGejbACInGP9rYeRWIQGAABcK6UCmsQIGgAAAICzV8oFNDYJARAbf9thxFpWAADgXikV0Pw3qgaA6Dn2dEADAABwq5QKaJJhiiOAuBDQAACAm6VYQGOTEACxCmwSYhmJBwAA7pX0gGaMucIYs8kYs9UYc09TxzusHQEAAABwlkpqQDPGeCX9SdKVkgZLutkYMzjs8aLnG0BsbO0aNEM7AgAAXCvZI2hjJG211m631lZJelbStY09gCmOAOLBGjQAAOBmGUkuv5uknXX+XSppbPjDjfZmWE17fKg81sjIyCMjj/X/aayRx/83GRv4Ux5ZOf7NRYzVGf8z/m1H6v/99P3Wgn/WPludck3g7/XLMw2e2/9sjpza53dqzyVQbm35/lfpL0OB1+aRkWRs7SurU67n9KObem3SGWX6X+npskzY11b71TrP7ZxRltPgPax71zorG3g21flZ1S3TU68s1Z5nqJ9bcJv02p9sndd/+r08/bNSvfLqvJO1PzfVeR0Nf371n9cGOgnql2Vs/TpS92fV2Gvzl+HU+fnX/qt2K/j69fH0e1n3faz/M/PU+/nZwM0p6tbHuj8zqWH9r1/7TaCW1Pt51S0r8G/VKy9EnQzWf+PU1hFbr3z/+9jwtZ1RXuDriuB325GVz1hVG0cnPD4p0//T3lOnHfE0LK9BO+Jp0I6cfp/8NcExdd7TMO9l8HWGbEfq1A1Pvd/t+u+jc0b5ocsJVR+DZanuexn2tQXKq/O6nEbKCjQtjb+PZ/yu6cyfW5jft4btiZVt4n2s3x5H87sd6vUlsh0J10YGp+7H2o4k9H2s2ybb4HsY5rXVlq/a16dAW9OwnTxds+u/j2e2//7y6r8ep96/w72PTdX/UL9rTb22uvUi+NoallvbRkb9ex19O3L6rKMrzwnxPsbfjpxuj5PTjjT9MwtXTyJpj+t+jrq9HXHqvI8hy6qtF2HqY+AHUP99rNfKhH19qdCOqJE6Gfz9i7T+h2tH6v+sQl/XObXXJY58TSzZSnZAa5Ix5jZJt0lSl+7tNLg6q8GLtKoJXLr4/+0PQD6p9u+ewA/T4//51/7bqH4YOt3oKdAInZ4O5S/TUY0UKEuBc5B8snKMf3SvYXmewHN4Q5Tlr1iq++tZ+wN1Aq/LJ5+sJF+gLCdQlq9OWf7nUu15h3ttOuP1+b8aLMsGXottUEb41xb4e6Asj+q+ltOVO1iyAu+jzzinX0vtz0y1f/epbpir/z4Gv2ZsndcZ/HrdCxoZ/8/HWNUEyqn7Mwv+u255dcuqX2dOv4+151H7egMXSoH6WL+OnPk+1oR8baffR1PvfTz9wa/a4OJ/L0//Djgx1ce6r63ue1u3fgRrTbD+15j6daTuzy34Om0TdeT0+1j/9yz4Pir4+xto4HxRvLZQv9seSZnWoxbyKNeXoUG+HA3uOE4fHZyrYFgMNpbOGa8tdDtiGryP9X/X6teXur/f8bUj4X7XFPigaNCO1KnnPo8TeF0N2pEQr62xOnL6g1Dy6vSHVTBg2Ebex1C/a6aR8kyI13dm/Q/9PjZ8bZH+bjf8mQXrZFPtiE8K1P+my2r4Pga/llmnrDNfW6TtSIzvo6xqPPXbkaba/vrvmQIdNKdfc213jT3dvtjA89QELvDiaUfCvY/12+P69T+edqT+NYKkBuWGex/rfq41LCueduTMz5rY2pEmr0ciaEdCvbYz62OduhJHOxLJ71rIn5k1MnUuuGuvfZpoRxq+NhOiPLe0IxkKhufg8/p/10L9Xoerj3XrXvC9NLbuv898fZG2I6F+r0P9rkXUjjR4H2NpR8641jrjGrZ+/Q/1ux3J71rda5Hg17zWo2bKlDeYqMMwwXUZyWCMGS/pfmvt5YF//0iSrLW/CnX8qFGj7NKlSz/DMwQAAACAxDLGLLPWjgr1vWSvQVsiqZ8xppcxppmkmyS9luRzAgAAAICkSOoUR2ttjTHmO5LmSPJKmmGtXZfMcwIAAACAZEn6GjRr7VuS3kr2eQAAAABAsiV7iiMAAAAAIICABgAAAAAuQUADAAAAAJcgoAEAAACASxDQAAAAAMAlCGgAAAAA4BIENAAAAABwCQIaAAAAALgEAQ0AAAAAXIKABgAAAAAuQUADAAAAAJcgoAEAAACASxDQAAAAAMAlCGgAAAAA4BLGWpvsc4iYMeaApB3JPg+4WgdJB5N9EnA16giaQh1BU6gjaAp1BE3paa3tGOobKRXQgKYYY5Zaa0cl+zzgXtQRNIU6gqZQR9AU6gjiwRRHAAAAAHAJAhoAAAAAuAQBDWebx5N9AnA96giaQh1BU6gjaAp1BDFjDRoAAAAAuAQjaAAAAADgEgQ0AAAAAHAJAhoAAAAAuAQBDQAAAABcgoAGAAAAAC5BQAMAAAAAl8hI9glEo0OHDjY/Pz/ZpwEAAAAAMVu2bNlBa23HUN9LqYCWn5+vpUuXJvs0AAAAACBmxpgd4b7HFEcAAAAAcAkCGgAAAAC4BAENAAAAAFwipdagAQAAAEi+6upqlZaWqqKiItmn4mpZWVnKy8tTZmZmxI8hoAEAAACISmlpqVq1aqX8/HwZY5J9Oq5krdWhQ4dUWlqqXr16Rfw4pjgCAAAAiEpFRYXat29POGuEMUbt27ePepSRgAYAAAAgaoSzpsXyHhHQAAAAAMAlCGgAAAAAUk55ebkuuOAC+Xw+SdIVV1yhNm3aaMqUKfWOs9bq3nvvVf/+/TVo0CD9/ve/b/K5wz3XxIkTNXz4cA0fPlxdu3bV1KlTJUlvvPGGfvrTnybkdRHQAAAAAKScGTNmaNq0afJ6vZKku+++W08++eQZx82aNUs7d+7Uxo0btWHDBt10001NPne451qwYIFWrlyplStXavz48Zo2bZok6aqrrtLrr7+usrKyOF8VuzgCAAAAiMPPXl+n9buPJ/Q5B3dtrfuuLmj0mKeeekpPP/107b8nT56s+fPnn3HcY489pqeffloej39sqlOnTk2WH+65go4fP665c+dq5syZkvxrzS688EK98cYb+vznP9/k8zeGETQAAAAAKaWqqkrbt29Xfn5+k8du27ZNzz33nEaNGqUrr7xSW7Zsibv82bNna/LkyWrdunXt10aNGqUFCxbE/dyMoAEAAACIWVMjXf8OBw8eVJs2bSI6trKyUllZWVq6dKlefvll3XrrrXEHqWeeeUZf//rX632tU6dO2r17d1zPKzGCBgAAACDFZGdnR3x/sby8vNq1Ytddd51Wr14dV9kHDx7U4sWLddVVV9X7ekVFhbKzs+N6bomABgAAACDFtG3bVj6fL6KQNnXqVM2bN0+S9MEHH6h///6SpMWLF+srX/lK1GW/+OKLmjJlirKysup9ffPmzSosLIz6+RoioAFIG0eOHdDSdfOTfRoAACABLrvsMi1cuLD23xMnTtSNN96o999/X3l5eZozZ44k6Z577tFLL72kIUOG6Ec/+pH+/ve/S5JKSkrCjniFey5JevbZZ3XzzTef8Zh58+adMaoWC9agAUgbf3j1Dr1ds0qfFKxL9qkAAIA43X777XrkkUd0ySWXSFLYdWVt2rTRm2++ecbXFy1apNtvvz3kYxpboxZqd8d9+/apvLxcQ4YMieDMG0dAA5A2ympO6qSXiQMAAJwNRowYoYsuukg+n6/2XmjReOihhxJ2LiUlJfrNb36TkOcioAFIG1ZWkuT4fPLE0JADAAB3ufXWW5N9CpKk0aNHJ+y56EoGkEZs4P+dJJ8HAABAaAQ0AGnj9AgaAQ0AALgTAQ1A+vDnMzmMoAEAAJcioAFIG7UjaA4BDQCAVHfrrbeqU6dO9e499oUvfEHDhw/X8OHDlZ+fr+HDhyfvBGPEJiEA0oYN/mkJaAAApLpbbrlF3/nOd+rdbPq5556r/fv3v/995ebmJuPU4kJAA5BGGEEDAOBsMWnSJBUXF4f8nrVWzz//vObOnfvZnlQCENAApI3aKY7yJflMAAA4i7x9j7R3TWKfs/MQ6coHYn74ggULdM4556hfv34JPKnPBmvQAKSPwBxHywgaAABntWeeeUY333xzsk8jJoygAUgbwRE0a20TRwIAgIjFMdL171BTU6OXX35Zy5YtS/apxIQRNABpJDDF0dYk+TwAAMC/y3vvvaeBAwcqLy8v2acSEwIagLQRHDdzfIygAQCQ6m6++WaNHz9emzZtUl5enqZPny5JevbZZ1N2eqPEFEcAaYRNQgAAOHs888wzIb8+a9asz/ZEEowRNABpJLAGzWEEDQAAuBMBDUDaOL1JCLs4AgAAdyKgAUgfgYEzh10cAQCASxHQAKSN0yNorEEDAADuREADkD6M/w8rpjgCAAB3IqABSBvBG1Q7bBICAABcioAGIO1YhxE0AABSXWlpqa699lr169dPffr00R133KGqqqqwxx89elR//vOfa/+9e/du3XDDDQk5l/vvv18PP/xwQp6LgAYgbbCLIwAAZwdrraZNm6apU6dqy5Yt2rx5s06ePKl777037GMaBrSuXbvqxRdf/CxONyrcqBpA2mENGgAAqW3u3LnKysrSV7/6VUmS1+vVI488ol69eqlXr16aM2eOjh07pl27dulLX/qS7rvvPt1zzz3atm2bhg8frksvvVS33367pkyZorVr12rWrFmaPXu2Tp06pS1btuiuu+5SVVWVnnzySTVv3lxvvfWW2rVrp7/97W96/PHHVVVVpb59++rJJ59UTk5OQl8bAQ1A2giOoDlMcQQAIGEeXPygNh7emNDnHNhuoH445odhv79u3TqNHDmy3tdat26tHj16qKamRosXL9batWuVk5Oj0aNH66qrrtIDDzygtWvXauXKlZKk4uLieo9fu3atVqxYoYqKCvXt21cPPvigVqxYoTvvvFNPPPGEvve972natGn6xje+IUn6yU9+ounTp+u73/1uQl87UxwBpJFAQOM+aAAAnNUuvfRStW/fXtnZ2Zo2bZoWLlzY5GMuuugitWrVSh07dlRubq6uvvpqSdKQIUNqw9zatWs1ceJEDRkyRE899ZTWrVuX8HNnBA1A2gjGMtagAQCQOI2NdP27DB48+Iz1Y8ePH1dJSYkyMjJkjKn3vYb/DqV58+a1f/d4PLX/9ng8qqmpkSTdcsstmj17toYNG6ZZs2Zp/vz5cb6SMzGCBiCNBDcJYQQNAIBUNnnyZJWVlemJJ56QJPl8Pn3/+9/XLbfcopycHL377rs6fPiwysvLNXv2bE2YMEGtWrXSiRMn4ir3xIkT6tKli6qrq/XUU08l4qWcgYAGIG0Ec5nDCBoAACnNGKNXXnlFL7zwgvr166f+/fsrKytLv/zlLyVJY8aM0fXXX6+hQ4fq+uuv16hRo9S+fXtNmDBBhYWFuvvuu2Mq9+c//7nGjh2rCRMmaODAgYl8SbVMKvUkjxo1yi5dujTZpwEgRX37bxO1sNlRPX/+3zWoz9hknw4AAClrw4YNGjRoULJPI6RZs2Zp6dKl+uMf/5jsU5EU+r0yxiyz1o4KdTwjaADSRu0ujmyzDwAAXCqlNgnZf2SnamqqlZGRmexTAZCCghMGLNvsAwBw1rrlllt0yy23JPs0YpZSI2gHnOOqqqlK9mkASFlsEgIAANwtpQKaRM83gHgEAxrtCAAA8aLDs2mxvEcpF9Ac60v2KQBIUcEmkhtVAwAQn6ysLB06dIiQ1ghrrQ4dOqSsrKyoHpdSa9AkyefUJPsUAKSo0x8hjKABABCPvLw8lZaW6sCBA8k+FVfLyspSXl5eVI9JuYAmUjqAmAV2caQdAQAgLpmZmerVq1eyT+OslHpTHFmDBiBGwVhmHaZKAwAAd0q9gCYurADEKjiCRjsCAADcKfUCmo8LKwCxqd0kxGGKIwAAcKekBjRjzGBjzPPGmMeMMTdE8hjWjgCIFZuEAAAAt4s5oBljZhhj9htj1jb4+hXGmE3GmK3GmHuaeJorJf3BWvttSV+JpFyH+xcBiBmbhAAAAHeLZxfHWZL+KOmJ4BeMMV5Jf5J0qaRSSUuMMa9J8kr6VYPH3yrpSUn3GWOukdQ+kkIJaABiVRvLCGgAAMClYg5o1toPjTH5Db48RtJWa+12STLGPCvpWmvtryRNCfNUtweC3csRFcwujgBiZgP/TzsCAADcKdFr0LpJ2lnn36WBr4VkjMk3xjwu/yjcQ2GOuc0Ys9QYs1SSHLbHBhCj05uEENAAAIA7JfVG1dbaYkm3NXHM45Iel6TsXtmW7bEBxC44gsYURwAA4E6JHkHbJal7nX/nBb6WMJbtsQHEqPZG1axlBQAALpXogLZEUj9jTC9jTDNJN0l6LZEFOKwdARAnNhsCAABuFc82+89I+kTSAGNMqTHma9baGknfkTRH0gZJz1tr1yXmVP1YgwYgVrVTGxmIBwAALhXPLo43h/n6W5LeivmMmiyXnm8A8aEdAQAAbpXoKY7/dg5r0ADEiDVoAADA7VIuoFkxxRFArAK7OHKjagAA4FKpF9Do+QYQo9r7oLHZEAAAcKmUC2g+NgkBEKPaKY5MlQYAAC6VcgFNXFgBiBk3qgYAAO6WcgHNYQ0agBjVjqAxxREAALhU6gU0Or4BxIuGBAAAuFQKBjRG0ADEJji10WEXRwAA4FIpF9Asm4QAiNHpKY60IwAAwJ1SL6DR8w0gTrQjAADArVIwoLG4H0BsakfQCGgAAMClUi6gOUxxBBAz2+BPAAAAd0m5gMb9iwDEKth6OA4j8QAAwJ1SLqBxYQUgZsb/B/dBAwAAbpVyAY0RNACxCi49Yy0rAABwq5QLaA4XVgBiZI0/odHRAwAA3CrlAprlRtUAYlS7RYhDQAMAAO6UcgGNETQA8XIYQQMAAC6VcgFN3L8IQIxOtx509AAAAHdKuYDGDWYBxIt2BAAAuFXKBTRuVA0gVsHNQQhoAADArVIuoLE9NoBY1W4SQkADAAAuRUADkHa4UTUAAHCrlAto7I4NIFa1I2js4ggAAFwq5QIaI2gAYhcIZkxxBAAALpVyAc3hRtUAYsQaNAAA4HYpF9DECBqAODHFEQAAuFXKBTQurADE6vQIGh09AADAnVIuoDlMTQIQI6Y4AgAAt0u5gGZZgwYgVsb/ByNoAADArVIwoNHzDSA2tB4AAMDtCGgA0gb3QQMAAG6XggGNqUkAYuUPZnT0AAAAt0q5gOYQ0ADE6PQIGu0IAABwp5QLaPR8A4gX7QgAAHCr1Ato9HwDiBFr0AAAgNulXkBjiiOAGHEfNAAA4HapF9CSfQIAUh73UwQAAG6VegGNCysAMWKKIwAAcLsUDGhMcQQQG2uCf0nqaQAAAISVegGNKysAcaKjBwAAuFXqBTSuqwDEKNh80NEDAADcKuUCmiPWoAGIlQ38PwENAAC4U8oFNLE9NoAYnd5mP6mnAQAAEFbKBTTWjgCIlQ3xNwAAADdJvYCW7BMAkPIcOnoAAIBLpV5A4z5oAGLECBoAAHC7lAtoDhdWAGLEGjQAAOB2KRfQuLICELPAjaqtmOIIAADcKeUCmkNAAxCj2taDdgQAALhUygU01o4AiFXtFEfaEQAA4FIpF9Ach01CAMSHeAYAANwq5QIal1YAYnV6kxDaEQAA4E4pF9CYmgQgVqdbDzYJAQAA7pR6AY2ebwAxYg0aAABwu5QLaA493wDiRD8PAABwq5QLaFxZAYiVNbV/S+ZpAAAAhJVyAY37oAGI1elNQhiJBwAA7pRyAY2ebwCxsg3+BAAAcJuUC2gs7gcQP9oRAADgTqkX0JiaBCBG7OIIAADcLgUDGhdWAGJj5d8lhHYEAAC4VcoFNHZxBBArNgkBAABul3IBzWFqEoA40YoAAAC3SrmAZrlRNYAYsQYNAAC4XQoGNC6sAMSm9kbVTJUGAAAulXIBjQsrALFiBA0AALhdygU0dl8DECsCGgAAcLvUC2hcWAGIkQ3xNwAAADdJwYDGJiEAYnN6m30CGgAAcKeUC2h0fAOIlTWBG1Un+TwAAADCSbmARs83gPjRjgAAAHdKvYDGhRWAGNTt3KGjBwAAuFXKBTSHNWgAYmDt6baDjh4AAOBWKRfQuK4CEAvr1OncYQQNAAC4VOoFNBIagBjU3QGWVgQAALhVygU0pjgCiEXdKY5ENAAA4FYpF9CYmgQgJnU3CSGgAQAAl0q5gMaFFYBY1N8kBAAAwJ1SMKABQPSs9dX9V9LOAwAAoDEpGNC4sAIQvXojaEyVBgAALpVyAY01aABiUe9G1Uk8DwAAgMakXEBzLLs4AoieFbs4AgAA90u5gAYAMXHqbhJCQAMAAO6UcgGNCysAsah/o2raEQAA4E6fWUAzxvQ2xkw3xrzY2NcafQ5xYQUgNvU2BqEZAQAALhVRQDPGzDDG7DfGrG3w9SuMMZuMMVuNMfc09hzW2u3W2q819bWmENAAxKL+fdBoRwAAgDtlRHjcLEl/lPRE8AvGGK+kP0m6VFKppCXGmNckeSX9qsHjb7XW7o/7bMX22ABiQ0ADAACpIKKAZq390BiT3+DLYyRttdZulyRjzLOSrrXW/krSlISeJQDEqX4oI6ABAAB3imcNWjdJO+v8uzTwtZCMMe2NMX+RdK4x5kfhvhbicbcZY5YaY5YaS883gBhxo2oAAJACIp3iGDdr7SFJ32rqayEe97ikxyWpRX62tdwHDUAMuFE1AABIBfGMoO2S1L3Ov/MCXwMA16nfuUNEAwAA7hRPQFsiqZ8xppcxppmkmyS9lpjTCo8pjgBiUbftoBUBAABuFek2+89I+kTSAGNMqTHma9baGknfkTRH0gZJz1tr1/37TtWPgAYgFo7jq/077QgAAHCrSHdxvDnM19+S9FZCz6jJk/lMSwNw1mAXRwAA4H7xTHH8zBlJVmwSAiB61ql7HzQAAAB3SqmAJnFhBSA29Tp32GYfAAC4VAoGNC6sAESPbfYBAEAqSLmABgCxqD89mogGAADcKeUCGmvQAMTEYQQNAAC4X+oFNK6sAMSgbucOU6UBAIBbpVRA8+/iyIUVgOhZy+g7AABwv5QKaAAQq7qdO3T0AAAAt0q5gObmCyvrOKqsOPaZleerqZLjq/nMyvssy/LVVH2mZdW9RxZiYx3nM30fo/251bsPWpRzpZPx2j4r1ZWnPrPXZh3nM21H3Fwf4+H4alRRfuQz/bmdrWVVlB/5zOqkr6ZK1ZWnPpOypM/2M7uy4thn9nOrri5TRfmRz6Qs6bN9Hx1fzWf2PvpqqlRdXfaZlCVJ5WWHP7PPts/6M/vfISPZJxCtSAPaB5/+VjM2PqU1qpTXSoUmS1/qf6MuHne3jCexufTA/nX689z/1pzyXTrhMermk65uW6ivTH5YrVp3S2hZjq9Gb3zwU/1zx1vaZGqUIel8b65uG/19FQycltCyJGnT5jf010UPaFHNUZ0wUl/r1bTO43XTJb9TRmZWQss6dXKv/j7nO3r72Cbt8kqdfFYX5uTptot+rXPOGZrQsiTpoyV/1Ix1s7RCFbKSzlWWvl7wVZ03+vaEl7V/31o9ueB/9O7xrdrtsersSFe3LdDXLv2Dclp2SmhZNdUVevH9u/X8ng9VZHzKsdLYjLb6+ujva/DAqQktS5I2b31bf/z4//Sp75iqjFRom+kL+Z/T5yb+VN6MZgktq6zsoP7xzh169fBq7fJKuY7Vpdnd9K2LHmqyjsTSuTP/099o1sZntNZWyBppiLJ0y8CbdeG478f6EsLas3uZ/jT/h/qgcq+Oeox6+KSr2hbqlksfTXgd8dVU6aX379Yzu+drq8dRtmN1fkYbfWv8verf98qEliVJ6za+rOlLfquFNUdVYaTejkdfzLtYN0x+WB5vYj+Gjh0r0az3/ltvHdukPR6rtla6OLubvnnBA+rc5dyElmUdR3M/fUgzNj2rdaZaRtJIk63/HPRlTRzz/xJaliTt27daf533A80pL9Vxj1Enn9UN7Ybqq5f/SVnZbRNaVnXlKT0/9y69svdjbTU+NbPSGG8rfXv0XSoYdH1Cy5KkFav/qb+s+L2W2jI5kgbYDF3f7SJdd9GvEv5ZU3Zyv/7+zu16+egGHfIatXGsrszpqdsuflgdOg5KaFnWcTR/0W/1xKZntVIVciQV2kzdNujLumDcfye0LEkqLv5Aj310nz6uOqhjRurmGF2RO0C3Xvpowq9Haqor9M8539Fz+xep1Cu1cKzOz2ynb477sfr1vSKhZUnS2vUv6B/L/6C5NYdVZYwGOV59scfluubCXyS8HTlyeJtmzr1L7wQ+s1tY6ZLmnfX/LnlUHTsVJLQs6zh644P/0TPFb2mDqZZH0kDbTF8bcJMuPu8HCS1LknbvXqo/zLtb71cdULnHKN8nXdthhP7jkkeUndMuoWVVV5fptfn/o6dL39Nmj6Nm1mqiN1ffPe9+9elzaULLkqTlq57QrFV/1RLfMZ30GPX2Gd3c9QLdeMlvEn49cuTwNv353e/qnbISHTFSJ0e6ICdP37jgVwn5rDHR9iQnU6v8bHvLT8bqD1+fH/YYx1ejB1+aqqfLd6iHT7qwVW851tGHJ4tV4pWuzTxH9934mjIzcxJyThs3vaZvffRjHfdIVzY7R91bdNGqo1u1UKfU3Sf9+eI/Kj//goSUdexYie6afYM+VbkGOB5Nyu2vUzXleutUsU4a6Z4uF+sLl/8+IWVJ0rP/+q4e3DtPOVa6NKur2jXP1dLj27XCVGmUba5Hr3tFrXO7J6SsnTs/0n+9+y0Ve6ULTSsNaNVDxad2a17NYTW30q8Lvqnzx3w3IWX5aqr00MvX66nyYnXzSZe06iNJeu/ENu3ySjdlddc9189O2C/zouWP679X/V5lRhrvaamBLXto88md+sCeVA+fNP3KJxJ24XjyxB597+VrtEgVGupkaFTr3jpWdULvVezWCSPd0/lC3XzFHxNSliS98t7d+t/St9XSSpfn9FCLjGzNPbZZxV5pvLL122mvqmWrLgkpq6h4vr4z97sq8UoTlKOhrXtrZ9levVN9QNlW+t25d2nU8FvCPn7nzo/1ubnflCRNqm6jP319QdhjfTVVuv/5z2l29T718EmTWvWSVx7NO7FNJV7pC1nd9aME1pGPl/xJd619TNWSLmt+jjpnd9C648X6SGXq6ZP+cPEf1Cv/woSUdexYib4/+/raOnJem4E6UnlUb5XvVLmRftT1En3+st8lpCxJ+ufb39LD+xb660h2nnKbtdaiY1u12lOt85St317/mlq07JyQsrYXzdV/zbtDuz1WF3haq1/LPO0q36/3qg+quZV+N/x7GnPu1xNSVk11hX7x0rV6sXK38n1Gk3P7q9qp1nsntmu3V/p882768Q2vJayOLFj8e/1w3eOqNNJlmR3Vu1V3rTq6RR/Yk+rjM/rzFTPUteuohJR15PA2fefVG7TaU6OhTqZGte6l8poKzSnboaNG+knXS3XjZY8kpCxJevKtb+qh/R+pgyNd3rKXmnmb6ZPj27TB49MY21y/m/ZqwsJFUfF83T73uyr1WF3szVVBbh9tOb5D79YcUisr/baJdiQa1ZWn9JMXr9JbNYfU3SdNbt1XzbzN9M6R9Sr2Sl/J6a3vT3spYeHi/Y8f1D2bnpRX0qXNO6tjVjttPrlTHzon1NMx+svl09Wt25iElHXsaLH+3+zrtdxUaayyNKrNAO0rP6A55btUbqQfdr5IN13xh4SUZR1Hz71zR+31yJU5PdS+eRvNO7JeGzw+TVCOHrru5YTVkQ2bXtV3PrpXBz3SJE9rDWjVQ/srDurNyr1qYaVHR96jc4d+KSFlOb4a/ez5K/Vy1V71dzya0LqPfI5PH54oUrHX6gtZ3fXjG15LWB1ZuPgPumvdX+VImpKdpw7N22r58a1apAr19EmPXfoXde8+ISFlHT68VXe89nmtNNUa4Hh0abuhOlJ5VK+dKlKFkR7q9yVNnnBPQsqSpMdmf1F/PrZG7RyrS7Lz1KZ5rhYd3aJVnmpNMi318A1vJiyA7tixQLe+/20d9kiXZrRXXs452lG2Rx9UH1EzSY8M+38aO+K2Jp/HGLPMWhu64bbWpsx/LXtm2e/8bZJtzAPPX20LZxXaB5+/xlZVnar9enVVuf3jyzfZwlmF9t6nJlvH52v0eSKxau2zdtyMAnvJ9AK7Zeucet9btvIfdtKMAnvR9AK7a9eSuMuqKD9qvzxzhB0+s8A+P+d79c7/2NES+1//GGcLZxXa5+bcEXdZ1lr72tx7beGsQvudf4y3R48U1fveq+//yA6fWWC/MnOEraw4HndZ+/ettZdML7Dnzyiwi5f/vd73SkoW2htmDLUjZhbY5auejLssa639+TNX2MJZhfaB56+ud/6VFcftr5+/xhbOKrT/+8zlCSlrxZqn7IiZBXbq9CG2qGh+ve8tXjHdjptRYKdMH2IPHtgUd1lVFSftVwJ15OX37q5XR44fK7Xf+cd4Wzir0L787l1xl2WttS+8c6ctnFVob5s12h45vL32676aavvCO3fa4TML7JcTVEd271pqL5peYCeFqCNFRfPt1dOH2JEzCuzqtc+HfY4dJQtt4axCWzir0P7X385vtLyfPXO5LZxVaB996UZbXVVe+/WqqlP2oeev9def56bE96ICNmx81Y6eUWCnzRhqS0o+rve9xSum20kzCuzk6QV23941cZdVXnbY/seMc+25Mwvsy+/eVa+OHDm83X77H2Nt4axC+9K734+7LGut/edb37aFswrt/3viPHv8WGnt1x2fzz4/53t22MwCe+vMkbaq4mTcZe3Zs6K2jqxc80y975WUfGynTh9iR88osGvXvxh3WY7PZ//n6cm2cFahfeTF68+oI7958bqEtiMfL33MDp9ZYG+YMdTu2LGg3vc+WvxHO35Ggb18eqE9sH993GVVlB+1N84YZkfOKLBzPvx5ve8dP1ZaW0den/eTuMuy1tpn//VdWzir0H7viQn21KkDtV93fD47+/0f1n7WJKKOlJR8bC8M1JGlK2fV+9627e/Zq6cPsSNmnll/YuH4fPb7T060hbMK7WOz/6N+Hak4aX/x7Ods4axC++vnr4m7LGutXbPueTtiZoH94ozhdv++tfW+t2TFzNo6kqjPmi/PHGHPnVlgX5t7b73vHT601d4euB5J1GfN31+7xd9u/2OcPXa0pPbrjs9nn/3Xd+3wmQX2P2eOTMhnTUnJQjthRoG9dHqBXb9xdr3vbS+aZ6dML7TjZxTYbdvfj7ssx+ez9z19aeCz5gbrq6mu/V51VXntZ83DL0yNuyxr/W1FsB0pLV1U73ufLvurPT/wWdOw/sTixPHdduqMoXbkjAL7xrz/qfdZc/DAJvvFGefaYTP930uE5+d8zxbOKrQ/fupiW3bqUO3Xg3VkyMwC+81ZY2xNdWXcZe3ZvdxeOr3ATpxRYDdsfLXe90pKFtqpgeuRTVveavK5JC21YTJP0kNXNP+16pllb//bxLAv9M35P7WFswrtr56bEjaABUPaW/Pva/KNa8yhQ1vsxdML7BXTC+2e3ctDHrNl6xw7dkaB/dLMc+OuFA8GgsPbH/ws5Perqk7Zb/9jrB0+s8CuWRf+IjUSRUXz7egZ/gavbsit6+0P7k/IRWpNdaX9z5kj7egZZzaGQUcOb7dXTS+0F08vsIcPbY2rvNfm/tgWziq0v2mkwQteXL383t1xlXX06A578fQCe+X0wnoBpq5lK/9hR83wX4DEW0ceeG5Ko3W7quqU/cas0XbEzMgajsasWvusHT6zwH5r1tiwF05vf/CzhNWRL844146bUWA3b3k75DGHDm2xlwfqyNGjO0IeU1z8YW1A+/bfJoQt79X3f2QLZxXa3744LewxTb3XkTp4YJOdPL3xD8VggLtl5sh6H+Cx+Nkzl9shMwvsuwt+GfL7VVWn7G2zRtvhMwvsug2vxFXWqrXP2mEzC+x3/jE+bN0O/j4+8PzVcZXlq6m2X5812o5upI4c2L/eXja90F4+vbDeRV4sghcDv3/582GP+e2L02zhrMK4L0D271trJ8wosFNnDLUnju8Oecza9S/a0YF2JN468psXptrCWYV23icPh/x+ZcVxe8vMkXbkjAK7des7cZW1actbdvjMAvvtf4ytF2DqCn6uN/b7GImqipP2xhnD7HkzCuy27e+FPObwoa32ikA7UrdDIRZPvf1ftnBWoZ3+2ldDft/x+WpDWrztyIH96+3F0/0BLNxn5Oq1/gB326zRcdeR/w10YL39wf0hv19Vdcp+PfBZE28dWbxiuh0ys8De/eSksOf91vz7EhJ2fTXV9iszR9jxMwrO6CwL2rVriZ00o8B+bnph2M+aSL3y3g9qO3lCXbM6Pp/9+bNX2sJZhfa9hb+Kq6w9u5fbcYGOwHB1O/hZ87VZo+IexLj7yUl22MwC+9GSP4X8/qkT++wtM0cm5Hpk5Zpn7PAmAlgkbXYk/Ncjw+24GeE/Iw8e2GQvmO5vsyvKjzb6fI0FtLNmk5Ajh7fpV9tf0jAnU3dd90LYdWbfuvofKnC8enDbizp+bGfM5/Hnd76rQx7pkQm/CDs9rW+fy/STXtdppanW8+/FPtd8w6ZX9WTZdn0hq7uumPTTkMdkZubogWtfUDtH+p9F/xfzwk9fTZV+OO8ONZP0wBV/DzsV9IpJ9+nmrB76Z3mxVqz+Z0xlSdIL731fy0ylftzjKg0acG3IY9q07aWHJ/xChz3S7+Z8K+ayDh/eql8Vv6oRtpnumPpc2OPuuPZZjbTN9VDJWzp0cHPM5T385q067JEePu/natO2V8hjRgz7iv6n5zVabqr07Lvfi7mslWue0lNlRbopq7uuvOD+kMdkZubogaufVitH+umCH8W8WLemukL3Lf6lOjrSA1OfV2bzFiGPu2LST3VzVg89VVakVWufjaksSXr23Tu02lOt/+l9fdh1De3a9dVvzvuZDnmkX7/51ZDH1N1mP9zE7oMHNuiBHa9phG2m/3ftM2HP6fvXvaBhTqZ+vv1FHTm8LeLX0tCv59ymwx7pDxN+EXZdw8AB1+hH3a/UUlOpV+b+MOayFi1/XC9U7tItrfrrkvN/FPKYzMwc/fra59XGke7/5P746siiX6iDI/1y6gthp/ldfdEvdFNWd/2zrEgr1z4dU1mS9Ny739OnKtddXSeHrSMdOg7Sr8fcq70eq0ff/kbMZe3bt1oP7XpX45Wt2695Kuxx373mKQ11MvVg0cs6eqQo5vIeeOdbqpD024seDTtduGDQ9bq35xQtN1V6Lo52ZPmqJzTr5Bbd2Lxb2HWWzZq30kNXPakWkn764Q9i3kChurpMP1nwI7W20v9N+WfYdWafu+Bnur5ZF806sUkbNr0aU1mSNHPOt7TB49PPB3xFvXtNDnlM23Z99PD4+3XQI/0+jjpy5PA2/XHPBxqvbH31qr+HPMZ4PPrBtJc03PrbkXjqyK/nfEtHPdKjEx9Q23Z9Qh4zpOBG/aDLxfpY5Xp1Xujf/0h88Olv9XzlLt3asr+umHRfyGMyM3P0wFX/VI6V7l/ww5jrSGXFMf10+SPKc4zub2Qq6JUX3K/PN++mJ09t07oNL8VUliQ9/c53tNxU6Yc9p6h79/Ehj+nadZR+N/Ie7fJYPfp201PYwtm/b61+XfKm/7Nm6rMhr1mNx6MfTn1Bgxyvfr7pnzp2rCTm8v733W/LJ+l3l/wl7FTQgQOu0V3dLtEiVej1+T+Juaxlq/6ht32H9c02Q3XeqP8KeUxOy056eMrTamml+xf8OOY6Erwe6eQYPXjtc2E/a2687BFdk9lJ04+t0/qNs2MqSwpej9ToJ72mhV3T375Df/1f4Te11ePo969/JeayUi6ghfPX976n40a6f9IDjS4o9mY000/H368jHukP//pmTGUVFc/XixU7dUN2Dw0ccE2jx1416Wcap2z9Yc98nTi+K6by/rDoV2rtWN1x5d8aPa51bnf9eMCXtNXj6PUPQge5prw2/16t9/h0b+8b1Lnz8EaP/d7V/1Ann9Wvl/0mpt1yTp7Yoz/umaexytK1F/2q0WMHDrhG/9Gir16p3KNNW96MuizJH6rLjXTfBb9udF2IN6OZfnrBgyoz0l/fvzOmstZvnK1Xq/bqyy37Nbkxx9UX/p/GKVt/3vuhjh0tjros6zh6aOnD6uRId141q9Fj27Xrq7t7T9M6j0+vzb836rIk6eV592irx9EPB35Zubk9Gj32jqumq6MjPbTk1zHVkePHduqxvQs0Ttm6cmLoi4GggoHT9JVW/fV61b6QdSSSTUIee/9OlRvp/gsbX1CckZmln03y15E/vxvb2siVa57SWzWH9LXcIWE7J4KmXvygRthmerR0jspO7o+6LMdXo4dX/UldfdLtV81s9NjcNvn6QZ8btMHj09sLfx51WZL09sL/01av1Q/7f7HJdSF3Xv2EOvqsHlryUEx15OiRIv1+z3ydp2zdeGnj66KGFd6km3N66YWK0pjbkUff+558Rvrp5N83ui4kIzNLPz3/5zpmpOnvx9ZBt2nLm3rHd1S3tClscg3iNRf+UmNsc/05xs8a6zh6ePkj6uxId015otFjO3QcpLvyr9VqT03M7ciz796pDR6fftLvi2rXrm+jx975ub+rjZUe/iS2+njwwAb9/dAKTfa0bnLThYJB1+vG7B56obxERcXzYyrvT+98R2VG+uH5v2h0U7KMzCzdN/EBlRnpL+/GtqnM8lVP6G3fYX29zVAN6HdVo8feeMlvNcI20yM7346pHamprtDD62cp32f0nWuebPTY9h366797fE4rTbXe/bjxz/dwnpt7t0q90v8Mu105OR0aPfbOq2aqrZV+s+hXMbUjx46V6I97F2qiaaFrLvxlo8eeO/RLujmnl16sKNWWrf+KuixJevDdb6ta0v9e9LtG25HM5i10//j7ddgjTX/3jpjK+mTZX7TAntJ/dRwXNngG3TD5YRU6GXq0+LWYdsp0fDV6ePnv1Mlndctlja93b9+hv+7Kv1ZrPDV6a8HPoi5LkmbP/7G2ea3u7v9F5bbJb/TYH141S20c6eFP/y+msvbuWaFH9y7QBOXoc5Pub/TY88d8V9c366KnT23Tzp0fxVReygW0UBdZ+/at1nNlRbqueVf17XNZk88xeOBUXZ+VpxfLS7R378qoz+HRBfcqy0rfnvy7Jo81Ho/uHPtjnfAYPT0v+sWQK9c8pQX2lG7tMDqiBbAXj/+BhjgZerxkjmqqK6Iqq7q6TI+VvK0hToaumNh0wMvJ6aDv9Pyc1npqtGDJo1GVJUlPz/uBjnmM7hxzT0Q7a37jst+rhZX++mn0jf3evSv1csVOXZeVF7b3tK7evSZravOueqF8R0x15C+LH1JrK32jiQZK8teRu8b/VMc9Rs9+8D9Rl7VgyR+02lOjb3e/PKLd/j436X4VOF49XvKvmOrI30vf01AnQxePu7vJ41u07Kzbul2sVZ5qfbL8L1GVJUnPfvBjHfMY/fe4eyOqI1+75HdqGaaO1B9BO7Md2bVrsV6qKNX12T0i2pCjT59LdV1WN71UXqL9+9Y2eXxDf17+qNo5Vl+9vOmF9Mbj0X+PultHPEZPz4t+V68PlzyqjR5Ht+dfreZZuU0ef/n5P9EAx6O/bJ8ddc+mr6ZKjxe9pv6OR5PHN32uOTkd9F/dL9NqT40+XfF4VGVJ0j/m3q1TRrprwv9GVEe+dfmfYm5Hdu78SG9W79fNLfoqL29ck8cP6HeVpjTrpGdObNHBgxujLu9vix5UC8fqyxc90OSxxuPRf4/7sY56jF6IoR1ZtOJvWuOp0de7TY6oHZlywc812PHqbzveirodqSg/oul7P9JYZenS83/c5PG5uT309XMmaLGp1JKVM6IqS5KeW/i/qjDS9yY2fuEd9O3Jv1MzK/31o+gvGnfu/EQvVOzU57N7RrRLXd8+l+na5l304qkiHT68Nery/rDi9+oQwcWwJHm8Gfr+6B/E3I688/GvVOy1+t6AL0a00do1F/yffwObLS9E3Y5UVhzT9H0fa5yyNX5k0zNnWrbqots6T9QSU6kVa6Kf1fPs/Ht1ymN0x7ifRNSOfPPS3yvbSn/9NLI6VdeWrf/SO76j+s82herZc2KTxw8eOFVTMjvpqZNbdPDAhqjL+8uav6mLz+qLTXRgSf468t/Dv6P9XqNXYmhH3vv4Aa311Oj/5U+JaEOOKRf8XH18Rk8WvR51sC47uV9/3PmORthmmnxe07NLWud21ze6TNISU6klK6ZHVZYkTf/wXlUb6SeTH42ojtw++RFlWukvC2IbMEnBgHam5z76uRxJX5/4vxE/z9cm/q+spH8uuD+q8ktKFup957i+3GaI2nfoH9FjBg+cqommhZ4+vEJVlSeiKu/Pyx9Ve5/VzZMfiuh44/HoawNu0i6vNPfTh6Mq652PHtAer9Ftg74U8a0Ipky6X118VtM3RNcgVlee0jMHV2iCciLesjk3t4duzh2sd51j2rnzk6jKe3rhz+TI/3OP1NfO/5l8kl74JLoLueLiDzTfOaab2hRGvKvUgP5TdL5a6JlD0deRJzb+U+f4rK65MLLeZePx6BsDblapV3rvk19HVdZ7H/9ae7xG34iijlx34S/UwWf1z/WN98o3VFlxTE8dWqHz1aLJEaag3Nwe+nzrgXrfd1SlpZ82+G7jI2j//Pj/ZCR9/YLIP3BvnXC/HEn/XBhdA7x12zv6ROX6codRTfYMBw0rvEkTlKOnDyyNegrzrI3PqIvP6sqJkU1b8Xgz9LXe12mHV1qwJLqdYd/56Jcq9lrd1veGiHceu2bSz9TBZ/WPtY2P7jVUXnZYzx/fqEu8bSLe1jueduSJj38hr6T/vOAXET/mG+fdp0qP0QsLI297JGl70ft6p+awvpg7qMme4aCCgdM0Vll6+sDiqOvI39b8TZ18VtdeENl5Go9H3+j3BZV4pfmLotvR8c2F/6dDXqNvDo18yvqNFz2gdo7VE6tDTxkMp7q6TC8eWaPzPS0j3lG5fYf+ur5FL82pPqB9+1ZHVd6Lix+WkfS1CyP/3PjPcT9SpcfouQ+ja0fWbXxZS02lvtr5vIh3pxta8AWdp2w9E2U7Yh1HM7fPVm+f0UXj7oroMd6MZvp672u13WujbkfeWvh/Ouwx+vqQyHddnXbBL9TGsZq5KrrOwPKyw3rq8ApNMi01oP+UiB7Tpm0v3dR6gN6pOay9e1ZEVd4/Fj+sbMfqS1HUkW+e/zNVGaMXPopuFHndxpe13FTpP845T82at4roMaOGfVVDnUw9sfuDqKe5P7tttvJ80tUXRDZKZTwe3dztQq33+LRqfXRLIWYv/JkOeY3uHPX9iK9HbrjoV2rnWD25JrqOnqNHivRKWYmubt45os45SerYqUDXtcjXW1X7YuroT8GAVv8iq7rylF48tkEXenMjftMkqVu3MZqc0Vavntwa1c2lX1zyW3mt1Y3nRTet4z8GfUmHPUZzPn4w4sfs3PmRPlG5bm5/bsQXcZJ04Zg7lefz/6JE4/niN5XvkyaNjnwYPTMzRzd3Gqvlpkrbi+ZG/Lh3P/21DnqNvjQouq1qvzDhJ/Jaq5cW/ybix1RVntDsE1t0kbdNVFsMd+8+XhM9rfTSkXVRfZC9tPR38kq6aeL9ET9Gkr40+Es65DWavzjy0cjtRe9rkSp0U8dRUd064sIxd6qrT3qx6PWozvHFojfULco60qx5K93YdogWOiejGup/f9Fvddhj9OWC6OZw33z+T2UkvdygjtTtnXMa3F6kvOywXjm5XZdldmhyam9d3buP1wXeXL16fHNUdeSFZb9XprWaNiG6ef5fHHiTDniN3v8k8s6XouL5WmYq9YWOo6OqI5ec9wN18lk9syn8es1Qntr+mvJ9RpeeF/k6l2Ad+die0p7dyyJ+3Fsf/ULHPUZfGhrdWpDPn/djeaJsR8rLDuvNshJdltkxqvsg5edfoImmhZ47vDqqOvL8kt8pQ9KXL2x69Kyum/vdoH1eo4+WPRbxY9ZtfFmLTaX+s/N5EY2wBl049k518lm9sv21iB9jHUfPlb6vvo5Ho4aFXi8aSlZ2W93QpkAfOMejakfmfvobHfQa3TTgCxE/RpK+OP7H8kl6KYrpedWVpzT7+CZN8uRGde/O3r0u1nnK1iuHV0d1Qfzcij8r27G67vzGp383dFP/z2u/1+iDRZF/1mzY/Jo2ehzd3PWCqLZ8v3zCj9Q5hnbk+Z3vqZ/j0ZjhkQe07Jx2uqH1QH3oHI9qVsPsD3+qIx6jrw+P7h6oN469W9YYzY6iHTl+bKfmVO7VVdndwq5ND6Vnz4maaFro+cOroxqxfmnl48pyrKY1sUSgLuPx6Mt9pqrUK32y/K8RP664+AMtMZW6vuPIqOrI1RN+opaO1dMrIy/LOo5e2L1AhU6Ghhd+MeLHNc/K1fW5g/WBcyyqz5q3F/1GlR6jL46Ibiryl8/7iXySXvk0us5wKSUDWn0Llz+mIx6j6/vfEPVzXT/wZh31GM1b/LuIjnd8NXrz2GZN9LRWp3MKoypr/IhvKc8nvV7yTsSPeWXJo/JYq6kRTCWry5vRTNe0G6olpjLinp2dOz/RclOla6P8xZKkq8feJa+1enX5nyJ+zOvFc9TFZ3XeyG9HVdY55wzVJE+uXj22MeIPsg+W/EFHPEY3DLwpqrIk6fq+1+mQ1+iT5Y2v/wuqqa7QG8e36HxPa3XoMDCqssade5s6+axeLYp8bczryx+T11pNHR/d9FlvRjNd32G4FqkixEhTaLt2LdZiU6lpHYZHXUemjfdPP3hjWeR15OXit9TN539fonHOOUM1zrTQG0c31JtWU79zp35LMm/JozrlMbp+cPT3trmu3zQd9hgtXPrniI6vri7TW6eKNTmjXZNrbxqaMPJ2dfZZvV78dsSPeWXZ75Vhra4dF92UpszMHF3bZpA+sad0YP+6iB5TVDxfqzzVur7TmKjryDWj75A1Rq8t+V3Ej3l91wfq7TM6d0h0P7fOnYdrkqe1Xj+2MeKpV+8vfkQnPEbXF3w5qrIk6Ya+03TIa/TpishGf6orT+nNU0W6OKNd2E0fwpk0+rtq51i9tuWViB/z+uqZamatpk6IbkpTRmaWrm0zSAudExFPvdq6/R1t8Ph0Q+cJEfd6B9047h5ZY/Tm8sjD53PbXlU3n/93Jxrdu4/XWJOjV4+sjbyOLPqNDnuMbhwYXRiUpOt6TdEer9GiFZF91lSUH9Gcir26Iqtz1Pf/mjT6/6mjz+rNKD5rXl39dzWzVleOj+56JDMzR9e0LYiqHdm67R2t9dTounPGRV1Hrh35XTnG6PUoQtNrez7SIMcb9b3N8vLGaayy9NqhVRFPz/vXot+owmN0w/Do90CY1vtaHfQaLVoZWTtSWXFM/yov1SXNOkZdRy4ee6faOFYvb3o+4se8tPR3yrBWU8dFt5lVTstOmtqil96tORTxplvrN72irV6rG/IujqosSZo25r/lGKN/LY/sM1uSXt/zkfo7nib3nWgoL2+cxphsvXZ4TdRTOFMqoBlJDS+s3tj2qto5VuNHRF/Zx517mzr4rN7Z8V5Ex69Y+5T2e42u7Bn93c893gxdkTtAi21ZRBXQOo7+dXSDxpqcqHrigq4a4Q8+by+L7KbEc1b4pwRMGRX9ItQOHQdpnGmhd45tjqgCHj1SpE/tSV2R2z+mmy9e1esKHfQaLVsT2ZS5d4r/pXaOjfpCX5ImjrxduY7VG1tejuj4pav/oYNeo2t6RzZNoi5vRjNNyR2gj5wTEW0WYh1Hbx3bpHGmRdRhUJKuPNc/vej9VZEN9b+z4q+Bx4XelakxnTsP10hl6e3DayOqIwcPbtRiW65r2hbGVEeu7nm59nhNvZ0BG9vF8a0d76izz2rU0FuiLuv8kbertWP1XtFbER2/ZOVMHfUYXdG78QX9oXgzmumK1v30sXMioh29rOPonWNbNN7TUh06Doq6vCnnfluOMXorwjWmb674izzW6qox0W+uk5c3TiNsM71zOLIpZXv3rtRyVejK9kOjvoiTpCt6XKL9XqPV6yPr2X+nZK46+axGDol+V65o25FPVj6uox6ja/pdF3VZmZk5urJFL833HdWpk3ubPL6mukJvnyrSBd42ap3bPeryrhz6NTnGaG6Ea0zfW/uEjLW6fFT0m+t07nKuRthmevvQ6ojakf371mqJqdTU9sNiumH41J5XaLfX/9kfiVeK3lBXn3TeiOh3G7547J1q4Vi9szWynSoXLHtMZR6jz/W/MeqyvBnNdEmLnlpQczSizUIcX43ePVmsSd42TW4MFcrV5/5XdO3IysfltVafGxN6J9HG5OdfoKFOpuYcjLRz+iOt9dToyo4joy5Lkq7sOkk7vdLGLZHNRnl/z8fq6ZMG958adVkTR/2XWjlWb26OrB1ZuPwvOuExunpA9HWkWfNWuqpFL833HYmoHamuLtNrJ7boQm+bmD5rrh76NdUYo/kRtiNz1v1TGdbqktHRtyN5eeNU6GRozoHIRtB2716qNZ4afa7DiKjLkqRrul+qUq+0en3kYVdKsYAmSXVnJlVXntLC6iO6OLtbVFN3gjzeDF2ck6eFNUci2q3m3U0vqrljdUGUoz5BlxV+WT5jNC+C3r9NW97QTq90WdfzYyqrR4/zNcjxat7BlREdP//QGhU6GWFvGdCUi7uMV6nX3zvaZFnL/6IaY3R5QfSjFZI0aeTtynas/rXpxSaPraw4pg+rD+vi7G4xfUBnNm+hS7K66sPqQxFNT5q79TVlOVbnx/ABLUkXD7hRPmO0MIKF8Ju2vKHdXunyvMjWVTTUvfsE9XM8mhthI/XugeUqcLxN7gIVzpVdJqjIa7W96P0mj523/K+yxmhyYWx15IKR31aGtZpXZxQh3Ahaedlhfeo7oUta9oopDGZkZumCZp00v3J/RFNP3t32mlrEUUeuKPiS/4NsWdO9f+s3z9Yur3Rpt0kxldW718Xq73g0/8DyiI6ff3SDhqt5VFMA67q440ht9jgRrQ2bv3K6rDG6bOitMZV1wchvK9NavbOx6Q/NspP79bHvmC5pmR9THcls3kIXZ3XWgqqDEbUj721/Uy0dq/HDY9vGe3K/qao2Rh9H0I6s2fCiDnuMLuvZ9AZbofTtfZnyfdI7ez+O6Ph3j6zTCGXFdBEnSVd0Hq/tXqvikg+bPHbeSv+mM5cW/mdMZQXbkflbZjd57Inju7TYluny3H4xfdY0a95KkzLba17F7ohmh7xbPEftHKtRQ2N7bZcOuF6VHqOFEWzMs3r9czrgNbqke/SjFZI/NPVzPPogwnbk/WObNcpkR7zOv6FLO47QBo8votkh76/yr3u9fERs13UXj/wvea3VO2sb39VS8u8UudiWaXJu/5g6lZpn5eqi5p20oGp/RHVkbvE7au1YjR52S9RlSdLk/tdF3I4sX/NPHfYYTelzdUxlDep/jbr5pHd2LWjyWOs4evf4Vo01LSJen9vQpR3O1TqPL6JZZvNW+TcUuSTmz5pvyWutPtgc3S0gUi6g1b2wWrr2SZV5jC7Ij+2DRZIu7jNF5R6jxaubHo1ZeLJYoz0t1aJl55jKGtjvanXyWS3cs6jJY+dteE7GWl08MvrRiqAL2gzSKlU2OWJ36OBmrTZVmtR2cMxlXTTcf8+YD9aHv3dU0Ie7P1Inn42pB0nyzzMfn5Grj8p2NdmLunSNv45cHMNoRdDEnpN1ymO0cm3jr806juae2qHzMnIjXrDd0JBBN6idY/VB6QdNHrtwk/+XfeLQyNdxNHRRm4FaqcomR2MOHdysNZ4aXdRuSMxlTQqMTi2M4IJ4/t5PleeT+ve5MqayWrbqojEmR/OPn94VLdwI2uLVs1TpMZrYK7JNJkK5qOclOu4xWrmu8UXO1nG0sGyXxme0iWqtT12D+l+r9j6rj3ZHEGI2vCCPtbooxosPSbogt79WqKLJOrJ791Jt8ji6qENsnTySdHGgLs9fM6vJYz/av0x5PqlXzwtjKqtlqy4abXL08Ymm7z+1aM0TqvQYXdw3uuktdU3qPlknPEar1jVe/301VZpXsVeTmnUIe4/Bppxb+B/KdazmRTA75MMts+W1VudFsR6sLuPx6KLcflpmy5scjdm3b7W2eBxd2GF4TGVJ0vkF/yFJ+mTjC00eO2/vIvX0KaKde0MJ1pH5x5ue9fLRyumqMUYX9ZsWU1mSdHGPyTrsMVqzofHX5vhq9En1IZ3fvFOjtxVqzLkFX1Qrx+qjCD5r5m1+WRnWalIMM5WCJrXupxWqaPIWEEXF81Xktbr4nMjXizc0edjXJEnzVje96dCCgyvVz/Goa9dRMZXVtl0fnassLTy+pcljP139D38d6R97HZnQbaKOeozWN3FPQF9NlT6o3KcLmnWKaQBD8teRSNuRD7a9qWbWanyM1yPG49HFrXprsT2p8rLDjR5bsvMjlXqlC+OoI5MG+5e8LIwgWM/bv1R9fSaiHTdDyc3toXOVpfnHoruvbsoFtLq94B9t/5eaWasxMfYgSdLIwv9QM2u1qKTxDS527vxIO7zS+Z1iG+KU/BXw/Owu+rTmSJM97YuPbtJAmxH1GpW6Lhx4gxxj9NHqWY0et2jdU7LGaGKMgUny71bT3/Fo8ZHG1yFUV57SxzVHNTG7a0w9SEHjO47Qbq+0s7TxXtuPit9VM2s1KsaRGEkaN/Q/lWGtFmxvfL5+0Y752uc1mth5bMxlebwZOr95J31afajJdQ8LDq/VIMcbc0+0JJ3X+3NyjNGSNY1P4fkk0IidH0cd6dzlXPV1PFrQxKhudXWZlvhOaEKL7nHVkUmdRqnYq9OjMTb0CNrCHe8p27EaNTT2G0qOHfJleazVp0WN3xNne9H72us1Ou+c0TGX5fFm6LwI68jHRzep0GZGtRi9oUn9r5PPGH2yalbjZa3zTyedVHBzzGV17z5e+T5p0cHGpzlWVZ7QIt/xuOvI+PZDtc1rm9xQ4JOSecp2rM6N47WNG3aLvx3Z1vhUqI1b39BRj9HEbrFdDEj+Ud3zMtvrk8r9TXZiLTi+RecqK6bpjUHj8y9TjTFauq7xTqyP1/p3+z1vYGQ794bSvft4dfdJH+9vfDSmqvKEljmndH7L/DjbkREq9lrt3r200eMWlH6gXMdq6ODPx1zW+KFfkbFWn2xrfLr0hi2v6ajHaFyX82IuKyMzS+My2uij8j1N1pFFx7dpqJpHvY6prol9r1aNMVq8pvEL4o83+KccXzAk9uu67t3Hq2cE7cjJE3u0XBWa1LpfzGVJ0nntBmujx2nyVhqf7lqolo5VYRz1f/wQfx1Z2MSo7vpNr+qYx2hiXmyzJ6TT7cinkbQjJ4o02rSI6BYd4UzIv1RVxmj5uqcbPe7TQOfM+EGx/6716XWJOvusPtq7uNHjKsqPaIUt14RWvWMuS5ImdRimLR4n4nWYUkoGtNOWnizWUGVFtcNhQ1nZbTVcWVp0srjR4z4JzB2dMCj6xb91nZc3SSc8Rms3hZ9DXF52WKtUobGtYr+okvwjdq0cq2VNVMBlexaphWM1qH9kW5mHM6pFd610ylRdeSrsMeu3vK5THqMJ3S+Mq6zgL+YnGxrvjf7kRJFGmJyYR7Qk/728hqq5lh5vvKd96WZ/j9aYAbH3jknS6HNG64jHaGvRu2GPqSg/otWq1LjW8TUaQwffqBzH6tPSxqcLfbL7I7VNQB05r2W+VtjyRm8lsHbDyyr3GI2L4wJVksYGwuTSzf5pjuFG0JaV7dJwT07EWxCH0jq3uwpsphY10UP2SWCKw4TC/4i5LEka33W8jniMNm8NfyF34vgurTVVGtcmtmlCQYUDpinbsVq2p/HpQsv2r1B7n1WvnhfFVd6YnG5a6jvRaCfW2o2vqNxjNL57bNN7g8b184+IfdrEBcEnp0o0ytsyrjrSslUXFaqZljXRjiwJ/EzHDo5+U6O6xp4zSge9RkU75oU95vixndpsfBrbNvo1rHWdO/gLEXV0frJnkTr4rPr1vjyu8sYF6khj07xWrX9eFR6jcT0ujKus0X3864mXbZrd6HHLKvZrVEZuTNMbg3Lb5KvAZurTo41f6C/a8oYkaXyc7ch5ncdoXxN15NjRYq03NRrXZkBcZQ0ZOE3NrNXyJkb+lxxcrW4+RbXjcihjcrppWRPtyIoNL6jGGI3vFfssLEk6r5//c3HR2ibakbLdGu3NjXnUU/KP2A2wXi1r4rNmUaBDeUxB5DschjK60wgd8BrtKAk/9fDgwY0q9lqNax/7DBtJGlHwRWVaq4+Lw1/7SNKn+5eri8+qR/cJMZdlPB6dl91Fi2qONtrRuWrDC6oyRmN6xPe5NjJQx5Y3cu3fUAoGNP+l1amTe7XB1GhkbuwjTEFj2w3SJo/T6MYMKw6uVgefVc8e8V00jghcvK8umR/2mDWbXlZ1AiqEN6OZRnhbaWnZnkaPW1a2W8M9LeL6YJGk0V0nqNxjtG7z7LDHrAp8gA+P80K/R/cJ6uizWnlwTdhjjh0t1lav1di2sY8wBY1s3VsbTLXKyg6GPWbJgRXq5LPqnhd7r6YkjRnkX9C7ZEv4ravXbHxZNcZoZLfY1igGZWbmaISnpZaWNT7tZHnFAY3MaBPT+pu6hncZqypjtLGRYLG4aI6MtRpVEN8Fap9el6itY7V0n7/n29GZAe3YsRJtNT6NiDPESNLY1n20RlWN1pGVh9ari8/GPJ0m6Nx+/nn+q4vDr+dbvv45OcZoXBxTwCV/L+owT46WN1JHrONoaeUBjWzWNq7RCkka022CTnmM1jVyQbyixH9BeW4cPdGS1L/v59TKsVqxP/w6zIMHNqjYK42N8+JDks5t2VPrTVWjt3ZZcnid8n0m5nV8QWMG+j9rFjfyPq7a9IqsMTq3e+y97JK/o3OYsrTk5I5Gj1tZdUijmrWLu46ce84onWqiE+vT4nfktVaj4rxA7dv7siY7OvfuXaldXmlk++h2dw5lXOs+Wq3KRqd5rTyyST19imv2hCSN6OsPn6u2hR/5X7b+eVljNKZXfKG6WfNWKlRzrTgZfqq046vRsppjGpV1TlxlSdKYruN10mO0YXP4EetVuz6Wx1oNiWNmiOTvDG/hWC2PoI6M6ZiAdiQnT6ud8kbD5+LD69XP8cS8ji9odOC9WdLIdd2Kjf7QcW7+JXGVlZ3TTsOVpaWNtCPWcbSi+qhGNu8YdzsyvNO5OuExKi4JP813UfF78lqrkQXxDc4M6n+1sh2r5REscQpKrYBWp9t75YYX5RijkXH2jknSkG7+FL6+kUZqZeVBDc9sE3eF6NipQF190urD4XvI1pT67/EytH/s6x2CRrYbrGKvDTv0fvRIkbZ5rUa2ja93TDp9sbSqkfC58tAGdfUp7osP4/FoSGau1lSGvxheE2iYh3aPL1RL0oi8SaoxRqs3hF/kuaLqsEY2ax93HenadZS6+qTlh8JPu1oeeI+HD4r+9hINDc3tre0eJ+xOTYcOblapVxoWZy+7JA0LjFis3BE+WKw5tlW9HU9c0/Ikfx0ZmdFGyyoOSJJsiCmOKze8KGuMRvaMbfF7XcO6jZfPGG3cEj58rqw6rOHN2sddVreuY9TOsVrVSB1Zs2exvNaqIMKbfDdmZJv+2mJ8On5sZ8jv7927Qnu9RiM7RL/j7BllDfTX6dUl4Xv1Vx7ZpHyfiWsKuOSfLjrEk6M15eF3KVsd2J1tWAI+a4Z3Ha9qY7Q+zEWjdRyt9J3QyOzY1jnXlddtvDr5rJY3Ms1rRelCea3VkIHxjfpL0rBW+dpiasIGi/371mqP12hY+9jXOgcN7+tfU7yqkU2pVh8vUn+boZatusRVljejmc71ttKyRurI8k3+UfoRcY4MStLQruNU00gnlnUcrfId07Cs2KeSBeX3mKRWjtWqA6vCHrN6z2JlWKuCBFyPnNuqlzaY6rB1pLjkAx31GI08J/alJLVlDfDvgNpYO7Lq+Hb1t964puVJ/joyxJOjVeXhO8PXBH6ew3rEth6yrnM7j1a5x2hTmKmwjq9Gq5wyjcyJfUpqUM8eE9XOsVrZSDuyfPcnynKsBveLbYOQuoa06qnNpiZsJ9au3Yt1yGs0LAGdIcP7fE6StHJb+NvWrD7hb0di3XsiKDMzR0M92VpxqjTix6RUQDM6PYK2LpBChw6YGvfzDu7j3xxg/e7QyfbggQ0q9UrD28X/wSJJQ5u11Zqq8LtGrju6VXk+xbw7Tb2yAj2j67fNCfn99YFGY2hefCMxktS+Q3918VmtPbIp7DGrq49oWLPYpxvWNaRNP+3w+kNmKGt2fypjrQb3jX2DkKBhgQuYVaULQ37/0MHN2uc1Kmgb/0iMJBVk5mpj1dGw3191bIv6+ExMWx6fUVaXsbLG1NaFM8oK9Jwl4gK10zmF6uKzWnU49FpF6zhaV3NCBVkd4y5Lkgrb9NMur380VSGmOK7ds0Qea1UYZw+qJBUGGvu1u0LXkb17Vmif12hY+/g6JyR/+Bzqba01gfAZytrjReprvXFNAQ8a2u08WWO0IcwH2frASEZhnCMxkn9UoJPPat2R0FN4/CHmuIYn4AJVkoa27qMtxhd2g4vgBerAvp+Lu6zhgXZk9c7QPba7di/WcY/R4ASEGOPxqCAjVxsb+axZc6JY/W1GYupIIFhsCEy/aygYdIfGOTNEkvK6jVV7n9WKMBeN1nG0zilTQXb8IzGSVNi6l3Z4nLCj4+v3r1Iza9W/T+wbDdWWFdgYaW1p6Cllpbs+0WGP0fAEdIZ4vBka6mmhVRX7wh6z5kSxBtgMZWW3jbu8oV3GqMYYbdoeujN8/Y75kqTCBHSYdepYqA4+q/VHQndOO74arXHKNCy7a9xlSdKw1r21xfjCdnSu2btEmdZqQN/468i5gRlIq8LMoCgu+VBlHqOCDvGP1hmPR4M8LbSxsc7wU7s02DSPeVOjuoZ2Hu2vI2EGTFYHPoOG9YpvtE7yd1DkOlYr9q8M+X1fTZXWOuUamh1fJ09QQcse2mJqGl0GVFdKBTTp9IXVxmPF6u5T3KlW8gehbj5/MAplfaAxGZKAECNJhW0HardXOnw4THnVR1XYLP7GUJL6Byrx5n2hF1Sv37tEkjQwAR8sklSY2UbrwlwQHDm8Tfu8RoPbxLcgNygYKteGuSBYe3y7ejueuHtQJalV627K80mbTxSH/P6G7f4APKhr7BuE1DUot7dKvAq749WmmpMa3Dz+iypJKuznD7BrAyO3Da0JXKAO7h9/75gkFWS20aYw4XPf/tU66DUqaBf/aJ0kDezsv7fNpqL35NQbQfPbeGKH8h1PXGsUgzp0HKRzfFZrD4fuoFgXqCOJuECVpMLcPiry2pAXBNZxtMY5pcIETBWSpAGBqSub9obeKGHD/pXyWqv+veObThlUkJGrdWEuCPbuXaGjHqPCBIQYSRrSdZwcY7Rua5hgcaJYA21mQi5Q27Xrq04+q83HQu8KuC4QdAt6xB90JWlQ63wVhxkdt46jTU6ZBiWoM2RIP/90udU7Q69nXb3Pf4GaiKDrD5+ttLEq9EhMyc6PdMJjVJiAXnZJGtBpuKwx2rI99G52m8p2q6/NiHm3vLo6dipQp0Y6OtcV+c+hMMbdSxsa2rq3thlfyPDpq6nSWluhITmJCTGD8v2jR5t2hV7PuuHAajV3bMw7s9YVrCPrKkK3I6W7PtUpj9HgDvF3mEnSsG7nyTFG67eE3kxs1ckSDbKZca1jDTrnnGFq41htPhJ658h1xf6lJAVxrgcOGtSyu7YbX8i1446vRptVpYE5iQkxhYH2YU2YmVhr9q9QlhP/OlYpUEc8OdpYGbqjs3jHBzrlMRrSaVjcZUnSoI5DVWOMtjWyNKGulAtoQZurj2pAZmzbVIcyOLONNlQfDV3Wfv/wf78Yt+ptqH9n//D9luIzF1QfO1qsXV4lLMS0at1N3XzSpjAL09cf3eYfrUvASIwkDW7TVzuDIxYNbAp8sARff7wGBMLn1v2hp2dsrjmhgc3jn05WW15ma22uCj3sviEYdBPQaEjSoM7+Xf42huhFOnx4q/Z7jQa0iX/9peS/aOzss9oQpoNi66ndync8MW8L31C/lt1V4rEhp7kEQ8zgvNgX/9Y1MLAwd8PuxfWmOAZH4jfWHNfA5okZ0ZWkwsxcrQ9z0bj5wGoZa9U3Ue1I4ENj244zR2N271mq4x6jggSM1kn+0fGOPqtNYerIxhM71MvxJCTESFJhm94qDtNBsTmwXqB/l/g2EQgaGLho3LL3zHVo1nG0yVZoYHZiRuskqZ+3hTZXHgr5vXX7VyjDWvXrdWlCyiroMkrWGG3aduZUwAMH1uuIx6h/gj5rOnQYqHN8VpvChM/NJ3ept/Um5AJVkvq16KZi4wvZG72uOBhiEnOBOjDfP6KzadeZG1wEg+7ABAVdyd9Bsb4yTDtycJ281qpPfvyjTJLUv+NQWWO0vfjMqYAlpR+rzGNU2DH+0TpJ6tz5XLV2rDaGCZ8bTu1Sf2XGtYlGXQWtw0/f37LTP9Ohf4I6VQcERv22hOgMt46jzbZSgxIUYozHo/4mS5vDzKBYf2CVshIUdCVpYKdhqjFGW0Pcw7R016cq9xj1T8AyGUk655yhaudYbToaOnxuKdujvgmsIwNadNM24wt5f8o1gXZkSILa4wE9/JtabQgzE6uhlAtoVlZlJ/erxGM1oHV+wp63X6vu2uWxIW9YvfX4DnX22bi2mK1XVuCXJtQv8vYS/w+uT4IaRMkfLMKNWGyoPqpBmW0SVtagzv7ND7YUzz/je5sCF0AD4lxIGpTbJl8dfFbbjhef8b2TJ/Zor9eob6vEBE9J6t+yh0o8TshgsfF4kfJ8imur6roGBYLexj1nLjoOBt0BgdGhROjjbaGiMB0UW2tOqE+zNgkrq1/HIf4LghA7h20/6N+Ctn+C6kj7Dv3VyWe18egWOXWmOEr+qbF7vUYDc/skpCxJ6tuyu3Z6bMj585tPlKinYxIyWidJfQMhduueJWd8b3ugh7rPObHfk6yh/t4W2hQmWGxIdGdIJ/95bwuxeHvTfv+NRfv3Tkwd6dhxsFo5VtuOnhksDh7coOMeo7658e2WWlf/luEvCDaf3KU+CQwxA/P9FxYbQyxM37TD30E4IEFBV5L6eltoW5gZFFt8p9QvQdPbJal/hwLVGKPtIXratx7aIK+16p2ggNal8wi1cqw2hJgul+igK0l9W3bVTo8TMnxuOVmqno4nYXWkf2Djsy27z/ysCbYjfbvEfluQuozHo4EmS5vKz5xObB1HG22FBiZoWqok9e/kD5/FO8+cHRLsMOuTn5gOs8bakX37Vumkx6hfgjpVJal/i67aouqQO5luKtuT0KA7KPB7tCnELJvNgd0dB3Qbl5CyJKmvydK2itAdFFt95eqbwM+a/h0KVW2MinecOfK/7chmNbNWPROwj4Ek9ex+vrIdq42H1kd0fAoGNH+PsTVG/RMYYnq1GyBrjHaEuK/WlqrD6uttmbCyOnQYqHaO1ZYQv8jb9/kvPnp3S0yvjuQPFjs8zhkXjRXlR7TLY9UvgSGmV+CXtCjEqNbmY9vUwWfj3lWorj7ebG0LcdG4vcT/y9Y7QdMXJH9PoxNmeLqo+rj6ZCSujrTv0F+5jlXR8TN3M9ocDLoJmIMd1Cens4rkO6OxLys7qFKv1KdlYoKnJPULBIvNIdZ8Fp8sVSefjXvRdl19vDkqqjpyxghacAR7QAIWpAf1bjdATph2ZHP1MfVLYGdIt66jle1YbQmxVmv7Af/mIb3j3HW2rgEt87TN+M7YOezUyb3a7zXq07pnwsrKD1wQFu87sx3ZdLxYeQma3i75Lxr7mebaGqI3elugl71Pp+EJKUuS+rcvCHtBsMNXpl4JnBnSseNg5ThWJcfP3DlvU6CDsH+CRnQlqXdOZxWp5oxtq48dK9F+r1G/1vFt/FNXv27jJUlbQkyXKz61W90dk5A1MdLpOrI9xHS5rcER3QR2mPVqO0A+Y1QS6nqk5oT6JbDDLK/bOGU7VptDbFy27ZC/w6xXgi5QpdPBomEdOXR4s054jPrkJq6O5Afa9lDtSKI7zIzHo75h2pEtO/0hpm8C60j/dgNV4QldR4qdCvVKYIjp1nWMMqxV8bHtZ3wv0UFXknpnd9J2VZ1x77Ujh7fpkDfBHWaBXbdDhc/tZXvV03rj3uE8yOPNUB9lalt5+DWf9Y5PSKmfGSMrq+LAxX9+lwQ2iF38Iz9Fe+qvsaiprlCR8alfi8QMTQf182Rrc4jGvujoNjV3rLp2iW8b7rp6tOkjxxjt2lN/Cs+O0o9ljVGvdokLTJ3PGa4sx6ooxC/ytspD6ueNf45+XX2yz9E2VZ/xi7wtEGL6BD7EE6F34L4sxfvrL0z31VRph/GpV05iLhiD8tVMxSHqSPGJErV1rNq2S9zIT5+2/VTpMdrdYDSmKDB9rl+HxKzlkKTueePV3LHaGmKtVnHlEfXyZiesLEnqkdVBJaqpN4JmJe0IjNb17JqY3mFJ6h34AN6+u/77WFZ2UDsT3BkSbOy3hLiNRtHxYrV1bNw7YdbVM7eXaozR3n0r6319R6n/Ajk/QVNcJH/4zLBWRSGmVG6vOqa+GYkZPQjqk9VRW23lme1IYPF43wStCZOkPoG2vXhv/RkUVZUntNtj1bNFYtb7SP6Lxp7KUHGIEYsdJ0rV0WcTNuovSb3b9FGFx2h3g8/RLUX+zpB+5wxPWFn5PScpw1ptPXTmhkPbq48rP8F1pEeztipxKs/4+o5A+T0TNFVOknp38QeLhtcjZSf3a5dX6tcqcZ0hHm+G+ipTW0LsUrn9RKm6JLjDLL91vio8RgcO1h9FKNnlH8HrmaC1pZLUPW+cjLUqDrFWa2v1cfVNYGeIJPXJ6qBtIdqR4DKMvj3ju29jXX0DyyCKG9SRkyf26IDXKL9VXsLK8mY0Uw/Hox1lZ9aR4lO71TWBQVeSeuf21kmP0f4D9XcpDnaG9O2UwMGZnheEbUeKak6qd4LrSM9mbVTiK4/o2BQLaH4lR7fJWKu8rombmtEz7zwZa1XU4KJxz94VqjZGvRI4NC1J+VkdVaLqM76+vXyv8uWN+35TdXXv6G/wShuMagUvEHom8EPT481QvrwqKjuzh6BUNeqRwF4dSeqT20dlHqN9DXrIth/ZombWqlsCL767BtbOlR6rv55v955lqjJGvdokLjBJUq/m7VTknHmfk52Vh9VdmQktq09gaurW0vprLLbvDY7oJu53zZvRTHnWo9IG4dM6jopUrZ4JriM9W3XXCY/R0ZP11zOVHCtSprXqnMiLxh4TA+1I/d7oXbuXJrwzRJJ6N2+r4hCNfVHlIfUyzRNaVvcO/nakpEGwKAm0Kz06D09YWRmZWerheFTc4ILAOo5KjaMe2Ylb7yNJfXJ767jH6NCh+u3/tmNFynWs2rdPXPjMCwS00gYzKHaWfirHGOW3TdxUOUnqmdlaJb4zp1OWVB1Rd09i60ifwIjFtga9+tsDQbdPnPeIrCszM0fdHKOdDXqja6ortMPjqHeCO1V7tuymg15zxnqmkuM7lO1YdeyYuGDRK9AhsP1wwxDj7wzp1S5x9VGSejVvqx0h2pHtVUfU25uYUcig7u39G0CVNAgWOw76L8Z7dkncjIZmzVupq2O049Tuel/31VRpl8dR95zEBU9J6pPbS8c85owN4LYeL1ZHn03IztxBPbr5r21KDtefQVEcGPXv1T7++7/W1TOjlXZUn7lJSGn1cXVPcKdqn8Bn8rYGN8cuClzn9UnQGnXJ3450cYx2NejEqqw4pl0eq14tErO0Kahniy7a61Gj98IMSrmAZmVVUrZHXRyTsDnYkv9Gm90co+0n69+jIBhq8tonZle5oLwWXXXcY85YBF9UcyqhU1wkqXvg4ntng1/kHYGpUT3juBt7KL0y26jIV3/u/Inju3TMY9StZeJ6hyUpL3DhVNogoO0s369ujidhc7Alfx3p5LMqPVX/A7ooMHe/dwLX+0hSfqvuOug1Onmi/gjJTl+Fuidwiosk5Xf3XziVNOig2B2YYtk1QRu7BOVltFBpzcl6Xzt8eKtOeIzyEzhVTpJ6Bn53d9R5bVbSjvL96u54EjZ9QfLXka6OUVGDMFga6AnslsDeYUnqln2O9nt0xu5axbYyoVNcJKl7sIOiQYgJ9k73SOAaBEnqldlKRQ0uCA4cWK8Kj1H3BI5ESlL3QHAuDUwxDyqtPKweyoz73oZ1tWrdTW0cq50N6khxYMphfgJ7hyWpR4su2uWxZ6xn2ulUqkeCdgsO6pnnrwM7G0y73X2iVBnW6pwEv7Y8b45KG9SRXbuXqObf0KnaMxCKSnbVn5pdUnFQPeRNaB3JyemgLj6rohMNrkcO+Ef98zombkaDJHUNtCN164h1HBWrRr0SuEGOJPUItiMH649Y7Di6XRnWqksCpwFKUr43R8XV9S+G9+9fo2pj1D2BI5GSlBfoXNnd4HqktOpowjtDctvkq5VjtbPBNWtRYIZDrwStGwzKz+mkEo9zxjKInapW9wRutCVJPQODLzsbXI+UnihRM2vVqVP8tw+oK8+brV0N2pEdpR/LMUa9E9wZ0qNNX1ljtHPXmUs8GkqpgOa/D5pUUnVMPRKc2CWpuzdbuxv8kIIXI3kJ7GWXpK65+ZKk3XtPXxD4aqq012OVl+AGsV27vspxrHY2aOyLT+zSOT6bkHvg1NWjRRftbnBBEJxemZfgUaZuHf2/qLsbhM89NafU9d9QR/I8zbWzwSL44sA8/fwE9g5LUn4gWAR7xCT/B+hej1X3BE+nbN0qTy0cq92n6ofB3WV71cFnE7Y7X1BeVgeVyldvKsjOwBbuPRPcGdIz0EGx40TddThWJdUn1COB6waD8rxZZ7QjuwJT9fIS2DssSd1ye8oaoz17V9Z+raL8iA57jLq1SGwd6dSxUM0dq5IG6yJ3nNylzv+GOtIj5xzt9Dj11qrsDExd7p7AES1J6hoYHdxzqEE74itXl8x/Qx1RpnY22KVvR+CzpmeC25Geuf4p7qV1pi+XlR3UAa9R95aJHWVq26a3shyrPScbtCPlB9TFMQntDJGkvKz22qn6a5l2BaagB0d8E6XHOf5dU3c0uPguqTmpHgmeTilJXT1Z2tPweiQw6pqXwOUdktStdQ85xmhvnftBHTu2Q+Ueo64J7lTtfM5wZVirkgYzUUrK9iovwZ2qktQzu6NKGtSR0kCIyUtwO9Il8Nm1q8F0uT1OpboluONdknooQzsbzETZcXSbPNaqewKn3EpSz9zeqjJGe+rMoDh+bKeOeoy6t0zsKFOH9gOVYa32nqw/8llaflBdHZPQGWaS1K15W5U2mNG2K9AZ0r1j4vYxkKSegXC5o0FnYCgpFdAk/wjajn/DNChJ6tystfbYBj+kEzuV8W9I7N06+Iefd9WZh33o0GbVGKMuCa7sxuNRd3nP+EXeWX1UPTyJbQwlqUvLbrLGaH9gjY9Ut+cvsZW9S+fhMtZqV4OLxr2qUZfmbRJaliTlNWuj0gbrEPae2qdsxyo3N7G9cd0CUxR21xmx2LVnqRxj1D2BC6klfx3pYj3aU1E/fO6qOqquJrEXVZKU1+r/s/fe0XJc15X371Z1Dq9fzsiZBJiDSIqUGJRlJStHy5YsyR5nj8c5yPJo7BlLHkkOkmVZOUtWzoFiziRIgiCIDDzg5dA5V31/VN3u6n7dr7tf133ro0ZnLS0CEIBCV1ede87e++wzQUYTLK9UD+kZWxYy6nKDNj5+ObppcsZREJuYnFUglQMY8fYwY9aijFPJc4QMk95ed7+3CXtf3DnHXOTMrPXjUZdZJk33MGlqnK0bgj9biCvJI6PhMUpCsLxcnWc9a+fLTW4DZvbfd87hCGsaBtPCZDzgLoAFsMnbw1SdpGw6M0PUcM8tWIZUf5x3zHNM2TOSm11mmYSmMWpqTNc5sJ0rJhjX3X9GNkUmSGqC+Eo1/8/GTwEwOuiuxGuzPc98xmH/XSrmmNJMNrsMmAGMeCPM1p01U6lzxAx35wYBJmwG+dxc9RmZtnPKuMtnjccbYMIQnKmTpp4tJdnkcXdGHWA0NEJaq1WinLUbKFV5ZNpRjxSLGWY1GAu5f9Zs8vasmmeayS4waOCaQY4M2cw688hZG/TZ7LIsW/f4GDYE07laA7ipUpIJl30MwFK0LWu18uUZmUdcZqul0uTsUuM1As542jVoOcokNcG4y/pygLHgMPO6qJELTWXnGFeA/E3YNP85xxzCtP3gj7qoU5axyRNlqlQrcZk1Cox6e1y/1liv5bAz45AwSORvwmWpnM8fZciAc46ZN8kgjLmsLweYDI0yp4sa/fBsfokRU7gqcQEYtmca5h1SqClF6DDAmCfEdLlWdni+nGPC6z46LKUg56araNxs8izgfkL0ekMMGDDnKHYSokheE4y7DIYAjAYHmdeocTucyi0w6bIMCmDSRvWnHEPw03bxMdrnntNV5XqeMOfqpKmzZoFRn/t5ZCRqFaGzDhDrbOIUmmky5rKcOBQZps8wOe+QLy8uPUVeE4wqOGsmQ8NMa2aN1f5cIc6I6f6RPDxgFd9zDifHszKPuPyuAYzpAWbqnpFzZpFJl+WUAJN9VoM55ZhnmrHz5bCLDr4AwVA/vYbJnGOh88Lik5SEYNxFQwYZI4F+ZjWzRmUwlV9iEnfZA4BxG4A+51CiTNvA4OiAu3Oz0FiaOkeZEZ/7LNOI/d3MOfNI/BQel+ePwZIvRw2Tcw4lytzc4xhCMB5x/xnZFBpdlUfmiwmGhbsz6gDDdhM/69hxWwHeXSYwAEY1HzP1ShRKTLospwSYsEGIKYeR3kx6Go9p0t/vbvPZE9tE2DCZbeDTUB9PuwZtRSsDMOQy7Q4war/Isw4UaaqYYFKBVC4W20LIMDnvoHCn7eToNoMAMOSLMS+qid4ol5jXYDjg/sM+Omj9+2eWq83nVPo8UQXIH8CE5ue8Y8+bZBDGXGYQAMZ7NtVcA2CulGbYZX05WHIhr1n7Is/ZyJzb6DDAuK+P85QrPy+XCkxrJuMKWKYJu3iacrCs0+kZQoZJNOp+0zQoPMyJqs3+oma9C7IJcDNGw+MYQjA/X/1s50ppJhXIKYeGLsRjmpyzm1uAmRWLcRpT0MQP+XqYdzwjRrnEggbDCg7NkT5LDj27XB24n87MM6IAHQYYw8P5fJVBnpl7DIDxXvcb3fHoJspCsDBfBbFmS2lGFJw1Q3aumHPIDucS1vMy4rKiAWDMF6tRomQzSyzqgvGwe/utZMhZrClH8T2bXWCgbCp5RgbRmS8mKj+fX7SAkeEe9/PISGiUoqg1nJgqZ5hUAKqODF+EXpdHpm0J4pjLc4MAQ94oC2ZVdljIJ1nSBMMK2OoRCRg7lSjZeUYM4bqcEmAcnWlHHpGM07jLhT5YaqWyECw6pNlz5RzDCpjIEfs8mXMAxnP22Myogjwy6o0y4wBVk4lzJBT4GEDVSO+c48yeyS0yokBOCTBkaszmV1r+vqddgzavW/8dUpAQx+z5qBlnsjdLjCpAdYSmMW5qnHfIriSDoCQhBgdIaqKyiHtp+RglIRhxeU4FYNSeC5txJPvFQoJhBegwwLi3h/OOF1kyCGMu0+4AQ3YTv+DQz88ZRYYVsExC0xg2BHMO2eF82mrWBhSgmmPhURIOmn9+4Ql16LCdEOcc7loz+SVGTc11lglgSA+S00Tl5wndusaQy5JDgFH773QyyLPCYFhBHtE9PsYMwXS2iurPJKcQpsnIkPuo5qC/n2VRZQeXlo5SEoJhBXmkUhA4mJ+FUopBBegwwIQnwnmHXEhKi8dVAGY2CLGwUpVvzpklhn3u5xF/IGYxP9mqNHU+M4dumvT3uStxBBgLjbDgUKJM27MW4z1bXb/WsP3dLDiAzplCnBHhflEFMKT5mS852Ar7HBiyZ8rdjNEeC2CUDLJpGMwKk1EFYIjHG2DEEEw7npHp1DQBw6RPAUAxFOhjUaNiOLFgv2sjLs9EAozY0jwpfQVYLKUZ1tyX7gOM6xHOO9RK03aDPe4yowswGLWalUUHGK7qrAlFhonU5ZGF7AJe06Snx30wfCwwyKxmVmaQpV/DhMuSW4Ah2whkwdF8zhSTjCoA3gFGdD/zdUZ6jeJp16CZwiqyhhQkjTEbaZy2H3ajXGJZgwEFs0wAfbqflVK1IJhOzxBRMIMAMGTLdOYXLPtvmfRVIH+hyDA9hsm0g/lZLGcZUJQQ66Ug0zbiPuai7bGMQfsgXrARaKNcYk4zGQm4PxMJMKz5mHPQ/Au5RXoM01UHUxnjtnvitM0OqkSHo9FJfKbJYraqMZ8ppRlVMKcCMNikgR5WgGqO2lKQGfs5LObTJDXBgAK2GmBQ87LksFGfzs4pmUEAGAoNYzpQ/VkbDFHxjPT370I3TWYdcqFFI8+AApYJrDwy41AZTNuN4eiI+4DZoP2uzcctRrxYzLCgwUjAfbYaYBiduUKV+VnILzFgoAQdHrMBnRnbTGPRlkSpAFVjsS3odXlk1sgx4rI1vIwhb4R5Bzs4bzMIQy47vcFqBjmbWSCnCQaCas6aAeFhydF8TucXlQFmg6FhykKwYj8bc3aDNqSg0B+22Z1ZRxO/YBQYVJVH/DFmnXlESvcV5pEFO1dlM0skNcGIAtULwLCpMedgfhbyywwaKHlG5AyyXH2yYDfYKsAQuVN20SFfnjUKjCgwiAIY8kSYM1av2aqPp1WDJhw/HhxUkBBtHa18oeLx05SFYCDoPu0O0KuHWHEk+2mbQVAR8nBcsJvPOXvwflQBggowil5D4S4YBQY8ag7N/kA/JSFI2/MjC3ZjOKRABjhoH5oLtlxIMpHDCuQ7AMOecM3s1GIhwZCqZ8ROfPM2qr9sH2h9Cua0hKYxYMCi4xmZMUuMubw+QMZQkwZ6UAE7MmbPhUkGWRqh9Ctq4vu1IItG1ZRktpBgVBHLNGAjtgt20SjzyIgCwEz3+BgyYNZhOLFAmQFFh2a/v5esVp0vXc4t4TFNehQwyNU8Yr1jiwtHMBUxkQBDWoA5RxM/X0gxqIplsovsefvZWExaqHS/guJb0z30G7DokJTNUmZUEag65O9nQaMCBs5n5tBMk/5+98/REZtxmbWb+EV7zrRfgdkEQJ8eYNlx1syV0ozoahiEIftMWbDHOmbtM2e4z12XZ7Dm1PsNk1kn8yMMBhTMzYKVR5KaoFi0wPfl/AoRw8QfcJ/VGrTVGgv2OzZnS/SGFDCRAEO6nzkHO7hQVKdokKDf3KJFKizZNVe/y2ZsYM2pxwyzkkeMcolZzWRUFfAe6Geubr60UTytGjQZPkWHZiDYR8QwWc5LGaCVNPpDaorvPl+UFapf0FI5y4CihChf5DlbkiFlQ8MKClSAET3IrKMgWBQmA373ExRAr91Ay0J4OR8nrIhl6u3bjsc0mbeT/ZzNSKqYZQIY9vcxJ6ov8nw5w6CiZ6TPll3FbRnlclomRDWfbVB4WLCTfamYY1EXDCtKiIOOokaY1ixav6FmTiUSHSNgmCzZjcWSXXz0Kyq++71hlhxzYctGgX5VTKREbO2isZpH3AdDAEaEj1l75qdcKrAiYFARE9lnP3vLy1YeWSkk6FOEDvcP7EaYJgv2uzZjM5EjCtBhgBFfD3OOmZ8FI8uQIgahzy4OV2zAbDljLYDtU2B+BTAgdJaKVh6RDMKwIlB1KDRESQhW7LNmPrdIv4GSWab+/p0I02TeXqC7aL9z/QpmcAD6PWEWHc/IilGiV9EzMmQX2fP2fZSzTCMK5mYBRvAwU7CAl0I+SUITDCo6a3rt/BSPW7lxuZikzxRr/ZF1hxx1kHlkzm7ih1XlEW+UOSeDbOQZVOCqCNXnfEWC4Rmr5lKWR0yNpYKlVlqJn7KAdwVGcwDDoeGaPNIsnpYN2pDhvmOejJgpiBcsB6olu/joj6pJiL2BXlY0gWFr9eNGiZiiwmpoQGpsLcR2Nj1tzSAokHgB9HhCJE2raMxmlsgolHj12ezVcsJK8iuFJL2KEqLm8TNgmCzYTbycRRtUlRBDw2Q1QdJGyBaMojImMmYjVst2Ily26X4VMwgAA5qfhbKF2MrDrE+RfGfQYTwiM8cQupJrAfSYELelqUu2HLZfgfkJWIjtsoByyTo4V8wSMQVD4gBDNlOwYLODs+kZdNNUMhMJ0K8HWbbZweXl4xgKFQ3VPGIXVqU0vULNM+L1helz5hHbJn5IUfExFBhgUaPi9jZvlpvKfruNPjuPrMg8YssPexXlyH7Nz6I9Oxi3m5heVXnELholqj9fTDKkiInUPT56TJO4XTQu2nlkQAETCdDn72HZwQ7GhUGvorNGMsjzdh6Zy8zhM91fVSNjQPOzbJ810lBjUFHx3WeDgcv2s7hcytCn6BnxBWL0GAaL9py6fEZUjACBZQa14JgdXKTMoIK5WYBe+7yUAI9UNKgwEQMY0Hws2qRC3K4lY6qAHptBnqtb1l4fT8sGTRWlCtAjdBJ2slcpzQDoCw5iCEHSRmxVJsTe2FaL+bEPzaV8nD4D19cHyIh4QqRsdnDRljEMKEqIvRJpSVrN53Ipo6ywAhjEw4J9aMbtJqZXUdLoCVjW1InkOUzDYFGYDCoYAAaI2UzZii07XMov4TVNworkmwPeCIv2AtF4UiZENYWVU7deadA0NegwQEzolfnSRYXSDLCkk6YQrNiNxYqAXkUywAEb0JEy4qX8itI8EvMESNhAjxyEH1TEIPTZf++y/SyulHP0KjxrBtCZt+fCEva+n5iq4iM4iCkEifgUpWKOJa257LfbkEX2iv2ZlgpxYoaphGUCGHAwP3EbgFRWWEkGWTJoZXVMJECvqRG32cEl27ypXxWDEBigKASp1AxGuURcQI+i4ntQAsY2y7pUiDOgiK0G6NGDJOxnZMFWRg0qetcqQI9dP64YBXoVAe9gMT8LRYsdjGfV5pH+4AAlIUilZygWMyxpgiFVwHvMqrtX7BprqbBCv8JnZMATYtGeC0vY71qPojwyLBVtDpOoRvG0bNAGPOoSYo/mJ24jtotpmRDVoBG9tnRyOX4K0zCIC4gp0kVruodBA+ZtxDZZzhJV+PVHfVFSmsAs5itOZYMKZKkAfXZjsWzT/CtGnl5F7jtg6bDnDcvFLmHL2HoUsayyQUul50inZ8lqgiFFA8BeX5ioYRDP2zM4eXUSL4BBXy/LwqRslInbzXWvoia+P1YFWTTbbb/fqwYMAYgJL3EbsV22JUp9fe67TwH0h617thQ/SSGfJKsJehXJif2BGFHDZN4uBBKlLD0K80iPN0LcJsOlxGtAVR7psf7eJSnNM4rKJF5gOQJKxDaRWwGgR1FhFbVnshLpGRaXnsIUgiFF71owNEjAMFiReaSYpF/R3CzAgC/GomZimmalsIqFVeURq0GTZ82SWWZAaR7xEC9bZ82iLavvVzCnBdBvnyvLKydIpaYxhKA30KvkWoFgX10eyRFVCKrGvCES9pqVBXtVzaAiwKzPzk9yRGDJLNGnCHgHGNT8LNpgYNJ+53p61OTISh5Jnq8YRakC3qM9m9DM6sjRcjFDv8JnZMDXw6Jt7pKwWbuYInC6x5aBJxymJI3iadmgxRQ2aBZiayEtS7lFNNOkVxFi1WcX9SvxsyST5ygrTIhgsYNJ+0VOlPP0KKLdASK+HkpCkEvPKpdmSOnMim01vmKW6VMk8QIY8EQqO1wSdkJURbtHbEYpmV1gyWYQ+hUlRLAQ2+WiJfFdLqXVJsRgP4YQLCfPEbcZmVhEzZxW1DE0rWEd1FGFz0hM95OwtfpLWXVmEwAD9mdbip9lxZbKxRShmgD9pqig+kkjT1RhHon5omQ1QbGYqwzCDypYwA3QJ5kf+9CMC4M+hcX3oCdccQRMFBJoCtnqHplH0jOs2Pm4T9G1EIKYKVixVQZLpSx9mkImMthPXgjSmXniaVlYqckjkYh1z1J2Q50UEFVYfMc0Hys2YLyUWyaqaLYaqrODS4kzxG02vlfBXjIZMVOQsF0jU0aBqEpllDdCQoBhlFm0WdYBRY1uReKbnsc0DFaE5TegKgY9IRbsZyRRSOAz1RiSAESD1rmSTM+wZLPIA4reNc3jI2aYxPOWymCpnKVPIfA+4O8jpQny+SRxW2nWo6oesXNvqsUutKdlgxZWWFj1eMLEbWneUn6FXlOdfKdXonGp6Q1JiGHhISNfZKNAj67mcwFEJfOTPK9cmhEJj+BxIi3CpFdhQuzxRUnbaFyikCSsUL4TtfXsycwiKbtwlElSRfQKnbh9aC6Xc2oTos0gLy4fZ8UurHoUydcaFb4RhcV3rydE3JbmqZZmSAn2UvIcK/ZMR68iaQZAWOikbLe3pFEgqmh9BkCPLeeNJ6dYtgGYXkXId09sM5ppmbsY5ZIlFVXERAJEvWFSNliQKKaImgolXiHreUhk5klnLNYirBAM7ENjxTYAskxr1IGqEsFfXDpG3H5GehS52EmgJ1lIUCxmyGqCiCI5MUCvJ0jcloEvFhMMKJqtBuiXDHJiqqJoiIXU5ZGI0EjbKoOkWVSbR/wxTCFIpWcreaRPwQ5MqALGS7lFsrkl8pqgV5GrKFhAY0oyP8U0PWsbA3YVUvKXTM+TstnPqMJnpBeN5ZLtCWGWlALv0h11celoVRmlqB6JOPLIWvG0bNAiKhErXw8JW5q3XEzRp1Ca0Wcv3FvJzLGSsCVeYTXyNYCQ5iVtMz9Js0yPwkMzIpGW1DRpG0mNKkIjhKbRa1qua/lcnIwm6FNYWAU9QfJCUCoXSZTS9JjKLkXULj6SuSXSdkKM2M2viujV/BVTBtUJMWrLkNLpWeL2kHNvTA3L6vFWn/WcvUsxqrKJ90aJa2CaJsvFDH0qmUhbgr2YmalKRRW9awBR4SVla/WTZpmoIldRgJidRxLJ82Rs1k4Vy6TpXnoNk5VCnGRyypJ4KSysQp4gGWE9I4limh6FxXePfc+S2UVS9rsWUTTvCRbzI00ZloVBn8ImRhaNqdRMJY/EFOxcA0vi6zNNksUU6ZTF+kcVMVoAMU+YuN3Er5Rz9CpkIqV8cyk9y4qUiirMI2HhIWWfNSnTIKpwTitmn5nxxBSZYgaPaeJTlP+9wRhRw2Alv8KydAJXCZh5AqTt1KFccm6f2YnMPGn7XQsrBIz7hKcyy70sTPoVjQAB9DjYwbiUnMfUqF4CgV48pknKNiRsFk+rBk3WwRGfwmQf6KUkBNnUNDmjREhhYSWbsaVCghVbr9yjSnYChHU/aRvVTwiTqEKpaMRuLFLp2UphFVSYpHrRWS6mWZEuXooG4AHCNvOSzS6TKOXoUfiMyKY2mY9XCquwwsKq1xMkbjfxy8KkX5HTG0DIbqIzuRXi+WV006wgSypDLruPKEz2MX8PBSHI5pZJGQXCCmWAUbupTebirKSlVFTdfQxrXlIS6BEmPSoVDfaznkhNky1lCBimMkUDQB86y4UUyyvSDVAdYBb2hjGEIJdPkCznNySPJLLLlcIqohD57tMDxM1ihYlUCZiF7Pc4k48TL8TxmCZBhZ8takCymCZpNzERRaZNYAHGaU1QLObJGCXCCmWA0twlnltiRc7gKGIQACKarwIYJ4RJRKW3QEDmkRnSpSwhhWw1QK8pWC6mKnLiXoV1XdATtgDjUp6EkVMqOZfMdDK3XJH5RhTmSAkYF/JJ0qqBd6+VR7K5OIlikpBh4vWqOduEphExIeXYKdconl4Nmi0rU1pY2bMbicRZ8mYZn8JDM+gJ4jFN0uVcReLVq2ApsIyQHiCNgVEukVTo0ARVdiSVWSBTyhI0TDRdXeLo03ysGDlWpF27wjmtkI0Gp9NzJIw8PQoPTScVXkmIKiUF3gjLwsQol0hrgqhC5DtkS6wy+QTxQpKY4kOzPiIKJV4xv+2+GT9D1iwTVHho6t4gPtMkW8pWrM17FTEIABHdTwoD0zCsGRyVJgm2DDaRmbcKK2VXsq+neVkpZ1mxnRyVzWkBYZlHMvMkVEtFZR7Jx0nbspqQUqAnzDJl8vkEhhCEFapegva8TSWPKJQTA0QRpEpZUnYTE1WpaLBzVDx5lgxlQgoZtIDNFudKuYoboMo8Etb8pMyyddYIiCoE3mO2fC2eniVdzhFSqHoByfxkWLYVDX0qATM7/2Yy8ySMotrRFds3IZlfqdQjYYWqrz5PmBXKZO3nMaywHgnaTHg2HydRTBFT/IxETFHxhGgWT6sGTUprwwq7aKnVjyfPkzfLBBQ2aEIIgiZkyjniOTlfoUbiBRD2BMkKS1JmCFGZ71ARlcYiu0hmAxJiUHjJmmXiabUuXlB9/jK5RTshqpN4eXwhgoYtqbENScIqTUJ8MTKaqBQffo862UnQLggyhQQrpTQ9CuXEjSKq0Egj5sgjWcWFFUIQNE1y5TxxWzuvak4LIOIJksIkm1uiJARRlbITu0GKZ+fJlPMEFcoAAYLCQ84sV1y8elTmERsgy2QWSJglpXnEHxzAZ5okismK5DyisPns9UVJCCqy7IBXHTsScuSRRClLTHFZExU6yXKuOhOsEDCL2cxPPDlF2jQJKWziha4TNEyy5VxFKtqjEujxBEgLk0xmHkMIogrVGj2RKtCTLecJK35GAsJDziiRtk0gQgplgGG7sc2kF5SProRCw2imSbyQIFXciDxiAcbZrPU8BhSqNYJ2XZfNJ5UrowCiQiNly8CbhTpYV0HIBk3lDI50f0qkZ8hj4FOIfAMEEWTLBeK5OELhEj6AkDdMWggSK6cAa3BWVUhJTSq/TKacJ4TawsqveSiUDHIFizIOKGQHQ36bCs8sksCgR6E0AyBqQqqYribEiLqEGLKTvdxwH1DYoEkEP1NIES/niCl+1+pDqVTUbqLjqWmypklQYWEFEDCFVVgVEgQMdS5eYO04TAtIJi1ZdsSvUNHQYyG2iewSGaNASKgvrGbJVfOIws8m80g6u0hCGEqlomgaPYZJopjCb79noZBC+aYvgikEcdt5M6jws4WCvQBkCykSRo6YSjAEiGhekmaRpJwJVijdl8zPSnKajDAJK8zHQAXoKRpFoorlxGFPkJSwZgcBogrrESnVTOSWSBsFwoqL74DQSRoF8kWLIVFZj4SlxDe3pHx0RdM9RE2TZCGFaZTxmCZ+hd9b2BulJAQJWxkSVMiyBm22OltMETfyxBQqowAiwluZwWwWTy8Gza7xIwrRCImYxrNL5E2DgKa2aAwhyBoFMqUMQYWOkWDRw4YQzNvby3sUFqgROyGlcnEyZfWFlU/3kcekaFPGPoVJSs5OpXPLJAT0eNQlDYAeNJKlHOlCSulwM4DPLgDkfIVf5X0M2Q1aMU3CKBJTyCAAhIxae6uoQmmGRGzjmTmywiSo+LMFEeSMItlyHrVwgeV+aQjB3LK1B6dHIWAWsSXf8XycjFFUX1hpHnKmQb60AYWVzfyks0vKpaIAUTQSpQypUpqwYsm5z0bx5eLogMLPFgzIPJIibhSIKXSeBYhqflJmqSLxUplH5B6mRHqWrLDGFFRGAEG2nCdfLhBULfHyRigIwaK9l0yl5FzuKU3kl0kbJYKK6zq/8JDDIGc7IvuVAj1WPZLKLCgfXQGImhrJUoZUKUNY8ViCz2O9y3G7HlGbR6xzzAJ6ivQoftcimo+kPYPZLJ5WDVrFJEQh8ie/pFwpTR4Tn2I0LohOxiiRN4qoPVYgbCeJmRW7sFJ4H0PeEMKEZDlHxiwQUsyO+DUfBUwKJWupp8+n7kWWcoWV9Aw5TdCj0MULICI8JI08qVKGiGkqToh2YWWbTfgVIt/+QB+aaZItZciahloZIBCuKzgiIXVMpN8eOM6XsmRhAxo0jaxRoGgU8SourKQ07/zSUwBEFQI9uj9CtGwQLyTIGEXleSSg+cgJk1xRfWEVDlpnzVLyHEUh6FEoFQXoQSdZzpMpZVe9C26H3y6spGlNQCHyLfNxppghaRqEFb9rUT1IEoOkLV+LKNoDBVTAuFR+hZIQhFSyrMg8UiRvFPEpVr1Iad7M4lFAbR7xh4bwGwbxfIIMZcKKFQ1B3UseB9CjskGzG9u5leOYikdXwJLmJco50qUcEcWSc7/dJMUzdoOmkkGz80i2mCaFQURxgxbVA6TMtXciPK0aNBkqGzTNdm0pF3MUBARUN2hCJ2uWKBgFfMoLK+vFnbadhVQ6RmpCI4K1gDJrlJQXVj7dTx6TQtlq0LwqJTX27NKMvbuux9er7FoAUc1L0iiSLuUIK57TkoxZ0pYUBBS5GAEIj5+QaZIpZSlhoqvWfNelu0hUYWFlz9zkihnymiCoWAYbFDpZo0TBKCkvrKQUaSZ+yvq5wnyMEISAXClLxiwrncEBCOg+8kC+vHGF1bTNIPQotPQHK48kjAKpck75DE61sLLziMLCyhuI4TFNMqUMRUx8muI84g2RAlJyli+qzgBCAo0rWWu2NKQwHwMEhWzQSvgV5xFp9jaTOAVAVKEbIJpG2IRsMUPGNAgrZln9mo8cJnl7xkipDNAmFSr1iMJrAfQIH0mjQKqcJ6xYGVUBeux5z5BKN1gbIMiWMhQF+BSzrBFvkJRYu+h/WjZoYYWD2x6bDSmX8uSwpHMqI6h57AatrLywklr96Yy9v0XhjhOAsClImSXSpmKTBKwXuSAEBdvSXymDZkvzlisD8GoPzYjuJ0lpQxKiz/4sCbsg8KuUXdkmOdlSjjImHsUNWn1RGlRoEuKz71tCDomrLqw0nZxZIr8BDZo0yZm2V4NEFQI9AB4ERaNEBpOQ4nwc0H1kheVkB4oLK7sgWJTzFQodygB69ABJs0S6XCCi+F3z28+7dAMMqpRdaTohwyRbylmFlerZEW+ErCZYzscJKLTihqqiYdk2/wkpPNfAmp3KmiUKZgmf4rNGShpnUjKPqKvrwMojJbNERpiEFLOsAc1HDsiXNqBBs01qFjdgTgugR/eTMIukjTwR1coo+/lfkbWWwjzi9YXxmCa5UpYCKFfPRT0RUi2O6qdlg6ZyuFm3C4BS2WLQ/Iq/pJDwkjENCkZROWJVQVoKlhtgj0JDEgA/goJZJoOhXOLl0wPkhaCQtxb/+RQ2FhIgiNumHV7Fny2iB0ljbkhClAWBbCwCiguCEIJMOUcJ8CguCOp3CCmVikqzFdt5M6i4QQsILxmzTNEs4xOKGTRbCjKbl3v51JkkAHgRFM0yGWESVCw78esBSkKQsaVJKgurkG0kkyhaOcuruPn06z4KpknaLBJSPYMjC6tKHlErAw9huSEXAa/izyZdS2fyS0QUq1689jkWl6sRFDodgu1iapTIm2X8qvOxzRjP5GyzFYXmVwBeoGhYlv4hha6iYDPxAvLlHH5D7ViClPjGK3lEca2leSmYJimzRFg58C7rEfscVTin6ASMNyaPRCo7WZvF07JBU2mkIWVWhWKGkhBKbcbB0ipnMe2da4oToo3YzpSzaKZJWDHyXS2sUI5Y+b1BDCHI2geZSgZNDqXHbbZOeWHlDZBnYxJihfmx76NfMaofQiNTLlAWoCt+/vdoaptNZ/h9NhNpH5pBxQYQQc1LDsNCvlHMRNrP/4rdxHi8anOkM4+EVUtFbUlNophSX1jZyPeKvazU61GbI3WhUxImKbNMRLFUtMKg2TLAgGLZVRBBppynIMCrK0a+bYfU6VKaiGqpqN8Geuw8ElLc6AaEhywGBbOMXzHLGrHrkaWyPe+p+LN5bUO2guK9fGC5H5eFIFXOKfcWkITFil2PeBTXIx6hUQbSZpmIYqmoVPSs2GB4QGWDBlaDVskjau9jO+7HT8sGTWV47K45aydEv+rhfs1PVpgUNqJBsxHbaWEQ3YClwD4EBdOwGjTFhVVAzk4VJYOmLtnrHi8BwyRemXdT7KzlCZETYkMSot9ubGVjoXJ2BOyhdLNoMWiKEatf3fUr/MvMHBdli/gNtdC3RL7loaladhLQfWQxKZiG8jwi9z4lzCIAuuLvzSqsihQ2wCShwvwU08oLK48vTMAwWJF5RHlhpVcKq7BqJlI2aHbzGVC49gEghE7aLr59iptPj33vEmZJvTuxvI/2TGRI4UwkQFD32Q2agVc10GM3aHHDziOKAQovonJmq5acyxnMlWKGgOodsMEBhGmSMGQeUXsfPUKjhEkK9Wsf5N6zFdsNUymDhgX0JMtZTCHwKgbD2/menlZ70IKGQDfVPu2SQcvYhZVqBi2k+8kINgSxCtnSvBVdZ1NZ6aUA8AmNjFmiuAGFlWR+Urb7mkexhCGEfbDo6hNiwBuhLARxysoTomwsksWNQTVDmpcVo0QJlJuElA68jt/4RoTkcogXHlA7f6l5AnhNs1J8B72qCys/Oaw8ElEty640aGUQoKk+yIQgbhRAqC+sKgVBOau8sEIIQibWZ9PAsyGFFaSEtWxcZcjZVVkQqy6sQvbeKUB5YaXZJiRFQFc8luC1FQwr5TwICPvVrbQACEpzCwz8is1WIvZ6ghWsYsSrcMEygBeNFaMIWtWJVlVIU6hEOad8JlhoGiHTBsw08ChudD1Cpywgg7UTU2VUAQqZR9Q5fYJlkpOwjV1UAz2ijXrnacWglc3NXCH+U+k1dDsppe0Fg37FSGPQY81OZc0yPtUmCQ4UU/WWdACvsBMiG4BY2X9/spzDp9iKHqzZqbg8WBQnRDkHtqLryiVefpvpkUlKNfIdFB4yZpky4FFcEGBCEus5UYzzgKbjN03iplU0BhWvYgjqAbICChj4FM8peu1iu4BlEayrbtDQiNv7YkKKJbeSiU8YBeUzwQBhBAn7PipHvjUPJdiQfVoyH6/YTVNA4a48gJDwkLDPGtXGXlKKXRImmuJnRPME8Jgmy/L5t42+VEVQ91t5xFSfR3y27DVrL1BSzaB5hKg0g6qlon5b9h03CwQ2Io+YEDetz+ZR3Fjomk4ByGlCuTKqAvQYBXTTVA68B4VuAWaAT+EoFbQ30vG0atBAfWHlsZNSxu7Y/YobC/mAx9mABs0bxmPfvx7FLzGAD424XXyoLqwqDFo5r3xdAUAYnRXbItWruthxHCYhxbuSpLlF0pavqZ4dCek+MhiUBMpdHJ2PhfIGDfCZsGIfmkHVMzgeawYzhYFX8X2UhVTR/rmmeObHKxx5RPUMjgRDzJJykwSwnEXjMo8oZsetGTQobYB8R+asuFlCmGZln5eqCGreyjOiegZNIt9FQFdde2saPtNkRdjPv0LnWbCZeCHIYio3SJOARAEQptrF6WDlkYR9CoQUr7QI2DNu8Q3KIyFEJY+oZ9A85OznXn0esfMxBsENGMsJCI+lDAG8imtk7eetQRPUFlkqQjJoGRuN8ysfSrdnHjCVI1aa0BixrxFVjNaCzaDZT5hyxMpuLFJmCfWtp4XYZu1k4VWNIjnYl5BiqZAspBI2YqvSxQ4gpPlJY1AWAl3x8+8MU3kmAR9UDs2QYgZBukTGMfErngnT7INLNmi64oPMKzSSmlURhBUzun5ZWGES2IDjMSB08raTl+oGzaPplOxrqZ73rDDxwiSwAYVVSPNWADOf4jldKcUugXIGDcBvQsH+3qRjn6qQeSS5AQ7Wus0y5QWKp92s8KKRs/OIyn1aAAE5g4ypfHQFLOYnrW1MHtGFtuF5JG7nEdUR1LwkZB5RXCNrP28SRwBTMfStCSvlZmw0zq+aUrVf5IwmlCdEgDHN+jw9irXDAD6hU5QHi+rCSjI/GHg34EV2omLKJY6Ow0Tl7i6oNmRJIX+ulrELeQKVXSCqk70zdWwUgyaff9UzOBWTHE0oX7Cp2wxF0f7elDNojmMqqJhBlmYuGU1sSGHlVE2on0GrPheq3zUJ9GSFQO0JakVID1Qsq1XnYzmDVhIb06DJt0uYJgHFDZrMI1lNqJeK2s+7KURF2aMyvI4zW7XkXDLxWU0Q2Ig84siRyvOI5swjql2lrXxcEoLgBrxrQc1XAQNV30etjXU4T78GbQOuoSPI2F+S0kW9QMjx96surAD6deuB1wy1KAvUFh+qbcZ9diOR0oTyoVwAv6PYUc2gOec3gooPaLmeIKEJfBsgOwl6qoWVrngGbSNYM2c4n0PV35tzybF6kwTr7y/b35um2sXRkUdU52O/w21zIworZ9HoVQwGOmc8VTdozr1nAXMDCitHU6Z6lk9zSBw3okGTeSRommiqZ1kdIx2qF/Xqju9pQxg0x7umck8q1OYpv+LF6UCNc69HNRPvyIuqHXyd6qHABkhFgw5QwqcY6Pm5MwmBjUG+PQgy9sOguiBw2m+rRqwAtJL18mbSGyDxcjyAAeWFlfUipzRtQxo0ZzOturDyO9iXUFjdknaoJqWyEPg3gmVyzO+pbixqGDSlV7KitkFT6z4VqAF6FBcEmobHvpnaBhjy1DRoPsUujo6CQLVUFKiRtauXOG4c8u31RRD2M7IRJgnOBebKpUl2o2sKga54KTxU80jINEExiOXMI37F9Yhw5JGNELfX5hHF62McTH9gA/JIDdCzoXlENdBTvY/BDWhXavKIYuD959MkZAOuoQutoudV/SI7Z7P8G2DcERDW4VUyiy1+Z/exkci3dIRKaZryPVBQ16CpZtAc7EtQ8XJxj/BUC6uNkJ04igDVDJozNgLo8dvp1WOaeBUuTgcIOqSoyhs0qgfHRhwgG5lHnIWVfwNmImsljqpnRxyFlWojDW8Qv8wjG4F8O5ifjTBbkSE2kEELbQATWaPo2YA5dSlt3BgGrXoV5Qyao27ciNEVJ9CjmkFzPv+qHSM9DqAnuAH5OOi4d+qZ+J/HBm0DKisdjYyNCm8k0rIRhZVPSOekgvJrebWNkzg699X5NuCx9tcwaKpXCFQbQNWzTEKIyoLejbAZdzZoHsVSEHONn6kIn42uRw0TFCPtQSfQswFMvG7W/ldlOPOIcomjo9ENKG5ioJ6JV5tHnGi3arYa3VNx090IqWjAMVPtU1ygOgsr1XvQoNqghTeCiXTmEcUSL6g2Zhsyg+bMI6rdYB15ZCMaNO9GShy1DQR6PP4q0LMBTGTQAbb7FCujfu5MQjZATQBYCz0zQjJoal/kmEP6pFrzCrB54u1sz0FP5NeUX8uJ6vgVMwh+B9qxIQyao5lQLXEMOhZ4qt4nB+C1C4GNkCbVMmiqTUJMx4+VXgqoAgWRjdiD42jcvRshlbYb3I1h0KrPhU8xYBZw3MeNUDRspFRa30CJI1ABejYC+Q44Z6cUKxo0R6HfzqB/tyHPs+AG8ExhhyGVTzGjC+CRO9CUX6k2j6iuR2oatA3Ix94NBXoctc8GyOnlqEVwA3JW0AH0qF6f9HPKoKm/hi40chUGTW2D1hOqzhT5N0BS4Atv4+DJ/0XBt1/9tRxJI+BVex+d83uq98lZ13MkKcWOmE4kM6i4+ADw21Kajdjf4pRIbKiLo9IrWeG3C7noBkiTog7p64bMstr/3ZDCqoZBU9ygOQrUwIasIqnmEdXIt3cjGTSoFFYbgnw7zhf1Esfq59kYBs1620IbcK71OfKIX/F9BNDt3LgR99F5vvgUuxPXAD0bkkcc77bixmIjGTSoAj39inM/1El8FQNmoo2Rjqdfg9aktIpni3zuvjN8/9AMj03Fu7qGk3psZjN+eDrBbCLHF+4/w1cfmlr3tYLR8cqPm2m+f/jELP/4gyMcOt/d5wIqaXAtR7sjM0l+5/MPc9exha6u5ZRsBpog35lCie88Ns0PDs2QzK1/Ls6ZBJst6s0UStxzYpFvPzrNTDy37msB+B27drxNZFePTcX54I+P8oNDM5TKxvqvpbdu0HLFMt969Dxfe/gcqXxp3deCqjRvLZtx0zSJZ4p897Fpzixm1n0tpyW2p0ljsZIpcGwu2dU9bDdM0+Tu44t86p7TnFvJdvV3yecw2qKwOrWQ5qnZZFfX6umZrPx4rT1QZcPk3Eq2a6m4/ERrHSDpfIlcsdzVdaC2IGgmOTcMk3tOLHb1LAJovjBe+96sVViVDZN0vkS+1N3nqwF6FMs3a8CQJoWVaZqcXcoQz3Q/oywl0iNrgHOZQomDZ1dYSncnuQ/6HS6mG1hYbcgMmp0/Qms01aZpMpvIkS109zz2xrZWr9ui0E/nS13nEU/df1WGbGI008TThGUyTZOZeA7D6O5z+Z0mIWsooxK5ImeXMhRK3Z1tTjDcs6FMfOMzu1Q2uq5DZMhMNBpobrSVypd48PRyVzUk1Jr2NWMiy4bJHUcXuP3oPMUuahK9DcBl4zbDuhSN8sGZxQyv/cjdnHcU3b/x7B389+ftQaxDguC0I27UoN16ZI5f+c/7a34tGvDynAs6N3AQIafEcXVC/PKDU/zhlw4C8MGfHOOSTb1curmXdz17B8PRzpESeTua5dVP33Oad3/zCQplg28cPM/LL5ngD5+3h/Hezl96Z9JoNJT7jz84wr/eepySnQzDPp0PveEybtwz3PG1nCyTrwEyMbWc4U3/cR8nF9IAeDTBtTsHef+rL2Yg0jnC5WQp6hOiaZp85t4z/M03D1EsW5+tL+Tlfa+5ZF2fLeA4KEMN2Lq7ji/wzk89SCJnJcSAV+PdL9nPq6/c1PG1QCK2RsPZkWyhzF9/4xBfP3iOUtmkZJiEfTqf+NWruGJr51byrSSOH739BO/97pOUDZOgV+fARIxXXjHJqy6fXNe7LaNRYZErlnn7Jx/g9qMWMPEPfg8ffvPlXLN9YF3X8gsdTIg0kXgtpPL8jy8/yo+fnAPglZdP8js372JTf+eMrNM8ppFU+thcig/+5Ch3HltgIVVg22CYt12/jTdcvaXja4FjBq3B/2eaJn/zzSf4zL2nKZZNxmIBnnfhKP/j+XsJ+jpnAZxsj6dBHplazvBbn3uYh8+sAHDl1j7++fWXMdyzDiRZ0/GbJkUhGjJopmnyrUenec+3n2A2kcerC/78RRfwlmu3dn4t6gqrBuDLlx+c4ksPnCVXLDMQ8TMaC/COG7azZaDzZq6msGoAhpxdyvDfPvcwB8+uEA14+G837uRN12wh5FtfmZC1X5nJYOOc9+RMgrd94gGmlrNoAv7guXv4zRt3rutaTlv/RqZN51ayfP2Rc/zg0Cwz8RzRgIc/fsFebt7X+Zldw6A1yAvFssEHf3KMrzw4xb6xKM/aPcRzLhhlNLY+ZkMCPeEmDdpsIsfbPvEAj52LEw14+Lc3Xs51OwfXda1grHpmNGMQHjqzzOfuPcOXHpxisi/I3750Pzfu7fxcg2oB2oxBOzKT5NP3nObuE4tcNBHD59H4u5cfQNc6z8eSQfabjWeCHz8X5/e+8AhH51I8Y3s/v33TLq5d530UDrdZv974Ph6fT/GKf7mLeLZIyKfzkTddwTN3re963hZ5pFAy+PZj57n3xBLffmyaHUMRPvi6S9d11nha5JFjc0ne9emHmEnkeM6+EaIBD6+6YhP7J9a3C3fF/q5HwqMN//+DZ1d4+ycfYC6ZZ1N/kC/8+jXrqlehdgazUR4xTZP//uWDfPWhcwBct3OAT7z1Kjx651yXaIMfe1oxaILVjUWxbPCrn7ifTLHMZ99+NV/7zet43VWb+Jdbj/Pubz2xLoRHdxQBTlTTNE0+cdcpfutzD+PVBb91006+9M5r2D/Rwx988RHOLq0DvdU9aBKxrXsgTi2k+fOvPcY12wd48M9v4fefsxufrvHpe07zlo/dv67uXSJ+je7KfSeX+MuvP841Owa4/Y9u5B037OBbj03z0n++k/PrYBOcL7Lw1hY7Pz48ywd/coznXDDC597+DL7w689g62CYd37qwUoT1Un4NKfEsbagyBXLvONTD7KQyvPPr7+Mr/3mdbzt+u3ce2KRt33ygXWh/M6G0Gkzbhgmf/pfj/PnX3ucZ+4c5ME/v4UPv+lyxmJB3vaJB/jXW493da16Bi2eLfL7XzjIYMTPZ952NV9+5zVcvqWPP/rKo3z23jMdXwuqMw/RumawVDZ4+ycf4IsPnuVFB8Z5x7O288lfvYrBqJ/f+fwj60KvnHKM+rmYu44v8J5vH+bmvcP846su5rVXbSKRK/JHX36UD992ouNrtZI4/uMPjnD70QX+8sUX8N3fuZ6eoJfX//u9/NnXHl9XHpHPYbRBYXXofJyXfuhO7ji2wH9/3h7e9sxtfOPgeV7/0XtIrOM+Cse+uvoZnLNLGV75b3fxk8NzPHPnIH/6wr30h3382X89zsfuONnxtaBaUGkNbst/3HGSj991ipdeMsHvP2c3l23u4xN3n+I1H7mbuUTnzLVEvnXTRNQ1n5lCibd87D6OzaZ47ysO8Mcv2Muh8wle/9F7181KXpG1/40NWKZ3f+sJfutzDzMU9fMnL9jLdTsH+atvHOKffvTUuq4lgR7RYOfg1x85xx9+6SALqTw9QS9nlzL810PnePEH7+DYXKrjazlZs3rk2zRN/uSrj3FiLsWfv2gfF0/28t7vPsmLP3AHdxxdn5Jizk6Lk9HJVf/f2aUMb/6P+yiWDf7vay/huReM8r+/f4TP3be+nOWc+fHV5a2Hzyxz4/++lX/43hE0AdfsGEATgnd86kEeOLXU8bVqZtDqSijTNHn7Jx/gAz8+yrbBME/NpviLrx/iGe/9MX/7rSfWxcxIqXSoAWCQK5b59U8+wPH5FH/2wn2Mx4K85WP3rV/V463mY3/dfTQMk3+99Tiv+Je7+PJDU7z2yk1E/B7e+ekHOTa3vndN5hFPg4bps/ee4YUfuJ0vPnCWoFfnqw+f4/P3n+Ufvm8Bdp2GbGIatbmlssFvfvYhkrkSv3njDh6divP6j97LX3zt8fWxW5rORbk8UJubZRybS/LGj96LRxP83cv3M94b5Lc//zDT8fWpNqRaSW+QR+46tsAN//BTfu8LB/n2Y9Nct2OQE/Mpfv1TD65LAaA7AbO6HDmXzPH6f7+X5UyRXcMRbju6wJcenOKXPnTHus8auSd1NLoacM4USvzO5x/Gq2v8/S8fYCVd5KX/fCfv/c5hMoXOGbwaN+QGDNoX7j/LVx86xzuftYO/+qULuPPYIv/ru092fB1oz7X6acagiVXSvM/ff5Zjcyk++uYruHaHhT5cPBkj6PXwsTtPMh4L8vYbtnd0Fd1jHV4+zVtTfH/szlP87bee4Ppdg/ztS/ezddBq3v759Zfxog/cwV98/XE+/tarOv5UAdMkI8QqScHff+9JvJrG+19zCQMRP7998y5+++ZdfO/xGd756Qf5xF2neNv1nX02mjBo0/Esv/GZh9jcH+Kf33AZEb+FML7s0nFe9a9387ZPPMCX3nkNYX/7j4yzacKBtCyk8vzRlx9l31gP//TaS/B7rAf1P3/lSm5+38/49U8+wD+/4TJ2j7Q/t6ZrOh4EJcxVC7//53cOc+h8go+++QpusVnOSzb1csmmXt71mQf5068+xvtec0nb17I+WxM56uFZPnffGX79hu38j+fvRdcEz7twlGt3DPCHXzrIP3z/SZ5zwTA7h9v/bE4Gof6lfs+3nmA+leer77qWizf1AvAfb7mSd336Qf7sa4+xdTBUeS/avl4xB16N8YE9Nb/+qXtOc8exBf7XKw7w2qs2V379fa++hFf921389Tee4B9ffXFn13IU3Loj2RuGyd99+zATvUE+8LpLCXh1fvnySUzT5J2ffpD3//Apnn/haOUdbCecuaP++X/w9DL/ccdJ3nD1Zn71mdsA+N7vXs/7f3iUj915kv6Qjz98Xu39aBWyQYvUPSsz8Rxv/o/78Hk0vvzOazkwaSGLLzgwxqs/fDd/9l+P84HXXrJuhrBeKv2XX3+cctnkG7/1TLbZ9+vXnrmd3/jMg/zddw5z0WSsY/az2QzauZUs/+cHR7hl3wj/+5UXVT7DD5+Y5Xc+/zC/9bmH+fyvP6OjzyYLKwFQt3Ptb7/1BCcW0nzm166uoN0XTcb47c89zOv//V6+8zvP7Fhp8LKhK7g18wRps/aA/9rD5/jPO0/xlmu28Je/dCG6Jvi1Z27jf3zlMf7pR0e5etsA1+zobN+d186RZt39mE3k+NOvPsYVW/r4zNuvruTIM4sZXv4vd/Kbn3mI7/zO9R0xCWsVVt8/NMsdxxb4m5dcyFuu3crbrt/OXccW+OOvPsabPnYvn3jrVdywu7MdjCX7M22K7aj59eV0gbf8533kimW+/K5r2T0S5fn7R/n1Tz7In3z1MfpCPp6/vzFa3iyCTnMLhwFEoWTw+188yFDUz8ffeiW77DMlkSvy/Pffxl9/8xDf+M1nonVyHx3KgnqTkFuPzHPrkXn+7IX7KnXHsbkkH7vzFP9xx0lGewId1yMyjzRq0P7y64/z6Lk4H37j5Tz3wlFefeUm3vXpB/n9Lx7k/EqW37xx57rziL+uQH33t57g43ed4kUXjfG3L91Pf9jHXDLH895/G7/7hUf46ruuw+fpDPP3WLD7KgZtajnDu791iGu2D/DB111KX9hH2TD5k68+yod/dgJM+JMX7uvoWvJda8TWfeWhKU4vZvj3N1/Bcy4Y4bdu2sX7f/QUH/7ZCZ6cSfCvb7ycwQ6VNr/qn+R3mUerY/2zhTLv/PRDFMsGn/q1q7lgvIertw3w0g/dwds+8QAfftPlTPZ1xmzJHFnvhnlyIc2vfuJ+JvtCfPyXr+RZu4cQQvDjw7P82ice4N9vO8F/u2lXh9dy5pHae/KZe84wn8rz7d+6ngvGrWYnkSvyh188yLu/9QTP2jPEjqH1zZKN9Na+N2XD5Dc+8xBnljJ8+m1Xc+2OQS7Z1MdffO1xPnL7CWYSOf7pNZ2do0FfNY84vQUKJYNf+c/7uOv4ItfvGuSPnrcHTROcXszw0TtOcmAyxksvmejo8/zcm4Sk8yX+74+OctW2fm7eV6XYhRD8xYv3WUXCD47wxPlER9eQCdgpvzJNk4/fdZKrtvXzibdeVVMYbhkI87u37OLWI/P85MnZjj9T0P5Qzo79zGKG7x+a4U3XbFkljXj+/lGu3zXIv9x6vGOdb6MZNCntyhXLfOTNVxBxNGF7R3v44Osv5fBMomP2p2ZtgONefvWhKRbTBd736osrhQfAcE+Af3nDZSylC/zBFw92zFrImSnnDNqRmSSfvPs0v/bMbZXmTMbz94/yrmft4KsPn+t4vq+Z4+Zn7z3DaE+AP3renpriKRrw8t5XXETAo/N/f3yso2s1i588OcuXHpzinc/aXmnOAAJenX9+w2VsGwjzu5/vnNlNYKFqExPPqPxavlTmAz8+yjN3DvKaOunk5Vv6+M0bd/KVh6b4fIcIuHPXiJNBs76TBH/0/D0EvI6ZDyF490v349M1/uxrj617BsL5p3LFMn/05YOMxYI1h3404OUvXryP1165iQ/99Bj3nFjs6BrS3CJad4j93XcOkymU+dSvXVVpzsC6j793yy6+efA8X3qwcwRcVPJIlUF7dGqFnx6Z553P3lFpzgB0TfB/XnUxI1E/7/n24Y7vY7MZtPf/8ClME/7mpRfWHIzPuWCEP3nhPu49ucQPnugsR0oZTf21fnpkjs/dd5Z3PmtHjRTp2h2DfPbtzyCVL/K7n3+kY7T9pld8hr/f9BLe+sy/qfzacrrAX379cS7f0ldpzqx/m8Z7Xrafzf0h/vBLB1nucJaqmaHLlx+cIl0o8w+vvKgmR24eCPE3L72QI7NJvv3YdEfX8jaRJhVKBu/59hPsHY3yhqurwMu1Owf53u9ez67hCH/wpYPrnimZGNxb+bFpmrzrMw8ytZzlo2+5sgLC+T06H3nz5RyYiPFHXz7I4enOzmzn+hGnNOkLD5zl5EKav33ZhZXmDKAn4OV/vGAvj59L8J93neroWkJ3Mmi1xd+//ew447FAjeR153CUv3vZfm7eO8z7f/QUC6l8R9eT31uojhk/eHaFLz4wxTtu2MFzL7Qa2ljQy8ffehWvuHSC//ODp/j8/Wc7upYznGMJZ5cyfPqe07zmik186HWX0h+2np/haID3vuIAj59L8MGfHO34GhWb/br7+NHbT2IY8L9++QB99rV0TfD3v3wRL7pojM/ee6ZjhsSrO4AeR0zHs7zn24e5Yksft9h1ZMCr8ycv2McHXncpj07F+eOvPNbxZ7v5zT/k4xf/Hq+6/q8qv2YYJr/3hUc4Npfin15zaaWJ2Tkc4UOvv4wzixne8NF7O1ajyOazPkf+++0nMEz49K9dzbP3DFdy8s37RnjRgTE++JNjHc/tNpNKl8oGX7j/LNfvGqp8LrDetb97+QF8usYnOnzXnDHcX9tIfvLuU9x6ZJ53v3R/BYTeMxrli++8ht+7ZTdff+R8x2dNMNAY6Pnk3ae46/gib3zGZj70+ssqgM6fvWgfV23r579/+VHe98OnOjpHxc9lg+b48SfvPs1CKs8fv2Dvqi5ZCMF7X3GA/pCPd3z6gY5oainNcyIFD5xe5uxSltdeuakh2vbma7ayfSjMu7/5RMe0ccB2MnLOoH3k9uPomuDN12xt+Gf+4Ll7WEoXOi6IK/fJcSM/cdcpHj+X4P2vuaQha/XsPcPctGeYLzxwtiNZZU2D5mB+vvPYDPsnetg3tnq+7/pdQ/zh8/bw2Lk4Pzo81/a1oLpvxOd4Sb5/aAYh4B3PaoxavuNZO4gGPLz/h50dLvVyVLAOsduOzvPqKzc11CT3h328/fptfPPg+XXLhmSYpsnffuswu0ci/PbNqxGwkM/Dv73pcvIlg9/7wiMdJY4FvwUUjPdV50F+fHiO5UyRt9+wvSEi9Ts37+KZOwd597ee6Gjg3+m45kz2H739BPsnenjJxeOr/sxIT4A/fN4e7jy2WJkXaydqJI6On/z7bSc4Pp/mf/3ygRpwAqz35a9fciFDUT//90edPSNFOwGHHc/KdDzLdx6b5o3P2NyQRX3Xs3dyzfYB/urrhzpurOVicScT/4X7LXnQm69ZPWsWDXj57Zt38cjZFb5x8HxH15KFqRONPreS5WsPn+N1V21mosEMwOuu3MSu4Qjv/c7hjvKxLFCdcsqyYfK/vvMkWwdC/N4tu1f9md0jUd79kv3cdXyxY9mc0D288Ka/o6e3es++9eh5ErkS737phatYq6BP5wOvu5T5ZJ6//fYTHV2rkTGUaZp85cEprtrWz/YGaPML94+xazjCh35ytCPJnF5jElL98bcePc/Ucpb/8YK9q/JWyOfh73/5IuaTef5tHfJsqJ1ruu/kEvecWOJPX7CXq7bVsrZ+j86/vOEywn4Pb/9kZ2d2wN9X+XFNYXXXKS7d3Ntw9vclF49zy75h/uF7TzKXbF9622wG7dhcintPLvGma7auYpKEEPzJC/eSKZT5cofgi6/SoFUB3LJh8lffOER/2Mdv3ljLUPo8Gv/46ou5ZvsA//PbhztuCIOGdd+dQM8n7jqFEPC7z9m1Kv8/f/8Yr7x8kn/+6TEePL3c0bW89t+lO4rVYtngmwfP85wLRlYxSUIIfuXarSTzJb7QYfMp67l6WfZn7jlDOl/i/7zq4lWf7SUXj/NbN+3kR4dneeTsSkfXQ9O5/JJfrTE2+s7j03zv0Ax/9sJ9q+bNbtw7zMfeeiVnlzL8w/eOdHQpbwM5djpf4isPTvHySyYazj/+xYsvwKMJ/vBLBzurj53GRo789dMj88wkcrzeoa6RMRT189JLxvniA2fXJXMH8PZUa4HzK1n+z/eP8KzdQzWgkox3PXsHe0ejvPc7hzvKkTVAj/38l8oGH77tBM/cOch7XnaAWND5+TX+7Y2Xc8u+YT7w46OV2bR2oh2J49OuQZONhWmafOWhKa7a2s9lm/sa/tahqJ/3vGw/Z5ey/LCDTrrCoDkajB8+MYtP13jehY2lFz6Pxl+++AJOLWb4zztPtX0tgICdnOQS1ul4li/eP8WrrtjUdLD4kk29XLGlj0/efXpdemz5J/KlMh+57QTX7xpc0+TkdVdtZj6Z5+uPtF/IOecrZNz21DyPnF3hhQfGmv65V1w2wZ6RKL//xUc6ctIb8/Va1y1XkbUfPDHDZZv7msqcYkEvb79+Oz86PMujUyttX6sRg/b5+88ggNeuYc7xGzfuZDwW4N9v73yGyhlH51KcXEjzlmu31iDsztg9EuUPn7ubB04vc8+J9mctsoaF3k1Eq5T9fz18jtGeAM9sMjTt0TX+6pcuIFss8+Hb2i/knGi3lGCdWkjz5EySl1/a3AjkdVdtZjwW4P0/ah+1avS7TNPkiw+e5fpdg1y/q7GEK+DVeccN27n7xCL3nWz/Pubtf3rAMST+pQemMEyzKfCia4L3veZiNAF//Y1DbV8LwG9/QnmwlA2T7x+a4aZ9w0QDjQ0GXnn5JJdu7uUvv36IlUz7jXUjBu2L95+lbJpNJVweXeNPX7iPU4uZjhpCiQ47n4S7jy9yZDbJ79yyq6ms6lVXTHJgIsbH7zrVtdvcNw6eZ/dIhAvHGw+6X7Kpl1+5biv/9fC5jmbfGjVoD51Z5sRCmldevnp2C0DTBP/tpp08NZvi+4dm2r6Wsynz2rJb0zT599tPsms4wrObSBgv3dzH8y4c4bP3nemokPv0+RneNzsPkeq58om7T9EX8vKaK1cXVQCb+kP8z1ccYGo5y1c6mKMKhqo1gJQmnVxIc3QuxUsuHm+YR4SwDF6KZYOP/Kz9fFy7B6367H3+vjN4NNH0e9s5HOXKrX18/r4zHRWNcuemcwfmlx44yyNnV/irX7qg4bsthOA9L99PpljmQz/pTLERtP9psrEolg2+9sg5bt47wlissfnCX/3SBYz3Bvn9Lz7S0Uy33gDouePYAovpAi+7tLFk7IotfTxz5yDv+8FTHbkxexsw8YZh8rVHznHdzsGmcvm3XreNkE/niw+sn42U8e+3nWDbYLgio6+PK7f284art/DZ+850NIsvay3nU3XPiUXyJYOXXrIa5AQYjQX4n684wH2nlnh/BzO0ut4Y6PncfWcYjvpr1GzO+K2bdlEqm3zop509j7+3tMxLkylwNLp//70nKZsm73nZ/obvtlfX+PUbtnNqMcO9HZzZwWAVNPLZ7rM/PTLPfDLf1AiqP+zjg6+7jMs29/K/v3+kbbdp8fO2qBqq0rwnZ5Icm0vxS00ePhk37h1mojfIZ+873fY1ZGfrlJ/cemSOq7b1rzmD9ew9w9y8d5gP/vhoRyhB0P4aNI+VaP/11uMYpsm7nrVjrT/G267fxpmlDP95Z/vDl4ZdqMiC5ZEzKyymC7zpGWu7ud20d5iLJ2P87+8/2XYClglRPoaGYfK7X3iEvaNR3rjG9fwenQ+/6XJS+RJf7AAl2xmxErrPsBq04/MpHj+X4PlNmmoZb71uK70hL+/7YftJqn4Q3TBMvvrQOZ69Z3hNB6GAV+cVl01y+1HrpV9vSMDhlhYuZK+6YhODER8fv6vzAd3xsPVu5Utl7jy2wHMvHFlz5mXXSJRXXDrJf9x+kiMz7RWpnhqbfevHsuh83oXNP5vPo/GbN+3k4TMr3NYFG/nQGYsZf1kL/fgbrt7CYMTX0eEiGzSfY/D+O49Nc8WWvjXds8ZiQd717B38+Mm5jobvK/vrbKDnwdPLLKQKvGCNeR6PrvE/X36AeLbIp+/pIEdWCisrDMPkqw9Pcd2OwYbsmYxn7xlix1C4o2vV5xGwWJ+wT+cF+5sDPUII3nzNFo7Npbi7Q3mqMxZTee4/tcyLL1r7rHnns3YQ9nl43w/azyONdnZ9+cEpgl59TRDrxReNs30wzAd+cqzt5rPGJMR+7+4+vsjh6QRvu37bmrMar71qM0vpAj863D7QeXG+wHMyWbCvlSuW+emT87z4ovE13TyfvXuIizf18qGfHGu7IfQ5GDSvbbn/IztHrgU8bh0M88uXTfLxu061vZ7HuYZHMsn5UpmvPDTFcy8cYSjafFbpzdds5dRihu8+3n5j7ddlg1YtUL/56Hm2D4UbKgxk7BiK8IpLJ/jcfRZD1G6EZD1iA2bS+fWXmzSeYLHxf/fyA5xezPD1R9pnETz2tZxM5HcenSbq93DD7sZgoBCC97xsP2XT5He/8HDbz38joOdnT80ztZzlFZc1z/9hv4db9o3w3cemu7JVP7WQ5uBUnDc+Y8ua5+hv3bQT0zT52sPt38fKLKvj124/ukDAq3H51sYEBsBLL5ng5ZdO8LE7Trbd7Nas67Df7eV0gZ89Nc8rLpvE28TRcPNAiFdfuYnP3XemI3XIr8aTvGdhqeK8mSuW+cGhWV55+eSa5+gL9o8RDXg6aqyDgWqDJt25v/v4NP1hHzfuaT6Dq2uCdzxrBzOJHLcemW/rWvrPm8RRiKpM6VP3nMana7ywxTCxrglee+Um7jy2yKk2EQmPqJU4nl/J8tRsime1MST95y++gELZ4H9/v32KWi7yzOVTJHJFPn//WX75srUfPoDnXTjKLfuG+ccfPNW2ZrkeuXvAliRc2cIkQNMEv/uc3cwm8m3L8yq6aPuSR+dSLKULvP367fQ0QfRlbB0Mc+2OAf7r4XNtJ+CtYSvJJssWE/BfD51DEzRFkGREA17eccMObj0y37ZEo36J58GpFabjOV58UfOiSsbLLp3AMOEL96/PsQzg9qPzXDjew0gLK3HZEP748FzbDaFEhQP2Z3zg1DKZQrmt5//PXrQPv0fj421qzZ0Mmiwgv3dohgMTsZaD0q+6fBPjsUDb0ivncyR/+OPDc3g0wXPXaAbBkrG94eot3H50vm2nLclHSVdFyQw+f42mQsZrrtyMRxN88YH2WYQAUiptXe9nT82ha6KlucO+sR6etXuIj991um3wRav817rmo+fiVqPbBPWWIYTgDVdv4ZGzKzx+rr2CWMp3ZElj2MzgLReM1MwnNopfunic3pCXT97VfkNYH3cdt5q761tYYPeHfbzt+m1879BM2wBFPRNvmiY/ODTLcy8cWSW3dYauCX7zxp0cnk60XezXmoRYufkz955hIOxrOeB+w64hxmKBzmRl+14CDle0u48vki2WV80C14cQgt+9ZZclmW2z2Bce52ez8tZtR+fZPRJpmUf+/EUX0B/28d7vHm7rWppjBkfmyh8cmmU5U+R1DeRdznjhgTG2D4X5l1vbb6xlHRK2LcCX0wXuObHEC/aPtjRA+OXLJ8mXDH56pP1xgRsiFngq5V53n1jEq4um6onKn9s1yAVjPfz77SfbZghlYyYbtWLZ4IeHZ7l533BTZQhY9cGfvnAf95xY4s5j7YEvcsbZWfS+/0dPMdkX5EUH1q4RXnLxOMuZYkdKrPr42VNW4X5LE4ZJxnBPgEs29XJrB9+ZZOJNx+Nw29F5nrF9YM37CPD7z9lNsWzwmXvby5G1NvvWdX/4xCxlw+RFa4BKYDWfQgg+8OMOxgVe82l44f+p/LSSR1qA00GfzssumeA7j00Tz7ZXHwcCvQjTxGuaFYPAQ+cSXLKpt6WV/k17hxmM+Ph6m+qQn1MGDZbSBb784BS/fPlEWzusXn3lJnRN8Lk2C2LJoMkHUb5Yz16jg5axbTDMKy/fxLcenW672HnJppsB2DRyMfeeWKJQMnj5GoiODCEE73r2TrLFctuHtNw5JtPn/aeW2DUcqQzirhXX7Rgk6vfwgyfau5YsPnT7ag+fsZqfSzf3tvXnX3HpJGeWMm03Tdt6rMPxlGkhQd9+bJrrdg62tQ/pLddaDMn7ftheY12/1+17h2bw6qKtvTo7hyPctHeYj95xsm1kMzf9MrLnXwVYQ/2PnF1ZNcPRLF55+SQlw+S7j7dnKvCtl3+LT73gU5Wf33pkDp+uteVQ1x/2cd3OQW57ar6tAqS2QfMxE8/x8JmVNdkzGT6Pxuuv3szdJ9oDX8yaH1s/u/PYApds6m0qAXTGKy6bwDThaw+3l4AL9jWkG9rDZ63nuFWhD5Y8++Z9w3zlwam2WQS/nc7lZ7v96AKXbuptCYYA/PoN21lI5fmvNlFbWVhJF7sfPjGDromWxQdYRWPAq7VdEFSlSdbnOj6fYjlTbFkwggVQvOaKTfzw8Oy6Geu7ji8QDXg40MYenzfZ6Pg3DrZ3H+ude4/OpVhMF9raY/XSS8bZOxrlb7/1RFsLir010iQ/hmFy5/EFbto73LLR1TXBqy6f5Laj8+2vXHnNp+BPqg3dbUfnCXp1nrG9dd569u4hNveH+F4HTJMMoWnkS2XuP7XU1n2Mhby8+Zot3HV8kRPzrdcXOBtdySR/+9FphqN+rmvhmKtrgrdet41D5xMcbJOxk0qekN3s3n5sgbJh8pwLWjtdXrm1n8GIr6P7+N9f/mW+fsM/MTJyEQD3nlji4sneljsMhRC8/YZtHJtLVWqmVuGxG1z533tPLLGSKbYFYr3y8kkGwj4+efeptq4l56UkqHRmMcOjU3Heet22lu6TN+4dZstAiA//7Pi65dI/e2qerQOhtnYY3rhnmINT8baVWPKzyX/Z1HKGE/PpprJ9Z2zqD/Gs3UN88YGzbcnzPDV5xMpf3318msm+IPsnVvsKOGMsFuSNV2/hKw9NcbyNdw2Afb8EV7298tOfPSXzSOt65DVXbiJfMvhGu0CPphEwwWffyGyhzNG5JPvH1/5cYMkqr981xN3HF9p6RrSfywbNNLn/lNXEvPLy9hbxjtizM99/fKatG1c/g/azI/OMxwLsHG7PHvS5F46QLZbbdn17+c3/wIOvvYvx8Su4+/gifo/WdhNz2eZetg2G2957UpU4Wj9/5OwKl29pToE7w+fRuHHvMD98YratorEyg2b//KEzy/SGvDVucmvF8/ePVvaftBMHNt0AwDOGLubsUoaTC2luanOBZsjn4deeuZ07jy225WpUvyPjsak4F4zHagZI14p33LCdlUyxbclQceUZlOKXA9YOrVzRaMl6ytg1HGHLQKht6n1TdBOXDF9S+fmtR+a5alt/2wtrb9g9xLmVLMfnWzdNXof8T9d9lea/XZvtV11hgS/tuJXVmoRAPFPk0XPxtpe6bhkIc/mWPr760FRbeeSW8FYA9kSsPHV4OonPo7G9zef/tVduZjFdaNsZtt8+pEulAsvpAo+di7d1QANcu2OAC8Z62t6dp9VJHH/0xBxXbu2jN9Qa6IkFvbzk4nG+9vD5tna+1RdWD9lAz2Vt5q1XXDZJuQOAoj7uObHE1dsG2lpGOhDxc+2OAb716HRbz0j9zjp5ZlzTRvHh0TX+7EX7mI7n2sojel2D9uRMkpVMsa1CB6x3zTTp2ORCxhPnE+wbi7ZE9MEq9m/aO8ydxxbaaj7r46HTK+SKRsuGScar7TzSzmfT6mz2M4UStz41x/P3j7Zl1/+yS8YJ+3Q+3uZoglxXE/JZReIDp5YI+/S2ikZdEzznglF++uRc24Cxxxtg+zYLNE7nSzx2Ls7VbTTVYElvR3sCbTdNVYmj9d/vPj5N0Ku3pdaQq1d+emSuLQWR11Nbj9xxzFICtXMtXRO8/frtHJyKr0subZomD51Zbvtde5GtxPl0m/lYguEy40jzrGc1kYnWxysv38RsIs/DbRih1OQRj59ErsgdxxZ4/oWtGV2A37hxB36Pzgc7YdEccf+pJS7b0tsSVALYPxHjwvGejtxMg1R35T05k8Aw4cI2l2xfu2OAhVSBI23MIf9cmoSYWMWwRxNc2EaCknHLvmFOLWbaKhrljfPqXkplgzuPLfAsh0Vpq7hm+wAhn96RxafPb8kX7j6xyOVb+to6xMA6yF5x6QT3nFhiarl1Y1EqVxm0lUyBlUyx7cYT4OWXTbRN9ctdYfKTPHxmhUs39bZ9H8N+D8+9cITvPDbdlmRieHAvd738+7zphR+tJKh2C1SozirIxL1W1O+IOTGfZsdQ+zu5rrCRzU6dKoEKo3hFmwWqEIIb9wxz1/GFjpdyn1vJcnQu1RZ7LONGuyn+9qOtC2KPY5ZP1318/9AMO4bCbe+JG+kJcOOeYb784FRH8wGmCQ+dXcY0abv4AItFOzqX4lAbqzt+KbaHh06eYZM9G3l4OsHukUhbhT5Yje5w1N+2ocZ7X/gJfiN2gAv3vpw7jy9gmnB9mwe0EIIX7B/lsXPxtpimyqJqBCsZ60Dq5F17w9VbyBbL/FcbrleV2RE7BTx0eoXekLftRnfPaJRdwxG+dbDzBm05XeDkQprLtvS2/Weev3+U04uZthBip1MeWA3aRG+Qyb7mc3zOuHbHoMWQtGEW4txZ5PUGK81gu8//pv4Q1+0c4IsPnO144bJpmjwxnWjo3Nssbto7TL5kcPeJzmdMHzxtGQNc2abKYLgnwDXbB/huGyBurcRR576TS+SKxpqzbs6IBry84Rlb+MbB820ZQUgX2GjQKu7vO7nEZVv62s4jL9g/SrpQ7sjxVsZj5+KUDbNtENerazz3whHuPbnUFogrGzMdDdM0+eETs9y4d6glWyfjOReMUCyb3PZU689WBXqsuPPYAqM9gbbP7VdePslgxMdHbuvc4Gs2kWclU6yxn18rtg9FuGXfCJ++53Rb51o9g1b9bO3VdtftHEAISz7YKjx1DdpPDs9RLJu84EB7oOpgxM+brrGe/3ZqVmek8yUOTye4vIkxYKN47ZWbOHQ+0bYJXNAUFQbtcfuc399mgybB3tvaYJB/PiWOpjXvsGsk2lYHLeMmW3rWDhotZ9B8mo/peI5kvsTFk+19QWAhO8+7cJRvHjzfEfqXL5V5ajbZNnsmQ859tDNU6jQJOWUzRe1Q7jJu2DXERG+Qz7chF5VLiIUJ8WyRo3Oppo6bzeJZu4dYyRQ5PNPeXpxozzia7uGeE4sdJV+AHUNhxmIB7jjW+uXyORyFUvkSM4lcRwsYdc1CiG/tANmUcf+pJTb3h9qSbsq4ae8wuaLRVuJwxr12EVdvCbxWTPQGeebOQb74wNmWDqNeR6ObL+ncc2Kp4yW1r7tqEwupfBufzTGDhskhewaq3eQL8OID4/h0rT2HOd1nIXH2Zzw8nWDfaPsFqq4JWzKx2FZBPDi0j3e97LNouofbn1qgJ+Dhog4+27NtK/Lbj7Z+Rpw2+4/aUq1LHbv4WsXFm3rZP9HT1kyTzCPysHr0XJyLJ9sHesBC9u8/vdSR6xvAI/ahfkkHn00i8u0w1s5lqKZpcu+JJa7e1t/2Z+uEIXEugvfoPh4/H2c46u9oKe6rr9jE1HK2MpfXbkwtZ0nmSh01aFdv7yfk0/nJk52DWI9Oxdk+GG5b0QDwggOjnLTnRNcKp4ujjqiANRdN9rZ9rbdfvx1NiLbO0Ztje/in2XnGezaRzBU5Mpvkii3tg0rX7BigN+TlK+tgPqVxSief7dodA2QK5bYKYsmgeYTGuZUsc8k817TJegJctrmPvpCXH7fBIHvqGrRHzq5wZQfvWsCr85orN3H70YWOVsmAxcQA7GmwxqhZvObKTSylC9zbhgOzHBWQp8Th6QQXTcba/my9IR/7Rnu463jrRrfGJEQPcNfxBfpCXi7d1H5t98art2CY7YG4znjk7AqGCZe3qR4CeOmlE0T8Hj52R3uMdVBoeO3z7dC5OH0hL+NN3NTrY7w3yIGJGN9+rDVg9nPMoK10VHiAVTTuG+tpi7FwShyl28zmgc42u7/myk0kc6WObJBPzKcpGyZ7OijiwEI2L56MtYUiOWfQ5NzOtsH2P5uuCV5yyTh3HV9smaTkXjcdk4M2dd6uLEmGnHtqB9lxxsGpFS7pgK0Di0W4bucgdx5bbNlY+B0zaCdtVraTZhAs6VUyX+poKbFpmjx4epkr1nBmahTX7BigL+TteLntkdkkPl1jZwfNJ1gW5+dWsi13x3gdDMLUSpGyYXLN9vYPaLCax3YKuXpg/PFzCbYOhNqa0ZIRC3m5ed8w33jkfGtkUxpA+EIspPIspArsGW3/gAYL2VzOFHmiw8W9dx5f4Nodg22j7AAXjvcwGPG11VhUZtAQlXd7fwcgFsDLLpngielEy7kfrz3noGGtDjg+n2L3SGfP44svHsM06fj5P3h2BSE6K1An+0LsGAq35S7qZNCO2fNn7cqgZLxg/yiZQrklQFE/O/LkdJK9HTRMYBlTxYJevtCh5bhcPN1Jg+b36Fy3c5CfPtnePKszHjsXr1kC305IOXyr0YRaiaPGofNxNveHOmoGh6J+rtkx0JYSJeQNcXMmC94QpxczmCYd5RGvrvGGqzfz/Sdm2pqxc8bBqRUmeoMMtjHrL+Pqbe2zMRUGTWgV06B2Zj0rf16zz+w25n4qgDGCdL7EuZUsuztQD4HlDFg2zIpDaLshm/69HdR21+8aJOjV25r59zokjvlSmVOLmYY7bdeKa3cM8NCZlZZAT826Do+fx88lODDZ25a8V8bmgRAXTcb4VocNmswjnTwjPQEvr7nS8oVYbGMnYIhqg/b4+Tj7J9pvdMGSpx48u9LSqfLnblG1AOYSOZYzRfaNdfbwAdy8d5gHTy+33PcjO1vD0DkjG7QWjor1cfW2fvpCXu5sQy4nQ+7P6QRlkfGM7QM8cnalJWNXaTxMOLWYRgg6QlABXnTASlI/aNF8ehzb7R86s2wXOp0dmmOxIFsHQm3JDmWsZAqcXsxw0abOrgVWUoxnixw6v/YAt89heXxiwTr0OmHQwHpGLp6M8ZkOLMdPLWZYSBXanj+T4dU1nr9/lB89MdsRY/fUTJLtQ+GOCn2gYuBwdwtEzskgLKatJNiuvEuG36Nz7Y5BftbCmKTGJMSEQ9PxtrXlznj5pRMspgutn0nJWHjDFSnTjg4LAimZaHfoHixGd2o523GBqmmCG3YNcdvR+ZYARcVmXwgOTsXZMRTuqNEFi9USojWK6pQmTS1nKJQMdrUpgZWxYyjCBWM9fLPDhdyHzifYMRRZ01GxUTxr9zD3nlhs+a4513XcY+/r6bRBu2bHAD0BT0sjCOdSWaF5OTafYm+HgEHAq/PSS8b5/qGZjtQhR+esHNlpY33T3mHOrWTbmumQMZfMMR3PdVTEgXXWjMcCLU2pnEyk1aAlOhq3kPHcC0Y4MZ/m2FyLpik8BEKH8OC665FfuXYbAjraYwpWo9vpmd0XlmxMG3K5SoOm86g9utLpM3nNjgFmE/mKIqhZyJUWAgsMh87z8YXjPUz2BTueZz0yk2QsFiAWaj9HBuxZvO88NtPSvEPOsppCVID+3eu4j4WSUZnxbRa6p9qglUwfT822Z6JRHzftHeaxc/GOVkBMLWeJ+D30dXAfwXLhLBlmW3VkUPPgE4JCyeDITLLp7stm8Vxb6nxrizNb+/9TgyaE2C6E+A8hxJcdv7ZPCPFvQogvCyHe1c7fM21LVHato4m5ed8wZcNsiWxKBu2Oo8ucWszg0UTTBY3NQgjBFVv7Kzb27cSRmSQeTbRtouGMZ2wfoFA2Kk6JzaJcYdBMTi9mGI8FO5KKgpWkNveH+E4rZyjdKmp0E47Pp9nUF2rLLa8+btk3wp3HFohn2rNKlZKriztAvWVca8srWun15cwgwNHZFB5NdMyyWoPwIxyZTZJqM0lJlHE9n+1FB8ZJF8od2fc+NZvqmPUByyxh31jrQ9rjkDjOpw2EgLHe9qWbMp69Z4ip5faMSQDShRJnl7Jc0CGDANZsWNintwQokEijL1RBrncMdlYQjPQEuHhTb0dM/HoZXYBn7bEkxa3kSZpjBu3UYrrjhgmsRakXjPW0HLp3ShxlMdtpYQWW5f4jbSCbzjg21zlbB3DD7kHyJaPlklSfr/odHZ1NEg142NTf2Vnj1TWevWe4ZfGhOxq080mTQslYFxh4095hCiWDB063vwD2xHyakR5/x/n/Rlt2247M8TnBSbZrQQ5PW81cp4UVWAqPh1qc2c4ZNNOE04uZdeUROat7RytJ8d4XwX+7HyLDlQat02dkKOpn/0SsLQmbjFyxzJmlzLry/zU7BnjwzHJrNsautTxC4/HzCXZ3OLoCVUCjFfPpZOKPzVvPSCfz92Cd2c+/cJQ7jy22ZXAk4+RCmu3ryMcvv2zCku+3eEac+xQl0N9p3rpyWz+agHtandmOPHJyuUTJMDsGQ4DKO9MJ+HJ2KcNkX7AjRgusMYaegKctwmR3aJydvj6emk1SLJsdgy/bBsNM9Aa5s1WfobUG/dpq0IQQHxNCzAkhHq/79ecLIY4IIY4JIf54rb/DNM0Tpmn+Wt2vHTZN853Aq4Hr2vm3yOiUrQBLphILelsmxIo21NQ5dD7ORF9wzcWCzeLKrX2cXEi3be98dC7FtsFwS8vXRnHF1j7r5WqRpGSDZhjWw95pogfbUODAKHcdW1iTjRzw99FfLvNH8TTTK1nG2tTx1sdLLhmnWDb53qH2UCu5g2g9qOZQ1M/e0WjLF9nvmEE7PG2h7O0auzjjwGSPxea0uRPqzDoltwDP2N7PQNjHN9uUFSRzRUsGso4iDizJxAOn1z6khV5NUnOpMsNR/7ruozQxWav5dJJr51csoKdTtg4sZPPZtpvpmkzTxOWw7Qbo28qJhTQ+XWNiHdd74f5RHp2Kt91YSHOK9eRIafTR6vmvShxheiW75nL2teLKrf08fGZlTbmoLAgE1Qat08IKqOwo/E6bMsdcsczpxXTH8l7A3j+k8bMWclGnG+ypxQxbB8IdFx9gzcjNJfPMrmHL7SysTi1a7+R6iu+rtvXj1UVHqoYTCym2dwhOgNXEXzjew0/baNDe9+rv8vU33cdTdv5fz2e7fEsf5+O5Nc0LnBLHctn6rrauA1Sd7AuxuT/Ena2YJk2HgR2Alf/7w751AZ3X7hjk4TMrbTMWU8uWnHI9gPG1ko1p0exWbfZ1Ti2k1/Vebx8MMxz1t5RUSvdBIQTH59LommBrB/P3Mp6/f5RC2WjrmZRxejHd0ay/jJv2DjMQ9vFfLVa7ON1g1wv09wS8HJiItQTMpMRRM02Ozlu1bSfSZRnyzzw53UGDtpzpWPEFlhT22h2D3HG0tRT2j171df7+Dbdywla9dFr/CGHtDLzr+MKazKebJiEfB55f94/QgX8GXgBcALxOCHGBEOKAEOJbdf9r6nUuhHgJ8G3gOy3/Ffa5FfF7GOlpXxMtw/qSBlp+SZJBw9Q5eHalYzmBDClDa9eWdTaRW3ehE7VfrntaDJRKk5CyaTKXzLdcdNwsXnRgjJJhrolser1BfnbmHM/LFpmOr/+zHZiIMRYLtO1CdT6eJezTO5oJcMb1uwZ54NTymhIen6/60j4xnWDvOiS3UDWoeKzNBu3UQppY0Nux5AosW+5b9o1w21Pzbe07OW1LRtp1y6uPdg9pGdMJk4l1PiOTfSF2DkfWlAKaDpGjnJ/slBmXceOeYRZShbWd+ob2wFu+Cb4wJ+bTbBkIrQvokbv12i2Ij8+n0NfB6IK1x27PSJT7TrVgERwMWrpQZnwdrCdYwFK2WOaJNVwxhV6VSp+YTzMY8a/r3d7Ubz0j7a4/ObWYxjBh5zoAioBX5+rtA/zsqbWLOK9jltUq4tZ31kgZ2mNr7NaS0iTdNJlOWUX6et63kM/DZZv72pbvm6bJ8bnUuhgEsJ7/B04vt70T6qnZJENRP/1t7PasDykpXuuzORm0gu2KvN6z7dodA9xzovXMswwLVF3fM3LdzgFKhsl9p9pjPk8tdG4iJkM28a0WZEswXNM0zq9k1wVgCSF4xnbrPq4pcZfXssc7JvuC6wLDL9vcR9Tv4YEWOVJGPFtkOVNkyzq+N69urTa6vYXs3LlP9PHzCXaNtLfOoj6esaP1qIwEejwmTMWLCLG+53+iN0jE76kYqLQK0zSZWs6ui1QAa1b9fDzXUgor47TdoK2n/n/e/hESubX9BVwzCTFN8zag/q2+CjhmM2MF4PPAS03TfMw0zRfX/a/pW2qa5jdM03wB8IZ2/i1gyVvWgzKCJU86H8+tKT0RtjG8aXpI5ErrLhovmuxlIOxry2EIYCGZ72gYtz7amUOTJiGlssFsIsdwdH3X2z8eI+zT1zaBsA8yU2jMJHLrZtCkXLTdhdWziRwjscC6n5Hrdg5SKBvcv8ZBpjmYn+l4bl0IEsBwNMBYLNB2g3Z6MbPuYgCsJJXMldq6nnS8G13n93bVtn50TXBnm7Ka84nyutAxGdfvGuS+k0tNm89GZ/d6n0nJzh5u07zj5EJ6XUg0WFLFoai/7cbixHyazf2hdR3QAFdu6+PBU83vI1SH+zGtd2y9z6R0o1vr3S5r1WbwfHx9RVz1en08eHq5LVfMo7M2W7cOBg3ghl2DHJ9Pr8nGOF1Mp5az60L0AS4Y70ETlsNls6gWViYzyTI+j0Zvh7McMq7bOcih84m23OwW0wUSudK6GF2w5kdMk7bXTTw1m1yXLBWsnZEjPf41xyCc0qRSyXqO1sPEg7VuJZkrcXKhPfOOM0uZdQPGV2zpx6dr3NVmY31q0SpQt64DNIgGvFy7Y5AfPDG7ZtMkJY6moVEy1g/QPWP7AHPJ/JprCwwboNMEFjgdXV/u1zTB7tFoRanTKs5U3LLX973dsLu17Nznq/7dh87F1zUTBtaKqGLZXFO+LKXSOibn41YNuZ5GV7PnDdtZWQMWqJoplNm0zhpBzsW3lBTbcXIxzVgs0PbKB2fcuGeYyzb38i+3Hmv6e1Tb7E8ATiunKfvXmvxjxIAQ4t+AS4UQf2L/2rOFEB8QQnyYJgyaEOLXhRAPCCEeKBSsw2A9CUPGyy6ZYCwW4L3ffbLp70nn7cLEtG7gelkmaaX+0yfnWjq+mabJfCrP0DobJrBsiQtlg4fPNi92ZGGynCmSLxkMd5GkLhyPrV3oVxo0QdkwGeuisbhiSx/T8RznVrItf+9MPMfoOr8zsFyofLrWkYSn08FmZ+yfaHEfHXFyMb3uQwwsxBZoa4B7JtFdgxYNeLloMta2A+f5hNFV83nRZIx8yahIE1qFEOv/bDuGInh10dKSGyww5PRimu3rLFAlQnz38bURYhnnVrLrLhgBrto2QLpQrszyNAppEiJJyfV+b6OxAMNR/5rP/1DAkl2+Pm+BIWNdvNtXbO0nkStVTCvWCulyu17mR8pu13LXda7rKBvmuou4kM/DruEoj61RxFUaNGA6WWS0pzsQyzTbc+qTsuz1fradwxEuHO9paYIC1vl2dC61blm2JU8a4o6jC033eAlHg1YsgVcXDK0TWJXnRjt5xDRNpldybVt+10fQp3PZll7uPNZePj69mCEW9La1fL5RPPfCEU4vZtY0QZENmmFYz+F6wZeK2/MaIFbI3su6zdBZSHZXa+0ZjXJkNtlWPj69ZOWR9TCRANe3werWmm0VOjaIknHl1n48mlizPvB4qnnk/Mr6lVFgzXw+NhVvy7hM1n7rPdu2DISs2bAOnv/15iwhBC+6aJyzS9mmsnPt/082+6ZpLpqm+U7TNHeYpvle+9duNU3zt03TfIdpmv/c5M99xDTNK0zTvMLvsx6M9SZDsJLUG5+xhYNnV4hnGw95ZvLS6bC7Bg0s9CORK7XU2cazRYpls6ukIXeMPXxmpenvkQzaefthH16HVFTG/okYh6cTzZF22+1KgtXrPViAyqLM+9dgPnPFMlv/+Ns8dGZl3YU3WM/I5Vv6Wkoq/3z0Rv5o9LeB9UmFZFw0EePEfJpkG0PH88l8V8X3QMTPruFIW2zkbCKHJrp73y7d1McTaz0jjsiVdAYj6ysGAC4Ysw6lZnK5+rN0KOLH26E7pQyfR2PHUKQtBu3cSpZi2Vy3VBQsZLMVQixjMd0dE3+VLc2+92Tzg2w1g7b+9+2iyd410eFooJfHTp7h9QXNAl9cyCOtzJQAphM5+sO+jk0LZOwYijAeC6xpf++USsP6iziwAIrHzsWbFo0er3XfPCbMJPLrGhOQcfFkjIjf09YS6bkugR6wQLPHzsVb5pGVbJFMobxulgnghQdGiWeLTb83J4OWL5mMxYIdWYw7Y+dwBF0TbbExK5kihbLRVT1y3Y5BnphONK19nHGqC8ktVBmLtdRKcpykZNfnk+s8R7cOhBjp8a854rEtNMK/zMzxV6UI8102aHtHo8SzRWYTrf0F1uu8KaMv7GPHUHhNtZJTKg3rm78HCPs9XLNjgG88cr6ppFIyaF7TqiO7adCu2mqRCgdbrOMBmLPvdSf7X50hhOCSTb1tSypPdaF6AbjEdhFv9tk0xQzaOWCT4+eT9q8pCzk/NdBF8QFUtrk/2aS4Mk3N/q+ViLs5yOTS6bVYLYAFez9DNwVqb8jH9qHwmsWHfOnmbOOS9TJoYBUEuaLBsWZzOJrdoNlo+3rnfcBy/BkI+9Y0gVhw7LjohkEDSwp4eDpR83fWx2ue9wHMnucAVhJdb8j9UY+fay9xdFMMA+wd62mrIJhN5BiM+Du22HfG/okecsX2WK0S3nXPDYLFdPg8WtOdYSa1B8565Y0y9o31tDXgLC2d18vEgGXwArScMQVYTBUY6OJ5HI0F2Nwf4r41CivNZl5Mw2IQBsPrz5EXTcY4sbAGQGE3gwaCVL7U1fO/pT9E2Ke31VjPxnNdFcNCCJ61Z4g7jy00VVA4pdLQXd66aDLGQqpQcTpefS0fmmniobv5Y7DmWS9oO49YObSb60l2vBXzuVg5R9f/PN6we4i+kLeppLJmBq20flkeWLOKWwdCa7LVMmaT1vfazX2UZ02z2scZ51eyXX22zf0hBiP+NcFAjyYbNOsdXy+DJoTgmlYqg4EdXJ/NoV/zeyTzpa4aNMnQtlPszyXyRPwewuuYG5dxyaY+HjnbHHxx7hOFzlcnOeO1V27m3Eq2qXOk18HEn+vyGblyaz9CrN3Ey5C1WDff246hMGeWMuRLazN2qXyJxXSBzf3rP7MvHI+ha6LiKl4fqhu0+4FdQohtQggf8FrgG138fS1Dsj/dNDFQtfdsdkjLBg26Z9AmeoMMRf08sgarBdWGqZuHDywW7aEzK01f5HpUpFsGDdYYTLcPMsO+n900upomePaeYW5dw+DCOXvXbfEth8Vbzf3IGYzeLhoLaVH7eJsyx26aarDQv3Mr2ZaM3Uwi3xXqDZ1+Nq2rBs2ra+wdjTa9Vv0r0Q1gALBvLMpMIsdyizmcE5WF8OtP9tukU1mL5zFTKJEplLsGsa7a1s/9p5aa5hENCWJZTOR6GQSwim/TXAugsOdm7dd+tIvvTdME+8Z62lr8PZPIMdpFzgK4YdcQyXyp5cL2FxoW1jnQxdl2wF690ZSN1Dzo2AxalzJwgJ0jEZ6aTbWUec0mcng0Qf86pXJARbK1lgkKwELKehe7ASi8usZ1Oweb74MSGrr9mQul7s+avWM97QEGdqM7Glv/M7nPXpTcjqRyNtFdEy+E4IotfWvOcks2sliCvpCXkG/9Tcwztg+wkMo3BwMDMfjrOLMTzwO6q7WkNPWpNiziF9OFrmvWSzbFWEjlOd8EfHFKpYF1GeTIeM4FIwS9enMG2SFxzJeMrpRRsZCX7YPhlntnodqgdfNu7xiOYJhVA7RmMRO3FGbdgIEBr87e0SgHm+RjN232PwfcDewRQkwJIX7NNM0S8N+A7wOHgS+apnmozX/7ukIW5oNdNjHDtsNTM9SqcuAYVoPWTRMjadVWB7Q8WLqRk4E1q7WULjRFGst1h+l6TULAcvcL+/TmxbeNDpcRCMG6tewynm3vaGo2VJp2mqOsc7ZCxgVjPfh0reVs2EqmSDTg6YplGoz4GY8F1hzwd8Z6HBydIdG/p2bXRqO7ZRAAtg9FCHhb30cZ3T4jF03GeHQq3pYrWn+Xh+Zeu9g53AJFPTGfIhb0dnVoyjm0B1o4sC3aeaTbguCqrf0sZ4pN50ecEsduv7MDFSfTlca/wbTyvmzQui2ILxjv4fB0sqVRyGyiOzklwNX2jqa1WITH3vIYsZF/xO/RCK1jIF3G3tEonjUQWzQPHtPEgyBbLHf9bu8ajhDPFitnV7OYTeQZjnbXxG8bCBPxe3i02TNix2LaLuK6PEf3jfUwtZxtvOtKSA9TS5rX7fN/yWQv51ayzCXXdqmctYvzbgC6kR4/fSFvy4YwlS+Rype6fv6v2NrH1HLzORyPsM6yQkl0DTxeZsuXW8nl5lPyPq7/GekN+Rjp8bfV6C6m8l0/jxJ8aQZQOCWOvSHvuqX7YMn3D0zGmo7KaB4/mmmi2+mz22dk53Ck9bJ2rBo5GvCsW3IO1dUzJ9ZyXwZm4t2z/mDJ9w+eXWl41ggXXRxfZ5rmmGmaXtM0J03T/A/7179jmuZue67s7zr9x3cakkHrtokRwnKPebIJ+lE2pEmIlTwGupDvgCVzPLGQXnNn2LxLDNoNu63B9Gb7d8rl6oMS8GpdFfvSKKRpY6FVZ9BiQe+6LMadIQu5ZrKCjL3fxe/ReMH+0a6u5fNo7BmNcqiF7HA5U6CvywMaLIS4XQYt5F9/goL20T+LQeguQema4KLJXh5qwSDL6IZBA4tBTuVLbSGbPevYJeSMdve4TC1n2dwfWrchg4y9Y1Gm47k1mc95FyReYDFoQFNLbk1UGbS+cHf3cSDiZ6I32Lyx6NsKwxdw7wV/CnQvX75grIdUvsTUcnPDoXypzEKqwGhPdyxrf9jHpv5gy8XfCylrbrCbZyTg1dkzGm0OhmgePKaFfEN3wCNQWU5+tMW7NpfMrXtuRIamCfZP9LRk0KSioRsmEqoqm4bvtoNBK5UhGugOMLt8q9VYPNjCtl02Od0CxvvaYOykg2+3YMgV9jxrM0t6KXEslmEw2t13tmMoQsint27QXKq19oy2J/G13u3uPpuUx0tnzfqQKzSGS2bXuR+smvWJ84nGUkDJxNswxXp28jljx1CE04uZlkZ688l817W/VLEcn1975EK+a92eNZdsipHIlRp+b/IMXSs2zCTEzeg2+YL1UJycbyzPKNuIrWnfnm4bi0s29QKsyaItpPJ4NNF1gTreG2T3SIRbm+zfcTJoPQFv10XjmkYh9gNYNruTt8jY3B8i6NWbolYZm0H78juvdSVJ7Z/o4fHzzXXfYLlhdjN/JuPARIyTC+mGiG09+tItgzbRGyTk09c8XKaWM8Szxa7mpmRcsaWPQ+fia65/kNHt8y9NIBrJk+q/xm6vNRT1MxjxtSx2VrLuPCMS/VvrcJEMWrc5cstAiKGov+kcmkdKHA1Bb7D7z3bxpljzBs3jh9+4mycClwHdF1a7bAb52Hzz53/OBTmZjIsnezl4tnVj0Q3DKkMyyA1zlhB4MPHY/1e3zI+0sm81FzabyHUlb5dx8WQvh6eTTd0VwULZhaBr0GzfWmMQmu4onDR6uswj+8dj+D0aD7QwbppN5ugLede9PkPG7pEoR+fWlqbKBq1bBuHC8R4CXq2pzNHJoHV7ZuuaYP9EjIMtmnjXGrSRCEfnUi3VGoupQtcMWk/Ay0DYV3GWbRT/uu/X2Zz/064kgDIu3dRHoWw0NtwSGh7TrDj5dluP7ByOUDLM4pAk2AAAXClJREFUlrLD+VR35ldgmaBM9AZbMp/Swbrb5/9iu/ZvdLZpbkkc//8W3TJaAFsHwyRypYZ7XCSDdsXmAW6xl8R2ExdN9iLE2g1aPFskFuy+YQJLi32wyUCpM5l0M7QqY/dIhFzRqDzQNWE3ugZi3ft2nCH3jzRjLNIFi0HrlmGSsX8ixkqmuCbSvpwu0OfCZ5MShkYsWr0stRudPtj3cWTtPS7SjOIZtkSrm7hyaz8lw2wp8wW6fk4294cYCPtaznxC9w0a2EYhLZJ9wn63u42dw3aDtkZBLE0Sui0IhBBc1cbuwVLZdOXdPjDRy5mlzJoqg6V0gZBP70riAtagOMDxuebFzqxLBzRYjcW5leyahkNL6YIrwOOBiV7i2SJnlxrnLItBs86Yni6Zn6Gon56Ah6Nzaz//3c4yyTgwGaNQNtZkxxdTefpCvq5B1TWlgEKrFk6m6JpB83k0Lp7sbd2guXQfdwxHyBTKjc9sO2ZcYhC8usYlm3qbGpfp9hhEodg96w+Wu2gr1+DljAWCdtvE7xntoVAymrJaYI3lLGUKrny2rYPhNV18n3nVb3E6M971CBA493w2YpAFHqgAPd3WkfJcO9Yijyx0uYZKRjsM8mwiR0/As64daM7YNRwl4NUa1nU/twzaepbi1Ye0vG70wEsG7YUHxvnoW67o+loRv4fdw9HmCDGQzJW6RuJkbB0Ik8o3az6rxX438w4ypFtQwyYmZMkbPut7lSsyQIC9I833j0gGLdxlAyNDMp9Nh8VxUeK4huFKPULXLWIFsGckumahc/fxRfrDPvasc5+QMyrrH1o4mfo8WtfFtxDCmjFqIIOtd3HsCXZ/H/eOWvdxrYIgni12XQyD1Xx6ddHcNRV3BqllXDBuzeE0klSmK6tINFee/4ukCcQaMl+33rXekI+BsI/ja9zHilTOBTBwty0pPtGC+XSDQbvYtnZulrN0pPUVXZ83Qgh2jUQrC70bRaFkEM8WXSlQq7OKzZ+Rbh1MZawpBRQaWiWVCFfe7cu3tlYZrLj0/HcCUHQ7X2RdL1Kxmq8Pjz0GUTJ0V56RfWOyaWrOxqTyJQJeras5LaiOCqwFdC5niphm9zPBYNV1azWDYMspXXj+J/uChH06R5qMk3jM6i7MbgGKXcNRogEPn7z79Jqs7kKye6koWM3nifnUmu+aG/PHYLG6m/pCnF1e/Txq4ueMQQt0Se07Y9uaDZr1xXk0927PloEQ59ZgYhIuFXHyWgCnGyRFJxvjRiMjd3I1bNC8QfjrOJ8xnuOKxAusYmcpXWjYfKbz7jJoe0d7iPg9a7pQrWSKrjAI/WGfNYfToPioz1lufL7do1EW04WK3KM+Dk8nuHgy1tVgv4xYyMt4LLBmIQfuMFogm6bUqqbJbYmjda0e8mugqKZpusageXWNLQPhNQeq55P5rgepZewZaT6r6LOLG0H3rCdUHWHXArGW04Wu591k7BiKrNmgSTY+4kJO3mLvP1rrGel2d52MvaM9xILepgukPYBuulNYgWUUspbEUTb3bjz/k30hdE0w1aDYkbGYzrvS6IJV7B+ZTa6WsAkN3QZ7TLSuZ1nBkoG3UhkkcyVXVC9VqXTz723OZhDcyCOjPQGWM8WGy4ilxNE0dVcY5N1r5CwZyVyx67kpsJgfTazdoC24NBMMsG0wxGwiT8bOTfVRKBkkciVXriWEpVY60uQ+6oBm55Fun8mgT+e/P28Pdx1fbAosyc/WrTIELODRMGn62UDuiey+QQOrRm5UHwtNR7RwwH1aNWg7hyM8/jfPc+XvmuwL4tFEQ0tWKXHU23BZaTdGegKVPSaNIuFS0oBqg3amAYrkNAnplr4FGOsNIARrHpoW8u3OZ5MzUY2+N8mghVw4VMBCPy7b0td0wLlQMkjlS67M14HFIrQlcXTh87UyCsmVyoRcKAZk7GohqYTuVhU4Q6Ko9eBLfSp0o7Cqzqo0n4ssGaZrzefOFo3F2eVsVztwnLFnVO76Wf3ZKvIMU+t6lgmsAn7bYHhNM43lTNE1Jn7HcHhNRiuVt9l4F8CQib4guiYa5mOwnpFc0XClsdA1wdXb+rnzeOMF0h5EBfl24/nfORxhKV2oSGvrI5mzikk3mkFdE4z2BDi/0vwcXXRJKgpWjswVG4AvQlQKJ2EKV87ttWZnZaQLJVfu43DUT8TvWdPJLpkvuVaPjNhMxFyDpc7SatxE69oAAtprmpK5ElEXzjZrh114zWsturD2QcZWm1RoNqvlloOpjD32md2I1fJgMWhCuFOP3LhnGGjO6qZs8N0NEqPVmi2w2Do35JRgAUtnGzHITql0k3haNWhCuCPvAmvR5kSTztawJY7taETbjZEePytNUCSQEkd3PttkXwghGr/INQyaC8WH36MzEg00ndPK2sWHG0UcwI7B5jap6UIJn0fryvK+Pi6ZjHFktvFg+krW3oHmUvO5fyLG6cUM8UytpKwewXXj8222Uf2GiQOr+fS7eB/3jEY5Nt94oHrIvrfuMWjS/n7thtCN6+0YDuPRRNNkH89a36Vb8uWdw5bjVTOjhDNLGTb3d+c8KGOyL0jE72lYgDhKVNfAF2lw0SyWMwX38shQhMV0oekOO8nGu3HeeHWNid5gQ0UDVOWUbgE91+wYYGo5y3R8dU72YCHfbsiJocpYNEOjpemRW8X+eG+A8yvNlSjpfImo3z2gBxoXclLiaKK5cm73hiwFxVrMTzpfduXMFkKwYyi8ptlQtuDOtaA6x9lo5s2jS6dndySOAa/OloHwmvcxlS+5woyDda6txcQs2zO1biiItg7YTo5N5tASWStnuXWO7h6JspxpvEZDN608EvZ5XFHZjMUCeDTRVGVQVUd1/72N9wbx6dqactF0oeRar7GpP0giV6rUApVwAD3N4mnVoLkdY7EA0w2SvWTQ3GzQpM1wM0mZJXF058UKeHXGegKcXmrEDjpn0Nx7AJsxaDJBuSU7megL4vNoDQ+XTL5M2AVW0BmTfSFMk4Z7XGSR7MZMJFRZrfoZo1aLYNcTo7EAmqBpsVMoGa59LrCkUIWSwekGSTGw8l7EkT9wj2UajuDVVzdN9ffRjev5PTrbBsNNd8olXJR4gfXZyobJmQbvtmmanF3KsMklBk0IwY7hSEOmSbMnmYRLDBpYM0bT8VzTfVDL6QL9LjWDlX04C42/t1SuhCYg6BIbv2UgxJkmBYG0snZD0QDVxqKRpNiDQDeFa2eNnAtrJs2TDJpb8v3x3iDnGzSeMjL5smv3UTIWjcBHmRlNU3Ot+dw+tLYJRCrvjsQR2pH4ll2rD6TRSKMzVLdn0ExT79pmX8bukciaTVMy5w4TCdY806nFdEsG2Y33TT6PJ5vkkWxR5hF3zm05vtII6PEi0BCuEiab+kNN2cGK5NyF6+maYLI/yOmF5qqvTN69518qWlaNOAkN7edJ4uh2jMeCDQtUaRIi6B4ZkDGyRpICKXF0T1K2dbAxQlbj4ujSQTbZF2oq35HosFsou64Jtg2EmzJobr1UMuSgaKPnRK7L01xw3gSHNLWu+G5n6XKn4dU1RnsCTDVr0MoGfhcbtIoDYaPG2oiSMIZ463XbXLmWz6OxYyjCk/UNWt3vc+t92z0SbepAJdlQtxo02Vg0mkObT+bJlww2D7jToAFM9gY51/AZEZX/unVIX7SGk2mpbM0guNUMbm9hlCCLYTdcdcFirJsxaLmilUjcet/WmjF6Z07wkrTPNbVGX9jHjqFw0x1eiazbDFqQmXiu4eJX0zTJFMuumF+BVQxG/Z6K5bwzqt9U9y6OMrYNhjk5n24IyBVKBoWSQcSl823HcITpeK4iHauPTL7k2n1cq0HzOBo0t/LInpEopxczTdVKqZx77MgNu4cwTbjtaOO9s8kKg9z99SJ+D0NRf1MGTX5et7waxmKyQVv9vQUAr6G5xrKCzJHNGDR7fMUt8GUg3DQfl8oGhbLh2rWqPg111/t5kzi6HeO9QWaT+VUFsGGbhLg5g1ZNUquRlkLJIFc0XEM1wS4aG7gd1jBoLiWpbYNhzsdzDV1xJIPglsRLXq+RS5ObsgwZ473N5RlSLurR3SnimklT62fQ3Irx3mBT45p80V0GrYoirf7eSobJKy6b4Jm7Bl27nuXAVts01d9Gt6SwO4ctl7JGBYGUNbjWoA1bjUWjBk06RbnFoIHFWJ9bya4qiCviDFOrHEDdxoXjPWiChjvDVuz76BYTP9kXwqdrTVmEdN69Ik5ebyVTrEh1nJG3mXi/S2zdYMRHLOht+IzcXPawN+9z9ay5fEsfD55ZbthYVBgElxrC8d4gxbLZcGVBoWxQNkzXWCawALpGDZr8pnRN79oNUMa2wTDJfInFNQyw3JLmSSfHk01kjm4yaD1BDwGv1vA+Vho0undVlLF7NErZMJvOmKbyJSIuyWD3j8cYjPj46ZONG7REroiuCdeK/W0DYU41YX7k+eNWHpHgdCOV2V9lNV6RjBBxMY9sHQhxeiHTMI+4KTkHuxlcbAyGZIruNoOy9jm7qtb6hcRxzRjrDVA2zFWSGsP+0txl0Cx9dSMUKamgidk1EiFdKK9Cv2saNJdeZIlGN5JnpOSQuEsJEWAw6mvs4ujioSJDokiNBtPlvXSLQZPS1Ho20mju4N5VyOK7URTK7jZogxEffo/W8Hplw8Tjgo7dGfvGoswkck1njNyMXSMRDLOxjXplBs2lgyzks1DURrIr+WubXJpBA2upeaFksJCuK4htB68Lx2OuFcRhv4ftQxGeaDDzI79Ht+Y9dU2wrYnKACw23s1Cf0wWOw3kQlLi6BaDJmeMGrp9ah7yhu7qWXPxpl5WMsWG77brM2j2fWzE/EuA0C1ZKtgNWoMzW35TXn1jnKUl0+XWM7m9hZNjplByDewUwjJ3aTiD5rEAl7LprTjDdhtruc+Cu2olTRNcubW/6eoHKad0i4nfOhhqKnGUTLxbz/9A2IdP15hu8L3tN70MFH1EXATEtwxYAEWj2k46V7pV320dCJEplBvO18k84ta1+kJewj69AYMmHOs6Gsf/0w3aeK8svuuaGFviqAv3Hr5Y0IvPozU8oBMuOl3JkMPb9XMIzgbNLa3+9sHm8xwpl5E/sIbpVzKFVcxnJu/eoSIj7PfQE/A0/N5kI9/tUlRnbB4IrRpeNRQxaBO2XKj+PpYNk7Jh4nOx+BBCMNFELlcsm+gurrQAa4ko1B/Sau7jrmFplLC6sZDvtlsMGtizsw3Q6MoeQBcbi4nexgCFxP48LqoMwNpP2WhO0a3lss6wnBybzKDly4oatOazrG5Lihs2n5qXvOHO7i4Z22zzgkYyd/n8uzdw39zcKF1wF/kGazRhLYmjV3fxPg42Z7XcnMEBS06va6KhQytYkjI3wc6RnsCaM2gC3RWzCbDGO7y6aDiHZpomqbx7M2hgNRZTy5mGowhueguAxcZYUvbVao2KxNHrTh7RNMFIzM90I9dUX4SkGXBVZSBHPBqpo6SrrlvX22YDFE822PNWMSRxKY8IIZjsC60GVYWG1qIm+X+7QWvCjoTZbP3/kXHXriWEYNdwpGFCrDBobkochxujSE65nBsuXlA9WBoxCG5T02DNPRhmdb6hcq1CmaDXXQYNLBZtLQZNdwkdA1sbXS9xVDCDBhbNXzJMjtbNT1UKRpcSvYyJvsaSyrJh4HVJJlq5VgNpqnz0P/Kmy11b1wGWXCjq93DfydVzOPFsESHcBV9GewINAYOS4T5gIEGs1d+blTvcBLHAKq5OL2ZWSSrlALybAMz2wQinlxo7YloSR/euJe9jo2In77LZEFhF40Iqv3rGyB9lxQi6yqBtrszOri6skrkiUb/HtWdSus82MhPIFtxzepMxFgswn1o9BqGiQZvoDeLVG6/+cfsc9Xt0Ltvcy+1NZqeyhZKrhlsjzRg03QJchHDvefTqGpv7Qw0b3UyhjGm6W49sGQhRLJsN59TdNCSBah5pBBpUGzT3vrexWLDhtXjFR/iQ9gZXQawtEuhpMIeWrjDI7ny2K7f24fNo3Hpk9fMvgU63CAxosgvtFy6Oa8dEkyXLI8bzGEr8MZcMX+Lq9aSNdL3uVdqjunloxkJeekPeVZ/NedC4hdgGfToTvcGGcomkggZNzqEsZWrpaTdlGc4Y7w00leYBriF/YCHfi+lCzYyFKgbtOReM4PNofPbeMzW/LtE5tyQnMpotbCwZpqtNBTisnR2Hi7yLQZ97A+lgzbJdta2fe06sXg6cypWIuGRFLGO8N9iQiZFNjcdFNlLmyHMr9QWxdQ0353TBAijyJWNVMVdxTHWR1d0xHG7qiJnOlwi7zCAADR0IKzNoLg33QxWNXsU0vfzf+NviG10tGsdiVmPRaOg+kXW3QA14dUZ7Ag0bNLf3YIL1vZWN1TNvup1MdBednj12Y9HIBELO8rlZED97zzCHzidWj3gY7pqtgCUVnU3kV9U+E0P7CRomSWOza9cCu7FoOE4i1Uru1Vpb1mB1k7mSq8C7nIlvVI/IBs1Nie9YLMB0osEYxNAejhf6XNknJ2NTfxAhaDhjJxlkt57/kM/DNdsH+MmTc6v+vwoY6GL+39QfYmqpbr5OaL+QOK4VEb+H/rBvFfJXNgVhtrh+vQMTvcSzxVXXS7jo9OOMoYh/la1/TYPm4ou8b6ynoQ47nS+ha8I12h2qDVr9fFGmUHY1OcnYNhjh5EJqFapfkTi6yKBdMG5J8w6dr1Lvqhi0gYifF+wf5ZsHz9f8utvrA2RM9AZZTBdWmcmUyu7PoEUDlu67kSmPm7OlMq7ZMcDJhfQqZitTKBFyGTQYjQVI5kqr2BEVDFosaN3H1Q2hlDi6+4xslTKXuiJVxTNZdcRsXBC7Kcv2eTQGI43lQvmiuzNoAFv6Gy+1Nfu2crbU62ozqGuWhKcZg+Ym8AgWY9e4qXZf4ijNveqff5lDNOHumW2dNc0/m5vA0vW2KdN9J5dqfj1XslgmN5nIkZ4AhZLBSt2Oz82bn8ktvZ9jif2uXUter5GkMpW3ru/muy0Z5IYAhcvu3M1UXwBZewZNBYNWX/tIqaibgIHfozMeCzaUuMs60s0ced1O68xeqQP6JVvnNoOWzJcqZAzwC4ljO7G5f3WyL5YN15z5nHHRpLUzpr6RUSEDBBiK+plPNW/Q3GRILt3cy4n51Q+7tLR1a0gWqnMo9W5XZcNU8r3tHI6QKxpNDVfcLIgvHLOekUPnq8+IMzf+8+svc+1aYBWpy5lijcxLheQKnLa9q++jm8vFZdQf0oqISMAyy4DV8yMpl5kYqM4zzay6j9b35nazOxJrUOzYJiEqJI6weg6hULZZXRefybWMEtxcVCpjvDfQcOA+r0BS3GwRvWzivS4/I5v7G69acbtABYuxaOjiW3Rf4jgaW83Eg8PF0UUGDexdaIvpVQWx2xIvqErK6qV5shl0U+I4usay6kLJwOfyuT0a8zPXwKG7wqC5KoO1GeQGz6QlcXQPoFjLWTGnAOgZiwUols2GtVbZMF1tBqH5OhJrJlJ3tY6U7or14EtWwSyrdDo+W2MU0hoq/kWD1r8a+SuWDdcsX2uuZSMt9ShqTtHMz1C0BYPm4ot86eZeAB4+s1Lz66l82fVCpxmDVjZMV9ksGbtGGu+ekgyam/K1WMjLRG+whkGT1/nQ6y/lRReNuXYtcNxLR2NdKLtvWgCOYqfukC4ahutNBayee5DyAgWPCEP2ktV6QCRTcNdsAprvp1HBoAGMRAOrmEizwqC5vHewJ4CuiVWSShUMWsTvYbQnwPEGbodpl9FhsOVCDQqrggKJYyzkJRb0rtorVCrL1SDuvttbbHOjegmb2wUqWE38fDJfmd2WkVFQWMmcVQ9QyLunufz8bxsMUygZq6Swki130w25J+Ah6NWZidfnLHcd88BqmKBxg1YsG3jdPmtsaWr9AmkVpmW6Juw59QYGcNmiaysmwGLHBiO+hlLpXKmMz6O5Wo+MNQEo5FnjNiC+qb/xGITba0/A0eyuUr24L3Gc6LVq/5rPJjRaZar/5xu0LQMhzq/kKJarDEKpbLpuWgAWauPTtVWW1VWJi7tohJQ4Og9Np0mIm8XOxZO9aAIePlM1SphN5JhJZF1/sSSDVj+DZhjuuwEC7LSR9nozDfnIuN0U7h6J1DAxKsxIZAzYDdqiw2427/LiXBmNlrUbholput9UwOodRvLJV9CfMRixCpB6296UiwtfZchDc9V8qSy+Xb6XjXdBqZlB0zRBf3j1Go3qDJq7z+SukQhP1b3X+VKZYtl0PW+NxRrPDuYVuDiCdbbVo/pFm2V1+3zbMRQhmSutAgQzBXdnmaCqRHnwdK0pT0aBzX5/yIdXF6u+N93OIm4//7JonEs2bizcZNCEEPZsWO1nq7rBujvLBzDb4Pkvlg3X3+uRJtJUVXlkMOJjsa6uMwyTVMF9gGK8t3ETky8aro94VNYMNVC9gPtnTV/YcuiuB3rSBXXnaP0zIveguSlxrM5y1zZov5hBaxGb+0OUjVoHnmLZcH22AqyEOBDx1RTDUD2g3ZzTAotByxbLNbMqTgZNDpK7EY12GF39P3/MnccWXUWrwHpxgl59FYNmmU24einAShqDER/H62ZVqiYh7l6vP+yvkYqqMCOpXstudtOrGTS3JY5VuVD1IKtIrhRJHOeSq/XzKjq0WNCLRxOrzAQyLu/TAuuA9unaqnUMqhi04R4/c8lczaFpmraLo4I8ORD2rWp0Vclu94xEOTqbqsmLKiReYBUEqXypMnMsQ5Upz3A0sOo+FktqZLA7hxurDPLFsusyqMu39OHVBfecqJ2dyri8Kwxsq/EG80yi8v+7+9mkoYSU4slI50v4PZrrzOdIj38Vq6WCQRuOBhACzjdZM+F2/m+m1lCVIwcjfhaSdeBcoYRp4upKC7By1mPn4qudbgtl12vIsd4mDFpZ3kd3r9cX8lEsm5WVGTLSCpRYw1FLrVH/2TIu2+yDtQst6NVrWVYhfjGD1irknp9zNQ2aGgYNsBu02iIuVywjhPsH9FDUQvWdqGbZMHnZJeM88pfPqWhw3YoLx3t4wiHNk+F2gQpWY7FKF22aSpoYsBJw/fVUmIQA9Ie9lb1PUJ2dcmshtjMGInKer/qMqHDMA0tSFvF7aoqdko3oq2DQhqN+imWzsixa5QyaBF8W6pDvtMv7tMC6V5sHVru9lQ0TTeCqTh8suVCxbNayWqaVqzSXZ9DAftfqcqQq2e2e0Sj5klEzmC5dvFxfet/EIjtfshgEt3NXX8jbEMQC9yWOFcOVunm+XMlwvWgM+TxcPNnL3XWuqZmi+xJHsJ7/1TNoamYwZTFfv0Im57KrooxGn02F2YrPo7GpL9Rw72ChbCqROMJqaWpZESA4EPGvAueSCvbbgmVItZIpcrhuh1eu5D4Y0h+yllXXM2glRfPOfSELoKjPW+l8yfV8rGuC4ah/leGKCiZeCLF6zZDQfmGz3yp6bbmcMyGWDDUzaGAjLXWoZq5YJuBxdwASmjdouqZVPrebccFYD+fjuVUvl5sDuTKGon7mEqslBSpkgGAxJPWHpgqTELAYu2yxXBlWLVcWYrt6GetaoQYMmqKZSLAR27izQVMjlYDqcmjJWJg2WqXCxRHku13foLm7T0jG1oHwKre3kmEqYf6r0tTqZ5MzaG4XqGCDWBskcdxrLzQ/4thPqcrFdNxG9etnVfJFw/XGE6w8slwnA5dSfvclZX4ifs8qBk2ebW7HgckYx2aTNaxutlBGEwqk2bHVO7zkFXSXZ9B66nKWjFzRcH0EAqzPVq8yUMGggbUvstHy9GLJwK+gYRKCVZJb+fy7fWYPRXwsZQo1TLyKvWRgNWgAdx+vBShUvGuaJhpK3MuKZtBkXVrv9plWMMsNtny/bo1Atmi5gbsNmE30BldJHMUvJI5rR6/dsTsfiGJZjascwEB4NTqcLxlKiuFKg5aqb9BcvxRQdbJ7YjpRM9OngtWa6AuudlU03d+nJSMW9FaYGOf1wP3PJ5smWVxVJI4Kms/ekA8hahErVZIrkAmxmuxVzU2Bo9jJ1sqFFPXwDcEXFSYhANsGQ6sWOhuKnv+Gs4MKGTQrR65u0DyacP1dk9I8p5OjbNDcBukkg7ZqLqZcVpL/+0I+8iWjZq1F1STE3fsohLAcCOtAA1Vn20RvkHShXPNuW/Nu7joGA4zZLJOzGaw0aC6rDCTbUi9xzJfUPCMVdtzRyFckvi6vB9kxFOHE/Op1NYWygdfj7nema4K+UAOVTYVBc1niGPVjmk2ATgVuyOOxAI/XuYFniwYBBWBgPagK6oBVWfusZFfvuFXBII/FAqvycVrB3Dg0qFmFQP+FxHHtkCi7s/gulg3XbYhlDEZ8LKRrhyBVoYxSz55yJPuSIiMNqFqJzsRzFZoYVtPVrlzLRiNksjdNy2xCRRMDjRs0eW23Wbt6Vss01TB18u+sP8hUMQgAoz3BGtckaVqgK2gGK3IhiUbbr5yi/mwVg2aaJumCIgZt0Fro7JSeqNgnB9YBDY0bNLdNEsBi0FL5UgWBBtuKW8HzGPTp9Id9NbMxRUUzmMNRC9Wvd3LMF903SYCqXMhZfFekSUqu5yPhOGuKZcOy4lZwtsnRhCmH22emUHJ1sF/GaCxAtljbDMpzxm0GOejV8WhilVojX1LDslbs7x3Pf0bBwmOwwJB8afW6GlWu2QNhH0t1QE91dsr9GTSgJv+rPEc3D4Q4W2cUYtWRat7rVeB0RT3k9gyaLXGsY9DyRfel0lDd81bPxKvII5v6QiylCzX38hc2+y0i5NPx6oIVp8SxbCqTOA5EfBRKRo1xR07RwydRAOfApYWyu34pwIn+FWtQ23oUy40Y7w1SKBkVR0xVrkIyGjJoiiSO0rhDsroqGTR5vY0wCQHYNxZlNpFnzi72K4imUgZNShzVxmDUMgCSyT5bdH/hq4y9o1EAHj/nXGhuoCuYnR2Orh64N5UyaKv3HBbKaho0WG1/r8qQxKtrjEQDTNU3aCUDv8vFMFgSR6gFyIplde9bJOAh5ZDmqZJ4gZX/oXZhb6ZQVgKGNHKykzNoHt3dd1sIQU/Q28BIRp3EEWAuWb2PFVdpl7+3HU2MZFSYhICcU69VK6kypZI5q6ZBK6uZ5YbG66FUGPKApTJrJpV2u96qShzrTaLUfLaxWIBMAybe7d2lUD2znXL6X9jstwghBLGgr0biWDLULKqGKtIiC7kDf/19vnHwvJLkK1GAbKHWxVHFnApQsZNN5kqkHdfcP97j+rUq5i42iiQTryqTkFjQS7ZYrlnoXNmD5jqDVot8lxVdR8ZA2Fdj66zK9hvgsi19ADxkr2NQhWjC6nkOCZK5LYGSMRTxUygblWSfUuAqJ2P/RAyfrlXuI8gZNPc/m8+jMRD21cygVRk09z/bQCVH1qLRKlgmWG1/X5U4un8vtw02kgGW1cyghVbvOFS1Bw2sWWMn8KhiAbeMaoNWbZosFzsVzeDqfUnyyfAoYJCjAU9jiaNSBk19/t9jF6j15hZFReBLo1lWVaZUg9FqXSdDrqtRwqD1h5hP5muA8JwCm32w8kj9TJgqcLq3YhLSaAZTzcgFwLRjDi1bdN8NE2DfmFUHP+l4/jVz7fv3/3yDBtZDEc/WSrxUMWhynuPcShbDrGrNVTwQPl1D10SN3NByelNToPo8Gn6PRjJfImPr2H//Obv525ftd/1acq+ERFANhTJAsBa/Qq0UtrIHTYFJCFSRb0PRdWTsGonw1EyyItlUxSCA5fTp82iVHUaqFl6C0xFt42bQoDrzmVFk1w7WzsQDk7GaXVDWfKmaD1dvNa50Bi2yejefKokjWChq/ZoVUANQ7BgOc3wuVSOpUSVf6w+vlgsVKxJHBQya31Mjp68waArAx8GID59Hq3NfVnMfxytOz9XnXzJomssMGlijCatdHA0lzeeQLbt1suOqGrSegJdN/cFVTs8FBXvQwJplrd+nWFI08zwYbiBxLNuz3AqeyU39lgP32eUqi6aqsehtNMuqaJbPq2tE/Z4aUMk0TRugUMeOOwE6a95TzSxfb8jL4ekqg/YLiWMbUS9fU4VEg1UMg0VzSjQH3JcTgMUUhHz6qgZNFTsIFouWzBUrTlBXbOlTcrBUF/9ZCUrlMmdoPKtYRePcvVZvUBZWdoNWYdDcvY6M/eMxkvlSJdlXhpsVSDP8Hp0Lxnoq0rxyxa7X/VQU9nnQxGoXR1VRP4egkkEDax/UY1NxSnZDocrFEazDpbZBk3vQ1CC2UDsonlcpcewNkMiVSNvfl6o1E2AZJSRypRozmYIi+ZqUCzkljqWKxNH9exkJeEgXypVcnCuqY9CEEJYr2rKzQVMzmjAY8ePRRI0MVrNLK68CBrkn6KmZ5QN1DJpX1xiM+GsWSOdLZXweTYnS4IKx1at4iiU1a436wxbz4zQsq7oPunsv5a5XJ4OsynkWLAYN4IxjEX1OocQRapl4VTNoAL1hb43EsWSYGKYawKyyrHqlFqBQcS0hBHtHoxx27Ar+hcSxjegNemsljgr2csgYivgZCPt4ciZRY8mq4sUCaw4tu0EMGlisRSJXqu6SUMAeWNfxEvV7Kge07HVVSRx7GjRoVdbO3WfFo2v0BDwV9E+VW6QM6b55yD44VQ43g4X+yXmOokIXR00TRB1odEXi6PqVrBiM1s4hyHdAhZ4drPtYKBvV58QwXV+aLmM0FqiROJYVMmgSDHHmZJUSx/E6FFXOjrjtLAfVfWFO10hVTof1QA9QaeZVMWhARd4u3WBVNJ+wGjRQpXzR7WXVTpRdrurwKGjQon4L5HRGvqjmGQF7F5qTQVMkJwO4YCzGycV0BQwBtRJHqH3+i4r2d+maBYanG0h8VXw2ucN2all9g9bX0OlczX0Ea/fakuNaKqXSw1E/moAZh3w5r2ilBVhrXY441Eq/YNDaiFjIy6HzCb7y4BSmaVq2r4qKYSEEe0ajNoNWbdBUJcSQz1MzD1Y21bGDUNXPV4pTRewB1NqWVnaFKfposTrDCXBIHBU0vNayXilxVMsO7h6N4NEEh85btr2qG7Rx29rWNE1lWnYZTjRavm2qJY7ye5PvXchlu2oZI1Hprmg1TioZtOFogMV0vnIwG4a6GTQpTXWCIQVFqCZU5xCkk51K5HtHA1v/fKms5FoS6KkxCVEkTYKqSZSUOUoGTYXsCmzZrcPcwrJrV5SzemtlsPIqbpuEgJ2zsvUMmrqisV6+rPJaO4bDmGatNE9VYz1gyw6dMkeVa10idTOYqmz2wZob92iiZnY8pwjoiQVXG3eoPLet2scxE6nQbMijawxHAw0kjmryyL6xKNliuWLw8gsGrY2QxfcffOlgpbFQtQcNrGHZp2ZTFB2GE6oYtKC3yqDJglgVEwNViaMsTlUMrcqY6A0yVTEJUWfXDo0ljkbFmMT96w1F/RVnLdVNjN+jMxz1VwbF86UyHk0ou95YLEChZLCYLihz1ZLRaJ5DFYfWF/KhiSqDJtFUVQzacN1+srJhKPvORmMBTJNKQVCZQVPQoHl0jYjfs6pBUwUYSNdUibSrdDEd6wkQ9Oocn6sahahkR/rDvtoZtJI6SXHEb691sZ97lYUVWOj3XCJfmecrKpplAouxOO2Qk2mKXBzByln1DFquqEbiCPD/tXfusZZd9X3//vbe53HPfc69c8eepz1+4RiDDTEOBAiPEB4hhJKqjaPSEAFKUHBVJVEkorRJpEQqatVWqE2b0oBCq5KIVnk4DzUF1Ma0SYhJAhgCxtjY2GObec/cua9zzt6rf+y99l7neDz3ztz7+51z9v1+JMvj65lZe5+9ztrrt76/3/d3/XxrqAZNb6zhQyxArwbNf6/DsXqK79KZIXMXzXUkigT7Z1oDAVqaOZXU5X2XqWXVrB3fP9MaaDC+oRjoAs83k9FKcQQqoxCf5kgFbRuEeex/+XjenV1rwwjkJ1brvbRsCAlApX8FkDeb9EGnF+xMFDTl+hsgV9D8qWamqGYBlw/QUkVjkgNz7WAznP9MMTMV80GvE83NMBA07D2/UaZcqSlo7Ubg4qhbgxZHgsXpqheaP0HVUxDyzY6fJ6li7azvcehrHvqKfdCA59cFa9rs+1TA88H8B/Q2VjctTz8/xVFJsVjoNAdTHDOdJtxAVYfjN6mabrBArupu9rNSIc/XLZ35f9eReTx3caPM2NBV0BpY7aYDtVObfR2TEABYnG7h/FqvXB+1Um6B3NwFGDTT0EpxnJuq2v540ixveK9RXzfsYqqpxAPAgbnBAC1zTqVOfWHq+TXBVVuj3b+35dkWzqx2K9Oynm6qdKcZD/Tc1FyPbz0wi0iArxVW+9EWIRoDNADvfc1x3HUkr8P5P4+cAqCTAuLxL8eNfhCgaSlozaRsPKllMRuSB2i9ckyNjuyeQwtTuLjRx8pGLwiWdMZamGogiWQgFUTTmOTAbHWKpO1QCQDzU0mpNGluhoGq5ueZC+uqJ3HAYLqQdoojkG9ATq3kL7Ky9YPSgPtncge27wQ95bTmyE1DtVNpln+vI9E5gJmfGlQ+NWvQhvvlaW+sbl6eeV6Ko1YQkytol+mDpliD5jepmn3QgHyDCgCnikwDrYbHAHDPjYsAgC88cRZAUIMWN3Z9rMv1r9OcIz7LxQfUmjU4lZFSsUamGTKndGBQzsfAfTDVWyPzPoCXSXFUCnZzBTmf+845OKfTQmbhMjVofUUlcnm2hTRz5bqlfdDTbgwa6W0qqtVTzRjHFjt4rOgFyBTHbfDKm5bwB/e/BrdfP4uHT+R1OJoqk385huYdajVojbjsg1YaaSjuUPMUx9xmPxK9+wKCXmjn16t0Q6V7S+IIR/ZN4cmgOWSmaN6xPNvCWjfFpc2+ukMlMKhYaG6Ggdw1DwCePb+uehIH5BvUkyt5vZuP0BTjMyzPVgpaqhx8NuJooIedpvvswbk22o0Ij5/KU/MuZDfjur7DDQdfrjLe/JBxk6aq227EaCVROf97iqlJQB6gnTi/Xq7/mvV1C53GQE+hfmmzr9AHbbgGra8boC0P1WBquTgCeZPZmVaCh4oAzb9nNBS0/WXT43yDmtuM682RqSKA8PNRMxica+cHnb7GqDowUHDxLQK0taAGX3ONfKEaNK136fJsuzzE9ckhGvufdiPGbCvBH37pmbKer69oEjLcrkbTJAR4AQVNaSwgz47y98YUx6uglUTlZNCsQfOL0XowKdQmXysuUykzZZUJyF/Sa90UKxs9dJqJWlNgILDaP7euXqcFAMeWpvHkmap2RFtBA4CTFzdUA0HP/FSjTGHQXqCWpptoxhGevbhRboa1ntsdB+dwbq2HZ0IHNsU5uTTdxJnVKmACdOfkgdl2eYqqqaBFkeD4/hk8fjo/+Tub3Yjb2p/A0aOvVhnv8imOemr8QqeydlZX0AqjBP9ZbmrW13Uur6BpmSQAwKXN/Ln5Rr1am33fU9TX6moq/0kc4eblaXz7bJ7iKEWD2aZCgOZrp/xmuJtmcE6nFQ9QBdB+P6IZDEaRYHG6WdaFadZp+drfMGjqp5na3m6m1RioQdvsZ4hEby95oEgF7KWZeiueX3vXnfj6cyv44y8/A0BfQQNQBp+biv0UgVxBXgt8GjRTHIE8y8Yf4lJBuwqiSMrJoKkg+JdjGLUH6ea7SqcZ48T5dfzjj32+nITaChqQ18VopjcCwJFAQdOsB/PcuJQXivtc/TTTC5wOzPrNx2aw+Ord28JwDZri/BcRzBbpIGmml3IFAC85sgAAePjp8+p90IA8Xc6/pDNldRAorMaLDWo/1XNxBICbl6dLBa2fZqpjLXQazzcJUZyTAwpymkFEby25cWkaAPBUsdnX3BDsm25irZuW75q+omIxXIOmnuJYHmJVNZ+ac2Sh0yyD+LIPWrL7KY5L3khjdUhBUEy7AqrnlR/QaW5QqyyDUq1WWP/bjQiRYMD6XlNBm20PKWjKpQI+xffMpW5Zp651iPuOlx5CHEmpVqeK5l7DdYraCtpUMykPJ/yBgWbmV+jQLaxB2z5JJIGCprcZ9l9ab0MMYKAgeDfpFKdIn3v0ND764GMAtAO0fLznLm6oGoQA+URvxlEeoFkoaIsdrGz0Szcjzdqwqr5iU9XO3zM/1cBGL8NmPy1O9HWD66miP5+2ynT79bNIIsGXn76g3gcNqFwjnXMmCtpsu1GmlGkqaEAeWDx9bg1p5tBLdRveDytomirT8Hh+o6+ltB4KDpb6aYY0c2obgrLpd7FmVSmOu39vw4qFd1/TMsmZaSVoJlGpNOU1aHpzcl+nUaqRZYAWN3d9nKUh90FtJfJ5CppiDQ6Qu+adXh1UqzU2+iKC6VYyYMaWZnrrlk9x9Ae42gcG1SFulWWjtUXIXSObpVptqaBtKJuEhE7n2ochQN7+4cJ6D91+tmUAxgAtIBIpm2tqbnT8yfNmYBKiFaCFNvd/8MVcnta8Nz/e2dWu2smpJ4oEBxfagymOikHMDcXJd2WUALUxq5f0pqqdvydsxK198gfkyu5aNy1P9LXUmHYjxi0HZvDIcyv47NdPAtA1CZmbSpA5YLWbIlVqihrSbkTlQU9f0WYfyE82M5f3w9G0NAfy+bjZz8qXc1exLgbIe/34IEZ7/u/rNDDViPHM+XX102HfZNYHFmXNj8L3LY4E0824cnEsAwud94CIDJQlaJqEAIWCVtTz+W+ZRg3a/FQDcSRl4Fk2/FZsxQMg+K7ppTgCwPJMC6dXBhU0rec200qGmmLrZRnMtBOkmSvXY+2DzrIx/GZqkmVzYLZyltasQZtpJWglUVmDqa8gR1jvpXl6o1+zNBXk2SqFmS6OV0EcSXmio5m+czmTEK0AbTpokusXYM1aJr/Qrm6m6pt8IDcKCRU0zXt72bEFzLYS/Ks/fQRZ5oLasN0fy+etpw42KY4+QFvrqZ+gAnlawTe+s4IPfvJvAOgq1ovTTfzZN07hk5//NoCt0wp2wly7cgS0UNDajbg0Y9BW0KrUq7x/nbaCBmAg7VBbQbtomOLrGx9XzWz1UhyByhGw3FgpPbvQ3GWjn6IR6/VTBPLPbbOfIStUXd3AuomVzT56aVauIc3G7gdoUSTY12mapziud6vAQrMGZzGo09U25JluJWVPVqCw2VdU0ABgZbNaRzTfo/4z2+ynVYqj4uHjgdlWmeKo+W4TkTyjoVhHNpXXyE4zKbNCysMQZQUNyFM4qaBdBXEk5QmjppFGabMf1KB1+zr1MeFmtG+gMvngc6OXquSVD3N4YQonzq1X6YaK97Z/poUP/eDt+KtvncWfP3ZGVbXz655zzqS+bn5IQdMO0DqNGI+frgxXtHvz+bmvjVciVzb6SBUNGTxTjcqBSrO+AhhMveoZ1KABMKuLfF6Ko/L8P7yvgxOBgqY1nk9xPFemOOo6i+a1rHkwuNFL1Qr7PbmClqKn2N/NE87JMkBTsNkHCrOhS9XnCOhtUP0zqmrQUlWTqIXOYDo9oPfcppvxgM1+T/EQa9jFVPtQyb+ju/3MRkGba5UtLTRr0IDBGuTN0g1WOcW3m5qkOC7PVjV2MRW07ROJlEWCmhO9cnGsVLN3v/KYylinhhpCArqnLEngUKm5gfMc3jeFkyubZVqBZhADAH//5Uew0Gngtx/6tmrdm59/mXPqLQSAoQBNeTMMVKe2Hu06rRDNFEf/kr64YaOgtRoxNnpZHsibKWib6KdOtd4nnI++V5LmZmehUzUH1mqcG3K4UNC0T2wPzOa98r709HkAQUqZ0tq80GmUwaC22QSQp4Z2+1l5sKprEuL7QXUhxdapoRWgzTSDFEdtk4RBV+m8D5ruYQgAXFzvV89NqcH49FCKY5o6tbk/3Aew209V52MZoKUZnEELpeXZdp49kWbq77YBV2nlVGlvZrfeS9XHAioF7cylLm32r4Y4EvXeRcCgygQAn3z/9+Blx/apjHXT/rxu6vDCVLkYqqY4Fn+3ZjFuyMH5oqfWhdwRTfPegPy05S13XI//++hpZM5BRMe23S+0aQYTA5TwdNhCQRgO0DRPvn3QZEGY4ugDJk1bf3+quNnP1L9zSzOVgtbP9OyqgSBAW+upWnE/b7xCQdacj0DerP30pW55SqyZ4viuuw/jE3/+BE4WbS0i0Vsn9wVOhxsGqdLNOK9B65VKjKZJSKVGigMi59BQSHH0Y5WNeq1NQpRTHMN658rFUWe84QBNs063DNC8gqb8Hi1THHv6NvtA7hjsXN6fL1WsQQN8RsNgP0W1A4pi/q91+0G9p6KL42yQ4rjF3oABWkD4YWmeRCRDKY6aG+8ffcVRfOZnvw/fe/NS+TPNNMBw06atwgDVxsZ/lpopXp59002sd9N8A670Wfq/NnPOJL/cu32uFjK/RYpjiKWCponffHgFTfO7BgymJ+UBoW4NjkhuXNNLXXkYo4EPmM6v90p1XHM9mQ0s4i0UZN/D65nz+cGS5vftfa89js1+hv/32OlC+VQMdIPUpDOXuuVz1KLVyGvQqiBeL7DwAdq7f/PzyLJ885QkOgGad7kFwhQvfZOQLHPqKe7hGtlVDqxnhmrQNGtnyzYTm1YpjnE5jkWv1OUig+LkykaloKnVsjbLmuBN5fV/KlTQDFIc20l1qBptUXnBAC0gfP6aG8bmUICmeeotIrjlwOzA/ag6VAb3YqGg+XvxC71mYO2ZasToFqlQWguivy/nnMni68fLMmeioA33yNNKOwGAuSEFTdXF0ac4rveRKrsqAtWmbaOXqdegxYV5gU+b1lTQFqbyzfCF9R6+/uxFAMDx5Wm18cLTb21Lf6Ay73iuaKCueWJ7+/Vz6DRjfOmpC3lgrfjc9nVykxDnHL5y4gLuODSnNhZQ1KD1UvWNPlBlGWz2M9x2roH7z51Hoph2tVbsDzasFLRuWvWBUpyPPsvAZ2vk42kpaDFOnFvH14o1JNXsg9bK7+tS4GKqedBTKWiVSYhmtsZCp1qTy1pWVQWtSpVuxpHa/mcqmP/a9Z5AtddKM0cF7WoYCGJUVabCxdG7KhoEFeHk1hwuXJA0N3DlGMV9+ZMP7Q0xUOXsX9pM1eZJVYMGkxYCsVSLhoXN/lRzMGjSOokDnp/iqOni6NW6lY0e0kxf0Q3rR7Rr0IDcgc0HFZoHMLPtBCL5ZuDz3zoLEeC7b9BJA8/HK57bZs+kBm1xOh/v2YtFgKa8IXjJ4Xn87VPni9RUTTfYJvqZwze+cwlnVrt46ZF5tbGAPGjxh2WAfp2i58a0g/ddWEGilJo3VbQhAQKbfS2TkOCQx6IGp6pB65X3phXITLfytidv+8jnAEDV3MgraJeMFLRmWINmkOIYpoGXpUBKn+X8VAOXCsdUbdOajrGCJiIQKQK0LX4vA7SAgRRHAyt6fzJmYaYR3o6VgqaZAlWNV8nFgK77psefuFza7Kt9lv6vDVMcNZ+bD5BSr6ApbTw8wwqarovjYJqVVyQ1aCYRphoxLm4UCpqyihymOPazTD0gXJpu4n8/cgpAdRKuQRQJZlsJLq738NATZ3HHwTnV8UIHNosUR58u54Nd7YDw7mML+NozF3Fpo2/ivvm5R/M5cudh/QBts1elOGqqgzOtBPuLOsyu36AmOnOy00jQLepKfaPl4brd3SKOBM0kKjao+jbjgwGabmDdCWoEvZGS1gGFb2lUmYTopooOujjmP7MyEusrOxT7dcTPEc0Dg8u5OGo5RnqSSJA6xz5oV0O4Adbc6AybhFioPqH6oqoOBi9/7UL7fLxBBc1CjfRf6NXNvtqJlQQKmg8oNG+tVNCcUz+xAgYbqN+41DGpL/L4Pk2a4/k+aNoBU7sxWIOmbZLzA3dcByBX0n7k5YdVx5rvNHB+rYuHT1zAy44tqI4VOrBZKMiLRYrjsz7FUXm81992AN00wx89/KxyGmB+Xw89cRYA8F3Xa6c4xrnNfl/fxVFE8Nmfez0AwBswN5Sd5da6fTx5ZhXNJML1Rd2iBr5dh4WCMDeVf9cuBAGa1nhPnq1auax1U/RSvSyDVhKjmURlo3btUoEkypWYzb6NSUjovtnPMoii2ZAf67t/7TP4/ONnVOfjQA2aQYojkO9Ts2zrAM3O3mwCiK0VNN8U26BWK7wf3XsLa9AMArR4sAbNJsWxOinTvMdI8powkxTH4nPrp7lltZXN/q0HZvDpn32d6ljDCtr+og+JFnNTDVzc6GGu3VCfjz6QtqhBA4D3v/Ym3Lw8g6OLndJYRouFqSaeOreOlY0+bljUqz8DBtOTLBS0uXYDkQQ1aMoB2vccX8TRxSk8dXZd9X2zrzj5fvLMGtqNSE318fgUx1JBU/4cK2tzAQRqNWj+c/vco6fxpafP4/jStHLD+6hQELyLnd5zayUx2o0IF9Z7ZUCvNf/ffMd1+N2/OQEgP1BNM90azJlWgkubQe2UcqpcM44G+qBpOwY3Ysn7AIquiBGaCz12ahWHF6bUxipTHLtpWVunvR57x3jWoF0FYeBiUYO20R2NgmbhUAnoFmx74lJBs/sspwYUNL3xIhFkzpnY7Pu/u3TMMzIJsVA8vYL22lv34y9+4Y24XflUf66dFKeMTj19uVTQ+ilSxdPhkDfcfgC3HJhRH2d+qoGvnLgAADi6qPeCBioFbWUj782kvdGPCsOV53wNmnK/sCgSvO62ZQC6hjw+Nemps2sm7qmtRp7iWPZ3U37nlAGaV9BinUMKvz7+9H/7G/zl42dxk6JBDlAoaP1U3ZDEMz/VwMX1fqCg6cz/t955EB+5724AubtiL9U1bpppJQONqrU/x7xRewZnkOIoIqV5R6r8bpsLArR7jy/iHXcdUhurstlP1eejJxaf4nhlqKAFDKQBWrg49u2s4QddHPXGCevOLGrrGs+rQbMN0DQ/yygSZA5lAbDm6Zj/2HxhurrNfrEBsXhePkCbn2rg4LzuRh/IXy7nVrtYnm2p319pkd1NkTp9Bc2S+alG+b0+sq+jOlYryU+HrRQ0IHdyPFM0I9b+vgEo574/JdbAKyKr3RTXzeul5Hl8HzSfQaH93EQErSRCVmytIqV33HCN7vH9ugFauxEP1OBoH9DNtRsDLo6a44X1pbmCphygBTVo2vOxmcRmKY5AlR0y1YhV3zU+BfwnvvdG/MoPv1htHGAwxdFvsbRLPKIoT3FMmOK4fQbSABU3wz6oWDdU0KzvDQAaiV3gWaY4WtSglSmOKZqKi30kRWGz058jIoI4Eqz38peL9obRuzhazH1vLjGn3JMpHO/JM2u2NWj9PD1Dsw+aNeHzOqocoIlIefptYbMPAIudKtXWYjzfe+1sERRqEKYm2ShoRQ2agYtjOWYSIesX3+tIK8VxcGs209bdqk01Y6z3UvRTm0DXKzEWAdqMt7/f7KuvkTPtBCsbfTx1dg0rGz0sTrfUxgKKFF8jkxDAK5897J9uqhpgHd8/jd//4KvxEmWTISCf660kwvm1bpm2rz3/Y5qEXD3hM9HM0y9THEsFTf8xWKmDgy6OBgpaNKigaZskAIOd5zXHq1IcbQLPWKRU0NRt9ovP0OJ5tZIIC50GDioW2Yd4k5A00+uT52kHNWiaPX5Gwc1BWtd8R3+zP9NOCgUtNVG09k1X92Qx3nVz+WbRn/Br0IgjzBbposP9BzXwG9SqD5pBgNaIkfmNlegraPfcsA/vfuUNKuN4vElI6vTT6YFcaT231sVmP0USiXraIQC8+2Ofx7dOr+o6BhcK2kcffBxJFOFHX3FUbSzApzimJkZiQBVY9wzeNXcfXTA5wBUR3Lg0jW+dXlXvueaJRJBmWyueDNACrOq0fFCx3rVLy7OqrwtfkLaNqgs10qhRNZCnA2o+uzxAy10cLYSROJJS1dUO0PxjMpgiEBH84f2vwftfe5P+YKjSQPqpgYJW5Mr/xp89ZtIHzZIfu/eY6XgzrQZWNvpY76Xq5hZAlcYD6J/YAlB1AQzxwfSwe6oGrSRC5qrUbIsArd2I1AO00OX2l9/xYtUWE34830sR0C+7WJ5t4fSlTXWnQ6AK0Hydlua9+UOeh09cwL3HF3G9cppvszigqPqg6T43n5pqVe9sxU3L03j89Co2jNb+OEJ+gEsFbfsMBDGaG+/ixMjb7JvUoAVfXM1apvBeTGz2Y28SYu/iCOgGhL6ZYbYNt5/dIE9x9I1DdRcpC+OTkKOLHZOFF8hfYr3UYbWr1yfP4+/pyTNrAGzWEiumWwn+8P7X4Pc/+GqT8WZbCc6tddFLHaYN5sr+mVzRasSiuiZ7LGrCgKrH22xLX/X0m3uvCloEuq0kRlnerxWgBfNv3iA126fm9Y3W5eWZvP5yraevVg+nh2oeHPs06TRzJqq4dzEtMlPNUhwtDLAsOb5/Gt8+s4aVjf7A4YgWSRQhzYAPpFdO3WcNWoBVrzAgfyn7AM0izSt8b1m4AQI2Lo5lH7SeXYDWDr7Ams8ujqSqQTMK0KxMQu4+uoB7b1zEL73jDtVxRoHv83NutWfmKufRboxtzUuO6NcgeGbaCR49uQLg+TVAGvgArZfqmXaE+NRDbRZMFbTB5sBWNWipcoDWMQ7QSne+sgGx7ue4PNuCc3mbCe1n5htIezTvbaadmLhFeppFo3Yrk5D5qQYubuR90CwypKw4vn8a/czh0ZMrJge5UZRnRs3iymPVJwTeBcIvlPbhQCOKytMqi1PvQXVQbxwRKTelFicsSVmDZm+zD+gGTmWKo0EDYsA2xbHdiPGpD7wKdxoUAVvj05HOrXVNzF1CLAL5ujLTSnDy4iYAmChoy7O6BgLDWKh0QOXkaGISMqSgWRwK5i6OPsVRqVF1owpuLQJdr4x4sxXtV7c/nDhxbl3d0nz479dck2dbCbr9DOu91CSAaRYKWhmgKb9vZtoJ0sxhZUM/O8QS38bi7565OHAAr0UseR+0rQ54qKAFhJNbO7hoJBGQ7wVq1QcNyFMbe2lqo6D5RtX+xWKwCWnEUjUaVK1BQ7Hw6hZRV+MFKY4GJ9F1xbsPnl3tqrsPDlOnl6Y1M+2kTJXuGKhNfpNqyUfuu1vdzXRhylBBK0xyVjby5sDa/esAn+KoXIPWtMnS8MxPNZA54GLxOVooaABw4vy6ep3WMJr7kuli3biw3jNx1G0lMS6s90z6oAFAOzgQqVM6/VLhttnPHKaULfaB/DudOgZoV8VAEKP8jJKBYNDOTAPQ/xL7+zGpQRu22Tdy/ZlqxLik3AdNCgXNwamnLgD5Z2mloNUZvzHd7NukuYTU6aVpTRhQdAxOUffPNLf+TbvMO+8+rD7GPsMUR18r65sDW9Sg5SYhPsVR5/tmvf561d/35dNet/zhxKXNvskzC9EMnPyeZ6OXmqzFzdjb7NukOLaDHrB1qkGbDg7kTExCJO+DttX6UZ9PeBewcjoEBoMXK3XEajx/b4mJSchQo2qjNB6/UOmmOObpjd1+ZtOKIRKsdW36oNWZ0HHNOk8/Nt7s1Imw1qfTql+KoxXzI01xtFEtMkie5liTlOJS9b+UB2gWLo4e7abAw2jem1fnNnp2NWiWfdAGArQa1aDNhAGaRYpjtL0UR77NA6x6hQHVCVkc2Th4mSposVfQ7O6rNAkxWjSmmvnzs+iD9vS5NRzeN6U2jid0cWSAdu14kxDA5vDl0z/zfbj1wAwAKmg7IQysOwYmITNGph3WeAXNpA9asbk/tbKJ6WZs8n1rlTb79Vkj/eHE2TUbBW26lZQbYWsFzZdDaBAepFrVQ24GCpr2VtL33by0qdtiyJp2IyrVR4saNL+3Y4B2FYTrhHbet99IWU1yqxYCQLVI2ZiEeJt9uz5oQFXEbWES8uSZNdywpF/LFEdSOspp2+zXmXCjbzEfb71utixyrtNL05pQQbMwCbEy7bDm5uUZJJHg6KL+muUNIE6cX8eSUU1fM47QR4xMySAkxOrAZT6omwVslP/9s7nS2jLYEP/1P3sT/un33wogV3+0CD83SwXNqg9aayDFsT7rl4hgujiUs1LQ+jQJuToGTUKM0gCtAjS5/K81aBgqaKVJSN/GfcrTLjZwqgpaBKz3+nj2wgZuWJxWG6ccL7gV1qBdO+1GXKYwWAVM0waKT92ZG0hxtPs8LTYEltx1dAEP/8pbTGo5/Dp1+lIXLz9mZ8jz39PX4UV3vgJvUhzjwZ9/g0mqLVCp/j5AszhYWuw08dTZdRMFbWmmVR4Y+DprDcJDaYsDavMUx+JAZL1XLwUNyFXdlc2+UaPqIsVxi6H4Vg+wdTq0VdAGDVBsgk8bk5DR1KB5px9tBc03IL5xv/7mI3yhMEDbGe0kwmrXxmoZqIqcNTcfdWegBs0oaPrSL73Z7FDJEqum8GEqtpWCljqHJ9xBnDj2YtVxjhlkTXiGFTSLfcm+aa+g2XwBfG+5NcU1MjbMVAJyBXmzn+WGE7AwCQlTOOu1cPnDECsFbTspjgzQAiy/XOYKmqEBSlKahNjUoImg7ClnFfDOtBrq40Ui+NbpVQDADUsGClpwLwzQdka7EWO1m5pYLQPVy2W1q5e+U3fCmikr5WK+o2+kUWfChs5WbQv8ZrhjFIRaMNNKEEdSpTgarFuLhZlMy2ijXwZoPb0ALcwaMnFxLPqgpWUNmo1JCFC/dHqfhWLZB+3Zle4Vfx93YQEDTodGRhpWGzhLA5QqxdHm3vxCKGJX1+E3c5pqpEh12nd4Qd8kJHyhWKSn1hl/sm91ADNTvFw06yvqTqigWRsXkGvj0MJU+T6zalvgDwPrdIglIphrJ+X7xsJsyytoVp+jN/5ZU61Bs3Xn9u8Zb5JmZbMP1M+Qyj8vC/U/ioAsA1Y3r3xYUJ8VZhcYcDo0UtCs9gGW91b1QbP5AlemJHYLxkwRoGmOGQbVFi+xcF406ph3ZUjZhsFoTvqaqa0WfPLChDVodTXwqBuNOMJisdG3UtB8U+DaKQhB3aXFu9Q/N6uv2ncdnEUzifDBN9yiNsZAf1uDzZ1XBX2Dce29XZjiWLf572/HzGbfOaS48mfIFMcAP7ktFqcqxdFmIxx+cbVvLzG+N/+8tOsGQ3wTVs0xLXvXAeHnqL/Q1x3vdmV1aHDfK47iy0+fx/1v1Nt81J261VTsFZammzi1soklIwUtLRS0uikITWP1Z6FI77U6VJptN/CNX3ub6hgDAZrBZ3isMD7xpRDqClpSBS/TNWsTUipoRjb7aeaQOgZo26bcoJoEaKMzCdFvwl0EukYKWmz8WQJVE1bNnirhY7IwP/FjcKO6c1pBn0MLplsJPnLfy0zGImScyJWzldJyX5t+ZmNpbs2ARbyRiyMArNWobtbaZv/4/rw2/bFTeYBmWYMWpoTXAf/ZtY1cHDPnSvfNF4I7sQC/KFksTtYmIZY93vy9WdVxeKXOysERqJrMauazhxsACzHSj8EAbef4VJC6nbITMm541filR+ZNxnvR9XlT+Ovm2ibjWeHXfTHKoPApxZdqVDc7aLOv/xkeXewgjgSPnbwEwKAPWlBqEfb7rAOWKY5JJOinVNCuCr8oWZx8eMcYs0bVlgYovibM2CTEMi3PpzhqWvaGQZlF8Fk9NwYVO8WfNDJVlBBdXnnTEp748NvNxvuZN92G1912AHcdXTAb04LE+NDYp8hpvkOtsVbQGnGEY4sdPHbKB2i644Xvs7opaP55mdT7S66g9RmgbR8fT1isTwvT+jbtIQMmIVYpjkb3lowkxdG/XGwUNIt7q2owqaDtFGsXR7I7PPjzbxj1JZAxJ4kj3Ht8cdSXses0DA+oAWB5Njd1uXl5xmQ8C6wVNAC4cakT1KDZvW/mahag+c8uc1vkHe4CvlH1VimODNAC/AOyWKB8/nW3r1fDFDJgEqK8/04MG1UD1UI4ihq0VU0FrZiPVu0D/OfYpIK2YyoXRwa7k4Rlc2BCxglr47LDC1P41E+9CncenjMZz4JQQbPKIArdSy0DtLopaGWAtlXUtBtjFS6OfdagbZ+43Ojrfyz7igDt4oZN/rVpHzRrm/14dDVo66oBWv5vq/vyC5TVi6XOeLcrKmiEkElgFJko9x5fLPuT1QFrF0dguIWSyZAAql6wdeFtd14PALjJQNGNRZDRxfHqKE1CDCa5t5j1/Su0sUxxTGLbjf5oFLSi75RBiqNVHZP/HFmDtnNaDVsXR0II2QlN4xq0OmLdqHp4HFMFrVMvBe1HX3EUb3/pwTI7SpOyD9oWCXQ8Kg8oTUIsLGanjVMcLRW0MsXRtgbN8vRotpV/iTXTlSNDV1GgmhdsUr1zRtE8nRBCrpXqPco161pphAqaVZshwx63IXVzcRQRk+AMKExCMmxpEsKdWEBsqFgsdGyaanpsTUJsa9DiUdjsG8j7/nbMnD59gJbwBb1TGtzsEEImCGsXxzoSvqut6o/DMS1q1T11q0GzJI7yhvcM0K6C2DBVbp+xPDzQB0359spUOePUPMvNcGnJqhiE+jGsbqt6blwWdoo/PbUoOCaEkJ3i32VMy752whRHsxo0sTt8D+kYNHSuK3EUoZ85pHRx3D6WfdCsTx/8yUpk4AjYaSXoNGOz0xzrgNDzsffco2oRbOkqGo5nlZpaZ/zpaZ8BGiFkAhjVe7ROJAMKWr1THC3VuroRR7md/1YVTgzQAmLDmh9rp7zYcLP/nlfdgO+7db/6OJ4yd954wfj+77pO9e+3TnGkgrZ7+FqEfmZTY0oIITshoYK2Y8K6M6uDTmuTkAOzLZxc2VQfp87EIkWK45V/HwO0AL8vreMC5e/J4tRjaaaFpaA3hzY+oKjbcytdHK1s9ssaNAZoO8Vvdvpb5TAQQsgY4Ptf8oDu2gk/u9HUoOmP95mfex02FNsL7QWiSNBPM6QZbfa3TWy8If7NH78H+6btXGMAWyMNK0Zhs29BZKygeVG3UbPPcRT409MeAzRCyATgD5VobHTtxJFAJHd3HkkfNIP93Vy7UTsHR2tiEaz3UrgtVFYGaAGWJiEA8KY7dFPkQqzvzZJRpThqY62gldbwrEHbMQlTHAkhE0SDLo67QiOK0E0zu4PVEZmEkGsnjgSZAzLQxXHbWJqEWOPVkRreWhlYzNass731fPSLu3V9ZB3xnyEVNELIJOBV/zrufyzxn5+ZghaHAZrJkGSH+L0dA7SrwNJIw5pSjanhvfnndWh+asRXsrtYpzh65UyzdcBewW92+ikVNELI+OMPOinC7IzEONANFTQ6K04G1TNjgLZtyjTAGk7yOt9b5nKV4tBC3QI02z5opYJWwyDeGl8gntJmnxAyATSS4lSfS9aO8O/PhtFB56hs9sm1E1NBu3oqlWnEF6JAnRW0U4Xl66GF9oivZHex7oNW2uxTQdsxb3jRMg7MtvD+19406kshhJAtafiNj2OEthOs2xVYm4SQnVMFaFfea9WraGeH1NlIo84Kmg/QDtdMQfOPytxmnyYhO2ZppoW/+sU3jfoyCCFkW/h1nwrazmhY16AxQJs4/DPb6qtmdlQuIjeJyMdE5H8EP3u9iHxORH5DRF5vdS0vRFz2QaufglDn4PM7FzcA1C/F0fqZ1bkGkxBCyAvjlZ+MCtqOiK1r0MIArX5b11riA+mtFLRtPU4R+biInBSRrwz9/K0i8oiIfFNEPnSlv8M597hz7n3DPwZwCUAbwNPbuRZNql5hI74QBfy91fGAZbVomnj9PFMcd4IvbpYt8qIJIYTUC6+gMT7bGT5V1KrhN232Jw8vBrkt9lrbTXH8LQD/HsB/8T8QkRjArwP4AeTB1UMi8gCAGMC/GPrz73XOnbzM3/s559yfich1AP4NgH+0zetRoc4qU53v7eM/cQ8e+OIzaDfiUV/KrmKe4mhsSkIIIWQ8aFBB2xXKvZbRST9THCcP/5x2JUBzzj0oIjcO/fheAN90zj0OACLyOwDe6Zz7FwB+aJt/r/egPgegtZ0/o4l1Y2BLyvS1Gt7bG2+/Dm+83a7ptxXWCloZEDJCI4SQPQXNoXaHxLjhd7g/qOH2rpb4Z/al7MomYjv5Rh4G8FTw308XP7ssIrIkIr8B4GUi8gvFz35ERP4TgP+KXKG73J/7SRH5goh84dSpUzu43K2ps8rk1XZuvieHsg+a0arrD065yBNCyN7Cm1tQQNsZPlWUJiHkhfBz44Hs1Vf+fRYXAwDOuTMAPjD0s98F8Ltb/LmPAvgoANxzzz2qS0edAzR/TzW8tdpi3fbBp7ZwkSeEkL0FUxx3B7/XMqtBYx+0iWO7QslOZtAJAEeD/z5S/GxisU4ps6TO6Zt1JTI+MHDFi5kzhBBC9hZJabPPAG0neJMQsxo0moRMHNvNitpJgPYQgFtF5LiINAHcB+CBHfx9I6fOvcLqHHzWFf+orBZd3/+GizwhhOwtmoWCxvBsZ1QKGmvQyOXZVQVNRH4bwF8AeJGIPC0i73PO9QHcD+BPAXwNwKecc1+9xusdC+Iypax+s7zO6Zt1xTqorlIcTYYjhBAyJnhzCwpoOyMZYR80YYQ2EWxXBNqui+OPvcDP/wTAn2z/ssYbnzJcTwUt/ze/wJNDZOy8WZmEcI4QQsheIin7oDFC2wmNEbo4kslgu8+MvqoB1v0rLBERRFLPJtx1xdr2vqxB4xwhhJA9RbM0CRnxhUw4cSSIIzE76GSANnlYmITUjjrXoAHVwkEmA2sFjTVohBCyNykVNFah7YhGbLvP4p5u8ijLqbZ4dAzQAuKaG2lEItx8TxDWdYO+Bq2u858QQsjl8bbwWTbiC5lw4igyS28E6iso1Bm/x2o34iv+PgZoAVWvsHpOeCpok4V1iiNTWwghZG9SujiyBm1HNIz3WQnrViYOBmjXgIhABIhr+qnEVNAmiirF0WY8x0bVhBCyJ4nLFEeyE5JYTBU0vq8nDx9jtJMrBxs1DUWunVikljb7QK7E1PXe6khkrqDRZp8QQvYift2ngLYzlmZaWJxumo3HrKjJwwfVWylo27LZ30v87Jtvw2tvWR71ZagQR0IXxwnC2iTkzsPzAIDbrp81GY8QQsh4IMjfMxkjtB3xT954C9776uNm4zFAmzz8M2sxQLs6fvr1t4z6EtSIhDVok4R1o+ofvusQ7jw8j5uXZ0zGI4QQMh7MtvPt4A++5OCIr2Sy6TQTdJp2W2vu6SaPuFTQrpzEyABtDxFHbEI8SfgAzeqZiQiDM0II2YNMtxL87T//AcxNNUZ9KeQqsKx3I7uDN2SbooJGPLEILVknCL/u8pERQgjRZp9h7RTZHWgSMnls9FIAdHEkARFt9icKbw7CJ0YIIYSQYXz/OjI5bPTzAK1FF0fiieniOFEIFTRCCCGEvACMzyaPjV7eDZ4KGin58VfdiB++69CoL4NsE6YuEEIIIeSFYFbU5PHKmxYBAO9+5bEr/j7WoO0h3vcaO+tXsnN8vaAwyZEQQgghQzBAmzyO7OvgiQ+/fcvfRwWNkDGFKY6EEEIIeSFo/FZfGKARMqaUNvsjvg5CCCGEjB80CakvfLKEjDnsXUcIIYSQYRif1Rc+WkIIIYQQQiYMKmj1hU+WkDHFjfoCCCGEEDK2MD6rL3y0hIwpzuUhGjMcCSGEEDIMFbT6widLyJhDm31CCCGEDEOX/frCAI2QMaUQ0KigEUIIIeR50ESsvjBAI2RMcUUVGpdfQgghhJC9AwM0QgghhBBCCBkTGKARMqYwxZEQQgghZO/BAI2QMcXb7DPHnBBCCCFk78AAjZAxpVTQRnsZhBBCCCHEEAZohIwp3iSEERohhBBCyN6BARohYw77oBFCCCGE7B0YoBEypvgUR0IIIYQQsndggEbImEOPEEIIIYSQvQMDNELGFOfYqJoQQgghZK/BAI2QMYV90AghhBBC9h4M0AgZU8o+aNTQCCGEEEL2DAzQCCGEEEIIIWRMSEZ9AYSQy8MUR0IIIYRciQ+87mbsn2mO+jLILsMAjZAxxTeqZnxGCCGEkMvxobfdPupLIAowxZGQMeWHXnoIAPCOuw6N+EoIIYQQQogVVNAIGVNuOTCDJz789lFfBiGEEEIIMYQKGiGEEEIIIYSMCQzQCCGEEEIIIWRMYIBGCCGEEEIIIWMCAzRCCCGEEEIIGRMYoBFCCCGEEELImMAAjRBCCCGEEELGBAZohBBCCCGEEDImMEAjhBBCCCGEkDGBARohhBBCCCGEjAkM0AghhBBCCCFkTGCARgghhBBCCCFjAgM0QgghhBBCCBkTGKARQgghhBBCyJjAAI0QQgghhBBCxgQGaIQQQgghhBAyJjBAI4QQQgghhJAxgQEaIYQQQgghhIwJ4pwb9TVsGxE5BeDJUV8HGWv2Azg96osgYw3nCNkKzhGyFZwjZCs4R8hW3OCcW77c/5ioAI2QrRCRLzjn7hn1dZDxhXOEbAXnCNkKzhGyFZwjZCcwxZEQQgghhBBCxgQGaIQQQgghhBAyJjBAI3Xjo6O+ADL2cI6QreAcIVvBOUK2gnOEXDOsQSOEEEIIIYSQMYEKGiGEEEIIIYSMCQzQSC0QkX8gIl8VkUxE7hn6f78gIt8UkUdE5C2jukYyPojIr4jICRH5YvHPD476msh4ICJvLdaKb4rIh0Z9PWT8EJEnROThYu34wqivh4weEfm4iJwUka8EP1sUkU+LyKPFv/eN8hrJZMEAjdSFrwD4EQAPhj8UkTsA3AfgxQDeCuA/iEhsf3lkDPm3zrm7i3/+ZNQXQ0ZPsTb8OoC3AbgDwI8Vawghw7yhWDtoo04A4LeQ7zFCPgTgs865WwF8tvhvQrYFAzRSC5xzX3POPXKZ//VOAL/jnNt0zn0LwDcB3Gt7dYSQCeFeAN90zj3unOsC+B3kawghhLwgzrkHAZwd+vE7AXyi+PUnAPw9y2sikw0DNFJ3DgN4Kvjvp4ufEXK/iHy5SE1h6gkBuF6Q7eEA/C8R+WsR+clRXwwZW65zzj1b/Po5ANeN8mLIZJGM+gII2S4i8hkA11/mf/2ic+4PrK+HjDdXmi8A/iOAX0W+0fpVAP8awHvtro4QMsG8xjl3QkQOAPi0iHy9UFAIuSzOOScitE0n24YBGpkYnHNvuoY/dgLA0eC/jxQ/IzVnu/NFRP4zgD9SvhwyGXC9IFvinDtR/PukiPwe8tRYBmhkmO+IyEHn3LMichDAyVFfEJkcmOJI6s4DAO4TkZaIHAdwK4C/GvE1kRFTvCw970JuMkPIQwBuFZHjItJEbjD0wIiviYwRIjItIrP+1wDeDK4f5PI8AOA9xa/fA4CZPmTbUEEjtUBE3gXg3wFYBvDHIvJF59xbnHNfFZFPAfg7AH0AH3TOpaO8VjIW/EsRuRt5iuMTAH5qpFdDxgLnXF9E7gfwpwBiAB93zn11xJdFxovrAPyeiAD5HuqTzrn/OdpLIqNGRH4bwOsB7BeRpwH8MoAPA/iUiLwPwJMA/uHorpBMGuIcU2IJIYQQQgghZBxgiiMhhBBCCCGEjAkM0AghhBBCCCFkTGCARgghhBBCCCFjAgM0QgghhBBCCBkTGKARQgghhBBCyJjAAI0QQgghhBBCxgQGaIQQQgghhBAyJjBAI4QQQgghhJAx4f8DcOrC0R/sqQ8AAAAASUVORK5CYII=", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "targets = (16, 17)\n", "xmax = 15\n", @@ -256,6 +357,7 @@ "lanczos = eval_lanczos(x)\n", "rel_error = calc_rel_error(lanczos, mean_lag)\n", "rel_error_simple = evaluate(x, targets[-1])\n", + "rel_error_opt = evaluate2(x)\n", "# rel_error = evaluate(x, target)\n", "\n", "_, axs = plt.subplots(\n", @@ -265,6 +367,8 @@ "axs[1].semilogy(x, np.abs(rel_error), label=targets)\n", "axs[0].plot(x, rel_error_simple, label=targets[-1])\n", "axs[1].semilogy(x, np.abs(rel_error_simple), label=targets[-1])\n", + "axs[0].plot(x, rel_error_opt, label=\"Optimal\")\n", + "axs[1].semilogy(x, np.abs(rel_error_opt), label=\"Optimal\")\n", "axs[0].set_xlim(x[0], x[-1])\n", "# axs[0].set_ylim(*(np.array([-1, 1]) * 4.2e-8))\n", "# axs[1].set_ylim(1e-10, 5e-8)\n", @@ -287,9 +391,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 79, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "z = 0.5\n", "ns = [4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12] # np.arange(4, 13)\n", @@ -371,9 +501,44 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 81, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 3.53233831 4.88557214 6.2238806 7.56716418 8.90547264 10.23383085\n", + " 11.5721393 12.91044776 14.23880597 15.57711443 17. ]\n", + "Intercept=1.34093, Bias=0.854093\n", + "35.0\n" + ] + }, + { + "data": { + "image/png": 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", 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jXtcXKCdw128HrADODhWEbeluAtITtbQ43t2xl7Vv/J1LP/hXHmuewVXxC7g/598YXFTCrHEectPV91F6lk6/m4BzbqmZDTlu9WwC94kDeBRYDHzvuG0uBuY75/YEC50PlABPhaMuke6u2d/C29v2MK/Cx8trfFTvbyApPpvM7Mu4pe5xjpx/O9+/+PpIlykSlTrzHJzHOVcVfOwjcIPT4w0AdrRZrgyuE+mxGptbWLa5lnkVPl5ZW82eQ42kJMZx0ahcSsd7mZm6gd5/KYOpd5Ba/iCMukgXV4uE0CWTTJxzzsw6dCzUzOYAcwDy89XMVWJLfZOfpR/sYl6FjwXrAn0f05ITmD4ml9JCLxeOzqFXUkLghqLPXfdxi6yhU9T/UaQdnRlw1WaW55yrMrM8oCbENjv5+DAmwEAChzJP4Jx7AHgAAufgwluqSNc71NDMog01lFX4WLS+hsONfjJTE5k1zktpoZfPjGjT97HVzpXq/yhymjoz4F4ErgZ+Gvz9lxDbvAz8p5n1CS7PAu7qxJpEIqruSLDvY4WPpcG+j9lpSXx+4gBKC72cN6wfifEh+j62Uv9HkdMWrssEniIwEss2s0rgbgLB9qyZXQt8CFwe3LYIuME5d51zbo+Z/Rh4J/hW97ROOBGJFbsPNjB/bSDUlm0O9H3My0zhq5PyKS30UjREfR9FOkNYLhPoarpMQKJddWvfx9U+3tq6mxYH+X17UVropaTQy4SB6vsoEg6dfpmAiMCOPYePNjNe8WHgUs4RuWl8Z9oISgq9FOSp76NIV1LAiZxKiPZYbF0KO1eyefR1R5sZr94Z6PtYkJfB7cWjKB3vZUSu+j6KRIoCTuRUgu2x+MojuCFT2LHyZbLLrufu5H/hub8tAeDMQVncVTqGkkIvg/up76NINFDAiZyCGzKFLRfNJe+Jr/O8zeKzjWVc23Qz/pwi7p7s5eJxXvqr76NI1FHAiYTQ0uJYsX0vZasDLbJ27nPcnjidm+KfZfWI6/n1528hJz050mWKyEko4ESCmv0tvLV1D2UVVby8pppdBxpIio9jyshs/uPMvUx9fwmccwfjyx+E2kshXdeeiUQzBZz0aI3NLbyxqZayiirmr61m7+EmUhPjuWh0DiWFXqaPySW9ajk89124/BG1xxLpRhRw0uPUN/lZvGEX8yqqeHVdDQcaAn0fZ4wN9n0clUtqUpsWWWqPJdItKeCkRzjY0MzC9TXMq6hi0fpdHGnyk9UrkZJCL6XjA30fkxPiQ79Y7bFEuiUFnMSsusNNzF9XzbyKKpZurKWxuYXstGS+eNYASgvzOHdY35P3fRSRbk0BJzGl9mADr6yppqyiiuWbd9Pc4uifmcLXzs2ntDCPswf3Ud9HkR5CASfdnq+unnkVVZRV+Hhn2x5aHAzu14trpwyltDCPCQMz1SJLpAdSwEm3tGPPYcqCofbu9n0AjMxN48ZpIygpzGNsXrpCTaSH69SAM7PRwDNtVg0Dfuic+1WbbS4icK+4rcFVf3LO3dOZdUmUa6f3Y+0Hb/J04hcoq/Cx5qP9AIzrn8G/zBpFSWEeI3LTIlOviESlTg0459wG4EwAM4sncAfvF0Js+ppz7tLOrEW6kWDvR/flh1mXMpE1b/yV4rV3clPDTSxv+YCJ+Vn86yVjKBmXR36/XpGuVkSiVFceopwBbHbOfdiFnyndjHOO9xPOYE3+PXz2sauY3zyDq+IX8Ot+P+Disy/ml4Ve8jLV91FETq0rA+4K4Kl2njvfzN4HPgL+xTm35vgNzGwOMAcgPz+/04qUrudvcaz4cG+gRVaFj4/q6kmI60uv7M9xy/4nOHTebfyw5IZIlyki3UyX3NHbzJIIhNc451z1cc9lAC3OuYNmdglwr3Nu5MneT3f07v6a/S28uSXQ9/GVtcG+jwlxTB2ZTUlhHiW9PiDtr9dB0bVQ/qDaYolISNFwR+9SYOXx4QbgnNvf5vFLZnafmWU752q7qDbpIg3N/kDfx9U+5q+rZl+w7+O0MTmUFOYxbXQO6SmJgZuJPnfdx6Gm3o8i8il0VcB9lXYOT5qZF6h2zjkzmwTEAbu7qC7pZEca/Sz54Ni+j+nBvo8lhXlcOCrn2L6PoN6PIhIWnR5wZtYbKAaub7PuBgDn3P3Al4Fvm1kzcAS4wnXFcVPpNAfqm1gUbGbctu9j6XgvpYV5TB7Rr/2+j6DejyISFp0ecM65Q0C/49bd3+bxXGBuZ9chnStU38ec9GS+dHaw7+PQviSo76OIdCF1MpFPrb2+j1edO5jS8V7OylffRxGJHAWcfCKh+j4O6deL66YMo7TQyxnq+ygiUUIBJwHttMdi50p2FMw5oe/jKE8aN04fSWmhlzFe9X0UkeijgJOAYHus1tmLO999mb4vzeGelDt46m+LACgckMF3Lx5NSaGX4Tnq+ygi0U0BJwC4IVP4cPp95D7xdf4UdzGlDS/xraabaehzJt+/JI+SQi+D+qrvo4h0Hwq4Hsw5x/uVdZRVVDGvwseHu/3cljCNmxOe4f3hc/if2TfjzUyJdJkiIp+KAq6HCd330Zg8IpsfFu5m2qqlcM4dTCh/EPZ8DjJ17ZmIdE8KuB6gyd/CW8G+jy+vqab2YGvfxxxunzWamWM9ZFYvh+fugMsfUXssEYkJCrgYFarvY6+keKaNzqWk0Mu0MbmkJbf536/2WCISYxRwMSTQ97GGsgofC1v7PqYkMHOsh5JCLxeOyiElsZ0WWWqPJSIxRgHXzR2ob2Lh+hrmVfhYvCHQ97FPr0QuGZ9HyXgvnxmeTVKCWmSJSM+jgOuG9h1u5JW11cyr8PH6xloa/S3kpifz5bMHUlroZZL6PoqIdMndBLYBBwA/0Hz8jeks0ALjXuAS4DBwjXNuZWfX1d3sOtDAK2t9lK32sXzLbvwtjgFZqXz9/MGUFgb6Psap76OIyFFdNYKbdpIbmJYCI4M/5wK/C/6OfSdpj8UFt/LRviPMq/Axb02g76NzMDS7N3OmBvo+jh+gvo8iIu2JhkOUs4HHgveAe9PMsswszzlXFenCOt1x7bHYuhT/M1fz9zH/jwd/+wbv79gHwGhPOjdPH0npeC+jPer7KCJyOroi4Bzwipk54H+dcw8c9/wAYEeb5crgutgPuOBUfP8zV1Oe80XGVD7LDQ03sfzNdMYPcHz34tGUFnoZpr6PIiKfWFcE3AXOuZ1mlgvMN7P1zrmln/RNzGwOMAcgPz8/3DV2Keccaz7az7wKH2UVLVx28EJuqf89z/X+KjOmf5n/Hqe+jyIiHdUVd/TeGfxdY2YvAJOAtgG3ExjUZnlgcN3x7/MA8ABAUVGR67SCO0lLi+O9yn2Bc2oVPrbvOUycwTf77+D61MUcPOs2vrL6URh4JfQdFulyRUS6vU4NODPrDcQ55w4EH88C7jlusxeBG83saQKTS+pi5fybv8XxzrY9R0PNt7+exHhj8vBs/umi4ZSmbSTzb/8NVz4WOFw5ZpraY4mIhElnj+A8wAvBSREJwJPOuXlmdgOAc+5+4CUClwhsInCZwDc7uaZO1eRvYfnm3ZRV+Ji/1kftwUaSE+KYOiqHOwpHM2Osh8zUxMDGr/9J7bFERDqJBSYvdi9FRUWuvLw80mUcVd/k5/WNtZRV+Fiwrpq6I030Topn2phg38fRufROjoYJqyIiscXMVhx/fXUrfet+Socbm1m8YRdlFT4Wra/hYLDvY/FYD6Xj85gyMrv9vo8iItLpFHCfwP76Jhauq6GsooolH+yivqmFvr2TuPSMwB2vJ6vvo4hI1FDAncLeQ43MX1tNWUUVb2zaTaO/BU9GMv9QNIiSwjzOGdJHfR9FRKKQAi6EmgP1vLymmnkVVby5ZQ/+FsfAPqlcPXkwJYV5TByUpb6PIiJRrmcF3El6P+4svD44nb+K8g/34hwMy+nNDRcOo7Qwj3H9M9QiS0SkG+lZAXdc70ffe6+Q+fd/5D9S7+Dxvy0EYIw3nVtnjKJ0vJeRuWkKNRGRbqpnBVzwOrPGp7/Bc8yipP4lvtV0M4czJ/C9kjxKC70Mye4d6SpFRCQMelbAQWDkNvJrfK1iLu8Om8PPZ9/EgKzUSFclIiJh1vOm/21dSv6Wp2DqHUys/iMD9r4T6YpERKQT9KyA27r043Nw078f+P3cNYH1IiISU3pWwO1c2X7vRxERiSk96xzcBbeeuG7oVDU2FhGJQT1rBCciIj1Gt7ybgJntAj7s4NtkA7VhKCcWad+0T/smNO2X9mnftC8c+2awcy4n1BPdMuDCwczK27vFQk+nfdM+7ZvQtF/ap33Tvs7eNzpEKSIiMUkBJyIiMaknB9wDkS4gimnftE/7JjTtl/Zp37SvU/dNjz0HJyIisa0nj+BERCSGKeBERCQmKeBERCQmdctWXdnZ2W7IkCGRLkNERCJsxYoVte1d6N0tA27IkCGUl5dHugwREYkwM2u3q5UOUYqISExSwImIxLD7l2xm2eZj2z0u21zL/Us2R6iirqOAExGJYWcMzOTGJ989GnLLNtdy45PvcsbAzAhX1vm65Tk4EREJrdnfQu3BRnz76/HV1VNzoJ4pI7K55uF3GD8gk621h5h75UQmD8+OdKmdTgEnItINOOfYf6SZ6gOB4PLtr6dmf30wyBqoCa6vPdhAy3ENqhLijPg4Y8WHe/n6eYN7RLiBAk5EJOzuX7KZMwZmHhMkyzbXsqqyjhsuHH7C9g3Nfmr2N1B9NLDqqTnQcEKQ1Te1nPDaPr0S8WSk4MlIYaw3A09GMp7MFLzBdZ6MFD7wHeA7T66kobmFP66spHS8t0eEXLfsRVlUVOR0mYCIRKvW81y/uWIio/PSeWWNj/98aT3/cM4g0pITjgZZdTDU9hxqPOE9khPi8GQEgyozBW9G8tHA8mam4ElPITcjmZTE+NOqZe6VE/nx39bhWhw1Bxti5jClma1o755yGsGJiITZ2YP78Pkz+/P1h9465nDhg69vxQyy05LxZCQzICuFs/KzjgkyT0Yy3owUMlMTMbMO17Kqsu5omBWPzWXuok387qqzWVVZFxMBdzIKOBGRMGlo9vNceSX3LdrER3X1eDOS8e1v4JLxXv5xyjA8GSnkpCeTGN91E9jbHhItLvDy64WbOFDfHPJQaazRZQIiIh3U0Ozn8Tc/ZNrPFvODP1fgzUzhrtIxNPodN08fwZtb9nCkyU//rNQuDbfjFQ7IwJuRwoK11RGroStpBCci8ik1NPt5Njhiq6qr5+zBffivL59BvBk3PvXu0UOD5w3vd/Q8WCQPC5oZMwty+dPKndQ3+U95/q67C8s/JcysxMw2mNkmM7szxPPJZvZM8Pm3zGxIcH2xma0ws9XB39PDUY+ISGdqaPbzhzc/5KKfLebf/lxB/6xU/nDtJJ6/4XymjMxh1c66Y8Js8vBs5l45kVWVdRGuPHCY8nCj/4TuJrGowyM4M4sHfgsUA5XAO2b2onNubZvNrgX2OudGmNkVwH8B/wDUAp9zzn1kZoXAy8CAjtYkItIZQo3YfvblCXxmRL9jJoSEOr81eXh2VEzqOG9YX9KSE5i/tobpYzyRLqdTheMQ5SRgk3NuC4CZPQ3MBtoG3GzgR8HHzwNzzcycc++22WYNkGpmyc65hjDUJSISFqcbbN1BckI8F47KYcG6av6jpZC4uO5V/ycRjoAbAOxos1wJnNveNs65ZjOrA/oRGMG1+hKwsr1wM7M5wByA/Pz8MJQtInJyDc1+nn1nB/ct3tztg62t4gIPf19dxfuV+5iY3yfS5XSaqJhkYmbjCBy2nNXeNs65B4AHIHChdxeVJiI90PHBVhQjwdbqotE5xMcZC9ZVK+BOYScwqM3ywOC6UNtUmlkCkAnsBjCzgcALwDecc7F//wYRiVqxHmytsnolMWlIX+avrea7F4+JdDmdJhwB9w4w0syGEgiyK4Arj9vmReBqYDnwZWChc86ZWRbwd+BO59wbYahFROQTaw223y7ajG9/INh+/pUJTB4eW8HWVnGBh3v+tpYPdx9icL/ekS6nU3T4MgHnXDNwI4EZkOuAZ51za8zsHjO7LLjZg0A/M9sE3Aa0XkpwIzAC+KGZvRf8ye1oTSIip6O+yc9jy7dx4X8v5t/+soaBfVJ54rpzee6G8/nMiOyYDTcIBBzA/Bi+6FvNlkWkx6lv8vNs+Q7uC47YzhnSh1tnjorpEVsoJb9aSmZqIs9cf36kS/nU1GxZRITQwfaLy2P7UOTJFBd4uG/xZvYeaqRP76RIlxN2CjgRiXmhgu2Xl0/g/B4abK1mjvXwm4WbWLShhi+eNTDS5YSdAk5EYkKom4wu3lDDE29uZ9XOfVTvb1CwHWf8gEw8GcnMX1utgBMRiVZnDMw82tD4rPw+/LRsPY8u34ZzMGlIX/7n8jMVbMeJizNmjPXw53djs/myAk5EujXnHAcamslJS+b6qcO47tFyDDjU6GeMJ50ffq5AwXYSxQUennxrO8u37Gba6NiaxK6AE5Go1djcQs2Beqr311O9vwFfXevjenzBddX76znc6D/htV+YOIBfXj5BwXYKk4f3o3dSPAvWVivgREQg9DmvZZtrWVVZd8q7RTvn2Hu4KURgHRtkuw81nvDapIQ4PBnJeDNSKOifwfQxuXgzUsjNSKb2YAO/fnUT3zh/ME8ERyXR0ME/miUnxDM12Hz5x7Njq/myAk5EPpW257wmD89m2eZabnzyXX75lQlsqz3UJrDq8dU1UH2gnuq6QJDV7G+g0d9ywntmpyXhyUghLzOFCYOy8Gak4M1MJjcjJfA4I4WsXokhR2XLNtfy739dy++uOovJw7M5P0puMtodFBd4KKvwsXpnHRMGZUW6nLBRwInIafG3OHYfbMC3vz4wwjrQwNSR2Vzz8Dt4MpL5aO8RkhPiuOaRd054ba+keLwZKXgyUiga3AdPZsrRZU9GCt7MFHLSkklK+PTNlVZVtn+TUQXcyU0bnXu0+XIsBZw6mYj0cM45DjY0Hx1pHTvyCgRZdV09uw424G859vsiPs5ISYjjUKOfYTm9uWBEdiCwjgZXMp6MFNKSE3QuLMr9w/8up+5IE/NunRrpUj4RdTIRiRGf9LxXY3MLuw6GmJxR9/EEDV87kzQyUhLwZgaCamRudiC0MlPwpCfjDY7APqg+yM1Pv8u1Fwzl8be2U1Lo1Wipmyou8PCTv69jx57DDOrbK9LlhIUCTqQbOXre66sTGZOXwStrfPzk7+v46qRB3Ltg4zGjr+r99dQeDDFJIz6O3OAkjbH9M7hodO7RkVbb0Vdq0smviVq2uZabn/74HNd5OufVrbUG3Py11XzrgqGRLicsdIhSpBtp8rfws5c38PvXttAS4q9udloSuekpR0derbMNAyOvwPo+7UzS+KQ6MotSotOs/1lCv97JPDXnvEiXctp0iFKkm2vyt/DCuzuZu3AT2/ccJjc9mZoDDZQWerluyjA8Gcnkpqd0aJLGJxUqxCYPz9borRsrLvBw/5It1B1uIrNXYqTL6bCu+9sQBe5fspllm2uPWbdscy33L9GNxCU6NflbePadHUz/xWLueH4VmamJfHfWKJpbHDdPH8FbW/fQ0OxnYJ9eXRpuEptmjvXgb3Es2lAT6VLCokf9jWg9f9Eacq3X7ZwxMDPClYkc65hg++MqslKTePDqIu4qHcODb2xj7pUTuW3WaOZeOfGYP9MiHTFhYBY56ckxcxPUHnWIsvW6mG8/vpL8vqns2HOE+4IXhYpEgyZ/Cy+s3MlvFm1kx54jjB+QyY+uHsf0MbmYGfcv2axrvaTTxMUZM8fm8tf3q2ho9pOc0L2bL/eogIPAF8I5Q/qwYF0NBvzl3Y8YkJXK4H69I12a9GDHB9sZAzP598vGMW107jETQnTeSzpbcYGHp97ewZtb9nDhqJxIl9MhPS7glm2uZeX2fXxz8hCefHs7f1xZyfMrK5k9oT/fmT6C4TlpkS5RepAmfwt/WlnJ3EWbThpsIl1l8vBsUhPjmb/W1+0DLizn4MysxMw2mNkmM7szxPPJZvZM8Pm3zGxIm+fuCq7fYGYXh6Oe9rSec5t75UTuvmwcD3/zHNKSE5hV4OGliipm/nIJNz31Lht8BzqzDBGa/C088852pv18Md/742r69ErioWuK+Mt3PsP0MR6Fm0RMSmI8U0dls2BtDd3xMrK2OjyCM7N44LdAMVAJvGNmLzrn1rbZ7Fpgr3NuhJldAfwX8A9mVgBcAYwD+gMLzGyUc+7EtgphEKpX3X1XncWqyjp+/PlCfv/aVv6wfBt/ff8jSsZ5uXH6CAoHaAKKhE/riO03CzdRuTcwYrtntkZsEl2KC7y8vKaaip37Gd+NJ+GF4xDlJGCTc24LgJk9DcwG2gbcbOBHwcfPA3Mt8Ld5NvC0c64B2Gpmm4LvtzwMdZ3gVOcv7iwdw/VTh/HwG1t5eNk25q3xMWNMLjfNGMmZMdSAVLre8cE2YWAmP55dyEWjcxRsEnWmj8klzmD+uuoeH3ADgB1tliuBc9vbxjnXbGZ1QL/g+jePe+2AUB9iZnOAOQD5+flhKDu0Pr2TuG3WaK6dMoxHl23joTe28vnfvsGUkdncPGMk5wzp22mfLbFHwSbdUd/eSRQN7sv8tdXcVjwq0uV8at1mkolz7gHgAQi06ursz8tMTeTmGSP51gVD+cPyD/n9a1v4yv3LOW9YX26eMZLzh/XTF5S0q8nfwh9XBCaPKNikOyou8PAfL3Xv5svhmGSyExjUZnlgcF3IbcwsAcgEdp/mayMqLTmBb180nNe+N40ffHYsW3Yd4sr/e4uv3L+cJR/s6vYnYSW8mvwtPP12YPLInX9aTb/eSTx8zTn8+TufYdoYnWeT7mNmgQeAV9d134u+O9xsORhYHwAzCITTO8CVzrk1bbb5DjDeOXdDcJLJF51zl5vZOOBJAufd+gOvAiNPNckkks2W65v8PFu+g/sXb+ajunomDMripmkjmDFWX149WWPzx9P9K/ceYcKgLG6dOZKLRmnEJt3XzF8uwZORzBPXRW/z5U5tthw8p3Yj8DIQDzzknFtjZvcA5c65F4EHgT8EJ5HsITBzkuB2zxKYkNIMfKezZlCGS0piPN84fwhXnJPPH1dWct/iTVz3WDkFeRncNH0EF4/zEhenL7SeIlSw/fjzhQo2iQnFBR7+b+kW6o40kZna/Zov63Y5HdTkb+Ev733EbxdtYmvtIUZ50rhx+kg+Oz6PeAVdTAh1W5ilH+ziybe3s7qyjp37NGKT2LTiw7186XfLuPeKM5l9Zsj5fxF3shFcj2q23BkS4+P48tkDWXDbhdx7xZk4Bzc/9S7F/7OEP66opNnfEukST4vutNC+tk26G5tb+Mnf13LNw28zr8JHdnoyD3/zHP78T5N1LZvEnImDsshOS+q2zZe7zSzKaBcfZ8w+cwCfO6M/89b4+M3CTdz+3Pvc++pG/umi4XzxrIFRfTuTo3eKDl4I37brS092sKGZ3PQUvn3hMK57tJx4Mw40NDM8pzf/dmkBF2rEJjEsLs6YMcbDS6uraGxuiervsFB0iLKTOOdYsK6G3yzcyKrKOgZkpXLDhcP4StEgUhIj06G72d/CroMN+Orqqd5fT/X+Bnz766muq6f6QD1bdx2iqq6ehHjD3+IYlZvO8Nw0ctKTyU5LIic9OfCTlkJOejL90pJIjO9ef+BbNflb2HWgIbgf6vHV1ePb30DN/np8wZ+a/Q0cbGg+4bWXTejPvVecqWCTHmHB2mque6ycP1w7iSkjo683pe7oHQFmRnGBh5ljc1nywS5+s3AT//aXNcxdtInrpw7nq5PyeXT5thPO7SzbXMuqyrqQXVfa45xj/5Hmo1/M1cHQ8gVDrDq4vvZgA8f/eyYhzvBkpODJSGbCoCxy0o/wfmUdIz1pZPVOZL1vP69tbGB//Ylf9BC4IDQnLfnj8EtPPrqc3WZ9VmriaU++CXXO63T3i3OOuiNNH/+317XZJ/s/3ien2hejPelMHZmDNzOwXHuwgbkLN/ON8wfzxFvbWb5ltzr4S49wwchsUhLjmL+2OioD7mQ0gusizjmWb97Nva9u5K2te8hOS2JWgYeyCh+//dpZJxwWbP3ybGj2U9M60gqONAJf1B+PPqr311PfdOK5vj69EvFkpAS+pNNT8GSm4A1+gbeu79sr6WjwtH7+Vefm8/hb24+po77JT+3BBnYdCP60fRxcrj3YQM3+BhqaT6wlIc6OCbwTQrFNIK7asY8bnzrxcOkvL5/AsOw0qg+02Q919VQfODbIQn3+J90XbR3//yXU/yeRWPaPj5WzZmcdb9w5PeqOXJxsBKeAi4C3t+7hNws38trGWtKS4/G3wHnD+rF8y27OG9oXjKNf4HsPN53w+uSEuODIIvDjDX5Jt35RezMChxA/yaHQcH2JO+c42NB80iBsfbz7UCP+lhP//KUmxpOeksCeQ43kZaXw0d56UpPiONhw4hUkbffF8YHVuu6T7ovjdWREKRILni3fwR3Pr+JvN10QdQ3oFXBRauX2vcxduImF62uOrstJTw5+UQe+rL0ZgdFG65e1NyOFjNSEsP8rKhJf4i0tjr2HG08MwWAQrvhwL5V7jzA0uzeTh/frsn0hIsfafbCBov9YwM3TR/LPUdabUufgotRZ+X24bspQVn64ly+cNYA/v7uTe684MyKHvSJxp+i4OKNfWjL90pIZ4z32uWWba3ltYy03Tx/B429t57Nn5OlwoEiE9EtL5uz8PixYVx11AXcy3XMKXIxoPQx431VncffnxvHbr5119Hqrnqzt4dHbZo1m7pUTtV9EIqy4wMOaj/azc9+RSJdy2hRwERTqBqxzr5zIqsq6CFcWWdovItGnOzZf1jk4ERE5LdN/sZgBWan84drjb/kZOWrVJSIiHVZc4OHNLbvZX3/i7O5opIATEZHTUjzWQ5PfsWTDrkiXcloUcCIiclom5vehX+/u03xZASciIqclPs6YMTaXRRtqaOoGd0pRwImIyGmbOdbDgfpm3t66J9KlnJICTkRETtuUkTkkJ8R1i8OUCjgRETltqUnxTBmZzfy11UT7ZWYKOBER+USKCzzs3HeEdVUHIl3KSXUo4Mysr5nNN7ONwd992tnu6uA2G83s6uC6Xmb2dzNbb2ZrzOynHalFRES6xvQxHsyI+sOUHR3B3Qm86pwbCbwaXD6GmfUF7gbOBSYBd7cJwp8758YAE4HPmFlpB+sREZFOlpOezMRBWSyI8rZdHQ242cCjwcePAp8Psc3FwHzn3B7n3F5gPlDinDvsnFsE4JxrBFYCAztYj4iIdIHiAi+rd9ZRVRe9zZc7GnAe51xV8LEP8ITYZgCwo81yZXDdUWaWBXyOwCgwJDObY2blZla+a1f3uIpeRCRWFRfkArAgig9TnjLgzGyBmVWE+JnddjsXmE7ziafUmFkC8BTwa+fclva2c8494Jwrcs4V5eTkfNKPERGRMBqek8bQ7N7MX1dz6o0j5JQ3PHXOzWzvOTOrNrM851yVmeUBof5LdwIXtVkeCCxus/wAsNE596vTKVhERCLPzCgu8PDwG1s5UN9EekpipEs6QUcPUb4IXB18fDXwlxDbvAzMMrM+wckls4LrMLOfAJnArR2sQ0REutjMYPPlpR9E582IOxpwPwWKzWwjMDO4jJkVmdnvAZxze4AfA+8Ef+5xzu0xs4HA94ECYKWZvWdm13WwHhER6SJnD+5D395JzF/ri3QpIZ3yEOXJOOd2AzNCrC8Hrmuz/BDw0HHbVALWkc8XEZHIiY8zpo/J5ZU1Ppr8LSTGR1fvkOiqRkREupWZYz3sr2/mnW3R13xZASciIp/a1FHZJEVp82UFnIiIfGq9khK4YER0Nl9WwImISIcUF3io3HuEDdXR1XxZASciIh0yY2ygq8n8NdF1mFIBJyIiHZKbnsKZUdh8WQEnIiIdVlzg4f3KOqr310e6lKMUcCIi0mGzCgK99qNpNqUCTkREOmxEbhqD+/WKqsOUCjgREekwM6N4rIdlm3ZzsKE50uUACjgREQmTmQUeGv0tLP0gOu7ZqYATEZGwKBrch6xeiVFzE1QFnIiIhEVCfBzTx+SycEMNzf6WSJejgBMRkfApHuth3+Emyj/cG+lSFHAiIhI+U0flkBQfHc2XFXAiIhI2vZMTmDyiX1Q0X1bAiYhIWBUXeNi+5zAbaw5GtA4FnIiIhNXMsdHR1UQBJyIiYeXJSGHCwExe6c4BZ2Z9zWy+mW0M/u7TznZXB7fZaGZXh3j+RTOr6EgtIiISPYoLPLy/Yx81EWy+3NER3J3Aq865kcCrweVjmFlf4G7gXGAScHfbIDSzLwKRPVArIiJhVVzgBWDBupqI1dDRgJsNPBp8/Cjw+RDbXAzMd87tcc7tBeYDJQBmlgbcBvykg3WIiEgUGeVJY1Df1Ig2X+5owHmcc1XBxz7AE2KbAcCONsuVwXUAPwZ+ARw+1QeZ2RwzKzez8l27oqPPmYiIhBZovuzl9U21HIpQ8+VTBpyZLTCzihA/s9tu5wIXPJz2RQ9mdiYw3Dn3wuls75x7wDlX5JwrysnJOd2PERGRCJlZkEtjcwuvbYzMoCThVBs452a295yZVZtZnnOuyszygFAHW3cCF7VZHggsBs4HisxsW7COXDNb7Jy7CBER6fYmDelLZmoi89fWUFKY1+Wf39FDlC8CrbMirwb+EmKbl4FZZtYnOLlkFvCyc+53zrn+zrkhwAXABwo3EZHYcbT58vrqiDRf7mjA/RQoNrONwMzgMmZWZGa/B3DO7SFwru2d4M89wXUiIhLjZo71sPdwEysi0Hz5lIcoT8Y5txuYEWJ9OXBdm+WHgIdO8j7bgMKO1CIiItHnwtGB5ssL1lVz7rB+XfrZ6mQiIiKdJi05gfOHR6b5sgJOREQ61cwCD9t2H2bzrq7t6aGAExGRTjVzbC5Al/emVMCJiEinystMZfyAzC6/u4ACTkREOl1xgYf3duyj5kDXNV9WwImISKcrLvDgHCzswubLCjgREel0Y7zpDMhK7dLDlAo4ERHpdGZGcYGH1zfVcrixa5ovK+BERKRLFBd4aGhu4bWNtV3yeQo4ERHpEpOG9iUjJYEFXXSYUgEnIiJdIjE+jmljclm4vgZ/S+d3NVHAiYhIl5k51sPuQ42s3N75zZcVcCIi0mW27DpIfBzHHKZctrmW+5dsDvtnKeBERKTLnDO0L2bGi+99BATC7cYn3+WMgZlh/ywFnIiIdJnJw7O56tzBVO2v5wcvrObGJ99l7pUTmTw8O+yfpYATEZEuNWfqMLJ6JfL4W9u56tz8Tgk3UMCJiEgX27b7EHFm3Dx9BI+/tZ1lmzvnujgFnIiIdJnWc25zr5zIbbNGM/fKidz45LudEnIKOBER6TKrKuuOOec2eXg2c6+cyKrKurB/lnX1LcTDoaioyJWXl0e6DBERiTAzW+GcKwr1nEZwIiISk7rlCM7MdgEfdvBtsoGu6fjZ/WjftE/7JjTtl/Zp37QvHPtmsHMuJ9QT3TLgwsHMytsb1vZ02jft074JTfulfdo37evsfaNDlCIiEpMUcCIiEpN6csA9EOkCopj2Tfu0b0LTfmmf9k37OnXf9NhzcCIiEtt68ghORERiWI8LODMbZGaLzGytma0xs1siXVM0MbN4M3vXzP4W6VqiiZllmdnzZrbezNaZ2fmRrilamNk/B/8uVZjZU2aWEumaIsXMHjKzGjOraLOur5nNN7ONwd99IlljJLSzX34W/Pu0ysxeMLOscH9ujws4oBm43TlXAJwHfMfMCiJcUzS5BVgX6SKi0L3APOfcGGAC2kcAmNkA4GagyDlXCMQDV0S2qoh6BCg5bt2dwKvOuZHAq8HlnuYRTtwv84FC59wZwAfAXeH+0B4XcM65KufcyuDjAwS+qAZEtqroYGYDgc8Cv490LdHEzDKBqcCDAM65RufcvogWFV0SgFQzSwB6AR9FuJ6Icc4tBfYct3o28Gjw8aPA57uypmgQar84515xzjUHF98EBob7c3tcwLVlZkOAicBbES4lWvwKuANoiXAd0WYosAt4OHj49vdm1jvSRUUD59xO4OfAdqAKqHPOvRLZqqKOxzlXFXzsAzyRLCZKfQsoC/eb9tiAM7M04I/Arc65/ZGuJ9LM7FKgxjm3ItK1RKEE4Czgd865icAheuZhphMEzyfNJvCPgP5AbzO7KrJVRS8XmLauqettmNn3CZw6eiLc790jA87MEgmE2xPOuT9Fup4o8RngMjPbBjwNTDezxyNbUtSoBCqdc60j/ecJBJ7ATGCrc26Xc64J+BMwOcI1RZtqM8sDCP6uiXA9UcPMrgEuBb7mOuGatR4XcGZmBM6lrHPO/TLS9UQL59xdzrmBzrkhBCYJLHTO6V/igHPOB+wws9HBVTOAtREsKZpsB84zs17Bv1sz0ASc470IXB18fDXwlwjWEjXMrITAKZHLnHOHO+MzelzAERipfJ3ACOW94M8lkS5Kot5NwBNmtgo4E/jPyJYTHYKj2ueBlcBqAt8pPbZzh5k9BSwHRptZpZldC/wUKDazjQRGvD+NZI2R0M5+mQukA/OD38P3h/1z1clERERiUU8cwYmISA+ggBMRkZikgBMRkZikgBMRkZikgBMRkZikgBMRkZikgBMRkZikgBMRkZj0/wFhGivRNtCNJgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "bests = []\n", "N = 200\n", @@ -442,7 +607,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.10" + "version": "3.8.3" }, "orig_nbformat": 4 }, diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 90843b1..9c8f3ee 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -37,11 +37,42 @@ def find_shift(z, target): return zs, factor -def laguerre_gamma_shift(z, x=None, w=None, n=8, target=11): +def find_optimal_shift(z, n): + mhat = 1.34093 * n + 0.854093 + steps = int(np.ceil(mhat - np.real(z))) - 1 + return steps + + +def get_shifting_factor(z, steps): + if steps > 0: + factor = 1 / pochhammer(z, steps) + elif steps < 0: + factor = pochhammer(z + steps, -steps) + return factor + + +def laguerre_gamma_shifted(z, x=None, w=None, n=8, target=11): x, w = _prep_zeros_and_weights(x, w, n) + n = len(x) z += 0j z_shifted, correction_factor = find_shift(z, target) + + res = np.sum(x ** (z_shifted - 1) * w) + res *= correction_factor + res = drop_imag(res) + return res + + +def laguerre_gamma_opt_shifted(z, x=None, w=None, n=8): + x, w = _prep_zeros_and_weights(x, w, n) + n = len(x) + + z += 0j + opt_shift = find_optimal_shift(z, n) + correction_factor = get_shifting_factor(z, opt_shift) + z_shifted = z + opt_shift + res = np.sum(x ** (z_shifted - 1) * w) res *= correction_factor res = drop_imag(res) @@ -72,8 +103,10 @@ def eval_laguerre_gamma(z, x=None, w=None, n=8, func="simple", **kwargs): f = laguerre_gamma_simple elif func == "mirror": f = laguerre_gamma_mirror + elif func == "optimal_shifted": + f = laguerre_gamma_opt_shifted else: - f = laguerre_gamma_shift + f = laguerre_gamma_shifted return np.array([f(zi, x, w, n, **kwargs) for zi in z]) @@ -81,11 +114,10 @@ def calc_rel_error(x, y): return (y - x) / x -ns = np.arange(2, 12, 2) - # Simple / naive xmin = -5 xmax = 30 +ns = np.arange(2, 12, 2) ylim = np.array([-11, 6]) x = np.linspace(xmin + EPSILON, xmax - EPSILON, 400) gamma = scipy.special.gamma(x) @@ -104,7 +136,7 @@ ax.set_xlabel(r"$z$") ax.set_ylabel("Relativer Fehler") ax.legend(ncol=3, fontsize="small") ax.grid(1, "both") -fig.savefig(f"{img_path}/rel_error_simple.pgf") +# fig.savefig(f"{img_path}/rel_error_simple.pgf") # Mirrored @@ -130,7 +162,7 @@ ax2.set_xlabel(r"$z$") ax2.set_ylabel("Relativer Fehler") ax2.legend(ncol=1, loc="upper left", fontsize="small") ax2.grid(1, "both") -fig2.savefig(f"{img_path}/rel_error_mirror.pgf") +# fig2.savefig(f"{img_path}/rel_error_mirror.pgf") # Move to target @@ -163,12 +195,14 @@ v = ax3.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest") plt.colorbar(v, ax=ax3, label=r"$m$") ticks = np.arange(0, N + 1, N // 5) ax3.set_xlim(0, 1) -ax3.set_xticks(ticks, [f"{v:.2f}" for v in ticks / N]) +ax3.set_xticks(ticks) +ax3.set_xticklabels([f"{v:.2f}" for v in ticks / N]) ax3.set_xticks(np.arange(0, N + 1, N // 20), minor=True) -ax3.set_yticks(np.arange(len(ns)), ns) +ax3.set_yticks(np.arange(len(ns))) +ax3.set_yticklabels(ns) ax3.set_xlabel(r"$z$") ax3.set_ylabel(r"$n$") -fig3.savefig(f"{img_path}/targets.pdf") +# fig3.savefig(f"{img_path}/targets.pdf") targets = np.mean(bests, -1) intercept, bias = np.polyfit(ns, targets, 1) @@ -178,9 +212,7 @@ fig4, axs4 = plt.subplots( xl = np.array([ns[0] - 0.5, ns[-1] + 0.5]) axs4[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$") axs4[0].plot(ns, targets, "x", label=r"$\bar{m}$") -axs4[1].plot( - ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \bar{m}$" -) +axs4[1].plot(ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \bar{m}$") axs4[0].set_xlim(*xl) # axs4[0].set_title("Schätzung von Mittelwert") # axs4[1].set_title("Fehler") @@ -188,10 +220,49 @@ axs4[-1].set_xlabel(r"$z$") for ax in axs4: ax.grid(1) ax.legend() -fig4.savefig(f"{img_path}/schaetzung.pgf") +# fig4.savefig(f"{img_path}/schaetzung.pgf") print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") predicts = np.ceil(intercept * ns[:, None] + bias - x) print(f"Error: {int(np.sum(np.abs(bests-predicts)))}") +# Comparison relative error between methods +N = 200 +step = 1 / (N - 1) +x = np.linspace(step, 1 - step, N + 1) +gamma = scipy.special.gamma(x)[:, None] +n = 8 +targets = np.arange(10, 14) +gamma = scipy.special.gamma(x) +fig5, ax5 = plt.subplots(num=1, clear=True, constrained_layout=True) +for target in targets: + gamma_lag = eval_laguerre_gamma(x, target=target, n=n, func="shifted") + rel_error = np.abs(calc_rel_error(gamma, gamma_lag)) + ax5.semilogy(x, rel_error, label=f"$m={target}$") +gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") +rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) +ax5.semilogy(x, rel_error, label="$m^*$") +ax5.set_xlim(x[0], x[-1]) +ax5.set_ylim(5e-9, 5e-8) +ax5.set_xlabel(r"$z$") +ax5.grid(1, "both") +ax5.legend() +fig5.savefig(f"{img_path}/rel_error_shifted.pgf") + +N = 200 +x = np.linspace(-5+ EPSILON, 5-EPSILON, N) +gamma = scipy.special.gamma(x)[:, None] +n = 8 +gamma = scipy.special.gamma(x) +fig6, ax6 = plt.subplots(num=1, clear=True, constrained_layout=True) +gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") +rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) +ax6.semilogy(x, rel_error, label="$m^*$") +ax6.set_xlim(x[0], x[-1]) +ax6.set_ylim(5e-9, 5e-8) +ax6.set_xlabel(r"$z$") +ax6.grid(1, "both") +ax6.legend() +fig6.savefig(f"{img_path}/rel_error_range.pgf") + # plt.show() -- cgit v1.2.1 From 85e7d741f78ca0874b42db5cfbd18f4c28a933b3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 2 Jun 2022 15:23:21 +0200 Subject: Add presentation --- buch/papers/laguerre/definition.tex | 3 + buch/papers/laguerre/gamma.tex | 2 +- buch/papers/laguerre/images/estimate.pgf | 1160 +++++++++++++++++ buch/papers/laguerre/images/gammaplot.pdf | Bin 0 -> 23297 bytes buch/papers/laguerre/images/rel_error_range.pgf | 887 +++++++++++++ buch/papers/laguerre/images/rel_error_shifted.pgf | 1329 ++++++++++++++++++++ buch/papers/laguerre/images/schaetzung.pgf | 1160 ----------------- buch/papers/laguerre/images/targets.pdf | Bin 12940 -> 12940 bytes buch/papers/laguerre/main.tex | 2 +- buch/papers/laguerre/presentation/presentation.tex | 134 ++ .../laguerre/presentation/sections/gamma.tex | 50 + .../presentation/sections/gamma_approx.tex | 176 +++ .../laguerre/presentation/sections/gaussquad.tex | 67 + .../laguerre/presentation/sections/laguerre.tex | 88 ++ buch/papers/laguerre/scripts/gamma_approx.py | 36 +- 15 files changed, 3919 insertions(+), 1175 deletions(-) create mode 100644 buch/papers/laguerre/images/estimate.pgf create mode 100644 buch/papers/laguerre/images/gammaplot.pdf create mode 100644 buch/papers/laguerre/images/rel_error_range.pgf create mode 100644 buch/papers/laguerre/images/rel_error_shifted.pgf delete mode 100644 buch/papers/laguerre/images/schaetzung.pgf create mode 100644 buch/papers/laguerre/presentation/presentation.tex create mode 100644 buch/papers/laguerre/presentation/sections/gamma.tex create mode 100644 buch/papers/laguerre/presentation/sections/gamma_approx.tex create mode 100644 buch/papers/laguerre/presentation/sections/gaussquad.tex create mode 100644 buch/papers/laguerre/presentation/sections/laguerre.tex diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index 3e5d423..e511f43 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -18,6 +18,9 @@ x \in \mathbb{R} . \label{laguerre:dgl} \end{align} +Spannenderweise wurde die verallgemeinerte Laguerre-Differentialgleichung +zuerst von Yacovlevich Sonine (1849 - 1915) beschrieben, +aber auf Grund ihrer Ähnlichkeit wurde sie nach Laguerre benannt. Die klassische Laguerre-Diffentialgleichung erhält man, wenn $\nu = 0$. Hier wird die verallgemeinerte Laguerre-Differentialgleichung verwendet, weil die Lösung mit der selben Methode berechnet werden kann, diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index da2fa93..a04ec47 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -295,7 +295,7 @@ m^* \begin{figure} \centering -\input{papers/laguerre/images/schaetzung.pgf} +\input{papers/laguerre/images/estimate.pgf} \caption{Schätzung Mittelwert von $m$ und Fehler} \label{laguerre:fig:schaetzung} \end{figure} diff --git a/buch/papers/laguerre/images/estimate.pgf b/buch/papers/laguerre/images/estimate.pgf new file mode 100644 index 0000000..3d11371 --- /dev/null +++ b/buch/papers/laguerre/images/estimate.pgf @@ -0,0 +1,1160 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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Binary files /dev/null and b/buch/papers/laguerre/images/gammaplot.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_range.pgf b/buch/papers/laguerre/images/rel_error_range.pgf new file mode 100644 index 0000000..ff73501 --- /dev/null +++ b/buch/papers/laguerre/images/rel_error_range.pgf @@ -0,0 +1,887 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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a/buch/papers/laguerre/images/targets.pdf and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex index 9f836ef..f4263de 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -12,7 +12,7 @@ benannt nach Edmond Laguerre (1834 - 1886), sind Lösungen der ebenfalls nach Laguerre benannten Differentialgleichung. Laguerre entdeckte diese Polynome als er Approximationsmethoden -für das Integral $\int_0^\infty exp(-x)\, dx$ suchte. +für das Integral $\int_0^\infty \exp(-x) / x \, dx$ suchte. Darum möchten wir in diesem Kapitel uns, ganz im Sinne des Entdeckers, den Laguerre-Polynomen für Approximationen von Integralen mit diff --git a/buch/papers/laguerre/presentation/presentation.tex b/buch/papers/laguerre/presentation/presentation.tex new file mode 100644 index 0000000..f49cf1e --- /dev/null +++ b/buch/papers/laguerre/presentation/presentation.tex @@ -0,0 +1,134 @@ +\documentclass[ngerman, aspectratio=169, xcolor={rgb}]{beamer} + +% style +\mode{ + \usetheme{Frankfurt} +} +%packages +\usepackage[utf8]{inputenc}\DeclareUnicodeCharacter{2212}{-} +\usepackage[ngerman]{babel} +\usepackage{graphicx} +\usepackage{array} + +\newcolumntype{L}[1]{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{#1}} +\usepackage{ragged2e} + +\usepackage{bm} % bold math +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{mathtools} +\usepackage{amsmath} +\usepackage{multirow} % multi row in tables +\usepackage{booktabs} %toprule midrule bottomrue in tables +\usepackage{scrextend} +\usepackage{textgreek} +\usepackage[rgb]{xcolor} + +\usepackage{ marvosym } % \Lightning + +\usepackage{multimedia} % embedded videos + +\usepackage{tikz} +\usepackage{pgf} +\usepackage{pgfplots} + +\usepackage{algorithmic} + +%citations +\usepackage[style=verbose,backend=biber]{biblatex} +\addbibresource{references.bib} + + +%math font +\usefonttheme[onlymath]{serif} + +%Beamer Template modifications +%\definecolor{mainColor}{HTML}{0065A3} % HSR blue +\definecolor{mainColor}{HTML}{D72864} % OST pink +\definecolor{invColor}{HTML}{28d79b} % OST pink +\definecolor{dgreen}{HTML}{38ad36} % Dark green + +%\definecolor{mainColor}{HTML}{000000} % HSR blue +\setbeamercolor{palette primary}{bg=white,fg=mainColor} +\setbeamercolor{palette secondary}{bg=orange,fg=mainColor} +\setbeamercolor{palette tertiary}{bg=yellow,fg=red} +\setbeamercolor{palette quaternary}{bg=mainColor,fg=white} %bg = Top bar, fg = active top bar topic +\setbeamercolor{structure}{fg=black} % itemize, enumerate, etc (bullet points) +\setbeamercolor{section in toc}{fg=black} % TOC sections +\setbeamertemplate{section in toc}[sections numbered] +\setbeamertemplate{subsection in toc}{% + \hspace{1.2em}{$\bullet$}~\inserttocsubsection\par} + +\setbeamertemplate{itemize items}[circle] +\setbeamertemplate{description item}[circle] +\setbeamertemplate{title page}[default][colsep=-4bp,rounded=true] +\beamertemplatenavigationsymbolsempty + +\setbeamercolor{footline}{fg=gray} +\setbeamertemplate{footline}{% + \hfill\usebeamertemplate***{navigation symbols} + \hspace{0.5cm} + \insertframenumber{}\hspace{0.2cm}\vspace{0.2cm} +} + +\usepackage{caption} +\captionsetup{labelformat=empty} + +%Title Page +\title{Laguerre-Polynome} +\subtitle{Anwendung: Approximation der Gamma-Funktion} +\author{Patrik Müller} +% \institute{OST Ostschweizer Fachhochschule} +% \institute{\includegraphics[scale=0.3]{../img/ost_logo.png}} +\date{\today} + +\input{../packages.tex} + +\newcommand*{\QED}{\hfill\ensuremath{\blacksquare}}% + +\newcommand*{\HL}{\textcolor{mainColor}} +\newcommand*{\RD}{\textcolor{red}} +\newcommand*{\BL}{\textcolor{blue}} +\newcommand*{\GN}{\textcolor{dgreen}} + +\definecolor{darkgreen}{rgb}{0,0.6,0} + + +\makeatletter +\newcount\my@repeat@count +\newcommand{\myrepeat}[2]{% + \begingroup + \my@repeat@count=\z@ + \@whilenum\my@repeat@count<#1\do{#2\advance\my@repeat@count\@ne}% + \endgroup +} +\makeatother + +\usetikzlibrary{automata,arrows,positioning,calc,shapes.geometric, fadings} + +\begin{document} + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame}{Inhaltsverzeichnis} + \tableofcontents +\end{frame} + +\input{sections/laguerre} + +\input{sections/gaussquad} + +\input{sections/gamma} + +\input{sections/gamma_approx} + +\appendix +\begin{frame} + \centering + \Large + \textbf{Vielen Dank für die Aufmerksamkeit} +\end{frame} + +\end{document} diff --git a/buch/papers/laguerre/presentation/sections/gamma.tex b/buch/papers/laguerre/presentation/sections/gamma.tex new file mode 100644 index 0000000..37f4a0b --- /dev/null +++ b/buch/papers/laguerre/presentation/sections/gamma.tex @@ -0,0 +1,50 @@ +\section{Gamma-Funktion} + +\begin{frame}{Gamma-Funktion} +\begin{columns} + +\begin{column}{0.48\textwidth} +\begin{figure}[h] +\centering +% \scalebox{0.51}{\input{../images/gammaplot.pdf}} +\includegraphics[width=1\textwidth]{../images/gammaplot.pdf} +% \caption{Gamma-Funktion} +\end{figure} +\end{column} + +\begin{column}{0.52\textwidth} +Verallgemeinerung der Fakultät +\begin{align*} +\Gamma(n) = (n-1)! +\end{align*} + +Integralformel +\begin{align*} +\Gamma(z) += +\int_0^\infty x^{z-1} e^{-x} \, dx +,\quad +\operatorname{Re} z > 0 +\end{align*} + +Funktionalgleichung +\begin{align*} +z \Gamma(z) += +\Gamma(z + 1) +\end{align*} + +Reflektionsformel +\begin{align*} +\Gamma(z) \Gamma(1 - z) += +\frac{\pi}{\sin \pi z} +, \quad +\text{für } +z \notin \mathbb{Z} +\end{align*} + +\end{column} +\end{columns} + +\end{frame} \ No newline at end of file diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex new file mode 100644 index 0000000..f5f889e --- /dev/null +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -0,0 +1,176 @@ +\section{Approximieren der Gamma-Funktion} + +\begin{frame}{Anwenden der Gauss-Laguerre-Quadratur auf $\Gamma(z)$} + +\begin{align*} +\Gamma(z) + & = +\int_0^\infty x^{z-1} e^{-x} \, dx +\approx +\sum_{i=1}^{n} f(x_i) A_i += +\sum_{i=1}^{n} x^{z-1} A_i +\\\\ + & \text{wobei } +A_i = \frac{x_i}{(n+1)^2 \left[ L_{n+1}(x_i) \right]^2} +\text{ und $x_i$ die Nullstellen von $L_n(x)$} +\end{align*} + +\end{frame} + +\begin{frame}{Fehlerabschätzung} +\begin{align*} +R_n(\xi) + & = +\frac{(n!)^2}{(2n)!} f^{(2n)}(\xi) +\\ + & = +(z - 2n)_{2n} \frac{(n!)^2}{(2n)!} \xi^{z - 2n - 1} +,\quad +0 < \xi < \infty +\end{align*} + +% \textbf{Probleme:} +\begin{itemize} +\item Funktion ist unbeschränkt +\item Maximum von $R_n$ gibt oberes Limit des Fehlers an +\uncover<2->{\item[$\Rightarrow$] Schwierig ein Maximum von $R_n(\xi)$ zu finden} +\end{itemize} +\end{frame} + +\begin{frame}{Einfacher Ansatz} + +\begin{figure}[h] +\centering +\scalebox{0.91}{\input{../images/rel_error_simple.pgf}} +\caption{Relativer Fehler des einfachen Ansatzes für verschiedene reele Werte +von $z$ und Grade $n$ der Laguerre-Polynome} +\end{figure} + +\end{frame} + +\begin{frame}{Wieso sind die Resultate so schlecht?} + +\textbf{Beobachtungen} +\begin{itemize} +\item Wenn $z \in \mathbb{Z}$ relativer Fehler $\rightarrow 0$ +\item Gewisse Periodizität zu erkennen +\item Für grosse und kleine $z$ ergibt sich ein schlechter relativer Fehler +\item Es gibt Intervalle $[a,a+1]$ mit minimalem relativem Fehler +\item $a$ ist abhängig von $n$ +\end{itemize} + +\uncover<2->{ +\textbf{Ursache?} +\begin{itemize} +\item Vermutung: Integrand ist problematisch +} +\uncover<3->{ +\item[$\Rightarrow$] Analysieren des Integranden +} +\end{itemize} +\end{frame} + +\begin{frame}{$f(x) = x^z$} +\begin{figure}[h] +\centering +\scalebox{0.91}{\input{../images/integrands.pgf}} +% \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} +\end{figure} +\end{frame} + +\begin{frame}{Integrand $x^z e^{-x}$} +\begin{figure}[h] +\centering +\scalebox{0.91}{\input{../images/integrands_exp.pgf}} +% \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} +\end{figure} +\end{frame} + +\begin{frame}{Neuer Ansatz?} + +\textbf{Vermutung} +\begin{itemize} +\item Es gibt Intervalle $[a(n), a(n+1)]$ in denen der relative Fehler minimal +ist +\item $a(n) > 0$ +\end{itemize} + +\uncover<2->{ +\textbf{Idee} +\begin{itemize} +\item[$\Rightarrow$] Berechnen von $\Gamma(z)$ im geeigneten Intervall und dann +mit Funktionalgleichung zurückverschieben +\end{itemize} +} + +\uncover<3->{ +\textbf{Wie finden wir $\boldsymbol{a(n)}$?} +\begin{itemize} +\item Minimieren des Fehlerterms mit zusätzlichem Verschiebungsterm +} +\uncover<4->{$\Rightarrow$ Schwierig das Maximum des Fehlerterms zu bestimmen} +\uncover<5->{\item Emprisch $a(n)$ bestimmen} +\uncover<6->{$\Rightarrow$ Sinnvoll, +da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} +\end{itemize} +\end{frame} + +\begin{frame}{Verschiebungsterm} +\begin{align*} +\Gamma(z) +\approx +\frac{1}{(z-m)_m} \sum_{i=1}^{n} x_i^{z + m - 1} A_i +\end{align*} + +\begin{figure}[h] +\centering +\includegraphics[width=0.5\textwidth]{../images/targets.pdf} +\caption{Verschiebungsterm $m$ in Abhängigkeit von $z$ und $n$} +\end{figure} +\end{frame} + +\begin{frame}{Schätzen von $m^*$} +\begin{columns} +\begin{column}{0.6\textwidth} +\begin{figure} +\centering +\vspace{-24pt} +\scalebox{0.7}{\input{../images/estimate.pgf}} +% \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} +\end{figure} +\end{column} +\begin{column}{0.39\textwidth} +\begin{align*} +m^* += +\lceil \hat{m} - \operatorname{Re}z \rceil +\end{align*} +\end{column} +\end{columns} + +\end{frame} + +\begin{frame}{} +\begin{figure}[h] +\centering +\scalebox{0.6}{\input{../images/rel_error_shifted.pgf}} +\caption{Relativer Fehler mit $n=8$, unterschiedlichen Verschiebungstermen $m$ und $z\in(0, 1)$} +\end{figure} +\end{frame} + +\begin{frame}{} +\begin{figure}[h] +\centering +\scalebox{0.6}{\input{../images/rel_error_range.pgf}} +\caption{Relativer Fehler mit $n=8$, Verschiebungsterm $m^*$ und $z\in(-5, 5)$} +\end{figure} +\end{frame} + +\begin{frame}{Vergleich mit Lanczos-Methode} +Maximaler relativer Fehler für $n=6$ +\begin{itemize} + \item Lanczos-Methode $< 10^{-12}$ + \item Unsere Methode $\approx 10^{-6}$ +\end{itemize} +\end{frame} \ No newline at end of file diff --git a/buch/papers/laguerre/presentation/sections/gaussquad.tex b/buch/papers/laguerre/presentation/sections/gaussquad.tex new file mode 100644 index 0000000..4d973b8 --- /dev/null +++ b/buch/papers/laguerre/presentation/sections/gaussquad.tex @@ -0,0 +1,67 @@ +\section{Gauss-Quadratur} + +\begin{frame}{Gauss-Quadratur} +\textbf{Idee} +\begin{itemize}[<+->] +\item Polynome können viele Funktionen approximieren +\item Wenn Verfahren gut für Polynome funktioniert, +sollte es auch für andere Funktionen funktionieren +\item Integrieren eines Interpolationspolynom +\item Interpolationspolynom ist durch Funktionswerte $f(x_i)$ bestimmt +$\Rightarrow$ Integral kann durch Funktionswerte berechnet werden +\item Evaluation der Funktionswerte an geeigneten Stellen +\end{itemize} +\end{frame} + +\begin{frame}{Gauss-Quadratur} +\begin{align*} +\int_{-1}^{1} f(x) \, dx +\approx +\sum_{i=1}^n f(x_i) A_i +\end{align*} + +\begin{itemize}[<+->] +\item Exakt für Polynome mit Grad $2n-1$ +\item Interpolationspolynome müssen orthogonal sein +\item Stützstellen $x_i$ sind Nullstellen des Polynoms +\item Fehler: +\begin{align*} +E += +\frac{f^{(2n)}(\xi)}{(2n)!} \int_{-1}^{1} l(x)^2 \, dx +,\quad +\text{wobei } +l(x) = \prod_{i=1}^n (x-x_i) +\end{align*} +\end{itemize} +\end{frame} + +\begin{frame}{Gauss-Laguerre-Quadratur} +\begin{itemize}[<+->] +\item Erweiterung des Integrationsintervall von $[-1, 1]$ auf $(a, b)$ +\item Hinzufügen einer Gewichtsfunktion +\item Bei uneigentlichen Integralen muss Gewichtsfunktion schneller als jedes +Integrationspolynom gegen $0$ gehen +\item[$\Rightarrow$] Für Laguerre-Polynome haben wir den Definitionsbereich +$(0, \infty)$ und die Gewichtsfunktion $w(x) = e^{-x}$ +\begin{align*} +\int_0^\infty & f(x) e^{-x} \, dx +\approx +\sum_{i=1}^n f(x_i) A_i +\\ + & \text{wobei } +A_i = \frac{x_i}{(n+1)^2 \left[ L_{n+1}(x_i) \right]^2} +\text{ und $x_i$ die Nullstellen von $L_n(x)$} +\end{align*} +\end{itemize} +\end{frame} + +\begin{frame}{Fehler der Gauss-Laguerre-Quadratur} +\begin{align*} +R_n += +\frac{(n!)^2}{(2n)!} f^{(2n)}(\xi) +,\quad +0 < \xi < \infty +\end{align*} +\end{frame} \ No newline at end of file diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex new file mode 100644 index 0000000..cba9ffb --- /dev/null +++ b/buch/papers/laguerre/presentation/sections/laguerre.tex @@ -0,0 +1,88 @@ +\section{Laguerre-Polynome} + +\begin{frame}{Laguerre-Differentialgleichung} + +\begin{itemize} +\item Benannt nach Edmond Nicolas Laguerre (1834-1886) +\item Aus Artikel von 1879, +in dem er $\int_0^\infty \exp(-x)/x \, dx$ analysierte +\end{itemize} + +\begin{align*} +x y''(x) + (1 - x) y'(x) + n y(x) + & = +0 +, \quad +n \in \mathbb{N}_0 +, \quad +x \in \mathbb{R} +\end{align*} + +\end{frame} + +\begin{frame}{Lösen der Differentialgleichung} + +\begin{align*} +x y''(x) + (1 - x) y'(x) + n y(x) + & = +0 +\\ +\end{align*} + +\uncover<2->{ +\centering +\begin{tikzpicture}[remember picture,overlay] +%% use here too +\path[draw=mainColor, very thick,->](0, 1.1) to +node[anchor=west]{Potenreihenansatz} (0, -0.8); +\end{tikzpicture} +} + +\begin{align*} +\uncover<3->{ +L_n(x) + & = +\sum_{k=0}^{n} \frac{(-1)^k}{k!} \binom{n}{k} x^k +} +\end{align*} +\uncover<4->{ +\begin{itemize} + \item Die Lösungen der DGL sind die Laguerre-Polynome +\end{itemize} +} +\end{frame} + +\begin{frame} +\begin{figure}[h] +\centering +\scalebox{0.66}{\input{../images/laguerre_polynomes.pgf}} +\caption{Laguerre-Polynome vom Grad $0$ bis $7$} +\end{figure} +\end{frame} + +\begin{frame}{Orthogonalität} +\begin{itemize}[<+->] +\item Beweis: Umformen in Sturm-Liouville-Problem (siehe Paper) +\begin{alignat*}{5} +((p(x) &y'(x)))' + q(x) &y(x) +&= +\lambda &w(x) &y(x) +\\ +((x e^{-x} &y'(x)))' + 0 &y(x) +&= +n &e^{-x} &y(x) +\end{alignat*} +\item Definitionsbereich $(0, \infty)$ +\item Gewichtsfunktion $w(x) = e^{-x}$ +\end{itemize} + +\only<4>{ +\begin{align*} +\int_0^\infty e^{-x} L_n(x) L_m(x) \, dx += +0 +,\quad +n, m \in \mathbb{N} +\end{align*} +} +\end{frame} \ No newline at end of file diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 9c8f3ee..dd50d92 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -39,7 +39,7 @@ def find_shift(z, target): def find_optimal_shift(z, n): mhat = 1.34093 * n + 0.854093 - steps = int(np.ceil(mhat - np.real(z))) - 1 + steps = int(np.floor(mhat - np.real(z))) return steps @@ -136,7 +136,7 @@ ax.set_xlabel(r"$z$") ax.set_ylabel("Relativer Fehler") ax.legend(ncol=3, fontsize="small") ax.grid(1, "both") -# fig.savefig(f"{img_path}/rel_error_simple.pgf") +fig.savefig(f"{img_path}/rel_error_simple.pgf") # Mirrored @@ -162,7 +162,7 @@ ax2.set_xlabel(r"$z$") ax2.set_ylabel("Relativer Fehler") ax2.legend(ncol=1, loc="upper left", fontsize="small") ax2.grid(1, "both") -# fig2.savefig(f"{img_path}/rel_error_mirror.pgf") +fig2.savefig(f"{img_path}/rel_error_mirror.pgf") # Move to target @@ -202,7 +202,7 @@ ax3.set_yticks(np.arange(len(ns))) ax3.set_yticklabels(ns) ax3.set_xlabel(r"$z$") ax3.set_ylabel(r"$n$") -# fig3.savefig(f"{img_path}/targets.pdf") +fig3.savefig(f"{img_path}/targets.pdf") targets = np.mean(bests, -1) intercept, bias = np.polyfit(ns, targets, 1) @@ -211,16 +211,16 @@ fig4, axs4 = plt.subplots( ) xl = np.array([ns[0] - 0.5, ns[-1] + 0.5]) axs4[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$") -axs4[0].plot(ns, targets, "x", label=r"$\bar{m}$") -axs4[1].plot(ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \bar{m}$") +axs4[0].plot(ns, targets, "x", label=r"$\overline{m}$") +axs4[1].plot(ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \overline{m}$") axs4[0].set_xlim(*xl) # axs4[0].set_title("Schätzung von Mittelwert") # axs4[1].set_title("Fehler") -axs4[-1].set_xlabel(r"$z$") +axs4[-1].set_xlabel(r"$n$") for ax in axs4: ax.grid(1) ax.legend() -# fig4.savefig(f"{img_path}/schaetzung.pgf") +fig4.savefig(f"{img_path}/estimate.pgf") print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") predicts = np.ceil(intercept * ns[:, None] + bias - x) @@ -234,14 +234,14 @@ gamma = scipy.special.gamma(x)[:, None] n = 8 targets = np.arange(10, 14) gamma = scipy.special.gamma(x) -fig5, ax5 = plt.subplots(num=1, clear=True, constrained_layout=True) +fig5, ax5 = plt.subplots(num=5, clear=True, constrained_layout=True) for target in targets: gamma_lag = eval_laguerre_gamma(x, target=target, n=n, func="shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lag)) - ax5.semilogy(x, rel_error, label=f"$m={target}$") + ax5.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3) gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax5.semilogy(x, rel_error, label="$m^*$") +ax5.semilogy(x, rel_error, "c", linestyle="dotted", label="$m^*$", linewidth=3) ax5.set_xlim(x[0], x[-1]) ax5.set_ylim(5e-9, 5e-8) ax5.set_xlabel(r"$z$") @@ -254,10 +254,10 @@ x = np.linspace(-5+ EPSILON, 5-EPSILON, N) gamma = scipy.special.gamma(x)[:, None] n = 8 gamma = scipy.special.gamma(x) -fig6, ax6 = plt.subplots(num=1, clear=True, constrained_layout=True) +fig6, ax6 = plt.subplots(num=6, clear=True, constrained_layout=True) gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax6.semilogy(x, rel_error, label="$m^*$") +ax6.semilogy(x, rel_error, label="$m^*$", linewidth=3) ax6.set_xlim(x[0], x[-1]) ax6.set_ylim(5e-9, 5e-8) ax6.set_xlabel(r"$z$") @@ -265,4 +265,14 @@ ax6.grid(1, "both") ax6.legend() fig6.savefig(f"{img_path}/rel_error_range.pgf") +N = 2001 +x = np.linspace(-5, 5, N) +gamma = scipy.special.gamma(x) +fig7, ax7 = plt.subplots(num=7, clear=True, constrained_layout=True) +ax7.plot(x, gamma) +ax7.set_xlim(x[0], x[-1]) +ax7.set_ylim(-7.5, 25) +ax7.grid(1, "both") +fig7.savefig(f"{img_path}/gamma.pgf") + # plt.show() -- cgit v1.2.1 From fac45f54d4cee5018c063b4a720695cbf3040fa9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 2 Jun 2022 15:53:49 +0200 Subject: Correct typos in presentation --- .../presentation/sections/gamma_approx.tex | 23 +++++++++++++++++----- .../laguerre/presentation/sections/laguerre.tex | 4 ++-- buch/papers/laguerre/scripts/gamma_approx.py | 2 +- 3 files changed, 21 insertions(+), 8 deletions(-) diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex index f5f889e..2e4e4e2 100644 --- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -6,14 +6,20 @@ \Gamma(z) & = \int_0^\infty x^{z-1} e^{-x} \, dx +\uncover<2->{ \approx \sum_{i=1}^{n} f(x_i) A_i +} +\uncover<3->{ = \sum_{i=1}^{n} x^{z-1} A_i +} \\\\ +\uncover<4->{ & \text{wobei } A_i = \frac{x_i}{(n+1)^2 \left[ L_{n+1}(x_i) \right]^2} \text{ und $x_i$ die Nullstellen von $L_n(x)$} +} \end{align*} \end{frame} @@ -66,7 +72,7 @@ von $z$ und Grade $n$ der Laguerre-Polynome} \item Vermutung: Integrand ist problematisch } \uncover<3->{ -\item[$\Rightarrow$] Analysieren des Integranden +\item[$\Rightarrow$] Analysieren von $f(x)$ und dem Integranden } \end{itemize} \end{frame} @@ -110,7 +116,7 @@ mit Funktionalgleichung zurückverschieben \item Minimieren des Fehlerterms mit zusätzlichem Verschiebungsterm } \uncover<4->{$\Rightarrow$ Schwierig das Maximum des Fehlerterms zu bestimmen} -\uncover<5->{\item Emprisch $a(n)$ bestimmen} +\uncover<5->{\item Empirisch $a(n)$ bestimmen} \uncover<6->{$\Rightarrow$ Sinnvoll, da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \end{itemize} @@ -120,13 +126,13 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \begin{align*} \Gamma(z) \approx -\frac{1}{(z-m)_m} \sum_{i=1}^{n} x_i^{z + m - 1} A_i +\frac{1}{(z-m)_{m}} \sum_{i=1}^{n} x_i^{z + m - 1} A_i \end{align*} \begin{figure}[h] \centering \includegraphics[width=0.5\textwidth]{../images/targets.pdf} -\caption{Verschiebungsterm $m$ in Abhängigkeit von $z$ und $n$} +\caption{Optimaler Verschiebungsterm $m^*$ in Abhängigkeit von $z$ und $n$} \end{figure} \end{frame} @@ -142,8 +148,15 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \end{column} \begin{column}{0.39\textwidth} \begin{align*} +\hat{m} +&= +\alpha n + \beta +\\ +&\approx +1.34093 n + 0.854093 +\\ m^* -= +&= \lceil \hat{m} - \operatorname{Re}z \rceil \end{align*} \end{column} diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex index cba9ffb..faa50e5 100644 --- a/buch/papers/laguerre/presentation/sections/laguerre.tex +++ b/buch/papers/laguerre/presentation/sections/laguerre.tex @@ -34,7 +34,7 @@ x y''(x) + (1 - x) y'(x) + n y(x) \begin{tikzpicture}[remember picture,overlay] %% use here too \path[draw=mainColor, very thick,->](0, 1.1) to -node[anchor=west]{Potenreihenansatz} (0, -0.8); +node[anchor=west]{Potenzreihenansatz} (0, -0.8); \end{tikzpicture} } @@ -76,7 +76,7 @@ n &e^{-x} &y(x) \item Gewichtsfunktion $w(x) = e^{-x}$ \end{itemize} -\only<4>{ +\uncover<4->{ \begin{align*} \int_0^\infty e^{-x} L_n(x) L_m(x) \, dx = diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index dd50d92..857c735 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -192,7 +192,7 @@ bests = np.stack(bests, 0) fig3, ax3 = plt.subplots(num=3, clear=True, constrained_layout=True, figsize=(5, 3)) v = ax3.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest") -plt.colorbar(v, ax=ax3, label=r"$m$") +plt.colorbar(v, ax=ax3, label=r"$m^*$") ticks = np.arange(0, N + 1, N // 5) ax3.set_xlim(0, 1) ax3.set_xticks(ticks) -- cgit v1.2.1 From fb20b12bd912595deb6ad98a6428842f893edcda Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 2 Jun 2022 16:13:14 +0200 Subject: Add n != m to presentation at orthogonality section --- buch/papers/laguerre/presentation/sections/laguerre.tex | 2 ++ 1 file changed, 2 insertions(+) diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex index faa50e5..1add511 100644 --- a/buch/papers/laguerre/presentation/sections/laguerre.tex +++ b/buch/papers/laguerre/presentation/sections/laguerre.tex @@ -81,6 +81,8 @@ n &e^{-x} &y(x) \int_0^\infty e^{-x} L_n(x) L_m(x) \, dx = 0 +,\quad +n \neq m ,\quad n, m \in \mathbb{N} \end{align*} -- cgit v1.2.1 From 83d215597b5df724022de2a08ae1dfa1e8d59497 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 2 Jun 2022 23:01:38 +0200 Subject: phases --- vorlesungen/slides/hermite/hermiteentwicklung.tex | 15 +++++++----- vorlesungen/slides/hermite/loesung.tex | 19 +++++++++++---- vorlesungen/slides/hermite/normalhermite.tex | 29 +++++++++++++++++------ vorlesungen/slides/hermite/normalintegrale.tex | 9 ++++--- vorlesungen/slides/hermite/skalarprodukt.tex | 22 ++++++++++++----- 5 files changed, 67 insertions(+), 27 deletions(-) diff --git a/vorlesungen/slides/hermite/hermiteentwicklung.tex b/vorlesungen/slides/hermite/hermiteentwicklung.tex index e1ced30..5f6e1c9 100644 --- a/vorlesungen/slides/hermite/hermiteentwicklung.tex +++ b/vorlesungen/slides/hermite/hermiteentwicklung.tex @@ -17,6 +17,7 @@ P(x) = p_0 + p_1x + p_2x^2 + \dots + p_nx^n \] +\uncover<2->{% als Linearkombination von Hermite-Polynome schreiben: \begin{align*} P(x) @@ -38,10 +39,11 @@ a_0\cdot 1 &\quad\;\;\vdots \\ &\quad + a_n(2^nx^n + \dots) -\end{align*} +\end{align*}} \end{block} \end{column} \begin{column}{0.48\textwidth} +\uncover<3->{% \begin{block}{Koeffizientenvergleich} führt auf ein Gleichungssystem \begin{center} @@ -58,11 +60,12 @@ a_0&a_1&a_2&a_3&a_4&\dots&\\ \hline \end{tabular} \end{center} -Dreiecksmatrix, Diagonalelement -$\ne 0$ -$\Rightarrow$ -$\exists$ eindeutige Lösung -\end{block} +\uncover<4->{% +Dreiecksmatrix}\uncover<5->{, Diagonalelement +$\ne 0$} +\uncover<6->{$\Rightarrow$ +$\exists$ eindeutige Lösung} +\end{block}} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/hermite/loesung.tex b/vorlesungen/slides/hermite/loesung.tex index 7d4741f..68ee32e 100644 --- a/vorlesungen/slides/hermite/loesung.tex +++ b/vorlesungen/slides/hermite/loesung.tex @@ -20,36 +20,45 @@ P(t)e^{-\frac{t^2}2} \] in geschlossener Form angeben? \end{block} +\uncover<2->{% \begin{block}{``Hermite-Antwort''} \[ \int H_n(x)e^{-x^2}\,dx \] kann genau für $n>0$ in geschlossener Form angegeben werden. -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<3->{% \begin{block}{Allgemein} \begin{align*} \int P(x)e^{-x^2}\,dx -&= -\int \sum_{k=0}^n a_kH_k(x)e^{-x^2}\,dx +&\uncover<4->{= +\int \sum_{k=0}^n a_kH_k(x)e^{-x^2}\,dx} \\ +\uncover<5->{ &= \sum_{k=0}^n a_k \int H_k(x)e^{-x^2}\,dx +} \\ +\uncover<6->{ &= a_0\operatorname{erf}(x) + C +} \\ +\uncover<6->{ &\hspace*{2mm} + \sum_{k=1}^n a_k\int H_k(x)e^{-x^2}\,dx +} \end{align*} -\end{block} +\end{block}} +\uncover<7->{% \begin{theorem} Das Integral von $P(x)e^{-x^2}$ ist genau dann elementar darstellbar, wenn $a_0=0$ -\end{theorem} +\end{theorem}} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/hermite/normalhermite.tex b/vorlesungen/slides/hermite/normalhermite.tex index 16a314c..98721dc 100644 --- a/vorlesungen/slides/hermite/normalhermite.tex +++ b/vorlesungen/slides/hermite/normalhermite.tex @@ -19,6 +19,7 @@ H_n(x) \] \end{block} \vspace{-10pt} +\uncover<2->{% \begin{block}{Orthogonalität} $H_n(x)$ sind orthogonale Polynome bezüglich $w(x)=e^{-x^2}$, d.~h. \begin{align*} @@ -37,8 +38,9 @@ $H_n(x)$ sind orthogonale Polynome bezüglich $w(x)=e^{-x^2}$, d.~h. = \delta_{mn} \end{align*} -\end{block} +\end{block}} \vspace{-10pt} +\uncover<3->{% \begin{block}{Rekursion: Auf-/Absteigeoperatoren} Rekursionsformel: \[ @@ -46,33 +48,46 @@ H_n(x) = 2x\cdot H_{n-1}(x) - H_{n-1}'(x) \] -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<4->{% \begin{block}{Stammfunktion} \begin{align*} -\int H_n(x) e^{-x^2}\,dx -&= -\int \bigl({\color{red}2x}H_{n-1}(x) +\uncover<4->{ +\int H_n(x) e^{-x^2}\,dx} +&\uncover<5->{= +\int \bigl({\color{red}2x}H_{n-1}(x)} \\ +\uncover<5->{ &\qquad -H_{n-1}'(x)\bigr) e^{-x^2}\,dx +} \\ +\uncover<6->{ {\color{gray}((e^{-x^2})'=-2x)} &= {\color{red}-}\int {\color{red}(e^{-x^2})'} H_{n-1}(x)\,dx +} \\ +\uncover<6->{ &\qquad - \int H_{n-1}'(x) e^{-x^2}\,dx +} \\ +\uncover<7->{ \text{\color{gray}(Produktregel)} &= \int (e^{-x^2}H_{n-1}(x))'\,dx +} \\ +\uncover<8->{ \text{\color{gray}(Ableitung)} &= e^{-x^2}H_{n-1}(x) +} \end{align*} +\uncover<9->{% ausser für $n=0$: \[ \int @@ -80,8 +95,8 @@ H_0(x)e^{-x^2}\,dx = \int e^{-x^2}\,dx -\] -\end{block} +\]} +\end{block}} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/hermite/normalintegrale.tex b/vorlesungen/slides/hermite/normalintegrale.tex index 88abbe8..32333cd 100644 --- a/vorlesungen/slides/hermite/normalintegrale.tex +++ b/vorlesungen/slides/hermite/normalintegrale.tex @@ -20,12 +20,14 @@ P(t)e^{-t^2} \] in geschlossener Form angeben? \end{block} +\uncover<4->{% \begin{block}{Allgemeine Antwort} Satz von Liouville und Risch- Algorithmus können entscheiden, ob es eine elementare Stammfunktion gibt -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<2->{% \begin{block}{Negativbeispiel} $P(t) = 1$, das Normalverteilungsintegral \[ @@ -34,7 +36,8 @@ F(x) \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-t^2}\,dt \] ist nicht elementar darstellbar. -\end{block} +\end{block}} +\uncover<3->{% \begin{block}{Positivbeispiel} $P(t)=t$. Wegen \begin{align*} @@ -47,7 +50,7 @@ $P(t)=t$. Wegen -e^{-x^2}+C \end{align*} elementar darstellbar. -\end{block} +\end{block}} \end{column} \end{columns} \end{frame} diff --git a/vorlesungen/slides/hermite/skalarprodukt.tex b/vorlesungen/slides/hermite/skalarprodukt.tex index 32b933f..a51e9f6 100644 --- a/vorlesungen/slides/hermite/skalarprodukt.tex +++ b/vorlesungen/slides/hermite/skalarprodukt.tex @@ -18,6 +18,7 @@ Orthogonale $H_k$ normalisieren: \] mit Gewichtsfunktion $w(x)=e^{-x^2}$ \end{block} +\uncover<2->{% \begin{block}{``Hermite''-Analyse} \begin{align*} P(x) @@ -26,46 +27,55 @@ P(x) = \sum_{k=1}^\infty \tilde{a}_k \tilde{H}_k(x) \\ +\uncover<3->{ \tilde{a}_k &= \| H_k\|_w\, a_k +} \\ +\uncover<4->{ a_k &= \frac{1}{\|H_k\|} \langle \tilde{H}_k, P\rangle_w -= +}\uncover<5->{= \frac{1}{\|H_k\|^2} \langle H_k, P\rangle_w +} \end{align*} -\end{block} +\end{block}} \end{column} \begin{column}{0.48\textwidth} +\uncover<6->{% \begin{block}{Integrationsproblem} Bedingung: \begin{align*} a_0=0 +\uncover<7->{% \qquad\Leftrightarrow\qquad \langle H_0,P\rangle_w &= -0 +0} \\ +\uncover<8->{% \int_{-\infty}^\infty P(t) w(t) \,dt +}\uncover<9->{% = \int_{-\infty}^\infty P(t) e^{-t^2} \,dt &= -0 +0} \end{align*} -\end{block} +\end{block}} +\uncover<10->{% \begin{theorem} Das Integral von $P(t)e^{-t^2}$ ist in geschlossener Form darstellbar genau dann, wenn \[ \int_{-\infty}^\infty P(t)e^{-t^2}\,dt = 0 \] -\end{theorem} +\end{theorem}} \end{column} \end{columns} \end{frame} -- cgit v1.2.1 From 8fb46098cb8e42a94b8e01ecc809f536d5c7efaf Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Fri, 3 Jun 2022 07:23:21 +0200 Subject: Minor tweaks of presentation --- buch/papers/laguerre/images/rel_error_shifted.pgf | 4 ++-- buch/papers/laguerre/images/targets.pdf | Bin 12940 -> 13199 bytes .../papers/laguerre/presentation/sections/gamma.tex | 5 +++-- .../laguerre/presentation/sections/gamma_approx.tex | 20 +++++++++++++------- .../laguerre/presentation/sections/laguerre.tex | 2 +- buch/papers/laguerre/scripts/gamma_approx.py | 2 +- 6 files changed, 20 insertions(+), 13 deletions(-) diff --git a/buch/papers/laguerre/images/rel_error_shifted.pgf b/buch/papers/laguerre/images/rel_error_shifted.pgf index c11b676..707d492 100644 --- a/buch/papers/laguerre/images/rel_error_shifted.pgf +++ b/buch/papers/laguerre/images/rel_error_shifted.pgf @@ -1050,7 +1050,7 @@ \pgfsetbuttcap% \pgfsetroundjoin% \pgfsetlinewidth{3.011250pt}% -\definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}% +\definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{{3.000000pt}{4.950000pt}}{0.000000pt}% \pgfpathmoveto{\pgfqpoint{0.712295in}{0.453273in}}% @@ -1310,7 +1310,7 @@ \pgfsetbuttcap% \pgfsetroundjoin% \pgfsetlinewidth{3.011250pt}% -\definecolor{currentstroke}{rgb}{0.000000,0.750000,0.750000}% +\definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{{3.000000pt}{4.950000pt}}{0.000000pt}% \pgfpathmoveto{\pgfqpoint{5.398422in}{3.760989in}}% diff --git a/buch/papers/laguerre/images/targets.pdf b/buch/papers/laguerre/images/targets.pdf index adaeeef..df11068 100644 Binary files a/buch/papers/laguerre/images/targets.pdf and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/presentation/sections/gamma.tex b/buch/papers/laguerre/presentation/sections/gamma.tex index 37f4a0b..7dca39b 100644 --- a/buch/papers/laguerre/presentation/sections/gamma.tex +++ b/buch/papers/laguerre/presentation/sections/gamma.tex @@ -3,8 +3,9 @@ \begin{frame}{Gamma-Funktion} \begin{columns} -\begin{column}{0.48\textwidth} +\begin{column}{0.55\textwidth} \begin{figure}[h] +\vspace{-16pt} \centering % \scalebox{0.51}{\input{../images/gammaplot.pdf}} \includegraphics[width=1\textwidth]{../images/gammaplot.pdf} @@ -12,7 +13,7 @@ \end{figure} \end{column} -\begin{column}{0.52\textwidth} +\begin{column}{0.45\textwidth} Verallgemeinerung der Fakultät \begin{align*} \Gamma(n) = (n-1)! diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex index 2e4e4e2..4073b3c 100644 --- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -48,7 +48,8 @@ R_n(\xi) \begin{figure}[h] \centering -\scalebox{0.91}{\input{../images/rel_error_simple.pgf}} +% \scalebox{0.91}{\input{../images/rel_error_simple.pgf}} +\resizebox{!}{0.72\textheight}{\input{../images/rel_error_simple.pgf}} \caption{Relativer Fehler des einfachen Ansatzes für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} \end{figure} @@ -123,17 +124,22 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \end{frame} \begin{frame}{Verschiebungsterm} +\begin{columns} +\begin{column}{0.625\textwidth} +\begin{figure}[h] +\centering +\includegraphics[width=1\textwidth]{../images/targets.pdf} +\caption{Optimaler Verschiebungsterm $m^*$ in Abhängigkeit von $z$ und $n$} +\end{figure} +\end{column} +\begin{column}{0.375\textwidth} \begin{align*} \Gamma(z) \approx \frac{1}{(z-m)_{m}} \sum_{i=1}^{n} x_i^{z + m - 1} A_i \end{align*} - -\begin{figure}[h] -\centering -\includegraphics[width=0.5\textwidth]{../images/targets.pdf} -\caption{Optimaler Verschiebungsterm $m^*$ in Abhängigkeit von $z$ und $n$} -\end{figure} +\end{column} +\end{columns} \end{frame} \begin{frame}{Schätzen von $m^*$} diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex index 1add511..07cafb8 100644 --- a/buch/papers/laguerre/presentation/sections/laguerre.tex +++ b/buch/papers/laguerre/presentation/sections/laguerre.tex @@ -55,7 +55,7 @@ L_n(x) \begin{frame} \begin{figure}[h] \centering -\scalebox{0.66}{\input{../images/laguerre_polynomes.pgf}} +\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_polynomes.pgf}} \caption{Laguerre-Polynome vom Grad $0$ bis $7$} \end{figure} \end{frame} diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 857c735..53ba76b 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -241,7 +241,7 @@ for target in targets: ax5.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3) gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax5.semilogy(x, rel_error, "c", linestyle="dotted", label="$m^*$", linewidth=3) +ax5.semilogy(x, rel_error, "m", linestyle="dotted", label="$m^*$", linewidth=3) ax5.set_xlim(x[0], x[-1]) ax5.set_ylim(5e-9, 5e-8) ax5.set_xlabel(r"$z$") -- cgit v1.2.1 From 5dcd1898f505fb707e8a7630c807f522fd549279 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Fri, 3 Jun 2022 07:25:42 +0200 Subject: Bugfix --- buch/papers/laguerre/presentation/presentation.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/buch/papers/laguerre/presentation/presentation.tex b/buch/papers/laguerre/presentation/presentation.tex index f49cf1e..3db69f5 100644 --- a/buch/papers/laguerre/presentation/presentation.tex +++ b/buch/papers/laguerre/presentation/presentation.tex @@ -126,9 +126,9 @@ \appendix \begin{frame} - \centering - \Large - \textbf{Vielen Dank für die Aufmerksamkeit} + % \centering + % \Large + % \textbf{Vielen Dank für die Aufmerksamkeit} \end{frame} \end{document} -- cgit v1.2.1 From 374bb4a4dbc16598329cb777600c531c8c848330 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sun, 5 Jun 2022 11:24:46 +0200 Subject: fix trigo definition graph --- buch/chapters/030-geometrie/chapter.tex | 3 +- .../030-geometrie/images/einheitskreis.pdf | Bin 19706 -> 20005 bytes .../030-geometrie/images/einheitskreis.tex | 4 + buch/chapters/030-geometrie/uebungsaufgaben/3.tex | 169 +++++++++++++++++++++ 4 files changed, 175 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/030-geometrie/uebungsaufgaben/3.tex diff --git a/buch/chapters/030-geometrie/chapter.tex b/buch/chapters/030-geometrie/chapter.tex index f3f1d39..0b2842b 100644 --- a/buch/chapters/030-geometrie/chapter.tex +++ b/buch/chapters/030-geometrie/chapter.tex @@ -42,7 +42,7 @@ wie die Berechnung der Länge von Ellipsen- oder Hyperbelbögen auf die Notwendigkeit führt, neue spezielle Funktionen zu definieren. \input{chapters/030-geometrie/trigonometrisch.tex} -\input{chapters/030-geometrie/sphaerisch.tex} +%\input{chapters/030-geometrie/sphaerisch.tex} \input{chapters/030-geometrie/hyperbolisch.tex} \input{chapters/030-geometrie/laenge.tex} \input{chapters/030-geometrie/flaeche.tex} @@ -54,5 +54,6 @@ die Notwendigkeit führt, neue spezielle Funktionen zu definieren. %\uebungsaufgabe{0} \uebungsaufgabe{1} \uebungsaufgabe{2} +\uebungsaufgabe{3} \end{uebungsaufgaben} diff --git a/buch/chapters/030-geometrie/images/einheitskreis.pdf b/buch/chapters/030-geometrie/images/einheitskreis.pdf index 0b514eb..d708377 100644 Binary files a/buch/chapters/030-geometrie/images/einheitskreis.pdf and b/buch/chapters/030-geometrie/images/einheitskreis.pdf differ diff --git a/buch/chapters/030-geometrie/images/einheitskreis.tex b/buch/chapters/030-geometrie/images/einheitskreis.tex index c38dc19..a194190 100644 --- a/buch/chapters/030-geometrie/images/einheitskreis.tex +++ b/buch/chapters/030-geometrie/images/einheitskreis.tex @@ -41,6 +41,7 @@ \fill[color=blue] (\a:\r) circle[radius=0.05]; \draw[color=blue,line width=1.4pt] (\r,0) -- (\r,{\r*tan(\a)}); +\fill[color=blue] (\r,{\r*tan(\a)}) circle[radius=1.0pt]; \node[color=blue] at (\r,{0.5*\r*tan(\a)}) [right] {$\tan\alpha$}; \draw[color=blue,line width=0.4pt] ({\r*cos(\a)},0) -- (\a:\r); @@ -53,6 +54,7 @@ \draw[color=blue] (-0.1,{\r*sin(\a)}) -- (0.1,{\r*sin(\a)}); \draw[color=blue,line width=1.4pt] (0,\r) -- ({\r/tan(\a)},\r); +\fill[color=blue] ({\r/tan(\a)},\r) circle[radius=1.0pt]; \node[color=blue] at ({0.5*\r/tan(\a)},\r) [above] {$\cot\alpha$}; \draw[color=darkgreen,line width=1pt] (0,0) -- (\b:\r); @@ -61,9 +63,11 @@ \fill[color=darkgreen] (\b:\r) circle[radius=0.05]; \draw[color=darkgreen,line width=1.4pt] (0,\r) -- ({\r/tan(\b)},\r); +\fill[color=darkgreen] ({\r/tan(\b)},\r) circle[radius=1.0pt]; \node[color=darkgreen] at ({0.5*\r/tan(\b)},\r) [above] {$\cot\beta$}; \draw[color=darkgreen,line width=1.4pt] (\r,0) -- (\r,{\r*tan(\b)}); +\fill[color=darkgreen] (\r,{\r*tan(\b)}) circle[radius=1.0pt]; \node[color=darkgreen] at (\r,{0.5*\r*tan(\b)}) [right] {$\tan\beta$}; \draw[color=darkgreen,line width=0.4pt] (\b:\r) -- (0,{\r*sin(\b)}); diff --git a/buch/chapters/030-geometrie/uebungsaufgaben/3.tex b/buch/chapters/030-geometrie/uebungsaufgaben/3.tex new file mode 100644 index 0000000..6a501fb --- /dev/null +++ b/buch/chapters/030-geometrie/uebungsaufgaben/3.tex @@ -0,0 +1,169 @@ +\def\cas{\operatorname{cas}} +Die Funktion $\cas$ definiert durch +$\cas x = \cos x + \sin x$ hat einige interessante Eigenschaften. +Wie die gewöhnlichen trigonometrischen Funktionen $\sin x$ und $\cos x$ +ist $\cas x$ $2\pi$-periodisch. +Die Ableitung und das Additionstheorem benötigen bei den gewöhnlichen +trigonometrischen Funktionen aber beide Funktionen, im Gegensatz zu den +im folgenden hergeleiteten Formeln, die nur die Funktion $\cas x$ brauchen. +\begin{teilaufgaben} +\item +Drücken Sie die Ableitung von $\cas x$ allein durch Werte der +$\cas$-Funktion aus. +\item +Zeigen Sie, dass +\[ +\cas x += +\sqrt{2} \sin\biggl(x+\frac{\pi}4\biggr) += +\sqrt{2} \cos\biggl(x-\frac{\pi}4\biggr). +\] +\item +Beweisen Sie das Additionstheorem für die $\cas$-Funktion +\begin{equation} +\cas(x+y) += +\frac12\bigl( +\cas(x)\cas(y) + \cas x\cas (-y) + \cas(-x)\cas(y) -\cas(-x)\cas(-y) +\bigr) +\label{buch:geometrie:uebung3:eqn:addition} +\end{equation} +\end{teilaufgaben} +Youtuber Dr Barker hat die Funktion $\cas$ im Video +{\small\url{https://www.youtube.com/watch?v=bn38o3u0lDc}} vorgestellt. + +\begin{loesung} +\begin{teilaufgaben} +\item +Die Ableitung ist +\[ +\frac{d}{dx}\cas x += +\frac{d}{dx}(\cos x + \sin x) += +-\sin x + \cos x += +\sin(-x) + \cos(-x) += +\cas(x). +\] +\item +Die Additionstheoreme angewendet auf die trigonometrischen Funktionen +auf der rechten Seite ergibt +\begin{align*} +\sin\biggl(x+\frac{\pi}4\biggr) +&= +\sin x \cos\frac{\pi}4 + \cos x \sin\frac{\pi}4 +&&& +\cos\biggl(x-\frac{\pi}4\biggr) +&= +\cos(x)\cos\frac{\pi}4 -\sin x \sin\biggl(-\frac{\pi}4\biggr) +\\ +&= +\frac{1}{\sqrt{2}} \sin x ++ +\frac{1}{\sqrt{2}} \cos x +&&& +&= +\frac{1}{\sqrt{2}} \cos x ++ +\frac{1}{\sqrt{2}} \sin x +\\ +&=\frac{1}{\sqrt{2}} \cas x +&&& +&= +\frac{1}{\sqrt{2}} \cas x. +\end{align*} +Multiplikation mit $\sqrt{2}$ ergibt die behaupteten Relationen. +\item +Substituiert man die Definition von $\cas(x)$ auf der rechten Seite von +\eqref{buch:geometrie:uebung3:eqn:addition} und multipliziert aus, +erhält man +\begin{align*} +\eqref{buch:geometrie:uebung3:eqn:addition} +&= +{\textstyle\frac12}\bigl( +(\cos x + \sin x) +(\cos y + \sin y) ++ +(\cos x + \sin x) +(\cos y - \sin y) +\\ +&\qquad ++ +(\cos x - \sin x) +(\cos y + \sin y) +- +(\cos x - \sin x) +(\cos y - \sin y) +\bigr) +\\ +&= +\phantom{-\mathstrut} +{\textstyle\frac12}\bigl( +\cos x\cos y ++ +\cos x\sin y ++ +\sin x\cos y ++ +\sin x\sin y +\\ +& +\phantom{=-\mathstrut{\textstyle\frac12}\bigl(}\llap{$\mathstrut +\mathstrut$} +\cos x\cos y +- +\cos x\sin y ++ +\sin x\cos y +- +\sin x\sin y +\\ +& +\phantom{=-\mathstrut{\textstyle\frac12}\bigl(}\llap{$\mathstrut +\mathstrut$} +\cos x\cos y ++ +\cos x\sin y +- +\sin x\cos y +- +\sin x\sin y +\bigr) +\\ +& +\phantom{=} +-\mathstrut{\textstyle\frac12}\bigl( +\cos x\cos y +- +\cos x\sin y +- +\sin x\cos y ++ +\sin x\sin y +\bigr) +\\ +&= \cos x \cos y ++ +\cos x \sin y ++ +\sin x \cos y +- +\sin x \sin y. +\intertext{Die äussersten zwei Terme passen zum Additionstheorem für den +Kosinus, die beiden inneren Terme dagegen zum Sinus. +Fasst man sie zusammen, erhält man} +&= +(\sin x\cos y + \cos x \sin y) ++ +(\cos x\cos y - \sin x \sin y) +\\ +&= +\sin (x+y) + \cos(x+y) += +\cas(x+y). +\end{align*} +Damit ist das Additionstheorem für die Funktion $\cas$ bewiesen. +\qedhere +\end{teilaufgaben} +\end{loesung} -- cgit v1.2.1 From d3c217cdb6106f2082097dd9e76f200885c853cb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 7 Jun 2022 11:45:38 +0200 Subject: add polynomials with elementary w-integrals paper --- buch/chapters/010-potenzen/polynome.tex | 239 ++++++++++++++++++++++++++++++-- buch/papers/dreieck/main.tex | 18 +-- buch/papers/dreieck/references.bib | 36 ++--- buch/papers/dreieck/teil0.tex | 45 +++++- buch/papers/dreieck/teil1.tex | 88 +++++++++++- buch/papers/dreieck/teil2.tex | 109 ++++++++++++++- buch/papers/dreieck/teil3.tex | 70 +++++++++- 7 files changed, 542 insertions(+), 63 deletions(-) diff --git a/buch/chapters/010-potenzen/polynome.tex b/buch/chapters/010-potenzen/polynome.tex index 5f119e5..981e444 100644 --- a/buch/chapters/010-potenzen/polynome.tex +++ b/buch/chapters/010-potenzen/polynome.tex @@ -13,20 +13,30 @@ Operationen konstruieren lassen, sind die Polynome. \index{Polynom}% Ein {\em Polynome} vom Grad $n$ ist die Funktion \[ -p(x) = a_nx^2n + a_{n-1}x^{n-1} + \dots + a_2x^2 + a_1x + a_0, +p(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_2x^2 + a_1x + a_0, \] wobei $a_n\ne 0$ sein muss. Das Polynom heisst {\em normiert}, wenn $a_n=1$ ist. \index{normiert}% +\index{Grad eines Polynoms}% Die Menge aller Polynome mit Koeffizienten in der Menge $K$ wird mit $K[x]$ bezeichnet. \end{definition} Die Menge $K[x]$ ist heisst auch der {\em Polynomring}, weil $K[x]$ -mit der Addition, Subtraktion und Multiplikation von Polynomen ein -Ring mit $1$ ist. -Im Folgenden werden wir uns auf die Fälle $K=\mathbb{R}$ und $K=\mathbb{C}$ -beschränken. +mit der Addition, Subtraktion und Multiplikation von Polynomen eine +algebraische Struktur bildet, die man einen Ring mit $1$ nennt. +\index{Ring}% +Im Folgenden werden wir uns auf die Fälle $K=\mathbb{Q}$, $K=\mathbb{R}$ +und $K=\mathbb{C}$ beschränken. + +Für den Grad eines Polynoms gelten die bekannten Rechenregeln +\begin{align*} +\deg (a(x) + b(x)) &\le \operatorname{max}(\deg a(x), \deg b(x)) +\\ +\deg (a(x)\cdot b(x)) &=\deg a(x) + \deg b(x) +\end{align*} +für beliebige Polynome $a(x),b(x)\in K[x]$. In Abschnitt~\ref{buch:orthogonalitaet:section:orthogonale-funktionen} werden Familien von Polynomen konstruiert werden, die sich durch eine @@ -35,12 +45,14 @@ Diese Polynome lassen sich typischerweise auch als Lösungen von Differentialgleichungen finden. Ausserdem werden hypergeometrische Funktionen \[ -\mathstrut_pF_q\biggl(\begin{matrix}a_1,\dots,a_p\\b_1,\dots,b_q\end{matrix};z\biggr), +\mathstrut_pF_q\biggl( +\begin{matrix}a_1,\dots,a_p\\b_1,\dots,b_q\end{matrix};z +\biggr), \] die in Abschnitt~\ref{buch:rekursion:section:hypergeometrische-funktion} definiert werden, zu Polynomen, wenn mindestens einer der Parameter $a_k$ negativ ganzzahlig ist. -Polynome sind also bereits eine Vielfältige Quelle von speziellen +Polynome sind also bereits eine vielfältige Quelle von speziellen Funktionen. Viele spezielle Funktionen werden aber komplizierter sein und @@ -53,6 +65,7 @@ Dank des folgenden Satzes kann dies immer mit Polynomen geschehen. \begin{satz}[Weierstrass] \label{buch:potenzen:satz:weierstrass} +\index{Weierstrass, Satz von}% Eine auf einem kompakten Intervall $[a,b]$ stetige Funktion $f(x)$ lässt sich durch eine Folge $p_n(x)$ von Polynomen gleichmässig approximieren. @@ -69,6 +82,189 @@ ebenfalls als Approximationen dienen können. Weitere Möglichkeiten liefern Interpolationsmethoden der numerischen Mathematik. +\subsection{Polynomdivision, Teilbarkeit und grösster gemeinsamer Teiler} +Der schriftliche Divisionsalgorithmus für Zahlen funktioniert +auch für die Division von Polynomen. +Zu zwei beliebigen Polynomen $p(x)$ und $q(x)$ lassen sich also +immer zwei Polynome $a(x)$ und $r(x)$ finden derart, dass +$p(x) = a(x) q(x) + r(x)$. +Das Polynom $a(x)$ heisst der {\em Quotient}, $r(x)$ der {\em Rest} +der Division. +Das Polynom $p(x)$ heisst {\em teilbar} durch $q(x)$, geschrieben +$q(x)\mid p(x)$, wenn $r(x)=0$ ist. + +\subsubsection{Grösster gemeinsamer Teiler} +Mit dem Begriff der Teilbarkeit geht auch die Idee des grössten +gemeinsamen Teilers einher. +Ein gemeinsamer Teiler zweier Polynome $a(x)$ und $b(x)$ +ist ein Polynom $g(x)$, welches beide Polynome teilt, also +$g(x)\mid a(x)$ und $g(x)\mid b(x)$. +\index{grösster gemeinsamer Teiler}% +Ein Polynome $g(x)$ heisst grösster gemeinsamer Teiler von $a(x)$ +und $b(x)$, wenn jeder andere gemeinsame Teiler $f(x)$ von $a(x)$ +und $b(x)$ auch ein Teiler von $g(x)$ ist. +Man beachte, dass die skalaren Vielfachen eines grössten gemeinsamen +Teilers ebenfalls grösste gemeinsame Teiler sind, der grösste gemeinsame +Teiler ist also nicht eindeutig bestimmt. + +\subsubsection{Der euklidische Algorithmus} +Zur Berechnung eines grössten gemeinsamen Teilers steht wie bei den +ganzen Zahlen der euklidische Algorithmus zur Verfügung. +Dazu bildet man die Folgen von Polynomen +\[ +\begin{aligned} +a_0(x)&=a(x) & b_0(x) &= b(x) +& +&\Rightarrow& +a_0(x)&=b_0(x) q_0(x) + r_0(x) && +\\ +a_1(x)&=b_0(x) & b_1(x) &= r_0(x) +& +&\Rightarrow& +a_1(x)&=b_1(x) q_1(x) + r_1(x) && +\\ +a_2(x)&=b_1(x) & b_2(x) &= r_1(x) +& +&\Rightarrow& +a_2(x)&=b_2(x) q_2(x) + r_2(x) && +\\ +&&&&&\hspace*{2mm}\vdots&& +\\ +a_{m-1}(x)&=b_{m-2}(x) & b_{m-1}(x) &= r_{m-2}(x) +& +&\Rightarrow& +a_{m-1}(x)&=b_{m-1}(x)q_{m-1}(x) + r_{m-1}(x) &\text{mit }r_{m-1}(x)&\ne 0 +\\ +a_m(x)&=b_{m-1}(x) & b_m(x)&=r_{m-1}(x) +& +&\Rightarrow& +a_m(x)&=b_m(x)q_m(x).&& +\end{aligned} +\] +Der Index $m$ ist der Index, bei dem zum ersten Mal $r_m(x)=0$ ist. +Dann ist $g(x)=r_{m-1}(x)$ ein grösster gemeinsamer Teiler. + +\subsubsection{Der erweiterte euklidische Algorithmus} +Die Konstruktion der Folgen $a_n(x)$ und $b_n(x)$ kann in Matrixform +kompakter geschrieben werden als +\[ +\begin{pmatrix} +a_k(x)\\ +b_k(x) +\end{pmatrix} += +\begin{pmatrix} +b_{k-1}(x)\\ +r_{k-1}(x) +\end{pmatrix} += +\begin{pmatrix} +0 & 1\\ +1 & -q_{k-1}(x) +\end{pmatrix} +\begin{pmatrix} +a_{k-1}(x)\\ +b_{k-1}(x) +\end{pmatrix}. +\] +Kürzen wir die $2\times 2$-Matrix als +\[ +Q_k(x) = \begin{pmatrix} 0&1\\1&-q_k(x)\end{pmatrix} +\] +ab, dann ergibt das Produkt der Matrizen $Q_0(x)$ bis $Q_{m}(x)$ +\[ +\begin{pmatrix} +g(x)\\ +0 +\end{pmatrix} += +\begin{pmatrix} +r_{m-1}(x)\\ +r_{m}(x) +\end{pmatrix} += +Q_{m}(x) +Q_{m-1}(x) +\cdots +Q_1(x) +Q_0(x) +\begin{pmatrix} +a(x)\\ +b(x) +\end{pmatrix}. +\] +Zur Berechnung des Produktes der Matrizen $Q_k(x)$ kann man rekursiv +vorgehen mit der Rekursionsformel +\[ +S_{k}(x) = Q_{k}(x) S_{k-1}(x) +\qquad\text{mit}\qquad +S_{-1}(x) += +\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}. +\] +Ausgeschrieben bedeutet dies Matrixrekursionsformel +\[ +S_{k-1}(x) += +\begin{pmatrix} +c_{k-1} & d_{k-1} \\ +c_k & d_k +\end{pmatrix} +\qquad\Rightarrow\qquad +Q_{k}(x) S_{k-1}(x) += +\begin{pmatrix} +0&1\\1&-q_k(x) +\end{pmatrix} +\begin{pmatrix} +c_{k-1} & d_{k-1} \\ +c_k & d_k +\end{pmatrix} += +\begin{pmatrix} +c_k&d_k\\ +c_{k+1}&d_{k+1} +\end{pmatrix}. +\] +Daraus lässt sich für die Matrixelemente die Rekursionsformel +\[ +\begin{aligned} +c_{k+1} &= c_{k-1} - q_k(x) c_k(x) \\ +d_{k+1} &= d_{k-1} - q_k(x) d_k(x) +\end{aligned} +\quad +\bigg\} +\qquad +\text{mit Startwerten} +\qquad +\bigg\{ +\begin{aligned} +\quad +c_{-1} &= 1, & c_0 &= 0 \\ +d_{-1} &= 0, & d_0 &= 1. +\end{aligned} +\] +Wendet man die Matrix $S_m(x)$ auf den Vektor mit den Komponenten +$a(x)$ und $b(x)$, erhält man die Beziehungen +\[ +g(x) = c_{k-1}(x) a(x) + d_{k-1}(x) b(x) +\qquad\text{und}\qquad +0 = c_k(x) a(x) + d_k(x) b(x). +\] +Dieser Algorithmus heisst der erweiterte euklidische Algorithmus. +Wir fassen die Resultate zusammen im folgenden Satz. + +\begin{satz} +Zu zwei Polynomen $a(x),b(x) \in K[x]$ gibt es Polynome +$g(x),c(x),d(x)\in K[x]$ +derart, dass $g(x)$ ein grösster gemeinsamer Teiler von $a(x)$ und $b(x)$ +ist, und ausserdem +\[ +g(x) = c(x)a(x)+d(x)b(x) +\] +gilt. +\end{satz} + \subsection{Faktorisierung und Nullstellen} % wird später gebraucht um bei der Definition der hypergeometrischen Reihe % die Zaehler- und Nenner-Polynome als Pochhammer-Symbole zu entwickeln @@ -77,11 +273,24 @@ numerischen Mathematik. % Wird gebraucht für die Potenzreihen-Methode % Muss später ausgedehnt werden auf Potenzreihen -\subsection{Polynom-Berechnung} -Die naive Berechnung der Werte eines Polynoms beginnt mit der Berechnung -der Potenzen. -Die Anzahl nötiger Multiplikationen kann minimiert werden, indem man -das Polynom als +\subsection{Berechnung von Polynom-Werten} +Die naive Berechnung der Werte eines Polynoms $p(x)$ vom Grad $n$ +beginnt mit der Berechnung der Potenzen von $x$. +Da alle Potenzen benötigt werden, wird man dazu $n-1$ Multiplikationen +benötigen. +Die Potenzen müssen anschliessend mit den Koeffizienten multipliziert +werden, dazu sind weitere $n$ Multiplikationen nötig. +Der Wert des Polynoms kann also erhalten werden mit $2n-1$ Multiplikationen +und $n$ Additionen. + +Die Anzahl nötiger Multiplikationen kann mit dem folgenden Vorgehen +reduziert werden, welches auch als das {\em Horner-Schema} bekannt ist. +\index{Horner-Schema}% +Statt erst am Schluss alle Terme zu addieren, addiert man so früh +wie möglich. +Zum Beispiel multipliziert man $(a_nx+a_{n-1})$ mit $x$, was auf +die Multiplikationen beider Terme mit $x$ hinausläuft. +Mit dieser Idee kann man das Polynom als \[ a_nx^n + @@ -95,10 +304,10 @@ a_0 = ((\dots((a_nx+a_{n-1})x+a_{n-2})x+\dots )x+a_1)x+a_0 \] -schreibt. +schreiben. Beginnend bei der innersten Klammer sind genau $n$ Multiplikationen -und $n+1$ Additionen nötig, im Gegensatz zu $2n$ Multiplikationen -und $n$ Additionen bei der naiven Vorgehensweise. +und $n$ Additionen nötig, man spart mit diesem Vorgehen also +$n-1$ Multiplikationen. diff --git a/buch/papers/dreieck/main.tex b/buch/papers/dreieck/main.tex index 75ba410..b9f8c3b 100644 --- a/buch/papers/dreieck/main.tex +++ b/buch/papers/dreieck/main.tex @@ -3,19 +3,19 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Dreieckstest und Beta-Funktion\label{chapter:dreieck}} -\lhead{Dreieckstest und Beta-Funktion} +\chapter{$\int P(t) e^{-t^2} \,dt$ in geschlossener Form? +\label{chapter:dreieck}} +\lhead{Integrierbarkeit in geschlossener Form} \begin{refsection} \chapterauthor{Andreas Müller} \noindent -Mit dem Dreieckstest kann man feststellen, wie gut ein Geruchs- -oder Geschmackstester verschiedene Gerüche oder Geschmäcker -unterscheiden kann. -Seine wahrscheinlichkeitstheoretische Erklärung benötigt die Beta-Funktion, -man kann die Beta-Funktion als durchaus als die mathematische Grundlage -der Weindegustation -bezeichnen. +Der Risch-Algorithmus erlaubt, eine definitive Antwort darauf zu geben, +ob eine elementare Funktion eine Stammfunktion in geschlossener Form hat. +Der Algorithmus ist jedoch ziemlich kompliziert. +In diesem Kapitel soll ein spezieller Fall mit Hilfe der Theorie der +orthogonale Polynome, speziell der Hermite-Polynome, behandelt werden, +wie er in der Arbeit \cite{dreieck:polint} behandelt wurde. \input{papers/dreieck/teil0.tex} \input{papers/dreieck/teil1.tex} diff --git a/buch/papers/dreieck/references.bib b/buch/papers/dreieck/references.bib index d2bbe08..47bd865 100644 --- a/buch/papers/dreieck/references.bib +++ b/buch/papers/dreieck/references.bib @@ -4,32 +4,12 @@ % (c) 2020 Autor, Hochschule Rapperswil % -@online{dreieck:bibtex, - title = {BibTeX}, - url = {https://de.wikipedia.org/wiki/BibTeX}, - date = {2020-02-06}, - year = {2020}, - month = {2}, - day = {6} +@article{dreieck:polint, + author = { George Stoica }, + title = { Polynomials and Integration in Finite Terms }, + journal = { Amer. Math. Monthly }, + volume = 129, + year = 2022, + number = 1, + pages = {80--81} } - -@book{dreieck:numerical-analysis, - title = {Numerical Analysis}, - author = {David Kincaid and Ward Cheney}, - publisher = {American Mathematical Society}, - year = {2002}, - isbn = {978-8-8218-4788-6}, - inseries = {Pure and applied undegraduate texts}, - volume = {2} -} - -@article{dreieck:mendezmueller, - author = { Tabea Méndez and Andreas Müller }, - title = { Noncommutative harmonic analysis and image registration }, - journal = { Appl. Comput. Harmon. Anal.}, - year = 2019, - volume = 47, - pages = {607--627}, - url = {https://doi.org/10.1016/j.acha.2017.11.004} -} - diff --git a/buch/papers/dreieck/teil0.tex b/buch/papers/dreieck/teil0.tex index bcf2cf8..584f12b 100644 --- a/buch/papers/dreieck/teil0.tex +++ b/buch/papers/dreieck/teil0.tex @@ -3,7 +3,48 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Testprinzip\label{dreieck:section:testprinzip}} -\rhead{Testprinzip} +\section{Problemstellung\label{dreieck:section:problemstellung}} +\rhead{Problemstellung} +Es ist bekannt, dass das Fehlerintegral +\[ +\frac{1}{\sqrt{2\pi}\sigma} \int_{-\infty}^x e^{-\frac{t^2}{2\sigma}}\,dt +\] +nicht in geschlossener Form dargestellt werden kann. +Mit der in Kapitel~\ref{buch:chapter:integral} skizzierten Theorie von +Liouville und dem Risch-Algorithmus kann dies strengt gezeigt werden. +Andererseits gibt es durchaus Integranden, die $e^{-t^2}$ enthalten, +für die eine Stammfunktion in geschlossener Form gefunden werden kann. +Zum Beispiel folgt aus der Ableitung +\[ +\frac{d}{dt} e^{-t^2} += +-2te^{-t^2} +\] +die Stammfunktion +\[ +\int te^{-t^2}\,dt += +-\frac12 e^{-t^2}. +\] +Leitet man $e^{-t^2}$ zweimal ab, erhält man +\[ +\frac{d^2}{dt^2} e^{-t^2} += +(4t^2-2) e^{-t^2} +\qquad\Rightarrow\qquad +\int (t^2-\frac12) e^{-t^2}\,dt += +\frac14 +e^{-t^2}. +\] +Es gibt also eine viele weitere Polynome $P(t)$, für die der Integrand +$P(t)e^{-t^2}$ eine Stammfunktion in geschlossener Form hat. +Damit stellt sich jetzt das folgende allgemeine Problem. + +\begin{problem} +\label{dreieck:problem} +Für welche Polynome $P(t)$ hat der Integrand $P(t)e^{-t^2}$ +eine elementare Stammfunktion? +\end{problem} diff --git a/buch/papers/dreieck/teil1.tex b/buch/papers/dreieck/teil1.tex index 4abe2e1..f03c425 100644 --- a/buch/papers/dreieck/teil1.tex +++ b/buch/papers/dreieck/teil1.tex @@ -3,9 +3,91 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Ordnungsstatistik und Beta-Funktion -\label{dreieck:section:ordnungsstatistik}} -\rhead{} +\section{Hermite-Polynome +\label{dreieck:section:hermite-polynome}} +\rhead{Hermite-Polyome} +In Abschnitt~\ref{dreieck:section:problemstellung} hat sich schon angedeutet, +dass die Polynome, die man durch Ableiten von $e^{-t^2}$ erhalten +kann, bezüglich des gestellten Problems besondere Eigenschaften +haben. +Zunächst halten wir fest, dass die Ableitung einer Funktion der Form +$P(t)e^{-t^2}$ mit einem Polynom $P(t)$ +\begin{equation} +\frac{d}{dt} P(t)e^{-t^2} += +P'(t)e^{-t^2} -2tP(t)e^{-t^2} += +(P'(t)-2tP(t)) e^{-t^2} +\label{dreieck:eqn:ableitung} +\end{equation} +ist. +Insbesondere hat die Ableitung wieder die Form $Q(t)e^{-t^2}$ +mit einem Polynome $Q(t)$, welches man auch als +\[ +Q(t) += +e^{t^2}\frac{d}{dt}P(t)e^{-t^2} +\] +erhalten kann. +Die Polynome, die man aus der Funktion $H_0(t)=e^{-t^2}$ durch +Ableiten erhalten kann, wurden bereits in +Abschnitt~\ref{buch:orthogonalitaet:section:rodrigues} +bis auf ein Vorzeichen hergeleitet, sie heissen die Hermite-Polynome +und es gilt +\[ +H_n(t) += +(-1)^n +e^{t^2} \frac{d^n}{dt^n} e^{-t^2}. +\] +Das Vorzeichen dient dazu sicherzustellen, dass der Leitkoeffizient +immer $1$ ist. +Das Polynom $H_n(t)$ hat den Grad $n$. + +In Abschnitt wurde auch gezeigt, dass die Polynome $H_n(t)$ +bezüglich des Skalarproduktes +\[ +\langle f,g\rangle_{w} += +\int_{-\infty}^\infty f(t)g(t)e^{-t^2}\,dt, +\qquad +w(t)=e^{-t^2}, +\] +orthogonal sind. +Ausserdem folgt aus \eqref{dreieck:eqn:ableitung} +die Rekursionsbeziehung +\begin{equation} +H_{n}(t) += +2tH_{n-1}(t) +- +H_{n-1}'(t) +\label{dreieck:eqn:rekursion} +\end{equation} +für $n>0$. + +Im Hinblick auf die Problemstellung ist jetzt die Frage interessant, +ob die Integranden $H_n(t)e^{-t^2}$ eine Stammfunktion in geschlossener +Form haben. +Mit Hilfe der Rekursionsbeziehung~\eqref{dreieck:eqn:rekursion} +kann man für $n>0$ unmittelbar verifizieren, dass +\begin{align*} +\int H_n(t)e^{-t^2}\,dt +&= +\int \bigl( 2tH_{n-1}(t) - H'_{n-1}(t)\bigr)e^{-t^2}\,dt +\\ +&= +-\int \bigl( \exp'(-t^2) H_{n-1}(t) + H'_{n-1}(t)\bigr)e^{-t^2}\,dt +\\ +&= +-\int \bigl( e^{-t^2}H_{n-1}(t)\bigr)' \,dt += +-e^{-t^2}H_{n-1}(t) +\end{align*} +ist. +Für $n>0$ hat also $H_n(t)e^{-t^2}$ eine elementare Stammfunktion. +Die Hermite-Polynome sind also Lösungen für das +Problem~\ref{dreieck:problem}. diff --git a/buch/papers/dreieck/teil2.tex b/buch/papers/dreieck/teil2.tex index 83ea3cb..c5a2826 100644 --- a/buch/papers/dreieck/teil2.tex +++ b/buch/papers/dreieck/teil2.tex @@ -3,7 +3,110 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Wahrscheinlichkeiten im Dreieckstest -\label{dreieck:section:wahrscheinlichkeiten}} -\rhead{Wahrscheinlichkeiten} +\section{Beliebige Polynome +\label{dreieck:section:beliebig}} +\rhead{Beliebige Polynome} +Im Abschnitt~\ref{dreieck:section:hermite-polynome} wurden die +Hermite-Polynome $H_n(t)$ mit $n>0$ als Lösungen des gestellten +Problems erkannt. +Eine Linearkombination von solchen Polynomen hat natürlich +ebenfalls eine elementare Stammfunktion. +Das Problem kann daher neu formuliert werden: + +\begin{problem} +\label{dreieck:problem2} +Welche Polynome $P(t)$ lassen sich aus den Hermite-Polynomen +$H_n(t)$ mit $n>0$ linear kombinieren. +\end{problem} + +Sei jetzt +\[ +P(t) = p_0 + p_1t + \ldots + p_{n-1}t^{n-1} + p_nt^n +\] +ein beliebiges Polynom vom Grad $n$. +Eine elementare Stammfunktion von $P(t)e^{-t^2}$ existiert sicher, +wenn sich $P(t)$ aus den Funktionen $H_n(t)$ mit $n>0$ linear +kombinieren lässt. +Gesucht ist also zunächst eine Darstellung von $P(t)$ als Linearkombination +von Hermite-Polynomen. + +\begin{lemma} +Jedes Polynome $P(t)$ vom Grad $n$ lässt sich auf eindeutige Art und +Weise als Linearkombination +\begin{equation} +P(t) = a_0H_0(t) + a_1H_1(t) + \ldots + a_nH_n(t) += +\sum_{k=0}^n a_nH_n(t) +\label{dreieck:lemma} +\end{equation} +von Hermite-Polynomen schreiben. +\end{lemma} + +\begin{proof}[Beweis] +Zunächst halten wir fest, dass aus der +Rekursionsformel~\eqref{dreieck:rekursion} +folgt, dass der Leitkoeffizient bei jedem Rekursionsschnitt +mit $2$ multipliziert wird. +Der Leitkoeffizient von $H_n(t)$ ist also $2^n$. + +Wir führen den Beweis mit vollständiger Induktion. +Für $n=0$ ist $P(t)=p_0 = p_0 H_0(t)$ als Linearkombination von +Hermite-Polynomen darstellbar, dies ist die Induktionsverankerung. + +Nehmen wir jetzt an, dass sich ein Polynom vom Grad $n-1$ als +Linearkombination der Polynome $H_0(t),\dots,H_{n-1}(t)$ schreiben +lässt und untersuchen wir $P(t)$ vom Grad $n$. +Da der Leitkoeffizient des Polynoms $H_n(t)$ ist $2^n$, ist +\[ +P(t) += +\underbrace{\biggl(P(t) - \frac{p_n}{2^n} H_n(t)\biggr)}_{\displaystyle = Q(t)} ++ +\frac{p_n}{2^n} H_n(t). +\] +Das Polynom $Q(t)$ hat Grad $n-1$, besitzt also nach Induktionsannahme +eine Darstellung +\[ +Q(t) = a_0H_0(t)+a_1H_1(t)+\ldots+a_{n-1}H_{n-1}(t) +\] +als Linearkombination der Polynome $H_0(t),\dots,H_{n-1}(t)$. +Somit ist +\[ +P(t) += a_0H_0(t)+a_1H_1(t)+\ldots+a_{n-1}H_{n-1}(t) + +\frac{p_n}{2^n} H_n(t) +\] +eine Darstellung von $P(t)$ als Linearkombination der Polynome +$H_0(t),\dots,H_n(t)$. +Damit ist der Induktionsschritt vollzogen und das Lemma für alle +$n$ bewiesen. +\end{proof} + +\begin{satz} +\label{dreieck:satz1} +Die Funktion $P(t)e^{-t^2}$ hat genau dann eine elementare Stammfunktion, +wenn in der Darstellung~\eqref{dreieck:lemma} +von $P(t)$ als Linearkombination von Hermite-Polynome $a_0=0$ gilt. +\end{satz} + +\begin{proof}[Beweis] +Es ist +\begin{align*} +\int P(t)e^{-t^2}\,dt +&= +a_0\int e^{-t^2}\,dt ++ +\int +\sum_{k=1} a_kH_k(t)\,dt +\\ +&= +\frac{\sqrt{\pi}}2 +\operatorname{erf}(t) ++ +\sum_{k=1} a_k\int H_k(t)\,dt. +\end{align*} +Da die Integrale in der Summe alle elementar darstellbar sind, +ist das Integral genau dann elementar, wenn $a_0=0$ ist. +\end{proof} + diff --git a/buch/papers/dreieck/teil3.tex b/buch/papers/dreieck/teil3.tex index e2dfd6b..888ceb6 100644 --- a/buch/papers/dreieck/teil3.tex +++ b/buch/papers/dreieck/teil3.tex @@ -3,8 +3,72 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Erweiterungen -\label{dreieck:section:erweiterungen}} -\rhead{Erweiterungen} +\section{Integralbedingung +\label{dreieck:section:integralbedingung}} +\rhead{Lösung} +Die Tatsache, dass die Hermite-Polynome orthogonal sind, erlaubt, das +Kriterium von Satz~\ref{dreieck:satz1} etwas anders zu formulieren. + +Aus den Polynomen $H_n(t)$ lassen sich durch Normierung die +orthonormierten Polynome +\[ +\tilde{H}_n(t) += +\frac{1}{\| H_n\|_w} H_n(t) +\qquad\text{mit}\quad +\|H_n\|_w^2 += +\int_{-\infty}^\infty H_n(t)e^{-t^2}\,dt +\] +bilden. +Da diese Polynome eine orthonormierte Basis des Vektorraums der Polynome +bilden, kann die gesuchte Zerlegung eines Polynoms $P(t)$ auch mit +Hilfe des Skalarproduktes gefunden werden: +\begin{align*} +P(t) +&= +\sum_{k=1}^n +\langle \tilde{H}_k, P\rangle_w +\tilde{H}_k(t) += +\sum_{k=1}^n +\biggl\langle \frac{H_k}{\|H_k\|_w}, P\biggr\rangle_w +\frac{H_k(t)}{\|H_k\|_w} += +\sum_{k=1}^n +\underbrace{ +\frac{ \langle H_k, P\rangle_w }{\|H_k\|_w^2} +}_{\displaystyle =a_k} +H_k(t). +\end{align*} +Die Darstellung von $P(t)$ als Linearkombination von Hermite-Polynomen +hat die Koeffizienten +\[ +a_k = \frac{\langle H_k,P\rangle_w}{\|H_k\|_w^2}. +\] +Aus dem Kriterium $a_0=0$ dafür, dass eine elementare Stammfunktion +von $P(t)e^{-t^2}$ existiert, wird daher die Bedingung, dass +$\langle H_0,P\rangle_w=0$ ist. +Da $H_0(t)=1$ ist, folgt als Bedingung +\[ +a_0 += +\langle H_0,P\rangle_w += +\int_{-\infty}^\infty P(t) e^{-t^2}\,dt += +0. +\] + +\begin{satz} +Ein Integrand der Form $P(t)e^{-t^2}$ mit einem Polynom $P(t)$ +hat genau dann eine elementare Stammfunktion, wenn +\[ +\int_{-\infty}^\infty P(t)e^{-t^2}\,dt = 0 +\] +ist. +\end{satz} + + -- cgit v1.2.1 From 54ab4af72ff10d4e5b739ac0e9d727482b9d5a15 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 7 Jun 2022 12:43:02 +0200 Subject: fix typos --- buch/papers/dreieck/main.tex | 2 +- buch/papers/dreieck/teil0.tex | 4 ++-- buch/papers/dreieck/teil2.tex | 17 ++++++++++------- buch/papers/dreieck/teil3.tex | 5 +++-- 4 files changed, 16 insertions(+), 12 deletions(-) diff --git a/buch/papers/dreieck/main.tex b/buch/papers/dreieck/main.tex index b9f8c3b..fecaf93 100644 --- a/buch/papers/dreieck/main.tex +++ b/buch/papers/dreieck/main.tex @@ -15,7 +15,7 @@ ob eine elementare Funktion eine Stammfunktion in geschlossener Form hat. Der Algorithmus ist jedoch ziemlich kompliziert. In diesem Kapitel soll ein spezieller Fall mit Hilfe der Theorie der orthogonale Polynome, speziell der Hermite-Polynome, behandelt werden, -wie er in der Arbeit \cite{dreieck:polint} behandelt wurde. +wie er in der Arbeit \cite{dreieck:polint} untersucht wurde. \input{papers/dreieck/teil0.tex} \input{papers/dreieck/teil1.tex} diff --git a/buch/papers/dreieck/teil0.tex b/buch/papers/dreieck/teil0.tex index 584f12b..65eff7a 100644 --- a/buch/papers/dreieck/teil0.tex +++ b/buch/papers/dreieck/teil0.tex @@ -33,9 +33,9 @@ Leitet man $e^{-t^2}$ zweimal ab, erhält man = (4t^2-2) e^{-t^2} \qquad\Rightarrow\qquad -\int (t^2-\frac12) e^{-t^2}\,dt +\int (t^2-{\textstyle\frac12}) e^{-t^2}\,dt = -\frac14 +{\textstyle\frac14} e^{-t^2}. \] Es gibt also eine viele weitere Polynome $P(t)$, für die der Integrand diff --git a/buch/papers/dreieck/teil2.tex b/buch/papers/dreieck/teil2.tex index c5a2826..8e89f6a 100644 --- a/buch/papers/dreieck/teil2.tex +++ b/buch/papers/dreieck/teil2.tex @@ -16,10 +16,10 @@ Das Problem kann daher neu formuliert werden: \begin{problem} \label{dreieck:problem2} Welche Polynome $P(t)$ lassen sich aus den Hermite-Polynomen -$H_n(t)$ mit $n>0$ linear kombinieren. +$H_n(t)$ mit $n>0$ linear kombinieren? \end{problem} -Sei jetzt +Sei also \[ P(t) = p_0 + p_1t + \ldots + p_{n-1}t^{n-1} + p_nt^n \] @@ -44,7 +44,7 @@ von Hermite-Polynomen schreiben. \begin{proof}[Beweis] Zunächst halten wir fest, dass aus der -Rekursionsformel~\eqref{dreieck:rekursion} +Rekursionsformel~\eqref{dreieck:eqn:rekursion} folgt, dass der Leitkoeffizient bei jedem Rekursionsschnitt mit $2$ multipliziert wird. Der Leitkoeffizient von $H_n(t)$ ist also $2^n$. @@ -53,10 +53,12 @@ Wir führen den Beweis mit vollständiger Induktion. Für $n=0$ ist $P(t)=p_0 = p_0 H_0(t)$ als Linearkombination von Hermite-Polynomen darstellbar, dies ist die Induktionsverankerung. -Nehmen wir jetzt an, dass sich ein Polynom vom Grad $n-1$ als +Wir nehmen jetzt im Sinne der Induktionsannahme an, +dass sich ein Polynom vom Grad $n-1$ als Linearkombination der Polynome $H_0(t),\dots,H_{n-1}(t)$ schreiben -lässt und untersuchen wir $P(t)$ vom Grad $n$. -Da der Leitkoeffizient des Polynoms $H_n(t)$ ist $2^n$, ist +lässt und untersuchen ein Polynom $P(t)$ vom Grad $n$. +Da der Leitkoeffizient des Polynoms $H_n(t)$ ist $2^n$, ist zerlegen +wir \[ P(t) = @@ -86,7 +88,7 @@ $n$ bewiesen. \label{dreieck:satz1} Die Funktion $P(t)e^{-t^2}$ hat genau dann eine elementare Stammfunktion, wenn in der Darstellung~\eqref{dreieck:lemma} -von $P(t)$ als Linearkombination von Hermite-Polynome $a_0=0$ gilt. +von $P(t)$ als Linearkombination von Hermite-Polynomen $a_0=0$ gilt. \end{satz} \begin{proof}[Beweis] @@ -100,6 +102,7 @@ a_0\int e^{-t^2}\,dt \sum_{k=1} a_kH_k(t)\,dt \\ &= +a_0 \frac{\sqrt{\pi}}2 \operatorname{erf}(t) + diff --git a/buch/papers/dreieck/teil3.tex b/buch/papers/dreieck/teil3.tex index 888ceb6..556a9d9 100644 --- a/buch/papers/dreieck/teil3.tex +++ b/buch/papers/dreieck/teil3.tex @@ -7,7 +7,8 @@ \label{dreieck:section:integralbedingung}} \rhead{Lösung} Die Tatsache, dass die Hermite-Polynome orthogonal sind, erlaubt, das -Kriterium von Satz~\ref{dreieck:satz1} etwas anders zu formulieren. +Kriterium von Satz~\ref{dreieck:satz1} in einer besonders attraktiven +Integralform zu formulieren. Aus den Polynomen $H_n(t)$ lassen sich durch Normierung die orthonormierten Polynome @@ -42,7 +43,7 @@ P(t) H_k(t). \end{align*} Die Darstellung von $P(t)$ als Linearkombination von Hermite-Polynomen -hat die Koeffizienten +hat somit die Koeffizienten \[ a_k = \frac{\langle H_k,P\rangle_w}{\|H_k\|_w^2}. \] -- cgit v1.2.1 From 4220519090661503f243902aa58f48343920e89c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 7 Jun 2022 12:47:03 +0200 Subject: index entries added --- buch/papers/dreieck/main.tex | 2 ++ buch/papers/dreieck/teil1.tex | 1 + buch/papers/dreieck/teil3.tex | 2 ++ 3 files changed, 5 insertions(+) diff --git a/buch/papers/dreieck/main.tex b/buch/papers/dreieck/main.tex index fecaf93..d7bc769 100644 --- a/buch/papers/dreieck/main.tex +++ b/buch/papers/dreieck/main.tex @@ -11,6 +11,8 @@ \noindent Der Risch-Algorithmus erlaubt, eine definitive Antwort darauf zu geben, +\index{Risch-Algorithmus}% +\index{elementare Stammfunktion}% ob eine elementare Funktion eine Stammfunktion in geschlossener Form hat. Der Algorithmus ist jedoch ziemlich kompliziert. In diesem Kapitel soll ein spezieller Fall mit Hilfe der Theorie der diff --git a/buch/papers/dreieck/teil1.tex b/buch/papers/dreieck/teil1.tex index f03c425..45c1a23 100644 --- a/buch/papers/dreieck/teil1.tex +++ b/buch/papers/dreieck/teil1.tex @@ -34,6 +34,7 @@ Die Polynome, die man aus der Funktion $H_0(t)=e^{-t^2}$ durch Ableiten erhalten kann, wurden bereits in Abschnitt~\ref{buch:orthogonalitaet:section:rodrigues} bis auf ein Vorzeichen hergeleitet, sie heissen die Hermite-Polynome +\index{Hermite-Polynome}% und es gilt \[ H_n(t) diff --git a/buch/papers/dreieck/teil3.tex b/buch/papers/dreieck/teil3.tex index 556a9d9..c0c046a 100644 --- a/buch/papers/dreieck/teil3.tex +++ b/buch/papers/dreieck/teil3.tex @@ -11,6 +11,8 @@ Kriterium von Satz~\ref{dreieck:satz1} in einer besonders attraktiven Integralform zu formulieren. Aus den Polynomen $H_n(t)$ lassen sich durch Normierung die +\index{orthogonale Polynome}% +\index{Polynome, orthogonale}% orthonormierten Polynome \[ \tilde{H}_n(t) -- cgit v1.2.1 From a5f6eeefeab2d84d51b94f780387be6e5264f0ca Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 7 Jun 2022 15:30:25 +0200 Subject: synch --- buch/papers/nav/bilder/sextant.jpg | Bin 8280 -> 244565 bytes buch/papers/nav/nautischesdreieck.tex | 28 +--------------------------- buch/papers/nav/trigo.tex | 14 +++++++------- 3 files changed, 8 insertions(+), 34 deletions(-) diff --git a/buch/papers/nav/bilder/sextant.jpg b/buch/papers/nav/bilder/sextant.jpg index 53dd784..472e61f 100644 Binary files a/buch/papers/nav/bilder/sextant.jpg and b/buch/papers/nav/bilder/sextant.jpg differ diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index 36e9c99..d8a14af 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -39,7 +39,7 @@ Unser eigener Standort ist der gesuchte Ecke $P$ und die Ecke $A$ ist in unserem Der Vorteil an der Idee des nautischen Dreiecks ist, dass eine Ecke immer der Nordpol ist. Somit ist diese Ecke immer bekannt und nur deswegen sind die Zusammenhänge von Rektaszension, Sternzeit und Deklination so einfach. -\subsection{Ecke $B$ und $C$ - Bildpunkt $X$ und $Y$} +\subsection{Ecke $B$ und $C$ - Bildpunkt von $X$ und $Y$} Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. seinen Bildpunkt auf der Erdkugel. Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mond oder die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn. @@ -85,32 +85,6 @@ Man benutzt ihn vor allem für die astronomische Navigation auf See. \caption[Sextant]{Sextant} \end{center} \end{figure} -\subsubsection{Eingeschaften} -Für das nautische Dreieck gibt es folgende Eigenschaften: -\begin{center} - \begin{tabular}{ l c l } - Legende && Name / Beziehung \\ - \hline - $\alpha$ && Rektaszension \\ - $\delta$ && Deklination \\ - $\theta$ && Sternzeit von Greenwich\\ - $\phi$ && Geographische Breite\\ - $\tau=\theta-\alpha$ && Stundenwinkel und Längengrad des Gestirns. \\ - $a$ && Azimut\\ - $h$ && Höhe - \end{tabular} -\end{center} -\begin{center} - \begin{tabular}{ l c l } - Eigenschaften \\ - \hline - Seitenlänge Zenit zu Himmelspol= && $\frac{\pi}{2} - \phi$ \\ - Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - \delta$ \\ - Seitenlänge Himmelspol zu Gestirn= && $\frac{\pi}{2} - h$ \\ - Winkel von Zenit zu Himmelsnordpol zu Gestirn= && $\pi-\alpha$\\ - Winkel von Himmelsnordpol zu Zenit zu Gestirn= && $\tau$\\ - \end{tabular} -\end{center} \subsection{Bestimmung des eigenen Standortes $P$} Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index aca8bd2..fa53189 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -87,20 +87,21 @@ So kann mit dem Taylorpolynom 2. Grades den Sinus und den Kosinus vom Sphärisch Es gibt ebenfalls folgende Approximierung der Seiten von der Sphäre in die Ebene: \begin{align} a &\approx \sin(a) \nonumber \intertext{und} - a^2 &\approx 1-\cos(a). \nonumber + \frac{a^2}{2} &\approx 1-\cos(a). \nonumber \end{align} Die Korrespondenzen zwischen der ebenen- und sphärischen Trigonometrie werden in den kommenden Abschnitten erläutert. \subsubsection{Sphärischer Satz des Pythagoras} -Die Korrespondenz \[ a^2 \approx 1-cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich +Die Korrespondenz \[ a^2 \approx 1- \cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich \begin{align} \cos(a)\cdot \cos(b) &= \cos(c) \\ - \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \\ - \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} + \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} + \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \\ -a^2-b^2 &=-c^2\\ a^2+b^2&=c^2 \end{align} +Dies ist der wohlbekannte ebener Satz des Pythagoras. \subsubsection{Sphärischer Sinussatz} Den sphärischen Sinussatz @@ -116,7 +117,6 @@ In der sphärischen Trigonometrie gibt es den Seitenkosinussatz \cos \ a = \cos b \cdot \cos c + \sin b \cdot \sin c \cdot \cos \alpha \nonumber \end{align} %Seitenkosinussatz und den Winkelkosinussatz - \begin{align} \cos \gamma = -\cos \alpha \cdot \cos \beta + \sin \alpha \cdot \sin \beta \cdot \cos c, \nonumber \end{align} der nur in der sphärischen Trigonometrie vorhanden ist. @@ -124,8 +124,8 @@ und den Winkelkosinussatz Analog gibt es auch beim Seitenkosinussatz eine Korrespondenz zu \[ a^2 \leftrightarrow 1-\cos(a),\] die den ebenen Kosinussatz herleiten lässt, nämlich \begin{align} \cos(a)&= \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha) \\ - 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha) \\ - \xcancel{1}-\frac{a^2}{2} &= \xcancel{1}-\frac{b^2}{2}-\frac{c^2}{2} \xcancel{+\frac{b^2c^2}{4}}+bc \cdot \cos(\alpha)\intertext{Höhere Potenzen vernachlässigen} + 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha) \intertext{Höhere Potenzen vernachlässigen} + \xcancel{1}-\frac{a^2}{2} &= \xcancel{1}-\frac{b^2}{2}-\frac{c^2}{2} \xcancel{+\frac{b^2c^2}{4}}+bc \cdot \cos(\alpha)\\ a^2&=b^2+c^2-2bc \cdot \cos(\alpha) \end{align} -- cgit v1.2.1 From fe2c26ed9605f3576abedfd8f0e2068e0c2d40e5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 8 Jun 2022 18:50:57 +0200 Subject: add additional measurements --- buch/papers/nav/beispiel.txt | 22 +++++++++++++++++++--- 1 file changed, 19 insertions(+), 3 deletions(-) diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt index 70e3ce2..12d9e9e 100644 --- a/buch/papers/nav/beispiel.txt +++ b/buch/papers/nav/beispiel.txt @@ -5,15 +5,31 @@ Sternzeit: 7h 54m 26.593s 7.90738694h Deneb RA 20h 42m 12.14s 20.703372h -DEC 45 21' 40.3" 45.361194 +DEC 45g 21' 40.3" 45.361194 -H 50g 15' 17.1" 50.254750h +H 50g 15' 21.7" 50.256027 Azi 59g 36' 02.0" 59.600555 +Altair + +RA 19h 51' 53.39" 19.864831h +DEC 8g 55' 42.3 8.928416 + +H 45g 27' 48.1" 45.463361 +Azi 117g 16' 14.1" 117.270583 + +Arktur + +RA 14h 16' 42.14" 14.278372 +DEC 19g 03' 47.6 19.063222 + +H 47g 25' 38.8" 47.427444 +Azi 259g 09' 38.4" 259.160666 + Spica RA 13h 26m 23.44s 13.439844h -DEC -11g 16' 46.8" 11.279666 +DEC -11g 16' 46.8" -11.279666 H 18g 27' 30.0" 18.458333 Azi 240g 23' 52.5" 240.397916 -- cgit v1.2.1 From b116b6ce1b2988cddd9fff3ae4b2008062438ca2 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Wed, 8 Jun 2022 20:54:01 +0200 Subject: =?UTF-8?q?=EF=BB=BFasd?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/nav/beispiel.txt | 22 +++------------------- 1 file changed, 3 insertions(+), 19 deletions(-) diff --git a/buch/papers/nav/beispiel.txt b/buch/papers/nav/beispiel.txt index 12d9e9e..b8716fc 100644 --- a/buch/papers/nav/beispiel.txt +++ b/buch/papers/nav/beispiel.txt @@ -5,31 +5,15 @@ Sternzeit: 7h 54m 26.593s 7.90738694h Deneb RA 20h 42m 12.14s 20.703372h -DEC 45g 21' 40.3" 45.361194 +DEC 45 21' 40.3" 45.361194 -H 50g 15' 21.7" 50.256027 +H 50g 15' 17.1" 50.254750 Azi 59g 36' 02.0" 59.600555 -Altair - -RA 19h 51' 53.39" 19.864831h -DEC 8g 55' 42.3 8.928416 - -H 45g 27' 48.1" 45.463361 -Azi 117g 16' 14.1" 117.270583 - -Arktur - -RA 14h 16' 42.14" 14.278372 -DEC 19g 03' 47.6 19.063222 - -H 47g 25' 38.8" 47.427444 -Azi 259g 09' 38.4" 259.160666 - Spica RA 13h 26m 23.44s 13.439844h -DEC -11g 16' 46.8" -11.279666 +DEC -11g 16' 46.8" 11.279666 H 18g 27' 30.0" 18.458333 Azi 240g 23' 52.5" 240.397916 -- cgit v1.2.1 From 6f3d0a8adb483394383123e2f4645bdaabba4c32 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Thu, 9 Jun 2022 19:47:33 +0200 Subject: new chapter beispiel --- buch/papers/nav/bsp.tex | 81 ++++++++++++++++++++++++++++++++++++++++++++++++ buch/papers/nav/main.tex | 1 + 2 files changed, 82 insertions(+) create mode 100644 buch/papers/nav/bsp.tex diff --git a/buch/papers/nav/bsp.tex b/buch/papers/nav/bsp.tex new file mode 100644 index 0000000..6f30022 --- /dev/null +++ b/buch/papers/nav/bsp.tex @@ -0,0 +1,81 @@ +\section{Beispielrechnung} + +\subsection{Einführung} +In diesem Abschnitt wird die Theorie vom Abschnitt 21.6 in einem Praxisbeispiel angewendet. +Wir haben die Deklination, Rektaszension, Höhe der beiden Planeten Deneb und Arktur und die Sternzeit von Greenwich als Ausgangslage. +Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden von einem uns unbekannten Ort aus gemessen. +Diesen Punkt gilt es mit dem erlangten Wissen herauszufinden. + +\subsection{Vorgehen} + +\begin{center} + \begin{tabular}{l l l} + 1. & Koordinaten der Bildpunkte der Gestirne bestimmen \\ + 2. & Dreiecke aufzeichnen und richtig beschriften\\ + 3. & Dreieck ABC bestimmmen\\ + 4. & Dreieck BPC bestimmen \\ + 5. & Dreieck ABP bestimmen \\ + 6. & Geographische Breite bestimmen \\ + 7. & Geographische Länge bestimmen \\ + \end{tabular} +\end{center} + +\subsection{Ausgangslage} +Die Rektaszension und die Sternzeit sind in der Regeln in Stunden angegeben. +Für die Umrechnung in Grad kann folgender Zusammenhang verwendet werden: +\[ Stunden \cdot 15 = Grad\]. +Dies wurde hier bereits gemacht. +\begin{center} + \begin{tabular}{l l l} + Sternzeit $s$ & $118.610804^\circ$ \\ + Deneb&\\ + & Rektaszension $RA_{Deneb}$& $310.55058^\circ$ \\ + & Deklination $DEC_{Deneb}$& $45.361194^\circ$ \\ + & Höhe $H_{Deneb}$ & $50.256027^\circ$ \\ + Arktur &\\ + & Rektaszension $RA_{Arktur}$& $214.17558^\circ$ \\ + & Deklination $DEC_{Arktur}$& $19.063222^\circ$ \\ + & Höhe $H_{Arktur}$ & $47.427444^\circ$ \\ + \end{tabular} +\end{center} +\subsection{Koordinaten der Bildpunkte} +Als erstes benötigen wir die Koordinaten der Bildpunkte von Arktur und Deneb. +$\delta$ ist die Breite, $\lambda$ die Länge. +\begin{align} +\delta_{Deneb}&=DEC_{Deneb} = \underline{\underline{45.361194^\circ}} \nonumber \\ +\lambda_{Deneb}&=RA_{Deneb} - s = 310.55058^\circ -118.610804^\circ =\underline{\underline{191.939776^\circ}} \nonumber \\ +\delta_{Arktur}&=DEC_{Arktur} = \underline{\underline{19.063222^\circ}} \nonumber \\ +\lambda_{Arktur}&=RA_{Arktur} - s = 214.17558^\circ -118.610804^\circ = \underline{\underline{5.5647759^\circ}} \nonumber +\end{align} + + +\subsection{Dreiecke definieren} +Das Festlegen der Dreiecke ist essenziell für die korrekten Berechnungen. +BILD +\subsection{Dreieck ABC} +Nun berechnen wir alle Seitenlängen $a$, $b$, $c$ und die Innnenwinkel $\alpha$, $\beta$ und $\gamma$ +Wir können $b$ und $c$ mit den geltenten Zusammenhängen des nautischen Dreiecks wie folgt bestimmen: +\begin{align} + b=90^\circ-DEC_{Deneb} = 90^\circ - 45.361194^\circ = \underline{\underline{44.638806^\circ}}\nonumber \\ + c=90^\circ-DEC_{Arktur} = 90^\circ - 19.063222^\circ = \underline{\underline{70.936778^\circ}} \nonumber +\end{align} +Um $a$ zu bestimmen, benötigen wir zuerst den Winkel \[\alpha= RA_{Deneb} - RA_{Arktur} = 310.55058^\circ -214.17558^\circ = \underline{\underline{96.375^\circ}}.\] +Danach nutzen wir den sphärischen Winkelkosinussatz, um $a$ zu berechnen: +\begin{align} + a &= \cos^{-1}(\cos(b) \cdot \cos(c) + \sin(b) \cdot \sin(c) \cdot \cos(\alpha)) \nonumber \\ + &= \cos^{-1}(\cos(44.638806) \cdot \cos(70.936778) + \sin(44.638806) \cdot \sin(70.936778) \cdot \cos(96.375)) \nonumber \\ + &= \underline{\underline{80.8707801^\circ}} \nonumber +\end{align} +Für $\beta$ und $\gamma$ nutzen wir den sphärischen Seitenkosinussatz: +\begin{align} + \beta &= \cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg] \nonumber \\ + &= \cos^{-1} \bigg[\frac{\cos(44.638806)-\cos(80.8707801) \cdot \cos(70.936778)}{\sin(80.8707801) \cdot \sin(70.936778)}\bigg] \nonumber \\ + &= \underline{\underline{45.0115314^\circ}} \nonumber +\end{align} + + \begin{align} + \gamma &= \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}\bigg] \nonumber \\ + &= \cos^{-1} \bigg[\frac{\cos(70.936778)-\cos(44.638806) \cdot \cos(80.8707801)}{\sin(80.8707801) \cdot \sin(44.638806)}\bigg] \nonumber \\ + &=\underline{\underline{72.0573328^\circ}} \nonumber +\end{align} + diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 4c52547..37bc83a 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -15,6 +15,7 @@ \input{papers/nav/sincos.tex} \input{papers/nav/trigo.tex} \input{papers/nav/nautischesdreieck.tex} +\input{papers/nav/bsp.tex} \printbibliography[heading=subbibliography] -- cgit v1.2.1 From 332ac4d8384eb8afee67e290e7660bffa9887263 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 10 Jun 2022 15:50:16 +0200 Subject: add position subdirectory --- buch/papers/nav/images/Makefile | 27 +- buch/papers/nav/images/common.inc | 156 +----------- buch/papers/nav/images/dreieck3d1.pdf | Bin 90451 -> 85369 bytes buch/papers/nav/images/dreieck3d1.pov | 3 + buch/papers/nav/images/dreieck3d2.pdf | Bin 69523 -> 64256 bytes buch/papers/nav/images/dreieck3d2.pov | 2 + buch/papers/nav/images/dreieck3d3.pdf | Bin 82512 -> 77179 bytes buch/papers/nav/images/dreieck3d3.pov | 2 + buch/papers/nav/images/dreieck3d4.pdf | Bin 85037 -> 84768 bytes buch/papers/nav/images/dreieck3d4.pov | 2 + buch/papers/nav/images/dreieck3d5.pdf | Bin 70045 -> 64209 bytes buch/papers/nav/images/dreieck3d5.pov | 2 + buch/papers/nav/images/dreieck3d6.pov | 2 + buch/papers/nav/images/dreieck3d7.pov | 2 + buch/papers/nav/images/dreieck3d8.jpg | Bin 93432 -> 90015 bytes 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create mode 100644 buch/papers/nav/images/position/position3.pov create mode 100644 buch/papers/nav/images/position/position3.tex create mode 100644 buch/papers/nav/images/position/position4.pdf create mode 100644 buch/papers/nav/images/position/position4.pov create mode 100644 buch/papers/nav/images/position/position4.tex create mode 100644 buch/papers/nav/images/position/position5.pdf create mode 100644 buch/papers/nav/images/position/position5.pov create mode 100644 buch/papers/nav/images/position/position5.tex diff --git a/buch/papers/nav/images/Makefile b/buch/papers/nav/images/Makefile index da4defa..39bfbcf 100644 --- a/buch/papers/nav/images/Makefile +++ b/buch/papers/nav/images/Makefile @@ -51,73 +51,80 @@ DREIECKE3D = \ dreieck3d5.pdf \ dreieck3d6.pdf \ dreieck3d7.pdf \ - dreieck3d8.pdf + dreieck3d8.pdf dreiecke3d: $(DREIECKE3D) POVRAYOPTIONS = -W1080 -H1080 #POVRAYOPTIONS = -W480 -H480 -dreieck3d1.png: dreieck3d1.pov common.inc +dreieck3d1.png: dreieck3d1.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d1.png dreieck3d1.pov dreieck3d1.jpg: dreieck3d1.png convert dreieck3d1.png -density 300 -units PixelsPerInch dreieck3d1.jpg dreieck3d1.pdf: dreieck3d1.tex dreieck3d1.jpg pdflatex dreieck3d1.tex -dreieck3d2.png: dreieck3d2.pov common.inc +dreieck3d2.png: dreieck3d2.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d2.png dreieck3d2.pov dreieck3d2.jpg: dreieck3d2.png convert dreieck3d2.png -density 300 -units PixelsPerInch dreieck3d2.jpg dreieck3d2.pdf: dreieck3d2.tex dreieck3d2.jpg pdflatex dreieck3d2.tex -dreieck3d3.png: dreieck3d3.pov common.inc +dreieck3d3.png: dreieck3d3.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d3.png dreieck3d3.pov dreieck3d3.jpg: dreieck3d3.png convert dreieck3d3.png -density 300 -units PixelsPerInch dreieck3d3.jpg dreieck3d3.pdf: dreieck3d3.tex dreieck3d3.jpg pdflatex dreieck3d3.tex -dreieck3d4.png: dreieck3d4.pov common.inc +dreieck3d4.png: dreieck3d4.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d4.png dreieck3d4.pov dreieck3d4.jpg: dreieck3d4.png convert dreieck3d4.png -density 300 -units PixelsPerInch dreieck3d4.jpg dreieck3d4.pdf: dreieck3d4.tex dreieck3d4.jpg pdflatex dreieck3d4.tex -dreieck3d5.png: dreieck3d5.pov common.inc +dreieck3d5.png: dreieck3d5.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d5.png dreieck3d5.pov dreieck3d5.jpg: dreieck3d5.png convert dreieck3d5.png -density 300 -units PixelsPerInch dreieck3d5.jpg dreieck3d5.pdf: dreieck3d5.tex dreieck3d5.jpg pdflatex dreieck3d5.tex -dreieck3d6.png: dreieck3d6.pov common.inc +dreieck3d6.png: dreieck3d6.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d6.png dreieck3d6.pov dreieck3d6.jpg: dreieck3d6.png convert dreieck3d6.png -density 300 -units PixelsPerInch dreieck3d6.jpg dreieck3d6.pdf: dreieck3d6.tex dreieck3d6.jpg pdflatex dreieck3d6.tex -dreieck3d7.png: dreieck3d7.pov common.inc +dreieck3d7.png: dreieck3d7.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d7.png dreieck3d7.pov dreieck3d7.jpg: dreieck3d7.png convert dreieck3d7.png -density 300 -units PixelsPerInch dreieck3d7.jpg dreieck3d7.pdf: dreieck3d7.tex dreieck3d7.jpg pdflatex dreieck3d7.tex -dreieck3d8.png: dreieck3d8.pov common.inc +dreieck3d8.png: dreieck3d8.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d8.png dreieck3d8.pov dreieck3d8.jpg: dreieck3d8.png convert dreieck3d8.png -density 300 -units PixelsPerInch dreieck3d8.jpg dreieck3d8.pdf: dreieck3d8.tex dreieck3d8.jpg pdflatex dreieck3d8.tex -dreieck3d9.png: dreieck3d9.pov common.inc +dreieck3d9.png: dreieck3d9.pov common.inc macros.inc povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d9.png dreieck3d9.pov dreieck3d9.jpg: dreieck3d9.png convert dreieck3d9.png -density 300 -units PixelsPerInch dreieck3d9.jpg dreieck3d9.pdf: dreieck3d9.tex dreieck3d9.jpg pdflatex dreieck3d9.tex +dreieck3d10.png: dreieck3d10.pov common.inc macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Odreieck3d10.png dreieck3d10.pov +dreieck3d10.jpg: dreieck3d10.png + convert dreieck3d10.png -density 300 -units PixelsPerInch dreieck3d10.jpg +dreieck3d10.pdf: dreieck3d10.tex dreieck3d10.jpg macros.inc + pdflatex dreieck3d10.tex + diff --git a/buch/papers/nav/images/common.inc b/buch/papers/nav/images/common.inc index 2c0ae6e..7b861de 100644 --- a/buch/papers/nav/images/common.inc +++ b/buch/papers/nav/images/common.inc @@ -5,6 +5,7 @@ // #version 3.7; #include "colors.inc" +#include "macros.inc" global_settings { assumed_gamma 1 @@ -12,12 +13,6 @@ global_settings { #declare imagescale = 0.034; -#declare O = <0, 0, 0>; -#declare A = vnormalize(< 0, 1, 0>); -#declare B = vnormalize(< 1, 2, -8>); -#declare C = vnormalize(< 5, 1, 0>); -#declare P = vnormalize(< 5, -1, -7>); - camera { location <40, 20, -20> look_at <0, 0.24, -0.20> @@ -26,7 +21,7 @@ camera { } light_source { - <10, 10, -40> color White + <30, 10, -40> color White area_light <1,0,0> <0,0,1>, 10, 10 adaptive 1 jitter @@ -38,150 +33,3 @@ sky_sphere { } } -// -// draw an arrow from to with thickness with -// color -// -#macro arrow(from, to, arrowthickness, c) -#declare arrowdirection = vnormalize(to - from); -#declare arrowlength = vlength(to - from); -union { - sphere { - from, 1.1 * arrowthickness - } - cylinder { - from, - from + (arrowlength - 5 * arrowthickness) * arrowdirection, - arrowthickness - } - cone { - from + (arrowlength - 5 * arrowthickness) * arrowdirection, - 2 * arrowthickness, - to, - 0 - } - pigment { - color c - } - finish { - specular 0.9 - metallic - } -} -#end - -#macro grosskreis(normale, staerke) -union { - #declare v1 = vcross(normale, ); - #declare v1 = vnormalize(v1); - #declare v2 = vnormalize(vcross(v1, normale)); - #declare phisteps = 100; - #declare phistep = pi / phisteps; - #declare phi = 0; - #declare p1 = v1; - #while (phi < 2 * pi - phistep/2) - sphere { p1, staerke } - #declare phi = phi + phistep; - #declare p2 = v1 * cos(phi) + v2 * sin(phi); - cylinder { p1, p2, staerke } - #declare p1 = p2; - #end -} -#end - -#macro seite(p, q, staerke) - #declare n = vcross(p, q); - intersection { - grosskreis(n, staerke) - plane { -vcross(n, q) * vdot(vcross(n, q), p), 0 } - plane { -vcross(n, p) * vdot(vcross(n, p), q), 0 } - } -#end - -#macro winkel(w, p, q, staerke, r) - #declare n = vnormalize(w); - #declare pp = vnormalize(p - vdot(n, p) * n); - #declare qq = vnormalize(q - vdot(n, q) * n); - intersection { - sphere { O, 1 + staerke } - cone { O, 0, 1.2 * vnormalize(w), r } - plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 } - plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 } - } -#end - -#macro punkt(p, staerke) - sphere { p, 1.5 * staerke } -#end - -#macro dreieck(p, q, r, farbe) - #declare n1 = vnormalize(vcross(p, q)); - #declare n2 = vnormalize(vcross(q, r)); - #declare n3 = vnormalize(vcross(r, p)); - intersection { - plane { n1, 0 } - plane { n2, 0 } - plane { n3, 0 } - sphere { <0, 0, 0>, 1 + 0.001 } - pigment { - color farbe - } - finish { - metallic - specular 0.4 - } - } -#end - -#macro ebenerwinkel(a, p, q, s, r, farbe) - #declare n = vnormalize(-vcross(p, q)); - #declare np = vnormalize(-vcross(p, n)); - #declare nq = -vnormalize(-vcross(q, n)); -// arrow(a, a + n, 0.02, White) -// arrow(a, a + np, 0.01, Red) -// arrow(a, a + nq, 0.01, Blue) - intersection { - cylinder { a - (s/2) * n, a + (s/2) * n, r } - plane { np, vdot(np, a) } - plane { nq, vdot(nq, a) } - pigment { - farbe - } - finish { - metallic - specular 0.5 - } - } -#end - -#macro komplement(a, p, q, s, r, farbe) - #declare n = vnormalize(-vcross(p, q)); -// arrow(a, a + n, 0.015, Orange) - #declare m = vnormalize(-vcross(q, n)); -// arrow(a, a + m, 0.015, Pink) - ebenerwinkel(a, p, m, s, r, farbe) -#end - -#declare fett = 0.015; -#declare fein = 0.010; - -#declare klein = 0.3; -#declare gross = 0.4; - -#declare dreieckfarbe = rgb<0.6,0.6,0.6>; -#declare rot = rgb<0.8,0.2,0.2>; -#declare gruen = rgb<0,0.6,0>; -#declare blau = rgb<0.2,0.2,0.8>; - -#declare kugelfarbe = rgb<0.8,0.8,0.8>; -#declare kugeltransparent = rgbt<0.8,0.8,0.8,0.5>; - -#macro kugel(farbe) -sphere { - <0, 0, 0>, 1 - pigment { - color farbe - } -} -#end - diff --git a/buch/papers/nav/images/dreieck3d1.pdf b/buch/papers/nav/images/dreieck3d1.pdf index 015bce7..fecaece 100644 Binary files a/buch/papers/nav/images/dreieck3d1.pdf and b/buch/papers/nav/images/dreieck3d1.pdf differ diff --git a/buch/papers/nav/images/dreieck3d1.pov b/buch/papers/nav/images/dreieck3d1.pov index e491075..336161c 100644 --- a/buch/papers/nav/images/dreieck3d1.pov +++ b/buch/papers/nav/images/dreieck3d1.pov @@ -3,8 +3,11 @@ // // (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule // +#version 3.7; #include "common.inc" +kugel(kugeldunkel) + union { seite(A, B, fett) seite(B, C, fett) diff --git a/buch/papers/nav/images/dreieck3d2.pdf b/buch/papers/nav/images/dreieck3d2.pdf index 6b3f09d..28af5fe 100644 Binary files a/buch/papers/nav/images/dreieck3d2.pdf and b/buch/papers/nav/images/dreieck3d2.pdf differ diff --git a/buch/papers/nav/images/dreieck3d2.pov b/buch/papers/nav/images/dreieck3d2.pov index c0625ce..9e57d22 100644 --- a/buch/papers/nav/images/dreieck3d2.pov +++ b/buch/papers/nav/images/dreieck3d2.pov @@ -5,6 +5,8 @@ // #include "common.inc" +kugel(kugeldunkel) + union { seite(A, B, fett) seite(B, C, fett) diff --git a/buch/papers/nav/images/dreieck3d3.pdf b/buch/papers/nav/images/dreieck3d3.pdf index 7d79455..4fc4fc1 100644 Binary files a/buch/papers/nav/images/dreieck3d3.pdf and b/buch/papers/nav/images/dreieck3d3.pdf differ diff --git a/buch/papers/nav/images/dreieck3d3.pov b/buch/papers/nav/images/dreieck3d3.pov index b6f64d5..bde780b 100644 --- a/buch/papers/nav/images/dreieck3d3.pov +++ b/buch/papers/nav/images/dreieck3d3.pov @@ -5,6 +5,8 @@ // #include "common.inc" +kugel(kugeldunkel) + union { seite(A, B, fett) seite(B, C, fett) diff --git a/buch/papers/nav/images/dreieck3d4.pdf b/buch/papers/nav/images/dreieck3d4.pdf index e1ea757..0d57fc2 100644 Binary files a/buch/papers/nav/images/dreieck3d4.pdf and b/buch/papers/nav/images/dreieck3d4.pdf differ diff --git a/buch/papers/nav/images/dreieck3d4.pov b/buch/papers/nav/images/dreieck3d4.pov index b6f17e3..08f266b 100644 --- a/buch/papers/nav/images/dreieck3d4.pov +++ b/buch/papers/nav/images/dreieck3d4.pov @@ -5,6 +5,8 @@ // #include "common.inc" +kugel(kugelfarbe) + union { seite(A, B, fein) seite(A, C, fein) diff --git a/buch/papers/nav/images/dreieck3d5.pdf b/buch/papers/nav/images/dreieck3d5.pdf index 0c86d36..a5dd0ae 100644 Binary files a/buch/papers/nav/images/dreieck3d5.pdf and b/buch/papers/nav/images/dreieck3d5.pdf differ diff --git a/buch/papers/nav/images/dreieck3d5.pov b/buch/papers/nav/images/dreieck3d5.pov index 188f181..1aac0dc 100644 --- a/buch/papers/nav/images/dreieck3d5.pov +++ b/buch/papers/nav/images/dreieck3d5.pov @@ -5,6 +5,8 @@ // #include "common.inc" +kugel(kugeldunkel) + union { seite(A, B, fein) seite(A, C, fein) diff --git a/buch/papers/nav/images/dreieck3d6.pov b/buch/papers/nav/images/dreieck3d6.pov index 191a1e7..6bbd1a9 100644 --- a/buch/papers/nav/images/dreieck3d6.pov +++ b/buch/papers/nav/images/dreieck3d6.pov @@ -5,6 +5,8 @@ // #include "common.inc" +kugel(kugeldunkel) + union { seite(A, B, fett) seite(A, C, fett) diff --git a/buch/papers/nav/images/dreieck3d7.pov b/buch/papers/nav/images/dreieck3d7.pov index aae5c6c..45dc5d6 100644 --- a/buch/papers/nav/images/dreieck3d7.pov +++ b/buch/papers/nav/images/dreieck3d7.pov @@ -5,6 +5,8 @@ // #include "common.inc" +kugel(kugeldunkel) + union { seite(A, C, fett) seite(A, P, fett) diff --git a/buch/papers/nav/images/dreieck3d8.jpg b/buch/papers/nav/images/dreieck3d8.jpg index 52bd25e..f24ea33 100644 Binary files a/buch/papers/nav/images/dreieck3d8.jpg and b/buch/papers/nav/images/dreieck3d8.jpg differ diff --git a/buch/papers/nav/images/dreieck3d8.pdf b/buch/papers/nav/images/dreieck3d8.pdf index 9d630aa..da3b110 100644 Binary files a/buch/papers/nav/images/dreieck3d8.pdf and b/buch/papers/nav/images/dreieck3d8.pdf differ diff --git a/buch/papers/nav/images/dreieck3d8.pov b/buch/papers/nav/images/dreieck3d8.pov index 9e9921a..dae7f67 100644 --- a/buch/papers/nav/images/dreieck3d8.pov +++ b/buch/papers/nav/images/dreieck3d8.pov @@ -93,4 +93,5 @@ object { dreieck(A, B, C, White) +kugel(kugeldunkel) diff --git a/buch/papers/nav/images/macros.inc b/buch/papers/nav/images/macros.inc new file mode 100644 index 0000000..2def6fd --- /dev/null +++ b/buch/papers/nav/images/macros.inc @@ -0,0 +1,343 @@ +// +// macros.inc -- 3d Darstellung +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +// +// Dimensions +// +#declare fett = 0.015; +#declare fein = 0.010; + +#declare klein = 0.3; +#declare gross = 0.4; + +// +// colors +// +#declare dreieckfarbe = rgb<0.6,0.6,0.6>; +#declare rot = rgb<0.8,0.2,0.2>; +#declare gruen = rgb<0,0.6,0>; +#declare blau = rgb<0.2,0.2,0.8>; + +#declare bekannt = rgb<0.2,0.6,1>; +#declare unbekannt = rgb<1.0,0.6,0.8>; + +#declare kugelfarbe = rgb<0.8,0.8,0.8>; +#declare kugeldunkel = rgb<0.4,0.4,0.4>; +#declare kugeltransparent = rgbt<0.8,0.8,0.8,0.5>; + +#declare gitterfarbe = rgb<0.2,0.6,1>; + +// +// Points Points +// +#declare O = <0, 0, 0>; +#declare Nordpol = vnormalize(< 0, 1, 0>); +#declare A = vnormalize(< 0, 1, 0>); +#declare B = vnormalize(< 1, 2, -8>); +#declare C = vnormalize(< 5, 1, 0>); +#declare P = vnormalize(< 5, -1, -7>); + +// +// \brief convert spherical coordinates to recctangular coordinates +// +// \param phi +// \param theta +// +#macro kugelpunkt(phi, theta) + < sin(theta) * cos(phi - pi), cos(theta), sin(theta) * sin(phi - pi) > +#end + +#declare Sakura = kugelpunkt(radians(140.2325498), radians(90 - 35.71548014)); +#declare Deneb = kugelpunkt(radians(191.9397759), radians(90 - 45.361194)); +#declare Spica = kugelpunkt(radians(82.9868559), radians(90 - (-11.279666))); +#declare Altair = kugelpunkt(radians(179.3616609), radians(90 - 8.928416)); +#declare Arktur = kugelpunkt(radians(95.5647759), radians(90 - 19.063222)); + +// +// draw an arrow from to with thickness with +// color +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare ntsteps = 100; + +// +// \brief Draw a circle +// +// \param b1 basis vector for a coordinate system of the plane containing +// the circle +// \param b2 the other basis vector +// \param o center of the circle +// \param thick diameter of the circular tube +// +#macro kreis(b1, b2, o, thick, maxwinkel) + #declare tpstep = pi / ntsteps; + #declare tp = tpstep; + #declare p1 = b1 + o; + sphere { p1, thick } + #declare tpstep = pi/ntsteps; + #while (tp < (maxwinkel - tpstep/2)) + #declare p2 = cos(tp) * b1 + sin(tp) * b2 + o; + cylinder { p1, p2, thick } + sphere { p2, thick } + #declare p1 = p2; + #declare tp = tp + tpstep; + #end + #if ((tp - tpstep) < maxwinkel) + #declare p2 = cos(maxwinkel) * b1 + sin(maxwinkel) * b2 + o; + cylinder { p1, p2, thick } + sphere { p2, thick } + #end +#end + +// +// \brief Draw a great circle +// +// \param normale the normal of the plane containing the great circle +// \param thick diameter +// +#macro grosskreis(normale, thick) + #declare other = < normale.y, -normale.x, normale.z >; + #declare b1 = vnormalize(vcross(other, normale)); + #declare b2 = vnormalize(vcross(normale, b1)); + kreis(b1, b2, <0,0,0>, thick, 2*pi) +#end + +// +// \brief Draw a circle of latitude +// +// \param theta latitude +// \param thick diameter +// +#macro breitenkreis(theta, thick) + #declare b1 = sin(theta) * kugelpunkt(0, pi/2); + #declare b2 = sin(theta) * kugelpunkt(pi/2, pi/2); + #declare o = < 0, cos(theta), 0 >; + kreis(b1, b2, o, thick, 2*pi) +#end + +// +// \brief Draw the great circle connecting the two points +// +// \param p first point +// \param q second point +// \param staerke diameter +// + +#macro seite(p, q, staerke) + #declare s1 = vnormalize(p); + #declare s2 = vnormalize(q); + #declare w = acos(vdot(s1, s2)); + #declare n = vnormalize(vcross(p, q)); + #declare s2 = vnormalize(vcross(n, s1)); + kreis(s1, s2, O, staerke, w) +#end + +// +// \brief Draw an angle +// +// \param w the edge where the angle is located +// \param p point on the first leg +// \param q point on the second leg +// \param r diameter of the angle +// +#macro winkel(w, p, q, staerke, r) + #declare n = vnormalize(w); + #declare pp = vnormalize(p - vdot(n, p) * n); + #declare qq = vnormalize(q - vdot(n, q) * n); + intersection { + sphere { O, 1 + staerke } + cone { O, 0, 1.2 * vnormalize(w), r } + plane { -vcross(n, qq) * vdot(vcross(n, qq), pp), 0 } + plane { -vcross(n, pp) * vdot(vcross(n, pp), qq), 0 } + } +#end + +// +// \brief Draw a point on the sphere as a circle +// +// \param p the point +// \param staerke the diameter of the point +// +#macro punkt(p, staerke) + sphere { p, 1.5 * staerke } +#end + +// +// \brief Draw a circle as a part of the differently colored cutout from +// the sphere +// +// \param p first point of the triangle +// \param q second point of the triangle +// \param r third point of the triangle +// \param farbe color +// +#macro dreieck(p, q, r, farbe) + #declare n1 = vnormalize(vcross(p, q)); + #declare n2 = vnormalize(vcross(q, r)); + #declare n3 = vnormalize(vcross(r, p)); + intersection { + plane { n1, 0 } + plane { n2, 0 } + plane { n3, 0 } + sphere { <0, 0, 0>, 1 + 0.001 } + pigment { + color farbe + } + finish { + metallic + specular 0.4 + } + } +#end + +// +// \brief +// +// \param a axis of the angle +// \param p first leg +// \param q second leg +// \param s thickness of the angle disk +// \param r radius of the angle disk +// \param farbe color +// +#macro ebenerwinkel(a, p, q, s, r, farbe) + #declare n = vnormalize(-vcross(p, q)); + #declare np = vnormalize(-vcross(p, n)); + #declare nq = -vnormalize(-vcross(q, n)); +// arrow(a, a + n, 0.02, White) +// arrow(a, a + np, 0.01, Red) +// arrow(a, a + nq, 0.01, Blue) + intersection { + cylinder { a - (s/2) * n, a + (s/2) * n, r } + plane { np, vdot(np, a) } + plane { nq, vdot(nq, a) } + pigment { + farbe + } + finish { + metallic + specular 0.5 + } + } +#end + +// +// \brief Show the complement angle +// +// +#macro komplement(a, p, q, s, r, farbe) + #declare n = vnormalize(-vcross(p, q)); +// arrow(a, a + n, 0.015, Orange) + #declare m = vnormalize(-vcross(q, n)); +// arrow(a, a + m, 0.015, Pink) + ebenerwinkel(a, p, m, s, r, farbe) +#end + +// +// \brief Show a coordinate grid on the sphere +// +// \param farbe the color of the grid +// \param thick the line thickness +// +#macro koordinatennetz(farbe, netzschritte, thick) +union { + // circles of latitude + #declare theta = pi/(2*netzschritte); + #declare thetastep = pi/(2*netzschritte); + #while (theta < pi - thetastep/2) + breitenkreis(theta, thick) + #declare theta = theta + thetastep; + #end + // cirles of longitude + #declare phi = 0; + #declare phistep = pi/(2*netzschritte); + #while (phi < pi-phistep/2) + grosskreis(kugelpunkt(phi, pi/2), thick) + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +// +// \brief Display a color of given color +// +// \param farbe the color +// +#macro kugel(farbe) +sphere { + <0, 0, 0>, 1 + pigment { + color farbe + } +} +#end + +// +// \brief Display the earth +// +#macro erde() +sphere { + <0, 0, 0>, 1 + pigment { + image_map { + png "2k_earth_daymap.png" gamma 1.0 + map_type 1 + } + } +} +#end + +// +// achse +// +#macro achse(durchmesser, farbe) + cylinder { + < 0, -1.2, 0 >, <0, 1.2, 0 >, durchmesser + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } + } +#end diff --git a/buch/papers/nav/images/position/Makefile b/buch/papers/nav/images/position/Makefile new file mode 100644 index 0000000..280e59c --- /dev/null +++ b/buch/papers/nav/images/position/Makefile @@ -0,0 +1,54 @@ +# +# Makefile to build images +# +# (c) 2022 +# +all: position + +POSITION = \ + position1.pdf \ + position2.pdf \ + position3.pdf \ + position4.pdf \ + position5.pdf + +position: $(POSITION) + +POVRAYOPTIONS = -W1080 -H1080 +#POVRAYOPTIONS = -W480 -H480 + +position1.png: position1.pov common.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Oposition1.png position1.pov +position1.jpg: position1.png + convert position1.png -density 300 -units PixelsPerInch position1.jpg +position1.pdf: position1.tex common.tex position1.jpg + pdflatex position1.tex + +position2.png: position2.pov common.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Oposition2.png position2.pov +position2.jpg: position2.png + convert position2.png -density 300 -units PixelsPerInch position2.jpg +position2.pdf: position2.tex common.tex position2.jpg + pdflatex position2.tex + +position3.png: position3.pov common.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Oposition3.png position3.pov +position3.jpg: position3.png + convert position3.png -density 300 -units PixelsPerInch position3.jpg +position3.pdf: position3.tex common.tex position3.jpg + pdflatex position3.tex + +position4.png: position4.pov common.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Oposition4.png position4.pov +position4.jpg: position4.png + convert position4.png -density 300 -units PixelsPerInch position4.jpg +position4.pdf: position4.tex common.tex position4.jpg + pdflatex position4.tex + +position5.png: position5.pov common.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Oposition5.png position5.pov +position5.jpg: position5.png + convert position5.png -density 300 -units PixelsPerInch position5.jpg +position5.pdf: position5.tex common.tex position5.jpg + pdflatex position5.tex + diff --git a/buch/papers/nav/images/position/common.inc b/buch/papers/nav/images/position/common.inc new file mode 100644 index 0000000..b50b8d6 --- /dev/null +++ b/buch/papers/nav/images/position/common.inc @@ -0,0 +1,37 @@ +// +// common.inc -- 3d Darstellung +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" +#include "../macros.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.034; + +camera { + location <40, 20, -20> + look_at <0, 0.24, -0.20> + right x * imagescale + up y * imagescale +} + +light_source { + <30, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +kugel(kugeldunkel) +achse(fein, White) diff --git a/buch/papers/nav/images/position/common.tex b/buch/papers/nav/images/position/common.tex new file mode 100644 index 0000000..d72a981 --- /dev/null +++ b/buch/papers/nav/images/position/common.tex @@ -0,0 +1,32 @@ +% +% common.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% + +\def\labelA{\node at (0.7,3.8) {$A$};} +\def\labelB{\node at (-3.4,-0.8) {$B$};} +\def\labelC{\node at (3.3,-2.1) {$C$};} +\def\labelP{\node at (-1.4,-3.5) {$P$};} + +\def\labelc{\node at (-1.9,2.1) {$c$};} +\def\labela{\node at (-0.2,-1.2) {$a$};} +\def\labelb{\node at (2.6,1.5) {$b$};} + +\def\labelhb{\node at (-2.6,-2.2) {$h_b$};} +\def\labelhc{\node at (1,-2.9) {$h_c$};} +\def\labell{\node at (-0.7,0.3) {$l$};} + +\def\labelalpha{\node at (0.6,2.85) {$\alpha$};} +\def\labelbeta{\node at (-2.5,-0.5) {$\beta$};} +\def\labelgamma{\node at (2.3,-1.2) {$\gamma$};} +\def\labelomega{\node at (0.85,3.3) {$\omega$};} + +\def\labelgammaone{\node at (2.1,-2.0) {$\gamma_1$};} +\def\labelgammatwo{\node at (2.3,-1.3) {$\gamma_2$};} +\def\labelbetaone{\node at (-2.4,-1.4) {$\beta_1$};} +\def\labelbetatwo{\node at (-2.5,-0.8) {$\beta_2$};} + +\def\labelomegalinks{\node at (0.25,3.25) {$\omega$};} +\def\labelomegarechts{\node at (0.85,3.1) {$\omega$};} + diff --git a/buch/papers/nav/images/position/position1.pdf b/buch/papers/nav/images/position/position1.pdf new file mode 100644 index 0000000..1bd9a69 Binary files /dev/null and b/buch/papers/nav/images/position/position1.pdf differ diff --git a/buch/papers/nav/images/position/position1.pov b/buch/papers/nav/images/position/position1.pov new file mode 100644 index 0000000..a79a9f1 --- /dev/null +++ b/buch/papers/nav/images/position/position1.pov @@ -0,0 +1,71 @@ +// +// position1.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "common.inc" + +union { + seite(B, C, fett) + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +union { + seite(A, P, fett) + pigment { + color rot + } + finish { + specular 0.95 + metallic + } +} + + +union { + seite(A, B, fett) + seite(A, C, fett) + seite(B, P, fett) + seite(C, P, fett) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, C, fein, gross) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, P, C, fett, klein) + pigment { + color rot + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/position/position1.tex b/buch/papers/nav/images/position/position1.tex new file mode 100644 index 0000000..d6c21c3 --- /dev/null +++ b/buch/papers/nav/images/position/position1.tex @@ -0,0 +1,55 @@ +% +% dreieck3d1.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{position1.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelB +\labelC +\labelP + +\labelc +\labela +\labelb +\labell + +\labelhb +\labelhc + +\labelalpha +\labelomega + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position2.pdf b/buch/papers/nav/images/position/position2.pdf new file mode 100644 index 0000000..6015ba1 Binary files /dev/null and b/buch/papers/nav/images/position/position2.pdf differ diff --git a/buch/papers/nav/images/position/position2.pov b/buch/papers/nav/images/position/position2.pov new file mode 100644 index 0000000..2abcd94 --- /dev/null +++ b/buch/papers/nav/images/position/position2.pov @@ -0,0 +1,70 @@ +// +// position3.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "common.inc" + +dreieck(A, B, C, kugelfarbe) + +union { + punkt(A, fett) + punkt(B, fett) + punkt(C, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +union { + seite(A, B, fett) + seite(A, C, fett) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +union { + seite(B, C, fett) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, C, fein, gross) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +union { + winkel(B, C, A, fein, gross) + winkel(C, A, B, fein, gross) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + + diff --git a/buch/papers/nav/images/position/position2.tex b/buch/papers/nav/images/position/position2.tex new file mode 100644 index 0000000..339592c --- /dev/null +++ b/buch/papers/nav/images/position/position2.tex @@ -0,0 +1,53 @@ +% +% position2.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{position2.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelB +\labelC + +\labelc +\labela +\labelb + +\begin{scope}[yshift=0.3cm,xshift=0.1cm] +\labelalpha +\end{scope} +\labelbeta +\labelgamma + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position3.pdf b/buch/papers/nav/images/position/position3.pdf new file mode 100644 index 0000000..dea8c28 Binary files /dev/null and b/buch/papers/nav/images/position/position3.pdf differ diff --git a/buch/papers/nav/images/position/position3.pov b/buch/papers/nav/images/position/position3.pov new file mode 100644 index 0000000..f6823eb --- /dev/null +++ b/buch/papers/nav/images/position/position3.pov @@ -0,0 +1,48 @@ +// +// position3.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "common.inc" + +dreieck(B, P, C, kugelfarbe) + +union { + punkt(B, fett) + punkt(C, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +union { + seite(B, C, fett) + seite(B, P, fett) + seite(C, P, fett) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +union { + winkel(B, P, C, fein, gross) + winkel(C, B, P, fein, gross) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/position/position3.tex b/buch/papers/nav/images/position/position3.tex new file mode 100644 index 0000000..d5480da --- /dev/null +++ b/buch/papers/nav/images/position/position3.tex @@ -0,0 +1,51 @@ +% +% dreieck3d1.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{position3.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelB +\labelC +\labelP + +\labela + +\labelhb +\labelhc + +\labelbetaone +\labelgammaone + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position4.pdf b/buch/papers/nav/images/position/position4.pdf new file mode 100644 index 0000000..59cd05c Binary files /dev/null and b/buch/papers/nav/images/position/position4.pdf differ diff --git a/buch/papers/nav/images/position/position4.pov b/buch/papers/nav/images/position/position4.pov new file mode 100644 index 0000000..80628f9 --- /dev/null +++ b/buch/papers/nav/images/position/position4.pov @@ -0,0 +1,69 @@ +// +// position4.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "common.inc" + +dreieck(A, B, P, kugelfarbe) + +union { + punkt(A, fett) + punkt(B, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +union { + seite(A, P, fett) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + + +union { + seite(A, B, fett) + seite(B, P, fett) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(B, P, A, fein, gross) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, B, P, fein, gross) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/position/position4.tex b/buch/papers/nav/images/position/position4.tex new file mode 100644 index 0000000..27c1757 --- /dev/null +++ b/buch/papers/nav/images/position/position4.tex @@ -0,0 +1,50 @@ +% +% position4.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{position4.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelB +\labelP + +\labelc +\labell +\labelhb + +\labelomegalinks +\labelbetatwo + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position5.pdf b/buch/papers/nav/images/position/position5.pdf new file mode 100644 index 0000000..5960392 Binary files /dev/null and b/buch/papers/nav/images/position/position5.pdf differ diff --git a/buch/papers/nav/images/position/position5.pov b/buch/papers/nav/images/position/position5.pov new file mode 100644 index 0000000..7ed33c5 --- /dev/null +++ b/buch/papers/nav/images/position/position5.pov @@ -0,0 +1,69 @@ +// +// position5.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "common.inc" + +dreieck(A, P, C, kugelfarbe) + +union { + punkt(A, fett) + punkt(C, fett) + punkt(P, fett) + pigment { + color dreieckfarbe + } + finish { + specular 0.95 + metallic + } +} + +union { + seite(A, P, fett) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + + +union { + seite(A, C, fett) + seite(C, P, fett) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(C, P, A, fein, gross) + pigment { + color bekannt + } + finish { + specular 0.95 + metallic + } +} + +object { + winkel(A, C, P, fein, gross) + pigment { + color unbekannt + } + finish { + specular 0.95 + metallic + } +} + diff --git a/buch/papers/nav/images/position/position5.tex b/buch/papers/nav/images/position/position5.tex new file mode 100644 index 0000000..b234429 --- /dev/null +++ b/buch/papers/nav/images/position/position5.tex @@ -0,0 +1,50 @@ +% +% position5.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{position5.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelC +\labelP + +\labelb +\labell +\labelhc + +\labelomegarechts +\labelgammatwo + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From d9a3a1717553c1287fdbefbf2bf4a1de03c88851 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 10 Jun 2022 17:17:20 +0200 Subject: neue Bilder --- buch/papers/nav/images/2k_earth_daymap.png | Bin 0 -> 1473323 bytes 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buch/papers/nav/images/position/position1.pdf | Bin 107297 -> 433631 bytes buch/papers/nav/images/position/position2.pdf | Bin 90563 -> 310650 bytes buch/papers/nav/images/position/position3.pdf | Bin 85020 -> 417714 bytes buch/papers/nav/images/position/position4.pdf | Bin 86376 -> 390348 bytes buch/papers/nav/images/position/position5.pdf | Bin 91680 -> 337310 bytes 22 files changed, 377 insertions(+), 4 deletions(-) create mode 100644 buch/papers/nav/images/2k_earth_daymap.png create mode 100644 buch/papers/nav/images/beispiele/2k_earth_daymap.png create mode 100644 buch/papers/nav/images/beispiele/Makefile create mode 100644 buch/papers/nav/images/beispiele/beispiele1.pdf create mode 100644 buch/papers/nav/images/beispiele/beispiele1.pov create mode 100644 buch/papers/nav/images/beispiele/beispiele1.tex create mode 100644 buch/papers/nav/images/beispiele/beispiele2.pdf create mode 100644 buch/papers/nav/images/beispiele/beispiele2.pov create mode 100644 buch/papers/nav/images/beispiele/beispiele2.tex create mode 100644 buch/papers/nav/images/beispiele/common.inc create mode 100644 buch/papers/nav/images/beispiele/common.tex create mode 100644 buch/papers/nav/images/beispiele/geometrie.inc create mode 100644 buch/papers/nav/images/dreieck3d10.pov create mode 100644 buch/papers/nav/images/position/2k_earth_daymap.png diff --git a/buch/papers/nav/images/2k_earth_daymap.png b/buch/papers/nav/images/2k_earth_daymap.png new file mode 100644 index 0000000..4d55da8 Binary files /dev/null and b/buch/papers/nav/images/2k_earth_daymap.png differ diff --git a/buch/papers/nav/images/beispiele/2k_earth_daymap.png b/buch/papers/nav/images/beispiele/2k_earth_daymap.png new file mode 100644 index 0000000..4d55da8 Binary files /dev/null and b/buch/papers/nav/images/beispiele/2k_earth_daymap.png differ diff --git a/buch/papers/nav/images/beispiele/Makefile b/buch/papers/nav/images/beispiele/Makefile new file mode 100644 index 0000000..6e95379 --- /dev/null +++ b/buch/papers/nav/images/beispiele/Makefile @@ -0,0 +1,30 @@ +# +# Makefile to build images +# +# (c) 2022 +# +all: beispiele + +POSITION = \ + beispiele1.pdf \ + beispiele2.pdf + +beispiele: $(POSITION) + +POVRAYOPTIONS = -W1080 -H1080 +#POVRAYOPTIONS = -W480 -H480 + +beispiele1.png: beispiele1.pov common.inc geometrie.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Obeispiele1.png beispiele1.pov +beispiele1.jpg: beispiele1.png + convert beispiele1.png -density 300 -units PixelsPerInch beispiele1.jpg +beispiele1.pdf: beispiele1.tex common.tex beispiele1.jpg + pdflatex beispiele1.tex + +beispiele2.png: beispiele2.pov common.inc geometrie.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Obeispiele2.png beispiele2.pov +beispiele2.jpg: beispiele2.png + convert beispiele2.png -density 300 -units PixelsPerInch beispiele2.jpg +beispiele2.pdf: beispiele2.tex common.tex beispiele2.jpg + pdflatex beispiele2.tex + diff --git a/buch/papers/nav/images/beispiele/beispiele1.pdf b/buch/papers/nav/images/beispiele/beispiele1.pdf new file mode 100644 index 0000000..d0fe3dc Binary files /dev/null and b/buch/papers/nav/images/beispiele/beispiele1.pdf differ diff --git a/buch/papers/nav/images/beispiele/beispiele1.pov b/buch/papers/nav/images/beispiele/beispiele1.pov new file mode 100644 index 0000000..7fb3de2 --- /dev/null +++ b/buch/papers/nav/images/beispiele/beispiele1.pov @@ -0,0 +1,12 @@ +// +// beispiele1.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +#declare Stern1 = Deneb; +#declare Stern2 = Arktur; + +#include "geometrie.inc" + diff --git a/buch/papers/nav/images/beispiele/beispiele1.tex b/buch/papers/nav/images/beispiele/beispiele1.tex new file mode 100644 index 0000000..5666ba6 --- /dev/null +++ b/buch/papers/nav/images/beispiele/beispiele1.tex @@ -0,0 +1,49 @@ +% +% beispiele1.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math,calc} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{beispiele1.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelP +\labelDeneb +\labelArktur +\labelhDeneb +\labelhArktur +\labellone +\labeldDeneb +\labeldArktur + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/beispiele/beispiele2.pdf b/buch/papers/nav/images/beispiele/beispiele2.pdf new file mode 100644 index 0000000..8579ee5 Binary files /dev/null and b/buch/papers/nav/images/beispiele/beispiele2.pdf differ diff --git a/buch/papers/nav/images/beispiele/beispiele2.pov b/buch/papers/nav/images/beispiele/beispiele2.pov new file mode 100644 index 0000000..b69f0f9 --- /dev/null +++ b/buch/papers/nav/images/beispiele/beispiele2.pov @@ -0,0 +1,12 @@ +// +// beispiele1.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +#declare Stern1 = Altair; +#declare Stern2 = Spica; + +#include "geometrie.inc" + diff --git a/buch/papers/nav/images/beispiele/beispiele2.tex b/buch/papers/nav/images/beispiele/beispiele2.tex new file mode 100644 index 0000000..c9b70bd --- /dev/null +++ b/buch/papers/nav/images/beispiele/beispiele2.tex @@ -0,0 +1,50 @@ +% +% beispiele2.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math,calc} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{beispiele2.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelP +\labelAltair +\labelSpica +\labelhAltair +\labelhSpica +\labelltwo +\labeldAltair +\labeldSpica + + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/beispiele/common.inc b/buch/papers/nav/images/beispiele/common.inc new file mode 100644 index 0000000..51fbd1f --- /dev/null +++ b/buch/papers/nav/images/beispiele/common.inc @@ -0,0 +1,50 @@ +// +// common.inc -- 3d Darstellung +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" +#include "../macros.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.034; + +camera { + location <40, 20, -20> + look_at <0, 0.24, -0.20> + right x * imagescale + up y * imagescale +} + +light_source { + <30, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +erde(0) +achse(fein, White) +koordinatennetz(gitterfarbe, 9, 0.001) + +union { + punkt(Sakura, fett) + pigment { + color rot + } + finish { + metallic + specular 0.9 + } +} + diff --git a/buch/papers/nav/images/beispiele/common.tex b/buch/papers/nav/images/beispiele/common.tex new file mode 100644 index 0000000..b7b3dac --- /dev/null +++ b/buch/papers/nav/images/beispiele/common.tex @@ -0,0 +1,79 @@ +% +% common.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% + +\def\labelA{\node at (0.7,3.8) {$A$};} + +\def\labelSpica{ + \node at (-3.6,-2.8) {Spica}; +} +\def\labelAltair{ + \node at (3.0,-2.3) {Altair}; +} +\def\labelArktur{ + \node at (-3.3,-0.7) {Arktur}; +} +\def\labelDeneb{ + \node at (3.4,0.9) {Deneb}; +} + +\def\labelP{\node at (0,-0.2) {$P$};} + +\def\labellone{\node at (0.1,1.9) {$l$};} +\def\labelltwo{\node at (0.1,2.0) {$l$};} + +\def\labelhSpica{ + \coordinate (Spica) at (-1.8,-0.3); + \node at (Spica) {$h_{\text{Spica}}\mathstrut$}; +} +\def\labelhAltair{ + \coordinate (Altair) at (1.1,-1.0); + \node at (Altair) {$h_{\text{Altair}}\mathstrut$}; +} +\def\labelhArktur{ + \coordinate (Arktur) at (-1.3,-0.3); + \node at (Arktur) {$h_{\text{Arktur}}\mathstrut$}; +} +\def\labelhDeneb{ + \coordinate (Deneb) at (1.6,0.45); + \node at (Deneb) {$h_{\text{Deneb}}\mathstrut$}; +} + +\def\labeldSpica{ + \coordinate (dSpica) at (-1.5,2.6); + \fill[color=white,opacity=0.5] + ($(dSpica)+(-1.8,0.08)$) + rectangle + ($(dSpica)+(-0.06,0.55)$); + \node at (dSpica) [above left] + {$90^\circ-\delta_{\text{Spica}}\mathstrut$}; +} +\def\labeldAltair{ + \coordinate (dAltair) at (2.0,2.1); + \fill[color=white,opacity=0.5] + ($(dAltair)+(0.10,0.05)$) + rectangle + ($(dAltair)+(1.8,0.5)$); + \node at (dAltair) [above right] + {$90^\circ-\delta_{\text{Altair}}\mathstrut$}; +} +\def\labeldArktur{ + \coordinate (dArktur) at (-1.2,2.5); + \fill[color=white,opacity=0.5] + ($(dArktur)+(-1.8,0.05)$) + rectangle + ($(dArktur)+(-0.06,0.5)$); + \node at (dArktur) [above left] + {$90^\circ-\delta_{\text{Arktur}}\mathstrut$}; +} +\def\labeldDeneb{ + \coordinate (dDeneb) at (2.0,2.8); + \fill[color=white,opacity=0.5] + ($(dDeneb)+(0.05,0.5)$) + rectangle + ($(dDeneb)+(1.87,0.05)$); + \node at (dDeneb) [above right] + {$90^\circ-\delta_{\text{Deneb}}\mathstrut$}; +} diff --git a/buch/papers/nav/images/beispiele/geometrie.inc b/buch/papers/nav/images/beispiele/geometrie.inc new file mode 100644 index 0000000..2f6084e --- /dev/null +++ b/buch/papers/nav/images/beispiele/geometrie.inc @@ -0,0 +1,41 @@ +union { + punkt(A, fett) + punkt(Stern1, fein) + punkt(Stern2, fein) + seite(Stern1, Stern2, fein) + pigment { + color kugelfarbe + } + finish { + metallic + specular 0.9 + } +} + +union { + seite(A, Stern1, fein) + seite(A, Stern2, fein) + seite(Stern1, Sakura, fein) + seite(Stern2, Sakura, fein) + winkel(A, Stern1, Stern2, 0.5*fein, gross) + pigment { + color bekannt + } + finish { + metallic + specular 0.9 + } +} + +union { + seite(A, Sakura, fein) + winkel(A, Sakura, Stern1, 0.5*fett, klein) + pigment { + color unbekannt + } + finish { + metallic + specular 0.9 + } +} + diff --git a/buch/papers/nav/images/dreieck3d10.pov b/buch/papers/nav/images/dreieck3d10.pov new file mode 100644 index 0000000..2dd7c79 --- /dev/null +++ b/buch/papers/nav/images/dreieck3d10.pov @@ -0,0 +1,46 @@ +// +// dreiecke3d10.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +erde() + +#declare Stern1 = Deneb; +#declare Stern2 = Spica; + +koordinatennetz(gitterfarbe, 9, 0.001) + +union { + seite(A, Stern1, 0.5*fein) + seite(A, Stern2, 0.5*fein) + seite(A, Sakura, 0.5*fein) + seite(Stern1, Sakura, 0.5*fein) + seite(Stern2, Sakura, 0.5*fein) + seite(Stern1, Stern2, 0.5*fein) + + punkt(A, fein) + punkt(Sakura, fett) + punkt(Deneb, fein) + punkt(Spica, fein) + punkt(Altair, fein) + punkt(Arktur, fein) + pigment { + color Red + } +} + +//arrow(<-1.3,0,0>, <1.3,0,0>, fein, White) +arrow(<0,-1.3,0>, <0,1.3,0>, fein, White) +//arrow(<0,0,-1.3>, <0,0,1.3>, fein, White) + +#declare imagescale = 0.044; + +camera { + location <40, 20, -20> + look_at <0, 0.24, -0.20> + right x * imagescale + up y * imagescale +} + diff --git a/buch/papers/nav/images/macros.inc b/buch/papers/nav/images/macros.inc index 2def6fd..20cb2ff 100644 --- a/buch/papers/nav/images/macros.inc +++ b/buch/papers/nav/images/macros.inc @@ -31,6 +31,7 @@ #declare kugeltransparent = rgbt<0.8,0.8,0.8,0.5>; #declare gitterfarbe = rgb<0.2,0.6,1>; +#declare gitterfarbe = rgb<1.0,0.8,0>; // // Points Points @@ -314,7 +315,7 @@ sphere { // // \brief Display the earth // -#macro erde() +#macro erde(winkel) sphere { <0, 0, 0>, 1 pigment { @@ -323,6 +324,7 @@ sphere { map_type 1 } } + rotate <0,winkel,0> } #end diff --git a/buch/papers/nav/images/position/2k_earth_daymap.png b/buch/papers/nav/images/position/2k_earth_daymap.png new file mode 100644 index 0000000..4d55da8 Binary files /dev/null and b/buch/papers/nav/images/position/2k_earth_daymap.png differ diff --git a/buch/papers/nav/images/position/common.inc b/buch/papers/nav/images/position/common.inc index b50b8d6..56e2836 100644 --- a/buch/papers/nav/images/position/common.inc +++ b/buch/papers/nav/images/position/common.inc @@ -33,5 +33,7 @@ sky_sphere { } } -kugel(kugeldunkel) +//kugel(kugeldunkel) +erde(-100) +koordinatennetz(gitterfarbe, 9, 0.001) achse(fein, White) diff --git a/buch/papers/nav/images/position/common.tex b/buch/papers/nav/images/position/common.tex index d72a981..9430608 100644 --- a/buch/papers/nav/images/position/common.tex +++ b/buch/papers/nav/images/position/common.tex @@ -13,8 +13,8 @@ \def\labela{\node at (-0.2,-1.2) {$a$};} \def\labelb{\node at (2.6,1.5) {$b$};} -\def\labelhb{\node at (-2.6,-2.2) {$h_b$};} -\def\labelhc{\node at (1,-2.9) {$h_c$};} +\def\labelhb{\node at (-2.6,-2.2) {$h_B$};} +\def\labelhc{\node at (1,-2.9) {$h_C$};} \def\labell{\node at (-0.7,0.3) {$l$};} \def\labelalpha{\node at (0.6,2.85) {$\alpha$};} diff --git a/buch/papers/nav/images/position/position1.pdf b/buch/papers/nav/images/position/position1.pdf index 1bd9a69..fc4f760 100644 Binary files a/buch/papers/nav/images/position/position1.pdf and b/buch/papers/nav/images/position/position1.pdf differ diff --git a/buch/papers/nav/images/position/position2.pdf b/buch/papers/nav/images/position/position2.pdf index 6015ba1..dbd2ea9 100644 Binary files a/buch/papers/nav/images/position/position2.pdf and b/buch/papers/nav/images/position/position2.pdf differ diff --git a/buch/papers/nav/images/position/position3.pdf b/buch/papers/nav/images/position/position3.pdf index dea8c28..2c940d2 100644 Binary files a/buch/papers/nav/images/position/position3.pdf and b/buch/papers/nav/images/position/position3.pdf differ diff --git a/buch/papers/nav/images/position/position4.pdf b/buch/papers/nav/images/position/position4.pdf index 59cd05c..8eeeaac 100644 Binary files a/buch/papers/nav/images/position/position4.pdf and b/buch/papers/nav/images/position/position4.pdf differ diff --git a/buch/papers/nav/images/position/position5.pdf b/buch/papers/nav/images/position/position5.pdf index 5960392..05a64cb 100644 Binary files a/buch/papers/nav/images/position/position5.pdf and b/buch/papers/nav/images/position/position5.pdf differ -- cgit v1.2.1 From eae6dffd6439f8ea5e5377e0e316b8da7f8df980 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 10 Jun 2022 17:31:19 +0200 Subject: another image --- buch/papers/nav/images/beispiele/Makefile | 10 ++++- buch/papers/nav/images/beispiele/beispiele3.pdf | Bin 0 -> 401946 bytes buch/papers/nav/images/beispiele/beispiele3.pov | 12 ++++++ buch/papers/nav/images/beispiele/beispiele3.tex | 49 ++++++++++++++++++++++++ 4 files changed, 70 insertions(+), 1 deletion(-) create mode 100644 buch/papers/nav/images/beispiele/beispiele3.pdf create mode 100644 buch/papers/nav/images/beispiele/beispiele3.pov create mode 100644 buch/papers/nav/images/beispiele/beispiele3.tex diff --git a/buch/papers/nav/images/beispiele/Makefile b/buch/papers/nav/images/beispiele/Makefile index 6e95379..9546c8e 100644 --- a/buch/papers/nav/images/beispiele/Makefile +++ b/buch/papers/nav/images/beispiele/Makefile @@ -7,7 +7,8 @@ all: beispiele POSITION = \ beispiele1.pdf \ - beispiele2.pdf + beispiele2.pdf \ + beispiele3.pdf beispiele: $(POSITION) @@ -28,3 +29,10 @@ beispiele2.jpg: beispiele2.png beispiele2.pdf: beispiele2.tex common.tex beispiele2.jpg pdflatex beispiele2.tex +beispiele3.png: beispiele3.pov common.inc geometrie.inc ../macros.inc + povray +A0.1 $(POVRAYOPTIONS) -Obeispiele3.png beispiele3.pov +beispiele3.jpg: beispiele3.png + convert beispiele3.png -density 300 -units PixelsPerInch beispiele3.jpg +beispiele3.pdf: beispiele3.tex common.tex beispiele3.jpg + pdflatex beispiele3.tex + diff --git a/buch/papers/nav/images/beispiele/beispiele3.pdf b/buch/papers/nav/images/beispiele/beispiele3.pdf new file mode 100644 index 0000000..a7189dd Binary files /dev/null and b/buch/papers/nav/images/beispiele/beispiele3.pdf differ diff --git a/buch/papers/nav/images/beispiele/beispiele3.pov b/buch/papers/nav/images/beispiele/beispiele3.pov new file mode 100644 index 0000000..af9a468 --- /dev/null +++ b/buch/papers/nav/images/beispiele/beispiele3.pov @@ -0,0 +1,12 @@ +// +// beispiele1.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +#declare Stern1 = Deneb; +#declare Stern2 = Altair; + +#include "geometrie.inc" + diff --git a/buch/papers/nav/images/beispiele/beispiele3.tex b/buch/papers/nav/images/beispiele/beispiele3.tex new file mode 100644 index 0000000..2573199 --- /dev/null +++ b/buch/papers/nav/images/beispiele/beispiele3.tex @@ -0,0 +1,49 @@ +% +% beispiele3.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math,calc} +\usepackage{ifthen} +\begin{document} + +\input{common.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{beispiele3.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelP +\labelDeneb +\labelAltair +\labelhDeneb +\labelhAltair +\labellone +%\labeldDeneb +%\labeldAltair + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From 021751ecb99962fc496b3ea0e5000f94b4e056c6 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Sat, 11 Jun 2022 12:57:40 +0200 Subject: no message --- buch/papers/nav/bsp.tex | 66 ++++++++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 62 insertions(+), 4 deletions(-) diff --git a/buch/papers/nav/bsp.tex b/buch/papers/nav/bsp.tex index 6f30022..ac749c5 100644 --- a/buch/papers/nav/bsp.tex +++ b/buch/papers/nav/bsp.tex @@ -3,9 +3,8 @@ \subsection{Einführung} In diesem Abschnitt wird die Theorie vom Abschnitt 21.6 in einem Praxisbeispiel angewendet. Wir haben die Deklination, Rektaszension, Höhe der beiden Planeten Deneb und Arktur und die Sternzeit von Greenwich als Ausgangslage. -Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden von einem uns unbekannten Ort aus gemessen. -Diesen Punkt gilt es mit dem erlangten Wissen herauszufinden. - +Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden von unserem Dozenten digital in einer Stadt in Japan mit den Koordinaten 35.716672 N, 140.233336 E bestimmt. +Wir werden rechnerisch beweisen, dass wir mit diesen Ergebnissen genau auf diese Koordinaten kommen. \subsection{Vorgehen} \begin{center} @@ -52,7 +51,7 @@ $\delta$ ist die Breite, $\lambda$ die Länge. \subsection{Dreiecke definieren} Das Festlegen der Dreiecke ist essenziell für die korrekten Berechnungen. BILD -\subsection{Dreieck ABC} +\subsection{Dreieck $ABC$} Nun berechnen wir alle Seitenlängen $a$, $b$, $c$ und die Innnenwinkel $\alpha$, $\beta$ und $\gamma$ Wir können $b$ und $c$ mit den geltenten Zusammenhängen des nautischen Dreiecks wie folgt bestimmen: \begin{align} @@ -78,4 +77,63 @@ Für $\beta$ und $\gamma$ nutzen wir den sphärischen Seitenkosinussatz: &= \cos^{-1} \bigg[\frac{\cos(70.936778)-\cos(44.638806) \cdot \cos(80.8707801)}{\sin(80.8707801) \cdot \sin(44.638806)}\bigg] \nonumber \\ &=\underline{\underline{72.0573328^\circ}} \nonumber \end{align} +\subsection{Dreieck $BPC$} +Als nächstes berechnen wir die Seiten $pb$, $pc$ und die Innenwinkel $\beta_1$ und $\gamma_1$. +\begin{align} + pb&=90^\circ - H_{Arktur} \nonumber \\ + &= 90^\circ - 47.42744^\circ \nonumber \\ + &= \underline{\underline{42.572556^\circ}} \nonumber +\end{align} +\begin{align} + pc &= 90^\circ - H_{Deneb} \nonumber \\ + &= 90^\circ - 50.256027^\circ \nonumber \\ + &= \underline{\underline{39.743973^\circ}} \nonumber +\end{align} +\begin{align} + \beta_1 &= \cos^{-1} \bigg[\frac{\cos(pc)-\cos(a) \cdot \cos(pb)}{\sin(a) \cdot \sin(pb)}\bigg] \nonumber \\ + &= \cos^{-1} \bigg[\frac{\cos(39.743973)-\cos(80.8707801) \cdot \cos(42.572556)}{\sin(80.8707801) \cdot \sin(42.572556)}\bigg] \nonumber \\ + &=\underline{\underline{12.5211127^\circ}} \nonumber +\end{align} +\begin{align} + \gamma_1 &= \cos^{-1} \bigg[\frac{\cos(pb)-\cos(a) \cdot \cos(pc)}{\sin(a) \cdot \sin(pc)}\bigg] \nonumber \\ + &= \cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(80.8707801) \cdot \cos(39.743973)}{\sin(80.8707801) \cdot \sin(39.743973)}\bigg] \nonumber \\ + &=\underline{\underline{13.2618475^\circ}} \nonumber +\end{align} + +\subsection{Dreieck $ABP$} +Als erster müssen wir den Winkel $\kappa$ berechnen: +\begin{align} + \kappa &= \beta + \beta_1 = 45.011513^\circ + 12.5211127^\circ \nonumber \\ + &=\underline{\underline{44.6687451^\circ}} \nonumber +\end{align} +Danach können wir mithilfe von $\kappa$, $c$ und $pb$ die Seite $l$ berechnen: +\begin{align} + l &= \cos^{-1}(\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)) \nonumber \\ + &= \cos^{-1}(\cos(70.936778) \cdot \cos(42.572556) + \sin(70.936778) \cdot \sin(42.572556) \cdot \cos(57.5326442)) \nonumber \\ + &= \underline{\underline{54.2833404^\circ}} \nonumber +\end{align} +Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Winkel $\omega$: +\begin{align} + \omega &= \cos^{-1} \bigg[\frac{\cos(pb)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \nonumber \\ + &=\cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(70.936778) \cdot \cos(54.2833404)}{\sin(70.936778) \cdot \sin(54.2833404)}\bigg] \nonumber \\ + &= \underline{\underline{44.6687451^\circ}} \nonumber +\end{align} + +\subsection{Längengrad und Breitengrad bestimmen} + +\begin{align} + \delta &= 90^\circ - l \nonumber \\ + &= 90^\circ - 54.2833404 \nonumber \\ + &= \underline{\underline{35.7166596^\circ}} \nonumber +\end{align} +\begin{align} + \lambda &= \lambda_{Arktur} + \omega \nonumber \\ + &= 95.5647759^\circ + 44.6687451^\circ \nonumber \\ + &= \underline{\underline{140.233521^\circ}} \nonumber +\end{align} +Wie wir sehen, stimmen die berechneten Koordinaten mit den Koordinaten des Punktes, an welchem gemessen wurde überein. +Unsere Methode scheint also zu funktionieren. + + + -- cgit v1.2.1 From 8d317ba95f733584dd51abb331506c9cacedf1ed Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 11 Jun 2022 14:18:48 +0200 Subject: flow --- buch/common/packages.tex | 1 + buch/papers/nav/images/position/Makefile | 25 +++- buch/papers/nav/images/position/common-small.tex | 32 +++++ .../papers/nav/images/position/position1-small.pdf | Bin 0 -> 433626 bytes .../papers/nav/images/position/position1-small.tex | 55 +++++++++ .../papers/nav/images/position/position2-small.pdf | Bin 0 -> 310645 bytes .../papers/nav/images/position/position2-small.tex | 53 ++++++++ .../papers/nav/images/position/position3-small.pdf | Bin 0 -> 417713 bytes .../papers/nav/images/position/position3-small.tex | 51 ++++++++ .../papers/nav/images/position/position4-small.pdf | Bin 0 -> 390331 bytes .../papers/nav/images/position/position4-small.tex | 50 ++++++++ .../papers/nav/images/position/position5-small.pdf | Bin 0 -> 337308 bytes .../papers/nav/images/position/position5-small.tex | 50 ++++++++ buch/papers/nav/images/position/test.tex | 135 +++++++++++++++++++++ 14 files changed, 447 insertions(+), 5 deletions(-) create mode 100644 buch/papers/nav/images/position/common-small.tex create mode 100644 buch/papers/nav/images/position/position1-small.pdf create mode 100644 buch/papers/nav/images/position/position1-small.tex create mode 100644 buch/papers/nav/images/position/position2-small.pdf create mode 100644 buch/papers/nav/images/position/position2-small.tex create mode 100644 buch/papers/nav/images/position/position3-small.pdf create mode 100644 buch/papers/nav/images/position/position3-small.tex create mode 100644 buch/papers/nav/images/position/position4-small.pdf create mode 100644 buch/papers/nav/images/position/position4-small.tex create mode 100644 buch/papers/nav/images/position/position5-small.pdf create mode 100644 buch/papers/nav/images/position/position5-small.tex create mode 100644 buch/papers/nav/images/position/test.tex diff --git a/buch/common/packages.tex b/buch/common/packages.tex index 2ab2ad8..eef17c1 100644 --- a/buch/common/packages.tex +++ b/buch/common/packages.tex @@ -43,6 +43,7 @@ \usepackage{wasysym} \usepackage{environ} \usepackage{appendix} +\usepackage{wrapfig} \usepackage{placeins} \usepackage[all]{xy} \usetikzlibrary{calc,intersections,through,backgrounds,graphs,positioning,shapes,arrows,fit,math} diff --git a/buch/papers/nav/images/position/Makefile b/buch/papers/nav/images/position/Makefile index 280e59c..eed2e56 100644 --- a/buch/papers/nav/images/position/Makefile +++ b/buch/papers/nav/images/position/Makefile @@ -6,11 +6,11 @@ all: position POSITION = \ - position1.pdf \ - position2.pdf \ - position3.pdf \ - position4.pdf \ - position5.pdf + position1.pdf position1-small.pdf \ + position2.pdf position2-small.pdf \ + position3.pdf position3-small.pdf \ + position4.pdf position4-small.pdf \ + position5.pdf position5-small.pdf position: $(POSITION) @@ -52,3 +52,18 @@ position5.jpg: position5.png position5.pdf: position5.tex common.tex position5.jpg pdflatex position5.tex +position1-small.pdf: position1-small.tex common.tex position1.jpg + pdflatex position1-small.tex +position2-small.pdf: position2-small.tex common.tex position2.jpg + pdflatex position2-small.tex +position3-small.pdf: position3-small.tex common.tex position3.jpg + pdflatex position3-small.tex +position4-small.pdf: position4-small.tex common.tex position4.jpg + pdflatex position4-small.tex +position5-small.pdf: position5-small.tex common.tex position5.jpg + pdflatex position5-small.tex + +test: test.pdf + +test.pdf: test.tex $(POSITION) + pdflatex test.tex diff --git a/buch/papers/nav/images/position/common-small.tex b/buch/papers/nav/images/position/common-small.tex new file mode 100644 index 0000000..9430608 --- /dev/null +++ b/buch/papers/nav/images/position/common-small.tex @@ -0,0 +1,32 @@ +% +% common.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% + +\def\labelA{\node at (0.7,3.8) {$A$};} +\def\labelB{\node at (-3.4,-0.8) {$B$};} +\def\labelC{\node at (3.3,-2.1) {$C$};} +\def\labelP{\node at (-1.4,-3.5) {$P$};} + +\def\labelc{\node at (-1.9,2.1) {$c$};} +\def\labela{\node at (-0.2,-1.2) {$a$};} +\def\labelb{\node at (2.6,1.5) {$b$};} + +\def\labelhb{\node at (-2.6,-2.2) {$h_B$};} +\def\labelhc{\node at (1,-2.9) {$h_C$};} +\def\labell{\node at (-0.7,0.3) {$l$};} + +\def\labelalpha{\node at (0.6,2.85) {$\alpha$};} +\def\labelbeta{\node at (-2.5,-0.5) {$\beta$};} +\def\labelgamma{\node at (2.3,-1.2) {$\gamma$};} +\def\labelomega{\node at (0.85,3.3) {$\omega$};} + +\def\labelgammaone{\node at (2.1,-2.0) {$\gamma_1$};} +\def\labelgammatwo{\node at (2.3,-1.3) {$\gamma_2$};} +\def\labelbetaone{\node at (-2.4,-1.4) {$\beta_1$};} +\def\labelbetatwo{\node at (-2.5,-0.8) {$\beta_2$};} + +\def\labelomegalinks{\node at (0.25,3.25) {$\omega$};} +\def\labelomegarechts{\node at (0.85,3.1) {$\omega$};} + diff --git a/buch/papers/nav/images/position/position1-small.pdf b/buch/papers/nav/images/position/position1-small.pdf new file mode 100644 index 0000000..ba7755f Binary files /dev/null and b/buch/papers/nav/images/position/position1-small.pdf differ diff --git a/buch/papers/nav/images/position/position1-small.tex b/buch/papers/nav/images/position/position1-small.tex new file mode 100644 index 0000000..05fad44 --- /dev/null +++ b/buch/papers/nav/images/position/position1-small.tex @@ -0,0 +1,55 @@ +% +% position1-small.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common-small.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick,scale=0.625] + +% Povray Bild +\node at (0,0) {\includegraphics[width=5cm]{position1.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelB +\labelC +\labelP + +\labelc +\labela +\labelb +\labell + +\labelhb +\labelhc + +\labelalpha +\labelomega + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position2-small.pdf b/buch/papers/nav/images/position/position2-small.pdf new file mode 100644 index 0000000..3333dd4 Binary files /dev/null and b/buch/papers/nav/images/position/position2-small.pdf differ diff --git a/buch/papers/nav/images/position/position2-small.tex b/buch/papers/nav/images/position/position2-small.tex new file mode 100644 index 0000000..e5c33cf --- /dev/null +++ b/buch/papers/nav/images/position/position2-small.tex @@ -0,0 +1,53 @@ +% +% position2-small.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common-small.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick,scale=0.625] + +% Povray Bild +\node at (0,0) {\includegraphics[width=5cm]{position2.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelB +\labelC + +\labelc +\labela +\labelb + +\begin{scope}[yshift=0.3cm,xshift=0.1cm] +\labelalpha +\end{scope} +\labelbeta +\labelgamma + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position3-small.pdf b/buch/papers/nav/images/position/position3-small.pdf new file mode 100644 index 0000000..fae0b85 Binary files /dev/null and b/buch/papers/nav/images/position/position3-small.pdf differ diff --git a/buch/papers/nav/images/position/position3-small.tex b/buch/papers/nav/images/position/position3-small.tex new file mode 100644 index 0000000..4f7b0e9 --- /dev/null +++ b/buch/papers/nav/images/position/position3-small.tex @@ -0,0 +1,51 @@ +% +% position3-small.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common-small.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick,scale=0.625] + +% Povray Bild +\node at (0,0) {\includegraphics[width=5cm]{position3.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelB +\labelC +\labelP + +\labela + +\labelhb +\labelhc + +\labelbetaone +\labelgammaone + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position4-small.pdf b/buch/papers/nav/images/position/position4-small.pdf new file mode 100644 index 0000000..ac80c46 Binary files /dev/null and b/buch/papers/nav/images/position/position4-small.pdf differ diff --git a/buch/papers/nav/images/position/position4-small.tex b/buch/papers/nav/images/position/position4-small.tex new file mode 100644 index 0000000..e06523b --- /dev/null +++ b/buch/papers/nav/images/position/position4-small.tex @@ -0,0 +1,50 @@ +% +% position4-small.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common-small.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick,scale=0.625] + +% Povray Bild +\node at (0,0) {\includegraphics[width=5cm]{position4.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelB +\labelP + +\labelc +\labell +\labelhb + +\labelomegalinks +\labelbetatwo + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/position5-small.pdf b/buch/papers/nav/images/position/position5-small.pdf new file mode 100644 index 0000000..afe120e Binary files /dev/null and b/buch/papers/nav/images/position/position5-small.pdf differ diff --git a/buch/papers/nav/images/position/position5-small.tex b/buch/papers/nav/images/position/position5-small.tex new file mode 100644 index 0000000..0a0e229 --- /dev/null +++ b/buch/papers/nav/images/position/position5-small.tex @@ -0,0 +1,50 @@ +% +% position5-small.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\input{common-small.tex} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick,scale=0.625] + +% Povray Bild +\node at (0,0) {\includegraphics[width=5cm]{position5.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\labelA +\labelC +\labelP + +\labelb +\labell +\labelhc + +\labelomegarechts +\labelgammatwo + +\end{tikzpicture} + +\end{document} + diff --git a/buch/papers/nav/images/position/test.tex b/buch/papers/nav/images/position/test.tex new file mode 100644 index 0000000..8f4b341 --- /dev/null +++ b/buch/papers/nav/images/position/test.tex @@ -0,0 +1,135 @@ +% +% test.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[12pt]{article} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{etex} +\usepackage[ngerman]{babel} +\usepackage{times} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{graphicx} +\usepackage{wrapfig} +\begin{document} + +\begin{wrapfigure}{R}{5.2cm} +\includegraphics{position1-small.pdf} +\end{wrapfigure} +Lorem ipsum dolor sit amet, consectetuer adipiscing elit. +Aenean +commodo ligula eget dolor. +Aenean massa. +Cum sociis natoque penatibus +et magnis dis parturient montes, nascetur ridiculus mus. +Donec quam +felis, ultricies nec, pellentesque eu, pretium quis, sem. +Nulla +consequat massa quis enim. +Donec pede justo, fringilla vel, aliquet +nec, vulputate eget, arcu. +In enim justo, rhoncus ut, imperdiet a, +venenatis vitae, justo. +Nullam dictum felis eu pede mollis pretium. +Integer tincidunt. +Cras dapibus. +Vivamus elementum semper nisi. +Aenean vulputate eleifend tellus. +Aenean leo ligula, porttitor eu, +consequat vitae, eleifend ac, enim. +Aliquam lorem ante, dapibus in, +viverra quis, feugiat a, tellus. + +\begin{wrapfigure}{R}{5.2cm} +\includegraphics{position2-small.pdf} +\end{wrapfigure} +Maecenas tempus, tellus eget condimentum rhoncus, sem quam semper +libero, sit amet adipiscing sem neque sed ipsum. Nam quam nunc, +blandit vel, luctus pulvinar, hendrerit id, lorem. Maecenas nec +odio et ante tincidunt tempus. Donec vitae sapien ut libero venenatis +faucibus. Nullam quis ante. Etiam sit amet orci eget eros faucibus +tincidunt. Duis leo. Sed fringilla mauris sit amet nibh. Donec +sodales sagittis magna. Sed consequat, leo eget bibendum sodales, +augue velit cursus nunc, quis gravida magna mi a libero. Fusce +vulputate eleifend sapien. Vestibulum purus quam, scelerisque ut, +mollis sed, nonummy id, metus. Nullam accumsan lorem in dui. Cras +ultricies mi eu turpis hendrerit fringilla. Vestibulum ante ipsum +primis in faucibus orci luctus et ultrices posuere cubilia Curae; + +\pagebreak + +\begin{wrapfigure}{R}{5.2cm} +\includegraphics{position3-small.pdf} +\end{wrapfigure} +Integer ante arcu, accumsan a, consectetuer eget, posuere ut, mauris. +Praesent adipiscing. Phasellus ullamcorper ipsum rutrum nunc. Nunc +nonummy metus. Vestibulum volutpat pretium libero. Cras id dui. +Aenean ut eros et nisl sagittis vestibulum. Nullam nulla eros, +ultricies sit amet, nonummy id, imperdiet feugiat, pede. Sed lectus. +Donec mollis hendrerit risus. Phasellus nec sem in justo pellentesque +facilisis. Etiam imperdiet imperdiet orci. Nunc nec neque. Phasellus +leo dolor, tempus non, auctor et, hendrerit quis, nisi. Curabitur +ligula sapien, tincidunt non, euismod vitae, posuere imperdiet, +leo. Maecenas malesuada. Praesent congue erat at massa. Sed cursus +turpis vitae tortor. Donec posuere vulputate arcu. Phasellus accumsan +cursus velit. Vestibulum ante ipsum primis in faucibus orci luctus +et ultrices posuere cubilia Curae; Sed aliquam, nisi quis porttitor +congue, elit erat euismod orci, ac placerat dolor lectus quis orci. +Phasellus consectetuer vestibulum elit. + +\begin{wrapfigure}{R}{5.2cm} +\includegraphics{position4-small.pdf} +\end{wrapfigure} +Aenean tellus metus, bibendum sed, posuere ac, mattis non, nunc. +Vestibulum fringilla pede sit amet augue. In turpis. Pellentesque +posuere. Praesent turpis. Aenean posuere, tortor sed cursus feugiat, +nunc augue blandit nunc, eu sollicitudin urna dolor sagittis lacus. +Donec elit libero, sodales nec, volutpat a, suscipit non, turpis. +Nullam sagittis. Suspendisse pulvinar, augue ac venenatis condimentum, +sem libero volutpat nibh, nec pellentesque velit pede quis nunc. +Vestibulum ante ipsum primis in faucibus orci luctus et ultrices +posuere cubilia Curae; Fusce id purus. Ut varius tincidunt libero. +Phasellus dolor. Maecenas vestibulum mollis diam. Pellentesque ut +neque. Pellentesque habitant morbi tristique senectus et netus et +malesuada fames ac turpis egestas. In dui magna, posuere eget, +vestibulum et, tempor auctor, justo. In ac felis quis tortor malesuada +pretium. Pellentesque auctor neque nec urna. + +\pagebreak + +\begin{wrapfigure}{R}{5.2cm} +\includegraphics{position5-small.pdf} +\end{wrapfigure} +Proin sapien ipsum, porta a, auctor quis, euismod ut, mi. Aenean +viverra rhoncus pede. Pellentesque habitant morbi tristique senectus +et netus et malesuada fames ac turpis egestas. Ut non enim eleifend +felis pretium feugiat. Vivamus quis mi. Phasellus a est. Phasellus +magna. In hac habitasse platea dictumst. Curabitur at lacus ac velit +ornare lobortis. Curabitur a felis in nunc fringilla tristique. +Morbi mattis ullamcorper velit. Phasellus gravida semper nisi. +Nullam vel sem. Pellentesque libero tortor, tincidunt et, tincidunt +eget, semper nec, quam. Sed hendrerit. Morbi ac felis. Nunc egestas, +augue at pellentesque laoreet, felis eros vehicula leo, at malesuada +velit leo quis pede. Donec interdum, metus et hendrerit aliquet, +dolor diam sagittis ligula, eget egestas libero turpis vel mi. Nunc +nulla. Fusce risus nisl, viverra et, tempor et, pretium in, sapien. +Donec venenatis vulputate lorem. Morbi nec metus. Phasellus blandit +leo ut odio. Maecenas ullamcorper, dui et placerat feugiat, eros +pede varius nisi, condimentum viverra felis nunc et lorem. Sed magna +purus, fermentum eu, tincidunt eu, varius ut, felis. In auctor +lobortis lacus. Quisque libero metus, condimentum nec, tempor a, +commodo mollis, magna. Vestibulum ullamcorper mauris at ligula. +Fusce fermentum. Nullam cursus lacinia erat. Praesent blandit laoreet +nibh. Fusce convallis metus id felis luctus adipiscing. Pellentesque +egestas, neque sit amet convallis pulvinar, justo nulla eleifend +augue, ac auctor orci leo non est. Quisque id mi. Ut tincidunt +tincidunt erat. Etiam feugiat lorem non metus. Vestibulum dapibus +nunc ac augue. Curabitur vestibulum aliquam leo. Praesent egestas +neque eu enim. In hac habitasse platea dictumst. Fusce a quam. Etiam +ut purus mattis mauris + +\end{document} -- cgit v1.2.1 From fee7a11b5b0309e89aae17485c24fe250c55d548 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Sun, 12 Jun 2022 18:31:01 +0200 Subject: Abgabe --- buch/papers/nav/bilder/beispiele1.pdf | Bin 0 -> 399907 bytes buch/papers/nav/bilder/beispiele2.pdf | Bin 0 -> 404679 bytes buch/papers/nav/bilder/position1.pdf | Bin 0 -> 433626 bytes buch/papers/nav/bilder/position2.pdf | Bin 0 -> 310645 bytes buch/papers/nav/bilder/position3.pdf | Bin 0 -> 417713 bytes buch/papers/nav/bilder/position4.pdf | Bin 0 -> 390331 bytes buch/papers/nav/bilder/position5.pdf | Bin 0 -> 337308 bytes buch/papers/nav/bsp.tex | 70 ++++++++++++++++++++++++------- buch/papers/nav/images/position/test.tex | 2 +- buch/papers/nav/nautischesdreieck.tex | 13 ++---- buch/papers/nav/packages.tex | 2 +- 11 files changed, 62 insertions(+), 25 deletions(-) create mode 100644 buch/papers/nav/bilder/beispiele1.pdf create mode 100644 buch/papers/nav/bilder/beispiele2.pdf create mode 100644 buch/papers/nav/bilder/position1.pdf create mode 100644 buch/papers/nav/bilder/position2.pdf create mode 100644 buch/papers/nav/bilder/position3.pdf create mode 100644 buch/papers/nav/bilder/position4.pdf create mode 100644 buch/papers/nav/bilder/position5.pdf diff --git a/buch/papers/nav/bilder/beispiele1.pdf b/buch/papers/nav/bilder/beispiele1.pdf new file mode 100644 index 0000000..d0fe3dc Binary files /dev/null and b/buch/papers/nav/bilder/beispiele1.pdf differ diff --git a/buch/papers/nav/bilder/beispiele2.pdf b/buch/papers/nav/bilder/beispiele2.pdf new file mode 100644 index 0000000..8579ee5 Binary files /dev/null and b/buch/papers/nav/bilder/beispiele2.pdf differ diff --git a/buch/papers/nav/bilder/position1.pdf b/buch/papers/nav/bilder/position1.pdf new file mode 100644 index 0000000..ba7755f Binary files /dev/null and b/buch/papers/nav/bilder/position1.pdf differ diff --git a/buch/papers/nav/bilder/position2.pdf b/buch/papers/nav/bilder/position2.pdf new file mode 100644 index 0000000..3333dd4 Binary files /dev/null and b/buch/papers/nav/bilder/position2.pdf differ diff --git a/buch/papers/nav/bilder/position3.pdf b/buch/papers/nav/bilder/position3.pdf new file mode 100644 index 0000000..fae0b85 Binary files /dev/null and b/buch/papers/nav/bilder/position3.pdf differ diff --git a/buch/papers/nav/bilder/position4.pdf b/buch/papers/nav/bilder/position4.pdf new file mode 100644 index 0000000..ac80c46 Binary files /dev/null and b/buch/papers/nav/bilder/position4.pdf differ diff --git a/buch/papers/nav/bilder/position5.pdf b/buch/papers/nav/bilder/position5.pdf new file mode 100644 index 0000000..afe120e Binary files /dev/null and b/buch/papers/nav/bilder/position5.pdf differ diff --git a/buch/papers/nav/bsp.tex b/buch/papers/nav/bsp.tex index ac749c5..d544588 100644 --- a/buch/papers/nav/bsp.tex +++ b/buch/papers/nav/bsp.tex @@ -20,6 +20,10 @@ Wir werden rechnerisch beweisen, dass wir mit diesen Ergebnissen genau auf diese \end{center} \subsection{Ausgangslage} +\begin{wrapfigure}{R}{5.6cm} + \includegraphics{papers/nav/bilder/position1.pdf} + \caption{Ausgangslage} +\end{wrapfigure} Die Rektaszension und die Sternzeit sind in der Regeln in Stunden angegeben. Für die Umrechnung in Grad kann folgender Zusammenhang verwendet werden: \[ Stunden \cdot 15 = Grad\]. @@ -30,11 +34,11 @@ Dies wurde hier bereits gemacht. Deneb&\\ & Rektaszension $RA_{Deneb}$& $310.55058^\circ$ \\ & Deklination $DEC_{Deneb}$& $45.361194^\circ$ \\ - & Höhe $H_{Deneb}$ & $50.256027^\circ$ \\ + & Höhe $h_c$ & $50.256027^\circ$ \\ Arktur &\\ & Rektaszension $RA_{Arktur}$& $214.17558^\circ$ \\ & Deklination $DEC_{Arktur}$& $19.063222^\circ$ \\ - & Höhe $H_{Arktur}$ & $47.427444^\circ$ \\ + & Höhe $h_b$ & $47.427444^\circ$ \\ \end{tabular} \end{center} \subsection{Koordinaten der Bildpunkte} @@ -49,9 +53,25 @@ $\delta$ ist die Breite, $\lambda$ die Länge. \subsection{Dreiecke definieren} +\begin{figure} + \begin{center} + \includegraphics[width=6cm]{papers/nav/bilder/beispiele1.pdf} + \includegraphics[width=6cm]{papers/nav/bilder/beispiele2.pdf} + \caption{Arktur-Deneb; Spica-Altiar} +\end{center} +\end{figure} Das Festlegen der Dreiecke ist essenziell für die korrekten Berechnungen. -BILD +Ein Problem, welches in der Theorie nicht berücksichtigt wurde ist, dass der Punkt $P$ nicht zwingend unterhalb der Seite $a$ sein muss. +Wenn man das nicht berücksichtigt, erhält man falsche oder keine Ergebnisse. +In der Realität weiss man jedoch ungefähr auf welchem Breitengrad man ist, so kann man relativ einfach entscheiden, ob der eigene Standort über $a$ ist oder nicht. +Beim unserem genutzten Paar Arktur-Deneb ist dies kein Problem, da der Punkt unterhalb der Seite $a$ liegt. +Würde man aber das Paar Altair-Spica nehmen, liegt $P$ über $a$ (vgl. Abbildung 21.11) und man müsste trigonometrisch anders vorgehen. + \subsection{Dreieck $ABC$} +\begin{wrapfigure}{R}{5.6cm} + \includegraphics{papers/nav/bilder/position2.pdf} + \caption{Dreieck ABC} +\end{wrapfigure} Nun berechnen wir alle Seitenlängen $a$, $b$, $c$ und die Innnenwinkel $\alpha$, $\beta$ und $\gamma$ Wir können $b$ und $c$ mit den geltenten Zusammenhängen des nautischen Dreiecks wie folgt bestimmen: \begin{align} @@ -78,43 +98,51 @@ Für $\beta$ und $\gamma$ nutzen wir den sphärischen Seitenkosinussatz: &=\underline{\underline{72.0573328^\circ}} \nonumber \end{align} \subsection{Dreieck $BPC$} -Als nächstes berechnen wir die Seiten $pb$, $pc$ und die Innenwinkel $\beta_1$ und $\gamma_1$. +\begin{wrapfigure}{R}{5.6cm} + \includegraphics{papers/nav/bilder/position3.pdf} + \caption{Dreieck BPC} +\end{wrapfigure} +Als nächstes berechnen wir die Seiten $h_b$, $h_c$ und die Innenwinkel $\beta_1$ und $\gamma_1$. \begin{align} - pb&=90^\circ - H_{Arktur} \nonumber \\ + h_b&=90^\circ - h_b \nonumber \\ &= 90^\circ - 47.42744^\circ \nonumber \\ &= \underline{\underline{42.572556^\circ}} \nonumber \end{align} \begin{align} - pc &= 90^\circ - H_{Deneb} \nonumber \\ + h_c &= 90^\circ - h_c \nonumber \\ &= 90^\circ - 50.256027^\circ \nonumber \\ &= \underline{\underline{39.743973^\circ}} \nonumber \end{align} \begin{align} - \beta_1 &= \cos^{-1} \bigg[\frac{\cos(pc)-\cos(a) \cdot \cos(pb)}{\sin(a) \cdot \sin(pb)}\bigg] \nonumber \\ + \beta_1 &= \cos^{-1} \bigg[\frac{\cos(h_c)-\cos(a) \cdot \cos(h_b)}{\sin(a) \cdot \sin(h_b)}\bigg] \nonumber \\ &= \cos^{-1} \bigg[\frac{\cos(39.743973)-\cos(80.8707801) \cdot \cos(42.572556)}{\sin(80.8707801) \cdot \sin(42.572556)}\bigg] \nonumber \\ &=\underline{\underline{12.5211127^\circ}} \nonumber \end{align} \begin{align} - \gamma_1 &= \cos^{-1} \bigg[\frac{\cos(pb)-\cos(a) \cdot \cos(pc)}{\sin(a) \cdot \sin(pc)}\bigg] \nonumber \\ + \gamma_1 &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(a) \cdot \cos(h_c)}{\sin(a) \cdot \sin(h_c)}\bigg] \nonumber \\ &= \cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(80.8707801) \cdot \cos(39.743973)}{\sin(80.8707801) \cdot \sin(39.743973)}\bigg] \nonumber \\ &=\underline{\underline{13.2618475^\circ}} \nonumber \end{align} \subsection{Dreieck $ABP$} -Als erster müssen wir den Winkel $\kappa$ berechnen: +\begin{wrapfigure}{R}{5.6cm} + \includegraphics{papers/nav/bilder/position4.pdf} + \caption{Dreieck ABP} +\end{wrapfigure} +Als erster müssen wir den Winkel $\beta_2$ berechnen: \begin{align} - \kappa &= \beta + \beta_1 = 45.011513^\circ + 12.5211127^\circ \nonumber \\ + \beta_2 &= \beta + \beta_1 = 45.011513^\circ + 12.5211127^\circ \nonumber \\ &=\underline{\underline{44.6687451^\circ}} \nonumber \end{align} -Danach können wir mithilfe von $\kappa$, $c$ und $pb$ die Seite $l$ berechnen: +Danach können wir mithilfe von $\beta_2$, $c$ und $h_b$ die Seite $l$ berechnen: \begin{align} - l &= \cos^{-1}(\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)) \nonumber \\ + l &= \cos^{-1}(\cos(c) \cdot \cos(h_b) + \sin(c) \cdot \sin(h_b) \cdot \cos(\beta_2)) \nonumber \\ &= \cos^{-1}(\cos(70.936778) \cdot \cos(42.572556) + \sin(70.936778) \cdot \sin(42.572556) \cdot \cos(57.5326442)) \nonumber \\ &= \underline{\underline{54.2833404^\circ}} \nonumber \end{align} Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Winkel $\omega$: \begin{align} - \omega &= \cos^{-1} \bigg[\frac{\cos(pb)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \nonumber \\ + \omega &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \nonumber \\ &=\cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(70.936778) \cdot \cos(54.2833404)}{\sin(70.936778) \cdot \sin(54.2833404)}\bigg] \nonumber \\ &= \underline{\underline{44.6687451^\circ}} \nonumber \end{align} @@ -132,7 +160,21 @@ Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Wink &= \underline{\underline{140.233521^\circ}} \nonumber \end{align} Wie wir sehen, stimmen die berechneten Koordinaten mit den Koordinaten des Punktes, an welchem gemessen wurde überein. -Unsere Methode scheint also zu funktionieren. + +\subsection{Fazit} +Die theoretische Anleitung im Abschnitt 21.6 scheint grundsätzlich zu funktionieren. +Allerdings gab es zwei interessante Probleme. + +Einerseits das Problem, ob der Punkt P sich oberhalb oder unterhalb von $a$ befindet. +Da wir eigentlich wussten, wo der gesuchte Punkt P ist, konnten wir das Dreieck anhand der Koordinaten der Bildpunkte richtig aufstellen. +In der Praxis muss man aber schon wissen, auf welchem Breitengrad man ungefähr ist. +Dies weis man in der Regeln aber, da die eigene Breite die Höhe des Polarsterns ist. +Diese Höhe wird mit dem Sextant gemessen. + +Andererseits ist da noch ein Problem mit dem Sinussatz. +Beim Sinussatz gibt es immer zwei Lösungen, weil \[ \sin(\pi-a)=\sin(a).\] +Da kann es sein (und war in unserem Fall auch so), dass man das falsche Ergebnis erwischt. +Durch diese Erkenntnis haben wir nur Kosinussätze verwendet und dies ebenfalls im Abschnitt 21.6 abgeändert, da es für den Leser auch relevant sein kann, wenn er es Probieren möchte. diff --git a/buch/papers/nav/images/position/test.tex b/buch/papers/nav/images/position/test.tex index 8f4b341..3247ed1 100644 --- a/buch/papers/nav/images/position/test.tex +++ b/buch/papers/nav/images/position/test.tex @@ -17,7 +17,7 @@ \usepackage{wrapfig} \begin{document} -\begin{wrapfigure}{R}{5.2cm} +\begin{wrapfigure}{R}{5.6cm} \includegraphics{position1-small.pdf} \end{wrapfigure} Lorem ipsum dolor sit amet, consectetuer adipiscing elit. diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index d8a14af..44153bd 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -97,7 +97,6 @@ Mithilfe dieser Dreiecken können wir die einfachen Sätze der sphärischen Trig \end{center} \end{figure} - \subsubsection{Dreieck $ABC$} \begin{center} @@ -140,12 +139,9 @@ können wir nun die dritte Seitenlänge bestimmen. Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. Jetzt fehlen noch die beiden anderen Innenwinkel $\beta$ und\ $\gamma$. -Diese bestimmen wir mithilfe des Sinussatzes \[\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}.\] -Hier muss man aufpassen, dass man Seite von Winkel unterscheiden kann. -Im Zähler sind die Seiten, im Nenner die Winkel. -Somit ist \[\beta =\sin^{-1} [\sin(b) \cdot \frac{\sin(\alpha)}{\sin(a)}].\] +Diese bestimmen wir mithilfe des Kosinussatzes: \[\beta=\cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg]\] und \[\gamma = \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}.\bigg]\] -Schlussendlich haben wir die Seiten $a,b\ und \ c$, die Ecken A,B und C und die Winkel $\alpha$, $\beta$ und $\gamma$ bestimmt und somit das ganze Kugeldreieck $ABC$ berechnet. +Schlussendlich haben wir die Seiten $a$ $b$ und $c$, die Ecken A,B und C und die Winkel $\alpha$, $\beta$ und $\gamma$ bestimmt und somit das ganze Kugeldreieck $ABC$ berechnet. \subsubsection{Dreieck $BPC$} Wir bilden nun ein zweites Dreieck, welches die Ecken $B$ und $C$ des ersten Dreiecks besitzt. @@ -167,8 +163,7 @@ und \delta =\cos^{-1} [\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)]. \] -Für die Geographische Länge $\lambda$ des eigenen Standortes muss man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet. -Mithilfe des Sinussatzes \[\frac{\sin (a)}{\sin (\alpha)} =\frac{\sin (b)}{\sin (\beta)} = \frac{\sin (c)}{\sin (\gamma)}\] können wir das bestimmen. -Somit ist \[ \omega=\sin^{-1}[\sin(pc) \cdot \frac{\sin(\gamma)}{\sin(l)}] \]und unsere gesuchte geographische Länge schlussendlich +Für die Geographische Länge $\lambda$ des eigenen Standortes nutzt man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet. +Mithilfe des Kosinussatzes können wir \[\omega = \cos^{-1} \bigg[\frac{\cos(pb)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}.\bigg]\] berechnen und schlussentlich dann \[\lambda=\lambda_1 - \omega\] wobei $\lambda_1$ die Länge des Bildpunktes $X$ von $C$ ist. diff --git a/buch/papers/nav/packages.tex b/buch/papers/nav/packages.tex index f2e6132..bedaccd 100644 --- a/buch/papers/nav/packages.tex +++ b/buch/papers/nav/packages.tex @@ -9,4 +9,4 @@ %\usepackage{packagename} \usepackage{amsmath} -\usepackage{cancel} \ No newline at end of file +\usepackage{cancel} -- cgit v1.2.1 From 9fb1f740b7d00b350a008e957d28ecf7daf53797 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 14 Jun 2022 16:24:13 +0200 Subject: new image --- buch/chapters/110-elliptisch/images/Makefile | 11 ++ buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 0 -> 139626 bytes buch/chapters/110-elliptisch/images/kegelpara.pov | 225 ++++++++++++++++++++++ buch/chapters/110-elliptisch/images/kegelpara.tex | 41 ++++ 4 files changed, 277 insertions(+) create mode 100644 buch/chapters/110-elliptisch/images/kegelpara.pdf create mode 100644 buch/chapters/110-elliptisch/images/kegelpara.pov create mode 100644 buch/chapters/110-elliptisch/images/kegelpara.tex diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index a7c9e74..7e4fa0c 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -78,3 +78,14 @@ slcldata.tex: slcl ./slcl --outfile=slcldata.tex --a=0 --b=13.4 --steps=200 slcl.pdf: slcl.tex slcldata.tex pdflatex slcl.tex + +POVRAYOPTIONS = -W1920 -H1080 +kegelpara.png: kegelpara.pov + povray +A0.1 -W1080 -H1080 -Okegelpara.png kegelpara.pov + +kegelpara.jpg: kegelpara.png Makefile + convert -extract 1080x1000+0+40 kegelpara.png \ + -density 300 -units PixelsPerInch kegelpara.jpg + +kegelpara.pdf: kegelpara.tex kegelpara.jpg + pdflatex kegelpara.tex diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf new file mode 100644 index 0000000..4b03119 Binary files /dev/null and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pov b/buch/chapters/110-elliptisch/images/kegelpara.pov new file mode 100644 index 0000000..5d85eed --- /dev/null +++ b/buch/chapters/110-elliptisch/images/kegelpara.pov @@ -0,0 +1,225 @@ +// +// kegelpara.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +#declare O = <0,0,0>; + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.08; + +camera { + location <28, 20, -40> + look_at <0, 0.1, 0> + right x * imagescale + up y * imagescale +} + +light_source { + <30, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + + +// +// draw an arrow from to with thickness with +// color +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +arrow(<-2,0,0>,<2,0,0>,0.02,White) +arrow(<0,-2,0>,<0,2,0>,0.02,White) +arrow(<0,0,-2>,<0,0,2>,0.02,White) + +#declare epsilon = 0.001; +#declare l = 1.5; + +#macro Kegel(farbe) +union { + difference { + cone { O, 0, , l } + cone { O + , 0, , l } + } + difference { + cone { O, 0, <-l, 0, 0>, l } + cone { O + <-epsilon, 0, 0>, 0, <-l-epsilon, 0, 0>, l } + } + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro F(w, r) + +#end + +#macro Paraboloid(farbe) +mesh { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 100; + #declare phistep = pi / phisteps; + #declare rsteps = 100; + #declare rmax = 1.5; + #declare rstep = rmax / rsteps; + #while (phi < phimax - phistep/2) + #declare r = rstep; + #declare h = r * r / sqrt(2); + triangle { + O, F(phi, r), F(phi + phistep, r) + } + #while (r < rmax - rstep/2) + // ring + triangle { + F(phi, r), + F(phi + phistep, r), + F(phi + phistep, r + rstep) + } + triangle { + F(phi, r), + F(phi + phistep, r + rstep), + F(phi, r + rstep) + } + #declare r = r + rstep; + #end + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare a = sqrt(2); +#macro G(phi,sg) + < a*sg*sqrt(cos(2*phi))*cos(phi), a*cos(2*phi), a*sqrt(cos(2*phi))*sin(phi)> +#end + +#macro Lemniskate3D(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G(phi,1), s } + cylinder { G(phi,1), G(phi+phistep,1), s } + sphere { G(phi,-1), s } + cylinder { G(phi,-1), G(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare a = sqrt(2); +#macro G2(phi,sg) + a * sqrt(cos(2*phi)) * < sg * cos(phi), 0, sin(phi)> +#end + +#macro Lemniskate(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G2(phi,1), s } + cylinder { G2(phi,1), G2(phi+phistep,1), s } + sphere { G2(phi,-1), s } + cylinder { G2(phi,-1), G2(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Projektion(s, farbe) +union { + #declare phistep = pi / 16; + #declare phi = -pi / 4 + phistep; + #declare phimax = pi / 4; + #while (phi < phimax - phistep/2) + cylinder { G(phi, 1), G2(phi, 1), s } + cylinder { G(phi, -1), G2(phi, -1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare kegelfarbe = rgbt<0.2,0.6,0.2,0.2>; +#declare paraboloidfarbe = rgbt<0.2,0.6,1.0,0.2>; + +Paraboloid(paraboloidfarbe) +Kegel(kegelfarbe) +Lemniskate3D(0.02, Blue) +Lemniskate(0.02, Red) +Projektion(0.01, Yellow) diff --git a/buch/chapters/110-elliptisch/images/kegelpara.tex b/buch/chapters/110-elliptisch/images/kegelpara.tex new file mode 100644 index 0000000..5a724ee --- /dev/null +++ b/buch/chapters/110-elliptisch/images/kegelpara.tex @@ -0,0 +1,41 @@ +% +% kegelpara.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{4} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=8cm]{kegelpara.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (3.3,-1.0) {$X$}; +\node at (0.2,3.4) {$Z$}; +\node at (-2.5,-1.4) {$-Y$}; + +\end{tikzpicture} + +\end{document} + -- cgit v1.2.1 From fbcf8833aef79694e448010520f2253e93f2cd4e Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 14 Jun 2022 16:59:48 +0200 Subject: more info about the lemniskate --- buch/chapters/110-elliptisch/images/Makefile | 12 +- .../110-elliptisch/images/torusschnitt.pdf | Bin 0 -> 137159 bytes .../110-elliptisch/images/torusschnitt.pov | 185 +++++++++++++++++++++ .../110-elliptisch/images/torusschnitt.tex | 41 +++++ buch/chapters/110-elliptisch/lemniskate.tex | 162 ++++++++++++++++++ 5 files changed, 399 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/110-elliptisch/images/torusschnitt.pdf create mode 100644 buch/chapters/110-elliptisch/images/torusschnitt.pov create mode 100644 buch/chapters/110-elliptisch/images/torusschnitt.tex diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 7e4fa0c..2a23d88 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -79,7 +79,6 @@ slcldata.tex: slcl slcl.pdf: slcl.tex slcldata.tex pdflatex slcl.tex -POVRAYOPTIONS = -W1920 -H1080 kegelpara.png: kegelpara.pov povray +A0.1 -W1080 -H1080 -Okegelpara.png kegelpara.pov @@ -89,3 +88,14 @@ kegelpara.jpg: kegelpara.png Makefile kegelpara.pdf: kegelpara.tex kegelpara.jpg pdflatex kegelpara.tex + +torusschnitt.png: torusschnitt.pov + povray +A0.1 -W1920 -H1080 -Otorusschnitt.png torusschnitt.pov + +torusschnitt.jpg: torusschnitt.png Makefile + convert -extract 1560x1080+180+0 torusschnitt.png \ + -density 300 -units PixelsPerInch torusschnitt.jpg + +torusschnitt.pdf: torusschnitt.tex torusschnitt.jpg + pdflatex torusschnitt.tex + diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf new file mode 100644 index 0000000..430447c Binary files /dev/null and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pov b/buch/chapters/110-elliptisch/images/torusschnitt.pov new file mode 100644 index 0000000..94190be --- /dev/null +++ b/buch/chapters/110-elliptisch/images/torusschnitt.pov @@ -0,0 +1,185 @@ +// +// kegelpara.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +#declare O = <0,0,0>; + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.060; + +camera { + location <28, 20, -40> + look_at <0, 0.55, 0> + right (16/9) * x * imagescale + up y * imagescale +} + +light_source { + <30, 10, -40> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + + +// +// draw an arrow from to with thickness with +// color +// +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +arrow(<-2,0,0>,<2,0,0>,0.02,White) +arrow(<0,-1.1,0>,<0,2.2,0>,0.02,White) +arrow(<0,0,-1.6>,<0,0,2.4>,0.02,White) + +#declare epsilon = 0.001; +#declare l = 1.5; + + +#declare a = sqrt(2); +#macro G2(phi,sg) + a * sqrt(cos(2*phi)) * < sg * cos(phi), 0, sin(phi)> +#end + +#macro Lemniskate(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G2(phi,1), s } + cylinder { G2(phi,1), G2(phi+phistep,1), s } + sphere { G2(phi,-1), s } + cylinder { G2(phi,-1), G2(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Projektion(s, farbe) +union { + #declare phistep = pi / 16; + #declare phi = -pi / 4 + phistep; + #declare phimax = pi / 4; + #while (phi < phimax - phistep/2) + cylinder { G(phi, 1), G2(phi, 1), s } + cylinder { G(phi, -1), G2(phi, -1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Ebene(farbe) +box { + <-1.8, 0, -1.4>, <1.8, 0.001, 1.4> + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare b = 0.5; +#macro T(phi, theta) + b * < (2 + cos(theta)) * cos(phi), (2 + cos(theta)) * sin(phi) + 1, sin(theta) > +#end + +#macro Torus(farbe) +mesh { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 200; + #declare phistep = phimax/phisteps; + #while (phi < phimax - phistep/2) + #declare theta = 0; + #declare thetamax = 2 * pi; + #declare thetasteps = 200; + #declare thetastep = thetamax / thetasteps; + #while (theta < thetamax - thetastep/2) + triangle { + T(phi, theta), + T(phi + phistep, theta), + T(phi + phistep, theta + thetastep) + } + triangle { + T(phi, theta), + T(phi + phistep, theta + thetastep), + T(phi, theta + thetastep) + } + #declare theta = theta + thetastep; + #end + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare torusfarbe = rgbt<0.2,0.6,0.2,0.2>; +#declare ebenenfarbe = rgbt<0.2,0.6,1.0,0.2>; + +Lemniskate(0.02, Red) +Ebene(ebenenfarbe) +Torus(torusfarbe) diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.tex b/buch/chapters/110-elliptisch/images/torusschnitt.tex new file mode 100644 index 0000000..3053ac5 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/torusschnitt.tex @@ -0,0 +1,41 @@ +% +% torusschnitt.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{times} +\usepackage{amsmath} +\usepackage{txfonts} +\usepackage[utf8]{inputenc} +\usepackage{graphics} +\usetikzlibrary{arrows,intersections,math} +\usepackage{ifthen} +\begin{document} + +\newboolean{showgrid} +\setboolean{showgrid}{false} +\def\breite{6} +\def\hoehe{4} + +\begin{tikzpicture}[>=latex,thick] + +% Povray Bild +\node at (0,0) {\includegraphics[width=11.4cm]{torusschnitt.jpg}}; + +% Gitter +\ifthenelse{\boolean{showgrid}}{ +\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe); +\draw (-\breite,-\hoehe) grid (\breite, \hoehe); +\fill (0,0) circle[radius=0.05]; +}{} + +\node at (4.4,-2.4) {$X$}; +\node at (3.5,0.6) {$Y$}; +\node at (0.3,3.8) {$Z$}; + +\end{tikzpicture} + +\end{document} + diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index f750a82..d76a963 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -12,6 +12,9 @@ veröffentlich hat. In diesem Abschnitt soll die Verbindung zu den Jacobischen elliptischen Funktionen hergestellt werden. +% +% Lemniskate +% \subsection{Lemniskate \label{buch:gemotrie:subsection:lemniskate}} \begin{figure} @@ -71,6 +74,165 @@ Sie gilt für Winkel $\varphi\in[-\frac{\pi}4,\frac{\pi}4]$ für das rechte Blatt und $\varphi\in[\frac{3\pi}4,\frac{5\pi}4]$ für das linke Blatt der Lemniskate. +% +% Schnitt eines Kegels mit einem Paraboloid +% +\subsubsection{Schnitt eines Kegels mit einem Paraboloid} +\begin{figure} +\center +\includegraphics{chapters/110-elliptisch/images/kegelpara.pdf} +\caption{Leminiskate (rot) als Projektion (gelb) der Schnittkurve (blau) +eines geraden +Kreiskegels (grün) mit einem Rotationsparaboloid (hellblau). +\label{buch:elliptisch:lemniskate:kegelpara}} +\end{figure}% +Schreibt man in der Gleichung~\eqref{buch:elliptisch:eqn:lemniskate} +für die Klammer auf der rechten Seite $Z^2 = X^2 - Y^2$, dann wird die +Lemniskate die Projektion in die $X$-$Y$-Ebene der Schnittmenge der Flächen, +die durch die Gleichungen +\begin{equation} +X^2-Y^2 = Z^2 +\qquad\text{und}\qquad +(X^2+Y^2) = R^2 = \sqrt{2}aZ +\label{buch:elliptisch:eqn:kegelparabolschnitt} +\end{equation} +beschrieben wird. +Die linke Gleichung in +\eqref{buch:elliptisch:eqn:kegelparabolschnitt} +beschreibt einen geraden Kreiskegel, die rechte ist ein Rotationsparaboloid. +Die Schnittkurve ist in Abbildung~\ref{buch:elliptisch:lemniskate:kegelpara} +dargestellt. + +\subsubsection{Schnitt eines Torus mit einer Ebene} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/torusschnitt.pdf} +\caption{Die Schnittkurve (rot) eines Torus (grün) +mit einer zur Torusachse parallelen Ebene (blau), +die den inneren Äquator des Torus berührt, ist eine Lemniskate. +\label{buch:elliptisch:lemniskate:torusschnitt}} +\end{figure} +Schneidet man einen Torus mit einer Ebene, die zur Achse des Torus +parallel ist und den inneren Äquator des Torus berührt, entsteht +ebenfalls eine Lemniskate. +Die Situation ist in Abbildung~\ref{buch:elliptisch:lemniskate:torusschnitt} +dargestellt. + +Der Torus kann mit den Radien $2$ und $1$ mit der $y$-Achse als Torusachse +kann mit der Parametrisierung +\[ +(s,t) +\mapsto +\begin{pmatrix} +(2+\cos s) \cos t \\ +\sin s \\ +(2+\cos s) \sin t +\end{pmatrix} +\] +beschrieben werden. +Die Gleichung $z=1$ beschreibt eine +achsparallele Ebene, die den inneren Äquator berührt. +Die Schnittkurve erfüllt daher +\[ +(2+\cos s)\sin t = 1, +\] +was wir auch als $2 +\cos s = 1/\sin t$ schreiben können. +Wir müssen nachprüfen dass die Koordinaten +$X=(2+\cos s)\cos t$ und $Y=\sin s$ die Gleichung einer Lemniskate +erfüllen. + +Zunächst können wir in der $X$-Koordinate den Klammerausdruck durch +\begin{equation} +X += +(2+\cos s) \cos t += +\frac{1}{\sin t}\cos t += +\frac{\cos t}{\sin t} +\qquad\Rightarrow\qquad +X^2 += +\frac{\cos^2t}{\sin^2 t} += +\frac{1-\sin^2t}{\sin^2 t} +\label{buch:elliptisch:lemniskate:Xsin} +\end{equation} +ersetzen. +Auch die $Y$-Koordinaten können wir durch $t$ ausdrücken, +nämlich +\begin{equation} +Y^2=\sin^2 s = 1-\cos^2 s += +1- +\biggl( +\frac{1}{\sin t} +-2 +\biggr)^2 += +\frac{-3\sin^2 t+4\sin t-1}{\sin^2 t}. +\label{buch:elliptisch:lemniskate:Ysin} +\end{equation} +Die Gleichungen +\eqref{buch:elliptisch:lemniskate:Xsin} +und +\eqref{buch:elliptisch:lemniskate:Ysin} +zeigen, dass man $X^2$ und $Y^2$ sogar einzig durch $\sin t$ +parametrisieren kann. +Um die Ausdrücke etwas zu vereinfachen, schreiben wir $S=\sin t$ +und erhalten zusammenfassend +\begin{equation} +\begin{aligned} +X^2 +&= +\frac{1-S^2}{S^2} +\\ +Y^2 +&= +\frac{-3S^2+4S-1}{S^2}. +\end{aligned} +\end{equation} +Daraus kann man jetzt die Summen und Differenzen der Quadrate +berechnen, sie sind +\begin{equation} +\begin{aligned} +X^2+Y^2 +&= +\frac{-4S^2+4S}{S^2} += +\frac{4S(1-S)}{S^2} += +\frac{4(1-S)}{S} += +4\frac{1-S}{S} +\\ +X^2-Y^2 +&= +\frac{2-4S+2S^2}{S^2} += +\frac{2(1-S)^2}{S^2} += +2\biggl(\frac{1-S}{S}\biggr)^2. +\end{aligned} +\end{equation} +Durch Berechnung des Quadrates von $X^2+Y^2$ kann man jetzt +die Gleichung +\[ +(X^2+Y^2) += +16 +\biggl(\frac{1-S}{S}\biggr)^2 += +8 \cdot 2 +\biggl(\frac{1-S}{S}\biggr)^2 += +2\cdot 2^2\cdot (X-Y)^2. +\] +Dies ist eine Lemniskaten-Gleichung für $a=2$. + +% +% Bogenlänge der Lemniskate +% \subsection{Bogenlänge} Die Funktionen \begin{equation} -- cgit v1.2.1 From f62b44e41eb5d9afe46e56c335b96cb48ae3a492 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 14 Jun 2022 17:02:23 +0200 Subject: finalize lemniscate as sections --- buch/chapters/110-elliptisch/images/Makefile | 2 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 139626 -> 139626 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 137159 -> 137159 bytes buch/chapters/110-elliptisch/lemniskate.tex | 4 ++-- 5 files changed, 3 insertions(+), 3 deletions(-) diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 2a23d88..30642fe 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -5,7 +5,7 @@ # all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ - sncnlimit.pdf slcl.pdf + sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index f0e6e78..4c74a5c 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 4b03119..6683709 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 430447c..2f8c204 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index d76a963..f81f0e2 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -215,7 +215,7 @@ X^2-Y^2 2\biggl(\frac{1-S}{S}\biggr)^2. \end{aligned} \end{equation} -Durch Berechnung des Quadrates von $X^2+Y^2$ kann man jetzt +Die Berechnung des Quadrates von $X^2+Y^2$ ergibt die Gleichung \[ (X^2+Y^2) @@ -228,7 +228,7 @@ die Gleichung = 2\cdot 2^2\cdot (X-Y)^2. \] -Dies ist eine Lemniskaten-Gleichung für $a=2$. +Sie ist eine Lemniskaten-Gleichung für $a=2$. % % Bogenlänge der Lemniskate -- cgit v1.2.1 From 864b17ee949de5c14ebc3bbf50a90178b4b804f3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 15 Jun 2022 20:25:27 +0200 Subject: fix some minor issues --- buch/chapters/110-elliptisch/images/Makefile | 7 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 139626 -> 202828 bytes buch/chapters/110-elliptisch/images/kegelpara.pov | 122 +++++++++++++++++++-- buch/chapters/110-elliptisch/images/kegelpara.tex | 6 +- .../110-elliptisch/images/torusschnitt.pdf | Bin 137159 -> 301677 bytes .../110-elliptisch/images/torusschnitt.pov | 88 ++++++++++++++- buch/chapters/110-elliptisch/lemniskate.tex | 12 +- 8 files changed, 211 insertions(+), 24 deletions(-) diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 30642fe..c8f98cb 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -79,11 +79,14 @@ slcldata.tex: slcl slcl.pdf: slcl.tex slcldata.tex pdflatex slcl.tex +KEGELSIZE = -W256 -H256 +KEGELSIZE = -W128 -H128 +KEGELSIZE = -W1080 -H1080 kegelpara.png: kegelpara.pov - povray +A0.1 -W1080 -H1080 -Okegelpara.png kegelpara.pov + povray +A0.1 $(KEGELSIZE) -Okegelpara.png kegelpara.pov kegelpara.jpg: kegelpara.png Makefile - convert -extract 1080x1000+0+40 kegelpara.png \ + convert -extract 1080x1040+0+0 kegelpara.png \ -density 300 -units PixelsPerInch kegelpara.jpg kegelpara.pdf: kegelpara.tex kegelpara.jpg diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 4c74a5c..c11affc 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 6683709..2f76593 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pov b/buch/chapters/110-elliptisch/images/kegelpara.pov index 5d85eed..13b66cc 100644 --- a/buch/chapters/110-elliptisch/images/kegelpara.pov +++ b/buch/chapters/110-elliptisch/images/kegelpara.pov @@ -67,11 +67,11 @@ union { } #end -arrow(<-2,0,0>,<2,0,0>,0.02,White) -arrow(<0,-2,0>,<0,2,0>,0.02,White) -arrow(<0,0,-2>,<0,0,2>,0.02,White) +arrow(<-2.6,0,0>,<2.5,0,0>,0.02,White) +arrow(<0,-2,0>,<0,2.3,0>,0.02,White) +arrow(<0,0,-3.2>,<0,0,3.7>,0.02,White) -#declare epsilon = 0.001; +#declare epsilon = 0.0001; #declare l = 1.5; #macro Kegel(farbe) @@ -94,6 +94,54 @@ union { } #end +#macro Kegelpunkt(xx, phi) + < xx, xx * sin(phi), xx * cos(phi) > +#end + +#macro Kegelgitter(farbe, r) +union { + #declare s = 0; + #declare smax = 2 * pi; + #declare sstep = pi / 6; + #while (s < smax - sstep/2) + cylinder { Kegelpunkt(l, s), Kegelpunkt(-l, s), r } + #declare s = s + sstep; + #end + #declare phimax = 2 * pi; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #declare xxstep = 0.5; + #declare xxmax = 2; + #declare xx = xxstep; + #while (xx < xxmax - xxstep/2) + #declare phi = 0; + #while (phi < phimax - phistep/2) + cylinder { + Kegelpunkt(xx, phi), + Kegelpunkt(xx, phi + phistep), + r + } + sphere { Kegelpunkt(xx, phi), r } + cylinder { + Kegelpunkt(-xx, phi), + Kegelpunkt(-xx, phi + phistep), + r + } + sphere { Kegelpunkt(-xx, phi), r } + #declare phi = phi + phistep; + #end + #declare xx = xx + xxstep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + #macro F(w, r) #end @@ -139,6 +187,50 @@ mesh { } #end +#macro Paraboloidgitter(farbe, gr) +union { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phistep = pi / 6; + + #declare rmax = 1.5; + #declare rsteps = 100; + #declare rstep = rmax / rsteps; + + #while (phi < phimax - phistep/2) + #declare r = rstep; + #while (r < rmax - rstep/2) + cylinder { F(phi, r), F(phi, r + rstep), gr } + sphere { F(phi, r), gr } + #declare r = r + rstep; + #end + #declare phi = phi + phistep; + #end + + #declare rstep = 0.2; + #declare r = rstep; + + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (r < rmax) + #declare phi = 0; + #while (phi < phimax - phistep/2) + cylinder { F(phi, r), F(phi + phistep, r), gr } + sphere { F(phi, r), gr } + #declare phi = phi + phistep; + #end + #declare r = r + rstep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + #declare a = sqrt(2); #macro G(phi,sg) < a*sg*sqrt(cos(2*phi))*cos(phi), a*cos(2*phi), a*sqrt(cos(2*phi))*sin(phi)> @@ -215,11 +307,23 @@ union { } #end -#declare kegelfarbe = rgbt<0.2,0.6,0.2,0.2>; -#declare paraboloidfarbe = rgbt<0.2,0.6,1.0,0.2>; +#declare kegelfarbe = rgbf<0.2,0.6,0.2,0.2>; +#declare kegelgitterfarbe = rgb<0.2,0.8,0.2>; +#declare paraboloidfarbe = rgbf<0.2,0.6,1.0,0.2>; +#declare paraboloidgitterfarbe = rgb<0.4,1,1>; + +//intersection { +// union { + Paraboloid(paraboloidfarbe) + Paraboloidgitter(paraboloidgitterfarbe, 0.004) + + Kegel(kegelfarbe) + Kegelgitter(kegelgitterfarbe, 0.004) +// } +// plane { <0, 0, -1>, 0.6 } +//} + -Paraboloid(paraboloidfarbe) -Kegel(kegelfarbe) -Lemniskate3D(0.02, Blue) +Lemniskate3D(0.02, rgb<0.8,0.0,0.8>) Lemniskate(0.02, Red) Projektion(0.01, Yellow) diff --git a/buch/chapters/110-elliptisch/images/kegelpara.tex b/buch/chapters/110-elliptisch/images/kegelpara.tex index 5a724ee..8fcefbf 100644 --- a/buch/chapters/110-elliptisch/images/kegelpara.tex +++ b/buch/chapters/110-elliptisch/images/kegelpara.tex @@ -31,9 +31,9 @@ \fill (0,0) circle[radius=0.05]; }{} -\node at (3.3,-1.0) {$X$}; -\node at (0.2,3.4) {$Z$}; -\node at (-2.5,-1.4) {$-Y$}; +\node at (4.1,-1.4) {$X$}; +\node at (0.2,3.8) {$Z$}; +\node at (4.0,1.8) {$Y$}; \end{tikzpicture} diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 2f8c204..11bd353 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pov b/buch/chapters/110-elliptisch/images/torusschnitt.pov index 94190be..43d50c6 100644 --- a/buch/chapters/110-elliptisch/images/torusschnitt.pov +++ b/buch/chapters/110-elliptisch/images/torusschnitt.pov @@ -123,9 +123,34 @@ union { } #end -#macro Ebene(farbe) -box { - <-1.8, 0, -1.4>, <1.8, 0.001, 1.4> +#macro Ebene(l, b, farbe) +mesh { + triangle { <-l, 0, -b>, < l, 0, -b>, < l, 0, b> } + triangle { <-l, 0, -b>, < l, 0, b>, <-l, 0, b> } + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Ebenengitter(l, b, s, r, farbe) +union { + #declare lmax = floor(l / s); + #declare ll = -lmax; + #while (ll <= lmax) + cylinder { , , r } + #declare ll = ll + 1; + #end + #declare bmax = floor(b / s); + #declare bb = -bmax; + #while (bb <= bmax) + cylinder { <-l, 0, bb * s>, , r } + #declare bb = bb + 1; + #end pigment { color farbe } @@ -141,6 +166,59 @@ box { b * < (2 + cos(theta)) * cos(phi), (2 + cos(theta)) * sin(phi) + 1, sin(theta) > #end +#macro breitenkreis(theta, r) + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 200; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + cylinder { T(phi, theta), T(phi + phistep, theta), r } + sphere { T(phi, theta), r } + #declare phi = phi + phistep; + #end +#end + +#macro laengenkreis(phi, r) + #declare theta = 0; + #declare thetamax = 2 * pi; + #declare thetasteps = 200; + #declare thetastep = thetamax / thetasteps; + #while (theta < thetamax - thetastep/2) + cylinder { T(phi, theta), T(phi, theta + thetastep), r } + sphere { T(phi, theta), r } + #declare theta = theta + thetastep; + #end +#end + +#macro Torusgitter(farbe, r) +union { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phistep = pi / 6; + #while (phi < phimax - phistep/2) + laengenkreis(phi, r) + #declare phi = phi + phistep; + #end + #declare thetamax = pi; + #declare thetastep = pi / 6; + #declare theta = thetastep; + #while (theta < thetamax - thetastep/2) + breitenkreis(theta, r) + breitenkreis(thetamax + theta, r) + #declare theta = theta + thetastep; + #end + breitenkreis(0, 1.5 * r) + breitenkreis(pi, 1.5 * r) + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + #macro Torus(farbe) mesh { #declare phi = 0; @@ -181,5 +259,7 @@ mesh { #declare ebenenfarbe = rgbt<0.2,0.6,1.0,0.2>; Lemniskate(0.02, Red) -Ebene(ebenenfarbe) +Ebene(1.8, 1.4, ebenenfarbe) +Ebenengitter(1.8, 1.4, 0.5, 0.005, rgb<0.4,1,1>) Torus(torusfarbe) +Torusgitter(Yellow, 0.005) diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index f81f0e2..fceaadf 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -81,7 +81,7 @@ Blatt der Lemniskate. \begin{figure} \center \includegraphics{chapters/110-elliptisch/images/kegelpara.pdf} -\caption{Leminiskate (rot) als Projektion (gelb) der Schnittkurve (blau) +\caption{Leminiskate (rot) als Projektion (gelb) der Schnittkurve (pink) eines geraden Kreiskegels (grün) mit einem Rotationsparaboloid (hellblau). \label{buch:elliptisch:lemniskate:kegelpara}} @@ -126,7 +126,7 @@ kann mit der Parametrisierung \begin{pmatrix} (2+\cos s) \cos t \\ \sin s \\ -(2+\cos s) \sin t +(2+\cos s) \sin t + 1 \end{pmatrix} \] beschrieben werden. @@ -134,9 +134,9 @@ Die Gleichung $z=1$ beschreibt eine achsparallele Ebene, die den inneren Äquator berührt. Die Schnittkurve erfüllt daher \[ -(2+\cos s)\sin t = 1, +(2+\cos s)\sin t + 1 = 0, \] -was wir auch als $2 +\cos s = 1/\sin t$ schreiben können. +was wir auch als $2 +\cos s = -1/\sin t$ schreiben können. Wir müssen nachprüfen dass die Koordinaten $X=(2+\cos s)\cos t$ und $Y=\sin s$ die Gleichung einer Lemniskate erfüllen. @@ -147,9 +147,9 @@ X = (2+\cos s) \cos t = -\frac{1}{\sin t}\cos t +-\frac{1}{\sin t}\cos t = -\frac{\cos t}{\sin t} +-\frac{\cos t}{\sin t} \qquad\Rightarrow\qquad X^2 = -- cgit v1.2.1 From b9af31ecb07acd4d34a13aa99d6170c9ca96af87 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 17:00:34 +0200 Subject: some improvements --- buch/chapters/110-elliptisch/images/Makefile | 2 +- .../110-elliptisch/images/torusschnitt.pdf | Bin 301677 -> 312677 bytes .../110-elliptisch/images/torusschnitt.pov | 55 ++++++++++++++++++--- .../110-elliptisch/images/torusschnitt.tex | 2 +- 4 files changed, 51 insertions(+), 8 deletions(-) diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index c8f98cb..7bbc8af 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -96,7 +96,7 @@ torusschnitt.png: torusschnitt.pov povray +A0.1 -W1920 -H1080 -Otorusschnitt.png torusschnitt.pov torusschnitt.jpg: torusschnitt.png Makefile - convert -extract 1560x1080+180+0 torusschnitt.png \ + convert -extract 1640x1080+140+0 torusschnitt.png \ -density 300 -units PixelsPerInch torusschnitt.jpg torusschnitt.pdf: torusschnitt.tex torusschnitt.jpg diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 11bd353..f5de617 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pov b/buch/chapters/110-elliptisch/images/torusschnitt.pov index 43d50c6..e5602df 100644 --- a/buch/chapters/110-elliptisch/images/torusschnitt.pov +++ b/buch/chapters/110-elliptisch/images/torusschnitt.pov @@ -67,14 +67,51 @@ union { } #end -arrow(<-2,0,0>,<2,0,0>,0.02,White) -arrow(<0,-1.1,0>,<0,2.2,0>,0.02,White) -arrow(<0,0,-1.6>,<0,0,2.4>,0.02,White) + +#macro Ticks(tl, tr) +union { + #declare s = 1; + #while (s <= 3.1) + cylinder { <-0.5*s-tl, 0, 0>, <-0.5*s+tl, 0, 0>, tr } + cylinder { < 0.5*s-tl, 0, 0>, < 0.5*s+tl, 0, 0>, tr } + #declare s = s + 1; + #end + + #declare s = 1; + #while (s <= 4.1) + cylinder { <0, 0.5*s-tl, 0>, <0, 0.5*s+tl, 0>, tr } + #declare s = s + 1; + #end + #declare s = 1; + #while (s <= 2.1) + cylinder { <0,-0.5*s-tl, 0>, <0,-0.5*s+tl, 0>, tr } + #declare s = s + 1; + #end + + #declare s = 1; + #while (s <= 4) + cylinder { <0, 0, 0.5*s-tl>, <0, 0, 0.5*s+tl>, tr } + #declare s = s + 1; + #end + #declare s = 1; + #while (s <= 3) + cylinder { <0, 0, -0.5*s-tl>, <0, 0, -0.5*s+tl>, tr } + #declare s = s + 1; + #end + + pigment { + color White + } + finish { + specular 0.9 + metallic + } +} +#end #declare epsilon = 0.001; #declare l = 1.5; - #declare a = sqrt(2); #macro G2(phi,sg) a * sqrt(cos(2*phi)) * < sg * cos(phi), 0, sin(phi)> @@ -258,8 +295,14 @@ mesh { #declare torusfarbe = rgbt<0.2,0.6,0.2,0.2>; #declare ebenenfarbe = rgbt<0.2,0.6,1.0,0.2>; +arrow(<-2,0,0>,<2,0,0>,0.02,White) +arrow(<0,-1.1,0>,<0,2.2,0>,0.02,White) +arrow(<0,0,-1.7>,<0,0,2.4>,0.02,White) +Ticks(0.007,0.036) + Lemniskate(0.02, Red) -Ebene(1.8, 1.4, ebenenfarbe) -Ebenengitter(1.8, 1.4, 0.5, 0.005, rgb<0.4,1,1>) +Ebene(1.8, 1.6, ebenenfarbe) +Ebenengitter(1.8, 1.6, 0.5, 0.005, rgb<0.4,1,1>) Torus(torusfarbe) Torusgitter(Yellow, 0.005) + diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.tex b/buch/chapters/110-elliptisch/images/torusschnitt.tex index 3053ac5..63351ad 100644 --- a/buch/chapters/110-elliptisch/images/torusschnitt.tex +++ b/buch/chapters/110-elliptisch/images/torusschnitt.tex @@ -21,7 +21,7 @@ \begin{tikzpicture}[>=latex,thick] % Povray Bild -\node at (0,0) {\includegraphics[width=11.4cm]{torusschnitt.jpg}}; +\node at (0,0) {\includegraphics[width=11.98cm]{torusschnitt.jpg}}; % Gitter \ifthenelse{\boolean{showgrid}}{ -- cgit v1.2.1 From 88031a6a5bad428cb3bf03dea6f0f95d79484723 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 17:02:24 +0200 Subject: new plots --- buch/chapters/110-elliptisch/images/Makefile | 13 ++- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 59737 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 202828 -> 203620 bytes buch/chapters/110-elliptisch/images/lemnispara.cpp | 126 +++++++++++++++++++++ buch/chapters/110-elliptisch/images/lemnispara.pdf | Bin 0 -> 28447 bytes buch/chapters/110-elliptisch/images/lemnispara.tex | 90 +++++++++++++++ buch/chapters/110-elliptisch/images/slcl.pdf | Bin 28233 -> 31823 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 301677 -> 302496 bytes buch/chapters/110-elliptisch/lemniskate.tex | 92 +++++++++++---- 9 files changed, 295 insertions(+), 26 deletions(-) create mode 100644 buch/chapters/110-elliptisch/images/lemnispara.cpp create mode 100644 buch/chapters/110-elliptisch/images/lemnispara.pdf create mode 100644 buch/chapters/110-elliptisch/images/lemnispara.tex diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index c8f98cb..3094877 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -5,7 +5,7 @@ # all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ - sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf + sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemnispara.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex @@ -102,3 +102,14 @@ torusschnitt.jpg: torusschnitt.png Makefile torusschnitt.pdf: torusschnitt.tex torusschnitt.jpg pdflatex torusschnitt.tex +lemnispara: lemnispara.cpp + g++ -O2 -Wall -g -o lemnispara `pkg-config --cflags gsl` \ + lemnispara.cpp `pkg-config --libs gsl` + +lemnisparadata.tex: lemnispara + ./lemnispara + +lemnispara.pdf: lemnispara.tex lemnisparadata.tex + pdflatex lemnispara.tex + +ltest: lemnispara.pdf diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index c11affc..fdd3d1f 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 2f76593..2dbe39d 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/lemnispara.cpp b/buch/chapters/110-elliptisch/images/lemnispara.cpp new file mode 100644 index 0000000..6f4d55d --- /dev/null +++ b/buch/chapters/110-elliptisch/images/lemnispara.cpp @@ -0,0 +1,126 @@ +/* + * lemnispara.cpp -- Display parametrisation of the lemniskate + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include +#include +#include +#include +#include + +const static double s = sqrt(2); +const static double k = 1 / s; +const static double m = k * k; + +typedef std::pair point_t; + +point_t operator*(const point_t& p, double s) { + return point_t(s * p.first, s * p.second); +} + +static double norm(const point_t& p) { + return hypot(p.first, p.second); +} + +static point_t normalize(const point_t& p) { + return p * (1/norm(p)); +} + +static point_t normal(const point_t& p) { + return std::make_pair(p.second, -p.first); +} + +class lemniscate : public point_t { + double sn, cn, dn; +public: + lemniscate(double t) { + gsl_sf_elljac_e(t, m, &sn, &cn, &dn); + first = s * cn * dn; + second = cn * sn; + } + point_t tangent() const { + return std::make_pair(-s * sn * (1.5 - sn * sn), + dn * (1 - 2 * sn * sn)); + } + point_t unittangent() const { + return normalize(tangent()); + } + point_t normal() const { + return ::normal(tangent()); + } + point_t unitnormal() const { + return ::normal(unittangent()); + } +}; + +std::ostream& operator<<(std::ostream& out, const point_t& p) { + char b[1024]; + snprintf(b, sizeof(b), "({%.4f*\\dx},{%.4f*\\dy})", p.first, p.second); + out << b; + return out; +} + +int main(int argc, char *argv[]) { + std::ofstream out("lemnisparadata.tex"); + + // the curve + double tstep = 0.01; + double tmax = 4.05; + out << "\\def\\lemnispath{ "; + out << lemniscate(0); + for (double t = tstep; t < tmax; t += tstep) { + out << std::endl << "\t" << "-- " << lemniscate(t); + } + out << std::endl; + out << "}" << std::endl; + + out << "\\def\\lemnispathmore{ "; + out << lemniscate(tmax); + double tmax2 = 7.5; + for (double t = tmax + tstep; t < tmax2; t += tstep) { + out << std::endl << "\t" << "-- " << lemniscate(t); + } + out << std::endl; + out << "}" << std::endl; + + // individual points + tstep = 0.2; + int i = 0; + char name[3]; + strcpy(name, "L0"); + for (double t = 0; t <= tmax; t += tstep) { + char c = 'A' + i++; + char buffer[128]; + lemniscate l(t); + name[0] = 'L'; + name[1] = c; + out << "\\coordinate (" << name << ") at "; + out << l << ";" << std::endl; + name[0] = 'T'; + out << "\\coordinate (" << name << ") at "; + out << l.unittangent() << ";" << std::endl; + name[0] = 'N'; + out << "\\coordinate (" << name << ") at "; + out << l.unitnormal() << ";" << std::endl; + name[0] = 'C'; + out << "\\def\\" << name << "{ "; + out << "\\node[color=red] at ($(L" << c << ")+0.06*(N" << c << ")$) "; + out << "[rotate={"; + double w = 180 * atan2(l.unitnormal().second, + l.unitnormal().first) / M_PI; + snprintf(buffer, sizeof(buffer), "%.1f", w); + out << buffer; + out << "-90}]"; + snprintf(buffer, sizeof(buffer), "%.1f", t); + out << " {$\\scriptstyle " << buffer << "$};" << std::endl; + out << "}" << std::endl; + } + + out.close(); + return EXIT_SUCCESS; +} diff --git a/buch/chapters/110-elliptisch/images/lemnispara.pdf b/buch/chapters/110-elliptisch/images/lemnispara.pdf new file mode 100644 index 0000000..b03997e Binary files /dev/null and b/buch/chapters/110-elliptisch/images/lemnispara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/lemnispara.tex b/buch/chapters/110-elliptisch/images/lemnispara.tex new file mode 100644 index 0000000..48557cf --- /dev/null +++ b/buch/chapters/110-elliptisch/images/lemnispara.tex @@ -0,0 +1,90 @@ +% +% lemnispara.tex -- parametrization of the lemniscate +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\def\skala{1} + +\begin{tikzpicture}[>=latex,thick,scale=\skala] +\def\dx{4} +\def\dy{4} +\input{lemnisparadata.tex} + +% add image content here +\draw[color=red!20,line width=1.4pt] \lemnispathmore; +\draw[color=red,line width=1.4pt] \lemnispath; + +\draw[->] ({-1.6*\dx},0) -- ({1.6*\dx},0) coordinate[label={$X$}]; +\draw[->] (0,{-0.7*\dy}) -- (0,{0.7*\dy}) coordinate[label={right:$Y$}]; +\draw ({1.5*\dx},-0.05) -- ({1.5*\dx},0.05); +\draw ({\dx},-0.05) -- ({\dx},0.05); +\draw ({0.5*\dx},-0.05) -- ({0.5*\dx},0.05); +\draw ({-0.5*\dx},-0.05) -- ({-0.5*\dx},0.05); +\draw ({-\dx},-0.05) -- ({-\dx},0.05); +\draw ({-1.5*\dx},-0.05) -- ({-1.5*\dx},0.05); +\draw (-0.05,{0.5*\dy}) -- (0.05,{0.5*\dy}); +\draw (-0.05,{-0.5*\dy}) -- (0.05,{-0.5*\dy}); + +\node at ({\dx},0) [above] {$1$}; +\node at ({-\dx},0) [above] {$-1$}; +\node at ({-0.5*\dx},0) [above] {$-\frac12$}; +\node at ({0.5*\dx},0) [above] {$\frac12$}; +\node at (0,{0.5*\dy}) [left] {$\frac12$}; +\node at (0,{-0.5*\dy}) [left] {$-\frac12$}; + +\def\s{0.02} + +\draw[color=red] ($(LA)-\s*(NA)$) -- ($(LA)+\s*(NA)$); +\draw[color=red] ($(LB)-\s*(NB)$) -- ($(LB)+\s*(NB)$); +\draw[color=red] ($(LC)-\s*(NC)$) -- ($(LC)+\s*(NC)$); +\draw[color=red] ($(LD)-\s*(ND)$) -- ($(LD)+\s*(ND)$); +\draw[color=red] ($(LE)-\s*(NE)$) -- ($(LE)+\s*(NE)$); +\draw[color=red] ($(LF)-\s*(NF)$) -- ($(LF)+\s*(NF)$); +\draw[color=red] ($(LG)-\s*(NG)$) -- ($(LG)+\s*(NG)$); +\draw[color=red] ($(LH)-\s*(NH)$) -- ($(LH)+\s*(NH)$); +\draw[color=red] ($(LI)-\s*(NI)$) -- ($(LI)+\s*(NI)$); +\draw[color=red] ($(LJ)-\s*(NJ)$) -- ($(LJ)+\s*(NJ)$); +\draw[color=red] ($(LK)-\s*(NK)$) -- ($(LK)+\s*(NK)$); +\draw[color=red] ($(LL)-\s*(NL)$) -- ($(LL)+\s*(NL)$); +\draw[color=red] ($(LM)-\s*(NM)$) -- ($(LM)+\s*(NM)$); +\draw[color=red] ($(LN)-\s*(NN)$) -- ($(LN)+\s*(NN)$); +\draw[color=red] ($(LO)-\s*(NO)$) -- ($(LO)+\s*(NO)$); +\draw[color=red] ($(LP)-\s*(NP)$) -- ($(LP)+\s*(NP)$); +\draw[color=red] ($(LQ)-\s*(NQ)$) -- ($(LQ)+\s*(NQ)$); +\draw[color=red] ($(LR)-\s*(NR)$) -- ($(LR)+\s*(NR)$); +\draw[color=red] ($(LS)-\s*(NS)$) -- ($(LS)+\s*(NS)$); +\draw[color=red] ($(LT)-\s*(NT)$) -- ($(LT)+\s*(NT)$); +\draw[color=red] ($(LU)-\s*(NU)$) -- ($(LU)+\s*(NU)$); + +\CB +\CC +\CD +\CE +\CF +\CG +\CH +\CI +\CJ +\CK +\CL +\CM +\CN +\CO +\CP +\CQ +\CR +\CS +\CT +\CU + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/110-elliptisch/images/slcl.pdf b/buch/chapters/110-elliptisch/images/slcl.pdf index c15051b..71645e3 100644 Binary files a/buch/chapters/110-elliptisch/images/slcl.pdf and b/buch/chapters/110-elliptisch/images/slcl.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 11bd353..fde5268 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index fceaadf..fd998b3 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -86,9 +86,11 @@ eines geraden Kreiskegels (grün) mit einem Rotationsparaboloid (hellblau). \label{buch:elliptisch:lemniskate:kegelpara}} \end{figure}% +\index{Kegel}% +\index{Paraboloid}% Schreibt man in der Gleichung~\eqref{buch:elliptisch:eqn:lemniskate} für die Klammer auf der rechten Seite $Z^2 = X^2 - Y^2$, dann wird die -Lemniskate die Projektion in die $X$-$Y$-Ebene der Schnittmenge der Flächen, +Lemniskate die Projektion in die $X$-$Y$-Ebene der Schnittkurve der Flächen, die durch die Gleichungen \begin{equation} X^2-Y^2 = Z^2 @@ -112,14 +114,18 @@ mit einer zur Torusachse parallelen Ebene (blau), die den inneren Äquator des Torus berührt, ist eine Lemniskate. \label{buch:elliptisch:lemniskate:torusschnitt}} \end{figure} +\index{Torus}% Schneidet man einen Torus mit einer Ebene, die zur Achse des Torus parallel ist und den inneren Äquator des Torus berührt, entsteht ebenfalls eine Lemniskate. Die Situation ist in Abbildung~\ref{buch:elliptisch:lemniskate:torusschnitt} dargestellt. -Der Torus kann mit den Radien $2$ und $1$ mit der $y$-Achse als Torusachse -kann mit der Parametrisierung +Der in Abbildung~\ref{buch:elliptisch:lemniskate:torusschnitt} +dargestellte Torus mit den Radien $2$ und $1$ hat als Achse die +um eine Einheit in $Z$-Richtung verschobene $Y$-Achse und die +$X$-$Z$-Ebene als Äquatorebene. +Sie kann mit \[ (s,t) \mapsto @@ -129,9 +135,10 @@ kann mit der Parametrisierung (2+\cos s) \sin t + 1 \end{pmatrix} \] -beschrieben werden. -Die Gleichung $z=1$ beschreibt eine -achsparallele Ebene, die den inneren Äquator berührt. +parametrisiert werden, die $s$- und $t$-Koordinatenlinien sind +in der Abbildung gelb eingezeichnet. +Die Gleichung $Z=0$ beschreibt eine achsparallele Ebene, die den +inneren Äquator berührt. Die Schnittkurve erfüllt daher \[ (2+\cos s)\sin t + 1 = 0, @@ -141,7 +148,8 @@ Wir müssen nachprüfen dass die Koordinaten $X=(2+\cos s)\cos t$ und $Y=\sin s$ die Gleichung einer Lemniskate erfüllen. -Zunächst können wir in der $X$-Koordinate den Klammerausdruck durch +Zunächst können wir in der $X$-Koordinate den Klammerausdruck durch +$\sin t$ ausdrücken und erhalten \begin{equation} X = @@ -155,10 +163,9 @@ X^2 = \frac{\cos^2t}{\sin^2 t} = -\frac{1-\sin^2t}{\sin^2 t} +\frac{1-\sin^2t}{\sin^2 t}. \label{buch:elliptisch:lemniskate:Xsin} \end{equation} -ersetzen. Auch die $Y$-Koordinaten können wir durch $t$ ausdrücken, nämlich \begin{equation} @@ -218,7 +225,7 @@ X^2-Y^2 Die Berechnung des Quadrates von $X^2+Y^2$ ergibt die Gleichung \[ -(X^2+Y^2) +(X^2+Y^2)^2 = 16 \biggl(\frac{1-S}{S}\biggr)^2 @@ -226,7 +233,7 @@ die Gleichung 8 \cdot 2 \biggl(\frac{1-S}{S}\biggr)^2 = -2\cdot 2^2\cdot (X-Y)^2. +2\cdot 2^2\cdot (X^2-Y^2). \] Sie ist eine Lemniskaten-Gleichung für $a=2$. @@ -279,7 +286,7 @@ Kettenregel berechnen kann: &&\Rightarrow& \dot{y}(r)^2 &= -\frac{1-r^2}{2} -r^2 + \frac{r^4}{2(1-r^2)} +\frac{1-r^2}{2} -r^2 + \frac{r^4}{2(1-r^2)}. \end{align*} Die Summe der Quadrate ist \begin{align*} @@ -342,6 +349,13 @@ $\varpi/2$. % Bogenlängenparametrisierung % \subsection{Bogenlängenparametrisierung} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/lemnispara.pdf} +\caption{Parametrisierung der Lemniskate mit Jacobischen elliptischen +Funktion wie in \eqref{buch:elliptisch:lemniskate:bogeneqn} +\label{buch:elliptisch:lemniskate:bogenpara}} +\end{figure} Die Lemniskate mit der Gleichung \[ (X^2+Y^2)^2=2(X^2-Y^2) @@ -350,7 +364,7 @@ Die Lemniskate mit der Gleichung kann mit Jacobischen elliptischen Funktionen parametrisiert werden. Dazu schreibt man -\[ +\begin{equation} \left. \begin{aligned} X(t) @@ -364,9 +378,17 @@ Y(t) \end{aligned} \quad\right\} \qquad\text{mit $k=\displaystyle\frac{1}{\sqrt{2}}$} -\] -und berechnet die beiden Seiten der definierenden Gleichung der -Lemniskate. +\label{buch:elliptisch:lemniskate:bogeneqn} +\end{equation} +Abbildung~\ref{buch:elliptisch:lemniskate:bogenpara} zeigt die +Parametrisierung. +Dem Parameterwert $t=0$ entspricht der Punkt +$(\sqrt{2},0)$ der Lemniskate. + +Dass \eqref{buch:elliptisch:lemniskate:bogeneqn} +tatsächlich eine Parametrisierung ist kann nachgewiesen werden dadurch, +dass man die beiden Seiten der definierenden Gleichung der +Lemniskate berechnet. Zunächst ist \begin{align*} X(t)^2 @@ -436,7 +458,7 @@ Dazu berechnen wir die Ableitungen &= -\sqrt{2}\operatorname{sn}(t,k)\bigl( 1-{\textstyle\frac12}\operatorname{sn}(t,k)^2 -+{\textstyle\frac12}-{\textstyle\frac12}\operatorname{sn}(u,t)^2 ++{\textstyle\frac12}-{\textstyle\frac12}\operatorname{sn}(t,k)^2 \bigr) \\ &= @@ -507,6 +529,7 @@ Gleichung \] hat daher eine Bogenlängenparametrisierung mit \begin{equation} +\left. \begin{aligned} x(t) &= @@ -515,8 +538,13 @@ x(t) \\ y(t) &= -\frac{1}{\sqrt{2}}\operatorname{cn}(\sqrt{2}t,k)\operatorname{sn}(\sqrt{2}t,k) +\frac{1}{\sqrt{2}} +\operatorname{cn}(\sqrt{2}t,k)\operatorname{sn}(\sqrt{2}t,k) \end{aligned} +\quad +\right\} +\qquad +\text{mit $\displaystyle k=\frac{1}{\sqrt{2}}$} \label{buch:elliptisch:lemniskate:bogenlaenge} \end{equation} @@ -527,7 +555,7 @@ die Bogenlänge zuordnet. Daher ist es naheliegend, die Umkehrfunktion von $s(r)$ in \eqref{buch:elliptisch:eqn:lemniskatebogenlaenge} den {\em lemniskatischen Sinus} zu nennen mit der Bezeichnung -$r=\operatorname{sl} s$. +$r=r(s)=\operatorname{sl} s$. Der Kosinus ist der Sinus des komplementären Winkels. Auch für die lemniskatische Bogenlänge $s(r)$ lässt sich eine @@ -537,9 +565,9 @@ Da die Bogenlänge zwischen $(0,0)$ und $(1,0)$ in in \eqref{buch:elliptisch:eqn:varpi} bereits bereichnet wurde. ist sie $\varpi/2-s$. Der {\em lemniskatische Kosinus} ist daher -$\operatorname{cl}(s) = \operatorname{sl}(\varpi/2-s)$ +$\operatorname{cl}(s) = \operatorname{sl}(\varpi/2-s)$. Graphen des lemniskatische Sinus und Kosinus sind in -Abbildung~\label{buch:elliptisch:figure:slcl} dargestellt. +Abbildung~\ref{buch:elliptisch:figure:slcl} dargestellt. Da die Parametrisierung~\eqref{buch:elliptisch:lemniskate:bogenlaenge} eine Bogenlängenparametrisierung ist, darf man $t=s$ schreiben. @@ -551,18 +579,32 @@ r(s)^2 x(s)^2 + y(s)^2 = \operatorname{cn}(s\sqrt{2},k)^2 -\qquad\Rightarrow\qquad +\biggl( +\operatorname{dn}(\sqrt{2}t,k)^2 ++ +\frac12 +\operatorname{sn}(\sqrt{2}t,k)^2 +\biggr) += +\operatorname{cn}(s\sqrt{2},k)^2. +\] +Die Wurzel ist +\[ r(s) = -\operatorname{cn}(s\sqrt{2},k) +\operatorname{sl} s += +\operatorname{cn}(s\sqrt{2},{\textstyle\frac{1}{\sqrt{2}}}). \] +Damit ist der lemniskatische Sinus durch eine Jacobische elliptische +Funktion darstellbar. \begin{figure} \centering \includegraphics[width=\textwidth]{chapters/110-elliptisch/images/slcl.pdf} \caption{ Lemniskatischer Sinus und Kosinus sowie Sinus und Kosinus -mit derart skaliertem Argument, dass die Funktionen die gleichen Nullstellen -haben. +mit derart skaliertem Argument, dass die Funktionen die +gleichen Nullstellen haben. \label{buch:elliptisch:figure:slcl}} \end{figure} -- cgit v1.2.1 From abb439719da913ee1bf14ee088748662fef3cd76 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 19:27:16 +0200 Subject: new stuff --- buch/chapters/020-exponential/chapter.tex | 4 +- buch/chapters/020-exponential/lambertw.tex | 32 +++- buch/chapters/110-elliptisch/images/lemnispara.pdf | Bin 28447 -> 28820 bytes buch/chapters/110-elliptisch/images/lemnispara.tex | 6 +- buch/chapters/110-elliptisch/lemniskate.tex | 199 ++++++++++++++------- 5 files changed, 166 insertions(+), 75 deletions(-) diff --git a/buch/chapters/020-exponential/chapter.tex b/buch/chapters/020-exponential/chapter.tex index 1ab4769..eaa777d 100644 --- a/buch/chapters/020-exponential/chapter.tex +++ b/buch/chapters/020-exponential/chapter.tex @@ -12,8 +12,8 @@ \input{chapters/020-exponential/zins.tex} \input{chapters/020-exponential/log.tex} \input{chapters/020-exponential/lambertw.tex} -\input{chapters/020-exponential/dilog.tex} -\input{chapters/020-exponential/eili.tex} +%\input{chapters/020-exponential/dilog.tex} +%\input{chapters/020-exponential/eili.tex} \section*{Übungsaufgaben} \rhead{Übungsaufgaben} diff --git a/buch/chapters/020-exponential/lambertw.tex b/buch/chapters/020-exponential/lambertw.tex index 2b023cc..9077c6f 100644 --- a/buch/chapters/020-exponential/lambertw.tex +++ b/buch/chapters/020-exponential/lambertw.tex @@ -17,6 +17,11 @@ der Unbekannten und der Exponentialfunktion, also $xe^x$ auftreten. Die Lambert $W$-Funktion ermöglicht, die Lösungen solcher Gleichungen darzustellen. +Als Anwendung der Theorie der Lambert-$W$-Funktion wird in +Kapitel~\ref{chapter:lambertw} +eine Parametrisierung einer Verfolgungskurve mit Hilfe von $W(x)$ +bestimmt. + % % Die Funktion xe^x % @@ -57,8 +62,10 @@ invertierbar. \begin{definition} Die inverse Funktion der Funktion $[-1,\infty)\to[-1/e,\infty):x\mapsto xe^x=y$ heisst die Lambert $W$-Funktion, geschrieben $W(y)$ oder $W_0(y)$. +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Definition}% Die inverse Funktion der Funktion $(-\infty,-1)\to[-1/e,0)$ wird mit $W_{-1}$ bezeichnet. +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Graph}% \end{definition} \begin{figure} @@ -78,7 +85,11 @@ erfüllen sie W(x) e^{W(x)} = x. \] +% +% Ableitung der W-Funktion +% \subsubsection{Ableitung der Funktionen $W(x)$ und $W_{-1}(x)$} +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Ableitung} Die Umkehrfunktion $f^{-1}(y)$ einer Funktion $f(x)$ erfüllt \( f^{-1}(f(x)) = x. @@ -204,7 +215,11 @@ P_{n+1}(t) \] mit $P_1(t)=1$. +% +% Differentialgleichung und Stammfunktion +% \subsubsection{Differentialgleichung und Stammfunktion} +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Differentialgleichung}% Die Ableitungsformel \eqref{buch:lambert:eqn:ableitung} bedeutet auch, dass die $W$-Funktion eine Lösung der Differentialgleichung \[ @@ -223,6 +238,7 @@ Diese Gleichung kann separiert werden in \] Eine Stammfunktion +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Stammfunktion}% \[ F(y) = @@ -260,6 +276,8 @@ für die Stammfunktion von $W(y)$. \label{buch:subsection:loesung-von-exponentialgleichungen}} Die Lambert $W$-Funktion kann zur Lösung von Exponentialgleichungen verwendet werden. +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Exponentialgleichungen}% +\index{Exponentialgleichungen}% \begin{aufgabe} Gesucht ist eine Lösung der Gleichung @@ -319,7 +337,10 @@ W(-cbe^{ac}) Die Gleichung hat eine Lösung wenn $-cbe^{ac} > -1/e$ ist. \end{proof} -\subsection{Numerische Berechnung +% +% Numerische Berechnung +% +\subsection{Numerische Berechnung der Lambert-$W$-Funktion \label{buch:subsection:lambertberechnung}} Die $W$-Funktionen sind nur dann nützlich, wenn man sie effizient berechnen kann. @@ -327,6 +348,9 @@ Leider ist sie nicht Teil der C- oder C++-Standardbibliothek, man muss sich also mit einer spezialisierten Bibliothek oder einer eigenen Implementation behelfen. +% +% Berechnung mit dem Newton-Algorithmus +% \subsubsection{Berechnung mit dem Newton-Algorithmus} Für $x>-1$ ist die Funktion $W(x)$ ist die Umkehrfunktion der streng monoton wachsenden und konvexen Funktion $f(x)=xe^x$. @@ -334,6 +358,7 @@ In dieser Situation konvergiert der Newton-Algorithmus zur Bestimmung der Nullstelle $x=W_0(y)$ von $f(x)-y$ für alle Werte von $y>-1/e$. Für $W_{-1}(y)$ ist die Situation etwas komplizierter, da für $x<-1$ die Funktion $f(x)$ nicht konvex ist. +\index{Lambert-W-Funktion@Lambert-$W$-Funktion!Newton-Algorithmus} Ausgehend vom Startwert $x_0$ ist die Iterationsfolge definiert durch @@ -362,11 +387,6 @@ bestimmt werden. Die Lambert $W$-Funktionen $W_0(x)$ und $W_{-1}(x)$ sind auch in der GNU scientific library \cite{buch:library:gsl} implementiert. -% -% Verfolgungskurven -% -\subsection{Verfolgungskurven -\label{buch:subsection:verfolgungskurven}} diff --git a/buch/chapters/110-elliptisch/images/lemnispara.pdf b/buch/chapters/110-elliptisch/images/lemnispara.pdf index b03997e..633df34 100644 Binary files a/buch/chapters/110-elliptisch/images/lemnispara.pdf and b/buch/chapters/110-elliptisch/images/lemnispara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/lemnispara.tex b/buch/chapters/110-elliptisch/images/lemnispara.tex index 48557cf..c6e32d7 100644 --- a/buch/chapters/110-elliptisch/images/lemnispara.tex +++ b/buch/chapters/110-elliptisch/images/lemnispara.tex @@ -22,8 +22,9 @@ \draw[color=red!20,line width=1.4pt] \lemnispathmore; \draw[color=red,line width=1.4pt] \lemnispath; -\draw[->] ({-1.6*\dx},0) -- ({1.6*\dx},0) coordinate[label={$X$}]; +\draw[->] ({-1.6*\dx},0) -- ({1.8*\dx},0) coordinate[label={$X$}]; \draw[->] (0,{-0.7*\dy}) -- (0,{0.7*\dy}) coordinate[label={right:$Y$}]; + \draw ({1.5*\dx},-0.05) -- ({1.5*\dx},0.05); \draw ({\dx},-0.05) -- ({\dx},0.05); \draw ({0.5*\dx},-0.05) -- ({0.5*\dx},0.05); @@ -85,6 +86,9 @@ \CT \CU +\fill[color=blue] (LA) circle[radius=0.07]; +\node[color=blue] at (LA) [above right] {$S$}; + \end{tikzpicture} \end{document} diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index fd998b3..a284f75 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -32,6 +32,13 @@ mit der Gleichung \end{equation} Sie ist in Abbildung~\ref{buch:elliptisch:fig:lemniskate} dargestellt. +Der Fall $a=1/\sqrt{2}$ ist eine Kurve mit der Gleichung +\[ +(x^2+y^2)^2 = x^2-y^2, +\] +wir nennen sie die {\em Standard-Lemniskate}. + +\subsubsection{Scheitelpunkte} Die beiden Scheitel der Lemniskate befinden sich bei $X_s=\pm a\sqrt{2}$. Dividiert man die Gleichung der Lemniskate durch $X_s^2=4a^4$ entsteht \begin{equation} @@ -53,10 +60,12 @@ Dividiert man die Gleichung der Lemniskate durch $X_s^2=4a^4$ entsteht \label{buch:elliptisch:eqn:lemniskatenormiert} \end{equation} wobei wir $x=X/a\sqrt{2}$ und $y=Y/a\sqrt{2}$ gesetzt haben. -In dieser Normierung liegen die Scheitel bei $\pm 1$. +In dieser Normierung, der Standard-Lemniskaten, liegen die Scheitel +bei $\pm 1$. Dies ist die Skalierung, die für die Definition des lemniskatischen Sinus und Kosinus verwendet werden soll. +\subsubsection{Polarkoordinaten} In Polarkoordinaten $x=r\cos\varphi$ und $y=r\sin\varphi$ gilt nach Einsetzen in \eqref{buch:elliptisch:eqn:lemniskatenormiert} \begin{equation} @@ -116,77 +125,80 @@ die den inneren Äquator des Torus berührt, ist eine Lemniskate. \end{figure} \index{Torus}% Schneidet man einen Torus mit einer Ebene, die zur Achse des Torus -parallel ist und den inneren Äquator des Torus berührt, entsteht -ebenfalls eine Lemniskate. -Die Situation ist in Abbildung~\ref{buch:elliptisch:lemniskate:torusschnitt} -dargestellt. +parallel ist und den inneren Äquator des Torus berührt, wie in +Abbildung~\ref{buch:elliptisch:lemniskate:torusschnitt}, +entsteht ebenfalls eine Lemniskate, wie in diesem Abschnitt nachgewiesen +werden soll. Der in Abbildung~\ref{buch:elliptisch:lemniskate:torusschnitt} dargestellte Torus mit den Radien $2$ und $1$ hat als Achse die um eine Einheit in $Z$-Richtung verschobene $Y$-Achse und die $X$-$Z$-Ebene als Äquatorebene. -Sie kann mit +Der Torus kann mit \[ -(s,t) +(u,v) \mapsto \begin{pmatrix} -(2+\cos s) \cos t \\ -\sin s \\ -(2+\cos s) \sin t + 1 +(2+\cos u) \cos v \\ + \sin u \\ +(2+\cos u) \sin v + 1 \end{pmatrix} \] -parametrisiert werden, die $s$- und $t$-Koordinatenlinien sind +parametrisiert werden, die $u$- und $v$-Koordinatenlinien sind in der Abbildung gelb eingezeichnet. +Die $v$-Koordinatenlinien sind Breitenkreise um die Achse des Torus. +Aus $u=0$ und $u=\pi$ ergeben sich die Äquatoren des Torus. + Die Gleichung $Z=0$ beschreibt eine achsparallele Ebene, die den inneren Äquator berührt. Die Schnittkurve erfüllt daher \[ -(2+\cos s)\sin t + 1 = 0, +(2+\cos u)\sin v + 1 = 0, \] -was wir auch als $2 +\cos s = -1/\sin t$ schreiben können. -Wir müssen nachprüfen dass die Koordinaten -$X=(2+\cos s)\cos t$ und $Y=\sin s$ die Gleichung einer Lemniskate +was wir auch als $2 +\cos u = -1/\sin v$ schreiben können. +Wir müssen nachprüfen, dass die Koordinaten +$X=(2+\cos u)\cos v$ und $Y=\sin u$ die Gleichung einer Lemniskate erfüllen. Zunächst können wir in der $X$-Koordinate den Klammerausdruck durch -$\sin t$ ausdrücken und erhalten +$\sin v$ ausdrücken und erhalten \begin{equation} X = -(2+\cos s) \cos t +(2+\cos u) \cos v = --\frac{1}{\sin t}\cos t +-\frac{1}{\sin v}\cos v = --\frac{\cos t}{\sin t} +-\frac{\cos v}{\sin v} \qquad\Rightarrow\qquad X^2 = -\frac{\cos^2t}{\sin^2 t} +\frac{\cos^2v}{\sin^2 v} = -\frac{1-\sin^2t}{\sin^2 t}. +\frac{1-\sin^2v}{\sin^2 v}. \label{buch:elliptisch:lemniskate:Xsin} \end{equation} -Auch die $Y$-Koordinaten können wir durch $t$ ausdrücken, +Auch die $Y$-Koordinaten können wir durch $v$ ausdrücken, nämlich \begin{equation} -Y^2=\sin^2 s = 1-\cos^2 s +Y^2=\sin^2 u = 1-\cos^2 u = 1- \biggl( -\frac{1}{\sin t} +\frac{1}{\sin v} -2 \biggr)^2 = -\frac{-3\sin^2 t+4\sin t-1}{\sin^2 t}. +\frac{-3\sin^2 v+4\sin v-1}{\sin^2 v}. \label{buch:elliptisch:lemniskate:Ysin} \end{equation} Die Gleichungen \eqref{buch:elliptisch:lemniskate:Xsin} und \eqref{buch:elliptisch:lemniskate:Ysin} -zeigen, dass man $X^2$ und $Y^2$ sogar einzig durch $\sin t$ +zeigen, dass man $X^2$ und $Y^2$ sogar einzig durch $\sin v$ parametrisieren kann. -Um die Ausdrücke etwas zu vereinfachen, schreiben wir $S=\sin t$ +Um die Ausdrücke etwas zu vereinfachen, schreiben wir $S=\sin v$ und erhalten zusammenfassend \begin{equation} \begin{aligned} @@ -222,8 +234,7 @@ X^2-Y^2 2\biggl(\frac{1-S}{S}\biggr)^2. \end{aligned} \end{equation} -Die Berechnung des Quadrates von $X^2+Y^2$ ergibt -die Gleichung +Die Berechnung des Quadrates von $X^2+Y^2$ ergibt die Gleichung \[ (X^2+Y^2)^2 = @@ -260,7 +271,7 @@ r^4 = (x(r)^2 + y(r)^2)^2, \end{align*} -sie stellen also eine Parametrisierung der Lemniskate dar. +sie stellen also eine Parametrisierung der Standard-Lemniskate dar. Mit Hilfe der Parametrisierung~\eqref{buch:geometrie:eqn:lemniskateparam} kann man die Länge $s$ des in Abbildung~\ref{buch:elliptisch:fig:lemniskate} @@ -382,9 +393,13 @@ Y(t) \end{equation} Abbildung~\ref{buch:elliptisch:lemniskate:bogenpara} zeigt die Parametrisierung. -Dem Parameterwert $t=0$ entspricht der Punkt -$(\sqrt{2},0)$ der Lemniskate. +Dem Parameterwert $t=0$ entspricht der Scheitelpunkt +$S=(\sqrt{2},0)$ der Lemniskate. +% +% Lemniskatengleichung +% +\subsubsection{Verfikation der Lemniskatengleichung} Dass \eqref{buch:elliptisch:lemniskate:bogeneqn} tatsächlich eine Parametrisierung ist kann nachgewiesen werden dadurch, dass man die beiden Seiten der definierenden Gleichung der @@ -441,6 +456,11 @@ X(t)^2-Y(t)^2 = 2(X(t)^2-Y(t)^2). \end{align*} + +% +% Berechnung der Bogenlänge +% +\subsubsection{Berechnung der Bogenlänge} Wir zeigen jetzt, dass dies tatsächlich eine Bogenlängenparametrisierung der Lemniskate ist. Dazu berechnen wir die Ableitungen @@ -509,19 +529,22 @@ Dazu berechnen wir die Ableitungen &= 1. \end{align*} -Dies bedeutet, dass die Bogenlänge zwischen den Parameterwerten $0$ und $s$ +Dies bedeutet, dass die Bogenlänge zwischen den Parameterwerten $0$ und $t$ \[ -\int_0^s -\sqrt{\dot{X}(t)^2 + \dot{Y}(t)^2} -\,dt +\int_0^t +\sqrt{\dot{X}(\tau)^2 + \dot{Y}(\tau)^2} +\,d\tau = -\int_0^s\,dt +\int_0^s\,d\tau = -s, +t, \] -der Parameter $t$ ist also ein Bogenlängenparameter, man darf also -$s=t$ schreiben. +der Parameter $t$ ist also ein Bogenlängenparameter. +% +% Bogenlängenparametrisierung der Standard-Lemniskate +% +\subsubsection{Bogenlängenparametrisierung der Standard-Lemniskate} Die mit dem Faktor $1/\sqrt{2}$ skalierte Standard-Lemniskate mit der Gleichung \[ @@ -547,7 +570,13 @@ y(t) \text{mit $\displaystyle k=\frac{1}{\sqrt{2}}$} \label{buch:elliptisch:lemniskate:bogenlaenge} \end{equation} +Der Punkt $t=0$ entspricht dem Scheitelpunkt $S=(1,0)$ der Lemniskate. +Der Parameter misst also die Bogenlänge entlang der Lemniskate ausgehend +vom Scheitel. +% +% der lemniskatische Sinus und Kosinus +% \subsection{Der lemniskatische Sinus und Kosinus} Der Sinus berechnet die Gegenkathete zu einer gegebenen Bogenlänge des Kreises, er ist die Umkehrfunktion der Funktion, die der Gegenkathete @@ -555,30 +584,53 @@ die Bogenlänge zuordnet. Daher ist es naheliegend, die Umkehrfunktion von $s(r)$ in \eqref{buch:elliptisch:eqn:lemniskatebogenlaenge} den {\em lemniskatischen Sinus} zu nennen mit der Bezeichnung +\index{lemniskatischer Sinus}% +\index{Sinus, lemniskatischer}% $r=r(s)=\operatorname{sl} s$. +\index{komplementäre Bogenlänge} +% +% die komplementäre Bogenlänge +% +\subsubsection{Die komplementäre Bogenlänge} Der Kosinus ist der Sinus des komplementären Winkels. Auch für die lemniskatische Bogenlänge $s(r)$ lässt sich eine -komplementäre Bogenlänge definieren, nämlich die Bogenlänge zwischen -dem Punkt $(x(r), y(r))$ und $(1,0)$. -Da die Bogenlänge zwischen $(0,0)$ und $(1,0)$ in -in \eqref{buch:elliptisch:eqn:varpi} bereits bereichnet wurde. -ist sie $\varpi/2-s$. +komplementäre Bogenlänge $t$ definieren, nämlich die Bogenlänge +zwischen dem Punkt $(x(r), y(r))$ und dem Scheitelpunkt $S=(1,0)$. +Dies ist der Parameter der Parametrisierung +\eqref{buch:elliptisch:lemniskate:bogenlaenge} +des vorangegangenen Abschnittes. +Die Bogenlänge zwischen $O=(0,0)$ und $S=(1,0)$ wurde in +\eqref{buch:elliptisch:eqn:varpi} bereits bereichnet, +sie ist $\varpi/2$. +Damit folgt für die beiden Parameter $s$ und $t$ die Beziehung +$t = \varpi/2 - s$. + +\subsubsection{Der lemniskatische Kosinus} +\begin{figure} +\centering +\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/slcl.pdf} +\caption{ +Lemniskatischer Sinus und Kosinus sowie Sinus und Kosinus +mit derart skaliertem Argument, dass die Funktionen die +gleichen Nullstellen haben. +\label{buch:elliptisch:figure:slcl}} +\end{figure} Der {\em lemniskatische Kosinus} ist daher $\operatorname{cl}(s) = \operatorname{sl}(\varpi/2-s)$. Graphen des lemniskatische Sinus und Kosinus sind in Abbildung~\ref{buch:elliptisch:figure:slcl} dargestellt. -Da die Parametrisierung~\eqref{buch:elliptisch:lemniskate:bogenlaenge} -eine Bogenlängenparametrisierung ist, darf man $t=s$ schreiben. -Dann kann man aber auch $r(s)$ daraus berechnen, -es ist +Die Parametrisierung~\eqref{buch:elliptisch:lemniskate:bogenlaenge} +ist eine Bogenlängenparametrisierung der Standard-Lemniskate. +Man kann sie verwenden, um $r(t)$ zu berechnen. +Es ist \[ -r(s)^2 +r(t)^2 = -x(s)^2 + y(s)^2 +x(t)^2 + y(t)^2 = -\operatorname{cn}(s\sqrt{2},k)^2 +\operatorname{cn}(\sqrt{2}t,k)^2 \biggl( \operatorname{dn}(\sqrt{2}t,k)^2 + @@ -586,25 +638,40 @@ x(s)^2 + y(s)^2 \operatorname{sn}(\sqrt{2}t,k)^2 \biggr) = -\operatorname{cn}(s\sqrt{2},k)^2. +\operatorname{cn}(\sqrt{2}t,k)^2. \] Die Wurzel ist \[ +r(t) += +\operatorname{cn}(\sqrt{2}t,{\textstyle\frac{1}{\sqrt{2}}}) +. +\] +Der lemniskatische Sinus wurde aber in Abhängigkeit von +$s=\varpi/2-t$ mittels +\[ +\operatorname{sl}s += r(s) = -\operatorname{sl} s +\operatorname{cn}(\sqrt{2}(\varpi/2-s),k)^2 +\] +definiert. +Der lemniskatische Kosinus ist definiert als der lemniskatische Sinus +\index{lemniskatischer Kosinus}% +\index{Kosinus, lemniskatischer}% +der komplementären Bogenlänge, also +\[ +\operatorname{cl}(s) += +\operatorname{sl}(\varpi/2-s) = -\operatorname{cn}(s\sqrt{2},{\textstyle\frac{1}{\sqrt{2}}}). +\operatorname{cn}(\sqrt{2}s,k)^2. \] -Damit ist der lemniskatische Sinus durch eine Jacobische elliptische -Funktion darstellbar. +Die Funktion $\operatorname{sl}(s)$ und $\operatorname{cl}(s)$ sind +in Abbildung~\ref{buch:elliptisch:figure:slcl} dargestellt. +Sie sind beide $2\varpi$-periodisch. +Die Abbildung zeigt ausserdem die Funktionen $\sin (\pi s/\varpi)$ +und $\cos(\pi s/\varpi)$, die ebenfalls $2\varpi$-periodisch sind. + -\begin{figure} -\centering -\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/slcl.pdf} -\caption{ -Lemniskatischer Sinus und Kosinus sowie Sinus und Kosinus -mit derart skaliertem Argument, dass die Funktionen die -gleichen Nullstellen haben. -\label{buch:elliptisch:figure:slcl}} -\end{figure} -- cgit v1.2.1 From 4764f8b481629a2f733c6025ec66a34a31d50222 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 20:01:13 +0200 Subject: more on polynomials --- buch/chapters/010-potenzen/polynome.tex | 61 ++++++++++++++++++++++++++++++++- 1 file changed, 60 insertions(+), 1 deletion(-) diff --git a/buch/chapters/010-potenzen/polynome.tex b/buch/chapters/010-potenzen/polynome.tex index 981e444..2086078 100644 --- a/buch/chapters/010-potenzen/polynome.tex +++ b/buch/chapters/010-potenzen/polynome.tex @@ -24,6 +24,7 @@ $K[x]$ bezeichnet. \end{definition} Die Menge $K[x]$ ist heisst auch der {\em Polynomring}, weil $K[x]$ +\index{Polynomring}% mit der Addition, Subtraktion und Multiplikation von Polynomen eine algebraische Struktur bildet, die man einen Ring mit $1$ nennt. \index{Ring}% @@ -82,32 +83,47 @@ ebenfalls als Approximationen dienen können. Weitere Möglichkeiten liefern Interpolationsmethoden der numerischen Mathematik. +% +% Polynomdivision, Teilbarkeit und ggT +% \subsection{Polynomdivision, Teilbarkeit und grösster gemeinsamer Teiler} Der schriftliche Divisionsalgorithmus für Zahlen funktioniert auch für die Division von Polynomen. +\index{Polynome!Divisionsalgorithmus}% Zu zwei beliebigen Polynomen $p(x)$ und $q(x)$ lassen sich also immer zwei Polynome $a(x)$ und $r(x)$ finden derart, dass $p(x) = a(x) q(x) + r(x)$. Das Polynom $a(x)$ heisst der {\em Quotient}, $r(x)$ der {\em Rest} der Division. Das Polynom $p(x)$ heisst {\em teilbar} durch $q(x)$, geschrieben +\index{teilbar}% +\index{Polynome!teilbar}% $q(x)\mid p(x)$, wenn $r(x)=0$ ist. +% +% Grösster gemeinsamer Teiler +% \subsubsection{Grösster gemeinsamer Teiler} Mit dem Begriff der Teilbarkeit geht auch die Idee des grössten gemeinsamen Teilers einher. Ein gemeinsamer Teiler zweier Polynome $a(x)$ und $b(x)$ +\index{gemeinsamer Teiler}% ist ein Polynom $g(x)$, welches beide Polynome teilt, also $g(x)\mid a(x)$ und $g(x)\mid b(x)$. \index{grösster gemeinsamer Teiler}% -Ein Polynome $g(x)$ heisst grösster gemeinsamer Teiler von $a(x)$ +Ein Polynom $g(x)$ heisst {\em grösster gemeinsamer Teiler} von $a(x)$ und $b(x)$, wenn jeder andere gemeinsame Teiler $f(x)$ von $a(x)$ und $b(x)$ auch ein Teiler von $g(x)$ ist. Man beachte, dass die skalaren Vielfachen eines grössten gemeinsamen Teilers ebenfalls grösste gemeinsame Teiler sind, der grösste gemeinsame Teiler ist also nicht eindeutig bestimmt. +% +% Der euklidische Algorithmus +% \subsubsection{Der euklidische Algorithmus} +\index{Algorithmus!euklidisch}% +\index{euklidischer Algorithmus}% Zur Berechnung eines grössten gemeinsamen Teilers steht wie bei den ganzen Zahlen der euklidische Algorithmus zur Verfügung. Dazu bildet man die Folgen von Polynomen @@ -144,6 +160,9 @@ a_m(x)&=b_m(x)q_m(x).&& Der Index $m$ ist der Index, bei dem zum ersten Mal $r_m(x)=0$ ist. Dann ist $g(x)=r_{m-1}(x)$ ein grösster gemeinsamer Teiler. +% +% Der erweiterte euklidische Algorithmus +% \subsubsection{Der erweiterte euklidische Algorithmus} Die Konstruktion der Folgen $a_n(x)$ und $b_n(x)$ kann in Matrixform kompakter geschrieben werden als @@ -265,10 +284,50 @@ g(x) = c(x)a(x)+d(x)b(x) gilt. \end{satz} +% +% Faktorisierung und Nullstellen +% \subsection{Faktorisierung und Nullstellen} % wird später gebraucht um bei der Definition der hypergeometrischen Reihe % die Zaehler- und Nenner-Polynome als Pochhammer-Symbole zu entwickeln +Ist $\alpha$ eine Nullstelle des Polynoms $a(x)$, also $a(\alpha)=0$. +Der Divisionsalgorithmus mit für die Polynome $a(x)$ und $b(x)=x-\alpha$ +liefert zwei Polynome $q(x)$ für den Quotienten und $r(x)$ für den Rest +mit den Eigenschaften +\[ +a(x) += +q(x) b(x) ++r(x) += +q(x)(x-\alpha)+r(x) +\qquad\text{mit}\qquad +\deg r < \deg b(x)=1. +\] +Der Rest $r(x)$ ist somit eine Konstante. +Setzt man $x=\alpha$ ein, folgt +\[ +0 += +a(\alpha) += +q(\alpha)(\alpha-\alpha)+r(\alpha) += +r(\alpha), +\] +der Rest $r(x)$ muss also verschwinden. +Für eine Nullstelle $\alpha$ von $a(x)$ ist $a(x)$ durch $(x-\alpha)$ +teilbar. +Wenn zwei Polynome $a(x)$ und $b(x)$ eine gemeinsame Nullstelle $\alpha$ +haben, dann ist $(x-\alpha)$ ein Teiler beider Polynome und somit auch +ein Teiler eines grössten gemeinsamer Teiler. +Insbesondere sind die Nullstellen des grössten gemeinsamen Teilers +gemeinsame Nullstellen von $a(x)$ und $b(x)$. + +% +% Koeffizienten-Vergleich +% \subsection{Koeffizienten-Vergleich} % Wird gebraucht für die Potenzreihen-Methode % Muss später ausgedehnt werden auf Potenzreihen -- cgit v1.2.1 From ddf0b2a3125ce9c161c327cd61b22aba339a7c7b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 20:13:21 +0200 Subject: add missing file --- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 59737 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 203620 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a/buch/chapters/110-elliptisch/images/lemnispara.pdf and b/buch/chapters/110-elliptisch/images/lemnispara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf new file mode 100644 index 0000000..b94286a Binary files /dev/null and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From f89f84ab92053e53f4760d92ae311444bb5a7986 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 20:17:52 +0200 Subject: Reorganisation --- buch/chapters/110-elliptisch/mathpendel.tex | 38 +++++++++++++++-------------- 1 file changed, 20 insertions(+), 18 deletions(-) diff --git a/buch/chapters/110-elliptisch/mathpendel.tex b/buch/chapters/110-elliptisch/mathpendel.tex index d61bcf6..39cb418 100644 --- a/buch/chapters/110-elliptisch/mathpendel.tex +++ b/buch/chapters/110-elliptisch/mathpendel.tex @@ -94,6 +94,24 @@ Für $E>2mgl$ wird sich das Pendel im Kreis bewegen, für sehr grosse Energie ist die kinetische Energie dominant, die Verlangsamung im höchsten Punkt wird immer weniger ausgeprägt sein. +\begin{figure} +\centering +\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} +\caption{% +Abhängigkeit der elliptischen Funktionen von $u$ für +verschiedene Werte von $k^2=m$. +Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, +$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese +sind in allen Plots in einer helleren Farbe eingezeichnet. +Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig +von den trigonometrischen Funktionen ab, +es ist aber klar erkennbar, dass die anharmonischen Terme in der +Differentialgleichung die Periode mit steigender Amplitude verlängern. +Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass +die Energie des Pendels fast ausreicht, dass es den höchsten Punkt +erreichen kann, was es für $m$ macht. +\label{buch:elliptisch:fig:jacobiplots}} +\end{figure} % % Koordinatentransformation auf elliptische Funktionen % @@ -160,24 +178,6 @@ $1$ sein muss. % Der Fall E < 2mgl % \subsubsection{Der Fall $E<2mgl$} -\begin{figure} -\centering -\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} -\caption{% -Abhängigkeit der elliptischen Funktionen von $u$ für -verschiedene Werte von $k^2=m$. -Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, -$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese -sind in allen Plots in einer helleren Farbe eingezeichnet. -Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig -von den trigonometrischen Funktionen ab, -es ist aber klar erkennbar, dass die anharmonischen Terme in der -Differentialgleichung die Periode mit steigender Amplitude verlängern. -Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass -die Energie des Pendels fast ausreicht, dass es den höchsten Punkt -erreichen kann, was es für $m$ macht. -\label{buch:elliptisch:fig:jacobiplots}} -\end{figure} Wir verwenden als neue Variable @@ -234,6 +234,8 @@ Dies ist genau die Form der Differentialgleichung für die elliptische Funktion $\operatorname{sn}(u,k)$ mit $k^2 = 2gml/E< 1$. +XXX Verbindung zur Abbildung + %% %% Der Fall E > 2mgl %% -- cgit v1.2.1 From 07724dd7774994996b3dc1b2955ef9a30cb59a44 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 16 Jun 2022 21:47:35 +0200 Subject: more complete chapter 1 --- buch/chapters/010-potenzen/loesbarkeit.tex | 68 ++++++++++++++++++++++ buch/chapters/010-potenzen/polynome.tex | 93 +++++++++++++++++++++++++++++- 2 files changed, 160 insertions(+), 1 deletion(-) diff --git a/buch/chapters/010-potenzen/loesbarkeit.tex b/buch/chapters/010-potenzen/loesbarkeit.tex index 692192d..f93a84b 100644 --- a/buch/chapters/010-potenzen/loesbarkeit.tex +++ b/buch/chapters/010-potenzen/loesbarkeit.tex @@ -20,8 +20,21 @@ für ein Polynome $p(x)$ und eine Konstante $c\in\mathbb{C}$. % Fundamentalsatz der Algebra % \subsection{Fundamentalsatz der Algebra} +In Abschnitt~\ref{buch:polynome:subsection:faktorisierung-und-nullstellen} +wurde gezeigt, dass sich jede Nullstellen $\alpha$ eines Polynoms als +Faktor $x-\alpha$ abspalten lässt. +Jedes Polynom liess sich in ein Produkt von Linearfaktoren und +einen Faktor zerlegen, der keine Nullstellen hat. +Zum Beispiel hat das Polynom $x^2+1\in\mathbb{R}[x]$ keine +Nullstellen in $\mathbb{R}$. +Eine solche Nullstelle müsste eine Quadratwurzel von $-1$ sein. +Die komplexen Zahlen $\mathbb{C}$ wurden genau mit dem Ziel konstruiert, +dass $i=\sqrt{-1}$ sinnvoll wird. +Der Fundamentalsatz der Algebra zeigt, dass $\mathbb{C}$ alle +Nullstellen von Polynomen enthält. \begin{satz}[Gauss] +\index{Fundamentalsatz der Algebra}% \label{buch:potenzen:satz:fundamentalsatz} Jedes Polynom $p(x)=a_nx^n+\dots + a_2x^2 + a_1x + a_0\in\mathbb{C}[x]$ zerfällt in ein Produkt @@ -34,6 +47,7 @@ a_n für Nullstellen $\alpha_k\in\mathbb{C}$. \end{satz} + % % Lösbarkeit durch Wurzelausdrücke % @@ -148,3 +162,57 @@ Für Polynomegleichungen vom Grad $n\ge 5$ gibt es keine allgemeine Lösung durch Wurzelausdrücke. \end{satz} + + +% +% Algebraische Zahlen +% +\subsection{Algebraische Zahlen} +Die Verwendung der komplexen Zahlen ist für numerische Rechnungen +zweckmässig. +In den Anwendungen der Computer-Algebra hingegen erwartet man zum +Beispiel exakte Formeln für eine Stammfunktion. +Nicht rationale Zahlen können nur exakt verarbeitet werden, wenn +Sie sich algebraisch in endlich vielen Schritten charakterisieren +lassen. +Dies ist zum Beispiel für rationale Zahlen $\mathbb{Q}$ möglich. +Gewisse irrationale Zahlen kann man charakterisieren durch +die Eigenschaft, Nullstelle eines Polynoms $p(x)\in\mathbb{Q}[x]$ +mit rationalen Koeffizienten zu sein. + +\begin{definition} +Eine Zahl $\alpha$ heisst {\em algebraisch} über $\mathbb{Q}$, +wenn es ein Polynom +\index{algebraische Zahl}% +$p(x)\in \mathbb{Q}[x]$ gibt, welches $\alpha$ als Nullstelle hat. +Eine Zahl heisst transzendent über $\mathbb{Q}$, wenn sie nicht algebraisch ist +über $\mathbb{Q}$. +\end{definition} + +Die Zahlen $i=\sqrt{-1}$ und $\sqrt{n\mathstrut}$ für $n\in\mathbb{N}$ +sind also algebraisch über $\mathbb{Z}$. +Es ist gezeigt worden, dass $\pi$ und $e$ nicht nur irrational +sind, sondern sogar transzendent. + +Eine Polynomgleichung $p(\alpha)=0$ mit $p(x)\in\mathbb{Q}[x]$ +hat eine Rechenregel für $\alpha$ zur Folge. +Dazu schreibt man +\[ +p_n\alpha^n + p_{n-1}\alpha^{n-1} + \dots + a_1\alpha + a_0 =0 +\qquad\Rightarrow\qquad +\alpha^n = -\frac{1}{p_n}\bigl( +p_{n-1}\alpha^{n-1}+\dots+a_1\alpha+a_0 +\bigr). +\] +Diese Regel erlaubt, jede Potenz $\alpha^k$ mit $k\ge n$ durch +Potenzen von $\alpha^l$ mit $l Date: Thu, 16 Jun 2022 22:17:47 +0200 Subject: some fixes in chapter 4 --- buch/chapters/040-rekursion/beta.tex | 3 ++- buch/chapters/040-rekursion/chapter.tex | 19 +++++++++++++++++++ buch/chapters/040-rekursion/gamma.tex | 6 +++--- 3 files changed, 24 insertions(+), 4 deletions(-) diff --git a/buch/chapters/040-rekursion/beta.tex b/buch/chapters/040-rekursion/beta.tex index ff59bad..13e074f 100644 --- a/buch/chapters/040-rekursion/beta.tex +++ b/buch/chapters/040-rekursion/beta.tex @@ -13,7 +13,8 @@ Man kann Sie aber auch als Grenzfall der Beta-Funktion verstehen, die in diesem Abschnitt dargestellt wird. -\subsection{Beta-Integral} +\subsection{Beta-Integral +\label{buch:rekursion:gamma:subsection:integralbeweis}} In diesem Abschnitt wird das Beta-Integral eingeführt, eine Funktion von zwei Variablen, welches eine Integral-Definition mit einer reichaltigen Menge von Rekursionsbeziehungen hat, die sich direkt auf diff --git a/buch/chapters/040-rekursion/chapter.tex b/buch/chapters/040-rekursion/chapter.tex index 165c48e..1771200 100644 --- a/buch/chapters/040-rekursion/chapter.tex +++ b/buch/chapters/040-rekursion/chapter.tex @@ -8,6 +8,25 @@ \label{buch:chapter:rekursion}} \lhead{Spezielle Funktionen und Rekursion} \rhead{} +Die Fakultät $n!=1\cdot 2\cdots n$ ist eine ersten Funktionen, für die +man normalerweise auch eine rekursive Definition kennenlernt. +Rekursion ist eine besonders gut der numerischen Berechnung zugängliche +Art, spezielle Funktionen zu definieren. +In diesem Kapitel sollen daher in +Abschnitt~\ref{buch:rekursion:section:gamma} +zunächst die Gamma-Funktion als Verallgemeinerung konstruiert +und charakterisiert werden. +Die Beta-Funktion in +Abschnitt~\ref{buch:rekursion:gamma:section:beta} +verallgemeinert diese Rekursionsbeziehungen. +Abschnitt~\ref{buch:rekursion:section:linear} +erinnert an die Methoden, mit denen lineare Rekursionsgleichungen +gelöst werden können. +Erfüllten die Koeffizienten einer Potenzreihe eine spezielle +Rekursionsbeziehung, entsteht die besonders vielfältige Familie +der hypergeometrischen Funktionen, die in +Abschnitt~\ref{buch:rekursion:section:hypergeometrische-funktion} +eingeführt werden. \input{chapters/040-rekursion/gamma.tex} \input{chapters/040-rekursion/beta.tex} diff --git a/buch/chapters/040-rekursion/gamma.tex b/buch/chapters/040-rekursion/gamma.tex index 7d4453b..8c02752 100644 --- a/buch/chapters/040-rekursion/gamma.tex +++ b/buch/chapters/040-rekursion/gamma.tex @@ -480,8 +480,8 @@ ganzzahlige Argumente übereinstimmen. Der folgende Abschnitt macht deutlich, dass es sehr viele Funktionen gibt, die ebenfalls die Funktionalgleichung erfüllen. Eine vollständige Rechtfertigung für diese Definition wird später -in Abschnitt~\ref{buch:rekursion:gamma:subsection:beta} -\eqref{buch:rekursion:gamma:integralbeweis} +in Abschnitt~\ref{buch:rekursion:gamma:subsection:integralbeweis} +in Formel~\eqref{buch:rekursion:gamma:integralbeweis} auf Seite~\pageref{buch:rekursion:gamma:integralbeweis} gegeben. @@ -511,7 +511,7 @@ der Gamma-Funktion und berechnen \int_{-\infty}^\infty e^{-s^2}\,ds = \sqrt{\pi}. -\label{buch:rekursion:gamma:betagamma} +\label{buch:rekursion:gamma:wert12} \end{align} Der Integrand im letzten Integral ist die Wahrscheinlichkeitsdichte einer Normalverteilung, deren Integral wohlbekannt ist. -- cgit v1.2.1 From dcd6d6037a84343f19333fe86a904bdc0bb8a36f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 17 Jun 2022 11:20:00 +0200 Subject: new section, cleanup --- buch/chapters/010-potenzen/Makefile.inc | 1 + buch/chapters/010-potenzen/chapter.tex | 1 + buch/chapters/010-potenzen/rational.tex | 60 ++++++++ buch/chapters/030-geometrie/chapter.tex | 1 + buch/chapters/040-rekursion/hypergeometrisch.tex | 170 +++++++++++++++++++-- .../chapters/050-differential/hypergeometrisch.tex | 5 +- 6 files changed, 220 insertions(+), 18 deletions(-) create mode 100644 buch/chapters/010-potenzen/rational.tex diff --git a/buch/chapters/010-potenzen/Makefile.inc b/buch/chapters/010-potenzen/Makefile.inc index 27ccdae..87afe38 100644 --- a/buch/chapters/010-potenzen/Makefile.inc +++ b/buch/chapters/010-potenzen/Makefile.inc @@ -8,6 +8,7 @@ CHAPTERFILES += \ chapters/010-potenzen/loesbarkeit.tex \ chapters/010-potenzen/polynome.tex \ chapters/010-potenzen/tschebyscheff.tex \ + chapters/010-potenzen/rational.tex \ chapters/010-potenzen/potenzreihen.tex \ chapters/010-potenzen/uebungsaufgaben/101.tex \ chapters/010-potenzen/uebungsaufgaben/102.tex \ diff --git a/buch/chapters/010-potenzen/chapter.tex b/buch/chapters/010-potenzen/chapter.tex index 7dc30d4..2628e33 100644 --- a/buch/chapters/010-potenzen/chapter.tex +++ b/buch/chapters/010-potenzen/chapter.tex @@ -40,6 +40,7 @@ Abschnitt~\ref{buch:potenzen:section:potenzreihen} erinnert. \input{chapters/010-potenzen/polynome.tex} \input{chapters/010-potenzen/loesbarkeit.tex} \input{chapters/010-potenzen/tschebyscheff.tex} +\input{chapters/010-potenzen/rational.tex} \input{chapters/010-potenzen/potenzreihen.tex} \section*{Übungsaufgaben} diff --git a/buch/chapters/010-potenzen/rational.tex b/buch/chapters/010-potenzen/rational.tex new file mode 100644 index 0000000..a5612e9 --- /dev/null +++ b/buch/chapters/010-potenzen/rational.tex @@ -0,0 +1,60 @@ +% +% rational.tex +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\section{Rationale Funktionen +\label{buch:polynome:section:rationale-funktionen}} +\rhead{Rationale Funktionen} +Polynome sind sehr einfach auszuwerten und können auf einem +Interval jede stetige Funktion beliebig gut approximieren. +Auf einem unbeschränkten Definitionsbereich wachsen Polynome aber +immer unbeschränkt an. +Der führende Term $a_nx^n$ dominiert das Verhalten eines Polynoms +für $x\to\infty$ wegen +\[ +\lim_{x\to\infty} a_nx^n += +\sign a_n \cdot\infty +\qquad\text{und}\qquad +\lim_{x\to-\infty} a_nx^n += +(-1)^n \sign a_n\cdot \infty. +\] +Insbesondere kann man nicht erwarten, dass sich eine beschränkte +Funktion wie $\sin x$ durch Polynome auf dem ganzen Definitionsbereich +gut approximieren lässt. +Der Unterschied $p(x)-\sin x$ wird für jedes beliebige Polynome $p(x)$ +für $x\to\pm\infty$ unbeschränkt anwachsen. + +Eine weitere Einschränkung ist, dass die Menge der Polynome bezüglich +der arithmetischen Operationen nicht abgeschlossen ist. +Man kann zwar Polynome addieren und multiplizieren, aber der Quotient +ist nicht notwendigerweise ein Polynome. +Abhilfe schafft nur, wenn man Quotienten von Polynomen zulässt. + +\begin{definition} +Eine Funktion $f(x)$ heisst {\em rationale Funktion}, wenn sie Quotient +\index{rationale Funktion}% +zweier Polynome ist, wenn es also Polynome $p(x), q(x)\in K[x]$ gibt mit +\[ +f(x) = \frac{p(x)}{q(x)}. +\] +Die Menge der rationalen Funktione mit Koeffizienten in $K$ wird mit +$K(x)$ bezeichnet. +\end{definition} + +Polynome sind rationale Funktionen, deren Nennergrad $1$ ist. +Rationale Funktionen können ebenfalls zur Approximation von Funktionen +verwendet werden. +Da sie beschränkt sein können, haben sie das Potential, +beschränkte Funktionen besser zu approximieren, als dies mit +Polynomen allein möglich wäre. +Die Theorie der Padé-Approximation, wie sie zum Beispiel im Buch +\cite{buch:pade} dargestellt ist, ist zum Beispiel auch in der +Regelungstechnik von Interesse, da sich rationale Funktionen mit +linearen Komponenten schaltungstechnisch realisieren lassen. +Weitere Anwendungen werden in Kapitel~\ref{chapter:transfer} +gezeigt. + + diff --git a/buch/chapters/030-geometrie/chapter.tex b/buch/chapters/030-geometrie/chapter.tex index 0b2842b..24fc089 100644 --- a/buch/chapters/030-geometrie/chapter.tex +++ b/buch/chapters/030-geometrie/chapter.tex @@ -32,6 +32,7 @@ der Strahlensatz muss durch den Satz von Menelaos ersetzt werden. Es ergibt sich eine Methode, beliebige Dreiecke auf einer Kugeloberfläche ganz analog zum Vorgehen bei ebenen Dreiecken zu berechnen. Diese sphärische Trigonometrie ist die Basis der Navigation +(siehe Kapitel~\ref{chapter:nav}) und aller astrometrischer Berechnungen. Die Analysis hat die Möglichkeit geschaffen, die Länge von Kurven diff --git a/buch/chapters/040-rekursion/hypergeometrisch.tex b/buch/chapters/040-rekursion/hypergeometrisch.tex index d92e594..39efc6b 100644 --- a/buch/chapters/040-rekursion/hypergeometrisch.tex +++ b/buch/chapters/040-rekursion/hypergeometrisch.tex @@ -16,22 +16,38 @@ n^3S_{n} mit Anfangswerten $S_0=1$ und $S_1=8$ angeben? Dies scheint auf den ersten Blick unmöglich kompliziert, man kann aber zeigen, dass -\[ +\begin{equation} S_n = \sum_{k=0}^n \binom{2n-2k}{n-k}^2 \binom{2k}{k}^2 -\] +\label{buch:rekursion:hypergeometrisch:eqn:Sn} +\end{equation} gilt (\cite[p.~xi]{buch:ab}). Die Lösung ist also eine Summe von Summanden, die sehr viel einfacher aussehen und vor allem die besondere Eigenschaft haben, dass die -Quotienten aufeinanderfolgender Terme rationale Funktionen von von $k$ +Quotienten aufeinanderfolgender Terme rationale Funktionen von $k$ sind. -% XXX Quotient berechnen -Eine besonders simple solche Funktion ist die geometrische Reihe, die -im Abschnitt~\ref{buch:rekursion:hypergeometrisch:geometrisch} -in Erinnerung gerufen wird. +\begin{definition} +Ein Folge heisst {\em hypergeometrisch}, wenn der Quotient aufeinanderfolgender +\index{hypergeometrische Folge}% +\index{Folge, hypergeometrisch}% +Terme eine rationale Funktion des Folgenindex ist. +\end{definition} + +Die Terme der Reihenentwicklungen aller bisher behandelten speziellen +Funktionen waren hypergeometrisch. +Im aktuellen Abschnitt soll daher die Klasse der sogenannten +hypergeometrischen Funktionen untersucht werden, die durch diese +Eigenschaft charakterisiert sind. + +In Abschnitt~\ref{buch:rekursion:hypergeometrisch:binomialkoeffizienten} +wird klar, dass Folgen, deren Terme aus Fakultäten und Binomialkoeffizienten +immer hypergeometrisch sind. +Die Untersuchung der geometrischen Reihe in +Abschnitt~\ref{buch:rekursion:hypergeometrisch:geometrisch} +motiviert die Namensgebung. Abschnitt~\ref{buch:rekursion:hypergeometrisch:reihen} definiert den Begriff der hypergeometrischen Reihe und zeigt, wie sie in eine Standardform gebracht werden können. @@ -39,22 +55,99 @@ In Abschnitt~\ref{buch:rekursion:hypergeometrisch:beispiele} schliesslich wird an Hand von Beispielen gezeigt, wie bekannte Funktionen als hypergeometrische Funktionen interpretiert werden können. +% +% Quotienten von Binomialkoeffizienten +% +\subsection{Quotienten von Binomialkoeffizienten +\label{buch:rekursion:hypergeometrisch:binomialkoeffizienten}} +Aufeinanderfolgende Terme der Summe +\eqref{buch:rekursion:hypergeometrisch:eqn:Sn} +sollen als Quotienten eine rationale Funktion haben. +Dies ist eine allgemeine Eigenschaft von Folgen, die durch Fakultäten +oder Binomialkoeffizienten definiert sind, wie die beiden folgenden +Sätze zeigen. + +\begin{satz} +\label{buch:rekursion:hypergeometrisch:satz:fakquo} +Der Quotient aufeinanderfolgender Folgenglieder +der Folge $c_k=(a+bk)!$ ist der ein Polynom vom Grad $b$. +\end{satz} +\begin{proof}[Beweis] +\begin{align*} +\frac{c_{k+1}}{c_k} +&= +\frac{(a+b(k+1))!}{(a+bk)!} += +\frac{(a+bk+b)!}{(a+b)!} +\\ +&= +(a+bk+1)(a+bk+2)\cdots(a+bk+b) += +(a+bk+1)_b +\end{align*} +Das Pochhammer-Symbol hat $b$ Faktoren, es ist ein Polynom vom Grad $b$. +\end{proof} + +\begin{satz} +\label{buch:rekursion:hypergeometrisch:satz:binomquo} +Die Quotienten aufeinanderfolgender Werte der Binomialkoeffizienten +\[ +f_k += +\binom{a+bk}{c+dk} +\] +ist eine rationale Funktion von $k$ mit Zähler- und Nennergrad $b$. +\end{satz} + +\begin{proof}[Beweis] +Indem man die Binomialkoeffizienten mit Fakultäten als +\[ +\binom{a+bk}{c+dk} += +\frac{(a+bk)!}{(c+dk)!(a-c+(b-d)k)!} +\] +ausschreibt, findet man mit +Satz~\ref{buch:rekursion:hypergeometrisch:satz:fakquo} +für die Quotienten +\begin{align} +\frac{f_{k+1}}{f_k} +&= +\frac{(a+bk+1)_b}{(c+dk+1)_d\cdot(a-c+(b-d)k+1)_{b-d}} +\label{buch:rekursion:eqn:binomquotient} +\end{align} +Die Pochhammer-Symbole sind Polynome vom Grad $b$, $d$ bzw.~$b-d$. +Insbesondere ist auch das Nenner-Polynom vom Grad $d+(b-d)=b$. +\end{proof} + +Aus den Sätzen~\ref{buch:rekursion:hypergeometrisch:satz:fakquo} +und +\ref{buch:rekursion:hypergeometrisch:satz:binomquo} +folgt jetzt sofort, dass auch der Quotient aufeinanderfolgender +Summanden der Summe~\eqref{buch:rekursion:hypergeometrisch:eqn:Sn} +eine rationale Funktion von $k$ ist. + +% +% Die geometrische Reihe +% \subsection{Die geometrische Reihe \label{buch:rekursion:hypergeometrisch:geometrisch}} -Die besonders einfache Potenzreihe +Die Reihe \[ f(q) = \sum_{k=0}^\infty aq^k \] -heisst die {\em geometrische Reihe}. +heisst die {\em geometrische Reihe} ist besonders einfache +Reihe mit einer hypergeometrischen Folge von Termen. +\index{geometrische Reihe}% +\index{Reihe!geometrische}% Die Partialsummen \[ S_n = \sum_{k=0}^n aq^k \] -kann mit der Differenz +können aus der Differenz \begin{equation} (1-q)S_n = @@ -75,8 +168,7 @@ a\frac{1-q^{n+1}}{1-q} \label{buch:rekursion:hypergeometrisch:eqn:geomsumme} \end{equation} auflösen kann. - -Fü $q<1$ geht $q^n\to 0$ und damit konvergiert +Für $q<1$ geht $q^n\to 0$ und damit konvergiert $S_n$ gegen \[ \sum_{k=0}^\infty aq^k @@ -97,6 +189,9 @@ Die Berechnung der Summe in beruht darauf, dass die Multiplikation mit $q$ einen ``anderen'' Teil der Summe ergibt, der sich in der Differenze weghebt. +% +% Hypergeometrische Reihen +% \subsection{Hypergeometrische Reihen \label{buch:rekursion:hypergeometrisch:reihen}} Es ist plausibel, dass eine etwas lockerere Bedingung an die @@ -105,11 +200,14 @@ ermöglichen wird, interessante Aussagen über die durch die Reihe beschriebenen Funktionen zu machen. \begin{definition} -Eine Reihe +Eine durch die Reihe \[ f(x) = \sum_{k=0}^\infty a_k x^k \] -heisst {\em hypergeometrisch}, wenn der Quotient aufeinanderfolgender +definierte Funktion $f(x)$ heisst {\em hypergeometrisch}, +wenn der Quotient aufeinanderfolgender +\index{hypergeometrisch} +\index{Reihe!hypergeometrisch} Koeffizienten eine rationale Funktion von $k$ ist, wenn also \[ @@ -485,6 +583,7 @@ x\cdot \subsubsection{Trigonometrische Funktionen} +\index{trigonometrische Funktionen!als hypergeometrische Funktionen}% Die Kosinus-Funktion wurde bereits als hypergeometrische Funktion erkannt, im Folgenden soll dies auch noch für die Sinus-Funktion durchgeführt werden. @@ -586,6 +685,7 @@ x\cdot\mathstrut_0F_1\biggl( durch eine hypergeometrische Funktion ausdrücken. \subsubsection{Hyperbolische Funktionen} +\index{hyperbolische Funktionen!als hypergeometrische Funktionen}% Die für die Sinus-Funktion angewendete Methode lässt sich auch auf die Funktion \begin{align*} @@ -619,9 +719,47 @@ Dies illustriert die Rolle der hypergeometrischen Funktionen als ``grosse Vereinheitlichung'' der bekannten speziellen Funktionen. \subsubsection{Tschebyscheff-Polynome} +\index{Tschebyscheff-Polynome}% +Man kann zeigen, dass auch die Tschebyscheff-Polynome sich durch die +hypergeometrischen Funktionen +\begin{equation} +T_n(x) += +\mathstrut_2F_1\biggl( +\begin{matrix}-n,n\\\frac12\end{matrix} +; +\frac12(1-x) +\biggr) +\label{buch:rekursion:hypergeometrisch:tschebyscheff2f1} +\end{equation} +ausdrücken lassen. +Beweisen kann man diese Beziehung zum Beispiel mit Hilfe der +Differentialgleichungen, denen die Funktionen genügen. +Diese Methode wird in +Abschnitt~\ref{buch:differentialgleichungen:section:hypergeometrisch} +von Kapitel~\ref{buch:chapter:differential} vorgestellt. -TODO -\url{https://en.wikipedia.org/wiki/Chebyshev_polynomials} +Die Tschebyscheff-Polynome sind nicht die einzigen Familien von Polynomen, +\index{Tschebyscheff-Polynome!als hypergeometrische Funktion} +die sich durch $\mathstrut_pF_q$ ausdrücken lassen. +Für die zahlreichen Familien von orthogonalen Polynomen, die in +Kapitel~\ref{buch:chapter:orthogonalitaet} untersucht werden, +trifft dies auch zu. +Ein Funktion +\[ +\mathstrut_pF_q +\biggl( +\begin{matrix} +a_1,\dots,a_p\\ +b_1,\dots,b_q +\end{matrix} +;z +\biggr) +\] +ist genau dann ein Polynom, wenn mindestens einer der Parameter +$a_k$ eine negative ganze Zahl ist. +Der Grad des Polynoms ist der kleinste Betrag der negativ ganzzahligen +Werte unter den Parametern $a_k$. % % Ableitung und Stammfunktion diff --git a/buch/chapters/050-differential/hypergeometrisch.tex b/buch/chapters/050-differential/hypergeometrisch.tex index e187b68..65b3be7 100644 --- a/buch/chapters/050-differential/hypergeometrisch.tex +++ b/buch/chapters/050-differential/hypergeometrisch.tex @@ -1757,6 +1757,7 @@ T_n(x) \biggr). \end{equation} Auch die Tschebyscheff-Polynome lassen sich also mit Hilfe einer -hypergeometrischen Funktion schreiben. +hypergeometrischen Funktion schreiben, wie schon in +\eqref{buch:rekursion:hypergeometrisch:tschebyscheff2f1} +bemerkt wurde. -%\url{https://en.wikipedia.org/wiki/Chebyshev_polynomials} -- cgit v1.2.1 From 0a24e24dc7b997d054be086aa2c021decf0a01f5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 17 Jun 2022 20:09:36 +0200 Subject: info on rational functions --- buch/chapters/010-potenzen/rational.tex | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/buch/chapters/010-potenzen/rational.tex b/buch/chapters/010-potenzen/rational.tex index a5612e9..f1957ac 100644 --- a/buch/chapters/010-potenzen/rational.tex +++ b/buch/chapters/010-potenzen/rational.tex @@ -15,11 +15,11 @@ für $x\to\infty$ wegen \[ \lim_{x\to\infty} a_nx^n = -\sign a_n \cdot\infty +\operatorname{sgn} a_n \cdot\infty \qquad\text{und}\qquad \lim_{x\to-\infty} a_nx^n = -(-1)^n \sign a_n\cdot \infty. +(-1)^n \operatorname{sgn} a_n\cdot \infty. \] Insbesondere kann man nicht erwarten, dass sich eine beschränkte Funktion wie $\sin x$ durch Polynome auf dem ganzen Definitionsbereich @@ -30,7 +30,7 @@ für $x\to\pm\infty$ unbeschränkt anwachsen. Eine weitere Einschränkung ist, dass die Menge der Polynome bezüglich der arithmetischen Operationen nicht abgeschlossen ist. Man kann zwar Polynome addieren und multiplizieren, aber der Quotient -ist nicht notwendigerweise ein Polynome. +ist nicht notwendigerweise ein Polynom. Abhilfe schafft nur, wenn man Quotienten von Polynomen zulässt. \begin{definition} @@ -51,6 +51,7 @@ Da sie beschränkt sein können, haben sie das Potential, beschränkte Funktionen besser zu approximieren, als dies mit Polynomen allein möglich wäre. Die Theorie der Padé-Approximation, wie sie zum Beispiel im Buch +\index{Pade-Approximation@Padé-Approximation}% \cite{buch:pade} dargestellt ist, ist zum Beispiel auch in der Regelungstechnik von Interesse, da sich rationale Funktionen mit linearen Komponenten schaltungstechnisch realisieren lassen. -- cgit v1.2.1 From 6893688fccb63844102d8f1d728302d4eb823d68 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 18 Jun 2022 11:01:07 +0200 Subject: add new graphs --- buch/chapters/030-geometrie/trigonometrisch.tex | 12 +- buch/chapters/040-rekursion/gamma.tex | 130 +++++++++++++++++---- buch/chapters/040-rekursion/gammalimit/Makefile | 11 ++ buch/chapters/040-rekursion/gammalimit/l.cpp | 26 +++++ buch/chapters/040-rekursion/gammalimit/l.m | 19 +++ buch/chapters/040-rekursion/images/Makefile | 6 +- buch/chapters/040-rekursion/images/loggammaplot.m | 43 +++++++ .../chapters/040-rekursion/images/loggammaplot.pdf | Bin 0 -> 30948 bytes .../chapters/040-rekursion/images/loggammaplot.tex | 89 ++++++++++++++ 9 files changed, 309 insertions(+), 27 deletions(-) create mode 100644 buch/chapters/040-rekursion/gammalimit/Makefile create mode 100644 buch/chapters/040-rekursion/gammalimit/l.cpp create mode 100644 buch/chapters/040-rekursion/gammalimit/l.m create mode 100644 buch/chapters/040-rekursion/images/loggammaplot.m create mode 100644 buch/chapters/040-rekursion/images/loggammaplot.pdf create mode 100644 buch/chapters/040-rekursion/images/loggammaplot.tex diff --git a/buch/chapters/030-geometrie/trigonometrisch.tex b/buch/chapters/030-geometrie/trigonometrisch.tex index dc1f46a..047e6cb 100644 --- a/buch/chapters/030-geometrie/trigonometrisch.tex +++ b/buch/chapters/030-geometrie/trigonometrisch.tex @@ -167,11 +167,11 @@ und umgekehrt: \[ \sin\alpha = -\sqrt{1-\cos^2\alpha\mathstrut} +\sqrt{1-{\cos\mathstrut\!}^2\,\alpha\mathstrut} \qquad\text{und}\qquad \cos\alpha = -\sqrt{1-\sin^2\alpha\mathstrut} +\sqrt{1-{\sin\mathstrut\!}^2\,\alpha\mathstrut} \] Da sich alle Funktionen durch $\cos\alpha$ und $\sin\alpha$ ausdrücken lassen, können alle auch nur durch eine ausgedrückt werden. @@ -197,7 +197,7 @@ Tabelle~\ref{buch:geometrie:tab:trigo} zusammengestellt ist. &\displaystyle\frac{\sqrt{\csc^2\alpha-1}}{\csc\alpha} \\ \cos\alpha - &\sqrt{1-\sin^2\alpha\mathstrut} + &\sqrt{1-\sin{\!}^2\,\alpha\mathstrut} &\cos\alpha &\displaystyle\frac{1}{\sqrt{1+\tan^2\alpha}} &\displaystyle\frac{\cot\alpha}{\sqrt{1+\cot^2\alpha}} @@ -205,7 +205,7 @@ Tabelle~\ref{buch:geometrie:tab:trigo} zusammengestellt ist. &\displaystyle\frac{1}{\csc\alpha} \\ \tan\alpha - &\displaystyle\frac{\sin\alpha}{\sqrt{1-\sin^2\alpha\mathstrut}} + &\displaystyle\frac{\sin\alpha}{\sqrt{1-\sin{\!}^2\,\alpha\mathstrut}} &\displaystyle\frac{\sqrt{1-\cos^2\alpha\mathstrut}}{\cos\alpha} &\tan\alpha &\displaystyle\frac{1}{\cot\alpha} @@ -213,7 +213,7 @@ Tabelle~\ref{buch:geometrie:tab:trigo} zusammengestellt ist. &\displaystyle\sqrt{\csc^2\alpha-1} \\ \cot\alpha - &\displaystyle\frac{\sqrt{1-\sin^2\alpha\mathstrut}}{\sin\alpha} + &\displaystyle\frac{\sqrt{1-\sin{\!}^2\,\alpha\mathstrut}}{\sin\alpha} &\displaystyle\frac{\cos\alpha}{\sqrt{1-\cos^2\alpha\mathstrut}} &\displaystyle\frac{1}{\tan\alpha} &\cot\alpha @@ -229,7 +229,7 @@ Tabelle~\ref{buch:geometrie:tab:trigo} zusammengestellt ist. &\displaystyle\frac{\csc\alpha}{\sqrt{\csc^2\alpha-1}} \\ \csc\alpha - &\displaystyle\frac{1}{\sqrt{1-\sin^2\alpha\mathstrut}} + &\displaystyle\frac{1}{\sqrt{1-\sin{\!}^2\,\alpha\mathstrut}} &\displaystyle\frac{1}{\cos\alpha} &\displaystyle\sqrt{1+\tan^2\alpha} &\displaystyle\frac{\sqrt{1+\cot^2\alpha}}{\cot\alpha} diff --git a/buch/chapters/040-rekursion/gamma.tex b/buch/chapters/040-rekursion/gamma.tex index 8c02752..e4dfa9a 100644 --- a/buch/chapters/040-rekursion/gamma.tex +++ b/buch/chapters/040-rekursion/gamma.tex @@ -203,7 +203,41 @@ x\lim_{n\to\infty} Weil $n/(n+1)\to 1$ ist und die Funktion $z\mapsto z^{x-1}$ für alle nach der Definition zulässigen Werte von $x$ eine stetige Funktion ist. +% +% +% \subsubsection{Numerische Unzulänglichkeiten der Grenzwertdefinition} +\begin{table} +\centering +%\renewcommand{\arraystretch}{1.1} +\begin{tabular}{|>{$}c<{$}|>{$}r<{$}|>{$}l<{$}|>{$}l<{$}|} +\hline +\log_{10} n& n&n!n^{x-1}/(x)_n\mathstrut & \text{Fehler% +\vrule height12pt depth6pt width0pt} \\ +\hline +\text{\vrule height12pt depth0pt width0pt} + 1& 10&1.\underline{7}947392559855804&0.0222854050800643\\ + 2& 100&1.\underline{77}46707942830697&0.0022169433775536\\ + 3& 1000&1.\underline{772}6754214755178&0.0002215705700017\\ + 4& 10000&1.\underline{7724}760067171375&0.0000221558116213\\ + 5& 100000&1.\underline{77245}60664742375&0.0000022155687214\\ + 6& 1000000&1.\underline{77245}40724623101&0.0000002215567940\\ + 7& 10000000&1.\underline{7724538}730613721&0.0000000221558560\\ + 8& 100000000&1.\underline{77245385}31233258&0.0000000022178097\\ + 9& 1000000000&1.\underline{77245385}11320680&0.0000000002265519\\ + 10& 10000000000&1.\underline{772453850}9261316&0.0000000000206155\\ + 11&100000000000&1.\underline{77245385}14549788&0.0000000005494627\\ + & \infty&1.\underline{7724538509055161}& +\text{\vrule height12pt depth6pt width0pt} \\ +\hline +\end{tabular} +\caption{Numerische Berechnung mit der Grenzwertdefinition +und rekursiver Berechnung von $n!/(x)_n$ mit Hilfe der Folge +\eqref{buch:rekursion:gamma:pnfolge}. +Die Konvergenz ist sehr langsam, die Anzahl korrekter Stellen +wächst logarithmisch mit $n$. +\label{buch:rekursion:gamma:produktberechnung}} +\end{table} Die Grenzwertdefinition~\ref{buch:rekursion:gamma:def:definition} ist zwar zweifellos richtig, kann aber nicht für die numerische Berechnung der Gamma-Funktion verwendet werden. @@ -237,6 +271,24 @@ ist. Die Approximation mit Hilfe der Grenzwertdefinition kann also grundsätzlich nicht mehr als zwei korrekte Nachkommastellen liefern. +Den Quotienten $n!/(x)_n$ kann man mit Hilfe der Rekursionsformel +\begin{equation} +p_n = p_{n-1}\cdot \frac{n}{x+n-1},\qquad +p_0 = 0 +\label{buch:rekursion:gamma:pnfolge} +\end{equation} +etwas effizienter berechnen. +Insbesondere umgeht man damit das Problem, dass $n!$ den Wertebereich +des \texttt{double} Datentyps sprengt. +Der Wert der Gamma-Funktion kann dann durch $p_nn^{x-1}$ approximiert +werden. +Die Tabelle~\ref{buch:rekursion:gamma:produktberechnung} fasst die +Resultate zusammen und zeigt, dass die Konvergenz logarithmisch ist: +die Anzahl korrekter Nachkommastellen ist $\log_{10}n$. + +% +% Produktformel +% \subsection{Produktformel} Ein möglicher Ausweg aus den numerischen Schwierigkeiten mit der Grenzwertdefinition ist, den schnell wachsenden Faktor $n!$ @@ -253,8 +305,10 @@ xe^{\gamma x} \prod_{k=1}^\infty \biggl(1+\frac{x}k\biggr)\,e^{-\frac{x}{k}}, \label{buch:rekursion:gamma:eqn:produktformel} +\index{Gamma-Funktion!Produktformel}% \end{equation} wobei $\gamma$ die Euler-Mascheronische Konstante +\index{Euler-Mascheronische Konstante}% \[ \gamma = @@ -368,16 +422,20 @@ vollständig bewiesen. \begin{table} \centering -\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\begin{tabular}{|>{$}c<{$}|>{$}r<{$}|>{$}c<{$}|>{$}c<{$}|} \hline -k & \Gamma(\frac12,n) & \Gamma(\frac12) - \Gamma(\frac12,n) \\ +k & n & \Gamma(\frac12,n) & \Gamma(\frac12) - \Gamma(\frac12,n)% +\text{\vrule height12pt depth6pt width0pt} \\ \hline -1 & 1.\underline{7}518166478 & -0.0206372031 \\ -2 & 1.\underline{77}02543372 & -0.0021995137 \\ -3 & 1.\underline{772}2324556 & -0.0002213953 \\ -4 & 1.\underline{7724}316968 & -0.0000221541 \\ -5 & 1.\underline{77245}16354 & -0.0000022156 \\ -6 & 1.\underline{772453}6293 & -0.0000002216 \\ +\text{\vrule height12pt depth0pt width0pt} + 1& 10& 1.\underline{7}518166478& -0.0206372031 \\ + 2& 100& 1.\underline{77}02543372& -0.0021995137 \\ + 3& 1000& 1.\underline{772}2324556& -0.0002213953 \\ + 4& 10000& 1.\underline{7724}316968& -0.0000221541 \\ + 5& 100000& 1.\underline{77245}16354& -0.0000022156 \\ + 6&1000000& 1.\underline{772453}6293& -0.0000002216 \\ +\infty& & 1.\underline{7724538509}& +\text{\vrule height12pt depth6pt width0pt} \\ \hline \end{tabular} \caption{Werte $\Gamma(\frac12,n)$ von $\Gamma(\frac12)$ berechnet mit @@ -385,6 +443,9 @@ $n=10^k$ Faktoren der Produktformel~\eqref{buch:rekursion:gamma:eqn:produktformel} und der zugehörige Fehler. Die korrekten Nachkommastellen sind unterstrichen. +Die Konvergenz ist genau gleich langsam wie in der Berechnung mit +Hilfe der Grenzwert-Definition in +Tabelle~\ref{buch:rekursion:gamma:produktberechnung}. \label{buch:rekursion:gamma:gammatabelle}} \end{table} @@ -436,6 +497,9 @@ die richtigen Werte für natürliche Argumente hat, es wird aber auch gezeigt, dass dies nicht ausreicht um zu schliessen, dass die Integralformel mit der früher definierten Gamma-Funktion übereinstimmt. +% +% Funktionalgleichung für die Integraldefinition +% \subsubsection{Funktionalgleichung für die Integraldefinition} Tatsächlich ist es einfach nachzuprüfen, dass die Funktionalgleichung der Gamma-Funktion auch für die Definition~\ref{buch:rekursion:def:gamma} @@ -494,6 +558,9 @@ die Werte der Fakultät annimmt. \label{buch:rekursion:fig:gamma}} \end{figure} +% +% Der Wert Gamma(1/2) +% \subsubsection{Der Wert $\Gamma(\frac12)$} Die Integraldarstellung kann dazu verwendet werden, $\Gamma(\frac12)$ zu berechnen. @@ -516,7 +583,11 @@ der Gamma-Funktion und berechnen Der Integrand im letzten Integral ist die Wahrscheinlichkeitsdichte einer Normalverteilung, deren Integral wohlbekannt ist. -\subsubsection{Alternative Lösungen} +% +% Alternative Lösungen +% +\subsubsection{Alternative Lösungen der +Funktionalgleichung~\ref{buch:rekursion:eqn:gammadef}} Die Funktion $\Gamma(z)$ ist nicht die einzige Funktion, die natürlichen Zahlen die Werte $\Gamma(n+1) = n!$ der Fakultät annimmt. Indem man eine beliebige Funktion $f(z)$ addiert, die auf alle @@ -560,6 +631,9 @@ Dann ist $ f(z) = \Gamma(z) $. % XXX Gamma in the interval (1,2) %Man beachte, dass +% +% Laplace-Transformierte der Potenzfunktion +% \subsubsection{Laplace-Transformierte der Potenzfunktion} Die Integraldarstellung der Gamma-Funktion erlaubt jetzt auch, die Laplace-Transformation der Potenzfunktion zu berechnen. @@ -594,6 +668,9 @@ Durch die Substitution $st = u$ oder $t=\frac{u}{s}$ wird daraus \] \end{proof} +% +% Pol erster Ordnung bei z=0 +% \subsubsection{Pol erster Ordnung bei $z=0$} Wir haben zu prüfen, dass sowohl der Wert $\Gamma(1)$ korrekt ist als auch die Rekursionsformel~\eqref{buch:rekursion:eqn:gammadef} gilt. @@ -644,6 +721,9 @@ Daraus ergibt sich für $\Gamma(z)$ der Ausdruck \] Die Gamma-Funktion hat daher an der Stelle $z=0$ einen Pol erster Ordnung. +% +% Ausdehnung auf Re(z) < 0 +% \subsubsection{Ausdehnung auf $\operatorname{Re}z<0$} Die Integralformel konvergiert nicht für $\operatorname{Re}z\le 0$. Durch analytische Fortsetzung, wie sie im @@ -683,22 +763,29 @@ Somit hat $\Gamma(z)$ Pole erster Ordnung bei den negativen ganzen Zahlen und bei $0$, wie sie in Abbildung~\ref{buch:rekursion:fig:gamma} gezeigt werden. +% +% Numerische Berechnung +% \subsubsection{Numerische Berechnung} \begin{table} \centering -\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}|} +\begin{tabular}{|>{$}c<{$}|>{$}r<{$}|>{$}c<{$}>{$}c<{$}|} \hline -k & y(10^k) & y(10^k) - \Gamma(\frac{5}{2}) \\ +k & n=10^k & y(n) & y(n) - \Gamma(\frac{5}{3})  +\text{\vrule height12pt depth6pt width0pt} \\ \hline -1 & 0.0000000000 & -0.9027452930 \\ -2 & 0.3319129461 & -0.5708323468 \\ -3 & 0.\underline{902}5209490 & -0.0002243440 \\ -4 & 0.\underline{902745}1207 & -0.0000001723 \\ -5 & 0.\underline{902745}0962 & -0.0000001968 \\ -6 & 0.\underline{902745}0962 & -0.0000001968 \\ +\text{\vrule height12pt depth0pt width0pt} +1 & 10 & 0.0000000000 & -0.9027452930 \\ +2 & 100 & 0.3319129461 & -0.5708323468 \\ +3 & 1000 & 0.\underline{902}5209490 & -0.0002243440 \\ +4 & 10000 & 0.\underline{902745}1207 & -0.0000001723 \\ +5 & 100000 & 0.\underline{902745}0962 & -0.0000001968 \\ +6 & 1000000 & 0.\underline{902745}0962 & -0.0000001968 \\ + & \infty & 0.\underline{9027452929} & +\text{\vrule height12pt depth6pt width0pt} \\ \hline \end{tabular} -\caption{Resultate der Berechnung von $\Gamma(\frac{5}{2})$ mit Hilfe +\caption{Resultate der Berechnung von $\Gamma(\frac{5}{3})$ mit Hilfe der Differentialgleichung \eqref{buch:rekursion:gamma:eqn:gammadgl}. Die korrekten Stellen sind unterstrichen. Es sind immerhin sechs korrekte Stellen gefunden, wobei nur 337 @@ -708,7 +795,7 @@ Auswertungen des Integranden notwendig waren. Im Prinzip könnte die Integraldefinition der numerischen Berechnung entgegenkommen. Um diese Hypothese zu prüfen, berechnen wir das Integral für -$z=\frac52$ mit Hilfe der äquivalenten Differentialgleichungen +$z=\frac53$ mit Hilfe der äquivalenten Differentialgleichungen \begin{equation} \dot{y}(t) = t^{z-1}e^{-t} \qquad\text{mit Anfangsbedingung $y(0)=0$}. @@ -717,10 +804,13 @@ $z=\frac52$ mit Hilfe der äquivalenten Differentialgleichungen Der gesuchte Wert ist der Grenzwert $\lim_{t\to\infty} y(t)$. In der Tabelle~\ref{buch:rekursion:gamma:table:gammaintegral} sind die Werte von $y(10^k)$ sowie die Differenzen -$y(10^k) - \Gamma(\frac{5}{2})$ zusammengefasst. +$y(10^k) - \Gamma(\frac{5}{3})$ zusammengefasst. Die Genauigkeit erreicht sechs korrekte Nachkommastellen mit nur 337 Auswertungen des Integranden. +Eine noch wesentlich effizientere Auswertung des $\Gamma$-Integrals +mit Hilfe der Gauss-Laguerre-Quadratur wird in Kapitel~\ref{chapter:laguerre} +von Patrick Müller dargestellt. % % diff --git a/buch/chapters/040-rekursion/gammalimit/Makefile b/buch/chapters/040-rekursion/gammalimit/Makefile new file mode 100644 index 0000000..0804e74 --- /dev/null +++ b/buch/chapters/040-rekursion/gammalimit/Makefile @@ -0,0 +1,11 @@ +# +# Makefile -- build gamma limit test programm +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +l: l.cpp + g++ -O2 -g -Wall `pkg-config --cflags gsl` `pkg-config --libs gsl` \ + -o l l.cpp + +test: l + ./l diff --git a/buch/chapters/040-rekursion/gammalimit/l.cpp b/buch/chapters/040-rekursion/gammalimit/l.cpp new file mode 100644 index 0000000..7a86800 --- /dev/null +++ b/buch/chapters/040-rekursion/gammalimit/l.cpp @@ -0,0 +1,26 @@ +/* + * l.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include + +int main(int argc, char *argv[]) { + double x = 0.5; + double g = tgamma(x); + printf("limit: %20.16f\n", g); + double p = 1; + long long N = 100000000000; + long long n = 10; + for (long long k = 1; k <= N; k++) { + p = p * k / (x + k - 1); + if (0 == k % n) { + double gval = p * pow(k, x-1); + printf("%12ld %20.16f %20.16f\n", k, gval, gval - g); + n = n * 10; + } + } + return EXIT_SUCCESS; +} diff --git a/buch/chapters/040-rekursion/gammalimit/l.m b/buch/chapters/040-rekursion/gammalimit/l.m new file mode 100644 index 0000000..32b6442 --- /dev/null +++ b/buch/chapters/040-rekursion/gammalimit/l.m @@ -0,0 +1,19 @@ +# +# l.m -- Berechnung der Gamma-Funktion +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +global N; +N = 10000; + +function retval = gamma(x, n) + p = 1; + for k = (1:n) + p = p * k / (x + k - 1); + end + retval = p * n^(x-1); +endfunction + +for n = (100:100:N) + printf("Gamma(%4d) = %10f\n", n, gamma(0.5, n)); +end diff --git a/buch/chapters/040-rekursion/images/Makefile b/buch/chapters/040-rekursion/images/Makefile index 86dfa1e..a1884f4 100644 --- a/buch/chapters/040-rekursion/images/Makefile +++ b/buch/chapters/040-rekursion/images/Makefile @@ -3,7 +3,7 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf +all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf loggammaplot.pdf gammaplot.pdf: gammaplot.tex gammapaths.tex pdflatex gammaplot.tex @@ -29,4 +29,8 @@ beta.pdf: beta.tex betapaths.tex betapaths.tex: betadist.m octave betadist.m +loggammaplot.pdf: loggammaplot.tex loggammadata.tex + pdflatex loggammaplot.tex +loggammadata.tex: loggammaplot.m + octave loggammaplot.m diff --git a/buch/chapters/040-rekursion/images/loggammaplot.m b/buch/chapters/040-rekursion/images/loggammaplot.m new file mode 100644 index 0000000..5456e4f --- /dev/null +++ b/buch/chapters/040-rekursion/images/loggammaplot.m @@ -0,0 +1,43 @@ +# +# loggammaplot.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +xmax = 10; +xmin = 0.1; +N = 500; + +fn = fopen("loggammadata.tex", "w"); + +fprintf(fn, "\\def\\loggammapath{\n ({%.4f*\\dx},{%.4f*\\dy})", + xmax, log(gamma(xmax))); +xstep = (xmax - 1) / N; +for x = (xmax:-xstep:1) + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", x, log(gamma(x))); +endfor +for k = (0:0.2:10) + x = exp(-k); + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", x, log(gamma(x))); +endfor +fprintf(fn, "\n}\n"); + +function retval = lgp(fn, x0, name) + fprintf(fn, "\\def\\loggammaplot%s{\n", name); + fprintf(fn, "\\draw[color=red,line width=1pt] "); + for k = (-7:0.1:7) + x = x0 + 0.5 * tanh(k); + if (k > -5) + fprintf(fn, "\n\t-- "); + end + fprintf(fn, "({%.4f*\\dx},{%.4f*\\dy})", x, log(gamma(x))); + endfor + fprintf(fn, ";\n}\n"); +endfunction + +lgp(fn, -0.5, "zero"); +lgp(fn, -1.5, "one"); +lgp(fn, -2.5, "two"); +lgp(fn, -3.5, "three"); +lgp(fn, -4.5, "four"); + +fclose(fn); diff --git a/buch/chapters/040-rekursion/images/loggammaplot.pdf b/buch/chapters/040-rekursion/images/loggammaplot.pdf new file mode 100644 index 0000000..8ac9eb4 Binary files /dev/null and b/buch/chapters/040-rekursion/images/loggammaplot.pdf differ diff --git a/buch/chapters/040-rekursion/images/loggammaplot.tex b/buch/chapters/040-rekursion/images/loggammaplot.tex new file mode 100644 index 0000000..c3c17ea --- /dev/null +++ b/buch/chapters/040-rekursion/images/loggammaplot.tex @@ -0,0 +1,89 @@ +% +% tikztemplate.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\input{loggammadata.tex} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +% add image content here + +\def\dx{1} +\def\dy{0.6} +\def\xmax{7.8} +\def\xmin{-4.9} +\def\ymax{8} +\def\ymin{-3.1} + +\fill[color=blue!20] ({\xmin*\dx},{\ymin*\dy}) rectangle ({-4*\dx},{\ymax*\dy}); +\fill[color=blue!20] ({-3*\dx},{\ymin*\dy}) rectangle ({-2*\dx},{\ymax*\dy}); +\fill[color=blue!20] ({-1*\dx},{\ymin*\dy}) rectangle ({-0*\dx},{\ymax*\dy}); + +\draw[->] ({\xmin*\dx-0.1},0) -- ({\xmax*\dx+0.3},0) + coordinate[label={$x$}]; +\draw[->] (0,{\ymin*\dy-0.1}) -- (0,{\ymax*\dy+0.3}) + coordinate[label={right:$y$}]; + +\begin{scope} +\clip ({\xmin*\dx},{\ymin*\dy}) rectangle ({\xmax*\dx},{\ymax*\dy}); + +\foreach \x in {-1,-2,-3,-4}{ + \draw[color=blue,line width=0.3pt] + ({\x*\dx},{\ymin*\dy}) -- ({\x*\dx},{\ymax*\dy}); +} + +\draw[color=red,line width=1pt] \loggammapath; + +\loggammaplotzero +\loggammaplotone +\loggammaplottwo +\loggammaplotthree +\loggammaplotfour + +\end{scope} + +\foreach \y in {0.1,10,100,1000,1000}{ + \draw[line width=0.3pt] + ({\xmin*\dx},{ln(\y)*\dy}) + -- + ({\xmax*\dx},{ln(\y)*\dy}) ; +} + +\foreach \x in {1,...,8}{ + \draw ({\x*\dx},{-0.05}) -- ({\x*\dx},{0.05}); + \node at ({\x*\dx},0) [below] {$\x$}; +} + +\foreach \x in {-1,...,-4}{ + \draw ({\x*\dx},{-0.05}) -- ({\x*\dx},{0.05}); +} +\foreach \x in {-1,...,-3}{ + \node at ({\x*\dx},0) [below right] {$\x$}; +} +\node at ({-4*\dx},0) [below left] {$-4$}; + +\def\htick#1#2{ + \draw (-0.05,{ln(#1)*\dy}) -- (0.05,{ln(#1)*\dy}); + \node at (0,{ln(#1)*\dy}) [above right] {#2}; +} + +\htick{10}{$10^1$} +\htick{100}{$10^2$} +\htick{1000}{$10^3$} +\htick{0.1}{$10^{-1}$} + +\node[color=red] at ({3*\dx},{ln(30)*\dy}) {$y=\log|\Gamma(x)|$}; + + +\end{tikzpicture} +\end{document} + -- cgit v1.2.1 From 3a95957a38a1cc8bcd865459a75cda87a2a8b56c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 18 Jun 2022 21:41:57 +0200 Subject: add new image, stuff about hypergeometrich series --- buch/chapters/040-rekursion/beta.tex | 16 +- buch/chapters/040-rekursion/bohrmollerup.tex | 17 ++ buch/chapters/040-rekursion/gamma.tex | 21 ++- buch/chapters/040-rekursion/hypergeometrisch.tex | 184 +++++++++++++++++++-- buch/chapters/040-rekursion/images/0f1.cpp | 94 +++++++++++ buch/chapters/040-rekursion/images/0f1.pdf | Bin 0 -> 49497 bytes buch/chapters/040-rekursion/images/0f1.tex | 86 ++++++++++ buch/chapters/040-rekursion/images/Makefile | 12 +- .../chapters/040-rekursion/images/loggammaplot.pdf | Bin 30948 -> 30943 bytes .../chapters/040-rekursion/images/loggammaplot.tex | 2 +- .../080-funktionentheorie/gammareflektion.tex | 2 + 11 files changed, 412 insertions(+), 22 deletions(-) create mode 100644 buch/chapters/040-rekursion/images/0f1.cpp create mode 100644 buch/chapters/040-rekursion/images/0f1.pdf create mode 100644 buch/chapters/040-rekursion/images/0f1.tex diff --git a/buch/chapters/040-rekursion/beta.tex b/buch/chapters/040-rekursion/beta.tex index 13e074f..35ff758 100644 --- a/buch/chapters/040-rekursion/beta.tex +++ b/buch/chapters/040-rekursion/beta.tex @@ -8,7 +8,8 @@ Die Eulersche Integralformel für die Gamma-Funktion in Definition~\ref{buch:rekursion:def:gamma} wurde in Abschnitt~\ref{buch:subsection:integral-eindeutig} -mit dem Satz von Mollerup gerechtfertigt. +mit dem Satz~\ref{buch:satz:bohr-mollerup} +von Bohr-Mollerup gerechtfertigt. Man kann Sie aber auch als Grenzfall der Beta-Funktion verstehen, die in diesem Abschnitt dargestellt wird. @@ -31,6 +32,7 @@ B(x,y) \int_0^1 t^{x-1} (1-t)^{y-1}\,dt \] für $\operatorname{Re}x>0$, $\operatorname{Re}y>0$. +\index{Beta-Integral}% \end{definition} Aus der Definition kann man sofort ablesen, dass $B(x,y)=B(y,x)$. @@ -321,6 +323,9 @@ $(-\frac12)!$ als Wert \] der Gamma-Funktion interpretiert. +% +% Alternative Parametrisierung +% \subsubsection{Alternative Parametrisierungen} Die Substitution $t=\sin^2 s$ hat im vorangegangenen Abschnitt ermöglicht, $\Gamma(\frac12)$ zu ermitteln. @@ -383,8 +388,10 @@ wobei wir \] verwendet haben. Diese Darstellung des Beta-Integrals wird später -% XXX Ort ergänzen +in Satz~\ref{buch:funktionentheorie:satz:spiegelungsformel} dazu verwendet, die Spiegelungsformel für die Gamma-Funktion +\index{Gamma-Funktion!Spiegelungsformel}% +\index{Spiegelungsformel der Gamma-Funktion}% herzuleiten. Eine weitere mögliche Parametrisierung verwendet $t = (1+s)/2$ @@ -408,6 +415,9 @@ B(x,y) \label{buch:rekursion:gamma:beta:symm} \end{equation} +% +% +% \subsubsection{Die Verdoppelungsformel von Legendre} Die trigonometrische Substitution kann dazu verwendet werden, die Legendresche Verdoppelungsformel für die Gamma-Funktion herzuleiten. @@ -419,6 +429,8 @@ Legendresche Verdoppelungsformel für die Gamma-Funktion herzuleiten. 2^{1-2x}\sqrt{\pi} \Gamma(2x) \] +\index{Verdoppelungsformel}% +\index{Gamma-Funktion!Verdoppelungsformel von Legendre}% \end{satz} \begin{proof}[Beweis] diff --git a/buch/chapters/040-rekursion/bohrmollerup.tex b/buch/chapters/040-rekursion/bohrmollerup.tex index cd9cadc..57e503a 100644 --- a/buch/chapters/040-rekursion/bohrmollerup.tex +++ b/buch/chapters/040-rekursion/bohrmollerup.tex @@ -5,12 +5,27 @@ % \subsection{Der Satz von Bohr-Mollerup \label{buch:rekursion:subsection:bohr-mollerup}} +\begin{figure} +\centering +\includegraphics{chapters/040-rekursion/images/loggammaplot.pdf} +\caption{Der Graph der Funktion $\log|\Gamma(x)|$ ist für $x>0$ konvex. +Die blau hinterlegten Bereiche zeigen an, wo die Gamma-Funktion +negative Werte annimmt. +\label{buch:rekursion:gamma:loggammaplot}} +\end{figure} Die Integralformel und die Grenzwertdefinition für die Gamma-Funktion zeigen beide, dass das Problem der Ausdehnung der Fakultät zu einer Funktion $\mathbb{C}\to\mathbb{C}$ eine Lösung hat, aber es ist noch nicht klar, in welchem Sinn dies die einzig mögliche Lösung ist. Der Satz von Bohr-Mollerup gibt darauf eine Antwort. +Der Graph +in Abbildung~\ref{buch:rekursion:gamma:loggammaplot} +zeigt, dass die Werte der Gamma-Funktion für $x>0$ so schnell +anwachsen, dass sogar die Funktion $\log|\Gamma(x)|$ konvex ist. +Der Satz von Bohr-Mollerup besagt, dass diese Eigenschaft zur +Charakterisierung der Gamma-Funktion verwendet werden kann. + \begin{satz} \label{buch:satz:bohr-mollerup} Eine Funktion $f\colon \mathbb{R}^+\to\mathbb{R}$ mit den Eigenschaften @@ -20,6 +35,8 @@ Eine Funktion $f\colon \mathbb{R}^+\to\mathbb{R}$ mit den Eigenschaften \item die Funktion $\log f(t)$ ist konvex \end{enumerate} ist die Gamma-Funktion: $f(t)=\Gamma(t)$. +\index{Satz!von Bohr-Mollerup}% +\index{Bohr-Mollerup, Satz von}% \end{satz} Für den Beweis verwenden wir die folgende Eigenschaft einer konvexen diff --git a/buch/chapters/040-rekursion/gamma.tex b/buch/chapters/040-rekursion/gamma.tex index e4dfa9a..45acf9f 100644 --- a/buch/chapters/040-rekursion/gamma.tex +++ b/buch/chapters/040-rekursion/gamma.tex @@ -20,6 +20,8 @@ für alle natürlichen Zahlen $x\in\mathbb{N}$ definiert werden. \end{equation} Kann man eine reelle oder komplexe Funktion finden, die die Funktionalgleichung~\eqref{buch:rekursion:eqn:gammadef} +\index{Gamma-Funktion!Funktionalgleichung}% +\index{Funktionalgleichung der Gamma-Funktion}% erfüllt und damit die Fakultät auf beliebige Argumente ausdehnt? \subsection{Definition als Grenzwert} @@ -141,6 +143,8 @@ $x\in\mathbb{C}\setminus\{0,-1,-2,-3,\dots\}$ ist der Grenzwert \[ \Gamma(x) = \lim_{n\to\infty} \frac{n!\,n^{x-1}}{(x)_n}. \] +\index{Grenzwertdefinition der Gamma-Funktion}% +\index{Gamma-Funktion!Grenzwertdefinition}% \end{definition} \subsubsection{Rekursionsgleichung für $\Gamma(x)$} @@ -204,7 +208,7 @@ Weil $n/(n+1)\to 1$ ist und die Funktion $z\mapsto z^{x-1}$ für alle nach der Definition zulässigen Werte von $x$ eine stetige Funktion ist. % -% +% Numerische Unzulänglichkeit der Grenzwertdefinition % \subsubsection{Numerische Unzulänglichkeiten der Grenzwertdefinition} \begin{table} @@ -316,6 +320,8 @@ wobei $\gamma$ die Euler-Mascheronische Konstante \biggl(\sum_{k=1}^n\frac{1}{k}-\log n\biggr) \] ist. +\index{Gamma-Funktion!Produktformel}% +\index{Produktformel für die Gamma-Funkion}% \end{satz} \begin{proof}[Beweis] @@ -483,6 +489,8 @@ z \mapsto \Gamma(z) = \int_0^\infty t^{z-1}e^{-t}\,dt \] +\index{Gamma-Funktion!Integraldefinition}% +\index{Integraldefinition der Gamma-Funktion}% \end{definition} Man beachte, dass das Integral für $x=0$ nicht definiert ist, eine @@ -564,6 +572,7 @@ die Werte der Fakultät annimmt. \subsubsection{Der Wert $\Gamma(\frac12)$} Die Integraldarstellung kann dazu verwendet werden, $\Gamma(\frac12)$ zu berechnen. +\index{Gamma-Funktion!WertGamma12@Wert von $\Gamma(\frac12)$}% Dazu verwendet man die Substition $t=s^2$ in der Integraldefinition der Gamma-Funktion und berechnen \begin{align} @@ -618,6 +627,8 @@ Von Wielandt stammt das folgende, noch etwas speziellere Resultat, welches hier nicht bewiesen wird. \begin{satz}[Wielandt] +\index{Satz!von Wielandt}% +\index{Wielandt, Satz von}% Ist $f(z)$ eine für $\operatorname{Re}z>0$ definiert Funktion mit den folgenden drei Eigenschaften \begin{enumerate} @@ -637,6 +648,7 @@ Dann ist $ f(z) = \Gamma(z) $. \subsubsection{Laplace-Transformierte der Potenzfunktion} Die Integraldarstellung der Gamma-Funktion erlaubt jetzt auch, die Laplace-Transformation der Potenzfunktion zu berechnen. +\index{Laplace-Transformierte der Potenzfunktion}% \begin{satz} Die Laplace-Transformierte der Potenzfunktion $f(t)=t^\alpha$ ist @@ -672,6 +684,7 @@ Durch die Substitution $st = u$ oder $t=\frac{u}{s}$ wird daraus % Pol erster Ordnung bei z=0 % \subsubsection{Pol erster Ordnung bei $z=0$} +\index{Gamma-Funktion!Pol@Pol bei $z=0$}% Wir haben zu prüfen, dass sowohl der Wert $\Gamma(1)$ korrekt ist als auch die Rekursionsformel~\eqref{buch:rekursion:eqn:gammadef} gilt. Der Wert für $z=1$ ist @@ -725,6 +738,8 @@ Die Gamma-Funktion hat daher an der Stelle $z=0$ einen Pol erster Ordnung. % Ausdehnung auf Re(z) < 0 % \subsubsection{Ausdehnung auf $\operatorname{Re}z<0$} +\index{Gamma-Funktion!analytische Fortsetzung}% +\index{analytische Fortsetzung der Gamma-Funktion}% Die Integralformel konvergiert nicht für $\operatorname{Re}z\le 0$. Durch analytische Fortsetzung, wie sie im Abschnitt~\ref{buch:funktionentheorie:section:fortsetzung} @@ -798,9 +813,11 @@ Um diese Hypothese zu prüfen, berechnen wir das Integral für $z=\frac53$ mit Hilfe der äquivalenten Differentialgleichungen \begin{equation} \dot{y}(t) = t^{z-1}e^{-t} -\qquad\text{mit Anfangsbedingung $y(0)=0$}. +\qquad +\text{mit Anfangsbedingung $y(0)=0$}. \label{buch:rekursion:gamma:eqn:gammadgl} \end{equation} +\index{Gamma-Funktion!Loesung@Lösung mit Differentialgleichung} Der gesuchte Wert ist der Grenzwert $\lim_{t\to\infty} y(t)$. In der Tabelle~\ref{buch:rekursion:gamma:table:gammaintegral} sind die Werte von $y(10^k)$ sowie die Differenzen diff --git a/buch/chapters/040-rekursion/hypergeometrisch.tex b/buch/chapters/040-rekursion/hypergeometrisch.tex index 39efc6b..1f42ade 100644 --- a/buch/chapters/040-rekursion/hypergeometrisch.tex +++ b/buch/chapters/040-rekursion/hypergeometrisch.tex @@ -200,6 +200,7 @@ ermöglichen wird, interessante Aussagen über die durch die Reihe beschriebenen Funktionen zu machen. \begin{definition} +\label{buch:rekursion:hypergeometrisch:def:allg} Eine durch die Reihe \[ f(x) = \sum_{k=0}^\infty a_k x^k @@ -218,9 +219,13 @@ wenn also mit Polynomen $p(k)$ und $q(k)$ ist. \end{definition} +% +% Beispiele von hypergeometrischen Funktionen +% +\subsubsection{Beispiele von hypergeometrischen Funktionen} Die geometrische Reihe ist natürlich eine hypergeometrische Reihe, wobei $p(k)/q(k)=1$ ist. -Etwas interessanter ist die Exponentialfunktion, durch die Taylor-Reihe +Etwas interessanter ist die Exponentialfunktion, die durch die Taylor-Reihe \[ e^x = \sum_{k=0}^\infty \frac{x^k}{k!} \] @@ -263,7 +268,30 @@ eine rationale Funktion mit Zählergrad $0$ und Nennergrad $2$. Es gibt also eine hypergeometrische Reihe $f(z)$ derart, dass $\cos x = f(x^2)$ ist. -Seien $p(k)$ und $q(k)$ zwei Polynome derart, dass +% +% Die hypergeometrischen Funktione pFq +% +\subsubsection{Die hypergeometrischen Funktionen $\mathstrut_pF_q$} +Die Definition~\ref{buch:rekursion:hypergeometrisch:def:allg} +einer hypergeometrischen Funktion wie auch die Verschiedenartigkeit +der Beispiele kännen den Eindruck vermitteln, dass die diese Klasse +von Funktionen unübersichtlich gross sein könnte. +Dem ist jedoch nicht so. +In diesem Abschnitt soll gezeigt werden, dass alle hypergeometrischen +Funktionen durch die in +Definition~\ref{buch:rekursion:hypergeometrisch:def} definierten +Funktionen $\mathstrut_pF_q$ ausgedrückt werden. +Die hypergeometrischen Funktionen können also vollständig parametrisiert +werden. + +Zu diesem Zweick sie +\[ +f(x) += +\sum_{k=0}^\infty a_kx^k +\] +eine hypergeometrische Funktion und +seien $p(k)$ und $q(k)$ zwei Polynome derart, dass \[ \frac{a_{k+1}}{a_k} = \frac{p(k)}{q(k)}. \] @@ -299,12 +327,12 @@ Dazu nehmen wir an, dass $a_i$, $i=1,\dots,n$ die Nullstellen von $p(k)$ sind und $b_j$, $j=1,\dots,m$ die Nullstellen von $q(k)$, dass man also die Polynome als \begin{align*} -p(k) &= x(k-a_1)(k-a_2)\cdots(k-a_n) +p(k) &= s(k-a_1)(k-a_2)\cdots(k-a_n) \\ q(k) &= (k-b_1)(k-b_2)\cdots(k-b_m) \end{align*} schreiben kann. -Der Faktor $x$ ist nötig, weil die Polynome $p(k)$ und $q(k)$ nicht +Der Faktor $s$ ist nötig, weil die Polynome $p(k)$ und $q(k)$ nicht notwendigerweise normiert sind. Um das Produkt der Quotienten zu vereinfachen, nehmen wir für den Moment @@ -314,14 +342,14 @@ Dann ist nach \[ a_{k} = -x^{k} +s^{k} \frac{ (k-1-a_1) \cdots (2-a_1)(1-a_1)(0-a_1) }{ (k-1-b_1) \cdots (2-b_1)(1-b_1)(0-b_1) } = -\frac{(-a_1)_k}{(-b_1)_k} x^k. +\frac{(-a_1)_k}{(-b_1)_k} s^k. \] Die Koeffizienten können daher als Quotienten von Pochhammer-Symbolen geschrieben werden. @@ -331,13 +359,16 @@ von der Form a_k = \frac{(-a_1)_k(-a_2)_k\cdots (-a_n)_k}{(-b_1)_k(-b_2)_k\cdots(-b_m)_k} -x^ka_0. +s^ka_0. \] -Jede hypergeometrische Reihe kann daher in der Form +Jede hypergeometrische Funktion kann daher in der Form \[ +f(x) += a_0 \sum_{k=0}^\infty \frac{(-a_1)_k(-a_2)_k\cdots (-a_n)_k}{(-b_1)_k(-b_2)_k\cdots(-b_m)_k} +s^k x^k \] geschrieben werden. @@ -371,9 +402,10 @@ zusätzlichen Faktor $(1)_k$ im Zähler des Bruchs von Pochhammer-Symbolen kompensieren, wodurch sich der Grad $p$ des Zählers natürlich um $1$ erhöht. -Die oben analysierte Summe $S$ kann mit der Definition als +Die oben analysierte Summe für $f(x)$ kann mit der +Definition~\ref{buch:rekursion:hypergeometrisch:def} als \[ -S +f(x) = a_0 \cdot @@ -381,11 +413,69 @@ a_0 \begin{matrix} -a_1,-a_2,\dots,-a_n,1\\ -b_1,-b_2,\dots,-a_m -\end{matrix}; x +\end{matrix}; sx \biggr) \] beschrieben werden. +% +% Elementare Rechenregeln +% +\subsubsection{Elementare Rechenregeln} +Die Funktionen $\mathstrut_pF_q$ sind nicht alle unabhängig. +In Abschnitt~\ref{buch:rekursion:hypergeometrisch:stammableitung} +wird gezeigt werden, dass Ableitung und Stammfunktion einer hypergeometrischen +Funktion durch Manipulation der Parameter $a_k$ und $b_k$ bestimmt werden +können. +Viel einfacher sind jedoch die folgenden, aus +Definition~\ref{buch:rekursion:hypergeometrisch:def} +offensichtlichen Regeln: + +\begin{satz}[Permutationsregel] +Sei $\pi$ eine beliebige Permutation der Zahlen $1,\dots,p$ und $\sigma$ eine +beliebige Permutation der Zahlen $1,\dots,q$, dann ist +\[ +\mathstrut_pF_q\biggl( +\begin{matrix} +a_1,\dots,a_p\\b_1,\dots,a_q +\end{matrix} +;x +\biggr) += +\mathstrut_pF_q\biggl( +\begin{matrix} +a_{\pi(1)},\dots,a_{\pi(p)}\\b_{\sigma(1)},\dots,b_{\sigma(q)} +\end{matrix} +;x +\biggr). +\] +\end{satz} + +\begin{satz}[Kürzungsformel] +Stimmt einer der Koeffizienten $a_k$ mit einem der Koeffizienten $b_i$ +überein, dann können sie weggelassen werden: +\[ +\mathstrut_{p+1}F_{q+1}\biggl( +\begin{matrix} +c,a_1,\dots,a_p\\ +c,b_1,\dots,b_q +\end{matrix}; +x +\biggr) += +\mathstrut_{p}F_{q}\biggl( +\begin{matrix} +a_1,\dots,a_p\\ +b_1,\dots,b_q +\end{matrix}; +x +\biggr). +\] +\end{satz} + +% +% Beispiele von hypergeometrischen Funktionen +% \subsection{Beispiele von hypergeometrischen Funktionen \label{buch:rekursion:hypergeometrisch:beispiele}} Viele der bekannten Reihenentwicklungen häufig verwendeter Funktionen @@ -393,6 +483,9 @@ lassen sich durch die hypergeometrischen Funktionen von Definition~\ref{buch:rekursion:hypergeometrisch:def} ausdrücken. In diesem Abschnitt werden einige Beispiel dazu gegeben. +% +% Die geometrische Reihe +% \subsubsection{Die geometrische Reihe} In der geometrischen Reihe fehlt der Nenner $k!$, es braucht daher einen Term $(1)_k$ im Zähler, um den Nenner zu kompensieren. @@ -410,6 +503,9 @@ a\sum_{k=0}^\infty a\cdot\mathstrut_1F_0(1,x). \] +% +% Die Exponentialfunktion +% \subsubsection{Exponentialfunktion} Die Exponentialfunktion ist die Reihe \[ @@ -421,7 +517,10 @@ benötigt, es ist daher e^x = \mathstrut_0F_0(x). \] -\subsubsection{Wurzelfunktion} +% +% Wurzelfunktionen +% +\subsubsection{Wurzelfunktionen} Die Wurzelfunktion $x\mapsto \sqrt{x}$ hat keine Taylor-Entwicklung in $x=0$, aber die Funktion $x\mapsto\sqrt{1+x}$ hat die Taylor-Reihe \[ @@ -510,11 +609,27 @@ Die Wurzelfunktion ist daher die hypergeometrische Funktion \sqrt{1\pm x} = \sum_{k=0}^\infty -\biggl(-\frac12\biggr)_k \frac{(-x)^k}{k!} +\biggl(-\frac12\biggr)_k \frac{(\pm x)^k}{k!} = \mathstrut_1F_0(-{\textstyle\frac12};\mp x). \] +Mit der Newtonschen Binomialreihe +\begin{align*} +(1+x)^\alpha +&= +1+\alpha x + \frac{\alpha(\alpha-1)}{2!}x^2 + \frac{\alpha(\alpha-1)(\alpha-2)}{3!}x^3+\dots +\\ +&= +\sum_{k=0}^\infty \frac{(-\alpha)_k}{k!}x^k += +\mathstrut_1F_0\biggl(\begin{matrix}-\alpha\\\text{---}\end{matrix};-x\biggr) +\end{align*} +kann man ganz analog jede beliebige Wurzelfunktion +durch $\mathstrut_1F_0$ ausdrücken. +% +% Logarithmusfunktion +% \subsubsection{Logarithmusfunktion} Für $x\in (-1,1)$ konvergiert die Taylor-Reihe \[ @@ -581,7 +696,9 @@ x\cdot \mathstrut_2F_1\biggl(\begin{matrix}1,1\\2\end{matrix};-x\biggr). \] - +% +% Trigonometrische Funktionen +% \subsubsection{Trigonometrische Funktionen} \index{trigonometrische Funktionen!als hypergeometrische Funktionen}% Die Kosinus-Funktion wurde bereits als hypergeometrische Funktion erkannt, @@ -684,6 +801,9 @@ x\cdot\mathstrut_0F_1\biggl( \end{equation} durch eine hypergeometrische Funktion ausdrücken. +% +% Hyperbolische Funktionen +% \subsubsection{Hyperbolische Funktionen} \index{hyperbolische Funktionen!als hypergeometrische Funktionen}% Die für die Sinus-Funktion angewendete Methode lässt sich auch @@ -718,6 +838,9 @@ ist diese Darstellung identisch mit der von $\sin x$. Dies illustriert die Rolle der hypergeometrischen Funktionen als ``grosse Vereinheitlichung'' der bekannten speziellen Funktionen. +% +% Tschebyscheff-Polynome +% \subsubsection{Tschebyscheff-Polynome} \index{Tschebyscheff-Polynome}% Man kann zeigen, dass auch die Tschebyscheff-Polynome sich durch die @@ -761,13 +884,39 @@ $a_k$ eine negative ganze Zahl ist. Der Grad des Polynoms ist der kleinste Betrag der negativ ganzzahligen Werte unter den Parametern $a_k$. +% +% Die Funktionen 0F1 +% +\subsubsection{Die Funktionen $\mathstrut_0F_1$} +\begin{figure} +\centering +\includegraphics{chapters/040-rekursion/images/0f1.pdf} +\caption{Graphen der Funktionen $\mathstrut_0F_1(;\alpha;x)$ für +verschiedene Werte von $\alpha$. +\label{buch:rekursion:hypergeometrisch:0f1}} +\end{figure} +Die Funktionen $\mathstrut_0F_1$ sind in den Beispielen mit der +beschränkten trigonometrischen Funktion $\sin x$ und mit der +exponentiell unbeschränkten Funktion $\sinh x$ mit dem gleichen +Wert des Parameters und nur einem Wechsel des Vorzeichens des +Arguments verbunden worden. +Die Graphen der Funktionen $\mathstrut_0F_1$, die in +Abbildung~\ref{buch:rekursion:hypergeometrisch:0f1} dargestellt sind, +machen dieses Verhalten plausibel. +Es wird sich später zeigen, dass $\mathstrut_0F_1$ auch mit den Bessel- +und den Airy-Funktionen verwandt sind. + + % % Ableitung und Stammfunktion % -\subsection{Ableitung und Stammfunktion hypergeometrischer Funktionen} +\subsection{Ableitung und Stammfunktion hypergeometrischer Funktionen +\label{buch:rekursion:hypergeometrisch:stammableitung}} Sowohl Ableitung wie auch Stammfunktion einer hypergeometrischen Funktion lässt sich immer durch hypergeometrische Reihen ausdrücken. - +% +% Ableitung +% \subsubsection{Ableitung} Wir gehen aus von der Funktion \begin{equation} @@ -909,6 +1058,9 @@ Funktion $\mathstrut_0F_1$ überein, es ist also wie erwartet} \end{align*} \end{beispiel} +% +% Stammfunktion +% \subsubsection{Stammfunktion} Eine Stammfunktion kann man auf die gleiche Art und Weise wie die Ableitung finden. diff --git a/buch/chapters/040-rekursion/images/0f1.cpp b/buch/chapters/040-rekursion/images/0f1.cpp new file mode 100644 index 0000000..24ca3f1 --- /dev/null +++ b/buch/chapters/040-rekursion/images/0f1.cpp @@ -0,0 +1,94 @@ +/* + * 0f1.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include +#include +#include + +static int N = 100; +static double xmin = -50; +static double xmax = 30; +static int points = 200; + +double f(double b, double x) { + double s = 1; + double p = 1; + for (int k = 1; k < N; k++) { + p = p * x / (k * (b + k - 1.)); + s += p; + } + return s; +} + +typedef std::pair point_t; + +point_t F(double b, double x) { + return std::make_pair(x, f(b, x)); +} + +std::string ff(double f) { + if (f > 1000) { f = 1000; } + if (f < -1000) { f = -1000; } + char b[128]; + snprintf(b, sizeof(b), "%.4f", f); + return std::string(b); +} + +std::ostream& operator<<(std::ostream& out, const point_t& p) { + char b[128]; + out << "({" << ff(p.first) << "*\\dx},{" << ff(p.second) << "*\\dy})"; + return out; +} + +void curve(std::ostream& out, double b, const std::string& name) { + double h = (xmax - xmin) / points; + out << "\\def\\kurve" << name << "{"; + out << std::endl << "\t" << F(b, xmin); + for (int i = 1; i <= points; i++) { + double x = xmin + h * i; + out << std::endl << "\t-- " << F(b, x); + } + out << std::endl; + out << "}" << std::endl; +} + +int main(int argc, char *argv[]) { + std::ofstream out("0f1data.tex"); + + double s = 13/(xmax-xmin); + out << "\\def\\dx{" << ff(s) << "}" << std::endl; + out << "\\def\\dy{" << ff(s) << "}" << std::endl; + out << "\\def\\xmin{" << ff(s * xmin) << "}" << std::endl; + out << "\\def\\xmax{" << ff(s * xmax) << "}" << std::endl; + + curve(out, 0.5, "one"); + curve(out, 1.5, "two"); + curve(out, 2.5, "three"); + curve(out, 3.5, "four"); + curve(out, 4.5, "five"); + curve(out, 5.5, "six"); + curve(out, 6.5, "seven"); + curve(out, 7.5, "eight"); + curve(out, 8.5, "nine"); + curve(out, 9.5, "ten"); + + curve(out,-0.5, "none"); + curve(out,-1.5, "ntwo"); + curve(out,-2.5, "nthree"); + curve(out,-3.5, "nfour"); + curve(out,-4.5, "nfive"); + curve(out,-5.5, "nsix"); + curve(out,-6.5, "nseven"); + curve(out,-7.5, "neight"); + curve(out,-8.5, "nnine"); + curve(out,-9.5, "nten"); + + out.close(); + return EXIT_SUCCESS; +} diff --git a/buch/chapters/040-rekursion/images/0f1.pdf b/buch/chapters/040-rekursion/images/0f1.pdf new file mode 100644 index 0000000..2c35813 Binary files /dev/null and b/buch/chapters/040-rekursion/images/0f1.pdf differ diff --git a/buch/chapters/040-rekursion/images/0f1.tex b/buch/chapters/040-rekursion/images/0f1.tex new file mode 100644 index 0000000..1bc8b87 --- /dev/null +++ b/buch/chapters/040-rekursion/images/0f1.tex @@ -0,0 +1,86 @@ +% +% 0f1.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\input{0f1data.tex} +\definecolor{darkgreen}{rgb}{0,0.6,0} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\begin{scope} +\clip (\xmin,-1) rectangle (\xmax,5); +\draw[color=blue!5!red,line width=1.4pt] \kurveone; +\draw[color=blue!16!red,line width=1.4pt] \kurvetwo; +\draw[color=blue!26!red,line width=1.4pt] \kurvethree; +\draw[color=blue!37!red,line width=1.4pt] \kurvefour; +\draw[color=blue!47!red,line width=1.4pt] \kurvefive; +\draw[color=blue!57!red,line width=1.4pt] \kurvesix; +\draw[color=blue!68!red,line width=1.4pt] \kurveseven; +\draw[color=blue!78!red,line width=1.4pt] \kurveeight; +\draw[color=blue!89!red,line width=1.4pt] \kurvenine; +\draw[color=blue!100!red,line width=1.4pt] \kurveten; +\def\ds{0.4} +\begin{scope}[yshift=0.5cm] +\node[color=blue!5!red] at (\xmin,{1*\ds}) [right] {$\alpha=0.5$}; +\node[color=blue!16!red] at (\xmin,{2*\ds}) [right] {$\alpha=1.5$}; +\node[color=blue!26!red] at (\xmin,{3*\ds}) [right] {$\alpha=2.5$}; +\node[color=blue!37!red] at (\xmin,{4*\ds}) [right] {$\alpha=2.5$}; +\node[color=blue!47!red] at (\xmin,{5*\ds}) [right] {$\alpha=3.5$}; +\node[color=blue!57!red] at (\xmin,{6*\ds}) [right] {$\alpha=5.5$}; +\node[color=blue!68!red] at (\xmin,{7*\ds}) [right] {$\alpha=6.5$}; +\node[color=blue!78!red] at (\xmin,{8*\ds}) [right] {$\alpha=7.5$}; +\node[color=blue!89!red] at (\xmin,{9*\ds}) [right] {$\alpha=8.5$}; +\node[color=blue!100!red]at (\xmin,{10*\ds}) [right] {$\alpha=9.5$}; +\end{scope} +\node at (-1.7,4.5) {$\displaystyle +y=\mathstrut_0F_1\biggl(\begin{matrix}\text{---}\\\alpha\end{matrix};x\biggr)$}; +\end{scope} + +\draw[->] (\xmin-0.2,0) -- (\xmax+0.3,0) coordinate[label=$x$]; +\draw[->] (0,-0.5) -- (0,5.3) coordinate[label={right:$y$}]; + +\begin{scope}[yshift=-6.5cm] +\begin{scope} +\clip (\xmin,-5) rectangle (\xmax,5); + +\draw[color=darkgreen!5!red,line width=1.4pt] \kurvenone; +\draw[color=darkgreen!16!red,line width=1.4pt] \kurventwo; +\draw[color=darkgreen!26!red,line width=1.4pt] \kurventhree; +\draw[color=darkgreen!37!red,line width=1.4pt] \kurvenfour; +\draw[color=darkgreen!47!red,line width=1.4pt] \kurvenfive; +\draw[color=darkgreen!57!red,line width=1.4pt] \kurvensix; +\draw[color=darkgreen!68!red,line width=1.4pt] \kurvenseven; +\draw[color=darkgreen!78!red,line width=1.4pt] \kurveneight; +\draw[color=darkgreen!89!red,line width=1.4pt] \kurvennine; +\draw[color=darkgreen!100!red,line width=1.4pt] \kurventen; +\end{scope} + +\draw[->] (\xmin-0.2,0) -- (\xmax+0.3,0) coordinate[label=$x$]; +\draw[->] (0,-5.2) -- (0,5.3) coordinate[label={right:$y$}]; +\def\ds{-0.4} +\begin{scope}[yshift=-0.5cm] +\node[color=darkgreen!5!red] at (\xmax,{1*\ds}) [left] {$\alpha=-0.5$}; +\node[color=darkgreen!16!red] at (\xmax,{2*\ds}) [left] {$\alpha=-1.5$}; +\node[color=darkgreen!26!red] at (\xmax,{3*\ds}) [left] {$\alpha=-2.5$}; +\node[color=darkgreen!37!red] at (\xmax,{4*\ds}) [left] {$\alpha=-2.5$}; +\node[color=darkgreen!47!red] at (\xmax,{5*\ds}) [left] {$\alpha=-3.5$}; +\node[color=darkgreen!57!red] at (\xmax,{6*\ds}) [left] {$\alpha=-5.5$}; +\node[color=darkgreen!68!red] at (\xmax,{7*\ds}) [left] {$\alpha=-6.5$}; +\node[color=darkgreen!78!red] at (\xmax,{8*\ds}) [left] {$\alpha=-7.5$}; +\node[color=darkgreen!89!red] at (\xmax,{9*\ds}) [left] {$\alpha=-8.5$}; +\node[color=darkgreen!100!red]at (\xmax,{10*\ds}) [left] {$\alpha=-9.5$}; +\end{scope} +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/040-rekursion/images/Makefile b/buch/chapters/040-rekursion/images/Makefile index a1884f4..54ed23b 100644 --- a/buch/chapters/040-rekursion/images/Makefile +++ b/buch/chapters/040-rekursion/images/Makefile @@ -3,7 +3,8 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # -all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf loggammaplot.pdf +all: gammaplot.pdf fibonacci.pdf order.pdf beta.pdf loggammaplot.pdf \ + 0f1.pdf gammaplot.pdf: gammaplot.tex gammapaths.tex pdflatex gammaplot.tex @@ -34,3 +35,12 @@ loggammaplot.pdf: loggammaplot.tex loggammadata.tex loggammadata.tex: loggammaplot.m octave loggammaplot.m + +0f1: 0f1.cpp + g++ -O -Wall -g -o 0f1 0f1.cpp + +0f1data.tex: 0f1 + ./0f1 + +0f1.pdf: 0f1.tex 0f1data.tex + pdflatex 0f1.tex diff --git a/buch/chapters/040-rekursion/images/loggammaplot.pdf b/buch/chapters/040-rekursion/images/loggammaplot.pdf index 8ac9eb4..a2963f2 100644 Binary files a/buch/chapters/040-rekursion/images/loggammaplot.pdf and b/buch/chapters/040-rekursion/images/loggammaplot.pdf differ diff --git a/buch/chapters/040-rekursion/images/loggammaplot.tex b/buch/chapters/040-rekursion/images/loggammaplot.tex index c3c17ea..8ca4e1c 100644 --- a/buch/chapters/040-rekursion/images/loggammaplot.tex +++ b/buch/chapters/040-rekursion/images/loggammaplot.tex @@ -19,7 +19,7 @@ \def\dx{1} \def\dy{0.6} -\def\xmax{7.8} +\def\xmax{8} \def\xmin{-4.9} \def\ymax{8} \def\ymin{-3.1} diff --git a/buch/chapters/080-funktionentheorie/gammareflektion.tex b/buch/chapters/080-funktionentheorie/gammareflektion.tex index 537fd96..017c850 100644 --- a/buch/chapters/080-funktionentheorie/gammareflektion.tex +++ b/buch/chapters/080-funktionentheorie/gammareflektion.tex @@ -12,12 +12,14 @@ die durch Spiegelung an der Geraden $\operatorname{Re}x=\frac12$ auseinander hervorgehen, und einem speziellen Beta-Integral her. \begin{satz} +\label{buch:funktionentheorie:satz:spiegelungsformel} Für $0 Date: Mon, 20 Jun 2022 10:58:52 +0200 Subject: fix some typos --- buch/chapters/040-rekursion/hypergeometrisch.tex | 83 +++++++++++++++------- .../chapters/040-rekursion/uebungsaufgaben/404.tex | 2 +- .../050-differential/potenzreihenmethode.tex | 4 +- 3 files changed, 61 insertions(+), 28 deletions(-) diff --git a/buch/chapters/040-rekursion/hypergeometrisch.tex b/buch/chapters/040-rekursion/hypergeometrisch.tex index 1f42ade..3b72ffa 100644 --- a/buch/chapters/040-rekursion/hypergeometrisch.tex +++ b/buch/chapters/040-rekursion/hypergeometrisch.tex @@ -432,9 +432,10 @@ Definition~\ref{buch:rekursion:hypergeometrisch:def} offensichtlichen Regeln: \begin{satz}[Permutationsregel] +\label{buch:rekursion:hypergeometrisch:satz:permuationsregel} Sei $\pi$ eine beliebige Permutation der Zahlen $1,\dots,p$ und $\sigma$ eine beliebige Permutation der Zahlen $1,\dots,q$, dann ist -\[ +\begin{equation} \mathstrut_pF_q\biggl( \begin{matrix} a_1,\dots,a_p\\b_1,\dots,a_q @@ -448,13 +449,15 @@ a_{\pi(1)},\dots,a_{\pi(p)}\\b_{\sigma(1)},\dots,b_{\sigma(q)} \end{matrix} ;x \biggr). -\] +\label{buch:rekursion:hypergeometrisch:eqn:permuationsregel} +\end{equation} \end{satz} \begin{satz}[Kürzungsformel] +\label{buch:rekursion:hypergeometrisch:satz:kuerzungsregel} Stimmt einer der Koeffizienten $a_k$ mit einem der Koeffizienten $b_i$ überein, dann können sie weggelassen werden: -\[ +\begin{equation} \mathstrut_{p+1}F_{q+1}\biggl( \begin{matrix} c,a_1,\dots,a_p\\ @@ -470,7 +473,8 @@ b_1,\dots,b_q \end{matrix}; x \biggr). -\] +\label{buch:rekursion:hypergeometrisch:eqn:kuerzungsregel} +\end{equation} \end{satz} % @@ -613,19 +617,25 @@ Die Wurzelfunktion ist daher die hypergeometrische Funktion = \mathstrut_1F_0(-{\textstyle\frac12};\mp x). \] -Mit der Newtonschen Binomialreihe +Mit der Newtonschen Binomialreihe, die in +Abschnitt~\ref{buch:differentialgleichungen:subsection:newtonschereihe} +hergleitet wird, +kann man ganz analog jede beliebige Wurzelfunktion \begin{align*} (1+x)^\alpha &= 1+\alpha x + \frac{\alpha(\alpha-1)}{2!}x^2 + \frac{\alpha(\alpha-1)(\alpha-2)}{3!}x^3+\dots -\\ -&= +%\\ +%& += \sum_{k=0}^\infty \frac{(-\alpha)_k}{k!}x^k = \mathstrut_1F_0\biggl(\begin{matrix}-\alpha\\\text{---}\end{matrix};-x\biggr) \end{align*} -kann man ganz analog jede beliebige Wurzelfunktion durch $\mathstrut_1F_0$ ausdrücken. +Dieses Resultat ist der Inhalt von +Satz~\ref{buch:differentialgleichungen:satz:newtonschereihe} + % % Logarithmusfunktion @@ -725,7 +735,7 @@ x f(-x^2). Die Funktion $f(z)$ soll jetzt als hypergeometrische Funktion geschrieben werden. Dazu muss zunächst wieder der Nenner $k!$ wiederhergestellt werden: -\[ +\begin{equation*} f(z) = 1 @@ -737,7 +747,7 @@ f(z) \frac{3!}{7!}\cdot \frac{z^3}{3!} + \dots -\] +\end{equation*} Die Koeffizienten $k!/(2k+1)!$ müssen jetzt durch Pochhammer-Symbole mit jeweils $k$ Faktoren ausgedrückt werden. Dazu muss die Fakultät $(2k+1)!$ in zwei Produkte @@ -777,15 +787,27 @@ müssen wird mit $2^{2k}$ kompensieren: (1)_k\cdot \biggl(\frac{3}{2}\biggr)_k \end{align*} Setzt man dies in die Reihe ein, wird -\[ +\begin{equation} f(z) = \sum_{k=0}^\infty \frac{(1)_k}{(1)_k\cdot (\frac{3}{2})_k\cdot 4^k} z^k = -\mathstrut_1F_2\biggl(1;1,\frac{3}{2};\frac{z}4\biggr). -\] +\mathstrut_1F_2\biggl( +\begin{matrix}1\\1,\frac{3}{2}\end{matrix};\frac{z}4 +\biggr) += +\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac{3}{2}\end{matrix};\frac{z}4 +\biggr). +\label{buch:rekursion:hyperbolisch:eqn:hilfsfunktionf} +\end{equation} +Im letzten Schritt wurde die Kürzungsregel +\eqref{buch:rekursion:hypergeometrisch:eqn:kuerzungsregel} +von +Satz~\ref{buch:rekursion:hypergeometrisch:satz:kuerzungsregel} +angewendet. Damit lässt sich die Sinus-Funktion als \begin{equation} \sin x @@ -812,21 +834,24 @@ auf die Funktion \sinh x &= \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!} -\\ -&= +%\\ +%& += x \, \biggl( 1+\frac{x^2}{3!} + \frac{x^4}{5!}+\frac{x^6}{7!}+\dots \biggr) -\\ +\intertext{Die Reihe in der Klammer lässt sich mit der Funktion +$f$ von \eqref{buch:rekursion:hyperbolisch:eqn:hilfsfunktionf} +schreiben als} &= -xf(-x^2) -= -x\,\mathstrut_1F_2\biggl( -\begin{matrix}1\\1,\frac{3}{2}\end{matrix} -;\frac{x^2}{4} -\biggr) +x\,f(-x^2) +%= +%x\cdot\mathstrut_1F_2\biggl( +%\begin{matrix}1\\1,\frac{3}{2}\end{matrix} +%;\frac{x^2}{4} +%\biggr) = x\cdot\mathstrut_0F_1\biggl( \begin{matrix}\text{---}\\\frac{3}{2}\end{matrix} @@ -1030,7 +1055,7 @@ Damit kann jetzt die Kosinus-Funktion als \frac{1}{(\frac12)_k} \frac{1}{k!}\biggl(\frac{-x^2}{4}\biggr)^k = -\mathstrut_0F_1\biggl(;\frac12;-\frac{x^2}4\biggr) +\mathstrut_0F_1\biggl(\begin{matrix}\text{---}\\\frac12\end{matrix};-\frac{x^2}4\biggr) \end{align*} geschrieben werden kann. @@ -1039,16 +1064,22 @@ Die Ableitung der Kosinus-Funktion ist daher \frac{d}{dx} \cos x &= \frac{d}{dx} -\mathstrut_0F_1\biggl(;\frac12;-\frac{x^2}4\biggr) +\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac12\end{matrix};-\frac{x^2}4 +\biggr) = \frac{1}{\frac12} \, -\mathstrut_0F_1\biggl(;\frac32;-\frac{x^2}4\biggr) +\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac32\end{matrix};-\frac{x^2}4 +\biggr) \cdot\biggl(-\frac{x}2\biggr) = -x \cdot -\mathstrut_0F_1\biggl(;\frac32;-\frac{x^2}4\biggr) +\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac32\end{matrix};-\frac{x^2}4 +\biggr) \intertext{Dies stimmt mit der in \eqref{buch:rekursion:hypergeometrisch:eqn:sinhyper} gefundenen Darstellung der Sinusfunktion mit Hilfe der hypergeometrischen diff --git a/buch/chapters/040-rekursion/uebungsaufgaben/404.tex b/buch/chapters/040-rekursion/uebungsaufgaben/404.tex index f9d014e..5d76598 100644 --- a/buch/chapters/040-rekursion/uebungsaufgaben/404.tex +++ b/buch/chapters/040-rekursion/uebungsaufgaben/404.tex @@ -1,5 +1,5 @@ Finden Sie einen einfachen Ausdruck für $(\frac12)_n$, der nur -Fakultäten und andere elmentare Funktionen verwendet. +Fakultäten und andere elementare Funktionen verwendet. \begin{loesung} Das Pochhammer-Symbol $(\frac12)_n$ kann wie folgt durch bekanntere diff --git a/buch/chapters/050-differential/potenzreihenmethode.tex b/buch/chapters/050-differential/potenzreihenmethode.tex index 2d95fb2..e6613dd 100644 --- a/buch/chapters/050-differential/potenzreihenmethode.tex +++ b/buch/chapters/050-differential/potenzreihenmethode.tex @@ -176,7 +176,8 @@ b_2\,2!\,a_{2+k} + b_1\, a_{1+k} + b_0\, a_k % % Die Newtonsche Reihe % -\subsection{Die Newtonsche Reihe} +\subsection{Die Newtonsche Reihe +\label{buch:differentialgleichungen:subsection:newtonschereihe}} Wir lösen die Differentialgleichung~\eqref{buch:differentialgleichungen:eqn:wurzeldgl1} mit der Anfangsbedingung $y(t)=1$ mit der Potenzreihenmethode. @@ -333,6 +334,7 @@ wir die Darstellung Damit haben wir den folgenden Satz gezeigt. \begin{satz} +\label{buch:differentialgleichungen:satz:newtonschereihe} Die Newtonsche Reihe für $(1-t)^\alpha$ ist der Wert \[ (1-t)^\alpha -- cgit v1.2.1 From 9f8e0b23aa9897b429ef997d7de8224844b60880 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 20 Jun 2022 21:27:44 +0200 Subject: fix all the Bessel stuff --- buch/chapters/040-rekursion/gamma.tex | 46 +++- buch/chapters/050-differential/bessel.tex | 277 +++++++++++++++++---- .../chapters/050-differential/hypergeometrisch.tex | 2 +- buch/chapters/070-orthogonalitaet/bessel.tex | 3 +- buch/chapters/070-orthogonalitaet/chapter.tex | 58 ++++- .../070-orthogonalitaet/gaussquadratur.tex | 5 +- buch/chapters/070-orthogonalitaet/legendredgl.tex | 31 ++- buch/chapters/070-orthogonalitaet/orthogonal.tex | 8 +- buch/chapters/070-orthogonalitaet/rekursion.tex | 41 ++- buch/chapters/070-orthogonalitaet/rodrigues.tex | 145 ++++++++--- buch/chapters/070-orthogonalitaet/sturm.tex | 45 +++- .../chapters/080-funktionentheorie/anwendungen.tex | 1 + .../080-funktionentheorie/singularitaeten.tex | 3 +- 13 files changed, 555 insertions(+), 110 deletions(-) diff --git a/buch/chapters/040-rekursion/gamma.tex b/buch/chapters/040-rekursion/gamma.tex index 45acf9f..2b0700e 100644 --- a/buch/chapters/040-rekursion/gamma.tex +++ b/buch/chapters/040-rekursion/gamma.tex @@ -73,6 +73,9 @@ gilt. Der Plan ist, dies so umzuformen, dass man für $x$ eine beliebige komplexe Zahl einsetzen kann. +% +% Pochhammer-Symbol +% \subsubsection{Pochhammer-Symbol} Die spezielle Form des Nenners und des zweiten Faktors im Zähler von \eqref{buch:rekursion:gamma:eqn:fakultaet} @@ -115,6 +118,9 @@ x! Der erste Faktor in diesem Ausdruck enthält jetzt nur noch Dinge, die für beliebige $x\in\mathbb{C}$ definiert sind. +% +% Grenwertdefinition +% \subsubsection{Grenzwertdefinition} Der zweite Bruch in \eqref{buch:rekursion:gamma:eqn:produkt3} besteht aus Termen, die zwar nur für natürliches $x$ definiert sind, @@ -147,6 +153,9 @@ $x\in\mathbb{C}\setminus\{0,-1,-2,-3,\dots\}$ ist der Grenzwert \index{Gamma-Funktion!Grenzwertdefinition}% \end{definition} +% +% Rekursionsgleichung für Gamma(x) +% \subsubsection{Rekursionsgleichung für $\Gamma(x)$} Es ist aus der Herleitung klar, dass $\Gamma(n)=(n-1)!$ sein muss. Wir sollten dies aber auch direkt aus der @@ -199,14 +208,49 @@ x\lim_{n\to\infty} \frac{n^{x-1}}{(n+1)^{x-1}} \\ &= +x \Gamma(x) \lim_{n\to\infty} \biggl(\frac{n}{n+1}\biggr)^{x-1} = -\Gamma(x), +x\Gamma(x), \end{align*} Weil $n/(n+1)\to 1$ ist und die Funktion $z\mapsto z^{x-1}$ für alle nach der Definition zulässigen Werte von $x$ eine stetige Funktion ist. +% +% Gamma-Funktion und Pochhammer-Symbol +% +\subsubsection{Gamma-Funktion und Pochhammer-Symbol} +Durch Iteration der Rekursionsformel für $\Gamma(x)$ folgt jetzt +\begin{align*} +\Gamma(x+n) +&= +(x+n-1) \Gamma(x+n-1) +\\ +&= +(x+n-1)(x+n-2)\Gamma(x+n-2) +\\ +&= +\underbrace{ +(x+n-1)(x+n-2)\cdots(x-1)(x) +}_{\text{$n$ Faktoren}} \Gamma(x) +\\ +&=(x)_n \Gamma(x). +\end{align*} +Damit folgt + +\begin{satz} +\label{buch:rekursion:gamma:satz:gamma-pochhammer} +Die Rekursionsformel für die Gamma-Funktion kann geschrieben werden als +\[ +\Gamma(x+n) = (x)_n \Gamma(x). +\] +Das Pochhammer-Symbol $(x)_n$ ist für alle natürlichen $n$ gegeben durch +\[ +(x)_n = \frac{\Gamma(x+n)}{\Gamma(x)}. +\] +\end{satz} + % % Numerische Unzulänglichkeit der Grenzwertdefinition % diff --git a/buch/chapters/050-differential/bessel.tex b/buch/chapters/050-differential/bessel.tex index 383c360..a3237fe 100644 --- a/buch/chapters/050-differential/bessel.tex +++ b/buch/chapters/050-differential/bessel.tex @@ -18,6 +18,9 @@ die sich durch bekannte Funktionen ausdrücken lassen, es ist also nötig, eine neue Familie von speziellen Funktionen zu definieren, die Bessel-Funktionen. +% +% Besselsche Differentialgleichung +% \subsection{Die Besselsche Differentialgleichung} % XXX Wo taucht diese Gleichung auf Die Besselsche Differentialgleichung ist die Differentialgleichung @@ -30,6 +33,9 @@ für eine auf dem Interval $[0,\infty)$ definierte Funktion $y(x)$. Der Parameter $\alpha$ ist eine beliebige komplexe Zahl $\alpha\in \mathbb{C}$, die Lösungsfunktionen hängen daher von $\alpha$ ab. +% +% Eigenwertproblem +% \subsubsection{Eigenwertproblem} Die Besselsche Differentialgleichung \eqref{buch:differentialgleichungen:eqn:bessel} @@ -46,12 +52,15 @@ erfüllt \[ By = -x^2y''+xy+x^2y +x^2y''+xy'+x^2y =\alpha^2 y, \] ist also eine Eigenfunktion des Bessel-Operators zum Eigenwert $\alpha^2$. +% +% Indexgleichung +% \subsubsection{Indexgleichung} Die Besselsche Differentialgleichung ist eine Differentialgleichung der Art~\eqref{buch:differentialgleichungen:eqn:dglverallg} mit @@ -117,8 +126,9 @@ Nur eine Lösung kann man finden, wenn \] ist. - - +% +% Bessel-Funktionen erster Art +% \subsection{Bessel-Funktionen erster Art} Für $\alpha \ge 0$ gibt es immer mindestens eine Lösung der Besselgleichung als verallgemeinerte Potenzreihe mit $\varrho=\alpha$. @@ -138,6 +148,9 @@ Da $F(\varrho+1)\ne 0$ ist, folgt dass $a_1=0$ sein muss. % Fall n=1 gesondert behandeln +% +% Der allgemeine Fall +% \subsubsection{Der allgemeine Fall} Für die höheren Potenzen $n>1$ wird die Rekursionsformel für die Koeffizienten $a_n$ der verallgemeinerten Potenzreihe @@ -201,10 +214,11 @@ x^\varrho\biggl( x^\varrho \sum_{k=0}^\infty \frac{1}{(\varrho+1)_k} \frac{(-x^2/4)}{k!} = +x^\varrho +\cdot \mathstrut_0F_1\biggl(;\varrho+1;-\frac{x^2}{4}\biggr) \end{align*} -Falls also $\alpha$ kein ganzzahliges Vielfaches von $\frac12$ ist, finden -wir zwei Lösungsfunktionen +Wir finden also zwei Lösungsfunktionen \begin{align} y_1(x) %J_\alpha(x) @@ -214,8 +228,10 @@ x^{\alpha\phantom{-}} \frac{1}{(\alpha+1)_k} \frac{(-x^2/4)^k}{k!} = +x^\alpha +\cdot \mathstrut_0F_1\biggl(;\alpha+1;-\frac{x^2}{4}\biggr), -\label{buch:differentialgleichunge:bessel:erste} +\label{buch:differentialgleichunge:bessel:eqn:erste} \\ y_2(x) %J_{-\alpha}(x) @@ -223,32 +239,50 @@ y_2(x) x^{-\alpha} \sum_{k=0}^\infty \frac{1}{(-\alpha+1)_k} \frac{(-x^2/4)^k}{k!} = +x^{-\alpha} +\cdot \mathstrut_0F_1\biggl(;-\alpha+1;-\frac{x^2}{4}\biggr). -\label{buch:differentialgleichunge:bessel:zweite} +\label{buch:differentialgleichunge:bessel:eqn:zweite} \end{align} +Man beachte, dass die zweite Lösung für ganzzahliges $\alpha>0$ nicht +definiert ist. +Man kann auch direkt nachrechnen, dass diese Funktionen Lösungen +der Besselschen Differentialgleichung sind. +% +% Bessel-Funktionen +% \subsubsection{Bessel-Funktionen} Da die Besselsche Differentialgleichung linear ist, ist auch jede Linearkombination der Funktionen -\eqref{buch:differentialgleichunge:bessel:erste} +\eqref{buch:differentialgleichunge:bessel:eqn:erste} und -\eqref{buch:differentialgleichunge:bessel:zweite} +\eqref{buch:differentialgleichunge:bessel:eqn:zweite} eine Lösung. -Man kann zum Beispiel das Pochhammer-Symbol im Nenner loswerden, -wenn man im Nenner mit $\Gamma(\alpha+1)$ -multipliziert: +Satz~\ref{buch:rekursion:gamma:satz:gamma-pochhammer} +ermöglicht, das Pochhammer-Symbol durch Werte der Gamma-Funktion +wie in \[ -\frac{(1/2)^\alpha}{\Gamma(\alpha+1)} +(\alpha+1)_n = \frac{\Gamma(\alpha+k+1)}{\Gamma(\alpha+1)} +\] +auszudrücken. +Damit wird +\begin{align} y_1(x) +&= +x^\alpha +\sum_{k=0}^\infty +\frac{\Gamma(\alpha+1)}{\Gamma(\alpha+k+1)} +\frac{(-x^2/4)^k}{k!} = +\Gamma(\alpha+1) 2^{\alpha} \biggl(\frac{x}{2}\biggr)^\alpha \sum_{k=0}^\infty -\frac{(-1)^k}{k!\,\Gamma(\alpha+k+1)} -\biggl(\frac{x}{2}\biggr)^{2k}. -\] -Dabei haben wir es durch -Multiplikation mit $(\frac12)^\alpha$ auch geschafft, die Funktion -einheitlich als Funktion von $x/2$ auszudrücken. +\frac{(-1)^k}{k!\,\Gamma(\alpha+k+1)} \biggl(\frac{x}{2}\biggr)^{2k} +\label{buch:differentialgleichungen:bessel:normierungsgleichung} +\end{align} +Nur gerade der Faktor $2^\alpha\Gamma(\alpha+1)$ ist von $k$ und $x$ +unabhängig, daher ist die folgende Definition sinnvoll: \begin{definition} \label{buch:differentialgleichungen:bessel:definition} @@ -262,8 +296,26 @@ J_{\alpha}(x) \biggl(\frac{x}{2}\biggr)^{2k} \] heisst {\em Bessel-Funktion erster Art der Ordnung $\alpha$}. +\index{Bessel-Funktion!erster Art}% \end{definition} +Die Bessel-Funktion $J_\alpha(x)$ der Ordnung $\alpha$ unterscheidet sich +nur durch einen Normierungsfaktor von der Lösung $y_1(x)$. +Dasselbe gilt für $J_{-\alpha}(x)$ und $y_2(x)$: +\begin{align*} +J_{\alpha}(x) +&= +\frac{1}{2^\alpha\Gamma(\alpha+1)} +\cdot +y_1(x) +\\ +J_{-\alpha}(x) +&= +\frac{1}{2^{-\alpha}\Gamma(-\alpha+1)} +\cdot +y_2(x). +\end{align*} + Man beachte, dass diese Definition für beliebige ganzzahlige $\alpha$ funktioniert. Ist $\alpha=-n<0$, $n\in\mathbb{N}$, dann hat der Nenner Pole @@ -285,6 +337,8 @@ J_{-n}(x) (-1)^n J_{n}(x). \end{align*} +Insbesondere unterscheiden sich $J_n(x)$ und $J_{-n}(x)$ nur durch +ein Vorzeichen. \subsubsection{Erzeugende Funktion} \begin{figure} @@ -388,6 +442,9 @@ Die beiden Exponentialreihen sind \notag \end{align} +% +% Additionstheorem +% \subsubsection{Additionstheorem} Die erzeugende Funktion kann dazu verwendet werden, das Additionstheorem für die Besselfunktionen zu beweisen. @@ -438,7 +495,9 @@ J_l(x+y) &= \sum_{m=-\infty}^\infty J_m(x)J_{l-m}(y) für alle $l$. \end{proof} - +% +% Der Fall \alpha=0 +% \subsubsection{Der Fall $\alpha=0$} Im Fall $\alpha=0$ hat das Indexpolynom eine doppelte Nullstelle, wir können daher nur eine Lösung erwarten. @@ -453,8 +512,19 @@ J_0(x) \] geschrieben werden kann. -% XXX Zweite Lösung explizit durchrechnen +Als lineare Differentialgleichung zweiter Ordnung erwarten wir noch +eine zweite, linear unabhängige Lösung. +Diese kann jedoch nicht allein mit der Potenzreihenmethode, +dazu sind die Methoden der Funktionentheorie nötig. +Im Abschnitt~\ref{buch:funktionentheorie:subsection:dglsing} +wird gezeigt, wie dies möglich ist und auf +Seite~\pageref{buch:funktionentheorie:subsubsection:bessel2art} +werden die damit zu findenden Bessel-Funktionen 0-ter Ordnung und +zweiter Art vorgestellt. +% +% Der Fall \alpha=p, p\in \mathbb{N} +% \subsubsection{Der Fall $\alpha=p$, $p\in\mathbb{N}, p > 0$} In diesem Fall kann nur die erste Lösung~\eqref{buch:differentialgleichunge:bessel:erste} @@ -467,8 +537,9 @@ J_p(x) \frac{(-1)^k}{k!(p+k)!}\biggl(\frac{x}{2}\biggr)^{p+2k}. \] -TODO: Lösung für $\alpha=-n$ - +% +% Der Fall $\alpha=n+\frac12$ +% \subsubsection{Der Fall $\alpha=n+\frac12$, $n\in\mathbb{N}$} Obwohl $2\alpha$ eine Ganzzahl ist, sind die beiden Lösungen \label{buch:differentialgleichunge:bessel:erste} @@ -491,7 +562,7 @@ Es ist = \frac{1}{2^k}\bigl(3\cdot 5\cdot\ldots\cdot (2k+1)\bigr) = -\frac{(2k+1)!}{2^{2k+1}\cdot k!} +\frac{(2k+1)!}{2^{2k}\cdot k!} \\ \biggl(-\frac12 + 1\biggr)_k &= @@ -508,63 +579,181 @@ Es ist = \frac{1}{2^k}\bigl(1\cdot 3 \cdot\ldots\cdot (2(k-1)+1)\bigr) = -\frac{(2k-1)!}{2^{2k}\cdot (k-1)!} +\frac{(2k-1)!}{2^{2k-1}\cdot (k-1)!} \end{align*} Damit können jetzt die Reihenentwicklungen der Lösung wie folgt umgeformt werden \begin{align*} y_1(x) &= -\sqrt{x} +x^\alpha \sum_{k=0}^\infty \frac{1}{(\alpha+1)_k} \frac{(-x^2/4)^k}{k!} = \sqrt{x} \sum_{k=0}^\infty -\frac{2^{2k+1}k!}{(2k+1)!} +\frac{2^{2k}k!}{(2k+1)!} \frac{(-x^2/4)^k}{k!} = \sqrt{x} \sum_{k=0}^\infty (-1)^k -\frac{2\cdot x^{2k}}{(2k+1)!} +\frac{x^{2k}}{(2k+1)!} \\ &= -\frac{1}{2\sqrt{x}} +\frac{1}{\sqrt{x}} \sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!} = -\frac{1}{2\sqrt{x}} \sin x +\frac{1}{\sqrt{x}} \sin x \\ y_2(x) &= -\frac{1}{\sqrt{x}} +x^{-\alpha} \sum_{k=0}^\infty -\frac{2^{2k}\cdot (k-1)!}{(2k-1)!} +\frac{1}{(-\alpha+1)_k} \frac{(-x^2/4)^k}{k!} = -\frac{1}{\sqrt{x}} +x^{-\frac12} \sum_{k=0}^\infty -(-1)^k -\frac{x^{2k}}{(2k-1)!\cdot k} +\frac{2^{2k-1}\cdot (k-1)!}{(2k-1)!} +\frac{(-x^2/4)^k}{k!} \\ &= -\frac{2}{\sqrt{x}} +\frac{1}{\sqrt{x}} \sum_{k=0}^\infty (-1)^k \frac{x^{2k}}{(2k-1)!\cdot 2k} = -\frac{2}{\sqrt{x}} \cos x. +\frac{1}{\sqrt{x}} \cos x. \end{align*} -% XXX Nachrechnen, dass diese Funktionen -% XXX Lösungen der Differentialgleichung sind - -\subsection{Analytische Fortsetzung und Bessel-Funktionen zweiter Art} - - - +Die Bessel-Funktionen verwenden aber eine andere Normierung. +Die Gleichung~\eqref{buch:differentialgleichungen:bessel:normierungsgleichung} +zeigt, dass die Bessel-Funktionen durch Division +der Funktion $y_1(x)$ und $y_2(x)$ durch $2^\alpha \Gamma(\alpha+1)$ +erhalten werden können. +Dies ergibt +\begin{equation*} +\renewcommand{\arraycolsep}{1pt} +\begin{array}{rclclclcl} +J_{\frac12}(x) +&=& +\displaystyle\frac{1}{2^{\frac12}\Gamma(\frac12+1)} +y_1(x) +&=& +\displaystyle\frac{1}{2^{\frac12}\frac12\Gamma(\frac12)} +y_1(x) +&=& +\displaystyle\frac{\sqrt{2}}{\Gamma(\frac12)} +y_1(x) +&=& +\displaystyle\frac{1}{\Gamma(\frac12)} +\sqrt{ \frac{2}{x}} +\sin x, +\\ +J_{-\frac12}(x) +&=& +\displaystyle\frac{1}{2^{-\frac12}\Gamma(-\frac12+1)} +y_2(x) +&=& +\displaystyle\frac{2^{\frac12}}{\Gamma(\frac12)} +y_2(x) +&=& +\displaystyle\frac{\sqrt{2}}{\Gamma(\frac12)} +y_2(x) +&=& +\displaystyle\frac{1}{\Gamma(\frac12)} +\sqrt{\frac{2}{x}} +\cos x. +\end{array} +\end{equation*} +Wegen $\Gamma(\frac12)=\sqrt{\pi}$ sind die +halbzahligen Bessel-Funktionen daher +\begin{align*} +J_{\frac12}(x) +&= +\sqrt{\frac{2}{\pi x}} \sin x += +\sqrt{\frac{2}{\pi}} x^{-\frac12}\sin x +& +&\text{und}& +J_{-\frac12}(x) +&= +\sqrt{\frac{2}{\pi x}} \cos x += +\sqrt{\frac{2}{\pi}} x^{-\frac12}\cos x. +\end{align*} +% +% Direkte Verifikation der Lösungen +% +\subsubsection{Direkte Verifikation der Lösungen für $\alpha=\pm\frac12$} +Tatsächlich führt die Anwendung des Bessel-Operators auf die beiden +Funktionen auf +\begin{align*} +\sqrt{\frac{\pi}2} +BJ_{\frac12}(x) +&= +\sqrt{\frac{\pi}2} +\biggl( +x^2J_{\frac12}''(x) + xJ_{\frac12}'(x) + x^2J_{\frac12}(x) +\biggr) +\\ +&= +x^2(x^{-\frac12}\sin x)'' ++ +x(x^{-\frac12}\sin x)' ++ +x^2(x^{-\frac12}\sin x) +\\ +&= +x^2( +x^{-{\textstyle\frac12}}\cos x +-{\textstyle\frac12}x^{-\frac32}\sin x +)' ++ +x( +x^{-\frac12}\cos x +-{\textstyle\frac12}x^{-\frac32}\sin x +) ++ +x^{\frac32}\sin x +\\ +&= +x^2( +-x^{-\frac12}\sin x +-{\textstyle\frac12}x^{-\frac32}\cos x +-{\textstyle\frac12}x^{-\frac32}\cos x ++{\textstyle\frac{3}{4}}x^{-\frac52}\sin x +) ++ +x^{\frac12}\cos x ++ +x^{-\frac12}(x-{\textstyle\frac12})\sin x +\\ +&= +( +-x^{\frac32} ++{\textstyle\frac34}x^{-\frac12} ++x^{\frac32} +-{\textstyle\frac12}x^{-\frac12} +) +\sin x += +\frac14x^{-\frac12}\sin x += +\frac14 +\sqrt{\frac{\pi}2} +J_{\frac12}(x) +\\ +BJ_{\frac12}(x) +&= +\biggl(\frac12\biggr)^2 J_{\frac12}(x). +\end{align*} +Dies zeigt, dass $J_{\frac12}(x)$ tatsächlich eine Eigenfunktion +des Bessel-Operators zum Eigenwert $\alpha^2 = \frac14$. +Analog kann man die Lösung $y_2(x)$ für $-\frac12$ verifizieren. diff --git a/buch/chapters/050-differential/hypergeometrisch.tex b/buch/chapters/050-differential/hypergeometrisch.tex index 65b3be7..87b9318 100644 --- a/buch/chapters/050-differential/hypergeometrisch.tex +++ b/buch/chapters/050-differential/hypergeometrisch.tex @@ -1591,7 +1591,7 @@ x\cdot \end{align*} als Lösungen. Die Differentialgleichung von $\mathstrut_0F_1$ sollte sich in diesem -Fall also auf die Airy-Differentialgleichung reduzieren lassen. +Fall also auf die Airy-Dif\-fe\-ren\-tial\-glei\-chung reduzieren lassen. Bei der Substition der Parameter in die Differentialgleichung \eqref{buch:differentialgleichungen:0F1:dgl} beachten wird, dass diff --git a/buch/chapters/070-orthogonalitaet/bessel.tex b/buch/chapters/070-orthogonalitaet/bessel.tex index 3e9412a..0ef28fd 100644 --- a/buch/chapters/070-orthogonalitaet/bessel.tex +++ b/buch/chapters/070-orthogonalitaet/bessel.tex @@ -1,7 +1,8 @@ % % Besselfunktionen also orthogonale Funktionenfamilie % -\section{Bessel-Funktionen als orthogonale Funktionenfamilie} +\section{Bessel-Funktionen als orthogonale Funktionenfamilie +\label{buch:orthogonalitaet:section:bessel}} \rhead{Bessel-Funktionen} Auch die Besselfunktionen sind eine orthogonale Funktionenfamilie. Sie sind Funktionen differenzierbaren Funktionen $f(r)$ für $r>0$ diff --git a/buch/chapters/070-orthogonalitaet/chapter.tex b/buch/chapters/070-orthogonalitaet/chapter.tex index 4756844..fba1298 100644 --- a/buch/chapters/070-orthogonalitaet/chapter.tex +++ b/buch/chapters/070-orthogonalitaet/chapter.tex @@ -8,20 +8,66 @@ \label{buch:chapter:orthogonalitaet}} \lhead{Orthogonalität} \rhead{} +In der linearen Algebra lernt man, dass orthonormierte Basen für die +Lösung vektorgeometrischer Probleme, bei denen auch das Skalarprodukt +involviert ist, besonders günstig sind. +Die Zerlegung eines Vektors in einer Basis verlangt normalerweise nach +der Lösung eines linearen Gleichungssystems, für orthonormierte +Basisvektoren beschränkt sie sich auf die Berechnung von Skalarprodukten. + +Oft dienen spezielle Funktionen als Basis der Lösungen einer linearen +partiellen Differentialgleichung (siehe Kapitel~\ref{buch:chapter:pde}). +Die Randbedingungen müssen dazu in der gewählten Basis von Funktionen +zerlegt werden. +Fourier ist es gelungen, die Idee des Skalarproduktes und der Orthogonalität +auf Funktionen zu verallgemeinern und so zum Beispiel das Wärmeleitungsproblem +zu lösen. + +Der Orthonormalisierungsprozess von Gram-Schmidt wird damit auch auf +Funktionen anwendbar +(Abschnitt~\ref{buch:orthogonalitaet:section:orthogonale-funktionen}), +der Nutzen führt aber noch viel weiter. +Da $K[x]$ ein Vektorraum ist, führt er von der Basis der Monome +$\{1,x,x^2,\dots,x^n\}$ +auf orthonormierte Polynome. +Diese haben jedoch eine ganze Reihe weiterer nützlicher Eigenschaften. +So wird in Abschnitt~\ref{buch:orthogonal:section:drei-term-rekursion} +gezeigt, dass sich die Werte aller Polynome einer solchen Familie mit +einer Rekursionsformel effizient berechnen lassen, die höchstens drei +Terme umfasst. +In Abschnitt~\ref{buch:orthogonalitaet:section:rodrigues} werden +die Rodrigues-Formeln vorgeführt, die Polynome durch Anwendung eines +Differentialoperators hervorbringen. +In Abschnitt~\ref{buch:orthogonal:section:orthogonale-polynome-und-dgl} +schliesslich wird gezeigt, dass diese Polynome auch Eigenfunktionen +eines selbstadjungierten Operators sind. +Da man in der linearen Algebra auch lernt, dass die Eigenvektoren einer +symmetrischen Matrix zu verschiedenen Eigenwerten orthogonal sind, +ist die Orthogonalität plötzlich nicht mehr überraschend. + +Die Bessel-Funktionen von +Abschnitt~\ref{buch:differntialgleichungen:section:bessel} +sind auch Eigenfunktionen eines Differentialoperators. +Abschnitt~\ref{buch:orthogonalitaet:section:bessel} findet das zugehörige +Skalarprodukt, welches andeutet, dass auch für andere Funktionenfamilien +eine entsprechende Konstruktion möglich ist. +Das in Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem} +präsentierte Sturm-Liouville-Problem führt sie durch. +Das Kapitel schliesst mit dem +Abschnitt~\ref{buch:orthogonal:section:gauss-quadratur} +über die Gauss-Quadratur, welche die Eigenschaften orthogonaler Polynome +für einen besonders effizienten numerischen Integrationsalgorithmus +ausnutzt. + \input{chapters/070-orthogonalitaet/orthogonal.tex} \input{chapters/070-orthogonalitaet/rekursion.tex} \input{chapters/070-orthogonalitaet/rodrigues.tex} -%\input{chapters/070-orthogonalitaet/jacobi.tex} \input{chapters/070-orthogonalitaet/legendredgl.tex} \input{chapters/070-orthogonalitaet/bessel.tex} \input{chapters/070-orthogonalitaet/sturm.tex} \input{chapters/070-orthogonalitaet/gaussquadratur.tex} -%\section{TODO} -%\begin{itemize} -%\end{itemize} - -\section*{Übungsaufgaben} +\section*{Übungsaufgabe} \rhead{Übungsaufgaben} \aufgabetoplevel{chapters/070-orthogonalitaet/uebungsaufgaben} \begin{uebungsaufgaben} diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index 2e43cec..4a25678 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -1,7 +1,8 @@ % % Anwendung: Gauss-Quadratur % -\section{Anwendung: Gauss-Quadratur} +\section{Anwendung: Gauss-Quadratur +\label{buch:orthogonal:section:gauss-quadratur}} \rhead{Gauss-Quadratur} Orthogonale Polynome haben eine etwas unerwartet Anwendung in einem von Gauss erdachten numerischen Integrationsverfahren. @@ -284,7 +285,7 @@ $p(x)$ sein. Der Satz~\ref{buch:integral:satz:gaussquadratur} begründet das {\em Gausssche Quadraturverfahren}. -Die in Abschnitt~\ref{buch:integral:section:orthogonale-polynome} +Die in Abschnitt~\ref{buch:orthogonal:subsection:legendre-polynome} bestimmten Legendre-Polynome $P_n$ haben die im Satz verlangte Eigenschaft, dass sie auf allen Polynomen geringeren Grades orthogonal sind. diff --git a/buch/chapters/070-orthogonalitaet/legendredgl.tex b/buch/chapters/070-orthogonalitaet/legendredgl.tex index de8f63f..6401e98 100644 --- a/buch/chapters/070-orthogonalitaet/legendredgl.tex +++ b/buch/chapters/070-orthogonalitaet/legendredgl.tex @@ -3,7 +3,8 @@ % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % -\section{Orthogonale Polynome und Differentialgleichungen} +\section{Orthogonale Polynome und Differentialgleichungen +\label{buch:orthogonal:section:orthogonale-polynome-und-dgl}} \rhead{Differentialgleichungen orthogonaler Polynome} Legendre hat einen ganz anderen Zugang zu den nach ihm benannten Polynomen gefunden. @@ -16,6 +17,9 @@ Die Orthogonalität wird dann aus einer Verallgemeinerung der bekannten Eingeschaft folgen, dass Eigenvektoren einer symmetrischen Matrix zu verschiedenen Eigenwerten orthogonal sind. +% +% Legendre-Differentialgleichung +% \subsection{Legendre-Differentialgleichung} Die {\em Legendre-Differentialgleichung} ist die Differentialgleichung \begin{equation} @@ -61,7 +65,10 @@ zerlegen, die als Linearkombinationen der beiden Lösungen $y(x)$ und $y_s(x)$ ebenfalls Lösungen der Differentialgleichung sind. -\subsection{Potenzreihenlösung} +% +% Potenzreihenlösungen +% +\subsubsection{Potenzreihenlösung} Wir suchen eine Lösung in Form einer Potenzreihe um $x=0$ und verwenden dazu den Ansatz \[ @@ -170,7 +177,10 @@ eine Polynomlösung $\bar{P}_n(x)$ vom Grad $n$ gibt. Dies kann aber nicht erklären, warum die so gefundenen Polynome orthogonal sind. -\subsection{Eigenfunktionen} +% +% Eigenfunktionen +% +\subsubsection{Eigenfunktionen} Die Differentialgleichung \eqref{buch:integral:eqn:legendre-differentialgleichung} Kann mit dem Differentialoperator @@ -198,7 +208,10 @@ des Operators $D$ zum Eigenwert $n(n+1)$ sind: D\bar{P}_n = -n(n+1) \bar{P}_n. \] -\subsection{Orthogonalität von $\bar{P}_n$ als Eigenfunktionen} +% +% Orthogonalität von P_n als Eigenfunktionen +% +\subsubsection{Orthogonalität von $\bar{P}_n$ als Eigenfunktionen} Ein Operator $A$ auf Funktionen heisst {\em selbstadjungiert}, wenn für zwei beliebige Funktionen $f$ und $g$ gilt \[ @@ -274,7 +287,10 @@ die $\bar{P}_n$ orthogonale Polynome vom Grad $n$ sind, die die gleiche Standardierdisierungsbedingung wie die Legendre-Polyonome erfüllen, also ist $\bar{P}_n(x)=P_n(x)$. -\subsection{Legendre-Funktionen zweiter Art} +% +% Legendre-Funktionen zweiter Art +% +\subsubsection{Legendre-Funktionen zweiter Art} %Siehe Wikipedia-Artikel \url{https://de.wikipedia.org/wiki/Legendre-Polynom} % Die Potenzreihenmethode liefert natürlich auch Lösungen der @@ -368,7 +384,7 @@ Q_1(x) = x \operatorname{artanh}x-1 verwendet werden. % -% +% Laguerre-Differentialgleichung % \subsection{Laguerre-Differentialgleichung \label{buch:orthogonal:subsection:laguerre-differentialgleichung}} @@ -429,6 +445,9 @@ ein anderer Weg zu einer zweiten Lösung gesucht werden. XXX TODO: zweite Lösung der Differentialgleichung. +% +% +% \subsubsection{Die assoziierte Laguerre-Differentialgleichung} \index{assoziierte Laguerre-Differentialgleichung}% \index{Laguerre-Differentialgleichung, assoziierte}% diff --git a/buch/chapters/070-orthogonalitaet/orthogonal.tex b/buch/chapters/070-orthogonalitaet/orthogonal.tex index 677e865..97cd06b 100644 --- a/buch/chapters/070-orthogonalitaet/orthogonal.tex +++ b/buch/chapters/070-orthogonalitaet/orthogonal.tex @@ -11,9 +11,13 @@ Funktionenreihen mit Summanden zu bilden, die im Sinne eines Skalarproduktes orthogonal sind, welches mit Hilfe eines Integrals definiert sind. Solche Funktionenfamilien treten jedoch auch als Lösungen von -Differentialgleichungen. +Differentialgleichungen auf. Besonders interessant wird die Situation, wenn die Funktionen Polynome sind. +In diesem Abschnitt soll zunächst das Skalarprodukt definiert +und an Hand von Beispielen gezeigt werden, wie verschiedenartige +interessante Familien von orthogonalen Polynomen gewonnen werden +können. % % Skalarprodukt @@ -520,7 +524,7 @@ Tabelle~\ref{buch:integral:table:legendre-polynome}. Die Graphen sind in Abbildung~\ref{buch:integral:orthogonal:legendregraphen} dargestellt. Abbildung~\ref{buch:integral:orthogonal:legendreortho} illustriert, -dass die die beiden Polynome $P_4(x)$ und $P_7(x)$ orthogonal sind. +dass die beiden Polynome $P_4(x)$ und $P_7(x)$ orthogonal sind. Das Produkt $P_4(x)\cdot P_7(x)$ hat Integral $=0$. % diff --git a/buch/chapters/070-orthogonalitaet/rekursion.tex b/buch/chapters/070-orthogonalitaet/rekursion.tex index dc5531b..c0efc6d 100644 --- a/buch/chapters/070-orthogonalitaet/rekursion.tex +++ b/buch/chapters/070-orthogonalitaet/rekursion.tex @@ -31,7 +31,17 @@ für alle $n$, $m$. \end{definition} \subsubsection{Allgemeine Drei-Term-Rekursion für orthogonale Polynome} -Der folgende Satz besagt, dass $p_n$ eine Rekursionsbeziehung erfüllt. +Die Multiplikation mit $x$ macht aus einem Polynom vom Grad $n$ ein +Polynom vom Grad $n+1$. +Das Polynom $xp_n(x)$ lässt sich daher als Linearkombination der +Polynome $p_k(x)$ mit $k\le n+1$ schreiben. +Es muss also eine lineare Beziehung zwischen den Polynomen $p_k(x)$ und +$xp_n(x)$ geben, die man nach $p_{n+1}(x)$ auflösen kann, um eine lineare +Darstellung von $p_{n+1}(x)$ durch die $p_k(x)$ und $p_n(x)$ zu +bekommen. +A priori muss man damit rechnen, dass sehr viele Summanden nötig sind. +Der folgende Satz besagt, dass $p_n(x)$ eine Rekursionsbeziehung mit +nur drei Termen erfüllt. \begin{satz} \label{buch:orthogonal:satz:drei-term-rekursion} @@ -55,9 +65,13 @@ C_{n+1} = \frac{A_{n+1}}{A_n}\frac{h_{n+1}}{h_n}. \end{equation} \end{satz} +Die Rekursionsbeziehung~\eqref{buch:orthogonal:eqn:rekursion} bedeutet, +dass sich die Werte $p_n(x)$ für alle $n$ ausgehend von $p_1(x)$ und +$p_0(x)$ mit nur $O(n)$ Operationen ermitteln lassen. + \subsubsection{Multiplikationsoperator mit $x$} -Man kann die Relation auch nach dem Produkt $xp_n(x)$ auflösen, dann -wird sie +Man kann die Relation \eqref{buch:orthogonal:eqn:rekursion} +auch nach dem Produkt $xp_n(x)$ auflösen, dann wird sie \begin{equation} xp_n(x) = @@ -68,9 +82,12 @@ xp_n(x) \frac{C_n}{A_n}p_{n-1}(x). \label{buch:orthogonal:eqn:multixrelation} \end{equation} -Die Multiplikation mit $x$ ist eine lineare Abbildung im Raum der Funktionen. +Die Multiplikation mit $x$ ist eine lineare Abbildung im Raum der Funktionen, +die wir weiter unten auch $M_x$ abkürzen. Die Relation~\eqref{buch:orthogonal:eqn:multixrelation} besagt, dass diese Abbildung in der Basis der Polynome $p_k$ tridiagonale Form hat. +Ein Beispiel dafür ist im nächsten Abschnitt in +\eqref{buch:orthogonal:eqn:Mx} \subsubsection{Drei-Term-Rekursion für die Tschebyscheff-Polynome} Eine Relation der Form~\eqref{buch:orthogonal:eqn:multixrelation} @@ -84,6 +101,22 @@ T_{n+1}(x) = 2x\,T_n(x)-T_{n-1}(x), \] also $A_n=2$, $B_n=0$ und $C_n=1$. +Die Matrixdarstellung des Multiplikationsoperators $M_x$ in der +Basis der Tschebyscheff-Polynome hat wegen +\eqref{buch:orthogonal:eqn:multixrelation} die Form +\begin{equation} +M_x += +\begin{pmatrix} + 0&\frac12& 0& 0& 0&\dots  \\ +\frac12& 0&\frac12& 0& 0&\dots  \\ + 0&\frac12& 0&\frac12& 0&\dots  \\ + 0& 0&\frac12& 0&\frac12&\dots  \\ + 0& 0& 0&\frac12& 0&\dots  \\ + \vdots& \vdots& \vdots& \vdots& \vdots&\ddots +\end{pmatrix}. +\label{buch:orthogonal:eqn:Mx} +\end{equation} \subsubsection{Beweis von Satz~\ref{buch:orthogonal:satz:drei-term-rekursion}} Die Relation~\eqref{buch:orthogonal:eqn:multixrelation} zeigt auch, diff --git a/buch/chapters/070-orthogonalitaet/rodrigues.tex b/buch/chapters/070-orthogonalitaet/rodrigues.tex index 9fded85..9a36bdc 100644 --- a/buch/chapters/070-orthogonalitaet/rodrigues.tex +++ b/buch/chapters/070-orthogonalitaet/rodrigues.tex @@ -14,7 +14,8 @@ mit der Ableitung kann man den Grad aber auch senken, man könnte daher auch nach einer Rekursionsformel fragen, die bei einem Polynom hohen Grades beginnt und mit Hilfe von Ableitungen zu geringeren Graden absteigt. -Solche Formeln heissen Rodrigues-Formeln nach dem Entdecker Olinde +Solche Formeln heissen {\em Rodrigues-Formeln} nach dem Entdecker Olinde +\index{Rodriguez, Olinde}% Rodrigues, der eine solche Formal als erster für Legendre-Polynome gefunden hat. @@ -27,12 +28,17 @@ Die Skalarprodukte sollen \] sein. +% +% Pearsonsche Differentialgleichung +% \subsection{Pearsonsche Differentialgleichung} Die {\em Pearsonsche Differentialgleichung} ist die Differentialgleichung \begin{equation} B(x) y' - A(x) y = 0, \label{buch:orthogonal:eqn:pearson} \end{equation} +\index{Differentialgleichung!Pearsonsche}% +\index{Pearsonsche Differentialgleichung}% wobei $B(x)$ ein Polynom vom Grad höchstens $2$ ist und $A(x)$ ein höchstens lineares Polynom. Die Gleichung~\eqref{buch:orthogonal:eqn:pearson} @@ -45,20 +51,31 @@ Dann kann man die Gleichung umstellen in = \frac{A(x)}{B(x)} \qquad\Rightarrow\qquad -y = \exp\biggl( \int\frac{A(x)}{B(x)}\biggr)\,dx. +y += +\exp\biggl( +\int\frac{A(x)}{B(x)} +\,dx +\biggr) +. \] -Im folgenden nehmen wir zusätzlich an, dass +Im Folgenden nehmen wir zusätzlich an, dass an den Intervallenden \begin{equation} \lim_{x\to a+} w(x)B(x) = 0, \qquad\text{und}\qquad -\lim_{x\to b-} w(x)B(x) = 0. +\lim_{x\to b-} w(x)B(x) = 0 \end{equation} +gilt. + Falls $w(x)$ an den Intervallenden einen von $0$ verschiedenen Grenzwert hat, bedeutet dies, dass $B(a)=B(b)=0$ sein muss. Falls $w(x)$ am Intervallende divergiert, muss $B(x)$ dort eine Nullstelle höherer Ordnung haben, was aber für ein Polynom zweiten Grades nicht möglich ist. +% +% Rekursionsformel +% \subsection{Rekursionsformel} Multiplikation mit $B(x)$ wird den Grad eines Polynomes typischerweise um $2$ erhöhen, die Ableitung wird ihn wieder um $1$ reduzieren. @@ -66,12 +83,13 @@ Etwas formeller kann man dies wie folgt formulieren: \begin{satz} Für alle $n\ge 0$ ist -\[ +\begin{equation} q_n(x) = \frac{1}{w(x)} \frac{d^n}{dx^n} B(x)^n w(x) -\] +\label{buch:orthogonalitaet:rodrigues:eqn:rekursion} +\end{equation} ein Polynom vom Grad höchstens $n$. \end{satz} @@ -85,50 +103,65 @@ r_0(x) B(x)^n w(x) \\ &= \frac{d^{n-1}}{dx^{n-1}} -\bigl(r_0'(x)B(x)+ nB'(x)B(x)^{n-1}w(x) + B(x)^n w'(x) \bigr) +\bigl(r_0'(x)B(x)+ nr_0(x)B'(x)B(x)^{n-1}w(x) + r_0(x)B(x)^n w'(x) \bigr) \\ &= \frac{d^{n-1}}{dx^{n-1}} -(r_0'(x)B(x)+nB'(x)+A(x)) B(x)^{n-1} w(x) -= +(\underbrace{r_0'(x)B(x)+nr_0(x)B'(x)+r_0(x)A(x)}_{\displaystyle = r_1(x)}) +B(x)^{n-1} w(x) +\\ +&= \frac{d^{n-1}}{dx^{n-1}} r_1(x)B^{n-1}(x) w(x). \end{align*} -Für die Funktionen $r_k$ gilt die Rekursionsformel +Iterativ lässt sich eine Folge von +Funktionen $r_k(x)$ definieren, für die Rekursionsformel \begin{equation} -r_k(x) = r_{k-1}'(x)B(x) + kB'(x) + A(x). +r_k(x) = r_{k-1}'(x)B(x) + \bigl((n+1-k)B'(x) + A(x)\bigr)r_{k-1}(x) \label{buch:orthogonal:rodrigues:rekursion:beweis1} \end{equation} +gilt. Wenn $r_0(x)$ ein Polynom ist, dann sind alle Funktionen $r_k(x)$ ebenfalls Polynome. -Durch wiederholte Anwendung dieser Formel kann man schliessen, dass +Aus der Konstruktion kann man schliessen, dass \[ \frac{d^n}{dx^n} r_0(x) B(x)^n w(x) = r_n(x) w(x). \] -Insbesondere folgt für $r_0(x)=1$, dass man durch $w(x)$ dividieren kann -und dass $r_n(x)=q_n(x)$. +Insbesondere folgt für $r_0(x)=1$, dass die $n$-te Ableitung den +Faktor $w(x)$ enthält und dass somit $r_n(x)=q_n(x)$ ein Polynom ist. + +Wir müssen auch noch den Grad von $r_k(x)$ bestimmen, wobei wir +wieder von $r_0(x)=1$ ausgehen. +Wir behaupten, dass $\deg r_k(x)\le k$ ist, und beweisen dies +mit vollständiger Induktion. +Für $k=0$ ist $\deg r_0(x) = 0 \le k$ die Induktionsverankerung. -Wir müssen auch noch den Grad von $r_k(x)$ bestimmen. -Dazu verwenden wir -\eqref{buch:orthogonal:rodrigues:rekursion:beweis1} und berechnen den -Grad: +Wir nehmen jetzt also an, dass $\deg r_{k-1}(x)\le k-1$ ist und +verwenden +\eqref{buch:orthogonal:rodrigues:rekursion:beweis1} um den Grad zu berechnen: \begin{equation*} \deg r_k(x) = \max \bigl( -\underbrace{\deg(r_{k-1}'(x) B(x))}_{\displaystyle \deg r_{k-1}(x) -1 + 2} +\underbrace{\deg(r_{k-1}'(x) B(x))}_{\displaystyle (k-1) -1 + 2} , -\underbrace{\deg(B'(x))}_{\displaystyle \le 1} +\underbrace{\deg(r_{k-1}(x)B'(x))}_{\displaystyle \le (k-1)+1} , -\underbrace{\deg(A(x))}_{\displaystyle \le 1} +\underbrace{\deg(r_{k-1}(x)A(x))}_{\displaystyle \le (k-1)+1} \bigr) -\le \max r_{k-1}(x) + 1. +\le k. \end{equation*} -Aus $\deg r_0(x)=0$ kann man jetzt ablesen, dass $\deg r_k(x)\le k$ ist. -Damit ist gezeigt, dass $\deg q_n(x)\le n$. +Damit ist der Induktionsschritt und $\deg r_k(x)\le k$ bewiesen. +Damit ist auch gezeigt, dass $\deg q_n(x)\le n$. \end{proof} +Die Rodrigues-Formel~\eqref{buch:orthogonalitaet:rodrigues:eqn:rekursion} +produziert eine Folge von Polynomen aufsteigenden Grades, es ist aber +noch nicht klar, dass diese Polynome bezüglich des gewählten Skalarproduktes +orthogonal sind. +Dies ist der Inhalt des folgenden Satzes. + \begin{satz} Es gibt Konstanten $c_n$ derart, dass \[ @@ -140,7 +173,7 @@ gilt. \end{satz} \begin{proof}[Beweis] -Wir müssen zeigen, dass die Polynome orthogonal sind auf allen Monomen +Wir zeigen, dass die Polynome orthogonal sind auf allen Monomen von geringerem Grad. \begin{align*} \langle q_n, x^k\rangle_w @@ -148,15 +181,17 @@ von geringerem Grad. \int_a^b q_n(x)x^kw(x)\,dx \\ &= -\int_a^b \frac{1}{w(x)}\frac{d^n}{dx^n}(B(x)^n w(x)) x^k w(x)\,dx +\int_a^b \frac{1}{w(x)} +\biggl(\frac{d^n}{dx^n}\bigl(B(x)^n w(x)\bigr)\biggr) +x^k w(x)\,dx \\ &= -\int_a^b \frac{d^n}{dx^n}(B(x)^n w(x)) x^k \,dx +\int_a^b \frac{d^n}{dx^n}\bigl(B(x)^n w(x)\bigr) x^k \,dx \\ &= -\biggl[\frac{d^{n-1}}{dx^{n-1}}(B(x)^n w(x)) x^k \biggr]_a^b +\biggl[\frac{d^{n-1}}{dx^{n-1}}\bigl(B(x)^n w(x)\bigr) x^k \biggr]_a^b - -\int_a^b \frac{d^{n-1}}{dx^{n-1}}(B(x)^n w(x))kx^{k-1}\,dx +\int_a^b \frac{d^{n-1}}{dx^{n-1}}\bigl(B(x)^n w(x)\bigr)kx^{k-1}\,dx \end{align*} Durch $n$-fache Iteration wird das Integral auf $0$ reduziert. Es bleiben nur die eckigen Klammern stehen, doch wenn man die Produktregel @@ -164,9 +199,20 @@ auswertet, bleibt immer mindestens ein Produkt $B(x)w(x)$ stehen, nach den Voraussetzungen an den Grenzwert dieses Produktes an den Intervallenden verschwinden diese Terme alle. Damit sind die $q_n(x)$ Polynome, die $w$-orthogonal sind auf allen -$x^k$ mit $k0$ im Innerend es Intervalls sein. +% +% Der Vektorraum H +% \subsection{Der Vektorraum $H$} Damit können wir jetzt die Eigenschaften der in Frage kommenden Funktionen zusammenstellen. @@ -346,7 +361,10 @@ f\in L^2([a,b],w)\;\bigg|\; \biggr\}. \] -\subsection{Differentialoperator} +% +% Der Sturm-Liouville-Differentialoperator +% +\subsection{Der Sturm-Liouville-Differentialoperator} Das verallgemeinerte Eigenwertproblem für $A$ und $B$ ist ein gewöhnliches Eigenwertproblem für die Operator $\tilde{A}=B^{-1}A$ bezüglich des modifizierten Skalarproduktes. @@ -366,12 +384,18 @@ $\lambda$ ist der zu $y(x)$ gehörige Eigenwert. Der Operator ist definiert auf Funktionen des im vorangegangenen Abschnitt definierten Vektorraumes $H$. +% +% Beispiele +% \subsection{Beispiele} Die meisten der früher vorgestellten Funktionenfamilien stellen sich als Lösungen eines geeigneten Sturm-Liouville-Problems heraus. Alle Eigenschaften aus der Sturm-Liouville-Theorie gelten daher automatisch für diese Funktionenfamilien. +% +% Trignometrische Funktionen +% \subsubsection{Trigonometrische Funktionen} Die trigonometrischen Funktionen sind Eigenfunktionen des Operators $d^2/dx^2$, also eines Sturm-Liouville-Operators mit $p(x)=1$, $q(x)=0$ @@ -434,6 +458,9 @@ Dann ist wegen die Bedingung~\eqref{buch:integrale:sturm:sabedingung} ebenfalls erfüllt, $L_0$ ist in diesem Raum selbstadjungiert. +% +% Bessel-Funktionen J_n(x) +% \subsubsection{Bessel-Funktionen $J_n(x)$} Der Bessel-Operator \eqref{buch:differentialgleichungen:bessel-operator} kann wie folgt in die Form eines Sturm-Liouville-Operators gebracht @@ -478,6 +505,9 @@ Es folgt damit sofort, dass die Besselfunktionen orthogonale Funktionen bezüglich des Skalarproduktes mit der Gewichtsfunktion $w(x)=1/x$ sind. +% +% Bessel-Funktionen J_n(sx) +% \subsubsection{Bessel-Funktionen $J_n(s x)$} Das Sturm-Liouville-Problem mit den Funktionen \eqref{buch:orthogonal:sturm:bessel:n} @@ -608,6 +638,9 @@ Damit sind geeignete Randbedingungen für das Sturm-Liouville-Problem gefunden. \end{proof} +% +% Laguerre-Polynome +% \subsubsection{Laguerre-Polynome} Die Laguerre-Polynome sind orthogonal bezüglich des Skalarprodukts mit der Laguerre-Gewichtsfunktion $w(x)=e^{-x}$ und erfüllen die @@ -646,6 +679,9 @@ also die Laguerre-Differentialgleichung. Somit folgt, dass die Laguerre-Polynome orthogonal sind bezüglich des Skalarproduktes mit der Laguerre-Gewichtsfunktion. +% +% Tschebyscheff-Polynome +% \subsubsection{Tschebyscheff-Polynome} Die Tschebyscheff-Polynome sind Lösungen der Tschebyscheff-Differentialgleichung @@ -685,10 +721,15 @@ bezüglich des Skalarproduktes \langle f,g\rangle = \int_{-1}^1 f(x)g(x)\frac{dx}{\sqrt{1-x^2}}. \] +% +% Jacobi-Polynome +% \subsubsection{Jacobi-Polynome} TODO - +% +% Hypergeometrische Differentialgleichungen +% \subsubsection{Hypergeometrische Differentialgleichungen} %\url{https://encyclopediaofmath.org/wiki/Hypergeometric_equation} Auch die Eulersche hypergeometrische Differentialgleichung diff --git a/buch/chapters/080-funktionentheorie/anwendungen.tex b/buch/chapters/080-funktionentheorie/anwendungen.tex index 4cdf9be..04c597e 100644 --- a/buch/chapters/080-funktionentheorie/anwendungen.tex +++ b/buch/chapters/080-funktionentheorie/anwendungen.tex @@ -5,6 +5,7 @@ % \section{Anwendungen \label{buch:funktionentheorie:section:anwendungen}} +\rhead{Anwendungen} \input{chapters/080-funktionentheorie/gammareflektion.tex} \input{chapters/080-funktionentheorie/carlson.tex} diff --git a/buch/chapters/080-funktionentheorie/singularitaeten.tex b/buch/chapters/080-funktionentheorie/singularitaeten.tex index 71d1844..07204ab 100644 --- a/buch/chapters/080-funktionentheorie/singularitaeten.tex +++ b/buch/chapters/080-funktionentheorie/singularitaeten.tex @@ -421,7 +421,8 @@ in die ursprüngliche Differentialgleichung ein, verschwindet der $\log(z)$-Term und für die verbleibenden Koeffizienten kann die bekannte Methode des Koeffizientenvergleichs verwendet werden. -\subsubsection{Bessel-Funktionen zweiter Art} +\subsubsection{Bessel-Funktionen zweiter Art +\label{buch:funktionentheorie:subsubsection:bessel2art}} -- cgit v1.2.1 From add0becdcdfee17ceb8e002684011c5895dc469b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 21 Jun 2022 07:46:06 +0200 Subject: typo --- buch/chapters/050-differential/potenzreihenmethode.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/chapters/050-differential/potenzreihenmethode.tex b/buch/chapters/050-differential/potenzreihenmethode.tex index e6613dd..84c52c2 100644 --- a/buch/chapters/050-differential/potenzreihenmethode.tex +++ b/buch/chapters/050-differential/potenzreihenmethode.tex @@ -372,7 +372,7 @@ entwickeln lassen. \subsubsection{Die Potenzreihenmethode funktioniert nicht} Für die Differentialgleichung \eqref{buch:differentialgleichungen:eqn:dglverallg} -funktioniert die Potenzreihenmethod oft nicht. +funktioniert die Potenzreihenmethode oft nicht. Sind die Funktionen $p(x)$ und $q(x)$ zum Beispiel Konstante $p(x)=p_0$ und $q(x)=q_0$, dann führt der Potenzreihenansatz \[ -- cgit v1.2.1 From c982d50db43bc3254f3b158e17c679d5ef3253e2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 21 Jun 2022 08:34:19 +0200 Subject: typos --- buch/chapters/050-differential/bessel.tex | 11 +++- .../050-differential/potenzreihenmethode.tex | 61 ++++++++++++++-------- 2 files changed, 49 insertions(+), 23 deletions(-) diff --git a/buch/chapters/050-differential/bessel.tex b/buch/chapters/050-differential/bessel.tex index a3237fe..cf271e3 100644 --- a/buch/chapters/050-differential/bessel.tex +++ b/buch/chapters/050-differential/bessel.tex @@ -316,10 +316,14 @@ J_{-\alpha}(x) y_2(x). \end{align*} +% +% Ganzzahlige Ordnung +% +\subsubsection{Besselfunktionen ganzzahliger Ordnung} Man beachte, dass diese Definition für beliebige ganzzahlige $\alpha$ funktioniert. Ist $\alpha=-n<0$, $n\in\mathbb{N}$, dann hat der Nenner Pole -an den Stellen $k=0,1,\dots,n-$. +an den Stellen $k=0,1,\dots,n-1$. Die Summe beginnt also erst bei $k=n$ oder \begin{align*} J_{-n}(x) @@ -340,6 +344,9 @@ J_{n}(x). Insbesondere unterscheiden sich $J_n(x)$ und $J_{-n}(x)$ nur durch ein Vorzeichen. +% +% Erzeugende Funktione +% \subsubsection{Erzeugende Funktion} \begin{figure} \centering @@ -754,6 +761,6 @@ BJ_{\frac12}(x) \biggl(\frac12\biggr)^2 J_{\frac12}(x). \end{align*} Dies zeigt, dass $J_{\frac12}(x)$ tatsächlich eine Eigenfunktion -des Bessel-Operators zum Eigenwert $\alpha^2 = \frac14$. +des Bessel-Operators zum Eigenwert $\alpha^2 = \frac14$ ist. Analog kann man die Lösung $y_2(x)$ für $-\frac12$ verifizieren. diff --git a/buch/chapters/050-differential/potenzreihenmethode.tex b/buch/chapters/050-differential/potenzreihenmethode.tex index 84c52c2..d046f06 100644 --- a/buch/chapters/050-differential/potenzreihenmethode.tex +++ b/buch/chapters/050-differential/potenzreihenmethode.tex @@ -290,7 +290,7 @@ Für ganzzahliges $\alpha$ wird daraus die binomische Formel \] % -% Lösung als hypergeometrische Riehe +% Lösung als hypergeometrische Reihe % \subsubsection{Lösung als hypergeometrische Funktion} Die Newtonreihe verwendet ein absteigendes Produkt im Zähler. @@ -420,25 +420,43 @@ $a_k=0$ sein, die einzige Potenzreihe ist die triviale Funktion $y(x)=0$. Für Differentialgleichungen der Art \eqref{buch:differentialgleichungen:eqn:dglverallg} ist also ein anderer Ansatz nötig. -Die Schwierigkeit bestand darin, dass die Gleichungen für die einzelnen -Koeffizienten $a_k$ voneinander unabhängig waren. -Mit einem zusätzlichen Potenzfaktor $x^\varrho$ mit nicht -notwendigerweise ganzzahligen Wert kann die nötige Flexibilität -erreicht werden. -Wir verwenden daher den Ansatz -\[ +Ursache für das Versagen des Potenzreihenansatzes ist, dass die +Koeffizienten der Differentialgleichung bei $x=0$ eine +Singularität haben. +Ist ist daher damit zu rechnen, dass auch die Lösung $y(x)$ an dieser +Stelle singuläres Verhalten zeigen wird. +Die Terme einer Potenzreihe um den Punkt $x=0$ sind nicht singulär, +können eine solche Singularität also nicht wiedergeben. +Der neue Ansatz sollte ähnlich einfach sein, aber auch gewisse ``einfache'' +Singularitäten darstellen können. +Die Potenzfunktionen $x^\varrho$ mit $\varrho<1$ erfüllen beide +Anforderungen. + +\begin{definition} +\label{buch:differentialgleichungen:def:verallpotenzreihe} +Eine {\em verallgemeinerte Potenzreihe} ist eine Funktion der Form +\begin{equation} y(x) = x^\varrho \sum_{k=0}^\infty a_kx^k = \sum_{k=0}^\infty a_k x^{\varrho+k} -\] -und versuchen nicht nur die Koeffizienten $a_k$ sondern auch den -Exponenten $\varrho$ zu bestimmen. -Durch Modifikation von $\varrho$ können wir immer erreichen, dass -$a_0\ne 0$ ist. - -Die Ableitungen von $y(x)$ mit der zugehörigen Potenz von x sind +\label{buch:differentialgleichungen:eqn:verallpotenzreihe} +\end{equation} +mit $a_0\ne 0$. +\end{definition} + +Die Forderung $a_0\ne 0$ kann nötigenfalls durch Modifikation des +Exponenten $\varrho$ immer erreicht werden. + +Wir verwenden also eine verallgemeinerte Potenzreihe der Form +\eqref{buch:differentialgleichungen:eqn:verallpotenzreihe} +als Lösungsansatz für die +Differentialgleichung~\eqref{buch:differentialgleichungen:eqn:dglverallg}. +Wir berechnen die Ableitungen von $y(x)$ und um sie in der +Differentialgleichung einzusetzen, versehen wir sie auch gleich mit den +benötigten Potenzen von $x$. +So erhalten wir \begin{align*} xy'(x) &= @@ -453,8 +471,9 @@ x^2y''(x) \sum_{k=0}^\infty (\varrho+k)(\varrho+k-1)a_kx^{\varrho+k}. \end{align*} -Diese Ableitungen setzen wir jetzt in die Differentialgleichung ein, -die dadurch zu +Diese Ausdrücke setzen wir jetzt in die +Differentialgleichung~\eqref{buch:differentialgleichungen:eqn:dglverallg} +ein, die dadurch zu \begin{equation} \sum_{k=0}^\infty (\varrho+k)(\varrho+k-1) a_k x^{\varrho+k} + @@ -489,6 +508,7 @@ Ausgeschrieben geben die einzelnen Terme \bigl((\varrho +2)a_2p_0 + (\varrho+1)a_1p_1 + \varrho a_0 p_2\bigr) x^{\varrho+2} + \dots +\label{buch:differentialgleichungen:eqn:dglverallg} \\ &+ q_0a_0x^{\varrho} @@ -685,18 +705,17 @@ Kapitel~\ref{buch:chapter:funktionentheorie} dargestellt werden. \item -Fall 3: $\varrho_1-\varrho-2$ ist eine positive ganze Zahl. +Fall 3: $\varrho_1-\varrho_2$ ist eine positive ganze Zahl. In diesem Fall ist im Allgemeinen nur eine Lösung in Form einer verallgemeinerten Potenzreihe möglich. Auch hier müssen Techniken der Funktionentheorie aus Kapitel~\ref{buch:chapter:funktionentheorie} verwendet werden, um eine zweite Lösung zu finden. -\end{itemize} - Wenn $\varrho_1-\varrho_2$ eine negative ganze Zahl ist, kann man die beiden Nullstellen vertauschen. -Es folgt dann, dass es eine +\end{itemize} + -- cgit v1.2.1 From 8a570ddc78a49006c1e6ad15bf05a19e62038f16 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 21 Jun 2022 16:16:07 +0200 Subject: jacobi stuff completed --- buch/chapters/010-potenzen/tschebyscheff.tex | 78 ++++++++++++++++++++++ buch/chapters/070-orthogonalitaet/orthogonal.tex | 2 +- buch/chapters/070-orthogonalitaet/rodrigues.tex | 12 ++++ buch/chapters/070-orthogonalitaet/sturm.tex | 83 +++++++++++++++++++++++- buch/chapters/references.bib | 8 +++ 5 files changed, 179 insertions(+), 4 deletions(-) diff --git a/buch/chapters/010-potenzen/tschebyscheff.tex b/buch/chapters/010-potenzen/tschebyscheff.tex index 29d1d4b..780be1b 100644 --- a/buch/chapters/010-potenzen/tschebyscheff.tex +++ b/buch/chapters/010-potenzen/tschebyscheff.tex @@ -241,6 +241,9 @@ Die Rekursionsformel kann auch dazu verwendet werden, Werte der Tschebyscheff-Polynome sehr effizient zu berechnen. +% +% Multiplikationsformel +% \subsubsection{Multiplikationsformel} Aus der Definition mit Hilfe trigonometrischer Funktionen lässt sich auch eine Multiplikationsformel ableiten. @@ -300,4 +303,79 @@ T_{mn}(x). Damit ist auch \eqref{buch:potenzen:tschebyscheff:mult2} bewiesen. \end{proof} +% +% Differentialgleichung +% +\subsubsection{Differentialgleichung} +Die Ableitungen der Tschebyscheff-Polynome sind +\begin{align*} +T_n(x) +&= +\cos (ny(x)) +&& +&& +\\ +\frac{d}{dx} T_n(x) +&= +\frac{d}{dx} \cos(ny(x)) += +n\sin(ny(x)) \cdot \frac{dy}{dx} +& +&\text{mit}& +\frac{dy}{dx} +&= +-\frac{1}{\sqrt{1-x^2}} +\\ +\frac{d^2}{dx^2} T_n(x) +&= +-n^2\cos(ny(x)) \biggl(\frac{dy}{dx}\biggr)^2 + n\sin(ny(x)) \frac{d^2y}{dx^2} +& +&\text{mit}& +\frac{d^2y}{dx^2} +&= +-\frac{x}{(1-x^2)^{\frac32}}. +\end{align*} +Wir suchen eine verschwindende Linearkombination dieser drei Terme +mit Funktionen von $x$ als Koeffizienten. +Wir setzen daher an +\begin{align*} +0 +&= +\alpha(x) T_n''(x) ++ +\beta(x) T_n'(x) ++ +\gamma(x) T_n(x) +\\ +&= +\biggl( +-\frac{n^2\alpha(x)}{1-x^2} ++ +\gamma(x) +\biggr) +\cos(ny(x)) ++ +\biggl( +-\frac{nx\alpha(x)}{(1-x^2)^{\frac32}} +-\frac{n\beta(x)}{\sqrt{1-x^2}} +\biggr) +\sin(ny(x)) +\end{align*} +Die grossen Klammern müssen verschwinden, was nur möglich ist, wenn zu +gegebenem $\alpha(x)$ die anderen beiden Koeffizienten +\begin{align*} +\beta(x) &= -\frac{x\alpha(x)}{1-x^2} \\ +\gamma(x) &= n^2 \frac{\alpha(x)}{1-x^2} +\end{align*} +sind. +Die Koeffizienten werden besonders einfach, wenn man $\alpha(x)=1-x^2$ wählt. +Die Tschebyscheff-Polynome sind Lösungen der Differentialgleichung +\begin{equation} +(1-x^2) T_n''(x) -x T_n'(x) +n^2 T_n(x) = 0. +\label{buch:potenzen:tschebyscheff:dgl} +\end{equation} + + + + diff --git a/buch/chapters/070-orthogonalitaet/orthogonal.tex b/buch/chapters/070-orthogonalitaet/orthogonal.tex index 97cd06b..df04514 100644 --- a/buch/chapters/070-orthogonalitaet/orthogonal.tex +++ b/buch/chapters/070-orthogonalitaet/orthogonal.tex @@ -638,7 +638,7 @@ Der Vektorraum $H_w$ von auf $(a,b)$ definierten Funktionen sei H_w = \biggl\{ -f:\colon(a,b) \to \mathbb{R} +f\colon(a,b) \to \mathbb{R} \;\bigg|\; \int_a^b |f(x)|^2 w(x)\,dx \biggr\}. diff --git a/buch/chapters/070-orthogonalitaet/rodrigues.tex b/buch/chapters/070-orthogonalitaet/rodrigues.tex index 9a36bdc..39b01b9 100644 --- a/buch/chapters/070-orthogonalitaet/rodrigues.tex +++ b/buch/chapters/070-orthogonalitaet/rodrigues.tex @@ -210,6 +210,18 @@ von Polynomen bilden. Durch Normierung müssen sich daraus die Polynome $p_n(x)$ ergeben. \end{proof} +\subsection{Differentialgleichung} +Man kann auch zeigen (siehe z.~B.~\cite{buch:pearsondgl}, +dass die orthogonalen Polynome, die die +Rodrigues-Formel liefert, einer Differentialgleichung zweiter +Ordnung genügen, deren möglicherweise nicht konstante Koeffizienten +sich direkt aus $A(x)$, $B(x)$ und $w(x)$ bestimmen lassen. + +\subsection{Beispiel} +Im folgenden zeigen wir, wie sich für viele der früher eingeführten +Gewichtsfunktionen Rodrigues-Formeln für die zugehörigen orthogonalen +Polynome konstruieren lassen. + % % Legendre-Polynome % diff --git a/buch/chapters/070-orthogonalitaet/sturm.tex b/buch/chapters/070-orthogonalitaet/sturm.tex index 1ba0ecb..613a491 100644 --- a/buch/chapters/070-orthogonalitaet/sturm.tex +++ b/buch/chapters/070-orthogonalitaet/sturm.tex @@ -371,9 +371,10 @@ bezüglich des modifizierten Skalarproduktes. Das Sturm-Liouville-Problem ist also ein Eigenwertproblem im Vektorraum $H$ mit dem Skalarprodukt $\langle\,\;,\;\rangle_w$. Der Operator -\[ +\begin{equation} L = \frac{1}{w(x)} \biggl(-\frac{d}{dx} p(x)\frac{d}{dx} + q(x)\biggr) -\] +\label{buch:orthogonal:sturm-liouville:opL1} +\end{equation} heisst der {\em Sturm-Liouville-Operator}. Eine Lösung des Sturm-Liouville-Problems ist eine Funktion $y(x)$ derart, dass @@ -383,6 +384,15 @@ Ly = \lambda y, $\lambda$ ist der zu $y(x)$ gehörige Eigenwert. Der Operator ist definiert auf Funktionen des im vorangegangenen Abschnitt definierten Vektorraumes $H$. +Führt man die Differentiation aus, bekommt der Operator die Form +\begin{equation} +L += +-\frac{p(x)}{w(x)} \frac{d^2}{dx^2} +-\frac{p'(x)}{w(x)} \frac{d}{dx} ++\frac{q(x)}{w(x)}. +\label{buch:orthogonal:sturm-liouville:opL2} +\end{equation} % % Beispiele @@ -725,7 +735,74 @@ bezüglich des Skalarproduktes % Jacobi-Polynome % \subsubsection{Jacobi-Polynome} -TODO +Die Jacobi-Polynome sind orthogonal bezüglich des Skalarproduktes +mit der Gewichtsfunktion +\( +w^{(\alpha,\beta)}(x) = (1-x)^\alpha(1+x)^\beta, +\) +definiert in Definition~\ref{buch:orthogonal:def:jacobi-gewichtsfunktion}. +%Bei der Herleitung der Rodrigues-Formel für die Jacobi-Polynome wurde erkannt, +%dass $B(x)=1-x^2$ und $A(x)=\beta-\alpha-(\alpha+\beta)x$ sein muss. +Man kann zeigen, dass die Jacobi-Polynome Lösungen der +Jacobi-Differentialgleichung +\begin{equation} +(1-x^2)y'' + (\beta-\alpha-(\alpha+\beta + 2)x)y' + n(n+\alpha+\beta+1)y=0 +\label{buch:orthogonal:jacobi:dgl} +\end{equation} +sind. +Es stellt sich die Frage, ob sich Funktionen $p(x)$ und $q(x)$ finden lassen +derart, dass die Differentialgleichung~\eqref{buch:orthogonal:jacobi:dgl} +eine Sturm-Liouville-Gleichung wird. +Gemäss der Form~\eqref{buch:orthogonal:sturm-liouville:opL2} muss +$p(x)$ so gefunden werden, dass +\begin{align*} +\frac{p(x)}{w^{(\alpha,\beta)}(x)} &= 1-x^2 \\ +\frac{p'(x)}{w^{(\alpha,\beta)}(x)} &= \beta-\alpha-(\alpha+\beta+2)x +\end{align*} +gilt. +Der Quotient der ersten beiden Gleichungen ist die logarithmische Ableitung +\[ +(\log p(x))' += +\frac{p'(x)}{p(x)} += +\frac{1-x^2}{\beta-\alpha-(\alpha+\beta+2)x} +\] +die sich in geschlossener Form integrieren lässt. +Man findet als Stammfunktion +\[ +p(x) += +(1-x)^{\alpha+1}(1+x)^{\beta+1}. +\] +Tatsächlich ist +\begin{align*} +\frac{p(x)}{w^{(\alpha,\beta)}(x)} +&= +\frac{(1-x)^{\alpha+1}(1+x)^{\beta+1}}{(1-x)^\alpha(1+x)^\beta} += +(1-x)(1+x)=1-x^2 +\\ +\frac{p'(x)}{w^{(\alpha,\beta)}(x)} +&= +\frac{ +-(\alpha+1) +(1-x)^{\alpha}(1+x)^{\beta+1} ++ +(\beta+1) +(1-x)^{\alpha+1}(1+x)^{\beta} +}{ +(1-x)^{\alpha}(1+x)^{\beta} +} +\\ +&= +-(\alpha+1)(1+x) + (\beta+1)(1-x) += +\beta-\alpha-(\alpha+\beta+2)x. +\end{align*} +Damit ist +die Jacobische Differentialgleichung +als Sturm-Liouville-Differentialgleichung erkannt. % % Hypergeometrische Differentialgleichungen diff --git a/buch/chapters/references.bib b/buch/chapters/references.bib index 32a86ec..0818f54 100644 --- a/buch/chapters/references.bib +++ b/buch/chapters/references.bib @@ -118,3 +118,11 @@ YEAR = 2022, url = {https://de.wikipedia.org/wiki/GNU_Multiple_Precision_Arithmetic_Library} } +@article{buch:pearsondgl, + title = {Orthogonal matrix polynomials, scalar-type Rordigues' formulas and Pearson equations}, + author = { Antion J. Dur\'an and F. Alberto Grünbaum }, + year = 2005, + journal = { Journal of Approximation theory }, + volume = 134, + pages = {267-280} +} -- cgit v1.2.1 From 98e2356f6d690fc6840c3ec5ae8b9eaf21771df2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 21 Jun 2022 17:54:12 +0200 Subject: bessel 2nd kind --- buch/chapters/050-differential/bessel.tex | 22 +-- buch/chapters/070-orthogonalitaet/legendredgl.tex | 2 +- buch/chapters/070-orthogonalitaet/sturm.tex | 17 +- buch/chapters/080-funktionentheorie/chapter.tex | 5 - .../080-funktionentheorie/singularitaeten.tex | 176 ++++++++++++++++++++- buch/chapters/references.bib | 11 ++ 6 files changed, 209 insertions(+), 24 deletions(-) diff --git a/buch/chapters/050-differential/bessel.tex b/buch/chapters/050-differential/bessel.tex index cf271e3..4e1c58c 100644 --- a/buch/chapters/050-differential/bessel.tex +++ b/buch/chapters/050-differential/bessel.tex @@ -129,7 +129,8 @@ ist. % % Bessel-Funktionen erster Art % -\subsection{Bessel-Funktionen erster Art} +\subsection{Bessel-Funktionen erster Art +\label{buch:differentialgleichungen:subsection:bessel1steart}} Für $\alpha \ge 0$ gibt es immer mindestens eine Lösung der Besselgleichung als verallgemeinerte Potenzreihe mit $\varrho=\alpha$. Die Funktion $q(x)=x^2-\alpha^2$ ist ein Polynom, die einzigen @@ -344,6 +345,16 @@ J_{n}(x). Insbesondere unterscheiden sich $J_n(x)$ und $J_{-n}(x)$ nur durch ein Vorzeichen. +Als lineare Differentialgleichung zweiter Ordnung erwarten wir noch +eine zweite, linear unabhängige Lösung. +Diese kann jedoch nicht allein mit der Potenzreihenmethode, +dazu sind die Methoden der Funktionentheorie nötig. +Im Abschnitt~\ref{buch:funktionentheorie:subsection:dglsing} +wird gezeigt, wie dies möglich ist und auf +Seite~\pageref{buch:funktionentheorie:subsubsection:bessel2art} +werden die damit zu findenden Bessel-Funktionen 0-ter Ordnung und +zweiter Art vorgestellt. + % % Erzeugende Funktione % @@ -519,15 +530,6 @@ J_0(x) \] geschrieben werden kann. -Als lineare Differentialgleichung zweiter Ordnung erwarten wir noch -eine zweite, linear unabhängige Lösung. -Diese kann jedoch nicht allein mit der Potenzreihenmethode, -dazu sind die Methoden der Funktionentheorie nötig. -Im Abschnitt~\ref{buch:funktionentheorie:subsection:dglsing} -wird gezeigt, wie dies möglich ist und auf -Seite~\pageref{buch:funktionentheorie:subsubsection:bessel2art} -werden die damit zu findenden Bessel-Funktionen 0-ter Ordnung und -zweiter Art vorgestellt. % % Der Fall \alpha=p, p\in \mathbb{N} diff --git a/buch/chapters/070-orthogonalitaet/legendredgl.tex b/buch/chapters/070-orthogonalitaet/legendredgl.tex index 6401e98..c4eaf97 100644 --- a/buch/chapters/070-orthogonalitaet/legendredgl.tex +++ b/buch/chapters/070-orthogonalitaet/legendredgl.tex @@ -443,7 +443,7 @@ schlägt eine zweite Lösung vor, im vorliegenden Fall mit $b=1$ ist die zweite Lösung jedoch identisch zu ersten, es muss daher ein anderer Weg zu einer zweiten Lösung gesucht werden. -XXX TODO: zweite Lösung der Differentialgleichung. +%XXX TODO: zweite Lösung der Differentialgleichung. % % diff --git a/buch/chapters/070-orthogonalitaet/sturm.tex b/buch/chapters/070-orthogonalitaet/sturm.tex index 613a491..164cd9a 100644 --- a/buch/chapters/070-orthogonalitaet/sturm.tex +++ b/buch/chapters/070-orthogonalitaet/sturm.tex @@ -694,7 +694,8 @@ des Skalarproduktes mit der Laguerre-Gewichtsfunktion. % \subsubsection{Tschebyscheff-Polynome} Die Tschebyscheff-Polynome sind Lösungen der -Tschebyscheff-Differentialgleichung +bereits in Kapitel~\ref{buch:chapter:potenzen} hergeleiteten +Tschebyscheff-Differentialgleichung~\eqref{buch:potenzen:tschebyscheff:dgl} \[ (1-x^2)y'' -xy' = n^2y \] @@ -737,14 +738,16 @@ bezüglich des Skalarproduktes \subsubsection{Jacobi-Polynome} Die Jacobi-Polynome sind orthogonal bezüglich des Skalarproduktes mit der Gewichtsfunktion -\( +\[ w^{(\alpha,\beta)}(x) = (1-x)^\alpha(1+x)^\beta, -\) +\] definiert in Definition~\ref{buch:orthogonal:def:jacobi-gewichtsfunktion}. %Bei der Herleitung der Rodrigues-Formel für die Jacobi-Polynome wurde erkannt, %dass $B(x)=1-x^2$ und $A(x)=\beta-\alpha-(\alpha+\beta)x$ sein muss. -Man kann zeigen, dass die Jacobi-Polynome Lösungen der -Jacobi-Differentialgleichung +Man kann zeigen, dass sie Lösungen der +{\em Jacobi-Diffe\-ren\-tial\-gleichung} +\index{Jacobi-Differentialgleichung}% +\index{Differentialgleichung!Jacobi}% \begin{equation} (1-x^2)y'' + (\beta-\alpha-(\alpha+\beta + 2)x)y' + n(n+\alpha+\beta+1)y=0 \label{buch:orthogonal:jacobi:dgl} @@ -760,7 +763,7 @@ $p(x)$ so gefunden werden, dass \frac{p'(x)}{w^{(\alpha,\beta)}(x)} &= \beta-\alpha-(\alpha+\beta+2)x \end{align*} gilt. -Der Quotient der ersten beiden Gleichungen ist die logarithmische Ableitung +Der Quotient der beiden Gleichungen ist die logarithmische Ableitung \[ (\log p(x))' = @@ -768,6 +771,7 @@ Der Quotient der ersten beiden Gleichungen ist die logarithmische Ableitung = \frac{1-x^2}{\beta-\alpha-(\alpha+\beta+2)x} \] +von $p(x)$, die sich in geschlossener Form integrieren lässt. Man findet als Stammfunktion \[ @@ -811,6 +815,7 @@ als Sturm-Liouville-Differentialgleichung erkannt. %\url{https://encyclopediaofmath.org/wiki/Hypergeometric_equation} Auch die Eulersche hypergeometrische Differentialgleichung lässt sich in die Form eines Sturm-Liouville-Operators +\index{Eulersche hypergeometrische Differentialgleichung!als Sturm-Liouville-Gleichung}% bringen. Dazu setzt man \begin{align*} diff --git a/buch/chapters/080-funktionentheorie/chapter.tex b/buch/chapters/080-funktionentheorie/chapter.tex index b7b5325..aa1041a 100644 --- a/buch/chapters/080-funktionentheorie/chapter.tex +++ b/buch/chapters/080-funktionentheorie/chapter.tex @@ -37,11 +37,6 @@ auf der rellen Achse hinaus fortsetzen. \input{chapters/080-funktionentheorie/fortsetzung.tex} \input{chapters/080-funktionentheorie/anwendungen.tex} -\section{TODO} -\begin{itemize} -\item Aurgument-Prinzip -\end{itemize} - \section*{Übungsaufgaben} \rhead{Übungsaufgaben} \aufgabetoplevel{chapters/080-funktionentheorie/uebungsaufgaben} diff --git a/buch/chapters/080-funktionentheorie/singularitaeten.tex b/buch/chapters/080-funktionentheorie/singularitaeten.tex index 07204ab..6742865 100644 --- a/buch/chapters/080-funktionentheorie/singularitaeten.tex +++ b/buch/chapters/080-funktionentheorie/singularitaeten.tex @@ -5,6 +5,9 @@ % \newcommand*\sk{\vcenter{\hbox{\includegraphics[scale=0.8]{chapters/080-funktionentheorie/images/operator-1.pdf}}}} +% +% Löesung linearer Differentialgleichunge mit Singularitäten +% \subsection{Lösungen von linearen Differentialgleichungen mit Singularitäten \label{buch:funktionentheorie:subsection:dglsing}} Die Potenzreihenmethode hat ermöglicht, mindestens eine Lösung gewisser @@ -19,6 +22,9 @@ Ziel dieses Abschnitts ist zu zeigen, warum dies nicht möglich war und wie diese Schwierigkeit mit Hilfe der analytischen Fortsetzung überwunden werden kann. +% +% Differentialgleichungen mit Singularitäten +% \subsubsection{Differentialgleichungen mit Singularitäten} Mit der Besselschen Differentialgleichung~\eqref{buch:differentialgleichungen:eqn:bessel} @@ -93,6 +99,9 @@ Klasse von Singularitäten beschreiben, aber es ist nicht klar, welche weiteren Arten von Singularitäten berücksichtigt werden sollten. Dies soll im Folgenden geklärt werden. +% +% Der Lösungsraum einer Differentialgleichung zweiter Ordnung +% \subsubsection{Der Lösungsraum einer Differentialgleichung zweiter Ordnung} Eine Differentialgleichung $n$-ter Ordnung hat lokal einen $n$-dimensionalen Vektorraum als Lösungsraum. @@ -126,6 +135,9 @@ Wenn der Punkt $x_0$ aus dem Kontext klar ist, kann er auch weggelassen werden: $\mathbb{L}_{x_0}=\mathbb{L}$. \end{definition} +% +% Analytische Fortsetzung auf dem Weg um 0 +% \subsubsection{Analytische Fortsetzung auf einem Weg um $0$} Die betrachteten Differentialgleichungen haben holomorphe Koeffizienten, Lösungen der Differentialgleichung lassen sich @@ -186,6 +198,9 @@ e^{2\pi i\varrho} z^\varrho \] schreiben. +% +% Rechenregeln für die analytische Fortsetzung +% \subsubsection{Rechenregeln für die analytische Fortsetzung} Der Operator $\sk$ ist ein Algebrahomomorphismus, d.~h.~für zwei analytische Funktionen $f$ und $g$ gilt @@ -215,7 +230,9 @@ vertauscht, dass also \sk(f^{(n)}). \] - +% +% Analytische Fortsetzung von Lösungen einer Differentialgleichung +% \subsubsection{Analytische Fortsetzung von Lösungen einer Differentialgleichung} Wir untersuchen jetzt die Wirkung des Operators $\sk$ auf den Lösungsraum $\mathbb{L}$ einer Differentialgleichung mit @@ -258,7 +275,9 @@ geeigneten Basis in besonders einfache Form gebracht. Wir führen diese Diskussion im folgenden nur für eine Differentialgleichung zweiter Ordnung $n=2$. - +% +% Fall A diagonalisierbar +% \subsubsection{Fall $A$ diagonalisierbar: verallgemeinerte Potenzreihen} In diesem Fall kann man die Lösungsfunktionen $w_1$ und $w_2$ so wählen, dass die Matrix @@ -326,6 +345,9 @@ Falls der Operator $\sk$ also diagonalisierbar ist, dann gibt es zwei linear unabhängige Lösungen der Differentialgleichung in der Form einer verallgemeinerten Potenzreihe. +% +% Fall $A$ nicht diagonalisierbar +% \subsubsection{Fall $A$ nicht diagonalisierbar: logarithmische Lösungen} Falls die Matrix $A$ nicht diagonalisierbar ist, hat sie nur einen Eigenwert $\lambda$ und kann durch geeignete Wahl einer Basis in @@ -421,8 +443,158 @@ in die ursprüngliche Differentialgleichung ein, verschwindet der $\log(z)$-Term und für die verbleibenden Koeffizienten kann die bekannte Methode des Koeffizientenvergleichs verwendet werden. +% +% Bessel-Funktionen zweiter Art +% \subsubsection{Bessel-Funktionen zweiter Art \label{buch:funktionentheorie:subsubsection:bessel2art}} +Im Abschnitt~\ref{buch:differentialgleichungen:subsection:bessel1steart} +waren wir nicht in der Lage, für ganzahlige $\alpha$ zwei linear unabhängige +Lösungen der Besselschen Differentialgleichung zu finden. +Die vorangegangenen Ausführungen erklären dies: der Ansatz als +verallgemeinerte Potenzreihe konnte die Singularität nicht wiedergeben. +Inzwischen wissen wir, dass wir nach einer Lösung mit einer logarithmischen +Singularität suchen müssen. +Um dies nachzuprüfen, setzen wir den Ansatz +\[ +y(x) = \log(x) J_n(x) + z(x) +\] +in die Besselsche Differentialgleichung ein. +Dazu benötigen wir erst die Ableitungen von $y(x)$: +\begin{align*} +y'(x) +&= +\frac{1}{x} J_n(x) + \log(x)J_n'(x) + z'(x) +\\ +xy'(x) +&= +J_n(x) + x\log(x)J_n'(x) + xz'(x) +\\ +y''(x) +&= +-\frac{1}{x^2} J_n(x) ++\frac2x J_n'(x) ++\log(x) J_n''(x) ++z''(x) +\\ +x^2y''(x) +&= +-J_n(x) + 2xJ'_n(x)+x^2\log(x)J_n''(x) + x^2z''(x). +\end{align*} +Die Wirkung des Bessel-Operators auf $y(x)$ ist +\begin{align*} +By +&= +x^2y''+xy'+x^2y +\\ +&= +\log(x) \bigl( +\underbrace{ +x^2J_n''(x) ++xJ_n'(x) ++x^2J_n(x) +}_{\displaystyle = n^2J_n(x)} +\bigr) +-J_n(x)+2xJ_n'(x) ++J_n(x) ++ +xz'(x) ++ +x^2z''(x) +\\ +&= +n^2 \log(x)J_n(x) ++ +2xJ_n(x) ++ +x^2z(x) ++ +xz'(x) ++ +x^2z''(x) +\end{align*} +Damit $y(x)$ eine Eigenfunktion zum Eigenwert $n^2$ wird, muss +dies mit $n^2y(x)$ übereinstimmen, also +\begin{align*} +n^2 \log(x)J_n(x) ++ +2xJ_n(x) ++ +x^2z(x) ++ +xz'(x) ++ +x^2z''(x) +&= +n^2\log(x)J_n(x) + n^2z(x). +\intertext{Die logarithmischen Terme heben sich weg und es bleibt} +x^2z''(x) ++ +xz'(x) ++ +(x^2-n^2)z(x) +&= +-2xJ_n(x). +\end{align*} +Eine Lösung für $z(x)$ kann mit Hilfe eines Potenzreihenansatzes +gefunden werden. +Sie ist aber nur bis auf einen Faktor festgelegt. +Tatsächlich kann man aber auch eine direkte Definition geben. + +\begin{definition} +Die Bessel-Funktionen zweiter Art der Ordnung $\alpha$ sind die Funktionen +\begin{equation} +Y_\alpha(x) += +\frac{J_\alpha(x) \cos \alpha\pi - J_{-\alpha}(x)}{\sin \alpha\pi }. +\label{buch:funktionentheorie:bessel:2teart} +\end{equation} +Für ganzzahliges $\alpha$ verschwindet der Nenner in +\eqref{buch:funktionentheorie:bessel:2teart}, +daher ist +\[ +Y_n(x) += +\lim_{\alpha\to n} Y_{\alpha}(x) += +\frac{1}{\pi}\biggl( +\frac{d}{d\alpha}J_{\alpha}(x)\bigg|_{\alpha=n} ++ +(-1)^n +\frac{d}{d\alpha}J_{\alpha}(x)\bigg|_{\alpha=-n} +\biggr). +\] +\end{definition} +Die Funktionen $Y_\alpha(x)$ sind Linearkombinationen der Lösungen +$J_\alpha(x)$ und $J_{-\alpha}(x)$ und damit automatisch auch Lösungen +der Besselschen Differentialgleichung. +Dies gilt auch für den Grenzwert im Falle ganzahliger Ordnung $\alpha$. +Da $J_{\alpha}(x)$ durch eine Reihenentwicklung definiert ist, kann man +diese Termweise nach $\alpha$ ableiten und damit auch eine +Reihendarstellung von $Y_n(x)$ finden. +Nach einiger Rechnung findet man: +\begin{align*} +Y_n(x) +&= +\frac{2}{\pi}J_n(x)\log\frac{x}2 +- +\frac1{\pi} +\sum_{k=0}^{n-1} \frac{(n-k-1)!}{k!}\biggl(\frac{x}2\biggr)^{2k-n} +\\ +&\qquad\qquad +- +\frac1{\pi} +\sum_{k=0}^\infty \frac{(-1)^k}{k!\,(n+k)!} +\biggl( +\frac{\Gamma'(n+k+1)}{\Gamma(n+k+1)} ++ +\frac{\Gamma'(k+1)}{\Gamma(k+1)} +\biggr) +\biggl( +\frac{x}2 +\biggr)^{2k+n} +\end{align*} +(siehe auch \cite[p.~200]{buch:specialfunctions}). diff --git a/buch/chapters/references.bib b/buch/chapters/references.bib index 0818f54..571831a 100644 --- a/buch/chapters/references.bib +++ b/buch/chapters/references.bib @@ -126,3 +126,14 @@ volume = 134, pages = {267-280} } + +@book{buch:specialfunctions, + author = { George E. Andrews and Richard Askey and Ranjan Roy }, + title = { Special Functions }, + series = { Encyclopedia of Mathematics and its applications }, + volume = { 71 }, + publisher = { Cambridge University Press }, + ISBN = { 0-521-78988-5 }, + year = 2004 +} + -- cgit v1.2.1 From 45e236bc519b62e8afc1aea7d2e625df4c145348 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 22 Jun 2022 11:49:27 +0200 Subject: add ell stuff --- buch/chapters/110-elliptisch/dglsol.tex | 59 +++++++++ buch/chapters/110-elliptisch/ellintegral.tex | 25 +++- buch/chapters/110-elliptisch/elltrigo.tex | 8 ++ buch/chapters/110-elliptisch/images/Makefile | 6 +- buch/chapters/110-elliptisch/images/ellpolnul.pdf | Bin 0 -> 19288 bytes buch/chapters/110-elliptisch/images/ellpolnul.tex | 57 +++++++++ .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 202828 -> 202828 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 312677 -> 312677 bytes buch/chapters/110-elliptisch/lemniskate.tex | 135 +++++++++++---------- 10 files changed, 222 insertions(+), 68 deletions(-) create mode 100644 buch/chapters/110-elliptisch/images/ellpolnul.pdf create mode 100644 buch/chapters/110-elliptisch/images/ellpolnul.tex diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index 7eaab38..3ef1eef 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -339,6 +339,65 @@ y(u) = F^{-1}(u+C). Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen der unvollständigen elliptischen Integrale. +% +% +% +\subsubsection{Pole und Nullstellen der Jacobischen elliptischen Funktionen} +Für die Funktion $y=\operatorname{sn}(u,k)$ erfüllt die Differentialgleichung +\[ +\frac{dy}{du} += +\sqrt{(1-y^2)(1-k^2y^2)}, +\] +welche mit dem unbestimmten Integral +\begin{equation} +u + C = \int\frac{dy}{\sqrt{(1-y^2)(1-k^2y^2)}} +\label{buch:elliptisch:eqn:uyintegral} +\end{equation} +gelöst werden kann. +Der Wertebereich des Integrals in \eqref{buch:elliptisch:eqn:uyintegral} +wurde bereits in +Abschnitt~\ref{buch:elliptisch:subsection:unvollstintegral} +auf Seite~\pageref{buch:elliptische:subsubsection:wertebereich} +diskutiert. +Daraus können jetzt Nullstellen und Pole der Funktion $\operatorname{sn}(u,k)$ +und mit Hilfe von Tabelle~\ref{buch:elliptisch:fig:jacobi-relationen} +auch für $\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$ +abgelesen werden: +\begin{equation} +\begin{aligned} +\operatorname{sn}(0,k)&=0 +& +\operatorname{cn}(0,k)&=1 +& +\operatorname{dn}(0,k)&=1 +\\ +\operatorname{sn}(iK',k)&=\infty +& +\operatorname{cn}(iK',k)&=\infty +& +\operatorname{dn}(iK',k)&=\infty +\\ +\operatorname{sn}(K,k)&=1 +& +\operatorname{cn}(K,k)&=0 +& +\operatorname{dn}(K,k)&=k' +\\ +\operatorname{sn}(K+iK',k)&=\frac{1}{k} +& +\operatorname{cn}(K+iK',k)&=\frac{ik'}{k} +& +\operatorname{dn}(K+iK',k)&=0 +\end{aligned} +\label{buch:elliptische:eqn:eckwerte} +\end{equation} +Daraus lassen sich jetzt auch die Werte der abgeleiteten Jacobischen +elliptischen Funktionen ablesen. + + + + % % Differentialgleichung des anharmonischen Oszillators diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 3acce2f..bc597d6 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -355,9 +355,9 @@ K(k) dies beweist die Behauptung. \end{proof} - - - +% +% Umfang einer Ellipse +% \subsubsection{Umfang einer Ellipse} \begin{figure} \centering @@ -451,13 +451,20 @@ Hilfe einer Entwicklung der Wurzel mit der Binomialreihe gefunden werden. \end{proof} +% +% +% \subsubsection{Komplementäre Integrale} \subsubsection{Ableitung} XXX Ableitung \\ XXX Stammfunktion \\ -\subsection{Unvollständige elliptische Integrale} +% +% Unvollständige elliptische Integrale +% +\subsection{Unvollständige elliptische Integrale +\label{buch:elliptisch:subsection:unvollstintegral}} Die Funktionen $K(k)$ und $E(k)$ sind als bestimmte Integrale über ein festes Intervall definiert. Die {\em unvollständigen elliptischen Integrale} entstehen, indem die @@ -522,12 +529,18 @@ Die Abbildung~\ref{buch:elliptisch:fig:unvollstaendigeintegrale} zeigt Graphen der unvollständigen elliptischen Integrale für verschiedene Werte des Parameters. +% +% Symmetrieeigenschaften +% \subsubsection{Symmetrieeigenschaften} Die Integranden aller drei unvollständigen elliptischen Integrale sind gerade Funktionen der reellen Variablen $t$. Die Funktionen $F(x,k)$, $E(x,k)$ und $\Pi(n,x,k)$ sind daher ungeraden Funktionen von $x$. +% +% Elliptische Integrale als komplexe Funktionen +% \subsubsection{Elliptische Integrale als komplexe Funktionen} Die unvollständigen elliptischen Integrale $F(x,k)$, $F(x,k)$ und $\Pi(n,x,k)$ in Jacobi-Form lassen sich auch für komplexe Argumente interpretieren. @@ -541,7 +554,11 @@ $\pm 1/\sqrt{n}$ XXX Additionstheoreme \\ XXX Parameterkonventionen \\ +% +% Wertebereich +% \subsubsection{Wertebereich} +\label{buch:elliptische:subsubsection:wertebereich} Die unvollständigen elliptischen Integrale betrachtet als reelle Funktionen haben nur positive relle Werte. Zum Beispiel nimmt das unvollständige elliptische Integral erster Art diff --git a/buch/chapters/110-elliptisch/elltrigo.tex b/buch/chapters/110-elliptisch/elltrigo.tex index d600243..583e00a 100644 --- a/buch/chapters/110-elliptisch/elltrigo.tex +++ b/buch/chapters/110-elliptisch/elltrigo.tex @@ -18,6 +18,14 @@ auf einer Ellipse. \end{figure} % based on Willliam Schwalm, Elliptic functions and elliptic integrals % https://youtu.be/DCXItCajCyo +Die Ellipse wurde in Abschnitt~\ref{buch:geometrie:subsection:kegelschnitte} +als Kegelschnitt erkannt und auf verschiedene Arten parametrisiert. +In diesem Abschnitt soll gezeigt werden, wie man die Parametrisierung +eines Kreises mit trigonometrischen Funktionen verallgemeinern kann +auf eine Parametrisierung einer Ellipse mit den drei +Funktionen $\operatorname{sn}(u,k)$, +$\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$, +die ähnliche Eigenschaften haben wie die trigonometrischen Funktionen. % % Geometrie einer Ellipse diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index e6e5b09..3074994 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -5,7 +5,8 @@ # all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ - sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemnispara.pdf + sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemnispara.pdf \ + ellpolnul.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex @@ -113,3 +114,6 @@ lemnispara.pdf: lemnispara.tex lemnisparadata.tex pdflatex lemnispara.tex ltest: lemnispara.pdf + +ellpolnul.pdf: ellpolnul.tex + pdflatex ellpolnul.tex diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf new file mode 100644 index 0000000..ca52cdf Binary files /dev/null and b/buch/chapters/110-elliptisch/images/ellpolnul.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex new file mode 100644 index 0000000..831b477 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex @@ -0,0 +1,57 @@ +% +% tikztemplate.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{rot}{rgb}{0.8,0,0} +\definecolor{blau}{rgb}{0,0,1} +\definecolor{gruen}{rgb}{0,0.6,0} + +\draw (-1,-1) rectangle (1,1); +\node at (-1,-1) [below left] {$0$}; +\node at (1,-1) [below right] {$K$}; +\node at (1,1) [above right] {$K+iK'$}; +\node at (-1,1) [above left] {$iK'$}; +\node at (0,0) {$u$}; + +\begin{scope}[xshift=4cm] +\fill[color=rot!20] (-1,-1) rectangle (1,1); +\node at (-1,-1) {$0$}; +\node at (1,-1) {$1$}; +\node at (1,1) {$\frac1k$}; +\node at (-1,1) {$\infty$}; +\node[color=rot] at (0,0) {$\operatorname{sn}(u,k)$}; +\end{scope} + +\begin{scope}[xshift=7cm] +\fill[color=blau!20] (-1,-1) rectangle (1,1); +\node at (-1,-1) {$1$}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\frac{ik'}k$}; +\node at (-1,1) {$\infty$}; +\node[color=blau] at (0,0) {$\operatorname{cn}(u,k)$}; +\end{scope} + +\begin{scope}[xshift=10cm] +\fill[color=gruen!20] (-1,-1) rectangle (1,1); +\node at (-1,-1) {$1$}; +\node at (1,-1) {$k'$}; +\node at (1,1) {$0$}; +\node at (-1,1) {$\infty$}; +\node[color=gruen] at (0,0) {$\operatorname{dn}(u,k)$}; +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index c51e916..d30f670 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index c6456ce..65b097f 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index b94286a..2eba07e 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index a284f75..61476a0 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -32,26 +32,26 @@ mit der Gleichung \end{equation} Sie ist in Abbildung~\ref{buch:elliptisch:fig:lemniskate} dargestellt. -Der Fall $a=1/\sqrt{2}$ ist eine Kurve mit der Gleichung +Der Fall $a=1/\!\sqrt{2}$ ist eine Kurve mit der Gleichung \[ (x^2+y^2)^2 = x^2-y^2, \] wir nennen sie die {\em Standard-Lemniskate}. \subsubsection{Scheitelpunkte} -Die beiden Scheitel der Lemniskate befinden sich bei $X_s=\pm a\sqrt{2}$. +Die beiden Scheitel der Lemniskate befinden sich bei $X_s=\pm a\!\sqrt{2}$. Dividiert man die Gleichung der Lemniskate durch $X_s^2=4a^4$ entsteht \begin{equation} \biggl( -\biggl(\frac{X}{a\sqrt{2}}\biggr)^2 +\biggl(\frac{X}{a\!\sqrt{2}}\biggr)^2 + -\biggl(\frac{Y}{a\sqrt{2}}\biggr)^2 +\biggl(\frac{Y}{a\!\sqrt{2}}\biggr)^2 \biggr)^2 = 2\frac{a^2}{2a^2}\biggl( -\biggl(\frac{X}{a\sqrt{2}}\biggr)^2 +\biggl(\frac{X}{a\!\sqrt{2}}\biggr)^2 - -\biggl(\frac{Y}{a\sqrt{2}}\biggr)^2 +\biggl(\frac{Y}{a\!\sqrt{2}}\biggr)^2 \biggr). \qquad \Leftrightarrow @@ -59,7 +59,7 @@ Dividiert man die Gleichung der Lemniskate durch $X_s^2=4a^4$ entsteht (x^2+y^2)^2 = x^2-y^2, \label{buch:elliptisch:eqn:lemniskatenormiert} \end{equation} -wobei wir $x=X/a\sqrt{2}$ und $y=Y/a\sqrt{2}$ gesetzt haben. +wobei wir $x=X/a\!\sqrt{2}$ und $y=Y/a\!\sqrt{2}$ gesetzt haben. In dieser Normierung, der Standard-Lemniskaten, liegen die Scheitel bei $\pm 1$. Dies ist die Skalierung, die für die Definition des lemniskatischen @@ -104,7 +104,7 @@ die durch die Gleichungen \begin{equation} X^2-Y^2 = Z^2 \qquad\text{und}\qquad -(X^2+Y^2) = R^2 = \sqrt{2}aZ +(X^2+Y^2) = R^2 = \!\sqrt{2}aZ \label{buch:elliptisch:eqn:kegelparabolschnitt} \end{equation} beschrieben wird. @@ -254,9 +254,9 @@ Sie ist eine Lemniskaten-Gleichung für $a=2$. \subsection{Bogenlänge} Die Funktionen \begin{equation} -x(r) = \frac{r}{\sqrt{2}}\sqrt{1+r^2}, +x(r) = \frac{r}{\!\sqrt{2}}\sqrt{1+r^2}, \quad -y(r) = \frac{r}{\sqrt{2}}\sqrt{1-r^2} +y(r) = \frac{r}{\!\sqrt{2}}\sqrt{1-r^2} \label{buch:geometrie:eqn:lemniskateparam} \end{equation} erfüllen @@ -281,9 +281,9 @@ Kettenregel berechnen kann: \begin{align*} \dot{x}(r) &= -\frac{\sqrt{1+r^2}}{\sqrt{2}} +\frac{\!\sqrt{1+r^2}}{\!\sqrt{2}} + -\frac{r^2}{\sqrt{2}\sqrt{1+r^2}} +\frac{r^2}{\!\sqrt{2}\sqrt{1+r^2}} &&\Rightarrow& \dot{x}(r)^2 &= @@ -291,7 +291,7 @@ Kettenregel berechnen kann: \\ \dot{y}(r) &= -\frac{\sqrt{1-r^2}}{\sqrt{2}} +\frac{\!\sqrt{1-r^2}}{\!\sqrt{2}} - \frac{r^2}{\sqrt{2}\sqrt{1-r^2}} &&\Rightarrow& @@ -316,7 +316,7 @@ Durch Einsetzen in das Integral für die Bogenlänge bekommt man s(r) = \int_0^r -\frac{1}{\sqrt{1-t^4}}\,dt. +\frac{1}{\!\sqrt{1-t^4}}\,dt. \label{buch:elliptisch:eqn:lemniskatebogenlaenge} \end{equation} @@ -329,11 +329,11 @@ $k^2=-1$ oder $k=i$ ist \[ K(r,i) = -\int_0^x \frac{dt}{\sqrt{(1-t^2)(1-i^2 t^2)}} +\int_0^x \frac{dt}{\!\sqrt{(1-t^2)(1-i^2 t^2)}} = -\int_0^x \frac{dt}{\sqrt{(1-t^2)(1-(-1)t^2)}} +\int_0^x \frac{dt}{\!\sqrt{(1-t^2)(1-(-1)t^2)}} = -\int_0^x \frac{dt}{\sqrt{1-t^4}} +\int_0^x \frac{dt}{\!\sqrt{1-t^4}} = s(r). \] @@ -388,23 +388,23 @@ Y(t) \operatorname{cn}(t,k) \operatorname{sn}(t,k) \end{aligned} \quad\right\} -\qquad\text{mit $k=\displaystyle\frac{1}{\sqrt{2}}$} +\qquad\text{mit $k=\displaystyle\frac{1}{\sqrt{2}}.$} \label{buch:elliptisch:lemniskate:bogeneqn} \end{equation} Abbildung~\ref{buch:elliptisch:lemniskate:bogenpara} zeigt die Parametrisierung. Dem Parameterwert $t=0$ entspricht der Scheitelpunkt -$S=(\sqrt{2},0)$ der Lemniskate. +$S=(\!\sqrt{2},0)$ der Lemniskate. % % Lemniskatengleichung % \subsubsection{Verfikation der Lemniskatengleichung} Dass \eqref{buch:elliptisch:lemniskate:bogeneqn} -tatsächlich eine Parametrisierung ist kann nachgewiesen werden dadurch, +tatsächlich eine Parametrisierung ist, kann dadurch nachgewiesen werden, dass man die beiden Seiten der definierenden Gleichung der Lemniskate berechnet. -Zunächst ist +Zunächst sind die Quadrate von $X(t)$ und $Y(t)$ \begin{align*} X(t)^2 &= @@ -414,8 +414,8 @@ X(t)^2 Y(t)^2 &= \operatorname{cn}(t,k)^2 -\operatorname{sn}(t,k)^2 -\\ +\operatorname{sn}(t,k)^2. +\intertext{Für Summe und Differenz der Quadrate findet man jetzt} X(t)^2+Y(t)^2 &= 2\operatorname{cn}(t,k)^2 @@ -447,15 +447,18 @@ X(t)^2-Y(t)^2 \bigr) \\ &= -2\operatorname{cn}(t,k)^4 -\\ +2\operatorname{cn}(t,k)^4. +\intertext{Beide lassen sich also durch $\operatorname{cn}(t,k)^2$ +ausdrücken. +Zusammengefasst erhält man} \Rightarrow\qquad (X(t)^2+Y(t)^2)^2 &= 4\operatorname{cn}(t,k)^4 = -2(X(t)^2-Y(t)^2). +2(X(t)^2-Y(t)^2), \end{align*} +eine Lemniskaten-Gleichung. % % Berechnung der Bogenlänge @@ -467,39 +470,26 @@ Dazu berechnen wir die Ableitungen \begin{align*} \dot{X}(t) &= -\sqrt{2}\operatorname{cn}'(t,k)\operatorname{dn}(t,k) +\!\sqrt{2}\operatorname{cn}'(t,k)\operatorname{dn}(t,k) + -\sqrt{2}\operatorname{cn}(t,k)\operatorname{dn}'(t,k) +\!\sqrt{2}\operatorname{cn}(t,k)\operatorname{dn}'(t,k) \\ &= --\sqrt{2}\operatorname{sn}(t,k)\operatorname{dn}(t,k)^2 +-\!\sqrt{2}\operatorname{sn}(t,k)\operatorname{dn}(t,k)^2 -\frac12\sqrt{2}\operatorname{sn}(t,k)\operatorname{cn}(t,k)^2 \\ &= --\sqrt{2}\operatorname{sn}(t,k)\bigl( +-\!\sqrt{2}\operatorname{sn}(t,k)\bigl( 1-{\textstyle\frac12}\operatorname{sn}(t,k)^2 +{\textstyle\frac12}-{\textstyle\frac12}\operatorname{sn}(t,k)^2 \bigr) \\ &= -\sqrt{2}\operatorname{sn}(t,k) +\!\sqrt{2}\operatorname{sn}(t,k) \bigl( {\textstyle \frac32}-\operatorname{sn}(t,k)^2 \bigr) \\ -\dot{X}(t)^2 -&= -2\operatorname{sn}(t,k)^2 -\bigl( -{\textstyle \frac32}-\operatorname{sn}(t,k)^2 -\bigr)^2 -\\ -&= -{\textstyle\frac{9}{2}}\operatorname{sn}(t,k)^2 -- -6\operatorname{sn}(t,k)^4 -+2\operatorname{sn}(t,k)^6 -\\ \dot{Y}(t) &= \operatorname{cn}'(t,k)\operatorname{sn}(t,k) @@ -514,6 +504,19 @@ Dazu berechnen wir die Ableitungen \\ &= \operatorname{dn}(t,k)\bigl(1-2\operatorname{sn}(t,k)^2\bigr) +\intertext{und davon die Quadrate} +\dot{X}(t)^2 +&= +2\operatorname{sn}(t,k)^2 +\bigl( +{\textstyle \frac32}-\operatorname{sn}(t,k)^2 +\bigr)^2 +\\ +&= +{\textstyle\frac{9}{2}}\operatorname{sn}(t,k)^2 +- +6\operatorname{sn}(t,k)^4 ++2\operatorname{sn}(t,k)^6 \\ \dot{Y}(t)^2 &= @@ -523,22 +526,22 @@ Dazu berechnen wir die Ableitungen &= 1-{\textstyle\frac{9}{2}}\operatorname{sn}(t,k)^2 +6\operatorname{sn}(t,k)^4 --2\operatorname{sn}(t,k)^6 -\\ +-2\operatorname{sn}(t,k)^6. +\intertext{Für das Bogenlängenintegral wird die Quadratsumme der Ableitungen +benötigt, diese ist} \dot{X}(t)^2 + \dot{Y}(t)^2 &= 1. -\end{align*} -Dies bedeutet, dass die Bogenlänge zwischen den Parameterwerten $0$ und $t$ -\[ +\intertext{Dies bedeutet, dass die Bogenlänge zwischen den +Parameterwerten $0$ und $t$} \int_0^t \sqrt{\dot{X}(\tau)^2 + \dot{Y}(\tau)^2} \,d\tau -= +&= \int_0^s\,d\tau = t, -\] +\end{align*} der Parameter $t$ ist also ein Bogenlängenparameter. % @@ -556,18 +559,18 @@ hat daher eine Bogenlängenparametrisierung mit \begin{aligned} x(t) &= -\phantom{\frac{1}{\sqrt{2}}} -\operatorname{cn}(\sqrt{2}t,k)\operatorname{dn}(\sqrt{2}t,k) +\phantom{\frac{1}{\!\sqrt{2}}} +\operatorname{cn}(\!\sqrt{2}t,k)\operatorname{dn}(\!\sqrt{2}t,k) \\ y(t) &= -\frac{1}{\sqrt{2}} -\operatorname{cn}(\sqrt{2}t,k)\operatorname{sn}(\sqrt{2}t,k) +\frac{1}{\!\sqrt{2}} +\operatorname{cn}(\!\sqrt{2}t,k)\operatorname{sn}(\!\sqrt{2}t,k) \end{aligned} \quad \right\} \qquad -\text{mit $\displaystyle k=\frac{1}{\sqrt{2}}$} +\text{mit $\displaystyle k=\frac{1}{\!\sqrt{2}}.$} \label{buch:elliptisch:lemniskate:bogenlaenge} \end{equation} Der Punkt $t=0$ entspricht dem Scheitelpunkt $S=(1,0)$ der Lemniskate. @@ -630,21 +633,21 @@ r(t)^2 = x(t)^2 + y(t)^2 = -\operatorname{cn}(\sqrt{2}t,k)^2 +\operatorname{cn}(\!\sqrt{2}t,k)^2 \biggl( -\operatorname{dn}(\sqrt{2}t,k)^2 +\operatorname{dn}(\!\sqrt{2}t,k)^2 + \frac12 -\operatorname{sn}(\sqrt{2}t,k)^2 +\operatorname{sn}(\!\sqrt{2}t,k)^2 \biggr) = -\operatorname{cn}(\sqrt{2}t,k)^2. +\operatorname{cn}(\!\sqrt{2}t,k)^2. \] Die Wurzel ist \[ r(t) = -\operatorname{cn}(\sqrt{2}t,{\textstyle\frac{1}{\sqrt{2}}}) +\operatorname{cn}(\!\sqrt{2}t,{\textstyle\frac{1}{\!\sqrt{2}}}) . \] Der lemniskatische Sinus wurde aber in Abhängigkeit von @@ -654,7 +657,7 @@ $s=\varpi/2-t$ mittels = r(s) = -\operatorname{cn}(\sqrt{2}(\varpi/2-s),k)^2 +\operatorname{cn}(\!\sqrt{2}(\varpi/2-s),k)^2 \] definiert. Der lemniskatische Kosinus ist definiert als der lemniskatische Sinus @@ -666,7 +669,7 @@ der komplementären Bogenlänge, also = \operatorname{sl}(\varpi/2-s) = -\operatorname{cn}(\sqrt{2}s,k)^2. +\operatorname{cn}(\!\sqrt{2}s,k)^2. \] Die Funktion $\operatorname{sl}(s)$ und $\operatorname{cl}(s)$ sind in Abbildung~\ref{buch:elliptisch:figure:slcl} dargestellt. @@ -674,4 +677,10 @@ Sie sind beide $2\varpi$-periodisch. Die Abbildung zeigt ausserdem die Funktionen $\sin (\pi s/\varpi)$ und $\cos(\pi s/\varpi)$, die ebenfalls $2\varpi$-periodisch sind. +Die Darstellung des lemniskatischen Sinus und Kosinus durch die +Jacobische elliptische Funktion $\operatorname{cn}(\!\sqrt{2}s,k)$ +zeigt einmal mehr den Nutzen der Jacobischen elliptischen Funktionen. + + + -- cgit v1.2.1 From 17f90bd131bdf24110d8933fd804413d53e17bc5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 22 Jun 2022 13:07:36 +0200 Subject: add graph for all functions --- buch/chapters/110-elliptisch/images/Makefile | 6 +- buch/chapters/110-elliptisch/images/ellall.pdf | Bin 0 -> 22616 bytes buch/chapters/110-elliptisch/images/ellall.tex | 148 +++++++++++++++++++++ buch/chapters/110-elliptisch/images/ellpolnul.pdf | Bin 19288 -> 23281 bytes buch/chapters/110-elliptisch/images/ellpolnul.tex | 24 ++-- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 59737 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 202828 -> 203620 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 312677 -> 313517 bytes 8 files changed, 164 insertions(+), 14 deletions(-) create mode 100644 buch/chapters/110-elliptisch/images/ellall.pdf create mode 100644 buch/chapters/110-elliptisch/images/ellall.tex diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 3074994..cd8e905 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -6,7 +6,7 @@ all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemnispara.pdf \ - ellpolnul.pdf + ellpolnul.pdf ellall.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex @@ -115,5 +115,7 @@ lemnispara.pdf: lemnispara.tex lemnisparadata.tex ltest: lemnispara.pdf -ellpolnul.pdf: ellpolnul.tex +ellpolnul.pdf: ellpolnul.tex ellcommon.tex pdflatex ellpolnul.tex +ellall.pdf: ellall.tex ellcommon.tex + pdflatex ellall.tex diff --git a/buch/chapters/110-elliptisch/images/ellall.pdf b/buch/chapters/110-elliptisch/images/ellall.pdf new file mode 100644 index 0000000..0047a52 Binary files /dev/null and b/buch/chapters/110-elliptisch/images/ellall.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex new file mode 100644 index 0000000..5d63322 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellall.tex @@ -0,0 +1,148 @@ +% +% ellpolnul.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math,calc} +\begin{document} +\input{ellcommon.tex} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +%\draw (-1,-1) rectangle (1,1); +%\node at (-1,-1) [below left] {$0$}; +%\node at (1,-1) [below right] {$K$}; +%\node at (1,1) [above right] {$K+iK'$}; +%\node at (-1,1) [above left] {$iK'$}; +%\node at (0,0) {$u$}; + +\begin{scope}[xshift=-3cm,yshift=0cm] +\rechteck{gray}{1} +\end{scope} + +\definecolor{sccolor}{rgb}{0.8,0.2,0.8} +\definecolor{sdcolor}{rgb}{0.8,0.8,0.2} +\definecolor{cdcolor}{rgb}{0.2,0.8,0.8} + +\begin{scope}[xshift=0cm] +\rechteck{rot}{\operatorname{sn}(u,k)} +\nullstelle{(-1,-1)}{rot} +\pol{(-1,1)}{rot} +\node at (-1,-1) {$0$}; +\node at (1,-1) {$1$}; +\node at (1,1) {$\frac1k$}; +\node at (-1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=3cm] +\rechteck{blau}{\operatorname{cn}(u,k)} +\nullstelle{(1,-1)}{blau} +\pol{(-1,1)}{blau} +\node at (-1,-1) {$1$}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\frac{ik'}k$}; +\node at (-1,1) {$\infty$}; +\end{scope} + +\begin{scope}[xshift=6cm] +\rechteck{gruen}{\operatorname{dn}(u,k)} +\nullstelle{(1,1)}{gruen} +\pol{(-1,1)}{gruen} +\node at (-1,-1) {$1$}; +\node at (1,-1) {$k'$}; +\node at (1,1) {$0$}; +\node at (-1,1) {$\infty$}; +\end{scope} + +% +% start row with denominator sn(u,k) +% + +\begin{scope}[xshift=-3cm,yshift=-3cm] +\rechteck{rot}{\operatorname{ns}(u,k)} +\pol{(-1,-1)}{rot} +\nullstelle{(-1,1)}{rot} +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-3cm] +\rechteck{gray}{1} +\end{scope} + +\begin{scope}[xshift=3cm,yshift=-3cm] +\rechteck{sccolor}{\operatorname{cs}(u,k)} +\pol{(1,-1)}{sccolor} +\nullstelle{(-1,-1)}{sccolor} +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-3cm] +\rechteck{sdcolor}{\operatorname{ds}(u,k)} +\pol{(-1,1)}{sdcolor} +\nullstelle{(-1,-1)}{sdcolor} +\nullstelle{(1,1)}{sdcolor} +\end{scope} + +% +% start row with denominator cn(u,k) +% + +\begin{scope}[xshift=-3cm,yshift=-6cm] +\rechteck{blau}{\operatorname{nc}(u,k)} +\pol{(1,-1)}{blau} +\nullstelle{(-1,1)}{blau} +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-6cm] +\rechteck{sccolor}{\operatorname{sc}(u,k)} +\nullstelle{(1,-1)}{sccolor} +\pol{(-1,-1)}{sccolor} +\end{scope} + +\begin{scope}[xshift=3cm,yshift=-6cm] +\rechteck{gray}{1} +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-6cm] +\rechteck{cdcolor}{\operatorname{dc}(u,k)} +\nullstelle{(1,1)}{cdcolor} +\nullstelle{(1,-1)}{cdcolor} +\pol{(-1,1)}{cdcolor} +\end{scope} + +% +% start row with denominator dn(u,k) +% + +\begin{scope}[xshift=-3cm,yshift=-9cm] +\rechteck{gruen}{\operatorname{nd}(u,k)} +\pol{(1,1)}{gruen} +\nullstelle{(-1,1)}{gruen} +\end{scope} + +\begin{scope}[xshift=0cm,yshift=-9cm] +\rechteck{sdcolor}{\operatorname{sd}(u,k)} +\nullstelle{(-1,1)}{sdcolor} +\pol{(-1,-1)}{sdcolor} +\pol{(1,1)}{sdcolor} +\end{scope} + +\begin{scope}[xshift=3cm,yshift=-9cm] +\rechteck{cdcolor}{\operatorname{cd}(u,k)} +\pol{(1,1)}{cdcolor} +\pol{(1,-1)}{cdcolor} +\nullstelle{(-1,1)}{cdcolor} +\end{scope} + +\begin{scope}[xshift=6cm,yshift=-9cm] +\rechteck{gray}{1} +\end{scope} + + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf index ca52cdf..d6549c4 100644 Binary files a/buch/chapters/110-elliptisch/images/ellpolnul.pdf and b/buch/chapters/110-elliptisch/images/ellpolnul.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex index 831b477..1ed6b22 100644 --- a/buch/chapters/110-elliptisch/images/ellpolnul.tex +++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex @@ -1,5 +1,5 @@ % -% tikztemplate.tex -- template for standalon tikz images +% ellpolnul.tex -- template for standalon tikz images % % (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule % @@ -9,15 +9,12 @@ \usepackage{txfonts} \usepackage{pgfplots} \usepackage{csvsimple} -\usetikzlibrary{arrows,intersections,math} +\usetikzlibrary{arrows,intersections,math,calc} \begin{document} +\input{ellcommon.tex} \def\skala{1} \begin{tikzpicture}[>=latex,thick,scale=\skala] -\definecolor{rot}{rgb}{0.8,0,0} -\definecolor{blau}{rgb}{0,0,1} -\definecolor{gruen}{rgb}{0,0.6,0} - \draw (-1,-1) rectangle (1,1); \node at (-1,-1) [below left] {$0$}; \node at (1,-1) [below right] {$K$}; @@ -26,30 +23,33 @@ \node at (0,0) {$u$}; \begin{scope}[xshift=4cm] -\fill[color=rot!20] (-1,-1) rectangle (1,1); +\rechteck{rot}{\operatorname{sn}(u,k)} +\nullstelle{(-1,-1)}{rot} +\pol{(-1,1)}{rot} \node at (-1,-1) {$0$}; \node at (1,-1) {$1$}; \node at (1,1) {$\frac1k$}; \node at (-1,1) {$\infty$}; -\node[color=rot] at (0,0) {$\operatorname{sn}(u,k)$}; \end{scope} \begin{scope}[xshift=7cm] -\fill[color=blau!20] (-1,-1) rectangle (1,1); +\rechteck{blau}{\operatorname{cn}(u,k)} +\nullstelle{(1,-1)}{blau} +\pol{(-1,1)}{blau} \node at (-1,-1) {$1$}; \node at (1,-1) {$0$}; \node at (1,1) {$\frac{ik'}k$}; \node at (-1,1) {$\infty$}; -\node[color=blau] at (0,0) {$\operatorname{cn}(u,k)$}; \end{scope} \begin{scope}[xshift=10cm] -\fill[color=gruen!20] (-1,-1) rectangle (1,1); +\rechteck{gruen}{\operatorname{dn}(u,k)} +\nullstelle{(1,1)}{gruen} +\pol{(-1,1)}{gruen} \node at (-1,-1) {$1$}; \node at (1,-1) {$k'$}; \node at (1,1) {$0$}; \node at (-1,1) {$\infty$}; -\node[color=gruen] at (0,0) {$\operatorname{dn}(u,k)$}; \end{scope} \end{tikzpicture} diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index d30f670..49bfeb2 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 65b097f..65a5b45 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 2eba07e..519a5a3 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From 43a21e525fe5f9f2e81113ed84742c42178c7114 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 22 Jun 2022 16:02:19 +0200 Subject: new images --- buch/chapters/110-elliptisch/dglsol.tex | 28 ++++++++++++++++++++++++- buch/chapters/110-elliptisch/images/ellall.pdf | Bin 22616 -> 24694 bytes buch/chapters/110-elliptisch/images/ellall.tex | 28 +++++++++++++++++++++++++ 3 files changed, 55 insertions(+), 1 deletion(-) diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index 3ef1eef..c4b990e 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -343,6 +343,28 @@ der unvollständigen elliptischen Integrale. % % \subsubsection{Pole und Nullstellen der Jacobischen elliptischen Funktionen} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/ellpolnul.pdf} +\caption{Werte der grundlegenden Jacobischen elliptischen Funktionen +$\operatorname{sn}(u,k)$, +$\operatorname{cn}(u,k)$ +und +$\operatorname{dn}(u,k)$ +in den Ecken des Rechtecks mit Ecken $(0,0)$ und $(K,K+iK')$. +Links der Definitionsbereich, rechts die Werte der drei Funktionen. +Pole sind mit einem Kreuz ($\times$) bezeichnet, Nullstellen mit einem +Kreis ($\ocircle$). +\label{buch:elliptisch:fig:ellpolnul}} +\end{figure} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/ellall.pdf} +\caption{Pole und Nullstellen aller Jacobischen elliptischen Funktionen +mit den gleichen Darstellungskonventionen wie in +Abbildung~\ref{buch:elliptisch:fig:ellpolnul} +\label{buch:elliptisch:fig:ellall}} +\end{figure} Für die Funktion $y=\operatorname{sn}(u,k)$ erfüllt die Differentialgleichung \[ \frac{dy}{du} @@ -392,8 +414,12 @@ abgelesen werden: \end{aligned} \label{buch:elliptische:eqn:eckwerte} \end{equation} +Abbildung~\ref{buch:elliptisch:fig:ellpolnul} zeigt diese Werte +an einer schematischen Darstellung des Definitionsbereiches auf. Daraus lassen sich jetzt auch die Werte der abgeleiteten Jacobischen -elliptischen Funktionen ablesen. +elliptischen Funktionen ablesen, Pole und Nullstellen sind in +Abbildung~\ref{buch:elliptisch:fig:ellall} +zusammengestellt. diff --git a/buch/chapters/110-elliptisch/images/ellall.pdf b/buch/chapters/110-elliptisch/images/ellall.pdf index 0047a52..a57be97 100644 Binary files a/buch/chapters/110-elliptisch/images/ellall.pdf and b/buch/chapters/110-elliptisch/images/ellall.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex index 5d63322..b694441 100644 --- a/buch/chapters/110-elliptisch/images/ellall.tex +++ b/buch/chapters/110-elliptisch/images/ellall.tex @@ -22,6 +22,34 @@ %\node at (-1,1) [above left] {$iK'$}; %\node at (0,0) {$u$}; +\fill[color=rot!10,opacity=0.5] (-5.5,-4.3) rectangle (7.3,-1.7); +\fill[color=blau!10,opacity=0.5] (-5.5,-7.3) rectangle (7.3,-4.7); +\fill[color=gruen!10,opacity=0.5] (-5.5,-10.3) rectangle (7.3,-7.7); + +\fill[color=rot!10,opacity=0.5] (-1.3,-10.5) rectangle (1.3,2.5); +\fill[color=blau!10,opacity=0.5] (1.7,-10.5) rectangle (4.3,2.5); +\fill[color=gruen!10,opacity=0.5] (4.7,-10.5) rectangle (7.3,2.5); + +\begin{scope}[xshift=1.5cm,yshift=2cm] +\node at (0,0) {Zähler}; +\draw[<-] (-4.5,0) -- (-1,0); +\draw[->] (1,0) -- (4.5,0); +\node[color=black] at (-4.5,-0.4) {\Large n}; +\node[color=rot] at (-1.5,-0.4) {\Large s}; +\node[color=blau] at (1.5,-0.4) {\Large c}; +\node[color=gruen] at (4.5,-0.4) {\Large d}; +\end{scope} + +\begin{scope}[xshift=-5.1cm,yshift=-4.5cm] +\node at (0,0) [rotate=90] {Nenner}; +\draw[<-] (0,-4.5) -- (0,-1); +\draw[->] (0,1) -- (0,4.5); +\node[color=gruen] at (0.4,-4.5) [rotate=90] {\Large d}; +\node[color=blau] at (0.4,-1.5) [rotate=90] {\Large c}; +\node[color=rot] at (0.4,1.5) [rotate=90] {\Large s}; +\node[color=black] at (0.4,4.5) [rotate=90] {\Large n}; +\end{scope} + \begin{scope}[xshift=-3cm,yshift=0cm] \rechteck{gray}{1} \end{scope} -- cgit v1.2.1 From 67a73f883b582591f1bd94c68e07868ae2e4440d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Wed, 22 Jun 2022 19:27:02 +0200 Subject: add missing file --- buch/chapters/110-elliptisch/images/ellcommon.tex | 24 +++++++++++++++++++++++ 1 file changed, 24 insertions(+) create mode 100644 buch/chapters/110-elliptisch/images/ellcommon.tex diff --git a/buch/chapters/110-elliptisch/images/ellcommon.tex b/buch/chapters/110-elliptisch/images/ellcommon.tex new file mode 100644 index 0000000..90bc486 --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellcommon.tex @@ -0,0 +1,24 @@ +% +% ellcommon.tex -- common macros/definitions for elliptic function +% values display +% +% (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\definecolor{rot}{rgb}{0.8,0,0} +\definecolor{blau}{rgb}{0,0,1} +\definecolor{gruen}{rgb}{0,0.6,0} +\def\l{0.2} + +\def\pol#1#2{ + \draw[color=#2!40,line width=2.4pt] + ($#1+(-\l,-\l)$) -- ($#1+(\l,\l)$); + \draw[color=#2!40,line width=2.4pt] + ($#1+(-\l,\l)$) -- ($#1+(\l,-\l)$); +} +\def\nullstelle#1#2{ + \draw[color=#2!40,line width=2.4pt] #1 circle[radius=\l]; +} +\def\rechteck#1#2{ + \fill[color=#1!20] (-1,-1) rectangle (1,1); + \node[color=#1] at (0,0) {$#2$}; +} -- cgit v1.2.1 From 0a0f36f71e9dff9b9c87a66a669e0d2f388d21c6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 23 Jun 2022 19:23:58 +0200 Subject: poles and zeros --- buch/chapters/110-elliptisch/images/ellall.pdf | Bin 24694 -> 22593 bytes buch/chapters/110-elliptisch/images/ellall.tex | 79 +++++++++++++++------ buch/chapters/110-elliptisch/images/ellcommon.tex | 8 +-- buch/chapters/110-elliptisch/images/ellpolnul.pdf | Bin 23281 -> 19647 bytes buch/chapters/110-elliptisch/images/ellpolnul.tex | 2 +- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 59737 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 203620 -> 202828 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 313517 -> 312677 bytes 8 files changed, 64 insertions(+), 25 deletions(-) diff --git a/buch/chapters/110-elliptisch/images/ellall.pdf b/buch/chapters/110-elliptisch/images/ellall.pdf index a57be97..fd0a5dd 100644 Binary files a/buch/chapters/110-elliptisch/images/ellall.pdf and b/buch/chapters/110-elliptisch/images/ellall.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellall.tex b/buch/chapters/110-elliptisch/images/ellall.tex index b694441..b37fe12 100644 --- a/buch/chapters/110-elliptisch/images/ellall.tex +++ b/buch/chapters/110-elliptisch/images/ellall.tex @@ -51,12 +51,13 @@ \end{scope} \begin{scope}[xshift=-3cm,yshift=0cm] -\rechteck{gray}{1} +\node at (0,0) {$1$}; +\draw[color=gray!20] (-1,-1) rectangle (1,1); \end{scope} -\definecolor{sccolor}{rgb}{0.8,0.2,0.8} -\definecolor{sdcolor}{rgb}{0.8,0.8,0.2} -\definecolor{cdcolor}{rgb}{0.2,0.8,0.8} +\definecolor{sccolor}{rgb}{0.8,0.0,1.0} +\definecolor{sdcolor}{rgb}{0.6,0.6,0.0} +\definecolor{cdcolor}{rgb}{0.0,0.6,1.0} \begin{scope}[xshift=0cm] \rechteck{rot}{\operatorname{sn}(u,k)} @@ -74,7 +75,7 @@ \pol{(-1,1)}{blau} \node at (-1,-1) {$1$}; \node at (1,-1) {$0$}; -\node at (1,1) {$\frac{ik'}k$}; +\node at (1,1) {$\frac{k'}{ik}$}; \node at (-1,1) {$\infty$}; \end{scope} @@ -96,23 +97,36 @@ \rechteck{rot}{\operatorname{ns}(u,k)} \pol{(-1,-1)}{rot} \nullstelle{(-1,1)}{rot} +\node at (-1,-1) {$\infty$}; +\node at (1,-1) {$1$}; +\node at (1,1) {$k$}; +\node at (-1,1) {$0$}; \end{scope} \begin{scope}[xshift=0cm,yshift=-3cm] -\rechteck{gray}{1} +%\rechteck{gray}{1} +\fill[color=white] (-1,-1) rectangle (1,1); +\node[color=gray] at (0,0) {$1$}; \end{scope} \begin{scope}[xshift=3cm,yshift=-3cm] \rechteck{sccolor}{\operatorname{cs}(u,k)} -\pol{(1,-1)}{sccolor} -\nullstelle{(-1,-1)}{sccolor} +\pol{(-1,-1)}{sccolor} +\nullstelle{(1,-1)}{sccolor} +\node at (-1,-1) {$\infty$}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\frac{k'}{i}$}; +\node at (-1,1) {$ $}; \end{scope} \begin{scope}[xshift=6cm,yshift=-3cm] \rechteck{sdcolor}{\operatorname{ds}(u,k)} -\pol{(-1,1)}{sdcolor} -\nullstelle{(-1,-1)}{sdcolor} +\pol{(-1,-1)}{sdcolor} \nullstelle{(1,1)}{sdcolor} +\node at (-1,-1) {$\infty$}; +\node at (1,-1) {$k'$}; +\node at (1,1) {$0$}; +\node at (-1,1) {$ $}; \end{scope} % @@ -123,23 +137,36 @@ \rechteck{blau}{\operatorname{nc}(u,k)} \pol{(1,-1)}{blau} \nullstelle{(-1,1)}{blau} +\node at (-1,-1) {$1$}; +\node at (-1,1) {$0$}; +\node at (1,-1) {$\infty$}; +\node at (1,1) {$\frac{ik}{k'}$}; \end{scope} \begin{scope}[xshift=0cm,yshift=-6cm] \rechteck{sccolor}{\operatorname{sc}(u,k)} -\nullstelle{(1,-1)}{sccolor} -\pol{(-1,-1)}{sccolor} +\nullstelle{(-1,-1)}{sccolor} +\pol{(1,-1)}{sccolor} +\node at (-1,-1) {$0$}; +\node at (1,-1) {$\infty$}; +\node at (-1,1) {$ $}; +\node at (1,1) {$\frac{i}{k'}$}; \end{scope} \begin{scope}[xshift=3cm,yshift=-6cm] -\rechteck{gray}{1} +%\rechteck{gray}{1} +\fill[color=white] (-1,-1) rectangle (1,1); +\node[color=gray] at (0,0) {$1$}; \end{scope} \begin{scope}[xshift=6cm,yshift=-6cm] \rechteck{cdcolor}{\operatorname{dc}(u,k)} \nullstelle{(1,1)}{cdcolor} -\nullstelle{(1,-1)}{cdcolor} -\pol{(-1,1)}{cdcolor} +\pol{(1,-1)}{cdcolor} +\node at (-1,-1) {$1$}; +\node at (1,-1) {$\infty$}; +\node at (-1,1) {$k$}; +\node at (1,1) {$0$}; \end{scope} % @@ -150,24 +177,36 @@ \rechteck{gruen}{\operatorname{nd}(u,k)} \pol{(1,1)}{gruen} \nullstelle{(-1,1)}{gruen} +\node at (-1,-1) {$1$}; +\node at (-1,1) {$0$}; +\node at (1,-1) {$\frac{1}{k'}$}; +\node at (1,1) {$\infty$}; \end{scope} \begin{scope}[xshift=0cm,yshift=-9cm] \rechteck{sdcolor}{\operatorname{sd}(u,k)} -\nullstelle{(-1,1)}{sdcolor} -\pol{(-1,-1)}{sdcolor} +\nullstelle{(-1,-1)}{sdcolor} \pol{(1,1)}{sdcolor} +\node at (-1,-1) {$0$}; +\node at (1,-1) {$\frac{1}{k'}$}; +\node at (-1,1) {$ $}; +\node at (1,1) {$\infty$}; \end{scope} \begin{scope}[xshift=3cm,yshift=-9cm] \rechteck{cdcolor}{\operatorname{cd}(u,k)} \pol{(1,1)}{cdcolor} -\pol{(1,-1)}{cdcolor} -\nullstelle{(-1,1)}{cdcolor} +\nullstelle{(1,-1)}{cdcolor} +\node at (-1,-1) {$1$}; +\node at (-1,1) {$\frac1k $}; +\node at (1,-1) {$0$}; +\node at (1,1) {$\infty$}; \end{scope} \begin{scope}[xshift=6cm,yshift=-9cm] -\rechteck{gray}{1} +%\rechteck{gray}{1} +\fill[color=white] (-1,-1) rectangle (1,1); +\node[color=gray] at (0,0) {$1$}; \end{scope} diff --git a/buch/chapters/110-elliptisch/images/ellcommon.tex b/buch/chapters/110-elliptisch/images/ellcommon.tex index 90bc486..cd3245d 100644 --- a/buch/chapters/110-elliptisch/images/ellcommon.tex +++ b/buch/chapters/110-elliptisch/images/ellcommon.tex @@ -10,15 +10,15 @@ \def\l{0.2} \def\pol#1#2{ - \draw[color=#2!40,line width=2.4pt] + \draw[color=#2!50,line width=3.0pt] ($#1+(-\l,-\l)$) -- ($#1+(\l,\l)$); - \draw[color=#2!40,line width=2.4pt] + \draw[color=#2!50,line width=3.0pt] ($#1+(-\l,\l)$) -- ($#1+(\l,-\l)$); } \def\nullstelle#1#2{ - \draw[color=#2!40,line width=2.4pt] #1 circle[radius=\l]; + \draw[color=#2!50,line width=3.0pt] #1 circle[radius=\l]; } \def\rechteck#1#2{ \fill[color=#1!20] (-1,-1) rectangle (1,1); - \node[color=#1] at (0,0) {$#2$}; + \node[color=#1] at (0,0) {$#2\mathstrut$}; } diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf index d6549c4..9143d2d 100644 Binary files a/buch/chapters/110-elliptisch/images/ellpolnul.pdf and b/buch/chapters/110-elliptisch/images/ellpolnul.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex index 1ed6b22..16730f9 100644 --- a/buch/chapters/110-elliptisch/images/ellpolnul.tex +++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex @@ -38,7 +38,7 @@ \pol{(-1,1)}{blau} \node at (-1,-1) {$1$}; \node at (1,-1) {$0$}; -\node at (1,1) {$\frac{ik'}k$}; +\node at (1,1) {$\frac{k'}{ik}$}; \node at (-1,1) {$\infty$}; \end{scope} diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 49bfeb2..331270e 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 65a5b45..b23654c 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 519a5a3..f70f362 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From 4093fce68a051cb36b95609f68e2319d14615d39 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 23 Jun 2022 19:26:58 +0200 Subject: typo --- buch/chapters/110-elliptisch/dglsol.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index c4b990e..b1b7db3 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -408,7 +408,7 @@ abgelesen werden: \\ \operatorname{sn}(K+iK',k)&=\frac{1}{k} & -\operatorname{cn}(K+iK',k)&=\frac{ik'}{k} +\operatorname{cn}(K+iK',k)&=\frac{k'}{ik} & \operatorname{dn}(K+iK',k)&=0 \end{aligned} -- cgit v1.2.1 From a14385eccb4fa12d22c88f2955b39bee7ee482c7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 12:51:42 +0200 Subject: Funktionsauswahl --- buch/chapters/110-elliptisch/dglsol.tex | 14 +++ buch/chapters/110-elliptisch/images/Makefile | 6 +- .../110-elliptisch/images/ellselection.pdf | Bin 0 -> 20323 bytes .../110-elliptisch/images/ellselection.tex | 122 +++++++++++++++++++++ .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 202828 -> 202828 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 312677 -> 312677 bytes 7 files changed, 141 insertions(+), 1 deletion(-) create mode 100644 buch/chapters/110-elliptisch/images/ellselection.pdf create mode 100644 buch/chapters/110-elliptisch/images/ellselection.tex diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index b1b7db3..74f2f8c 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -365,6 +365,20 @@ mit den gleichen Darstellungskonventionen wie in Abbildung~\ref{buch:elliptisch:fig:ellpolnul} \label{buch:elliptisch:fig:ellall}} \end{figure} +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/ellselection.pdf} +\caption{Auswahl einer Jacobischen elliptischen Funktion mit bestimmten +Nullstellen und Polen. +Nullstellen und Pole können in jeder der vier Ecken des fundamentalen +Rechtecks (gelb, oberer rechter Viertel des Periodenrechtecks) liegen. +Der erste Buchstabe des Namens der gesuchten Funktion ist der Buchstabe +der Ecke der Nullstelle, der zweite Buchstabe ist der Buchstabe der +Ecke des Poles. +Im Beispiel die Funktion $\operatorname{cd}(u,k)$, welche eine +Nullstelle in $K$ hat und einen Pol in $K+iK'$. +\label{buch:elliptisch:fig:selectell}} +\end{figure} Für die Funktion $y=\operatorname{sn}(u,k)$ erfüllt die Differentialgleichung \[ \frac{dy}{du} diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index cd8e905..43ca35e 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -6,7 +6,7 @@ all: lemniskate.pdf ellipsenumfang.pdf unvollstaendig.pdf rechteck.pdf \ ellipse.pdf pendel.pdf jacobiplots.pdf jacobidef.pdf jacobi12.pdf \ sncnlimit.pdf slcl.pdf torusschnitt.pdf kegelpara.pdf lemnispara.pdf \ - ellpolnul.pdf ellall.pdf + ellpolnul.pdf ellall.pdf ellselection.pdf lemniskate.pdf: lemniskate.tex pdflatex lemniskate.tex @@ -119,3 +119,7 @@ ellpolnul.pdf: ellpolnul.tex ellcommon.tex pdflatex ellpolnul.tex ellall.pdf: ellall.tex ellcommon.tex pdflatex ellall.tex + +ellselection.pdf: ellselection.tex + pdflatex ellselection.tex + diff --git a/buch/chapters/110-elliptisch/images/ellselection.pdf b/buch/chapters/110-elliptisch/images/ellselection.pdf new file mode 100644 index 0000000..bc9af35 Binary files /dev/null and b/buch/chapters/110-elliptisch/images/ellselection.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex new file mode 100644 index 0000000..9e822ec --- /dev/null +++ b/buch/chapters/110-elliptisch/images/ellselection.tex @@ -0,0 +1,122 @@ +% +% ellselection.tex -- Wahl einer elliptischen Funktion +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\l{0.45} +\pgfmathparse{\l*72/2.54} +\xdef\L{\pgfmathresult} + +\def\sx{4.1} +\pgfmathparse{\sx*72/2.54} +\xdef\Sx{\pgfmathresult} + +\def\sy{3.2} +\pgfmathparse{\sy*72/2.54} +\xdef\Sy{\pgfmathresult} + +\pgfmathparse{\sx/2-\l} +\xdef\linksx{\pgfmathresult} +\pgfmathparse{\sy/2-\l} +\xdef\linksy{\pgfmathresult} + +\pgfmathparse{\sx/2+2*\l} +\xdef\rechtsx{\pgfmathresult} +\pgfmathparse{\sy/2} +\xdef\rechtsy{\pgfmathresult} + +\fill[color=red!20] ({-\sx},0) rectangle (\sx,\sy); +\fill[color=blue!20] ({-\sx},{-\sy}) rectangle (\sx,0); +\fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy); + +\draw (-\sx,-\sy) rectangle (\sx,\sy); + +\draw[->] ({-1.4*\sx},0) -- ({1.4*\sx},0) coordinate[label={$\Re u$}]; +\draw[->] (0,{-\sy-1}) -- (0,{\sy+1}) coordinate[label={right:$\Im u$}]; + +\definecolor{darkgreen}{rgb}{0,0.6,0} + +\draw[->,line width=1.9pt,color=darkgreen] + (\sx,0) to[out=180,in=-79] (\linksx,\linksy); +\draw[->,line width=1.9pt,color=darkgreen] + (\sx,{\sy-\l}) to[out=-90,in=0] (\rechtsx,\rechtsy); + +\def\rect#1#2{ + \fill[color=white] (-\l,-\l) rectangle (\l,\l); + #2 + \draw (-\l,-\l) rectangle (\l,\l); + \node at (0,0) {\Huge #1\strut}; +} + +\def\kreuz{ + \begin{scope} + \clip ({-\l},{-\l}) rectangle ({\l},{\l}); + \fill[color=white] ({-2*\l},{-2*\l}) rectangle ({2*\l},{2*\l}); + \draw[color=darkgreen!30,line width=3pt] (-\l,-\l) -- (\l,\l); + \draw[color=darkgreen!30,line width=3pt] (-\l,\l) -- (\l,-\l); + \end{scope} +} + +\def\kreis{ + \begin{scope} + \clip ({-\l},{-\l}) rectangle ({\l},{\l}); + \fill[color=white] ({-2*\l},{-2*\l}) rectangle ({2*\l},{2*\l}); + \draw[color=darkgreen!30,line width=3pt] + (0,0) circle[radius={\l*(\L-1.5)/\L}]; + \end{scope} +} + +\begin{scope}[xshift={0},yshift={0}] + \rect{s}{} +\end{scope} + +\begin{scope}[xshift={\Sx},yshift={0}] + \rect{c}{\kreis} +\end{scope} + +\begin{scope}[xshift={\Sx},yshift={\Sy}] + \rect{d}{\kreuz} +\end{scope} + +\begin{scope}[xshift={0},yshift={\Sy}] + \rect{n}{} +\end{scope} + +\node at ({-\l+0.1},{\sy+\l-0.1}) [above left] {$iK'\mathstrut$}; +\node at ({-\l+0.1},{-\l+0.1}) [below left] {$0\mathstrut$}; +\node at ({\sx+\l-0.1},{-\l+0.1}) [below right] {$K\mathstrut$}; +\node at ({\sx+\l-0.1},{\sy+\l-0.1}) [above right] {$K+iK'\mathstrut$}; +\node at ({-\sx},0) [below left] {$-K\mathstrut$}; +\node at (0,{-\sy+0.05}) [below left] {$-iK'\mathstrut$}; +\node at ({\sx-0.1},{-\sy+0.1}) [below right] {$K-iK'\mathstrut$}; +\node at ({-\sx+0.1},{-\sy+0.1}) [below left] {$-K-iK'\mathstrut$}; +\node at ({-\sx+0.1},{\sy-0.1}) [above left] {$-K+iK'\mathstrut$}; + +\begin{scope}[xshift={-\L+0.5*\Sx},yshift={0.5*\Sy}] + \node at ({-\l},{\l-0.1}) [above] {Nullstelle\strut}; + \kreis + \node[color=darkgreen] at (0,0) {\Huge c\strut}; + \draw[line width=0.2pt] (-\l,-\l) rectangle (\l,\l); +\end{scope} + +\begin{scope}[xshift={\L+0.5*\Sx},yshift={0.5*\Sy}] + \node at ({\l},{\l-0.1}) [above] {Pol\strut}; + \kreuz + \node[color=darkgreen] at (0,0) {\Huge d\strut}; + \draw[line width=0.2pt] (-\l,-\l) rectangle (\l,\l); +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 331270e..59aea81 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index b23654c..59f9f50 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index f70f362..61293f3 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From 3a7e2cef27bd78a96b20751db2a53f7291fcd2a6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 20:18:48 +0200 Subject: add grid to images --- buch/chapters/110-elliptisch/dglsol.tex | 16 +++++------ buch/chapters/110-elliptisch/images/Makefile | 7 ++++- buch/chapters/110-elliptisch/images/ellpolnul.pdf | Bin 19647 -> 86072 bytes buch/chapters/110-elliptisch/images/ellpolnul.tex | 9 ++++++ .../110-elliptisch/images/ellselection.pdf | Bin 20323 -> 76094 bytes .../110-elliptisch/images/ellselection.tex | 15 ++++++++-- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 202828 -> 202828 bytes buch/chapters/110-elliptisch/images/rechteck.cpp | 31 +++++++++++++++------ buch/chapters/110-elliptisch/images/rechteck.pdf | Bin 91639 -> 94300 bytes buch/chapters/110-elliptisch/images/rechteck.tex | 2 ++ .../110-elliptisch/images/torusschnitt.pdf | Bin 312677 -> 312677 bytes 12 files changed, 60 insertions(+), 20 deletions(-) diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index 74f2f8c..3303aee 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -403,27 +403,27 @@ abgelesen werden: \begin{equation} \begin{aligned} \operatorname{sn}(0,k)&=0 -& +&&\qquad& \operatorname{cn}(0,k)&=1 -& +&&\qquad& \operatorname{dn}(0,k)&=1 \\ \operatorname{sn}(iK',k)&=\infty -& +&&\qquad& \operatorname{cn}(iK',k)&=\infty -& +&&\qquad& \operatorname{dn}(iK',k)&=\infty \\ \operatorname{sn}(K,k)&=1 -& +&&\qquad& \operatorname{cn}(K,k)&=0 -& +&&\qquad& \operatorname{dn}(K,k)&=k' \\ \operatorname{sn}(K+iK',k)&=\frac{1}{k} -& +&&\qquad& \operatorname{cn}(K+iK',k)&=\frac{k'}{ik} -& +&&\qquad& \operatorname{dn}(K+iK',k)&=0 \end{aligned} \label{buch:elliptische:eqn:eckwerte} diff --git a/buch/chapters/110-elliptisch/images/Makefile b/buch/chapters/110-elliptisch/images/Makefile index 43ca35e..7636e65 100644 --- a/buch/chapters/110-elliptisch/images/Makefile +++ b/buch/chapters/110-elliptisch/images/Makefile @@ -120,6 +120,11 @@ ellpolnul.pdf: ellpolnul.tex ellcommon.tex ellall.pdf: ellall.tex ellcommon.tex pdflatex ellall.tex -ellselection.pdf: ellselection.tex +rechteckpfade2.tex: rechteck Makefile + ./rechteck --outfile rechteckpfade2.tex --k 0.87 --vsteps=1 +ellselection.pdf: ellselection.tex rechteckpfade2.tex pdflatex ellselection.tex +rechteckpfade3.tex: rechteck + ./rechteck --outfile rechteckpfade3.tex --k 0.70710678118654752440 \ + --vsteps=4 diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf index 9143d2d..a60a51b 100644 Binary files a/buch/chapters/110-elliptisch/images/ellpolnul.pdf and b/buch/chapters/110-elliptisch/images/ellpolnul.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex index 16730f9..fe1d235 100644 --- a/buch/chapters/110-elliptisch/images/ellpolnul.tex +++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex @@ -15,6 +15,15 @@ \def\skala{1} \begin{tikzpicture}[>=latex,thick,scale=\skala] +\input rechteckpfade3.tex + +\pgfmathparse{1/\xmax} +\xdef\dx{\pgfmathresult} +\xdef\dy{\dx} + +\netz{0.1pt} +\draw[line width=0.1pt] (-1,0) -- (1,0); +\fill[color=white,opacity=0.5] (-1,-1) rectangle (1,1); \draw (-1,-1) rectangle (1,1); \node at (-1,-1) [below left] {$0$}; \node at (1,-1) [below right] {$K$}; diff --git a/buch/chapters/110-elliptisch/images/ellselection.pdf b/buch/chapters/110-elliptisch/images/ellselection.pdf index bc9af35..bad342c 100644 Binary files a/buch/chapters/110-elliptisch/images/ellselection.pdf and b/buch/chapters/110-elliptisch/images/ellselection.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex index 9e822ec..0dd1e04 100644 --- a/buch/chapters/110-elliptisch/images/ellselection.tex +++ b/buch/chapters/110-elliptisch/images/ellselection.tex @@ -14,15 +14,22 @@ \def\skala{1} \begin{tikzpicture}[>=latex,thick,scale=\skala] +\input{rechteckpfade2.tex} + \def\l{0.45} \pgfmathparse{\l*72/2.54} \xdef\L{\pgfmathresult} +\pgfmathparse{4.1/\xmax} +\xdef\dx{\pgfmathresult} +\xdef\dy{\dx} + \def\sx{4.1} \pgfmathparse{\sx*72/2.54} \xdef\Sx{\pgfmathresult} -\def\sy{3.2} +\pgfmathparse{\dx*\ymax} +\xdef\sy{\pgfmathresult} \pgfmathparse{\sy*72/2.54} \xdef\Sy{\pgfmathresult} @@ -36,8 +43,10 @@ \pgfmathparse{\sy/2} \xdef\rechtsy{\pgfmathresult} -\fill[color=red!20] ({-\sx},0) rectangle (\sx,\sy); -\fill[color=blue!20] ({-\sx},{-\sy}) rectangle (\sx,0); +\hintergrund +\netz{0.7pt} +\fill[color=red!14,opacity=0.7] ({-\sx},0) rectangle (\sx,\sy); +\fill[color=blue!14,opacity=0.7] ({-\sx},{-\sy}) rectangle (\sx,0); \fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy); \draw (-\sx,-\sy) rectangle (\sx,\sy); diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 59aea81..3ac9fe5 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 59f9f50..0d6f63d 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/rechteck.cpp b/buch/chapters/110-elliptisch/images/rechteck.cpp index c65ae0f..b5ad0ec 100644 --- a/buch/chapters/110-elliptisch/images/rechteck.cpp +++ b/buch/chapters/110-elliptisch/images/rechteck.cpp @@ -163,7 +163,7 @@ curvetracer::curve_t curvetracer::trace(const std::complex& startz, } catch (const toomanyiterations& x) { std::cerr << "iterations exceeded after "; std::cerr << result.size(); - std::cerr << " points"; + std::cerr << " points" << std::endl; maxsteps = 0; } } @@ -230,7 +230,7 @@ void curvedrawer::operator()(const curvetracer::curve_t& curve) { double first = true; for (auto z : curve) { if (first) { - *_out << "\\draw[color=" << _color << "] "; + *_out << "\\draw[color=" << _color << ",line width=#1] "; first = false; } else { *_out << std::endl << " -- "; @@ -244,6 +244,7 @@ static struct option longopts[] = { { "outfile", required_argument, NULL, 'o' }, { "k", required_argument, NULL, 'k' }, { "deltax", required_argument, NULL, 'd' }, +{ "vsteps", required_argument, NULL, 'v' }, { NULL, 0, NULL, 0 } }; @@ -252,7 +253,8 @@ static struct option longopts[] = { */ int main(int argc, char *argv[]) { double k = 0.625; - double deltax = 0.2; + double Deltax = 0.2; + int vsteps = 4; int c; int longindex; @@ -261,7 +263,7 @@ int main(int argc, char *argv[]) { &longindex))) switch (c) { case 'd': - deltax = std::stod(optarg); + Deltax = std::stod(optarg); break; case 'o': outfilename = std::string(optarg); @@ -269,6 +271,9 @@ int main(int argc, char *argv[]) { case 'k': k = std::stod(optarg); break; + case 'v': + vsteps = std::stoi(optarg); + break; } double kprime = integrand::kprime(k); @@ -293,15 +298,21 @@ int main(int argc, char *argv[]) { curvetracer ct(f); // fill + (*cdp->out()) << "\\def\\hintergrund{" << std::endl; (*cdp->out()) << "\\fill[color=red!10] ({" << (-xmax) << "*\\dx},0) " << "rectangle ({" << xmax << "*\\dx},{" << ymax << "*\\dy});" << std::endl; (*cdp->out()) << "\\fill[color=blue!10] ({" << (-xmax) << "*\\dx},{" << (-ymax) << "*\\dy}) rectangle ({" << xmax << "*\\dx},0);" << std::endl; + (*cdp->out()) << "}" << std::endl; + + // macro for grid + (*cdp->out()) << "\\def\\netz#1{" << std::endl; // "circles" std::complex dir(0.01, 0); + double deltax = Deltax; for (double im = deltax; im < 3; im += deltax) { std::complex startz(0, im); std::complex startw = ct.startpoint(startz); @@ -316,9 +327,9 @@ int main(int argc, char *argv[]) { } // imaginary axis - (*cdp->out()) << "\\draw[color=red] (0,0) -- (0,{" << ymax + (*cdp->out()) << "\\draw[color=red,line width=#1] (0,0) -- (0,{" << ymax << "*\\dy});" << std::endl; - (*cdp->out()) << "\\draw[color=blue] (0,0) -- (0,{" << (-ymax) + (*cdp->out()) << "\\draw[color=blue,line width=#1] (0,0) -- (0,{" << (-ymax) << "*\\dy});" << std::endl; // arguments between 0 and 1 @@ -353,7 +364,8 @@ int main(int argc, char *argv[]) { // arguments between 1 and 1/k { - for (double x0 = 1 + deltax; x0 < 1/k; x0 += deltax) { + deltax = (1/k - 1) / vsteps; + for (double x0 = 1 + deltax; x0 < 1/k + 0.00001; x0 += deltax) { double y0 = sqrt(1-1/(x0*x0))/kprime; //std::cout << "y0 = " << y0 << std::endl; double y = gsl_sf_ellint_F(asin(y0), kprime, @@ -389,8 +401,9 @@ int main(int argc, char *argv[]) { // arguments larger than 1/k { + deltax = Deltax; dir = std::complex(0, 0.01); - double x0 = 1; + double x0 = 1/k; while (x0 <= 1/k + 0.0001) { x0 += deltax; } for (; x0 < 4; x0 += deltax) { std::complex startz(x0); @@ -407,6 +420,8 @@ int main(int argc, char *argv[]) { } } + (*cdp->out()) << "}" << std::endl; + // border (*cdp->out()) << "\\def\\xmax{" << xmax << "}" << std::endl; (*cdp->out()) << "\\def\\ymax{" << ymax << "}" << std::endl; diff --git a/buch/chapters/110-elliptisch/images/rechteck.pdf b/buch/chapters/110-elliptisch/images/rechteck.pdf index 6209897..46f2376 100644 Binary files a/buch/chapters/110-elliptisch/images/rechteck.pdf and b/buch/chapters/110-elliptisch/images/rechteck.pdf differ diff --git a/buch/chapters/110-elliptisch/images/rechteck.tex b/buch/chapters/110-elliptisch/images/rechteck.tex index 622a9e9..12535ba 100644 --- a/buch/chapters/110-elliptisch/images/rechteck.tex +++ b/buch/chapters/110-elliptisch/images/rechteck.tex @@ -18,6 +18,8 @@ \def\dy{3} \input{rechteckpfade.tex} +\hintergrund +\netz{0.7pt} \begin{scope} \clip ({-\xmax*\dx},{-\ymax*\dy}) rectangle ({\xmax*\dx},{\ymax*\dy}); diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 61293f3..2948e76 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From b2d8e88a2517a5d15b01f4e34ac12dfc8723c265 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 20:30:36 +0200 Subject: improve elliptic domain images --- buch/chapters/110-elliptisch/images/ellpolnul.pdf | Bin 86072 -> 130369 bytes buch/chapters/110-elliptisch/images/ellpolnul.tex | 9 ++++++--- .../chapters/110-elliptisch/images/jacobiplots.pdf | Bin 56975 -> 56975 bytes buch/chapters/110-elliptisch/images/kegelpara.pdf | Bin 202828 -> 202828 bytes .../110-elliptisch/images/torusschnitt.pdf | Bin 312677 -> 312677 bytes 5 files changed, 6 insertions(+), 3 deletions(-) diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf index a60a51b..4453703 100644 Binary files a/buch/chapters/110-elliptisch/images/ellpolnul.pdf and b/buch/chapters/110-elliptisch/images/ellpolnul.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex index fe1d235..b3183fc 100644 --- a/buch/chapters/110-elliptisch/images/ellpolnul.tex +++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex @@ -17,12 +17,15 @@ \input rechteckpfade3.tex -\pgfmathparse{1/\xmax} +\pgfmathparse{2/\xmax} \xdef\dx{\pgfmathresult} \xdef\dy{\dx} -\netz{0.1pt} -\draw[line width=0.1pt] (-1,0) -- (1,0); +\begin{scope}[xshift=-1cm,yshift=-1cm] +\clip (0,0) rectangle (2,2); +\netz{0.4pt} +\draw[line width=0.4pt] (-1,0) -- (1,0); +\end{scope} \fill[color=white,opacity=0.5] (-1,-1) rectangle (1,1); \draw (-1,-1) rectangle (1,1); \node at (-1,-1) [below left] {$0$}; diff --git a/buch/chapters/110-elliptisch/images/jacobiplots.pdf b/buch/chapters/110-elliptisch/images/jacobiplots.pdf index 3ac9fe5..eb9d7f1 100644 Binary files a/buch/chapters/110-elliptisch/images/jacobiplots.pdf and b/buch/chapters/110-elliptisch/images/jacobiplots.pdf differ diff --git a/buch/chapters/110-elliptisch/images/kegelpara.pdf b/buch/chapters/110-elliptisch/images/kegelpara.pdf index 0d6f63d..2bbd428 100644 Binary files a/buch/chapters/110-elliptisch/images/kegelpara.pdf and b/buch/chapters/110-elliptisch/images/kegelpara.pdf differ diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pdf b/buch/chapters/110-elliptisch/images/torusschnitt.pdf index 2948e76..9b64ab2 100644 Binary files a/buch/chapters/110-elliptisch/images/torusschnitt.pdf and b/buch/chapters/110-elliptisch/images/torusschnitt.pdf differ -- cgit v1.2.1 From e1e6149b020ef102e257adb9898d5ba5242bac05 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 24 Jun 2022 20:47:33 +0200 Subject: more improvements --- buch/chapters/110-elliptisch/images/ellpolnul.pdf | Bin 130369 -> 130369 bytes buch/chapters/110-elliptisch/images/ellpolnul.tex | 2 +- .../110-elliptisch/images/ellselection.pdf | Bin 76094 -> 165928 bytes .../110-elliptisch/images/ellselection.tex | 14 ++++++++++++-- 4 files changed, 13 insertions(+), 3 deletions(-) diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.pdf b/buch/chapters/110-elliptisch/images/ellpolnul.pdf index 4453703..d798169 100644 Binary files a/buch/chapters/110-elliptisch/images/ellpolnul.pdf and b/buch/chapters/110-elliptisch/images/ellpolnul.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellpolnul.tex b/buch/chapters/110-elliptisch/images/ellpolnul.tex index b3183fc..dfa04d3 100644 --- a/buch/chapters/110-elliptisch/images/ellpolnul.tex +++ b/buch/chapters/110-elliptisch/images/ellpolnul.tex @@ -26,7 +26,7 @@ \netz{0.4pt} \draw[line width=0.4pt] (-1,0) -- (1,0); \end{scope} -\fill[color=white,opacity=0.5] (-1,-1) rectangle (1,1); +\fill[color=white,opacity=0.7] (-1,-1) rectangle (1,1); \draw (-1,-1) rectangle (1,1); \node at (-1,-1) [below left] {$0$}; \node at (1,-1) [below right] {$K$}; diff --git a/buch/chapters/110-elliptisch/images/ellselection.pdf b/buch/chapters/110-elliptisch/images/ellselection.pdf index bad342c..7c98db1 100644 Binary files a/buch/chapters/110-elliptisch/images/ellselection.pdf and b/buch/chapters/110-elliptisch/images/ellselection.pdf differ diff --git a/buch/chapters/110-elliptisch/images/ellselection.tex b/buch/chapters/110-elliptisch/images/ellselection.tex index 0dd1e04..d8afeb1 100644 --- a/buch/chapters/110-elliptisch/images/ellselection.tex +++ b/buch/chapters/110-elliptisch/images/ellselection.tex @@ -43,8 +43,18 @@ \pgfmathparse{\sy/2} \xdef\rechtsy{\pgfmathresult} -\hintergrund -\netz{0.7pt} +\begin{scope} + \clip (-\sx,-\sy) rectangle (\sx,\sy); + \begin{scope}[xshift={-\Sx}] + \hintergrund + \netz{0.7pt} + \end{scope} + \begin{scope}[xshift={\Sx}] + \hintergrund + \netz{0.7pt} + \end{scope} +\end{scope} + \fill[color=red!14,opacity=0.7] ({-\sx},0) rectangle (\sx,\sy); \fill[color=blue!14,opacity=0.7] ({-\sx},{-\sy}) rectangle (\sx,0); \fill[color=yellow!40,opacity=0.5] (0,0) rectangle (\sx,\sy); -- cgit v1.2.1 From 7cc8f34f003ecb25ade7f1ff2287fe12b5a22c40 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 25 Jun 2022 14:36:04 +0200 Subject: arithmetic-geometric-mean --- buch/chapters/110-elliptisch/agm.m | 20 ++ buch/chapters/110-elliptisch/ellintegral.tex | 320 ++++++++++++++++++++- .../chapters/110-elliptisch/experiments/agm.maxima | 26 ++ 3 files changed, 357 insertions(+), 9 deletions(-) create mode 100644 buch/chapters/110-elliptisch/agm.m create mode 100644 buch/chapters/110-elliptisch/experiments/agm.maxima diff --git a/buch/chapters/110-elliptisch/agm.m b/buch/chapters/110-elliptisch/agm.m new file mode 100644 index 0000000..2f0a1ea --- /dev/null +++ b/buch/chapters/110-elliptisch/agm.m @@ -0,0 +1,20 @@ +# +# agm.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +format long + +n = 10; +a = 1; +b = sqrt(0.5); + +for i = (1:n) + printf("%20.16f %20.16f\n", a, b); + A = (a+b)/2; + b = sqrt(a*b); + a = A; +end + +E = 2 / (pi * a) + diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index bc597d6..970d8fa 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -451,14 +451,310 @@ Hilfe einer Entwicklung der Wurzel mit der Binomialreihe gefunden werden. \end{proof} +Die Darstellung von $E(k)$ als hypergeometrische Reihe ermöglicht +jetzt zum Beispiel auch die Berechnung der Ableitung nach dem +Parameter $k$ mit der Ableitungsformel für die Funktion $\mathstrut_2F_1$. + + % +% Berechnung mit dem arithmetisch-geometrischen Mittel +% +\subsection{Berechnung mit dem arithmetisch-geometrischen Mittel} +Die numerische Berechnung von elliptischer Integrale mit gewöhnlichen +numerischen Integrationsroutinen ist nicht sehr effizient. +Das in diesem Abschnitt vorgestellte arithmetisch-geometrische Mittel +\index{arithmetisch-geometrisches Mittel}% +liefert einen Algorithmus mit sehr viel besserer Konvergenz. +Die Methode lässt sich auch auf die unvollständigen elliptischen +Integrale von Abschnitt~\eqref{buch:elliptisch:subsection:unvollstintegral} +verallgemeinern. +Sie ist ein Speziallfall der sogenannten Landen-Transformation, +\index{Landen-Transformation}% +welche ausser für die elliptischen Integrale auch für die +Jacobischen elliptischen Funktionen formuliert werden kann und +für letztere ebenfalls sehr schnelle numerische Algorithmen liefert. + % +% Das arithmetisch-geometrische Mittel % -\subsubsection{Komplementäre Integrale} +\subsubsection{Das arithmetisch-geometrische Mittel} +Seien $a$ und $b$ zwei nichtnegative reelle Zahlen. +Aus $a$ und $b$ werden jetzt zwei Folgen konstruiert, deren Glieder +durch +\begin{align*} +a_0&=a &&\text{und}& a_{n+1} &= \frac{a_n+b_n}2 &&\text{arithmetisches Mittel} +\\ +b_0&=b &&\text{und}& b_{n+1} &= \sqrt{a_nb_n} &&\text{geometrisches Mittel} +\end{align*} +definiert sind. + +\begin{satz} +Falls $a>b>0$ ist, nimmt die Folge $(a_k)_{k\ge 0}$ monoton ab und +$(b_k)_{k\ge 0}$ nimmt monoton zu. +Beide konvergieren quadratisch gegen einen gemeinsamen Grenzwert. +\end{satz} + +\begin{definition} +Der gemeinsame Grenzwert von $a_n$ und $b_n$ heisst das +{\em arithmetisch-geometrische Mittel} und wird mit +\[ +M(a,b) += +\lim_{n\to\infty} a_n += +\lim_{n\to\infty} b_n +\] +bezeichnet. +\index{arithmetisch-geometrisches Mittel}% +\end{definition} -\subsubsection{Ableitung} -XXX Ableitung \\ -XXX Stammfunktion \\ +\begin{proof}[Beweis] +Zunächst ist zu zeigen, dass die Folgen monoton sind. +Dies folgt sofort aus der Definition der Folgen: +\begin{align*} +a_{n+1} &= \frac{a_n+b_n}{2} \ge \frac{a_n+a_n}{2} = a_n +\\ +b_{n+1} &= \sqrt{a_nb_n} \ge \sqrt{b_nb_n} = b_n. +\end{align*} +Die Konvergenz folgt aus +\[ +a_{n+1}-b_{n+1} +\le +a_{n+1}-b_n += +\frac{a_n+b_n}{2}-b_n += +\frac{a_n-b_n}2 +\le +\frac{a-b}{2^{n+1}}. +\] +Dies zeigt jedoch nur, dass die Konvergenz mindestens ein +Bit in jeder Iteration ist. +Aus +\[ +a_{n+1}^2 - b_{n+1}^2 += +\frac{(a_n+b_n)^2}{4} - a_nb_n += +\frac{a_n^2 -2a_nb_n+b_n^2}{4} += +\frac{(a_n-b_n)^2}{4} +\] +folgt +\[ +a_{n+1}-b_{n+1} += +\frac{(a_n-b_n)^2}{2(a_{n+1}+b_{n+1})}. +\] +Da der Nenner gegen $2M(a,b)$ konvergiert, wird der Fehler für in +jeder Iteration quadriert, es liegt also quadratische Konvergenz vor. +\end{proof} + +% +% Transformation des elliptischen Integrals +% +\subsubsection{Transformation des elliptischen Integrals} +In diesem Abschnitt soll das Integral +\[ +I(a,b) += +\int_0^{\frac{\pi}2} +\frac{dt}{\sqrt{a^2\cos^2 t + b^2\sin^2t}} +\] +berechnet werden. +Es ist klar, dass +\[ +I(sa,sb) += +\frac{1}{s} I(a,b). +\] + +Gauss hat gefunden, dass die Substitution +\begin{equation} +\sin t += +\frac{2a\sin t_1}{a+b+(a-b)\sin t_1} +\label{buch:elliptisch:agm:subst} +\end{equation} +zu +\begin{equation} +\frac{dt}{a^2\cos^2 t + b^2 \sin^2 t} += +\frac{dt_1}{a_1^2\cos^2 t_1 + b_1^2 \sin^2 t_1} +\label{buch:elliptisch:agm:dtdt1} +\end{equation} +führt. +Um dies nachzuprüfen, muss man zunächst +\eqref{buch:elliptisch:agm:subst} +nach $t_1$ ableiten, was +\[ +\frac{d}{dt_1}\sin t += +\cos t +\frac{dt}{dt_1} +\qquad\Rightarrow\qquad +\biggl( +\frac{d}{dt_1}\sin t +\biggr)^2 += +(1-\sin^2t)\biggl(\frac{dt}{dt_1}\biggr)^2 +\] +ergibt. +Die Ableitung von $t$ nach $t_1$ kann auch aus +\eqref{buch:elliptisch:agm:dtdt1} +ableiten, es ist +\[ +\biggl( +\frac{dt}{dt_1} +\biggr)^2 += +\frac{a^2 \cos^2 t + b^2 \sin^2 t}{a_1^2 \cos^2 t_1 + b_1^2 \sin^2 t_1}. +\] +Man muss also nachprüfen, dass +\begin{equation} +\frac{1}{1-\sin^2 t} +\frac{d}{dt_1}\sin t += +\frac{a^2 \cos^2 t + b^2 \sin^2 t}{a_1^2 \cos^2 t_1 + b_1^2 \sin^2 t_1}. +\label{buch:elliptisch:agm:deq} +\end{equation} +Dazu muss man zunächst $a_1=(a+b)/2$, $b_1=\sqrt{ab}$ setzen. +Ausserdem muss man $\cos^2 t$ durch $1-\sin^2t$ ersetzen und +$\sin t$ durch \eqref{buch:elliptisch:agm:subst}. +Auch $\cos^2 t_1$ muss man durch $1-\sin^2t_1$ ersetzt werden. +Dann kann man nach einer langwierigen Rechnung, die sich am leichtesten +mit einem Computer-Algebra-System ausführen lässt finden, dass +\eqref{buch:elliptisch:agm:deq} +tatsächlich korrekt ist. + +\begin{satz} +\label{buch:elliptisch:agm:integrale} +Für $a_1=(a+b)/2$ und $b_1=\sqrt{ab}$ gilt +\[ +\int_0^{\frac{\pi}2} +\frac{dt}{a^2\cos^2 t + b^2 \sin^2 t} += +\int_0^{\frac{\pi}2} +\frac{dt_1}{a_1^2\cos^2 t_1 + b_1^2 \sin^2 t_1}. +\] +\end{satz} + +Der Satz~\ref{buch:elliptisch:agm:integrale} zeigt, dass die Ersetzung +von $a$ und $b$ durch $a_1$ und $b_1$ das Integral $I(a,b)$ nicht ändert. +Dies gilt natürlich für alle Glieder der Folge zur Bestimmung des +arithmetisch-geometrischen Mittels. + +\begin{satz} +Für $a\ge b>0$ gilt +\begin{equation} +I(a,b) += +\int_0^{\frac{\pi}2} +\frac{dt}{a^2\cos^2 t + b^2\sin^2t} += +\frac{\pi}{2M(a,b)} +\end{equation} +\end{satz} + +\begin{proof}[Beweis] +Zunächst folgt aus Satz~\ref{buch:elliptisch:agm:integrale}, dass +\[ +I(a,b) += +I(a_1,b_1) += +\dots += +I(a_n,b_n). +\] +Ausserdem ist $a_n\to M(a,b)$ und $b_n\to M(a,b)$, +damit wird +\[ +I(a,b) += +\frac{1}{M(a,b)} +\int_0^{\frac{\pi}2} +\frac{dt}{\sqrt{\cos^2 t + \sin^2 t}} += +\frac{\pi}{2M(a,b)}. +\qedhere +\] +\end{proof} + +% +% Berechnung des elliptischen Integrals +% +\subsubsection{Berechnung des elliptischen Integrals} +Das elliptische Integral erster Art hat eine Form, die dem Integral +$I(a,b)$ bereits sehr ähnlich ist. +Im die Verbindung herzustellen, berechnen wir +\begin{align*} +I(a,b) +&= +\int_0^{\frac{\pi}2} +\frac{dt}{\sqrt{a^2\cos^2 t + b^2 \sin^2 t}} +\\ +&= +\frac{1}{a} +\int_0^{\frac{\pi}2} +\frac{dt}{\sqrt{1-\sin^2 t + \frac{b^2}{a^2} \sin^2 t}} +\\ +&= +\frac{1}{a} +\int_0^{\frac{\pi}2} +\frac{dt}{\sqrt{1-(1-\frac{b^2}{a^2})\sin^2 t}} += +K(k) +\qquad\text{mit}\qquad +k'=\frac{b^2}{a^2},\; +k=\sqrt{1-k^{\prime 2}} +\end{align*} + +\begin{satz} +\label{buch:elliptisch:agm:satz:Ek} +Für $0{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\hline +n& a_n & b_n \\ +\hline +0 & 1.0000000000000000 & 0.7071067811865476\\ +1 & 0.\underline{8}535533905932737 & 0.\underline{84}08964152537146\\ +2 & 0.\underline{8472}249029234942 & 0.\underline{8472}012667468916\\ +3 & 0.\underline{847213084}8351929 & 0.\underline{8472130847}527654\\ +4 & 0.\underline{847213084793979}2 & 0.\underline{847213084793979}1\\ +\hline +\end{tabular} +\caption{Die Berechnung des arithmetisch-geometrischen Mittels für +$a=1$ und $b=\sqrt{2}/2$ zeigt die sehr rasche Konvergenz. +\label{buch:elliptisch:agm:numerisch}} +\end{table} +In diesem Abschnitt soll als Zahlenbeispiel $E(k)$ für $k=\sqrt{2}/2$ +berechnet werden. +In diesem speziellen Fall ist $k'=k$. +Tabelle~\ref{buch:elliptisch:agm:numerisch} zeigt die sehr rasche +Konvergenz der Berechnung des arithmetisch-geometrischen Mittels +von $1$ und $\sqrt{2}/2$. +Mit Satz~\ref{buch:elliptisch:agm:satz:Ek} folgt jetzt +\[ +K(\sqrt{2}/2) += +\frac{\pi}{2M(1,\sqrt{2}/2)} += +0.751428163461842. +\] +Die Berechnung hat nur 4 Mittelwerte, 4 Produkte, 4 Quadratwurzeln und +eine Division erfordert. % % Unvollständige elliptische Integrale @@ -551,7 +847,7 @@ Die Faktoren, die in den Integranden der unvollständigen elliptischen Integrale vorkommen, haben Nullstellen bei $\pm1$, $\pm1/k$ und $\pm 1/\sqrt{n}$ -XXX Additionstheoreme \\ +% XXX Additionstheoreme \\ XXX Parameterkonventionen \\ % @@ -648,6 +944,9 @@ l({\textstyle\frac{1}{k}})=\int_1^{\frac1{k}} \end{equation} ausgewertet werden. +% +% Komplementärmodul +% \subsubsection{Komplementärmodul} Im vorangegangen Abschnitt wurde gezeigt, dass der Wertebereicht des unvollständigen elliptischen Integrals der ersten Art als komplexe @@ -751,6 +1050,9 @@ in das blaue. \label{buch:elliptisch:fig:rechteck}} \end{figure} +% +% Reelle Argument > 1/k +% \subsubsection{Reelle Argument $> 1/k$} Für Argument $x> 1/k$ sind beide Faktoren im Integranden des unvollständigen elliptischen Integrals negativ, das Integral kann @@ -797,7 +1099,7 @@ F(x,k) = iK(k') - F\biggl(\frac1{kx},k\biggr) für die Werte des elliptischen Integrals erster Art für grosse Argumentwerte fest. -\subsection{Potenzreihe} -XXX Potenzreihen \\ -XXX Als hypergeometrische Funktionen \url{https://www.youtube.com/watch?v=j0t1yWrvKmE} \\ -XXX Berechnung mit der Landen-Transformation https://en.wikipedia.org/wiki/Landen%27s_transformation +%\subsection{Potenzreihe} +%XXX Potenzreihen \\ +%XXX Als hypergeometrische Funktionen \url{https://www.youtube.com/watch?v=j0t1yWrvKmE} \\ +%XXX Berechnung mit der Landen-Transformation https://en.wikipedia.org/wiki/Landen%27s_transformation diff --git a/buch/chapters/110-elliptisch/experiments/agm.maxima b/buch/chapters/110-elliptisch/experiments/agm.maxima new file mode 100644 index 0000000..c7facd4 --- /dev/null +++ b/buch/chapters/110-elliptisch/experiments/agm.maxima @@ -0,0 +1,26 @@ +/* + * agm.maxima + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ + +S: 2*a*sin(theta1) / (a+b+(a-b)*sin(theta1)^2); + +C2: ratsimp(diff(S, theta1)^2 / (1 - S^2)); +C2: ratsimp(subst(sqrt(1-sin(theta1)^2), cos(theta1), C2)); +C2: ratsimp(subst(S, sin(theta), C2)); +C2: ratsimp(subst(sqrt(1-S^2), cos(theta), C2)); + +D2: (a^2 * cos(theta)^2 + b^2 * sin(theta)^2) + / + (a1^2 * cos(theta1)^2 + b1^2 * sin(theta1)^2); +D2: subst((a+b)/2, a1, D2); +D2: subst(sqrt(a*b), b1, D2); +D2: ratsimp(subst(1-S^2, cos(theta)^2, D2)); +D2: ratsimp(subst(S, sin(theta), D2)); +D2: ratsimp(subst(1-sin(theta1)^2, cos(theta1)^2, D2)); + +Q: D2/C2; +Q: ratsimp(subst(x, sin(theta1), Q)); + +Q: ratsimp(expand(ratsimp(Q))); -- cgit v1.2.1 From 335c3a23f09759be380291ec89b0f2c43c2d3db6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 25 Jun 2022 22:46:16 +0200 Subject: fix agm --- buch/chapters/110-elliptisch/agm.m | 20 ------------- buch/chapters/110-elliptisch/agm/Makefile | 10 +++++++ buch/chapters/110-elliptisch/agm/agm.cpp | 42 ++++++++++++++++++++++++++++ buch/chapters/110-elliptisch/agm/agm.m | 20 +++++++++++++ buch/chapters/110-elliptisch/ellintegral.tex | 34 ++++++++++++---------- 5 files changed, 91 insertions(+), 35 deletions(-) delete mode 100644 buch/chapters/110-elliptisch/agm.m create mode 100644 buch/chapters/110-elliptisch/agm/Makefile create mode 100644 buch/chapters/110-elliptisch/agm/agm.cpp create mode 100644 buch/chapters/110-elliptisch/agm/agm.m diff --git a/buch/chapters/110-elliptisch/agm.m b/buch/chapters/110-elliptisch/agm.m deleted file mode 100644 index 2f0a1ea..0000000 --- a/buch/chapters/110-elliptisch/agm.m +++ /dev/null @@ -1,20 +0,0 @@ -# -# agm.m -# -# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule -# -format long - -n = 10; -a = 1; -b = sqrt(0.5); - -for i = (1:n) - printf("%20.16f %20.16f\n", a, b); - A = (a+b)/2; - b = sqrt(a*b); - a = A; -end - -E = 2 / (pi * a) - diff --git a/buch/chapters/110-elliptisch/agm/Makefile b/buch/chapters/110-elliptisch/agm/Makefile new file mode 100644 index 0000000..e7975e1 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/Makefile @@ -0,0 +1,10 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# + +agm: agm.cpp + g++ -O -Wall -g -std=c++11 agm.cpp -o agm `pkg-config --cflags gsl` `pkg-config --libs gsl` + ./agm + diff --git a/buch/chapters/110-elliptisch/agm/agm.cpp b/buch/chapters/110-elliptisch/agm/agm.cpp new file mode 100644 index 0000000..fdb0441 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/agm.cpp @@ -0,0 +1,42 @@ +/* + * agm.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include + + + +int main(int argc, char *argv[]) { + long double a = 1; + long double b = sqrtl(2.)/2; + if (argc >= 3) { + a = std::stod(argv[1]); + b = std::stod(argv[2]); + } + + { + long double an = a; + long double bn = b; + for (int i = 0; i < 10; i++) { + printf("%d %24.18Lf %24.18Lf %24.18Lf\n", + i, an, bn, a * M_PI / (2 * an)); + long double A = (an + bn) / 2; + bn = sqrtl(an * bn); + an = A; + } + } + + { + double k = b/a; + k = sqrt(1 - k*k); + double K = gsl_sf_ellint_Kcomp(k, GSL_PREC_DOUBLE); + printf(" %24.18f %24.18f\n", k, K); + } + + return EXIT_SUCCESS; +} diff --git a/buch/chapters/110-elliptisch/agm/agm.m b/buch/chapters/110-elliptisch/agm/agm.m new file mode 100644 index 0000000..dcb3ad8 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/agm.m @@ -0,0 +1,20 @@ +# +# agm.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +format long + +n = 10; +a = 1; +b = sqrt(0.5); + +for i = (1:n) + printf("%20.16f %20.16f\n", a, b); + A = (a+b)/2; + b = sqrt(a*b); + a = A; +end + +K = pi / (2 * a) + diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 970d8fa..79ed91e 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -578,9 +578,9 @@ Gauss hat gefunden, dass die Substitution \end{equation} zu \begin{equation} -\frac{dt}{a^2\cos^2 t + b^2 \sin^2 t} +\frac{dt}{\sqrt{a^2_{\phantom{1}}\cos^2 t + b^2_{\phantom{1}} \sin^2 t}} = -\frac{dt_1}{a_1^2\cos^2 t_1 + b_1^2 \sin^2 t_1} +\frac{dt_1}{\sqrt{a_1^2\cos^2 t_1 + b_1^2 \sin^2 t_1}} \label{buch:elliptisch:agm:dtdt1} \end{equation} führt. @@ -608,7 +608,7 @@ ableiten, es ist \frac{dt}{dt_1} \biggr)^2 = -\frac{a^2 \cos^2 t + b^2 \sin^2 t}{a_1^2 \cos^2 t_1 + b_1^2 \sin^2 t_1}. +\frac{a^2_{\phantom{1}} \cos^2 t + b^2_{\phantom{1}} \sin^2 t}{a_1^2 \cos^2 t_1 + b_1^2 \sin^2 t_1}. \] Man muss also nachprüfen, dass \begin{equation} @@ -618,7 +618,7 @@ Man muss also nachprüfen, dass \frac{a^2 \cos^2 t + b^2 \sin^2 t}{a_1^2 \cos^2 t_1 + b_1^2 \sin^2 t_1}. \label{buch:elliptisch:agm:deq} \end{equation} -Dazu muss man zunächst $a_1=(a+b)/2$, $b_1=\sqrt{ab}$ setzen. +Dazu muss man zunächst $a_1=(a+b)/2$, $b_1=\!\sqrt{ab}$ setzen. Ausserdem muss man $\cos^2 t$ durch $1-\sin^2t$ ersetzen und $\sin t$ durch \eqref{buch:elliptisch:agm:subst}. Auch $\cos^2 t_1$ muss man durch $1-\sin^2t_1$ ersetzt werden. @@ -724,15 +724,19 @@ K(k) = I(1,\sqrt{1-k^2}) = \frac{\pi}{2M(1,\sqrt{1-k^2})} \subsubsection{Numerisches Beispiel} \begin{table} \centering -\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} \hline -n& a_n & b_n \\ +n& a_n & b_n & \pi/2a_n \mathstrut +\text{\vrule height12pt depth6pt width0pt}\\ \hline -0 & 1.0000000000000000 & 0.7071067811865476\\ -1 & 0.\underline{8}535533905932737 & 0.\underline{84}08964152537146\\ -2 & 0.\underline{8472}249029234942 & 0.\underline{8472}012667468916\\ -3 & 0.\underline{847213084}8351929 & 0.\underline{8472130847}527654\\ -4 & 0.\underline{847213084793979}2 & 0.\underline{847213084793979}1\\ +\text{\vrule height12pt depth0pt width0pt} + 0 & 1.0000000000000000000 & 0.7071067811865475243 & 1.5707963267948965579 \\ + 1 & 0.8535533905932737621 & 0.8408964152537145430 & 1.\underline{8}403023690212201581 \\ + 2 & 0.8472249029234941526 & 0.8472012667468914603 & 1.\underline{8540}488143993356315 \\ + 3 & 0.8472130848351928064 & 0.8472130847527653666 & 1.\underline{854074677}2111781089 \\ + 4 & 0.8472130847939790865 & 0.8472130847939790865 & 1.\underline{854074677301371}8463 \\ +\infty& & & 1.8540746773013719184  +\text{\vrule height12pt depth6pt width0pt}\\ \hline \end{tabular} \caption{Die Berechnung des arithmetisch-geometrischen Mittels für @@ -747,11 +751,11 @@ Konvergenz der Berechnung des arithmetisch-geometrischen Mittels von $1$ und $\sqrt{2}/2$. Mit Satz~\ref{buch:elliptisch:agm:satz:Ek} folgt jetzt \[ -K(\sqrt{2}/2) +K(\!\sqrt{2}/2) = -\frac{\pi}{2M(1,\sqrt{2}/2)} +\frac{\pi}{2M(1,\!\sqrt{2}/2)} = -0.751428163461842. +1.854074677301372. \] Die Berechnung hat nur 4 Mittelwerte, 4 Produkte, 4 Quadratwurzeln und eine Division erfordert. @@ -848,7 +852,7 @@ Integrale vorkommen, haben Nullstellen bei $\pm1$, $\pm1/k$ und $\pm 1/\sqrt{n}$ % XXX Additionstheoreme \\ -XXX Parameterkonventionen \\ +% XXX Parameterkonventionen \\ % % Wertebereich -- cgit v1.2.1 From 753507e2be9ce6019b934b8422980c62b55ef1fe Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 25 Jun 2022 22:52:08 +0200 Subject: final agm --- buch/chapters/110-elliptisch/ellintegral.tex | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 79ed91e..4589ffa 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -547,7 +547,8 @@ a_{n+1}-b_{n+1} \frac{(a_n-b_n)^2}{2(a_{n+1}+b_{n+1})}. \] Da der Nenner gegen $2M(a,b)$ konvergiert, wird der Fehler für in -jeder Iteration quadriert, es liegt also quadratische Konvergenz vor. +jeder Iteration quadriert, die Zahl korrekter Stellen verdoppelt sich +in jeder Iteration, es liegt also quadratische Konvergenz vor. \end{proof} % @@ -726,16 +727,15 @@ K(k) = I(1,\sqrt{1-k^2}) = \frac{\pi}{2M(1,\sqrt{1-k^2})} \centering \begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} \hline -n& a_n & b_n & \pi/2a_n \mathstrut -\text{\vrule height12pt depth6pt width0pt}\\ +n& a_n & b_n & \pi/2a_n \mathstrut\text{\vrule height12pt depth6pt width0pt}\\ \hline -\text{\vrule height12pt depth0pt width0pt} - 0 & 1.0000000000000000000 & 0.7071067811865475243 & 1.5707963267948965579 \\ - 1 & 0.8535533905932737621 & 0.8408964152537145430 & 1.\underline{8}403023690212201581 \\ - 2 & 0.8472249029234941526 & 0.8472012667468914603 & 1.\underline{8540}488143993356315 \\ - 3 & 0.8472130848351928064 & 0.8472130847527653666 & 1.\underline{854074677}2111781089 \\ - 4 & 0.8472130847939790865 & 0.8472130847939790865 & 1.\underline{854074677301371}8463 \\ -\infty& & & 1.8540746773013719184  +\text{\vrule height12pt depth0pt width0pt}% +0 & 1.0000000000000000000 & 0.7071067811865475243 & 1.5707963267948965579 \\ +1 & 0.8535533905932737621 & 0.8408964152537145430 & 1.\underline{8}403023690212201581 \\ +2 & 0.8472249029234941526 & 0.8472012667468914603 & 1.\underline{8540}488143993356315 \\ +3 & 0.8472130848351928064 & 0.8472130847527653666 & 1.\underline{854074677}2111781089 \\ +4 & 0.8472130847939790865 & 0.8472130847939790865 & 1.\underline{854074677301371}8463 \\ +\infty& & & 1.8540746773013719184% \text{\vrule height12pt depth6pt width0pt}\\ \hline \end{tabular} -- cgit v1.2.1 From 05d75b0f467b2535db538ecaee461cf0c8b637d1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 27 Jun 2022 20:17:16 +0200 Subject: add stuff for elliptic filters --- buch/chapters/110-elliptisch/Makefile.inc | 3 + buch/chapters/110-elliptisch/agm/Makefile | 5 + buch/chapters/110-elliptisch/agm/agm.cpp | 37 ++++- buch/chapters/110-elliptisch/agm/agm.maxima | 26 +++ buch/chapters/110-elliptisch/agm/sn.cpp | 52 ++++++ buch/chapters/110-elliptisch/chapter.tex | 7 +- buch/chapters/110-elliptisch/dglsol.tex | 89 +++++++++++ buch/chapters/110-elliptisch/ellintegral.tex | 141 +++++++++++++++- buch/chapters/110-elliptisch/elltrigo.tex | 2 +- buch/chapters/110-elliptisch/experiments/KK.pdf | Bin 0 -> 23248 bytes buch/chapters/110-elliptisch/experiments/KK.tex | 66 ++++++++ buch/chapters/110-elliptisch/experiments/KN.cpp | 177 +++++++++++++++++++++ buch/chapters/110-elliptisch/experiments/Makefile | 15 ++ .../chapters/110-elliptisch/experiments/agm.maxima | 26 --- buch/chapters/110-elliptisch/uebungsaufgaben/2.tex | 61 +++++++ buch/chapters/110-elliptisch/uebungsaufgaben/3.tex | 135 ++++++++++++++++ .../110-elliptisch/uebungsaufgaben/landen.m | 60 +++++++ buch/chapters/references.bib | 9 ++ buch/papers/dreieck/teil0.tex | 2 +- 19 files changed, 878 insertions(+), 35 deletions(-) create mode 100644 buch/chapters/110-elliptisch/agm/agm.maxima create mode 100644 buch/chapters/110-elliptisch/agm/sn.cpp create mode 100644 buch/chapters/110-elliptisch/experiments/KK.pdf create mode 100644 buch/chapters/110-elliptisch/experiments/KK.tex create mode 100644 buch/chapters/110-elliptisch/experiments/KN.cpp create mode 100644 buch/chapters/110-elliptisch/experiments/Makefile delete mode 100644 buch/chapters/110-elliptisch/experiments/agm.maxima create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/2.tex create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/3.tex create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/landen.m diff --git a/buch/chapters/110-elliptisch/Makefile.inc b/buch/chapters/110-elliptisch/Makefile.inc index 639cb8f..ef6ea51 100644 --- a/buch/chapters/110-elliptisch/Makefile.inc +++ b/buch/chapters/110-elliptisch/Makefile.inc @@ -12,4 +12,7 @@ CHAPTERFILES += \ chapters/110-elliptisch/mathpendel.tex \ chapters/110-elliptisch/lemniskate.tex \ chapters/110-elliptisch/uebungsaufgaben/1.tex \ + chapters/110-elliptisch/uebungsaufgaben/2.tex \ + chapters/110-elliptisch/uebungsaufgaben/3.tex \ + chapters/110-elliptisch/uebungsaufgaben/4.tex \ chapters/110-elliptisch/chapter.tex diff --git a/buch/chapters/110-elliptisch/agm/Makefile b/buch/chapters/110-elliptisch/agm/Makefile index e7975e1..8dab511 100644 --- a/buch/chapters/110-elliptisch/agm/Makefile +++ b/buch/chapters/110-elliptisch/agm/Makefile @@ -3,6 +3,11 @@ # # (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule # +all: sn + +sn: sn.cpp + g++ -O -Wall -g -std=c++11 sn.cpp -o sn `pkg-config --cflags gsl` `pkg-config --libs gsl` + agm: agm.cpp g++ -O -Wall -g -std=c++11 agm.cpp -o agm `pkg-config --cflags gsl` `pkg-config --libs gsl` diff --git a/buch/chapters/110-elliptisch/agm/agm.cpp b/buch/chapters/110-elliptisch/agm/agm.cpp index fdb0441..8abb4b2 100644 --- a/buch/chapters/110-elliptisch/agm/agm.cpp +++ b/buch/chapters/110-elliptisch/agm/agm.cpp @@ -9,23 +9,54 @@ #include #include +inline long double sqrl(long double x) { + return x * x; +} +long double Xn(long double a, long double b, long double x) { + double long epsilon = fabsl(a - b); + if (epsilon > 0.001) { + return (a - sqrtl(sqrl(a) - sqrl(x) * (a + b) * (a - b))) + / (x * (a - b)); + } + long double d = a + b; + long double x1 = 0; + long double y2 = sqrl(x/a); + long double c = 1; + long double s = 0; + int k = 1; + while (c > 0.0000000000001) { + c *= (0.5 - (k - 1)) / k; + c *= (d - epsilon) * y2; + s += c; + c *= epsilon; + c = -c; + k++; + } + return s * a / x; +} int main(int argc, char *argv[]) { long double a = 1; long double b = sqrtl(2.)/2; + long double x = 0.7; if (argc >= 3) { a = std::stod(argv[1]); b = std::stod(argv[2]); } + if (argc >= 4) { + x = std::stod(argv[3]); + } { long double an = a; long double bn = b; + long double xn = x; for (int i = 0; i < 10; i++) { - printf("%d %24.18Lf %24.18Lf %24.18Lf\n", - i, an, bn, a * M_PI / (2 * an)); + printf("%d %24.18Lf %24.18Lf %24.18Lf %24.18Lf\n", + i, an, bn, xn, a * asin(xn) / an); long double A = (an + bn) / 2; + xn = Xn(an, bn, xn); bn = sqrtl(an * bn); an = A; } @@ -36,6 +67,8 @@ int main(int argc, char *argv[]) { k = sqrt(1 - k*k); double K = gsl_sf_ellint_Kcomp(k, GSL_PREC_DOUBLE); printf(" %24.18f %24.18f\n", k, K); + double F = gsl_sf_ellint_F(asinl(x), k, GSL_PREC_DOUBLE); + printf(" %24.18f %24.18f\n", k, F); } return EXIT_SUCCESS; diff --git a/buch/chapters/110-elliptisch/agm/agm.maxima b/buch/chapters/110-elliptisch/agm/agm.maxima new file mode 100644 index 0000000..c7facd4 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/agm.maxima @@ -0,0 +1,26 @@ +/* + * agm.maxima + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ + +S: 2*a*sin(theta1) / (a+b+(a-b)*sin(theta1)^2); + +C2: ratsimp(diff(S, theta1)^2 / (1 - S^2)); +C2: ratsimp(subst(sqrt(1-sin(theta1)^2), cos(theta1), C2)); +C2: ratsimp(subst(S, sin(theta), C2)); +C2: ratsimp(subst(sqrt(1-S^2), cos(theta), C2)); + +D2: (a^2 * cos(theta)^2 + b^2 * sin(theta)^2) + / + (a1^2 * cos(theta1)^2 + b1^2 * sin(theta1)^2); +D2: subst((a+b)/2, a1, D2); +D2: subst(sqrt(a*b), b1, D2); +D2: ratsimp(subst(1-S^2, cos(theta)^2, D2)); +D2: ratsimp(subst(S, sin(theta), D2)); +D2: ratsimp(subst(1-sin(theta1)^2, cos(theta1)^2, D2)); + +Q: D2/C2; +Q: ratsimp(subst(x, sin(theta1), Q)); + +Q: ratsimp(expand(ratsimp(Q))); diff --git a/buch/chapters/110-elliptisch/agm/sn.cpp b/buch/chapters/110-elliptisch/agm/sn.cpp new file mode 100644 index 0000000..ff2ed17 --- /dev/null +++ b/buch/chapters/110-elliptisch/agm/sn.cpp @@ -0,0 +1,52 @@ +/* + * ns.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include +#include + +static const int N = 10; + +inline long double sqrl(long double x) { + return x * x; +} + +int main(int argc, char *argv[]) { + long double u = 0.6; + long double k = 0.9; + long double kprime = sqrt(1 - sqrl(k)); + + long double a[N], b[N], x[N+1]; + a[0] = 1; + b[0] = kprime; + + for (int n = 0; n < N-1; n++) { + printf("a[%d] = %22.18Lf b[%d] = %22.18Lf\n", n, a[n], n, b[n]); + a[n+1] = (a[n] + b[n]) / 2; + b[n+1] = sqrtl(a[n] * b[n]); + } + + x[N] = sinl(u * a[N-1]); + printf("x[%d] = %22.18Lf\n", N, x[N]); + + for (int n = N - 1; n >= 0; n--) { + x[n] = 2 * a[n] * x[n+1] / (a[n] + b[n] + (a[n] - b[n]) * sqrl(x[n+1])); + printf("x[%2d] = %22.18Lf\n", n, x[n]); + } + + printf("sn(%7.4Lf, %7.4Lf) = %20.24Lf\n", u, k, x[0]); + + double sn, cn, dn; + double m = sqrl(k); + gsl_sf_elljac_e((double)u, m, &sn, &cn, &dn); + printf("sn(%7.4Lf, %7.4Lf) = %20.24f\n", u, k, sn); + printf("cn(%7.4Lf, %7.4Lf) = %20.24f\n", u, k, cn); + printf("dn(%7.4Lf, %7.4Lf) = %20.24f\n", u, k, dn); + + return EXIT_SUCCESS; +} diff --git a/buch/chapters/110-elliptisch/chapter.tex b/buch/chapters/110-elliptisch/chapter.tex index e05f3bd..d65570b 100644 --- a/buch/chapters/110-elliptisch/chapter.tex +++ b/buch/chapters/110-elliptisch/chapter.tex @@ -35,11 +35,14 @@ wieder hergestellt. \input{chapters/110-elliptisch/lemniskate.tex} -\section*{Übungsaufgabe} -\rhead{Übungsaufgabe} +\section*{Übungsaufgaben} +\rhead{Übungsaufgaben} \aufgabetoplevel{chapters/110-elliptisch/uebungsaufgaben} \begin{uebungsaufgaben} %\uebungsaufgabe{0} \uebungsaufgabe{1} +\uebungsaufgabe{2} +\uebungsaufgabe{3} +\uebungsaufgabe{4} \end{uebungsaufgaben} diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index 3303aee..3709300 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -340,7 +340,96 @@ Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen der unvollständigen elliptischen Integrale. % +% Numerische Berechnung mit dem arithmetisch-geometrischen Mittel % +\subsubsection{Numerische Berechnung mit dem arithmetisch-geometrischen Mittel} +\begin{table} +\centering +\begin{tikzpicture}[>=latex,thick] + +\begin{scope}[xshift=-2.4cm,yshift=1.2cm] +\fill[color=red!20] + (-1.0,0) -- (-1.0,-2.1) -- (-1.8,-2.1) -- (0,-3.0) + -- (1.8,-2.1) -- (1.0,-2.1) -- (1.0,0) -- cycle; +\node[color=white] at (0,-1.2) [scale=7] {\sf 1}; +\end{scope} + +\begin{scope}[xshift=2.9cm,yshift=-1.8cm] +\fill[color=blue!20] + (0.8,0) -- (0.8,2.1) -- (1.4,2.1) -- (0,3.0) -- (-1.4,2.1) + -- (-0.8,2.1) -- (-0.8,0) -- cycle; +\node[color=white] at (0,1.2) [scale=7] {\sf 2}; +\end{scope} + +\node at (0,0) { +\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}|>{$}c<{$}>{$}l<{$}|} +\hline +n & a_n & b_n & x_n & +\mathstrut\text{\vrule height12pt depth6pt width0pt}\\ +\hline +0 & 1.0000000000000000 & 0.4358898943540673 & 0.5422823228691580 & = \operatorname{sn}(u,k)% +\mathstrut\text{\vrule height12pt depth0pt width0pt}\\ +1 & 0.7179449471770336 & 0.6602195804079634 & 0.4157689781689663 & \mathstrut\\ +2 & 0.6890822637924985 & 0.6884775317911533 & 0.4017521410983242 & \mathstrut\\ +3 & 0.6887798977918259 & 0.6887798314243237 & 0.4016042867931862 & \mathstrut\\ +4 & 0.6887798646080748 & 0.6887798646080740 & 0.4016042705654757 & \mathstrut\\ +5 & 0.6887798646080744 & 0.6887798646080744 & 0.4016042705654755 & \mathstrut\\ +6 & & & 0.4016042705654755 & = \sin(a_5u) +\mathstrut\text{\vrule height0pt depth6pt width0pt}\\ +\hline +\end{tabular} +}; +\end{tikzpicture} +\caption{Berechnung von $\operatorname{sn}(u,k)$ für $u=0.6$ und $k=0.$2 +mit Hilfe des arithmetisch-geo\-me\-tri\-schen Mittels. +In der ersten Phase des Algorithmus (rot) wird die Folge der arithmetischen +und geometrischen Mittel berechnet, in der zweiten Phase werden die +Approximationen von $x_0=\operatorname{sn}(u,k)$. +Bei $n=5$ erreicht die Iteration des arithmetisch-geometrischen Mittels +Maschinengenauigkeit, was sich auch darin äussert, dass sich $x_5$ und +$x_6=\sin(a_5u)$ nicht unterscheiden. +\label{buch:elliptisch:agm:table:snberechnung}} +\end{table} +In Abschnitt~\ref{buch:elliptisch:subsection:agm} auf +Seite~\pageref{buch:elliptisch:subsubection:berechnung-fxk-agm} +wurde erklärt, wie das unvollständige elliptische Integral $F(x,k)$ mit +Hilfe des arithmetisch-geometrischen Mittels berechnet werden kann. +Da $\operatorname{sn}^{-1}(x,k) = F(x,k)$ die Umkehrfunktion ist, kann +man den Algorithmus auch zur Berechnung von $\operatorname{sn}(u,k)$ +verwenden. +Dazu geht man wie folgt vor: +\begin{enumerate} +\item +$k'=\sqrt{1-k^2}$. +\item +Berechne die Folgen des arithmetisch-geometrischen Mittels +$a_n$ und $b_n$ mit $a_0=1$ und $b_0=k'$, bis zum Folgenindex $N$, +bei dem ausreichende Konvergenz eintegreten ist. +\item +Setze $x_N = \sin(a_N \cdot u)$. +\item +Berechnet für absteigende $n=N-1,N-2,\dots$ die Folge $x_n$ mit Hilfe +der Rekursionsformel +\begin{equation} +x_{n} += +\frac{2a_nx_{n+1}}{a_n+b_n+(a_n-b_n)x_{n+1}^2}, +\label{buch:elliptisch:agm:xnrek} +\end{equation} +die aus \eqref{buch:elliptisch:agm:subst} +durch die Substitution $x_n = \sin t_n$ entsteht. +\item +Setze $\operatorname{sn}(u,k) = x_0$. +\end{enumerate} +Da die Formel \eqref{buch:elliptisch:agm:xnrek} nicht unter den +numerischen Stabilitätsproblemen leidet, die früher auf +Seite~\pageref{buch:elliptisch:agm:ellintegral-stabilitaet} +diskutiert wurden, ist die Berechnung stabil und sehr schnell. +Tabelle~\ref{buch:elliptisch:agm:table:snberechnung} +zeigt die Berechnung am Beispiel $u=0.6$ und $k=0.2$. + +% +% Pole und Nullstellen der Jacobischen elliptischen Funktionen % \subsubsection{Pole und Nullstellen der Jacobischen elliptischen Funktionen} \begin{figure} diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 4589ffa..cc99218 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -459,7 +459,8 @@ Parameter $k$ mit der Ableitungsformel für die Funktion $\mathstrut_2F_1$. % % Berechnung mit dem arithmetisch-geometrischen Mittel % -\subsection{Berechnung mit dem arithmetisch-geometrischen Mittel} +\subsection{Berechnung mit dem arithmetisch-geometrischen Mittel +\label{buch:elliptisch:subsection:agm}} Die numerische Berechnung von elliptischer Integrale mit gewöhnlichen numerischen Integrationsroutinen ist nicht sehr effizient. Das in diesem Abschnitt vorgestellte arithmetisch-geometrische Mittel @@ -472,7 +473,11 @@ Sie ist ein Speziallfall der sogenannten Landen-Transformation, \index{Landen-Transformation}% welche ausser für die elliptischen Integrale auch für die Jacobischen elliptischen Funktionen formuliert werden kann und -für letztere ebenfalls sehr schnelle numerische Algorithmen liefert. +für letztere ebenfalls sehr schnelle numerische Algorithmen liefert +(siehe dazu auch die +Aufgaben~\ref{buch:elliptisch:aufgabe:2}--\ref{buch:elliptisch:aufgabe:4}). +Sie kann auch verwendet werden, um die Werte der Jacobischen elliptischen +Funktionen für komplexe Argument zu berechnen. % % Das arithmetisch-geometrische Mittel @@ -574,7 +579,7 @@ Gauss hat gefunden, dass die Substitution \begin{equation} \sin t = -\frac{2a\sin t_1}{a+b+(a-b)\sin t_1} +\frac{2a\sin t_1}{a+b+(a-b)\sin^2 t_1} \label{buch:elliptisch:agm:subst} \end{equation} zu @@ -1103,6 +1108,136 @@ F(x,k) = iK(k') - F\biggl(\frac1{kx},k\biggr) für die Werte des elliptischen Integrals erster Art für grosse Argumentwerte fest. +% +% AGM und Berechnung von F(x,k) +% +\subsubsection{Berechnung von $F(x,k)$ mit dem arithmetisch-geometrischen Mittel\label{buch:elliptisch:subsubection:berechnung-fxk-agm}} +Wie das vollständige elliptische Integral $K(k)$ kann auch das +unvollständige elliptische Integral +\begin{align*} +F(x,k) +&= +\int_0^x \frac{d\xi}{\sqrt{(1-\xi^2)(1-k^{\prime 2}\xi^2)}} += +\int_0^{\varphi} +\frac{dt}{\sqrt{1-k^2 \sin^2 t}} +\\ +&= +a +\int_0^{\varphi} \frac{dt}{a^2 \cos^2 t + b^2 \sin^2 t} +\qquad\text{mit $k=b/a$} +\end{align*} +mit dem arithmetisch-geometrischen Mittel berechnet werden. +Dazu muss die Substitution +\eqref{buch:elliptisch:agm:subst} +verwendet werden, um auch den Winkel $\varphi_1$ zu berechnen. +Dazu muss \eqref{buch:elliptisch:agm:subst} nach $x_1=\sin t_1$ +aufgelöst werden. +Durch Multiplikation mit dem Nenner erhält man mit der Abkürzung +$x=\sin t$ und $x_1=\sin t_1$ die quadratische Gleichung +\[ +(a-b)x x_1 +- +2ax_1 +(a+b)x += +0, +\] +mit der Lösung +\begin{equation} +x_1 += +\frac{a-\sqrt{a^2-(a^2-b^2)x^2}}{(a-b)x}. +\label{buch:elliptisch:unvollstagm:xrek} +\end{equation} +Der Algorithmus zur Berechnung des arithmetisch-geometrischen Mittels +muss daher verallgemeinert werden zu +\begin{equation} +\left. +\begin{aligned} +a_{n+1} &= \frac{a_n+b_n}2, &\qquad a_0 &= a +\\ +b_{n+1} &= \sqrt{a_nb_n}, & b_0 &= b +\\ +x_{n+1} &= \frac{a_n-\sqrt{a_n^2-(a_n^2-b_n^2)x_n^2}}{(a_n-b_n)x_n}, & x_0 &= x +\end{aligned} +\quad +\right\} +\label{buch:elliptisch:unvollstagm:rek} +\end{equation} +Die Folge $x_n$ konvergiert gegen einen Wert $x_{\infty} = \lim_{n\to\infty} x_n$. +Der Wert des unvollständigen elliptischen Integrals ist dann der Grenzwert +\[ +F(x,k) += +\lim_{n\to\infty} +\frac{\arcsin x_n}{M(a_n,b_n)} += +\frac{\arcsin x_{\infty}}{M(1,\sqrt{1-k^2})}. +\] + +In dieser Form ist die Berechnung allerdings nicht praktisch durchführbar. +Das Problem ist, dass die Differenz $a_n-b_n$, die in +\eqref{buch:elliptisch:unvollstagm:rek} +im Nenner vorkommt, sehr schnell gegen Null geht. +Ausserdem ist die Quadratwurzel im Zähler fast gleich gross wie +$a_n$, was zu Auslöschung und damit ungenauen Resultaten führt. +\label{buch:elliptisch:agm:ellintegral-stabilitaet} + +Eine Möglichkeit, das Problem zu entschärfen, ist, die Rekursionsformel +nach $\varepsilon = a-b$ zu entwickeln. +Mit $a+b=2a+\varepsilon$ kann man $b$ aus der Formel elimineren und erhält +mit Hilfe der binomischen Reihe +\begin{align*} +x_1 +&= +\frac{a}{x\varepsilon} +\left(1-\sqrt{1-\varepsilon(2a-\varepsilon)x^2/a^2}\right) +\\ +&= +\frac{a}{x\varepsilon} +\biggl( +1-\sum_{k=0}^\infty +(-1)^k +\frac{(\frac12)_k}{k!} \varepsilon^k(2a-\varepsilon)^k\frac{x^{2k}}{a^{2k}} +\biggr) +\\ +&= +\sum_{k=1}^\infty +(-1)^{k-1} +\frac{(\frac12)_k}{k!} \varepsilon^{k-1}(2a-\varepsilon)^k\frac{x^{2k-1}}{a^{2k-1}} +\\ +&= +\frac{\frac12}{1!}(2a-\varepsilon)\frac{x}{a} +- +\frac{\frac12\cdot(\frac12-1)}{2!}\varepsilon(2a-\varepsilon)^2\frac{x^3}{a^3} ++ +\frac{\frac12\cdot(\frac12-1)(\frac12-2)}{3!}\varepsilon^2(2a-\varepsilon)^3\frac{x^5}{a^5} +- +\dots +\\ +&= +x\biggl(1-\frac{\varepsilon}{2a}\biggr) +\biggl( +1 +- +\frac{\frac12-1}{2!}\varepsilon(2a-\varepsilon)\frac{x^2}{a^2} ++ +\frac{(\frac12-1)(\frac12-2)}{3!}\varepsilon^2(2a-\varepsilon)^2\frac{x^4}{a^4} +- +\dots +\biggr) +\\ +&= +x\biggl(1-\frac{\varepsilon}{2a}\biggr) +\cdot +\mathstrut_2F_1\biggl( +\begin{matrix}-\frac12,1\\2\end{matrix};-\varepsilon(2a-\varepsilon)\frac{x^2}{a^2} +\biggr). +\end{align*} +Diese Form ist wesentlich besser, aber leider kann es bei der numerischen +Rechnung passieren, dass $\varepsilon < 0$ wird. + %\subsection{Potenzreihe} %XXX Potenzreihen \\ %XXX Als hypergeometrische Funktionen \url{https://www.youtube.com/watch?v=j0t1yWrvKmE} \\ diff --git a/buch/chapters/110-elliptisch/elltrigo.tex b/buch/chapters/110-elliptisch/elltrigo.tex index 583e00a..c67870f 100644 --- a/buch/chapters/110-elliptisch/elltrigo.tex +++ b/buch/chapters/110-elliptisch/elltrigo.tex @@ -169,7 +169,7 @@ x^2(k^2-1) + y^2 = 1. an einer Ellipse mit Halbachsen $a$ und $1$. \label{buch:elliptisch:fig:jacobidef}} \end{figure} -\subsubsection{Definition der elliptischen Funktionen} +\subsubsection{Definition der Jacobischen elliptischen Funktionen} Die elliptischen Funktionen für einen Punkt $P$ auf der Ellipse mit Modulus $k$ können jetzt als Verhältnisse der Koordinaten des Punktes definieren. Es stellt sich aber die Frage, was man als Argument verwenden soll. diff --git a/buch/chapters/110-elliptisch/experiments/KK.pdf b/buch/chapters/110-elliptisch/experiments/KK.pdf new file mode 100644 index 0000000..13a2739 Binary files /dev/null and b/buch/chapters/110-elliptisch/experiments/KK.pdf differ diff --git a/buch/chapters/110-elliptisch/experiments/KK.tex b/buch/chapters/110-elliptisch/experiments/KK.tex new file mode 100644 index 0000000..a3ae425 --- /dev/null +++ b/buch/chapters/110-elliptisch/experiments/KK.tex @@ -0,0 +1,66 @@ +% +% KK.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\def\dx{10} +\def\dy{3} +\input{KKpath.tex} + +\draw[->] (-0.1,0) -- (10.3,0) coordinate[label={$k$}]; +\draw[->] (0,-0.1) -- (0,{2*\dy+0.3}) coordinate[label={right:$y$}]; + +\node at (3,{1.2*\dy}) {$\displaystyle y = \frac{K(k)}{K(\!\sqrt{1-k^2})}$}; + +\begin{scope} +\clip (0,0) rectangle (10,{2*\dy}); +\draw[color=red,line width=1.4pt] \KKpath; +\end{scope} + +\draw[line width=0.2pt] (10,0) -- (10,{2*\dy}); + +\foreach \y in {0.0,0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0}{ + \draw (-0.05,{\y*\dy}) -- (0.05,{\y*\dy}); + \node at (0,{\y*\dy}) [left] {$\y\mathstrut$}; +} + +\foreach \k in {1,...,9}{ + \draw ({\k*\dx/10},-0.05) -- ({\k*\dx/10},0.05); + \node at ({\k*\dx/10},0) [below] {$0.\k\mathstrut$}; +} +\node at (0,0) [below] {$0\mathstrut$}; +\node at (10,0) [below] {$1\mathstrut$}; + +\draw[color=blue] ({\knull*\dx},0) -- ({\knull*\dx},{\KKnull*\dy}); +\foreach \y in {1,2,3,4}{ + \draw[color=blue] + ({\knull*\dx-0.05},{\y*\KKnull*\dy/5}) + -- + ({\knull*\dx+0.05},{\y*\KKnull*\dy/5}); +} +\draw[color=black,line width=0.1pt] (0,{\KKnull*\dy}) -- ({\knull*\dx},{\KKnull*\dy}); +\draw[color=black,line width=0.1pt] (0,{\KKnull*\dy/5}) -- ({\kone*\dx},{\KKnull*\dy/5}); +\node at ({0.6*\dx},{\KKnull*\dy}) [above] {$y=1.7732$}; +\node at ({0.6*\dx},{\KKnull*\dy/5}) [above] {$y=0.3546$}; +\draw[color=blue] ({\kone*\dx},0) -- ({\kone*\dx},{\KKnull*\dy/5}); +\draw[color=blue] ({\kone*\dx},{\KKnull*\dy/5}) -- ({\knull*\dx},{\KKnull*\dy/5}); +\fill[color=blue] ({\kone*\dx},{\KKnull*\dy/5}) circle[radius=0.05]; +\fill[color=blue] ({\knull*\dx},{\KKnull*\dy/5}) circle[radius=0.05]; +\fill[color=blue] ({\knull*\dx},{\KKnull*\dy}) circle[radius=0.05]; +\node[color=blue] at ({\knull*\dx},0) [left,rotate=90] {$k=0.97\mathstrut$}; +\node[color=blue] at ({\kone*\dx},0) [left,rotate=90] {$k_1=0.0477$}; + +\end{tikzpicture} +\end{document} + diff --git a/buch/chapters/110-elliptisch/experiments/KN.cpp b/buch/chapters/110-elliptisch/experiments/KN.cpp new file mode 100644 index 0000000..1dcca9e --- /dev/null +++ b/buch/chapters/110-elliptisch/experiments/KN.cpp @@ -0,0 +1,177 @@ +/* + * KN.cpp + * + * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule + */ +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace KN { + +bool debug = false; + +static struct option longopts[] { +{ "debug", no_argument, NULL, 'd' }, +{ "N", required_argument, NULL, 'N' }, +{ "outfile", required_argument, NULL, 'o' }, +{ "min", required_argument, NULL, 'm' }, +{ NULL, 0, NULL, 0 } +}; + +double KprimeK(double k) { + double kprime = sqrt(1-k*k); + if (debug) + printf("%s:%d: k = %f, k' = %f\n", __FILE__, __LINE__, k, kprime); + double v + = + gsl_sf_ellint_Kcomp(k, GSL_PREC_DOUBLE) + / + gsl_sf_ellint_Kcomp(kprime, GSL_PREC_DOUBLE) + ; + if (debug) + printf("%s:%d: KprimeK(k = %f) = %f\n", __FILE__, __LINE__, k, v); + return v; +} + +static const int L = 100000000; +static const double h = 1. / L; + +double Kd(double k) { + double m = 0; + if (k < h) { + m = 2 * (KprimeK(k) - KprimeK(k / 2)) / k; + } else if (k > 1-h) { + m = 2 * (KprimeK((1 + k) / 2) - KprimeK(k)) / (1 - k); + + } else { + m = L * (KprimeK(k + h) - KprimeK(k)); + } + if (debug) + printf("%s:%d: Kd(%f) = %f\n", __FILE__, __LINE__, k, m); + return m; +} + +double k1(double y) { + if (debug) + printf("%s:%d: Newton for y = %f\n", __FILE__, __LINE__, y); + double kn = 0.5; + double delta = 1; + int n = 0; + while ((fabs(delta) > 0.000001) && (n < 10)) { + double yn = KprimeK(kn); + if (debug) + printf("%s:%d: k%d = %f, y%d = %f\n", __FILE__, __LINE__, n, kn, n, yn); + delta = (yn - y) / Kd(kn); + if (debug) + printf("%s:%d: delta = %f\n", __FILE__, __LINE__, delta); + double kneu = kn - delta; + if (kneu <= 0) { + kneu = kn / 4; + } + if (kneu >= 1) { + kneu = (3 + kn) / 4; + } + kn = kneu; + if (debug) + printf("%s:%d: kneu = %f, kn = %f\n", __FILE__, __LINE__, kneu, kn); + n++; + } + if (debug) + printf("%s:%d: Newton result: k = %f\n", __FILE__, __LINE__, kn); + return kn; +} + +double k1(int N, double k) { + return k1(KprimeK(k) / N); +} + +/** + * \brief Main function for the slcl program + */ +int main(int argc, char *argv[]) { + int longindex; + int c; + int N = 5; + double kmin = 0.01; + std::string outfilename; + while (EOF != (c = getopt_long(argc, argv, "d:N:o:m:", + longopts, &longindex))) + switch (c) { + case 'd': + debug = true; + break; + case 'N': + N = std::stoi(optarg); + break; + case 'o': + outfilename = std::string(optarg); + break; + case 'm': + kmin = std::stod(optarg); + break; + } + + double d = 0.01; + if (outfilename.size() > 0) { + FILE *fn = fopen(outfilename.c_str(), "w"); + fprintf(fn, "\\def\\KKpath{ "); + double k = d; + fprintf(fn, " (0,0)"); + double k0 = k/16; + while (k0 < k) { + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", k0, KprimeK(k0)); + k0 *= 2; + } + while (k < 1-0.5*d) { + fprintf(fn, "\n\t-- ({%.4f*\\dx},{%.4f*\\dy})", k, KprimeK(k)); + k += d; + } + fprintf(fn, "}\n"); + + k0 = 0.97; + fprintf(fn, "\\def\\knull{%.4f}\n", k0); + double KK = KprimeK(k0); + fprintf(fn, "\\def\\KKnull{%.4f}\n", KK); + fprintf(fn, "\\def\\kone{%.4f}\n", k1(N, k0)); + + fclose(fn); + return EXIT_SUCCESS; + } + + for (double k = kmin; k < (1 - d/2); k += d) { + if (debug) + printf("%s:%d: k = %f\n", __FILE__, __LINE__, k); + double y = KprimeK(k); + double k0 = k1(y); + double kone = k1(N, k0); + printf("g(%4.2f) = %10.6f,", k, y); + printf(" g'(%.2f) = %10.6f,", k, Kd(k)); + printf(" g^{-1} = %10.6f,", k0); + printf(" k1 = %10.6f,", kone); + printf(" g(k1) = %10.6f\n", KprimeK(kone)); + } + + return EXIT_SUCCESS; +} + +} // namespace KN + +int main(int argc, char *argv[]) { + try { + return KN::main(argc, argv); + } catch (const std::exception& e) { + std::cerr << "terminated by exception: " << e.what(); + std::cerr << std::endl; + } catch (...) { + std::cerr << "terminated by unknown exception" << std::endl; + } + return EXIT_FAILURE; +} diff --git a/buch/chapters/110-elliptisch/experiments/Makefile b/buch/chapters/110-elliptisch/experiments/Makefile new file mode 100644 index 0000000..fac4fbc --- /dev/null +++ b/buch/chapters/110-elliptisch/experiments/Makefile @@ -0,0 +1,15 @@ +# +# Makefile +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschlue +# +all: KK.pdf + +KN: KN.cpp + g++ -O -Wall -std=c++11 KN.cpp -o KN `pkg-config --cflags gsl` `pkg-config --libs gsl` + +KKpath.tex: KN + ./KN --outfile KKpath.tex + +KK.pdf: KK.tex KKpath.tex + pdflatex KK.tex diff --git a/buch/chapters/110-elliptisch/experiments/agm.maxima b/buch/chapters/110-elliptisch/experiments/agm.maxima deleted file mode 100644 index c7facd4..0000000 --- a/buch/chapters/110-elliptisch/experiments/agm.maxima +++ /dev/null @@ -1,26 +0,0 @@ -/* - * agm.maxima - * - * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule - */ - -S: 2*a*sin(theta1) / (a+b+(a-b)*sin(theta1)^2); - -C2: ratsimp(diff(S, theta1)^2 / (1 - S^2)); -C2: ratsimp(subst(sqrt(1-sin(theta1)^2), cos(theta1), C2)); -C2: ratsimp(subst(S, sin(theta), C2)); -C2: ratsimp(subst(sqrt(1-S^2), cos(theta), C2)); - -D2: (a^2 * cos(theta)^2 + b^2 * sin(theta)^2) - / - (a1^2 * cos(theta1)^2 + b1^2 * sin(theta1)^2); -D2: subst((a+b)/2, a1, D2); -D2: subst(sqrt(a*b), b1, D2); -D2: ratsimp(subst(1-S^2, cos(theta)^2, D2)); -D2: ratsimp(subst(S, sin(theta), D2)); -D2: ratsimp(subst(1-sin(theta1)^2, cos(theta1)^2, D2)); - -Q: D2/C2; -Q: ratsimp(subst(x, sin(theta1), Q)); - -Q: ratsimp(expand(ratsimp(Q))); diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex new file mode 100644 index 0000000..9a1cafc --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex @@ -0,0 +1,61 @@ +\label{buch:elliptisch:aufgabe:2}% +Die Landen-Transformation basiert auf der Iteration +\begin{equation} +\begin{aligned} +k_{n+1} +&= +\frac{1-k_n'}{1+k_n'} +& +&\text{und}& +k_{n+1}' +&= +\sqrt{1-k_{n+1}^2} +\end{aligned} +\label{buch:elliptisch:aufgabe:2:iteration} +\end{equation} +mit den Startwerten $k_0 = k$ und $k_0' = \sqrt{1-k_0^2}$. +Zeigen Sie, dass $k_n\to 0$ und $k_n'\to 1$ mit quadratischer Konvergenz. + +\begin{loesung} +\begin{table} +\centering +\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\hline +n & k & k' \\ +\hline +0 & 0.200000000000000 & 0.979795897113271 \\ +1 & 0.010205144336438 & 0.999947926158694 \\ +2 & 0.000026037598592 & 0.999999999661022 \\ +3 & 0.000000000169489 & 1.000000000000000 \\ +4 & 0.000000000000000 & 1.000000000000000 \\ +\hline +\end{tabular} +\caption{Numerisches Experiment zur Folge $(k_n,k_n')$ +gemäss \eqref{buch:elliptisch:aufgabe:2:iteration} +mit $k_0=0.2$ +\label{buch:ellptisch:aufgabe:2:numerisch}} +\end{table} +Es ist klar, dass $k'_n\to 1$ folgt, wenn man zeigen kann, dass +$k_n\to 0$ gilt. +Wir berechnen daher +\begin{align*} +k_{n+1} +&= +\frac{1-k_n'}{1+k_n'} += +\frac{1-\sqrt{1-k_n^2}}{1+\sqrt{1-k_n^2}} +\intertext{und erweitern mit dem Nenner $1+\sqrt{1-k_n^2}$ um} +&= +\frac{1-(1-k_n^2)}{(1+\sqrt{1-k_n^2})^2} += +\frac{ k_n^2 }{(1+\sqrt{1-k_n^2})^2} +\le +k_n^2 +\end{align*} +zu erhalten. +Daraus folgt jetzt sofort die quadratische Konvergenz von $k_n$ gegen $0$. + +Ein einfaches numerisches Experiment (siehe +Tabelle~\ref{buch:ellptisch:aufgabe:2:numerisch}) +bestätigt die quadratische Konvergenz der Folgen. +\end{loesung} diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/3.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/3.tex new file mode 100644 index 0000000..a5d118f --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/3.tex @@ -0,0 +1,135 @@ +\label{buch:elliptisch:aufgabe:3}% +Aus der in Aufgabe~\ref{buch:elliptisch:aufgabe:2} konstruierten Folge +$k_n$ kann zu einem vorgegebenen $u$ ausserdem die Folge $u_n$ +mit der Rekursionsformel +\[ +u_{n+1} = \frac{u_n}{1+k_{n+1}} +\] +und Anfangswert $u_0=u$ konstruiert werden. +Die Landen-Transformation (siehe \cite[80]{buch:ellfun-applications}) +\index{Landen-Transformation}% +führt auf die folgenden Formeln für die Jacobischen elliptischen Funktionen: +\begin{equation} +\left.\qquad +\begin{aligned} +\operatorname{sn}(u_n,k_n) +&= +\frac{ +(1+k_{n+1})\operatorname{sn}(u_{n+1},k_{n+1}) +}{ +1 + k_{n+1} \operatorname{sn}(u_{n+1},k_{n+1})^2 +} +\\ +\operatorname{cn}(u_n,k_n) +&= +\frac{ +\operatorname{cn}(u_{n+1},k_{n+1}) +\operatorname{dn}(u_{n+1},k_{n+1}) +}{ +1 + k_{n+1} \operatorname{sn}(u_{n+1},k_{n+1})^2 +} +\\ +\operatorname{dn}(u_n,k_n) +&= +\frac{ +1 - k_{n+1} \operatorname{sn}(u_{n+1},k_{n+1})^2 +}{ +1 + k_{n+1} \operatorname{sn}(u_{n+1},k_{n+1})^2 +} +\end{aligned} +\qquad\right\} +\label{buch:elliptisch:aufgabe:3:gauss} +\end{equation} +Die Transformationsformeln +\eqref{buch:elliptisch:aufgabe:3:gauss} +sind auch als Gauss-Transformation bekannt. +\index{Gauss-Transformation}% +Konstruieren Sie daraus einen numerischen Algorithmus, mit dem sich +gleichzeitig die Werte aller drei Jacobischen elliptischen Funktionen +für vorgegebene Parameterwerte $u$ und $k$ berechnen lassen. + +\begin{loesung} +In der ersten Phase des Algorithmus werden die Folgen $k_n$ und $k_n'$ +sowie $u_n$ bis zum Folgenindex $N$ berechnet, bis $k_N\approx 0$ +angenommen werden darf. +Dann gilt +\begin{align*} +\operatorname{sn}(u_N, k_N) &= \operatorname{sn}(u_N,0) = \sin u_N +\\ +\operatorname{cn}(u_N, k_N) &= \operatorname{cn}(u_N,0) = \cos u_N +\\ +\operatorname{dn}(u_N, k_N) &= \operatorname{dn}(u_N,0) = 1. +\end{align*} +In der zweiten Phase des Algorithmus können für absteigende +$n$ jeweils die Formeln~\eqref{buch:elliptisch:aufgabe:3:gauss} +angewendet werden um nacheinander die Werte der Jacobischen +elliptischen Funktionen für Argument $u_n$ und Parameter $k_n$ +für $n=N-1,N-2,\dots,0$ zu bekommen. +\end{loesung} +\begin{table} +\centering +\begin{tikzpicture}[>=latex,thick] +\def\pfeil#1#2{ + \fill[color=#1!30] (-0.5,1) -- (-0.5,-1) -- (-0.8,-1) + -- (0,-1.5) -- (0.8,-1) -- (0.5,-1) -- (0.5,1) -- cycle; + \node[color=white] at (0,-0.2) [scale=5] {\sf #2\strut}; +} +\begin{scope}[xshift=-4.9cm,yshift=0.2cm] +\pfeil{red}{1} +\end{scope} + +\begin{scope}[xshift=-2.3cm,yshift=0.2cm] +\pfeil{red}{1} +\end{scope} + +\begin{scope}[xshift=0.35cm,yshift=-0.3cm,yscale=-1] +\pfeil{blue}{2} +\end{scope} + +\begin{scope}[xshift=2.92cm,yshift=-0.3cm,yscale=-1] +\pfeil{blue}{2} +\end{scope} + +\begin{scope}[xshift=5.60cm,yshift=-0.3cm,yscale=-1] +\pfeil{blue}{2} +\end{scope} + +\node at (0,0) { +\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\hline +n & k_n & u_n & \operatorname{sn}(u_n,k_n) & \operatorname{cn}(u_n,k_n) & \operatorname{dn}(u_n,k_n)% +\mathstrut\text{\vrule height12pt depth6pt width0pt} \\ +\hline +\mathstrut\text{\vrule height12pt depth0pt width0pt}% +%\small +0 & 0.90000000000 & 0.60000000000 & 0.54228232286 & 0.84019633556 & 0.87281338478 \\ +1 & 0.39286445838 & 0.43076696830 & 0.41576897816 & 0.90947026163 & 0.98656969610 \\ +2 & 0.04188568608 & 0.41344935827 & 0.40175214109 & 0.91574844642 & 0.99985840483 \\ +3 & 0.00043898784 & 0.41326793867 & 0.40160428679 & 0.91581329801 & 0.99999998445 \\ +4 & 0.00000004817 & 0.41326791876 & 0.40160427056 & 0.91581330513 & 1.00000000000 \\ +5 & 0.00000000000 & 0.41326791876 & 0.40160427056 & 0.91581330513 & 1.00000000000 \\ +%N & 0.00000000000 & 0.41326791876 & 0.40160427056 & 0.91581330513 & 1.00000000000% +N & & 0.41326791876 & \sin u_N & \cos u_N & 1% +%0 & 0.900000000000000 & 0.600000000000000 & 0.542282322869158 & 0.840196335569032 & 0.872813384788490 \\ +%1 & 0.392864458385019 & 0.430766968306220 & 0.415768978168966 & 0.909470261631645 & 0.986569696107075 \\ +%2 & 0.041885686080039 & 0.413449358275499 & 0.401752141098324 & 0.915748446421239 & 0.999858404836479 \\ +%3 & 0.000438987841605 & 0.413267938675096 & 0.401604286793186 & 0.915813298019491 & 0.999999984459261 \\ +%4 & 0.000000048177586 & 0.413267918764845 & 0.401604270565476 & 0.915813305135699 & 1.000000000000000 \\ +%5 & 0.000000000000001 & 0.413267918764845 & 0.401604270565476 & 0.915813305135699 & 1.000000000000000 \\ +%N & 0.000000000000000 & 0.413267918764845 & 0.401604270565476 & 0.915813305135699 & 1.000000000000000 \\ +\mathstrut\text{\vrule height12pt depth6pt width0pt} \\ +\hline +\end{tabular} +}; +\end{tikzpicture} +\caption{Durchführung des auf der Landen-Transformation basierenden +Algorithmus zur Berechnung der Jacobischen elliptischen Funktionen +für $u=0.6$ und $k=0.9$. +Die erste Phase (rot) berechnet die Folgen $k_n$ und $u_n$, die zweite +(blau) +transformiert die Wert der trigonometrischen Funktionen in die Werte +der Jacobischen elliptischen Funktionen. +\label{buch:elliptisch:aufgabe:3:resultate}} +\end{table} + + diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/landen.m b/buch/chapters/110-elliptisch/uebungsaufgaben/landen.m new file mode 100644 index 0000000..bba5549 --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/landen.m @@ -0,0 +1,60 @@ +# +# landen.m +# +# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# +N = 10; + +function retval = M(a,b) + for i = (1:10) + A = (a+b)/2; + b = sqrt(a*b); + a = A; + endfor + retval = a; +endfunction; + +function retval = EllipticKk(k) + retval = pi / (2 * M(1, sqrt(1-k^2))); +endfunction + +k = 0.5; +kprime = sqrt(1-k^2); + +EK = EllipticKk(k); +EKprime = EllipticKk(kprime); + +u = EK + EKprime * i; + +K = zeros(N,3); +K(1,1) = k; +K(1,2) = kprime; +K(1,3) = u; + +format long + +for n = (2:N) + K(n,1) = (1-K(n-1,2)) / (1+K(n-1,2)); + K(n,2) = sqrt(1-K(n,1)^2); + K(n,3) = K(n-1,3) / (1 + K(n,1)); +end + +K(:,[1,3]) + +pi / 2 + +scd = zeros(N,3); +scd(N,1) = sin(K(N,3)); +scd(N,2) = cos(K(N,3)); +scd(N,3) = 1; + +for n = (N:-1:2) + nenner = 1 + K(n,1) * scd(n, 1)^2; + scd(n-1,1) = (1+K(n,1)) * scd(n, 1) / nenner; + scd(n-1,2) = scd(n, 2) * scd(n, 3) / nenner; + scd(n-1,3) = (1 - K(n,1) * scd(n,1)^2) / nenner; +end + +scd(:,1) + +cosh(2.009459377005286) diff --git a/buch/chapters/references.bib b/buch/chapters/references.bib index 571831a..fbbbf30 100644 --- a/buch/chapters/references.bib +++ b/buch/chapters/references.bib @@ -137,3 +137,12 @@ year = 2004 } +@book{buch:ellfun-applications, + author = { Derek F. Lawden }, + title = { Elliptic Functions and Applications }, + series = { Applied Mathematical Sciences }, + volume = { 80 }, + publisher = { Springer-Verlag }, + year = 2010, + ISBN = { 978-1-4419-3090-3 } +} diff --git a/buch/papers/dreieck/teil0.tex b/buch/papers/dreieck/teil0.tex index 65eff7a..f9affe7 100644 --- a/buch/papers/dreieck/teil0.tex +++ b/buch/papers/dreieck/teil0.tex @@ -38,7 +38,7 @@ Leitet man $e^{-t^2}$ zweimal ab, erhält man {\textstyle\frac14} e^{-t^2}. \] -Es gibt also eine viele weitere Polynome $P(t)$, für die der Integrand +Es gibt also viele weitere Polynome $P(t)$, für die der Integrand $P(t)e^{-t^2}$ eine Stammfunktion in geschlossener Form hat. Damit stellt sich jetzt das folgende allgemeine Problem. -- cgit v1.2.1 From 7cf7e37298a732b1a900b5eed59c442461e43a6d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 27 Jun 2022 21:02:10 +0200 Subject: add more problems to chapter 11 --- buch/chapters/110-elliptisch/Makefile.inc | 1 + buch/chapters/110-elliptisch/chapter.tex | 1 + buch/chapters/110-elliptisch/uebungsaufgaben/4.tex | 80 ++++++++++++++++++++++ buch/chapters/110-elliptisch/uebungsaufgaben/5.tex | 58 ++++++++++++++++ buch/chapters/references.bib | 9 +++ 5 files changed, 149 insertions(+) create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/4.tex create mode 100644 buch/chapters/110-elliptisch/uebungsaufgaben/5.tex diff --git a/buch/chapters/110-elliptisch/Makefile.inc b/buch/chapters/110-elliptisch/Makefile.inc index ef6ea51..4e2644c 100644 --- a/buch/chapters/110-elliptisch/Makefile.inc +++ b/buch/chapters/110-elliptisch/Makefile.inc @@ -15,4 +15,5 @@ CHAPTERFILES += \ chapters/110-elliptisch/uebungsaufgaben/2.tex \ chapters/110-elliptisch/uebungsaufgaben/3.tex \ chapters/110-elliptisch/uebungsaufgaben/4.tex \ + chapters/110-elliptisch/uebungsaufgaben/5.tex \ chapters/110-elliptisch/chapter.tex diff --git a/buch/chapters/110-elliptisch/chapter.tex b/buch/chapters/110-elliptisch/chapter.tex index d65570b..21fc986 100644 --- a/buch/chapters/110-elliptisch/chapter.tex +++ b/buch/chapters/110-elliptisch/chapter.tex @@ -44,5 +44,6 @@ wieder hergestellt. \uebungsaufgabe{2} \uebungsaufgabe{3} \uebungsaufgabe{4} +\uebungsaufgabe{5} \end{uebungsaufgaben} diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex new file mode 100644 index 0000000..b48192d --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex @@ -0,0 +1,80 @@ +\label{buch:elliptisch:aufgabe:4} +Es ist bekannt, dass $\operatorname{sn}(K+iK', k) = 1/k$ gilt. +Verwenden Sie den Algorithmus von Aufgabe~\ref{buch:elliptisch:aufgabe:3}, +um dies für $k=\frac12$ nachzurechnen. + +\begin{loesung} +Zunächst müssen wir mit dem Algorithmus des arithmetisch-geometrischen +Mittels +\[ +K(k) +\approx +1.685750354812596 +\qquad\text{und}\qquad +K(k') +\approx +2.156515647499643 +\] +berechnen. +Aus $k=\frac12$ kann man jetzt die Folgen $k_n$ und $u_n$ berechnen, die innert +$N=5$ Iterationen konvergiert. +\end{loesung} + +\begin{table} +\centering +\renewcommand{\tabcolsep}{5pt} +\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\hline + n & k_n & u_n & \operatorname{sn}(u_n,k_n)% +\mathstrut\text{\vrule height12pt depth6pt width0pt}% +\\ +\hline +\mathstrut\text{\vrule height12pt depth0pt width0pt}% + 0 & 0.500000000000000 & 1.685750354812596 + 2.156515647499643i & 2.000000000000000 \\ + 1 & 0.071796769724491 & 1.572826493259468 + 2.012056490946491i & 3.732050807568877 \\ + 2 & 0.001292026239995 & 1.570796982340579 + 2.009460215619685i & 3.796651109009551 \\ + 3 & 0.000000417333300 & 1.570796326794965 + 2.009459377005374i & 3.796672364209438 \\ + 4 & 0.000000000000044 & 1.570796326794897 + 2.009459377005286i & 3.796672364211658 \\ + N & 0.000000000000000 & 1.570796326794897 + 2.009459377005286i & 3.796672364211658% +\mathstrut\text{\vrule height12pt depth6pt width0pt}% +\\ +\hline +\end{tabular} +\caption{Berechnung von $\operatorname{sn}(K+iK',k)=1/k$ mit Hilfe der Landen-Transformation. +Konvergenz der Folge $k_n$ ist bei $N=5$ eintegreten. +\label{buch:elliptisch:aufgabe:4:table}} +\end{table} + +\begin{loesung} +Sie führt auf +\[ +u_N += +\frac{\pi}2 + 2.009459377005286i += +\frac{\pi}2 + bi. +\] +Jetzt muss der Sinus von $u_N$ berechnet werden. +Dazu verwenden wir die komplexe Darstellung: +\[ +\sin u_N += +\frac{e^{i\frac{\pi}2-b} - e^{-i\frac{\pi}2+b}}{2i} += +\frac{ie^{-b}+ie^{b}}{2i} += +\cosh b += +3.796672364211658. +\] + +Da der Wert $\operatorname{sn}(u_N,k_N) = \sin u_N$ reell ist, wird auch +die daraus wie in Aufgabe~\ref{buch:elliptisch:aufgabe:3} +konstruierte Folge $\operatorname{sn}(u_n,k_n)$ reell sein. +Die Werte von $\operatorname{cn}(u_n,k_n)$ und $\operatorname{dn}(u_n,k_n)$ +werden für die Iterationsformeln~\eqref{buch:elliptisch:aufgabe:3:gauss} +für $\operatorname{sn}(u_n,k_n)$ nicht benötigt. +Die Berechnung ist in Tabelle~\ref{buch:elliptisch:aufgabe:4:table} +zusammengefasst. +Man liest ab, dass $\operatorname{sn}(K+iK',k)=2 = 1/k$, wie erwartet. +\end{loesung} diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex new file mode 100644 index 0000000..4a8c15c --- /dev/null +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex @@ -0,0 +1,58 @@ +\label{buch:elliptisch:aufgabe:5} +Die sehr schnelle Konvergenz des arithmetisch-geometrische Mittels +kann auch dazu ausgenutzt werden, eine grosse Zahl von Stellen der +Kreiszahl $\pi$ zu berechnen. +Almkvist und Berndt haben gezeigt \cite{buch:almkvist-berndt}, dass +\[ +\pi += +\frac{4 M(1,\sqrt{2}/2)^2}{ +\displaystyle 1-\sum_{n=1}^\infty 2^{n+1}(a_n^2-b_n^2) +} +\] +Verwenden Sie diese Formel, um Approximationen von $\pi$ zu berechnen. + +\begin{loesung} +\begin{table} +\centering +\begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +\hline +n & a_n & b_n & \pi_n% +\mathstrut\text{\vrule height12pt depth6pt width0pt}\\ +\hline +\mathstrut\text{\vrule height12pt depth0pt width0pt}% +0 & 1.000000000000000 & 0.707106781186548 & +\mathstrut\text{\vrule height12pt depth0pt width0pt}\\ +1 & 0.853553390593274 & 0.840896415253715 & 3.\underline{1}87672642712106 \\ +2 & 0.847224902923494 & 0.847201266746892 & 3.\underline{141}680293297648 \\ +3 & 0.847213084835193 & 0.847213084752765 & 3.\underline{141592653}895451 \\ +4 & 0.847213084793979 & 0.847213084793979 & 3.\underline{141592653589}822 \\ +5 & 0.847213084793979 & 0.847213084793979 & 3.\underline{141592653589}871 \\ +\hline +\infty & & & 3.141592653589793% +\mathstrut\text{\vrule height12pt depth6pt width0pt}\\ +\hline +\end{tabular} +\caption{Approximationen der Kreiszahl $\pi$ mit Hilfe des Algorithmus +des arithmetisch-geometrischen Mittels. +In nur 4 Schritten werden 12 Stellen Genauigkeit erreicht. +\label{buch:elliptisch:aufgabe:5:table}} +\end{table} +Wir schreiben +\[ +\pi_n += +\frac{4 a_k^2}{ +\displaystyle +1-\sum_{k=1}^\infty 2^{k+1}(a_k^2-b_k^2) +} +\] +für die Approximationen von $\pi$, +wobei $a_k$ und $b_k$ die Folgen der arithmetischen und geometrischen +Mittel von $1$ und $\!\sqrt{2}/2$ sind. +Die Tabelle~\ref{buch:elliptisch:aufgabe:5:table} zeigt die Resultat. +In nur 4 Schritten können 12 Stellen Genauigkeit erreicht werden, +dann beginnen jedoch bereits Rundungsfehler das Resultat zu beinträchtigen. +Für die Berechnung einer grösseren Zahl von Stellen muss daher mit +grösserer Präzision gerechnet werden. +\end{loesung} diff --git a/buch/chapters/references.bib b/buch/chapters/references.bib index fbbbf30..e8f3494 100644 --- a/buch/chapters/references.bib +++ b/buch/chapters/references.bib @@ -146,3 +146,12 @@ year = 2010, ISBN = { 978-1-4419-3090-3 } } + +@article{buch:almkvist-berndt, + author = { Gert Almkvist und Bruce Berndt }, + title = { Gauss, Landen, Ramanjujan, the Arithmetic-Geometric Mean, Ellipses $\pi$, and the {\em Ladies Diary} }, + journal = { The American Mathematical Monthly }, + volume = { 95 }, + pages = { 585--608 }, + year = 1988 +} -- cgit v1.2.1 From 3d742539c034e5b9569722e95395fd5ede33d770 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 27 Jun 2022 21:19:31 +0200 Subject: some improvements in tables --- buch/chapters/110-elliptisch/ellintegral.tex | 2 ++ buch/chapters/110-elliptisch/uebungsaufgaben/2.tex | 8 ++++-- buch/chapters/110-elliptisch/uebungsaufgaben/4.tex | 33 +++++++++------------- buch/chapters/110-elliptisch/uebungsaufgaben/5.tex | 7 +++-- 4 files changed, 26 insertions(+), 24 deletions(-) diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index cc99218..27724fd 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -478,6 +478,8 @@ für letztere ebenfalls sehr schnelle numerische Algorithmen liefert Aufgaben~\ref{buch:elliptisch:aufgabe:2}--\ref{buch:elliptisch:aufgabe:4}). Sie kann auch verwendet werden, um die Werte der Jacobischen elliptischen Funktionen für komplexe Argument zu berechnen. +Eine weiter Anwendung ist die Berechnung einer grossen Zahl von +Stellen der Kreiszahl $\pi$, siehe Aufgaben~\ref{buch:elliptisch:aufgabe:5}. % % Das arithmetisch-geometrische Mittel diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex index 9a1cafc..dbf184a 100644 --- a/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/2.tex @@ -21,13 +21,17 @@ Zeigen Sie, dass $k_n\to 0$ und $k_n'\to 1$ mit quadratischer Konvergenz. \centering \begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} \hline -n & k & k' \\ +n & k & k'% +\mathstrut\text{\vrule height12pt depth6pt width0pt}% +\\ \hline +\mathstrut\text{\vrule height12pt depth0pt width0pt}% 0 & 0.200000000000000 & 0.979795897113271 \\ 1 & 0.010205144336438 & 0.999947926158694 \\ 2 & 0.000026037598592 & 0.999999999661022 \\ 3 & 0.000000000169489 & 1.000000000000000 \\ -4 & 0.000000000000000 & 1.000000000000000 \\ +4 & 0.000000000000000 & 1.000000000000000% +\mathstrut\text{\vrule height0pt depth6pt width0pt}\\ \hline \end{tabular} \caption{Numerisches Experiment zur Folge $(k_n,k_n')$ diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex index b48192d..8814090 100644 --- a/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/4.tex @@ -4,22 +4,6 @@ Verwenden Sie den Algorithmus von Aufgabe~\ref{buch:elliptisch:aufgabe:3}, um dies für $k=\frac12$ nachzurechnen. \begin{loesung} -Zunächst müssen wir mit dem Algorithmus des arithmetisch-geometrischen -Mittels -\[ -K(k) -\approx -1.685750354812596 -\qquad\text{und}\qquad -K(k') -\approx -2.156515647499643 -\] -berechnen. -Aus $k=\frac12$ kann man jetzt die Folgen $k_n$ und $u_n$ berechnen, die innert -$N=5$ Iterationen konvergiert. -\end{loesung} - \begin{table} \centering \renewcommand{\tabcolsep}{5pt} @@ -44,8 +28,20 @@ $N=5$ Iterationen konvergiert. Konvergenz der Folge $k_n$ ist bei $N=5$ eintegreten. \label{buch:elliptisch:aufgabe:4:table}} \end{table} - -\begin{loesung} +Zunächst müssen wir mit dem Algorithmus des arithmetisch-geometrischen +Mittels +\[ +K(k) +\approx +1.685750354812596 +\qquad\text{und}\qquad +K(k') +\approx +2.156515647499643 +\] +berechnen. +Aus $k=\frac12$ kann man jetzt die Folgen $k_n$ und $u_n$ berechnen, die innert +$N=5$ Iterationen konvergiert. Sie führt auf \[ u_N @@ -67,7 +63,6 @@ Dazu verwenden wir die komplexe Darstellung: = 3.796672364211658. \] - Da der Wert $\operatorname{sn}(u_N,k_N) = \sin u_N$ reell ist, wird auch die daraus wie in Aufgabe~\ref{buch:elliptisch:aufgabe:3} konstruierte Folge $\operatorname{sn}(u_n,k_n)$ reell sein. diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex index 4a8c15c..fa018ca 100644 --- a/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/5.tex @@ -6,9 +6,9 @@ Almkvist und Berndt haben gezeigt \cite{buch:almkvist-berndt}, dass \[ \pi = -\frac{4 M(1,\sqrt{2}/2)^2}{ +\frac{4 M(1,\!\sqrt{2}/2)^2}{ \displaystyle 1-\sum_{n=1}^\infty 2^{n+1}(a_n^2-b_n^2) -} +}. \] Verwenden Sie diese Formel, um Approximationen von $\pi$ zu berechnen. @@ -27,7 +27,8 @@ n & a_n & b_n & \pi_n% 2 & 0.847224902923494 & 0.847201266746892 & 3.\underline{141}680293297648 \\ 3 & 0.847213084835193 & 0.847213084752765 & 3.\underline{141592653}895451 \\ 4 & 0.847213084793979 & 0.847213084793979 & 3.\underline{141592653589}822 \\ -5 & 0.847213084793979 & 0.847213084793979 & 3.\underline{141592653589}871 \\ +5 & 0.847213084793979 & 0.847213084793979 & 3.\underline{141592653589}871% +\mathstrut\text{\vrule height0pt depth6pt width0pt}\\ \hline \infty & & & 3.141592653589793% \mathstrut\text{\vrule height12pt depth6pt width0pt}\\ -- cgit v1.2.1 From 9b417043f748aaa2c5b802c0b4550104d59c5b37 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 28 Jun 2022 07:24:55 +0200 Subject: typo --- buch/chapters/110-elliptisch/elltrigo.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/chapters/110-elliptisch/elltrigo.tex b/buch/chapters/110-elliptisch/elltrigo.tex index c67870f..670b1de 100644 --- a/buch/chapters/110-elliptisch/elltrigo.tex +++ b/buch/chapters/110-elliptisch/elltrigo.tex @@ -120,7 +120,7 @@ Punktes auf dem Einheitskreis interpretieren. Für die Koordinaten eines Punktes auf der Ellipse ist dies nicht so einfach, weil es nicht nur eine Ellipse gibt, sondern für jede numerische Exzentrizität -mindestens eine mit Halbeachse $1$. +mindestens eine mit Halbachse $1$. Wir wählen die Ellipsen so, dass $a$ die grosse Halbachse ist, also $a>b$. Als Normierungsbedingung verwenden wir, dass $b=1$ sein soll, wie in Abbildung~\ref{buch:elliptisch:fig:jacobidef}. -- cgit v1.2.1 From b751d10130f923c1399a9eca58cfeb62c3a7a0e2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 28 Jun 2022 07:27:57 +0200 Subject: cleanup --- buch/chapters/110-elliptisch/ellintegral.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 27724fd..6dd1ef6 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -1113,7 +1113,8 @@ fest. % % AGM und Berechnung von F(x,k) % -\subsubsection{Berechnung von $F(x,k)$ mit dem arithmetisch-geometrischen Mittel\label{buch:elliptisch:subsubection:berechnung-fxk-agm}} +\subsubsection{Berechnung von $F(x,k)$ mit dem arithmetisch-geometrischen +Mittel\label{buch:elliptisch:subsubection:berechnung-fxk-agm}} Wie das vollständige elliptische Integral $K(k)$ kann auch das unvollständige elliptische Integral \begin{align*} @@ -1123,11 +1124,12 @@ F(x,k) = \int_0^{\varphi} \frac{dt}{\sqrt{1-k^2 \sin^2 t}} +&&\text{mit $x=\sin\varphi$} \\ &= a \int_0^{\varphi} \frac{dt}{a^2 \cos^2 t + b^2 \sin^2 t} -\qquad\text{mit $k=b/a$} +&&\text{mit $k=b/a$} \end{align*} mit dem arithmetisch-geometrischen Mittel berechnet werden. Dazu muss die Substitution -- cgit v1.2.1 From 9fd9ca9c2071b0911f08d434aa0fa722d7037640 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 28 Jun 2022 07:29:32 +0200 Subject: Formulierung --- buch/chapters/110-elliptisch/ellintegral.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index 6dd1ef6..f509fcb 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -1135,8 +1135,8 @@ mit dem arithmetisch-geometrischen Mittel berechnet werden. Dazu muss die Substitution \eqref{buch:elliptisch:agm:subst} verwendet werden, um auch den Winkel $\varphi_1$ zu berechnen. -Dazu muss \eqref{buch:elliptisch:agm:subst} nach $x_1=\sin t_1$ -aufgelöst werden. +Zunächst wird \eqref{buch:elliptisch:agm:subst} nach $x_1=\sin t_1$ +aufgelöst. Durch Multiplikation mit dem Nenner erhält man mit der Abkürzung $x=\sin t$ und $x_1=\sin t_1$ die quadratische Gleichung \[ -- cgit v1.2.1 From 971770c50241f483ba0f880dc6fafdd3f91d4983 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 28 Jun 2022 07:56:22 +0200 Subject: typos --- buch/chapters/110-elliptisch/ellintegral.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/buch/chapters/110-elliptisch/ellintegral.tex b/buch/chapters/110-elliptisch/ellintegral.tex index f509fcb..25f7083 100644 --- a/buch/chapters/110-elliptisch/ellintegral.tex +++ b/buch/chapters/110-elliptisch/ellintegral.tex @@ -1138,11 +1138,13 @@ verwendet werden, um auch den Winkel $\varphi_1$ zu berechnen. Zunächst wird \eqref{buch:elliptisch:agm:subst} nach $x_1=\sin t_1$ aufgelöst. Durch Multiplikation mit dem Nenner erhält man mit der Abkürzung -$x=\sin t$ und $x_1=\sin t_1$ die quadratische Gleichung +$x=\sin t$ %und $x_1=\sin t_1$ +die quadratische Gleichung \[ -(a-b)x x_1 +(a-b)x x_1^2 - 2ax_1 ++ (a+b)x = 0, -- cgit v1.2.1 From 6c3d3784c6d03fd89450bcf05b60cdf888d23333 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 28 Jun 2022 18:14:35 +0200 Subject: typos --- buch/chapters/110-elliptisch/agm/sn.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/chapters/110-elliptisch/agm/sn.cpp b/buch/chapters/110-elliptisch/agm/sn.cpp index ff2ed17..9e1b047 100644 --- a/buch/chapters/110-elliptisch/agm/sn.cpp +++ b/buch/chapters/110-elliptisch/agm/sn.cpp @@ -1,5 +1,5 @@ /* - * ns.cpp + * sn.cpp * * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule */ -- cgit v1.2.1 From 2400bd7fe87b268a8bb10ab503c3e0948c4dd6f2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 1 Jul 2022 17:18:14 +0200 Subject: Einleitung fertig --- buch/chapters/000-einleitung/Makefile.inc | 5 +- buch/chapters/000-einleitung/chapter.tex | 108 +-------------- buch/chapters/000-einleitung/funktionsbegriff.tex | 74 ++++++++++ buch/chapters/000-einleitung/inhalt.tex | 153 +++++++++++++++++++++ .../000-einleitung/speziellefunktionen.tex | 150 ++++++++++++++++++++ .../070-orthogonalitaet/gaussquadratur.tex | 2 +- 6 files changed, 385 insertions(+), 107 deletions(-) create mode 100644 buch/chapters/000-einleitung/funktionsbegriff.tex create mode 100644 buch/chapters/000-einleitung/inhalt.tex create mode 100644 buch/chapters/000-einleitung/speziellefunktionen.tex diff --git a/buch/chapters/000-einleitung/Makefile.inc b/buch/chapters/000-einleitung/Makefile.inc index 5840050..2c4e046 100644 --- a/buch/chapters/000-einleitung/Makefile.inc +++ b/buch/chapters/000-einleitung/Makefile.inc @@ -5,4 +5,7 @@ # CHAPTERFILES += \ - chapters/000-einleitung/chapter.tex + chapters/000-einleitung/chapter.tex \ + chapters/000-einleitung/funktionsbegriff.tex \ + chapters/000-einleitung/speziellefunktionen.tex \ + chapters/000-einleitung/inhalt.tex diff --git a/buch/chapters/000-einleitung/chapter.tex b/buch/chapters/000-einleitung/chapter.tex index 559a468..e53eafb 100644 --- a/buch/chapters/000-einleitung/chapter.tex +++ b/buch/chapters/000-einleitung/chapter.tex @@ -7,110 +7,8 @@ \lhead{Einleitung} \rhead{} \addcontentsline{toc}{chapter}{Einleitung} -Eine Polynomgleichung wie etwa -\begin{equation} -p(x) = ax^2+bx+c = 0 -\label{buch:einleitung:quadratisch} -\end{equation} -kann manchmal dadurch gelöst werden, dass man die Nullstellen errät -und damit eine Faktorisierung $p(x)=a(x-x_1)(x-x_2)$ konstruiert. -Doch im Allgemeinen wird man die Lösungsformel für quadratische -Gleichungen verwenden, die auf quadratischem Ergänzen basiert. -Es erlaubt die Gleichung~\eqref{buch:einleitung:quadratisch} umzwandeln in -\[ -\biggl(x + \frac{b}{2a}\biggr)^2 -= --\frac{c}{a} + \frac{b^2}{4a^2} -= -\frac{b^2-4ac}{4a^2}. -\] -Um diese Gleichung nach $x$ aufzulösen, muss man die inverse Funktion -der Quadratfunktion zur Verfügung haben, die Wurzelfunktion. -Dies ist wohl das älteste Beispiel einer speziellen Funktion, -die man zu dem Zweck eingeführt hat, spezielle algebraische Gleichungen -lösen zu können. -Sie liefert die bekannte Lösungsformel -\[ -x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} -\] -für die quadratische Gleichung. - -Durch die Definition der Wurzelfunktion ist das Problem der numerischen -Berechnung der Nullstelle natürlich noch nicht gelöst, aber man hat -ein handliches mathematisches Symbol gewonnen, mit dem man die Lösungen -übersichtlich beschreiben und algebraisch manipulieren kann. -Diese Idee steht hinter allen weiteren in diesem Buch diskutierten -Funktionen: wann immer ein wichtiges mathematisches Konzept sich nicht -direkt durch die bereits entwickelten Funktionen ausdrücken lässt, -erfindet man dafür eine neue Funktion oder Familie von Funktionen. -Beispielsweise hat sich die Darstellung von Zahlen $x$ als Potenzen -einer gemeinsamen Basis, zum Beispiel $x=10^y$, als sehr nützlich -herausgestellt, um Multiplikationen auf die von Hand leichter -ausführbaren Additionen zurückzuführen. -Man braucht also die Fähigkeit, die Abhängigkeit des Exponenten $y$ -von $x$ auszudrücken, mit anderen Worten, man braucht die Logarithmusfunktion. - -Spezielle Funktionen wie die Wurzelfunktion und die Logarithmusfunktion -werden also zu Bausteinen, die in der Lösung algebraischer oder auch -analytischer Probleme verwendet werden können. -Die Erfahrung zeigt, dass diese Funktionen immer wieder nützlich -sind, es lohnt sich also, ihre Berechnung zum Beispiel in einer -Bibliothek zu implementieren. -Spezielle Funktionen sind in diesem Sinn eine mathematische Form -des informatischen Prinzips des ``code reuse''. - -Die trigonometrischen Funktionen kann man als Lösungen des geometrischen -Problems der Parametrisierung eines Kreises verstehen. -Alternativ kann man $\sin x$ und $\cos x$ als spezielle Lösungen der -Differentialgleichung $y''=-y$ verstehen. -Viele andere Funktionen wie die hyperbolischen Funktionen oder die -Bessel-Funktionen sind ebenfalls Lösungen spezieller Differentialgleichungen. -Auch die Theorie der partiellen Differentialgleichungen gibt Anlass -zu interessanten Lösungsfunktionen. -Die Separation des Poisson-Problems in Kugelkoordinaten führt zum Beispiel -auf die Kugelfunktionen, mit denen sich beliebige Funktionen auf einer -Kugeloberfläche analysieren und synthetisieren lassen. - -Die Lösungen einer linearer gewöhnlicher Differentialgleichung können -oft mit Hilfe von Potenzreihen dargestellt werden. -So kann man zum Beispiel die Potenzreihenentwicklung der Exponentialfunktion -und der trigonometrischen Funktionen finden. -Die Konvergenz einer Potenzreihe wird aber durch Singularitäten -eingeschränkt. -Komplexe Potenzreihen ermöglichen aber, solche Stellen zu ``umgehen''. -Die Theorie der komplex differenzierbaren Funktionen bildet einen -allgemeinen Rahmen, mit solchen Funktionen umzugehen und ist zum -Beispiel nötig, um die Bessel-Funktionen der zweiten Art zu konstruieren, -die ebenfalls Lösungen ger Bessel-Gleichung sind, aber bei $x=0$ -eine Singularität aufweisen. - -Die Stammfunktion $F(x)$ einer gegebenen Funktion $f(x)$ ist natürlich -auch die Lösung der besonders einfachen Differentialgleichung $F'=f$. -Ein bekanntes Beispiel ist die Stammfunktion der Wahrscheinlichkeitsdichte -\[ -\varphi(x) -= -\frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}, -\] -der Normalverteilung, für die aber keine geschlossene Darstellung -mit bekannten Funktionen bekannt ist. -Sie kann aber durch die Fehlerfunktion -\[ -\operatorname{erf}(x) -= -\frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2}\,dt -\] -dargestellt werden. -Mit dem Risch-Algorithmus kann man nachweisen, dass es tatsächlich -keine Möglichkeit gibt, die Stammfunktion in geschlossener Form durch -die bereits bekannten Funktionen darzustellen, die Definition einer -neuen speziellen Funktion ist also der einzige Ausweg. -Die Fehlerfunktion ist heute in der Standardbibliothek enthalten auf -gleicher Stufe wie Wurzeln, trigonometrische Funktionen, -Exponentialfunktionen oder Logarithmen. - -Die nachstehenden Kapitel sollen die vielfältigen Arten illustrieren, -wie diese Prinzipien zu neuen und nützlichen speziellen Funktionen -und ihren Anwendungen führen können. +\input{chapters/000-einleitung/funktionsbegriff.tex} +\input{chapters/000-einleitung/speziellefunktionen.tex} +\input{chapters/000-einleitung/inhalt.tex} diff --git a/buch/chapters/000-einleitung/funktionsbegriff.tex b/buch/chapters/000-einleitung/funktionsbegriff.tex new file mode 100644 index 0000000..e684f82 --- /dev/null +++ b/buch/chapters/000-einleitung/funktionsbegriff.tex @@ -0,0 +1,74 @@ +% +% Der Funktionsbegriff +% +\subsection*{Der mathematische Funktionsbegriff} +Der moderne mathematische Funktionsbegriff ist die Krönungn einer +langen Entwicklung. +Erste Ansätze sind in der Darstellung voneinander abhängiger Grössen +in einem Koordinatensystem durch Nikolaus von Oresme im 14.~Jahrhundert +zu erkennen. +Dieser Ansatz, Funktionen einfach nur als Kurven zu betrachten, +war bis ins 17.~Jahrhundert verbreitet. +Der Begriff {\em Funktion} selbst geht wahrscheinlich auf Leibniz +zurück. + +Euler verwendete den Begriff oft austauschbar für zwei im Prinzip +verschiedene Vorstellungen. +Einerseits sah er jeden ``analytischen Ausdruck'' in einer Variablen +$x$ als eine Funktion an, andererseits betrachtete er eine in einem +Koordinatensystem freihändig gezeichnete Kurve als eine Funktion. +Heute unterscheiden wir zwischen der Funktion, also der Zuordnung +von $x$ zu den Funktionswerten $f(x)$ und dem Graphen, also der +von Paaren $(x,f(x))$ gebildeten Kurve in einem Koordinatensystem. +Nach letzterer Vorstellung ist auch die Wurzelfunktion, +die Umkehrfunktion der Quadratfunktion, $f(x)=x^2$ eine Funktion. +Da zu jedem Argument zwei verschiedene Werte $\pm\sqrt{x}$ +für die Wurzel möglich sind, lässt sich diese ``Funktion'' nicht +durch einen ``analytischen Ausdruck'' beschrieben. +Euler beschrieb diese Situation als {\em mehrdeutige Funktion}. + +Was ``analytische Ausdrücke'' alles umfassen sollen, ist ebenfalls +nicht scharf definiert. +Dahinter verbergen sich viele versteckte Annahmen, zum Beispiel +dass Funktionen automatisch stetig und möglicherweise sogar +differenzierbar sind. +Für Lagrange waren nur Funktionen akzeptabel, die durch Potenzreihen +definiert waren, solche Funktionen nennen wir heute {\em analytisch}. +Die Wahl von Potenzreihen zur Definition von Funktion ist einerseits +willkürlich, warum nicht Linearkombinationen von trigonometrischen +Funktionen? +Andererseits gibt es beliebig oft differenzierbare Funktionen, +deren Potenzreihe nicht gegen die Funktion konvergiert. + +Im 19.~Jahrhundert erfuhr die Analysis eine Reformierung. +Ausgehend vom nun präzis gefassten Grenzwertbegriff wurden Stetigkeit +und Differenzierbarkeit als eigenständige Eigenschaften von +Funktionen erkannt. +Eine Funktion war jetzt nur noch eine eindeutige Zuordnung +$x\mapsto f(x)$. +Stetigkeit ist die Eigenschaft, dass der Grenzwert in einem +Punkt des Definitionsbereichs existiert und mit dem Funktionswert +in diesem Punkt übereinstimmt. +Später wurden auch Differenzierbarkeit und Integrierbarkeit als +Eigenschaften von Funktionen erkannt, die vorhanden sein können, +aber nicht müssen. + +Der nun präzis gefasste Funktionsbegriff ist nur selten direkt anwendbar. +In der Physik treten Funktionen als Lösungen von Differentialgleichungen +auf. +Sie sind also immer mindestens differenzierbar, haben aber typischerweise +noch viele weitere Eigenschaften. +So sind zum Beispiel die Lösungen der Differentialgleichung +$y''=-n^2 y$ auf dem Intervall $[-\pi,\pi]$ die Funktionen +$\sin(nx)$ und $\cos(nx)$ für $n\in\mathbb{N}$. +Wie Fourier herausgefunden hat, lässt sich jede stetige $2\pi$-periodische +Funktion als Linearkombination dieser Funktionen approximieren. + +Eine Familie von Differentialgleichungen, die durch wenige Parameter +charakterisiert ist, führt auch zu einer Familie von Lösungsfunktionen, die +sich durch die gleichen Parameter beschreiben lassen. +Sie ist unmittelbar nützlich, da sie jedes Anwendungsproblem löst, +welches durch diese Differentialgleichung modelliert werden kann. +In diesem Sinne ist eine solche spezielle Funktionenfamilie interessanter +als eine beliebige differenzierbare Funktion. + diff --git a/buch/chapters/000-einleitung/inhalt.tex b/buch/chapters/000-einleitung/inhalt.tex new file mode 100644 index 0000000..1b9f35b --- /dev/null +++ b/buch/chapters/000-einleitung/inhalt.tex @@ -0,0 +1,153 @@ +% +% Was ist zu erwarten +% +\subsection*{Was ist zu erwarten?} +Spezielle Funktionen wie die eben angedeuteten werden also zu +Bausteinen, die in der Lösung algebraischer oder auch analytischer +Probleme verwendet werden können. +Die Erfahrung zeigt, dass diese Funktionen immer wieder nützlich +sind, es lohnt sich also, ihre Berechnung zum Beispiel in einer +Bibliothek zu implementieren. +Spezielle Funktionen sind in diesem Sinn eine mathematische Form +des informatischen Prinzips des ``code reuse''. + +Die nachstehenden Kapitel sollen die vielfältigen Arten illustrieren, +wie diese Prinzipien zu neuen und nützlichen speziellen Funktionen +und ihren Anwendungen führen können. +Hier eine kurze Übersicht über ihren Inhalt. +\begin{enumerate} +\item +Potenzen und Wurzeln: Potenzen und Polynome sind die einfachsten +Funktionen, die sich unmittelbar aus den arithmetischen Operationen +konstruieren lassen. +Die zugehörigen Umkehrfunktionen sind die Wurzelfunktionen, +sie lösen gewisse algebraische Gleichungen. +Aus den Polynomen lassen sich weiter rationale Funktionen und +Potenzreihen konstruieren, die als wichtige Werkzeuge zur Konstruktion +spezieller Funktionen in späteren Kapiteln sind. +\item +Exponentialfunktion und Exponentialgleichungen. +Die Exponentialfunktion entsteht aus dem Zinsproblem durch Grenzwert, +die Jost Bürgi zur Berechnung seiner Logarithmentabelle verwendet hat. +Hier zeigt sich die Nützlichkeit spezieller Funktionen als Grundlage +für die numerische Rechnung: Logarithmentafeln waren über Jahrhunderte +das zentrale Werkzeug für die Durchführung numerischer Rechnung. +Besonders nützlich ist aber auch die Potenzreihendarstellung der +Exponentialdarstellung, die meist für die numerische Berechnung +verwendet wird. +Die Lambert-$W$-schliesslich löst gewisse Exponentialgleichungen. +\item +Spezielle Funktionen aus der Geometrie. +Dieses Kapitel startet mit der langen Geschichte der trigonometrischen +Funktionen, den wahrscheinlich wichtigsten speziellen Funktionen für +geometrische Anwendungen. +Es führt aber auch die Kegelschnitte, die hyperbolischen Funktionen +und andere Parametrisierungen der Kegelschnitte ein, die später +wichtig werden. +Es beginnt auch die Diskussion einiger geometrischer Fragestellungen +die sich oft nur durch Definition neuer spezieller Funktionen lösen +lassen, wie zum Beispiel das Problem der Kurvenlänge auf einer +Ellipse. +\item +Spezielle Funktionen und Rekursion. +Viele Probleme lassen eine Lösung in rekursiver Form zu. +Zum Beispiel lässt sich die Fakultät durch eine Rekursionsbeziehung +vollständig definieren. +Dieses Kapitel zeigt, wie sich die Fakultät zur Gamma-Funktion +$\Gamma(x)$ erweitern lässt, die für beliebige reelle $x$ +definiert ist. +Sie ist aber nur die Spitze eines Eisbergs von weiteren wichtigen +Funktionen. +Die Beta-Integrale sind ebenfalls durch Rekursionsbeziehungen +charakterisiert, lassen sich durch Gamma-Funktionen ausdrücken und +haben als Anwendung die Verteilungsfunktionen der Ordnungsstatistiken. +Lineare Differenzengleichungen sind Rekursionsgleichungen, die sich +besonders leicht mit Potenzfunktionen lösen lassen. +Alle diese Funktionen sind Speziallfälle einer sehr viel grösseren +Klasse von Funktionen, den hypergeometrischen Funktionen, die sich +durch eine Rekursionsbeziehung der Koeffizienten ihrer +Potenzreihenentwicklung auszeichnen. +Es wird sich in nächsten Kapitel zeigen, dass sie besonders gut +geeignet sind, Lösungen von linearen Differentialgleichungen zu +beschreiben. +\item +Differentialgleichungen. +Lösungsfunktionen von Differentialgleichungen sind meistens die +erste Anwendung, in der man die klassschen speziellen Funktionen +kennenlernt. +Sie entstehen mit Hilfe der Potenzreihenmethode und können daher +als hypergeometrische Funktionen geschrieben werden. +Sie sind aber von derart grosser Bedeutung für die Anwendung, +dass viele dieser Funktionen als eigenständige Funktionenfamilien +definiert worden sind. +Die Bessel-Funktionen werden in diesem Zusammenhang eingehend +behandelt. +\item +Integrale können als Lösungen sehr spezieller Differentialgleichungen +betrachtet werden. +Eine Stammfunktion $F(x)$ der Funktion $f(x)$ hat als Ableitung die +ursprüngliche Funktion: $F'(x)=f(x)$. +Während Ableiten ein einfacher, algebraischer Prozess ist, +scheint das Finden einer Stammfunktion sehr viel anspruchsvoller +zu sein. +Spezielle Funktionen sinnvoll sein, wenn eine Stammfunktion sich nicht +mit den bereits definierten Funktionen ausdrücken lässt. +Es gibt eine systematische Methode zu entscheiden, ob eine Stammfunktion +sich durch ``elementare Funktionen'' ausdrücken lässt, sie wird oft +der Risch-Algorithmus genannt. +\item +Orthogonalität. +Mit dem Integral lassen sich auch für Funktionen Skalarprodukte +definieren. +Orthogonalität zwischen Funktionen zeichnet dann Funktionen aus, die +sich besonders gut zur Darstellung beliebiger stetiger oder +integrierbarer Funktionen eignen. +Die Fourier-Theorie und ihre vielen Varianten sind ein Resultat. +Besonders einfache orthogonale Funktionenfamilien sind die orthogonalen +Polynome, die ausserdem zu ausserordentlich genauen numerischen +Integrationsverfahren führen. +\item +Integraltransformationen. +Die trigonometrischen Funktionen sind die Grundlage der Fourier-Theorie. +Doch auch andere spezielle Funktionenfamilien können ähnlich +nützliche Integraltransformationen hergeben. +Die Bessel-Funktionen stellen sich in diesem Zusammenhang als die +Polarkoordinaten-Variante der Fourier-Theorie in der Ebene heraus. +\item +Funktionentheorie. +Einige Eigenschaften der Lösungen gewöhnlicher Differentialgleichung +sind allein mit der reellen Analysis nicht zu bewältigen. +In der Welt der speziellen Funktionen hat man aber strengere +Anforderungen an Funktionen, sie lassen sich immer als Funktionen +einer komplexen Variablen verstehen. +Dieses Kapitel stellt die wichtigsten Eigenschaften komplex +differenzierbarer Funktionen zusammen und wendet sie zum Beispiel +auf das Problem an, weitere Lösungen der Bessel-Differentialgleichung +zu finden. +\item +Partielle Differentialgleichungen sind eine der wichtigsten Quellen +der gewöhnlichen Differentialgleichungen, die nur mit speziellen +Funktionen gelöst werden können. +So führen rotationssymmetrische Wellenprobleme in der Ebene +ganz natürlich auf die Besselsche Differentialgleichung und damit +auf die Bessel-Funktionen als Lösungsfunktionen. +\item +Elliptische Funktionen. +Einige der in Kapitel~\ref{buch:chapter:geometrie} angesprochenen +Fragestellungen wie der Berechnung der Bogenlänge auf einer Ellipse +lassen sich mit keiner der bisher vorgestellten Technik lösen. +In diesem Kapitel werden die elliptischen Integrale und die +zugehörigen Umkehrfunktionen vorgestellt. +Die Jacobischen elliptischen Funktionen verallgemeinern +die trigonometrischen Funktionen und können gewisse nichtlineare +Differentialgleichungen lösen. +Sie finden auch Anwendungen im Design elliptischer Filter +(siehe Kapitel~\ref{chapter:ellfilter}). +\end{enumerate} + +Natürlich ist damit das weite Gebiet der speziellen Funktionen +nur ganz grob umrissen. +Weitere Aspekte und Anwendungen werden in den Artikeln im zweiten +Teil vorgestellt. +Eine Übersicht dazu findet der Leser auf Seite~\pageref{buch:uebersicht}. + diff --git a/buch/chapters/000-einleitung/speziellefunktionen.tex b/buch/chapters/000-einleitung/speziellefunktionen.tex new file mode 100644 index 0000000..8ca71bc --- /dev/null +++ b/buch/chapters/000-einleitung/speziellefunktionen.tex @@ -0,0 +1,150 @@ +% +% Spezielle Funktionen +% +\subsection*{Spezielle Funktionen} +Der abstrakte Funktionsbegriff auferlegt einer Funktion nur ganz wenige +Einschränkungen. +Damit lässt sich zwar eine mathematische Theorie entwickeln, die +klärt, unter welchen Umständen zusätzliche Eigenschaften wie Stetigkeit +und Differenzierbarkeit zu erwarten sind. +Allgemeine Berechnungen kann man mit diesem Begriff aber nicht durchführen, +seine Anwendbarkeit ist beschränkt. +Praktisch nützlich wird der Funktionsbegriff also erst, wenn man ihn +einschränkt auf anwendungsrelevante Eigenschaften. +Die Mathematik hat in ihrer Geschichte genau dies immer wieder +getan, wie im Folgenden kurz skizziert werden soll. + +% +% Polynome und Wurzeln +% +\subsubsection{Polynome und Wurzeln} +Eine Polynomgleichung wie etwa +\begin{equation} +p(x) = ax^2+bx+c = 0 +\label{buch:einleitung:quadratisch} +\end{equation} +kann manchmal dadurch gelöst werden, dass man die Nullstellen errät +und damit eine Faktorisierung $p(x)=a(x-x_1)(x-x_2)$ konstruiert. +Doch im Allgemeinen wird man die Lösungsformel für quadratische +Gleichungen verwenden, die auf quadratischem Ergänzen basiert. +Es erlaubt die Gleichung~\eqref{buch:einleitung:quadratisch} umzwandeln in +\[ +\biggl(x + \frac{b}{2a}\biggr)^2 += +-\frac{c}{a} + \frac{b^2}{4a^2} += +\frac{b^2-4ac}{4a^2}. +\] +Um diese Gleichung nach $x$ aufzulösen, muss man die inverse Funktion +der Quadratfunktion zur Verfügung haben, die Wurzelfunktion. +Dies ist wohl das älteste Beispiel einer speziellen Funktion, +die man zu dem Zweck eingeführt hat, spezielle algebraische Gleichungen +lösen zu können. +Sie liefert die bekannte Lösungsformel +\[ +x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} +\] +für die quadratische Gleichung. + +% +% Exponential- und Logarithmusfunktion +% +\subsubsection{Exponential- und Logarithmusfunktion} +Durch die Definition der Wurzelfunktion ist das Problem der numerischen +Berechnung der Nullstelle natürlich noch nicht gelöst, aber man hat +ein handliches mathematisches Symbol gewonnen, mit dem man die Lösungen +übersichtlich beschreiben und algebraisch manipulieren kann. +Diese Idee steht hinter allen weiteren in diesem Buch diskutierten +Funktionen: wann immer ein wichtiges mathematisches Konzept sich nicht +direkt durch die bereits entwickelten Funktionen ausdrücken lässt, +erfindet man dafür eine neue Funktion oder Familie von Funktionen. +Beispielsweise hat sich die Darstellung von Zahlen $x$ als Potenzen +einer gemeinsamen Basis, zum Beispiel $x=10^y$, als sehr nützlich +herausgestellt, um Multiplikationen auf die von Hand leichter +ausführbaren Additionen zurückzuführen. +Man braucht also die Fähigkeit, die Abhängigkeit des Exponenten $y$ +von $x$ auszudrücken, mit anderen Worten, man braucht die +Logarithmusfunktion. + +Auch die Logarithmusfunktion erlaubt nicht, die Gleichungen $xe^x=y$ +nach $x$ aufzulösen. +Solche Exponentialgleichungen treten in verschiedenster Form auch in +Anwendungen auf. +Die Lambert-$W$-Funktion, die in Abschnitt~\ref{buch:section:lambertw} +eingeführt wird, löst genau diese Aufgabe. + + +% +% Geometrisch definierte spezielle Funktionen +% +\subsubsection{Geometrisch definierte spezielle Funktionen} +Die trigonometrischen Funktionen entstanden bereits im Altertum +um das Problem der Vermessung der Himmelskugel zu lösen. +Man kann sie aber auch zur Parametrisierung eines Kreises oder +zur Beschreibung von Drehungen mit Drehmatrizen verwenden. +Sie stellen auch eine Zusammenhang zwischen der Bogenlänge +entlang eines Kreises und der zugehörigen Sehne her. +Diese Ideen lassen sich auf eine grössere Klasse von Kurven, +nämlich die Kegelschnitte verallgemeinern. +Diese werden in Kapitel~\ref{buch:chapter:geometrie} eingeführt. +Die Parametrisierungen der Hyperbeln zum Beispiel führt auf +hyperbolische Funktion und macht eine Verbindung zu Exponential- +und Logarithmusfunktion sichtbar. + +% +% Lösungen von Differentialgleichungen +% +\subsubsection{Lösungen von Differentialgleichungen} +Alternativ kann man $\sin x$ und $\cos x$ als spezielle Lösungen der +Differentialgleichung $y''=-y$ verstehen. +Viele andere Funktionen wie die hyperbolischen Funktionen oder die +Bessel-Funktionen sind ebenfalls Lösungen spezieller Differentialgleichungen. + +Auch die Theorie der partiellen Differentialgleichungen, auf die +im Kapitel~\ref{buch:chapter:pde} eingegangen wird, gibt Anlass +zu interessanten Lösungsfunktionen. +Die Separation des Poisson-Problems in Kugelkoordinaten führt zum Beispiel +auf die Kugelfunktionen, mit denen sich beliebige Funktionen auf einer +Kugeloberfläche analysieren und synthetisieren lassen. +Die Lösungen einer linearer gewöhnlicher Differentialgleichung können +oft mit Hilfe von Potenzreihen dargestellt werden. +So kann man zum Beispiel die Potenzreihenentwicklung der Exponentialfunktion +und der trigonometrischen Funktionen finden. +Die Konvergenz einer Potenzreihe wird aber durch Singularitäten +eingeschränkt. +Komplexe Potenzreihen ermöglichen aber, solche Stellen zu ``umgehen''. +Die Theorie der komplex differenzierbaren Funktionen bildet einen +allgemeinen Rahmen, mit solchen Funktionen umzugehen und ist zum +Beispiel nötig, um die Bessel-Funktionen der zweiten Art zu konstruieren, +die ebenfalls Lösungen ger Bessel-Gleichung sind, aber bei $x=0$ +eine Singularität aufweisen. + +% +% Stammfunktionen +% +\subsubsection{Stammfunktionen} +Die Stammfunktion $F(x)$ einer gegebenen Funktion $f(x)$ ist natürlich +auch die Lösung der besonders einfachen Differentialgleichung $F'=f$. +Ein bekanntes Beispiel ist die Stammfunktion der Wahrscheinlichkeitsdichte +\[ +\varphi(x) += +\frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}}, +\] +der Normalverteilung, für die aber keine geschlossene Darstellung +mit bekannten Funktionen bekannt ist. +Sie kann aber durch die Fehlerfunktion +\[ +\operatorname{erf}(x) += +\frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2}\,dt +\] +dargestellt werden. +Mit dem Risch-Algorithmus kann man nachweisen, dass es tatsächlich +keine Möglichkeit gibt, die Stammfunktion in geschlossener Form durch +die bereits bekannten Funktionen darzustellen, die Definition einer +neuen speziellen Funktion ist also der einzige Ausweg. +Die Fehlerfunktion ist heute in der Standardbibliothek enthalten auf +gleicher Stufe wie Wurzeln, trigonometrische Funktionen, +Exponentialfunktionen oder Logarithmen. + diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index 4a25678..480a37d 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -552,7 +552,7 @@ w(x)=e^{-x} \text{ und } g(x)=f(x)e^x. \] -Dann approximiert $g(x)$ man durch ein Interpolationspolynom, +Dann approximiert man $g(x)$ durch ein Interpolationspolynom, so wie man das bei der Gauss-Quadratur gemacht hat. Als Stützstellen müssen dazu die Nullstellen der Laguerre-Polynome verwendet werden. -- cgit v1.2.1 From 70287f9b87cf4492e639ce2a191708c3265e75a3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 1 Jul 2022 18:40:19 +0200 Subject: complete chapter 9 --- buch/chapters/080-funktionentheorie/analytisch.tex | 33 +++++++++++++++++++++- .../chapters/080-funktionentheorie/anwendungen.tex | 3 ++ buch/chapters/080-funktionentheorie/cauchy.tex | 10 +++++++ buch/chapters/080-funktionentheorie/holomorph.tex | 3 +- 4 files changed, 47 insertions(+), 2 deletions(-) diff --git a/buch/chapters/080-funktionentheorie/analytisch.tex b/buch/chapters/080-funktionentheorie/analytisch.tex index 15ca2e4..3095cc1 100644 --- a/buch/chapters/080-funktionentheorie/analytisch.tex +++ b/buch/chapters/080-funktionentheorie/analytisch.tex @@ -140,7 +140,38 @@ von $\mathbb{C}$ gegen $f(z)=\overline{z}$ konvergiert. % \subsection{Konvergenzradius \label{buch:funktionentheorie:subsection:konvergenzradius}} +In der Theorie der Potenzreihen, die man in einem grundlegenden +Analysiskurs lernt, wird auch genauer untersucht, wie gross +eine Umgebung des Punktes $z_0$ ist, in der die Potenzreihe +im Punkt $z_0$ einer analytischen Funktion konvergiert. -% XXX auf dem Rand des Konvergenzkreises gibt es immer eine Singularität +\begin{satz} +\label{buch:funktionentheorie:satz:konvergenzradius} +Die Potenzreihe +\[ +f(z) = \sum_{k=0}^\infty a_0(z-z_0)^k +\] +ist konvergent auf einem Kreis mit Radius $\varrho$ und +\[ +\frac{1}{\varrho} += +\limsup_{n\to\infty} \sqrt[k]{|a_k|}. +\] +Falls $a_k\ne 0$ für alle $k$ und der folgende Grenzwert existiert, +dann gilt auch +\[ +\varrho = \lim_{n\to\infty} \biggl| \frac{a_n}{a_{n+1}}\biggr|. +\] +\end{satz} + +\begin{definition} +\label{buch:funktionentheorie:definition:konvergenzradius} +\index{Konvergenzradius}% +Der in Satz~\ref{buch:funktionentheorie:satz:konvergenzradius} +Radius $\varrho$ des Konvergenzkreises heisst {\em Konvergenzradius}. +\end{definition} +Man kann auch zeigen, dass der Konvergenzkreis immer so gross ist, +dass auf seinem Rand ein Wert $z$ liegt, für den die Potenzreihe nicht +konvergiert. diff --git a/buch/chapters/080-funktionentheorie/anwendungen.tex b/buch/chapters/080-funktionentheorie/anwendungen.tex index 04c597e..440d2d3 100644 --- a/buch/chapters/080-funktionentheorie/anwendungen.tex +++ b/buch/chapters/080-funktionentheorie/anwendungen.tex @@ -6,6 +6,9 @@ \section{Anwendungen \label{buch:funktionentheorie:section:anwendungen}} \rhead{Anwendungen} +In diesem Abschnitt wird die Theorie der komplex differenzierbaren +Funktionen dazu verwendet, einige früher bereits verwendete oder +angedeutete Resultate herzuleiten. \input{chapters/080-funktionentheorie/gammareflektion.tex} \input{chapters/080-funktionentheorie/carlson.tex} diff --git a/buch/chapters/080-funktionentheorie/cauchy.tex b/buch/chapters/080-funktionentheorie/cauchy.tex index 21d8dcf..58504db 100644 --- a/buch/chapters/080-funktionentheorie/cauchy.tex +++ b/buch/chapters/080-funktionentheorie/cauchy.tex @@ -6,6 +6,16 @@ \section{Cauchy-Integral \label{buch:funktionentheorie:section:cauchy}} \rhead{Cauchy-Integral} +In Abschnitt~\ref{buch:funktionentheorie:section:holomorph} hat sich +bereits gezeigt, dass komplexe Differenzierbarkeit einer komplexen +Funktion weit mehr Einschränkungen auferlegt als reelle Differenzierbarkeit. +Sowohl der Real- wie auch der Imaginärteil müssenharmonische Funktionen +sein. +In diesem Abschnitt wird die Cauchy-In\-te\-gral\-formel etabliert, die +sogar zeigt, dass eine komplex differenzierbare Funktion bereits durch +die Werte auf dem Rand eines einfach zusammenhängenden Gebietes +gegeben ist, beliebig oft differenzierbar ist und ausserdem immer +analytisch ist. % % Wegintegrale und die Cauchy-Formel diff --git a/buch/chapters/080-funktionentheorie/holomorph.tex b/buch/chapters/080-funktionentheorie/holomorph.tex index c87b083..dfe2744 100644 --- a/buch/chapters/080-funktionentheorie/holomorph.tex +++ b/buch/chapters/080-funktionentheorie/holomorph.tex @@ -83,6 +83,7 @@ Der Term $x-x_0$ und die Gleichung \eqref{komplex:abldef} sind aber auch für komplexe Argument sinnvoll, wir definieren daher \begin{definition} +\label{buch:funktionentheorie:definition:differenzierbar} Die komplexe Funktion $f(z)$ heisst im Punkt $z_0$ komplex differenzierbar und hat die komplexe Ableitung $f'(z_0)\in\mathbb C$, wenn \index{komplex differenzierbar}% @@ -258,11 +259,11 @@ Der Operator \frac{\partial^2}{\partial y^2} \] heisst der {\em Laplace-Operator} in zwei Dimensionen. - \index{Laplace-Operator}% \end{definition} \begin{definition} +\label{buch:funktionentheorie:definition:harmonisch} Eine Funktion $h(x,y)$ von zwei Variablen heisst {\em harmonisch}, wenn sie die Gleichung \[ -- cgit v1.2.1 From 7e3f893dcf57b6114b7e9124e77f56c59e1e067d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 1 Jul 2022 19:29:32 +0200 Subject: chapter PDE completed --- buch/chapters/090-pde/gleichung.tex | 150 ++++++++++++++++++++++++++++++------ 1 file changed, 128 insertions(+), 22 deletions(-) diff --git a/buch/chapters/090-pde/gleichung.tex b/buch/chapters/090-pde/gleichung.tex index 583895d..271dc44 100644 --- a/buch/chapters/090-pde/gleichung.tex +++ b/buch/chapters/090-pde/gleichung.tex @@ -6,10 +6,26 @@ \section{Gleichungen und Randbedingungen \label{buch:pde:section:gleichungen-und-randbedingungen}} \rhead{Gebiete, Gleichungen und Randbedingungen} +Gewöhnliche Differentialgleichungen sind immer auf einem +Intervall als Definitionsgebiet definiert. +Partielle Differentialgleichungen sind Gleichungen, die verschiedene +partielle Ableitungen einer Funktion mehrerer Variablen involvieren, +das Definitionsgebiet ist daher immer eine höherdimensionale Teilmenge +von $\mathbb{R}^n$. +Sowohl das Gebiet wie auch dessen Rand können wesentlich komplexer sein. +Eine sorgfältige Definition ist unabdingbar, um Widersprüchen vorzubeugen. +% +% Gebiete, Differentialoperatoren, Randbedingungen +% \subsection{Gebiete, Differentialoperatoren, Randbedingungen} +In diesem Abschnitt sollen die Begriffe geklärt werden, die zur +korrekten Formulierung eines partiellen Differentialgleichungsproblems +notwendig sind. - +% +% Gebiete +% \subsubsection{Gebiete} Gewöhnliche Differentialgleichungen haben nur eine unabhängige Variable, die gesuchte Lösungsfunktion ist auf eine @@ -20,6 +36,7 @@ ermöglicht wesentlich vielfältigere und kompliziertere Situationen. \begin{definition} +\label{buch:pde:definition:gebiet} Ein Gebiet $G\subset\mathbb{R}^n$ ist eine offene Teilmenge von $\mathbb{R}^n$, d.~h.~für jeden Punkt $x\in G$ gibt es eine kleine Umgebung @@ -29,8 +46,12 @@ U_{\varepsilon}(x) \{y\in\mathbb{R}^n\mid |x-y|<\varepsilon\} \), die ebenfalls in $G$ in enthalten ist, also $U_{\varepsilon}(x)\subset G$. +\index{Gebiet}% \end{definition} +% +% Differentialoperatoren +% \subsubsection{Differentialoperatoren} Eine gewöhnliche Differentialgleichung für eine Funktion ist eine Beziehung zwischen den Werten der Funktion und ihrer @@ -66,9 +87,13 @@ schreiben. Die Koeffizienten $a$, $b_i$, $c_{ij}$ können dabei durchaus auch Funktionen der unabhängigen Variablen sein. +% +% Laplace-Operator +% \subsubsection{Laplace-Operator} -Der Laplace-Operator hat in einem karteischen Koordinatensystem die +Der {\em Laplace-Operator} hat in einem karteischen Koordinatensystem die Form +\index{Laplace-Operator}% \[ \Delta = @@ -86,28 +111,109 @@ nicht ändert. Man könnte sagen, der Laplace-Operator ist symmetrisch bezüglich aller Bewegungen des Raumes. +% +% Wellengleichung +% \subsubsection{Wellengleichung} +Da die physikalischen Gesetze invariant sein müssen unter solchen +Bewegungen, ist zu erwarten, dass der Laplace-Operator in partiellen +Differentialgleichungen +Als Beispiel betrachten wir die Ausbreitung einer Welle, welche sich +in einem Medium mit der Geschwindigkeit $c$ ausbreitet. +Ist $u(x,t)$ die Auslenkung der Welle im Punkt $x\in\mathbb{R}^n$ +zur Zeit $t\in\mathbb{R}$, dann erfüllt die Funktion $u(x,t)$ +die partielle Differentialgleichung +\begin{equation} +\frac{1}{c^2} +\frac{\partial^2 u}{\partial t^2} += +\Delta u. +\label{buch:pde:eqn:waveequation} +\end{equation} +In dieser Gleichung treten nicht nur die partiellen Ableitungen +nach den Ortskoordinaten auf, die der Laplace-Operator miteinander +verknüpft. +Die Funktion $u(x,t)$ ist definiert auf einem Gebiet in +$\mathbb{R}^{n}\times\mathbb{R}=\mathbb{R}^{n+1}$ mit den Koordinaten +$(x_1,\dots,x_n,t)$. +Der Gleichung~\eqref{buch:pde:eqn:waveequation} ist daher eigentlich +die Gleichung +\[ +\square u = 0 +\qquad\text{mit}\quad +\square += +\frac{1}{c^2}\frac{^2}{\partial t^2} +- +\Delta += +\frac{1}{c^2}\frac{\partial^2}{\partial t^2} +- +\frac{\partial^2}{\partial x_1^2} +- +\frac{\partial^2}{\partial x_2^2} +-\dots- +\frac{\partial^2}{\partial x_n^2} +\] +wird. +Der Operator $\square$ heisst auch d'Alembert-Operator. +\index{dAlembertoperator@d'Alembert-Operator}% -\subsubsection{Eigenfunktionen} -Eine besonders einfache - -\subsubsection{Trigonometrische Funktionen} -Die trigonometrischen Funktionen - -\subsection{Orthogonalität} -In der linearen Algebra lernt man, dass die Eigenvektoren einer -symmetrischen Matrix zu verschiedenen Eigenwerten orthgonal sind. -Dies hat zur Folge, dass die Transformation in eine Eigenbasis -mit einer orthogonalen Matrix möglich ist, was wiederum die Basis -von Diagonalisierungsverfahren wie dem Jacobi-Verfahren ist. - -Das Separationsverfahren wird zeigen, wie sich das Finden einer -Lösung der Wellengleichung auf Lösungen des Eigenwertproblems -$\Delta u = \lambda u$ zurückführen lässt. -Damit stellt sich die Frage, welche Eigenschaften - +% +% Randbedingungen +% +\subsubsection{Randbedingungen} +Die Differentialgleichung oder der Differentialoperator legen die +Lösung nicht fest. +Wie bei gewöhnlichen Differentialgleichungen ist dazu die Spezifikation +geeigneter Randbedingungen nötig. -\subsubsection{Gewöhnliche Differentialglichung} +\begin{definition} +\label{buch:pde:definition:randbedingungen} +Eine {\em Randbedingung} für das Gebiet $\Omega$ ist eine Teilmenge +$F\subset\partial\Omega$ sowie eine auf $F$ definierte Funktion +$f\colon F\to\mathbb{R}$. +Eine Funktion $u\colon \overline{\Omega} \to\mathbb{R}$ erfüllt eine +{\em Dirichlet-Randbedingung}, wenn +\index{Dirichlet-Randbedingung}% +\index{Randbedingung!Dirichlet-}% +\( +u(x) = f(x) +\) +für $x\in F$. +Sie erfüllt eine {\em Neumann-Randbedingung}, wenn +\index{Neumann-Randbedingung}% +\index{Randbedingung!Neumann-}% +\[ +\frac{\partial u}{\partial n} += +f(x)\qquad\text{für $x\in F$}. +\] +Dabei ist +\[ +\frac{\partial u}{\partial n} += +\frac{d}{dt} +u(x+tn) +\bigg|_{t=0} += +\operatorname{grad}u\cdot n +\] +\index{Normalableitung}% +die {\em Normalableitung}, die Richtungsableitung in Richtung des +Vektors $n$, der senkrecht ist auf dem Rand $\partial\Omega$ von +$\Omega$. +\end{definition} +Die Vorgabe nur von Ableitungen kann natürlich die Lösung $u(x)$ +einer linearen partiellen Differentialgleichung nicht eindeutig +festlegen, dazu ist noch mindestens ein Funktionswert notwendig. +Die Vorgabe von anderen Ableitungen in Richtungen tangential an den +Rand liefert keine neue Information, denn ausgehend von dem einen +Funktionswert auf dem Rand kann man durch Integration entlang +einer Kurve auf dem Rand eine Neumann-Randbedingung konstruieren, +die die gleiche Information beinhaltet wie Anforderungen an die +tangentialen Ableitungen. +Dirichlet- und Neumann-Randbedingungen sind daher die einzigen +sinnvollen linearen Randbedingungen. -\subsubsection{$n$-dimensionaler Fall} -- cgit v1.2.1 From 931871e8c8e9b266b9b626d816a803bbd2c56653 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Fri, 1 Jul 2022 20:55:53 +0200 Subject: more index stuff --- buch/chapters/010-potenzen/chapter.tex | 4 ++ buch/chapters/010-potenzen/loesbarkeit.tex | 2 + buch/chapters/010-potenzen/polynome.tex | 13 +++++ buch/chapters/010-potenzen/potenzreihen.tex | 14 +++++- buch/chapters/010-potenzen/tschebyscheff.tex | 8 +++- buch/chapters/020-exponential/lambertw.tex | 5 +- buch/chapters/030-geometrie/hyperbolisch.tex | 1 + buch/chapters/030-geometrie/trigonometrisch.tex | 1 + buch/chapters/040-rekursion/beta.tex | 2 + buch/chapters/040-rekursion/gamma.tex | 3 ++ buch/chapters/040-rekursion/hypergeometrisch.tex | 4 ++ buch/chapters/050-differential/bessel.tex | 4 ++ .../chapters/050-differential/hypergeometrisch.tex | 2 + .../050-differential/potenzreihenmethode.tex | 2 + buch/chapters/060-integral/eulertransformation.tex | 2 + buch/chapters/060-integral/fehlerfunktion.tex | 4 +- .../070-orthogonalitaet/gaussquadratur.tex | 2 + buch/chapters/070-orthogonalitaet/legendredgl.tex | 3 ++ buch/chapters/070-orthogonalitaet/rekursion.tex | 1 + buch/chapters/070-orthogonalitaet/rodrigues.tex | 6 +++ buch/chapters/070-orthogonalitaet/saev.tex | 1 + buch/chapters/070-orthogonalitaet/sturm.tex | 21 ++++++++- buch/chapters/080-funktionentheorie/analytisch.tex | 55 ++++++++++++---------- buch/chapters/080-funktionentheorie/carlson.tex | 2 + buch/chapters/080-funktionentheorie/cauchy.tex | 1 + .../080-funktionentheorie/gammareflektion.tex | 1 + buch/chapters/080-funktionentheorie/holomorph.tex | 6 ++- .../080-funktionentheorie/singularitaeten.tex | 9 ++++ buch/chapters/110-elliptisch/dglsol.tex | 5 ++ buch/chapters/110-elliptisch/ellintegral.tex | 7 ++- buch/chapters/110-elliptisch/elltrigo.tex | 1 + 31 files changed, 157 insertions(+), 35 deletions(-) diff --git a/buch/chapters/010-potenzen/chapter.tex b/buch/chapters/010-potenzen/chapter.tex index 2628e33..a1cce60 100644 --- a/buch/chapters/010-potenzen/chapter.tex +++ b/buch/chapters/010-potenzen/chapter.tex @@ -18,10 +18,13 @@ Diskussion rechtfertigen. \begin{enumerate} \item Die Umkehrfunktion der Potenzfunktion sind viel schwieriger zu +\index{Potenzfunktion}% berechnen und können als eine besonders einfache Art von speziellen Funktionen betrachtet werden. Die in Abschnitt~\ref{buch:potenzen:section:loesungen} definierten Wurzelfunktionen sind der erste Schritt zur Lösung von Polynomgleichungen. +\index{Wurzelfunktion}% +\index{Polynomgleichung}% \item Es lassen sich interessante Familien von Funktionen definieren, die zum Teil aus Polynomen bestehen. @@ -32,6 +35,7 @@ Abschnitt~\ref{buch:polynome:section:tschebyscheff} vorgestellt. \item Alles speziellen Funktionen sind analytisch, sie haben eine konvergente Potenzreihenentwicklung. +\index{Potenzreihe}% Die Partialsummen einer Potenzreihenentwicklung sind Approximationen An die wichtigsten Eigenschaften von Potenzreihen wird in Abschnitt~\ref{buch:potenzen:section:potenzreihen} erinnert. diff --git a/buch/chapters/010-potenzen/loesbarkeit.tex b/buch/chapters/010-potenzen/loesbarkeit.tex index f93a84b..a9f273a 100644 --- a/buch/chapters/010-potenzen/loesbarkeit.tex +++ b/buch/chapters/010-potenzen/loesbarkeit.tex @@ -34,6 +34,7 @@ Der Fundamentalsatz der Algebra zeigt, dass $\mathbb{C}$ alle Nullstellen von Polynomen enthält. \begin{satz}[Gauss] +\index{Satz!Fundamentalsatz der Algebra}% \index{Fundamentalsatz der Algebra}% \label{buch:potenzen:satz:fundamentalsatz} Jedes Polynom $p(x)=a_nx^n+\dots + a_2x^2 + a_1x + a_0\in\mathbb{C}[x]$ @@ -157,6 +158,7 @@ höheren Grades nicht mit einer Lösung durch Wurzelausdrücke rechnen kann. \begin{satz}[Abel] +\index{Satz!von Abel} \label{buch:potenzen:satz:abel} Für Polynomegleichungen vom Grad $n\ge 5$ gibt es keine allgemeine Lösung durch Wurzelausdrücke. diff --git a/buch/chapters/010-potenzen/polynome.tex b/buch/chapters/010-potenzen/polynome.tex index 9edb012..ce5e521 100644 --- a/buch/chapters/010-potenzen/polynome.tex +++ b/buch/chapters/010-potenzen/polynome.tex @@ -19,6 +19,7 @@ wobei $a_n\ne 0$ sein muss. Das Polynom heisst {\em normiert}, wenn $a_n=1$ ist. \index{normiert}% \index{Grad eines Polynoms}% +\index{Polynom!Grad}% Die Menge aller Polynome mit Koeffizienten in der Menge $K$ wird mit $K[x]$ bezeichnet. \end{definition} @@ -65,6 +66,8 @@ Berechnungsverfahren für die speziellen Funktionen zu konstruieren. Dank des folgenden Satzes kann dies immer mit Polynomen geschehen. \begin{satz}[Weierstrass] +\index{Satz!Weierstrass}% +\index{Weierstrasse, Karl}% \label{buch:potenzen:satz:weierstrass} \index{Weierstrass, Satz von}% Eine auf einem kompakten Intervall $[a,b]$ stetige Funktion $f(x)$ @@ -74,7 +77,9 @@ approximieren. Der Satz sagt in dieser Form nichts darüber aus, wie die Approximationspolynome konstruiert werden sollen. +\index{Approximationspolynom}% Von Bernstein gibt es konstruktive Beweise dieses Satzes, +\index{Bernstein-Polynom}% welche auch explizit eine Folge von Approximationspolynomen konstruieren. In der späteren Entwicklung werden wir für die meisten @@ -127,6 +132,7 @@ Ein gemeinsamer Teiler zweier Polynome $a(x)$ und $b(x)$ ist ein Polynom $g(x)$, welches beide Polynome teilt, also $g(x)\mid a(x)$ und $g(x)\mid b(x)$. \index{grösster gemeinsamer Teiler}% +\index{Polynome!grösster gemeinsamer Teiler}% Ein Polynom $g(x)$ heisst {\em grösster gemeinsamer Teiler} von $a(x)$ und $b(x)$, wenn jeder andere gemeinsame Teiler $f(x)$ von $a(x)$ und $b(x)$ auch ein Teiler von $g(x)$ ist. @@ -180,6 +186,9 @@ Dann ist $g(x)=r_{m-1}(x)$ ein grösster gemeinsamer Teiler. % Der erweiterte euklidische Algorithmus % \subsubsection{Der erweiterte euklidische Algorithmus} +\index{Polynome!erweiterter euklidischer Algorithmus}% +\index{erweiterter euklidischer Algorithmus}% +\index{euklidischer Algorithmus!erweitert}% Die Konstruktion der Folgen $a_n(x)$ und $b_n(x)$ kann in Matrixform kompakter geschrieben werden als \[ @@ -401,8 +410,11 @@ p_n so dass $p_n=0$ sein muss, was schliesslich dazu führt, dass alle Koeffizienten von $a(x)-b(x)$ verschwinden. Daraus folgt das Prinzip des Koeffizientenvergleichs: +\index{Koeffizientenvergleich}% +\index{Polynome!Koeffizientenvergleich}% \begin{satz}[Koeffizientenvergleich] +\index{Satz!Koeffizientenvergleich}% \label{buch:polynome:satz:koeffizientenvergleich} Zwei Polynome $a(x)$ und $b(x)$ stimmen genau dann überein, wenn sie die gleichen Koeffizienten haben. @@ -436,6 +448,7 @@ und $n$ Additionen. Die Anzahl nötiger Multiplikationen kann mit dem folgenden Vorgehen reduziert werden, welches auch als das {\em Horner-Schema} bekannt ist. \index{Horner-Schema}% +\index{Polynome!Horner-Schema}% Statt erst am Schluss alle Terme zu addieren, addiert man so früh wie möglich. Zum Beispiel multipliziert man $(a_nx+a_{n-1})$ mit $x$, was auf diff --git a/buch/chapters/010-potenzen/potenzreihen.tex b/buch/chapters/010-potenzen/potenzreihen.tex index a003fcb..994f99f 100644 --- a/buch/chapters/010-potenzen/potenzreihen.tex +++ b/buch/chapters/010-potenzen/potenzreihen.tex @@ -105,6 +105,7 @@ Für $|z|<1$ geht $z^n\to 0$ für $n\to\infty$, die Partialsummen konvergieren und wir erhalten das Resultat des folgenden Satzes. \begin{satz} +\index{Satz!geometrische Reihe}% \label{buch:polynome:satz:geometrischereihe} Die geometrische Reihe $a+az+az^2+\dots$ konvergiert für $|z|<1$ und hat die Summe @@ -124,6 +125,7 @@ als konvergent erkannten Reihen nachweisbar. Dies ist der Inhalt des folgenden, wohlbekannten Majorantenkriteriums. \begin{satz}[Majorantenkriterium] +\index{Satz!Majorantenkriterium}% \label{buch:polynome:satz:majorantenkriterium} \index{Majorantenkriterium} Seien $a_k$ und $b_k$ die Glieder zweier unendlicher Reihen. @@ -142,6 +144,7 @@ Potenzreihen mit der geometrischen Reihe zu vergleichen und liefert damit einfach anzuwende Kriterien für die Konvergenz. \begin{satz}[Quotientenkriterium] +\index{Satz!Quotientenkriterium}% \label{buch:polynome:satz:quotientenkriterium} \index{Quotientenkriterium}% Eine Reihe @@ -175,6 +178,7 @@ die unter der gegebenen Voraussetzung konvergiert. \end{proof} \begin{satz}[Wurzelkriterium] +\index{Satz!Wurzelkriterium}% \label{buch:polynome:satz:wurzelkriterium} \index{Wurzelkriterium} Falls @@ -203,6 +207,9 @@ das Reststück der Reihe ab Index $N$ ist daher wieder majorisiert durch eine konvergente geometrische Reihe. \end{proof} +% +% Konvergenzradius +% \subsubsection{Konvergenzradius} Das Quotienten- und das Wurzel-Kriterium ist auf beliebige Reihen anwendbar, es berücksichtigt nicht, dass in einer Potenzreihe @@ -224,6 +231,7 @@ um den Punkt $z_0$ ist \end{definition} \begin{satz} +\index{Satz!Konvergenzradius}% \label{buch:polynome:satz:konvergenzradius} Der Konvergenzradius $\varrho$ einer Potenzreihe $\sum_{k=0}^\infty a_k(z-z_0)^k$ ist @@ -420,7 +428,7 @@ $z_0$ ist die Summe \frac{f^{(k)}(z_0)}{k!} (z-z_0)^k \label{buch:polynome:eqn:taylor-polynom} \end{equation} -\index{Taylor-Reihe} +\index{Taylor-Reihe}% Die {\em Taylor-Reihe} der Funktion $f(z)$ ist die Reihe \begin{equation} \mathscr{T}_{z_0}f (z) @@ -431,7 +439,9 @@ Die {\em Taylor-Reihe} der Funktion $f(z)$ ist die Reihe \end{equation} \end{definition} - +% +% Analytische Funktionen +% \subsubsection{Analytische Funktionen} Das Taylor-Polynom $\mathscr{T}_{z_0}^nf(z)$ hat an der Stelle $z_0$ die gleichen Funktionswerte und Ableitungen wie die Funktion $f(z)$, diff --git a/buch/chapters/010-potenzen/tschebyscheff.tex b/buch/chapters/010-potenzen/tschebyscheff.tex index 780be1b..ccc2e97 100644 --- a/buch/chapters/010-potenzen/tschebyscheff.tex +++ b/buch/chapters/010-potenzen/tschebyscheff.tex @@ -250,6 +250,7 @@ lässt sich auch eine Multiplikationsformel ableiten. \index{Multiplikationsformel}% \begin{satz} +\index{Satz!Multiplikationsformel für Tschebyscheff-Polynome}% Es gilt \begin{align} T_m(x)T_n(x)&=\frac12\bigl(T_{m+n}(x) + T_{m-n}(x)\bigr) @@ -306,7 +307,7 @@ Damit ist auch \eqref{buch:potenzen:tschebyscheff:mult2} bewiesen. % % Differentialgleichung % -\subsubsection{Differentialgleichung} +\subsubsection{Tschebyscheff-Differentialgleichung} Die Ableitungen der Tschebyscheff-Polynome sind \begin{align*} T_n(x) @@ -374,7 +375,10 @@ Die Tschebyscheff-Polynome sind Lösungen der Differentialgleichung (1-x^2) T_n''(x) -x T_n'(x) +n^2 T_n(x) = 0. \label{buch:potenzen:tschebyscheff:dgl} \end{equation} - +Die Differentialgleichung~\eqref{buch:potenzen:tschebyscheff:dgl} +heisst {\em Tschebyscheff-Differentialgleichung}. +\index{Tschebyscheff-Differentialgleichung}% +\index{Differentialgleichung!Tschebyscheff-}% diff --git a/buch/chapters/020-exponential/lambertw.tex b/buch/chapters/020-exponential/lambertw.tex index 9077c6f..d78fdc3 100644 --- a/buch/chapters/020-exponential/lambertw.tex +++ b/buch/chapters/020-exponential/lambertw.tex @@ -220,6 +220,7 @@ mit $P_1(t)=1$. % \subsubsection{Differentialgleichung und Stammfunktion} \index{Lambert-W-Funktion@Lambert-$W$-Funktion!Differentialgleichung}% +\index{Differentialgleichung!der Lambert-$W$-Funktion}% Die Ableitungsformel \eqref{buch:lambert:eqn:ableitung} bedeutet auch, dass die $W$-Funktion eine Lösung der Differentialgleichung \[ @@ -355,6 +356,8 @@ eigenen Implementation behelfen. Für $x>-1$ ist die Funktion $W(x)$ ist die Umkehrfunktion der streng monoton wachsenden und konvexen Funktion $f(x)=xe^x$. In dieser Situation konvergiert der Newton-Algorithmus zur Bestimmung +\index{Newton-Algorithmus}% +\index{Algorithmus!Newton-}% der Nullstelle $x=W_0(y)$ von $f(x)-y$ für alle Werte von $y>-1/e$. Für $W_{-1}(y)$ ist die Situation etwas komplizierter, da für $x<-1$ die Funktion $f(x)$ nicht konvex ist. @@ -386,7 +389,7 @@ bestimmt werden. \subsubsection{GNU scientific library} Die Lambert $W$-Funktionen $W_0(x)$ und $W_{-1}(x)$ sind auch in der GNU scientific library \cite{buch:library:gsl} implementiert. - +\index{GNU scientifi library}% diff --git a/buch/chapters/030-geometrie/hyperbolisch.tex b/buch/chapters/030-geometrie/hyperbolisch.tex index 72c2cb4..2938316 100644 --- a/buch/chapters/030-geometrie/hyperbolisch.tex +++ b/buch/chapters/030-geometrie/hyperbolisch.tex @@ -355,6 +355,7 @@ heissen der {\em hyperbolische Tangens} und der {\em hyperbolische Kotangens}. \end{definition} \begin{satz} +\index{Satz!hyperbolische Gruppe}% \label{buch:geometrie:hyperbolisch:Hparametrisierung} Die orientierungserhaltenden $2\times 2$-Matrizen, die das Minkowski-Skalarprodukt invariant lassen und die Zeitrichtung diff --git a/buch/chapters/030-geometrie/trigonometrisch.tex b/buch/chapters/030-geometrie/trigonometrisch.tex index 047e6cb..643c8f2 100644 --- a/buch/chapters/030-geometrie/trigonometrisch.tex +++ b/buch/chapters/030-geometrie/trigonometrisch.tex @@ -394,6 +394,7 @@ D_{\alpha}D_{\beta} Aus dem Vergleich der beiden Matrizen liest man die Additionstheoreme. \begin{satz} +\index{Satz!Drehmatrizen}% Für $\alpha,\beta\in\mathbb{R}$ gilt \begin{align*} \sin(\alpha\pm\beta) diff --git a/buch/chapters/040-rekursion/beta.tex b/buch/chapters/040-rekursion/beta.tex index 35ff758..20e3f0e 100644 --- a/buch/chapters/040-rekursion/beta.tex +++ b/buch/chapters/040-rekursion/beta.tex @@ -234,6 +234,7 @@ Durch Einsetzen der Integralformel im Ausdruck Satz. \begin{satz} +\index{Satz!Beta-Funktion und Gamma-Funktion}% Die Beta-Funktion kann aus der Gamma-Funktion nach \begin{equation} B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} @@ -423,6 +424,7 @@ Die trigonometrische Substitution kann dazu verwendet werden, die Legendresche Verdoppelungsformel für die Gamma-Funktion herzuleiten. \begin{satz}[Legendre] +\index{Satz!Verdoppelungsformel@Verdoppelungsformel für $\Gamma(x)$}% \[ \Gamma(x)\Gamma(x+{\textstyle\frac12}) = diff --git a/buch/chapters/040-rekursion/gamma.tex b/buch/chapters/040-rekursion/gamma.tex index 2b0700e..7f19637 100644 --- a/buch/chapters/040-rekursion/gamma.tex +++ b/buch/chapters/040-rekursion/gamma.tex @@ -240,6 +240,7 @@ Durch Iteration der Rekursionsformel für $\Gamma(x)$ folgt jetzt Damit folgt \begin{satz} +\index{Satz!Pochhammer-Symbol@Pochhammer-Symbol und $\Gamma(x)$}% \label{buch:rekursion:gamma:satz:gamma-pochhammer} Die Rekursionsformel für die Gamma-Funktion kann geschrieben werden als \[ @@ -344,6 +345,7 @@ in den Zähler zu bringen, so dass er der Konvergenz etwas nachhilft. Wir berechnen daher den Kehrwert $1/\Gamma(x)$. \begin{satz} +\index{Satz!Produktformel@Produktformel für $\Gamma(x)$}% \label{buch:rekursion:gamma:satz:produktformel} Der Kehrwert der Gamma-Funktion kann geschrieben werden als \begin{equation} @@ -695,6 +697,7 @@ Laplace-Transformation der Potenzfunktion zu berechnen. \index{Laplace-Transformierte der Potenzfunktion}% \begin{satz} +\index{Satz!Laplace-Transformierte der Potenzfunktion}% Die Laplace-Transformierte der Potenzfunktion $f(t)=t^\alpha$ ist \[ (\mathscr{L}f)(s) diff --git a/buch/chapters/040-rekursion/hypergeometrisch.tex b/buch/chapters/040-rekursion/hypergeometrisch.tex index 3b72ffa..13ba3b2 100644 --- a/buch/chapters/040-rekursion/hypergeometrisch.tex +++ b/buch/chapters/040-rekursion/hypergeometrisch.tex @@ -68,6 +68,7 @@ oder Binomialkoeffizienten definiert sind, wie die beiden folgenden Sätze zeigen. \begin{satz} +\index{Satz!Quotienten von Fakultäten}% \label{buch:rekursion:hypergeometrisch:satz:fakquo} Der Quotient aufeinanderfolgender Folgenglieder der Folge $c_k=(a+bk)!$ ist der ein Polynom vom Grad $b$. @@ -89,6 +90,7 @@ Das Pochhammer-Symbol hat $b$ Faktoren, es ist ein Polynom vom Grad $b$. \end{proof} \begin{satz} +\index{Satz!Quotienten von Binomialkoeffizienten}% \label{buch:rekursion:hypergeometrisch:satz:binomquo} Die Quotienten aufeinanderfolgender Werte der Binomialkoeffizienten \[ @@ -432,6 +434,7 @@ Definition~\ref{buch:rekursion:hypergeometrisch:def} offensichtlichen Regeln: \begin{satz}[Permutationsregel] +\index{Satz!Permutationsregel für hypergeometrische Funktionen}% \label{buch:rekursion:hypergeometrisch:satz:permuationsregel} Sei $\pi$ eine beliebige Permutation der Zahlen $1,\dots,p$ und $\sigma$ eine beliebige Permutation der Zahlen $1,\dots,q$, dann ist @@ -454,6 +457,7 @@ a_{\pi(1)},\dots,a_{\pi(p)}\\b_{\sigma(1)},\dots,b_{\sigma(q)} \end{satz} \begin{satz}[Kürzungsformel] +\index{Satz!Kürzungsformel für hypergeometrische Funktionen}% \label{buch:rekursion:hypergeometrisch:satz:kuerzungsregel} Stimmt einer der Koeffizienten $a_k$ mit einem der Koeffizienten $b_i$ überein, dann können sie weggelassen werden: diff --git a/buch/chapters/050-differential/bessel.tex b/buch/chapters/050-differential/bessel.tex index 4e1c58c..ac509ba 100644 --- a/buch/chapters/050-differential/bessel.tex +++ b/buch/chapters/050-differential/bessel.tex @@ -28,6 +28,8 @@ Die Besselsche Differentialgleichung ist die Differentialgleichung x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} + (x^2-\alpha^2)y = 0 \label{buch:differentialgleichungen:eqn:bessel} \end{equation} +\index{Differentialgleichung!Besselsche}% +\index{Besselsche Differentialgleichung}% zweiter Ordnung für eine auf dem Interval $[0,\infty)$ definierte Funktion $y(x)$. Der Parameter $\alpha$ ist eine beliebige komplexe Zahl $\alpha\in \mathbb{C}$, @@ -41,6 +43,7 @@ Die Besselsche Differentialgleichung \eqref{buch:differentialgleichungen:eqn:bessel} kann man auch als Eigenwertproblem für den Bessel-Operator \index{Bessel-Operator}% +\index{Operator!Bessel-}% \begin{equation} B = x^2\frac{d^2}{dx^2} + x\frac{d}{dx} + x^2 \label{buch:differentialgleichungen:bessel-operator} @@ -468,6 +471,7 @@ Die erzeugende Funktion kann dazu verwendet werden, das Additionstheorem für die Besselfunktionen zu beweisen. \begin{satz} +\index{Satz!Additionstheorem für Besselfunktionen}% Für $l\in\mathbb{Z}$ und $x,y\in\mathbb{R}$ gilt \[ J_l(x+y) = \sum_{m=-\infty}^\infty J_m(x)J_{l-m}(y). diff --git a/buch/chapters/050-differential/hypergeometrisch.tex b/buch/chapters/050-differential/hypergeometrisch.tex index 87b9318..2fe43c1 100644 --- a/buch/chapters/050-differential/hypergeometrisch.tex +++ b/buch/chapters/050-differential/hypergeometrisch.tex @@ -371,6 +371,7 @@ $c$ darf also kein natürliche Zahl $\ge 2$ sein. Wir fassen die Resultate dieses Abschnitts im folgenden Satz zusammen. \begin{satz} +\index{Satz!Lösung der eulerschen hypergeometrischen Differentialgleichung}% Die eulersche hypergeometrische Differentialgleichung \begin{equation} x(1-x)\frac{d^2y}{dx^2} @@ -906,6 +907,7 @@ Funktion wohldefiniert. Wir fassen diese Resultat zusammen: \begin{satz} +\index{Satz!1f1@Differentialgleichung von $\mathstrut_1F_1$}% \label{buch:differentialgleichungen:satz:1f1-dgl-loesungen} Die Differentialgleichung \[ diff --git a/buch/chapters/050-differential/potenzreihenmethode.tex b/buch/chapters/050-differential/potenzreihenmethode.tex index d046f06..9f2e0a6 100644 --- a/buch/chapters/050-differential/potenzreihenmethode.tex +++ b/buch/chapters/050-differential/potenzreihenmethode.tex @@ -44,6 +44,7 @@ Tatsächlich gilt der folgende sehr viel allgemeinere Satz von Cauchy und Kowalevskaja: \begin{satz}[Cauchy-Kowalevskaja] +\index{Satz!von Cauchy-Kowalevskaja}% Eine partielle Differentialgleichung der Ordnung $k$ für eine Funktion $u(x_1,\dots,x_n,t)=u(x,t)$ in expliziter Form @@ -334,6 +335,7 @@ wir die Darstellung Damit haben wir den folgenden Satz gezeigt. \begin{satz} +\index{Satz!Newtonsche Reihe}% \label{buch:differentialgleichungen:satz:newtonschereihe} Die Newtonsche Reihe für $(1-t)^\alpha$ ist der Wert \[ diff --git a/buch/chapters/060-integral/eulertransformation.tex b/buch/chapters/060-integral/eulertransformation.tex index a597892..65d48b2 100644 --- a/buch/chapters/060-integral/eulertransformation.tex +++ b/buch/chapters/060-integral/eulertransformation.tex @@ -93,6 +93,7 @@ Durch Auflösung nach der hypergeometrischen Funktion bekommt man die folgende Integraldarstellung. \begin{satz}[Euler] +\index{Satz!Eulertransformation}% \label{buch:integrale:eulertransformation:satz} Die hypergeometrische Funktion $\mathstrut_2F_1$ kann durch das Integral @@ -219,6 +220,7 @@ Funktionen $\mathstrut_{p+1}F_{q+1}$ durch ein Integral, dessen Integrand $\mathstrut_pF_q$ enthält, ausdrücken lässt. \begin{satz} +\index{Satz!Euler-Transformationformel}% Es gilt die sogennannte Euler-Transformationsformel \index{Euler-Transformation}% \[ diff --git a/buch/chapters/060-integral/fehlerfunktion.tex b/buch/chapters/060-integral/fehlerfunktion.tex index 581e56a..6b87044 100644 --- a/buch/chapters/060-integral/fehlerfunktion.tex +++ b/buch/chapters/060-integral/fehlerfunktion.tex @@ -622,7 +622,9 @@ Resultat für die Laplace-Transformierte von $f(t)$, sie ist \frac1s\biggl(1-\frac12e^{-a\sqrt{s}} \biggr). \] -\begin{satz} Die Laplace-Transformierte der Fehlerfunktion mit Argument +\begin{satz} +\index{Satz!Laplace-Transformierte der Fehlerfunktion}% +Die Laplace-Transformierte der Fehlerfunktion mit Argument $a/2\sqrt{t}$ ist \begin{equation} f(t) = \operatorname{erf}\biggl(\frac{a}{2\sqrt{t}}\biggr) diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index 480a37d..a5af7d2 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -230,6 +230,7 @@ Sei $R_n=\{p(X)\in\mathbb{R}[X] \mid \deg p\le n\}$ der Vektorraum der Polynome vom Grad $n$. \begin{satz} +\index{Satz!Gaussquadratur}% \label{buch:integral:satz:gaussquadratur} Sei $p$ ein Polynom vom Grad $n$, welches auf allen Polynomen in $R_{n-1}$ orthogonal sind. @@ -307,6 +308,7 @@ Für eine beliebige Funktion kann man die folgende Fehlerabschätzung angeben \cite[theorem 7.3.4, p.~497]{buch:numal}. \begin{satz} +\index{Satz!Gausssche Quadraturformel und Fehler}% Seien $x_i$ die Stützstellen und $A_i$ die Gewichte einer Gaussschen Quadraturformel mit $n+1$ Stützstellen und sei $f$ eine auf dem Interval $[-1,1]$ $2n+2$-mal stetig differenzierbare diff --git a/buch/chapters/070-orthogonalitaet/legendredgl.tex b/buch/chapters/070-orthogonalitaet/legendredgl.tex index c4eaf97..f3dd53f 100644 --- a/buch/chapters/070-orthogonalitaet/legendredgl.tex +++ b/buch/chapters/070-orthogonalitaet/legendredgl.tex @@ -22,6 +22,8 @@ verschiedenen Eigenwerten orthogonal sind. % \subsection{Legendre-Differentialgleichung} Die {\em Legendre-Differentialgleichung} ist die Differentialgleichung +\index{Differentialgleichung!Legendre-}% +\index{Legendre-Differentialgleichung}% \begin{equation} (1-x^2) y'' - 2x y' + n(n+1) y = 0 \label{buch:integral:eqn:legendre-differentialgleichung} @@ -451,6 +453,7 @@ ein anderer Weg zu einer zweiten Lösung gesucht werden. \subsubsection{Die assoziierte Laguerre-Differentialgleichung} \index{assoziierte Laguerre-Differentialgleichung}% \index{Laguerre-Differentialgleichung, assoziierte}% +\index{Differentialgleichung!assoziierte Laguerre-}% Die {\em assoziierte Laguerre-Differentialgleichung} ist die Differentialgleichung \begin{equation} diff --git a/buch/chapters/070-orthogonalitaet/rekursion.tex b/buch/chapters/070-orthogonalitaet/rekursion.tex index c0efc6d..3dd9de5 100644 --- a/buch/chapters/070-orthogonalitaet/rekursion.tex +++ b/buch/chapters/070-orthogonalitaet/rekursion.tex @@ -44,6 +44,7 @@ Der folgende Satz besagt, dass $p_n(x)$ eine Rekursionsbeziehung mit nur drei Termen erfüllt. \begin{satz} +\index{Satz!Drei-Term-Rekursion}% \label{buch:orthogonal:satz:drei-term-rekursion} Eine Folge bezüglich $\langle\,\;,\;\rangle_w$ orthogonaler Polynome $p_n$ mit dem Grade $\deg p_n = n$ erfüllt eine Rekursionsbeziehung der Form diff --git a/buch/chapters/070-orthogonalitaet/rodrigues.tex b/buch/chapters/070-orthogonalitaet/rodrigues.tex index 39b01b9..4852624 100644 --- a/buch/chapters/070-orthogonalitaet/rodrigues.tex +++ b/buch/chapters/070-orthogonalitaet/rodrigues.tex @@ -82,6 +82,7 @@ um $2$ erhöhen, die Ableitung wird ihn wieder um $1$ reduzieren. Etwas formeller kann man dies wie folgt formulieren: \begin{satz} +\index{Satz!Rodrigues-Rekursionsformel}% Für alle $n\ge 0$ ist \begin{equation} q_n(x) @@ -163,6 +164,7 @@ orthogonal sind. Dies ist der Inhalt des folgenden Satzes. \begin{satz} +\index{Satz!Rodrigues-Formel für orthonormierte Polynome}% Es gibt Konstanten $c_n$ derart, dass \[ p_n(x) @@ -464,6 +466,8 @@ hat die Ableitung w'(x) = -e^{-x}, \] die Pearsonsche Differentialgleichung ist daher +\index{Pearsonsche Differentialgleichung}% +\index{Differentialgleichung!Pearsonsche}% \[ \frac{w'(x)}{w(x)}=\frac{-1}{1}. \] @@ -562,6 +566,8 @@ an der Stelle $0$. Wir fassen die Resultate im folgenden Satz zusammen. \begin{satz} +\index{Satz!Laguerre-Polynome}% +\index{Polynome!Laguerre-}% Die Laguerre-Polynome vom Grad $n$ haben die Form \begin{equation} L_n(x) diff --git a/buch/chapters/070-orthogonalitaet/saev.tex b/buch/chapters/070-orthogonalitaet/saev.tex index c667297..599d3a0 100644 --- a/buch/chapters/070-orthogonalitaet/saev.tex +++ b/buch/chapters/070-orthogonalitaet/saev.tex @@ -18,6 +18,7 @@ Der Beweis ist direkt übertragbar, wir halten das Resultat hier für spätere Verwendung fest. \begin{satz} +\index{Satz!orthogonale Eigenvektoren}% Sind $f$ und $g$ Eigenvektoren eines selbstadjungierten Operators $A$ zu verschiedenen Eigenwerten $\lambda$ und $\mu$, dann sind $f$ und $g$ orthogonal. diff --git a/buch/chapters/070-orthogonalitaet/sturm.tex b/buch/chapters/070-orthogonalitaet/sturm.tex index 164cd9a..742ec0a 100644 --- a/buch/chapters/070-orthogonalitaet/sturm.tex +++ b/buch/chapters/070-orthogonalitaet/sturm.tex @@ -7,6 +7,7 @@ \label{buch:integrale:subsection:sturm-liouville-problem}} \rhead{Das Sturm-Liouville-Problem} Sowohl bei den Bessel-Funktionen wie bei den Legendre-Polynomen +\index{Bessel-Funktion}% konnte die Orthogonalität der Funktionen dadurch gezeigt werden, dass sie als Eigenfunktionen eines bezüglich eines geeigneten Skalarproduktes selbstadjungierten Operators erkannt wurden. @@ -57,6 +58,7 @@ Für symmetrische Matrizen lässt sich dieses Problem auf ein Optimierungsproblem reduzieren. \begin{satz} +\index{Satz!verallgemeinertes Eigenwertproblem}% Seien $A$ und $B$ symmetrische $n\times n$-Matrizen und sei ausserdem $B$ positiv definit. Ist $v$ ein Vektor, der die Grösse @@ -127,6 +129,7 @@ Eigenwert $\lambda$ ist. \end{proof} \begin{satz} +\index{Satz!Orthogonalität verallgemeinerter Eigenvektoren}% Verallgemeinerte Eigenvektoren $u$ und $v$ von $A$ und $B$ zu verschiedenen Eigenwerten erfüllen $u^tBv=0$. \end{satz} @@ -153,6 +156,8 @@ dass $u^tBv=0$ sein muss. Verallgemeinerte Eigenwerte und Eigenvektoren verhalten sich also ganz analog zu den gewöhnlichen Eigenwerten und Eigenvektoren. Da $B$ positiv definit ist, ist $B$ auch invertierbar. +\index{verallgemeinertes Skalarprodukt}% +\index{Skalarprodukt!verallgemeinertes}% Zudem kann $B$ zur Definition des verallgemeinerten Skalarproduktes \[ \langle u,v\rangle_B = u^tBv @@ -201,6 +206,7 @@ Bezüglich des gewöhnlichen Skalarproduktes für Funktionen auf dem Intervall $[a,b]$ ist der Operator $L_0$ tatsächlich selbstadjungiert. Mit partieller Integration rechnet man nach: +\index{partielle Integration}% \begin{align} \langle f,L_0g\rangle &= @@ -376,6 +382,8 @@ L = \frac{1}{w(x)} \biggl(-\frac{d}{dx} p(x)\frac{d}{dx} + q(x)\biggr) \label{buch:orthogonal:sturm-liouville:opL1} \end{equation} heisst der {\em Sturm-Liouville-Operator}. +\index{Sturm-Liouville-Operator}% +\index{Operator!Sturm-Liouville-}% Eine Lösung des Sturm-Liouville-Problems ist eine Funktion $y(x)$ derart, dass \[ @@ -529,7 +537,10 @@ Im Folgenden sollen hingegen die Funktionen $J_n(s x)$ für konstantes $n$, aber verschiedene $s$ untersucht und als orthogonal erkannt werden. -Die Funktion $y(x) = J_n(x)$ ist eine Lösung der Bessel-Differentialgleichung +Die Funktion $y(x) = J_n(x)$ ist eine Lösung der Besselschen +Differentialgleichung +\index{Besselsche Differentialgleichung}% +\index{Differentialgleichung!Besselsche}% \[ x^2y'' + xy' + x^2y = n^2y. \] @@ -616,6 +627,7 @@ des Sturm-Liouville-Problems für den Eigenwert $\lambda = -s^2$. \begin{satz}[Orthogonalität der Bessel-Funktionen] +\index{Satz!Orthogonalität der Bessel-Funktionen}% Die Bessel-Funktionen $J_n(sx)$ für verschiedene $s$ sind orthogonal bezüglich des Skalarproduktes mit der Gewichtsfunktion $w(x)=x$, d.~h. @@ -696,6 +708,8 @@ des Skalarproduktes mit der Laguerre-Gewichtsfunktion. Die Tschebyscheff-Polynome sind Lösungen der bereits in Kapitel~\ref{buch:chapter:potenzen} hergeleiteten Tschebyscheff-Differentialgleichung~\eqref{buch:potenzen:tschebyscheff:dgl} +\index{Tschebyscheff-Differentialgleichung}% +\index{Differentialgleichung!Tschebyscheff-}% \[ (1-x^2)y'' -xy' = n^2y \] @@ -727,6 +741,7 @@ xy'(x) \lambda y(x). \end{align*} Es folgt, dass die Tschebyscheff-Polynome orthogonal sind +\index{Tschebyscheff-Polynom}% bezüglich des Skalarproduktes \[ \langle f,g\rangle = \int_{-1}^1 f(x)g(x)\frac{dx}{\sqrt{1-x^2}}. @@ -737,6 +752,8 @@ bezüglich des Skalarproduktes % \subsubsection{Jacobi-Polynome} Die Jacobi-Polynome sind orthogonal bezüglich des Skalarproduktes +\index{Jacobi-Polynome}% +\index{Polynome!Jacobi-}% mit der Gewichtsfunktion \[ w^{(\alpha,\beta)}(x) = (1-x)^\alpha(1+x)^\beta, @@ -814,6 +831,8 @@ als Sturm-Liouville-Differentialgleichung erkannt. \subsubsection{Hypergeometrische Differentialgleichungen} %\url{https://encyclopediaofmath.org/wiki/Hypergeometric_equation} Auch die Eulersche hypergeometrische Differentialgleichung +\index{Eulersche hypergeometrische Differentialgleichung}% +\index{Differentialgleichung!Eulersche hypergeometrische}% lässt sich in die Form eines Sturm-Liouville-Operators \index{Eulersche hypergeometrische Differentialgleichung!als Sturm-Liouville-Gleichung}% bringen. diff --git a/buch/chapters/080-funktionentheorie/analytisch.tex b/buch/chapters/080-funktionentheorie/analytisch.tex index 3095cc1..08196f1 100644 --- a/buch/chapters/080-funktionentheorie/analytisch.tex +++ b/buch/chapters/080-funktionentheorie/analytisch.tex @@ -9,6 +9,9 @@ Holomorphe Funktionen zeichnen sich dadurch aus, dass sie auch immer eine konvergente Reihenentwicklung haben, sie sind also analytisch. +% +% Definition +% \subsection{Definition} \index{Taylor-Reihe}% \index{Exponentialfunktion}% @@ -90,29 +93,29 @@ Damit ist gezeigt, dass alle Ableitungen $f^{(n)}(0)=0$ sind. Die Taylorreihe von $f(x)$ ist daher die Nullfunktion. \end{beispiel} -Die Klasse der Funktionen, die sich durch ihre Taylor-Reihe darstellen -lassen, zeichnet sich also durch besondere Eigenschaften aus, die in -der folgenden Definition zusammengefasst werden. - -\index{analytisch in einem Punkt}% -\index{analytisch}% -\begin{definition} -Eine auf einem offenen Intervall $I\subset \mathbb {R}$ definierte Funktion -$f\colon U\to\mathbb{R}$ heisst {\em analytisch im Punkt $x_0\in I$}, wenn -es eine in einer Umgebung von $x_0$ konvergente Potenzreihe -\[ -\sum_{k=0}^\infty a_k(x-x_0)^k = f(x) -\] -gibt. -Sie heisst {\em analytisch}, wenn sie analytisch ist in jedem Punkt von $I$. -\end{definition} - -Es ist wohlbekannt aus der elementaren Theorie der Potenzreihen, dass +%Die Klasse der Funktionen, die sich durch ihre Taylor-Reihe darstellen +%lassen, zeichnet sich also durch besondere Eigenschaften aus, die in +%der folgenden Definition zusammengefasst werden. +% +%\index{analytisch in einem Punkt}% +%\index{analytisch}% +%\begin{definition} +%Eine auf einem offenen Intervall $I\subset \mathbb {R}$ definierte Funktion +%$f\colon U\to\mathbb{R}$ heisst {\em analytisch im Punkt $x_0\in I$}, wenn +%es eine in einer Umgebung von $x_0$ konvergente Potenzreihe +%\[ +%\sum_{k=0}^\infty a_k(x-x_0)^k = f(x) +%\] +%gibt. +%Sie heisst {\em analytisch}, wenn sie analytisch ist in jedem Punkt von $I$. +%\end{definition} + +Es ist bekannt aus der elementaren Theorie der Potenzreihen +in Kapitel~\ref{buch:potenzen:section:potenzreihen}, dass eine analytische Funktion beliebig oft differenzierbar ist und dass die Potenzreihe im Punkt $x_0$ die Taylor-Reihe sein muss. -Ausserdem sidn Summen, Differenzen und Produkte von analytischen Funktionen +Ausserdem sind Summen, Differenzen und Produkte von analytischen Funktionen wieder analytisch. - Für eine komplexe Funktion lässt sich der Begriff der analytischen Funktion genau gleich definieren. @@ -131,8 +134,8 @@ Die Verwendung einer offenen Teilmenge $U\subset\mathbb{C}$ ist wesentlich, denn die Funktion $f\colon z\mapsto \overline{z}$ kann in jedem Punkt $x_0\in\mathbb{R}$ der reellen Achse $\mathbb{R}\subset\mathbb{C}$ durch die Potenzreihe -$f(x) = x_0 + (x-x_0)$ dargestellt werden. -Es gibt aber keine Potenzreihe, die $f(z)$ in einer offenen Teilmenge +$f(x) = x_0 + (x-x_0)$ dargestellt werden, +es gibt aber keine Potenzreihe, die $f(z)$ in einer offenen Teilmenge von $\mathbb{C}$ gegen $f(z)=\overline{z}$ konvergiert. % @@ -140,18 +143,20 @@ von $\mathbb{C}$ gegen $f(z)=\overline{z}$ konvergiert. % \subsection{Konvergenzradius \label{buch:funktionentheorie:subsection:konvergenzradius}} -In der Theorie der Potenzreihen, die man in einem grundlegenden -Analysiskurs lernt, wird auch genauer untersucht, wie gross +In der Theorie der Potenzreihen, wie sie in Kapitel~\ref{buch:chapter:potenzen} +zusammengefasst wurde, wird auch untersucht, wie gross eine Umgebung des Punktes $z_0$ ist, in der die Potenzreihe im Punkt $z_0$ einer analytischen Funktion konvergiert. +Die Definition des Konvergenzradius gilt auch für komplexe Funktionen. \begin{satz} +\index{Satz!Konvergenzradius}% \label{buch:funktionentheorie:satz:konvergenzradius} Die Potenzreihe \[ f(z) = \sum_{k=0}^\infty a_0(z-z_0)^k \] -ist konvergent auf einem Kreis mit Radius $\varrho$ und +ist konvergent auf einem Kreis um $z_0$ mit Radius $\varrho$ und \[ \frac{1}{\varrho} = diff --git a/buch/chapters/080-funktionentheorie/carlson.tex b/buch/chapters/080-funktionentheorie/carlson.tex index 1923351..41fb5e8 100644 --- a/buch/chapters/080-funktionentheorie/carlson.tex +++ b/buch/chapters/080-funktionentheorie/carlson.tex @@ -24,6 +24,8 @@ beschränkt ist und an den Stellen $z=1,2,3,\dots$ verschwindet. Dann ist $f(z)=0$. \end{satz} +\index{Satz!von Carlson}% +\index{Carlson, Satz von}% \begin{figure} \centering \includegraphics{chapters/080-funktionentheorie/images/carlsonpath.pdf} diff --git a/buch/chapters/080-funktionentheorie/cauchy.tex b/buch/chapters/080-funktionentheorie/cauchy.tex index 58504db..bd07a2f 100644 --- a/buch/chapters/080-funktionentheorie/cauchy.tex +++ b/buch/chapters/080-funktionentheorie/cauchy.tex @@ -135,6 +135,7 @@ Wie Wahl der Parametrisierung der Kurve hat keinen Einfluss auf den Wert des Wegintegrals. \begin{satz} +\index{Satz!Kurvenparametrisierung}% Seien $\gamma_1(t), t\in[a,b],$ und $\gamma_2(s),s\in[c,d]$ verschiedene Parametrisierungen \index{Parametrisierung}% diff --git a/buch/chapters/080-funktionentheorie/gammareflektion.tex b/buch/chapters/080-funktionentheorie/gammareflektion.tex index 017c850..4a8f41f 100644 --- a/buch/chapters/080-funktionentheorie/gammareflektion.tex +++ b/buch/chapters/080-funktionentheorie/gammareflektion.tex @@ -12,6 +12,7 @@ die durch Spiegelung an der Geraden $\operatorname{Re}x=\frac12$ auseinander hervorgehen, und einem speziellen Beta-Integral her. \begin{satz} +\index{Satz!Spiegelungsformel für $\Gamma(x)$}% \label{buch:funktionentheorie:satz:spiegelungsformel} Für $0b>0$ ist, nimmt die Folge $(a_k)_{k\ge 0}$ monoton ab und $(b_k)_{k\ge 0}$ nimmt monoton zu. Beide konvergieren quadratisch gegen einen gemeinsamen Grenzwert. @@ -636,6 +638,7 @@ mit einem Computer-Algebra-System ausführen lässt finden, dass tatsächlich korrekt ist. \begin{satz} +\index{Satz!Gauss-Integrale}% \label{buch:elliptisch:agm:integrale} Für $a_1=(a+b)/2$ und $b_1=\sqrt{ab}$ gilt \[ @@ -653,6 +656,7 @@ Dies gilt natürlich für alle Glieder der Folge zur Bestimmung des arithmetisch-geometrischen Mittels. \begin{satz} +\index{Satz!Iab@$I(a,b)$ und arithmetisch geometrisches Mittel}% Für $a\ge b>0$ gilt \begin{equation} I(a,b) @@ -719,6 +723,7 @@ k=\sqrt{1-k^{\prime 2}} \end{align*} \begin{satz} +\index{Satz!vollständige elliptische Integrale und arithmetisch-geometrisches Mittel}% \label{buch:elliptisch:agm:satz:Ek} Für $0 Date: Mon, 4 Jul 2022 19:35:36 +0200 Subject: images updated, nav/bsp.tex -> nav/bsp2.tex --- buch/papers/nav/bilder/beispiele1.pdf | Bin 399907 -> 399925 bytes buch/papers/nav/bilder/beispiele2.pdf | Bin 404679 -> 404688 bytes buch/papers/nav/bsp2.tex | 235 ++++++++++++++++++++++++ buch/papers/nav/images/beispiele/beispiele1.pdf | Bin 399907 -> 399925 bytes buch/papers/nav/images/beispiele/beispiele1.tex | 4 +- buch/papers/nav/images/beispiele/beispiele2.pdf | Bin 404679 -> 404688 bytes buch/papers/nav/images/beispiele/beispiele2.tex | 4 +- buch/papers/nav/images/beispiele/beispiele3.pdf | Bin 401946 -> 401946 bytes buch/papers/nav/images/beispiele/common.tex | 16 +- buch/papers/nav/main.tex | 2 +- 10 files changed, 248 insertions(+), 13 deletions(-) create mode 100644 buch/papers/nav/bsp2.tex diff --git a/buch/papers/nav/bilder/beispiele1.pdf b/buch/papers/nav/bilder/beispiele1.pdf index d0fe3dc..1f91809 100644 Binary files a/buch/papers/nav/bilder/beispiele1.pdf and b/buch/papers/nav/bilder/beispiele1.pdf differ diff --git a/buch/papers/nav/bilder/beispiele2.pdf b/buch/papers/nav/bilder/beispiele2.pdf index 8579ee5..4b28f2f 100644 Binary files a/buch/papers/nav/bilder/beispiele2.pdf and b/buch/papers/nav/bilder/beispiele2.pdf differ diff --git a/buch/papers/nav/bsp2.tex b/buch/papers/nav/bsp2.tex new file mode 100644 index 0000000..fe8f423 --- /dev/null +++ b/buch/papers/nav/bsp2.tex @@ -0,0 +1,235 @@ +\section{Beispielrechnung} + +\subsection{Einführung} +In diesem Abschnitt wird die Theorie vom Abschnitt 21.6 in einem Praxisbeispiel angewendet. +Wir haben die Deklination, Rektaszension, Höhe der beiden Planeten Deneb und Arktur und die Sternzeit von Greenwich als Ausgangslage. +Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden von unserem Dozenten digital in einer Stadt in Japan mit den Koordinaten 35.716672 N, 140.233336 E bestimmt. +Wir werden rechnerisch beweisen, dass wir mit diesen Ergebnissen genau auf diese Koordinaten kommen. +\subsection{Vorgehen} + +\begin{compactenum} +\item +Koordinaten der Bildpunkte der Gestirne bestimmen +\item +Dreiecke aufzeichnen und richtig beschriften +\item +Dreieck ABC bestimmmen +\item +Dreieck BPC bestimmen +\item +Dreieck ABP bestimmen +\item +Geographische Breite bestimmen +\item +Geographische Länge bestimmen +\end{compactenum} + +\subsection{Ausgangslage} +\hbox to\textwidth{% +\begin{minipage}{8.4cm} +Die Rektaszension und die Sternzeit sind in der Regeln in Stunden angegeben. +Für die Umrechnung in Grad kann folgender Zusammenhang verwendet werden: +\[ +\text{Stunden} \cdot 15 = \text{Grad}. +\] +Dies wurde hier bereits gemacht. +\begin{center} +\begin{tabular}{l l >{$}l<{$}} +Sternzeit $s$ & $118.610804^\circ$ \\ +Deneb &\\ + & Rektaszension $RA_{\text{Deneb}}$ & 310.55058^\circ\\ + & Deklination $DEC_{\text{Deneb}}$ & \phantom{0}45.361194^\circ \\ + & Höhe $h_c$ & \phantom{0}50.256027^\circ \\ +Arktur &\\ + & Rektaszension $RA_{\text{Arktur}}$& 214.17558^\circ \\ + & Deklination $DEC_{\text{Arktur}}$ & \phantom{0}19.063222^\circ \\ + & Höhe $h_b$ & \phantom{0}47.427444^\circ \\ +\end{tabular} +\end{center} +\end{minipage}% +\hfill% +\raisebox{-2cm}{\includegraphics{papers/nav/bilder/position1.pdf}}% +} +\medskip + +\subsection{Koordinaten der Bildpunkte} +Als erstes benötigen wir die Koordinaten der Bildpunkte von Arktur und Deneb. +$\delta$ ist die Breite, $\lambda$ die Länge. +\begin{align} +\delta_{\text{Deneb}}&=DEC_{\text{Deneb}} = \underline{\underline{45.361194^\circ}} \nonumber \\ +\lambda_{\text{Deneb}}&=RA_{\text{Deneb}} - s = 310.55058^\circ -118.610804^\circ =\underline{\underline{191.939776^\circ}} \nonumber \\ +\delta_{\text{Arktur}}&=DEC_{\text{Arktur}} = \underline{\underline{19.063222^\circ}} \nonumber \\ +\lambda_{\text{Arktur}}&=RA_{\text{Arktur}} - s = 214.17558^\circ -118.610804^\circ = \underline{\underline{5.5647759^\circ}} \nonumber +\end{align} + + +\subsection{Dreiecke definieren} +\begin{figure} +\hbox{% +\includegraphics{papers/nav/bilder/beispiele1.pdf}% +\hfill% +\includegraphics{papers/nav/bilder/beispiele2.pdf}} +\caption{Arktur-Deneb; Spica-Altiar +\label{nav:beispiele}} +\end{figure} +Das Festlegen der Dreiecke ist essenziell für die korrekten Berechnungen. +Ein Problem, welches in der Theorie nicht berücksichtigt wurde ist, dass der Punkt $P$ nicht zwingend unterhalb der Seite $a$ sein muss. +Wenn man das nicht berücksichtigt, erhält man falsche oder keine Ergebnisse. +In der Realität weiss man jedoch ungefähr auf welchem Breitengrad man ist, so kann man relativ einfach entscheiden, ob der eigene Standort über $a$ ist oder nicht. +Beim unserem genutzten Paar Arktur-Deneb ist dies kein Problem, da der Punkt unterhalb der Seite $a$ liegt. +Würde man aber das Paar Altair-Spica nehmen, liegt $P$ über $a$ +(vgl. Abbildung\ref{nav:beispiele}) und man müsste trigonometrisch +anders vorgehen. + +\subsection{Dreieck $ABC$} +\vspace*{-3mm} +\hbox to\textwidth{% +\begin{minipage}{8.4cm}% +Nun berechnen wir alle Seitenlängen $a$, $b$, $c$ und die +Innnenwinkel $\alpha$, $\beta$ und $\gamma$. +Wir können $b$ und $c$ mit den geltenten Zusammenhängen des nautischen Dreiecks wie folgt bestimmen: +\begin{align*} +b +&= +90^\circ-DEC_{\text{Deneb}} += +90^\circ - 45.361194^\circ +\\ +&= +\underline{\underline{44.638806^\circ}} +\\ +c +&= +90^\circ-DEC_{\text{Arktur}} += +90^\circ - 19.063222^\circ +\\ +&= +\underline{\underline{70.936778^\circ}} +\end{align*} +\end{minipage}% +\hfill% +\raisebox{-2.4cm}{\includegraphics{papers/nav/bilder/position2.pdf}}% +} +Um $a$ zu bestimmen, benötigen wir zuerst den Winkel +\begin{align*} +\alpha +&= +RA_{\text{Deneb}} - RA_{\text{Arktur}} += +310.55058^\circ -214.17558^\circ +\\ +&= +\underline{\underline{96.375^\circ}}. +\end{align*} +Danach nutzen wir den sphärischen Winkelkosinussatz, um $a$ zu berechnen: +\begin{align*} + a &= \cos^{-1}(\cos(b) \cdot \cos(c) + \sin(b) \cdot \sin(c) \cdot \cos(\alpha)) \\ + &= \cos^{-1}(\cos(44.638806) \cdot \cos(70.936778) + \sin(44.638806) \cdot \sin(70.936778) \cdot \cos(96.375)) \\ + &= \underline{\underline{80.8707801^\circ}} +\end{align*} +Für $\beta$ und $\gamma$ nutzen wir den sphärischen Seitenkosinussatz: +\begin{align*} + \beta &= \cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(44.638806)-\cos(80.8707801) \cdot \cos(70.936778)}{\sin(80.8707801) \cdot \sin(70.936778)}\bigg] \\ + &= \underline{\underline{45.0115314^\circ}} +\\ +\gamma &= \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(70.936778)-\cos(44.638806) \cdot \cos(80.8707801)}{\sin(80.8707801) \cdot \sin(44.638806)}\bigg] \\ + &=\underline{\underline{72.0573328^\circ}} +\end{align*} + + + +\subsection{Dreieck $BPC$} +\vspace*{-4mm} +\hbox to\textwidth{% +\begin{minipage}{8.4cm}% +Als nächstes berechnen wir die Seiten $h_b$, $h_c$ und die Innenwinkel $\beta_1$ und $\gamma_1$. +\begin{align*} +h_b&=90^\circ - h_b + = 90^\circ - 47.42744^\circ \\ + &= \underline{\underline{42.572556^\circ}} +\\ + h_c &= 90^\circ - h_c + = 90^\circ - 50.256027^\circ \\ + &= \underline{\underline{39.743973^\circ}} +\end{align*} +\end{minipage}% +\hfill% +\raisebox{-2.8cm}{\includegraphics{papers/nav/bilder/position3.pdf}}% +} +\begin{align*} +\beta_1 &= \cos^{-1} \bigg[\frac{\cos(h_c)-\cos(a) \cdot \cos(h_b)}{\sin(a) \cdot \sin(h_b)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(39.743973)-\cos(80.8707801) \cdot \cos(42.572556)}{\sin(80.8707801) \cdot \sin(42.572556)}\bigg] \\ + &=\underline{\underline{12.5211127^\circ}} +\\ +\gamma_1 &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(a) \cdot \cos(h_c)}{\sin(a) \cdot \sin(h_c)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(80.8707801) \cdot \cos(39.743973)}{\sin(80.8707801) \cdot \sin(39.743973)}\bigg] \\ + &=\underline{\underline{13.2618475^\circ}} +\end{align*} + +\subsection{Dreieck $ABP$} +\vspace*{-2mm} +\hbox to\textwidth{% +\begin{minipage}{8.4cm}% +Als erstes müssen wir den Winkel $\beta_2$ berechnen: +\begin{align*} + \beta_2 &= \beta + \beta_1 = 45.011513^\circ + 12.5211127^\circ \\ + &=\underline{\underline{44.6687451^\circ}} +\end{align*} +Danach können wir mithilfe von $\beta_2$, $c$ und $h_b$ die Seite $l$ berechnen: +\begin{align*} +l +&= +\cos^{-1}(\cos(c) \cdot \cos(h_b) + + \sin(c) \cdot \sin(h_b) \cdot \cos(\beta_2)) \\ +&= +\cos^{-1}(\cos(70.936778) \cdot \cos(42.572556)\\ +&\qquad + \sin(70.936778) \cdot \sin(42.572556) \cdot \cos(57.5326442)) \\ +&= \underline{\underline{54.2833404^\circ}} +\end{align*} +\end{minipage}% +\hfill% +\raisebox{-2.0cm}{\includegraphics{papers/nav/bilder/position4.pdf}}% +} + +\medskip + +Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Winkel $\omega$: +\begin{align*} + \omega &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \\ + &=\cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(70.936778) \cdot \cos(54.2833404)}{\sin(70.936778) \cdot \sin(54.2833404)}\bigg] \\ + &= \underline{\underline{44.6687451^\circ}} +\end{align*} + +\subsection{Längengrad und Breitengrad bestimmen} + +\begin{align*} +\delta &= 90^\circ - l & + \lambda &= \lambda_{Arktur} + \omega \\ +&= 90^\circ - 54.2833404 & + &= 95.5647759^\circ + 44.6687451^\circ \\ +&= \underline{\underline{35.7166596^\circ}} & + &= \underline{\underline{140.233521^\circ}} +\end{align*} +Wie wir sehen, stimmen die berechneten Koordinaten mit den Koordinaten des Punktes, an welchem gemessen wurde überein. + +\subsection{Fazit} +Die theoretische Anleitung im Abschnitt 21.6 scheint grundsätzlich zu funktionieren. +Allerdings gab es zwei interessante Probleme. + +Einerseits das Problem, ob der Punkt P sich oberhalb oder unterhalb von $a$ befindet. +Da wir eigentlich wussten, wo der gesuchte Punkt P ist, konnten wir das Dreieck anhand der Koordinaten der Bildpunkte richtig aufstellen. +In der Praxis muss man aber schon wissen, auf welchem Breitengrad man ungefähr ist. +Dies weis man in der Regeln aber, da die eigene Breite die Höhe des Polarsterns ist. +Diese Höhe wird mit dem Sextant gemessen. + +Andererseits ist da noch ein Problem mit dem Sinussatz. +Beim Sinussatz gibt es immer zwei Lösungen, weil \[ \sin(\pi-a)=\sin(a).\] +Da kann es sein (und war in unserem Fall auch so), dass man das falsche Ergebnis erwischt. +Durch diese Erkenntnis haben wir nur Kosinussätze verwendet und dies ebenfalls im Abschnitt 21.6 abgeändert, da es für den Leser auch relevant sein kann, wenn er es Probieren möchte. + + + + diff --git a/buch/papers/nav/images/beispiele/beispiele1.pdf b/buch/papers/nav/images/beispiele/beispiele1.pdf index d0fe3dc..1f91809 100644 Binary files a/buch/papers/nav/images/beispiele/beispiele1.pdf and b/buch/papers/nav/images/beispiele/beispiele1.pdf differ diff --git a/buch/papers/nav/images/beispiele/beispiele1.tex b/buch/papers/nav/images/beispiele/beispiele1.tex index 5666ba6..0dfae2f 100644 --- a/buch/papers/nav/images/beispiele/beispiele1.tex +++ b/buch/papers/nav/images/beispiele/beispiele1.tex @@ -20,10 +20,10 @@ \def\breite{4} \def\hoehe{4} -\begin{tikzpicture}[>=latex,thick] +\begin{tikzpicture}[>=latex,thick,scale=0.8125] % Povray Bild -\node at (0,0) {\includegraphics[width=8cm]{beispiele1.jpg}}; +\node at (0,0) {\includegraphics[width=6.5cm]{beispiele1.jpg}}; % Gitter \ifthenelse{\boolean{showgrid}}{ diff --git a/buch/papers/nav/images/beispiele/beispiele2.pdf b/buch/papers/nav/images/beispiele/beispiele2.pdf index 8579ee5..4b28f2f 100644 Binary files a/buch/papers/nav/images/beispiele/beispiele2.pdf and b/buch/papers/nav/images/beispiele/beispiele2.pdf differ diff --git a/buch/papers/nav/images/beispiele/beispiele2.tex b/buch/papers/nav/images/beispiele/beispiele2.tex index c9b70bd..04c1e4d 100644 --- a/buch/papers/nav/images/beispiele/beispiele2.tex +++ b/buch/papers/nav/images/beispiele/beispiele2.tex @@ -20,10 +20,10 @@ \def\breite{4} \def\hoehe{4} -\begin{tikzpicture}[>=latex,thick] +\begin{tikzpicture}[>=latex,thick,scale=0.8125] % Povray Bild -\node at (0,0) {\includegraphics[width=8cm]{beispiele2.jpg}}; +\node at (0,0) {\includegraphics[width=6.5cm]{beispiele2.jpg}}; % Gitter \ifthenelse{\boolean{showgrid}}{ diff --git a/buch/papers/nav/images/beispiele/beispiele3.pdf b/buch/papers/nav/images/beispiele/beispiele3.pdf index a7189dd..049ccdf 100644 Binary files a/buch/papers/nav/images/beispiele/beispiele3.pdf and b/buch/papers/nav/images/beispiele/beispiele3.pdf differ diff --git a/buch/papers/nav/images/beispiele/common.tex b/buch/papers/nav/images/beispiele/common.tex index b7b3dac..81dc037 100644 --- a/buch/papers/nav/images/beispiele/common.tex +++ b/buch/papers/nav/images/beispiele/common.tex @@ -44,36 +44,36 @@ \def\labeldSpica{ \coordinate (dSpica) at (-1.5,2.6); \fill[color=white,opacity=0.5] - ($(dSpica)+(-1.8,0.08)$) + ($(dSpica)+(-1.8,0.13)$) rectangle - ($(dSpica)+(-0.06,0.55)$); + ($(dSpica)+(-0.06,0.60)$); \node at (dSpica) [above left] {$90^\circ-\delta_{\text{Spica}}\mathstrut$}; } \def\labeldAltair{ \coordinate (dAltair) at (2.0,2.1); \fill[color=white,opacity=0.5] - ($(dAltair)+(0.10,0.05)$) + ($(dAltair)+(0.10,0.10)$) rectangle - ($(dAltair)+(1.8,0.5)$); + ($(dAltair)+(2.0,0.60)$); \node at (dAltair) [above right] {$90^\circ-\delta_{\text{Altair}}\mathstrut$}; } \def\labeldArktur{ \coordinate (dArktur) at (-1.2,2.5); \fill[color=white,opacity=0.5] - ($(dArktur)+(-1.8,0.05)$) + ($(dArktur)+(-1.8,0.10)$) rectangle - ($(dArktur)+(-0.06,0.5)$); + ($(dArktur)+(-0.06,0.55)$); \node at (dArktur) [above left] {$90^\circ-\delta_{\text{Arktur}}\mathstrut$}; } \def\labeldDeneb{ \coordinate (dDeneb) at (2.0,2.8); \fill[color=white,opacity=0.5] - ($(dDeneb)+(0.05,0.5)$) + ($(dDeneb)+(0.05,0.60)$) rectangle - ($(dDeneb)+(1.87,0.05)$); + ($(dDeneb)+(1.87,0.10)$); \node at (dDeneb) [above right] {$90^\circ-\delta_{\text{Deneb}}\mathstrut$}; } diff --git a/buch/papers/nav/main.tex b/buch/papers/nav/main.tex index 37bc83a..f993559 100644 --- a/buch/papers/nav/main.tex +++ b/buch/papers/nav/main.tex @@ -15,7 +15,7 @@ \input{papers/nav/sincos.tex} \input{papers/nav/trigo.tex} \input{papers/nav/nautischesdreieck.tex} -\input{papers/nav/bsp.tex} +\input{papers/nav/bsp2.tex} \printbibliography[heading=subbibliography] -- cgit v1.2.1 From fb34a6ec01db936f85fc977ceee02dcc8525f208 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 4 Jul 2022 19:59:45 +0200 Subject: missing \text{} --- buch/papers/nav/bsp2.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/papers/nav/bsp2.tex b/buch/papers/nav/bsp2.tex index fe8f423..fde44b8 100644 --- a/buch/papers/nav/bsp2.tex +++ b/buch/papers/nav/bsp2.tex @@ -207,7 +207,7 @@ Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Wink \begin{align*} \delta &= 90^\circ - l & - \lambda &= \lambda_{Arktur} + \omega \\ + \lambda &= \lambda_{\text{Arktur}} + \omega \\ &= 90^\circ - 54.2833404 & &= 95.5647759^\circ + 44.6687451^\circ \\ &= \underline{\underline{35.7166596^\circ}} & -- cgit v1.2.1 From 3fbbafce1a5d906a12c1f8035fa2e16f6c187de0 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Tue, 5 Jul 2022 15:31:16 +0200 Subject: abschluss --- buch/papers/nav/bsp2.tex | 50 +++++++++++++-------------- buch/papers/nav/flatearth.tex | 3 +- buch/papers/nav/nautischesdreieck.tex | 63 ++++++++++++++++++----------------- buch/papers/nav/references.bib | 6 ++++ buch/papers/nav/sincos.tex | 10 +++--- buch/papers/nav/trigo.tex | 45 +++++++++++++------------ 6 files changed, 94 insertions(+), 83 deletions(-) diff --git a/buch/papers/nav/bsp2.tex b/buch/papers/nav/bsp2.tex index fde44b8..23380eb 100644 --- a/buch/papers/nav/bsp2.tex +++ b/buch/papers/nav/bsp2.tex @@ -1,12 +1,12 @@ \section{Beispielrechnung} \subsection{Einführung} -In diesem Abschnitt wird die Theorie vom Abschnitt 21.6 in einem Praxisbeispiel angewendet. +In diesem Abschnitt wird die Theorie vom Abschnitt \ref{sta} in einem Praxisbeispiel angewendet. Wir haben die Deklination, Rektaszension, Höhe der beiden Planeten Deneb und Arktur und die Sternzeit von Greenwich als Ausgangslage. -Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden von unserem Dozenten digital in einer Stadt in Japan mit den Koordinaten 35.716672 N, 140.233336 E bestimmt. -Wir werden rechnerisch beweisen, dass wir mit diesen Ergebnissen genau auf diese Koordinaten kommen. +Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden digital in einer Stadt in Japan mit den Koordinaten 35.716672 N, 140.233336 E bestimmt. +Wir werden nachrechnen, dass wir mit unserer Methode genau auf diese Koordinaten kommen. \subsection{Vorgehen} - +Unser vorgehen erschliesst sicht aus unserer Methode, die wir im Abschnitt \ref{p} theoretisch erklärt haben. \begin{compactenum} \item Koordinaten der Bildpunkte der Gestirne bestimmen @@ -27,7 +27,7 @@ Geographische Länge bestimmen \subsection{Ausgangslage} \hbox to\textwidth{% \begin{minipage}{8.4cm} -Die Rektaszension und die Sternzeit sind in der Regeln in Stunden angegeben. +Die Rektaszension und die Sternzeit sind in der Regel in Stunden angegeben. Für die Umrechnung in Grad kann folgender Zusammenhang verwendet werden: \[ \text{Stunden} \cdot 15 = \text{Grad}. @@ -125,17 +125,17 @@ RA_{\text{Deneb}} - RA_{\text{Arktur}} Danach nutzen wir den sphärischen Winkelkosinussatz, um $a$ zu berechnen: \begin{align*} a &= \cos^{-1}(\cos(b) \cdot \cos(c) + \sin(b) \cdot \sin(c) \cdot \cos(\alpha)) \\ - &= \cos^{-1}(\cos(44.638806) \cdot \cos(70.936778) + \sin(44.638806) \cdot \sin(70.936778) \cdot \cos(96.375)) \\ + &= \cos^{-1}(\cos(44.638806^\circ) \cdot \cos(70.936778^\circ) + \sin(44.638806^\circ) \cdot \sin(70.936778^\circ) \cdot \cos(96.375^\circ)) \\ &= \underline{\underline{80.8707801^\circ}} \end{align*} Für $\beta$ und $\gamma$ nutzen wir den sphärischen Seitenkosinussatz: \begin{align*} \beta &= \cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg] \\ - &= \cos^{-1} \bigg[\frac{\cos(44.638806)-\cos(80.8707801) \cdot \cos(70.936778)}{\sin(80.8707801) \cdot \sin(70.936778)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(44.638806^\circ)-\cos(80.8707801^\circ) \cdot \cos(70.936778^\circ)}{\sin(80.8707801^\circ) \cdot \sin(70.936778^\circ)}\bigg] \\ &= \underline{\underline{45.0115314^\circ}} \\ \gamma &= \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}\bigg] \\ - &= \cos^{-1} \bigg[\frac{\cos(70.936778)-\cos(44.638806) \cdot \cos(80.8707801)}{\sin(80.8707801) \cdot \sin(44.638806)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(70.936778^\circ)-\cos(44.638806^\circ) \cdot \cos(80.8707801^\circ)}{\sin(80.8707801^\circ) \cdot \sin(44.638806^\circ)}\bigg] \\ &=\underline{\underline{72.0573328^\circ}} \end{align*} @@ -145,13 +145,13 @@ Für $\beta$ und $\gamma$ nutzen wir den sphärischen Seitenkosinussatz: \vspace*{-4mm} \hbox to\textwidth{% \begin{minipage}{8.4cm}% -Als nächstes berechnen wir die Seiten $h_b$, $h_c$ und die Innenwinkel $\beta_1$ und $\gamma_1$. +Als nächstes berechnen wir die Seiten $h_B$, $h_B$ und die Innenwinkel $\beta_1$ und $\gamma_1$. \begin{align*} -h_b&=90^\circ - h_b +h_B&=90^\circ - pbb = 90^\circ - 47.42744^\circ \\ &= \underline{\underline{42.572556^\circ}} \\ - h_c &= 90^\circ - h_c + h_C &= 90^\circ - pc = 90^\circ - 50.256027^\circ \\ &= \underline{\underline{39.743973^\circ}} \end{align*} @@ -160,12 +160,12 @@ h_b&=90^\circ - h_b \raisebox{-2.8cm}{\includegraphics{papers/nav/bilder/position3.pdf}}% } \begin{align*} -\beta_1 &= \cos^{-1} \bigg[\frac{\cos(h_c)-\cos(a) \cdot \cos(h_b)}{\sin(a) \cdot \sin(h_b)}\bigg] \\ - &= \cos^{-1} \bigg[\frac{\cos(39.743973)-\cos(80.8707801) \cdot \cos(42.572556)}{\sin(80.8707801) \cdot \sin(42.572556)}\bigg] \\ +\beta_1 &= \cos^{-1} \bigg[\frac{\cos(h_c)-\cos(a) \cdot \cos(h_B)}{\sin(a) \cdot \sin(h_B)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(39.743973^\circ)-\cos(80.8707801^\circ) \cdot \cos(42.572556^\circ)}{\sin(80.8707801^\circ) \cdot \sin(42.572556^\circ)}\bigg] \\ &=\underline{\underline{12.5211127^\circ}} \\ -\gamma_1 &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(a) \cdot \cos(h_c)}{\sin(a) \cdot \sin(h_c)}\bigg] \\ - &= \cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(80.8707801) \cdot \cos(39.743973)}{\sin(80.8707801) \cdot \sin(39.743973)}\bigg] \\ +\gamma_1 &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(a) \cdot \cos(h_C)}{\sin(a) \cdot \sin(h_C)}\bigg] \\ + &= \cos^{-1} \bigg[\frac{\cos(42.572556^\circ)-\cos(80.8707801^\circ) \cdot \cos(39.743973^\circ)}{\sin(80.8707801^\circ) \cdot \sin(39.743973^\circ)}\bigg] \\ &=\underline{\underline{13.2618475^\circ}} \end{align*} @@ -178,15 +178,15 @@ Als erstes müssen wir den Winkel $\beta_2$ berechnen: \beta_2 &= \beta + \beta_1 = 45.011513^\circ + 12.5211127^\circ \\ &=\underline{\underline{44.6687451^\circ}} \end{align*} -Danach können wir mithilfe von $\beta_2$, $c$ und $h_b$ die Seite $l$ berechnen: +Danach können wir mithilfe von $\beta_2$, $c$ und $h_B$ die Seite $l$ berechnen: \begin{align*} l &= -\cos^{-1}(\cos(c) \cdot \cos(h_b) - + \sin(c) \cdot \sin(h_b) \cdot \cos(\beta_2)) \\ +\cos^{-1}(\cos(c) \cdot \cos(h_B) + + \sin(c) \cdot \sin(h_B) \cdot \cos(\beta_2)) \\ &= -\cos^{-1}(\cos(70.936778) \cdot \cos(42.572556)\\ -&\qquad + \sin(70.936778) \cdot \sin(42.572556) \cdot \cos(57.5326442)) \\ +\cos^{-1}(\cos(70.936778^\circ) \cdot \cos(42.572556^\circ)\\ +&\qquad + \sin(70.936778^\circ) \cdot \sin(42.572556^\circ) \cdot \cos(57.5326442^\circ)) \\ &= \underline{\underline{54.2833404^\circ}} \end{align*} \end{minipage}% @@ -199,7 +199,7 @@ l Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Winkel $\omega$: \begin{align*} \omega &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \\ - &=\cos^{-1} \bigg[\frac{\cos(42.572556)-\cos(70.936778) \cdot \cos(54.2833404)}{\sin(70.936778) \cdot \sin(54.2833404)}\bigg] \\ + &=\cos^{-1} \bigg[\frac{\cos(42.572556^\circ)-\cos(70.936778^\circ) \cdot \cos(54.2833404^\circ)}{\sin(70.936778^\circ) \cdot \sin(54.2833404^\circ)}\bigg] \\ &= \underline{\underline{44.6687451^\circ}} \end{align*} @@ -216,11 +216,11 @@ Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Wink Wie wir sehen, stimmen die berechneten Koordinaten mit den Koordinaten des Punktes, an welchem gemessen wurde überein. \subsection{Fazit} -Die theoretische Anleitung im Abschnitt 21.6 scheint grundsätzlich zu funktionieren. +Die theoretische Anleitung im Abschnitt \ref{sta} scheint grundsätzlich zu funktionieren. Allerdings gab es zwei interessante Probleme. -Einerseits das Problem, ob der Punkt P sich oberhalb oder unterhalb von $a$ befindet. -Da wir eigentlich wussten, wo der gesuchte Punkt P ist, konnten wir das Dreieck anhand der Koordinaten der Bildpunkte richtig aufstellen. +Einerseits das Problem, ob der Punkt $P$ sich oberhalb oder unterhalb von $a$ befindet. +Da wir eigentlich wussten, wo der gesuchte Punkt $P$ ist, konnten wir das Dreieck anhand der Koordinaten der Bildpunkte richtig aufstellen. In der Praxis muss man aber schon wissen, auf welchem Breitengrad man ungefähr ist. Dies weis man in der Regeln aber, da die eigene Breite die Höhe des Polarsterns ist. Diese Höhe wird mit dem Sextant gemessen. @@ -228,7 +228,7 @@ Diese Höhe wird mit dem Sextant gemessen. Andererseits ist da noch ein Problem mit dem Sinussatz. Beim Sinussatz gibt es immer zwei Lösungen, weil \[ \sin(\pi-a)=\sin(a).\] Da kann es sein (und war in unserem Fall auch so), dass man das falsche Ergebnis erwischt. -Durch diese Erkenntnis haben wir nur Kosinussätze verwendet und dies ebenfalls im Abschnitt 21.6 abgeändert, da es für den Leser auch relevant sein kann, wenn er es Probieren möchte. +Wegen dieser Erkenntnis haben wir nur Kosinussätze verwendet und dies ebenfalls im Abschnitt \ref{sta} abgeändert, da es für den Leser auch relevant sein kann, wenn er es Probieren möchte. diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index 3b08e8d..d1d5a9b 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -6,6 +6,7 @@ \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/projektion.png} \caption[Mercator Projektion]{Mercator Projektion} + \label{merc} \end{center} \end{figure} @@ -17,7 +18,7 @@ Eratosthenes konnte etwa 100 Jahre später den Erdumfang berechnen. Er beobachtete, dass die Sonne in Syene mittags im Zenit steht und gleichzeitig in Alexandria unter einem Winkel einfällt. Mithilfe der Trigonometrie konnte er mit dem Abstand der Städte und dem Einfallswinkel den Umfang berechnen. -Der Kartograph Gerhard Mercator projizierte die Erdkugel wie in Abbildung 21.1 dargestellt auf ein Papier und erstellte so eine winkeltreue Karte. +Der Kartograph Gerhard Mercator projizierte die Erdkugel wie in Abbildung \ref{merc} dargestellt auf ein Papier und erstellte so eine winkeltreue Karte. Jedoch wurden die Länder, die einen grösseren Abstand zum Äquator haben vergrössert, damit die Winkel stimmen können. Wurde man also nun davon ausgehen, dass die Erde flach ist so würden wir nie dort ankommen wo wir es wollen. Dies sieht man zum Beispiel sehr gut, wenn man die Anwendung Google Earth und eine Weltkarte vergleicht. diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index 44153bd..36674ee 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -2,9 +2,9 @@ \subsection{Definition des Nautischen Dreiecks} Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient. Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. -Ein Gestirn ist ein Planet oder ein Fixstern, zu welchen es diverse Jahrbücher mit allen astronomischen Eigenschaften gibt. +Als Gestirne kommen Sterne und Planeten in Frage, zu welchen in diversen Jahrbüchern die für die Navigation nötigen Daten publiziert sind. Der Himmelspol ist der Nordpol an die Himmelskugel projiziert. -Das nautische Dreieck hat die Ecken Zenit, Gestirn und Himmelspol, wie man in der Abbildung 21.5 sehen kann. +Das nautische Dreieck hat die Ecken Zenit, Gestirn und Himmelspol, wie man in der Abbildung \ref{naut} sehen kann. Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astronomie um die momentane Position eines Fixsterns oder Planeten an der Himmelskugel zu bestimmen. @@ -13,21 +13,24 @@ Ursprünglich ist das nautische Dreieck ein Hilfsmittel der sphärischen Astrono \begin{center} \includegraphics[width=8cm]{papers/nav/bilder/kugel3.png} \caption[Nautisches Dreieck]{Nautisches Dreieck} + \label{naut} \end{center} \end{figure} Man kann das nautische Dreieck auf die Erdkugel projizieren. Dieses Dreieck nennt man dann Bilddreieck. Als Bildpunkt wird in der astronomischen Navigation der Punkt bezeichnet, an dem eine gedachte Linie vom Mittelpunkt eines beobachteten Gestirns zum Mittelpunkt der Erde die Erdoberfläche schneidet. -Die Projektion auf der Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. +Die Projektion des nautischen Dreiecks auf die Erdkugel hat die Ecken Nordpol, Standort und Bildpunkt. \section{Standortbestimmung ohne elektronische Hilfsmittel} +\label{sta} Um den eigenen Standort herauszufinden, wird in diesem Kapitel die Projektion des nautische Dreiecks auf die Erdkugel zur Hilfe genommen. Mithilfe eines Sextanten, einem Jahrbuch und der sphärischen Trigonometrie kann man dann die Längen- und Breitengrade des eigenen Standortes bestimmen. -Was ein Sextant und ein Jahrbuch ist, wird im Abschnitt 21.6.3 erklärt. +Was ein Sextant und ein Jahrbuch ist, wird im Abschnitt \ref{ephe} erklärt. \begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/dreieck.pdf} \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} + \label{d1} \end{center} \end{figure} @@ -44,10 +47,11 @@ Für die Standortermittlung benötigt man als weiteren Punkt ein Gestirn bzw. se Damit das trigonometrische Rechnen einfacher wird, werden hier zwei Gestirne zur Hilfe genommen. Es gibt diverse Gestirne, die man nutzen kann wie zum Beispiel die Sonne, der Mond oder die vier Navigationsplaneten Venus, Mars, Jupiter und Saturn. -Die Bildpunkte von den beiden Gestirnen $X$ und $Y$ bilden die beiden Ecken $B$ und $C$ im Dreieck der Abbildung 21.5. +Die Bildpunkte von den beiden Gestirnen $X$ und $Y$ bilden die beiden Ecken $B$ und $C$ im Dreieck der Abbildung \ref{d1}. \subsection{Ephemeriden} -Zu all diesen Gestirnen gibt es Ephemeriden. -Diese enthalten die Rektaszensionen und Deklinationen in Abhängigkeit von der Zeit. +\label{ephe} +Zu all diesen Gestirnen gibt es Ephemeridentabellen. +Diese Tabellen enthalten die Rektaszensionen und Deklinationen in Abhängigkeit von der Zeit. \begin{figure} \begin{center} @@ -63,20 +67,19 @@ Die Deklination $\delta$ beschreibt den Winkel zwischen dem Himmelsäquator und Die Rektaszension $\alpha$ gibt an, in welchem Winkel das Gestirn zum Frühlingspunkt, welcher der Nullpunkt auf dem Himmelsäquator ist, steht und geht vom Koordinatensystem der Himmelskugel aus. Die Tatsache, dass sich die Himmelskugel ca. vier Minuten schneller um die eigene Achse dreht als die Erdkugel, stellt hier ein kleines Problem dar. -Die Lösung ist die Sternzeit. -Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen und können die am Frühlingspunkt (21. März) 12:00 Uhr ist die Sternzeit $\theta = 0$. - -Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet. +Die Lösung ist die Sternzeit $\theta$. +Mit dieser können wir die schnellere Drehung der Himmelskugel ausgleichen. +Die Sternzeit geht vom Frühlungspunkt aus, an welchem die Sonne den Himmelsäquator schneidet und $\theta=0$ ist. Für die Standortermittlung auf der Erdkugel ist es am einfachsten, wenn man die Sternzeit von Greenwich berechnet. Für die Sternzeit von Greenwich $\theta$ braucht man als erstes das Julianische Datum $T$ vom aktuellen Tag, welches sich leicht nachschlagen lässt. Im Anschluss berechnet man die Sternzeit von Greenwich -\[\theta = 6^h 41^m 50^s,54841 + 8640184^s,812866 \cdot T + 0^s,093104 \cdot T^2 - 0^s,0000062 \cdot T^3.\] +\[\theta = 6^h 41^m 50^s.54841 + 8640184^s.812866 \cdot T + 0^s.093104 \cdot T^2 - 0^s.0000062 \cdot T^3.\] Wenn man die Sternzeit von Greenwich ausgerechnet hat, kann man den Längengrad des Gestirns $\lambda = \theta - \alpha$ bestimmen, wobei $\alpha$ die Rektaszension und $\theta$ die Sternzeit von Greenwich ist. Dies gilt analog auch für das zweite Gestirn. \subsubsection{Sextant} -Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann. Es wird vor allem der Winkelabstand zu Gestirnen gemessen. +Ein Sextant ist ein nautisches Messinstrument, mit dem man den Winkel zwischen der Blickrichtung zu weit entfernten Objekten bestimmen kann. Es wird vor allem der Winkelabstand vom Horizont zum Gestirn gemessen. Man benutzt ihn vor allem für die astronomische Navigation auf See. \begin{figure} @@ -85,22 +88,24 @@ Man benutzt ihn vor allem für die astronomische Navigation auf See. \caption[Sextant]{Sextant} \end{center} \end{figure} -\subsection{Bestimmung des eigenen Standortes $P$} +\subsection{Bestimmung des eigenen Standortes $P$} \label{p} +Wir nehmen die Abbildung \ref{d2} zur Hilfe. Nun hat man die Koordinaten der beiden Gestirne und man weiss die Koordinaten des Nordpols. Damit wir unseren Standort bestimmen können, bilden wir zuerst das Dreieck $ABC$, dann das Dreieck $BPC$ und zum Schluss noch das Dreieck $ABP$. -Mithilfe dieser Dreiecken können wir die einfachen Sätze der sphärischen Trigonometrie anwenden und benötigen lediglich ein Ephemeride zu den Gestirnen und einen Sextant. +Auf diese Dreiecke können wir die einfachen Sätze der sphärischen Trigonometrie anwenden und benötigen lediglich ein Ephemeride zu den Gestirnen und einen Sextant. \begin{figure} \begin{center} \includegraphics[width=8cm]{papers/nav/bilder/dreieck.pdf} \caption[Dreieck für die Standortbestimmung]{Dreieck für die Standortbestimmung} + \label{d2} \end{center} \end{figure} \subsubsection{Dreieck $ABC$} \begin{center} - \begin{tabular}{ c c c } + \begin{tabular}{ l l l } Ecke && Name \\ \hline $A$ && Nordpol \\ @@ -111,18 +116,15 @@ Mithilfe dieser Dreiecken können wir die einfachen Sätze der sphärischen Trig Mit unserem erlangten Wissen können wir nun alle Seiten des Dreiecks $ABC$ berechnen. -Die Seite vom Nordpol zum Bildpunkt $X$ sei $c$. -Dann ist $c = \frac{\pi}{2} - \delta_1$. - -Die Seite vom Nordpol zum Bildpunkt $Y$ sei $b$. -Dann ist $b = \frac{\pi}{2} - \delta_2$. - -Der Innenwinkel bei der Ecke, wo der Nordpol ist sei $\alpha$. -Dann ist $ \alpha = |\lambda_1 - \lambda_2|$. +\begin{enumerate} + \item Die Seite vom Nordpol zum Bildpunkt $X$ sei $c$, dann ist $c = \frac{\pi}{2} - \delta_1$. + \item Die Seite vom Nordpol zum Bildpunkt $Y$ sei $b$, dann ist $b = \frac{\pi}{2} - \delta_2$. + \item Der Innenwinkel bei der Ecke, wo der Nordpol ist sei $\alpha$, dann ist $ \alpha = |\lambda_1 - \lambda_2|$. +\end{enumerate} mit \begin{center} - \begin{tabular}{ c c c } + \begin{tabular}{ l l l } Ecke && Name \\ \hline $\delta_1$ && Deklination vom Bildpunkt $X$ \\ @@ -141,7 +143,7 @@ Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sin Jetzt fehlen noch die beiden anderen Innenwinkel $\beta$ und\ $\gamma$. Diese bestimmen wir mithilfe des Kosinussatzes: \[\beta=\cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg]\] und \[\gamma = \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}.\bigg]\] -Schlussendlich haben wir die Seiten $a$ $b$ und $c$, die Ecken A,B und C und die Winkel $\alpha$, $\beta$ und $\gamma$ bestimmt und somit das ganze Kugeldreieck $ABC$ berechnet. +Schlussendlich haben wir die Seiten $a$, $b$ und $c$, die Ecken $A$,$B$ und $C$ und die Winkel $\alpha$, $\beta$ und $\gamma$ bestimmt und somit das ganze Kugeldreieck $ABC$ berechnet. \subsubsection{Dreieck $BPC$} Wir bilden nun ein zweites Dreieck, welches die Ecken $B$ und $C$ des ersten Dreiecks besitzt. @@ -150,12 +152,11 @@ Unser Standort definiere sich aus einer geographischen Breite $\delta$ und einer Die Seite von $P$ zu $B$ sei $pb$ und die Seite von $P$ zu $C$ sei $pc$. Die beiden Seitenlängen kann man mit dem Sextant messen und durch eine einfache Formel bestimmen, nämlich $pb=\frac{\pi}{2} - h_{B}$ und $pc=\frac{\pi}{2} - h_{C}$ - mit $h_B=$ Höhe von Gestirn in $B$ und $h_C=$ Höhe von Gestirn in $C$ mit Sextant gemessen. Zum Schluss müssen wir noch den Winkel $\beta_1$ mithilfe des Seiten-Kosinussatzes \[\cos(pb)=\cos(pc)\cdot\cos(a)+\sin(pc)\cdot\sin(a)\cdot\cos(\beta_1)\] mit den bekannten Seiten $pc$, $pb$ und $a$ bestimmen. \subsubsection{Dreieck $ABP$} -Nun muss man eine Verbindungslinie ziehen zwischen $P$ und $A$. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$, den bekannten Seiten $c$ und $pb$ und des Seiten-Kosinussatzes berechnen. +Nun muss man eine Verbindungslinie des Standorts zwischen $P$ und $A$ ziehen. Die Länge $l$ dieser Linie entspricht der gesuchten geographischen Breite $\delta$. Diese lässt sich mithilfe des Dreiecks $ABP$, den bekannten Seiten $c$ und $pb$ und des Seiten-Kosinussatzes berechnen. Für den Seiten-Kosinussatz benötigt es noch $\kappa=\beta + \beta_1$. Somit ist \[\cos(l) = \cos(c)\cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)\] und @@ -163,7 +164,7 @@ und \delta =\cos^{-1} [\cos(c) \cdot \cos(pb) + \sin(c) \cdot \sin(pb) \cdot \cos(\kappa)]. \] -Für die Geographische Länge $\lambda$ des eigenen Standortes nutzt man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet. -Mithilfe des Kosinussatzes können wir \[\omega = \cos^{-1} \bigg[\frac{\cos(pb)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}.\bigg]\] berechnen und schlussentlich dann -\[\lambda=\lambda_1 - \omega\] +Für die geographische Länge $\lambda$ des eigenen Standortes nutzt man den Winkel $\omega$, welcher sich im Dreieck $ACP$ in der Ecke bei $A$ befindet. +Mithilfe des Kosinussatzes können wir \[\omega = \cos^{-1} \bigg[\frac{\cos(pb)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg]\] berechnen und bekommen schlussendlich die geographische Länge +\[\lambda=\lambda_1 - \omega,\] wobei $\lambda_1$ die Länge des Bildpunktes $X$ von $C$ ist. diff --git a/buch/papers/nav/references.bib b/buch/papers/nav/references.bib index 236323b..10dbf66 100644 --- a/buch/papers/nav/references.bib +++ b/buch/papers/nav/references.bib @@ -32,4 +32,10 @@ pages = {607--627}, url = {https://doi.org/10.1016/j.acha.2017.11.004} } +@online{nav:winkel, + editor={Unbekannt}, + title = {Sphärische Trigonometrie}, + year={2022} + url = {https://de.wikipedia.org/wiki/Sphärische_Trigonometrie} +} diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index a1653e8..f82a057 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -2,18 +2,18 @@ \section{Sphärische Navigation und Winkelfunktionen} -Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren sich mit Problemen der sphärischen Trigonometrie beschäftigt haben um den Lauf von Gestirnen zu berechnen. +Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren mit Problemen der sphärischen Trigonometrie beschäftigt haben, um den Lauf von Gestirnen zu berechnen. Jedoch konnten sie dieses Problem nicht lösen. +Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 BCE dachten die Griechen über Kugelgeometrie nach,sie wurde damit zu einer Hilfswissenschaft der Astronomen. -Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 vor Christus dachten die Griechen über Kugelgeometrie nach und sie wurde zu einer Hilfswissenschaft der Astronomen. Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom names Hipparchos. -Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten und im Abschnitt 3.1.1 beschrieben sind. +Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten. Chord ist der Vorgänger der Sinusfunktion und galt damals als wichtigste Grundlage der Trigonometrie. In dieser Zeit wurden auch die ersten Sternenkarten angefertigt. Damals kannte man die Sinusfunktionen noch nicht. +Die Definition der trigonometrischen Funktionen aus Griechenland ermöglicht nur, rechtwinklige Dreiecke zu berechnen. Aus Indien stammten die ersten Ansätze zu den Kosinussätzen. -Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. -Die Definition der trigonometrischen Funktionen ermöglicht nur, rechtwinklige Dreiecke zu berechnen. +Aufbauend auf den indischen und griechischen Forschungen entwickeln die Araber um das 9. Jahrhundert den Sinussatz. Die Beziehung zwischen Seiten und Winkeln sind komplizierter und als Sinus- und Kosinussätze bekannt. Doch ein paar weitere Jahrhunderte vergingen bis zu diesem Thema wieder verstärkt Forschung betrieben wurde, da im 15. Jahrhundert grosse Entdeckungsreisen, hauptsächlich per Schiff, erfolgten und die Orientierung mit Sternen vermehrt an Wichtigkeit gewann. Man nutzte für die Kartographie nun die Kugelgeometrie, um die Genauigkeit zu erhöhen. diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index fa53189..c96aaa5 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -7,46 +7,48 @@ Sein Mittelpunkt fällt immer mit dem Mittelpunkt der Kugel zusammen und ein Sch Da es unendlich viele Möglichkeiten gibt, eine Kugel so zu zerschneiden, dass die Schnittebene den Kugelmittelpunkt trifft, gibt es auch unendlich viele Grosskreise. Grosskreisbögen sind die kürzesten Verbindungslinien zwischen zwei Punkten auf der Kugel. -Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden werden, so entsteht ein Kugeldreieck $ABC$. -Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. -$A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung 21.2). - Da die Länge der Grosskreisbögen wegen der Abhängigkeit vom Kugelradius ungeeignet ist, wird die Grösse einer Seite mit dem zugehörigen Mittelpunktwinkel des Grosskreisbogens angegeben. Laut dieser Definition ist die Seite $c$ der Winkel $AMB$, wobei der Punkt $M$ die Erdmitte ist. Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Aussen ist. Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. +Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden werden, so entsteht ein Kugeldreieck $ABC$. +Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. +$A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung \ref{kugel}). + \begin{figure} \begin{center} - \includegraphics[width=6cm]{papers/nav/bilder/kugel1.png} + \includegraphics[width=3.5cm]{papers/nav/bilder/kugel1.png} \caption[Das Kugeldreieck]{Das Kugeldreieck} + \label{kugel} \end{center} \end{figure} \subsection{Rechtwinkliges Dreieck und rechtseitiges Dreieck} -In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkel, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. +In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkeln, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. Wie auch im ebenen Dreieck gibt es beim Kugeldreieck auch ein rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. -Ein Rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss, wie man in der Abbildung 21.3 sehen kann. +Ein rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss, wie man in der Abbildung \ref{recht} sehen kann. \begin{figure} \begin{center} - \includegraphics[width=10cm]{papers/nav/bilder/recht.jpg} - \caption[Rechtseitiges Kugeldreieck]{Rechtseitiges Kugeldreieck} + \includegraphics[width=5cm]{papers/nav/bilder/recht.jpg} + \caption[Rechtseitiges und rechtwinkliges Kugeldreieck]{Rechtseitiges und rechtwinkliges Kugeldreieck} + \label{recht} \end{center} \end{figure} \subsection{Winkelsumme und Flächeninhalt} -\begin{figure} +%\begin{figure} ----- Brauche das Bild eigentlich nicht! - \begin{center} - \includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} - \caption[Winkelangabe im Kugeldreieck]{Winkelangabe im Kugeldreieck} - \end{center} -\end{figure} +% \begin{center} +% \includegraphics[width=8cm]{papers/nav/bilder/kugel2.png} +% \caption[Winkelangabe im Kugeldreieck]{Winkelangabe im Kugeldreieck} +% \end{center} +%\end{figure} Die Winkel eines Kugeldreiecks sind die, welche die Halbtangenten in den Eckpunkten einschliessen. @@ -64,12 +66,13 @@ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zu \subsubsection{Flächeninnhalt} Mithilfe des Radius $r$ und dem sphärischen Exzess $\epsilon$ gilt für den Flächeninhalt -\[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon\]. +\[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon = 2 \cdot r^2 \cdot \epsilon\]. +\cite{nav:winkel} \subsection{Seiten und Winkelberechnung} Es gibt in der sphärischen Trigonometrie eigentlich gar keinen Satz des Pythagoras, wie man ihn aus der zweidimensionalen Geometrie kennt. -Es gibt aber auch einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks, nicht aber für das rechtseitige Kugeldreieck, in eine Beziehung bringt und zum jetzigen Punkt noch unklar ist, weshalb dieser Satz so aussieht. -Die Approximation folgt noch. +Es gibt aber einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. Dieser Satz gilt jedoch nicht für das rechtseitige Kugeldreieck. +Die Approximation im nächsten Abschnitt wird erklären, warum man dies als eine Form des Satzes des Pythagoras sehen kann. Es gilt nämlich: \begin{align} \cos c = \cos a \cdot \cos b \quad \text{wenn} \nonumber & @@ -94,14 +97,14 @@ Die Korrespondenzen zwischen der ebenen- und sphärischen Trigonometrie werden i \subsubsection{Sphärischer Satz des Pythagoras} Die Korrespondenz \[ a^2 \approx 1- \cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich -\begin{align} +\begin{align*} \cos(a)\cdot \cos(b) &= \cos(c) \\ \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \\ -a^2-b^2 &=-c^2\\ a^2+b^2&=c^2 -\end{align} -Dies ist der wohlbekannte ebener Satz des Pythagoras. +\end{align*} +Dies ist der wohlbekannte ebene Satz des Pythagoras. \subsubsection{Sphärischer Sinussatz} Den sphärischen Sinussatz -- cgit v1.2.1 From e69e3df9a1e10de9e3122d694da2e923dad711a2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 5 Jul 2022 18:04:48 +0200 Subject: elliptic stuff complete --- buch/chapters/110-elliptisch/dglsol.tex | 7 +- buch/chapters/110-elliptisch/elltrigo.tex | 63 +++- buch/chapters/110-elliptisch/lemniskate.tex | 12 +- buch/chapters/110-elliptisch/mathpendel.tex | 323 +++++++++++++-------- buch/chapters/110-elliptisch/uebungsaufgaben/1.tex | 1 + buch/chapters/part1.tex | 1 + buch/chapters/references.bib | 17 +- 7 files changed, 286 insertions(+), 138 deletions(-) diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index 8a638a7..613f130 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -343,7 +343,8 @@ der unvollständigen elliptischen Integrale. % % Numerische Berechnung mit dem arithmetisch-geometrischen Mittel % -\subsubsection{Numerische Berechnung mit dem arithmetisch-geometrischen Mittel} +\subsubsection{Numerische Berechnung mit dem arithmetisch-geometrischen Mittel +\label{buch:elliptisch:jacobi:agm}} \begin{table} \centering \begin{tikzpicture}[>=latex,thick] @@ -685,3 +686,7 @@ x(t) = a\operatorname{zn}(b(t-t_0)), wobei die Funktion $\operatorname{zn}(u,k)$ auf Grund der Vorzeichen von $A$, $B$ und $C$ gewählt werden müssen. +Die Übungsaufgaben~\ref{buch:elliptisch:aufgabe:1} ist als +Lernaufgabe konzipiert, mit der die Lösung der Differentialgleichung +des harmonischen Oszillators beispielhaft durchgearbeitet +werden kann. diff --git a/buch/chapters/110-elliptisch/elltrigo.tex b/buch/chapters/110-elliptisch/elltrigo.tex index 0ff9cdb..49e6686 100644 --- a/buch/chapters/110-elliptisch/elltrigo.tex +++ b/buch/chapters/110-elliptisch/elltrigo.tex @@ -27,6 +27,11 @@ Funktionen $\operatorname{sn}(u,k)$, $\operatorname{cn}(u,k)$ und $\operatorname{dn}(u,k)$, die ähnliche Eigenschaften haben wie die trigonometrischen Funktionen. +Die nachstehende Darstellung ist stark inspiriert von William Schwalms +sehr zielorientierten Einführung +\cite{buch:schwalm}, welche auch als Youtube-Videovorlesung +\cite{buch:schwalm-youtube} zur Verfügung steht. + % % Geometrie einer Ellipse % @@ -1012,10 +1017,60 @@ finden. Man beachte, dass in jeder Identität alle Funktionen den gleichen zweiten Buchstaben haben. -\subsubsection{TODO} -XXX algebraische Beziehungen \\ -XXX Additionstheoreme \\ -XXX Perioden +\subsubsection{Weitere Beziehungen} +Für die Jacobischen elliptischen Funktionen lässt sich eine grosse +Zahl weiterer Eigenschaften und Identitäten beweisen. +Zum Beispiel gibt es Aditionstheoreme, die im Grenzfall $k\to 0$ zu +den Additionstheoremen für die trigonometrischen Funktionen werden. +\index{Additionstheorem}% +Ebenso kann man weitere algebraische Identitäten finden. +So lässt sich zum Beispiel die einzige reelle Nullstelle von $x^5+x=w$ +mit Jacobischen elliptischen Funktionen darstellen, während es +nicht möglich ist, diese Lösung als Wurzelausdruck zu schreiben. + +Die Jacobischen elliptischen Funktionen lassen sich statt auf dem +hier gewählten trigonometrischen Weg auch mit Hilfe der Jacobischen +Theta-Funktionen definieren, die Lösungen einer Wärmeleitungsgleichung +\index{Theta-Funktionen}% +\index{Wärmeleitungs-Gleichung}% +mit geeigneten Randbedingungen sind. +Diese Vorgehensweise hat den Vorteil, ziemlich direkt zu +Reihen- und Produktentwicklungen für die Funktionen zu führen. +Auch die Additionstheorem ergeben sich vergleichsweise leicht. +Dieser Zugang zu den Jacobischen elliptischen Funktionen wird in der +Standardreferenz~\cite{buch:ellfun-applications} gewählt. + +Bei anderen speziellen Funktionen waren Reihenentwicklungen ein +wichtiges Hilfsmittel zu deren numerischer Berechnung. +Bei den Jacobischen elliptischen Funktionen ist diese Methode +nicht zielführend. +Im Abschnitt~\ref{buch:elliptisch:subsection:differentialgleichungen} +wird gezeigt, dass Jacobische elliptische Funktionen gewisse nichtlineare +Differentialgleichungen zu lösen ermöglichen. +Dies zeigt auch, dass Jacobischen elliptischen Funktionen +Umkehrfunktionen der elliptischen Integrale sind, die in +Abschnitt~\ref{buch:elliptisch:subsection:agm} mit dem +arithmetisch-geometrischen Mittel berechnet wurden. +Die dort angetroffenen numerischen Schwierigkeiten treten bei der +Berechnung der Umkehrfunktion jedoch nicht auf. + +Die grundlegende Mechanik dieser Berechnungsmethode wird auf +Seite~\pageref{buch:elliptisch:jacobi:agm} dargestellt und +und in den Übungsaufgaben +\ref{buch:elliptisch:aufgabe:2} bis \ref{buch:elliptisch:aufgabe:5} +etwas näher untersucht wird. + +Aus der Theorie das arithmetisch-geometrischen Mittels lässt sich +die sogenannte Landen-Trans\-formation herleiten. +\index{Landen-Transformation}% +Sie stellt eine Verbindung zwischen +den Werten der elliptischen Funktionen zu verschiedenen Moduli $k$ her. +Sie ist die Basis aller effizienten Berechnungsmethoden. + + +% algebraische Beziehungen \\ +% Additionstheoreme \\ +% Perioden % use https://math.stackexchange.com/questions/3013692/how-to-show-that-jacobi-sine-function-is-doubly-periodic diff --git a/buch/chapters/110-elliptisch/lemniskate.tex b/buch/chapters/110-elliptisch/lemniskate.tex index 61476a0..04c137d 100644 --- a/buch/chapters/110-elliptisch/lemniskate.tex +++ b/buch/chapters/110-elliptisch/lemniskate.tex @@ -17,12 +17,6 @@ elliptischen Funktionen hergestellt werden. % \subsection{Lemniskate \label{buch:gemotrie:subsection:lemniskate}} -\begin{figure} -\centering -\includegraphics{chapters/110-elliptisch/images/lemniskate.pdf} -\caption{Bogenlänge und Radius der Lemniskate von Bernoulli. -\label{buch:elliptisch:fig:lemniskate}} -\end{figure} Die {\em Lemniskate von Bernoulli} ist die Kurve vierten Grades mit der Gleichung \index{Lemniskate von Bernoulli}% @@ -64,6 +58,12 @@ In dieser Normierung, der Standard-Lemniskaten, liegen die Scheitel bei $\pm 1$. Dies ist die Skalierung, die für die Definition des lemniskatischen Sinus und Kosinus verwendet werden soll. +\begin{figure} +\centering +\includegraphics{chapters/110-elliptisch/images/lemniskate.pdf} +\caption{Bogenlänge und Radius der Lemniskate von Bernoulli. +\label{buch:elliptisch:fig:lemniskate}} +\end{figure} \subsubsection{Polarkoordinaten} In Polarkoordinaten $x=r\cos\varphi$ und $y=r\sin\varphi$ diff --git a/buch/chapters/110-elliptisch/mathpendel.tex b/buch/chapters/110-elliptisch/mathpendel.tex index 39cb418..54b7531 100644 --- a/buch/chapters/110-elliptisch/mathpendel.tex +++ b/buch/chapters/110-elliptisch/mathpendel.tex @@ -53,7 +53,7 @@ enthält. Der Energieerhaltungssatz kann uns eine solche Gleichung geben. Die Summe von kinetischer und potentieller Energie muss konstant sein. Dies führt auf -\[ +\begin{equation} E_{\text{kinetisch}} + E_{\text{potentiell}} @@ -66,8 +66,9 @@ mgl(1-\cos\vartheta) + mgl(1-\cos\vartheta) = -E -\] +E. +\label{buch:elliptisch:mathpendel:energiegleichung} +\end{equation} Durch Auflösen nach $\dot{\vartheta}$ kann man jetzt die Differentialgleichung \[ @@ -94,159 +95,229 @@ Für $E>2mgl$ wird sich das Pendel im Kreis bewegen, für sehr grosse Energie ist die kinetische Energie dominant, die Verlangsamung im höchsten Punkt wird immer weniger ausgeprägt sein. -\begin{figure} -\centering -\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} -\caption{% -Abhängigkeit der elliptischen Funktionen von $u$ für -verschiedene Werte von $k^2=m$. -Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, -$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese -sind in allen Plots in einer helleren Farbe eingezeichnet. -Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig -von den trigonometrischen Funktionen ab, -es ist aber klar erkennbar, dass die anharmonischen Terme in der -Differentialgleichung die Periode mit steigender Amplitude verlängern. -Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass -die Energie des Pendels fast ausreicht, dass es den höchsten Punkt -erreichen kann, was es für $m$ macht. -\label{buch:elliptisch:fig:jacobiplots}} -\end{figure} + % % Koordinatentransformation auf elliptische Funktionen % \subsubsection{Koordinatentransformation auf elliptische Funktionen} Wir verwenden als neue Variable -\[ -y = \sin\frac{\vartheta}2 -\] -mit der Ableitung -\[ -\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. -\] -Man beachte, dass $y$ nicht eine Koordinate in -Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. - -Aus den Halbwinkelformeln finden wir -\[ +\begin{align} +y +&= +\sin\frac{\vartheta}2 +&&\Rightarrow& +\cos^2\frac{\vartheta}2 +&= +1-y^2. +\label{buch:elliptisch:mathpendel:ydef} +\intertext{Die Ableitung ist} +\dot{y} +&= +\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta} +&&\Rightarrow& +\dot{y}^2 +&= +\frac14\cos^2\frac{\vartheta}2\cdot\dot{\vartheta}^2. +\label{buch:elliptisch:mathpendel:yabl} +\intertext{% +Man beachte, dass die Koordinate senkrecht zur $x$-Achse in +Abbildung~\ref{buch:elliptisch:fig:mathpendel} die Auslenkung +$l\sin\vartheta$ ist, $y$ ist also nicht die Auslenkung senkrecht +zur $x$-Achse! +Aus den Halbwinkelformeln finden wir ausserdem +} \cos\vartheta -= +&= 1-2\sin^2 \frac{\vartheta}2 = -1-2y^2. -\] -Dies können wir zusammen mit der -Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ -in die Energiegleichung einsetzen und erhalten -\[ -\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E -\qquad\Rightarrow\qquad -\frac14 \dot{\vartheta}^2 = \frac{E}{2ml^2} - \frac{g}{2l}y^2. -\] -Der konstante Term auf der rechten Seite ist grösser oder kleiner als -$1$ je nachdem, ob das Pendel sich im Kreis bewegt oder nicht. +1-2y^2 +&&\Rightarrow& +1-\cos\vartheta +&= +2y^2. +\label{buch:elliptisch:mathpendel:halbwinkel} +\end{align} +Die Grösse $1-\cos\vartheta$ haben wir in der Energiegleichung +\eqref{buch:elliptisch:mathpendel:energiegleichung} +bereits angetroffen. -Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ +Die Identitäten +\eqref{buch:elliptisch:mathpendel:halbwinkel} +%und +%\eqref{buch:elliptisch:mathpendel:ydef} +können wir jetzt in die +Energiegleichung~\eqref{buch:elliptisch:mathpendel:energiegleichung} +einsetzen und erhalten +\begin{align} +\frac12ml^2\dot{\vartheta}^2 + 2mgly^2 +&= +E +\intertext{und nach Division durch $2ml^2$} +\frac14 \dot{\vartheta}^2 +&= +\frac{E}{2ml^2} - \frac{g}{l}y^2. +\label{buch:elliptisch:mathpendel:thetadgl} +\end{align} +%Der konstante Term auf der rechten Seite ist grösser oder kleiner als +%$1$ je nachdem, ob das Pendel sich im Kreis bewegt oder nicht. +Durch Multiplizieren mit der rechten Gleichung von +\eqref{buch:elliptisch:mathpendel:ydef} erhalten wir auf der linken Seite einen Ausdruck, den wir +mit Hilfe von \eqref{buch:elliptisch:mathpendel:yabl} als Funktion von $\dot{y}$ ausdrücken können. Wir erhalten -\begin{align*} -\frac14 +\begin{align} +\underbrace{\frac14 \cos^2\frac{\vartheta}2 \cdot -\dot{\vartheta}^2 +\dot{\vartheta}^2}_{\displaystyle=\dot{y}^2} &= -\frac14 (1-y^2) -\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) +\biggl(\frac{E}{2ml^2} -\frac{g}{l}y^2\biggr) +\notag \\ \dot{y}^2 &= -\frac{1}{4} (1-y^2) -\biggl(\frac{E}{2ml^2} -\frac{g}{2l}y^2\biggr) -\end{align*} +\biggl(\frac{E}{2ml^2} -\frac{g}{l}y^2\biggr) +\label{buch:elliptisch:mathpendel:ydgl} +\end{align} Die letzte Gleichung hat die Form einer Differentialgleichung für elliptische Funktionen. -Welche Funktion verwendet werden muss, hängt von der Grösse der -Koeffizienten in der zweiten Klammer ab. -Die Tabelle~\ref{buch:elliptisch:tabelle:loesungsfunktionen} -zeigt, dass in der zweiten Klammer jeweils einer der Terme -$1$ sein muss. +Welche Funktion verwendet werden muss, hängt von der relativen +Grösse der Koeffizienten in der zweiten Klammer ab. % -% Der Fall E < 2mgl +% Zeittransformation zur Elimination des konstanten Faktors % -\subsubsection{Der Fall $E<2mgl$} - - -Wir verwenden als neue Variable -\[ -y = \sin\frac{\vartheta}2 -\] -mit der Ableitung +\subsubsection{Zeittransformation} +Die Gleichung~\eqref{buch:elliptisch:mathpendel:ydgl} kann auch in +die Form +\begin{equation} +\frac{2ml^2}{E}\dot{y}^2 += +(1-y^2)\biggl(1-\frac{2mgl}{E}y^2\biggr) +\label{buch:elliptisch:mathpendel:ydgl2} +\end{equation} +gebracht werden. +Der konstante Faktor auf der linken Seite kann wie in der Diskussion +des anharmonischen Oszillators durch eine lineare +Transformation der Zeit zum Verschwinden gebracht werden. +Dazu setzt man $z(t) = y(bt)$ und bekommt \[ -\dot{y}=\frac12\cos\frac{\vartheta}{2}\cdot \dot{\vartheta}. +\frac{d}{dt}z(t) += +\frac{d}{dt}y(bt) \frac{d\,bt}{dt} += +b\dot{y}(bt). \] -Man beachte, dass $y$ nicht eine Koordinate in -Abbildung~\ref{buch:elliptisch:fig:mathpendel} ist. +Die Zeit muss also mit dem Faktor $\sqrt{2ml^2/E}$ skaliert werden. + +% +% Nullstellen der rechten Seite der Differentialgleichung +% +\subsubsection{Nullstellen der rechten Seite} +Die rechte Seite von \eqref{buch:elliptisch:mathpendel:ydgl2} +hat die beiden Nullstellen $1$ und +\begin{equation} +y_0=\sqrt{\frac{E}{2mgl}}. +\label{buch:elliptisch:mathpendel:y0} +\end{equation} +Die Differentialgleichung kann damit als +\begin{equation} +\dot{y}^2 += +(1-y^2)\biggl(1-\frac{1}{y_0^2}y^2\biggr) +\label{buch:elliptisch:mathpendel:y0dgl} +\end{equation} +geschrieben werden. +Da die linke Seite $\ge 0$ sein muss, muss +\( +y\le \min(1,y_0) +\) +sein. +Damit ergeben sich zwei Fälle. +Wenn $y_0<1$ ist, dann schwingt das Pendel. +Der Fall $y_0>1$ entspricht einer Bewegung, bei der das Pendel +um den Punkt $O$ rotiert. + + +\begin{figure} +\centering +\includegraphics[width=\textwidth]{chapters/110-elliptisch/images/jacobiplots.pdf} +\caption{% +Abhängigkeit der elliptischen Funktionen von $u$ für +verschiedene Werte von $k^2=m$. +Für $m=0$ ist $\operatorname{sn}(u,0)=\sin u$, +$\operatorname{cn}(u,0)=\cos u$ und $\operatorname{dn}(u,0)=1$, diese +sind in allen Plots in einer helleren Farbe eingezeichnet. +Für kleine Werte von $m$ weichen die elliptischen Funktionen nur wenig +von den trigonometrischen Funktionen ab, +es ist aber klar erkennbar, dass die anharmonischen Terme in der +Differentialgleichung die Periode mit steigender Amplitude verlängern. +Sehr grosse Werte von $m$ nahe bei $1$ entsprechen der Situation, dass +die Energie des Pendels fast ausreicht, dass es den höchsten Punkt +erreichen kann, was es für $m$ macht. +\label{buch:elliptisch:fig:jacobiplots}} +\end{figure} -Aus den Halbwinkelformeln finden wir +\subsubsection{Der Fall $E>2mgl$} +In diesem Fall ist die zweite Nullstelle $y_0>1$ oder $1/y_0^2 < 1$. +Die Differentialgleichung~\eqref{buch:elliptisch:mathpendel:y0dgl} +sieht ganz ähnlich aus wie die Differentialgleichung der +Funktion $\operatorname{sn}(u,k)$, tatsächlich wird sie zur +Differentialgleichung von $\operatorname{sn}(u,k)$ wenn man \[ -\cos\vartheta +k^2 = -1-2\sin^2 \frac{\vartheta}2 +1/y_0^2 = -1-2y^2. +\frac{2mgl}{E} \] -Dies können wir zusammen mit der -Identität $\cos^2\vartheta/2 = 1-\sin^2\vartheta/2 = 1-y^2$ -in die Energiegleichung einsetzen und erhalten -\[ -\frac12ml^2\dot{\vartheta}^2 + mgly^2 = E. -\] -Durch Multiplizieren mit $\cos^2\frac{\vartheta}{2}=1-y^2$ -erhalten wir auf der linken Seite einen Ausdruck, den wir -als Funktion von $\dot{y}$ ausdrücken können. -Wir erhalten -\begin{align*} -\frac12ml^2 -\cos^2\frac{\vartheta}2 -\dot{\vartheta}^2 -&= -(1-y^2) -(E -mgly^2) -\\ -\frac{1}{4}\cos^2\frac{\vartheta}{2}\dot{\vartheta}^2 -&= -\frac{1}{2} -(1-y^2) -\biggl(\frac{E}{ml^2} -\frac{g}{l}y^2\biggr) -\\ +wählt. +In diesem Fall ist also $y=\operatorname{sn}(u,1/y_0)$ eine Lösung +der Differentialgleichung, wobei $u$ eine lineare Funktion der Zeit +ist. + +Wenn $y_0 \gg 1$ ist, dann ist $k\approx 0$ und die Bewegung ist +entspricht einer gleichförmigen Kreisbewegung. +Je näher $y_0$ an $1$ liegt, desto näher an $1$ ist auch $k$ und +desto grösser wird die Verlangsamung der Bewgung in der Nähe des +Scheitels, das Pendel verweilt sehr lange. +Dies äussert sich in Abbildung~\ref{buch:elliptisch:fig:jacobiplots} +durch die lange Verweildauer der Funktion nahe der Extrema. + +% +% Der Fall E < 2mgl +% +\subsubsection{Der Fall $E<2mgl$} +In diesem Fall ist $y_0<1$ und die +Differentialgleichung~\eqref{buch:elliptisch:mathpendel:y0dgl} +sieht zwar immer noch wie eine Differentialgleichung für +$\operatorname{sn}(u,k)$ aus, aber die Lage der Nullstellen +der rechten Seite ist verkehrt. +Indem wir $y=y_0z$ schreiben, erhalten wir +\begin{equation} \dot{y}^2 -&= -\frac{E}{2ml^2} -(1-y^2)\biggl( -1-\frac{2gml}{E}y^2 -\biggr). -\end{align*} -Dies ist genau die Form der Differentialgleichung für die elliptische -Funktion $\operatorname{sn}(u,k)$ -mit $k^2 = 2gml/E< 1$. - -XXX Verbindung zur Abbildung - -%% -%% Der Fall E > 2mgl -%% -%\subsection{Der Fall $E > 2mgl$} -%In diesem Fall hat das Pendel im höchsten Punkte immer noch genügend -%kinetische Energie, so dass es sich im Kreise dreht. -%Indem wir die Gleichung - - -%\subsection{Soliton-Lösungen der Sinus-Gordon-Gleichung} - -%\subsection{Nichtlineare Differentialgleichung vierter Ordnung} -%XXX Möbius-Transformation \\ -%XXX Reduktion auf die Differentialgleichung elliptischer Funktionen += +y_0^2 \dot{z}^2 += +(1-y_0^2z^2)(1-z^2). +\end{equation} +Wieder kann durch eine lineare Transformation der Zeit der Faktor $y_0^2$ +auf der linken Seite zum Verschwinden gebracht werden, es bleibt +die Differentialgleichung der Funktion $\operatorname{sn}(u,k)$ +mit $k=y_0$. +Daraus liest man ab, dass $y_0\operatorname{sn}(u,k)$ die Bewegung +des Pendels im oszillatorischen Fall beschreibt, wobei $u$ wieder +eine lineare Funktion der Zeit ist. + +Wenn $y_0\ll 1$ ist, dann ist auch $k$ sehr klein und die lineare +Näherung ist sehr gut, das Pendel verhält sich wie ein harmonischer +Oszillator mit einer Sinus-Schwingung als Lösung. +Für $y_0=k$ nahe an $1$ dagegen erreicht die Schwingung fast den +die maximale Höhe und wird dort sehr langsam. +Dies äussert sich in Abbildung~ +Dies äussert sich in Abbildung~\ref{buch:elliptisch:fig:jacobiplots} +wiederum durch die lange Verweildauer der Funktion nahe der Extrema. + diff --git a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex index 694f18a..af094c6 100644 --- a/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex +++ b/buch/chapters/110-elliptisch/uebungsaufgaben/1.tex @@ -1,3 +1,4 @@ +\label{buch:elliptisch:aufgabe:1} In einem anharmonische Oszillator oszilliert eine Masse $m$ unter dem Einfluss einer Kraft, die nach dem Gesetz \[ diff --git a/buch/chapters/part1.tex b/buch/chapters/part1.tex index bee4416..52b18a0 100644 --- a/buch/chapters/part1.tex +++ b/buch/chapters/part1.tex @@ -35,6 +35,7 @@ %\end{appendices} \vfill \pagebreak + \ifodd\value{page}\else\null\clearpage\fi \lhead{Literatur} \rhead{} diff --git a/buch/chapters/references.bib b/buch/chapters/references.bib index e8f3494..d14a3d2 100644 --- a/buch/chapters/references.bib +++ b/buch/chapters/references.bib @@ -120,7 +120,7 @@ } @article{buch:pearsondgl, title = {Orthogonal matrix polynomials, scalar-type Rordigues' formulas and Pearson equations}, - author = { Antion J. Dur\'an and F. Alberto Grünbaum }, + author = { Antonio J. Dur\'an and F. Alberto Grünbaum }, year = 2005, journal = { Journal of Approximation theory }, volume = 134, @@ -155,3 +155,18 @@ pages = { 585--608 }, year = 1988 } + +@book{buch:schwalm, + author = { William A. Schwalm }, + title = { Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals }, + publisher = { IOP Science }, + year = 2015, + ISBN = { 978-1-6817-4166-6 } +} + +@misc{buch:schwalm-youtube, + author = { William A. Schwalm }, + title = { Elliptic Functions and Elliptic Integrals }, + howpublished = { \url{https://youtu.be/DCXItCajCyo} }, + year = 2018 +} -- cgit v1.2.1 From 7fb8462834ce37e6a468e42b4729c51fc821ffe9 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 5 Jul 2022 18:09:40 +0200 Subject: fix typo in nav/references.bib --- buch/papers/nav/references.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/buch/papers/nav/references.bib b/buch/papers/nav/references.bib index 10dbf66..c67aaac 100644 --- a/buch/papers/nav/references.bib +++ b/buch/papers/nav/references.bib @@ -35,7 +35,7 @@ @online{nav:winkel, editor={Unbekannt}, title = {Sphärische Trigonometrie}, - year={2022} + year={2022}, url = {https://de.wikipedia.org/wiki/Sphärische_Trigonometrie} } -- cgit v1.2.1 From a58f08028c11d87c3d45e10648fbb7e1e0f080b5 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 5 Jul 2022 19:37:34 +0200 Subject: minor fixes --- buch/papers/nav/bsp.tex | 1 + buch/papers/nav/bsp2.tex | 1 + 2 files changed, 2 insertions(+) diff --git a/buch/papers/nav/bsp.tex b/buch/papers/nav/bsp.tex index d544588..ff01828 100644 --- a/buch/papers/nav/bsp.tex +++ b/buch/papers/nav/bsp.tex @@ -1,4 +1,5 @@ \section{Beispielrechnung} +\rhead{Beispielrechnung} \subsection{Einführung} In diesem Abschnitt wird die Theorie vom Abschnitt 21.6 in einem Praxisbeispiel angewendet. diff --git a/buch/papers/nav/bsp2.tex b/buch/papers/nav/bsp2.tex index 23380eb..8ca214f 100644 --- a/buch/papers/nav/bsp2.tex +++ b/buch/papers/nav/bsp2.tex @@ -1,4 +1,5 @@ \section{Beispielrechnung} +\rhead{Beispielrechnung} \subsection{Einführung} In diesem Abschnitt wird die Theorie vom Abschnitt \ref{sta} in einem Praxisbeispiel angewendet. -- cgit v1.2.1 From fde57297b3efbef28d09a532e1b3895d2b2ad917 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 14 Jul 2022 15:03:28 +0200 Subject: Correct Makefile, add text to gamma.tex, separate python-scripts for each image --- buch/papers/laguerre/Makefile | 38 +- buch/papers/laguerre/Makefile.inc | 4 +- buch/papers/laguerre/definition.tex | 2 +- buch/papers/laguerre/gamma.tex | 212 +- buch/papers/laguerre/images/estimate.pgf | 1160 ------- buch/papers/laguerre/images/estimates.pgf | 1700 ++++++++++ buch/papers/laguerre/images/gammaplot.pdf | Bin 23297 -> 23297 bytes buch/papers/laguerre/images/integrand.pgf | 2670 ++++++++++++++++ buch/papers/laguerre/images/integrand_exp.pgf | 1916 +++++++++++ buch/papers/laguerre/images/integrands.pgf | 2865 ----------------- buch/papers/laguerre/images/integrands_exp.pgf | 1968 ------------ buch/papers/laguerre/images/laguerre_poly.pgf | 1838 +++++++++++ buch/papers/laguerre/images/laguerre_polynomes.pgf | 1838 ----------- buch/papers/laguerre/images/rel_error_mirror.pgf | 3381 ++++++++++---------- buch/papers/laguerre/images/rel_error_range.pgf | 2467 ++++++++++++-- buch/papers/laguerre/images/rel_error_shifted.pgf | 1446 +++++---- buch/papers/laguerre/images/rel_error_simple.pgf | 2648 ++++++++------- buch/papers/laguerre/images/rel_error_simple.png | Bin 61966 -> 0 bytes buch/papers/laguerre/images/targets-img0.png | Bin 0 -> 836 bytes buch/papers/laguerre/images/targets-img1.png | Bin 0 -> 429 bytes buch/papers/laguerre/images/targets.pdf | Bin 13199 -> 12530 bytes buch/papers/laguerre/images/targets.pgf | 1024 ++++++ buch/papers/laguerre/packages.tex | 2 +- .../presentation/sections/gamma_approx.tex | 8 +- .../laguerre/presentation/sections/laguerre.tex | 2 +- buch/papers/laguerre/quadratur.tex | 8 +- buch/papers/laguerre/scripts/estimates.py | 39 + buch/papers/laguerre/scripts/gamma_approx.ipynb | 616 ---- buch/papers/laguerre/scripts/gamma_approx.py | 181 +- buch/papers/laguerre/scripts/integrand.py | 74 +- buch/papers/laguerre/scripts/integrand_exp.py | 36 + buch/papers/laguerre/scripts/laguerre_plot.py | 101 - buch/papers/laguerre/scripts/laguerre_poly.py | 98 + buch/papers/laguerre/scripts/rel_error_mirror.py | 28 + buch/papers/laguerre/scripts/rel_error_range.py | 32 + buch/papers/laguerre/scripts/rel_error_shifted.py | 31 + buch/papers/laguerre/scripts/rel_error_simple.py | 29 + buch/papers/laguerre/scripts/targets.py | 48 + 38 files changed, 15675 insertions(+), 12835 deletions(-) delete mode 100644 buch/papers/laguerre/images/estimate.pgf create mode 100644 buch/papers/laguerre/images/estimates.pgf create mode 100644 buch/papers/laguerre/images/integrand.pgf create mode 100644 buch/papers/laguerre/images/integrand_exp.pgf delete mode 100644 buch/papers/laguerre/images/integrands.pgf delete mode 100644 buch/papers/laguerre/images/integrands_exp.pgf create mode 100644 buch/papers/laguerre/images/laguerre_poly.pgf delete mode 100644 buch/papers/laguerre/images/laguerre_polynomes.pgf delete mode 100644 buch/papers/laguerre/images/rel_error_simple.png create mode 100644 buch/papers/laguerre/images/targets-img0.png create mode 100644 buch/papers/laguerre/images/targets-img1.png create mode 100644 buch/papers/laguerre/images/targets.pgf create mode 100644 buch/papers/laguerre/scripts/estimates.py delete mode 100644 buch/papers/laguerre/scripts/gamma_approx.ipynb create mode 100644 buch/papers/laguerre/scripts/integrand_exp.py delete mode 100644 buch/papers/laguerre/scripts/laguerre_plot.py create mode 100644 buch/papers/laguerre/scripts/laguerre_poly.py create mode 100644 buch/papers/laguerre/scripts/rel_error_mirror.py create mode 100644 buch/papers/laguerre/scripts/rel_error_range.py create mode 100644 buch/papers/laguerre/scripts/rel_error_shifted.py create mode 100644 buch/papers/laguerre/scripts/rel_error_simple.py create mode 100644 buch/papers/laguerre/scripts/targets.py diff --git a/buch/papers/laguerre/Makefile b/buch/papers/laguerre/Makefile index 0f0985a..1ed87cc 100644 --- a/buch/papers/laguerre/Makefile +++ b/buch/papers/laguerre/Makefile @@ -3,9 +3,41 @@ # # (c) 2020 Prof Dr Andreas Mueller # +IMGFOLDER := images +PRESFOLDER := presentation -images: images/laguerre_polynomes.pdf +FIGURES := \ + images/targets.pdf \ + images/estimates.pgf \ + images/integrand.pgf \ + images/integrand_exp.pgf \ + images/laguerre_poly.pgf \ + images/rel_error_mirror.pgf \ + images/rel_error_range.pgf \ + images/rel_error_shifted.pgf \ + images/rel_error_simple.pgf \ + images/gammaplot.pdf -images/laguerre_polynomes.pdf: scripts/laguerre_plot.py - python3 scripts/laguerre_plot.py +.PHONY: all +all: images presentation +.PHONY: images +images: $(FIGURES) + +.PHONY: presentation +presentation: $(PRESFOLDER)/presentation.pdf + +images/%.pdf images/%.pgf: scripts/%.py + python3 $< + +images/gammaplot.pdf: images/gammaplot.tex images/gammapaths.tex + cd $(IMGFOLDER) && latexmk -quiet -pdf gammaplot.tex + +$(PRESFOLDER)/%.pdf: $(PRESFOLDER)/%.tex $(FIGURES) + cd $(PRESFOLDER) && latexmk -quiet -pdf $(.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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--- /dev/null +++ b/buch/papers/laguerre/images/estimates.pgf @@ -0,0 +1,1700 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.500000in}{3.600000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.400000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.400000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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\usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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-\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetroundjoin% -\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetfillcolor{currentfill}% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% -\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% -\pgfusepath{stroke,fill}% -}% -\begin{pgfscope}% -\pgfsys@transformshift{4.552273in}{0.463273in}% -\pgfsys@useobject{currentmarker}{}% -\end{pgfscope}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=4.552273in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{1}}\)}% -\end{pgfscope}% -\begin{pgfscope}% 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necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% 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packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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-\pgfpathlineto{\pgfqpoint{4.745673in}{2.064252in}}% -\pgfpathlineto{\pgfqpoint{4.781175in}{1.953370in}}% -\pgfpathlineto{\pgfqpoint{4.816677in}{1.835719in}}% -\pgfpathlineto{\pgfqpoint{4.858096in}{1.689983in}}% -\pgfpathlineto{\pgfqpoint{4.899515in}{1.535245in}}% -\pgfpathlineto{\pgfqpoint{4.940934in}{1.371677in}}% -\pgfpathlineto{\pgfqpoint{4.982353in}{1.199498in}}% -\pgfpathlineto{\pgfqpoint{5.029689in}{0.992518in}}% -\pgfpathlineto{\pgfqpoint{5.077024in}{0.775107in}}% -\pgfpathlineto{\pgfqpoint{5.124360in}{0.547814in}}% -\pgfpathlineto{\pgfqpoint{5.177613in}{0.281092in}}% -\pgfpathlineto{\pgfqpoint{5.225582in}{0.031670in}}% -\pgfpathlineto{\pgfqpoint{5.225582in}{0.031670in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetmiterjoin% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.579040in}{0.041670in}}% -\pgfpathlineto{\pgfqpoint{0.579040in}{3.958330in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetmiterjoin% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.041670in}{2.000000in}}% -\pgfpathlineto{\pgfqpoint{5.953330in}{2.000000in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetmiterjoin% -\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% -\pgfsetfillcolor{currentfill}% -\pgfsetfillopacity{0.800000}% -\pgfsetlinewidth{1.003750pt}% -\definecolor{currentstroke}{rgb}{0.800000,0.800000,0.800000}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetstrokeopacity{0.800000}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.813961in}{0.080837in}}% -\pgfpathlineto{\pgfqpoint{2.944352in}{0.080837in}}% -\pgfpathquadraticcurveto{\pgfqpoint{2.977686in}{0.080837in}}{\pgfqpoint{2.977686in}{0.114170in}}% -\pgfpathlineto{\pgfqpoint{2.977686in}{1.076018in}}% -\pgfpathquadraticcurveto{\pgfqpoint{2.977686in}{1.109352in}}{\pgfqpoint{2.944352in}{1.109352in}}% -\pgfpathlineto{\pgfqpoint{0.813961in}{1.109352in}}% -\pgfpathquadraticcurveto{\pgfqpoint{0.780627in}{1.109352in}}{\pgfqpoint{0.780627in}{1.076018in}}% -\pgfpathlineto{\pgfqpoint{0.780627in}{0.114170in}}% -\pgfpathquadraticcurveto{\pgfqpoint{0.780627in}{0.080837in}}{\pgfqpoint{0.813961in}{0.080837in}}% -\pgfpathlineto{\pgfqpoint{0.813961in}{0.080837in}}% -\pgfpathclose% -\pgfusepath{stroke,fill}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.847294in}{0.974391in}}% -\pgfpathlineto{\pgfqpoint{1.013961in}{0.974391in}}% -\pgfpathlineto{\pgfqpoint{1.180627in}{0.974391in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=1.313961in,y=0.916057in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=0\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.847294in}{0.729762in}}% -\pgfpathlineto{\pgfqpoint{1.013961in}{0.729762in}}% -\pgfpathlineto{\pgfqpoint{1.180627in}{0.729762in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=1.313961in,y=0.671429in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=1\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.847294in}{0.485133in}}% -\pgfpathlineto{\pgfqpoint{1.013961in}{0.485133in}}% -\pgfpathlineto{\pgfqpoint{1.180627in}{0.485133in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=1.313961in,y=0.426800in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=2\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.847294in}{0.240504in}}% -\pgfpathlineto{\pgfqpoint{1.013961in}{0.240504in}}% -\pgfpathlineto{\pgfqpoint{1.180627in}{0.240504in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=1.313961in,y=0.182171in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=3\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.580392,0.403922,0.741176}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.045823in}{0.974391in}}% -\pgfpathlineto{\pgfqpoint{2.212490in}{0.974391in}}% -\pgfpathlineto{\pgfqpoint{2.379157in}{0.974391in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=2.512490in,y=0.916057in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=4\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.549020,0.337255,0.294118}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.045823in}{0.729762in}}% -\pgfpathlineto{\pgfqpoint{2.212490in}{0.729762in}}% -\pgfpathlineto{\pgfqpoint{2.379157in}{0.729762in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=2.512490in,y=0.671429in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=5\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.890196,0.466667,0.760784}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.045823in}{0.485133in}}% -\pgfpathlineto{\pgfqpoint{2.212490in}{0.485133in}}% -\pgfpathlineto{\pgfqpoint{2.379157in}{0.485133in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=2.512490in,y=0.426800in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=6\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{1.505625pt}% -\definecolor{currentstroke}{rgb}{0.498039,0.498039,0.498039}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.045823in}{0.240504in}}% -\pgfpathlineto{\pgfqpoint{2.212490in}{0.240504in}}% -\pgfpathlineto{\pgfqpoint{2.379157in}{0.240504in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=2.512490in,y=0.182171in,left,base]{\color{textcolor}\sffamily\fontsize{12.000000}{14.400000}\selectfont \(\displaystyle n=7\)}% -\end{pgfscope}% -\end{pgfpicture}% -\makeatother% -\endgroup% diff --git a/buch/papers/laguerre/images/rel_error_mirror.pgf b/buch/papers/laguerre/images/rel_error_mirror.pgf index de1cd53..45d502e 100644 --- a/buch/papers/laguerre/images/rel_error_mirror.pgf +++ b/buch/papers/laguerre/images/rel_error_mirror.pgf @@ -56,16 +56,16 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetstrokeopacity{0.000000}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.458330in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{2.458330in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathclose% \pgfusepath{fill}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -73,8 +73,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.482258in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482258in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -92,7 +92,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.463273in}% +\pgfsys@transformshift{0.482258in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -100,10 +100,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.672226in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}15}% +\pgftext[x=0.482258in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}15}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -111,8 +111,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.371849in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.371849in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.213542in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.213542in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -130,7 +130,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.371849in}{0.463273in}% +\pgfsys@transformshift{1.213542in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -138,10 +138,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.371849in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}10}% +\pgftext[x=1.213542in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}10}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -149,8 +149,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.071472in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.071472in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.944827in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.944827in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -168,7 +168,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.071472in}{0.463273in}% +\pgfsys@transformshift{1.944827in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -176,10 +176,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.071472in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}5}% +\pgftext[x=1.944827in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}5}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -187,8 +187,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.771095in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.771095in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.676111in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.676111in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -206,7 +206,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.771095in}{0.463273in}% +\pgfsys@transformshift{2.676111in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -214,10 +214,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.771095in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}% +\pgftext[x=2.676111in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -225,8 +225,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.470718in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.470718in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.407396in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.407396in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -244,7 +244,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.470718in}{0.463273in}% +\pgfsys@transformshift{3.407396in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -252,10 +252,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.470718in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 5}% +\pgftext[x=3.407396in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 5}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -263,8 +263,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.170342in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.170342in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.138680in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.138680in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -282,7 +282,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.170342in}{0.463273in}% +\pgfsys@transformshift{4.138680in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -290,10 +290,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=4.170342in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 10}% +\pgftext[x=4.138680in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 10}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -331,7 +331,7 @@ \pgftext[x=4.869965in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 15}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -339,8 +339,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.812150in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.812150in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.628514in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.628514in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -358,12 +358,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.812150in}{0.463273in}% +\pgfsys@transformshift{0.628514in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -371,8 +371,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.952075in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.952075in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.774771in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.774771in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -390,12 +390,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.952075in}{0.463273in}% +\pgfsys@transformshift{0.774771in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -403,8 +403,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.092000in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.092000in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.921028in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.921028in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -422,12 +422,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.092000in}{0.463273in}% +\pgfsys@transformshift{0.921028in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -435,8 +435,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.231924in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.231924in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.067285in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.067285in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -454,12 +454,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.231924in}{0.463273in}% +\pgfsys@transformshift{1.067285in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -467,8 +467,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.511774in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.511774in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.359799in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.359799in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -486,12 +486,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.511774in}{0.463273in}% +\pgfsys@transformshift{1.359799in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -499,8 +499,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.651698in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.651698in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.506056in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.506056in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -518,12 +518,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.651698in}{0.463273in}% +\pgfsys@transformshift{1.506056in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -531,8 +531,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.791623in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.791623in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.652313in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.652313in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -550,12 +550,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.791623in}{0.463273in}% +\pgfsys@transformshift{1.652313in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -563,8 +563,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.931547in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.931547in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.798570in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.798570in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -582,12 +582,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.931547in}{0.463273in}% +\pgfsys@transformshift{1.798570in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -595,8 +595,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.211397in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.211397in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.091083in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.091083in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -614,12 +614,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.211397in}{0.463273in}% +\pgfsys@transformshift{2.091083in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -627,8 +627,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.351321in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.351321in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.237340in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.237340in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -646,12 +646,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.351321in}{0.463273in}% +\pgfsys@transformshift{2.237340in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -659,8 +659,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.491246in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.491246in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.383597in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.383597in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -678,12 +678,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.491246in}{0.463273in}% +\pgfsys@transformshift{2.383597in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -691,8 +691,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.631171in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.631171in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.529854in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.529854in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -710,12 +710,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.631171in}{0.463273in}% +\pgfsys@transformshift{2.529854in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -723,8 +723,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.911020in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.911020in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.822368in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.822368in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -742,12 +742,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.911020in}{0.463273in}% +\pgfsys@transformshift{2.822368in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -755,8 +755,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.050944in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.050944in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.968625in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.968625in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -774,12 +774,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.050944in}{0.463273in}% +\pgfsys@transformshift{2.968625in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -787,8 +787,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.190869in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.190869in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.114882in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.114882in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -806,12 +806,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.190869in}{0.463273in}% +\pgfsys@transformshift{3.114882in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -819,8 +819,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.330794in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.330794in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.261139in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.261139in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -838,12 +838,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.330794in}{0.463273in}% +\pgfsys@transformshift{3.261139in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -851,8 +851,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.610643in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.610643in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.553653in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.553653in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -870,12 +870,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.610643in}{0.463273in}% +\pgfsys@transformshift{3.553653in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -883,8 +883,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.750568in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.750568in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.699909in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.699909in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -902,12 +902,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.750568in}{0.463273in}% +\pgfsys@transformshift{3.699909in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -915,8 +915,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.890492in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.890492in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.846166in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.846166in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -934,12 +934,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.890492in}{0.463273in}% +\pgfsys@transformshift{3.846166in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -947,8 +947,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.030417in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.030417in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.992423in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.992423in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -966,12 +966,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.030417in}{0.463273in}% +\pgfsys@transformshift{3.992423in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -979,8 +979,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.310266in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.310266in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.284937in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.284937in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -998,12 +998,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.310266in}{0.463273in}% +\pgfsys@transformshift{4.284937in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1011,8 +1011,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.450191in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.450191in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.431194in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.431194in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1030,12 +1030,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.450191in}{0.463273in}% +\pgfsys@transformshift{4.431194in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1043,8 +1043,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.590115in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.590115in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.577451in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.577451in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1062,12 +1062,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.590115in}{0.463273in}% +\pgfsys@transformshift{4.577451in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1075,8 +1075,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.730040in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.730040in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.723708in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.723708in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1094,7 +1094,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.730040in}{0.463273in}% +\pgfsys@transformshift{4.723708in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1102,10 +1102,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.771095in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% +\pgftext[x=2.676111in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1113,7 +1113,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1132,7 +1132,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.463273in}% +\pgfsys@transformshift{0.482257in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1140,10 +1140,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.231638in, y=0.410512in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-11}}\)}% +\pgftext[x=0.041670in, y=0.410512in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-11}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1151,7 +1151,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.795783in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.795783in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.795783in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1170,7 +1170,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.795783in}% +\pgfsys@transformshift{0.482257in}{0.795783in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1178,10 +1178,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=0.743021in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-9}}\)}% +\pgftext[x=0.097033in, y=0.743021in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-9}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1189,7 +1189,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.128292in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.128292in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.128292in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1208,7 +1208,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.128292in}% +\pgfsys@transformshift{0.482257in}{1.128292in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1216,10 +1216,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=1.075531in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-7}}\)}% +\pgftext[x=0.097033in, y=1.075531in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-7}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1227,7 +1227,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.460802in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.460802in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.460802in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1246,7 +1246,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.460802in}% +\pgfsys@transformshift{0.482257in}{1.460802in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1254,10 +1254,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=1.408040in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-5}}\)}% +\pgftext[x=0.097033in, y=1.408040in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-5}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1265,7 +1265,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.793311in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.793311in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.793311in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1284,7 +1284,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.793311in}% +\pgfsys@transformshift{0.482257in}{1.793311in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1292,10 +1292,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=1.740550in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-3}}\)}% +\pgftext[x=0.097033in, y=1.740550in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-3}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1303,7 +1303,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{2.125821in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{2.125821in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.125821in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1322,7 +1322,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{2.125821in}% +\pgfsys@transformshift{0.482257in}{2.125821in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1330,16 +1330,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=2.073059in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-1}}\)}% +\pgftext[x=0.097033in, y=2.073059in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-1}}\)}% \end{pgfscope}% \begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=0.176083in,y=1.460802in,,bottom,rotate=90.000000]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Relativer Fehler}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1347,143 +1341,144 @@ \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.679275in}{2.468330in}}% -\pgfpathlineto{\pgfqpoint{1.797935in}{2.410308in}}% -\pgfpathlineto{\pgfqpoint{1.987307in}{2.317895in}}% -\pgfpathlineto{\pgfqpoint{2.050431in}{2.284509in}}% -\pgfpathlineto{\pgfqpoint{2.103034in}{2.254104in}}% -\pgfpathlineto{\pgfqpoint{2.145117in}{2.227040in}}% -\pgfpathlineto{\pgfqpoint{2.176679in}{2.204343in}}% -\pgfpathlineto{\pgfqpoint{2.208241in}{2.178651in}}% 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+\pgfpathlineto{\pgfqpoint{4.781991in}{0.724684in}}% +\pgfpathlineto{\pgfqpoint{4.792987in}{0.729021in}}% +\pgfpathlineto{\pgfqpoint{4.803984in}{0.729358in}}% +\pgfpathlineto{\pgfqpoint{4.814981in}{0.725625in}}% +\pgfpathlineto{\pgfqpoint{4.825978in}{0.717212in}}% +\pgfpathlineto{\pgfqpoint{4.836974in}{0.702610in}}% +\pgfpathlineto{\pgfqpoint{4.847971in}{0.678109in}}% +\pgfpathlineto{\pgfqpoint{4.858968in}{0.631528in}}% +\pgfpathlineto{\pgfqpoint{4.861012in}{0.453273in}}% +\pgfpathlineto{\pgfqpoint{4.861012in}{0.453273in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -2898,8 +2895,8 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -2920,7 +2917,7 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482258in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -2931,7 +2928,7 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.482258in}{2.458330in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -2946,16 +2943,16 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetstrokeopacity{0.800000}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.753212in}{1.516709in}}% -\pgfpathlineto{\pgfqpoint{1.470533in}{1.516709in}}% -\pgfpathquadraticcurveto{\pgfqpoint{1.493672in}{1.516709in}}{\pgfqpoint{1.493672in}{1.539848in}}% -\pgfpathlineto{\pgfqpoint{1.493672in}{2.377344in}}% -\pgfpathquadraticcurveto{\pgfqpoint{1.493672in}{2.400483in}}{\pgfqpoint{1.470533in}{2.400483in}}% -\pgfpathlineto{\pgfqpoint{0.753212in}{2.400483in}}% -\pgfpathquadraticcurveto{\pgfqpoint{0.730073in}{2.400483in}}{\pgfqpoint{0.730073in}{2.377344in}}% -\pgfpathlineto{\pgfqpoint{0.730073in}{1.539848in}}% -\pgfpathquadraticcurveto{\pgfqpoint{0.730073in}{1.516709in}}{\pgfqpoint{0.753212in}{1.516709in}}% -\pgfpathlineto{\pgfqpoint{0.753212in}{1.516709in}}% +\pgfpathmoveto{\pgfqpoint{0.579480in}{1.327933in}}% +\pgfpathlineto{\pgfqpoint{1.431363in}{1.327933in}}% +\pgfpathquadraticcurveto{\pgfqpoint{1.459141in}{1.327933in}}{\pgfqpoint{1.459141in}{1.355711in}}% +\pgfpathlineto{\pgfqpoint{1.459141in}{2.361108in}}% +\pgfpathquadraticcurveto{\pgfqpoint{1.459141in}{2.388886in}}{\pgfqpoint{1.431363in}{2.388886in}}% +\pgfpathlineto{\pgfqpoint{0.579480in}{2.388886in}}% +\pgfpathquadraticcurveto{\pgfqpoint{0.551702in}{2.388886in}}{\pgfqpoint{0.551702in}{2.361108in}}% +\pgfpathlineto{\pgfqpoint{0.551702in}{1.355711in}}% +\pgfpathquadraticcurveto{\pgfqpoint{0.551702in}{1.327933in}}{\pgfqpoint{0.579480in}{1.327933in}}% +\pgfpathlineto{\pgfqpoint{0.579480in}{1.327933in}}% \pgfpathclose% \pgfusepath{stroke,fill}% \end{pgfscope}% @@ -2966,16 +2963,16 @@ \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.776351in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{0.892045in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{1.007740in}{2.306797in}}% +\pgfpathmoveto{\pgfqpoint{0.607257in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{0.746146in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{2.276418in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.100295in,y=2.266304in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=2\)}% +\pgftext[x=0.996146in,y=2.227807in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=2\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -2984,16 +2981,16 @@ \definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.776351in}{2.136984in}}% -\pgfpathlineto{\pgfqpoint{0.892045in}{2.136984in}}% -\pgfpathlineto{\pgfqpoint{1.007740in}{2.136984in}}% +\pgfpathmoveto{\pgfqpoint{0.607257in}{2.072561in}}% +\pgfpathlineto{\pgfqpoint{0.746146in}{2.072561in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{2.072561in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.100295in,y=2.096491in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=4\)}% +\pgftext[x=0.996146in,y=2.023950in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=4\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -3002,16 +2999,16 @@ \definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.776351in}{1.967171in}}% -\pgfpathlineto{\pgfqpoint{0.892045in}{1.967171in}}% -\pgfpathlineto{\pgfqpoint{1.007740in}{1.967171in}}% +\pgfpathmoveto{\pgfqpoint{0.607257in}{1.868704in}}% +\pgfpathlineto{\pgfqpoint{0.746146in}{1.868704in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{1.868704in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.100295in,y=1.926678in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=6\)}% +\pgftext[x=0.996146in,y=1.820092in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=6\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -3020,16 +3017,16 @@ \definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.776351in}{1.797358in}}% -\pgfpathlineto{\pgfqpoint{0.892045in}{1.797358in}}% -\pgfpathlineto{\pgfqpoint{1.007740in}{1.797358in}}% +\pgfpathmoveto{\pgfqpoint{0.607257in}{1.664846in}}% +\pgfpathlineto{\pgfqpoint{0.746146in}{1.664846in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{1.664846in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.100295in,y=1.756865in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=8\)}% +\pgftext[x=0.996146in,y=1.616235in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=8\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -3038,16 +3035,16 @@ \definecolor{currentstroke}{rgb}{0.580392,0.403922,0.741176}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.776351in}{1.627545in}}% -\pgfpathlineto{\pgfqpoint{0.892045in}{1.627545in}}% -\pgfpathlineto{\pgfqpoint{1.007740in}{1.627545in}}% +\pgfpathmoveto{\pgfqpoint{0.607257in}{1.460989in}}% +\pgfpathlineto{\pgfqpoint{0.746146in}{1.460989in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{1.460989in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.100295in,y=1.587052in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=10\)}% +\pgftext[x=0.996146in,y=1.412378in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=10\)}% \end{pgfscope}% \end{pgfpicture}% \makeatother% diff --git a/buch/papers/laguerre/images/rel_error_range.pgf b/buch/papers/laguerre/images/rel_error_range.pgf index ff73501..7448afc 100644 --- a/buch/papers/laguerre/images/rel_error_range.pgf +++ b/buch/papers/laguerre/images/rel_error_range.pgf @@ -27,7 +27,7 @@ \begingroup% \makeatletter% \begin{pgfpicture}% -\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.000000in}{2.500000in}}% \pgfusepath{use as bounding box, clip}% \begin{pgfscope}% \pgfsetbuttcap% @@ -39,9 +39,9 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% \pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}% -\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}% +\pgfpathlineto{\pgfqpoint{5.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{5.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}% \pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% \pgfpathclose% \pgfusepath{fill}% @@ -56,16 +56,16 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetstrokeopacity{0.000000}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.758330in}}% -\pgfpathlineto{\pgfqpoint{0.426895in}{4.758330in}}% -\pgfpathlineto{\pgfqpoint{0.426895in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathclose% \pgfusepath{fill}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -73,8 +73,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.020038in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.020038in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{0.929865in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.929865in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -92,7 +92,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.020038in}{0.463273in}% +\pgfsys@transformshift{0.929865in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -100,10 +100,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.020038in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}4}% +\pgftext[x=0.929865in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}4}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -111,8 +111,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.206325in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.206325in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{1.825079in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.825079in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -130,7 +130,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.206325in}{0.463273in}% +\pgfsys@transformshift{1.825079in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -138,10 +138,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.206325in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}2}% +\pgftext[x=1.825079in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}2}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -149,8 +149,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.392612in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.392612in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{2.720294in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.720294in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -168,7 +168,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.392612in}{0.463273in}% +\pgfsys@transformshift{2.720294in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -176,10 +176,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.392612in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}% +\pgftext[x=2.720294in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -187,8 +187,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.578899in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.578899in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{3.615508in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.615508in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -206,7 +206,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.578899in}{0.463273in}% +\pgfsys@transformshift{3.615508in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -214,10 +214,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=4.578899in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 2}% +\pgftext[x=3.615508in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 2}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -225,8 +225,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.765187in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{5.765187in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{4.510723in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.510723in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -244,7 +244,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{5.765187in}{0.463273in}% +\pgfsys@transformshift{4.510723in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -252,16 +252,176 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.765187in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 4}% +\pgftext[x=4.510723in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 4}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.482257in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.377472in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.377472in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.377472in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.272687in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.272687in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.272687in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.167901in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.167901in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.167901in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.063116in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.063116in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{4.063116in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.392612in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% +\pgftext[x=2.720294in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -269,8 +429,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.756214in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.756214in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -288,7 +448,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.756214in}% +\pgfsys@transformshift{0.482257in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -296,10 +456,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.041670in, y=1.703453in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-8}}\)}% +\pgftext[x=0.041670in, y=0.410512in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-11}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -307,8 +467,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.870428in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{0.870428in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -316,22 +476,28 @@ \pgfsetroundjoin% \definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% \pgfsetfillcolor{currentfill}% -\pgfsetlinewidth{0.602250pt}% +\pgfsetlinewidth{0.803000pt}% \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.027778in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% \pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{-0.027778in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{0.463273in}% +\pgfsys@transformshift{0.482257in}{0.870428in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.097033in, y=0.817666in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-9}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -339,8 +505,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{0.803361in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.803361in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.277582in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{1.277582in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -348,22 +514,28 @@ \pgfsetroundjoin% \definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% \pgfsetfillcolor{currentfill}% -\pgfsetlinewidth{0.602250pt}% +\pgfsetlinewidth{0.803000pt}% \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.027778in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% \pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{-0.027778in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{0.803361in}% +\pgfsys@transformshift{0.482257in}{1.277582in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.097033in, y=1.224821in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-7}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -371,8 +543,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.090902in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.090902in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.684737in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{1.684737in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -380,22 +552,28 @@ \pgfsetroundjoin% \definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% \pgfsetfillcolor{currentfill}% -\pgfsetlinewidth{0.602250pt}% +\pgfsetlinewidth{0.803000pt}% \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.027778in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% \pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{-0.027778in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.090902in}% +\pgfsys@transformshift{0.482257in}{1.684737in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.097033in, y=1.631975in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-5}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -403,8 +581,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.339980in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.339980in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{2.091891in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{2.091891in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -412,22 +590,28 @@ \pgfsetroundjoin% \definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% \pgfsetfillcolor{currentfill}% -\pgfsetlinewidth{0.602250pt}% +\pgfsetlinewidth{0.803000pt}% \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.027778in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% \pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{-0.027778in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.339980in}% +\pgfsys@transformshift{0.482257in}{2.091891in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.097033in, y=2.039129in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-3}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -435,8 +619,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.559683in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.559683in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.666851in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{0.666851in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -454,12 +638,18 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.559683in}% +\pgfsys@transformshift{0.482257in}{0.666851in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.063892in, y=0.614089in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-10}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -467,8 +657,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{3.049155in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{3.049155in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.074005in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{1.074005in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -486,12 +676,18 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{3.049155in}% +\pgfsys@transformshift{0.482257in}{1.074005in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.119255in, y=1.021243in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-8}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -499,8 +695,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{3.805477in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{3.805477in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.481159in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{1.481159in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -518,12 +714,18 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{3.805477in}% +\pgfsys@transformshift{0.482257in}{1.481159in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.119255in, y=1.428398in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-6}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -531,8 +733,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{4.342096in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.342096in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.888314in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{1.888314in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -550,12 +752,18 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{4.342096in}% +\pgfsys@transformshift{0.482257in}{1.888314in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.119255in, y=1.835552in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-4}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -563,8 +771,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{4.758330in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{2.295468in}}% +\pgfpathlineto{\pgfqpoint{4.958330in}{2.295468in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -582,218 +790,1781 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{4.758330in}% +\pgfsys@transformshift{0.482257in}{2.295468in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.119255in, y=2.242707in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-2}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% -\pgfsetlinewidth{3.011250pt}% +\pgfsetlinewidth{1.505625pt}% \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.458685in}{0.453273in}}% -\pgfpathlineto{\pgfqpoint{0.486507in}{1.638360in}}% -\pgfpathlineto{\pgfqpoint{0.516313in}{2.356782in}}% -\pgfpathlineto{\pgfqpoint{0.546120in}{2.840564in}}% -\pgfpathlineto{\pgfqpoint{0.575926in}{3.188428in}}% -\pgfpathlineto{\pgfqpoint{0.605732in}{3.443795in}}% -\pgfpathlineto{\pgfqpoint{0.635538in}{3.629171in}}% -\pgfpathlineto{\pgfqpoint{0.665344in}{3.757206in}}% -\pgfpathlineto{\pgfqpoint{0.695151in}{3.835102in}}% -\pgfpathlineto{\pgfqpoint{0.724957in}{3.866571in}}% -\pgfpathlineto{\pgfqpoint{0.754763in}{3.852698in}}% -\pgfpathlineto{\pgfqpoint{0.784569in}{3.776490in}}% -\pgfpathlineto{\pgfqpoint{0.814375in}{3.639548in}}% -\pgfpathlineto{\pgfqpoint{0.844182in}{3.444211in}}% -\pgfpathlineto{\pgfqpoint{0.873988in}{3.177116in}}% -\pgfpathlineto{\pgfqpoint{0.903794in}{2.814351in}}% -\pgfpathlineto{\pgfqpoint{0.933600in}{2.309221in}}% -\pgfpathlineto{\pgfqpoint{0.963406in}{1.553036in}}% -\pgfpathlineto{\pgfqpoint{0.987233in}{0.453273in}}% -\pgfpathmoveto{\pgfqpoint{1.052213in}{0.453273in}}% -\pgfpathlineto{\pgfqpoint{1.052825in}{0.544877in}}% -\pgfpathlineto{\pgfqpoint{1.082631in}{1.726239in}}% -\pgfpathlineto{\pgfqpoint{1.112437in}{2.413343in}}% -\pgfpathlineto{\pgfqpoint{1.142244in}{2.880497in}}% -\pgfpathlineto{\pgfqpoint{1.172050in}{3.217645in}}% -\pgfpathlineto{\pgfqpoint{1.201856in}{3.465216in}}% -\pgfpathlineto{\pgfqpoint{1.231662in}{3.644402in}}% -\pgfpathlineto{\pgfqpoint{1.261469in}{3.767168in}}% -\pgfpathlineto{\pgfqpoint{1.291275in}{3.840302in}}% -\pgfpathlineto{\pgfqpoint{1.321081in}{3.867227in}}% -\pgfpathlineto{\pgfqpoint{1.350887in}{3.848787in}}% -\pgfpathlineto{\pgfqpoint{1.380693in}{3.765173in}}% -\pgfpathlineto{\pgfqpoint{1.410500in}{3.622808in}}% -\pgfpathlineto{\pgfqpoint{1.440306in}{3.421020in}}% -\pgfpathlineto{\pgfqpoint{1.470112in}{3.145674in}}% -\pgfpathlineto{\pgfqpoint{1.499918in}{2.771335in}}% -\pgfpathlineto{\pgfqpoint{1.529724in}{2.247687in}}% -\pgfpathlineto{\pgfqpoint{1.559531in}{1.454638in}}% -\pgfpathlineto{\pgfqpoint{1.579481in}{0.453273in}}% -\pgfpathmoveto{\pgfqpoint{1.646693in}{0.453273in}}% -\pgfpathlineto{\pgfqpoint{1.648949in}{0.705347in}}% -\pgfpathlineto{\pgfqpoint{1.678755in}{1.809737in}}% -\pgfpathlineto{\pgfqpoint{1.708562in}{2.467810in}}% -\pgfpathlineto{\pgfqpoint{1.738368in}{2.919164in}}% -\pgfpathlineto{\pgfqpoint{1.768174in}{3.245981in}}% -\pgfpathlineto{\pgfqpoint{1.797980in}{3.485961in}}% -\pgfpathlineto{\pgfqpoint{1.827786in}{3.659073in}}% -\pgfpathlineto{\pgfqpoint{1.857593in}{3.776635in}}% -\pgfpathlineto{\pgfqpoint{1.887399in}{3.845041in}}% -\pgfpathlineto{\pgfqpoint{1.917205in}{3.867431in}}% -\pgfpathlineto{\pgfqpoint{1.947011in}{3.844410in}}% -\pgfpathlineto{\pgfqpoint{1.976818in}{3.753346in}}% -\pgfpathlineto{\pgfqpoint{2.006624in}{3.605478in}}% -\pgfpathlineto{\pgfqpoint{2.036430in}{3.397101in}}% -\pgfpathlineto{\pgfqpoint{2.066236in}{3.113261in}}% -\pgfpathlineto{\pgfqpoint{2.096042in}{2.726873in}}% -\pgfpathlineto{\pgfqpoint{2.125849in}{2.183623in}}% -\pgfpathlineto{\pgfqpoint{2.155655in}{1.350328in}}% -\pgfpathlineto{\pgfqpoint{2.171959in}{0.453273in}}% -\pgfpathmoveto{\pgfqpoint{2.240700in}{0.453273in}}% -\pgfpathlineto{\pgfqpoint{2.245073in}{0.852675in}}% -\pgfpathlineto{\pgfqpoint{2.274880in}{1.889231in}}% 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+\pgfpathlineto{\pgfqpoint{0.746146in}{1.664846in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{1.664846in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.996146in,y=1.616235in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=8\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{1.505625pt}% +\definecolor{currentstroke}{rgb}{0.580392,0.403922,0.741176}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.607257in}{1.460989in}}% +\pgfpathlineto{\pgfqpoint{0.746146in}{1.460989in}}% +\pgfpathlineto{\pgfqpoint{0.885035in}{1.460989in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=6.047533in,y=4.527807in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m^*\)}% +\pgftext[x=0.996146in,y=1.412378in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=10\)}% \end{pgfscope}% \end{pgfpicture}% \makeatother% diff --git a/buch/papers/laguerre/images/rel_error_shifted.pgf b/buch/papers/laguerre/images/rel_error_shifted.pgf index 707d492..32f95e0 100644 --- a/buch/papers/laguerre/images/rel_error_shifted.pgf +++ b/buch/papers/laguerre/images/rel_error_shifted.pgf @@ -27,7 +27,7 @@ \begingroup% \makeatletter% \begin{pgfpicture}% -\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{6.400000in}{4.800000in}}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{5.000000in}{2.500000in}}% \pgfusepath{use as bounding box, clip}% \begin{pgfscope}% \pgfsetbuttcap% @@ -39,9 +39,9 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% \pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{6.400000in}{0.000000in}}% -\pgfpathlineto{\pgfqpoint{6.400000in}{4.800000in}}% -\pgfpathlineto{\pgfqpoint{0.000000in}{4.800000in}}% +\pgfpathlineto{\pgfqpoint{5.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{5.000000in}{2.500000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.500000in}}% \pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% \pgfpathclose% \pgfusepath{fill}% @@ -57,15 +57,15 @@ \pgfsetstrokeopacity{0.000000}% \pgfsetdash{}{0pt}% \pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.758330in}}% -\pgfpathlineto{\pgfqpoint{0.426895in}{4.758330in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{0.426895in}{2.458330in}}% \pgfpathlineto{\pgfqpoint{0.426895in}{0.463273in}}% \pgfpathclose% \pgfusepath{fill}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -73,8 +73,46 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.595116in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.595116in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.426895in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.426895in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.426895in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.0}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.311094in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.311094in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -92,7 +130,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.595116in}{0.463273in}% +\pgfsys@transformshift{1.311094in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -100,10 +138,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.595116in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.2}% +\pgftext[x=1.311094in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.2}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -111,8 +149,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.793447in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.793447in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{2.195293in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.195293in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -130,7 +168,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.793447in}{0.463273in}% +\pgfsys@transformshift{2.195293in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -138,10 +176,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.793447in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.4}% +\pgftext[x=2.195293in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.4}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -149,8 +187,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.991778in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.991778in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{3.079492in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.079492in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -168,7 +206,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.991778in}{0.463273in}% +\pgfsys@transformshift{3.079492in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -176,10 +214,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.991778in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.6}% +\pgftext[x=3.079492in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.6}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -187,8 +225,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.190108in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{5.190108in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{3.963691in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.963691in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -206,7 +244,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{5.190108in}{0.463273in}% +\pgfsys@transformshift{3.963691in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -214,16 +252,214 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.190108in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.8}% +\pgftext[x=3.963691in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.8}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.847890in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{4.847890in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=4.847890in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 1.0}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.868994in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.868994in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.868994in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.753193in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.753193in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.753193in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.637393in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.637393in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.637393in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.521592in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.521592in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.521592in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.405791in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.405791in}{2.458330in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.602250pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.027778in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.027778in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{4.405791in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.392612in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% +\pgftext[x=2.637393in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -231,8 +467,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.756214in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.756214in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{1.063845in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{1.063845in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -250,7 +486,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.756214in}% +\pgfsys@transformshift{0.426895in}{1.063845in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -258,10 +494,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.041670in, y=1.703453in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-8}}\)}% +\pgftext[x=0.041670in, y=1.011084in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-8}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -270,7 +506,7 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% \pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -293,7 +529,7 @@ \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -301,8 +537,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{0.803361in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.803361in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{0.621244in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.621244in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -320,12 +556,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{0.803361in}% +\pgfsys@transformshift{0.426895in}{0.621244in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -333,8 +569,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.090902in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.090902in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{0.754807in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.754807in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -352,12 +588,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.090902in}% +\pgfsys@transformshift{0.426895in}{0.754807in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -365,8 +601,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.339980in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.339980in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{0.870504in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.870504in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -384,12 +620,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.339980in}% +\pgfsys@transformshift{0.426895in}{0.870504in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -397,8 +633,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{1.559683in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{1.559683in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{0.972556in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.972556in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -416,12 +652,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{1.559683in}% +\pgfsys@transformshift{0.426895in}{0.972556in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -429,8 +665,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{3.049155in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{3.049155in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{1.664417in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{1.664417in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -448,12 +684,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{3.049155in}% +\pgfsys@transformshift{0.426895in}{1.664417in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -461,8 +697,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{3.805477in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{3.805477in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{2.015729in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.015729in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -480,12 +716,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{3.805477in}% +\pgfsys@transformshift{0.426895in}{2.015729in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -493,8 +729,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{4.342096in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.342096in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{2.264989in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.264989in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -512,12 +748,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{4.342096in}% +\pgfsys@transformshift{0.426895in}{2.264989in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -525,8 +761,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{4.758330in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -544,12 +780,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.426895in}{4.758330in}% +\pgfsys@transformshift{0.426895in}{2.458330in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{5.931435in}{4.295057in}}% +\pgfpathrectangle{\pgfqpoint{0.426895in}{0.463273in}}{\pgfqpoint{4.420996in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -557,125 +793,99 @@ \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.579662in}{0.453273in}}% -\pgfpathlineto{\pgfqpoint{0.604838in}{0.691883in}}% -\pgfpathlineto{\pgfqpoint{0.634495in}{0.934532in}}% -\pgfpathlineto{\pgfqpoint{0.664152in}{1.147779in}}% -\pgfpathlineto{\pgfqpoint{0.693809in}{1.337791in}}% -\pgfpathlineto{\pgfqpoint{0.723466in}{1.508975in}}% -\pgfpathlineto{\pgfqpoint{0.753124in}{1.664580in}}% -\pgfpathlineto{\pgfqpoint{0.782781in}{1.807081in}}% -\pgfpathlineto{\pgfqpoint{0.812438in}{1.938396in}}% -\pgfpathlineto{\pgfqpoint{0.842095in}{2.060050in}}% -\pgfpathlineto{\pgfqpoint{0.871752in}{2.173272in}}% -\pgfpathlineto{\pgfqpoint{0.901410in}{2.279065in}}% -\pgfpathlineto{\pgfqpoint{0.931067in}{2.378263in}}% -\pgfpathlineto{\pgfqpoint{0.960724in}{2.471563in}}% -\pgfpathlineto{\pgfqpoint{0.990381in}{2.559556in}}% -\pgfpathlineto{\pgfqpoint{1.020038in}{2.642744in}}% -\pgfpathlineto{\pgfqpoint{1.049695in}{2.721561in}}% -\pgfpathlineto{\pgfqpoint{1.079353in}{2.796383in}}% -\pgfpathlineto{\pgfqpoint{1.109010in}{2.867537in}}% -\pgfpathlineto{\pgfqpoint{1.138667in}{2.935310in}}% -\pgfpathlineto{\pgfqpoint{1.168324in}{2.999956in}}% -\pgfpathlineto{\pgfqpoint{1.197981in}{3.061700in}}% -\pgfpathlineto{\pgfqpoint{1.227638in}{3.120741in}}% -\pgfpathlineto{\pgfqpoint{1.286953in}{3.231415in}}% -\pgfpathlineto{\pgfqpoint{1.346267in}{3.333204in}}% -\pgfpathlineto{\pgfqpoint{1.405582in}{3.427112in}}% -\pgfpathlineto{\pgfqpoint{1.464896in}{3.513967in}}% -\pgfpathlineto{\pgfqpoint{1.524210in}{3.594465in}}% -\pgfpathlineto{\pgfqpoint{1.583525in}{3.669192in}}% -\pgfpathlineto{\pgfqpoint{1.642839in}{3.738646in}}% -\pgfpathlineto{\pgfqpoint{1.702153in}{3.803258in}}% -\pgfpathlineto{\pgfqpoint{1.761468in}{3.863396in}}% -\pgfpathlineto{\pgfqpoint{1.820782in}{3.919383in}}% -\pgfpathlineto{\pgfqpoint{1.880096in}{3.971501in}}% -\pgfpathlineto{\pgfqpoint{1.939411in}{4.019997in}}% -\pgfpathlineto{\pgfqpoint{1.998725in}{4.065088in}}% -\pgfpathlineto{\pgfqpoint{2.058039in}{4.106968in}}% -\pgfpathlineto{\pgfqpoint{2.117354in}{4.145809in}}% -\pgfpathlineto{\pgfqpoint{2.176668in}{4.181762in}}% -\pgfpathlineto{\pgfqpoint{2.235982in}{4.214965in}}% -\pgfpathlineto{\pgfqpoint{2.295297in}{4.245540in}}% -\pgfpathlineto{\pgfqpoint{2.354611in}{4.273595in}}% -\pgfpathlineto{\pgfqpoint{2.413926in}{4.299228in}}% -\pgfpathlineto{\pgfqpoint{2.473240in}{4.322529in}}% -\pgfpathlineto{\pgfqpoint{2.532554in}{4.343576in}}% -\pgfpathlineto{\pgfqpoint{2.591869in}{4.362440in}}% -\pgfpathlineto{\pgfqpoint{2.651183in}{4.379185in}}% -\pgfpathlineto{\pgfqpoint{2.710497in}{4.393866in}}% -\pgfpathlineto{\pgfqpoint{2.769812in}{4.406536in}}% -\pgfpathlineto{\pgfqpoint{2.829126in}{4.417240in}}% -\pgfpathlineto{\pgfqpoint{2.888440in}{4.426016in}}% -\pgfpathlineto{\pgfqpoint{2.947755in}{4.432901in}}% -\pgfpathlineto{\pgfqpoint{3.007069in}{4.437925in}}% -\pgfpathlineto{\pgfqpoint{3.066383in}{4.441112in}}% -\pgfpathlineto{\pgfqpoint{3.125698in}{4.442487in}}% -\pgfpathlineto{\pgfqpoint{3.185012in}{4.442066in}}% -\pgfpathlineto{\pgfqpoint{3.244326in}{4.439864in}}% -\pgfpathlineto{\pgfqpoint{3.303641in}{4.435891in}}% -\pgfpathlineto{\pgfqpoint{3.362955in}{4.430156in}}% -\pgfpathlineto{\pgfqpoint{3.422270in}{4.422660in}}% -\pgfpathlineto{\pgfqpoint{3.481584in}{4.413405in}}% -\pgfpathlineto{\pgfqpoint{3.540898in}{4.402386in}}% -\pgfpathlineto{\pgfqpoint{3.600213in}{4.389597in}}% -\pgfpathlineto{\pgfqpoint{3.659527in}{4.375027in}}% -\pgfpathlineto{\pgfqpoint{3.718841in}{4.358661in}}% -\pgfpathlineto{\pgfqpoint{3.778156in}{4.340483in}}% -\pgfpathlineto{\pgfqpoint{3.837470in}{4.320469in}}% -\pgfpathlineto{\pgfqpoint{3.896784in}{4.298594in}}% -\pgfpathlineto{\pgfqpoint{3.956099in}{4.274828in}}% -\pgfpathlineto{\pgfqpoint{4.015413in}{4.249135in}}% 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\begin{pgfscope}% @@ -1174,7 +1278,7 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% \pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.426895in}{4.758330in}}% +\pgfpathlineto{\pgfqpoint{0.426895in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1184,8 +1288,8 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{6.358330in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{4.847890in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1196,7 +1300,7 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% \pgfpathmoveto{\pgfqpoint{0.426895in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1206,8 +1310,8 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.426895in}{4.758330in}}% -\pgfpathlineto{\pgfqpoint{6.358330in}{4.758330in}}% +\pgfpathmoveto{\pgfqpoint{0.426895in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{4.847890in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1221,16 +1325,16 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetstrokeopacity{0.800000}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.370644in}{3.627933in}}% -\pgfpathlineto{\pgfqpoint{6.261108in}{3.627933in}}% -\pgfpathquadraticcurveto{\pgfqpoint{6.288886in}{3.627933in}}{\pgfqpoint{6.288886in}{3.655711in}}% -\pgfpathlineto{\pgfqpoint{6.288886in}{4.661108in}}% -\pgfpathquadraticcurveto{\pgfqpoint{6.288886in}{4.688886in}}{\pgfqpoint{6.261108in}{4.688886in}}% -\pgfpathlineto{\pgfqpoint{5.370644in}{4.688886in}}% -\pgfpathquadraticcurveto{\pgfqpoint{5.342866in}{4.688886in}}{\pgfqpoint{5.342866in}{4.661108in}}% -\pgfpathlineto{\pgfqpoint{5.342866in}{3.655711in}}% -\pgfpathquadraticcurveto{\pgfqpoint{5.342866in}{3.627933in}}{\pgfqpoint{5.370644in}{3.627933in}}% -\pgfpathlineto{\pgfqpoint{5.370644in}{3.627933in}}% +\pgfpathmoveto{\pgfqpoint{2.192161in}{0.532718in}}% +\pgfpathlineto{\pgfqpoint{3.082624in}{0.532718in}}% +\pgfpathquadraticcurveto{\pgfqpoint{3.110402in}{0.532718in}}{\pgfqpoint{3.110402in}{0.560496in}}% +\pgfpathlineto{\pgfqpoint{3.110402in}{1.565893in}}% +\pgfpathquadraticcurveto{\pgfqpoint{3.110402in}{1.593671in}}{\pgfqpoint{3.082624in}{1.593671in}}% +\pgfpathlineto{\pgfqpoint{2.192161in}{1.593671in}}% +\pgfpathquadraticcurveto{\pgfqpoint{2.164383in}{1.593671in}}{\pgfqpoint{2.164383in}{1.565893in}}% +\pgfpathlineto{\pgfqpoint{2.164383in}{0.560496in}}% +\pgfpathquadraticcurveto{\pgfqpoint{2.164383in}{0.532718in}}{\pgfqpoint{2.192161in}{0.532718in}}% +\pgfpathlineto{\pgfqpoint{2.192161in}{0.532718in}}% \pgfpathclose% \pgfusepath{stroke,fill}% \end{pgfscope}% @@ -1241,16 +1345,16 @@ \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.398422in}{4.576418in}}% -\pgfpathlineto{\pgfqpoint{5.537311in}{4.576418in}}% -\pgfpathlineto{\pgfqpoint{5.676200in}{4.576418in}}% +\pgfpathmoveto{\pgfqpoint{2.219938in}{1.481203in}}% +\pgfpathlineto{\pgfqpoint{2.358827in}{1.481203in}}% +\pgfpathlineto{\pgfqpoint{2.497716in}{1.481203in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.787311in,y=4.527807in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=10\)}% +\pgftext[x=2.608827in,y=1.432592in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=10\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -1259,16 +1363,16 @@ \definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.398422in}{4.372561in}}% -\pgfpathlineto{\pgfqpoint{5.537311in}{4.372561in}}% -\pgfpathlineto{\pgfqpoint{5.676200in}{4.372561in}}% +\pgfpathmoveto{\pgfqpoint{2.219938in}{1.277346in}}% +\pgfpathlineto{\pgfqpoint{2.358827in}{1.277346in}}% +\pgfpathlineto{\pgfqpoint{2.497716in}{1.277346in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.787311in,y=4.323950in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=11\)}% +\pgftext[x=2.608827in,y=1.228735in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=11\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -1277,16 +1381,16 @@ \definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.398422in}{4.168704in}}% -\pgfpathlineto{\pgfqpoint{5.537311in}{4.168704in}}% -\pgfpathlineto{\pgfqpoint{5.676200in}{4.168704in}}% +\pgfpathmoveto{\pgfqpoint{2.219938in}{1.073489in}}% +\pgfpathlineto{\pgfqpoint{2.358827in}{1.073489in}}% +\pgfpathlineto{\pgfqpoint{2.497716in}{1.073489in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.787311in,y=4.120092in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=12\)}% +\pgftext[x=2.608827in,y=1.024878in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=12\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -1295,16 +1399,16 @@ \definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{5.398422in}{3.964846in}}% -\pgfpathlineto{\pgfqpoint{5.537311in}{3.964846in}}% -\pgfpathlineto{\pgfqpoint{5.676200in}{3.964846in}}% +\pgfpathmoveto{\pgfqpoint{2.219938in}{0.869631in}}% +\pgfpathlineto{\pgfqpoint{2.358827in}{0.869631in}}% +\pgfpathlineto{\pgfqpoint{2.497716in}{0.869631in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.787311in,y=3.916235in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=13\)}% +\pgftext[x=2.608827in,y=0.821020in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m=13\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetbuttcap% @@ -1313,16 +1417,16 @@ \definecolor{currentstroke}{rgb}{0.750000,0.000000,0.750000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{{3.000000pt}{4.950000pt}}{0.000000pt}% -\pgfpathmoveto{\pgfqpoint{5.398422in}{3.760989in}}% -\pgfpathlineto{\pgfqpoint{5.537311in}{3.760989in}}% -\pgfpathlineto{\pgfqpoint{5.676200in}{3.760989in}}% +\pgfpathmoveto{\pgfqpoint{2.219938in}{0.665774in}}% +\pgfpathlineto{\pgfqpoint{2.358827in}{0.665774in}}% +\pgfpathlineto{\pgfqpoint{2.497716in}{0.665774in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=5.787311in,y=3.712378in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m^*\)}% +\pgftext[x=2.608827in,y=0.617163in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle m^*\)}% \end{pgfscope}% \end{pgfpicture}% \makeatother% diff --git a/buch/papers/laguerre/images/rel_error_simple.pgf b/buch/papers/laguerre/images/rel_error_simple.pgf index 9368616..2439d65 100644 --- a/buch/papers/laguerre/images/rel_error_simple.pgf +++ b/buch/papers/laguerre/images/rel_error_simple.pgf @@ -56,16 +56,16 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetstrokeopacity{0.000000}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.458330in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{2.458330in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{2.458330in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathclose% \pgfusepath{fill}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -73,8 +73,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.482258in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482258in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -92,7 +92,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.463273in}% +\pgfsys@transformshift{0.482258in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -100,10 +100,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.672226in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}5}% +\pgftext[x=0.482258in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}5}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -111,8 +111,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.271903in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.271903in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.109073in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.109073in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -130,7 +130,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.271903in}{0.463273in}% +\pgfsys@transformshift{1.109073in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -138,10 +138,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.271903in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}% +\pgftext[x=1.109073in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -149,8 +149,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.871580in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.871580in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.735888in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.735888in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -168,7 +168,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.871580in}{0.463273in}% +\pgfsys@transformshift{1.735888in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -176,10 +176,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=1.871580in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 5}% +\pgftext[x=1.735888in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 5}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -187,8 +187,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.471257in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.471257in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.362703in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.362703in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -206,7 +206,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.471257in}{0.463273in}% +\pgfsys@transformshift{2.362703in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -214,10 +214,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.471257in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 10}% +\pgftext[x=2.362703in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 10}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -225,8 +225,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.070934in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.070934in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.989519in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.989519in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -244,7 +244,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.070934in}{0.463273in}% +\pgfsys@transformshift{2.989519in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -252,10 +252,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.070934in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 15}% +\pgftext[x=2.989519in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 15}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -263,8 +263,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.670611in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.670611in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.616334in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.616334in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -282,7 +282,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.670611in}{0.463273in}% +\pgfsys@transformshift{3.616334in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -290,10 +290,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.670611in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 20}% +\pgftext[x=3.616334in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 20}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -301,8 +301,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.270288in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.270288in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.243149in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.243149in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -320,7 +320,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.270288in}{0.463273in}% +\pgfsys@transformshift{4.243149in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -328,10 +328,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=4.270288in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 25}% +\pgftext[x=4.243149in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 25}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -369,7 +369,7 @@ \pgftext[x=4.869965in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 30}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -377,8 +377,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.792161in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.792161in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.607621in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.607621in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -396,12 +396,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.792161in}{0.463273in}% +\pgfsys@transformshift{0.607621in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -409,8 +409,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.912097in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.912097in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.732984in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.732984in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -428,12 +428,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.912097in}{0.463273in}% +\pgfsys@transformshift{0.732984in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -441,8 +441,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.032032in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.032032in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.858347in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.858347in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -460,12 +460,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.032032in}{0.463273in}% +\pgfsys@transformshift{0.858347in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -473,8 +473,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.151967in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.151967in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.983710in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.983710in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -492,12 +492,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.151967in}{0.463273in}% +\pgfsys@transformshift{0.983710in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -505,8 +505,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.391838in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.391838in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.234436in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.234436in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -524,12 +524,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.391838in}{0.463273in}% +\pgfsys@transformshift{1.234436in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -537,8 +537,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.511774in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.511774in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.359799in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.359799in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -556,12 +556,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.511774in}{0.463273in}% +\pgfsys@transformshift{1.359799in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -569,8 +569,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.631709in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.631709in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.485162in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.485162in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -588,12 +588,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.631709in}{0.463273in}% +\pgfsys@transformshift{1.485162in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -601,8 +601,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.751644in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.751644in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.610525in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.610525in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -620,12 +620,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.751644in}{0.463273in}% +\pgfsys@transformshift{1.610525in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -633,8 +633,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{1.991515in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{1.991515in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.861251in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.861251in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -652,12 +652,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{1.991515in}{0.463273in}% +\pgfsys@transformshift{1.861251in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -665,8 +665,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.111451in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.111451in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{1.986614in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.986614in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -684,12 +684,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.111451in}{0.463273in}% +\pgfsys@transformshift{1.986614in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -697,8 +697,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.231386in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.231386in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.111977in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.111977in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -716,12 +716,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.231386in}{0.463273in}% +\pgfsys@transformshift{2.111977in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -729,8 +729,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.351321in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.351321in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.237340in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.237340in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -748,12 +748,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.351321in}{0.463273in}% +\pgfsys@transformshift{2.237340in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -761,8 +761,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.591192in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.591192in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.488066in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.488066in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -780,12 +780,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.591192in}{0.463273in}% +\pgfsys@transformshift{2.488066in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -793,8 +793,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.711128in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.711128in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.613430in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.613430in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -812,12 +812,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.711128in}{0.463273in}% +\pgfsys@transformshift{2.613430in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -825,8 +825,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.831063in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.831063in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.738793in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.738793in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -844,12 +844,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.831063in}{0.463273in}% +\pgfsys@transformshift{2.738793in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -857,8 +857,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.950998in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{2.950998in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{2.864156in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.864156in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -876,12 +876,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{2.950998in}{0.463273in}% +\pgfsys@transformshift{2.864156in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -889,8 +889,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.190869in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.190869in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.114882in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.114882in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -908,12 +908,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.190869in}{0.463273in}% +\pgfsys@transformshift{3.114882in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -921,8 +921,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.310805in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.310805in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.240245in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.240245in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -940,12 +940,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.310805in}{0.463273in}% +\pgfsys@transformshift{3.240245in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -953,8 +953,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.430740in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.430740in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.365608in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.365608in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -972,12 +972,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.430740in}{0.463273in}% +\pgfsys@transformshift{3.365608in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -985,8 +985,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.550675in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.550675in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.490971in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.490971in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1004,12 +1004,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.550675in}{0.463273in}% +\pgfsys@transformshift{3.490971in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1017,8 +1017,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.790546in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.790546in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.741697in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.741697in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1036,12 +1036,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.790546in}{0.463273in}% +\pgfsys@transformshift{3.741697in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1049,8 +1049,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.910481in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{3.910481in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.867060in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.867060in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1068,12 +1068,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{3.910481in}{0.463273in}% +\pgfsys@transformshift{3.867060in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1081,8 +1081,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.030417in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.030417in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{3.992423in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{3.992423in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1100,12 +1100,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.030417in}{0.463273in}% +\pgfsys@transformshift{3.992423in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1113,8 +1113,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.150352in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.150352in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.117786in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.117786in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1132,12 +1132,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.150352in}{0.463273in}% +\pgfsys@transformshift{4.117786in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1145,8 +1145,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.390223in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.390223in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.368512in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.368512in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1164,12 +1164,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.390223in}{0.463273in}% +\pgfsys@transformshift{4.368512in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1177,8 +1177,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.510158in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.510158in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.493875in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.493875in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1196,12 +1196,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.510158in}{0.463273in}% +\pgfsys@transformshift{4.493875in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1209,8 +1209,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.630094in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.630094in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.619239in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.619239in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1228,12 +1228,12 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.630094in}{0.463273in}% +\pgfsys@transformshift{4.619239in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1241,8 +1241,8 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.750029in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{4.750029in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{4.744602in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.744602in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -1260,7 +1260,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{4.750029in}{0.463273in}% +\pgfsys@transformshift{4.744602in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1268,10 +1268,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.771095in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% +\pgftext[x=2.676111in,y=0.176083in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle z\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1279,7 +1279,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1298,7 +1298,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.463273in}% +\pgfsys@transformshift{0.482257in}{0.463273in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1306,10 +1306,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.231638in, y=0.410512in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-11}}\)}% +\pgftext[x=0.041670in, y=0.410512in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-11}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1317,7 +1317,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.697986in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.697986in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.697986in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1336,7 +1336,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.697986in}% +\pgfsys@transformshift{0.482257in}{0.697986in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1344,10 +1344,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=0.645224in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-9}}\)}% +\pgftext[x=0.097033in, y=0.645224in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-9}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1355,7 +1355,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.932698in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.932698in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.932698in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1374,7 +1374,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{0.932698in}% +\pgfsys@transformshift{0.482257in}{0.932698in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1382,10 +1382,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=0.879937in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-7}}\)}% +\pgftext[x=0.097033in, y=0.879937in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-7}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1393,7 +1393,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.167411in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.167411in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.167411in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1412,7 +1412,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.167411in}% +\pgfsys@transformshift{0.482257in}{1.167411in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1420,10 +1420,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=1.114649in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-5}}\)}% +\pgftext[x=0.097033in, y=1.114649in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-5}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1431,7 +1431,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.402124in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.402124in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.402124in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1450,7 +1450,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.402124in}% +\pgfsys@transformshift{0.482257in}{1.402124in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1458,10 +1458,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=1.349362in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-3}}\)}% +\pgftext[x=0.097033in, y=1.349362in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-3}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1469,7 +1469,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.636836in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.636836in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.636836in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1488,7 +1488,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.636836in}% +\pgfsys@transformshift{0.482257in}{1.636836in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1496,10 +1496,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.287001in, y=1.584075in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-1}}\)}% +\pgftext[x=0.097033in, y=1.584075in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-1}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1507,7 +1507,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{1.871549in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{1.871549in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.871549in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1526,7 +1526,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{1.871549in}% +\pgfsys@transformshift{0.482257in}{1.871549in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1534,10 +1534,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.373807in, y=1.818787in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{1}}\)}% +\pgftext[x=0.183839in, y=1.818787in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{1}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1545,7 +1545,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{2.106261in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{2.106261in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.106261in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1564,7 +1564,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{2.106261in}% +\pgfsys@transformshift{0.482257in}{2.106261in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1572,10 +1572,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.373807in, y=2.053500in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{3}}\)}% +\pgftext[x=0.183839in, y=2.053500in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{3}}\)}% \end{pgfscope}% \begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% \pgfsetroundjoin% @@ -1583,7 +1583,7 @@ \definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{2.340974in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{2.340974in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.340974in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -1602,7 +1602,7 @@ \pgfusepath{stroke,fill}% }% \begin{pgfscope}% -\pgfsys@transformshift{0.672226in}{2.340974in}% +\pgfsys@transformshift{0.482257in}{2.340974in}% \pgfsys@useobject{currentmarker}{}% \end{pgfscope}% \end{pgfscope}% @@ -1610,16 +1610,10 @@ \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=0.373807in, y=2.288212in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{5}}\)}% +\pgftext[x=0.183839in, y=2.288212in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{5}}\)}% \end{pgfscope}% \begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=0.176083in,y=1.460802in,,bottom,rotate=90.000000]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont Relativer Fehler}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.672226in}{0.463273in}}{\pgfqpoint{4.197739in}{1.995057in}}% +\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.387707in}{1.995057in}}% \pgfusepath{clip}% \pgfsetrectcap% 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+\pgfpathlineto{\pgfqpoint{3.891253in}{1.274752in}}% +\pgfpathlineto{\pgfqpoint{3.935240in}{1.306188in}}% +\pgfpathlineto{\pgfqpoint{3.979227in}{1.334872in}}% +\pgfpathlineto{\pgfqpoint{4.023214in}{1.361236in}}% +\pgfpathlineto{\pgfqpoint{4.078198in}{1.391409in}}% +\pgfpathlineto{\pgfqpoint{4.133182in}{1.418930in}}% +\pgfpathlineto{\pgfqpoint{4.188166in}{1.444160in}}% +\pgfpathlineto{\pgfqpoint{4.254146in}{1.471806in}}% +\pgfpathlineto{\pgfqpoint{4.320127in}{1.496941in}}% +\pgfpathlineto{\pgfqpoint{4.386107in}{1.519873in}}% +\pgfpathlineto{\pgfqpoint{4.463085in}{1.544168in}}% +\pgfpathlineto{\pgfqpoint{4.540062in}{1.566117in}}% +\pgfpathlineto{\pgfqpoint{4.628036in}{1.588663in}}% +\pgfpathlineto{\pgfqpoint{4.716010in}{1.608807in}}% +\pgfpathlineto{\pgfqpoint{4.803984in}{1.626816in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.639057in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{1.639057in}}% \pgfusepath{stroke}% @@ -2784,8 +2778,8 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% -\pgfpathlineto{\pgfqpoint{0.672226in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.482257in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.482257in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% @@ -2806,7 +2800,7 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{0.463273in}}% +\pgfpathmoveto{\pgfqpoint{0.482258in}{0.463273in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{0.463273in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -2817,7 +2811,7 @@ \definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.672226in}{2.458330in}}% +\pgfpathmoveto{\pgfqpoint{0.482258in}{2.458330in}}% \pgfpathlineto{\pgfqpoint{4.869965in}{2.458330in}}% \pgfusepath{stroke}% \end{pgfscope}% @@ -2832,16 +2826,16 @@ \pgfsetstrokecolor{currentstroke}% \pgfsetstrokeopacity{0.800000}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.384851in}{2.026148in}}% -\pgfpathlineto{\pgfqpoint{4.788979in}{2.026148in}}% -\pgfpathquadraticcurveto{\pgfqpoint{4.812117in}{2.026148in}}{\pgfqpoint{4.812117in}{2.049287in}}% -\pgfpathlineto{\pgfqpoint{4.812117in}{2.377344in}}% -\pgfpathquadraticcurveto{\pgfqpoint{4.812117in}{2.400483in}}{\pgfqpoint{4.788979in}{2.400483in}}% -\pgfpathlineto{\pgfqpoint{2.384851in}{2.400483in}}% -\pgfpathquadraticcurveto{\pgfqpoint{2.361713in}{2.400483in}}{\pgfqpoint{2.361713in}{2.377344in}}% -\pgfpathlineto{\pgfqpoint{2.361713in}{2.049287in}}% -\pgfpathquadraticcurveto{\pgfqpoint{2.361713in}{2.026148in}}{\pgfqpoint{2.384851in}{2.026148in}}% -\pgfpathlineto{\pgfqpoint{2.384851in}{2.026148in}}% +\pgfpathmoveto{\pgfqpoint{1.911537in}{1.939504in}}% +\pgfpathlineto{\pgfqpoint{4.772742in}{1.939504in}}% +\pgfpathquadraticcurveto{\pgfqpoint{4.800520in}{1.939504in}}{\pgfqpoint{4.800520in}{1.967282in}}% +\pgfpathlineto{\pgfqpoint{4.800520in}{2.361108in}}% +\pgfpathquadraticcurveto{\pgfqpoint{4.800520in}{2.388886in}}{\pgfqpoint{4.772742in}{2.388886in}}% +\pgfpathlineto{\pgfqpoint{1.911537in}{2.388886in}}% +\pgfpathquadraticcurveto{\pgfqpoint{1.883759in}{2.388886in}}{\pgfqpoint{1.883759in}{2.361108in}}% +\pgfpathlineto{\pgfqpoint{1.883759in}{1.967282in}}% +\pgfpathquadraticcurveto{\pgfqpoint{1.883759in}{1.939504in}}{\pgfqpoint{1.911537in}{1.939504in}}% +\pgfpathlineto{\pgfqpoint{1.911537in}{1.939504in}}% \pgfpathclose% \pgfusepath{stroke,fill}% \end{pgfscope}% @@ -2852,16 +2846,16 @@ \definecolor{currentstroke}{rgb}{0.121569,0.466667,0.705882}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.407990in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{2.523685in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{2.639379in}{2.306797in}}% +\pgfpathmoveto{\pgfqpoint{1.939315in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{2.078204in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{2.217093in}{2.276418in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.731935in,y=2.266304in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=2\)}% +\pgftext[x=2.328204in,y=2.227807in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=2\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -2870,16 +2864,16 @@ \definecolor{currentstroke}{rgb}{1.000000,0.498039,0.054902}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{2.407990in}{2.136984in}}% -\pgfpathlineto{\pgfqpoint{2.523685in}{2.136984in}}% -\pgfpathlineto{\pgfqpoint{2.639379in}{2.136984in}}% +\pgfpathmoveto{\pgfqpoint{1.939315in}{2.072561in}}% +\pgfpathlineto{\pgfqpoint{2.078204in}{2.072561in}}% +\pgfpathlineto{\pgfqpoint{2.217093in}{2.072561in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=2.731935in,y=2.096491in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=4\)}% +\pgftext[x=2.328204in,y=2.023950in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=4\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -2888,16 +2882,16 @@ \definecolor{currentstroke}{rgb}{0.172549,0.627451,0.172549}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.251394in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{3.367088in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{3.482782in}{2.306797in}}% +\pgfpathmoveto{\pgfqpoint{2.943976in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{3.082865in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{3.221754in}{2.276418in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.575338in,y=2.266304in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=6\)}% +\pgftext[x=3.332865in,y=2.227807in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=6\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -2906,16 +2900,16 @@ \definecolor{currentstroke}{rgb}{0.839216,0.152941,0.156863}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{3.251394in}{2.136984in}}% -\pgfpathlineto{\pgfqpoint{3.367088in}{2.136984in}}% -\pgfpathlineto{\pgfqpoint{3.482782in}{2.136984in}}% +\pgfpathmoveto{\pgfqpoint{2.943976in}{2.072561in}}% +\pgfpathlineto{\pgfqpoint{3.082865in}{2.072561in}}% +\pgfpathlineto{\pgfqpoint{3.221754in}{2.072561in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=3.575338in,y=2.096491in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=8\)}% +\pgftext[x=3.332865in,y=2.023950in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=8\)}% \end{pgfscope}% \begin{pgfscope}% \pgfsetrectcap% @@ -2924,16 +2918,16 @@ \definecolor{currentstroke}{rgb}{0.580392,0.403922,0.741176}% \pgfsetstrokecolor{currentstroke}% \pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{4.094797in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{4.210491in}{2.306797in}}% -\pgfpathlineto{\pgfqpoint{4.326186in}{2.306797in}}% +\pgfpathmoveto{\pgfqpoint{3.948637in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{4.087526in}{2.276418in}}% +\pgfpathlineto{\pgfqpoint{4.226415in}{2.276418in}}% \pgfusepath{stroke}% \end{pgfscope}% \begin{pgfscope}% \definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% \pgfsetstrokecolor{textcolor}% \pgfsetfillcolor{textcolor}% -\pgftext[x=4.418741in,y=2.266304in,left,base]{\color{textcolor}\sffamily\fontsize{8.330000}{9.996000}\selectfont \(\displaystyle n=10\)}% +\pgftext[x=4.337526in,y=2.227807in,left,base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle n=10\)}% \end{pgfscope}% \end{pgfpicture}% \makeatother% diff --git a/buch/papers/laguerre/images/rel_error_simple.png b/buch/papers/laguerre/images/rel_error_simple.png deleted file mode 100644 index 8bcd8e0..0000000 Binary files a/buch/papers/laguerre/images/rel_error_simple.png and /dev/null differ diff --git a/buch/papers/laguerre/images/targets-img0.png b/buch/papers/laguerre/images/targets-img0.png new file mode 100644 index 0000000..6e110dd Binary files /dev/null and b/buch/papers/laguerre/images/targets-img0.png differ diff --git a/buch/papers/laguerre/images/targets-img1.png b/buch/papers/laguerre/images/targets-img1.png new file mode 100644 index 0000000..999a4d2 Binary files /dev/null and b/buch/papers/laguerre/images/targets-img1.png differ diff --git a/buch/papers/laguerre/images/targets.pdf b/buch/papers/laguerre/images/targets.pdf index df11068..c050efa 100644 Binary files a/buch/papers/laguerre/images/targets.pdf and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/images/targets.pgf b/buch/papers/laguerre/images/targets.pgf new file mode 100644 index 0000000..f5602fd --- /dev/null +++ b/buch/papers/laguerre/images/targets.pgf @@ -0,0 +1,1024 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.400000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{2.400000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.400000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.505591in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.982055in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{2.982055in}{2.358330in}}% +\pgfpathlineto{\pgfqpoint{0.505591in}{2.358330in}}% +\pgfpathlineto{\pgfqpoint{0.505591in}{0.463273in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.505591in}{0.463273in}}{\pgfqpoint{2.476464in}{1.895057in}}% +\pgfusepath{clip}% +\pgfsys@transformshift{0.505591in}{0.463273in}% +\pgftext[left,bottom]{\includegraphics[interpolate=true,width=2.480000in,height=1.900000in]{papers/laguerre/images/targets-img0.png}}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.505591in}{0.463273in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.505591in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont 0.00}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% 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+\pgfusepath{stroke}% +\end{pgfscope}% +\end{pgfpicture}% +\makeatother% +\endgroup% diff --git a/buch/papers/laguerre/packages.tex b/buch/papers/laguerre/packages.tex index 4ebc172..a80d091 100644 --- a/buch/papers/laguerre/packages.tex +++ b/buch/papers/laguerre/packages.tex @@ -6,4 +6,4 @@ % if your paper needs special packages, add package commands as in the % following example -\usepackage{derivative} +\DeclareMathOperator{\real}{Re} \ No newline at end of file diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex index 4073b3c..3d32aae 100644 --- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -81,7 +81,7 @@ von $z$ und Grade $n$ der Laguerre-Polynome} \begin{frame}{$f(x) = x^z$} \begin{figure}[h] \centering -\scalebox{0.91}{\input{../images/integrands.pgf}} +\scalebox{0.91}{\input{../images/integrand.pgf}} % \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \end{figure} \end{frame} @@ -89,7 +89,7 @@ von $z$ und Grade $n$ der Laguerre-Polynome} \begin{frame}{Integrand $x^z e^{-x}$} \begin{figure}[h] \centering -\scalebox{0.91}{\input{../images/integrands_exp.pgf}} +\scalebox{0.91}{\input{../images/integrand_exp.pgf}} % \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \end{figure} \end{frame} @@ -98,7 +98,7 @@ von $z$ und Grade $n$ der Laguerre-Polynome} \textbf{Vermutung} \begin{itemize} -\item Es gibt Intervalle $[a(n), a(n+1)]$ in denen der relative Fehler minimal +\item Es gibt Intervalle $[a(n), a(n)+1]$ in denen der relative Fehler minimal ist \item $a(n) > 0$ \end{itemize} @@ -148,7 +148,7 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \begin{figure} \centering \vspace{-24pt} -\scalebox{0.7}{\input{../images/estimate.pgf}} +\scalebox{0.7}{\input{../images/estimates.pgf}} % \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \end{figure} \end{column} diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex index 07cafb8..ed29387 100644 --- a/buch/papers/laguerre/presentation/sections/laguerre.tex +++ b/buch/papers/laguerre/presentation/sections/laguerre.tex @@ -55,7 +55,7 @@ L_n(x) \begin{frame} \begin{figure}[h] \centering -\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_polynomes.pgf}} +\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_poly.pgf}} \caption{Laguerre-Polynome vom Grad $0$ bis $7$} \end{figure} \end{frame} diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index b5ad316..851fe8a 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -6,10 +6,12 @@ \section{Gauss-Quadratur \label{laguerre:section:quadratur}} {\large \color{red} TODO: Einleitung und kurze Beschreibung Gauss-Quadratur} + +Siehe Abschnitt~\ref{buch:orthogonalitaet:section:gauss-quadratur} \begin{align} \int_a^b f(x) w(x) \, dx \approx -\sum_{i=1}^N f(x_i) A_i +\sum_{i=1}^n f(x_i) A_i \label{laguerre:gaussquadratur} \end{align} @@ -25,7 +27,7 @@ Gleichung~\eqref{laguerre:laguerrequadratur} lässt sich wie folgt umformulieren \begin{align} \int_{0}^{\infty} f(x) e^{-x} dx \approx -\sum_{i=1}^{N} f(x_i) A_i +\sum_{i=1}^{n} f(x_i) A_i \label{laguerre:laguerrequadratur} \end{align} @@ -45,7 +47,7 @@ l_i(x_j) 0 & \text{sonst.} \end{cases} \end{align*} -Laut \cite{abramowitz+stegun} sind die Gewichte also +Laut \cite{abramowitz+stegun} sind die Gewichte \begin{align} A_i = diff --git a/buch/papers/laguerre/scripts/estimates.py b/buch/papers/laguerre/scripts/estimates.py new file mode 100644 index 0000000..207bbd2 --- /dev/null +++ b/buch/papers/laguerre/scripts/estimates.py @@ -0,0 +1,39 @@ +if __name__ == "__main__": + import matplotlib.pyplot as plt + import numpy as np + + import gamma_approx as ga + import targets + + N = 200 + ns = np.arange(2, 13) + step = 1 / (N - 1) + x = np.linspace(step, 1 - step, N + 1) + + bests = targets.find_best_loc(N, ns=ns) + mean_m = np.mean(bests, -1) + + intercept, bias = np.polyfit(ns, mean_m, 1) + fig, axs = plt.subplots( + 2, num=1, sharex=True, clear=True, constrained_layout=True, figsize=(4.5, 3.6) + ) + xl = np.array([ns[0] - 0.5, ns[-1] + 0.5]) + axs[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$") + axs[0].plot(ns, mean_m, "x", label=r"$\overline{m}$") + axs[1].plot( + ns, ((intercept * ns + bias) - mean_m), "-x", label=r"$\hat{m} - \overline{m}$" + ) + axs[0].set_xlim(*xl) + axs[0].set_xticks(ns) + axs[0].set_yticks(np.arange(np.floor(mean_m[0]), np.ceil(mean_m[-1]) + 0.1, 2)) + # axs[0].set_title("Schätzung von Mittelwert") + # axs[1].set_title("Fehler") + axs[-1].set_xlabel(r"$n$") + for ax in axs: + ax.grid(1) + ax.legend() + fig.savefig(f"{ga.img_path}/estimates.pgf") + + print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") + predicts = np.ceil(intercept * ns[:, None] + bias - np.real(x)) + print(f"Error: {np.mean(np.abs(bests - predicts))}") diff --git a/buch/papers/laguerre/scripts/gamma_approx.ipynb b/buch/papers/laguerre/scripts/gamma_approx.ipynb deleted file mode 100644 index 82adca6..0000000 --- a/buch/papers/laguerre/scripts/gamma_approx.ipynb +++ /dev/null @@ -1,616 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Gauss-Laguerre Quadratur für die Gamma-Funktion\n", - "\n", - "$$\n", - " \\Gamma(z)\n", - " = \n", - " \\int_0^\\infty t^{z-1}e^{-t}dt\n", - "$$\n", - "\n", - "$$\n", - " \\int_0^\\infty f(x) e^{-x} dx \n", - " \\approx \n", - " \\sum_{i=1}^{N} f(x_i) w_i\n", - " \\qquad\\text{ wobei }\n", - " w_i = \\frac{x_i}{(n+1)^2 [L_{n+1}(x_i)]^2}\n", - "$$\n", - "und $x_i$ sind Nullstellen des Laguerre Polynoms $L_n(x)$\n", - "\n", - "Der Fehler ist gegeben als\n", - "\n", - "$$\n", - " E \n", - " =\n", - " \\frac{(n!)^2}{(2n)!} f^{(2n)}(\\xi) \n", - " = \n", - " \\frac{(-2n + z)_{2n}}{(z-m)_m} \\frac{(n!)^2}{(2n)!} \\xi^{z + m - 2n - 1}\n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from cmath import exp, pi, sin, sqrt\n", - "import scipy.special\n", - "\n", - "EPSILON = 1e-07\n" - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "metadata": {}, - "outputs": [], - "source": [ - "lanczos_p = [\n", - " 676.5203681218851,\n", - " -1259.1392167224028,\n", - " 771.32342877765313,\n", - " -176.61502916214059,\n", - " 12.507343278686905,\n", - " -0.13857109526572012,\n", - " 9.9843695780195716e-6,\n", - " 1.5056327351493116e-7,\n", - "]\n", - "\n", - "\n", - "def drop_imag(z):\n", - " if abs(z.imag) <= EPSILON:\n", - " z = z.real\n", - " return z\n", - "\n", - "\n", - "def lanczos_gamma(z):\n", - " z = complex(z)\n", - " if z.real < 0.5:\n", - " y = pi / (sin(pi * z) * lanczos_gamma(1 - z)) # Reflection formula\n", - " else:\n", - " z -= 1\n", - " x = 0.99999999999980993\n", - " for (i, pval) in enumerate(lanczos_p):\n", - " x += pval / (z + i + 1)\n", - " t = z + len(lanczos_p) - 0.5\n", - " y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x\n", - " return drop_imag(y)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [], - "source": [ - "zeros, weights = np.polynomial.laguerre.laggauss(8)\n", - "# zeros = np.array(\n", - "# [\n", - "# 1.70279632305101000e-1,\n", - "# 9.03701776799379912e-1,\n", - "# 2.25108662986613069e0,\n", - "# 4.26670017028765879e0,\n", - "# 7.04590540239346570e0,\n", - "# 1.07585160101809952e1,\n", - "# 1.57406786412780046e1,\n", - "# 2.28631317368892641e1,\n", - "# ]\n", - "# )\n", - "\n", - "# weights = np.array(\n", - "# [\n", - "# 3.69188589341637530e-1,\n", - "# 4.18786780814342956e-1,\n", - "# 1.75794986637171806e-1,\n", - "# 3.33434922612156515e-2,\n", - "# 2.79453623522567252e-3,\n", - "# 9.07650877335821310e-5,\n", - "# 8.48574671627253154e-7,\n", - "# 1.04800117487151038e-9,\n", - "# ]\n", - "# )\n", - "\n", - "\n", - "def pochhammer(z, n):\n", - " return np.prod(z + np.arange(n))\n", - "\n", - "\n", - "def find_shift(z, target):\n", - " factor = 1.0\n", - " steps = int(np.floor(target - np.real(z)))\n", - " zs = z + steps\n", - " if steps > 0:\n", - " factor = 1 / pochhammer(z, steps)\n", - " elif steps < 0:\n", - " factor = pochhammer(zs, -steps)\n", - " return zs, factor\n", - "\n", - "def find_optimal_shift(z, n):\n", - " mhat = 1.34093 * n + 0.854093\n", - " steps = int(np.ceil(mhat - np.real(z)))-1\n", - " return steps\n", - "\n", - "\n", - "def get_shifting_factor(z, steps):\n", - " zs = z + steps\n", - " factor = 1.0\n", - " if steps > 0:\n", - " factor = 1 / pochhammer(z, steps)\n", - " elif steps < 0:\n", - " factor = pochhammer(zs, -steps)\n", - " return factor\n", - "\n", - "\n", - "def laguerre_gamma_shift(z, x, w):\n", - " z = complex(z)\n", - " n = len(x)\n", - "\n", - " z += 0j\n", - " # z_shifted, correction_factor = find_shift(z, target)\n", - " opt_shift = find_optimal_shift(z, n)\n", - " correction_factor = get_shifting_factor(z, opt_shift)\n", - " z_shifted = z + opt_shift\n", - "\n", - " res = np.sum(x ** (z_shifted - 1) * w)\n", - " res *= correction_factor\n", - " res = drop_imag(res)\n", - " return res\n", - "\n", - "\n", - "def laguerre_gamma(z, x, w, target=11):\n", - " # res = 0.0\n", - " z = complex(z)\n", - " n = len(x)\n", - " # if z.real < 1e-3:\n", - " # res = pi / (\n", - " # sin(pi * z) * laguerre_gamma(1 - z, x, w, target)\n", - " # ) # Reflection formula\n", - " # else:\n", - " # z_shifted, correction_factor = find_shift(z, target)\n", - " # res = np.sum(x ** (z_shifted - 1) * w)\n", - " # res *= correction_factor\n", - " \n", - " z_shifted, correction_factor = find_shift(z, target)\n", - " \n", - " # opt_shift = find_optimal_shift(z, n)\n", - " # correction_factor = get_shifting_factor(z, opt_shift)\n", - " # z_shifted = z + opt_shift\n", - " \n", - " res = np.sum(x ** (z_shifted - 1) * w)\n", - " res *= correction_factor\n", - " res = drop_imag(res)\n", - " return res\n" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [], - "source": [ - "def eval_laguerre(x, target=12):\n", - " return np.array([laguerre_gamma(xi, zeros, weights, target) for xi in x])\n", - "\n", - "\n", - "def eval_laguerre2(x):\n", - " return np.array([laguerre_gamma_shift(xi, zeros, weights) for xi in x])\n", - "\n", - "\n", - "def eval_lanczos(x):\n", - " return np.array([lanczos_gamma(xi) for xi in x])\n", - "\n", - "\n", - "def eval_mean_laguerre(x, targets):\n", - " return np.mean([eval_laguerre(x, target) for target in targets], 0)\n", - "\n", - "\n", - "def calc_rel_error(x, y):\n", - " return (y - x) / x\n", - "\n", - "\n", - "def evaluate(x, target=12):\n", - " lanczos_gammas = eval_lanczos(x)\n", - " laguerre_gammas = eval_laguerre(x, target)\n", - " rel_error = calc_rel_error(lanczos_gammas, laguerre_gammas)\n", - " return rel_error\n", - "\n", - "def evaluate2(x):\n", - " lanczos_gammas = eval_lanczos(x)\n", - " laguerre_gammas = eval_laguerre2(x)\n", - " rel_error = calc_rel_error(lanczos_gammas, laguerre_gammas)\n", - " return rel_error\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test with real values" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Empirische Tests zeigen:\n", - "- $n=4 \\Rightarrow m=6$\n", - "- $n=5 \\Rightarrow m=7$ oder $m=8$\n", - "- $n=6 \\Rightarrow m=9$\n", - "- $n=7 \\Rightarrow m=10$\n", - "- $n=8 \\Rightarrow m=11$ oder $m=12$\n", - "- $n=9 \\Rightarrow m=13$\n", - "- $n=10 \\Rightarrow m=14$\n", - "- $n=11 \\Rightarrow m=15$ oder $m=16$\n", - "- $n=12 \\Rightarrow m=17$\n", - "- $n=13 \\Rightarrow m=18 \\Rightarrow $ Beginnt numerisch instabil zu werden \n" - ] - }, - { - "cell_type": "code", - "execution_count": 87, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "zeros, weights = np.polynomial.laguerre.laggauss(8)\n", - "targets = np.arange(9, 14)\n", - "mean_targets = ((9, 10),)\n", - "x = np.linspace(EPSILON, 1 - EPSILON, 101)\n", - "_, axs = plt.subplots(\n", - " 2, sharex=True, clear=True, constrained_layout=True, figsize=(12, 12)\n", - ")\n", - "\n", - "lanczos = eval_lanczos(x)\n", - "# for mean_target in mean_targets:\n", - "# vals = eval_mean_laguerre(x, mean_target)\n", - "# rel_error_mean = calc_rel_error(lanczos, vals)\n", - "# axs[0].plot(x, rel_error_mean, label=mean_target)\n", - "# axs[1].semilogy(x, np.abs(rel_error_mean), label=mean_target)\n", - "\n", - "mins = []\n", - "maxs = []\n", - "for target in targets:\n", - " rel_error = evaluate(x, target)\n", - " mins.append(np.min(np.abs(rel_error[(0.05 <= x) & (x <= 0.95)])))\n", - " maxs.append(np.max(np.abs(rel_error)))\n", - " axs[0].plot(x, rel_error, label=target)\n", - " axs[1].semilogy(x, np.abs(rel_error), label=target)\n", - " \n", - "rel_error = evaluate2(x)\n", - "axs[0].plot(x, rel_error, label=\"Optimal shift\")\n", - "axs[1].semilogy(x, np.abs(rel_error), label=\"Optimal shift\")\n", - "\n", - "# axs[0].set_ylim(*(np.array([-1, 1]) * 3.5e-8))\n", - "\n", - "axs[0].set_xlim(x[0], x[-1])\n", - "axs[1].set_ylim(np.min(mins), 1.04*np.max(maxs))\n", - "for ax in axs:\n", - " ax.legend()\n", - " ax.grid(which=\"both\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 82, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(-7.5, 25.0)" - ] - }, - "execution_count": 82, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "targets = (16, 17)\n", - "xmax = 15\n", - "x = np.linspace(-xmax + EPSILON, xmax - EPSILON, 1000)\n", - "\n", - "mean_lag = eval_mean_laguerre(x, targets)\n", - "lanczos = eval_lanczos(x)\n", - "rel_error = calc_rel_error(lanczos, mean_lag)\n", - "rel_error_simple = evaluate(x, targets[-1])\n", - "rel_error_opt = evaluate2(x)\n", - "# rel_error = evaluate(x, target)\n", - "\n", - "_, axs = plt.subplots(\n", - " 2, sharex=True, clear=True, constrained_layout=True, figsize=(12, 12)\n", - ")\n", - "axs[0].plot(x, rel_error, label=targets)\n", - "axs[1].semilogy(x, np.abs(rel_error), label=targets)\n", - "axs[0].plot(x, rel_error_simple, label=targets[-1])\n", - "axs[1].semilogy(x, np.abs(rel_error_simple), label=targets[-1])\n", - "axs[0].plot(x, rel_error_opt, label=\"Optimal\")\n", - "axs[1].semilogy(x, np.abs(rel_error_opt), label=\"Optimal\")\n", - "axs[0].set_xlim(x[0], x[-1])\n", - "# axs[0].set_ylim(*(np.array([-1, 1]) * 4.2e-8))\n", - "# axs[1].set_ylim(1e-10, 5e-8)\n", - "for ax in axs:\n", - " ax.legend()\n", - "\n", - "x2 = np.linspace(-5 + EPSILON, 5, 4001)\n", - "_, ax = plt.subplots(constrained_layout=True, figsize=(8, 6))\n", - "ax.plot(x2, eval_mean_laguerre(x2, targets))\n", - "ax.set_xlim(x2[0], x2[-1])\n", - "ax.set_ylim(-7.5, 25)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test with complex values" - ] - }, - { - "cell_type": "code", - "execution_count": 79, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "targets = (16, 17)\n", - "vals = np.linspace(-5 + EPSILON, 5, 100)\n", - "x, y = np.meshgrid(vals, vals)\n", - "mesh = x + 1j * y\n", - "input = mesh.flatten()\n", - "\n", - "mean_lag = eval_mean_laguerre(input, targets).reshape(mesh.shape)\n", - "lanczos = eval_lanczos(input).reshape(mesh.shape)\n", - "rel_error = np.abs(calc_rel_error(lanczos, mean_lag))\n", - "\n", - "lag = eval_laguerre(input, targets[-1]).reshape(mesh.shape)\n", - "rel_error_simple = np.abs(calc_rel_error(lanczos, lag))\n", - "# rel_error = evaluate(x, target)\n", - "\n", - "fig, axs = plt.subplots(\n", - " 2,\n", - " 2,\n", - " sharex=True,\n", - " sharey=True,\n", - " clear=True,\n", - " constrained_layout=True,\n", - " figsize=(12, 10),\n", - ")\n", - "_c = axs[0, 1].pcolormesh(x, y, np.log10(np.abs(lanczos - mean_lag)), shading=\"gouraud\")\n", - "_c = axs[0, 0].pcolormesh(x, y, np.log10(np.abs(lanczos - lag)), shading=\"gouraud\")\n", - "fig.colorbar(_c, ax=axs[0, :])\n", - "_c = axs[1, 1].pcolormesh(x, y, np.log10(rel_error), shading=\"gouraud\")\n", - "_c = axs[1, 0].pcolormesh(x, y, np.log10(rel_error_simple), shading=\"gouraud\")\n", - "fig.colorbar(_c, ax=axs[1, :])\n", - "_ = axs[0, 0].set_title(\"Absolute Error\")\n", - "_ = axs[1, 0].set_title(\"Relative Error\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 80, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "z = 0.5\n", - "ns = [4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12] # np.arange(4, 13)\n", - "ms = np.arange(6, 18)\n", - "xi = np.logspace(0, 2, 201)[:, None]\n", - "lanczos = eval_lanczos([z])[0]\n", - "\n", - "_, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(12, 8))\n", - "ax.grid(1)\n", - "for n, m in zip(ns, ms):\n", - " zeros, weights = np.polynomial.laguerre.laggauss(n)\n", - " c = scipy.special.factorial(n) ** 2 / scipy.special.factorial(2 * n)\n", - " e = np.abs(\n", - " scipy.special.poch(z - 2 * n, 2 * n)\n", - " / scipy.special.poch(z - m, m)\n", - " * c\n", - " * xi ** (z - 2 * n + m - 1)\n", - " )\n", - " ez = np.sum(\n", - " scipy.special.poch(z - 2 * n, 2 * n)\n", - " / scipy.special.poch(z - m, m)\n", - " * c\n", - " * zeros[:, None] ** (z - 2 * n + m - 1),\n", - " 0,\n", - " )\n", - " lag = eval_laguerre([z], m)[0]\n", - " err = np.abs(lanczos - lag)\n", - " # print(m+z,ez)\n", - " # for zi,ezi in zip(z[0], ez):\n", - " # print(f\"{m+zi}: {ezi}\")\n", - " # ax.semilogy(xi, e, color=color)\n", - " lines = ax.loglog(xi, e, label=str(n))\n", - " ax.axhline(err, color=lines[0].get_color())\n", - " # ax.set_xticks(np.arange(xi[-1] + 1))\n", - " # ax.set_ylim(1e-8, 1e5)\n", - "_ = ax.legend()\n", - "# _ = ax.legend([f\"z={zi}\" for zi in z[0]])\n", - "# _ = [ax.axvline(x) for x in zeros]\n" - ] - }, - { - "cell_type": "code", - "execution_count": 81, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 3.53233831 4.88557214 6.2238806 7.56716418 8.90547264 10.23383085\n", - " 11.5721393 12.91044776 14.23880597 15.57711443 17. ]\n", - "Intercept=1.34093, Bias=0.854093\n", - "35.0\n" - ] - }, - { - "data": { - "image/png": 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caTwlG/QFQwVXSFqT+746S1U9jD3N7N7s7/uAPYeU/STwXUkXEhT5OjP71SihFiiivO82s69lf3+xaMOjyDIKvhY4t9/v+XzeB+66S2O0WYL7vB2nCgoMWG40s+IJ9B7XvpmGW2KfJei4NvDHwMGSlpvZM4q0X0R5XyPp7cBHzCYaB/F7wI1m9vMJthk9klFSrp9G4w9EJ48R8giVwM8l7WVm90raC7h/SNn1ZvY3+Q2SCofOF1HeBwD/DThH0g3AWmCtmY1rhZ/MAJdJL8Ia40qQmrOvVSKLPxFRk4gh2mQA3wBOBc7P/v/6kLJrJZ1tZh9d2LCYscSRytvMjgeQtAPbFPnvMoYLRdJOwCuBPypepxkKrdPqRjuCP83EPiHDmSzB8h47VPBSwuDkCknrgfMISvsySWcAdwMnDmliT+AVks4BbgR+yCIM48Khgmb2KGGl9xuK1hnS1iOEUdZiCFoNSkwV9+JM04tb3vFQ+pmawCQdMzt5wE8vL1j/RNjqKjmQYBgfTkHDOI4ZlhhSM5R3U9IAVE06A4mImkX5b9rT8oabuUpuzD6FiUJ5N2WSDkCnswUrZyCl0UzLjeoUpOxQQVTWgGVlxKG8gaQhbpOQw8Wt70nT7SbuNomIStawjHwYLQrlLRlJQ3KbdDrzpJGvaj2NtNvz7jaJirKXQSstVLAyolDeEPc03MXQas2TlLQ6SZPZMt/2VYoiopqsgiX3UTJRKO9geTfjxmu1m/GGUTWtzWljIpac0bjlXSFNifNut+fdN1sCSZI2JmJpFoh4kk5l1KK8s+n2byY8AH8EnGZmjw2v04wbL/Eg71JotbqNMQBmggr0auxXQx2LMewN/ClwgJk9KukyQnbBiwdXgqYk/FDajIdU1XjaASePAfNueS+53x0kbQF2JKwiMYQG3XithuxnxUjWmEFvpxixuycr99hnScf/DvgpcC/wKzO7omo5HMdpLmYht8mwz7RTufKW9ETCahP7AU8FdpJ0Sp9yZ0paI2nNA495BIbjOJMlNQ39TDt1uE1eAdxpZr8AkPQV4H8QEpNvJb8YwyErdjA1xOftlIOSBrneKiZG90OYHh+f3HnqUN4/BY6QtCPwKCED15rhVRxnPHzAMi7KDxWE2EMD6lg9/npJXyJk0JoHfkBmYQ9CNCfO2ymHpNWl3Z6vW4yZwyyh241vsosR5xtDnlqiTczsPELi8mI0KLeJUw6tJG1MZsoqMbNycvFUoFe7kduD8cywdJ+3MwZJK/XUAyVgJS0vV7bbxGz8NMFLmWw4SeJQ3gK55e2MQdKepx3h6/20YybSMo5rJZb30jtZ0mTDCROF8m5SYiqnHFodzxlTBtZtoS3xvRUbExmwXORkw8kShfIGkPsrnTFwt0k5pLJSxhKqCFAYx/I2sw2SFiYbPgpcUfVkwziUtwy55e2MQdKZ94ilEujOt2hF6NI0Cq2ks0JSPox5dTb/pHey4UPAFyWdYmaffXwz5RCF8hbu83bGI2kLc+VdCrE+FAssxrDRzFYN+K3QZMMyiUJ5I482ccYjaaeYX0OlUMZ4VOkPhPHzl9Q+2bCufN5nA39IMKr/ycw+MryGNSYlrFMOolvB2lrNQ6mizLU/7oDlUiYbTpo68nkfRFDchwObgcsl/YuZ3Ta8XnwXiDNFtIDEQwUnTWJpOYZVBJN0Fj3ZcMLUYXk/D7jezH4LIOm7wBuADw2s4W4TZwIIHzeZNN35pCQXR/mrx8eQOXAYdZgiNwEvkvSkzF90DLBvDXI4jjMmMRtVXRv+mXbqSEx1i6QPAlcAjwBr4fEmkaQzgTMB9t3FX3cdx5kcITFV3VKMR12JqS4ELgSQ9NfA+j5ltubzPuypHfMBS8eZTmK1vmMfRasr2uTJZna/pKcR/N1HDK9gzYrzNmGpv204EVDSIhdle6MtEtfIMOqK8/6ypCcBW4C3mdlDwwqLeJ/uS8FSTwfgxIGUlpOuuYKJPwVmWE41dblNXrSoCjLUaVAi/W4Cbnk7EaB2SlLGvVmy6W245V0NMrSsQcp7UweL3iPnNAElKa0SlHcVU+7d8q4CgToNUmbpPMy36pbCcUaTpiSdybtNylbebnlXhUDL6haiOqxr8ZsFTiNQu1uOS7P03CYeKlgNCTAX92yoxaDNaSxnxmk6SUprbvPk263CbVJ6D+USh4pIBMsbZHo/ugm55e1EgCWUYnm722Q0cShvCZZ16paiMtTehLnydiJAqaESfN5VJKaK/RaLR3l3GmR5t+QpcJ1o0LISlHfJ179b3lUhQTsOUSdCW1Eu6uo0kARK8R5XYnnHfY+VphElXQQcC9xvZgdl23YHvgCsBO4CTjSzXxZoDWs3yG2SJOAzLJ1IUIR2lU+PH87FwAXAJblt7wG+Y2bnS3pP9v2ckS01zfJOVE+yXsdZCmVcq6Vb3oaVnDO8bErTiGZ2jaSVPZuPA47M/v4McDVFlXfSoEkrSeJLdjnxEKH7oeDq8UORtBvwKeCgrMnTzezacWUrStXm7J5mdm/2933AnoMK5vN5P23PBlndjhMbkRoa3fEfOh8FLjezEyQtA3YcX6ri1PZybmbGkLWOzGy1ma0ys1UrdnPl7TjO5FhYgHjYZxiSdgVeTLYugZltHpUdddJUrRV/LmkvM7tX0l7A/UUrWoMWj5X7vMvDx4GdjAKW9wpJa3LfV2eLxADsB/wC+LSkQ4AbgLPN7JHJS9qfqpX3N4BTgfOz/79euGaDlDftNrQblEWxSuYbtKhHzFSQErZAqOBGM1s14Lc2cBhwlpldL+mjhACMv5iclMMpM1TwUsLg5ApJ64HzCEr7MklnAHcDJxZsrFkDlq02tBu0v47TSwV+9O540SbrgfVmdn32/UsE5V0ZZUabnDzgp5cvqb2mWd4NSgdQGWkaPk7jMYx0DOVtZvdJukfSc8zsVoJeu3liAhYgjpFAJdBuzvR4WzaHXMlMnjR1t0kslL6I5URmWJ4FfC6LNLkDOG1suRZBJMq7WTMsWTYX+fSB6UTzW2BLCelLnRIoV3sb0B1z9NrM1gKDfOKlE4XyNsAa5PO2ZXNVpHZoHJYkaNNjdYvhFKECn/c4bpNpIArlHSzvJrlNljfLx18R2pygVhyXfOMpPdrExra86yaOK1lJo5R3umw5atCbRlUoTZsVcho1JWtvQSpX3tUQY+qyJWLtZc0KjawIS7vNSnAWMyW7TYLlHffgdRxXshKsPVe3FJVi5pN0Jk7aJfGHopPhPu8BDMjn/fvA+4DnAYeb2ZrBLWzXWqMsUWvPQdqc/a2M5FF3m8RCFQOW7jYZyMU8Pp/3TcAbgE8uqiWBJXG8JEwCQaMeVlUR3FGuvJ3gNpkn7rfbSvN5m9ktAIo0hWRVNOlBVSWWtPyhGAul64gwxzJmplZL5PN577v3TjVL4zjOLGEY84rb8p7ad8jt8nk/qVmDlY7jlI/RHfqZdqbW8t6eZg1YOiWhtk9+cgD3eVeGIfcDO2NjSQualCMnZirxeU+/dT2MqvN5Pwh8DNgD+FdJa83sqAKNNWqSjlMSSbtZCc5ipvRJOpD6gGV/huTz/uqSGnTL2xkTa89hy5bXLYZTBJXt3jK6bCm5j3KJQyMqgZbfdM54WPsx0mU71C2GUwCrwPL2UMFKECT+uuuMSWs51tmxbimcIlRheZtb3qUjJcgtb2dMLN1CunyXusVwilB6dNlkBiwltYA1wAYzO3bsBhdBFMob5MrbmQjWebhuEZwCmMpV3obRnUzyt7OBW4DKrYI4lLcSksSVtzMeKWBzT6xbDKcIJStvDMzGs7wl7QO8GvgA8I5JiLUY4lDeCHm0iTMmCcux9hPqFsMpgEr2eYfMJmMPWH4EeDew89gCLYEoNKIAeZy3MyZqtT1PeixUMGCZjh6wXCEpn7Z6tZmtBpC0kO76BklHliPjcKrO5/23wGuAzcDtwGlm9tDoxhJaiec3ccbDrAtueUeBKki7ZDbS8t5oZoNWh38h8FpJxwDLgV0kfdbMTpmkjMOoOp/3lcC5ZjYv6YPAucA5oxoSInHL2xmTFGiV7Ut1JkMVbpMxQgXN7FyC/iKzvN9VpeKG6vN5X5H7eh1wQln9O04vbgDEg8pegBgrYnlPNXVezacDX6ixf8dxmopBOqHxDzO7Grh6Io0tglqUt6T3AvPA54aU2boYw9Oe9qSKJHMcpxnEv5JO5cmNJb2JMJD5RjMbuHxzfjGGPfbwWXGO40wOIwxgD/tMO5Va3pKOJsRFvsTMfltl347jONuw6MNGS7O8s3ze1wLPkbRe0hmE6JOdgSslrZX0ibL6dxzHGUxwmwz7TDtV5/O+sKz+HMdxFkXklrfHTjmO00DiH7B05e04TjOJYFByGK68HcdpIIYxMNgtCjQkWm9qkPQb4L7s66+AXXM/935f2LYCtlukblC5hW0dYOOIMr3bOrk+ypRryyLaHyXXIFlnXa5B7S9Frn7XShPkWtiWPydLlatfufz3p5hZadn6JF1O2I9hbDSzo8uSYVxiUd5rgBsBzOxMSasXfuv9ntu2tc6IcgvbDjOzVSPK9G47rAq5gBsX0f5QuYbIOtNyDWl/0XLR51ppgly5bQPvx6JyjdjvrXVwBhKT2+SbA/7u930x5Ra2HVagTO+2wyqS65sDyi1VrqLbZk2uQW0tVq5B10oT5Oq3faly9dvWez86gzCzqf8Aa8quU0UfLtdsyNXkfZ9muZr2qXx6/BJZPbrI2HWq6GMpdVyuZvaxlDpNl6tRROHzdhzHcbYnFsvbcRzHyVO33wY4GrgVuA14T5/f5wh5v28DrgdOzZW/PPv/VuCoAeVXZn3cTlhM5WfAWuATuT5eTBg9nycsEJGX6TLgv7LPqf3K9+yH5fr4Rq6PdwA3A+uA7wBPz9X5OSGUamsfBeoM6uctwI+y7d8jpNUddrx6yx8w6njl+jo+k+OsYX30Kb+qwDl5E/CLbPta4M0FjldvnQ/n5Epz2/PH68TsGP8Y+PyoPkbUGXROPpzr+yfAwwy/vnrLP1Sgj6cBVwE/IFwvx+TqPJDty3bnpE+dv8jK3EUIBVyQ4RNZ+acTrsN1hPzV+xQ4J711/hm4H7gJ6PaeE8KStf+QHZt1hKiThbZO7T1WTf7UrbhbhBt4f2AZ8EPggJ4yf5y7eE7OLvz9gUOAR7P/98vaafWUPym7OW4HXkS42fr1sRI4mLBk24k5mfYENgEvAJ4I3JH9ny9/Qs9+PDygj5cCO2Z/vzUn16FZuzcBRyz0MaLOsH52yf39OuC3I45XvvxrCcp36PHKyu4MXENYEWn9sD76lD+8wDl5E3BBn2tl2PHaWofHX1vdPn08i6C4Fuo/pUAfg+oMPCc9ff4p8GuGXF895c8CPl3gvK8G3pr9fQBBAd8OvIqgBNcBr+w5J/k6BxEU9v7ZPj7ap48vsu0B8zLgswWOV2+dfyNEktwEPNzn+BwDfJugxI8Ars+27561u/ugY9W0T91uk8OB28zsDjPbTHgqH9dT5jjgM9nf9xBuxDsJJ/m7wDFmdifhSX14T/kvES7e27K61q8PM7vLzNYRrLNnLshEuNjWAkea2S8Ja3Ae3VN+u/3Ivvfr4yrblgb3OuC5mVzPzdr9HEFZX0mwZgbWGdHPr3NfDwYeycr3PV495XciTJIYerwy/gr4IOF83DOsj57yjwEHFuwjz+GMOF79yueurfk+ffwh8PHs3EJ44Izqo2+dYeekhzcDPxl2ffWUP5nwsBjVhwELie93JTwgbgP+O3Bp9lnF9uckX+cFBGV6B9sm7fT2cQDw79nfVwGvZ/Tx6q3zAuDBfgcm4zjgEgtcB+wmaS/gKOBKM3twyLFqFHUr770JN/AC67Ntg8o8hXDzPynbfmeu/ELdreUtJOx9jPCaBuFG+yPgTyS9aIBMu+f62xv4aZ8+hu3HcsINfrak1w3o4wyCxXlPru5C24P6yNcZ2o+kt0m6nWDlXZWTsd/xypf/EOEGXOij7/GSdBiwr5n9K8FN9fNhffSUB9hjVB8Zx0taJ+lLhAdRkeN1vKR1wN+zvZJoA2+XdF3ueD0beLak/5B0HfDqAn0MqgMjzr2kpwP7EiznheM18PrKyu9HmF08qo/3AadIWg98i2AVj9qXfJ0Ps/1SXrsB75D03dx5+SHwhuzv1wM7Eu6tYX301tk5axtguaQ1PedkkE4ooisaRd3Ku0ruJfj4/oLg2/28pDKW6Hk6cB5wBfARSc/I/yjpFIIF9PWiDQ6oM7AfM/u4mT2DcAM/f1T7ufLnsG1R6L7HS1JCUIzvLCr+kPLDzsk3gZVmdjDByvqTAn3l66wDXpL77e0Et9MfsO14tQkugiMJFu5bCG8SwxhWZ+i5J7jxroXCSTVOIrw95tPfDerjZOBiM9uH8AZ0VoH283X+GjgyO7/3Eo7XFwjjLgvn5V3ASyT9gHBsHyywL711NuT25+kWZlHmz4lTkLqV9waCJbLAPtm2QWXuI1geD2Tb98uVX6i7tbykdlb+yWa2ycweyMqtJfjqnt1Hpgdz/W0gKJfePgbuh5ltyMrdQrBkDl0oJOkVwHsJvuW7szoLdRfa3q6PAXWG9pPjsuwYLcjY73jl+WfCQ2LfIcdrZ4J/9GpJdxHcTEdLWjWgj1/2lD8C+D/AgcPOiZk9YGabsnY+lbU79Hj11LmEYOEvsBOwIXMLLByv9YSBsi2Zm+dOgmIedk4G1SlyTk4Cvkbx6+skgrujyPV1BuF8Y2bXEu7tZ4zYl611CG9oc8CK7Bjulh2vG8jOi5n9zMzeYGaHEq7JLsFvP+yc9NaB4NJZ2Bd6zskgnVBEVzSLOh3uBCvmDsKNuTBgeWBPmbexbQDyDwgDNvuxbXDs+dn3OwiDVPnyJxEGTO4g+P6WZ30cRTjxu/f0dTFhwHJBpt4BpTvzdbLyJ+T24xDgCVkfLySMih+QlT2UcBM8q2ffn5+1e1PWz9Y+htQZ1s+zcvIdl8k/7Hjly78GWFP0eGV1vktQaAP76Cl/NfC7o/oA9srVeT3B5z/qeOXrHE9wme0HPJlgiR9ISEb0X2yLqvlMVn4F4bX8rhF9DKoz8JxkZZ+blctf8wOvr1x5FTzv3wbelP39PEJEyh1sP2D5qvw56alzEGFcYD/gqVkfBxIGMDcQ3IkrgCQr/wHCOMaoc9Jb5/2EAf+bgblcmYVz8mq2H7D8flZm96zdJ/Yeq6Z+6hcgvOL9hKCk3pttez/w2uzv5QQFfBvwfeD0XPkrsv83Au8bUH7/rI+fAZsJr4Q3EiyahT5+h6CAHiFY9Xfn+vhy1taDwEcHlP9x1sdPCTfjvYTwu2/k+vi/BN/w2uzzjdy+35+1cxvBNTKqzrB+PprJs5ZgTb1lxPHqLX/gqOPVc/6uJvjWB/bRp/yqAufkb9gWiXIVQZmNOl69dc7Myq8nvLX9MDue/5CVX3Dp3Jwdx5MK9DGozsBzktV7H3B+n2v+cddXb/lcnWHn/QDgP7J9XEtQ1Av9PJB9biWMaQyq896s/H1su+7uBf4qK38CQcn+hPA2NFfgePXW+ULW5jxhYPQewsPhktzx/Xh2bH4ErModg9Oz9m8DTqtbd9X98RmWjuM4EVK3z9txHMdZAq68HcdxIsSVt+M4ToS48nYcx4kQV96O4zgR4srbcRwnQlx5O47jRIgrb2cqkfTvktZmn8cknVi3TI4zTfgkHWeqkfRWQprRk82sW7c8jjMttOsWwHEGIel/A78HHO+K23G2x5W3M5VI+n3gjcBxZralbnkcZ9pw5e1MHZKOJSxnd6yZPVa3PI4zjbjP25k6JD1AyLL3SLbpY2Z2YY0iOc7U4crbcRwnQjxU0HEcJ0JceTuO40SIK2/HcZwIceXtOI4TIa68HcdxIsSVt+M4ToS48nYcx4kQV96O4zgR8v8BcthPbE9QNgsAAAAASUVORK5CYII=", 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jXtcXKCdw128HrADODhWEbeluAtITtbQ43t2xl7Vv/J1LP/hXHmuewVXxC7g/598YXFTCrHEectPV91F6lk6/m4BzbqmZDTlu9WwC94kDeBRYDHzvuG0uBuY75/YEC50PlABPhaMuke6u2d/C29v2MK/Cx8trfFTvbyApPpvM7Mu4pe5xjpx/O9+/+PpIlykSlTrzHJzHOVcVfOwjcIPT4w0AdrRZrgyuE+mxGptbWLa5lnkVPl5ZW82eQ42kJMZx0ahcSsd7mZm6gd5/KYOpd5Ba/iCMukgXV4uE0CWTTJxzzsw6dCzUzOYAcwDy89XMVWJLfZOfpR/sYl6FjwXrAn0f05ITmD4ml9JCLxeOzqFXUkLghqLPXfdxi6yhU9T/UaQdnRlw1WaW55yrMrM8oCbENjv5+DAmwEAChzJP4Jx7AHgAAufgwluqSNc71NDMog01lFX4WLS+hsONfjJTE5k1zktpoZfPjGjT97HVzpXq/yhymjoz4F4ErgZ+Gvz9lxDbvAz8p5n1CS7PAu7qxJpEIqruSLDvY4WPpcG+j9lpSXx+4gBKC72cN6wfifEh+j62Uv9HkdMWrssEniIwEss2s0rgbgLB9qyZXQt8CFwe3LYIuME5d51zbo+Z/Rh4J/hW97ROOBGJFbsPNjB/bSDUlm0O9H3My0zhq5PyKS30UjREfR9FOkNYLhPoarpMQKJddWvfx9U+3tq6mxYH+X17UVropaTQy4SB6vsoEg6dfpmAiMCOPYePNjNe8WHgUs4RuWl8Z9oISgq9FOSp76NIV1LAiZxKiPZYbF0KO1eyefR1R5sZr94Z6PtYkJfB7cWjKB3vZUSu+j6KRIoCTuRUgu2x+MojuCFT2LHyZbLLrufu5H/hub8tAeDMQVncVTqGkkIvg/up76NINFDAiZyCGzKFLRfNJe+Jr/O8zeKzjWVc23Qz/pwi7p7s5eJxXvqr76NI1FHAiYTQ0uJYsX0vZasDLbJ27nPcnjidm+KfZfWI6/n1528hJz050mWKyEko4ESCmv0tvLV1D2UVVby8pppdBxpIio9jyshs/uPMvUx9fwmccwfjyx+E2kshXdeeiUQzBZz0aI3NLbyxqZayiirmr61m7+EmUhPjuWh0DiWFXqaPySW9ajk89124/BG1xxLpRhRw0uPUN/lZvGEX8yqqeHVdDQcaAn0fZ4wN9n0clUtqUpsWWWqPJdItKeCkRzjY0MzC9TXMq6hi0fpdHGnyk9UrkZJCL6XjA30fkxPiQ79Y7bFEuiUFnMSsusNNzF9XzbyKKpZurKWxuYXstGS+eNYASgvzOHdY35P3fRSRbk0BJzGl9mADr6yppqyiiuWbd9Pc4uifmcLXzs2ntDCPswf3Ud9HkR5CASfdnq+unnkVVZRV+Hhn2x5aHAzu14trpwyltDCPCQMz1SJLpAdSwEm3tGPPYcqCofbu9n0AjMxN48ZpIygpzGNsXrpCTaSH69SAM7PRwDNtVg0Dfuic+1WbbS4icK+4rcFVf3LO3dOZdUmUa6f3Y+0Hb/J04hcoq/Cx5qP9AIzrn8G/zBpFSWEeI3LTIlOviESlTg0459wG4EwAM4sncAfvF0Js+ppz7tLOrEW6kWDvR/flh1mXMpE1b/yV4rV3clPDTSxv+YCJ+Vn86yVjKBmXR36/XpGuVkSiVFceopwBbHbOfdiFnyndjHOO9xPOYE3+PXz2sauY3zyDq+IX8Ot+P+Disy/ml4Ve8jLV91FETq0rA+4K4Kl2njvfzN4HPgL+xTm35vgNzGwOMAcgPz+/04qUrudvcaz4cG+gRVaFj4/q6kmI60uv7M9xy/4nOHTebfyw5IZIlyki3UyX3NHbzJIIhNc451z1cc9lAC3OuYNmdglwr3Nu5MneT3f07v6a/S28uSXQ9/GVtcG+jwlxTB2ZTUlhHiW9PiDtr9dB0bVQ/qDaYolISNFwR+9SYOXx4QbgnNvf5vFLZnafmWU752q7qDbpIg3N/kDfx9U+5q+rZl+w7+O0MTmUFOYxbXQO6SmJgZuJPnfdx6Gm3o8i8il0VcB9lXYOT5qZF6h2zjkzmwTEAbu7qC7pZEca/Sz54Ni+j+nBvo8lhXlcOCrn2L6PoN6PIhIWnR5wZtYbKAaub7PuBgDn3P3Al4Fvm1kzcAS4wnXFcVPpNAfqm1gUbGbctu9j6XgvpYV5TB7Rr/2+j6DejyISFp0ecM65Q0C/49bd3+bxXGBuZ9chnStU38ec9GS+dHaw7+PQviSo76OIdCF1MpFPrb2+j1edO5jS8V7OylffRxGJHAWcfCKh+j4O6deL66YMo7TQyxnq+ygiUUIBJwHttMdi50p2FMw5oe/jKE8aN04fSWmhlzFe9X0UkeijgJOAYHus1tmLO999mb4vzeGelDt46m+LACgckMF3Lx5NSaGX4Tnq+ygi0U0BJwC4IVP4cPp95D7xdf4UdzGlDS/xraabaehzJt+/JI+SQi+D+qrvo4h0Hwq4Hsw5x/uVdZRVVDGvwseHu/3cljCNmxOe4f3hc/if2TfjzUyJdJkiIp+KAq6HCd330Zg8IpsfFu5m2qqlcM4dTCh/EPZ8DjJ17ZmIdE8KuB6gyd/CW8G+jy+vqab2YGvfxxxunzWamWM9ZFYvh+fugMsfUXssEYkJCrgYFarvY6+keKaNzqWk0Mu0MbmkJbf536/2WCISYxRwMSTQ97GGsgofC1v7PqYkMHOsh5JCLxeOyiElsZ0WWWqPJSIxRgHXzR2ob2Lh+hrmVfhYvCHQ97FPr0QuGZ9HyXgvnxmeTVKCWmSJSM+jgOuG9h1u5JW11cyr8PH6xloa/S3kpifz5bMHUlroZZL6PoqIdMndBLYBBwA/0Hz8jeks0ALjXuAS4DBwjXNuZWfX1d3sOtDAK2t9lK32sXzLbvwtjgFZqXz9/MGUFgb6Psap76OIyFFdNYKbdpIbmJYCI4M/5wK/C/6OfSdpj8UFt/LRviPMq/Axb02g76NzMDS7N3OmBvo+jh+gvo8iIu2JhkOUs4HHgveAe9PMsswszzlXFenCOt1x7bHYuhT/M1fz9zH/jwd/+wbv79gHwGhPOjdPH0npeC+jPer7KCJyOroi4Bzwipk54H+dcw8c9/wAYEeb5crgutgPuOBUfP8zV1Oe80XGVD7LDQ03sfzNdMYPcHz34tGUFnoZpr6PIiKfWFcE3AXOuZ1mlgvMN7P1zrmln/RNzGwOMAcgPz8/3DV2Keccaz7az7wKH2UVLVx28EJuqf89z/X+KjOmf5n/Hqe+jyIiHdUVd/TeGfxdY2YvAJOAtgG3ExjUZnlgcN3x7/MA8ABAUVGR67SCO0lLi+O9yn2Bc2oVPrbvOUycwTf77+D61MUcPOs2vrL6URh4JfQdFulyRUS6vU4NODPrDcQ55w4EH88C7jlusxeBG83saQKTS+pi5fybv8XxzrY9R0PNt7+exHhj8vBs/umi4ZSmbSTzb/8NVz4WOFw5ZpraY4mIhElnj+A8wAvBSREJwJPOuXlmdgOAc+5+4CUClwhsInCZwDc7uaZO1eRvYfnm3ZRV+Ji/1kftwUaSE+KYOiqHOwpHM2Osh8zUxMDGr/9J7bFERDqJBSYvdi9FRUWuvLw80mUcVd/k5/WNtZRV+Fiwrpq6I030Topn2phg38fRufROjoYJqyIiscXMVhx/fXUrfet+Socbm1m8YRdlFT4Wra/hYLDvY/FYD6Xj85gyMrv9vo8iItLpFHCfwP76Jhauq6GsooolH+yivqmFvr2TuPSMwB2vJ6vvo4hI1FDAncLeQ43MX1tNWUUVb2zaTaO/BU9GMv9QNIiSwjzOGdJHfR9FRKKQAi6EmgP1vLymmnkVVby5ZQ/+FsfAPqlcPXkwJYV5TByUpb6PIiJRrmcF3El6P+4svD44nb+K8g/34hwMy+nNDRcOo7Qwj3H9M9QiS0SkG+lZAXdc70ffe6+Q+fd/5D9S7+Dxvy0EYIw3nVtnjKJ0vJeRuWkKNRGRbqpnBVzwOrPGp7/Bc8yipP4lvtV0M4czJ/C9kjxKC70Mye4d6SpFRCQMelbAQWDkNvJrfK1iLu8Om8PPZ9/EgKzUSFclIiJh1vOm/21dSv6Wp2DqHUys/iMD9r4T6YpERKQT9KyA27r043Nw078f+P3cNYH1IiISU3pWwO1c2X7vRxERiSk96xzcBbeeuG7oVDU2FhGJQT1rBCciIj1Gt7ybgJntAj7s4NtkA7VhKCcWad+0T/smNO2X9mnftC8c+2awcy4n1BPdMuDCwczK27vFQk+nfdM+7ZvQtF/ap33Tvs7eNzpEKSIiMUkBJyIiMaknB9wDkS4gimnftE/7JjTtl/Zp37SvU/dNjz0HJyIisa0nj+BERCSGKeBERCQmKeBERCQmdctWXdnZ2W7IkCGRLkNERCJsxYoVte1d6N0tA27IkCGUl5dHugwREYkwM2u3q5UOUYqISExSwImIxLD7l2xm2eZj2z0u21zL/Us2R6iirqOAExGJYWcMzOTGJ989GnLLNtdy45PvcsbAzAhX1vm65Tk4EREJrdnfQu3BRnz76/HV1VNzoJ4pI7K55uF3GD8gk621h5h75UQmD8+OdKmdTgEnItINOOfYf6SZ6gOB4PLtr6dmf30wyBqoCa6vPdhAy3ENqhLijPg4Y8WHe/n6eYN7RLiBAk5EJOzuX7KZMwZmHhMkyzbXsqqyjhsuHH7C9g3Nfmr2N1B9NLDqqTnQcEKQ1Te1nPDaPr0S8WSk4MlIYaw3A09GMp7MFLzBdZ6MFD7wHeA7T66kobmFP66spHS8t0eEXLfsRVlUVOR0mYCIRKvW81y/uWIio/PSeWWNj/98aT3/cM4g0pITjgZZdTDU9hxqPOE9khPi8GQEgyozBW9G8tHA8mam4ElPITcjmZTE+NOqZe6VE/nx39bhWhw1Bxti5jClma1o755yGsGJiITZ2YP78Pkz+/P1h9465nDhg69vxQyy05LxZCQzICuFs/KzjgkyT0Yy3owUMlMTMbMO17Kqsu5omBWPzWXuok387qqzWVVZFxMBdzIKOBGRMGlo9vNceSX3LdrER3X1eDOS8e1v4JLxXv5xyjA8GSnkpCeTGN91E9jbHhItLvDy64WbOFDfHPJQaazRZQIiIh3U0Ozn8Tc/ZNrPFvODP1fgzUzhrtIxNPodN08fwZtb9nCkyU//rNQuDbfjFQ7IwJuRwoK11RGroStpBCci8ik1NPt5Njhiq6qr5+zBffivL59BvBk3PvXu0UOD5w3vd/Q8WCQPC5oZMwty+dPKndQ3+U95/q67C8s/JcysxMw2mNkmM7szxPPJZvZM8Pm3zGxIcH2xma0ws9XB39PDUY+ISGdqaPbzhzc/5KKfLebf/lxB/6xU/nDtJJ6/4XymjMxh1c66Y8Js8vBs5l45kVWVdRGuPHCY8nCj/4TuJrGowyM4M4sHfgsUA5XAO2b2onNubZvNrgX2OudGmNkVwH8B/wDUAp9zzn1kZoXAy8CAjtYkItIZQo3YfvblCXxmRL9jJoSEOr81eXh2VEzqOG9YX9KSE5i/tobpYzyRLqdTheMQ5SRgk3NuC4CZPQ3MBtoG3GzgR8HHzwNzzcycc++22WYNkGpmyc65hjDUJSISFqcbbN1BckI8F47KYcG6av6jpZC4uO5V/ycRjoAbAOxos1wJnNveNs65ZjOrA/oRGMG1+hKwsr1wM7M5wByA/Pz8MJQtInJyDc1+nn1nB/ct3tztg62t4gIPf19dxfuV+5iY3yfS5XSaqJhkYmbjCBy2nNXeNs65B4AHIHChdxeVJiI90PHBVhQjwdbqotE5xMcZC9ZVK+BOYScwqM3ywOC6UNtUmlkCkAnsBjCzgcALwDecc7F//wYRiVqxHmytsnolMWlIX+avrea7F4+JdDmdJhwB9w4w0syGEgiyK4Arj9vmReBqYDnwZWChc86ZWRbwd+BO59wbYahFROQTaw223y7ajG9/INh+/pUJTB4eW8HWVnGBh3v+tpYPdx9icL/ekS6nU3T4MgHnXDNwI4EZkOuAZ51za8zsHjO7LLjZg0A/M9sE3Aa0XkpwIzAC+KGZvRf8ye1oTSIip6O+yc9jy7dx4X8v5t/+soaBfVJ54rpzee6G8/nMiOyYDTcIBBzA/Bi+6FvNlkWkx6lv8vNs+Q7uC47YzhnSh1tnjorpEVsoJb9aSmZqIs9cf36kS/nU1GxZRITQwfaLy2P7UOTJFBd4uG/xZvYeaqRP76RIlxN2CjgRiXmhgu2Xl0/g/B4abK1mjvXwm4WbWLShhi+eNTDS5YSdAk5EYkKom4wu3lDDE29uZ9XOfVTvb1CwHWf8gEw8GcnMX1utgBMRiVZnDMw82tD4rPw+/LRsPY8u34ZzMGlIX/7n8jMVbMeJizNmjPXw53djs/myAk5EujXnHAcamslJS+b6qcO47tFyDDjU6GeMJ50ffq5AwXYSxQUennxrO8u37Gba6NiaxK6AE5Go1djcQs2Beqr311O9vwFfXevjenzBddX76znc6D/htV+YOIBfXj5BwXYKk4f3o3dSPAvWVivgREQg9DmvZZtrWVVZd8q7RTvn2Hu4KURgHRtkuw81nvDapIQ4PBnJeDNSKOifwfQxuXgzUsjNSKb2YAO/fnUT3zh/ME8ERyXR0ME/miUnxDM12Hz5x7Njq/myAk5EPpW257wmD89m2eZabnzyXX75lQlsqz3UJrDq8dU1UH2gnuq6QJDV7G+g0d9ywntmpyXhyUghLzOFCYOy8Gak4M1MJjcjJfA4I4WsXokhR2XLNtfy739dy++uOovJw7M5P0puMtodFBd4KKvwsXpnHRMGZUW6nLBRwInIafG3OHYfbMC3vz4wwjrQwNSR2Vzz8Dt4MpL5aO8RkhPiuOaRd054ba+keLwZKXgyUiga3AdPZsrRZU9GCt7MFHLSkklK+PTNlVZVtn+TUQXcyU0bnXu0+XIsBZw6mYj0cM45DjY0Hx1pHTvyCgRZdV09uw424G859vsiPs5ISYjjUKOfYTm9uWBEdiCwjgZXMp6MFNKSE3QuLMr9w/8up+5IE/NunRrpUj4RdTIRiRGf9LxXY3MLuw6GmJxR9/EEDV87kzQyUhLwZgaCamRudiC0MlPwpCfjDY7APqg+yM1Pv8u1Fwzl8be2U1Lo1Wipmyou8PCTv69jx57DDOrbK9LlhIUCTqQbOXre66sTGZOXwStrfPzk7+v46qRB3Ltg4zGjr+r99dQeDDFJIz6O3OAkjbH9M7hodO7RkVbb0Vdq0smviVq2uZabn/74HNd5OufVrbUG3Py11XzrgqGRLicsdIhSpBtp8rfws5c38PvXttAS4q9udloSuekpR0derbMNAyOvwPo+7UzS+KQ6MotSotOs/1lCv97JPDXnvEiXctp0iFKkm2vyt/DCuzuZu3AT2/ccJjc9mZoDDZQWerluyjA8Gcnkpqd0aJLGJxUqxCYPz9borRsrLvBw/5It1B1uIrNXYqTL6bCu+9sQBe5fspllm2uPWbdscy33L9GNxCU6NflbePadHUz/xWLueH4VmamJfHfWKJpbHDdPH8FbW/fQ0OxnYJ9eXRpuEptmjvXgb3Es2lAT6VLCokf9jWg9f9Eacq3X7ZwxMDPClYkc65hg++MqslKTePDqIu4qHcODb2xj7pUTuW3WaOZeOfGYP9MiHTFhYBY56ckxcxPUHnWIsvW6mG8/vpL8vqns2HOE+4IXhYpEgyZ/Cy+s3MlvFm1kx54jjB+QyY+uHsf0MbmYGfcv2axrvaTTxMUZM8fm8tf3q2ho9pOc0L2bL/eogIPAF8I5Q/qwYF0NBvzl3Y8YkJXK4H69I12a9GDHB9sZAzP598vGMW107jETQnTeSzpbcYGHp97ewZtb9nDhqJxIl9MhPS7glm2uZeX2fXxz8hCefHs7f1xZyfMrK5k9oT/fmT6C4TlpkS5RepAmfwt/WlnJ3EWbThpsIl1l8vBsUhPjmb/W1+0DLizn4MysxMw2mNkmM7szxPPJZvZM8Pm3zGxIm+fuCq7fYGYXh6Oe9rSec5t75UTuvmwcD3/zHNKSE5hV4OGliipm/nIJNz31Lht8BzqzDBGa/C088852pv18Md/742r69ErioWuK+Mt3PsP0MR6Fm0RMSmI8U0dls2BtDd3xMrK2OjyCM7N44LdAMVAJvGNmLzrn1rbZ7Fpgr3NuhJldAfwX8A9mVgBcAYwD+gMLzGyUc+7EtgphEKpX3X1XncWqyjp+/PlCfv/aVv6wfBt/ff8jSsZ5uXH6CAoHaAKKhE/riO03CzdRuTcwYrtntkZsEl2KC7y8vKaaip37Gd+NJ+GF4xDlJGCTc24LgJk9DcwG2gbcbOBHwcfPA3Mt8Ld5NvC0c64B2Gpmm4LvtzwMdZ3gVOcv7iwdw/VTh/HwG1t5eNk25q3xMWNMLjfNGMmZMdSAVLre8cE2YWAmP55dyEWjcxRsEnWmj8klzmD+uuoeH3ADgB1tliuBc9vbxjnXbGZ1QL/g+jePe+2AUB9iZnOAOQD5+flhKDu0Pr2TuG3WaK6dMoxHl23joTe28vnfvsGUkdncPGMk5wzp22mfLbFHwSbdUd/eSRQN7sv8tdXcVjwq0uV8at1mkolz7gHgAQi06ursz8tMTeTmGSP51gVD+cPyD/n9a1v4yv3LOW9YX26eMZLzh/XTF5S0q8nfwh9XBCaPKNikOyou8PAfL3Xv5svhmGSyExjUZnlgcF3IbcwsAcgEdp/mayMqLTmBb180nNe+N40ffHYsW3Yd4sr/e4uv3L+cJR/s6vYnYSW8mvwtPP12YPLInX9aTb/eSTx8zTn8+TufYdoYnWeT7mNmgQeAV9d134u+O9xsORhYHwAzCITTO8CVzrk1bbb5DjDeOXdDcJLJF51zl5vZOOBJAufd+gOvAiNPNckkks2W65v8PFu+g/sXb+ajunomDMripmkjmDFWX149WWPzx9P9K/ceYcKgLG6dOZKLRmnEJt3XzF8uwZORzBPXRW/z5U5tthw8p3Yj8DIQDzzknFtjZvcA5c65F4EHgT8EJ5HsITBzkuB2zxKYkNIMfKezZlCGS0piPN84fwhXnJPPH1dWct/iTVz3WDkFeRncNH0EF4/zEhenL7SeIlSw/fjzhQo2iQnFBR7+b+kW6o40kZna/Zov63Y5HdTkb+Ev733EbxdtYmvtIUZ50rhx+kg+Oz6PeAVdTAh1W5ilH+ziybe3s7qyjp37NGKT2LTiw7186XfLuPeKM5l9Zsj5fxF3shFcj2q23BkS4+P48tkDWXDbhdx7xZk4Bzc/9S7F/7OEP66opNnfEukST4vutNC+tk26G5tb+Mnf13LNw28zr8JHdnoyD3/zHP78T5N1LZvEnImDsshOS+q2zZe7zSzKaBcfZ8w+cwCfO6M/89b4+M3CTdz+3Pvc++pG/umi4XzxrIFRfTuTo3eKDl4I37brS092sKGZ3PQUvn3hMK57tJx4Mw40NDM8pzf/dmkBF2rEJjEsLs6YMcbDS6uraGxuiervsFB0iLKTOOdYsK6G3yzcyKrKOgZkpXLDhcP4StEgUhIj06G72d/CroMN+Orqqd5fT/X+Bnz766muq6f6QD1bdx2iqq6ehHjD3+IYlZvO8Nw0ctKTyU5LIic9OfCTlkJOejL90pJIjO9ef+BbNflb2HWgIbgf6vHV1ePb30DN/np8wZ+a/Q0cbGg+4bWXTejPvVecqWCTHmHB2mque6ycP1w7iSkjo683pe7oHQFmRnGBh5ljc1nywS5+s3AT//aXNcxdtInrpw7nq5PyeXT5thPO7SzbXMuqyrqQXVfa45xj/5Hmo1/M1cHQ8gVDrDq4vvZgA8f/eyYhzvBkpODJSGbCoCxy0o/wfmUdIz1pZPVOZL1vP69tbGB//Ylf9BC4IDQnLfnj8EtPPrqc3WZ9VmriaU++CXXO63T3i3OOuiNNH/+317XZJ/s/3ien2hejPelMHZmDNzOwXHuwgbkLN/ON8wfzxFvbWb5ltzr4S49wwchsUhLjmL+2OioD7mQ0gusizjmWb97Nva9u5K2te8hOS2JWgYeyCh+//dpZJxwWbP3ybGj2U9M60gqONAJf1B+PPqr311PfdOK5vj69EvFkpAS+pNNT8GSm4A1+gbeu79sr6WjwtH7+Vefm8/hb24+po77JT+3BBnYdCP60fRxcrj3YQM3+BhqaT6wlIc6OCbwTQrFNIK7asY8bnzrxcOkvL5/AsOw0qg+02Q919VQfODbIQn3+J90XbR3//yXU/yeRWPaPj5WzZmcdb9w5PeqOXJxsBKeAi4C3t+7hNws38trGWtKS4/G3wHnD+rF8y27OG9oXjKNf4HsPN53w+uSEuODIIvDjDX5Jt35RezMChxA/yaHQcH2JO+c42NB80iBsfbz7UCP+lhP//KUmxpOeksCeQ43kZaXw0d56UpPiONhw4hUkbffF8YHVuu6T7ovjdWREKRILni3fwR3Pr+JvN10QdQ3oFXBRauX2vcxduImF62uOrstJTw5+UQe+rL0ZgdFG65e1NyOFjNSEsP8rKhJf4i0tjr2HG08MwWAQrvhwL5V7jzA0uzeTh/frsn0hIsfafbCBov9YwM3TR/LPUdabUufgotRZ+X24bspQVn64ly+cNYA/v7uTe684MyKHvSJxp+i4OKNfWjL90pIZ4z32uWWba3ltYy03Tx/B429t57Nn5OlwoEiE9EtL5uz8PixYVx11AXcy3XMKXIxoPQx431VncffnxvHbr5119Hqrnqzt4dHbZo1m7pUTtV9EIqy4wMOaj/azc9+RSJdy2hRwERTqBqxzr5zIqsq6CFcWWdovItGnOzZf1jk4ERE5LdN/sZgBWan84drjb/kZOWrVJSIiHVZc4OHNLbvZX3/i7O5opIATEZHTUjzWQ5PfsWTDrkiXcloUcCIiclom5vehX+/u03xZASciIqclPs6YMTaXRRtqaOoGd0pRwImIyGmbOdbDgfpm3t66J9KlnJICTkRETtuUkTkkJ8R1i8OUCjgRETltqUnxTBmZzfy11UT7ZWYKOBER+USKCzzs3HeEdVUHIl3KSXUo4Mysr5nNN7ONwd992tnu6uA2G83s6uC6Xmb2dzNbb2ZrzOynHalFRES6xvQxHsyI+sOUHR3B3Qm86pwbCbwaXD6GmfUF7gbOBSYBd7cJwp8758YAE4HPmFlpB+sREZFOlpOezMRBWSyI8rZdHQ242cCjwcePAp8Psc3FwHzn3B7n3F5gPlDinDvsnFsE4JxrBFYCAztYj4iIdIHiAi+rd9ZRVRe9zZc7GnAe51xV8LEP8ITYZgCwo81yZXDdUWaWBXyOwCgwJDObY2blZla+a1f3uIpeRCRWFRfkArAgig9TnjLgzGyBmVWE+JnddjsXmE7ziafUmFkC8BTwa+fclva2c8494Jwrcs4V5eTkfNKPERGRMBqek8bQ7N7MX1dz6o0j5JQ3PHXOzWzvOTOrNrM851yVmeUBof5LdwIXtVkeCCxus/wAsNE596vTKVhERCLPzCgu8PDwG1s5UN9EekpipEs6QUcPUb4IXB18fDXwlxDbvAzMMrM+wckls4LrMLOfAJnArR2sQ0REutjMYPPlpR9E582IOxpwPwWKzWwjMDO4jJkVmdnvAZxze4AfA+8Ef+5xzu0xs4HA94ECYKWZvWdm13WwHhER6SJnD+5D395JzF/ri3QpIZ3yEOXJOOd2AzNCrC8Hrmuz/BDw0HHbVALWkc8XEZHIiY8zpo/J5ZU1Ppr8LSTGR1fvkOiqRkREupWZYz3sr2/mnW3R13xZASciIp/a1FHZJEVp82UFnIiIfGq9khK4YER0Nl9WwImISIcUF3io3HuEDdXR1XxZASciIh0yY2ygq8n8NdF1mFIBJyIiHZKbnsKZUdh8WQEnIiIdVlzg4f3KOqr310e6lKMUcCIi0mGzCgK99qNpNqUCTkREOmxEbhqD+/WKqsOUCjgREekwM6N4rIdlm3ZzsKE50uUACjgREQmTmQUeGv0tLP0gOu7ZqYATEZGwKBrch6xeiVFzE1QFnIiIhEVCfBzTx+SycEMNzf6WSJejgBMRkfApHuth3+Emyj/cG+lSFHAiIhI+U0flkBQfHc2XFXAiIhI2vZMTmDyiX1Q0X1bAiYhIWBUXeNi+5zAbaw5GtA4FnIiIhNXMsdHR1UQBJyIiYeXJSGHCwExe6c4BZ2Z9zWy+mW0M/u7TznZXB7fZaGZXh3j+RTOr6EgtIiISPYoLPLy/Yx81EWy+3NER3J3Aq865kcCrweVjmFlf4G7gXGAScHfbIDSzLwKRPVArIiJhVVzgBWDBupqI1dDRgJsNPBp8/Cjw+RDbXAzMd87tcc7tBeYDJQBmlgbcBvykg3WIiEgUGeVJY1Df1Ig2X+5owHmcc1XBxz7AE2KbAcCONsuVwXUAPwZ+ARw+1QeZ2RwzKzez8l27oqPPmYiIhBZovuzl9U21HIpQ8+VTBpyZLTCzihA/s9tu5wIXPJz2RQ9mdiYw3Dn3wuls75x7wDlX5JwrysnJOd2PERGRCJlZkEtjcwuvbYzMoCThVBs452a295yZVZtZnnOuyszygFAHW3cCF7VZHggsBs4HisxsW7COXDNb7Jy7CBER6fYmDelLZmoi89fWUFKY1+Wf39FDlC8CrbMirwb+EmKbl4FZZtYnOLlkFvCyc+53zrn+zrkhwAXABwo3EZHYcbT58vrqiDRf7mjA/RQoNrONwMzgMmZWZGa/B3DO7SFwru2d4M89wXUiIhLjZo71sPdwEysi0Hz5lIcoT8Y5txuYEWJ9OXBdm+WHgIdO8j7bgMKO1CIiItHnwtGB5ssL1lVz7rB+XfrZ6mQiIiKdJi05gfOHR6b5sgJOREQ61cwCD9t2H2bzrq7t6aGAExGRTjVzbC5Al/emVMCJiEinystMZfyAzC6/u4ACTkREOl1xgYf3duyj5kDXNV9WwImISKcrLvDgHCzswubLCjgREel0Y7zpDMhK7dLDlAo4ERHpdGZGcYGH1zfVcrixa5ovK+BERKRLFBd4aGhu4bWNtV3yeQo4ERHpEpOG9iUjJYEFXXSYUgEnIiJdIjE+jmljclm4vgZ/S+d3NVHAiYhIl5k51sPuQ42s3N75zZcVcCIi0mW27DpIfBzHHKZctrmW+5dsDvtnKeBERKTLnDO0L2bGi+99BATC7cYn3+WMgZlh/ywFnIiIdJnJw7O56tzBVO2v5wcvrObGJ99l7pUTmTw8O+yfpYATEZEuNWfqMLJ6JfL4W9u56tz8Tgk3UMCJiEgX27b7EHFm3Dx9BI+/tZ1lmzvnujgFnIiIdJnWc25zr5zIbbNGM/fKidz45LudEnIKOBER6TKrKuuOOec2eXg2c6+cyKrKurB/lnX1LcTDoaioyJWXl0e6DBERiTAzW+GcKwr1nEZwIiISk7rlCM7MdgEfdvBtsoGu6fjZ/WjftE/7JjTtl/Zp37QvHPtmsHMuJ9QT3TLgwsHMytsb1vZ02jft074JTfulfdo37evsfaNDlCIiEpMUcCIiEpN6csA9EOkCopj2Tfu0b0LTfmmf9k37OnXf9NhzcCIiEtt68ghORERiWI8LODMbZGaLzGytma0xs1siXVM0MbN4M3vXzP4W6VqiiZllmdnzZrbezNaZ2fmRrilamNk/B/8uVZjZU2aWEumaIsXMHjKzGjOraLOur5nNN7ONwd99IlljJLSzX34W/Pu0ysxeMLOscH9ujws4oBm43TlXAJwHfMfMCiJcUzS5BVgX6SKi0L3APOfcGGAC2kcAmNkA4GagyDlXCMQDV0S2qoh6BCg5bt2dwKvOuZHAq8HlnuYRTtwv84FC59wZwAfAXeH+0B4XcM65KufcyuDjAwS+qAZEtqroYGYDgc8Cv490LdHEzDKBqcCDAM65RufcvogWFV0SgFQzSwB6AR9FuJ6Icc4tBfYct3o28Gjw8aPA57uypmgQar84515xzjUHF98EBob7c3tcwLVlZkOAicBbES4lWvwKuANoiXAd0WYosAt4OHj49vdm1jvSRUUD59xO4OfAdqAKqHPOvRLZqqKOxzlXFXzsAzyRLCZKfQsoC/eb9tiAM7M04I/Arc65/ZGuJ9LM7FKgxjm3ItK1RKEE4Czgd865icAheuZhphMEzyfNJvCPgP5AbzO7KrJVRS8XmLauqettmNn3CZw6eiLc790jA87MEgmE2xPOuT9Fup4o8RngMjPbBjwNTDezxyNbUtSoBCqdc60j/ecJBJ7ATGCrc26Xc64J+BMwOcI1RZtqM8sDCP6uiXA9UcPMrgEuBb7mOuGatR4XcGZmBM6lrHPO/TLS9UQL59xdzrmBzrkhBCYJLHTO6V/igHPOB+wws9HBVTOAtREsKZpsB84zs17Bv1sz0ASc470IXB18fDXwlwjWEjXMrITAKZHLnHOHO+MzelzAERipfJ3ACOW94M8lkS5Kot5NwBNmtgo4E/jPyJYTHYKj2ueBlcBqAt8pPbZzh5k9BSwHRptZpZldC/wUKDazjQRGvD+NZI2R0M5+mQukA/OD38P3h/1z1clERERiUU8cwYmISA+ggBMRkZikgBMRkZikgBMRkZikgBMRkZikgBMRkZikgBMRkZikgBMRkZj0/wFhGivRNtCNJgAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "bests = []\n", - "N = 200\n", - "step = 1 / (N - 1)\n", - "a = 11 / 8\n", - "b = 1 / 2\n", - "x = np.linspace(step, 1 - step, N + 1)\n", - "ns = np.arange(2, 13)\n", - "for n in ns:\n", - " zeros, weights = np.polynomial.laguerre.laggauss(n)\n", - " est = np.ceil(b + a * n)\n", - " targets = np.arange(max(est - 2, 0), est + 3)\n", - " rel_errors = np.stack([np.abs(evaluate(x, target)) for target in targets], -1)\n", - " best = np.argmin(rel_errors, -1) + targets[0]\n", - " bests.append(best)\n", - "bests = np.stack(bests, 0)\n", - "\n", - "fig, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(5, 3))\n", - "v = ax.imshow(bests, cmap=\"inferno\", aspect=\"auto\")\n", - "plt.colorbar(v, ax=ax, label=r'$m$')\n", - "ticks = np.arange(0, N + 1, 10)\n", - "ax.set_xlim(0, 1)\n", - "ax.set_xticks(ticks, [f\"{v:.2f}\" for v in ticks / N])\n", - "ax.set_xticks(np.arange(N + 1), minor=True)\n", - "ax.set_yticks(np.arange(len(ns)), ns)\n", - "ax.set_xlabel(r\"$z$\")\n", - "ax.set_ylabel(r\"$n$\")\n", - "# for best in bests:\n", - "# print(\", \".join([f\"{int(b):2d}\" for b in best]))\n", - "# print(np.unique(bests, return_counts=True))\n", - "\n", - "targets = np.mean(bests, -1)\n", - "intercept, bias = np.polyfit(ns, targets, 1)\n", - "_, axs2 = plt.subplots(2, sharex=True, clear=True, constrained_layout=True)\n", - "xl = np.array([1, ns[-1] + 1])\n", - "axs2[0].plot(ns, intercept * ns + bias)\n", - "axs2[0].plot(ns, targets, \"x\")\n", - "axs2[1].plot(ns, ((intercept * ns + bias) - targets), \"-x\")\n", - "print(np.mean(bests, -1))\n", - "print(f\"Intercept={intercept:.6g}, Bias={bias:.6g}\")\n", - "\n", - "\n", - "predicts = np.ceil(intercept * ns[:, None] + bias - x)\n", - "print(np.sum(np.abs(bests-predicts)))\n", - "# for best in predicts:\n", - "# print(\", \".join([f\"{int(b):2d}\" for b in best]))\n" - ] - } - ], - "metadata": { - "interpreter": { - "hash": "767d51c1340bd893661ea55ea3124f6de3c7a262a8b4abca0554b478b1e2ff90" - }, - "kernelspec": { - "display_name": "Python 3.8.10 64-bit", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.3" - }, - "orig_nbformat": 4 - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 53ba76b..208f770 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -8,6 +8,7 @@ import scipy.special EPSILON = 1e-7 root = str(Path(__file__).parent) img_path = f"{root}/../images" +fontsize = "medium" def _prep_zeros_and_weights(x, w, n): @@ -26,17 +27,6 @@ def pochhammer(z, n): return np.prod(z + np.arange(n)) -def find_shift(z, target): - factor = 1.0 - steps = int(np.floor(target - np.real(z))) - zs = z + steps - if steps > 0: - factor = 1 / pochhammer(z, steps) - elif steps < 0: - factor = pochhammer(zs, -steps) - return zs, factor - - def find_optimal_shift(z, n): mhat = 1.34093 * n + 0.854093 steps = int(np.floor(mhat - np.real(z))) @@ -44,6 +34,7 @@ def find_optimal_shift(z, n): def get_shifting_factor(z, steps): + factor = 1.0 if steps > 0: factor = 1 / pochhammer(z, steps) elif steps < 0: @@ -56,7 +47,9 @@ def laguerre_gamma_shifted(z, x=None, w=None, n=8, target=11): n = len(x) z += 0j - z_shifted, correction_factor = find_shift(z, target) + steps = int(np.floor(target - np.real(z))) + z_shifted = z + steps + correction_factor = get_shifting_factor(z, steps) res = np.sum(x ** (z_shifted - 1) * w) res *= correction_factor @@ -112,167 +105,3 @@ def eval_laguerre_gamma(z, x=None, w=None, n=8, func="simple", **kwargs): def calc_rel_error(x, y): return (y - x) / x - - -# Simple / naive -xmin = -5 -xmax = 30 -ns = np.arange(2, 12, 2) -ylim = np.array([-11, 6]) -x = np.linspace(xmin + EPSILON, xmax - EPSILON, 400) -gamma = scipy.special.gamma(x) -fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) -for n in ns: - gamma_lag = eval_laguerre_gamma(x, n=n) - rel_err = calc_rel_error(gamma, gamma_lag) - ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$") -ax.set_xlim(x[0], x[-1]) -ax.set_ylim(*(10.0 ** ylim)) -ax.set_xticks(np.arange(xmin, xmax + EPSILON, 5)) -ax.set_xticks(np.arange(xmin, xmax), minor=True) -ax.set_yticks(10.0 ** np.arange(*ylim, 2)) -ax.set_yticks(10.0 ** np.arange(*ylim, 2)) -ax.set_xlabel(r"$z$") -ax.set_ylabel("Relativer Fehler") -ax.legend(ncol=3, fontsize="small") -ax.grid(1, "both") -fig.savefig(f"{img_path}/rel_error_simple.pgf") - - -# Mirrored -xmin = -15 -xmax = 15 -ylim = np.array([-11, 1]) -x = np.linspace(xmin + EPSILON, xmax - EPSILON, 400) -gamma = scipy.special.gamma(x) -fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(5, 2.5)) -for n in ns: - gamma_lag = eval_laguerre_gamma(x, n=n, func="mirror") - rel_err = calc_rel_error(gamma, gamma_lag) - ax2.semilogy(x, np.abs(rel_err), label=f"$n={n}$") -ax2.set_xlim(x[0], x[-1]) -ax2.set_ylim(*(10.0 ** ylim)) -ax2.set_xticks(np.arange(xmin, xmax + EPSILON, 5)) -ax2.set_xticks(np.arange(xmin, xmax), minor=True) -ax2.set_yticks(10.0 ** np.arange(*ylim, 2)) -# locmin = mpl.ticker.LogLocator(base=10.0,subs=0.1*np.arange(1,10),numticks=100) -# ax2.yaxis.set_minor_locator(locmin) -# ax2.yaxis.set_minor_formatter(mpl.ticker.NullFormatter()) -ax2.set_xlabel(r"$z$") -ax2.set_ylabel("Relativer Fehler") -ax2.legend(ncol=1, loc="upper left", fontsize="small") -ax2.grid(1, "both") -fig2.savefig(f"{img_path}/rel_error_mirror.pgf") - - -# Move to target -bests = [] -N = 200 -step = 1 / (N - 1) -a = 11 / 8 -b = 1 / 2 -x = np.linspace(step, 1 - step, N + 1) -gamma = scipy.special.gamma(x)[:, None] -ns = np.arange(2, 13) -for n in ns: - zeros, weights = np.polynomial.laguerre.laggauss(n) - est = np.ceil(b + a * n) - targets = np.arange(max(est - 2, 0), est + 3) - gamma_lag = np.stack( - [ - eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted") - for target in targets - ], - -1, - ) - rel_error = np.abs(calc_rel_error(gamma, gamma_lag)) - best = np.argmin(rel_error, -1) + targets[0] - bests.append(best) -bests = np.stack(bests, 0) - -fig3, ax3 = plt.subplots(num=3, clear=True, constrained_layout=True, figsize=(5, 3)) -v = ax3.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest") -plt.colorbar(v, ax=ax3, label=r"$m^*$") -ticks = np.arange(0, N + 1, N // 5) -ax3.set_xlim(0, 1) -ax3.set_xticks(ticks) -ax3.set_xticklabels([f"{v:.2f}" for v in ticks / N]) -ax3.set_xticks(np.arange(0, N + 1, N // 20), minor=True) -ax3.set_yticks(np.arange(len(ns))) -ax3.set_yticklabels(ns) -ax3.set_xlabel(r"$z$") -ax3.set_ylabel(r"$n$") -fig3.savefig(f"{img_path}/targets.pdf") - -targets = np.mean(bests, -1) -intercept, bias = np.polyfit(ns, targets, 1) -fig4, axs4 = plt.subplots( - 2, num=4, sharex=True, clear=True, constrained_layout=True, figsize=(5, 4) -) -xl = np.array([ns[0] - 0.5, ns[-1] + 0.5]) -axs4[0].plot(xl, intercept * xl + bias, label=r"$\hat{m}$") -axs4[0].plot(ns, targets, "x", label=r"$\overline{m}$") -axs4[1].plot(ns, ((intercept * ns + bias) - targets), "-x", label=r"$\hat{m} - \overline{m}$") -axs4[0].set_xlim(*xl) -# axs4[0].set_title("Schätzung von Mittelwert") -# axs4[1].set_title("Fehler") -axs4[-1].set_xlabel(r"$n$") -for ax in axs4: - ax.grid(1) - ax.legend() -fig4.savefig(f"{img_path}/estimate.pgf") - -print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") -predicts = np.ceil(intercept * ns[:, None] + bias - x) -print(f"Error: {int(np.sum(np.abs(bests-predicts)))}") - -# Comparison relative error between methods -N = 200 -step = 1 / (N - 1) -x = np.linspace(step, 1 - step, N + 1) -gamma = scipy.special.gamma(x)[:, None] -n = 8 -targets = np.arange(10, 14) -gamma = scipy.special.gamma(x) -fig5, ax5 = plt.subplots(num=5, clear=True, constrained_layout=True) -for target in targets: - gamma_lag = eval_laguerre_gamma(x, target=target, n=n, func="shifted") - rel_error = np.abs(calc_rel_error(gamma, gamma_lag)) - ax5.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3) -gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") -rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax5.semilogy(x, rel_error, "m", linestyle="dotted", label="$m^*$", linewidth=3) -ax5.set_xlim(x[0], x[-1]) -ax5.set_ylim(5e-9, 5e-8) -ax5.set_xlabel(r"$z$") -ax5.grid(1, "both") -ax5.legend() -fig5.savefig(f"{img_path}/rel_error_shifted.pgf") - -N = 200 -x = np.linspace(-5+ EPSILON, 5-EPSILON, N) -gamma = scipy.special.gamma(x)[:, None] -n = 8 -gamma = scipy.special.gamma(x) -fig6, ax6 = plt.subplots(num=6, clear=True, constrained_layout=True) -gamma_lgo = eval_laguerre_gamma(x, n=n, func="optimal_shifted") -rel_error = np.abs(calc_rel_error(gamma, gamma_lgo)) -ax6.semilogy(x, rel_error, label="$m^*$", linewidth=3) -ax6.set_xlim(x[0], x[-1]) -ax6.set_ylim(5e-9, 5e-8) -ax6.set_xlabel(r"$z$") -ax6.grid(1, "both") -ax6.legend() -fig6.savefig(f"{img_path}/rel_error_range.pgf") - -N = 2001 -x = np.linspace(-5, 5, N) -gamma = scipy.special.gamma(x) -fig7, ax7 = plt.subplots(num=7, clear=True, constrained_layout=True) -ax7.plot(x, gamma) -ax7.set_xlim(x[0], x[-1]) -ax7.set_ylim(-7.5, 25) -ax7.grid(1, "both") -fig7.savefig(f"{img_path}/gamma.pgf") - -# plt.show() diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py index 0cf43d1..f31f194 100644 --- a/buch/papers/laguerre/scripts/integrand.py +++ b/buch/papers/laguerre/scripts/integrand.py @@ -2,48 +2,32 @@ # -*- coding:utf-8 -*- """Plot for integrand of gamma function with shifting terms.""" -import os -from pathlib import Path - -import matplotlib.pyplot as plt -import numpy as np - -EPSILON = 1e-12 -xlims = np.array([-3, 3]) - -root = str(Path(__file__).parent) -img_path = f"{root}/../images" -os.makedirs(img_path, exist_ok=True) - -t = np.logspace(*xlims, 1001)[:, None] - -z = np.array([-4.5, -2, -1, -0.5, 0.0, 0.5, 1, 2, 4.5]) -r = t ** z - -fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 3)) -ax.semilogx(t, r) -ax.set_xlim(*(10.0 ** xlims)) -ax.set_ylim(1e-3, 40) -ax.set_xlabel(r"$x$") -ax.set_ylabel(r"$x^z$") -ax.grid(1, "both") -labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)] -ax.legend(labels, ncol=2, loc="upper left", fontsize="small") -fig.savefig(f"{img_path}/integrands.pgf") - -z2 = np.array([-1, -0.5, 0.0, 0.5, 1, 2, 3, 4, 4.5]) -e = np.exp(-t) -r2 = t ** z2 * e - -fig2, ax2 = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(5, 3)) -ax2.semilogx(t, r2) -# ax2.plot(t,np.exp(-t)) -ax2.set_xlim(10 ** (-2), 20) -ax2.set_ylim(1e-3, 10) -ax2.set_xlabel(r"$x$") -ax2.set_ylabel(r"$x^z e^{-x}$") -ax2.grid(1, "both") -labels =[f"$z={zi: 3.1f}$" for zi in np.squeeze(z2)] -ax2.legend(labels, ncol=2, loc="upper left", fontsize="small") -fig2.savefig(f"{img_path}/integrands_exp.pgf") -# plt.show() +if __name__ == "__main__": + import os + from pathlib import Path + + import matplotlib.pyplot as plt + import numpy as np + + EPSILON = 1e-12 + xlims = np.array([-3, 3]) + + root = str(Path(__file__).parent) + img_path = f"{root}/../images" + os.makedirs(img_path, exist_ok=True) + + t = np.logspace(*xlims, 1001)[:, None] + + z = np.array([-4.5, -2, -1, -0.5, 0.0, 0.5, 1, 2, 4.5]) + r = t ** z + + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(4, 2.4)) + ax.semilogx(t, r) + ax.set_xlim(*(10.0 ** xlims)) + ax.set_ylim(1e-3, 40) + ax.set_xlabel(r"$x$") + # ax.set_ylabel(r"$x^z$") + ax.grid(1, "both") + labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)] + ax.legend(labels, ncol=2, loc="upper left", fontsize="small") + fig.savefig(f"{img_path}/integrand.pgf") diff --git a/buch/papers/laguerre/scripts/integrand_exp.py b/buch/papers/laguerre/scripts/integrand_exp.py new file mode 100644 index 0000000..0e50f43 --- /dev/null +++ b/buch/papers/laguerre/scripts/integrand_exp.py @@ -0,0 +1,36 @@ +#!/usr/bin/env python3 +# -*- coding:utf-8 -*- +"""Plot for integrand of gamma function with shifting terms.""" + +if __name__ == "__main__": + import os + from pathlib import Path + + import matplotlib.pyplot as plt + import numpy as np + + EPSILON = 1e-12 + xlims = np.array([-3, 3]) + + root = str(Path(__file__).parent) + img_path = f"{root}/../images" + os.makedirs(img_path, exist_ok=True) + + t = np.logspace(*xlims, 1001)[:, None] + + z = np.array([-1, -0.5, 0.0, 0.5, 1, 2, 3, 4, 4.5]) + e = np.exp(-t) + r = t ** z * e + + fig, ax = plt.subplots(num=2, clear=True, constrained_layout=True, figsize=(4, 2.4)) + ax.semilogx(t, r) + # ax.plot(t,np.exp(-t)) + ax.set_xlim(10 ** (-2), 20) + ax.set_ylim(1e-3, 10) + ax.set_xlabel(r"$x$") + # ax.set_ylabel(r"$x^z e^{-x}$") + ax.grid(1, "both") + labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)] + ax.legend(labels, ncol=2, loc="upper left", fontsize="small") + fig.savefig(f"{img_path}/integrand_exp.pgf") + # plt.show() diff --git a/buch/papers/laguerre/scripts/laguerre_plot.py b/buch/papers/laguerre/scripts/laguerre_plot.py deleted file mode 100644 index 1be3552..0000000 --- a/buch/papers/laguerre/scripts/laguerre_plot.py +++ /dev/null @@ -1,101 +0,0 @@ -#!/usr/bin/env python3 -# -*- coding:utf-8 -*- -"""Some plots for Laguerre Polynomials.""" - -import os -from pathlib import Path - -import matplotlib.pyplot as plt -import numpy as np -import scipy.special as ss - - -def get_ticks(start, end, step=1): - ticks = np.arange(start, end, step) - return ticks[ticks != 0] - - -N = 1000 -step = 5 -t = np.linspace(-1.05, 10.5, N)[:, None] -root = str(Path(__file__).parent) -img_path = f"{root}/../images" -os.makedirs(img_path, exist_ok=True) - - -# fig = plt.figure(num=1, clear=True, tight_layout=True, figsize=(5.5, 3.7)) -# ax = fig.add_subplot(axes_class=AxesZero) -fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) -for n in np.arange(0, 8): - k = np.arange(0, n + 1)[None] - L = np.sum((-1) ** k * ss.binom(n, k) / ss.factorial(k) * t ** k, -1) - ax.plot(t, L, label=f"$n={n}$") - -ax.set_xticks(get_ticks(int(t[0]), t[-1]), minor=True) -ax.set_xticks(get_ticks(0, t[-1], step)) -ax.set_xlim(t[0], t[-1] + 0.1 * (t[1] - t[0])) -ax.set_xlabel(r"$x$", x=1.0, labelpad=-10, rotation=0, fontsize="large") - -ylim = 13 -ax.set_yticks(np.arange(-ylim, ylim), minor=True) -ax.set_yticks(np.arange(-step * (ylim // step), ylim, step)) -ax.set_ylim(-ylim, ylim) -ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large") - -ax.legend(ncol=2, loc=(0.125, 0.01), fontsize="large") - -# set the x-spine -ax.spines[["left", "bottom"]].set_position("zero") -ax.spines[["right", "top"]].set_visible(False) -ax.xaxis.set_ticks_position("bottom") -hlx = 0.4 -dx = t[-1, 0] - t[0, 0] -dy = 2 * ylim -hly = dy / dx * hlx -dps = fig.dpi_scale_trans.inverted() -bbox = ax.get_window_extent().transformed(dps) -width, height = bbox.width, bbox.height - -# manual arrowhead width and length -hw = 1.0 / 60.0 * dy -hl = 1.0 / 30.0 * dx -lw = 0.5 # axis line width -ohg = 0.0 # arrow overhang - -# compute matching arrowhead length and width -yhw = hw / dy * dx * height / width -yhl = hl / dx * dy * width / height - -# draw x and y axis -ax.arrow( - t[-1, 0] - hl, - 0, - hl, - 0.0, - fc="k", - ec="k", - lw=lw, - head_width=hw, - head_length=hl, - overhang=ohg, - length_includes_head=True, - clip_on=False, -) - -ax.arrow( - 0, - ylim - yhl, - 0.0, - yhl, - fc="k", - ec="k", - lw=lw, - head_width=yhw, - head_length=yhl, - overhang=ohg, - length_includes_head=True, - clip_on=False, -) - -fig.savefig(f"{img_path}/laguerre_polynomes.pgf") -# plt.show() diff --git a/buch/papers/laguerre/scripts/laguerre_poly.py b/buch/papers/laguerre/scripts/laguerre_poly.py new file mode 100644 index 0000000..954a0b1 --- /dev/null +++ b/buch/papers/laguerre/scripts/laguerre_poly.py @@ -0,0 +1,98 @@ +import numpy as np + + +def get_ticks(start, end, step=1): + ticks = np.arange(start, end, step) + return ticks[ticks != 0] + + +if __name__ == "__main__": + import os + from pathlib import Path + + import matplotlib.pyplot as plt + import scipy.special as ss + + N = 1000 + step = 5 + t = np.linspace(-1.05, 10.5, N)[:, None] + root = str(Path(__file__).parent) + img_path = f"{root}/../images" + os.makedirs(img_path, exist_ok=True) + + # fig = plt.figure(num=1, clear=True, tight_layout=True, figsize=(5.5, 3.7)) + # ax = fig.add_subplot(axes_class=AxesZero) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(6, 4)) + for n in np.arange(0, 8): + k = np.arange(0, n + 1)[None] + L = np.sum((-1) ** k * ss.binom(n, k) / ss.factorial(k) * t ** k, -1) + ax.plot(t, L, label=f"$n={n}$") + + ax.set_xticks(get_ticks(int(t[0]), t[-1]), minor=True) + ax.set_xticks(get_ticks(0, t[-1], step)) + ax.set_xlim(t[0], t[-1] + 0.1 * (t[1] - t[0])) + ax.set_xlabel(r"$x$", x=1.0, labelpad=-10, rotation=0, fontsize="large") + + ylim = 13 + ax.set_yticks(np.arange(-ylim, ylim), minor=True) + ax.set_yticks(np.arange(-step * (ylim // step), ylim, step)) + ax.set_ylim(-ylim, ylim) + ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large") + + ax.legend(ncol=2, loc=(0.125, 0.01), fontsize="large") + + # set the x-spine + ax.spines[["left", "bottom"]].set_position("zero") + ax.spines[["right", "top"]].set_visible(False) + ax.xaxis.set_ticks_position("bottom") + hlx = 0.4 + dx = t[-1, 0] - t[0, 0] + dy = 2 * ylim + hly = dy / dx * hlx + dps = fig.dpi_scale_trans.inverted() + bbox = ax.get_window_extent().transformed(dps) + width, height = bbox.width, bbox.height + + # manual arrowhead width and length + hw = 1.0 / 60.0 * dy + hl = 1.0 / 30.0 * dx + lw = 0.5 # axis line width + ohg = 0.0 # arrow overhang + + # compute matching arrowhead length and width + yhw = hw / dy * dx * height / width + yhl = hl / dx * dy * width / height + + # draw x and y axis + ax.arrow( + t[-1, 0] - hl, + 0, + hl, + 0.0, + fc="k", + ec="k", + lw=lw, + head_width=hw, + head_length=hl, + overhang=ohg, + length_includes_head=True, + clip_on=False, + ) + + ax.arrow( + 0, + ylim - yhl, + 0.0, + yhl, + fc="k", + ec="k", + lw=lw, + head_width=yhw, + head_length=yhl, + overhang=ohg, + length_includes_head=True, + clip_on=False, + ) + + fig.savefig(f"{img_path}/laguerre_poly.pgf") + # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_mirror.py b/buch/papers/laguerre/scripts/rel_error_mirror.py new file mode 100644 index 0000000..05e68e4 --- /dev/null +++ b/buch/papers/laguerre/scripts/rel_error_mirror.py @@ -0,0 +1,28 @@ +if __name__ == "__main__": + import matplotlib.pyplot as plt + import numpy as np + import scipy.special + + import gamma_approx as ga + + xmin = -15 + xmax = 15 + ns = np.arange(2, 12, 2) + ylim = np.array([-11, 1]) + x = np.linspace(xmin + ga.EPSILON, xmax - ga.EPSILON, 400) + gamma = scipy.special.gamma(x) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) + for n in ns: + gamma_lag = ga.eval_laguerre_gamma(x, n=n, func="mirror") + rel_err = ga.calc_rel_error(gamma, gamma_lag) + ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$") + ax.set_xlim(x[0], x[-1]) + ax.set_ylim(*(10.0 ** ylim)) + ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON, 5)) + ax.set_xticks(np.arange(xmin, xmax), minor=True) + ax.set_yticks(10.0 ** np.arange(*ylim, 2)) + ax.set_xlabel(r"$z$") + # ax.set_ylabel("Relativer Fehler") + ax.legend(ncol=1, loc="upper left", fontsize=ga.fontsize) + ax.grid(1, "both") + fig.savefig(f"{ga.img_path}/rel_error_mirror.pgf") diff --git a/buch/papers/laguerre/scripts/rel_error_range.py b/buch/papers/laguerre/scripts/rel_error_range.py new file mode 100644 index 0000000..7d017a7 --- /dev/null +++ b/buch/papers/laguerre/scripts/rel_error_range.py @@ -0,0 +1,32 @@ +if __name__ == "__main__": + import matplotlib.pyplot as plt + import numpy as np + import scipy.special + + import gamma_approx as ga + + N = 1000 + xmin = -5 + xmax = 5 + ns = np.arange(2, 12, 2) + ylim = np.array([-11, -1.2]) + + x = np.linspace(xmin + ga.EPSILON, xmax - ga.EPSILON, N) + gamma = scipy.special.gamma(x) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) + for n in ns: + gamma_lag = ga.eval_laguerre_gamma(x, n=n, func="optimal_shifted") + rel_err = ga.calc_rel_error(gamma, gamma_lag) + ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$") + ax.set_xlim(x[0], x[-1]) + ax.set_ylim(*(10.0 ** ylim)) + ax.set_xticks(np.arange(xmin + 1, xmax, 2)) + ax.set_xticks(np.arange(xmin, xmax), minor=True) + ax.set_yticks(10.0 ** np.arange(*ylim, 2)) + ax.set_yticks(10.0 ** np.arange(*ylim, 1), minor=True) + ax.set_xlabel(r"$z$") + # ax.set_ylabel("Relativer Fehler") + ax.legend(ncol=1, loc="upper left", fontsize=ga.fontsize) + ax.grid(1, "both") + fig.savefig(f"{ga.img_path}/rel_error_range.pgf") + # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_shifted.py b/buch/papers/laguerre/scripts/rel_error_shifted.py new file mode 100644 index 0000000..1515c6e --- /dev/null +++ b/buch/papers/laguerre/scripts/rel_error_shifted.py @@ -0,0 +1,31 @@ +if __name__ == "__main__": + import matplotlib.pyplot as plt + import numpy as np + import scipy.special + + import gamma_approx as ga + + n = 8 # order of Laguerre polynomial + N = 200 # number of points in interval + + step = 1 / (N - 1) + x = np.linspace(step, 1 - step, N + 1) + targets = np.arange(10, 14) + gamma = scipy.special.gamma(x) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) + for target in targets: + gamma_lag = ga.eval_laguerre_gamma(x, target=target, n=n, func="shifted") + rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lag)) + ax.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3) + gamma_lgo = ga.eval_laguerre_gamma(x, n=n, func="optimal_shifted") + rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lgo)) + ax.semilogy(x, rel_error, "m", linestyle="dotted", label="$m^*$", linewidth=3) + ax.set_xlim(x[0], x[-1]) + ax.set_ylim(5e-9, 5e-8) + ax.set_xlabel(r"$z$") + ax.set_xticks(np.linspace(0, 1, 6)) + ax.set_xticks(np.linspace(0, 1, 11), minor=True) + ax.grid(1, "both") + ax.legend(ncol=1, fontsize=ga.fontsize) + fig.savefig(f"{ga.img_path}/rel_error_shifted.pgf") + # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_simple.py b/buch/papers/laguerre/scripts/rel_error_simple.py new file mode 100644 index 0000000..0929976 --- /dev/null +++ b/buch/papers/laguerre/scripts/rel_error_simple.py @@ -0,0 +1,29 @@ +if __name__ == "__main__": + import matplotlib.pyplot as plt + import numpy as np + import scipy.special + + import gamma_approx as ga + + # Simple / naive + xmin = -5 + xmax = 30 + ns = np.arange(2, 12, 2) + ylim = np.array([-11, 6]) + x = np.linspace(xmin + ga.EPSILON, xmax - ga.EPSILON, 400) + gamma = scipy.special.gamma(x) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) + for n in ns: + gamma_lag = ga.eval_laguerre_gamma(x, n=n) + rel_err = ga.calc_rel_error(gamma, gamma_lag) + ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$") + ax.set_xlim(x[0], x[-1]) + ax.set_ylim(*(10.0 ** ylim)) + ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON, 5)) + ax.set_xticks(np.arange(xmin, xmax), minor=True) + ax.set_yticks(10.0 ** np.arange(*ylim, 2)) + ax.set_xlabel(r"$z$") + # ax.set_ylabel("Relativer Fehler") + ax.legend(ncol=3, fontsize=ga.fontsize) + ax.grid(1, "both") + fig.savefig(f"{ga.img_path}/rel_error_simple.pgf") diff --git a/buch/papers/laguerre/scripts/targets.py b/buch/papers/laguerre/scripts/targets.py new file mode 100644 index 0000000..73d6e03 --- /dev/null +++ b/buch/papers/laguerre/scripts/targets.py @@ -0,0 +1,48 @@ +import numpy as np +import scipy.special + +import gamma_approx as ga + + +def find_best_loc(N=200, a=1.375, b=0.5, ns=None): + if ns is None: + ns = np.arange(2, 13) + bests = [] + step = 1 / (N - 1) + x = np.linspace(step, 1 - step, N + 1) + gamma = scipy.special.gamma(x)[:, None] + for n in ns: + zeros, weights = np.polynomial.laguerre.laggauss(n) + est = np.ceil(b + a * n) + targets = np.arange(max(est - 2, 0), est + 3) + glag = [ + ga.eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted") + for target in targets + ] + gamma_lag = np.stack(glag, -1) + rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lag)) + best = np.argmin(rel_error, -1) + targets[0] + bests.append(best) + return np.stack(bests, 0) + + +if __name__ == "__main__": + import matplotlib.pyplot as plt + N = 200 + ns = np.arange(2, 13) + + bests = find_best_loc(N, ns=ns) + + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(4, 2.4)) + v = ax.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest") + plt.colorbar(v, ax=ax, label=r"$m^*$") + ticks = np.arange(0, N + 1, N // 5) + ax.set_xlim(0, 1) + ax.set_xticks(ticks) + ax.set_xticklabels([f"{v:.2f}" for v in ticks / N]) + ax.set_xticks(np.arange(0, N + 1, N // 20), minor=True) + ax.set_yticks(np.arange(len(ns))) + ax.set_yticklabels(ns) + ax.set_xlabel(r"$z$") + ax.set_ylabel(r"$n$") + fig.savefig(f"{ga.img_path}/targets.pgf") -- cgit v1.2.1 From 3cb2fa354f814fa98474610dac744281285dafc6 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Fri, 15 Jul 2022 11:40:55 +0200 Subject: First version of section 'Gauss Quadratur', fix to gamma_approx.py when z=0 --- buch/papers/laguerre/quadratur.tex | 148 ++++++++++++++++++++---- buch/papers/laguerre/references.bib | 11 ++ buch/papers/laguerre/scripts/gamma_approx.py | 18 ++- buch/papers/laguerre/scripts/rel_error_range.py | 2 +- 4 files changed, 151 insertions(+), 28 deletions(-) diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 851fe8a..7cbae48 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -5,25 +5,57 @@ % \section{Gauss-Quadratur \label{laguerre:section:quadratur}} - {\large \color{red} TODO: Einleitung und kurze Beschreibung Gauss-Quadratur} - -Siehe Abschnitt~\ref{buch:orthogonalitaet:section:gauss-quadratur} +Die Gauss-Quadratur ist ein numerisches Integrationsverfahren, +welches die Eigenschaften von orthogonalen Polynomen ausnützt. +Herleitungen und Analysen der Gauss-Quadratur können im +Abschnitt~\ref{buch:orthogonalitaet:section:gauss-quadratur} gefunden werden. +Als grundlegende Idee wird die Beobachtung, +dass viele Funktionen sich gut mit Polynomen approximieren lassen, +verwendet. +Stellt man also sicher, +dass ein Verfahren gut für Polynome gut funktioniert, +sollte es auch für andere Funktionen nicht schlecht funktionieren. +Es wird ein Polynom verwendet, +welches an den Punkten $x_0 < x_1 < \ldots < x_n$ +die Funktionwerte~$f(x_i)$ annimmt. +Als Resultat kann das Integral via eine gewichtete Summe der Form \begin{align} \int_a^b f(x) w(x) \, dx \approx \sum_{i=1}^n f(x_i) A_i \label{laguerre:gaussquadratur} \end{align} +berechnet werden. +Die Gauss-Quadratur ist exakt für Polynome mit Grad $2n -1$, +wenn ein Interpolationspolynom von Grad $n$ gewählt wurde. \subsection{Gauss-Laguerre-Quadratur \label{laguerre:subsection:gausslag-quadratur}} -Die Gauss-Quadratur kann auch auf Skalarprodukte mit Gewichtsfunktionen -ausgeweitet werden. -In unserem Falle möchten wir die Gauss Quadratur auf die Laguerre-Polynome -$L_n$ ausweiten. -Diese sind orthogonal im Intervall $(0, \infty)$ bezüglich -der Gewichtsfunktion $e^{-x}$. -Gleichung~\eqref{laguerre:laguerrequadratur} lässt sich wie folgt umformulieren: +Wir möchten nun die Gauss-Quadratur auf die Berechnung +von uneigentlichen Integralen erweitern, +spezifisch auf das Interval $(0, \infty)$. +Mit dem vorher beschriebenen Verfahren ist dies nicht direkt möglich. +Mit einer Transformation die das unendliche Intervall $(a, \infty)$ mit +\begin{align*} +x += +a + \frac{1 - t}{t} +\end{align*} +auf das Intervall $[0, 1]$ transformiert. +Für unser Fall gilt $a = 0$. +Das Integral eines Polynomes in diesem Intervall ist immer divergent, +darum müssen wir sie mit einer Funktion multiplizieren, +die schneller als jedes Polynom gegen $0$ geht, +damit das Integral immer noch konvergiert. +Die Laguerre-Polynome $L_n$ bieten hier Abhilfe, +da ihre Gewichtsfunktion $e^{-x}$ schneller +gegen $0$ konvergiert als jedes Polynom. +% In unserem Falle möchten wir die Gauss Quadratur auf die Laguerre-Polynome +% $L_n$ ausweiten. +% Diese sind orthogonal im Intervall $(0, \infty)$ bezüglich +% der Gewichtsfunktion $e^{-x}$. +Gleichung~\eqref{laguerre:gaussquadratur} lässt sich wie folgt +umformulieren: \begin{align} \int_{0}^{\infty} f(x) e^{-x} dx \approx @@ -43,20 +75,93 @@ l_i(x_j) \delta_{ij} = \begin{cases} -1 & i=j \\ -0 & \text{sonst.} +1 & i=j \\ +0 & \text{.} \end{cases} +% . \end{align*} -Laut \cite{abramowitz+stegun} sind die Gewichte -\begin{align} +die Lagrangschen Interpolationspolynome. +Laut \cite{hildebrand2013introduction} können die Gewicht mit +\begin{align*} A_i + & = +-\frac{C_{n+1} \gamma_n}{C_n \phi'_n(x_i) \phi_{n+1} (x_i)} +\end{align*} +berechnet werden. +$C_i$ entspricht dabei dem Koeffizienten von $x^i$ +des orthogonalen Polynoms $\phi_n(x)$, $\forall i =0,\ldots,n$ und +\begin{align*} +\gamma_n += +\int_0^\infty w(x) \phi_n^2(x)\,dx +\end{align*} +dem Normalisierungsfaktor. +Wir setzen nun $\phi_n(x) = L_n(x)$ und +nutzen den Vorzeichenwechsel der Laguerrekoeffizienten aus, +damit erhalten wir +\begin{align*} +A_i + & = +-\frac{C_{n+1} \gamma_n}{C_n L'_n(x_i) L_{n+1} (x_i)} +\\ + & = \frac{C_n}{C_{n-1}} \frac{\gamma_{n-1}}{L_{n-1}(x_i) L'_n(x_i)} +. +\end{align*} +Für Laguerre-Polynome gilt +\begin{align*} +\frac{C_n}{C_{n-1}} += +-\frac{1}{n} +\quad \text{und} \quad +\gamma_n = -\frac{x_i}{(n + 1)^2 \left[ L_{n + 1}(x_i)\right]^2} +1 +. +\end{align*} +Daraus folgt +\begin{align} +A_i +&= +- \frac{1}{n L_{n-1}(x_i) L'_n(x_i)} +. +\label{laguerre:gewichte_lag_temp} +\end{align} +Nun kann die Rekursionseigenschaft der Laguerre-Polynome +\begin{align*} +x L'_n(x) +&= +n L_n(x) - n L_{n-1}(x) +\\ +&= (x - n - 1) L_n(x) + (n + 1) L_{n+1}(x) +\end{align*} +umgeformt werden und da $x_i$ die Nullstellen von $L_n(x)$ sind, +folgt +\begin{align*} +x_i L'_n(x_i) +&= +- n L_{n-1}(x_i) +\\ +&= + (n + 1) L_{n+1}(x_i) +. +\end{align*} +Setzen wir das nun in \eqref{laguerre:gewichte_lag_temp} ein ergibt sicht +\begin{align} +\nonumber +A_i +&= +\frac{1}{x_i \left[ L'_n(x_i) \right]^2} +\\ +&= +\frac{x_i}{(n+1)^2 \left[ L_{n+1}(x_i) \right]^2} . \label{laguerre:quadratur_gewichte} \end{align} \subsubsection{Fehlerterm} +Die Gauss-Laguerre-Quadratur mit $n$ Stützstellen berechnet Integrale +von Polynomen bis zum Grad $2n - 1$ exakt. +Für beliebige Funktionen kann eine Fehlerabschätzung angegeben werden. Der Fehlerterm $R_n$ folgt direkt aus der Approximation \begin{align*} \int_0^{\infty} f(x) e^{-x} \, dx @@ -66,16 +171,15 @@ Der Fehlerterm $R_n$ folgt direkt aus der Approximation und \cite{abramowitz+stegun} gibt ihn als \begin{align} R_n -= + & = +\frac{f^{(2n)}(\xi)}{(2n)!} \int_0^\infty l(x)^2 e^{-x}\,dx +\\ + & = \frac{(n!)^2}{(2n)!} f^{(2n)}(\xi) ,\quad 0 < \xi < \infty \label{laguerre:lag_error} \end{align} an. - -{ -\large \color{red} -TODO: -Noch mehr Text / bessere Beschreibungen in allen Abschnitten -} +Der Fehler ist also abhängig von der $2n$-ten Ableitung +der zu integrierenden Funktion. diff --git a/buch/papers/laguerre/references.bib b/buch/papers/laguerre/references.bib index e12e218..2371922 100644 --- a/buch/papers/laguerre/references.bib +++ b/buch/papers/laguerre/references.bib @@ -4,6 +4,17 @@ % (c) 2020 Autor, Hochschule Rapperswil % +@book{hildebrand2013introduction, + title={Introduction to Numerical Analysis: Second Edition}, + author={Hildebrand, F.B.}, + isbn={9780486318554}, + series={Dover Books on Mathematics}, + url={https://books.google.ch/books?id=ic2jAQAAQBAJ}, + year={2013}, + publisher={Dover Publications}, + pages = {389} +} + @book{abramowitz+stegun, added-at = {2008-06-25T06:25:58.000+0200}, address = {New York}, diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 208f770..9f9dae7 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -1,7 +1,5 @@ from pathlib import Path -import matplotlib as mpl -import matplotlib.pyplot as plt import numpy as np import scipy.special @@ -58,6 +56,8 @@ def laguerre_gamma_shifted(z, x=None, w=None, n=8, target=11): def laguerre_gamma_opt_shifted(z, x=None, w=None, n=8): + if z == 0.0: + return np.infty x, w = _prep_zeros_and_weights(x, w, n) n = len(x) @@ -73,6 +73,8 @@ def laguerre_gamma_opt_shifted(z, x=None, w=None, n=8): def laguerre_gamma_simple(z, x=None, w=None, n=8): + if z == 0.0: + return np.infty x, w = _prep_zeros_and_weights(x, w, n) z += 0j res = np.sum(x ** (z - 1) * w) @@ -81,6 +83,8 @@ def laguerre_gamma_simple(z, x=None, w=None, n=8): def laguerre_gamma_mirror(z, x=None, w=None, n=8): + if z == 0.0: + return np.infty x, w = _prep_zeros_and_weights(x, w, n) z += 0j if z.real < 1e-3: @@ -90,8 +94,8 @@ def laguerre_gamma_mirror(z, x=None, w=None, n=8): return laguerre_gamma_simple(z, x, w) -def eval_laguerre_gamma(z, x=None, w=None, n=8, func="simple", **kwargs): - x, w = _prep_zeros_and_weights(x, w, n) +def eval_laguerre_gamma(z, x=None, w=None, n=8, func="simple", **kwargs): + x, w = _prep_zeros_and_weights(x, w, n) if func == "simple": f = laguerre_gamma_simple elif func == "mirror": @@ -104,4 +108,8 @@ def eval_laguerre_gamma(z, x=None, w=None, n=8, func="simple", **kwargs): def calc_rel_error(x, y): - return (y - x) / x + mask = np.abs(x) != np.infty + rel_error = np.zeros_like(y) + rel_error[mask] = (y[mask] - x[mask]) / x[mask] + rel_error[~mask] = 0.0 + return rel_error diff --git a/buch/papers/laguerre/scripts/rel_error_range.py b/buch/papers/laguerre/scripts/rel_error_range.py index 7d017a7..7c74d76 100644 --- a/buch/papers/laguerre/scripts/rel_error_range.py +++ b/buch/papers/laguerre/scripts/rel_error_range.py @@ -5,7 +5,7 @@ if __name__ == "__main__": import gamma_approx as ga - N = 1000 + N = 1001 xmin = -5 xmax = 5 ns = np.arange(2, 12, 2) -- cgit v1.2.1 From 7a8795dcb555a551fd09a3c9b15002675e30891f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Fri, 15 Jul 2022 16:24:48 +0200 Subject: Change image scripts to PDF format, update Makefile, add complex plane plot --- buch/papers/laguerre/Makefile | 17 +- buch/papers/laguerre/images/estimates.pdf | Bin 0 -> 13780 bytes buch/papers/laguerre/images/estimates.pgf | 1700 ----------- buch/papers/laguerre/images/gammaplot.pdf | Bin 23297 -> 23297 bytes buch/papers/laguerre/images/integrand.pdf | Bin 0 -> 16109 bytes buch/papers/laguerre/images/integrand.pgf | 2670 ----------------- buch/papers/laguerre/images/integrand_exp.pdf | Bin 0 -> 16951 bytes buch/papers/laguerre/images/integrand_exp.pgf | 1916 ------------ buch/papers/laguerre/images/laguerre_poly.pdf | Bin 0 -> 19815 bytes buch/papers/laguerre/images/laguerre_poly.pgf | 1838 ------------ buch/papers/laguerre/images/rel_error_complex.pdf | Bin 0 -> 198151 bytes buch/papers/laguerre/images/rel_error_mirror.pdf | Bin 0 -> 26866 bytes buch/papers/laguerre/images/rel_error_mirror.pgf | 3051 -------------------- buch/papers/laguerre/images/rel_error_range.pdf | Bin 0 -> 25704 bytes buch/papers/laguerre/images/rel_error_range.pgf | 2730 ------------------ buch/papers/laguerre/images/rel_error_shifted.pdf | Bin 0 -> 16231 bytes buch/papers/laguerre/images/rel_error_shifted.pgf | 1433 --------- buch/papers/laguerre/images/rel_error_simple.pdf | Bin 0 -> 23353 bytes buch/papers/laguerre/images/rel_error_simple.pgf | 2934 ------------------- buch/papers/laguerre/images/targets-img0.png | Bin 836 -> 0 bytes buch/papers/laguerre/images/targets-img1.png | Bin 429 -> 0 bytes buch/papers/laguerre/images/targets.pdf | Bin 12530 -> 14757 bytes buch/papers/laguerre/images/targets.pgf | 1024 ------- buch/papers/laguerre/presentation/presentation.pdf | Bin 0 -> 394774 bytes buch/papers/laguerre/scripts/estimates.py | 12 +- buch/papers/laguerre/scripts/integrand.py | 11 +- buch/papers/laguerre/scripts/integrand_exp.py | 12 +- buch/papers/laguerre/scripts/laguerre_poly.py | 16 +- buch/papers/laguerre/scripts/rel_error_complex.py | 43 + buch/papers/laguerre/scripts/rel_error_mirror.py | 12 +- buch/papers/laguerre/scripts/rel_error_range.py | 25 +- buch/papers/laguerre/scripts/rel_error_shifted.py | 13 +- buch/papers/laguerre/scripts/rel_error_simple.py | 14 +- buch/papers/laguerre/scripts/targets.py | 26 +- 34 files changed, 167 insertions(+), 19330 deletions(-) create mode 100644 buch/papers/laguerre/images/estimates.pdf delete mode 100644 buch/papers/laguerre/images/estimates.pgf create mode 100644 buch/papers/laguerre/images/integrand.pdf delete mode 100644 buch/papers/laguerre/images/integrand.pgf create mode 100644 buch/papers/laguerre/images/integrand_exp.pdf delete mode 100644 buch/papers/laguerre/images/integrand_exp.pgf create mode 100644 buch/papers/laguerre/images/laguerre_poly.pdf delete mode 100644 buch/papers/laguerre/images/laguerre_poly.pgf create mode 100644 buch/papers/laguerre/images/rel_error_complex.pdf create mode 100644 buch/papers/laguerre/images/rel_error_mirror.pdf delete mode 100644 buch/papers/laguerre/images/rel_error_mirror.pgf create mode 100644 buch/papers/laguerre/images/rel_error_range.pdf delete mode 100644 buch/papers/laguerre/images/rel_error_range.pgf create mode 100644 buch/papers/laguerre/images/rel_error_shifted.pdf delete mode 100644 buch/papers/laguerre/images/rel_error_shifted.pgf create mode 100644 buch/papers/laguerre/images/rel_error_simple.pdf delete mode 100644 buch/papers/laguerre/images/rel_error_simple.pgf delete mode 100644 buch/papers/laguerre/images/targets-img0.png delete mode 100644 buch/papers/laguerre/images/targets-img1.png delete mode 100644 buch/papers/laguerre/images/targets.pgf create mode 100644 buch/papers/laguerre/presentation/presentation.pdf create mode 100644 buch/papers/laguerre/scripts/rel_error_complex.py diff --git a/buch/papers/laguerre/Makefile b/buch/papers/laguerre/Makefile index 1ed87cc..48f8066 100644 --- a/buch/papers/laguerre/Makefile +++ b/buch/papers/laguerre/Makefile @@ -8,14 +8,15 @@ PRESFOLDER := presentation FIGURES := \ images/targets.pdf \ - images/estimates.pgf \ - images/integrand.pgf \ - images/integrand_exp.pgf \ - images/laguerre_poly.pgf \ - images/rel_error_mirror.pgf \ - images/rel_error_range.pgf \ - images/rel_error_shifted.pgf \ - images/rel_error_simple.pgf \ + images/rel_error_complex.pdf \ + images/estimates.pdf \ + images/integrand.pdf \ + images/integrand_exp.pdf \ + images/laguerre_poly.pdf \ + images/rel_error_mirror.pdf \ + images/rel_error_range.pdf \ + images/rel_error_shifted.pdf \ + images/rel_error_simple.pdf \ images/gammaplot.pdf .PHONY: all diff --git a/buch/papers/laguerre/images/estimates.pdf b/buch/papers/laguerre/images/estimates.pdf new file mode 100644 index 0000000..c93a4f0 Binary files /dev/null and b/buch/papers/laguerre/images/estimates.pdf differ diff --git a/buch/papers/laguerre/images/estimates.pgf b/buch/papers/laguerre/images/estimates.pgf deleted file mode 100644 index b82fa5d..0000000 --- a/buch/papers/laguerre/images/estimates.pgf +++ /dev/null @@ -1,1700 +0,0 @@ -%% Creator: Matplotlib, PGF backend -%% -%% To include the figure in your LaTeX document, write -%% \input{.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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document, write -%% \input{.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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-1,1838 +0,0 @@ -%% Creator: Matplotlib, PGF backend -%% -%% To include the figure in your LaTeX document, write -%% \input{.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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a/buch/papers/laguerre/images/rel_error_mirror.pgf b/buch/papers/laguerre/images/rel_error_mirror.pgf deleted file mode 100644 index 45d502e..0000000 --- a/buch/papers/laguerre/images/rel_error_mirror.pgf +++ /dev/null @@ -1,3051 +0,0 @@ -%% Creator: Matplotlib, PGF backend -%% -%% To include the figure in your LaTeX document, write -%% \input{.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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-\begin{pgfscope}% -\pgfsys@transformshift{0.482257in}{0.870428in}% -\pgfsys@useobject{currentmarker}{}% -\end{pgfscope}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=0.097033in, y=0.817666in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-9}}\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% -\pgfusepath{clip}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.482257in}{1.277582in}}% -\pgfpathlineto{\pgfqpoint{4.958330in}{1.277582in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetroundjoin% 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-\begin{pgfscope}% -\pgfsys@transformshift{0.482257in}{1.684737in}% -\pgfsys@useobject{currentmarker}{}% -\end{pgfscope}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=0.097033in, y=1.631975in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-5}}\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% -\pgfusepath{clip}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.482257in}{2.091891in}}% -\pgfpathlineto{\pgfqpoint{4.958330in}{2.091891in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetroundjoin% 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-\begin{pgfscope}% -\pgfsys@transformshift{0.482257in}{0.666851in}% -\pgfsys@useobject{currentmarker}{}% -\end{pgfscope}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=0.063892in, y=0.614089in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-10}}\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% -\pgfusepath{clip}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.482257in}{1.074005in}}% -\pgfpathlineto{\pgfqpoint{4.958330in}{1.074005in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetroundjoin% 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-\begin{pgfscope}% -\pgfsys@transformshift{0.482257in}{1.481159in}% -\pgfsys@useobject{currentmarker}{}% -\end{pgfscope}% -\end{pgfscope}% -\begin{pgfscope}% -\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% -\pgfsetstrokecolor{textcolor}% -\pgfsetfillcolor{textcolor}% -\pgftext[x=0.119255in, y=1.428398in, left, base]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{-6}}\)}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfpathrectangle{\pgfqpoint{0.482257in}{0.463273in}}{\pgfqpoint{4.476072in}{1.995057in}}% -\pgfusepath{clip}% -\pgfsetrectcap% -\pgfsetroundjoin% -\pgfsetlinewidth{0.803000pt}% -\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% -\pgfsetstrokecolor{currentstroke}% -\pgfsetdash{}{0pt}% -\pgfpathmoveto{\pgfqpoint{0.482257in}{1.888314in}}% -\pgfpathlineto{\pgfqpoint{4.958330in}{1.888314in}}% -\pgfusepath{stroke}% -\end{pgfscope}% -\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetroundjoin% 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and b/buch/papers/laguerre/images/rel_error_simple.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_simple.pgf b/buch/papers/laguerre/images/rel_error_simple.pgf deleted file mode 100644 index 2439d65..0000000 --- a/buch/papers/laguerre/images/rel_error_simple.pgf +++ /dev/null @@ -1,2934 +0,0 @@ -%% Creator: Matplotlib, PGF backend -%% -%% To include the figure in your LaTeX document, write -%% \input{.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. 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index c050efa..e1ec07c 100644 Binary files a/buch/papers/laguerre/images/targets.pdf and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/images/targets.pgf b/buch/papers/laguerre/images/targets.pgf deleted file mode 100644 index f5602fd..0000000 --- a/buch/papers/laguerre/images/targets.pgf +++ /dev/null @@ -1,1024 +0,0 @@ -%% Creator: Matplotlib, PGF backend -%% -%% To include the figure in your LaTeX document, write -%% \input{.pgf} -%% -%% Make sure the required packages are loaded in your preamble -%% \usepackage{pgf} -%% -%% Also ensure that all the required font packages are loaded; for instance, -%% the lmodern package is sometimes necessary when using math font. -%% \usepackage{lmodern} -%% -%% Figures using additional raster images can only be included by \input if -%% they are in the same directory as the main LaTeX file. For loading figures -%% from other directories you can use the `import` package -%% \usepackage{import} -%% -%% and then include the figures with -%% \import{}{.pgf} -%% -%% Matplotlib used the following preamble -%% \usepackage{fontspec} -%% \setmainfont{DejaVuSerif.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] -%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] -%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/mup/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] -%% -\begingroup% -\makeatletter% -\begin{pgfpicture}% -\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{2.400000in}}% -\pgfusepath{use as bounding box, clip}% -\begin{pgfscope}% -\pgfsetbuttcap% -\pgfsetmiterjoin% -\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% -\pgfsetfillcolor{currentfill}% -\pgfsetlinewidth{0.000000pt}% 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-\pgfusepath{stroke}% -\end{pgfscope}% -\end{pgfpicture}% -\makeatother% -\endgroup% diff --git a/buch/papers/laguerre/presentation/presentation.pdf b/buch/papers/laguerre/presentation/presentation.pdf new file mode 100644 index 0000000..3d00de3 Binary files /dev/null and b/buch/papers/laguerre/presentation/presentation.pdf differ diff --git a/buch/papers/laguerre/scripts/estimates.py b/buch/papers/laguerre/scripts/estimates.py index 207bbd2..21551f3 100644 --- a/buch/papers/laguerre/scripts/estimates.py +++ b/buch/papers/laguerre/scripts/estimates.py @@ -1,10 +1,19 @@ if __name__ == "__main__": + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import gamma_approx as ga import targets + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) + N = 200 ns = np.arange(2, 13) step = 1 / (N - 1) @@ -32,7 +41,8 @@ if __name__ == "__main__": for ax in axs: ax.grid(1) ax.legend() - fig.savefig(f"{ga.img_path}/estimates.pgf") + # fig.savefig(f"{ga.img_path}/estimates.pgf") + fig.savefig(f"{ga.img_path}/estimates.pdf") print(f"Intercept={intercept:.6g}, Bias={bias:.6g}") predicts = np.ceil(intercept * ns[:, None] + bias - np.real(x)) diff --git a/buch/papers/laguerre/scripts/integrand.py b/buch/papers/laguerre/scripts/integrand.py index f31f194..e970721 100644 --- a/buch/papers/laguerre/scripts/integrand.py +++ b/buch/papers/laguerre/scripts/integrand.py @@ -6,9 +6,18 @@ if __name__ == "__main__": import os from pathlib import Path + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) + EPSILON = 1e-12 xlims = np.array([-3, 3]) @@ -30,4 +39,4 @@ if __name__ == "__main__": ax.grid(1, "both") labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)] ax.legend(labels, ncol=2, loc="upper left", fontsize="small") - fig.savefig(f"{img_path}/integrand.pgf") + fig.savefig(f"{img_path}/integrand.pdf") diff --git a/buch/papers/laguerre/scripts/integrand_exp.py b/buch/papers/laguerre/scripts/integrand_exp.py index 0e50f43..e649b26 100644 --- a/buch/papers/laguerre/scripts/integrand_exp.py +++ b/buch/papers/laguerre/scripts/integrand_exp.py @@ -6,8 +6,17 @@ if __name__ == "__main__": import os from pathlib import Path + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np + + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) EPSILON = 1e-12 xlims = np.array([-3, 3]) @@ -32,5 +41,6 @@ if __name__ == "__main__": ax.grid(1, "both") labels = [f"$z={zi: 3.1f}$" for zi in np.squeeze(z)] ax.legend(labels, ncol=2, loc="upper left", fontsize="small") - fig.savefig(f"{img_path}/integrand_exp.pgf") + # fig.savefig(f"{img_path}/integrand_exp.pgf") + fig.savefig(f"{img_path}/integrand_exp.pdf") # plt.show() diff --git a/buch/papers/laguerre/scripts/laguerre_poly.py b/buch/papers/laguerre/scripts/laguerre_poly.py index 954a0b1..9700ab4 100644 --- a/buch/papers/laguerre/scripts/laguerre_poly.py +++ b/buch/papers/laguerre/scripts/laguerre_poly.py @@ -10,8 +10,17 @@ if __name__ == "__main__": import os from pathlib import Path + import matplotlib as mpl import matplotlib.pyplot as plt import scipy.special as ss + + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) N = 1000 step = 5 @@ -34,8 +43,8 @@ if __name__ == "__main__": ax.set_xlabel(r"$x$", x=1.0, labelpad=-10, rotation=0, fontsize="large") ylim = 13 - ax.set_yticks(np.arange(-ylim, ylim), minor=True) - ax.set_yticks(np.arange(-step * (ylim // step), ylim, step)) + ax.set_yticks(get_ticks(-ylim, ylim), minor=True) + ax.set_yticks(get_ticks(-step * (ylim // step), ylim, step)) ax.set_ylim(-ylim, ylim) ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large") @@ -94,5 +103,6 @@ if __name__ == "__main__": clip_on=False, ) - fig.savefig(f"{img_path}/laguerre_poly.pgf") + # fig.savefig(f"{img_path}/laguerre_poly.pgf") + fig.savefig(f"{img_path}/laguerre_poly.pdf") # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_complex.py b/buch/papers/laguerre/scripts/rel_error_complex.py new file mode 100644 index 0000000..5be79be --- /dev/null +++ b/buch/papers/laguerre/scripts/rel_error_complex.py @@ -0,0 +1,43 @@ +if __name__ == "__main__": + import matplotlib as mpl + import matplotlib.pyplot as plt + import numpy as np + import scipy.special + + import gamma_approx as ga + + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) + + xmax = 4 + vals = np.linspace(-xmax + ga.EPSILON, xmax, 100) + x, y = np.meshgrid(vals, vals) + mesh = x + 1j * y + input = mesh.flatten() + + lanczos = scipy.special.gamma(mesh) + lag = ga.eval_laguerre_gamma(input, n=8, func="optimal_shifted").reshape(mesh.shape) + rel_error = np.abs(ga.calc_rel_error(lanczos, lag)) + + fig, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(4, 2.4)) + _c = ax.pcolormesh( + x, y, rel_error, shading="gouraud", cmap="inferno", norm=mpl.colors.LogNorm() + ) + cbr = fig.colorbar(_c, ax=ax) + cbr.minorticks_off() + # ax.set_title("Relative Error") + ax.set_xlabel("Re($z$)") + ax.set_ylabel("Im($z$)") + minor_ticks = np.arange(-xmax, xmax + ga.EPSILON) + ticks = np.arange(-xmax, xmax + ga.EPSILON, 2) + ax.set_xticks(ticks) + ax.set_xticks(minor_ticks, minor=True) + ax.set_yticks(ticks) + ax.set_yticks(minor_ticks, minor=True) + fig.savefig(f"{ga.img_path}/rel_error_complex.pdf") + # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_mirror.py b/buch/papers/laguerre/scripts/rel_error_mirror.py index 05e68e4..7348d5e 100644 --- a/buch/papers/laguerre/scripts/rel_error_mirror.py +++ b/buch/papers/laguerre/scripts/rel_error_mirror.py @@ -1,9 +1,18 @@ if __name__ == "__main__": + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import scipy.special import gamma_approx as ga + + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) xmin = -15 xmax = 15 @@ -25,4 +34,5 @@ if __name__ == "__main__": # ax.set_ylabel("Relativer Fehler") ax.legend(ncol=1, loc="upper left", fontsize=ga.fontsize) ax.grid(1, "both") - fig.savefig(f"{ga.img_path}/rel_error_mirror.pgf") + # fig.savefig(f"{ga.img_path}/rel_error_mirror.pgf") + fig.savefig(f"{ga.img_path}/rel_error_mirror.pdf") diff --git a/buch/papers/laguerre/scripts/rel_error_range.py b/buch/papers/laguerre/scripts/rel_error_range.py index 7c74d76..43b5450 100644 --- a/buch/papers/laguerre/scripts/rel_error_range.py +++ b/buch/papers/laguerre/scripts/rel_error_range.py @@ -1,13 +1,21 @@ if __name__ == "__main__": + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import scipy.special import gamma_approx as ga - - N = 1001 - xmin = -5 - xmax = 5 + + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) + N = 1201 + xmax = 6 + xmin = -xmax ns = np.arange(2, 12, 2) ylim = np.array([-11, -1.2]) @@ -20,13 +28,14 @@ if __name__ == "__main__": ax.semilogy(x, np.abs(rel_err), label=f"$n={n}$") ax.set_xlim(x[0], x[-1]) ax.set_ylim(*(10.0 ** ylim)) - ax.set_xticks(np.arange(xmin + 1, xmax, 2)) - ax.set_xticks(np.arange(xmin, xmax), minor=True) + ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON, 2)) + ax.set_xticks(np.arange(xmin, xmax + ga.EPSILON), minor=True) ax.set_yticks(10.0 ** np.arange(*ylim, 2)) - ax.set_yticks(10.0 ** np.arange(*ylim, 1), minor=True) + ax.set_yticks(10.0 ** np.arange(*ylim, 1), "", minor=True) ax.set_xlabel(r"$z$") # ax.set_ylabel("Relativer Fehler") ax.legend(ncol=1, loc="upper left", fontsize=ga.fontsize) ax.grid(1, "both") - fig.savefig(f"{ga.img_path}/rel_error_range.pgf") + # fig.savefig(f"{ga.img_path}/rel_error_range.pgf") + fig.savefig(f"{ga.img_path}/rel_error_range.pdf") # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_shifted.py b/buch/papers/laguerre/scripts/rel_error_shifted.py index 1515c6e..dc9d177 100644 --- a/buch/papers/laguerre/scripts/rel_error_shifted.py +++ b/buch/papers/laguerre/scripts/rel_error_shifted.py @@ -1,10 +1,18 @@ if __name__ == "__main__": + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import scipy.special import gamma_approx as ga + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) n = 8 # order of Laguerre polynomial N = 200 # number of points in interval @@ -19,7 +27,7 @@ if __name__ == "__main__": ax.semilogy(x, rel_error, label=f"$m={target}$", linewidth=3) gamma_lgo = ga.eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lgo)) - ax.semilogy(x, rel_error, "m", linestyle="dotted", label="$m^*$", linewidth=3) + ax.semilogy(x, rel_error, "m", linestyle=":", label="$m^*$", linewidth=3) ax.set_xlim(x[0], x[-1]) ax.set_ylim(5e-9, 5e-8) ax.set_xlabel(r"$z$") @@ -27,5 +35,6 @@ if __name__ == "__main__": ax.set_xticks(np.linspace(0, 1, 11), minor=True) ax.grid(1, "both") ax.legend(ncol=1, fontsize=ga.fontsize) - fig.savefig(f"{ga.img_path}/rel_error_shifted.pgf") + # fig.savefig(f"{ga.img_path}/rel_error_shifted.pgf") + fig.savefig(f"{ga.img_path}/rel_error_shifted.pdf") # plt.show() diff --git a/buch/papers/laguerre/scripts/rel_error_simple.py b/buch/papers/laguerre/scripts/rel_error_simple.py index 0929976..686500b 100644 --- a/buch/papers/laguerre/scripts/rel_error_simple.py +++ b/buch/papers/laguerre/scripts/rel_error_simple.py @@ -1,10 +1,21 @@ if __name__ == "__main__": + import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np import scipy.special import gamma_approx as ga + # mpl.rc("text", usetex=True) + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) + # mpl.rcParams.update({"font.family": "serif", "font.serif": "TeX Gyre Termes"}) + # Simple / naive xmin = -5 xmax = 30 @@ -26,4 +37,5 @@ if __name__ == "__main__": # ax.set_ylabel("Relativer Fehler") ax.legend(ncol=3, fontsize=ga.fontsize) ax.grid(1, "both") - fig.savefig(f"{ga.img_path}/rel_error_simple.pgf") + # fig.savefig(f"{ga.img_path}/rel_error_simple.pgf") + fig.savefig(f"{ga.img_path}/rel_error_simple.pdf") diff --git a/buch/papers/laguerre/scripts/targets.py b/buch/papers/laguerre/scripts/targets.py index 73d6e03..206b3a1 100644 --- a/buch/papers/laguerre/scripts/targets.py +++ b/buch/papers/laguerre/scripts/targets.py @@ -10,24 +10,33 @@ def find_best_loc(N=200, a=1.375, b=0.5, ns=None): bests = [] step = 1 / (N - 1) x = np.linspace(step, 1 - step, N + 1) - gamma = scipy.special.gamma(x)[:, None] + gamma = scipy.special.gamma(x) for n in ns: zeros, weights = np.polynomial.laguerre.laggauss(n) est = np.ceil(b + a * n) targets = np.arange(max(est - 2, 0), est + 3) - glag = [ - ga.eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted") - for target in targets - ] - gamma_lag = np.stack(glag, -1) - rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lag)) + rel_error = [] + for target in targets: + gamma_lag = ga.eval_laguerre_gamma(x, target=target, x=zeros, w=weights, func="shifted") + rel_error.append(np.abs(ga.calc_rel_error(gamma, gamma_lag))) + rel_error = np.stack(rel_error, -1) best = np.argmin(rel_error, -1) + targets[0] bests.append(best) return np.stack(bests, 0) if __name__ == "__main__": + import matplotlib as mpl import matplotlib.pyplot as plt + + mpl.rcParams.update( + { + "mathtext.fontset": "stix", + "font.family": "serif", + "font.serif": "TeX Gyre Termes", + } + ) + N = 200 ns = np.arange(2, 13) @@ -45,4 +54,5 @@ if __name__ == "__main__": ax.set_yticklabels(ns) ax.set_xlabel(r"$z$") ax.set_ylabel(r"$n$") - fig.savefig(f"{ga.img_path}/targets.pgf") + # fig.savefig(f"{ga.img_path}/targets.pgf") + fig.savefig(f"{ga.img_path}/targets.pdf") -- cgit v1.2.1 From ac98ecfb4f0142b418cd501045ac797da564f059 Mon Sep 17 00:00:00 2001 From: "ENEZ-PC\\erdem" Date: Fri, 15 Jul 2022 20:38:18 +0200 Subject: finito --- buch/papers/nav/bsp2.tex | 4 ++-- buch/papers/nav/einleitung.tex | 1 + buch/papers/nav/flatearth.tex | 2 +- buch/papers/nav/nautischesdreieck.tex | 4 +++- buch/papers/nav/sincos.tex | 7 ++++--- buch/papers/nav/trigo.tex | 28 ++++++++++++++++------------ 6 files changed, 27 insertions(+), 19 deletions(-) diff --git a/buch/papers/nav/bsp2.tex b/buch/papers/nav/bsp2.tex index 8ca214f..8d9083b 100644 --- a/buch/papers/nav/bsp2.tex +++ b/buch/papers/nav/bsp2.tex @@ -7,7 +7,7 @@ Wir haben die Deklination, Rektaszension, Höhe der beiden Planeten Deneb und Ar Die Deklinationen und Rektaszensionen sind von einem vergangenen Datum und die Höhe der Gestirne und die Sternzeit wurden digital in einer Stadt in Japan mit den Koordinaten 35.716672 N, 140.233336 E bestimmt. Wir werden nachrechnen, dass wir mit unserer Methode genau auf diese Koordinaten kommen. \subsection{Vorgehen} -Unser vorgehen erschliesst sicht aus unserer Methode, die wir im Abschnitt \ref{p} theoretisch erklärt haben. +Unser Vorgehen erschliesst sich aus unserer Methode, die wir im Abschnitt \ref{p} theoretisch erklärt haben. \begin{compactenum} \item Koordinaten der Bildpunkte der Gestirne bestimmen @@ -199,7 +199,7 @@ l Damit wir gleich den Längengrad berechnen können, benötigen wir noch den Winkel $\omega$: \begin{align*} - \omega &= \cos^{-1} \bigg[\frac{\cos(h_b)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \\ + \omega &= \cos^{-1} \bigg[\frac{\cos(h_B)-\cos(c) \cdot \cos(l)}{\sin(c) \cdot \sin(l)}\bigg] \\ &=\cos^{-1} \bigg[\frac{\cos(42.572556^\circ)-\cos(70.936778^\circ) \cdot \cos(54.2833404^\circ)}{\sin(70.936778^\circ) \cdot \sin(54.2833404^\circ)}\bigg] \\ &= \underline{\underline{44.6687451^\circ}} \end{align*} diff --git a/buch/papers/nav/einleitung.tex b/buch/papers/nav/einleitung.tex index 8eb4481..c778d5c 100644 --- a/buch/papers/nav/einleitung.tex +++ b/buch/papers/nav/einleitung.tex @@ -1,6 +1,7 @@ \section{Einleitung} +\rhead{Einleitung} Heutzutage ist die Navigation ein Teil des Lebens. Man sendet dem Kollegen seinen eigenen Standort, um sich das ewige Erklären zu sparen oder gibt die Adresse des Ziels ein, damit man seinen Aufenthaltsort zum Beispiel auf einer riesigen Wiese am See findet. Dies wird durch Technologien wie Funknavigation, welches ein auf Laufzeitmessung beruhendes Hyperbelverfahren mit Langwellen ist, oder die verbreitete Satellitennavigation, welche vier Satelliten für eine Messung zur Standortbestimmung nutzt. diff --git a/buch/papers/nav/flatearth.tex b/buch/papers/nav/flatearth.tex index d1d5a9b..9745cdc 100644 --- a/buch/papers/nav/flatearth.tex +++ b/buch/papers/nav/flatearth.tex @@ -1,7 +1,7 @@ \section{Warum ist die Erde nicht flach?} - +\rhead{Warum ist die Erde nicht flach?} \begin{figure} \begin{center} \includegraphics[width=10cm]{papers/nav/bilder/projektion.png} diff --git a/buch/papers/nav/nautischesdreieck.tex b/buch/papers/nav/nautischesdreieck.tex index 36674ee..32d1b8b 100644 --- a/buch/papers/nav/nautischesdreieck.tex +++ b/buch/papers/nav/nautischesdreieck.tex @@ -1,4 +1,5 @@ \section{Das Nautische Dreieck} +\rhead{Das nautische Dreieck} \subsection{Definition des Nautischen Dreiecks} Die Himmelskugel ist eine gedachte Kugel, welche die Erde und dessen Beobachter umgibt und als Rechenfläche für Koordinaten in der Astronomie und Geodäsie dient. Der Zenit ist jener Punkt, der vom Erdmittelpunkt durch denn eigenen Standort an die Himmelskugel verlängert wird. @@ -115,6 +116,7 @@ Auf diese Dreiecke können wir die einfachen Sätze der sphärischen Trigonometr \end{center} Mit unserem erlangten Wissen können wir nun alle Seiten des Dreiecks $ABC$ berechnen. +Dazu sind die folgenden vorbereiteten Berechnungen nötigt: \begin{enumerate} \item Die Seite vom Nordpol zum Bildpunkt $X$ sei $c$, dann ist $c = \frac{\pi}{2} - \delta_1$. @@ -141,7 +143,7 @@ können wir nun die dritte Seitenlänge bestimmen. Es ist darauf zu achten, dass hier natürlich die Seitenlängen in Bogenmass sind und dementsprechend der Kosinus und Sinus verwendet wird. Jetzt fehlen noch die beiden anderen Innenwinkel $\beta$ und\ $\gamma$. -Diese bestimmen wir mithilfe des Kosinussatzes: \[\beta=\cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg]\] und \[\gamma = \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}.\bigg]\] +Diese bestimmen wir mithilfe des Kosinussatzes: \[\beta=\cos^{-1} \bigg[\frac{\cos(b)-\cos(a) \cdot \cos(c)}{\sin(a) \cdot \sin(c)}\bigg]\] und \[\gamma = \cos^{-1} \bigg[\frac{\cos(c)-\cos(b) \cdot \cos(a)}{\sin(a) \cdot \sin(b)}\bigg]\]. Schlussendlich haben wir die Seiten $a$, $b$ und $c$, die Ecken $A$,$B$ und $C$ und die Winkel $\alpha$, $\beta$ und $\gamma$ bestimmt und somit das ganze Kugeldreieck $ABC$ berechnet. diff --git a/buch/papers/nav/sincos.tex b/buch/papers/nav/sincos.tex index f82a057..b64d100 100644 --- a/buch/papers/nav/sincos.tex +++ b/buch/papers/nav/sincos.tex @@ -2,12 +2,13 @@ \section{Sphärische Navigation und Winkelfunktionen} +\rhead{Sphärische Navigation und Winkelfunktionen} Es gibt Hinweise, dass sich schon die Babylonier und Ägypter vor 4000 Jahren mit Problemen der sphärischen Trigonometrie beschäftigt haben, um den Lauf von Gestirnen zu berechnen. Jedoch konnten sie dieses Problem nicht lösen. -Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 BCE dachten die Griechen über Kugelgeometrie nach,sie wurde damit zu einer Hilfswissenschaft der Astronomen. +Die Geschichte der sphärischen Trigonometrie ist daher eng mit der Astronomie verknüpft. Ca. 350 BCE dachten die Griechen über Kugelgeometrie nach, sie wurde damit zu einer Hilfswissenschaft der Astronomen. -Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom names Hipparchos. -Dieser entwickelte unter anderem die Chordentafeln, welche die Chord - Funktionen, auch Chord genannt, beinhalten. +Zwischen 190 v. Chr. und 120 v. Chr. lebte ein griechischer Astronom namens Hipparchos. +Dieser entwickelte unter anderem die Chordentafeln, welche die Chordfunktionen, auch Chord genannt, beinhalten. Chord ist der Vorgänger der Sinusfunktion und galt damals als wichtigste Grundlage der Trigonometrie. In dieser Zeit wurden auch die ersten Sternenkarten angefertigt. Damals kannte man die Sinusfunktionen noch nicht. diff --git a/buch/papers/nav/trigo.tex b/buch/papers/nav/trigo.tex index c96aaa5..483b612 100644 --- a/buch/papers/nav/trigo.tex +++ b/buch/papers/nav/trigo.tex @@ -1,5 +1,7 @@ \section{Sphärische Trigonometrie} +\rhead{Sphärische Trigonometrie} + \subsection{Das Kugeldreieck} Damit man die Definition des Kugeldreiecks versteht, müssen wir zuerst Begriffe wie Grosskreisebene und Grosskreisbögen verstehen. Ein Grosskreis ist ein grösstmöglicher Kreis auf einer Kugeloberfläche. @@ -14,7 +16,7 @@ Man kann bei Kugeldreiecken nicht so einfach unterscheiden, was Innen oder Ausse Wenn man drei Eckpunkte miteinander verbindet, ergeben sich immer 16 Kugeldreiecke. Werden drei voneinander verschiedene Punkte, die sich nicht auf derselben Grosskreisebene befinden, mit Grosskreisbögen verbunden werden, so entsteht ein Kugeldreieck $ABC$. -Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $2\pi$ aber grösser als 0 ist. +Für ein Kugeldreieck gilt, dass die Summe der drei Seiten kleiner als $3\pi$ aber grösser als 0 ist. $A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskreisbögen zwischen den Eckpunkten (siehe Abbildung \ref{kugel}). \begin{figure} @@ -27,7 +29,7 @@ $A$, $B$ und $C$ sind die Ecken des Dreiecks und dessen Seiten sind die Grosskre \end{figure} \subsection{Rechtwinkliges Dreieck und rechtseitiges Dreieck} -In der sphärischen Trigonometrie gibt es eine Symetrie zwischen Seiten und Winkeln, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. +In der sphärischen Trigonometrie gibt es eine Symmetrie zwischen Seiten und Winkeln, also zu jedem Satz über Seiten und Winkel gibt es einen entsprechenden Satz, mit dem man Winkel durch Seiten und Seiten durch Winkel ersetzt hat. Wie auch im ebenen Dreieck gibt es beim Kugeldreieck auch ein rechtwinkliges Kugeldreieck, bei dem ein Winkel $\frac{\pi}{2}$ ist. Ein rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine Seitenlänge $\frac{\pi}{2}$ lang sein muss, wie man in der Abbildung \ref{recht} sehen kann. @@ -42,6 +44,7 @@ Ein rechtseitiges Dreieck gibt es jedoch nur beim Kugeldreieck, weil dort eine S \end{figure} \subsection{Winkelsumme und Flächeninhalt} +\label{trigo} %\begin{figure} ----- Brauche das Bild eigentlich nicht! % \begin{center} @@ -66,9 +69,9 @@ beschreibt die Abweichung der Innenwinkelsumme von $\pi$ und ist proportional zu \subsubsection{Flächeninnhalt} Mithilfe des Radius $r$ und dem sphärischen Exzess $\epsilon$ gilt für den Flächeninhalt -\[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon = 2 \cdot r^2 \cdot \epsilon\]. +\[ F=\frac{\pi \cdot r^2}{\frac{\pi}{2}} \cdot \epsilon = 2 \cdot r^2 \cdot \epsilon.\] -\cite{nav:winkel} +In diesem Kapitel sind keine Begründungen für die erhaltenen Resultate im Abschnitt \ref{trigo} zu erwarten und können in der Referenz \cite{nav:winkel} nachgeschlagen werden. \subsection{Seiten und Winkelberechnung} Es gibt in der sphärischen Trigonometrie eigentlich gar keinen Satz des Pythagoras, wie man ihn aus der zweidimensionalen Geometrie kennt. Es gibt aber einen Satz, der alle drei Seiten eines rechtwinkligen Kugeldreiecks in eine Beziehung bringt. Dieser Satz gilt jedoch nicht für das rechtseitige Kugeldreieck. @@ -76,7 +79,7 @@ Die Approximation im nächsten Abschnitt wird erklären, warum man dies als eine Es gilt nämlich: \begin{align} \cos c = \cos a \cdot \cos b \quad \text{wenn} \nonumber & - \quad \alpha = \frac{\pi}{2} \nonumber + \quad \alpha = \frac{\pi}{2}. \nonumber \end{align} \subsubsection{Approximation von kleinen Dreiecken} @@ -92,17 +95,18 @@ Es gibt ebenfalls folgende Approximierung der Seiten von der Sphäre in die Eben a &\approx \sin(a) \nonumber \intertext{und} \frac{a^2}{2} &\approx 1-\cos(a). \nonumber \end{align} -Die Korrespondenzen zwischen der ebenen- und sphärischen Trigonometrie werden in den kommenden Abschnitten erläutert. +Die Korrespondenzen zwischen der ebenen und sphärischen Trigonometrie werden in den kommenden Abschnitten erläutert. \subsubsection{Sphärischer Satz des Pythagoras} -Die Korrespondenz \[ a^2 \approx 1- \cos(a)\] liefert unter Anderem einen entsprechenden Satz des Pythagoras, nämlich +Die Korrespondenz \[ a^2 \approx 1- \cos(a)\] liefert unter anderem einen entsprechenden Satz des Pythagoras, nämlich \begin{align*} - \cos(a)\cdot \cos(b) &= \cos(c) \\ - \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2} \intertext{Höhere Potenzen vernachlässigen} + \cos(a)\cdot \cos(b) &= \cos(c), \\ + \bigg[1-\frac{a^2}{2}\bigg] \cdot \bigg[1-\frac{b^2}{2}\bigg] &= 1-\frac{c^2}{2}. + \intertext{Höhere Potenzen vernachlässigen:} \xcancel{1}- \frac{a^2}{2} - \frac{b^2}{2} + \xcancel{\frac{a^2b^2}{4}}&= \xcancel{1}- \frac{c^2}{2} \\ -a^2-b^2 &=-c^2\\ - a^2+b^2&=c^2 + a^2+b^2&=c^2. \end{align*} Dies ist der wohlbekannte ebene Satz des Pythagoras. @@ -127,9 +131,9 @@ und den Winkelkosinussatz Analog gibt es auch beim Seitenkosinussatz eine Korrespondenz zu \[ a^2 \leftrightarrow 1-\cos(a),\] die den ebenen Kosinussatz herleiten lässt, nämlich \begin{align} \cos(a)&= \cos(b)\cdot \cos(c) + \sin(b) \cdot \sin(c)\cdot \cos(\alpha) \\ - 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha) \intertext{Höhere Potenzen vernachlässigen} + 1-\frac{a^2}{2} &= \bigg[1-\frac{b^2}{2}\bigg]\bigg[1-\frac{c^2}{2}\bigg]+bc\cdot\cos(\alpha). \intertext{Höhere Potenzen vernachlässigen:} \xcancel{1}-\frac{a^2}{2} &= \xcancel{1}-\frac{b^2}{2}-\frac{c^2}{2} \xcancel{+\frac{b^2c^2}{4}}+bc \cdot \cos(\alpha)\\ - a^2&=b^2+c^2-2bc \cdot \cos(\alpha) + a^2&=b^2+c^2-2bc \cdot \cos(\alpha). \end{align} -- cgit v1.2.1 From 4a5bb7d7fa8ae99e2982ff30873b15a41a4f2a73 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 14:35:43 +0200 Subject: Kapitel unterteilung --- buch/papers/fm/01_AM-FM.tex | 22 +++++++++++++ buch/papers/fm/02_frequenzyspectrum.tex | 55 +++++++++++++++++++++++++++++++++ buch/papers/fm/03_bessel.tex | 40 ++++++++++++++++++++++++ buch/papers/fm/04_fazit.tex | 40 ++++++++++++++++++++++++ buch/papers/fm/main.tex | 46 ++++++++++++++------------- buch/papers/fm/teil0.tex | 22 ------------- buch/papers/fm/teil1.tex | 55 --------------------------------- buch/papers/fm/teil2.tex | 40 ------------------------ buch/papers/fm/teil3.tex | 40 ------------------------ 9 files changed, 181 insertions(+), 179 deletions(-) create mode 100644 buch/papers/fm/01_AM-FM.tex create mode 100644 buch/papers/fm/02_frequenzyspectrum.tex create mode 100644 buch/papers/fm/03_bessel.tex create mode 100644 buch/papers/fm/04_fazit.tex delete mode 100644 buch/papers/fm/teil0.tex delete mode 100644 buch/papers/fm/teil1.tex delete mode 100644 buch/papers/fm/teil2.tex delete mode 100644 buch/papers/fm/teil3.tex diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex new file mode 100644 index 0000000..55697df --- /dev/null +++ b/buch/papers/fm/01_AM-FM.tex @@ -0,0 +1,22 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 0\label{fm:section:teil0}} +\rhead{Teil 0} +Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +erat, sed diam voluptua \cite{fm:bibtex}. +At vero eos et accusam et justo duo dolores et ea rebum. +Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum +dolor sit amet. + +Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +erat, sed diam voluptua. +At vero eos et accusam et justo duo dolores et ea rebum. Stet clita +kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit +amet. + + diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex new file mode 100644 index 0000000..6f9edf1 --- /dev/null +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -0,0 +1,55 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 1 +\label{fm:section:teil1}} +\rhead{Problemstellung} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. +Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +aut fugit, sed quia consequuntur magni dolores eos qui ratione +voluptatem sequi nesciunt +\begin{equation} +\int_a^b x^2\, dx += +\left[ \frac13 x^3 \right]_a^b += +\frac{b^3-a^3}3. +\label{fm:equation1} +\end{equation} +Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +consectetur, adipisci velit, sed quia non numquam eius modi tempora +incidunt ut labore et dolore magnam aliquam quaerat voluptatem. + +Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +Quis autem vel eum iure reprehenderit qui in ea voluptate velit +esse quam nihil molestiae consequatur, vel illum qui dolorem eum +fugiat quo voluptas nulla pariatur? + +\subsection{De finibus bonorum et malorum +\label{fm:subsection:finibus}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. + +Et harum quidem rerum facilis est et expedita distinctio +\ref{fm:section:loesung}. +Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +impedit quo minus id quod maxime placeat facere possimus, omnis +voluptas assumenda est, omnis dolor repellendus +\ref{fm:section:folgerung}. +Temporibus autem quibusdam et aut officiis debitis aut rerum +necessitatibus saepe eveniet ut et voluptates repudiandae sint et +molestiae non recusandae. +Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +voluptatibus maiores alias consequatur aut perferendis doloribus +asperiores repellat. + + diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex new file mode 100644 index 0000000..6ab6fa0 --- /dev/null +++ b/buch/papers/fm/03_bessel.tex @@ -0,0 +1,40 @@ +% +% teil2.tex -- Beispiel-File für teil2 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 2 +\label{fm:section:teil2}} +\rhead{Teil 2} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +velit, sed quia non numquam eius modi tempora incidunt ut labore +et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +reprehenderit qui in ea voluptate velit esse quam nihil molestiae +consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +pariatur? + +\subsection{De finibus bonorum et malorum +\label{fm:subsection:bonorum}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +est et expedita distinctio. Nam libero tempore, cum soluta nobis +est eligendi optio cumque nihil impedit quo minus id quod maxime +placeat facere possimus, omnis voluptas assumenda est, omnis dolor +repellendus. Temporibus autem quibusdam et aut officiis debitis aut +rerum necessitatibus saepe eveniet ut et voluptates repudiandae +sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +sapiente delectus, ut aut reiciendis voluptatibus maiores alias +consequatur aut perferendis doloribus asperiores repellat. + + diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex new file mode 100644 index 0000000..3bcfc4d --- /dev/null +++ b/buch/papers/fm/04_fazit.tex @@ -0,0 +1,40 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Teil 3 +\label{fm:section:teil3}} +\rhead{Teil 3} +Sed ut perspiciatis unde omnis iste natus error sit voluptatem +accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +quae ab illo inventore veritatis et quasi architecto beatae vitae +dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +velit, sed quia non numquam eius modi tempora incidunt ut labore +et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +reprehenderit qui in ea voluptate velit esse quam nihil molestiae +consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +pariatur? + +\subsection{De finibus bonorum et malorum +\label{fm:subsection:malorum}} +At vero eos et accusamus et iusto odio dignissimos ducimus qui +blanditiis praesentium voluptatum deleniti atque corrupti quos +dolores et quas molestias excepturi sint occaecati cupiditate non +provident, similique sunt in culpa qui officia deserunt mollitia +animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +est et expedita distinctio. Nam libero tempore, cum soluta nobis +est eligendi optio cumque nihil impedit quo minus id quod maxime +placeat facere possimus, omnis voluptas assumenda est, omnis dolor +repellendus. Temporibus autem quibusdam et aut officiis debitis aut +rerum necessitatibus saepe eveniet ut et voluptates repudiandae +sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +sapiente delectus, ut aut reiciendis voluptatibus maiores alias +consequatur aut perferendis doloribus asperiores repellat. + + diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 00fb34b..1f8ebde 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -11,29 +11,31 @@ \chapterauthor{Joshua Bär} -Ein paar Hinweise für die korrekte Formatierung des Textes -\begin{itemize} -\item -Absätze werden gebildet, indem man eine Leerzeile einfügt. -Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -\item -Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -Optionen werden gelöscht. -Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -\item -Beginnen Sie jeden Satz auf einer neuen Zeile. -Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -anzuwenden. -\item -Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -\end{itemize} +Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). -\input{papers/fm/teil0.tex} -\input{papers/fm/teil1.tex} -\input{papers/fm/teil2.tex} -\input{papers/fm/teil3.tex} +%Ein paar Hinweise für die korrekte Formatierung des Textes +%\begin{itemize} +%\item +%Absätze werden gebildet, indem man eine Leerzeile einfügt. +%Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. +%\item +%Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende +%Optionen werden gelöscht. +%Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. +%\item +%Beginnen Sie jeden Satz auf einer neuen Zeile. +%Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen +%in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt +%anzuwenden. +%\item +%Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren +%Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. +%\end{itemize} + +\input{papers/fm/01_AM-FM.tex} +\input{papers/fm/02_frequenzyspectrum.tex} +\input{papers/fm/03_bessel.tex} +\input{papers/fm/04_fazit.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/fm/teil0.tex b/buch/papers/fm/teil0.tex deleted file mode 100644 index 55697df..0000000 --- a/buch/papers/fm/teil0.tex +++ /dev/null @@ -1,22 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 0\label{fm:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fm:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. - -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. - - diff --git a/buch/papers/fm/teil1.tex b/buch/papers/fm/teil1.tex deleted file mode 100644 index 6f9edf1..0000000 --- a/buch/papers/fm/teil1.tex +++ /dev/null @@ -1,55 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 1 -\label{fm:section:teil1}} -\rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{fm:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{fm:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{fm:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - - diff --git a/buch/papers/fm/teil2.tex b/buch/papers/fm/teil2.tex deleted file mode 100644 index 6ab6fa0..0000000 --- a/buch/papers/fm/teil2.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil2.tex -- Beispiel-File für teil2 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 2 -\label{fm:section:teil2}} -\rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - diff --git a/buch/papers/fm/teil3.tex b/buch/papers/fm/teil3.tex deleted file mode 100644 index 3bcfc4d..0000000 --- a/buch/papers/fm/teil3.tex +++ /dev/null @@ -1,40 +0,0 @@ -% -% teil3.tex -- Beispiel-File für Teil 3 -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{Teil 3 -\label{fm:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. - - -- cgit v1.2.1 From 24235f4b1ac1d6b837fc7740a69d8906ff2376eb Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 14:44:14 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 25 ++++----- buch/papers/fm/02_frequenzyspectrum.tex | 94 ++++++++++++++++----------------- buch/papers/fm/03_bessel.tex | 50 +++++++----------- 3 files changed, 78 insertions(+), 91 deletions(-) diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 55697df..58dd6e7 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -3,20 +3,17 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{fm:section:teil0}} -\rhead{Teil 0} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua \cite{fm:bibtex}. -At vero eos et accusam et justo duo dolores et ea rebum. -Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum -dolor sit amet. +\section{AM - FM\label{fm:section:teil0}} +\rhead{AM- FM} -Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam -nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -erat, sed diam voluptua. -At vero eos et accusam et justo duo dolores et ea rebum. Stet clita -kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit -amet. +TODO: +Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] + +%Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam +%nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam +%erat, sed diam voluptua \cite{fm:bibtex}. +%At vero eos et accusam et justo duo dolores et ea rebum. +%Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum +%dolor sit amet. diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex index 6f9edf1..1c6044d 100644 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -3,53 +3,53 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 1 +\section{AM-FM im Frequenzspektrum \label{fm:section:teil1}} \rhead{Problemstellung} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. -Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit -aut fugit, sed quia consequuntur magni dolores eos qui ratione -voluptatem sequi nesciunt -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\label{fm:equation1} -\end{equation} -Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, -consectetur, adipisci velit, sed quia non numquam eius modi tempora -incidunt ut labore et dolore magnam aliquam quaerat voluptatem. - -Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis -suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? -Quis autem vel eum iure reprehenderit qui in ea voluptate velit -esse quam nihil molestiae consequatur, vel illum qui dolorem eum -fugiat quo voluptas nulla pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:finibus}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - -Et harum quidem rerum facilis est et expedita distinctio -\ref{fm:section:loesung}. -Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil -impedit quo minus id quod maxime placeat facere possimus, omnis -voluptas assumenda est, omnis dolor repellendus -\ref{fm:section:folgerung}. -Temporibus autem quibusdam et aut officiis debitis aut rerum -necessitatibus saepe eveniet ut et voluptates repudiandae sint et -molestiae non recusandae. -Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis -voluptatibus maiores alias consequatur aut perferendis doloribus -asperiores repellat. - +Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. +%Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit +%aut fugit, sed quia consequuntur magni dolores eos qui ratione +%voluptatem sequi nesciunt +%\begin{equation} +%\int_a^b x^2\, dx +%= +%\left[ \frac13 x^3 \right]_a^b +%= +%\frac{b^3-a^3}3. +%\label{fm:equation1} +%\end{equation} +%Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, +%consectetur, adipisci velit, sed quia non numquam eius modi tempora +%incidunt ut labore et dolore magnam aliquam quaerat voluptatem. +% +%Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis +%suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? +%Quis autem vel eum iure reprehenderit qui in ea voluptate velit +%esse quam nihil molestiae consequatur, vel illum qui dolorem eum +%fugiat quo voluptas nulla pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:finibus}} +%At vero eos et accusamus et iusto odio dignissimos ducimus qui +%blanditiis praesentium voluptatum deleniti atque corrupti quos +%dolores et quas molestias excepturi sint occaecati cupiditate non +%provident, similique sunt in culpa qui officia deserunt mollitia +%animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. +% +%Et harum quidem rerum facilis est et expedita distinctio +%\ref{fm:section:loesung}. +%Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil +%impedit quo minus id quod maxime placeat facere possimus, omnis +%voluptas assumenda est, omnis dolor repellendus +%\ref{fm:section:folgerung}. +%Temporibus autem quibusdam et aut officiis debitis aut rerum +%necessitatibus saepe eveniet ut et voluptates repudiandae sint et +%molestiae non recusandae. +%Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis +%voluptatibus maiores alias consequatur aut perferendis doloribus +%asperiores repellat. diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index 6ab6fa0..fdaa0d1 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -3,38 +3,28 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 +\section{FM und Besselfunktion \label{fm:section:teil2}} \rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? -\subsection{De finibus bonorum et malorum -\label{fm:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +%aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +%eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +%est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +%velit, sed quia non numquam eius modi tempora incidunt ut labore +%et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +%veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +%nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +%reprehenderit qui in ea voluptate velit esse quam nihil molestiae +%consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +%pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:bonorum}} + -- cgit v1.2.1 From 49524d47d4705bf9b49568625976ad1f2ef67aff Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 16:30:50 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 2 ++ buch/papers/fm/04_fazit.tex | 66 ++++++++++++++++++++++----------------------- buch/papers/fm/main.tex | 7 +++-- 3 files changed, 40 insertions(+), 35 deletions(-) diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 58dd6e7..6f1c942 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -9,6 +9,8 @@ TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] + + %Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam %nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam %erat, sed diam voluptua \cite{fm:bibtex}. diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex index 3bcfc4d..8c6c002 100644 --- a/buch/papers/fm/04_fazit.tex +++ b/buch/papers/fm/04_fazit.tex @@ -3,38 +3,38 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 3 -\label{fm:section:teil3}} -\rhead{Teil 3} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? - -\subsection{De finibus bonorum et malorum -\label{fm:subsection:malorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\section{Fazit +\label{fm:section:fazit}} +\rhead{Zusamenfassend} +%Sed ut perspiciatis unde omnis iste natus error sit voluptatem +%accusantium doloremque laudantium, totam rem aperiam, eaque ipsa +%quae ab illo inventore veritatis et quasi architecto beatae vitae +%dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit +%aspernatur aut odit aut fugit, sed quia consequuntur magni dolores +%eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam +%est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci +%velit, sed quia non numquam eius modi tempora incidunt ut labore +%et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima +%veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, +%nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure +%reprehenderit qui in ea voluptate velit esse quam nihil molestiae +%consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla +%pariatur? +% +%\subsection{De finibus bonorum et malorum +%\label{fm:subsection:malorum}} +%At vero eos et accusamus et iusto odio dignissimos ducimus qui +%blanditiis praesentium voluptatum deleniti atque corrupti quos +%dolores et quas molestias excepturi sint occaecati cupiditate non +%provident, similique sunt in culpa qui officia deserunt mollitia +%animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis +%est et expedita distinctio. Nam libero tempore, cum soluta nobis +%est eligendi optio cumque nihil impedit quo minus id quod maxime +%placeat facere possimus, omnis voluptas assumenda est, omnis dolor +%repellendus. Temporibus autem quibusdam et aut officiis debitis aut +%rerum necessitatibus saepe eveniet ut et voluptates repudiandae +%sint et molestiae non recusandae. Itaque earum rerum hic tenetur a +%sapiente delectus, ut aut reiciendis voluptatibus maiores alias +%consequatur aut perferendis doloribus asperiores repellat. diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 1f8ebde..393daa5 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -5,14 +5,17 @@ % % !TeX root = buch.tex %\begin {document} -\chapter{Thema\label{chapter:fm}} -\lhead{Thema} +\chapter{FM\label{chapter:fm}} +\lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). +Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. +Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. + %Ein paar Hinweise für die korrekte Formatierung des Textes %\begin{itemize} %\item -- cgit v1.2.1 From 1001d7e685fbf99051c5cfe26abc800aa1ae1c2f Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Mon, 18 Jul 2022 17:15:22 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 2 +- buch/papers/fm/Makefile | 32 ++++++++++++++++++++++++++++++-- buch/papers/fm/main.tex | 4 ++-- buch/papers/fm/standalone.tex | 30 ++++++++++++++++++++++++++++++ 4 files changed, 63 insertions(+), 5 deletions(-) create mode 100644 buch/papers/fm/standalone.tex diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 6f1c942..a267322 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -13,7 +13,7 @@ Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequ %Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam %nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -%erat, sed diam voluptua \cite{fm:bibtex}. +erat, sed diam voluptua \cite{fm:bibtex}. %At vero eos et accusam et justo duo dolores et ea rebum. %Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum %dolor sit amet. diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index f43d497..fb42942 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -4,6 +4,34 @@ # (c) 2020 Prof Dr Andreas Mueller # -images: - @echo "no images to be created in fm" +SOURCES := \ + 01_AM-FM.tex \ + 02_frequenzyspectrum.tex \ + main.tex \ + 03_bessel.tex \ + 04_fazit.tex +#TIKZFIGURES := \ + tikz/atoms-grid-still.tex \ + +#FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) + +.PHONY: images +#images: $(FIGURES) + +#figures/%.pdf: tikz/%.tex +# mkdir -p figures +# pdflatex --output-directory=figures $< + +.PHONY: standalone +standalone: standalone.tex $(SOURCES) #$(FIGURES) + mkdir -p standalone + cd ../..; \ + pdflatex \ + --halt-on-error \ + --shell-escape \ + --output-directory=papers/fm/standalone \ + papers/fm/standalone.tex; + cd standalone; \ + bibtex standalone; \ + makeindex standalone; \ No newline at end of file diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 393daa5..be66a2f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -13,8 +13,8 @@ Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). -Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. -Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. +%Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. +%Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. %Ein paar Hinweise für die korrekte Formatierung des Textes %\begin{itemize} diff --git a/buch/papers/fm/standalone.tex b/buch/papers/fm/standalone.tex new file mode 100644 index 0000000..51a5c8c --- /dev/null +++ b/buch/papers/fm/standalone.tex @@ -0,0 +1,30 @@ +\documentclass{book} + +\input{common/packages.tex} + +% additional packages used by the individual papers, add a line for +% each paper +\input{papers/common/addpackages.tex} + +% workaround for biblatex bug +\makeatletter +\def\blx@maxline{77} +\makeatother +\addbibresource{chapters/references.bib} + +% Bibresources for each article +\input{papers/common/addbibresources.tex} + +% make sure the last index starts on an odd page +\AtEndDocument{\clearpage\ifodd\value{page}\else\null\clearpage\fi} +\makeindex + +%\pgfplotsset{compat=1.12} +\setlength{\headheight}{15pt} % fix headheight warning +\DeclareGraphicsRule{*}{mps}{*}{} + +\begin{document} + \input{common/macros.tex} + \def\chapterauthor#1{{\large #1}\bigskip\bigskip} + \input{papers/fm/main.tex} +\end{document} -- cgit v1.2.1 From e1f5d6267540ea8dc758696fb08cb7540362cf8f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Mon, 18 Jul 2022 17:34:37 +0200 Subject: First complete draft of Laguerre chapter --- .../070-orthogonalitaet/gaussquadratur.tex | 3 +- buch/papers/laguerre/Makefile | 2 +- buch/papers/laguerre/definition.tex | 6 +- buch/papers/laguerre/gamma.tex | 242 ++++++++++++++------- buch/papers/laguerre/images/estimates.pdf | Bin 13780 -> 13780 bytes buch/papers/laguerre/images/gammaplot.pdf | Bin 23297 -> 23297 bytes buch/papers/laguerre/images/integrand.pdf | Bin 16109 -> 16109 bytes buch/papers/laguerre/images/integrand_exp.pdf | Bin 16951 -> 16951 bytes buch/papers/laguerre/images/laguerre_poly.pdf | Bin 19815 -> 19815 bytes buch/papers/laguerre/images/rel_error_complex.pdf | Bin 198151 -> 195590 bytes buch/papers/laguerre/images/rel_error_mirror.pdf | Bin 26866 -> 26866 bytes buch/papers/laguerre/images/rel_error_range.pdf | Bin 25704 -> 25105 bytes buch/papers/laguerre/images/rel_error_shifted.pdf | Bin 16231 -> 16317 bytes buch/papers/laguerre/images/rel_error_simple.pdf | Bin 23353 -> 23353 bytes buch/papers/laguerre/images/targets.pdf | Bin 14757 -> 14462 bytes buch/papers/laguerre/main.tex | 2 +- .../presentation/sections/gamma_approx.tex | 24 +- .../laguerre/presentation/sections/laguerre.tex | 3 +- buch/papers/laguerre/quadratur.tex | 14 +- buch/papers/laguerre/references.bib | 18 +- buch/papers/laguerre/scripts/gamma_approx.py | 1 + buch/papers/laguerre/scripts/rel_error_complex.py | 4 +- buch/papers/laguerre/scripts/rel_error_range.py | 2 +- buch/papers/laguerre/scripts/rel_error_shifted.py | 2 +- buch/papers/laguerre/scripts/targets.py | 4 +- 25 files changed, 213 insertions(+), 114 deletions(-) diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index 2e43cec..25844df 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -1,7 +1,8 @@ % % Anwendung: Gauss-Quadratur % -\section{Anwendung: Gauss-Quadratur} +\section{Anwendung: Gauss-Quadratur +\label{buch:orthogonalitaet:section:gauss-quadratur}} \rhead{Gauss-Quadratur} Orthogonale Polynome haben eine etwas unerwartet Anwendung in einem von Gauss erdachten numerischen Integrationsverfahren. diff --git a/buch/papers/laguerre/Makefile b/buch/papers/laguerre/Makefile index 48f8066..85a1b83 100644 --- a/buch/papers/laguerre/Makefile +++ b/buch/papers/laguerre/Makefile @@ -28,7 +28,7 @@ images: $(FIGURES) .PHONY: presentation presentation: $(PRESFOLDER)/presentation.pdf -images/%.pdf images/%.pgf: scripts/%.py +images/%.pdf images/%.pgf: scripts/%.py scripts/gamma_approx.py python3 $< images/gammaplot.pdf: images/gammaplot.tex images/gammapaths.tex diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index 9ebc288..42cd6f6 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -125,10 +125,8 @@ Die Laguerre-Polynome von Grad $0$ bis $7$ sind in Abbildung~\ref{laguerre:fig:polyeval} dargestellt. \begin{figure} \centering -\scalebox{0.8}{\input{papers/laguerre/images/laguerre_poly.pgf}} -% \includegraphics[width=0.7\textwidth]{% -% papers/laguerre/images/laguerre_polynomes.eps% -% } +% \scalebox{0.8}{\input{papers/laguerre/images/laguerre_poly.pgf}} +\includegraphics[width=0.9\textwidth]{papers/laguerre/images/laguerre_poly.pdf} \caption{Laguerre-Polynome vom Grad $0$ bis $7$} \label{laguerre:fig:polyeval} \end{figure} diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index a28c180..eb64fa2 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -23,8 +23,8 @@ Integral der Form , \quad \text{wobei Realteil von $z$ grösser als $0$} -, \label{laguerre:gamma} +. \end{align} Der Term $e^{-t}$ ist genau die Gewichtsfunktion der Laguerre-Integration und der Definitionsbereich passt ebenfalls genau für dieses Verfahren. @@ -72,7 +72,7 @@ allerdings müssten die Gewichte und Nullstellen für jedes $z$ neu berechnet werden, da sie per Definition von $z$ abhängen. Dazu kommt, -dass die Berechnung der Gewichte $A_i$ nach \cite{Cassity1965AbcissasCA} +dass die Berechnung der Gewichte $A_i$ nach \cite{laguerre:Cassity1965AbcissasCA} \begin{align*} A_i = @@ -85,7 +85,7 @@ A_i } \end{align*} Evaluationen der Gamma-Funktion benötigen. -Somit scheint diese Methode nicht geeignet für unser Vorhaben. +Somit ist diese Methode eindeutig nicht geeignet für unser Vorhaben. Bei der zweiten Variante benötigen wir keine Neuberechung der Gewichte und Nullstellen für unterschiedliche $z$. @@ -95,10 +95,10 @@ Auch die Nullstellen können vorgängig, mittels eines geeigneten Verfahrens aus den Polynomen bestimmt werden. Als problematisch könnte sich höchstens die zu integrierende Funktion $f(x)=x^{z-1}$ für $|z| \gg 0$ erweisen. -Somit entscheiden wir uns auf Grund der vorherigen Punkte, +Somit entscheiden wir uns aufgrund der vorherigen Punkte, die zweite Variante weiterzuverfolgen. -\subsubsection{Naiver Ansatz} +\subsubsection{Direkter Ansatz} Wenden wir also die Gauss-Laguerre-Quadratur aus \eqref{laguerre:laguerrequadratur} auf die Gamma-Funktion \eqref{laguerre:gamma} an ergibt sich @@ -111,15 +111,16 @@ Wenden wir also die Gauss-Laguerre-Quadratur aus \begin{figure} \centering -\input{papers/laguerre/images/rel_error_simple.pgf} -\vspace{-12pt} -\caption{Relativer Fehler des naiven Ansatzes +% \input{papers/laguerre/images/rel_error_simple.pgf} +\includegraphics{papers/laguerre/images/rel_error_simple.pdf} +%\vspace{-12pt} +\caption{Relativer Fehler des direkten Ansatzes für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} \label{laguerre:fig:rel_error_simple} \end{figure} Bevor wir die Gauss-Laguerre-Quadratur anwenden, -möchten wir als erstes eine Fehlerabschätzung durchführen. +möchten wir als ersten Schritt eine Fehlerabschätzung durchführen. Für den Fehlerterm \eqref{laguerre:lag_error} wird die $2n$-te Ableitung der zu integrierenden Funktion $f(\xi)$ benötigt. Für das Integral der Gamma-Funktion ergibt sich also @@ -130,6 +131,7 @@ Für das Integral der Gamma-Funktion ergibt sich also \\ & = (z - 2n)_{2n} \xi^{z - 2n - 1} +. \end{align*} Eingesetzt im Fehlerterm \eqref{laguerre:lag_error} resultiert \begin{align} @@ -147,17 +149,19 @@ und für $z > 2n - 1$ bei $\xi \rightarrow \infty$ divergiert. Nur für den unwahrscheinlichen Fall $ z = 2n - 1$ wäre eine Fehlerabschätzung plausibel. -Wenden wir nun also naiv die Gauss-Laguerre-Quadratur auf die Gammafunktion an. +Wenden wir nun also direkt die Gauss-Laguerre-Quadratur auf die Gamma-Funktion +an. Dazu benötigen wir die Gewichte nach \eqref{laguerre:quadratur_gewichte} und als Stützstellen die Nullstellen des Laguerre-Polynomes $L_n$. Evaluieren wir den relativen Fehler unserer Approximation zeigt sich ein Bild wie in Abbildung~\ref{laguerre:fig:rel_error_simple}. Man kann sehen, -wie der relative Fehler Nullstellen aufweist für ganzzahlige $z < 2n$, +wie der relative Fehler Nullstellen aufweist für ganzzahlige $z \leq 2n$, was laut der Theorie der Gauss-Quadratur auch zu erwarten ist, denn die Approximation via Gauss-Quadratur -ist exakt für zu integrierende Polynome mit Grad $< 2n-1$. +ist exakt für zu integrierende Polynome mit Grad $\leq 2n-1$ +und von $z$ auch noch $1$ abgezogen wird im Exponenten. Es ist ersichtlich, dass sich für den Polynomgrad $n$ ein Interval gibt, in dem der relative Fehler minimal ist. @@ -168,9 +172,10 @@ könnten wir die Reflektionsformel der Gamma-Funktion ausnutzen. \begin{figure} \centering -\input{papers/laguerre/images/rel_error_mirror.pgf} -\vspace{-12pt} -\caption{Relativer Fehler des naiven Ansatz mit Spiegelung negativer Realwerte +% \input{papers/laguerre/images/rel_error_mirror.pgf} +\includegraphics{papers/laguerre/images/rel_error_mirror.pdf} +%\vspace{-12pt} +\caption{Relativer Fehler des Ansatzes mit Spiegelung negativer Realwerte für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} \label{laguerre:fig:rel_error_mirror} \end{figure} @@ -202,8 +207,9 @@ dadurch geeignete Gegenmassnahmen zu entwickeln. % und Abbildung~\ref{laguerre:fig:integrand_exp} grafisch dargestellt werden. \begin{figure} \centering -\input{papers/laguerre/images/integrand.pgf} -\vspace{-12pt} +% \input{papers/laguerre/images/integrand.pgf} +\includegraphics{papers/laguerre/images/integrand.pdf} +%\vspace{-12pt} \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \label{laguerre:fig:integrand} \end{figure} @@ -211,7 +217,7 @@ dadurch geeignete Gegenmassnahmen zu entwickeln. In Abbildung~\ref{laguerre:fig:integrand} ist der Integrand $x^z$ für unterschiedliche Werte von $z$ dargestellt. Dies entspricht der zu integrierenden Funktion $f(x)$ -der Gauss-Laguerre-Quadratur für die Gamma-Funktion- +der Gauss-Laguerre-Quadratur für die Gamma-Funktion. Man erkennt, dass für kleine $z$ sich ein singulärer Integrand ergibt und auch für grosse $z$ wächst der Integrand sehr schnell an. @@ -223,8 +229,9 @@ dass kleine Exponenten um $0$ genauere Resultate liefern sollten. \begin{figure} \centering -\input{papers/laguerre/images/integrand_exp.pgf} -\vspace{-12pt} +% \input{papers/laguerre/images/integrand_exp.pgf} +\includegraphics{papers/laguerre/images/integrand_exp.pdf} +%\vspace{-12pt} \caption{Integrand $x^z e^{-x}$ mit unterschiedlichen Werten für $z$} \label{laguerre:fig:integrand_exp} \end{figure} @@ -246,9 +253,9 @@ Damit formulieren wir die Vermutung, dass $a(n)$, welches das Intervall $[a(n), a(n) + 1]$ definiert, in dem der relative Fehler minimal ist, -grösser als $0$ ist. +grösser als $0$ und kleiner als $2n-1$ ist. -\subsubsection{Finden der optimalen Berechnungsstelle} +\subsubsection{Ansatz mit Verschiebungsterm} % Mittels der Funktionalgleichung \eqref{laguerre:gamma_funktional} % kann der Wert von $\Gamma(z)$ im Interval $z \in [a,a+1]$, % in dem der relative Fehler minimal ist, @@ -287,12 +294,13 @@ s(z, m) = \begin{cases} \displaystyle -\frac{1}{(z - m)_m} & \text{wenn } m \geq 0 \\ -(z + m)_{-m} & \text{wenn } m < 0 +\frac{1}{(z)_m} & \text{wenn } m \geq 0 \\ +(z + m)_{-m} & \text{wenn } m < 0 \end{cases} . \end{align*} +\subsubsection{Finden der optimalen Berechnungsstelle} Um die optimale Stelle $z^*(n) \in \left[a(n), a(n) + 1\right]$, $z^*(n) \in \mathbb{R}$, zu finden, @@ -305,9 +313,17 @@ s(z, m) \cdot (z - 2n)_{2n} \frac{(n!)^2}{(2n)!} \xi^{z + m - 2n - 1} ,\quad \text{für } \xi \in (0, \infty) -. \label{laguerre:gamma_err_shifted} +. \end{align} + +\begin{figure} +\centering +\includegraphics{papers/laguerre/images/targets.pdf} +% %\vspace{-12pt} +\caption{$a$ in Abhängigkeit von $z$ und $n$} +\label{laguerre:fig:targets} +\end{figure} % wobei ist % mit $z^*(n) \in \mathbb{R}$ wollen wir finden, % in dem wir den Fehlerterm \eqref{laguerre:lag_error} anpassen @@ -329,21 +345,14 @@ m^* \operatorname*{argmin}_m \max_\xi R_{n,m}(\xi) . \end{align*} -Allerdings ist die Funktion $R_{n,m}(\xi)$ unbeschränkt. +Allerdings ist die Funktion $R_{n,m}(\xi)$ unbeschränkt und +hat die gleichen Probleme wie die Fehlerabschätzung des direkten Ansatzes. Dazu müssten wir $\xi$ versuchen unter Kontrolle zu bringen, was ein äussersts schwieriges Unterfangen zu sein scheint. -Da die Gauss-Quadratur aber sowieso nur wirklich Sinn macht für kleine $n$, +Da die Gauss-Quadratur aber sowieso +nur wirklich praktisch sinnvoll für kleine $n$ ist, können die Intervalle $[a(n), a(n)+1]$ empirisch gesucht werden. -\begin{figure} -\centering -% \includegraphics{papers/laguerre/images/targets.pdf} -\input{papers/laguerre/images/targets.pgf} -\vspace{-12pt} -\caption{$a$ in Abhängigkeit von $z$ und $n$} -\label{laguerre:fig:targets} -\end{figure} - Wir bestimmen nun die optimalen Verschiebungsterme empirisch für $n = 2,\ldots, 12$ im Intervall $z \in (0, 1)$, da $z$ sowieso um den Term $m$ verschoben wird, @@ -369,11 +378,20 @@ Den linearen Regressor machen wir nur abhängig von $n$ in dem wir den Mittelwert $\overline{m}$ von $m^*$ über $z$ berechnen. +\begin{figure} +\centering +% \input{papers/laguerre/images/estimates.pgf} +\includegraphics{papers/laguerre/images/estimates.pdf} +%\vspace{-12pt} +\caption{Schätzung Mittelwert von $m$ und Fehler} +\label{laguerre:fig:schaetzung} +\end{figure} + In Abbildung~\ref{laguerre:fig:schaetzung} sind die Resultate der linearen Regression aufgezeigt mit $\alpha = 1.34094$ und $\beta = 0.854093$. Die lineare Beziehung ist ganz klar ersichtlich und der Fit scheint zu genügen. -Der optimalen Verschiebungsterm +Der optimalen Verschiebungsterm kann nun mit \begin{align*} m^* \approx @@ -381,61 +399,127 @@ m^* = \lceil \alpha n + \beta - z \rceil \end{align*} -kann nun mit dem linearen Regressor und $z$ gefunden werden. - -\begin{figure} -\centering -\input{papers/laguerre/images/estimates.pgf} -\vspace{-12pt} -\caption{Schätzung Mittelwert von $m$ und Fehler} -\label{laguerre:fig:schaetzung} -\end{figure} - -\subsection{Resultate} - -\subsubsection{Relativer Fehler} +% kann nun mit dem linearen Regressor und $z$ +gefunden werden. +\subsubsection{Evaluation des Schätzers} +In einem ersten Schritt möchten wir analysieren, +wie gut die Abschätzung des optimalen Verschiebungsterms ist. +Dazu bestimmen wir den relativen Fehler für verschiedene Verschiebungsterme $m$ +rund um $m^*$ bei gegebenem Polynomgrad $n = 8$ für $z \in (0, 1)$. +Abbildung~\ref{laguerre:fig:rel_error_shifted} sind die relativen Fehler +der Approximation dargestellt. +Man kann deutlich sehen, +dass der relative Fehler anwächst, +je weiter der Verschiebungsterm vom idealen Wert abweicht. +Zudem scheint der Schätzer den optimalen Verschiebungsterm gut zu bestimmen, +da der Schätzer zuerst der grünen Linie folgt und +dann beim Übergang auf die orange Linie wechselt. \begin{figure} \centering -\input{papers/laguerre/images/rel_error_shifted.pgf} -\vspace{-12pt} +% \input{papers/laguerre/images/rel_error_shifted.pgf} +\includegraphics{papers/laguerre/images/rel_error_shifted.pdf} +%\vspace{-12pt} \caption{Relativer Fehler des Ansatzes mit Verschiebungsterm für verschiedene reele Werte von $z$ und Verschiebungsterme $m$. Das verwendete Laguerre-Polynom besitzt den Grad $n = 8$. $m^*$ bezeichnet hier den optimalen Verschiebungsterm} \label{laguerre:fig:rel_error_shifted} \end{figure} - + +\subsubsection{Resultate} +Das Verfahren scheint für den Grad $n=8$ und $z \in (0,1)$ gut zu funktioneren. +Es stellt sich nun die Frage, +wie der relative Fehler sich für verschiedene $z$ und $n$ verhält. +In Abbildung~\ref{laguerre:fig:rel_error_range} sind die relativen Fehler für +unterschiedliche $n$ dargestellt. +Der relative Fehler scheint immer noch Nullstellen aufzuweisen, +bei für ganzzahlige $z$. +Durch das Verschieben ergibt sich jetzt aber, +wie zu erwarten war, +ein periodischer relativer Fehler mit einer Periodendauer von $1$. +Zudem lässt sich erkennen, +dass der Fehler abhängig von der Ordnung $n$ +des verwendeten Laguerre-Polynoms ist. +Wenn der Grad $n$ um $1$ erhöht wird, +verbessert sich die Genauigkeit des Resultats um etwa eine signifikante Stelle. + +In Abbildung~\ref{laguerre:fig:rel_error_complex} +ist der Betrag des relativen Fehlers in der komplexen Ebene dargestellt. +Je stärker der Imaginäranteil von $z$ von $0$ abweicht, +umso schlechter wird die Genauigkeit der Approximation. +Das erstaunt nicht weiter, +da die Gauss-Quadratur eigentlich nur für reelle Zahlen definiert ist. +Wenn der Imaginäranteil von $z$ ungefähr $0$ ist, +lässt sich das gleiche Bild beobachten wie in +Abbildung~\ref{laguerre:fig:rel_error_range}. + \begin{figure} \centering -\input{papers/laguerre/images/rel_error_range.pgf} -\vspace{-12pt} +% \input{papers/laguerre/images/rel_error_range.pgf} +\includegraphics{papers/laguerre/images/rel_error_range.pdf} +%\vspace{-12pt} \caption{Relativer Fehler des Ansatzes mit optimalen Verschiebungsterm -für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} +für verschiedene reele Werte von $z$ und Laguerre-Polynome vom Grad $n$} \label{laguerre:fig:rel_error_range} \end{figure} -\subsubsection{Vergleich mit Lanczos-Methode} -{\color{red} -$ $\newline -$n = 7$:\newline -Lanczos Polynomgrad auf 13 Stellen.\newline -Unsere Methode auf 7 Stellen -} - -% 2. Die Fehlerabschätzung ist problematisch, -% weil die Funktion R_n(\xi) unbeschränkt ist. -% Daher kann man nicht einfach nach dem Maximum von R_n(\xi) suchen. -% Man muss zunächst irgendwie das \xi unter Kontrolle bringen. -% Das scheint mir äusserst schwierig zu sein. +\begin{figure} +\centering +\includegraphics{papers/laguerre/images/rel_error_complex.pdf} +%\vspace{-12pt} +\caption{Absolutwert des relativen Fehlers in der komplexen Ebene} +\label{laguerre:fig:rel_error_complex} +\end{figure} -% Ich möchte daher folgendes anregen: -% Im Sinne der Formulierung des Problems, -% wie im Punkt 1 oben könnten Sie für verschiedene n -% nach den optimalen Intervallen [a(n),a(n)+1] suchen, -% und versuchen, einen empirischen Zusammenhang (Faustregel) -% zwischen n und a(n) zu formulieren. -% Das ist etwa gleich gut, -% da ja der Witz der Gauss-Integration ist, -% dass man eben nur sehr kleine n überhaupt in Betracht zieht, -% d.h. man braucht keine exakte Gesetzmässigkeit für a(n). +\subsubsection{Vergleich mit Lanczos-Methode} +Nun stellt sich die Frage, +wie das in diesem Abschnitt beschriebene Approximationsverfahren +der Gamma-Funktion sich gegenüber den üblichen Approximationsverfahren schlägt. +Eine häufig verwendete Methode ist die Lanczos-Approximation, +welche gegeben ist durch +\begin{align} +\Gamma(z + 1) +\approx +\sqrt{2\pi} \left( z + \sigma + \frac{1}{2} \right)^{z + 1/2} +e^{-(z + \sigma + 1/2)} \sum_{k=0}^n g_k H_k(z) +, +\end{align} +wobei +\begin{align*} +g_k = \frac{e^\sigma \varepsilon_k (-1)^k}{\sqrt{2\pi}} +\sum_{r=0}^k (-1)^r \, \binom{k}{r} \, (k)_r +\left( \frac{e}{r + \sigma + \frac{1}{2}}\right)^{r + 1/2} +, +\end{align*} +\begin{align*} +\varepsilon_k += +\begin{cases} +1 & \text{für } k = 0 \\ +2 & \text{sonst} +\end{cases} +\quad \text{und}\quad +H_k(z) += +\frac{(-1)^k (-z)_k}{(z+1)_k} +\end{align*} +mit $H_0 = 1$ und $\sum_0^n g_k = 1$ (siehe \cite{laguerre:lanczos}). +Diese Methode wurde zum Beispiel in +{\em GNU Scientific Library}, {\em Boost}, {\em CPython} und +{\em musl} implementiert. +Diese Methode erreicht für $n = 7$ typischerweise Genauigkeit von $13$ +korrekten, signifikanten Stellen für reele Argumente. +Zum Vergleich: die vorgestellte Methode erreicht für $n = 7$ +eine minimale Genauigkeit von $6$-$7$ korrekten, signifikanten Stellen +für reele Argumente. +Das Resultat ist etwas enttäuschend, +aber nicht unerwartet, +da die Lanczos-Methode spezifisch auf dieses Problem zugeschnitten ist und +unsere Methode eine erweiterte allgemeine Methode ist. +Was die Komplexität der Berechnungen im Betrieb angeht, +ist die Gauss-Laguerre-Quadratur wesentlich ressourcensparender, +weil sie nur aus $n$ Funktionasevaluationen, +wenigen Multiplikationen und Additionen besteht. +Also könnte diese Methode z.B. Anwendung in Systemen mit wenig Rechenleistung +und/oder knappen Energieressourcen finden. \ No newline at end of file diff --git a/buch/papers/laguerre/images/estimates.pdf b/buch/papers/laguerre/images/estimates.pdf index c93a4f0..bd995de 100644 Binary files a/buch/papers/laguerre/images/estimates.pdf and b/buch/papers/laguerre/images/estimates.pdf differ diff --git a/buch/papers/laguerre/images/gammaplot.pdf b/buch/papers/laguerre/images/gammaplot.pdf index b65cf1b..7c195f2 100644 Binary files a/buch/papers/laguerre/images/gammaplot.pdf and b/buch/papers/laguerre/images/gammaplot.pdf differ diff --git a/buch/papers/laguerre/images/integrand.pdf b/buch/papers/laguerre/images/integrand.pdf index 676ac98..76be412 100644 Binary files a/buch/papers/laguerre/images/integrand.pdf and b/buch/papers/laguerre/images/integrand.pdf differ diff --git a/buch/papers/laguerre/images/integrand_exp.pdf b/buch/papers/laguerre/images/integrand_exp.pdf index 5e021d5..5fe7a7b 100644 Binary files a/buch/papers/laguerre/images/integrand_exp.pdf and b/buch/papers/laguerre/images/integrand_exp.pdf differ diff --git a/buch/papers/laguerre/images/laguerre_poly.pdf b/buch/papers/laguerre/images/laguerre_poly.pdf index d74f652..21278f5 100644 Binary files a/buch/papers/laguerre/images/laguerre_poly.pdf and b/buch/papers/laguerre/images/laguerre_poly.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_complex.pdf b/buch/papers/laguerre/images/rel_error_complex.pdf index d23ebd1..c7bb37a 100644 Binary files a/buch/papers/laguerre/images/rel_error_complex.pdf and b/buch/papers/laguerre/images/rel_error_complex.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_mirror.pdf b/buch/papers/laguerre/images/rel_error_mirror.pdf index e51dd83..8a27d41 100644 Binary files a/buch/papers/laguerre/images/rel_error_mirror.pdf and b/buch/papers/laguerre/images/rel_error_mirror.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_range.pdf b/buch/papers/laguerre/images/rel_error_range.pdf index fca4019..bb8a2d7 100644 Binary files a/buch/papers/laguerre/images/rel_error_range.pdf and b/buch/papers/laguerre/images/rel_error_range.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_shifted.pdf b/buch/papers/laguerre/images/rel_error_shifted.pdf index d0c2ae0..b7e72dc 100644 Binary files a/buch/papers/laguerre/images/rel_error_shifted.pdf and b/buch/papers/laguerre/images/rel_error_shifted.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_simple.pdf b/buch/papers/laguerre/images/rel_error_simple.pdf index 24e11b6..3212e42 100644 Binary files a/buch/papers/laguerre/images/rel_error_simple.pdf and b/buch/papers/laguerre/images/rel_error_simple.pdf differ diff --git a/buch/papers/laguerre/images/targets.pdf b/buch/papers/laguerre/images/targets.pdf index e1ec07c..9514a6d 100644 Binary files a/buch/papers/laguerre/images/targets.pdf and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex index f4263de..d69fbed 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -13,7 +13,7 @@ benannt nach Edmond Laguerre (1834 - 1886), sind Lösungen der ebenfalls nach Laguerre benannten Differentialgleichung. Laguerre entdeckte diese Polynome als er Approximationsmethoden für das Integral $\int_0^\infty \exp(-x) / x \, dx$ suchte. -Darum möchten wir in diesem Kapitel uns, +Darum möchten wir uns in diesem Kapitel, ganz im Sinne des Entdeckers, den Laguerre-Polynomen für Approximationen von Integralen mit exponentiell-abfallenden Funktionen widmen. diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex index 3d32aae..ecd02ab 100644 --- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -49,7 +49,8 @@ R_n(\xi) \begin{figure}[h] \centering % \scalebox{0.91}{\input{../images/rel_error_simple.pgf}} -\resizebox{!}{0.72\textheight}{\input{../images/rel_error_simple.pgf}} +% \resizebox{!}{0.72\textheight}{\input{../images/rel_error_simple.pgf}} +\includegraphics[width=0.77\textwidth]{../images/rel_error_simple.pdf} \caption{Relativer Fehler des einfachen Ansatzes für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} \end{figure} @@ -81,7 +82,8 @@ von $z$ und Grade $n$ der Laguerre-Polynome} \begin{frame}{$f(x) = x^z$} \begin{figure}[h] \centering -\scalebox{0.91}{\input{../images/integrand.pgf}} +% \scalebox{0.91}{\input{../images/integrand.pgf}} +\includegraphics[width=0.8\textwidth]{../images/integrand.pdf} % \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \end{figure} \end{frame} @@ -89,7 +91,8 @@ von $z$ und Grade $n$ der Laguerre-Polynome} \begin{frame}{Integrand $x^z e^{-x}$} \begin{figure}[h] \centering -\scalebox{0.91}{\input{../images/integrand_exp.pgf}} +% \scalebox{0.91}{\input{../images/integrand_exp.pgf}} +\includegraphics[width=0.8\textwidth]{../images/integrand_exp.pdf} % \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \end{figure} \end{frame} @@ -144,15 +147,16 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \begin{frame}{Schätzen von $m^*$} \begin{columns} -\begin{column}{0.6\textwidth} +\begin{column}{0.65\textwidth} \begin{figure} \centering -\vspace{-24pt} -\scalebox{0.7}{\input{../images/estimates.pgf}} +\vspace{-12pt} +% \scalebox{0.7}{\input{../images/estimates.pgf}} +\includegraphics[width=1.0\textwidth]{../images/estimates.pdf} % \caption{Integrand $x^z$ mit unterschiedlichen Werten für $z$} \end{figure} \end{column} -\begin{column}{0.39\textwidth} +\begin{column}{0.34\textwidth} \begin{align*} \hat{m} &= @@ -173,7 +177,8 @@ m^* \begin{frame}{} \begin{figure}[h] \centering -\scalebox{0.6}{\input{../images/rel_error_shifted.pgf}} +% \scalebox{0.6}{\input{../images/rel_error_shifted.pgf}} +\includegraphics{../images/rel_error_shifted.pdf} \caption{Relativer Fehler mit $n=8$, unterschiedlichen Verschiebungstermen $m$ und $z\in(0, 1)$} \end{figure} \end{frame} @@ -181,7 +186,8 @@ m^* \begin{frame}{} \begin{figure}[h] \centering -\scalebox{0.6}{\input{../images/rel_error_range.pgf}} +% \scalebox{0.6}{\input{../images/rel_error_range.pgf}} +\includegraphics{../images/rel_error_range.pdf} \caption{Relativer Fehler mit $n=8$, Verschiebungsterm $m^*$ und $z\in(-5, 5)$} \end{figure} \end{frame} diff --git a/buch/papers/laguerre/presentation/sections/laguerre.tex b/buch/papers/laguerre/presentation/sections/laguerre.tex index ed29387..f99214e 100644 --- a/buch/papers/laguerre/presentation/sections/laguerre.tex +++ b/buch/papers/laguerre/presentation/sections/laguerre.tex @@ -55,7 +55,8 @@ L_n(x) \begin{frame} \begin{figure}[h] \centering -\resizebox{0.74\textwidth}{!}{\input{../images/laguerre_poly.pgf}} +% \resizebox{0.74\textwidth}{!}{\input{../images/laguerre_poly.pgf}} +\includegraphics[width=0.7\textwidth]{../images/laguerre_poly.pdf} \caption{Laguerre-Polynome vom Grad $0$ bis $7$} \end{figure} \end{frame} diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 7cbae48..4ca6913 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -48,13 +48,13 @@ darum müssen wir sie mit einer Funktion multiplizieren, die schneller als jedes Polynom gegen $0$ geht, damit das Integral immer noch konvergiert. Die Laguerre-Polynome $L_n$ bieten hier Abhilfe, -da ihre Gewichtsfunktion $e^{-x}$ schneller +da ihre Gewichtsfunktion $w(x) = e^{-x}$ schneller gegen $0$ konvergiert als jedes Polynom. % In unserem Falle möchten wir die Gauss Quadratur auf die Laguerre-Polynome % $L_n$ ausweiten. % Diese sind orthogonal im Intervall $(0, \infty)$ bezüglich % der Gewichtsfunktion $e^{-x}$. -Gleichung~\eqref{laguerre:gaussquadratur} lässt sich wie folgt +Die Gleichung~\eqref{laguerre:gaussquadratur} lässt sich wie folgt umformulieren: \begin{align} \int_{0}^{\infty} f(x) e^{-x} dx @@ -81,7 +81,7 @@ l_i(x_j) % . \end{align*} die Lagrangschen Interpolationspolynome. -Laut \cite{hildebrand2013introduction} können die Gewicht mit +Laut \cite{laguerre:hildebrand2013introduction} können die Gewichte mit \begin{align*} A_i & = @@ -97,7 +97,7 @@ des orthogonalen Polynoms $\phi_n(x)$, $\forall i =0,\ldots,n$ und \end{align*} dem Normalisierungsfaktor. Wir setzen nun $\phi_n(x) = L_n(x)$ und -nutzen den Vorzeichenwechsel der Laguerrekoeffizienten aus, +nutzen den Vorzeichenwechsel der Laguerre-Koeffizienten aus, damit erhalten wir \begin{align*} A_i @@ -135,7 +135,7 @@ n L_n(x) - n L_{n-1}(x) &= (x - n - 1) L_n(x) + (n + 1) L_{n+1}(x) \end{align*} umgeformt werden und da $x_i$ die Nullstellen von $L_n(x)$ sind, -folgt +vereinfacht sich der Term zu \begin{align*} x_i L'_n(x_i) &= @@ -145,7 +145,7 @@ x_i L'_n(x_i) (n + 1) L_{n+1}(x_i) . \end{align*} -Setzen wir das nun in \eqref{laguerre:gewichte_lag_temp} ein ergibt sicht +Setzen wir das nun in \eqref{laguerre:gewichte_lag_temp} ein ergibt sich \begin{align} \nonumber A_i @@ -168,7 +168,7 @@ Der Fehlerterm $R_n$ folgt direkt aus der Approximation = \sum_{i=1}^n f(x_i) A_i + R_n \end{align*} -und \cite{abramowitz+stegun} gibt ihn als +und \cite{laguerre:abramowitz+stegun} gibt ihn als \begin{align} R_n & = diff --git a/buch/papers/laguerre/references.bib b/buch/papers/laguerre/references.bib index 2371922..d21009b 100644 --- a/buch/papers/laguerre/references.bib +++ b/buch/papers/laguerre/references.bib @@ -3,19 +3,17 @@ % % (c) 2020 Autor, Hochschule Rapperswil % - -@book{hildebrand2013introduction, +@book{laguerre:hildebrand2013introduction, title={Introduction to Numerical Analysis: Second Edition}, author={Hildebrand, F.B.}, isbn={9780486318554}, series={Dover Books on Mathematics}, - url={https://books.google.ch/books?id=ic2jAQAAQBAJ}, year={2013}, publisher={Dover Publications}, pages = {389} } -@book{abramowitz+stegun, +@book{laguerre:abramowitz+stegun, added-at = {2008-06-25T06:25:58.000+0200}, address = {New York}, author = {Abramowitz, Milton and Stegun, Irene A.}, @@ -32,11 +30,21 @@ year = 1972 } -@article{Cassity1965AbcissasCA, +@article{laguerre:Cassity1965AbcissasCA, title={Abcissas, coefficients, and error term for the generalized Gauss-Laguerre quadrature formula using the zero ordinate}, author={C. Ronald Cassity}, journal={Mathematics of Computation}, year={1965}, volume={19}, pages={287-296} +} + +@online{laguerre:lanczos, + title = {Lanczos Approximation}, + author={Eric W. Weisstein}, + url = {https://mathworld.wolfram.com/LanczosApproximation.html}, + date = {2022-07-18}, + year = {2022}, + month = {7}, + day = {18} } \ No newline at end of file diff --git a/buch/papers/laguerre/scripts/gamma_approx.py b/buch/papers/laguerre/scripts/gamma_approx.py index 9f9dae7..5b09e59 100644 --- a/buch/papers/laguerre/scripts/gamma_approx.py +++ b/buch/papers/laguerre/scripts/gamma_approx.py @@ -7,6 +7,7 @@ EPSILON = 1e-7 root = str(Path(__file__).parent) img_path = f"{root}/../images" fontsize = "medium" +cmap = "plasma" def _prep_zeros_and_weights(x, w, n): diff --git a/buch/papers/laguerre/scripts/rel_error_complex.py b/buch/papers/laguerre/scripts/rel_error_complex.py index 5be79be..4a714fa 100644 --- a/buch/papers/laguerre/scripts/rel_error_complex.py +++ b/buch/papers/laguerre/scripts/rel_error_complex.py @@ -24,9 +24,9 @@ if __name__ == "__main__": lag = ga.eval_laguerre_gamma(input, n=8, func="optimal_shifted").reshape(mesh.shape) rel_error = np.abs(ga.calc_rel_error(lanczos, lag)) - fig, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(4, 2.4)) + fig, ax = plt.subplots(clear=True, constrained_layout=True, figsize=(3.5, 2.1)) _c = ax.pcolormesh( - x, y, rel_error, shading="gouraud", cmap="inferno", norm=mpl.colors.LogNorm() + x, y, rel_error, shading="gouraud", cmap=ga.cmap, norm=mpl.colors.LogNorm() ) cbr = fig.colorbar(_c, ax=ax) cbr.minorticks_off() diff --git a/buch/papers/laguerre/scripts/rel_error_range.py b/buch/papers/laguerre/scripts/rel_error_range.py index 43b5450..ece3b6d 100644 --- a/buch/papers/laguerre/scripts/rel_error_range.py +++ b/buch/papers/laguerre/scripts/rel_error_range.py @@ -21,7 +21,7 @@ if __name__ == "__main__": x = np.linspace(xmin + ga.EPSILON, xmax - ga.EPSILON, N) gamma = scipy.special.gamma(x) - fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2)) for n in ns: gamma_lag = ga.eval_laguerre_gamma(x, n=n, func="optimal_shifted") rel_err = ga.calc_rel_error(gamma, gamma_lag) diff --git a/buch/papers/laguerre/scripts/rel_error_shifted.py b/buch/papers/laguerre/scripts/rel_error_shifted.py index dc9d177..f53c89b 100644 --- a/buch/papers/laguerre/scripts/rel_error_shifted.py +++ b/buch/papers/laguerre/scripts/rel_error_shifted.py @@ -20,7 +20,7 @@ if __name__ == "__main__": x = np.linspace(step, 1 - step, N + 1) targets = np.arange(10, 14) gamma = scipy.special.gamma(x) - fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.5)) + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(5, 2.1)) for target in targets: gamma_lag = ga.eval_laguerre_gamma(x, target=target, n=n, func="shifted") rel_error = np.abs(ga.calc_rel_error(gamma, gamma_lag)) diff --git a/buch/papers/laguerre/scripts/targets.py b/buch/papers/laguerre/scripts/targets.py index 206b3a1..3bc7f52 100644 --- a/buch/papers/laguerre/scripts/targets.py +++ b/buch/papers/laguerre/scripts/targets.py @@ -42,8 +42,8 @@ if __name__ == "__main__": bests = find_best_loc(N, ns=ns) - fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(4, 2.4)) - v = ax.imshow(bests, cmap="inferno", aspect="auto", interpolation="nearest") + fig, ax = plt.subplots(num=1, clear=True, constrained_layout=True, figsize=(3.5, 2.1)) + v = ax.imshow(bests, cmap=ga.cmap, aspect="auto", interpolation="nearest") plt.colorbar(v, ax=ax, label=r"$m^*$") ticks = np.arange(0, N + 1, N // 5) ax.set_xlim(0, 1) -- cgit v1.2.1 From b7b2af20f16f6a5beac602046572067c462e5ff7 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Mon, 18 Jul 2022 20:03:57 +0200 Subject: Created some helpful graphics --- buch/papers/lambertw/Bilder/Strategie.png | Bin 0 -> 11049 bytes buch/papers/lambertw/Bilder/pursuerDGL.ggb | Bin 0 -> 36225 bytes buch/papers/lambertw/Bilder/pursuerDGL.svg | 1 + buch/papers/lambertw/Bilder/pursuerDGL2.ggb | Bin 0 -> 36225 bytes buch/papers/lambertw/Bilder/pursuerDGL2.svg | 1 + 5 files changed, 2 insertions(+) create mode 100644 buch/papers/lambertw/Bilder/Strategie.png create mode 100644 buch/papers/lambertw/Bilder/pursuerDGL.ggb create mode 100644 buch/papers/lambertw/Bilder/pursuerDGL.svg create mode 100644 buch/papers/lambertw/Bilder/pursuerDGL2.ggb create mode 100644 buch/papers/lambertw/Bilder/pursuerDGL2.svg diff --git a/buch/papers/lambertw/Bilder/Strategie.png b/buch/papers/lambertw/Bilder/Strategie.png new file mode 100644 index 0000000..e78abd3 Binary files /dev/null and b/buch/papers/lambertw/Bilder/Strategie.png differ diff --git a/buch/papers/lambertw/Bilder/pursuerDGL.ggb b/buch/papers/lambertw/Bilder/pursuerDGL.ggb new file mode 100644 index 0000000..3fb3a78 Binary files /dev/null and b/buch/papers/lambertw/Bilder/pursuerDGL.ggb differ diff --git a/buch/papers/lambertw/Bilder/pursuerDGL.svg b/buch/papers/lambertw/Bilder/pursuerDGL.svg new file mode 100644 index 0000000..d91e5e1 --- /dev/null +++ b/buch/papers/lambertw/Bilder/pursuerDGL.svg @@ -0,0 +1 @@ +–0.7–0.7–0.7–0.6–0.6–0.6–0.5–0.5–0.5–0.4–0.4–0.4–0.3–0.3–0.3–0.2–0.2–0.2–0.1–0.1–0.10.10.10.10.20.20.20.30.30.30.40.40.40.50.50.50.60.60.60.70.70.70.80.80.80.90.90.91111.11.11.11.21.21.21.31.31.31.41.41.41.51.51.51.61.61.61.71.71.71.81.81.81.91.91.92222.12.12.12.22.22.22.32.32.32.42.42.42.52.52.52.62.62.62.72.72.72.82.82.82.92.92.93333.13.13.13.23.23.23.33.33.30.10.10.10.20.20.20.30.30.30.40.40.40.50.50.50.60.60.60.70.70.70.80.80.80.90.90.91111.11.11.11.21.21.21.31.31.31.41.41.41.51.51.51.61.61.61.71.71.71.81.81.81.91.91.92222.12.12.12.22.22.22.32.32.32.42.42.4000AOAOAOPOPOPOPAPAPAPPPAAA \ No newline at end of file diff --git a/buch/papers/lambertw/Bilder/pursuerDGL2.ggb b/buch/papers/lambertw/Bilder/pursuerDGL2.ggb new file mode 100644 index 0000000..5bd816c Binary files /dev/null and b/buch/papers/lambertw/Bilder/pursuerDGL2.ggb differ diff --git a/buch/papers/lambertw/Bilder/pursuerDGL2.svg b/buch/papers/lambertw/Bilder/pursuerDGL2.svg new file mode 100644 index 0000000..0c4a11d --- /dev/null +++ b/buch/papers/lambertw/Bilder/pursuerDGL2.svg @@ -0,0 +1 @@ +–0.2–0.20.20.20.40.40.60.60.80.8111.21.21.41.41.61.61.81.8222.22.22.42.42.62.62.82.8333.23.2–0.2–0.20.20.20.40.40.60.60.80.8111.21.21.41.41.61.61.81.8222.22.22.42.42.62.62.82.83300Visierlinie \ No newline at end of file -- cgit v1.2.1 From 1badf707f9ebd0642bb6a1d282059b6e867a44af Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Mon, 18 Jul 2022 20:06:05 +0200 Subject: rearranged the introduction --- buch/papers/lambertw/Bilder/something.svg | 1 - buch/papers/lambertw/teil0.tex | 67 +++++++++++++++++++++++++++++-- buch/papers/lambertw/teil1.tex | 2 +- buch/papers/lambertw/teil2.tex | 39 ++++-------------- 4 files changed, 72 insertions(+), 37 deletions(-) delete mode 100644 buch/papers/lambertw/Bilder/something.svg diff --git a/buch/papers/lambertw/Bilder/something.svg b/buch/papers/lambertw/Bilder/something.svg deleted file mode 100644 index e9d5656..0000000 --- a/buch/papers/lambertw/Bilder/something.svg +++ /dev/null @@ -1 +0,0 @@ -–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888000OAOAOAOPOPOPPAPAPAPPPAAA \ No newline at end of file diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index ca172e5..f174ccb 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -3,14 +3,73 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Was sind Verfolgungskurven? \label{lambertw:section:teil0}} +\section{Was sind Verfolgungskurven? +\label{lambertw:section:teil0}} \rhead{Teil 0} +Verfolgungskurven tauchen oft auf bei fragen wie, welchen Pfad begeht ein Hund während er einer Katze nachrennt. Ein solches Problem hat im Kern immer ein Verfolger und sein Ziel. Der Verfolger versucht sein Ziel zu ergattern und das Ziel versucht zu entkommen. Der Pfad, der der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. Um diese Kurve zu bestimmen, kann das Verfolgungsproblem als DGL formuliert werden. Diese DGL entspringt der Verfolgungsstrategie des Verfolgers. -Verfolgungskurven entstehen immer, dann wenn ein Verfolger sein Ziel verfolgt. -Nämlich ist eine Verfolgungskurve die Kurve, die ein Verfolger abfährt während er sein Ziel verfolgt. -Zum Beispiel +\subsection{Verfolger und Verfolgungsstrategie +\label{lambertw:subsection:Verfolger}} +Wie bereits erwähnt, wird der Verfolger durch seine Verfolgungsstrategie definiert. Wir nehmen an, dass sich der Verfolger stur an eine Verfolgungsstrategie hält. Dabei gibt es viele mögliche Strategien, die der Verfolger wählen könnte. Die möglichen Strategien entstehen durch Festlegung einzelner Parameter, die der Verfolger kontrollieren kann. Der Verfolger hat nur einen direkten Einfluss auf seinen Geschwindigkeitsvektor. Mit diesem kann er neben Richtung und Betrag auch den Abstand zwischen Verfolger und Ziel kontrollieren. Wenn zwei dieser drei Parameter durch die Strategie definiert werden, ist der dritte nicht mehr frei. Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um den Verfolger komplett zu beschreiben. + +\begin{tabular}{|>{$}l<{$}|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + \hline + \text{}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ + \hline + \text{Strategie 1} + & \text{konstant} & \text{-} & \text{direkt auf Ziel hinzu}\\ + + \text{Strategie 2} + & \text{-} & \text{konstant} & \text{direkt auf Ziel hinzu}\\ + + \text{Strategie 3} + & \text{konstant} & \text{-} & \text{etwas voraus Zielen}\\ + \hline +\label{lambertw:Strategien} +\end{tabular} + +In der Tabelle \eqref{lambertw:Strategien} sind drei mögliche Strategien aufgezählt. Folgend wird nur noch auf die Strategie 1 eingegangen. Bei dieser Strategie ist die Geschwindigkeit konstant und der Verfolger bewegt sich immer direkt auf sein Ziel hinzu. In der Grafik \eqref{lambertw:pursuerDGL2} ist das Problem dargestellt. Wobei $\overrightarrow{V}$ der Ortsvektor des Verfolgers, $\overrightarrow{Z}$ der Ortsvektor des Ziels und $\overrightarrow{\dot{V}}$ der Richtungsvektor des Verfolgers ist. Die konstante Geschwindigkeit kann man mit der Gleichung +\begin{equation} + |\overrightarrow{\dot{V}}| + = + konst = A + \quad|A\in\mathbb{R}>0 +\end{equation} +darstellen. Der Richtungsvektor wiederum kann mit der Gleichung +\begin{equation} + \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|} + = + \frac{\overrightarrow{\dot{V}}}{|\overrightarrow{\dot{V}}|} +\end{equation} +beschrieben werden. Durch die Subtraktion der Ortsvektoren $\overrightarrow{V}$ und $\overrightarrow{Z}$ entsteht ein Vektor der vom Punkt $V$ auf $Z$ zeigt. Da die Länge dieses Vektors beliebig sein kann, wird durch Division mit dem Betrag, die Länge auf eins festgelegt. +Aus dem Verfolgungsproblem ist auch ersichtlich, dass die Punkte $V$ und $Z$ nicht am gleichen Ort starten und so eine Division durch Null ausgeschlossen ist. Wenn die Punkte $V$ und $Z$ trotzdem am gleichen Ort starten, ist die Lösung trivial. +Nun wird die Gleichung mit deren rechten Seite skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. +\begin{equation} + \label{pursuer:pursuerDGL} + \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot \frac{\overrightarrow{\dot{V}}}{|\overrightarrow{\dot{V}}|} + = + 1 +\end{equation} +Diese DGL ist der Kern des Verfolgungsproblems, insofern sich der Verfolger immer direkt auf sein Ziel zubewegt. + + + + + +\subsection{Ziel +\label{lambertw:subsection:Ziel}} +Als nächstes gehen wir auf das Ziel ein. Wie der Verfolger wird auch unser Ziel sich strikt an eine Fluchtstrategie halten, welche von Anfang an bekannt ist. Diese Strategie kann als Parameterdarstellung der Position nach der Zeit beschrieben werden. Zum Beispiel könnte ein Ziel auf einer Geraden flüchten, welches auf einer Ebene mit der Parametrisierung +\begin{equation} + \vec{r}(t) + = + \begin{Bmatrix} + 0\\ + t + \end{Bmatrix} +\end{equation} +beschrieben werden könnte. diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 493ec05..cc4a62a 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -3,7 +3,7 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Beispiel () +\section{Ziel \label{lambertw:section:teil1}} \rhead{Problemstellung} diff --git a/buch/papers/lambertw/teil2.tex b/buch/papers/lambertw/teil2.tex index 9d840ab..c95511a 100644 --- a/buch/papers/lambertw/teil2.tex +++ b/buch/papers/lambertw/teil2.tex @@ -3,38 +3,15 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 -\label{lambertw:section:teil2}} +\section{Verfolger +\label{lambertw:section:Verfolger}} \rhead{Teil 2} -Sed ut perspiciatis unde omnis iste natus error sit voluptatem -accusantium doloremque laudantium, totam rem aperiam, eaque ipsa -quae ab illo inventore veritatis et quasi architecto beatae vitae -dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit -aspernatur aut odit aut fugit, sed quia consequuntur magni dolores -eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam -est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci -velit, sed quia non numquam eius modi tempora incidunt ut labore -et dolore magnam aliquam quaerat voluptatem. Ut enim ad minima -veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, -nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure -reprehenderit qui in ea voluptate velit esse quam nihil molestiae -consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla -pariatur? -\subsection{De finibus bonorum et malorum -\label{lambertw:subsection:bonorum}} -At vero eos et accusamus et iusto odio dignissimos ducimus qui -blanditiis praesentium voluptatum deleniti atque corrupti quos -dolores et quas molestias excepturi sint occaecati cupiditate non -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis -est et expedita distinctio. Nam libero tempore, cum soluta nobis -est eligendi optio cumque nihil impedit quo minus id quod maxime -placeat facere possimus, omnis voluptas assumenda est, omnis dolor -repellendus. Temporibus autem quibusdam et aut officiis debitis aut -rerum necessitatibus saepe eveniet ut et voluptates repudiandae -sint et molestiae non recusandae. Itaque earum rerum hic tenetur a -sapiente delectus, ut aut reiciendis voluptatibus maiores alias -consequatur aut perferendis doloribus asperiores repellat. +\subsection{Strategie 1 +\label{lambertw:subsection:Strategie1}} + + +\subsection{Strategie 2 +\label{lambertw:subsection:Strategie2}} -- cgit v1.2.1 From f0ff46df0f4c212b44cbed4c01ad357c75f0bdbb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Tue, 19 Jul 2022 07:40:48 +0200 Subject: Fix typos in gamma.tex and quadratur.tex --- buch/papers/laguerre/gamma.tex | 2 +- buch/papers/laguerre/quadratur.tex | 9 +++++---- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index eb64fa2..b76daeb 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -245,7 +245,7 @@ Für negative $z$ ergeben sich immer noch Singularitäten, wenn $x \rightarrow 0$. Um $1$ wächst der Term $x^z$ schneller als die Dämpfung $e^{-x}$, aber für $x \rightarrow \infty$ geht der Integrand gegen $0$. -Das führt zu Glockenförmigen Kurven, +Das führt zu glockenförmigen Kurven, die für grosse Exponenten $z$ nach der Stelle $x=1$ schnell anwachsen. Zu grosse Exponenten $z$ sind also immer noch problematisch. Kleine positive $z$ scheinen nun also auch zulässig zu sein. diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 4ca6913..75858df 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -41,10 +41,11 @@ x = a + \frac{1 - t}{t} \end{align*} -auf das Intervall $[0, 1]$ transformiert. -Für unser Fall gilt $a = 0$. +auf das Intervall $[0, 1]$ transformiert, +kann dies behoben werden. +Für unseren Fall gilt $a = 0$. Das Integral eines Polynomes in diesem Intervall ist immer divergent, -darum müssen wir sie mit einer Funktion multiplizieren, +darum müssen wir das Polynome mit einer Funktion multiplizieren, die schneller als jedes Polynom gegen $0$ geht, damit das Integral immer noch konvergiert. Die Laguerre-Polynome $L_n$ bieten hier Abhilfe, @@ -76,7 +77,7 @@ l_i(x_j) = \begin{cases} 1 & i=j \\ -0 & \text{.} +0 & \text{sonst} \end{cases} % . \end{align*} -- cgit v1.2.1 From b72c171ecac28671740a594f89a02fd3bc4d0e96 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 19 Jul 2022 07:44:42 +0200 Subject: dependencies fixed --- buch/chapters/110-elliptisch/dglsol.tex | 34 +++++++++++++++++++++++------ buch/chapters/110-elliptisch/mathpendel.tex | 4 +++- buch/papers/fm/Makefile.inc | 6 +---- 3 files changed, 31 insertions(+), 13 deletions(-) diff --git a/buch/chapters/110-elliptisch/dglsol.tex b/buch/chapters/110-elliptisch/dglsol.tex index 613f130..c5b3a5c 100644 --- a/buch/chapters/110-elliptisch/dglsol.tex +++ b/buch/chapters/110-elliptisch/dglsol.tex @@ -230,7 +230,8 @@ folgenden Satz. \begin{satz} \index{Satz!Differentialgleichung von $1/\operatorname{pq}(u,k)$}% Wenn die Jacobische elliptische Funktion $\operatorname{pq}(u,k)$ -der Differentialgleichung genügt, dann genügt der Kehrwert +der Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} +genügt, dann genügt der Kehrwert $\operatorname{qp}(u,k) = 1/\operatorname{pq}(u,k)$ der Differentialgleichung \begin{equation} (\operatorname{qp}'(u,k))^2 @@ -277,8 +278,8 @@ vertauscht worden sind. % Differentialgleichung zweiter Ordnung % \subsubsection{Differentialgleichung zweiter Ordnung} -Leitet die Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} -man dies nochmals nach $u$ ab, erhält man die Differentialgleichung +Leitet man die Differentialgleichung~\eqref{buch:elliptisch:eqn:1storderdglell} +nochmals nach $u$ ab, erhält man die Differentialgleichung \[ 2\operatorname{pq}''(u,k)\operatorname{pq}'(u,k) = @@ -340,6 +341,25 @@ y(u) = F^{-1}(u+C). Die Jacobischen elliptischen Funktionen sind daher inverse Funktionen der unvollständigen elliptischen Integrale. +\begin{beispiel} +Die Differentialgleichung der Funktion $y=\operatorname{sn}(u,k)$ ist +\[ +(y')^2 += +(1-y^2)(1-k^2y^2). +\] +Aus \eqref{buch:elliptisch:eqn:yintegral} folgt daher, dass +\[ +u+C += +\int\frac{dy}{(1-y^2)(1-k^2y^2)}. +\] +Das Integral ist das unvollständige elliptische Integral erster Art. +Mit der Wahl der Konstanten $C$ so, dass $y(0)=0$ ist, ist +$y(u)=\operatorname{sn}(u,k)$ daher die Umkehrfunktion von +$y\mapsto F(y,k)=u$. +\end{beispiel} + % % Numerische Berechnung mit dem arithmetisch-geometrischen Mittel % @@ -545,7 +565,7 @@ Wir möchten die nichtlineare Differentialgleichung \biggr)^2 = Ax^4+Bx^2 + C -\label{buch:elliptisch:eqn:allgdgl} +\label{buch:elliptisch:eqn:anhdgl} \end{equation} mit Hilfe elliptischer Funktionen lösen. Wir nehmen also an, dass die gesuchte Lösung eine Funktion der Form @@ -562,7 +582,7 @@ a\operatorname{zn}'(bt,k). \] Indem wir diesen Lösungsansatz in die -Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} +Differentialgleichung~\eqref{buch:elliptisch:eqn:anhdgl} einsetzen, erhalten wir \begin{equation} a^2b^2 \operatorname{zn}'(bt,k)^2 @@ -672,13 +692,13 @@ Da alle Parameter im Lösungsansatz~\eqref{buch:elliptisch:eqn:loesungsansatz} bereits festgelegt sind stellt sich die Frage, woher man einen weiteren Parameter nehmen kann, mit dem Anfangsbedingungen erfüllen kann. -Die Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} ist +Die Differentialgleichung~\eqref{buch:elliptisch:eqn:anhdgl} ist autonom, die Koeffizienten der rechten Seite der Differentialgleichung sind nicht von der Zeit abhängig. Damit ist eine zeitverschobene Funktion $x(t-t_0)$ ebenfalls eine Lösung der Differentialgleichung. Die allgmeine Lösung der -Differentialgleichung~\eqref{buch:elliptisch:eqn:allgdgl} hat +Differentialgleichung~\eqref{buch:elliptisch:eqn:anhdgl} hat also die Form \[ x(t) = a\operatorname{zn}(b(t-t_0)), diff --git a/buch/chapters/110-elliptisch/mathpendel.tex b/buch/chapters/110-elliptisch/mathpendel.tex index 54b7531..e029ffd 100644 --- a/buch/chapters/110-elliptisch/mathpendel.tex +++ b/buch/chapters/110-elliptisch/mathpendel.tex @@ -209,7 +209,7 @@ Dazu setzt man $z(t) = y(bt)$ und bekommt = \frac{d}{dt}y(bt) \frac{d\,bt}{dt} = -b\dot{y}(bt). +b\,\dot{y}(bt). \] Die Zeit muss also mit dem Faktor $\sqrt{2ml^2/E}$ skaliert werden. @@ -240,6 +240,8 @@ Damit ergeben sich zwei Fälle. Wenn $y_0<1$ ist, dann schwingt das Pendel. Der Fall $y_0>1$ entspricht einer Bewegung, bei der das Pendel um den Punkt $O$ rotiert. +In den folgenden zwei Abschnitten werden die beiden Fälle ausführlicher +diskutiert. \begin{figure} diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index 0f144b6..dcdecd2 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,9 +6,5 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ - papers/fm/references.bib \ - papers/fm/teil0.tex \ - papers/fm/teil1.tex \ - papers/fm/teil2.tex \ - papers/fm/teil3.tex + papers/fm/references.bib -- cgit v1.2.1 From 36f9ca108e2cc08f68d7095b5e09b59bff90f98c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 19 Jul 2022 07:52:32 +0200 Subject: makefile fix --- buch/papers/fm/Makefile.inc | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index dcdecd2..e5cd9f6 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,5 +6,9 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ + papers/fm/01_AM-FM.tex \ + papers/fm/02_frequenzyspectrum.tex \ + papers/fm/03_bessel.tex \ + papers/fm/04_fazit.tex \ papers/fm/references.bib -- cgit v1.2.1 From eeecc5a6af897e52423b7b3538e4c1bee47f943f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Tue, 19 Jul 2022 07:55:06 +0200 Subject: Fix merge issue --- buch/chapters/070-orthogonalitaet/gaussquadratur.tex | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex index 25844df..2e43cec 100644 --- a/buch/chapters/070-orthogonalitaet/gaussquadratur.tex +++ b/buch/chapters/070-orthogonalitaet/gaussquadratur.tex @@ -1,8 +1,7 @@ % % Anwendung: Gauss-Quadratur % -\section{Anwendung: Gauss-Quadratur -\label{buch:orthogonalitaet:section:gauss-quadratur}} +\section{Anwendung: Gauss-Quadratur} \rhead{Gauss-Quadratur} Orthogonale Polynome haben eine etwas unerwartet Anwendung in einem von Gauss erdachten numerischen Integrationsverfahren. -- cgit v1.2.1 From 2b3fb7f75fd66876ed1a1d77f4fd0b16a6dfe772 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Tue, 19 Jul 2022 08:06:58 +0200 Subject: Add missing files --- buch/papers/laguerre/images/gammapaths.tex | 1024 ++++++++++++++++++++++++++++ buch/papers/laguerre/images/gammaplot.tex | 73 ++ buch/papers/laguerre/quadratur.tex | 2 +- 3 files changed, 1098 insertions(+), 1 deletion(-) create mode 100644 buch/papers/laguerre/images/gammapaths.tex create mode 100644 buch/papers/laguerre/images/gammaplot.tex diff --git a/buch/papers/laguerre/images/gammapaths.tex b/buch/papers/laguerre/images/gammapaths.tex new file mode 100644 index 0000000..efa0863 --- /dev/null +++ b/buch/papers/laguerre/images/gammapaths.tex @@ -0,0 +1,1024 @@ +\def\gammaplus{({\dx*0.0190},{\dy*52.0728}) + -- ({\dx*0.0200},{\dy*49.4422}) + -- ({\dx*0.0400},{\dy*24.4610}) + -- ({\dx*0.0600},{\dy*16.1457}) + -- ({\dx*0.0800},{\dy*11.9966}) + -- ({\dx*0.1000},{\dy*9.5135}) + -- ({\dx*0.1200},{\dy*7.8633}) + -- ({\dx*0.1400},{\dy*6.6887}) + -- ({\dx*0.1600},{\dy*5.8113}) + -- ({\dx*0.1800},{\dy*5.1318}) + -- ({\dx*0.2000},{\dy*4.5908}) + -- ({\dx*0.2200},{\dy*4.1505}) + -- ({\dx*0.2400},{\dy*3.7855}) + -- ({\dx*0.2600},{\dy*3.4785}) + -- ({\dx*0.2800},{\dy*3.2169}) + -- ({\dx*0.3000},{\dy*2.9916}) + -- ({\dx*0.3200},{\dy*2.7958}) + -- ({\dx*0.3400},{\dy*2.6242}) + -- ({\dx*0.3600},{\dy*2.4727}) + -- ({\dx*0.3800},{\dy*2.3383}) + -- ({\dx*0.4000},{\dy*2.2182}) + -- ({\dx*0.4200},{\dy*2.1104}) + -- ({\dx*0.4400},{\dy*2.0132}) + -- ({\dx*0.4600},{\dy*1.9252}) + -- ({\dx*0.4800},{\dy*1.8453}) + -- ({\dx*0.5000},{\dy*1.7725}) + -- ({\dx*0.5200},{\dy*1.7058}) + -- ({\dx*0.5400},{\dy*1.6448}) + -- ({\dx*0.5600},{\dy*1.5886}) + -- ({\dx*0.5800},{\dy*1.5369}) + -- ({\dx*0.6000},{\dy*1.4892}) + -- ({\dx*0.6200},{\dy*1.4450}) + -- ({\dx*0.6400},{\dy*1.4041}) + -- ({\dx*0.6600},{\dy*1.3662}) + -- ({\dx*0.6800},{\dy*1.3309}) + -- ({\dx*0.7000},{\dy*1.2981}) + -- ({\dx*0.7200},{\dy*1.2675}) + -- ({\dx*0.7400},{\dy*1.2390}) + -- ({\dx*0.7600},{\dy*1.2123}) + -- ({\dx*0.7800},{\dy*1.1875}) + -- ({\dx*0.8000},{\dy*1.1642}) + -- ({\dx*0.8200},{\dy*1.1425}) + -- ({\dx*0.8400},{\dy*1.1222}) + -- ({\dx*0.8600},{\dy*1.1031}) + -- ({\dx*0.8800},{\dy*1.0853}) + -- ({\dx*0.9000},{\dy*1.0686}) + -- ({\dx*0.9200},{\dy*1.0530}) + -- ({\dx*0.9400},{\dy*1.0384}) + -- ({\dx*0.9600},{\dy*1.0247}) + -- ({\dx*0.9800},{\dy*1.0119}) + -- ({\dx*1.0000},{\dy*1.0000}) + -- ({\dx*1.0200},{\dy*0.9888}) + -- ({\dx*1.0400},{\dy*0.9784}) + -- ({\dx*1.0600},{\dy*0.9687}) + -- ({\dx*1.0800},{\dy*0.9597}) + -- ({\dx*1.1000},{\dy*0.9514}) + -- ({\dx*1.1200},{\dy*0.9436}) + -- ({\dx*1.1400},{\dy*0.9364}) + -- ({\dx*1.1600},{\dy*0.9298}) + -- ({\dx*1.1800},{\dy*0.9237}) + -- ({\dx*1.2000},{\dy*0.9182}) + -- ({\dx*1.2200},{\dy*0.9131}) + -- ({\dx*1.2400},{\dy*0.9085}) + -- ({\dx*1.2600},{\dy*0.9044}) + -- ({\dx*1.2800},{\dy*0.9007}) + -- ({\dx*1.3000},{\dy*0.8975}) + -- ({\dx*1.3200},{\dy*0.8946}) + -- ({\dx*1.3400},{\dy*0.8922}) + -- ({\dx*1.3600},{\dy*0.8902}) + -- ({\dx*1.3800},{\dy*0.8885}) + -- ({\dx*1.4000},{\dy*0.8873}) + -- ({\dx*1.4200},{\dy*0.8864}) + -- ({\dx*1.4400},{\dy*0.8858}) + -- ({\dx*1.4600},{\dy*0.8856}) + -- ({\dx*1.4800},{\dy*0.8857}) + -- ({\dx*1.5000},{\dy*0.8862}) + -- ({\dx*1.5200},{\dy*0.8870}) + -- ({\dx*1.5400},{\dy*0.8882}) + -- ({\dx*1.5600},{\dy*0.8896}) + -- ({\dx*1.5800},{\dy*0.8914}) + -- ({\dx*1.6000},{\dy*0.8935}) + -- ({\dx*1.6200},{\dy*0.8959}) + -- ({\dx*1.6400},{\dy*0.8986}) + -- ({\dx*1.6600},{\dy*0.9017}) + -- ({\dx*1.6800},{\dy*0.9050}) + -- ({\dx*1.7000},{\dy*0.9086}) + -- ({\dx*1.7200},{\dy*0.9126}) + -- ({\dx*1.7400},{\dy*0.9168}) + -- ({\dx*1.7600},{\dy*0.9214}) + -- ({\dx*1.7800},{\dy*0.9262}) + -- ({\dx*1.8000},{\dy*0.9314}) + -- ({\dx*1.8200},{\dy*0.9368}) + -- ({\dx*1.8400},{\dy*0.9426}) + -- ({\dx*1.8600},{\dy*0.9487}) + -- ({\dx*1.8800},{\dy*0.9551}) + -- ({\dx*1.9000},{\dy*0.9618}) + -- ({\dx*1.9200},{\dy*0.9688}) + -- ({\dx*1.9400},{\dy*0.9761}) + -- ({\dx*1.9600},{\dy*0.9837}) + -- ({\dx*1.9800},{\dy*0.9917}) + -- ({\dx*2.0000},{\dy*1.0000}) + -- ({\dx*2.0200},{\dy*1.0086}) + -- ({\dx*2.0400},{\dy*1.0176}) + -- ({\dx*2.0600},{\dy*1.0269}) + -- ({\dx*2.0800},{\dy*1.0365}) + -- ({\dx*2.1000},{\dy*1.0465}) + -- ({\dx*2.1200},{\dy*1.0568}) + -- ({\dx*2.1400},{\dy*1.0675}) + -- ({\dx*2.1600},{\dy*1.0786}) + -- ({\dx*2.1800},{\dy*1.0900}) + -- ({\dx*2.2000},{\dy*1.1018}) + -- ({\dx*2.2200},{\dy*1.1140}) + -- ({\dx*2.2400},{\dy*1.1266}) + -- ({\dx*2.2600},{\dy*1.1395}) + -- ({\dx*2.2800},{\dy*1.1529}) + -- ({\dx*2.3000},{\dy*1.1667}) + -- ({\dx*2.3200},{\dy*1.1809}) + -- ({\dx*2.3400},{\dy*1.1956}) + -- ({\dx*2.3600},{\dy*1.2107}) + -- ({\dx*2.3800},{\dy*1.2262}) + -- ({\dx*2.4000},{\dy*1.2422}) + -- ({\dx*2.4200},{\dy*1.2586}) + -- ({\dx*2.4400},{\dy*1.2756}) + -- ({\dx*2.4600},{\dy*1.2930}) + -- ({\dx*2.4800},{\dy*1.3109}) + -- ({\dx*2.5000},{\dy*1.3293}) + -- ({\dx*2.5200},{\dy*1.3483}) + -- ({\dx*2.5400},{\dy*1.3678}) + -- ({\dx*2.5600},{\dy*1.3878}) + -- ({\dx*2.5800},{\dy*1.4084}) + -- ({\dx*2.6000},{\dy*1.4296}) + -- ({\dx*2.6200},{\dy*1.4514}) + -- ({\dx*2.6400},{\dy*1.4738}) + -- ({\dx*2.6600},{\dy*1.4968}) + -- ({\dx*2.6800},{\dy*1.5204}) + -- ({\dx*2.7000},{\dy*1.5447}) + -- ({\dx*2.7200},{\dy*1.5696}) + -- ({\dx*2.7400},{\dy*1.5953}) + -- ({\dx*2.7600},{\dy*1.6216}) + -- ({\dx*2.7800},{\dy*1.6487}) + -- ({\dx*2.8000},{\dy*1.6765}) + -- ({\dx*2.8200},{\dy*1.7051}) + -- ({\dx*2.8400},{\dy*1.7344}) + -- ({\dx*2.8600},{\dy*1.7646}) + -- ({\dx*2.8800},{\dy*1.7955}) + -- ({\dx*2.9000},{\dy*1.8274}) + -- ({\dx*2.9200},{\dy*1.8600}) + -- ({\dx*2.9400},{\dy*1.8936}) + -- ({\dx*2.9600},{\dy*1.9281}) + -- ({\dx*2.9800},{\dy*1.9636}) + -- ({\dx*3.0000},{\dy*2.0000}) + -- ({\dx*3.0200},{\dy*2.0374}) + -- ({\dx*3.0400},{\dy*2.0759}) + -- ({\dx*3.0600},{\dy*2.1153}) + -- ({\dx*3.0800},{\dy*2.1559}) + -- ({\dx*3.1000},{\dy*2.1976}) + -- ({\dx*3.1200},{\dy*2.2405}) + -- ({\dx*3.1400},{\dy*2.2845}) + -- ({\dx*3.1600},{\dy*2.3297}) + -- ({\dx*3.1800},{\dy*2.3762}) + -- ({\dx*3.2000},{\dy*2.4240}) + -- ({\dx*3.2200},{\dy*2.4731}) + -- ({\dx*3.2400},{\dy*2.5235}) + -- ({\dx*3.2600},{\dy*2.5754}) + -- ({\dx*3.2800},{\dy*2.6287}) + -- ({\dx*3.3000},{\dy*2.6834}) + -- ({\dx*3.3200},{\dy*2.7397}) + -- ({\dx*3.3400},{\dy*2.7976}) + -- ({\dx*3.3600},{\dy*2.8571}) + -- ({\dx*3.3800},{\dy*2.9183}) + -- ({\dx*3.4000},{\dy*2.9812}) + -- ({\dx*3.4200},{\dy*3.0459}) + -- ({\dx*3.4400},{\dy*3.1124}) + -- ({\dx*3.4600},{\dy*3.1807}) + -- ({\dx*3.4800},{\dy*3.2510}) + -- ({\dx*3.5000},{\dy*3.3234}) + -- ({\dx*3.5200},{\dy*3.3977}) + -- ({\dx*3.5400},{\dy*3.4742}) + -- ({\dx*3.5600},{\dy*3.5529}) + -- ({\dx*3.5800},{\dy*3.6338}) + -- ({\dx*3.6000},{\dy*3.7170}) + -- ({\dx*3.6200},{\dy*3.8027}) + -- ({\dx*3.6400},{\dy*3.8908}) + -- ({\dx*3.6600},{\dy*3.9814}) + -- ({\dx*3.6800},{\dy*4.0747}) + -- ({\dx*3.7000},{\dy*4.1707}) + -- ({\dx*3.7200},{\dy*4.2694}) + -- ({\dx*3.7400},{\dy*4.3711}) + -- ({\dx*3.7600},{\dy*4.4757}) + -- ({\dx*3.7800},{\dy*4.5833}) + -- ({\dx*3.8000},{\dy*4.6942}) + -- ({\dx*3.8200},{\dy*4.8083}) + -- ({\dx*3.8400},{\dy*4.9257}) + -- ({\dx*3.8600},{\dy*5.0466}) + -- ({\dx*3.8800},{\dy*5.1711}) + -- ({\dx*3.9000},{\dy*5.2993}) + -- ({\dx*3.9200},{\dy*5.4313}) + -- ({\dx*3.9400},{\dy*5.5673}) + -- ({\dx*3.9600},{\dy*5.7073}) + -- ({\dx*3.9800},{\dy*5.8515}) + -- ({\dx*4.0000},{\dy*6.0000}) + -- ({\dx*4.0200},{\dy*6.1530}) + -- ({\dx*4.0400},{\dy*6.3106}) + -- ({\dx*4.0600},{\dy*6.4730}) + -- ({\dx*4.0800},{\dy*6.6403}) + -- ({\dx*4.0810},{\dy*6.6488})} +\def\gammaone{({\dx*-0.9810},{\dy*-53.0814}) + -- ({\dx*-0.9800},{\dy*-50.4512}) + -- ({\dx*-0.9600},{\dy*-25.4802}) + -- ({\dx*-0.9400},{\dy*-17.1763}) + -- ({\dx*-0.9200},{\dy*-13.0397}) + -- ({\dx*-0.9000},{\dy*-10.5706}) + -- ({\dx*-0.8800},{\dy*-8.9355}) + -- ({\dx*-0.8600},{\dy*-7.7775}) + -- ({\dx*-0.8400},{\dy*-6.9182}) + -- ({\dx*-0.8200},{\dy*-6.2583}) + -- ({\dx*-0.8000},{\dy*-5.7386}) + -- ({\dx*-0.7800},{\dy*-5.3211}) + -- ({\dx*-0.7600},{\dy*-4.9809}) + -- ({\dx*-0.7400},{\dy*-4.7006}) + -- ({\dx*-0.7200},{\dy*-4.4678}) + -- ({\dx*-0.7000},{\dy*-4.2737}) + -- ({\dx*-0.6800},{\dy*-4.1114}) + -- ({\dx*-0.6600},{\dy*-3.9760}) + -- ({\dx*-0.6400},{\dy*-3.8636}) + -- ({\dx*-0.6200},{\dy*-3.7714}) + -- ({\dx*-0.6000},{\dy*-3.6969}) + -- ({\dx*-0.5800},{\dy*-3.6386}) + -- ({\dx*-0.5600},{\dy*-3.5950}) + -- ({\dx*-0.5400},{\dy*-3.5652}) + -- ({\dx*-0.5200},{\dy*-3.5487}) + -- ({\dx*-0.5000},{\dy*-3.5449}) + -- ({\dx*-0.4800},{\dy*-3.5538}) + -- ({\dx*-0.4600},{\dy*-3.5756}) + -- ({\dx*-0.4400},{\dy*-3.6105}) + -- ({\dx*-0.4200},{\dy*-3.6594}) + -- ({\dx*-0.4000},{\dy*-3.7230}) + -- ({\dx*-0.3800},{\dy*-3.8027}) + -- ({\dx*-0.3600},{\dy*-3.9004}) + -- ({\dx*-0.3400},{\dy*-4.0181}) + -- ({\dx*-0.3200},{\dy*-4.1590}) + -- ({\dx*-0.3000},{\dy*-4.3269}) + -- ({\dx*-0.2800},{\dy*-4.5267}) + -- ({\dx*-0.2600},{\dy*-4.7652}) + -- ({\dx*-0.2400},{\dy*-5.0514}) + -- ({\dx*-0.2200},{\dy*-5.3976}) + -- ({\dx*-0.2000},{\dy*-5.8211}) + -- ({\dx*-0.1800},{\dy*-6.3472}) + -- ({\dx*-0.1600},{\dy*-7.0135}) + -- ({\dx*-0.1400},{\dy*-7.8795}) + -- ({\dx*-0.1200},{\dy*-9.0442}) + -- ({\dx*-0.1000},{\dy*-10.6863}) + -- ({\dx*-0.0800},{\dy*-13.1627}) + -- ({\dx*-0.0600},{\dy*-17.3067}) + -- ({\dx*-0.0400},{\dy*-25.6183}) + -- ({\dx*-0.0200},{\dy*-50.5974}) + -- ({\dx*-0.0190},{\dy*-53.2279})} +\def\gammatwo{({\dx*-1.9810},{\dy*26.7952}) + -- ({\dx*-1.9800},{\dy*25.4804}) + -- ({\dx*-1.9600},{\dy*13.0001}) + -- ({\dx*-1.9400},{\dy*8.8538}) + -- ({\dx*-1.9200},{\dy*6.7915}) + -- ({\dx*-1.9000},{\dy*5.5635}) + -- ({\dx*-1.8800},{\dy*4.7529}) + -- ({\dx*-1.8600},{\dy*4.1815}) + -- ({\dx*-1.8400},{\dy*3.7599}) + -- ({\dx*-1.8200},{\dy*3.4386}) + -- ({\dx*-1.8000},{\dy*3.1881}) + -- ({\dx*-1.7800},{\dy*2.9894}) + -- ({\dx*-1.7600},{\dy*2.8301}) + -- ({\dx*-1.7400},{\dy*2.7015}) + -- ({\dx*-1.7200},{\dy*2.5976}) + -- ({\dx*-1.7000},{\dy*2.5139}) + -- ({\dx*-1.6800},{\dy*2.4473}) + -- ({\dx*-1.6600},{\dy*2.3952}) + -- ({\dx*-1.6400},{\dy*2.3559}) + -- ({\dx*-1.6200},{\dy*2.3280}) + -- ({\dx*-1.6000},{\dy*2.3106}) + -- ({\dx*-1.5800},{\dy*2.3029}) + -- ({\dx*-1.5600},{\dy*2.3045}) + -- ({\dx*-1.5400},{\dy*2.3151}) + -- ({\dx*-1.5200},{\dy*2.3346}) + -- ({\dx*-1.5000},{\dy*2.3633}) + -- ({\dx*-1.4800},{\dy*2.4012}) + -- ({\dx*-1.4600},{\dy*2.4490}) + -- ({\dx*-1.4400},{\dy*2.5073}) + -- ({\dx*-1.4200},{\dy*2.5770}) + -- ({\dx*-1.4000},{\dy*2.6593}) + -- ({\dx*-1.3800},{\dy*2.7556}) + -- ({\dx*-1.3600},{\dy*2.8679}) + -- ({\dx*-1.3400},{\dy*2.9986}) + -- ({\dx*-1.3200},{\dy*3.1508}) + -- ({\dx*-1.3000},{\dy*3.3283}) + -- ({\dx*-1.2800},{\dy*3.5365}) + -- ({\dx*-1.2600},{\dy*3.7819}) + -- ({\dx*-1.2400},{\dy*4.0737}) + -- ({\dx*-1.2200},{\dy*4.4243}) + -- ({\dx*-1.2000},{\dy*4.8510}) + -- ({\dx*-1.1800},{\dy*5.3790}) + -- ({\dx*-1.1600},{\dy*6.0461}) + -- ({\dx*-1.1400},{\dy*6.9118}) + -- ({\dx*-1.1200},{\dy*8.0752}) + -- ({\dx*-1.1000},{\dy*9.7148}) + -- ({\dx*-1.0800},{\dy*12.1877}) + -- ({\dx*-1.0600},{\dy*16.3271}) + -- ({\dx*-1.0400},{\dy*24.6330}) + -- ({\dx*-1.0200},{\dy*49.6053}) + -- ({\dx*-1.0190},{\dy*52.2354})} +\def\gammathree{({\dx*-2.9810},{\dy*-8.9887}) + -- ({\dx*-2.9800},{\dy*-8.5505}) + -- ({\dx*-2.9600},{\dy*-4.3919}) + -- ({\dx*-2.9400},{\dy*-3.0115}) + -- ({\dx*-2.9200},{\dy*-2.3259}) + -- ({\dx*-2.9000},{\dy*-1.9184}) + -- ({\dx*-2.8800},{\dy*-1.6503}) + -- ({\dx*-2.8600},{\dy*-1.4621}) + -- ({\dx*-2.8400},{\dy*-1.3239}) + -- ({\dx*-2.8200},{\dy*-1.2194}) + -- ({\dx*-2.8000},{\dy*-1.1386}) + -- ({\dx*-2.7800},{\dy*-1.0753}) + -- ({\dx*-2.7600},{\dy*-1.0254}) + -- ({\dx*-2.7400},{\dy*-0.9859}) + -- ({\dx*-2.7200},{\dy*-0.9550}) + -- ({\dx*-2.7000},{\dy*-0.9311}) + -- ({\dx*-2.6800},{\dy*-0.9132}) + -- ({\dx*-2.6600},{\dy*-0.9004}) + -- ({\dx*-2.6400},{\dy*-0.8924}) + -- ({\dx*-2.6200},{\dy*-0.8886}) + -- ({\dx*-2.6000},{\dy*-0.8887}) + -- ({\dx*-2.5800},{\dy*-0.8926}) + -- ({\dx*-2.5600},{\dy*-0.9002}) + -- ({\dx*-2.5400},{\dy*-0.9115}) + -- ({\dx*-2.5200},{\dy*-0.9264}) + -- ({\dx*-2.5000},{\dy*-0.9453}) + -- ({\dx*-2.4800},{\dy*-0.9682}) + -- ({\dx*-2.4600},{\dy*-0.9955}) + -- ({\dx*-2.4400},{\dy*-1.0276}) + -- ({\dx*-2.4200},{\dy*-1.0649}) + -- ({\dx*-2.4000},{\dy*-1.1080}) + -- ({\dx*-2.3800},{\dy*-1.1578}) + -- ({\dx*-2.3600},{\dy*-1.2152}) + -- ({\dx*-2.3400},{\dy*-1.2815}) + -- ({\dx*-2.3200},{\dy*-1.3581}) + -- ({\dx*-2.3000},{\dy*-1.4471}) + -- ({\dx*-2.2800},{\dy*-1.5511}) + -- ({\dx*-2.2600},{\dy*-1.6734}) + -- ({\dx*-2.2400},{\dy*-1.8186}) + -- ({\dx*-2.2200},{\dy*-1.9929}) + -- ({\dx*-2.2000},{\dy*-2.2050}) + -- ({\dx*-2.1800},{\dy*-2.4674}) + -- ({\dx*-2.1600},{\dy*-2.7991}) + -- ({\dx*-2.1400},{\dy*-3.2298}) + -- ({\dx*-2.1200},{\dy*-3.8091}) + -- ({\dx*-2.1000},{\dy*-4.6261}) + -- ({\dx*-2.0800},{\dy*-5.8595}) + -- ({\dx*-2.0600},{\dy*-7.9258}) + -- ({\dx*-2.0400},{\dy*-12.0750}) + -- ({\dx*-2.0200},{\dy*-24.5571}) + -- ({\dx*-2.0190},{\dy*-25.8719})} +\def\gammafour{({\dx*-3.9950},{\dy*8.3966}) + -- ({\dx*-3.9800},{\dy*2.1484}) + -- ({\dx*-3.9600},{\dy*1.1091}) + -- ({\dx*-3.9400},{\dy*0.7643}) + -- ({\dx*-3.9200},{\dy*0.5933}) + -- ({\dx*-3.9000},{\dy*0.4919}) + -- ({\dx*-3.8800},{\dy*0.4253}) + -- ({\dx*-3.8600},{\dy*0.3788}) + -- ({\dx*-3.8400},{\dy*0.3448}) + -- ({\dx*-3.8200},{\dy*0.3192}) + -- ({\dx*-3.8000},{\dy*0.2996}) + -- ({\dx*-3.7800},{\dy*0.2845}) + -- ({\dx*-3.7600},{\dy*0.2727}) + -- ({\dx*-3.7400},{\dy*0.2636}) + -- ({\dx*-3.7200},{\dy*0.2567}) + -- ({\dx*-3.7000},{\dy*0.2516}) + -- ({\dx*-3.6800},{\dy*0.2481}) + -- ({\dx*-3.6600},{\dy*0.2460}) + -- ({\dx*-3.6400},{\dy*0.2452}) + -- ({\dx*-3.6200},{\dy*0.2455}) + -- ({\dx*-3.6000},{\dy*0.2469}) + -- ({\dx*-3.5800},{\dy*0.2493}) + -- ({\dx*-3.5600},{\dy*0.2529}) + -- ({\dx*-3.5400},{\dy*0.2575}) + -- ({\dx*-3.5200},{\dy*0.2632}) + -- ({\dx*-3.5000},{\dy*0.2701}) + -- ({\dx*-3.4800},{\dy*0.2782}) + -- ({\dx*-3.4600},{\dy*0.2877}) + -- ({\dx*-3.4400},{\dy*0.2987}) + -- ({\dx*-3.4200},{\dy*0.3114}) + -- ({\dx*-3.4000},{\dy*0.3259}) + -- ({\dx*-3.3800},{\dy*0.3425}) + -- ({\dx*-3.3600},{\dy*0.3617}) + -- ({\dx*-3.3400},{\dy*0.3837}) + -- ({\dx*-3.3200},{\dy*0.4091}) + -- ({\dx*-3.3000},{\dy*0.4385}) + -- ({\dx*-3.2800},{\dy*0.4729}) + -- ({\dx*-3.2600},{\dy*0.5133}) + -- ({\dx*-3.2400},{\dy*0.5613}) + -- ({\dx*-3.2200},{\dy*0.6189}) + -- ({\dx*-3.2000},{\dy*0.6891}) + -- ({\dx*-3.1800},{\dy*0.7759}) + -- ({\dx*-3.1600},{\dy*0.8858}) + -- ({\dx*-3.1400},{\dy*1.0286}) + -- ({\dx*-3.1200},{\dy*1.2209}) + -- ({\dx*-3.1000},{\dy*1.4923}) + -- ({\dx*-3.0800},{\dy*1.9024}) + -- ({\dx*-3.0600},{\dy*2.5901}) + -- ({\dx*-3.0400},{\dy*3.9720}) + -- ({\dx*-3.0200},{\dy*8.1315}) + -- ({\dx*-3.0050},{\dy*33.1259})} +\def\gammafive{({\dx*-4.9990},{\dy*-8.3476}) + -- ({\dx*-4.9800},{\dy*-0.4314}) + -- ({\dx*-4.9600},{\dy*-0.2236}) + -- ({\dx*-4.9400},{\dy*-0.1547}) + -- ({\dx*-4.9200},{\dy*-0.1206}) + -- ({\dx*-4.9000},{\dy*-0.1004}) + -- ({\dx*-4.8800},{\dy*-0.0872}) + -- ({\dx*-4.8600},{\dy*-0.0779}) + -- ({\dx*-4.8400},{\dy*-0.0712}) + -- ({\dx*-4.8200},{\dy*-0.0662}) + -- ({\dx*-4.8000},{\dy*-0.0624}) + -- ({\dx*-4.7800},{\dy*-0.0595}) + -- ({\dx*-4.7600},{\dy*-0.0573}) + -- ({\dx*-4.7400},{\dy*-0.0556}) + -- ({\dx*-4.7200},{\dy*-0.0544}) + -- ({\dx*-4.7000},{\dy*-0.0535}) + -- ({\dx*-4.6800},{\dy*-0.0530}) + -- ({\dx*-4.6600},{\dy*-0.0528}) + -- ({\dx*-4.6400},{\dy*-0.0528}) + -- ({\dx*-4.6200},{\dy*-0.0531}) + -- ({\dx*-4.6000},{\dy*-0.0537}) + -- ({\dx*-4.5800},{\dy*-0.0544}) + -- ({\dx*-4.5600},{\dy*-0.0555}) + -- ({\dx*-4.5400},{\dy*-0.0567}) + -- ({\dx*-4.5200},{\dy*-0.0582}) + -- ({\dx*-4.5000},{\dy*-0.0600}) + -- ({\dx*-4.4800},{\dy*-0.0621}) + -- ({\dx*-4.4600},{\dy*-0.0645}) + -- ({\dx*-4.4400},{\dy*-0.0673}) + -- ({\dx*-4.4200},{\dy*-0.0704}) + -- ({\dx*-4.4000},{\dy*-0.0741}) + -- ({\dx*-4.3800},{\dy*-0.0782}) + -- ({\dx*-4.3600},{\dy*-0.0830}) + -- ({\dx*-4.3400},{\dy*-0.0884}) + -- ({\dx*-4.3200},{\dy*-0.0947}) + -- ({\dx*-4.3000},{\dy*-0.1020}) + -- ({\dx*-4.2800},{\dy*-0.1105}) + -- ({\dx*-4.2600},{\dy*-0.1205}) + -- ({\dx*-4.2400},{\dy*-0.1324}) + -- ({\dx*-4.2200},{\dy*-0.1467}) + -- ({\dx*-4.2000},{\dy*-0.1641}) + -- ({\dx*-4.1800},{\dy*-0.1856}) + -- ({\dx*-4.1600},{\dy*-0.2129}) + -- ({\dx*-4.1400},{\dy*-0.2485}) + -- ({\dx*-4.1200},{\dy*-0.2963}) + -- ({\dx*-4.1000},{\dy*-0.3640}) + -- ({\dx*-4.0800},{\dy*-0.4663}) + -- ({\dx*-4.0600},{\dy*-0.6380}) + -- ({\dx*-4.0400},{\dy*-0.9832}) + -- ({\dx*-4.0200},{\dy*-2.0228}) + -- ({\dx*-4.0010},{\dy*-41.6040})} +\def\gammasix{({\dx*-5.9998},{\dy*6.9470}) + -- ({\dx*-5.9800},{\dy*0.0721}) + -- ({\dx*-5.9600},{\dy*0.0375}) + -- ({\dx*-5.9400},{\dy*0.0260}) + -- ({\dx*-5.9200},{\dy*0.0204}) + -- ({\dx*-5.9000},{\dy*0.0170}) + -- ({\dx*-5.8800},{\dy*0.0148}) + -- ({\dx*-5.8600},{\dy*0.0133}) + -- ({\dx*-5.8400},{\dy*0.0122}) + -- ({\dx*-5.8200},{\dy*0.0114}) + -- ({\dx*-5.8000},{\dy*0.0108}) + -- ({\dx*-5.7800},{\dy*0.0103}) + -- ({\dx*-5.7600},{\dy*0.0099}) + -- ({\dx*-5.7400},{\dy*0.0097}) + -- ({\dx*-5.7200},{\dy*0.0095}) + -- ({\dx*-5.7000},{\dy*0.0094}) + -- ({\dx*-5.6800},{\dy*0.0093}) + -- ({\dx*-5.6600},{\dy*0.0093}) + -- ({\dx*-5.6400},{\dy*0.0094}) + -- ({\dx*-5.6200},{\dy*0.0095}) + -- ({\dx*-5.6000},{\dy*0.0096}) + -- ({\dx*-5.5800},{\dy*0.0098}) + -- ({\dx*-5.5600},{\dy*0.0100}) + -- ({\dx*-5.5400},{\dy*0.0102}) + -- ({\dx*-5.5200},{\dy*0.0105}) + -- ({\dx*-5.5000},{\dy*0.0109}) + -- ({\dx*-5.4800},{\dy*0.0113}) + -- ({\dx*-5.4600},{\dy*0.0118}) + -- ({\dx*-5.4400},{\dy*0.0124}) + -- ({\dx*-5.4200},{\dy*0.0130}) + -- ({\dx*-5.4000},{\dy*0.0137}) + -- ({\dx*-5.3800},{\dy*0.0145}) + -- ({\dx*-5.3600},{\dy*0.0155}) + -- ({\dx*-5.3400},{\dy*0.0166}) + -- ({\dx*-5.3200},{\dy*0.0178}) + -- ({\dx*-5.3000},{\dy*0.0192}) + -- ({\dx*-5.2800},{\dy*0.0209}) + -- ({\dx*-5.2600},{\dy*0.0229}) + -- ({\dx*-5.2400},{\dy*0.0253}) + -- ({\dx*-5.2200},{\dy*0.0281}) + -- ({\dx*-5.2000},{\dy*0.0316}) + -- ({\dx*-5.1800},{\dy*0.0358}) + -- ({\dx*-5.1600},{\dy*0.0413}) + -- ({\dx*-5.1400},{\dy*0.0483}) + -- ({\dx*-5.1200},{\dy*0.0579}) + -- ({\dx*-5.1000},{\dy*0.0714}) + -- ({\dx*-5.0800},{\dy*0.0918}) + -- ({\dx*-5.0600},{\dy*0.1261}) + -- ({\dx*-5.0400},{\dy*0.1951}) + -- ({\dx*-5.0200},{\dy*0.4029}) + -- ({\dx*-5.0002},{\dy*41.6525})} +\def\gammasinplus{({\dx*0.0190},{\dy*52.1325}) + -- ({\dx*0.0200},{\dy*49.5050}) + -- ({\dx*0.0400},{\dy*24.5863}) + -- ({\dx*0.0600},{\dy*16.3331}) + -- ({\dx*0.0800},{\dy*12.2453}) + -- ({\dx*0.1000},{\dy*9.8225}) + -- ({\dx*0.1200},{\dy*8.2314}) + -- ({\dx*0.1400},{\dy*7.1145}) + -- ({\dx*0.1600},{\dy*6.2930}) + -- ({\dx*0.1800},{\dy*5.6676}) + -- ({\dx*0.2000},{\dy*5.1786}) + -- ({\dx*0.2200},{\dy*4.7879}) + -- ({\dx*0.2400},{\dy*4.4701}) + -- ({\dx*0.2600},{\dy*4.2074}) + -- ({\dx*0.2800},{\dy*3.9874}) + -- ({\dx*0.3000},{\dy*3.8006}) + -- ({\dx*0.3200},{\dy*3.6401}) + -- ({\dx*0.3400},{\dy*3.5005}) + -- ({\dx*0.3600},{\dy*3.3776}) + -- ({\dx*0.3800},{\dy*3.2680}) + -- ({\dx*0.4000},{\dy*3.1692}) + -- ({\dx*0.4200},{\dy*3.0790}) + -- ({\dx*0.4400},{\dy*2.9955}) + -- ({\dx*0.4600},{\dy*2.9173}) + -- ({\dx*0.4800},{\dy*2.8433}) + -- ({\dx*0.5000},{\dy*2.7725}) + -- ({\dx*0.5200},{\dy*2.7039}) + -- ({\dx*0.5400},{\dy*2.6369}) + -- ({\dx*0.5600},{\dy*2.5709}) + -- ({\dx*0.5800},{\dy*2.5055}) + -- ({\dx*0.6000},{\dy*2.4402}) + -- ({\dx*0.6200},{\dy*2.3748}) + -- ({\dx*0.6400},{\dy*2.3090}) + -- ({\dx*0.6600},{\dy*2.2425}) + -- ({\dx*0.6800},{\dy*2.1752}) + -- ({\dx*0.7000},{\dy*2.1071}) + -- ({\dx*0.7200},{\dy*2.0380}) + -- ({\dx*0.7400},{\dy*1.9679}) + -- ({\dx*0.7600},{\dy*1.8969}) + -- ({\dx*0.7800},{\dy*1.8249}) + -- ({\dx*0.8000},{\dy*1.7520}) + -- ({\dx*0.8200},{\dy*1.6783}) + -- ({\dx*0.8400},{\dy*1.6039}) + -- ({\dx*0.8600},{\dy*1.5289}) + -- ({\dx*0.8800},{\dy*1.4534}) + -- ({\dx*0.9000},{\dy*1.3776}) + -- ({\dx*0.9200},{\dy*1.3017}) + -- ({\dx*0.9400},{\dy*1.2258}) + -- ({\dx*0.9600},{\dy*1.1501}) + -- ({\dx*0.9800},{\dy*1.0747}) + -- ({\dx*1.0000},{\dy*1.0000}) + -- ({\dx*1.0200},{\dy*0.9261}) + -- ({\dx*1.0400},{\dy*0.8531}) + -- ({\dx*1.0600},{\dy*0.7814}) + -- ({\dx*1.0800},{\dy*0.7110}) + -- ({\dx*1.1000},{\dy*0.6423}) + -- ({\dx*1.1200},{\dy*0.5755}) + -- ({\dx*1.1400},{\dy*0.5106}) + -- ({\dx*1.1600},{\dy*0.4480}) + -- ({\dx*1.1800},{\dy*0.3879}) + -- ({\dx*1.2000},{\dy*0.3304}) + -- ({\dx*1.2200},{\dy*0.2757}) + -- ({\dx*1.2400},{\dy*0.2240}) + -- ({\dx*1.2600},{\dy*0.1754}) + -- ({\dx*1.2800},{\dy*0.1302}) + -- ({\dx*1.3000},{\dy*0.0885}) + -- ({\dx*1.3200},{\dy*0.0503}) + -- ({\dx*1.3400},{\dy*0.0159}) + -- ({\dx*1.3600},{\dy*-0.0146}) + -- ({\dx*1.3800},{\dy*-0.0412}) + -- ({\dx*1.4000},{\dy*-0.0638}) + -- ({\dx*1.4200},{\dy*-0.0822}) + -- ({\dx*1.4400},{\dy*-0.0965}) + -- ({\dx*1.4600},{\dy*-0.1065}) + -- ({\dx*1.4800},{\dy*-0.1123}) + -- ({\dx*1.5000},{\dy*-0.1138}) + -- ({\dx*1.5200},{\dy*-0.1110}) + -- ({\dx*1.5400},{\dy*-0.1039}) + -- ({\dx*1.5600},{\dy*-0.0926}) + -- ({\dx*1.5800},{\dy*-0.0772}) + -- ({\dx*1.6000},{\dy*-0.0575}) + -- ({\dx*1.6200},{\dy*-0.0339}) + -- ({\dx*1.6400},{\dy*-0.0062}) + -- ({\dx*1.6600},{\dy*0.0254}) + -- ({\dx*1.6800},{\dy*0.0607}) + -- ({\dx*1.7000},{\dy*0.0996}) + -- ({\dx*1.7200},{\dy*0.1421}) + -- ({\dx*1.7400},{\dy*0.1879}) + -- ({\dx*1.7600},{\dy*0.2368}) + -- ({\dx*1.7800},{\dy*0.2888}) + -- ({\dx*1.8000},{\dy*0.3436}) + -- ({\dx*1.8200},{\dy*0.4010}) + -- ({\dx*1.8400},{\dy*0.4609}) + -- ({\dx*1.8600},{\dy*0.5229}) + -- ({\dx*1.8800},{\dy*0.5869}) + -- ({\dx*1.9000},{\dy*0.6527}) + -- ({\dx*1.9200},{\dy*0.7201}) + -- ({\dx*1.9400},{\dy*0.7887}) + -- ({\dx*1.9600},{\dy*0.8584}) + -- ({\dx*1.9800},{\dy*0.9289}) + -- ({\dx*2.0000},{\dy*1.0000}) + -- ({\dx*2.0200},{\dy*1.0714}) + -- ({\dx*2.0400},{\dy*1.1429}) + -- ({\dx*2.0600},{\dy*1.2142}) + -- ({\dx*2.0800},{\dy*1.2852}) + -- ({\dx*2.1000},{\dy*1.3555}) + -- ({\dx*2.1200},{\dy*1.4249}) + -- ({\dx*2.1400},{\dy*1.4933}) + -- ({\dx*2.1600},{\dy*1.5603}) + -- ({\dx*2.1800},{\dy*1.6258}) + -- ({\dx*2.2000},{\dy*1.6896}) + -- ({\dx*2.2200},{\dy*1.7514}) + -- ({\dx*2.2400},{\dy*1.8111}) + -- ({\dx*2.2600},{\dy*1.8685}) + -- ({\dx*2.2800},{\dy*1.9234}) + -- ({\dx*2.3000},{\dy*1.9757}) + -- ({\dx*2.3200},{\dy*2.0253}) + -- ({\dx*2.3400},{\dy*2.0719}) + -- ({\dx*2.3600},{\dy*2.1155}) + -- ({\dx*2.3800},{\dy*2.1560}) + -- ({\dx*2.4000},{\dy*2.1932}) + -- ({\dx*2.4200},{\dy*2.2272}) + -- ({\dx*2.4400},{\dy*2.2578}) + -- ({\dx*2.4600},{\dy*2.2851}) + -- ({\dx*2.4800},{\dy*2.3089}) + -- ({\dx*2.5000},{\dy*2.3293}) + -- ({\dx*2.5200},{\dy*2.3463}) + -- ({\dx*2.5400},{\dy*2.3599}) + -- ({\dx*2.5600},{\dy*2.3701}) + -- ({\dx*2.5800},{\dy*2.3770}) + -- ({\dx*2.6000},{\dy*2.3807}) + -- ({\dx*2.6200},{\dy*2.3812}) + -- ({\dx*2.6400},{\dy*2.3786}) + -- ({\dx*2.6600},{\dy*2.3731}) + -- ({\dx*2.6800},{\dy*2.3647}) + -- ({\dx*2.7000},{\dy*2.3537}) + -- ({\dx*2.7200},{\dy*2.3402}) + -- ({\dx*2.7400},{\dy*2.3242}) + -- ({\dx*2.7600},{\dy*2.3062}) + -- ({\dx*2.7800},{\dy*2.2861}) + -- ({\dx*2.8000},{\dy*2.2643}) + -- ({\dx*2.8200},{\dy*2.2409}) + -- ({\dx*2.8400},{\dy*2.2162}) + -- ({\dx*2.8600},{\dy*2.1903}) + -- ({\dx*2.8800},{\dy*2.1637}) + -- ({\dx*2.9000},{\dy*2.1364}) + -- ({\dx*2.9200},{\dy*2.1087}) + -- ({\dx*2.9400},{\dy*2.0810}) + -- ({\dx*2.9600},{\dy*2.0535}) + -- ({\dx*2.9800},{\dy*2.0264}) + -- ({\dx*3.0000},{\dy*2.0000}) + -- ({\dx*3.0200},{\dy*1.9746}) + -- ({\dx*3.0400},{\dy*1.9505}) + -- ({\dx*3.0600},{\dy*1.9280}) + -- ({\dx*3.0800},{\dy*1.9072}) + -- ({\dx*3.1000},{\dy*1.8886}) + -- ({\dx*3.1200},{\dy*1.8723}) + -- ({\dx*3.1400},{\dy*1.8587}) + -- ({\dx*3.1600},{\dy*1.8480}) + -- ({\dx*3.1800},{\dy*1.8404}) + -- ({\dx*3.2000},{\dy*1.8362}) + -- ({\dx*3.2200},{\dy*1.8356}) + -- ({\dx*3.2400},{\dy*1.8390}) + -- ({\dx*3.2600},{\dy*1.8464}) + -- ({\dx*3.2800},{\dy*1.8581}) + -- ({\dx*3.3000},{\dy*1.8744}) + -- ({\dx*3.3200},{\dy*1.8954}) + -- ({\dx*3.3400},{\dy*1.9213}) + -- ({\dx*3.3600},{\dy*1.9523}) + -- ({\dx*3.3800},{\dy*1.9885}) + -- ({\dx*3.4000},{\dy*2.0301}) + -- ({\dx*3.4200},{\dy*2.0773}) + -- ({\dx*3.4400},{\dy*2.1301}) + -- ({\dx*3.4600},{\dy*2.1886}) + -- ({\dx*3.4800},{\dy*2.2530}) + -- ({\dx*3.5000},{\dy*2.3234}) + -- ({\dx*3.5200},{\dy*2.3997}) + -- ({\dx*3.5400},{\dy*2.4821}) + -- ({\dx*3.5600},{\dy*2.5706}) + -- ({\dx*3.5800},{\dy*2.6652}) + -- ({\dx*3.6000},{\dy*2.7660}) + -- ({\dx*3.6200},{\dy*2.8729}) + -- ({\dx*3.6400},{\dy*2.9859}) + -- ({\dx*3.6600},{\dy*3.1051}) + -- ({\dx*3.6800},{\dy*3.2303}) + -- ({\dx*3.7000},{\dy*3.3616}) + -- ({\dx*3.7200},{\dy*3.4989}) + -- ({\dx*3.7400},{\dy*3.6421}) + -- ({\dx*3.7600},{\dy*3.7911}) + -- ({\dx*3.7800},{\dy*3.9459}) + -- ({\dx*3.8000},{\dy*4.1064}) + -- ({\dx*3.8200},{\dy*4.2724}) + -- ({\dx*3.8400},{\dy*4.4440}) + -- ({\dx*3.8600},{\dy*4.6209}) + -- ({\dx*3.8800},{\dy*4.8030}) + -- ({\dx*3.9000},{\dy*4.9903}) + -- ({\dx*3.9200},{\dy*5.1826}) + -- ({\dx*3.9400},{\dy*5.3799}) + -- ({\dx*3.9600},{\dy*5.5819}) + -- ({\dx*3.9800},{\dy*5.7887}) + -- ({\dx*4.0000},{\dy*6.0000}) + -- ({\dx*4.0200},{\dy*6.2158}) + -- ({\dx*4.0400},{\dy*6.4359}) + -- ({\dx*4.0600},{\dy*6.6603}) + -- ({\dx*4.0800},{\dy*6.8889}) + -- ({\dx*4.0810},{\dy*6.9005})} +\def\gammasinone{({\dx*-0.9810},{\dy*-53.1410}) + -- ({\dx*-0.9800},{\dy*-50.5140}) + -- ({\dx*-0.9600},{\dy*-25.6055}) + -- ({\dx*-0.9400},{\dy*-17.3637}) + -- ({\dx*-0.9200},{\dy*-13.2884}) + -- ({\dx*-0.9000},{\dy*-10.8796}) + -- ({\dx*-0.8800},{\dy*-9.3036}) + -- ({\dx*-0.8600},{\dy*-8.2033}) + -- ({\dx*-0.8400},{\dy*-7.3999}) + -- ({\dx*-0.8200},{\dy*-6.7941}) + -- ({\dx*-0.8000},{\dy*-6.3263}) + -- ({\dx*-0.7800},{\dy*-5.9586}) + -- ({\dx*-0.7600},{\dy*-5.6655}) + -- ({\dx*-0.7400},{\dy*-5.4296}) + -- ({\dx*-0.7200},{\dy*-5.2384}) + -- ({\dx*-0.7000},{\dy*-5.0827}) + -- ({\dx*-0.6800},{\dy*-4.9557}) + -- ({\dx*-0.6600},{\dy*-4.8523}) + -- ({\dx*-0.6400},{\dy*-4.7685}) + -- ({\dx*-0.6200},{\dy*-4.7012}) + -- ({\dx*-0.6000},{\dy*-4.6480}) + -- ({\dx*-0.5800},{\dy*-4.6072}) + -- ({\dx*-0.5600},{\dy*-4.5773}) + -- ({\dx*-0.5400},{\dy*-4.5573}) + -- ({\dx*-0.5200},{\dy*-4.5467}) + -- ({\dx*-0.5000},{\dy*-4.5449}) + -- ({\dx*-0.4800},{\dy*-4.5519}) + -- ({\dx*-0.4600},{\dy*-4.5677}) + -- ({\dx*-0.4400},{\dy*-4.5928}) + -- ({\dx*-0.4200},{\dy*-4.6279}) + -- ({\dx*-0.4000},{\dy*-4.6740}) + -- ({\dx*-0.3800},{\dy*-4.7325}) + -- ({\dx*-0.3600},{\dy*-4.8052}) + -- ({\dx*-0.3400},{\dy*-4.8944}) + -- ({\dx*-0.3200},{\dy*-5.0033}) + -- ({\dx*-0.3000},{\dy*-5.1359}) + -- ({\dx*-0.2800},{\dy*-5.2972}) + -- ({\dx*-0.2600},{\dy*-5.4942}) + -- ({\dx*-0.2400},{\dy*-5.7359}) + -- ({\dx*-0.2200},{\dy*-6.0350}) + -- ({\dx*-0.2000},{\dy*-6.4089}) + -- ({\dx*-0.1800},{\dy*-6.8830}) + -- ({\dx*-0.1600},{\dy*-7.4952}) + -- ({\dx*-0.1400},{\dy*-8.3052}) + -- ({\dx*-0.1200},{\dy*-9.4124}) + -- ({\dx*-0.1000},{\dy*-10.9953}) + -- ({\dx*-0.0800},{\dy*-13.4114}) + -- ({\dx*-0.0600},{\dy*-17.4941}) + -- ({\dx*-0.0400},{\dy*-25.7436}) + -- ({\dx*-0.0200},{\dy*-50.6602}) + -- ({\dx*-0.0190},{\dy*-53.2876})} +\def\gammasintwo{({\dx*-1.9810},{\dy*26.8549}) + -- ({\dx*-1.9800},{\dy*25.5432}) + -- ({\dx*-1.9600},{\dy*13.1254}) + -- ({\dx*-1.9400},{\dy*9.0411}) + -- ({\dx*-1.9200},{\dy*7.0402}) + -- ({\dx*-1.9000},{\dy*5.8725}) + -- ({\dx*-1.8800},{\dy*5.1211}) + -- ({\dx*-1.8600},{\dy*4.6073}) + -- ({\dx*-1.8400},{\dy*4.2416}) + -- ({\dx*-1.8200},{\dy*3.9745}) + -- ({\dx*-1.8000},{\dy*3.7759}) + -- ({\dx*-1.7800},{\dy*3.6268}) + -- ({\dx*-1.7600},{\dy*3.5146}) + -- ({\dx*-1.7400},{\dy*3.4305}) + -- ({\dx*-1.7200},{\dy*3.3681}) + -- ({\dx*-1.7000},{\dy*3.3229}) + -- ({\dx*-1.6800},{\dy*3.2916}) + -- ({\dx*-1.6600},{\dy*3.2715}) + -- ({\dx*-1.6400},{\dy*3.2607}) + -- ({\dx*-1.6200},{\dy*3.2578}) + -- ({\dx*-1.6000},{\dy*3.2616}) + -- ({\dx*-1.5800},{\dy*3.2715}) + -- ({\dx*-1.5600},{\dy*3.2868}) + -- ({\dx*-1.5400},{\dy*3.3072}) + -- ({\dx*-1.5200},{\dy*3.3327}) + -- ({\dx*-1.5000},{\dy*3.3633}) + -- ({\dx*-1.4800},{\dy*3.3993}) + -- ({\dx*-1.4600},{\dy*3.4412}) + -- ({\dx*-1.4400},{\dy*3.4896}) + -- ({\dx*-1.4200},{\dy*3.5456}) + -- ({\dx*-1.4000},{\dy*3.6103}) + -- ({\dx*-1.3800},{\dy*3.6854}) + -- ({\dx*-1.3600},{\dy*3.7727}) + -- ({\dx*-1.3400},{\dy*3.8749}) + -- ({\dx*-1.3200},{\dy*3.9951}) + -- ({\dx*-1.3000},{\dy*4.1374}) + -- ({\dx*-1.2800},{\dy*4.3070}) + -- ({\dx*-1.2600},{\dy*4.5109}) + -- ({\dx*-1.2400},{\dy*4.7583}) + -- ({\dx*-1.2200},{\dy*5.0617}) + -- ({\dx*-1.2000},{\dy*5.4387}) + -- ({\dx*-1.1800},{\dy*5.9148}) + -- ({\dx*-1.1600},{\dy*6.5279}) + -- ({\dx*-1.1400},{\dy*7.3376}) + -- ({\dx*-1.1200},{\dy*8.4433}) + -- ({\dx*-1.1000},{\dy*10.0238}) + -- ({\dx*-1.0800},{\dy*12.4364}) + -- ({\dx*-1.0600},{\dy*16.5145}) + -- ({\dx*-1.0400},{\dy*24.7583}) + -- ({\dx*-1.0200},{\dy*49.6681}) + -- ({\dx*-1.0190},{\dy*52.2951})} +\def\gammasinthree{({\dx*-2.9810},{\dy*-9.0483}) + -- ({\dx*-2.9800},{\dy*-8.6133}) + -- ({\dx*-2.9600},{\dy*-4.5173}) + -- ({\dx*-2.9400},{\dy*-3.1989}) + -- ({\dx*-2.9200},{\dy*-2.5746}) + -- ({\dx*-2.9000},{\dy*-2.2274}) + -- ({\dx*-2.8800},{\dy*-2.0184}) + -- ({\dx*-2.8600},{\dy*-1.8878}) + -- ({\dx*-2.8400},{\dy*-1.8057}) + -- ({\dx*-2.8200},{\dy*-1.7552}) + -- ({\dx*-2.8000},{\dy*-1.7264}) + -- ({\dx*-2.7800},{\dy*-1.7127}) + -- ({\dx*-2.7600},{\dy*-1.7099}) + -- ({\dx*-2.7400},{\dy*-1.7149}) + -- ({\dx*-2.7200},{\dy*-1.7255}) + -- ({\dx*-2.7000},{\dy*-1.7401}) + -- ({\dx*-2.6800},{\dy*-1.7575}) + -- ({\dx*-2.6600},{\dy*-1.7768}) + -- ({\dx*-2.6400},{\dy*-1.7972}) + -- ({\dx*-2.6200},{\dy*-1.8183}) + -- ({\dx*-2.6000},{\dy*-1.8397}) + -- ({\dx*-2.5800},{\dy*-1.8612}) + -- ({\dx*-2.5600},{\dy*-1.8825}) + -- ({\dx*-2.5400},{\dy*-1.9036}) + -- ({\dx*-2.5200},{\dy*-1.9245}) + -- ({\dx*-2.5000},{\dy*-1.9453}) + -- ({\dx*-2.4800},{\dy*-1.9663}) + -- ({\dx*-2.4600},{\dy*-1.9877}) + -- ({\dx*-2.4400},{\dy*-2.0099}) + -- ({\dx*-2.4200},{\dy*-2.0335}) + -- ({\dx*-2.4000},{\dy*-2.0591}) + -- ({\dx*-2.3800},{\dy*-2.0876}) + -- ({\dx*-2.3600},{\dy*-2.1200}) + -- ({\dx*-2.3400},{\dy*-2.1578}) + -- ({\dx*-2.3200},{\dy*-2.2024}) + -- ({\dx*-2.3000},{\dy*-2.2561}) + -- ({\dx*-2.2800},{\dy*-2.3216}) + -- ({\dx*-2.2600},{\dy*-2.4024}) + -- ({\dx*-2.2400},{\dy*-2.5032}) + -- ({\dx*-2.2200},{\dy*-2.6303}) + -- ({\dx*-2.2000},{\dy*-2.7928}) + -- ({\dx*-2.1800},{\dy*-3.0032}) + -- ({\dx*-2.1600},{\dy*-3.2809}) + -- ({\dx*-2.1400},{\dy*-3.6556}) + -- ({\dx*-2.1200},{\dy*-4.1772}) + -- ({\dx*-2.1000},{\dy*-4.9351}) + -- ({\dx*-2.0800},{\dy*-6.1082}) + -- ({\dx*-2.0600},{\dy*-8.1132}) + -- ({\dx*-2.0400},{\dy*-12.2003}) + -- ({\dx*-2.0200},{\dy*-24.6199}) + -- ({\dx*-2.0190},{\dy*-25.9316})} +\def\gammasinfour{({\dx*-3.9950},{\dy*8.4124}) + -- ({\dx*-3.9800},{\dy*2.2112}) + -- ({\dx*-3.9600},{\dy*1.2344}) + -- ({\dx*-3.9400},{\dy*0.9517}) + -- ({\dx*-3.9200},{\dy*0.8420}) + -- ({\dx*-3.9000},{\dy*0.8009}) + -- ({\dx*-3.8800},{\dy*0.7935}) + -- ({\dx*-3.8600},{\dy*0.8045}) + -- ({\dx*-3.8400},{\dy*0.8265}) + -- ({\dx*-3.8200},{\dy*0.8550}) + -- ({\dx*-3.8000},{\dy*0.8874}) + -- ({\dx*-3.7800},{\dy*0.9219}) + -- ({\dx*-3.7600},{\dy*0.9573}) + -- ({\dx*-3.7400},{\dy*0.9926}) + -- ({\dx*-3.7200},{\dy*1.0272}) + -- ({\dx*-3.7000},{\dy*1.0607}) + -- ({\dx*-3.6800},{\dy*1.0925}) + -- ({\dx*-3.6600},{\dy*1.1223}) + -- ({\dx*-3.6400},{\dy*1.1500}) + -- ({\dx*-3.6200},{\dy*1.1752}) + -- ({\dx*-3.6000},{\dy*1.1979}) + -- ({\dx*-3.5800},{\dy*1.2179}) + -- ({\dx*-3.5600},{\dy*1.2351}) + -- ({\dx*-3.5400},{\dy*1.2496}) + -- ({\dx*-3.5200},{\dy*1.2612}) + -- ({\dx*-3.5000},{\dy*1.2701}) + -- ({\dx*-3.4800},{\dy*1.2763}) + -- ({\dx*-3.4600},{\dy*1.2798}) + -- ({\dx*-3.4400},{\dy*1.2810}) + -- ({\dx*-3.4200},{\dy*1.2800}) + -- ({\dx*-3.4000},{\dy*1.2769}) + -- ({\dx*-3.3800},{\dy*1.2723}) + -- ({\dx*-3.3600},{\dy*1.2665}) + -- ({\dx*-3.3400},{\dy*1.2600}) + -- ({\dx*-3.3200},{\dy*1.2534}) + -- ({\dx*-3.3000},{\dy*1.2475}) + -- ({\dx*-3.2800},{\dy*1.2434}) + -- ({\dx*-3.2600},{\dy*1.2423}) + -- ({\dx*-3.2400},{\dy*1.2458}) + -- ({\dx*-3.2200},{\dy*1.2563}) + -- ({\dx*-3.2000},{\dy*1.2768}) + -- ({\dx*-3.1800},{\dy*1.3117}) + -- ({\dx*-3.1600},{\dy*1.3676}) + -- ({\dx*-3.1400},{\dy*1.4544}) + -- ({\dx*-3.1200},{\dy*1.5890}) + -- ({\dx*-3.1000},{\dy*1.8013}) + -- ({\dx*-3.0800},{\dy*2.1511}) + -- ({\dx*-3.0600},{\dy*2.7775}) + -- ({\dx*-3.0400},{\dy*4.0974}) + -- ({\dx*-3.0200},{\dy*8.1943}) + -- ({\dx*-3.0050},{\dy*33.1416})} +\def\gammasinfive{({\dx*-4.9990},{\dy*-8.3507}) + -- ({\dx*-4.9800},{\dy*-0.4942}) + -- ({\dx*-4.9600},{\dy*-0.3489}) + -- ({\dx*-4.9400},{\dy*-0.3421}) + -- ({\dx*-4.9200},{\dy*-0.3693}) + -- ({\dx*-4.9000},{\dy*-0.4094}) + -- ({\dx*-4.8800},{\dy*-0.4553}) + -- ({\dx*-4.8600},{\dy*-0.5037}) + -- ({\dx*-4.8400},{\dy*-0.5530}) + -- ({\dx*-4.8200},{\dy*-0.6021}) + -- ({\dx*-4.8000},{\dy*-0.6502}) + -- ({\dx*-4.7800},{\dy*-0.6969}) + -- ({\dx*-4.7600},{\dy*-0.7418}) + -- ({\dx*-4.7400},{\dy*-0.7846}) + -- ({\dx*-4.7200},{\dy*-0.8249}) + -- ({\dx*-4.7000},{\dy*-0.8626}) + -- ({\dx*-4.6800},{\dy*-0.8973}) + -- ({\dx*-4.6600},{\dy*-0.9291}) + -- ({\dx*-4.6400},{\dy*-0.9577}) + -- ({\dx*-4.6200},{\dy*-0.9829}) + -- ({\dx*-4.6000},{\dy*-1.0047}) + -- ({\dx*-4.5800},{\dy*-1.0230}) + -- ({\dx*-4.5600},{\dy*-1.0377}) + -- ({\dx*-4.5400},{\dy*-1.0488}) + -- ({\dx*-4.5200},{\dy*-1.0563}) + -- ({\dx*-4.5000},{\dy*-1.0600}) + -- ({\dx*-4.4800},{\dy*-1.0601}) + -- ({\dx*-4.4600},{\dy*-1.0566}) + -- ({\dx*-4.4400},{\dy*-1.0496}) + -- ({\dx*-4.4200},{\dy*-1.0390}) + -- ({\dx*-4.4000},{\dy*-1.0251}) + -- ({\dx*-4.3800},{\dy*-1.0080}) + -- ({\dx*-4.3600},{\dy*-0.9878}) + -- ({\dx*-4.3400},{\dy*-0.9647}) + -- ({\dx*-4.3200},{\dy*-0.9390}) + -- ({\dx*-4.3000},{\dy*-0.9110}) + -- ({\dx*-4.2800},{\dy*-0.8810}) + -- ({\dx*-4.2600},{\dy*-0.8495}) + -- ({\dx*-4.2400},{\dy*-0.8169}) + -- ({\dx*-4.2200},{\dy*-0.7841}) + -- ({\dx*-4.2000},{\dy*-0.7518}) + -- ({\dx*-4.1800},{\dy*-0.7215}) + -- ({\dx*-4.1600},{\dy*-0.6947}) + -- ({\dx*-4.1400},{\dy*-0.6742}) + -- ({\dx*-4.1200},{\dy*-0.6644}) + -- ({\dx*-4.1000},{\dy*-0.6730}) + -- ({\dx*-4.0800},{\dy*-0.7150}) + -- ({\dx*-4.0600},{\dy*-0.8253}) + -- ({\dx*-4.0400},{\dy*-1.1085}) + -- ({\dx*-4.0200},{\dy*-2.0855}) + -- ({\dx*-4.0010},{\dy*-41.6072})} +\def\gammasinsix{({\dx*-5.9998},{\dy*6.9477}) + -- ({\dx*-5.9800},{\dy*0.1349}) + -- ({\dx*-5.9600},{\dy*0.1629}) + -- ({\dx*-5.9400},{\dy*0.2134}) + -- ({\dx*-5.9200},{\dy*0.2691}) + -- ({\dx*-5.9000},{\dy*0.3260}) + -- ({\dx*-5.8800},{\dy*0.3829}) + -- ({\dx*-5.8600},{\dy*0.4391}) + -- ({\dx*-5.8400},{\dy*0.4940}) + -- ({\dx*-5.8200},{\dy*0.5472}) + -- ({\dx*-5.8000},{\dy*0.5985}) + -- ({\dx*-5.7800},{\dy*0.6477}) + -- ({\dx*-5.7600},{\dy*0.6945}) + -- ({\dx*-5.7400},{\dy*0.7387}) + -- ({\dx*-5.7200},{\dy*0.7800}) + -- ({\dx*-5.7000},{\dy*0.8184}) + -- ({\dx*-5.6800},{\dy*0.8537}) + -- ({\dx*-5.6600},{\dy*0.8856}) + -- ({\dx*-5.6400},{\dy*0.9142}) + -- ({\dx*-5.6200},{\dy*0.9392}) + -- ({\dx*-5.6000},{\dy*0.9606}) + -- ({\dx*-5.5800},{\dy*0.9783}) + -- ({\dx*-5.5600},{\dy*0.9923}) + -- ({\dx*-5.5400},{\dy*1.0024}) + -- ({\dx*-5.5200},{\dy*1.0086}) + -- ({\dx*-5.5000},{\dy*1.0109}) + -- ({\dx*-5.4800},{\dy*1.0094}) + -- ({\dx*-5.4600},{\dy*1.0039}) + -- ({\dx*-5.4400},{\dy*0.9947}) + -- ({\dx*-5.4200},{\dy*0.9816}) + -- ({\dx*-5.4000},{\dy*0.9648}) + -- ({\dx*-5.3800},{\dy*0.9443}) + -- ({\dx*-5.3600},{\dy*0.9203}) + -- ({\dx*-5.3400},{\dy*0.8929}) + -- ({\dx*-5.3200},{\dy*0.8621}) + -- ({\dx*-5.3000},{\dy*0.8283}) + -- ({\dx*-5.2800},{\dy*0.7914}) + -- ({\dx*-5.2600},{\dy*0.7519}) + -- ({\dx*-5.2400},{\dy*0.7098}) + -- ({\dx*-5.2200},{\dy*0.6655}) + -- ({\dx*-5.2000},{\dy*0.6193}) + -- ({\dx*-5.1800},{\dy*0.5717}) + -- ({\dx*-5.1600},{\dy*0.5230}) + -- ({\dx*-5.1400},{\dy*0.4741}) + -- ({\dx*-5.1200},{\dy*0.4260}) + -- ({\dx*-5.1000},{\dy*0.3804}) + -- ({\dx*-5.0800},{\dy*0.3405}) + -- ({\dx*-5.0600},{\dy*0.3135}) + -- ({\dx*-5.0400},{\dy*0.3204}) + -- ({\dx*-5.0200},{\dy*0.4657}) + -- ({\dx*-5.0002},{\dy*41.6531})} diff --git a/buch/papers/laguerre/images/gammaplot.tex b/buch/papers/laguerre/images/gammaplot.tex new file mode 100644 index 0000000..5a68f0a --- /dev/null +++ b/buch/papers/laguerre/images/gammaplot.tex @@ -0,0 +1,73 @@ +% +% gammaplot.tex -- template for standalon tikz images +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\documentclass[tikz]{standalone} +\usepackage{amsmath} +\usepackage{times} +\usepackage{txfonts} +\usepackage{pgfplots} +\usepackage{csvsimple} +\usetikzlibrary{arrows,intersections,math} +\input{gammapaths.tex} +\begin{document} +\def\skala{1} +\begin{tikzpicture}[>=latex,thick,scale=\skala] + +\definecolor{mainColor}{HTML}{D72864} % OST pink + +\draw[->] (-6.1,0) -- (5.3,0) coordinate[label={$z$}]; +\draw[->] (0,-5.1) -- (0,6.4) coordinate[label={right:$\Gamma(z)$}]; + +\foreach \x in {-1,-2,-3,-4,-5,-6}{ + \draw (\x,-0.1) -- (\x,0.1); + \draw[line width=0.1pt] (\x,-5) -- (\x,6.2); +} +\foreach \x in {1,2,3,4,5}{ + \draw (\x,-0.1) -- (\x,0.1); + \node at (\x,0) [below] {$\x$}; +} +\foreach \y in {-5,-4,-3,-2,-1,1,2,3,4,5,6}{ + \draw (-0.1,\y) -- (0.1,\y); +} +\foreach \y in {1,2,3,4,5,6}{ + \node at (0,\y) [left] {$\y$}; +} +\foreach \y in {-1,-2,-3,-4,-5}{ + \node at (0,\y) [right] {$\y$}; +} +\foreach \x in {-1,-3,-5}{ + \node at (\x,0) [below left] {$\x$}; +} +\foreach \x in {-2,-4,-6}{ + \node at (\x,0) [above left] {$\x$}; +} + +\def\dx{1} +\def\dy{1} + +\begin{scope} +\clip (-6.1,-5) rectangle (4.3,6.2); + +% \draw[color=darkgreen,line width=1.4pt] \gammasinplus; +% \draw[color=darkgreen,line width=1.4pt] \gammasinone; +% \draw[color=darkgreen,line width=1.4pt] \gammasintwo; +% \draw[color=darkgreen,line width=1.4pt] \gammasinthree; +% \draw[color=darkgreen,line width=1.4pt] \gammasinfour; +% \draw[color=darkgreen,line width=1.4pt] \gammasinfive; +% \draw[color=darkgreen,line width=1.4pt] \gammasinsix; + +\draw[color=mainColor,line width=1.4pt] \gammaplus; +\draw[color=mainColor,line width=1.4pt] \gammaone; +\draw[color=mainColor,line width=1.4pt] \gammatwo; +\draw[color=mainColor,line width=1.4pt] \gammathree; +\draw[color=mainColor,line width=1.4pt] \gammafour; +\draw[color=mainColor,line width=1.4pt] \gammafive; +\draw[color=mainColor,line width=1.4pt] \gammasix; + +\end{scope} + +\end{tikzpicture} +\end{document} + diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 75858df..27519d8 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -8,7 +8,7 @@ Die Gauss-Quadratur ist ein numerisches Integrationsverfahren, welches die Eigenschaften von orthogonalen Polynomen ausnützt. Herleitungen und Analysen der Gauss-Quadratur können im -Abschnitt~\ref{buch:orthogonalitaet:section:gauss-quadratur} gefunden werden. +Abschnitt~\ref{buch:orthogonal:section:gauss-quadratur} gefunden werden. Als grundlegende Idee wird die Beobachtung, dass viele Funktionen sich gut mit Polynomen approximieren lassen, verwendet. -- cgit v1.2.1 From e694c3a02296d4a0b551ad0be3f980a91a0e05f2 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 19 Jul 2022 13:53:55 +0200 Subject: save --- buch/papers/fm/01_AM-FM.tex | 6 ++++++ buch/papers/fm/main.tex | 47 ++++++++++++++++++------------------------- buch/papers/fm/standalone.tex | 1 + 3 files changed, 27 insertions(+), 27 deletions(-) diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index a267322..f1c59a9 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -6,6 +6,12 @@ \section{AM - FM\label{fm:section:teil0}} \rhead{AM- FM} +Das sinusförmige Trägersignal hat die übliche Form: +\(x-c(t) = A_c \cdot cos(\omega_ct+\psi)\). +Wobei die konstanten Amplitude \(A_c\) und Phase \(\psi\) vom Nachrichtensignal \(m(t)\) verändert wird. +Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), +steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. +\newblockpunct TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index be66a2f..24c645f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -3,37 +3,30 @@ % % (c) 2020 Hochschule Rapperswil % -% !TeX root = buch.tex -%\begin {document} -\chapter{FM\label{chapter:fm}} + +\chapter{FM \(\with\)Bessel\label{chapter:fm}} \lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} -Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Frequenz Modulatrion (FM)(acronym?). - -%Mit hilfe einer Modulation kann ein Übertragungs Signal \(m(t)\) auf einen Trägerfrequenz \( f_c \) kombiniert werden. -%Das Ziel ist es dieses modulierte Signal dan im Empfangsspektrum wieder demodulieren und so informationen im Signal \( m(t) \)zu Übertragen. - -%Ein paar Hinweise für die korrekte Formatierung des Textes -%\begin{itemize} -%\item -%Absätze werden gebildet, indem man eine Leerzeile einfügt. -%Die Verwendung von \verb+\\+ ist nur in Tabellen und Arrays gestattet. -%\item -%Die explizite Platzierung von Bildern ist nicht erlaubt, entsprechende -%Optionen werden gelöscht. -%Verwenden Sie Labels und Verweise, um auf Bilder hinzuweisen. -%\item -%Beginnen Sie jeden Satz auf einer neuen Zeile. -%Damit ermöglichen Sie dem Versionsverwaltungssysteme, Änderungen -%in verschiedenen Sätzen von verschiedenen Autoren ohne Konflikt -%anzuwenden. -%\item -%Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren -%Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. -%\end{itemize} +Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. +Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, +dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. +Durch die Modulation wird ein Nachrichtensignal \(m(t)\) auf ein Trägersignal (z.B. ein Sinus- oder Rechtecksignal) abgebildet (kombiniert). +Durch dieses Auftragen vom Nachrichtensignal \(m(t)\) kann das modulierte Signal in einem gewünschten Frequenzbereich übertragen werden. +Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 HZ bis zur Bandbreite \(B_m\). +\newline +Beim Empfänger wird dann durch Demodulation das ursprüngliche Nachrichtensignal \(m(t)\) so originalgetreu wie möglich zurückgewonnen. +\newline +Beim Trägersignal \(x_c(t)\) handelt es sich um ein informationsloses Hilfssignal. +Durch die Modulation mit dem Nachrichtensignal \(m(t)\) wird es zum modulierten zu übertragenden Signal. +Für alle Erklärungen wird ein sinusförmiges Trägersignal benutzt, jedoch kann auch ein Rechtecksignal, +welches Digital einfach umzusetzten ist, +genauso als Trägersignal genutzt werden kann. +Zuerst wird erklärt was \textit{FM-AM} ist, danach wie sich diese im Frequenzspektrum verhalten. +Erst dann erklär ich dir wie die Besselfunktion mit der Frequenzmodulation( acro?) zusammenhängt. +Nun zur Modulation im nächsten Abschnitt. \input{papers/fm/01_AM-FM.tex} \input{papers/fm/02_frequenzyspectrum.tex} @@ -43,4 +36,4 @@ Dieser Abschnitt beschreibt die Beziehung von der Besselfunktion(Ref) zur Freque \printbibliography[heading=subbibliography] \end{refsection} -%\end {document} + diff --git a/buch/papers/fm/standalone.tex b/buch/papers/fm/standalone.tex index 51a5c8c..c161ed5 100644 --- a/buch/papers/fm/standalone.tex +++ b/buch/papers/fm/standalone.tex @@ -1,5 +1,6 @@ \documentclass{book} +\def\IncludeBookCover{0} \input{common/packages.tex} % additional packages used by the individual papers, add a line for -- cgit v1.2.1 From 6c23215c9ad1209bee5d1d2704579b4761341b71 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 19 Jul 2022 14:36:41 +0200 Subject: add gitignore --- buch/.gitignore | 19 +++++++++++++++++++ buch/papers/fm/.gitignore | 1 + buch/papers/fm/01_AM-FM.tex | 5 +++-- buch/papers/fm/Makefile | 6 +++--- buch/papers/fm/main.tex | 6 +++--- 5 files changed, 29 insertions(+), 8 deletions(-) create mode 100644 buch/.gitignore create mode 100644 buch/papers/fm/.gitignore diff --git a/buch/.gitignore b/buch/.gitignore new file mode 100644 index 0000000..86604da --- /dev/null +++ b/buch/.gitignore @@ -0,0 +1,19 @@ +*.aux +*.bbl +*.bib +*.blg +*.idx +*.ilg +*.ind +*.log +*.out +*.rpt +buch*.pdf +*.run.xml +*.toc +.build/ +*.synctex.gz +*.DS_Store + + +*.synctex(busy) \ No newline at end of file diff --git a/buch/papers/fm/.gitignore b/buch/papers/fm/.gitignore new file mode 100644 index 0000000..eae2913 --- /dev/null +++ b/buch/papers/fm/.gitignore @@ -0,0 +1 @@ +standalone \ No newline at end of file diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index f1c59a9..b9d6167 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,11 +7,12 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x-c(t) = A_c \cdot cos(\omega_ct+\psi)\). -Wobei die konstanten Amplitude \(A_c\) und Phase \(\psi\) vom Nachrichtensignal \(m(t)\) verändert wird. +\(x_c(t) = A_c \cdot cos(\omega_ct+\varphi)\). +Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. \newblockpunct + TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index fb42942..c84963f 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -7,16 +7,16 @@ SOURCES := \ 01_AM-FM.tex \ 02_frequenzyspectrum.tex \ - main.tex \ 03_bessel.tex \ - 04_fazit.tex + 04_fazit.tex \ + main.tex #TIKZFIGURES := \ tikz/atoms-grid-still.tex \ #FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) -.PHONY: images +#.PHONY: images #images: $(FIGURES) #figures/%.pdf: tikz/%.tex diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 24c645f..56a7ac5 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -4,18 +4,18 @@ % (c) 2020 Hochschule Rapperswil % -\chapter{FM \(\with\)Bessel\label{chapter:fm}} +\chapter{FM Bessel\label{chapter:fm}} \lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} - +%$\with$ Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. Durch die Modulation wird ein Nachrichtensignal \(m(t)\) auf ein Trägersignal (z.B. ein Sinus- oder Rechtecksignal) abgebildet (kombiniert). Durch dieses Auftragen vom Nachrichtensignal \(m(t)\) kann das modulierte Signal in einem gewünschten Frequenzbereich übertragen werden. -Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 HZ bis zur Bandbreite \(B_m\). +Der ursprünglich Frequenzbereich des Nachrichtensignal \(m(t)\) erstreckt sich typischerweise von 0 Hz bis zur Bandbreite \(B_m\). \newline Beim Empfänger wird dann durch Demodulation das ursprüngliche Nachrichtensignal \(m(t)\) so originalgetreu wie möglich zurückgewonnen. \newline -- cgit v1.2.1 From 2625b1234dd68a9cc3ce50675ac0b1cb80eca275 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Tue, 19 Jul 2022 16:31:48 +0200 Subject: Correct typos, improve grammar --- buch/papers/laguerre/definition.tex | 14 +++++---- buch/papers/laguerre/eigenschaften.tex | 37 +++++++---------------- buch/papers/laguerre/gamma.tex | 55 +++++++++++++++++++--------------- buch/papers/laguerre/main.tex | 14 +++++---- buch/papers/laguerre/quadratur.tex | 19 ++++++------ 5 files changed, 68 insertions(+), 71 deletions(-) diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index 42cd6f6..4729a93 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -15,16 +15,16 @@ x y''(x) + (\nu + 1 - x) y'(x) + n y(x) n \in \mathbb{N}_0 , \quad x \in \mathbb{R} -. \label{laguerre:dgl} +. \end{align} Spannenderweise wurde die verallgemeinerte Laguerre-Differentialgleichung zuerst von Yacovlevich Sonine (1849 - 1915) beschrieben, -aber auf Grund ihrer Ähnlichkeit wurde sie nach Laguerre benannt. +aber aufgrund ihrer Ähnlichkeit nach Laguerre benannt. Die klassische Laguerre-Diffentialgleichung erhält man, wenn $\nu = 0$. Hier wird die verallgemeinerte Laguerre-Differentialgleichung verwendet, -weil die Lösung mit der selben Methode berechnet werden kann, -aber man zusätzlich die Lösung für den allgmeinen Fall erhält. +weil die Lösung mit derselben Methode berechnet werden kann. +Zusätzlich erhält man aber die Lösung für den allgmeinen Fall. Zur Lösung von \eqref{laguerre:dgl} verwenden wir einen Potenzreihenansatz. Da wir bereits wissen, dass die Lösung orthogonale Polynome sind, @@ -47,7 +47,7 @@ y''(x) = \sum_{k=1}^\infty (k+1) k a_{k+1} x^{k-1} \end{align*} -in die Differentialgleichung ein, erhält man: +in die Differentialgleichung ein, erhält man \begin{align*} \sum_{k=1}^\infty (k+1) k a_{k+1} x^k + @@ -138,8 +138,10 @@ Differentialgleichung mit der Form \Xi_n(x) = L_n(x) \ln(x) + \sum_{k=1}^\infty d_k x^k +. \end{align*} -Nach einigen mühsamen Rechnungen, +Nach einigen aufwändigen Rechnungen, +% die am besten ein Computeralgebrasystem übernimmt, die den Rahmen dieses Kapitel sprengen würden, erhalten wir \begin{align*} diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 9b901ae..4adbe86 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -3,24 +3,11 @@ % % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % -% \section{Eigenschaften -% \label{laguerre:section:eigenschaften}} -% { -% \large \color{red} -% TODO: -% Evtl. nur Orthogonalität hier behandeln, da nur diese für die Gauss-Quadratur -% benötigt wird. -% } - -% Die Laguerre-Polynome besitzen einige interessante Eigenschaften -% \rhead{Eigenschaften} - -% \subsection{Orthogonalität -% \label{laguerre:subsection:orthogonal}} \section{Orthogonalität \label{laguerre:section:orthogonal}} -Im Abschnitt~\ref{laguerre:section:definition} haben wir behauptet, -dass die Laguerre-Polynome orthogonale Polynome sind. +Im Abschnitt~\ref{laguerre:section:definition} +haben wir die Behauptung aufgestellt, +dass die Laguerre-Polynome orthogonal sind. Zu dieser Behauptung möchten wir nun einen Beweis liefern. Wenn wir \eqref{laguerre:dgl} in ein Sturm-Liouville-Problem umwandeln können, haben wir bewiesen, dass es sich @@ -40,7 +27,7 @@ und den Laguerre-Operator x \frac{d}{dx^2} + (\nu + 1 -x) \frac{d}{dx} \end{align} erhalten werden, -in dem wir diese Operatoren einander gleichsetzen. +indem wir diese Operatoren einander gleichsetzen. Aus der Beziehung \begin{align} S @@ -58,7 +45,7 @@ Ausserdem ist ersichtlich, dass $p(x)$ die Differentialgleichung \begin{align*} x \frac{dp}{dx} = --(\nu + 1 - x) p, +-(\nu + 1 - x) p \end{align*} erfüllen muss. Durch Separation erhalten wir dann @@ -76,6 +63,7 @@ Durch Separation erhalten wir dann p(x) & = -C x^{\nu + 1} e^{-x} +. \end{align*} Eingefügt in Gleichung~\eqref{laguerre:sl-lag} ergibt sich \begin{align*} @@ -117,14 +105,9 @@ Für den rechten Rand ist die Bedingung (Gleichung~\eqref{laguerre:sllag_randb}) 0 \end{align*} für beliebige Polynomlösungen erfüllt für $k_\infty=0$ und $h_\infty=1$. -Damit können wir schlussfolgern, dass die verallgemeinerten Laguerre-Polynome -orthogonal bezüglich des Skalarproduktes auf dem Intervall $(0, \infty)$ -mit der verallgemeinerten Laguerre\--Gewichtsfunktion $w(x)=x^\nu e^{-x}$ sind. +Damit können wir schlussfolgern: +Die verallgemeinerten Laguerre-Polynome sind orthogonal +bezüglich des Skalarproduktes auf dem Intervall $(0, \infty)$ +mit der verallgemeinerten Laguerre\--Gewichtsfunktion $w(x)=x^\nu e^{-x}$. Die Laguerre-Polynome ($\nu=0$) sind somit orthognal im Intervall $(0, \infty)$ mit der Gewichtsfunktion $w(x)=e^{-x}$. - -% \subsection{Rodrigues-Formel} - -% \subsection{Drei-Terme Rekursion} - -% \subsection{Beziehung mit der Hypergeometrischen Funktion} diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index b76daeb..2e5fc06 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -8,8 +8,8 @@ Die Gauss-Laguerre-Quadratur kann nun verwendet werden, um exponentiell abfallende Funktionen im Definitionsbereich $(0, \infty)$ zu berechnen. -Dabei bietet sich z.B. die Gamma-Funkion bestens an, wie wir in den folgenden -Abschnitten sehen werden. +Dabei bietet sich z.B. die Gamma-Funkion hervorragend an, +wie wir in den folgenden Abschnitten sehen werden. \subsection{Gamma-Funktion} Die Gamma-Funktion ist eine Erweiterung der Fakultät auf die reale und komplexe @@ -26,10 +26,12 @@ Integral der Form \label{laguerre:gamma} . \end{align} -Der Term $e^{-t}$ ist genau die Gewichtsfunktion der Laguerre-Integration und -der Definitionsbereich passt ebenfalls genau für dieses Verfahren. -Zu erwähnen ist auch, dass für die verallgemeinerte Laguerre-Integration die -Gewichtsfunktion $t^\nu e^{-t}$ genau dem Integranden für $\nu=z-1$ entspricht. +Der Term $e^{-t}$ im Integranden und der Integrationsbereich erfüllen +genau die Bedingungen der Laguerre-Integration. +% Der Term $e^{-t}$ ist genau die Gewichtsfunktion der Laguerre-Integration und +% der Definitionsbereich passt ebenfalls genau für dieses Verfahren. +Weiter zu erwähnen ist, dass für die verallgemeinerte Laguerre-Integration die +Gewichtsfunktion $t^\nu e^{-t}$ exakt dem Integranden für $\nu=z-1$ entspricht. \subsubsection{Funktionalgleichung} Die Gamma-Funktion besitzt die gleiche Rekursionsbeziehung wie die Fakultät, @@ -62,7 +64,8 @@ leicht in die linke Halbebene übersetzen und umgekehrt. \subsection{Berechnung mittels Gauss-Laguerre-Quadratur} In den vorherigen Abschnitten haben wir gesehen, dass sich die Gamma-Funktion bestens für die Gauss-Laguerre-Quadratur eignet. -Nun bieten sich uns zwei Optionen diese zu berechnen: +Nun bieten sich uns zwei Optionen, +diese zu berechnen: \begin{enumerate} \item Wir verwenden die verallgemeinerten Laguerre-Polynome, dann $f(x)=1$. \item Wir verwenden die Laguerre-Polynome, dann $f(x)=x^{z-1}$. @@ -92,7 +95,8 @@ und Nullstellen für unterschiedliche $z$. In \eqref{laguerre:quadratur_gewichte} ist ersichtlich, dass die Gewichte einfach zu berechnen sind. Auch die Nullstellen können vorgängig, -mittels eines geeigneten Verfahrens aus den Polynomen bestimmt werden. +mittels eines geeigneten Verfahrens, +aus den Polynomen bestimmt werden. Als problematisch könnte sich höchstens die zu integrierende Funktion $f(x)=x^{z-1}$ für $|z| \gg 0$ erweisen. Somit entscheiden wir uns aufgrund der vorherigen Punkte, @@ -101,7 +105,8 @@ die zweite Variante weiterzuverfolgen. \subsubsection{Direkter Ansatz} Wenden wir also die Gauss-Laguerre-Quadratur aus \eqref{laguerre:laguerrequadratur} auf die Gamma-Funktion -\eqref{laguerre:gamma} an ergibt sich +\eqref{laguerre:gamma} an, +ergibt sich \begin{align} \Gamma(z) \approx @@ -157,11 +162,12 @@ und als Stützstellen die Nullstellen des Laguerre-Polynomes $L_n$. Evaluieren wir den relativen Fehler unserer Approximation zeigt sich ein Bild wie in Abbildung~\ref{laguerre:fig:rel_error_simple}. Man kann sehen, -wie der relative Fehler Nullstellen aufweist für ganzzahlige $z \leq 2n$, -was laut der Theorie der Gauss-Quadratur auch zu erwarten ist, -denn die Approximation via Gauss-Quadratur -ist exakt für zu integrierende Polynome mit Grad $\leq 2n-1$ -und von $z$ auch noch $1$ abgezogen wird im Exponenten. +wie der relative Fehler Nullstellen aufweist für ganzzahlige $z \leq 2n$. +Laut der Theorie der Gauss-Quadratur auch ist das zu erwarten, +da die Approximation via Gauss-Quadratur +exakt ist für zu integrierende Polynome mit Grad $\leq 2n-1$ +und hinzukommt, +dass zudem von $z$ noch $1$ abgezogen wird im Exponenten. Es ist ersichtlich, dass sich für den Polynomgrad $n$ ein Interval gibt, in dem der relative Fehler minimal ist. @@ -347,7 +353,8 @@ m^* \end{align*} Allerdings ist die Funktion $R_{n,m}(\xi)$ unbeschränkt und hat die gleichen Probleme wie die Fehlerabschätzung des direkten Ansatzes. -Dazu müssten wir $\xi$ versuchen unter Kontrolle zu bringen, +Dazu müssten wir $\xi$ versuchen, +unter Kontrolle zu bringen, was ein äussersts schwieriges Unterfangen zu sein scheint. Da die Gauss-Quadratur aber sowieso nur wirklich praktisch sinnvoll für kleine $n$ ist, @@ -367,8 +374,8 @@ aus dieser Grafik nicht offensichtlich, aber sie scheint regelmässig zu sein. Es lässt die Vermutung aufkommen, dass die Restriktion von $m^* \in \mathbb{Z}$ Rundungsprobleme verursacht. -Wir versuchen dieses Problem via lineare Regression und -geeignete Rundung zu beheben. +Wir versuchen, +dieses Problem via lineare Regression und geeignete Rundung zu beheben. Den linearen Regressor \begin{align*} \hat{m} @@ -391,7 +398,7 @@ In Abbildung~\ref{laguerre:fig:schaetzung} sind die Resultate der linearen Regression aufgezeigt mit $\alpha = 1.34094$ und $\beta = 0.854093$. Die lineare Beziehung ist ganz klar ersichtlich und der Fit scheint zu genügen. -Der optimalen Verschiebungsterm kann nun mit +Der optimale Verschiebungsterm kann nun mit \begin{align*} m^* \approx @@ -423,7 +430,7 @@ dann beim Übergang auf die orange Linie wechselt. \caption{Relativer Fehler des Ansatzes mit Verschiebungsterm für verschiedene reele Werte von $z$ und Verschiebungsterme $m$. Das verwendete Laguerre-Polynom besitzt den Grad $n = 8$. -$m^*$ bezeichnet hier den optimalen Verschiebungsterm} +$m^*$ bezeichnet hier den optimalen Verschiebungsterm.} \label{laguerre:fig:rel_error_shifted} \end{figure} @@ -433,8 +440,8 @@ Es stellt sich nun die Frage, wie der relative Fehler sich für verschiedene $z$ und $n$ verhält. In Abbildung~\ref{laguerre:fig:rel_error_range} sind die relativen Fehler für unterschiedliche $n$ dargestellt. -Der relative Fehler scheint immer noch Nullstellen aufzuweisen, -bei für ganzzahlige $z$. +Der relative Fehler scheint immer noch Nullstellen aufzuweisen +für ganzzahlige $z$. Durch das Verschieben ergibt sich jetzt aber, wie zu erwarten war, ein periodischer relativer Fehler mit einer Periodendauer von $1$. @@ -511,7 +518,7 @@ Diese Methode wurde zum Beispiel in Diese Methode erreicht für $n = 7$ typischerweise Genauigkeit von $13$ korrekten, signifikanten Stellen für reele Argumente. Zum Vergleich: die vorgestellte Methode erreicht für $n = 7$ -eine minimale Genauigkeit von $6$-$7$ korrekten, signifikanten Stellen +eine minimale Genauigkeit von $6$ korrekten, signifikanten Stellen für reele Argumente. Das Resultat ist etwas enttäuschend, aber nicht unerwartet, @@ -519,7 +526,7 @@ da die Lanczos-Methode spezifisch auf dieses Problem zugeschnitten ist und unsere Methode eine erweiterte allgemeine Methode ist. Was die Komplexität der Berechnungen im Betrieb angeht, ist die Gauss-Laguerre-Quadratur wesentlich ressourcensparender, -weil sie nur aus $n$ Funktionasevaluationen, +weil sie nur aus $n$ Funktionsevaluationen, wenigen Multiplikationen und Additionen besteht. -Also könnte diese Methode z.B. Anwendung in Systemen mit wenig Rechenleistung +Demzufolge könnte diese Methode Anwendung in Systemen mit wenig Rechenleistung und/oder knappen Energieressourcen finden. \ No newline at end of file diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex index d69fbed..57a6560 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -11,15 +11,19 @@ {\parindent0pt Die} Laguerre\--Polynome, benannt nach Edmond Laguerre (1834 - 1886), sind Lösungen der ebenfalls nach Laguerre benannten Differentialgleichung. -Laguerre entdeckte diese Polynome als er Approximationsmethoden -für das Integral $\int_0^\infty \exp(-x) / x \, dx$ suchte. +Laguerre entdeckte diese Polynome, als er Approximations\-methoden +für das Integral +% $\int_0^\infty \exp(-x) / x \, dx $ +\begin{align*} +\int_0^\infty \frac{e^{-x}}{x} \, dx +\end{align*} +suchte. Darum möchten wir uns in diesem Kapitel, ganz im Sinne des Entdeckers, den Laguerre-Polynomen für Approximationen von Integralen mit exponentiell-abfallenden Funktionen widmen. -Namentlich werden wir versuchen, -eine geeignete Approximation für die Gamma-Funktion zu finden -mittels Laguerre-Polynomen und der Gauss-Quadratur. +Namentlich werden wir versuchen, mittels Laguerre-Polynomen und +der Gauss-Quadratur eine geeignete Approximation für die Gamma-Funktion zu finden. Laguerre-Polynome tauchen zudem auch in der Quantenmechanik im radialen Anteil der Lösung für die Schrödinger-Gleichung eines Wasserstoffatoms auf. diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 27519d8..a494362 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -6,19 +6,19 @@ \section{Gauss-Quadratur \label{laguerre:section:quadratur}} Die Gauss-Quadratur ist ein numerisches Integrationsverfahren, -welches die Eigenschaften von orthogonalen Polynomen ausnützt. +welches die Eigenschaften von orthogonalen Polynomen verwendet. Herleitungen und Analysen der Gauss-Quadratur können im Abschnitt~\ref{buch:orthogonal:section:gauss-quadratur} gefunden werden. Als grundlegende Idee wird die Beobachtung, dass viele Funktionen sich gut mit Polynomen approximieren lassen, verwendet. Stellt man also sicher, -dass ein Verfahren gut für Polynome gut funktioniert, -sollte es auch für andere Funktionen nicht schlecht funktionieren. +dass ein Verfahren gut für Polynome funktioniert, +sollte es auch für andere Funktionen angemessene Resultate liefern. Es wird ein Polynom verwendet, welches an den Punkten $x_0 < x_1 < \ldots < x_n$ die Funktionwerte~$f(x_i)$ annimmt. -Als Resultat kann das Integral via eine gewichtete Summe der Form +Als Resultat kann das Integral via einer gewichteten Summe der Form \begin{align} \int_a^b f(x) w(x) \, dx \approx @@ -44,11 +44,11 @@ a + \frac{1 - t}{t} auf das Intervall $[0, 1]$ transformiert, kann dies behoben werden. Für unseren Fall gilt $a = 0$. -Das Integral eines Polynomes in diesem Intervall ist immer divergent, -darum müssen wir das Polynome mit einer Funktion multiplizieren, +Das Integral eines Polynomes in diesem Intervall ist immer divergent. +Darum müssen wir das Polynom mit einer Funktion multiplizieren, die schneller als jedes Polynom gegen $0$ geht, damit das Integral immer noch konvergiert. -Die Laguerre-Polynome $L_n$ bieten hier Abhilfe, +Die Laguerre-Polynome $L_n$ schaffen hier Abhilfe, da ihre Gewichtsfunktion $w(x) = e^{-x}$ schneller gegen $0$ konvergiert als jedes Polynom. % In unserem Falle möchten wir die Gauss Quadratur auf die Laguerre-Polynome @@ -67,7 +67,7 @@ umformulieren: \subsubsection{Stützstellen und Gewichte} Nach der Definition der Gauss-Quadratur müssen als Stützstellen die Nullstellen des verwendeten Polynoms genommen werden. -Das heisst für das Laguerre-Polynom $L_n$ müssen dessen Nullstellen $x_i$ und +Für das Laguerre-Polynom $L_n$ müssen demnach dessen Nullstellen $x_i$ und als Gewichte $A_i$ die Integrale $l_i(x)e^{-x}$ verwendet werden. Dabei sind \begin{align*} @@ -146,7 +146,8 @@ x_i L'_n(x_i) (n + 1) L_{n+1}(x_i) . \end{align*} -Setzen wir das nun in \eqref{laguerre:gewichte_lag_temp} ein ergibt sich +Setzen wir das nun in \eqref{laguerre:gewichte_lag_temp} ein, +ergibt sich \begin{align} \nonumber A_i -- cgit v1.2.1 From 62f06c35b53971f99acdc4477da5e2be98a68c04 Mon Sep 17 00:00:00 2001 From: daHugen Date: Tue, 19 Jul 2022 16:43:52 +0200 Subject: made some changes --- buch/papers/lambertw/teil4.tex | 104 ++++++++++++++++++++++++++++++++++++----- 1 file changed, 93 insertions(+), 11 deletions(-) diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 598a57e..6c70174 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -10,15 +10,15 @@ In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve beschre \subsection{Ziel bewegt sich auf einer Gerade \label{lambertw:subsection:malorum}} -Das zu verfolgende Ziel \(A\) wandert auf einer Gerade, wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(P\) startet auf einem beliebigen Punkt auf dem ersten Quadrant.Um die Rechnungen zu vereinfachen wir die Geschwindigkeit \(v\) auf 1 gesetzt. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: +Das zu verfolgende Ziel \(\overrightarrow{Z}\) wandert auf einer Gerade, wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(\overrightarrow{V}\) startet auf einem beliebigen Punkt auf dem ersten Quadrant. Um die Rechnungen zu vereinfachen wir die Geschwindigkeit \(v\) auf 1 gesetzt. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: \begin{equation} - A + \overrightarrow{Z} = \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) = \left( \begin{array}{c} 0 \\ t \end{array} \right) ; - P + \overrightarrow{V} = \left( \begin{array}{c} x \\ y \end{array} \right) \label{lambertw:Anfangspunkte} @@ -79,12 +79,12 @@ Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich z = 0 \label{lambertw:equation5} \end{equation} -Um die Ableitung nach der Zeit wegzubringen wird beidseitig mit \(\dot{x}\) dividiert, wobei \(\frac{\dot{y}}{\dot{x}} = \frac{dy}{dt}/\frac{dx}{dt} = \frac{dy}{dx}\) entspricht. +Um die Ableitung nach der Zeit wegzubringen, wird beidseitig mit \(\dot{x}\) dividiert, wobei \(\frac{\dot{y}}{\dot{x}} = \frac{dy}{dt}/\frac{dx}{dt} = \frac{dy}{dx}\) entspricht. \[ x \frac{\dot{y}}{\dot{x}} + (t-y) \frac{\dot{x}}{\dot{x}} = 0 \] -Nach dem kürzen ergibt sich folgende DGL: +Nach dem Kürzen und Vereinfachen ergibt sich folgende DGL: \begin{equation} x y^{\prime} + t - y = 0 @@ -146,21 +146,103 @@ Diese kann mit den selben Methoden gelöst werden, diesmal in Kombination mit de &= \int \frac{1}{2} (e^{ln(x)+C} - e^{-(ln(x)+C)}) \\ &= - C_1 + C_2 x^2 - C_3 ln(x) + \frac{e^C}{4} x^2 - \frac{ln(x)}{2 \cdot e^C} + C_1 \\ + &= + C_1 + C_2 x^2 - \frac{ln(x)}{8 \cdot C_2} \end{align*} -Das Resultat wie ersichtlich ist folgende Funktion welche mittels Anfangsbedingungen parametrisiert werden kann: + +\begin{figure} + \centering + \includegraphics{papers/lambertw/Bilder/VerfolgungskurveBsp.png} + \caption[Graph der Verfolgungskurve]{Graph der Verfolgungskurve wobei, ({\color{red}rot}) die Funktion \ensuremath{y(x)} ist, ({\color{darkgreen}grün}) der quadratische Teil und ({\color{blue}blau}) dem \ensuremath{ln(x)}-Teil entspricht. + \label{lambertw:funkLoes} + } +\end{figure} + +Das Resultat, wie ersichtlich, ist folgende Funktion \eqref{lambertw:funkLoes} welche mittels Anfangsbedingungen parametrisiert werden kann: \begin{equation} - y(x) + {\color{red}{y(x)}} = - C_1 + C_2 x^2 - C_3 ln(x) + C_1 + C_2 {\color{darkgreen}{x^2}} {\color{blue}{-}} \frac{\color{blue}{ln(x)}}{8 \cdot C_2} \label{lambertw:funkLoes} \end{equation} -Für die Koeffizienten \(C_1, C_2\) und \(C_3\) ergibt sich ein Anfangswertproblem, welches für deren Bestimmung gelöst werden muss. Zuerst soll aber eine qualitative Intuition, oder Idee für das Aussehen der Funktion \(\bf{y(x)}\) geschaffen werden: +Für die Koeffizienten \(C_1\) und \(C_2\) ergibt sich ein Anfangswertproblem, welches für deren Bestimmung gelöst werden muss. Zuerst soll aber eine qualitative Intuition, oder Idee für das Aussehen der Funktion \(\bf{y(x)}\) geschaffen werden: \begin{itemize} \item Für grosse \(x\)-Werte welche in der Regel in der Nähe von \(x_0\) sein sollten, ist der quadratisch Term in der Funktion dominant und somit für immer kleiner werdende \(x\) geht der Verfolger in Richtung \(y\)-Achse wobei seine Steigung stetig sinkt, was Sinn macht wenn der Verfolgte entlang der \(y\)-Achse steigt. \item Für \(x\)-Werte in der Nähe von \(0\) ist das asymptotische Verhalten des Logarithmus dominant, dies macht auch Sinn da sich der Verfolgte auf der \(y\)-Achse bewegt und der Verfolger im nachgeht. \item - Aufgrund des Monotoniewechsels in der Kurve muss die Kurve auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? Durch eine logische Überlegung kann eine Abschätzung darüber getroffen werden und zwar, dass dieser dann entsteht, wenn \(A\) und \(P\) die gleiche \(y\)-Koordinaten besitzen. In diesem Moment ändert die Richtung der \(y\)-Komponente der Geschwindigkeit und somit auch sein Vorzeichen. + Aufgrund des Monotoniewechsels in der Kurve muss es auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? Durch eine logische Überlegung kann eine Abschätzung darüber getroffen werden und zwar, dass dieser dann entsteht, wenn \(A\) und \(P\) die gleiche \(y\)-Koordinaten besitzen. In diesem Moment ändert die Richtung der \(y\)-Komponente der Geschwindigkeit und somit auch sein Vorzeichen. \end{itemize} +Alle diese Eigenschafte stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde. Nun stellt sich die Frage wie die Kurve wirklich aussieht, dies wird durch das Einsetzen folgender Anfangsbedingungen erreicht: +\begin{equation} + y(x)\big \vert_{t=0} + = + y(x_0) + = + y_0 + \:;\: + \frac{dy}{dx}\bigg \vert_{t=0} + = + y^{\prime}(x_0) + = + \frac{y_0}{x_0} +\end{equation} +Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfangsbedingungen ein, dann ergibt sich folgendes Gleichungssystem: +\begin{subequations} + \begin{align} + y_0 + &= + C_1 + C_2 x^2_0 - \frac{ln(x_0)}{8 \cdot C_2} \\ + \frac{y_0}{x_0} + &= + 2 \cdot C_2 x_0 - \frac{ln(x_0)}{8 \cdot C_2} + \end{align} +\end{subequations} +... Mit folgenden Formeln geht es weiter: +\begin{align*} + \eta + &= + \left(\frac{x}{x_0}\right)^2 + \:;\: + r_0 + = + \sqrt{x_0^2+y_0^2} \\ + y + &= + \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)ln\left(\eta\right)-r_0+3y_0\right) \\ + y^\prime + &= + \frac{1}{2}\left(\left(y_0+r_0\right)\frac{x}{x_0^2}+\left(r_0-y_0\right)\frac{1}{x}\right) \\ + -4t + &= + \left(y_0+r_0\right)\left(\eta-1\right)+\left(r_0-y_0\right)ln\left(\eta\right) \\ + -4t+\left(y_0+r_0\right) + &= + \left(y_0+r_0\right)\eta+\left(r_0-y_0\right)ln\left(\eta\right) \\ + e^{-4t+\left(y_0+r_0\right)} + &= + e^{\left(y_0+r_0\right)\eta}\cdot\eta^{\left(r_0-y_0\right)} \\ + e^{\frac{-4t}{r_0-y_0}+\frac{y_0+r_0}{r_0-y_0}} + &= + e^{\frac{y_0+r_0}{r_0-y_0}\eta}\cdot\eta\ \\ + \chi + &= + \frac{y_0+r_0}{r_0-y_0}; \cdot\chi \\ + \chi\cdot e^{\chi-\frac{4t}{r_0-y_0}} + &= + \chi\eta\cdot e^{\chi\eta} \\ + W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) + &= + \chi\eta \\ + \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} + &= + \eta \\ + x\left(t\right) + &= + \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ + \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} + &= + \left(\frac{x}{x_0}\right)^2 +\end{align*} -- cgit v1.2.1 From 9421fec277f1671393a1a9c517e521f4b924e39d Mon Sep 17 00:00:00 2001 From: daHugen Date: Tue, 19 Jul 2022 16:46:02 +0200 Subject: added a picture --- buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png | Bin 0 -> 124329 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png diff --git a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png new file mode 100644 index 0000000..53eb2f9 Binary files /dev/null and b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png differ -- cgit v1.2.1 From c8634d0feb99ab7afc46c27831202cecc29c9252 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Tue, 19 Jul 2022 16:47:17 +0200 Subject: Excluded unused parts. --- buch/papers/lambertw/Bilder/pursuerDGL2.ggb | Bin 36225 -> 17954 bytes buch/papers/lambertw/Bilder/pursuerDGL2.pdf | Bin 0 -> 17941 bytes buch/papers/lambertw/main.tex | 6 +- buch/papers/lambertw/teil0.log | 3656 +++++++++++++++++++++++++++ buch/papers/lambertw/teil0.tex | 89 +- buch/papers/lambertw/teil1.log | 3259 ++++++++++++++++++++++++ buch/papers/lambertw/teil2.log | 1580 ++++++++++++ buch/papers/lambertw/teil3.log | 1580 ++++++++++++ 8 files changed, 10136 insertions(+), 34 deletions(-) create mode 100644 buch/papers/lambertw/Bilder/pursuerDGL2.pdf create mode 100644 buch/papers/lambertw/teil0.log create mode 100644 buch/papers/lambertw/teil1.log create mode 100644 buch/papers/lambertw/teil2.log create mode 100644 buch/papers/lambertw/teil3.log diff --git a/buch/papers/lambertw/Bilder/pursuerDGL2.ggb b/buch/papers/lambertw/Bilder/pursuerDGL2.ggb index 5bd816c..0bd39b2 100644 Binary files a/buch/papers/lambertw/Bilder/pursuerDGL2.ggb and b/buch/papers/lambertw/Bilder/pursuerDGL2.ggb differ diff --git a/buch/papers/lambertw/Bilder/pursuerDGL2.pdf b/buch/papers/lambertw/Bilder/pursuerDGL2.pdf new file mode 100644 index 0000000..284dd7d Binary files /dev/null and b/buch/papers/lambertw/Bilder/pursuerDGL2.pdf differ diff --git a/buch/papers/lambertw/main.tex b/buch/papers/lambertw/main.tex index 6e9bbe0..68b7a5d 100644 --- a/buch/papers/lambertw/main.tex +++ b/buch/papers/lambertw/main.tex @@ -28,9 +28,9 @@ Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren \end{itemize} \input{papers/lambertw/teil0.tex} -\input{papers/lambertw/teil1.tex} -\input{papers/lambertw/teil2.tex} -\input{papers/lambertw/teil3.tex} +%\input{papers/lambertw/teil1.tex} +%\input{papers/lambertw/teil2.tex} +%\input{papers/lambertw/teil3.tex} \input{papers/lambertw/teil4.tex} \printbibliography[heading=subbibliography] diff --git a/buch/papers/lambertw/teil0.log b/buch/papers/lambertw/teil0.log new file mode 100644 index 0000000..f5b3f0d --- /dev/null +++ b/buch/papers/lambertw/teil0.log @@ -0,0 +1,3656 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.23 (MiKTeX 21.8) (preloaded format=pdflatex 2021.9.21) 19 JUL 2022 16:20 +entering extended mode +**./teil0.tex +(teil0.tex +LaTeX2e <2021-06-01> patch level 1 +L3 programming layer <2021-08-27> +! 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LaTeX Error: Environment table undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \begin{table} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 \begin{tabular} + {|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 18. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <5> on input line 18. + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +! LaTeX Error: Illegal character in array arg. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 ...|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Undefined control sequence. + \text + +l.20 \text + {}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +! Undefined control sequence. +l.20 \text{}&\text + {Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no G in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.20 \text{}&\text{Geschwindigkeit}&\text + {Abstand}&\text{Richtung}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no A in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +! Undefined control sequence. +l.20 ...text{Geschwindigkeit}&\text{Abstand}&\text + {Richtung}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +! Undefined control sequence. + \text + +l.22 \text + {Strategie 1} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 1 in font nullfont! +! Undefined control sequence. +l.23 & \text + {konstant} & \text{-} & \text{direkt auf Ziel hinzu}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.23 & \text{konstant} & \text + {-} & \text{direkt auf Ziel hinzu}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no - in font nullfont! +! Undefined control sequence. +l.23 & \text{konstant} & \text{-} & \text + {direkt auf Ziel hinzu}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +! Undefined control sequence. +l.25 \text + {Strategie 2} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 2 in font nullfont! +! Undefined control sequence. +l.26 & \text + {-} & \text{konstant} & \text{direkt auf Ziel hinzu}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no - in font nullfont! +! Undefined control sequence. +l.26 & \text{-} & \text + {konstant} & \text{direkt auf Ziel hinzu}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.26 & \text{-} & \text{konstant} & \text + {direkt auf Ziel hinzu}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +! Undefined control sequence. +l.28 \text + {Strategie 3} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 3 in font nullfont! +! Undefined control sequence. +l.29 & \text + {konstant} & \text{-} & \text{etwas voraus Zielen}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +! Undefined control sequence. +l.29 & \text{konstant} & \text + {-} & \text{etwas voraus Zielen}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no - in font nullfont! +! Undefined control sequence. +l.29 & \text{konstant} & \text{-} & \text + {etwas voraus Zielen}\\ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{table}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.33 \end{table} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.00006pt too wide) in paragraph at lines 18--34 +[][] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 I + n der Tabelle \eqref{lambertw:Strategien} sind drei mögliche Strategi... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no I in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. +l.42 In der Tabelle \eqref + {lambertw:Strategien} sind drei mögliche Strategi... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no : in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no k in font nullfont! +! Undefined control sequence. +l.45 In der Grafik \eqref + {lambertw:pursuerDGL2} ist das Problem dargestellt. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no : in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no W in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 42--48 +[] + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 42--48 +\/cmr/m/n/10 o + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 42--48 +\/cmr/m/n/10 a + [] + + +Overfull \hbox (10.00023pt too wide) in paragraph at lines 42--48 +[]$ + [] + + +Overfull \hbox (10.00023pt too wide) in paragraph at lines 42--48 +[]$ + [] + + +Overfull \hbox (10.00023pt too wide) in paragraph at lines 42--48 +[]$ + [] + +! Undefined control sequence. +l.51 \quad|A\in\mathbb + {R}>0 +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (122.89459pt too wide) detected at line 52 +\OMS/cmsy/m/n/10 j[]j \/cmr/m/n/10 = \OML/cmm/m/it/10 konst \/cmr/m/n/10 = \OML +/cmm/m/it/10 A \OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 A \OMS/cmsy/m/n/10 2 \OML/cmm +/m/it/10 R > \/cmr/m/n/10 0 + [] + +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! + +Overfull \hbox (81.8452pt too wide) detected at line 58 +[] \OMS/cmsy/m/n/10  j[]j \/cmr/m/n/10 = [] + [] + +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no W in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment align undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.65 \begin{align} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no - in font nullfont! +! Missing $ inserted. + + $ +l.67 ...}{|\overrightarrow{Z}-\overrightarrow{V}|} + \cdot +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +\frac #1#2->{\begingroup #1\endgroup \over #2} + +l.67 ...}{|\overrightarrow{Z}-\overrightarrow{V}|} + \cdot +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Misplaced alignment tab character &. +l.69 & + = +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.73 & + = +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{document} ended by \end{align}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.75 \end{align} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.75 \end{align} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.75 \end{align} + +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no K in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (10.00023pt too wide) in paragraph at lines 58--77 + $[]$ + [] + + +Overfull \hbox (10.00023pt too wide) in paragraph at lines 58--77 +[]$ + [] + + +Overfull \hbox (8.05556pt too wide) in paragraph at lines 58--77 +\OML/cmm/m/it/10 V$ + [] + + +Overfull \hbox (7.54167pt too wide) in paragraph at lines 58--77 +\OML/cmm/m/it/10 Z$ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 58--77 +\/cmr/m/n/10 a + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 58--77 +\/cmr/m/n/10 a + [] + + +Overfull \hbox (8.05556pt too wide) in paragraph at lines 58--77 +\OML/cmm/m/it/10 V$ + [] + + +Overfull \hbox (7.54167pt too wide) in paragraph at lines 58--77 +\OML/cmm/m/it/10 Z$ + [] + + +Overfull \hbox (8.05556pt too wide) in paragraph at lines 58--77 +\OML/cmm/m/it/10 V$ + [] + + +Overfull \hbox (7.54167pt too wide) in paragraph at lines 58--77 +\OML/cmm/m/it/10 Z$ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 58--77 +\/cmr/m/n/10 o + [] + + +Overfull \hbox (152.45233pt too wide) in paragraph at lines 58--77 +[][]$[]$ + [] + +! Undefined control sequence. +l.79 \subsection + {Ziel +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.79 \subsection{Z + iel +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no W in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! 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Emergency stop. +<*> ./teil0.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 34 strings out of 478927 + 671 string characters out of 2852535 + 298175 words of memory out of 3000000 + 17993 multiletter control sequences out of 15000+600000 + 403430 words of font info for 27 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 23i,13n,32p,801b,95s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index f174ccb..73fe187 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -14,53 +14,78 @@ Verfolgungskurven tauchen oft auf bei fragen wie, welchen Pfad begeht ein Hund w \label{lambertw:subsection:Verfolger}} Wie bereits erwähnt, wird der Verfolger durch seine Verfolgungsstrategie definiert. Wir nehmen an, dass sich der Verfolger stur an eine Verfolgungsstrategie hält. Dabei gibt es viele mögliche Strategien, die der Verfolger wählen könnte. Die möglichen Strategien entstehen durch Festlegung einzelner Parameter, die der Verfolger kontrollieren kann. Der Verfolger hat nur einen direkten Einfluss auf seinen Geschwindigkeitsvektor. Mit diesem kann er neben Richtung und Betrag auch den Abstand zwischen Verfolger und Ziel kontrollieren. Wenn zwei dieser drei Parameter durch die Strategie definiert werden, ist der dritte nicht mehr frei. Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um den Verfolger komplett zu beschreiben. -\begin{tabular}{|>{$}l<{$}|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} - \hline - \text{}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ - \hline - \text{Strategie 1} - & \text{konstant} & \text{-} & \text{direkt auf Ziel hinzu}\\ - - \text{Strategie 2} - & \text{-} & \text{konstant} & \text{direkt auf Ziel hinzu}\\ - - \text{Strategie 3} - & \text{konstant} & \text{-} & \text{etwas voraus Zielen}\\ - \hline -\label{lambertw:Strategien} -\end{tabular} +\begin{table} + \centering + \begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + \hline + \text{}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ + \hline + \text{Strategie 1} + & \text{konstant} & \text{-} & \text{direkt auf Ziel hinzu}\\ + + \text{Strategie 2} + & \text{-} & \text{konstant} & \text{direkt auf Ziel hinzu}\\ + + \text{Strategie 3} + & \text{konstant} & \text{-} & \text{etwas voraus Zielen}\\ + \hline + \end{tabular} + \caption{mögliche Verfolgungsstrategien} + \label{lambertw:Strategien} +\end{table} -In der Tabelle \eqref{lambertw:Strategien} sind drei mögliche Strategien aufgezählt. Folgend wird nur noch auf die Strategie 1 eingegangen. Bei dieser Strategie ist die Geschwindigkeit konstant und der Verfolger bewegt sich immer direkt auf sein Ziel hinzu. In der Grafik \eqref{lambertw:pursuerDGL2} ist das Problem dargestellt. Wobei $\overrightarrow{V}$ der Ortsvektor des Verfolgers, $\overrightarrow{Z}$ der Ortsvektor des Ziels und $\overrightarrow{\dot{V}}$ der Richtungsvektor des Verfolgers ist. Die konstante Geschwindigkeit kann man mit der Gleichung + + + +%\begin{figure} +% \centering +% \includegraphics{.\papers\lambertw\Bilder\pursuerDGL2.pdf} +% \label{pursuer:pursuerDGL2} +%\end{figure} + +In der Tabelle \eqref{lambertw:Strategien} sind drei mögliche Strategien aufgezählt. +Folgend wird nur noch auf die Strategie 1 eingegangen. +Bei dieser Strategie ist die Geschwindigkeit konstant und der Verfolger bewegt sich immer direkt auf sein Ziel hinzu. +In der Grafik \eqref{lambertw:pursuerDGL2} ist das Problem dargestellt. +Wobei $\overrightarrow{V}$ der Ortsvektor des Verfolgers, $\overrightarrow{Z}$ der Ortsvektor des Ziels und $\overrightarrow{\dot{V}}$ der Geschwindigkeitsvektor des Verfolgers ist. +Die konstante Geschwindigkeit kann man mit der Gleichung \begin{equation} |\overrightarrow{\dot{V}}| - = - konst = A + = konst = A \quad|A\in\mathbb{R}>0 \end{equation} -darstellen. Der Richtungsvektor wiederum kann mit der Gleichung +darstellen. Der Geschwindigkeitsvektor wiederum kann mit der Gleichung \begin{equation} - \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|} + \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot|\overrightarrow{\dot{V}}| = - \frac{\overrightarrow{\dot{V}}}{|\overrightarrow{\dot{V}}|} + \overrightarrow{\dot{V}} \end{equation} -beschrieben werden. Durch die Subtraktion der Ortsvektoren $\overrightarrow{V}$ und $\overrightarrow{Z}$ entsteht ein Vektor der vom Punkt $V$ auf $Z$ zeigt. Da die Länge dieses Vektors beliebig sein kann, wird durch Division mit dem Betrag, die Länge auf eins festgelegt. -Aus dem Verfolgungsproblem ist auch ersichtlich, dass die Punkte $V$ und $Z$ nicht am gleichen Ort starten und so eine Division durch Null ausgeschlossen ist. Wenn die Punkte $V$ und $Z$ trotzdem am gleichen Ort starten, ist die Lösung trivial. +beschrieben werden. +Durch die Subtraktion der Ortsvektoren $\overrightarrow{V}$ und $\overrightarrow{Z}$ entsteht ein Vektor der vom Punkt $V$ auf $Z$ zeigt. +Da die Länge dieses Vektors beliebig sein kann, wird durch Division mit dem Betrag, die Länge auf eins festgelegt. +Aus dem Verfolgungsproblem ist auch ersichtlich, dass die Punkte $V$ und $Z$ nicht am gleichen Ort starten und so eine Division durch Null ausgeschlossen ist. +Wenn die Punkte $V$ und $Z$ trotzdem am gleichen Ort starten, ist die Lösung trivial. Nun wird die Gleichung mit deren rechten Seite skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. -\begin{equation} +\begin{align} \label{pursuer:pursuerDGL} + \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot + \overrightarrow{\dot{V}} + &= + |\overrightarrow{\dot{V}}|^2 + \\ \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot \frac{\overrightarrow{\dot{V}}}{|\overrightarrow{\dot{V}}|} - = + &= 1 -\end{equation} -Diese DGL ist der Kern des Verfolgungsproblems, insofern sich der Verfolger immer direkt auf sein Ziel zubewegt. - - - +\end{align} +Diese DGL ist der Kern des Verfolgungsproblems, insofern der Verfolger die Strategie 1 verwendet. \subsection{Ziel \label{lambertw:subsection:Ziel}} -Als nächstes gehen wir auf das Ziel ein. Wie der Verfolger wird auch unser Ziel sich strikt an eine Fluchtstrategie halten, welche von Anfang an bekannt ist. Diese Strategie kann als Parameterdarstellung der Position nach der Zeit beschrieben werden. Zum Beispiel könnte ein Ziel auf einer Geraden flüchten, welches auf einer Ebene mit der Parametrisierung +Als nächstes gehen wir auf das Ziel ein. +Wie der Verfolger wird auch unser Ziel sich strikt an eine Fluchtstrategie halten, welche von Anfang an bekannt ist. +Diese Strategie kann als Parameterdarstellung der Position nach der Zeit beschrieben werden. +Zum Beispiel könnte ein Ziel auf einer Geraden flüchten, welches auf einer Ebene mit der Parametrisierung \begin{equation} \vec{r}(t) = @@ -70,6 +95,8 @@ Als nächstes gehen wir auf das Ziel ein. Wie der Verfolger wird auch unser Ziel \end{Bmatrix} \end{equation} beschrieben werden könnte. +Mit dieser Gleichung ist das Ziel auch schon vollumfänglich definiert. +Die Fluchtkurve kann eine beliebige Form haben, jedoch wird die zu lösende DGL immer komplexer. diff --git a/buch/papers/lambertw/teil1.log b/buch/papers/lambertw/teil1.log new file mode 100644 index 0000000..d2eb5c6 --- /dev/null +++ b/buch/papers/lambertw/teil1.log @@ -0,0 +1,3259 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.23 (MiKTeX 21.8) (preloaded format=pdflatex 2021.9.21) 5 APR 2022 23:32 +entering extended mode +**./teil1.tex +(teil1.tex +LaTeX2e <2021-06-01> patch level 1 +L3 programming layer <2021-08-27> +! Undefined control sequence. +l.6 \section + {Beispiel () +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.20 J + e nach Verfolgungsstrategie die der Verfolger verwendet, entsteht eine... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no J in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no F in font nullfont! +LaTeX Font Info: Trying to load font information for +cmr on input line 21. +LaTeX Font Info: No file cmr.fd. on input line 21. + +LaTeX Font Warning: Font shape `/cmr/m/n' undefined +(Font) using `/cmr/m/n' instead on input line 21. + +! Corrupted NFSS tables. +wrong@fontshape ...message {Corrupted NFSS tables} + error@fontshape else let f... +l.21 Fü + r dieses konkrete Beispiel wird einfachheitshalber die simpelste Str... +This error message was generated by an \errmessage +command, so I can't give any explicit help. +Pretend that you're Hercule Poirot: Examine all clues, +and deduce the truth by order and method. + + +LaTeX Font Warning: Font shape `/cmr/m/n' undefined +(Font) using `OT1/cmr/m/n' instead on input line 21. + +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no W in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no j in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 20--24 +[] + [] + + +Overfull \hbox (10.55559pt too wide) in paragraph at lines 20--24 +\/cmr/m/n/10 u + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 20--24 +\/cmr/m/n/10 a + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.25 U + m die DGL dieses Problems herzuleiten wird der Sachverhalt in der Graf... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no U in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no k in font nullfont! +! Undefined control sequence. +l.25 ... wird der Sachverhalt in der Grafik \eqref + {pursuer_grafik1} aufgezeigt. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +! Missing $ inserted. + + $ +l.25 ... Sachverhalt in der Grafik \eqref{pursuer_ + grafik1} aufgezeigt. +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 25. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <5> on input line 25. +! Extra }, or forgotten $. +l.25 ...halt in der Grafik \eqref{pursuer_grafik1} + aufgezeigt. +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +! Missing $ inserted. + + $ +l.27 + +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 25--27 +[] + [] + + +Overfull \hbox (332.97824pt too wide) in paragraph at lines 25--27 +[]\OML/cmm/m/it/10 rafik\/cmr/m/n/10 1\OML/cmm/m/it/10 aufgezeigt:DerPunktPistd +erVerfolgerundderPunktAistseinZiel:$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.28 U + m dies mathematisch beschreiben zu können, wird der Richtungsvektor +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no U in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 28--29 +[] + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 28--29 +\/cmr/m/n/10 o + [] + + +Overfull \hbox (64.58458pt too wide) detected at line 33 +[] \/cmr/m/n/10 = [] + [] + +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! 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Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no B in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! 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+Missing character: There is no l in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no k in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no z in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no w in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no L in font nullfont! +! Undefined control sequence. +l.50 ...ieses Problem wurde bereits die DGL \eqref + {eq:PursuerDGL} hergeleitet. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no : in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no G in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 49--52 +[] + [] + + +Overfull \hbox (5.55557pt too wide) in paragraph at lines 49--52 +\/cmr/m/n/10 u + [] + + +Overfull \hbox (5.55557pt too wide) in paragraph at lines 49--52 +\/cmr/m/n/10 u + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.53 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 53--53 +[] + [] + + +Overfull \hbox (135.67946pt too wide) detected at line 57 +[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )[][] = [][][] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.59 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 59--59 +[] + [] + + +Overfull \hbox (61.57726pt too wide) detected at line 65 +[] \OMS/cmsy/m/n/10  [] \/cmr/m/n/10 = 1 = \OML/cmm/m/it/10 v[] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.79 S + ed ut perspiciatis unde omnis iste natus error sit voluptatem +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.98 U + t enim ad minima veniam, quis nostrum exercitationem ullam corporis +You're in trouble here. 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Undefined control sequence. +l.110 animi, id est laborum et dolorum fuga \eqref + {000tempmlate:equation1}. +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.112 E + t harum quidem rerum facilis est et expedita distinctio +You're in trouble here. 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Undefined control sequence. + ...ertw:section:loesung' on page \thepage + \space undefined\on@line . +l.113 \ref{lambertw:section:loesung} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. + ...tw:section:folgerung' on page \thepage + \space undefined\on@line . +l.117 \ref{lambertw:section:folgerung} + . +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.6 \section + {Teil 2 +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.6 \section{T + eil 2 +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no 2 in font nullfont! +! Undefined control sequence. +l.8 \rhead + {Teil 2} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.6 \section + {Teil 3 +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.6 \section{T + eil 3 +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no T in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no 3 in font nullfont! +! Undefined control sequence. +l.8 \rhead + {Teil 3} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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Undefined control sequence. +l.24 \subsection + {De finibus bonorum et malorum +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 \subsection{D + e finibus bonorum et malorum +You're in trouble here. 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Emergency stop. +<*> ./teil3.tex + +*** (job aborted, no legal \end found) + + +Here is how much of TeX's memory you used: + 18 strings out of 478927 + 531 string characters out of 2852535 + 291175 words of memory out of 3000000 + 17978 multiletter control sequences out of 15000+600000 + 403430 words of font info for 27 fonts, out of 8000000 for 9000 + 1141 hyphenation exceptions out of 8191 + 13i,0n,12p,86b,18s stack positions out of 5000i,500n,10000p,200000b,80000s +! ==> Fatal error occurred, no output PDF file produced! -- cgit v1.2.1 From 5d9ae555dc943ae5ec772b7b6efa6b44f131a785 Mon Sep 17 00:00:00 2001 From: daHugen Date: Tue, 19 Jul 2022 17:56:14 +0200 Subject: made some changes and added some text[C --- buch/papers/lambertw/teil4.tex | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 6c70174..e0f7731 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -6,11 +6,9 @@ \section{Beispiel Verfolgungskurve \label{lambertw:section:teil4}} \rhead{Beispiel Verfolgungskurve} -In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve beschreiben. +In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie 1 beschreiben. -\subsection{Ziel bewegt sich auf einer Gerade -\label{lambertw:subsection:malorum}} -Das zu verfolgende Ziel \(\overrightarrow{Z}\) wandert auf einer Gerade, wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(\overrightarrow{V}\) startet auf einem beliebigen Punkt auf dem ersten Quadrant. Um die Rechnungen zu vereinfachen wir die Geschwindigkeit \(v\) auf 1 gesetzt. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: +Das zu verfolgende Ziel \(\overrightarrow{Z}\) wandert auf einer Gerade mit konstanter Geschwindigkeit \(v = 1\), wobei diese Gerade der \(y\)-Achse entspricht. Der Verfolger \(\overrightarrow{V}\) startet auf einem beliebigen Punkt im ersten Quadrant und bewegt sich auch mit konstanter Geschwindigkeit. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: \begin{equation} \overrightarrow{Z} = @@ -23,7 +21,7 @@ Das zu verfolgende Ziel \(\overrightarrow{Z}\) wandert auf einer Gerade, wobei d \left( \begin{array}{c} x \\ y \end{array} \right) \label{lambertw:Anfangspunkte} \end{equation} -Wenn man diese Startpunkte in die Gleichung der Verfolgungskurve einfügt ergibt sich folgender Ausdruck: +Wenn man diese Startpunkte in die Gleichung der Verfolgungskurve \eqref{lambertw:pursuerDGL} einfügt ergibt sich folgender Ausdruck: \begin{equation} \frac{\left( \begin{array}{c} 0-x \\ t-y \end{array} \right)}{\sqrt{x^2 + (t-y)^2}} \circ @@ -155,7 +153,7 @@ Diese kann mit den selben Methoden gelöst werden, diesmal in Kombination mit de \centering \includegraphics{papers/lambertw/Bilder/VerfolgungskurveBsp.png} \caption[Graph der Verfolgungskurve]{Graph der Verfolgungskurve wobei, ({\color{red}rot}) die Funktion \ensuremath{y(x)} ist, ({\color{darkgreen}grün}) der quadratische Teil und ({\color{blue}blau}) dem \ensuremath{ln(x)}-Teil entspricht. - \label{lambertw:funkLoes} + \label{lambertw:BildFunkLoes} } \end{figure} @@ -175,7 +173,7 @@ Für die Koeffizienten \(C_1\) und \(C_2\) ergibt sich ein Anfangswertproblem, w \item Aufgrund des Monotoniewechsels in der Kurve muss es auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? Durch eine logische Überlegung kann eine Abschätzung darüber getroffen werden und zwar, dass dieser dann entsteht, wenn \(A\) und \(P\) die gleiche \(y\)-Koordinaten besitzen. In diesem Moment ändert die Richtung der \(y\)-Komponente der Geschwindigkeit und somit auch sein Vorzeichen. \end{itemize} -Alle diese Eigenschafte stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde. Nun stellt sich die Frage wie die Kurve wirklich aussieht, dies wird durch das Einsetzen folgender Anfangsbedingungen erreicht: +Alle diese Eigenschafte stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde, siehe \ref{lambertw:BildFunkLoes}. Nun stellt sich die Frage wie die Kurve wirklich aussieht, dies wird durch das Einsetzen folgender Anfangsbedingungen erreicht: \begin{equation} y(x)\big \vert_{t=0} = -- cgit v1.2.1 From a01266d1d515ffbb6d5a965cea415b65b092a64b Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 19 Jul 2022 18:01:20 +0200 Subject: not finished --- buch/papers/fm/01_AM-FM.tex | 12 ++++++++++-- buch/papers/fm/main.tex | 5 +++-- 2 files changed, 13 insertions(+), 4 deletions(-) diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index b9d6167..ef55d55 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,12 +7,20 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot cos(\omega_ct+\varphi)\). +\(x_c(t) = A_c \cdot cos(\omega_c(t)+\varphi)\). Wobei die konstanten Amplitude \(A_c\) und Phase \(\varphi\) vom Nachrichtensignal \(m(t)\) verändert wird. Der Parameter \(\omega_c\), die Trägerkreisfrequenz bzw. die Trägerfrequenz \(f_c = \frac{\omega_c}{2\pi}\), steht nicht für die modulation zur verfügung, statt dessen kann durch ihn die Frequenzachse frei gewählt werden. \newblockpunct - +Jedoch ist das für die Vilfalt der Modulationsarten keine Einschrenkung. +Ein Nachrichtensignal kann auch über die Momentanfrequenz (instantenous frequency) \(\omega_i\) eines trägers verändert werden. +Mathematisch wird dann daraus +\[ + \omega_i = \omega_c + \frac{d \varphi(t)}{dt} +\] +mit der Ableitung der Phase. +\newline +\newline TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[cos( cos x)\] diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 56a7ac5..fcf4d1a 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -1,15 +1,16 @@ +% !TeX root = ../../buch.tex % % main.tex -- Paper zum Thema % % (c) 2020 Hochschule Rapperswil % -\chapter{FM Bessel\label{chapter:fm}} +\chapter{FM Bessel\label{chapter:fm}} \lhead{FM} \begin{refsection} \chapterauthor{Joshua Bär} -%$\with$ + Die Frequenzmodulation ist eine Modulation die man auch schon im alten Radio findet. Falls du dich an die Zeit erinnerst, konnte man zwischen \textit{FM-AM} Umschalten, dies bedeutete so viel wie: \textit{F}requenz-\textit{M}odulation und \textit{A}mplituden-\textit{M}odulation. -- cgit v1.2.1 From d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd Mon Sep 17 00:00:00 2001 From: daHugen Date: Tue, 19 Jul 2022 18:35:13 +0200 Subject: added some equations and made some changes --- buch/papers/lambertw/teil4.tex | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index e0f7731..6184369 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -237,10 +237,16 @@ Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfang \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} &= \eta \\ - x\left(t\right) - &= - \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} &= - \left(\frac{x}{x_0}\right)^2 + \left(\frac{x}{x_0}\right)^2 \\ + x\left(t\right) + &= + \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \end{align*} +\begin{equation} + y(t) + = + \frac{1}{4}\left(\left(y_0+r_0\right)\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}+\left(r_0-y_0\right)\cdot\mathrm{ln}\ \left(\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}\right)-r_0+3y_0\right) + \label{lambertw:funkNachT} +\end{equation} -- cgit v1.2.1 From 5da2fa5a5e6a2fa2b8a23745b8c300d15a06669d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Sat, 23 Jul 2022 15:19:20 +0200 Subject: Restruct paper, correct typos, add positive conclusion, add more citations and references, small changes to plots --- buch/papers/laguerre/definition.tex | 86 +++++++--- buch/papers/laguerre/eigenschaften.tex | 129 +++++++++++---- buch/papers/laguerre/gamma.tex | 184 ++++++++++++++------- buch/papers/laguerre/images/estimates.pdf | Bin 13780 -> 13813 bytes buch/papers/laguerre/images/laguerre_poly.pdf | Bin 19815 -> 19815 bytes buch/papers/laguerre/images/rel_error_simple.pdf | Bin 23353 -> 24455 bytes buch/papers/laguerre/images/targets.pdf | Bin 14462 -> 14495 bytes buch/papers/laguerre/main.tex | 2 +- buch/papers/laguerre/presentation/presentation.pdf | Bin 394774 -> 0 bytes .../presentation/sections/gamma_approx.tex | 2 +- buch/papers/laguerre/quadratur.tex | 98 +++++++---- buch/papers/laguerre/references.bib | 4 +- buch/papers/laguerre/scripts/estimates.py | 2 +- buch/papers/laguerre/scripts/laguerre_poly.py | 2 +- buch/papers/laguerre/scripts/rel_error_simple.py | 2 +- buch/papers/laguerre/scripts/targets.py | 2 +- 16 files changed, 357 insertions(+), 156 deletions(-) delete mode 100644 buch/papers/laguerre/presentation/presentation.pdf diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index 4729a93..e2062d2 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -3,51 +3,80 @@ % % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % -\section{Definition - \label{laguerre:section:definition}} -\rhead{Definition} -Die verallgemeinerte Laguerre-Differentialgleichung ist gegeben durch +\section{Herleitung% +% \section{Einleitung +% \section{Definition +\label{laguerre:section:definition}} +\rhead{Definition}% +In einem ersten Schritt möchten wir die Laguerre-Polynome +aus der Laguerre-\-Differentialgleichung herleiten. +Zudem möchten wir die Lösung auch auf +die assoziierten Laguerre-Polynome ausweiten. +Im Anschluss möchten wir dann noch die Orthogonalität dieser Polynome beweisen. + +\subsection{Assoziierte Laguerre-Differentialgleichung} +Die assoziierte Laguerre-Differentialgleichung ist gegeben durch \begin{align} x y''(x) + (\nu + 1 - x) y'(x) + n y(x) = 0 , \quad -n \in \mathbb{N}_0 +n \in \mathbb{N} , \quad x \in \mathbb{R} \label{laguerre:dgl} . \end{align} -Spannenderweise wurde die verallgemeinerte Laguerre-Differentialgleichung +Spannenderweise wurde die assoziierte Laguerre-Differentialgleichung zuerst von Yacovlevich Sonine (1849 - 1915) beschrieben, aber aufgrund ihrer Ähnlichkeit nach Laguerre benannt. Die klassische Laguerre-Diffentialgleichung erhält man, wenn $\nu = 0$. -Hier wird die verallgemeinerte Laguerre-Differentialgleichung verwendet, + +{\subsection{Potenzreihenansatz} +\label{laguerre:subsection:potenzreihenansatz}} +Hier wird die assoziierte Laguerre-Differentialgleichung verwendet, weil die Lösung mit derselben Methode berechnet werden kann. Zusätzlich erhält man aber die Lösung für den allgmeinen Fall. -Zur Lösung von \eqref{laguerre:dgl} verwenden wir einen -Potenzreihenansatz. -Da wir bereits wissen, dass die Lösung orthogonale Polynome sind, -erscheint dieser Ansatz sinnvoll. -Setzt man nun den Ansatz +Wir stellen die Vermutung auf, +dass die Lösungen orthogonale Polynome sind. +Die Orthogonalität der Lösung werden wir im +Abschnitt~\ref{laguerre:subsection:orthogonal} beweisen. +Zur Lösung von \eqref{laguerre:dgl} verwenden wir aufgrund +der getroffenen Vermutungen einen Potenzreihenansatz. +Der Potenzreihenansatz ist gegeben als +% Da wir bereits wissen, +% dass die Lösung orthogonale Polynome sind, +% erscheint dieser Ansatz sinnvoll. \begin{align*} y(x) - & = +& = \sum_{k=0}^\infty a_k x^k -\\ +% \\ +. +\end{align*} +Für die 1. und 2. Ableitungen erhalten wir +\begin{align*} y'(x) - & = +& = \sum_{k=1}^\infty k a_k x^{k-1} = \sum_{k=0}^\infty (k+1) a_{k+1} x^k \\ y''(x) - & = +& = \sum_{k=2}^\infty k (k-1) a_k x^{k-2} = \sum_{k=1}^\infty (k+1) k a_{k+1} x^{k-1} +. \end{align*} -in die Differentialgleichung ein, erhält man + +\subsection{Lösen der Laguerre-Differentialgleichung} +Setzt man nun den Potenzreihenansatz in +\eqref{laguerre:dgl} +%die Differentialgleichung +ein, +% erhält man +resultiert \begin{align*} \sum_{k=1}^\infty (k+1) k a_{k+1} x^k + @@ -64,16 +93,18 @@ n \sum_{k=0}^\infty a_k x^k 0. \end{align*} Daraus lässt sich die Rekursionsbeziehung -\begin{align*} +\begin{align} a_{k+1} & = \frac{k-n}{(k+1) (k + \nu + 1)} a_k -\end{align*} +\label{laguerre:rekursion} +\end{align} ableiten. Für ein konstantes $n$ erhalten wir als Potenzreihenlösung ein Polynom vom Grad $n$, denn für $k=n$ wird $a_{n+1} = 0$ und damit auch $a_{n+2}=a_{n+3}=\ldots=0$. -Aus der Rekursionsbeziehung ist zudem ersichtlich, +Aus %der Rekursionsbeziehung +\eqref{laguerre:rekursion} ist zudem ersichtlich, dass $a_0 \neq 0$ beliebig gewählt werden kann. Wählen wir nun $a_0 = 1$, dann folgt für die Koeffizienten $a_1, a_2, a_3$ \begin{align*} @@ -114,7 +145,7 @@ L_n(x) \sum_{k=0}^{n} \frac{(-1)^k}{k!} \binom{n}{k} x^k \label{laguerre:polynom} \end{align} -und mit $\nu \in \mathbb{R}$ die verallgemeinerten Laguerre-Polynome +und mit $\nu \in \mathbb{R}$ die assoziierten Laguerre-Polynome \begin{align} L_n^\nu(x) = @@ -132,14 +163,19 @@ Abbildung~\ref{laguerre:fig:polyeval} dargestellt. \end{figure} \subsection{Analytische Fortsetzung} -Durch die analytische Fortsetzung erhalten wir zudem noch die zweite Lösung der -Differentialgleichung mit der Form +Durch die analytische Fortsetzung können wir zudem noch die zweite Lösung der +Differentialgleichung erhalten. +Laut \eqref{buch:funktionentheorie:singularitäten:eqn:w1} hat die Lösung +die Form \begin{align*} \Xi_n(x) = -L_n(x) \ln(x) + \sum_{k=1}^\infty d_k x^k +L_n(x) \log(x) + \sum_{k=1}^\infty d_k x^k . \end{align*} +Eine Herleitung dazu lässt sich im +Abschnitt \ref{buch:funktionentheorie:subsection:dglsing} +im ersten Teil des Buches finden. Nach einigen aufwändigen Rechnungen, % die am besten ein Computeralgebrasystem übernimmt, die den Rahmen dieses Kapitel sprengen würden, @@ -147,7 +183,7 @@ erhalten wir \begin{align*} \Xi_n = -L_n(x) \ln(x) +L_n(x) \log(x) + \sum_{k=1}^n \frac{(-1)^k}{k!} \binom{n}{k} (\alpha_{n-k} - \alpha_n - 2 \alpha_k)x^k diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 4adbe86..55d2276 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -3,32 +3,83 @@ % % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % -\section{Orthogonalität - \label{laguerre:section:orthogonal}} -Im Abschnitt~\ref{laguerre:section:definition} +\subsection{Orthogonalität% +\label{laguerre:subsection:orthogonal}} +\rhead{Orthogonalität}% +Im Abschnitt~\ref{laguerre:subsection:potenzreihenansatz} haben wir die Behauptung aufgestellt, dass die Laguerre-Polynome orthogonal sind. Zu dieser Behauptung möchten wir nun einen Beweis liefern. -Wenn wir \eqref{laguerre:dgl} in ein -Sturm-Liouville-Problem umwandeln können, haben wir bewiesen, dass es sich -bei den Laguerre-Polynomen um orthogonale Polynome handelt (siehe -Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem}). -Der Beweis kann äquivalent auch über den Sturm-Liouville-Operator +% +Um die Orthogonalität von Funktionen zu zeigen, +bieten sich folgende Möglichkeiten an: +\begin{enumerate} +\item Identifizieren der Funktion als Eigenfunktion eines Skalarproduktes +mit einem selbstadjungierten Operator. +Dafür muss aber zuerst bewiesen werden, +dass der verwendete Operator selbstadjungiert ist. +Die Theorie dazu findet sich in den +Abschnitten~\ref{buch:orthogonal:section:orthogonale-polynome-und-dgl} und +\ref{buch:orthogonalitaet:section:bessel}. +\item Umformen der Differentialgleichung in die Form der +Sturm-Liouville-Differentialgleichung, +denn für dieses verallgemeinerte Problem +ist die Orthogonalität bereits bewiesen. +Die Theorie dazu findet sich im Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem}. +\end{enumerate} + +% \subsubsection{Plan} +\subsubsection{Idee} +Für den Beweis der Orthogonalität der Laguerre-Polynome möchten +wir den zweiten Ansatz über das Sturm-Liouville-Problem verwenden. +% Dazu müssen wir die Laguerre-Differentialgleichung~\eqref{laguerre:dgl} +% in die Form der Sturm-Liouville-Differentialgleichung bringen. +Allerdings möchten wir nicht die Laguerre-Differentialgleichung +in die richtige Form bringen, +sondern den Laguerre-Operator \begin{align} -S +\Lambda = -\frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right). -\label{laguerre:slop} +x \frac{d}{dx^2} + (\nu + 1 -x) \frac{d}{dx} +\label{laguerre:lagop} +. \end{align} -und den Laguerre-Operator +Da es sich beim Sturm-Liouville-Problem um ein Eigenwertproblem handelt, +kann die Orthogonalität äquivalent über denn Sturm-Liouville-Operator \begin{align} -\Lambda +S = -x \frac{d}{dx^2} + (\nu + 1 -x) \frac{d}{dx} +\frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right). +\label{laguerre:slop} \end{align} -erhalten werden, -indem wir diese Operatoren einander gleichsetzen. -Aus der Beziehung +bewiesen werden. +Dazu müssen wir die Operatoren einander gleichsetzen. + +% Wenn wir \eqref{laguerre:dgl} in ein +% Sturm-Liouville-Problem umwandeln können, haben wir bewiesen, dass es sich +% bei den Laguerre-Polynomen um orthogonale Polynome handelt (siehe +% Abschnitt~\ref{buch:integrale:subsection:sturm-liouville-problem}). +% Der Beweis kann äquivalent auch über den Sturm-Liouville-Operator +% \begin{align} +% S +% = +% \frac{1}{w(x)} \left(-\frac{d}{dx}p(x) \frac{d}{dx} + q(x) \right). +% \label{laguerre:slop} +% \end{align} +% und den Laguerre-Operator +% \begin{align} +% \Lambda +% = +% x \frac{d}{dx^2} + (\nu + 1 -x) \frac{d}{dx} +% \end{align} +% erhalten werden, +% indem wir diese Operatoren einander gleichsetzen. + +\subsubsection{Umformen in Sturm-Liouville-Operator} +% Aus der Beziehung von +Setzen wir nun +\eqref{laguerre:lagop} und \eqref{laguerre:slop} +einander gleich \begin{align} S & = @@ -75,11 +126,13 @@ x^{\nu+1} e^{-x} \frac{d^2}{dx^2} + = x \frac{d^2}{dx^2} + (\nu + 1 - x) \frac{d}{dx}. \end{align*} -Mittels Koeffizientenvergleich kann nun abgelesen werden, dass $w(x) = x^\nu -e^{-x}$ und $C=1$ mit $\nu > -1$. +Mittels Koeffizientenvergleich kann nun abgelesen werden, +dass $w(x) = x^\nu e^{-x}$ und $C=1$ mit $\nu > -1$. Die Gewichtsfunktion $w(x)$ wächst für $x\rightarrow-\infty$ sehr schnell an, deshalb ist die Laguerre-Gewichtsfunktion nur geeignet für den Definitionsbereich $(0, \infty)$. + +\subsubsection{Randbedingungen} Bleibt nur noch sicherzustellen, dass die Randbedingungen, \begin{align} k_0 y(0) + h_0 p(0)y'(0) @@ -93,10 +146,12 @@ k_\infty y(\infty) + h_\infty p(\infty) y'(\infty) \label{laguerre:sllag_randb} \end{align} mit $|k_i|^2 + |h_i|^2 \neq 0,\,\forall i \in \{0, \infty\}$, erfüllt sind. -Am linken Rand (Gleichung~\eqref{laguerre:sllag_randa}) kann $y(0) = 1$, $k_0 = -0$ und $h_0 = 1$ verwendet werden, +% +Am linken Rand \eqref{laguerre:sllag_randa} kann $y(0) = 1$, $k_0 = 0$ und +$h_0 = 1$ verwendet werden, was auch die Laguerre-Polynome ergeben haben. -Für den rechten Rand ist die Bedingung (Gleichung~\eqref{laguerre:sllag_randb}) + +Für den rechten Rand ist die Bedingung \eqref{laguerre:sllag_randb} \begin{align*} \lim_{x \rightarrow \infty} p(x) y'(x) & = @@ -105,9 +160,27 @@ Für den rechten Rand ist die Bedingung (Gleichung~\eqref{laguerre:sllag_randb}) 0 \end{align*} für beliebige Polynomlösungen erfüllt für $k_\infty=0$ und $h_\infty=1$. -Damit können wir schlussfolgern: -Die verallgemeinerten Laguerre-Polynome sind orthogonal -bezüglich des Skalarproduktes auf dem Intervall $(0, \infty)$ -mit der verallgemeinerten Laguerre\--Gewichtsfunktion $w(x)=x^\nu e^{-x}$. -Die Laguerre-Polynome ($\nu=0$) sind somit orthognal im Intervall $(0, \infty)$ -mit der Gewichtsfunktion $w(x)=e^{-x}$. + +% Somit können wir schlussfolgern: +\begin{satz} +Die Laguerre-Polynome %($\nu=0$) +\eqref{laguerre:polynom} +% \begin{align*} +% L_n(x) +% = +% \sum_{k=0}^{n} \frac{(-1)^k}{k!} \binom{n}{k} x^k +% \end{align*} +sind orthognale Polynome bezüglich des Skalarproduktes +im Intervall~$(0, \infty)$ mit der Gewichts\-funktion~$w(x)=e^{-x}$. +\end{satz} + +\begin{satz} +Die assoziierten Laguerre-Polynome \eqref{laguerre:allg_polynom} +% \begin{align*} +% L_n^\nu(x) +% = +% \sum_{k=0}^{n} \frac{(-1)^k}{(\nu + 1)_k} \binom{n}{k} x^k. +% \end{align*} +sind orthogonale Polynome bezüglich des Skalarproduktes +im Intervall~$(0, \infty)$ mit der Gewichts\-funktion~$w(x)=x^\nu e^{-x}$. +\end{satz} diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index 2e5fc06..e40d8ca 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -3,17 +3,34 @@ % % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % -\section{Anwendung: Berechnung der Gamma-Funktion +\section{Anwendung: Berechnung der + Gamma-Funktion% \label{laguerre:section:quad-gamma}} +\rhead{Approximation der Gamma-Funktion}% Die Gauss-Laguerre-Quadratur kann nun verwendet werden, -um exponentiell abfallende Funktionen im Definitionsbereich $(0, \infty)$ zu -berechnen. -Dabei bietet sich z.B. die Gamma-Funkion hervorragend an, +um exponentiell abfallende Funktionen im Definitionsbereich~$(0, \infty)$ +zu berechnen. +Dabei bietet sich zum Beispiel die Gamma-Funktion hervorragend an, wie wir in den folgenden Abschnitten sehen werden. -\subsection{Gamma-Funktion} +Im ersten Abschnitt~\ref{laguerre:subsection:gamma} möchten wir noch einmal +die wichtigsten Eigenschaften der Gamma-Funktion betrachten, +bevor wir dann im zweiten Abschnitt~\ref{laguerre:subsection:gauss-lag-gamma} +diese Eigenschaften nutzen werden, +damit wir die Gauss-Laguerre-Quadratur für die Gamma-Funktion +markant verbessern können. +% damit wir sie dann in einem nächsten Schritt verwenden können, +% um unsere Approximationsmethode zu verbessern +% Im zweiten Abschnitt~\ref{laguerre:subsection:gauss-lag-gamma} +% wenden wir dann die Gauss-Laguerre-Quadratur auf die Gamma-Funktion und +% erweitern die Methode + +{\subsection{Gamma-Funktion} +\label{laguerre:subsection:gamma}} Die Gamma-Funktion ist eine Erweiterung der Fakultät auf die reale und komplexe Zahlenmenge. +Mehr Informationen zur Gamma-Funktion lassen sich im +Abschnitt~\ref{buch:rekursion:section:gamma} finden. Die Definition~\ref{buch:rekursion:def:gamma} beschreibt die Gamma-Funktion als Integral der Form \begin{align} @@ -22,24 +39,30 @@ Integral der Form \int_0^\infty x^{z-1} e^{-x} \, dx , \quad -\text{wobei Realteil von $z$ grösser als $0$} +\text{wobei } \operatorname{Re}(z) > 0 \label{laguerre:gamma} . \end{align} -Der Term $e^{-t}$ im Integranden und der Integrationsbereich erfüllen +Der Term $e^{-x}$ im Integranden und der Integrationsbereich erfüllen genau die Bedingungen der Laguerre-Integration. % Der Term $e^{-t}$ ist genau die Gewichtsfunktion der Laguerre-Integration und % der Definitionsbereich passt ebenfalls genau für dieses Verfahren. -Weiter zu erwähnen ist, dass für die verallgemeinerte Laguerre-Integration die -Gewichtsfunktion $t^\nu e^{-t}$ exakt dem Integranden für $\nu=z-1$ entspricht. +Weiter zu erwähnen ist, dass für die assoziierte Laguerre-Integration die +Gewichtsfunktion $x^\nu e^{-x}$ exakt dem Integranden +für $\nu = z - 1$ entspricht. \subsubsection{Funktionalgleichung} Die Gamma-Funktion besitzt die gleiche Rekursionsbeziehung wie die Fakultät, nämlich \begin{align} +\Gamma(z+1) += z \Gamma(z) +\quad +\text{mit } +\Gamma(1) = -\Gamma(z+1) +1 . \label{laguerre:gamma_funktional} \end{align} @@ -61,21 +84,64 @@ her. Dadurch lassen Werte der Gamma-Funktion sich für $z$ in der rechten Halbebene leicht in die linke Halbebene übersetzen und umgekehrt. -\subsection{Berechnung mittels Gauss-Laguerre-Quadratur} +{\subsection{Berechnung mittels Gauss-Laguerre-Quadratur} +\label{laguerre:subsection:gauss-lag-gamma}} In den vorherigen Abschnitten haben wir gesehen, -dass sich die Gamma-Funktion bestens für die Gauss-Laguerre-Quadratur eignet. +dass sich die Gamma-Funktion bestens für die Gauss-Laguerre-Quadratur +\begin{align*} +\int_0^\infty x^{z-1} e^{-x} \, dx += +\int_0^\infty f(x) w(x) \, dx +\approx +\sum_{i=1}^n f(x_i) A_i +\end{align*} +eignet. Nun bieten sich uns zwei Optionen, diese zu berechnen: \begin{enumerate} -\item Wir verwenden die verallgemeinerten Laguerre-Polynome, dann $f(x)=1$. -\item Wir verwenden die Laguerre-Polynome, dann $f(x)=x^{z-1}$. +\item Wir verwenden die assoziierten Laguerre-Polynome $L_n^\nu(x)$ mit +$w(x) = x^\nu e^{-x}$, $\nu = z - 1$ und $f(x) = 1$. +% $f(x)=1$. +% \begin{align*} +% \int_0^\infty x^{z-1} e^{-x} \, dx +% = +% \int_0^\infty f(x) w(x) \, dx +% \quad +% \text{mit } +% w(x) +% = +% x^\nu e^{-x}, +% \nu +% = +% z - 1 +% \text{ und } +% f(x) = 1 +% . +% \end{align*} +\item Wir verwenden die Laguerre-Polynome $L_n(x)$ mit +$w(x) = e^{-x}$ und $f(x) = x^{z - 1}$. +% $f(x)=x^{z-1}$ +% \begin{align*} +% \int_0^\infty x^{z-1} e^{-x} \, dx +% = +% \int_0^\infty f(x) w(x) \, dx +% \quad +% \text{mit } +% w(x) +% = +% e^{-x} +% \text{ und } +% f(x) = x^{z - 1} +% . +% \end{align*} \end{enumerate} Die erste Variante wäre optimal auf das Problem angepasst, allerdings müssten die Gewichte und Nullstellen für jedes $z$ neu berechnet werden, da sie per Definition von $z$ abhängen. Dazu kommt, -dass die Berechnung der Gewichte $A_i$ nach \cite{laguerre:Cassity1965AbcissasCA} +dass die Berechnung der Gewichte $A_i$ nach +\cite{laguerre:Cassity1965AbcissasCA} \begin{align*} A_i = @@ -113,7 +179,7 @@ ergibt sich \sum_{i=1}^n x_i^{z-1} A_i. \label{laguerre:naive_lag} \end{align} - +% \begin{figure} \centering % \input{papers/laguerre/images/rel_error_simple.pgf} @@ -123,7 +189,7 @@ ergibt sich für verschiedene reele Werte von $z$ und Grade $n$ der Laguerre-Polynome} \label{laguerre:fig:rel_error_simple} \end{figure} - +% Bevor wir die Gauss-Laguerre-Quadratur anwenden, möchten wir als ersten Schritt eine Fehlerabschätzung durchführen. Für den Fehlerterm \eqref{laguerre:lag_error} wird die $2n$-te Ableitung @@ -146,7 +212,7 @@ R_n , \label{laguerre:gamma_err_simple} \end{align} -wobei $\xi$ ein geeigneter Wert im Interval $(0, \infty)$ ist +wobei $\xi$ ein geeigneter Wert im Intervall $(0, \infty)$ ist und $n$ der Grad des verwendeten Laguerre-Polynoms. Eine Fehlerabschätzung mit dem Fehlerterm stellt sich als unnütz heraus, da $R_n$ für $z < 2n - 1$ bei $\xi \rightarrow 0$ eine Singularität aufweist @@ -169,12 +235,12 @@ exakt ist für zu integrierende Polynome mit Grad $\leq 2n-1$ und hinzukommt, dass zudem von $z$ noch $1$ abgezogen wird im Exponenten. Es ist ersichtlich, -dass sich für den Polynomgrad $n$ ein Interval gibt, +dass sich für den Polynomgrad $n$ ein Intervall gibt, in dem der relative Fehler minimal ist. Links steigt der relative Fehler besonders stark an, während er auf der rechten Seite zu konvergieren scheint. Um die linke Hälfte in den Griff zu bekommen, -könnten wir die Reflektionsformel der Gamma-Funktion ausnutzen. +könnten wir die Reflektionsformel der Gamma-Funktion verwenden. \begin{figure} \centering @@ -204,8 +270,8 @@ das Problem in den Griff zu bekommen. Wie wir im vorherigen Abschnitt gesehen haben, scheint der Integrand problematisch. Darum möchten wir jetzt den Integranden analysieren, -um ihn besser verstehen zu können und -dadurch geeignete Gegenmassnahmen zu entwickeln. +damit wir ihn besser verstehen und +dadurch geeignete Gegenmassnahmen zu entwickeln können. % Dieser Abschnitt soll eine grafisches Verständnis dafür schaffen, % wieso der Integrand so problematisch ist. @@ -263,7 +329,7 @@ grösser als $0$ und kleiner als $2n-1$ ist. \subsubsection{Ansatz mit Verschiebungsterm} % Mittels der Funktionalgleichung \eqref{laguerre:gamma_funktional} -% kann der Wert von $\Gamma(z)$ im Interval $z \in [a,a+1]$, +% kann der Wert von $\Gamma(z)$ im Intervall $z \in [a,a+1]$, % in dem der relative Fehler minimal ist, % evaluiert werden und dann mit der Funktionalgleichung zurückverschoben werden. Nun stellt sich die Frage, @@ -322,28 +388,15 @@ s(z, m) \cdot (z - 2n)_{2n} \frac{(n!)^2}{(2n)!} \xi^{z + m - 2n - 1} \label{laguerre:gamma_err_shifted} . \end{align} - +% \begin{figure} \centering \includegraphics{papers/laguerre/images/targets.pdf} % %\vspace{-12pt} -\caption{$a$ in Abhängigkeit von $z$ und $n$} +\caption{$m^*$ in Abhängigkeit von $z$ und $n$} \label{laguerre:fig:targets} \end{figure} -% wobei ist -% mit $z^*(n) \in \mathbb{R}$ wollen wir finden, -% in dem wir den Fehlerterm \eqref{laguerre:lag_error} anpassen -% und in einem nächsten Schritt minimieren. -% Zudem nehmen wir an, -% dass $z < z^*(n)$ ist. -% Wir fügen einen Verschiebungsterm um $m \in \mathbb{N}$ Stellen ein, -% daraus folgt -% -% Damit wir den idealen Verschiebungsterm $m^*$ finden können, -% müssen wir mittels des Fehlerterms \eqref{laguerre:gamma_err_shifted} -% ein Optimierungsproblem % -% Das Optimierungsproblem daraus lässt sich als Daraus formulieren wir das Optimierungproblem \begin{align*} m^* @@ -361,8 +414,8 @@ nur wirklich praktisch sinnvoll für kleine $n$ ist, können die Intervalle $[a(n), a(n)+1]$ empirisch gesucht werden. Wir bestimmen nun die optimalen Verschiebungsterme empirisch -für $n = 2,\ldots, 12$ im Intervall $z \in (0, 1)$, -da $z$ sowieso um den Term $m$ verschoben wird, +für $n = 1,\ldots, 12$ im Intervall $z \in (0, 1)$, +da $z$ sowieso mit den Term $m$ verschoben wird, reicht die $m^*$ nur in diesem Intervall zu analysieren. In Abbildung~\ref{laguerre:fig:targets} sind die empirisch bestimmten $m^*$ abhängig von $z$ und $n$ dargestellt. @@ -382,7 +435,7 @@ Den linearen Regressor = \alpha n + \beta \end{align*} -machen wir nur abhängig von $n$ +machen wir nur abhängig von $n$, in dem wir den Mittelwert $\overline{m}$ von $m^*$ über $z$ berechnen. \begin{figure} @@ -395,8 +448,8 @@ in dem wir den Mittelwert $\overline{m}$ von $m^*$ über $z$ berechnen. \end{figure} In Abbildung~\ref{laguerre:fig:schaetzung} sind die Resultate -der linearen Regression aufgezeigt mit $\alpha = 1.34094$ und $\beta = -0.854093$. +der linearen Regression aufgezeigt mit $\alpha = 1.34154$ und $\beta = +0.848786$. Die lineare Beziehung ist ganz klar ersichtlich und der Fit scheint zu genügen. Der optimale Verschiebungsterm kann nun mit \begin{align*} @@ -413,8 +466,8 @@ gefunden werden. In einem ersten Schritt möchten wir analysieren, wie gut die Abschätzung des optimalen Verschiebungsterms ist. Dazu bestimmen wir den relativen Fehler für verschiedene Verschiebungsterme $m$ -rund um $m^*$ bei gegebenem Polynomgrad $n = 8$ für $z \in (0, 1)$. -Abbildung~\ref{laguerre:fig:rel_error_shifted} sind die relativen Fehler +in der Nähe von $m^*$ bei gegebenem Polynomgrad $n = 8$ für $z \in (0, 1)$. +In Abbildung~\ref{laguerre:fig:rel_error_shifted} sind die relativen Fehler der Approximation dargestellt. Man kann deutlich sehen, dass der relative Fehler anwächst, @@ -512,21 +565,36 @@ H_k(z) \frac{(-1)^k (-z)_k}{(z+1)_k} \end{align*} mit $H_0 = 1$ und $\sum_0^n g_k = 1$ (siehe \cite{laguerre:lanczos}). -Diese Methode wurde zum Beispiel in -{\em GNU Scientific Library}, {\em Boost}, {\em CPython} und +Diese Methode wurde zum Beispiel in +{\em GNU Scientific Library}, {\em Boost}, {\em CPython} und {\em musl} implementiert. -Diese Methode erreicht für $n = 7$ typischerweise Genauigkeit von $13$ +Diese Methode erreicht für $n = 7$ typischerweise eine Genauigkeit von $13$ korrekten, signifikanten Stellen für reele Argumente. -Zum Vergleich: die vorgestellte Methode erreicht für $n = 7$ -eine minimale Genauigkeit von $6$ korrekten, signifikanten Stellen +Zum Vergleich: die vorgestellte Methode erreicht für $n = 7$ +eine minimale Genauigkeit von $6$ korrekten, signifikanten Stellen für reele Argumente. -Das Resultat ist etwas enttäuschend, -aber nicht unerwartet, -da die Lanczos-Methode spezifisch auf dieses Problem zugeschnitten ist und + +\subsubsection{Fazit} +% Das Resultat ist etwas enttäuschend, +Die Genauigkeit der vorgestellten Methode schneidet somit schlechter ab, +als die Lanczos-Methode. +Dieser Erkenntnis kommt nicht ganz unerwartet, +% aber nicht unerwartet, +da die Lanczos-Methode spezifisch auf dieses Problem zugeschnitten ist und unsere Methode eine erweiterte allgemeine Methode ist. -Was die Komplexität der Berechnungen im Betrieb angeht, -ist die Gauss-Laguerre-Quadratur wesentlich ressourcensparender, -weil sie nur aus $n$ Funktionsevaluationen, -wenigen Multiplikationen und Additionen besteht. +Allerdings besticht die vorgestellte Methode +durch ihre stark reduzierte Komplexität. % und Rechenaufwand. +% Was die Komplexität der Berechnungen im Betrieb angeht, +% ist die Gauss-Laguerre-Quadratur wesentlich ressourcensparender, +% weil sie nur aus $n$ Funktionsevaluationen, +% wenigen Multiplikationen und Additionen besteht. +Was den Rechenaufwand angeht, +benötigt die vorgestellte Methode, +für eine Genauigkeit von $n-1$ signifikanten Stellen, +nur $n$ Funktionsevaluationen +und wenige zusätzliche Multiplikationen und Additionen. Demzufolge könnte diese Methode Anwendung in Systemen mit wenig Rechenleistung -und/oder knappen Energieressourcen finden. \ No newline at end of file +und/oder knappen Energieressourcen finden. +Die vorgestellte Methode ist ein weiteres Beispiel dafür, +wie Verfahren durch die Kenntnis der Eigenschaften einer Funktion +verbessert werden können. \ No newline at end of file diff --git a/buch/papers/laguerre/images/estimates.pdf b/buch/papers/laguerre/images/estimates.pdf index bd995de..fe48f47 100644 Binary files a/buch/papers/laguerre/images/estimates.pdf and b/buch/papers/laguerre/images/estimates.pdf differ diff --git a/buch/papers/laguerre/images/laguerre_poly.pdf b/buch/papers/laguerre/images/laguerre_poly.pdf index 21278f5..f31d81d 100644 Binary files a/buch/papers/laguerre/images/laguerre_poly.pdf and b/buch/papers/laguerre/images/laguerre_poly.pdf differ diff --git a/buch/papers/laguerre/images/rel_error_simple.pdf b/buch/papers/laguerre/images/rel_error_simple.pdf index 3212e42..0072d28 100644 Binary files a/buch/papers/laguerre/images/rel_error_simple.pdf and b/buch/papers/laguerre/images/rel_error_simple.pdf differ diff --git a/buch/papers/laguerre/images/targets.pdf b/buch/papers/laguerre/images/targets.pdf index 9514a6d..dc61c88 100644 Binary files a/buch/papers/laguerre/images/targets.pdf and b/buch/papers/laguerre/images/targets.pdf differ diff --git a/buch/papers/laguerre/main.tex b/buch/papers/laguerre/main.tex index 57a6560..91c1475 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -9,7 +9,7 @@ \chapterauthor{Patrik Müller} {\parindent0pt Die} Laguerre\--Polynome, -benannt nach Edmond Laguerre (1834 - 1886), +benannt nach Edmond Laguerre (1834 -- 1886), sind Lösungen der ebenfalls nach Laguerre benannten Differentialgleichung. Laguerre entdeckte diese Polynome, als er Approximations\-methoden für das Integral diff --git a/buch/papers/laguerre/presentation/presentation.pdf b/buch/papers/laguerre/presentation/presentation.pdf deleted file mode 100644 index 3d00de3..0000000 Binary files a/buch/papers/laguerre/presentation/presentation.pdf and /dev/null differ diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex index ecd02ab..811fbfa 100644 --- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -163,7 +163,7 @@ da Gauss-Quadratur nur für kleine $n$ praktischen Nutzen hat} \alpha n + \beta \\ &\approx -1.34093 n + 0.854093 +1.34154 n + 0.848786 \\ m^* &= diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index a494362..841bc20 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -3,20 +3,21 @@ % % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % -\section{Gauss-Quadratur +\section{Gauss-Quadratur% \label{laguerre:section:quadratur}} +\rhead{Gauss-Quadratur}% Die Gauss-Quadratur ist ein numerisches Integrationsverfahren, welches die Eigenschaften von orthogonalen Polynomen verwendet. -Herleitungen und Analysen der Gauss-Quadratur können im +Herleitungen und Analysen der Gauss-Quadratur können im Abschnitt~\ref{buch:orthogonal:section:gauss-quadratur} gefunden werden. Als grundlegende Idee wird die Beobachtung, dass viele Funktionen sich gut mit Polynomen approximieren lassen, verwendet. Stellt man also sicher, -dass ein Verfahren gut für Polynome funktioniert, +dass ein Verfahren gut für Polynome funktioniert, sollte es auch für andere Funktionen angemessene Resultate liefern. -Es wird ein Polynom verwendet, -welches an den Punkten $x_0 < x_1 < \ldots < x_n$ +Es wird ein Polynom verwendet, +welches an den Punkten $x_0 < x_1 < \ldots < x_n$ die Funktionwerte~$f(x_i)$ annimmt. Als Resultat kann das Integral via einer gewichteten Summe der Form \begin{align} @@ -29,25 +30,35 @@ berechnet werden. Die Gauss-Quadratur ist exakt für Polynome mit Grad $2n -1$, wenn ein Interpolationspolynom von Grad $n$ gewählt wurde. -\subsection{Gauss-Laguerre-Quadratur +\subsection{Gauss-Laguerre-Quadratur% \label{laguerre:subsection:gausslag-quadratur}} Wir möchten nun die Gauss-Quadratur auf die Berechnung von uneigentlichen Integralen erweitern, -spezifisch auf das Interval $(0, \infty)$. +spezifisch auf das Intervall~$(0, \infty)$. Mit dem vorher beschriebenen Verfahren ist dies nicht direkt möglich. -Mit einer Transformation die das unendliche Intervall $(a, \infty)$ mit -\begin{align*} -x -= -a + \frac{1 - t}{t} -\end{align*} -auf das Intervall $[0, 1]$ transformiert, -kann dies behoben werden. -Für unseren Fall gilt $a = 0$. +% Mit einer Transformation +% \begin{align*} +% x +% = +% % a + +% \frac{1 - t}{t} +% \end{align*} +% die das unendliche Intervall~$(0, \infty)$ +% auf das Intervall~$[0, 1]$ transformiert, +% kann dies behoben werden. +% % Für unseren Fall gilt $a = 0$. Das Integral eines Polynomes in diesem Intervall ist immer divergent. -Darum müssen wir das Polynom mit einer Funktion multiplizieren, -die schneller als jedes Polynom gegen $0$ geht, -damit das Integral immer noch konvergiert. +Es ist also nötig, +den Integranden durch Funktionen zu approximieren, +die genügend schnell gegen $0$ gehen. +Man kann Polynome beliebigen Grades verwenden, +wenn sie mit einer Funktion multipliziert werden, +die schneller gegen $0$ geht als jedes Polynom. +Damit stellen wir sicher, +dass das Integral immer noch konvergiert. +% Darum müssen wir das Polynom mit einer Funktion multiplizieren, +% die schneller als jedes Polynom gegen $0$ geht, +% damit das Integral immer noch konvergiert. Die Laguerre-Polynome $L_n$ schaffen hier Abhilfe, da ihre Gewichtsfunktion $w(x) = e^{-x}$ schneller gegen $0$ konvergiert als jedes Polynom. @@ -55,20 +66,32 @@ gegen $0$ konvergiert als jedes Polynom. % $L_n$ ausweiten. % Diese sind orthogonal im Intervall $(0, \infty)$ bezüglich % der Gewichtsfunktion $e^{-x}$. -Die Gleichung~\eqref{laguerre:gaussquadratur} lässt sich wie folgt -umformulieren: +Um also das Integral einer Funktion $g(x)$ im Intervall~$(0,\infty)$ zu berechen, +formt man das Integral wie folgt um: +\begin{align*} +\int_0^\infty g(x) \, dx += +\int_0^\infty f(x) e^{-x} \, dx +\end{align*} +Wir approximieren dann $f(x)$ durch ein Interpolationspolynom +wie bei der Gauss-Quadratur. +% Die Gleichung~\eqref{laguerre:gaussquadratur} lässt sich daher wie folgt +% umformulieren: +Die Gleichung~\eqref{laguerre:gaussquadratur} wird also +für die Gauss-Laguerre-Quadratur zu \begin{align} \int_{0}^{\infty} f(x) e^{-x} dx \approx \sum_{i=1}^{n} f(x_i) A_i \label{laguerre:laguerrequadratur} +. \end{align} \subsubsection{Stützstellen und Gewichte} Nach der Definition der Gauss-Quadratur müssen als Stützstellen die Nullstellen des verwendeten Polynoms genommen werden. Für das Laguerre-Polynom $L_n$ müssen demnach dessen Nullstellen $x_i$ und -als Gewichte $A_i$ die Integrale $l_i(x)e^{-x}$ verwendet werden. +als Gewichte $A_i$ die Integrale von $l_i(x) e^{-x}$ verwendet werden. Dabei sind \begin{align*} l_i(x_j) @@ -76,7 +99,7 @@ l_i(x_j) \delta_{ij} = \begin{cases} -1 & i=j \\ +1 & i=j \\ 0 & \text{sonst} \end{cases} % . @@ -97,6 +120,7 @@ des orthogonalen Polynoms $\phi_n(x)$, $\forall i =0,\ldots,n$ und \int_0^\infty w(x) \phi_n^2(x)\,dx \end{align*} dem Normalisierungsfaktor. + Wir setzen nun $\phi_n(x) = L_n(x)$ und nutzen den Vorzeichenwechsel der Laguerre-Koeffizienten aus, damit erhalten wir @@ -122,39 +146,41 @@ Für Laguerre-Polynome gilt Daraus folgt \begin{align} A_i -&= + & = - \frac{1}{n L_{n-1}(x_i) L'_n(x_i)} -. \label{laguerre:gewichte_lag_temp} +. \end{align} Nun kann die Rekursionseigenschaft der Laguerre-Polynome +\cite{laguerre:hildebrand2013introduction} +% (siehe \cite{laguerre:hildebrand2013introduction}) \begin{align*} -x L'_n(x) -&= +x L'_n(x) + & = n L_n(x) - n L_{n-1}(x) \\ -&= (x - n - 1) L_n(x) + (n + 1) L_{n+1}(x) + & = (x - n - 1) L_n(x) + (n + 1) L_{n+1}(x) \end{align*} umgeformt werden und da $x_i$ die Nullstellen von $L_n(x)$ sind, -vereinfacht sich der Term zu +vereinfacht sich die Gleichung zu \begin{align*} x_i L'_n(x_i) -&= -- n L_{n-1}(x_i) + & = +- n L_{n-1}(x_i) \\ -&= - (n + 1) L_{n+1}(x_i) + & = +(n + 1) L_{n+1}(x_i) . \end{align*} -Setzen wir das nun in \eqref{laguerre:gewichte_lag_temp} ein, +Setzen wir diese Beziehung nun in \eqref{laguerre:gewichte_lag_temp} ein, ergibt sich \begin{align} \nonumber A_i -&= + & = \frac{1}{x_i \left[ L'_n(x_i) \right]^2} \\ -&= + & = \frac{x_i}{(n+1)^2 \left[ L_{n+1}(x_i) \right]^2} . \label{laguerre:quadratur_gewichte} diff --git a/buch/papers/laguerre/references.bib b/buch/papers/laguerre/references.bib index d21009b..1a4a903 100644 --- a/buch/papers/laguerre/references.bib +++ b/buch/papers/laguerre/references.bib @@ -10,15 +10,13 @@ series={Dover Books on Mathematics}, year={2013}, publisher={Dover Publications}, - pages = {389} + pages = {389-392} } @book{laguerre:abramowitz+stegun, added-at = {2008-06-25T06:25:58.000+0200}, address = {New York}, author = {Abramowitz, Milton and Stegun, Irene A.}, - biburl = {https://www.bibsonomy.org/bibtex/223ec744709b3a776a1af0a3fd65cd09f/a_olympia}, - description = {BibTeX - Wikipedia, the free encyclopedia}, edition = {ninth Dover printing, tenth GPO printing}, interhash = {d4914a420f489f7c5129ed01ec3cf80c}, intrahash = {23ec744709b3a776a1af0a3fd65cd09f}, diff --git a/buch/papers/laguerre/scripts/estimates.py b/buch/papers/laguerre/scripts/estimates.py index 21551f3..1acd7f7 100644 --- a/buch/papers/laguerre/scripts/estimates.py +++ b/buch/papers/laguerre/scripts/estimates.py @@ -15,7 +15,7 @@ if __name__ == "__main__": ) N = 200 - ns = np.arange(2, 13) + ns = np.arange(1, 13) step = 1 / (N - 1) x = np.linspace(step, 1 - step, N + 1) diff --git a/buch/papers/laguerre/scripts/laguerre_poly.py b/buch/papers/laguerre/scripts/laguerre_poly.py index 9700ab4..05db5d3 100644 --- a/buch/papers/laguerre/scripts/laguerre_poly.py +++ b/buch/papers/laguerre/scripts/laguerre_poly.py @@ -46,7 +46,7 @@ if __name__ == "__main__": ax.set_yticks(get_ticks(-ylim, ylim), minor=True) ax.set_yticks(get_ticks(-step * (ylim // step), ylim, step)) ax.set_ylim(-ylim, ylim) - ax.set_ylabel(r"$y$", y=0.95, labelpad=-18, rotation=0, fontsize="large") + ax.set_ylabel(r"$y$", y=0.95, labelpad=-14, rotation=0, fontsize="large") ax.legend(ncol=2, loc=(0.125, 0.01), fontsize="large") diff --git a/buch/papers/laguerre/scripts/rel_error_simple.py b/buch/papers/laguerre/scripts/rel_error_simple.py index 686500b..e1ea36a 100644 --- a/buch/papers/laguerre/scripts/rel_error_simple.py +++ b/buch/papers/laguerre/scripts/rel_error_simple.py @@ -18,7 +18,7 @@ if __name__ == "__main__": # Simple / naive xmin = -5 - xmax = 30 + xmax = 25 ns = np.arange(2, 12, 2) ylim = np.array([-11, 6]) x = np.linspace(xmin + ga.EPSILON, xmax - ga.EPSILON, 400) diff --git a/buch/papers/laguerre/scripts/targets.py b/buch/papers/laguerre/scripts/targets.py index 3bc7f52..69f94ba 100644 --- a/buch/papers/laguerre/scripts/targets.py +++ b/buch/papers/laguerre/scripts/targets.py @@ -38,7 +38,7 @@ if __name__ == "__main__": ) N = 200 - ns = np.arange(2, 13) + ns = np.arange(1, 13) bests = find_best_loc(N, ns=ns) -- cgit v1.2.1