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(-) (limited to 'buch') 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 (limited to 'buch') 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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+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! +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 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 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 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 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 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 m in font nullfont! +Missing character: There is no a 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 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 a 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 a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c 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 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 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(-) (limited to 'buch') 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 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 (limited to 'buch') 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 (limited to 'buch') 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 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 (limited to 'buch') 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 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 buch/papers/fm/RS presentation/images/bessel.png | Bin 0 -> 40393 bytes buch/papers/fm/RS presentation/images/bessel2.png | Bin 0 -> 102494 bytes .../fm/RS presentation/images/bessel_beta1.png | Bin 0 -> 40696 bytes .../fm/RS presentation/images/bessel_frequenz.png | Bin 0 -> 11264 bytes .../fm/RS presentation/images/beta_0.001.png | Bin 0 -> 6233 bytes buch/papers/fm/RS presentation/images/beta_0.1.png | Bin 0 -> 6630 bytes buch/papers/fm/RS presentation/images/beta_0.5.png | Bin 0 -> 8167 bytes buch/papers/fm/RS presentation/images/beta_1.png | Bin 0 -> 11303 bytes buch/papers/fm/RS presentation/images/beta_2.png | Bin 0 -> 14703 bytes buch/papers/fm/RS presentation/images/beta_3.png | Bin 0 -> 20377 bytes buch/papers/fm/RS presentation/images/fm_10Hz.png | Bin 0 -> 6781 bytes buch/papers/fm/RS presentation/images/fm_20hz.png | Bin 0 -> 7834 bytes buch/papers/fm/RS presentation/images/fm_30Hz.png | Bin 0 -> 8601 bytes buch/papers/fm/RS presentation/images/fm_3Hz.png | Bin 0 -> 6558 bytes buch/papers/fm/RS presentation/images/fm_40Hz.png | Bin 0 -> 8795 bytes buch/papers/fm/RS presentation/images/fm_5Hz.png | Bin 0 -> 5766 bytes buch/papers/fm/RS presentation/images/fm_7Hz.png | Bin 0 -> 6337 bytes .../fm/RS presentation/images/fm_frequenz.png | Bin 0 -> 11042 bytes .../fm/RS presentation/images/fm_in_time.png | Bin 0 -> 27400 bytes buch/papers/fm/main.tex | 4 +- 31 files changed, 318 insertions(+), 188 deletions(-) create mode 100644 buch/papers/fm/.vscode/settings.json create mode 100644 buch/papers/fm/RS presentation/FM_presentation.pdf create mode 100644 buch/papers/fm/RS presentation/FM_presentation.tex create mode 100644 buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf create mode 100644 buch/papers/fm/RS presentation/README.txt create mode 100644 buch/papers/fm/RS presentation/images/100HZ.png create mode 100644 buch/papers/fm/RS presentation/images/200HZ.png create mode 100644 buch/papers/fm/RS presentation/images/300HZ.png 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 (limited to 'buch') 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 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 (limited to 'buch') 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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+\pgfpathlineto{\pgfqpoint{0.505591in}{0.463273in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.505591in}{0.463273in}}{\pgfqpoint{5.352140in}{3.442295in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.505591in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{0.505591in}{3.905568in}}% +\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{0.505591in}{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 \(\displaystyle {10^{-3}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.505591in}{0.463273in}}{\pgfqpoint{5.352140in}{3.442295in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.397615in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{1.397615in}{3.905568in}}% +\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{1.397615in}{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=1.397615in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle 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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{3.181661in}{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=3.181661in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{0}}\)}% +\end{pgfscope}% +\begin{pgfscope}% 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+\begin{pgfscope}% +\pgfsys@transformshift{4.073685in}{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=4.073685in,y=0.366051in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle {10^{1}}\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.505591in}{0.463273in}}{\pgfqpoint{5.352140in}{3.442295in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{4.965708in}{0.463273in}}% +\pgfpathlineto{\pgfqpoint{4.965708in}{3.905568in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% 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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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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 +- 3 files changed, 2 insertions(+), 2 deletions(-) (limited to 'buch') 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} -- 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) (limited to 'buch') 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 -- 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 (limited to 'buch') 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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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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innfZbTTMNpZ6jmr5mCZCRTxH9q9hQldzdHO6AAV9xawRgiAIIqNcc801+Oyzz1p97O2338bKlSuxcuVKXHDBBTj//PMz9NM5p3MKNG2nVNtlB5ISAs79TKrKko8eScmHx8viidixPbCWuUrdRrR8rPtINvmwtpRvrIaDrAcs+dq0v4tI9ss3MXGmiRiAJan71/BPGss3sj97JYkYTRjyPtg5FmPrrteYlo/5AkzIaz8HT8o3MFep27CWj/UaA9TuYRsXPKnYBkDVXyNCxGeK0AVY4i+iT1H73fQYmRQr/jvkLSxUld3L5PuYVcB+h0I2etYA2cUtji4AdBvO3HHe4rNyO9sMafU81lwtAb+3g5vYMzF5jfQaI0YMEgRBEBnl+OOPR9euXXU/p6oq3nnnHd0Dpds7vkz/AELQdkqTE+JkYXHIafxi1e1n0yK7j2z98e4jxEyNrNwOdB3SUnIIJCXEm4HigfxiJRLUJActK5/1kYgQaAe3sKEFyXQ/BGj6LxMWufpvQEdUbmcOVvL90nbcKzkLtJoSVvKXnKAC7L6WCRBoZRtZsu31t3xMey+UbWjp8eOB1kPXbXjLxwK5QGF/oELA+WQHN7MjEZLpMZqNUQ/Ws/XJi/J4D2nye1u7jwfWtQzW4EHdPnauW7KoBpjTWrmDXxyNim1tRYz2O6zYCuR14xdLE2HJ4jO/J5tSKWqjZ/hJrT/WcxQb7hKLtjiUBEEQBD8+vZP/hmLvccBpzs+onTdvHnr16oURI0ak/+J2Rid10NazhvTkhD67kJW58HZHtEEgPVIEWteh7EBd3ocRV+1iAikZTUDxLs3TE2gAcxF473wH65kDmCp0tWut4pykVm4HivozJ0sjq4BNl6vYzjlW/GdPFjEAE5+V2/n3vJVvaF1OBrQk/rzXv/Z6mrjV6D6c/wHSTVVAczU7Sy4Z7VpFrP+igWwypUZBbyCriP8AIE3odk/5n0jXoWzt83aQq3ayjZ5kkgUaTw7qCF2AVRnwdpCbqtlgldRnVtdhrHe3hnOVAUEQBNFuefPNNzukewZ0VgetYlvbRAdgyT7vwQVGyUfXYQBUllz1HN3m2xyhqiyxSnWZ8roDOV35JzuVO9iEyIK+rT/edQg7QFpVW+/Au0FzW9rcxyEtP0tyn5NbKne0FRVA3LHgLGK0NddlUOuPdx8BqFH2O00V+E4JNzMRPyHlgVQ0EPD4BAjdbUBhP+aaJdNtOLD6Xb5rpEq7j4Nbf1zrESvfxHeNVGxlQjMZRQG6DubvamliNlXEdx3CnLWGcuY68SASFyqp97E4vkZ4C7SqXUBBn7ZrpOsQdl4ZTxLP4xSBpt3Xym1t34cEQRCEe1w4XSKIRCJ4//33sWzZskz/KI7onA5a9S79/wl3GcSSYZ5UbAP8eSwBSabb0JbP86KxkpXKpSZWAEtAeF9b1U6geBA7kymZLoOBSDPbqeZFwmVKKfES6aClOggA+73xdpmqS1g5ZarQ1Zwgnr+32j0AVPZ7S8brYwl4JWd3sGKrvtDtNoKd+9ZQzi9WtYFAK473UVXv5hdLi6f3XusyhP96rNjGzltrsxmild1yjFddAkBt60R6/WLWSPUu/dLrLoPZ+gjW84ulV3ILiHOQCYIgiHbJV199hVGjRqF///6Z/lEc0fkEWriJCYfiwW0/12UwO6w0EuQXr7aUlcqlugRd4wkBTzdGS+T1ksai/vzLd/TKKYGW5J+nsKiJJ9fJQwsAVl6W3wuo5BhLK5XTExZdBgMNZWwd8aJqF/v9eFMM64T43MkvVnV8SmnxgLaf6zqUf/KtVyoHiEmIE+s/RXz6slhJczXHCa3NtWydpApdgN3H6hJ23hwvDDdDNAeZ4+/N7DlSPLDlvciL6l3691GLz7OqQRPpRSn/Qy7owwQw7/VPEARBZJTLLrsMRx11FDZt2oT+/fvjxRdfBAC89dZbHba8EeiMJY5akqbroA0GoLL/iaeWLjmldm/LyO9kcorZlLQqjsmHtmtvJNA2zmITA1OTPCdo5ZR6AyUSwmJXy3lebqnezcanZxfqxOPsWCREjM4a0QRizR5+a6S6RH895vdkSSPPazMSugATFruX8Cs7jASZA1KoszulJci1e9zH0ajaxUamZxe1/VzxAL5HaBi5dQATpLEI25zR+7wTakr0XabigQAUvmvE9DkyANj8Ob9Y0Qh7L40zcNAA9pxJHujkhpoStqHjz279cUVh61/EwfAEQRBExnjzzTd1P/7KK6/I/UE40/kcNE0Qme3YcnV+9gBF/fQ/V9SfCThusUyS76IB7AyvxoN8YmnllHruiJZI8tz5rtmtf11aPJ67+jVx0aD3e0sINM7Jvt56VBS2Jrk6aLsBxaO/adBlCJs4ymuMet0+9qderML4veXp6hrdR4D93niWOBq5dYAYV6t6t77r6Qsw96eGo9Ct2Q14A0zIpFI8MO4gcxpuVLeX9VnqljgKKPGtNnuODOJfBksQBEEQAuh8As1s5zshLHbyiRUNs3LKQgOBVtiXr4NQs4e5B3qjxDXHgpeQ0ZImvYTYn81KyrgK3VLjxKqoH1C7j99B3NrvxMz54SUsIkG2Royurctgvv1FNbtZH1PyiH2NhKvF6dq0zQc9oZtdyA4L5rn+6/Ybv9eKB7LfGa81YrrRE/8YrzXSXMtKbg3Xf3++Gwa1e5no03PaExsUnK4tMdhF5z7mdAECBfxLpfWELhDfMOO4HgmCIAhCEJ1QoJWwg5z1Jp7l92LDGmr38YlVtx+AmkagcXTQavfoiwqAv7DQknijZKd4AGd3xCSxKuzHDrptKOMTq6aUHeSc10MnVl/mQPG6Ns1lMnJZebuD6e4jwG9Naq9juP778XV+6vYBBTquD8CuORYG6vfziVVdwgRmTpe2n8vvzf7kdR+137+ZsOD5XqvZ07ZHS6OYs4NsthmiKPHNF073MRaLX5vJRk+wlgligiAIgmjHdD6BVrefnVWk12Pj8bLPcUtQteTDKEHtz0oOeZUL1ZSal1MC/BLidMl3QZ8W8eGW5ho28c8oaeR+bXuAQgMHwetn18arFCpxH3XKAAG2aRCqB0INfOLV7Da5j5zLDhPr3+Daivrxc+siQaCxou201EQszs5P7Z64WNd5jvgCQF5Pfm5MYrCFwSHzRf3Z2ufpIBv+zjhPxEy3Rng+RxrKWZm3kUBLbFCQi0YQBMELlfc5nZ0QJ/eoEwq0fcZJHMAShTreAs0g+dA+zjOekWDK6QL4cvglH7V72Bloeg4C0OKO8Hhj1sVdj9QR48mxAH7Jfo2JEwnEE2LeAs3g96b1AdVzcAdVNb5BYbD+83qwc664OT97mMuUVaD/eU1Y8EA70qGgt/7ntWuu4+SgWXmOSHPQOPaXxmLxwUYmrj/ATzTV7mPDklLPQEuOx6uiQXv2pd3EosOqCYIgeJCdnY2KigoSaSaoqoqKigpkZ2en/+IkOt8Ux7r95hPBCvrwO9C5Lk3SqCU7tXv1R7rbIdzEHASj5ENRWPkXrwRVm05pNO2vsC8QbmAlQ3pT9eygiROjg3i5l+btAQZMNf58QW+gbAO/WIC5gwawe6A3kMUOTVUskTeK5YmfxcZTxJuKmCQHOXWqnl0SIt4gHm+BVrsPGDbK+POFfflNaK3bz8pq9UpugaSyw93uD6tuPMhKQY0EmtfPDr3nsWEAMKFntB4B9l6rPwDEomx9uoqVZo2QQCMIguBK//79UVpaivJyjmeedkKys7Ntn8fWOQXa8JOMP1/YD9j2DZ9YDWWslym72DgWwEdYJJwYk19wQR++As3I0QKSxOc+9wKtIY1Ay+3K3DweiZWqpk8a83oC9d+6jwWw+2jmMuXHk3Ie/XXaGpHl/NSXGW9OAC39YvUH9IdE2EFzdIzi5XZj7iAP5ycWZT9zuvu4a4H7WACLldfTWKAkJmLuAfpNdhdLew8ZbfQA7H3Iq98znYgv6MOmPDaUm68lKyTWiEG8/N5MCFOJI0EQBBf8fj+GDHG5uUzo0rlKHIP1bDS82f/oC/uynh8ejeL15fGyMYPbqCWoPERTQqCZJTu9+Q1JMDrfTSMh0DgkO/XxnZc8A4GmKPx6VZprgGjIOBbAEtTmaj4HmqdLUPOTRIxb0iWoAEvMeTkI9Qf0R7VraMM0uFzbgdavmYrHwz7H471WX8ZEg9l7rbAvWyM8egfrD5g7Y9rneIimhMtk8ozM68HPQatNsxmSXGXglrp95k6k18fWK6/yTYIgCIIQRLsQaIqieBVFWaEoykxXL5ToU0mTWAF8EoKGshYHRI+sQtYXxiNBbUgjYgB+CWoslt5l4nkf6w+w6ZpG/W5AfFefg4XecLDl9cxiAXzi1e4zT/RzuwNQ+CTEiXPJ0jgWvPrd6svM7yPPDYq6fcwhy+1mEq83n+Rb6xk1c5ALkhxkt9QfMBdM2jU3cOhB055FpsK6F581kjiGJE2JI8BvjeT1ZELMiPye/MQnQRAEQQiiXQg0AL8C4L7pJ10ZVPLneDhN9WXmgolnX5gmFkwT4t7MHQzWuYvVVMlcpnSlSQCfhLghnugbOZEA2xXnkaBqLkRed5NY8XvMI5GrP2Ds+gAsmczrzkfEa2LBLF5ej3jvYL27WME6INIk0UHbz17PbI0UcNqgqLUgdBOlqRxEfF0aB41nX1hio8dkY4nXZkj9AQBqmucIx0FK2gRfM/J78VmPBEEQBCGQjAs0RVH6AzgDwAuuX8xK+Y6WNNZx+J90fZl5gqrF4+WgKR5zl6mA07VZEYO+LOYQctnVLzdPGIG4QOPhoFlMUAH3CXHCZUpzbfm9Wso83VC3lzlyvoB5LMD9mkwMdjFZ/3nd2Zrl5Y6kS755lcFaKRXNjQt8t5MVY9H4BkU6YcGpL6y+jPWM+rKMvyavB5+jH6w8R7SNEh7PEbMJphrkoBEEQRAdgIwLNACPAvg9AN1DfhRFuUFRlKWKoixNOyXGVvLtMkFVVRYvXfLNy0GrL2NJodmks4RAc5mkWrmPACu94jH6uyFNqZz2szRWsITWDVpyZuZ85nEa3BGsZVMVzWIB8aSR04ZBWgeBU/lmolTO5No83vjAFR4CzYI7UtCL9YW5PXew4SAApUWE6cFLWDRWAGos/UYPTwfZynoE3AuZhgr2p9lzxOtngpGLQLMg4rXyTV5nyhEEQRCEADIq0BRFORNAmaqqy4y+RlXV51RVnaKq6pQePdIIhoZy1qdiNFURYNP0ePSFNVWxcdVpk53enEqTDqYXTLzdkbSuVneODpoFgabGgMZKd7ESybdJLxOvBLXegoMAxEUMp/I1s9LN5J/F9RqJi650wqKgFx+32krynXC1KtzFaihnk0PNepl4OWgJ19+CQONScltuwfWPf96tiNe+3+y9BrB76fZ3Fo2w17BybWqUlXETBEEQRDsl0w7aMQDOVhRlJ4C3APxYUZT/OX61hMtkcllaX5jr3WGLyXdBLyBYw84xcxXPQqkctwQ1nnSmddA4JFaqas1B49Xz01CWPvn258TLNzklqGmFddxBc3vQoy0R71Z8WihxBOIbFC4dtHAzc8bSCrS4EHC9/svS30d/NhAoaHGJ3MQCrLlaXEp8LTxHtGt3K+I18Zpu0yCvu3uh21RlLRavzReCIAiCEEhGBZqqqnepqtpfVdXBAC4F8I2qqlc6fkErCSoQL3NxmTRaKfECknreXMZrsNCnldMFgMLHQUjX7wYAed3cO2jN1WwgiZUSR8B92aGV+6jFc5ugpjvfTSO/FyuFDLo8+sHK+s/txn63PARausmbABMDbvvrtPdquv6iPE6ultXnSF43DiJeKwO0IGKCte7LN6241dxKHA8C3gDb7DAjt7t7oas983K7mn8dz2MtCIIgCEIQmXbQ+GKlJwzg0yhupZdJiwW4FzJWEiuvD8gpdh+roTy9Ewm0OGhunJ90Z6BpJAQaj/toVcS7FRZW1wgHVyvczM4ATFdO5vGy35trd6Qifjh0ujXSjZWTuVkj2uZGukEaCQfNbRmsxTWSy8H5SQiLNL+3PA69g+Fm5uZbddBci8+D7B4pivnX5XaVdx9JoBEEQRAdgHYj0FRVnauq6pmuXsRqYsVjsqLVEkdtR9eNqxVqYKPR0+2yA3zKDhsOpr8ugP08sTA7/NlxLIsuE7ek0eoa6cHHrUvX7wbw6QtrtFiWCvA550oTaOnI7cYc0pCLsf6JqYppyilzOQ3usCri83g4PweZE2nWNwvwcZCtrhFeY/0bDzKXMR15HDZ6tGtL2+/GqQyWIAiCIATSbgQaFywn371Yz0Ik5DxWfRng8adPrHgkBFbFoBaPR4mjVTEIuItntVQ0u5gNgOFRdmVJfHKYrFhfxn4fZv1uAB+Bluh3s/J76+p+jTRWWhdogMv1rx0unkag5RTDdYlvJMhcJqsCjUc5pRUnkocTn3CZLKwRHpNFrZaK5nYHYhFW7uwUqw5adhETxG5dVoIgCIIQSOcRaKEGINxoPUEF3E3yqo8PErBS4gXwSVAtJ40cBhdYSeJ4jBq3WuLo8cR7VTiUeFlZI/m9mDMYCTqP13jQmohJlF25uDY7ayS3q/spdo0V1twRnus/Xb+bx+u+XC4hBi0Ki4aDLp2fCmvrMTG4w42DZlHEaPF4uNW2niMu1oh2bTlpetAUha0jmuJIEARBtGM6j0CzOjEPSCo7dPE/aSvT0AAgkM8a5V25TBbH3gPs2lyfzVRpUehqybebhNjisAnA/VlQtsoAOZRUNlalH1oAxN1Bv7vBNQmBZuH3ltPVvYNgp8QRcBevsYLdI6/fWjw3ayQxGt6isHBd4mtRxHMpcYz/DqysSV5lsLaceDfv7Ur2rPVnW4jHwUEmCIIgCIF0HoFmZ3dYEwOuHTQLpXKK4r7s0Jb4dNnPEQ2zaXGWBBMPBy0+Yj+dEwm47wuzOrQj+WvclHk1VaXf0Qfi7iCnNWJFWOR2ZeVkTg/rjcXYe0dWiaNVMQjE179LMQhYvDYOJb5WRUwglwkQLiWOVlxdl4OUwk2s79CS+Ix/jdtrsyI8AT4bFARBEAQhkM4j0LRzcKwkxNrXaN/jhAYLB74mx3Pr1gHWSxzVqPNd/aZq9qeV+8hj51srFbWC27IrO2WAib4wF/GaKoFcC0IXiO/qu1gjTZXMhcsqSP+1OV3Zod9Oe36aq9n3WxIxHIbkNB60JmIAluy7WY+J54hFRxdw7+paEdVaPNcljkr6vlktVriBlY47wVbJLSeha1nEd3X37CcIgiAIwXQegdZoI7FyW+KoqnHnx6KwcNvz03CQnSVkqXzHpWNhJ0EN5AL+XPe9I5aTb5cljomJkTYEmlPHTlXZ+rIidIF4X0y1s1hA3K3rkn6kOZDUg+kwSU2UyllIiLO0oQxu1ohFt077mdzEsiXQXJb4RiMsnq3177LEMac4/dAaIGn9O9ygsHpIdfLXuCpxtCHQyEEjCIIg2jmdR6DZSawSDprD/0kHa1nvidWdb7dJox2Xye1utHZPLDs/LifZWS0DBOK7+o1A0OHIdluloi6FbriRHT5tuezK5eACTaBZiuVyg8LqocBAvHzTZc+P1T4toKXE0Wn5ZsJBtrLR47LEV3tmWb22/J4cygBtiBjA+RrRNm2sPCP9OYA/z/1Gj+U1QkNCCIIgiPbN/0+BFsgFfNnOkw87sQA+/UWWBVo8sXKbNFq9tjyXQxnsCAu3Z6HVl7NEMJCX/mv9uYA3y73LZFV8ui1xbKy0sR5dblDY6WXSvs7p+ldVm8l3t3iJb7WzeE1VrNfLF0j/tYkeTIfr0fZ7jUOJo537CLgQaDaOfQDcl6Y2VlrfMMvpCkSagVCj83gEQRAEIZBOJNAqWRmglfIdwJ1jYWcaGsCSnaYqIBZ1Fq/BTg+OSwfNtrBw4aDF4n1QtgWaw3h2EtTEOG6HAq3J5hrRYjkd7tJUbcNBi3+dawfNjkBz6VbLWv92Ngw058dpLE1E5hRb+/rcbmxdOXUH7ZTcar9bx89IGyWOQMuRBU4IN8cHkti8NprkSBAEQbRTOpFAq7Ke6ADxPgSnybcDB02NOR/c4WjnW5aD1t15aVKwlt0XO24d4PzamqttrhEXAs2u0M3pykoiww539e0IC+kOmosSRyexkr/PLnafI3kuhIXd91pOMXu/hOqcxbM7SEP7Hic0HIwPrSm09vVuDv1ObIbYvDYqcyQIgiDaKZ1HoNnZHQbcTfKyMzEScLdjq6r2hEUgD/DluOtBU7xAdpG1r8+NlyY5cX60BMlqgqpNn3M6TMO2iHcxuMOJgwa4W5NWY2UVAYrHnYPmy2ZloFZwU+LYaPe95rYvzEapKOBSWNgUaG7Wv6rGp4pavI/Z2hpxIdDyelgbWgPEz6+TJOLd9tcRBEEQhGA6j0Cz4yAA7kocbTtoWkmZgwQk3AREQ/auzU2yo4kYq4lVXvd4P4eDcdy2HYT41znuL6p2sEZkuawuksZIkI1Etyo+PR73Jb653Wwk3y4GdzQ7cKsBOSWOgLvSPJnrP9zI3qdWRYwnfni8YxF/sMXxtoKbjR6nLis5aARBEEQ7pXMJNKu7w4C7oQyNNp0fN0mjloxZObtII8+NY2HXiXTR82PbQShq/X1O4tm5j65KHG06P24mi9qZPJgcz42DZuu9Fh/cEXRQ4pu4tmJrX+92ZLvtjZ5idwNJoDBH02qsxPfZxK6IAeJrxIWrZSeWm40ectAIgiCITkYnEmg2S5M0B8FRaV6VvYEkbgRaQsQUW/8ebTfaCU4SVMBZkmpXWHjipZdOS7zsDCQB2LW5GRJidRog4K7E0a7QBdydzWc3+XYzEdDuBkVicIeDWKrq0Il3eih83K32WHwMuylxdCLQtKEkTrB9H12czWfnXD7AfTkxQRAEQQimcwi0WMxB+VpXIBYBgg4a7u2KQVcCrZr9acf5ye3urgfNjjviJmlMnANlM56TxCrcGC8VLbb+PTld2PeFm+3Hc9ITqX2fXZwINDdDchwLNBfr3+4GhZOyw1A9eybY+b1lFzNn0MmEVidiEHC2GWLn7DoNN9M3bT+Pi9mfbq7NajxfAAgUkINGEARBtFs6h0AL1gBQnSXEjkrKbCZWfu3cNRcljrYTVKcCrVqigxYXCLbKDovluHVA0hpx4mpVWj/sG0ja1XeyHm2W3AKSHTQXEwGbq9nQG1+W9e9x6nw6ErrF7E8nE1qdutWOHDSbLhPA1q/TwUZOyokB5+5gdrH1igbA+bURBEEQhAQ6h0Cz2xMGuC+psbMTrSjOd6OdOGg5Xdgo7mjYfjy7zo9bB81OqSjgfLKik14+N6VQdu+jL4uV5rlxIu26MU7WYzTC7qVMB83O5gTgQsQ7uI+J9e9QENrd6PH45ZQBAs7fa6F61nNo5/fm5j7aOaRdI8fFBgVBEARBCKZzCDQ37ojTkjI7ib4WT5aDltjVr7UXKzENUFZpUqX95NtpiaOTXj5XfWE2RTzgfHCN0x60SBObEuokliyB1lxt/72WXezM0XK00VPM/nQqCO3EUhTn4rOxgo3Nt3p8BsC+NtLEngt2cLSpFP9aJ9fWXGP/OeJmSBRBEARBCKaTCDSbZ04B7pJvJwmB06l5TdWwNekNaEmM7CY7ieTbRtIYyGfnpjl1fmzvfHeRV+Io00ED3JXmKV7rhwIDzifZ2e33AdjZfB6/8/VvW8Q7HCTjykFzGM/J+ndaBpjThQ3asUriOWJT7Dp1dAHn7rhdEU8OGkEQBNGO6SQCzeGQBMB+0qiqLGGxsxMNuHPQsousT3oDksbRV9uL5eQ+Jnb1JfTgAC0ixu70TUf9bg4FWizK7oddB81p0mj37DrAeQ+m9nu2I5q0NRK06egCDpPvYnkljk6dH22wkRN30OmYfbsbBk7FpxPXX9voceqgOXoe0xRHgiAIon3y/1igORzKEG4EYmEHiVWRswTVaQ8OYD/ZSZR42U3kiuSUeAHs62MR++clJZJGCQ5asza0xsG1OS1xtO3WOdygSPTy2bw2x66WA7c6u5idqWV3+qaTMlinIibodI0UO3yvOSi5dToAxUmJoybiHTnI1Q5KHLux34GTPl2CIAiCEEznEGhakmknIfD6WNmg7QQ1nqzY3bHNLnLmMjnqwSlq+V47OBG6QHxX32YsLZ6TWICza1O8QFaB9e8J5AMen/2k0anQze0qZ9iEFgtw7qC15/XvdIOiqYpNjPTnyIkFyCtxbK5x8RxxWuJoN16xi2uzux6L49/rYNOMIAiCIATTOQRaUxUTW3amAQKs18qROwJnCWo05GxX30miAzgocXQwJAFwtqufOBTY7q6+Q1dL22W3UwaoKPGE2G4sBz2RQLzE0WH5ppNEH3BQviZRoMWizHV2uv6dOD92f2f+HHaEhoxyYiBDIsZmPCdutfb1dmOFm4Fo0Nl6BJy5kQRBEAQhmE4i0BxMAwSc9XM46cEBXOxGV7twEBzufNtNUp0kjcG6+ChuB2IQcJYQ272PQItoshsLcJagqlH7v7dGJ06kw/WYKHG0MZBEi2c7liYGi23Gin+9kw0Ku/dRiydtjRQ7OxjbkUBz6sRXM7c6kG/v+5yUODo5PkOLBThzdQmCIAhCMJ1EoFXZFxWAs76wRH+FzWQny0VCbFcM+rIBb8BZD5rH5yyxsp3EOXTrnJ6X1FztLPnO6eKgDDC+ppwMLgCcJft2r82fy37XTta/3YOjAWcCzWmpnJuyQ0drpNiZiAGcO5927qWqsjXpRFQDzoaE2HWrAWcbPW4c3eTvJwiCIIh2ROcRaE7cEam7+g4SAlV15qApirOzoLQ+FaeJlZ3SPDcuE+AsIXbisjopcUzs6ttMGp0MromG2aHkdu+jojhf/47c6vggGTtrxKk74thBc1BOrMWTWeII2Fv/oQbmzNpdj/5sttnj6DliMxbgrMQxIXSL7X0fCTSCIAiiHdNJBFq1w9KkQvtN4jJ3bLWJkY6uzcHUvKCDXXaAJUdqFAjVW/8eNyVeyd9vJ55jB63a3vdorpSdc8mApDViY006dWIA9vPJSr6zi1kPZsRGD6bT5Nuxg1btUFgUuxgSUmw/VvL3W8HpM0v7Hts9aLX21z7QclxHLGYjlsQNM4IgCIKQROcQaE6FhSOXqTr+vQ4FWtBGPKcJqvY9thMrp8m3g1IopwItMVnRRizA2TRAwKGDVgN4s5gDYQcnSaOTM6eS40kTaC6uTVbyHax16MQXs+MA7NBUBQQKAK/f3vc5Ge7idMMAcOHEOxTxasxe2S2VOBIEQRCdkM4h0JprnCUfWYVAuAGIRuzF8ufZT6xkJqja99hOrBzufDuZmufUQUiUb1Zb/x7tUGCnJY6heiASsv49UkVM/Gsd/d6cCLRqedfmdIPC62fvUTsiJhpmjrW00jyHjq6TEke3Dpo0J95B+bLTZ2QgH1A8JNAIgiCIdknHF2jhZlY65SZptLVjW93+E1QtnpOGe6clXoDNxMrFrr5dVytYC0eHAgPOpr05GcgAtNwLGQ6C9j1O+xRtxypu+X7Lsapbf68d7DrIrtZjMfud2Zms2FQN5Lh4rzkqcSx2Fs/JGslyc23VNmLFv9bu+81pDyZBEARBSKDjC7Sgw4l5yd9j17FwIpj8OYDH78xlkpGgAu5KRQH7ZVcen71DgTVyip2VUzq5j05Fk5P16GRXP7H+ZTloEt3Bpmo2pMJuqShgf3CHVnrsZv3bFZ9uhK4tEeN2jdiIpcVzWuII2BefTqaKAiTQCIIgiHZLxxdorhyEwtavYQWngwQUJT6URHJ/ka2pebXudr7tOhZZhfYnRgL2z51yenAu4GyNOC259XiArAJ7Q0LcOD92E1RVldun6FTEaPFklQE6crUclhP7s5kgcVQGKMFljUZY2bjTYUOAvWtzWroMOBOfBEEQBCGBTiDQXCaogP3k20mio8VzMqHP6U67GmMHQlshGo4nVm52vqutf49Ttw6w3/Pj9Ow6wJmDFnToIAD2E2JXGxTFrO8qGrb29cE6tqZklcG6Sb7tlua5eo4Usz+lrf9im0LXTZ9isb3Jim4qGpwMQHH9PCYHjSAIgmh/dAKBVs3+lJV8y0wImmsAKM77YgDrCbEm5Bz3TinOHDQn2E1Q3VxbwkGTtEaybB6eHqwFoNg/XBywP9bfjRjMcuJEVrtw0IqdiRhX4tOmg+Z4jRTaf2Y5mSoKsJ9RjVk/QsOtGATsu4OuXFYSaARBEET7o+MLNLc9OIADB63Yfiwtnt3+oqxCVvrmJBZgPZ4boevxsPtv20FwmqAWxN0ci+WbbsaMZxW0fg0rOB0SAjgQ8W7WiCaaqi3Giv9cjnowHRx67NpBq7b+9a6eI8XsT6vrPxZreW87we75jW7ea3aH5Li5j/4cwBuw34PmeMOsmAQaQRAE0S7p+AKNS4mjxWQnFpPsoLlJ9IvZn1aTRjf3UYtn10Fz4yCoUSDcZO3rNQdNE1t2YwHW10gkCESaXKwRm8m32/WovYbVWMnf5ySetHLiYub6WC3fTAzSkFC+GaoHoDp/bztx0FyvkWrrsZK/zw6KYv9geCpxJAiCIDohnUCguSm7Kmj9GukI1YElVpISAle77JKTb9tlhy6uLeFqWeyvcyM+7ZbBJmJJXCNu3DpAjsuqfZ8tV6vOmajWYgH217+McwDdOLqAg0EyNe43eizfR8kbPa6GhBSzHkw7ZxwSBEEQhAQ6vkBz04Pj8bJEwm4S5zQhsLvzHax1nqDa7kFzUZoE2C8XcuMO2hVNwdr44eI++7G8Pva9VhNiN0MSgPgacVDi6IT27KCpalyguehTBOyJpkABeybYxZfFjtCwu2Hg+L1m10FzObQGsL754vo5YuP8Rq1U1O212bmXBEEQBCGBji/QtN1hJz04gD3R5GYaIGB/x1ZqiaPb5NvGfXTbg2O3L8yN0AXi1ybTZaq1MTUvEyWOxQ7jFVuPFWkGYmEXDlox+9PO+nf6XkscoWFTxDte/x2hDLbYYbxC60I3pE0VdRrLQQ8yQRAEQUigEwg0h2d3adjZ1efhIAA2hYUbl0mRV5qUZSexctmDo32fHcfCaSzA3rUl1ogbV0u1NzXPbYmj5fJNF2WAWjzLjpaLyZuA/cmKbkQMYG+jx02/m/Z9kSYb/XUOz+UD7DvxieeIQ2GtDQCyFIvT85jOQiMIgiDaGZ1AoLlMrDIh0OwkqU4TVG2yot3mfhm7+jx6cAAb8Vz0MgH23BHXybfNcfRuShwD+YDisR6rqZqVATopFQVsvtc4bBgkv0463GyGAPaEBQ8HDbB3bW5KbgF7z0h/LuD1O48nXaCRg0YQBEG0Lzq+QHMzJAGIJ9+yynfslgu5Lc2z41jUsoTdcfJdyEqOYtH0X+u2B8fukBDXybcdd4SDy5T8OmaoqrvkW1Hsb1Dw2AyxcjwCLxFvJ9l39RyxcQh9ogzWrYNs4fcWbmblok5/bx4vq1Cw3IPm1okskFhyTgKNIAiCaJ90fIHmxkEAbCao1S3f4zQWYC1eJAhEgxyEhZ0yQJeJFWCtNI+XgyCrxNFJf5Fbx8JKkhqqj/fgyFr/HARaLAKEGtJ/bWKNuCiVA+Suf9uTPiU4aG7XI8CuzXLJLYfNkHAjEI2k/9pEGSwJNIIgCKJz0QkEWgZ6RxwPLrBRLuQ2+QBsCrRq94kVYC1pdFsGaHtIiMsSR9sOmsOpooC9pNFtoq99rx2B5nSCKWDv2tycXZf8fXYcNFkua7AW8PjYwcxOyLYh4t2+1wCb4pODgwbEjzRJg1sRTwKNIAiCaKd0fIEW5FSaZKnsqo4l3k5GcWuxAIvJt1Yq50ZY2EiseJSKaq9jJRbgPCH2+gFfjs1hK26cHzs9aC6nito5PJ2HO2LXQXPrVmuvkzaWyzJYj5e9V60INLelooD9PsXsIlZi6gQ7DrLbklsAyLJ4HwF+zxFL618T8U57MPOYUCaBRhAEQbQzOrZAi8XclyZlFwFq1FrZVcjtsAk7DgIPd8TmRDQeO992kka3iZyVWLEoK89yNcXRxtQ8HusRkCNitHh2+hTdbhgAFstgXSbfWjwrIj7cyEovXa2R+HvNan+dK6Frx62ujn+PWwfNRqmo298ZYC2eWwfNbg8mQRAEQUiiYws0bVw7l2THYtmV09I1IP69isXkw+WYcUByYuXA+XGbyNnaZXc5xRGwmBDXuHPrEu6IHZfVjSAstp6ghuqZm+IUO6WpPH5vVtc/lzLAQrbRE260Fs/thgFgz612LdDsHPsgaaMnWAd4A4A/23k8EmgEQRBEO6RjCzS3Y5aTv9dSslPvLmFUFPtJo4wEFeAwAMJmX4ybHhzA+rVxEYM2RZOb++gLsPJNOy6r6xJHq6WiLtd/Ivm24qDVsPvgdFy7Fk/aGrFx9INUB42DW233CAFp4tNlRQNgrweTIAiCICTRsQVaIkHlMdzCooPmxkEA4hPRJAqLSDMQCZl/XaIHh0dpko0E1WkPDmB9AIpsB83tfQSsiyZepaKhuvRT8yIhNlU0wEOgWfy9ub2PljdDXB6fASRt9FjcfHEjqhM9mFaeWXEx7HpIjoXrCjcD0ZC8Eke3x5Bo8ay6gwRBEAQhiY4t0HhMsdOSMssCTVLSyGWKo8Wen0QPDofSPKtTHLkk33am2EkSn24dNMD62XxcBkDEvzfdGglxSPS18mCpybedEkceLqsEBw2wPpREu343pdnaplIsZv51PCoa7JbB8nDQrLqDBEEQBCGJDi7QeOx82xAWboeEANYny/EocbTaX8dD6AbyAMVjvaTMtdC166BJFJ+uk+8i64m+x++yVNSiaEo4uhx60KwOCZG1RngN0gCsD3dxvUFhcax/qB7w5zqfPAu0iLt0vzcuJbc2pzhy2TCzWOJLEARBEJLo2AKNS4mjnXN3XA4J0eLJ7MEB0iepPHa+E/11Vh00Di6TrZH+HIRuuniqykfEW+2L0RJ9V6WiFtcIj1I5O8cjuJ0YCVhfjzzKiRNrJM19jMXkO2g87qP2WmbwGLbiz7W50SPJZSUIgiAIiXRsgca1pCbN/6RV1f2QBC2ezB4c7bXSxQI47EZb7J3i4qBZHGvOZUiCxf6icCOgxtyvEauT5dyeSwZYd7V4lMoBsHymFs8etLSleZymOALpBaE2eVaWg8ZrUwmwsEY4nN1oZ5ASz5JzK8cjEARBEIQkOrZA4+GOWN2xjQSBWFhuX4ysnW/NPZR5bTySbzWW/vw6mUNCErFkuawcnEhbwgKS1z8P8akC4XRrpBZQvO6nigIW1ggHtw6w7qC5PRoBSFojElxWgG2ISOtBK2DP9UjQ3esQBEEQBEc6uECrY+PafS7OwVEUNpkuXULMI9HXvt/qFEcePTiADQfNrfNjdVefh/Nj9dq05DvXeSyrU/MSCaqs6YOchC4gb41YFp+cSkW117ISS0apKA9HF7DnoPFyWdPF47pGJJY4AlTmSBAEQbQrOrhAq2flO24SK8BaQsDLZdKGhKQtzeOZfMtyfiz0Tqmq/PJNt31agDXHgoejq31/uAGIRdPE45B8W52syKvEMWDhvcarT8tOf53bWB5v/L2dZo3wGMgDWD+KQXtGusGuiHdzFIMWL919jATjI/15iXgaFEIQBEG0Hzq2QAtxSKwAawkBtx6ceGleuDF9PFm7wzKdn1A9nz4tq4kVj1JRLZ4sB8Hq1LwQx/4iK7+35K93Ey9tL18DAFWig1brfnNCi2dVxLuZPKvFCjekP7+Oy9AaiyI+xGujp8BGObEkEU8QBEEQEunYAo3HwdGAtaSRW3+FVdFUC1ej4YF4f51XnjtipcSR1320OlmRx33U4qVLGjURw000pSu75TS0xlIsjhsU6Up8E2cASnKQQxzuI2Bx/XMsJwasxZPWg1YHeLMAX5a7eNkWjkfg6VYDJNAIgiCIdkUnEGg83BELk+V49lcA6RNiHiWOVieihbTEKuAunuYgmJVvJkSMLKHLaY0E8q1POpTlWPBIvj1ewJ9nLdH35wJen7t4VtYjjzMAk7/fyn10Kzy1eFY2DJJ/NsexrAo0DiWOiTJYC+ufy/PYyoYZ7+cxCTSCIAii/dCxBVqIQ/IBxHf1JQ4JAcwTq1iMT2kSAEuH9fJMrNJNRON9H9O5Ws017oWuFs/yIBlOA1DM1qQ2VZSbsLBQ4sgllp3NELcTKu30oMl6r2kOMge3GjBf/5EQEA26X4++ABvEZEUMcqtosNjLJ6uXlSAIgiAk0rEFmswSR56j6AHzeCFOib4WT1ZipY18N4vHcyBJ8uuZxeNxHwP51kvz3F5bwrEwu4+c+gYB644FLxEfDaUR8RzO00r+fhlOpBbPahmsP89lLAsOWoiTGAQkr5EiINLMBKZZLO3nchXLYhksQRAEQUikgws0mTvfvKbYWRgAwWt3GLA+AIXXfdRezwjufVqyku98aw6a22MfAGtlsIlSOVmuFi93RFsjZtfGuwfNgjvIQ+ha7cEM5AMel4/eLAtlh7yeWYANgcbpmQWYPyNpSAhBEATRiengAq3OfS8T0JJ8xGLmsaAAAbc73xYSAl67w9prWOrB4RQLMB+1z2tIiJ3eKZk9aG7P0wKs9aDxErqA3DVixR3k1YOWOL/OJJZ27AOX+2hho4fH5E2g5XdhScRw+r3JujZLzxFOa8SXzTZVSKARBEEQ7YiOK9BUld/0tUA+ADU+3tsA7awk18m3HZdJkkDj1e9mZbIcr1JRLZ5ZrGiY9eBwuY/58dI8k7KrUD2nWBZ60Hj1MmnxrIz057VhAFjcoODkxpiVHYY4jfQH2M8bbmTrzgiefVqAxBJHib2s2RaekbzEpzZIKd36JwiCIAiJdFyBlkiseCY7aXajeZWTaa9nFiv5a91gaWS1xBJHmWVXPO+jVceC24YBLPbyySyD5fhes+L8uHWrtXgy32vJr6kHz2ErQJpnFuc+RSs9mDJFPI9yYi0eOWgEQRBEO6LjCjTeiX7ya+rBy0GwUlIjvXyN866+mWMRrAcUD+DP4RPP1B3hfB+BNEkjp0OxfQF27IFZ8h2SKHQBvv2eQPr1789jZayu46W5thBHEROwsvnC6T5qQ0ZMhW5t65/LDZl4jphuUNTyqWgArLmDBEEQBCGRjivQeCZWVp0fHomOlbPJeJevhRuBaMQknuQhIQEOfVqA5PsoMfnW4km7tvh9THd+HVfnR4LQBdI7yFxFjIUBQLz6tDwe9j6yJD4lCLRoGIg0yX0ec3uvWXCQCYIgCEIiHVeg8SxNsrRjyzEhCKTpeeDdgwYYlydFIyyx4tWnZRYL4LfLDqTf+eY9JAGwUOLI69rSrBHe1xaLsNHmekTD7HM8J/SlFbqy1ginoTVAy3soXdkht2uzKuIl9LKKeK+lFWgc1iNAJY4EQRBEu6MTCDSOwkKaOyKxLyZdQsxzaIcvC/D44/2BBvAqFQXiybeFgSQ8hW7aPkWOIl5mGSxgfG0y1yPAz63T4kl7r1nYoOB5bekmiwZ5rv988/PrQjzFoNXNEEnPY4IgCIKQTMcVaCISVKkJQZreKY+fCR4esQDjXi2eQhdggx3SiRhpyTfHEq+AxeRb1q5+sA7w53Lq00ozfZPnGtF6p6RuhpiMa+cpLBLOTzsRFqE61vPq9XGIleb8Op49wYk1kqa/jgQaQRAE0UnpuAKNq4NmpXeKZ2KV5tBjrmVQaRwLniJGi5duPDyvWFp/kdH5dVxFfJrkOxbl7PykKV/jdcQEYMFl5Xgftd4pGX1aQPz8rnrj/jreLhNgfG3ReBmp1OcI7zUiQcR7POndwWYSaARBEETnJaMCTVGUAYqizFEUZb2iKOsURfmV5W8W0vNgkHzwPMwWsDZZjkfCCKQXn9wdNAvCgud9hGqcyHHtL0qTfPN0YrTXSefocr2PsLBGeK7/NJM+efZpqVHj0jyuz5E0paI8J28C1nowpa0RjkObAGvlmzxLpdMNUiIIgiAIiWTaQYsA+K2qqocCOBLAzYqiHGrpO3nu6vsCrBTIKPkINwJqTG4PGq8ENV1pXqIHjVdpXr55D5p24DeXWBb766T0aXEWaOmELm8RA8hLvtMOt+DZy5dGWCfO0+JRTpzmvcbbrQ7kWyi5lSXQ4oKb27WlKZUONfC/tnTnvBEEQRCEJDIq0FRV3aeq6vL43+sAbADQz9I3B+sAxcvnPC3APCHmnnxLdEe0w36NRBPP3hEtXrqzmXhO6APMnR9vFhPgbvH62WsZJt8iXKY0kz65CaY095G782PFQea8QWFWvpnF6dgHbUiOoYPGcVMJsFDiyHHSYcCqy8qxfNPoORKLxifPShKfBEEQBCGZTDtoCRRFGQzgMACLUz5+g6IoSxVFWVpeXt7yCc1B4JFYAeYJMffkIy7QYlH9z3Pd+U7TOyXE+TGIpaqcSxzTCTSO9xEwT4iDvJ3IAiDcYLxGgrX8E9S04pOngyyxTwswd9B4lRNr8WSU3Gqv015KHHmX+AZM1gh3oUsCjSAIgmhftAuBpihKPoAZAG5TVbVVc4qqqs+pqjpFVdUpPXr0aPkETwcBME92eI6iT34ds0SOm4OQLpYA58fIrYsE2Xlb3MuuDKb08RSDWjzDHrQMrJGOPEhGlluXbrIiz3JKII2wEHBtsbD56Hvu6zGNiOfpDhqWZcefL1p1gOtYJNAIgiCI9kXGBZqiKH4wcfa6qqrvW/5Gng4CYN5wLyL5AMx3iHklVl6feX8dzyl2QLzEMd0uOydhnW3FQeOdfEsctpL8uqnwXCO+bNaHJW2NmN1HAWIQMN+g4O2ypnXQeAtrCddmZZCMP4/PsQ9AvL/OYKMnIdAkOfEEQRAEIZlMT3FUALwIYIOqqv+29c3cy9dMJsuJKPFKft028Tg7P2YT0ULx87R4nJWkxTJMGGtbvoYH6c5443k0AmA+3IK7iLeQfPOKpSjpXS1fDr81klUgz4lJ9GBK2AwBzHtZhZXmGT23eDrxeQAU8/XP9T6aDAlJrBFODlq6Kb4EQRAEIZlMO2jHALgKwI8VRVkZ/+90S9/JOyEwTb55946Y7NiqqiBhISHR12LFwkAkpBOL9xQ7CwNQZAldEf1FgP4a4d2nBaR3tbiux3gsvbPJeLusVkocea9/WWvEbEJlNMIGafC6j4qSvsqA9xoxFNXx9zvvPl2z6bMEQRAEIRFOW+LOUFV1PgBnUz5C9UBhX34/jFlCkBghzTux0kl2wk3xkf48hYXZtQlwEAAWz9e19ed4Owhp++vqgS6D+cQC2O+kaqdBLFE9aDprhHe/G5DeHeRdBqjG2PEVqS6IiJ5IQO76r9mj/znu0zBNymBDnO+j9lqy1kggn62PWLRt2STvHrR0Gz0EQRAEIZlMO2jO4XmeFsCSNMNSOYnuCG8RA8hPrLTXbROL833U+uvMytekOWi17Gfx+vnFAgzuI+dEX3stw54fAcNWAH1Xi7uIlzwkxHSjp57fmWtAkhOvEy8o4jliUgbOu1TUbPqm7DVCEARBEJLpwAJNgLCIBllpkF4sT1wM8MBMoPF2YoA0woLjWUlAmsRKxLWZ9aqIKM0zKbuSJWJ4l4oC8eEuJqWiXNeISYkv72vzBQBvQN+JjMUE9aCl2TDgdTSImRPPe1NJey1ToctxjZiJJt4CLXHGIQk0giAIon3QMQWa1qfF20EA9P8nrfWp8DxzDZCTfADmPWjc76NWUqaT7AtzfnSuTVTyHao37p3iPbQGMHdZeQtdWZMOzYYy8J4YqcXTW4/hBgCqgB40g/467hsGFlxWEb2DenCfqmvyHOFd4qi9Fgk0giAIop3QMQVaok+Lc4IKGAg0zuWUlsoAZbkjvEVM/D7Kujajc9dEJd9QjZNGIQ6a3n3UpmHKKs0TUAYIpHFZOQtCUyeSsxhUY+wZlQrvzRBTl1WyQAs18H9mAQbuIOcx+9prUQ8aQRAE0U7omAKN9yCB5NfSdX5q+cbyBeJnk+k4CAkHjfOEPrOJaDx3omX2jgDxEkdZQjfNtfG8j2ZlV6JEfLrSPF6Yis96wOPn16cFGE9WFOJWm4hP3keDyO5TTCfQuDpaJiWOwbp4vyfHGVdm0zcJgiAIQjIdU6AJETFpkm+eO9FaPNPSJAGjv3VL8wQlVkYljjwPs9XimSbfPB0Ek94p3vcRMHY+hZQ4mjgIInr5AOPyTVnvtZBAEW8Uj6dg8njZGYZm65/3NFizYx+4u9UwuDZB7zUaEkIQBEG0EzqoQBPUgwAY79jyThqNSspE9WlpY82TicVYKaCIXj7D+8gxFhAXnyb9biJcVmkCzejaRDiR2pCccOuPJ87TkiTQeLtMgImDJuA5YurEi7g2A9GUcFk5T7oN1bHnRjJhEc9jsz5die81giAIgsgAJNA00jk/PJNhwDixErHznWUgmjTBJiRBleAgAMb9RULKKdOVOIoQFpKOYjDqwRRy5loaB42n6wmYrBGRzxGjNSLZiRfhaoVTnpFCha6k9xoNCSEIgiDaER1coIlIvo12vgU4aGY730ImK6Ym3wISK182oHiNB2nwdhACBiJGxAAII6ELSC5xbIj3aQX4xTJyfkQk+r5sdmyF0QAUES6TzKmigEQH2cCJD9Wx4wV4rhGjaxPyPDYZ2iRqo4cEGkEQBNFO6KACTRMxAkocdZN9QSWORg6CP5dvn5ZRaZ4IJ0ZRzKfm8XYQtBLH1P46IefJmU0flNyDJiIW0Pb3JmIgSWKNGAhrIe6IpGmARg6yqgpyWQ3OJhO1qQTobPQIeB77TUrORbzXjEqlCYIgCCIDdFCBJrF3RGhiZSAGRewOA3IcNMB8ap4IYRGLAJFgSiyBJV6pvzcRQxIA89I87oM0DM6dEjGQBGC9UYZDQgTdx1QRL7LEMfX3Fg2xdSqid0r2c6TNRo+A++jxmAwAoiEhBEEQROemgws0jgmI0Y5tuAnsPC1JiZWIBNWoNE+UQJOaWBns6sscsy9iSIIWT6bQ1V47GREHR2vxUnuZAEHOTz6gRpmITkZm75SIklvt9YyO6xBxH7XXbhVL4Po3HCQjYINCb0gOQRAEQWSADirQtKSR846tX6dRXLbLJKTEK11iJUAQyixNAvTLrhQPKxflRSAPgCJR6Jr0oMkSaCKG1mjxDMs3BbmDbX5v9eysOa9fTixA0CAZg/46EccVAMYuq5Bry/AGBUEQBEFkgA4q0BrYkAGeh9kC+kmjqOQjUMB29KORtvFEJVaGPWgihIXE6WuAvmjy57F+J15ovVOyhK7hfRQhdI1KHCWKT1UVdxQDoP97431dXh8bgpLagyZbxAstcZTpxMveoKA+NIIgCCLzdFyBFuCcfAP6CbHIxApoW+YlZKS/0c63qGvTGVyg9fKJ6C8C9J0f3rEA/d5BYUI331jEixK60lxWnTUSagArJ5Z4bbxjAfq9g8JEfD47py4WTYknsFRamvjUuY/RMCtFFDFsCCCBRhAEQbQLOqhAE5CgAvrlQqIFml48mSIGENOrkhor0swOyxbm/EhwR4B4+aakBNXo3KmgiBIvI3dEossqrJzS5NpErREZkw6TX0/vOSLNQYv/2y9g/bcRgwI3QwAaFEIQBEG0CzqoQBOUfOuWrwmYBpj8erqJFedr83hZL1YmSxxFlgEC+uPhRbkjsl1WGcm31qunF0vxsLI9nuiWEwt06wB5Il7PQe5MAk3vPvI+c02LJ7PfE6AeNIIgCKJdQAItGb1Ry1pCIGJIAiC37EovlsfHkivesdoIJgGDXbRYgLz7qDcAJZF8i+odlCAszIbkBPIFlRPL6vc0GQ8vzUET9RzR2ehJHA0iao1I2FQCzO+jrOcIQRAEQWSADizQRIkYSSWOeqPvVZWVswkrzTNI9Hkn31k6I6uFuyM6yb4od8RohLqMXf1YLL5GRJX4SioD1OudEv1ey+hmiCjxqbNGRJUTa/F0ha6k57Go4wqMKhoIgiAIIgN0UIEmMGmUXZqXnBAITayMkm8RiZVO0ii6NEmmOyKrB00vaQw3iomlvaZeQiwqFtA6nshBGqmxAIHPEbPyTQnOj6j7CMgX8eHGFBEvaDPESMQTBEEQRAbooAJNZkmN4KZ0aYmVwdQ8UYkV0DqeKAfBlwV4/BL7izLRgyZB6ALGPT+i3BEg5dokD4AQukb0BJoC+HL4x0q8vhZL0H3U4sm6j3qiSfhGDwk0giAIIvOQQEtG2/lW1daxRA1J0F4/EUubhsbxcOVEPL2JaKITKz13RJSwljAkQYsl48BjIE3yLbFPUahAk7BGfAHWZylr/esNydGcSA/nR65sEZ+lU+KbkY0eziWOfp3nMUEQBEFkiI4p0IRN6MsDYhEgEmz5mMghCdrrJ8dK/hzveNLcEZ2peTJ39UUNSQDYten110lzEASNogf0hYXIMkDt9ROxtPJNCWeTiezl095rrTZ6RJcTSygV1V5TVqm03vRNUc8RoyE5BEEQBJEBOp5AE518A20dC5G7w52yd0SnLywxxY7zzjfQ1h2MBAE1KlY0pV6b9ORbphMpqwdNS74FOMip619kL19WPlt/bTZ6ZN9HmRs9shw0wZtYJNAIgiCIdkDHE2jhJgCqvOEWooYkeP2sLE6ayySxB83M+ZEhLET38gFtr03EdWllV7oJqigHTZZAMyhxFFFODLRd/6J7+ZJjaH+XvtEjcfR9R+9B0+JRiSNBEATRDuh4Ak30DirQNiEQEUuLJ9MdCTew0q7keJ0i+c4z6FMRuauf6qCJEPE+dr8yVSoKSHAHU99rAsqJgbbCQmgvn961CSoD9AXiQ3JklUobbfTI2jCrYz26Hq+YeDQkhCAIgmgHdECBJjCxMhpuwbshXSN12puMXf1w6rUJHACRLGK0vkERyXdqX4wUd6SxdTxhIl7yGgkl9U6JLCfWOwdQVCygbfmalI0eCaXSWjxZg2RSN3piMYEbPfHnbqrzKfS9RgKNIAiCyDwdUKBJSL5buSMyk0YJ4lNLdmQk3zIcBKDtZDnRZYCAvvMjgtQ1EhTs/KhRdh4fED+XT1Avn1F/ncjkW3qJY0o8EYNdgLZHaMjc6IloJecinyMS+j0BEmgEQRBEu4EEWjIye0eAtiPbRZcmAS0JSLgpfii2gGTHnwtAkZh8SyxxNBSfshw0kSI+ZUiOSKGrN9Zc6HtNpog3EGiy3UEhx3Wk9EVK2TCTtNGj14NJEARBEBmgAwo0Gb0jEoWFXvmaiMQqdfqgyMRKUfQdi05RBpiJNZJyHz1+1nskIhbQEk/kSP/E2WQpkxVFuiPS+hSNShwlCYtQAxPAvM9cA9oOyRH5PNbd6JG4GUIQBEEQGaIDCrQMlCYJLamRlFilXpvIxAqID2VILRUVGCsaBCKheKxMrBGJLqtIMQjIcUe015WVfGtDQrT+OpkiXlUlb/TUiyunTC0DDwoUuh6P/gaFrPcaQRAEQWQIEmjJpJaviezTAvR70DpN8q1TmicyFtDSFyPTZRV54LEWr41bJzj5blPiKNH5FBkrub9OZoljJAjEIp3jPqY+I2WskdSJqcLEZ15rEU8QBEEQGaIDCjSBybcvm42C15IOkQceAwbJt8AeHEBeYqXn/IhMrLQYyX+KuDZfDlqVXYk88BjIjNDVnE/RLqve9E2/4GsLpjrIAh20NpshoqbBSnSZDEW8SCc+9VxKgesxWcQTBEEQRIbowAJNQu9UJhJU0e5IMIPJt2h3MDVpFNHLlyi7SoklsqQs1WUVNg1QtoMm0UFOnQgYagAUL+DL4h8rtXdK5DNLe11p/W4Sha4WT9pRDDpDogiCIAgiA3RAgRY/8NifI+b1kxNiGclHpBmIRuLxOllpkmzxmfx7E9XLB7QWFsKFrkx3JEXoiuwv0l5XWp9WqrCIr0cR5/IZifhOVeIoYdgQEJ++KavEV+cIDYIgCILIAB1ToIlKrICU5FuCgwAk9U4JTKy00jFZPWjJJY4yevmA1gmxqFhaPGnuSD4QDSUNQMmEOyJhSE40JLZPq80GhcD1CEgW8SmHR8sWuskfFxFPE4ORIBALi18jNCiEIAiCyDAdUKAJTqyy8tvufMvsnRJ1bR5P64RYivOj9WkJPHNNiwW0vjbRybfMSYeAHBHfxomUWOIoPNHXOeOt04h4vTUi0a1O/hm4x9NzIiU9RwiCIAgiQ3RAgSY6sZIpYnR6fkTF0uLJKk0K6AhdmYMLRIlqgCX7soRF6q6+yPXvy2J9Wa1+b4qYXj5Achmg5iAnrX/hz5GUNSJto0fgBoXHw9z45N+b4mEDlkSgJ3RFHyGQfDwIQRAEQWQAEmipBPLkHOYM6BweLcEdbOX8KAJ7+fJayq5kuHVASvmaSIGWAXdEhohXlNZT80SXE+u51TJ7MIVvhmRwg0LmM1JoyXnSfRTeE0lDQgiCIIj2QQcVaJ0lsZLdO5XfVsSI7OUD2Bj6jIgYWeVrEpNvTewKX/+y+rTy2fqIReX0MgGt++s6TQ9a0gZFJMT6+YSXgUu6j5qIj8WoxJEgCIL4f0MHFGgyEiuJfVoAixcNA9Gg2OQ7q0BigpokLESXePkzIXRl98XUiz9zTXttGeWUWiwtjoxhK4CcXj6g9XNExjRMgMULC16P2mtLXSMqEGkSv0a0syJpSAhBEASRYTqgQMtA74iMoQyiY2mvHZLYgwPEr02w0PX6WA+MtPI1PXeks6yRfIlCN1mgadcmqN/NFwA8/gyKeJG9fDqbIUJdrZQeTBlrJJi8/mnMPkEQBNG56XgCLSixpCZYD0ABfAL7tAB5iVXqzrfQQRpJyY408SlximNy8u3xAd6AoFjJybdgoQvo3EfBTgyQsv5lXZtgEZ/a7ymjnFiqiJfYywekbPSIGpKTzQaekEAjCIIgMkzHE2gy3BGo8d6p+O6wsAOPJbsjegMgRCFdfKYm34JjxcKs30eL1VmS76yCJJdVgtDV4ohOvoG4sGiMn8tXJ6cHTfQZgEDrSZ+yRLzMXj5AzgaFooBNaKUeNIIgCCKzdECBJrN3KhPJhywHTeJ9DMpIGvPlDUlI3dUX7cQAKSVenUXoSi7NC+TG10hz/Fw+wfdRjbLDlTvbfWyz0SO5DFa0808OGkEQBJFhOpZAU1WW9EgrqRHsMnn9gDdLrjsSaQKiEYmJlcRdfVlDErJS14jA+6j1LSWLeG2YgQjaDAmRVOKoDUDxSxCfUsopM7HRI0vEF0gcEpK60SOw5BxoXZpKEARBEBmigwm0KPtTSmmehORbiyezBw2Qc22pO9+Klx2ELDKezHJKoCWeyFgeLxNpUssAk3rQpPQp1rFYvmw28EVYvHyJbnXqc0TkRk+A9UHKEp9Z+UlnHMoqlU56ZokqOdfiUYkjQRAEkWE6mECLsT9l9HMkdr4FJh+ATtIow/mRcG2pZVcihyRo8aQL3QbxCSogX8S3Sr47idDV4skcpAEklcEKjKUoSWtEkogH5Fxbahm4lOcxOWgEQRBEZulYAi0mQaC1Sb4FJ41Z+UCwrhM7aPXiBzIAOi6TrF19wQkq0JI0ypp0CABNVUAs0gkFWiZKHAVPTNXiyexBA4DGinjJeSd6Hif36RIEQRBEhuhYAk1miaMmmmQljTIOIdZ6lxorxCffvixW1igtQc1kiaNsl1VC8l2/vyW2KGQOWwHYfQs3ZqjEUbI7KLSXT1sjB1r/W0gs2ZsheS19rARBEASRITqYQJPtoElKGpOTb9FDEgCgTkLyrSitd/U7ZS9fg/hz+YDWybfIM9cAneRbpIhPOjw61CDuIGcNqWWwSSI+KLlUWkYvH5D0HBG5RrSzySSXExMEQRBEBiGBlkpGytfiyYc3wJJWkbEAOcm39voyhiQA8d6pRqC5tuXfwmJJHAChxQvWtyT6Qnv54tdWX9b636LIkijitTLYoEQHLSjR+ZHl1mVJfI602ugRPLQGYFUGVOJIEARBZJgOJtC0EsdO0qcFSE6s4iWOMna+tdcPNbByURmxAKChvPW/RcYK1slJvluJGAliEJBTvqa9frAeCDXKuTY1xkp8tdiiSC4nFt2nBbTuU5QRC5C4RvJahLWsEket35kgCIIgMkDHEmiJISECEwJfgDlZjRKGJAApiZWEZBiQU+IItC47lCXQZOzqa2WoDQcBqBJdVkmOLiDPQUtsUMi8NglrpM16FHh2nRZPVll2YqNHphMv+Tmi9QQTBEEQRAboWAJNRomj9vpSd4clJd9tBkBILN+UJT41YSGyl8/jYa8vVcRIHFoDZGD9y7w2bY0I7Hnz5QBQJK8R2fcxExs9EoQuQKP2CYIgiIzSwQRavMRRxjABLUGVMR470gw018jpwVE8STvfkkqTpJbm7Rc/JEGLJ7MMUJqDJtGJ1F5ftrBoKGMCW+SBxx5PfI1kYjNEkhMpzUHLl+iyxgUgDQohCIIgMkgHE2gx9j9rkYkVEE+sJO58A0B9ufhYWsO9tKQxT+6QBID93kTH0uLJXCOxCDubTLYTKaUHrY71/ci8NulrRJLLFKyTeB9lOWj5Env5yEEjCIIgMk8HFGiyEiuJLhPA4omOBbAYTVUtfxcaK09unxYQv48y1ki+RJcpqXdQxnlyWqzkfwuLly9nsEvy68tcIzIH8kBl7zfRsbQS34aDSbEFEshruY9ZskocyUEjCIIgMkfHEmgxiQKtubrl7yJJTHuTkFgBrRN8Gcl3sKZtXCGx4tfSWCFJ6Oax3xkgT8Q3V4v/nXkD7Kw1bf0LLyfOYyWH2t+FxopfS8NBeWukqZL9Xfh4+PjrN0hyB7PyAajs7zLWiOznMY3aJwiCIDJIxxJoMkpcgNbJm6xdfRmxgNbXJiOxSsSSeR8lJd96fxdBcnKfVSg2lqK0XI/oPi1A7n1MrAsJjm6reJB4bRJiJceQskYy8DymEkeCIAgig3QwgRbLQPItyR2RESs5nuzkO6dYcCzJCWpyqZXM5Fu0QEuO1+lEjOzNkM78HJG5RpJiUIkjQRAE8f+ADijQZCdWnSxp1BIc2SImp6vYWLLvY263pHgSk+9sGQItr21c0bFkxMuoQOtk1ybzOZIcI7e74Fjx9zI5aARBEEQG6VgCLSa7xFFpnYgLjQW51yY9sRIs0HxZgOKNx5XgILQSaBKTbykOWjye6L4pAMguSoorOF5ySa+MNaLdP3+enKNBEn+X+RyR6NYB4p8jJNAIgiCIdkDHEmiySxzzewFev+BYskvzZCZWySWOghMr7QiB1LiiSBZo/hyxsZJ/V1IctHg8GWKwqH9SXNHTB70tQkmmiCnsy9an0FiSSxyzMrTRI/o54gsAHj+VOBIEQRAZRfBpvpyRXeKY00V8rPxeSXE7ce+I6B40gE3pC0o48BtoLdCEJ9/JPWiCe3AAdtA3APQaKz5W0YCWv8tak+FGueu/sK/4WMkxZF6b9FJRwU6kFs9AoIUiMawoqcKGfbXYdKAOjaEozhjXByeN7gWPh+9zIBZT8fXGMizdWQmvR0HA50FewIfjRnbHqN78N08O1gfx3wU7sXZvLYpy/Dj50F44YWQP5GWJSRO2ltXjvWWl2HGwHkU5fhwzvDvOGNcHPi//feO1e2qw42ADtpTVQ1VVKACOHNYNRw3tBoXz87u6MYQv1x/A8pJq9C7MRp/ibBw1tBsGdBWzdvfVNOHtH3Zja1k9+nXJwZFDu2HayB7crwsAItEY5m05iG3l9diwrw7dCwI45dDemDyIf64Ui6lYVVqNVbursauyEf275CLgVXDRlAHI9nu5x9teXo+3ftiNbWX1GN2nEOP7F+HYEd2RGxCz/rccqMMrC3aiqjGEngXZuOTwARjdh//7WlVVlFQ2YldFI3ZXsT/zAj5cMLkf+nfhvyb3VDdhxrJSHKhtxqjeBfB4FBzapxDj+hUJeW/XNIbx4vc78MOOSozuU4jLpg7A0B758HJ+HgNsTX6wYg8+XrUXMVXFtEN64sojByLLx389Ah1OoMkqcdQEWrH4WF4fkNeDnQXV6XpHkoSFR8wCbkWkmf3ZZZD4WLkSxLuG7BLHmlL2Z7/J4mO1ctAkuboN5XId5DzBfVNA680kKe/tDD1HZBDI1x2z/9na/fjLJ+uwr4Y9Z7rk+uH1KPho5V4c0qsAv/jRMG4Co6I+iJteX44lOyrh9ypQVSASix9rMBs4e0Jf3HfeWBRk86nwWLDtIG57ayUO1gcxslcBVpRU4YMVe5Dl8+C4Ed1x7mH9cMa4PlyS/uUlVXjim634ZmMZfB4Fg7vnoaohhHeWluLhLzbj1hNH4LzD+nFJsOqaw7jz/TWYtXpf4mMeBYipwGPfbMXp43rj7tNHc0tUl+2qxE9fXYrqxjAKsnyoC0YSnxvQNQfXHzsUVx05iIuYbwpF8fy87XhyzlaEozH065KDz9ftx7PfbsfIXvk4c3xfXHXkIHTJC7iOpaoqnpq7DS/M246qxjAAoHt+Fmqbwnj22+24aHJ/3HbySPQr5lNNUlLRiFveXI7VpeyYnoDXg1A0BgB46PNN+PkJw/CLacO4rEdVVfHp2v24473VCEZiGNQtF99sKoOqArkBL04+tBd+dtxQjO1XlP7FLLC6tBovzt+Bj1ftRZbPg37FOZizsRyvLtyJ08b2xpVHDuK2cbCrogG/eH051u2tTXws4PMgEo3hyblb8duTR+L644ZyEzNvLC7BHz9ai2hMRW7Ai8ZQNPG5XoVZeOmawzGmL5/7WNscxsvzd+KF+dtR1xzB+P5F+O/CnXjp+x3I8Xtx4eT+uH36ISjk8IzcW92Ef3y6EatLq7GzohFDu+ch4PPgbzPX4+Xvd+CXPx6OqUO6YUh3vv8/7GACTdJ4bG0kfHax+FgAcyq2z2E9dqLJlIMmg3OfZuegjb9UfCzRvYnJJPcvyShxLN/I/pQh0JIdEZnvbRmxNCdS1nOk2wigYgs7x040mSqVlkFWfpsetMe+3oJ/f7kZY/oW4s9nHYrDBnZBz4IsRGMqPlm9F0/N2YZfvbUSL3+/E49fdpgrt+RgfRBXPL8Yuyob8OAF43DBpP7weT2IxlRUNoTw2qJdeHLOViwvqcKDF4zHMcOdbwBEYyr+8/UWPP7NFgzpnodXrp2KQ/sWIhKNYemuKny+bj++WHcAX21YgRmHlOLxyych34WjNnP1Xtz21koU5fhx20kjcOWRg9A9PwuxmIovNxzA499swe/eXYWn527F3aePxomje6V/UQOqG0O4/PnF2HSgDr89eSR+PLonRvYqgN/rQXM4ihfn78B/vtqCrzeU4e7TR+PyIwbC70Jcf7n+AG55Yzn6Fufg5WsOx8QBxQhHVeysaMDCbRWYtWYf/vzxOqwqrcb9541z5QItL6nCza8vx76aZpw+rjfuOm00BnTNRTgaw/vLSzFj2R488tVmvPT9Dtw5fRQunTrQcaxQJIY7ZqzGByv24MRRPXHJ4QMweVAXdMvPQmMogoe/2Iz/LdqF2Wv24aIpA/Drk0eiKMd5Ury9vB6XPb8IzeEYHrxgHKYd0hPd87NwoLYZuyoa8eL87fjn55uwZEclfnfKIRjX33nCH4rE8LeZ6/Haol04tE8hnv/JFPQrzkFdcxhrSmvwyep9mL2G/ffA+eNx4eT+6V/UAFVV8eBnm/DMt9uQ4/fixuOH4Ybjh6JrXgDVjSE89932+H3cj6mDu+Lxyw9Dr8Jsx/H21zTjyhcXo645gr+cPQajehegf9dc9CnMxv7aZvzlk3V44NONeGNJCX5+wjBcMmWAq42Dp+duw4OfbcS0Q3rgb+eMRa/CbNQ0hRGKsqqD+2dtwPlPLcBvTxmJ644Z4moj650fduO+2RtQ0xTGqWN64baTRmJ0n0Lsr2nGt5vLsHRnFd5YUoLvtpTjlWunuhJOmw/U4fLnF6ExFMXUIV3x65NH4qzxfeHxKJi3pRwPzN6IO2asAQBcMmUA/nLOGH4Or6qqHea/yX08qrrwaVU4y15V1T8Xqur7N4qPpaqqunE2i7d3lfhYiWv7ufhYFdtYrD8Xio8lm6pdcq/tvr4sVn25+Fgf3MRiRaPiY6lqy32MxcTHev4kFmvpK+JjzfkHi/XlveJjqaqqrn2fxasqER9r/n9YrJm/FR9r7yq577XnfqSq/z0v8c83F+9SB90xU/312yvUYFj/PRGNxtQPV5SqY//8mTr2z5+ps1bvdRS6rLZZPenhueoh98xWv99i/F5fsqNC/fG/5qhD75ql3vHeKvVgXbPtWLFYTP3F68vUQXfMVH/z9kq1vjms+3XRaEx9af52dehds9RTH/lWLa1qtB1LVVX10zX71CF3zlQvfPp7taYpZPgzfbpmr3riw3PVQXfMVP/x6QY15uC5EIpE1YufWaCOuHu2OmfjAcOv21PVqF75wiJ10B0z1TMfm+f42t5YvEsdcudM9ezH5xn+LmKxmPqfrzarg+6YqZ76yLfq5v21jmJtL69XJ/7lc/W4B79RF247aPh1G/fVqpc8u0AddMdM9Z+fbXR0H1VVVf/04Rp10B0z1ce+2mz4GiUVDeqtby5Xh901Sz36ga/VpTsrHMXacqBWnfL3L9VJf/1C3bCvRvdrotGY+uy3W9UJf/lcHXLnTPXl+dsdxaptCqnTH/1OHXTHTPW+WevVcET/vV3VEFQvf36hOuiOmeoDszeoDUH990k6np67VR10x0z1zhmrDdd/UyiivrZwp3roHz9VT33kW3VfdZOjWJX1QfWkh+eqY/70mbqypEr3a2KxmDp79V71vCfnq4PumKne+N+lalMoYjtWLBZT75+9Xh10x0z1l28sN3xGHqhpUq9/9Qd10B0z1bMen+d4/X+2dp86+M6Z6iXPLlDXlFYbft2SHRXqxL98rh721y/UBVuN3ydm1DeH1Wn/nKMe/vcv1S0H9H/eaDSmrimtVu+bxe7BNS8tViNR6+81AEtVA83TsYaEAHJ2U5vjdrCsne9DTgP+sB/oM158rEydcdXZkOmgAUmTFSU4aGc9Bty1R/w5eamI7uUD5PZONbPynFaTKkUy5jzgT1VA8YD0X+uWTA0JkUFSD9oPOyvxx4/W4viRPfDQBeMR8Om/JzweBedM7IfZtx6HYT3y8YvXl+PZb7fZChuMRHH9qz+gtKoJL18zFUebOGOHD+6KD28+BhdPGYD3V+zB2U98j7V7amzFe37edsxavQ+3n3oIHr54gmGvmcej4NpjhuDlaw7HnqomnPnYPLy/vBQst7BGeV0Qd72/GuP6FeHV66Yalh0pioLpY/tg9q3H4bKpA/H03G24Y8ZqNIftVZfcN2sDFu+oxIMXMgfGiL7FOfjvdVPx1BWTsPNgA856fL7t+/jJqr246/01OH5kD7x5w5Holp9leG23njgCr1x7OA7WB3HWE/PxxuISW/exMRTBtS8vgaIo+O91U3HkUOP/Dx3SuwCvX38kLj18AJ6YsxU//98ylFY12rq2Wav34dWFu3D9sUPwyxNHGJbdDeiai/9cehjeu+loeD0KrnpxCRZvr7AVq6I+iMufXwwAeOuGIw37LD0eBTccPwzf/f5HOHF0L9z7yXrc+/E6ROIlkFZQVRW3v7samw/U4ZkrJ+Pu00cbOjrFuQG8+JPDcenhA/DMt9tw6qPfYcO+Wt2vNWJ1aTX++fkmnDGuD+4/b6zh+s/2e3HlkYPw9JWTsauiESc/8i3eXbrb1hqJxVTc/MZylFQ24oWfTMGEAcW6X6coCk4b1wczbjoa95wxGp+v349b3lhu+7320Oeb8Oy323HlkQPx6CUTDZ+RPQuz8dxVk/HE5YehtKoJZz7O1r8dNh+ow6/fXonx/YrwyrVTTctODx/cFe//4hgU5/hx+QuLcP/sDQhG7F3b32aux86KBjx22WEY3lO//9/jUTC2XxHuPn00/nbuWMzZVI7rX/0BNfFSYDeQQNNj4uXAqDOB434rPpaG6EmAGokJfZ2wNEkmosempxLIYyVzPvf9BGnx+uSsD43jfgf0GC0nVkKgSbi+yT8B8noC4y4UH0tDlqjOxJh9GaWbAOuvC9WjpjGMW99cgX7FOXj80sMsleQM6JqLd248CmdN6IsHPt2IO2esRmVDyFLYv36yHqtKa/DIJRNx1LD0G0AF2X48cP44zPj50VBVFZc+twirdldbirVydzUe/GwTThvbG7+YNszS9xw/sgc+uuUYDOmeh9+8swr3fLgWYYtJ8Z8/XouGUBQPXzzB0tCFgM+D+84di1t+NBzvLC3Fxc8utCwu3lm6G68s2Inrjx2C8w5LX5KmKApOH9cHH95yDHL8Xlzz8hLM21JuKVZZbTPuen8NJg0sxvNXT7F0bdMO6YnZvzoOhw/uirs/WINfvL4cTSFrieNz323HzopGPHn5JAy2ULbl9Sh44Pxx+N0pIzF/y0Gc88T3+GFnpaVYpVWNuPP91Zg4oBh3nDbK0vdMHFCM9246Cr0Ls3HFC4vx/HfbLYkLVVVxx4zVqG4K49Vrp2JEr/TDsAqz/Xjmysm4/tgheGXBTlz7ivWk+NUFO/HZuv24c/ooTB/bO+3XZ/u9+McF4/H2DUciFInhgqcX4LO1+9J+HwA0h6P47Tur0D0/gPvPH2ept+z4kT3w2W3HYXSfQtz+3mrc8Noy1DRZu7an5m7Fgm0V+PNZY0wFvIaiKLj+uKH42zlj8dWGMlz2/CKU1wUtxfpm4wE8PXcbLps6EH87Z2zaEklFUXDm+L747LbjcMTQbrj7gzV4b1mppViqquLu99cg2+/F81dPsVRGOKR7HmbeeiwunzoQz323Hec+uQC7KqxN6P1s7X689cNu3HTCMEv3EQCuOnIQ/nrOGHy/tQLnPf19q95XJ3RAgSbjjKuuwKWvA/k9xMeSjcydb9kiRiYy3J5kAvlyJjhmghP/CNy8SE4smQ5yj0OA27e0HoTSWchEL2tXa0KCRzw1VI8/fLgG5XVBPHbZYSjKtd5TE/B58OglE3Hj8UPx7rJSnPaf77Bkh3lS/MW6/Xh9cQluPGGopYQxmXH9izDjF0ejKMePi55ZiGe+3YZozDgpjsVU/PnjdeiWF8BDF463NYxgaI98vPfzo3HTtGF4fXEJrn5xCarSCNBZq/dh9pr9uO2kEYa70Hp4PAp+d+oheO6qydhRztyt+VsOmn5PSUUj7vlwLY4Z3g13WhQVGsN65DN3L8ePq15cgjtnrEZts3lS/PAXmxGMRPHviyfa6l/rWZCNV6+dirtOG4XP1u3H1S8txt7qJtPv2XKgDk/P3YYzxvWxJOA1FEXBLT8egY9/eSyKcvy4/PlFeHXBTlPhFInG8Ku3VgIq8Phlh9m+tg9uPgYnje6F+2ZvwPWvLsWB2mbT73l9cQm+2lCGO6ePwqF9rVeJeD0K7jnzUDx0wXgs2l6Bc5/6HitKqky/p7IhhIe/2IwTRvbA9ccNsRwLAI4Y2g0f33IsRvQqwM//txyPfrUZMZP3GgD85+st2FJWjwcvGG+rN29Qtzy89bMj8cczD8WcjWU4+4n5aZ27j1buwb++2IyzJvTFZVPtVVJceeQgPH3FJKzfW4sf/WsuXpi33fQ50hCM4O731+KQXgW49+xDbT1HehZk44Wrp+Cood3wu3dX4ck5W9PexxnL92DprircOX0UetrozcsN+HDfeePw4k+mYG91Ey56ZiF2HjQXaQdqm3Fn3PG/7aSRlmMBwNVHDcYr1x4OqMDNbyzHHz5Yg4akYUF2yLhAUxRluqIomxRF2aooyp1pv6EzuzIykLnzrSjAKfcBN84THysTXPwacP03cmIF8uWUN3Z2ZJY4dmZkbvRk5QPnPQtc/aH4WAAQyEOosQ4zV+/Dr08eifH9i22/hNej4K7TR+PjuCtz2fOL8NRc/SSkORzFXz5Zj1G9C3D7KYc4+pH7FOXg41uOwY9H9cQ/Pt2Ii59diDWl+qV6H67cg1W7q/H76aMcTYH0eBTcMX0U/n3xBCzbVYVznvweM1fv1b22ivog/vTRWozvX4QbjhtqOxYAnDKmNz665Rj0KMjC1S8tNryPAPDXmevh8yh4+KKJjoYQDO+Zj9m3HocbTxiKd5buxqmPfIelBo7Tur01eGfZblxz9GBLblYqHo+CG08YhscuPQxr99Ri2r/m4tGvNuuW6qmqit/PWI28LB/+fPahtmMBTIB+8ItjcPyIHvjzx+vwyzdXoLpRX1w/PXcblu2qwt/PG+to4E1Rjh9PXzkJ9551KOZvPYgzHpuPHQZJ8bbyevx91nocN6I7rjl6sO1YAHDx4QPwxs+ORHM4ivOfXoB7P16HeoOk+F9fbEJjOIp7zhjtaFJir8JsvH3DkTj/sH549KstuOG1pdh8oE73a1ftrsaz327DxVP6m5baGuHxKPjpsUPw9o3s2s576nu8v1zfcWoKRfGPTzdibL9CPHrJREfXdtq4Pph167GYOqQr/j5rAy59bqGhm/b64l3YX9uM+88f62jMfMDnwcvXHo5zJvbFPz/fhMP+9iVeXbBT971d0xTGA7M3YNLAYseDWk4c3Qvv/vwohKIxnPHYPLy2cKduOaeqqrj9vdUIhmN49FLjkk0zjh7eHV/8+njccPxQvLGkBJc+twj7asw3YPTIqEBTFMUL4EkApwE4FMBliqKYP30osXKHNo5bVn/d0bfI6a3LBIeeDfSXMOkQAIr6yekt6uzILHHszMh00ABgwqVyzpMDEPPnQQ3WYUTPfNx4vDNRoTGmbxE++eWxmD62Nx76bBMufW4R3l9eij1Jbsm7S3djT3UT7jnjUFeTzbrlZ+HpKyfh0UsmYsfBBpz1xHzc+uYK7K5sKQ1sCEbw4GcbMaF/Ec4/rJ+razt/Un+8deORUBTgljdW4Jwnv8dHK/cknJlYTMXdH6xBbXMYD1043tW1DY2Li9PH9cFDn23CSY98i3s/XoeN+1schTkby/DVhgO49cQR6F3kfPpdtt+Lu04bjfd/cQyy/V5c/sJiPPjZRqzdU4NQhIknVVVx36wNKM7x45Yfj3AcCwDOmtAXX/z6eJw6pjce/WoLTvjnXHy/tbVTOGP5Hqwoqcadp41CzwLn11aU68fzV0/BHdNHYfaafZh639e49+N1rcTT7spGPDmXHUFwzkTna0RRFFxzzBB8fMuxiKkqzn5iPh79ajNWl1a3EqH//mIzfB4PHr5ogqspgocP7oovfn08rj5yEF5duBOn/PtbfLKq9cbBipIqvLmkBNccPdhSGaUR2X4vHr54Au45YzS+31qBUx75Dr99Z1UrwdsUiuL291ahR0EW/nCGM1GtMXlQV3zyy2MxoX8xfvPOKvz8tWX4ZNVe1CU5vM/P2459Nc3405ljXI3NH96zAC/+ZAr+ddEErNlTg7OfmI8PVpSivC6YuJcNwQien7cDxwzvhsmDujqOle334tFLJuKpKyZhXL8i/Pnjdbj0+UVYt7emlcP74GcbUdUYwl8tlFGaMbJXAWb+8lhMGtQFf/xoHabe9xUe/3pLKzH/+boD+G5zOX4//RAM6+E8T/B5Pbj79NF48SdTsKWsDj/+17d4+ItNWLm72nK/pGKn+ZA3iqIcBeBeVVVPjf/7LgBQVfUBva+f0ter/vPd79Bj8FgM75kv5LBCjaqGEGYsL0VzOIqjh3fH2L5FjpS0FVRVxeIdlThYH8SQ7nkY1kPste1d8iG25k1Cty5F6JoXQNe8gLCD9hpDkUSN8RFDumFkr3whB2hqrNtbg23lDahvjuDE0T1djalNx46DDdi4rxahaAyDu+WhR0EW+nI6ByaVuppKfL+lDEFfAXoXZqN/11xuZ87osfNgA37YWYlITMWkgV2E/t6CkSgWba/EtrJ65Gf7cMLIHsJ+b+qcB6B8+w8sPm8e1IJ+6FmQhSHd84RdW11zGD/srESX3ADG9ityNcY7HaqqYuH2Cmwtq0f/Ljk4fkQPIQeDAgAiQYQ+/QN2jrkZu4O5yM/yYfKgLsLiaQdEK4qCrnkBDOmeJ+QgUgDYNeNPGLTmP5h13jqcMYFPeaqqqnjrh934z1dbsD9e7tW/Sw4m9C/GvC3lGNGrAO/9/Chu67CumZ1P9cJ8VqbUrzgHuQEfdhxsQFM4ihk3HeUqsUomFlMxY3kpnvtuO7aU1WNcvyL0K87B+n21KKlsxD1njMb1Dt2zVFRVxSer9+HtH0rww84qhCIxTB7UBYO75eGztfvQpzgHs289jtv/qysbQvjTR2sxa80+qCpQkOXDwG65mFRQjeat32HcmTfj6qMGc4mlqiq+2ViG+2dvwLbyBkzoX4Rehdmobgpj5e5qjO9XhLdvPIrbut+wrxavLtiJd5exgS8nH9oLA7rkYtaafahrjuDTXx3H7XDtXRUN+NNH6/DtZtbbV5zrx9TBXZHl92Lm6r34xbRhuP1UeyWpZizbVYU/fLAGG/fXoV9xDvuvSw4+XbsPRTl+fPWbE7idIVjVEMKz323Hc99tg8/rwfQxvVGU48cPOyux+UAdXrrmcEfumR6RaAyPfrUFbywpQWVDCFk+D86a0BcxVcXMVftw4uieePpKfpvGq3ZX4w8frsHaPWwjpDDbhwkDinGwPoQN+2ox46ajuR1Srqoq3l1air/NWo+65gj6FeegRwEbuLNydzWuP3YI7jnTndBNjjV/60G8umAXvtpwAF1y/ZgyuCt6FGRhxrJSDO6Wh1m3Hsvt/2e7Kxtx36wN+GzdfgBAfpYPZ03og6nhZTj/0uuWqao6Re/7Mi3QLgQwXVXV6+P/vgrAEaqq3pL0NTcAuAEAJvfxTvZc/QrK0AVej4JRvQtw6eEDcNnUgVwTg10VDTjvqQWtmrt7FGThqiMH4fIjBqK7wZQmp/z7i0147JutiX97FGBcvyLcfuooHDuC7yG3i7ZX4LLnFyH51+7zKLj6qMH4/fRDuArD5nAU5zzxPTYl2f9dcv340aieuOKIgZg0sAvXxPiLdftx4/+Wtbq2SQOLccPxw/DjUT25CuzdlY049dHvWh3EqCjAGeP64KZpw7gdxgiwBOj8pxdgZcoAgGE98vCLacNx/qR+XO/jsl1VuPrFxWhIurZhPfJwxvi+uGhyf27/0wbYg/Knry7FNxvLEh/zehRcMKkffvnjEVxjAcAX/70fJ2x7GIcFn0MjmAg8tE8hbpo2DGeO53MQr8buykZc+tyihFuSG/Cia14AJx/aC9cePQQDu/G9tke/2oxHv9qS+HePgixcMKk/Ljl8APcDNFeUVOHy5xejKalEZEj3PPz2lJE4fWwfLgfxatQ2h3HW4/Oxq6LFCcoNeHHS6F749ckjuV/bzGfuxpn7n0Tz73YiO5/vgfTRmIpN++uweEcFluyoxLq9tRjULRd/PWcs9+sA2FlIL3+/A/tqmtEQjGBfTTOOGtYNf+SU6CQTjal4beFOzF67H2W1zTikdwGOH9kDl08dKGQDpKohhPeWleL9FXtQ3RjCiF4F+OeF44Vs7uyvacaSnZVYtL0CJRWNmLbnWVyvzkD47gPwB/jGawhG8NYPu/F+fIO4e34W+hRl409njUFXDodOp3KgthlPz92GOZvKsLe6CYf2LcJ9547ldjBzMmW1zVi0oxJfbziAjfvqUB+MYOqQrvjLOWO4HCicTDSmYubqvZi9Zh/21zTjYD3L5+49ewxOPtT5+XpGbNpfh9cW7cSna/ajKRzF8J75uPaYwZYG1dglGlOxooSd9fXlugNoCkcxtl8RXr7mcC4HkycTi6n4emMZ9lQ1YnNZPVaWVGN/bTOuPHIQfnOyvf4sK1TUB/HF+gOYv+UgapvDCEZibFDN9FFCNuVW7a7Gs99tw+YD9SipaMTJh/bCvWePSYhDnpTVNWPJjkrM2ViOj1ftwd3KK7juvnc7rkBLZuJhk9U3Zn6DnZWNWL+3FvO2lGNVaQ3G9SvCgxeMt9VcasZv3lmJ2Wv2YcZNR6N7fhaW7arCO0t3Y+6mcgR8Hlx95CDcdfpoLotleUkVzn9qAc6f1A/XHzsU2w/WY9N+1v+w42ADJg0sxp/OGoOJBqNS7RCKxHD6Y/NQ1xzGvy+eiNqmMKoaw1hRUoV3l5Wid2E2Hr54gquDT5N57rttuH/2Rjx9xSSM61+EeVsOYunOKsxesw9N4SjOHN8HD5w/jstOVnldED9+eC4GdcvF/eeNQ5bPi682HMB/F+7EgdogDulVgH9cMA6HDXSfcKmqiqtfWoKlO6vw+GWHoX/XHOyqaMSKkmq8tnAnGkJRXHHEQPzprEO5OJMfrdyDX721En85ewyOHtYN+2ubsa2sHjOW78GaPTU4fmQPPHD+OC6OWiQaw/T/zENzOIoXfjIFuX4fvt1Sjlmr92Lxjkpk+7y458zR3JKuD1aU4tdvr8KvTxqJy48YiKrGEN5cUoLXF5cgFlPjB5+OcFXWo7GtvB5nP/o1LhmuYvq04xGJxrCtvB6vLtyFrWX1OHZ4d/z1nDEY6qKsIZmfv7YM320pxxOXH4amUAw/7KzE3uomfLOxDF6PgvvPG8dNXK8urcY5T36Pcyb0xd2nj8aq0hq8/UMJ5mwqRzSm4pjh3XDPGYdidB/3z8hgJIozH5uP+mAE95xxKPoUZ2NPVROe+GYrNh2ow7h+RbhjOr/NJW0D698XT0CvwmzsrW7Cit3V+HjlXoSiMdw8bTh+Pm0ol/daZUMIjz14F+71vAD8ZiNQ2IfDFbQjVr0NeLxyJ4t2Rj69E1j8NPD7HWyoWCdBVVWhFS5taKgA3rsWOP85oMDecJz2CjvDClw3qdIRisTg9yryfncr32BHDY08VU48Schc/+FoDJ6Pb4Hv/KfbrUCzV+I4ZYq6dOnSxL9VVcXsNfvx54/XoroxjBtPGIpbTxzh6n/Uq3ZX4/ynF+Caowe32WXcWlaPZ7/dhneXleLwwV1w/3njXNUxR6IxXPjMQuypbsLc301rdQ5NYyiCNxaX4Pl521FWF8Qvpg3D7045xNXieXLOVvzz8014+ZrD8aNRrS33xdsr8IcP12JrWT3OHN8H958/ztWOVnVjCMc/NAeTBnXBK9dObfW5uuYwXvl+Jx79egv6FefgicsPc9SIn8yv3lqBT9fsx6e3HdeqbjgcjeGr9Qfw15nrsb+2GT89Zgh+P32UKzft3aW7cft7q/HXc8a0KW+paQrj8a+34IX5OzChfxGevGIS+ndx7pQ0h6M48eFvUZzrxye3HNvqoR+Lqfjf4l34x6cboQC46/TRuOIId8Lple934N5P1uOZKydh+tjWyWlpVSPunLEG87cexJnj++ChC8dbGittRFldM0595DsM6Z6Hd39+dKsNj301TXhyzla8/cNuFOX48eglh7lK+FVVxU9e/gErdlXhm99Na7U7FoupeH1JCR78dCMaQxFcd8wQ3D79EFfPkcXbK3DJc4vw25NH4pcntu5R2V/TjF+9tQKLd1Ti9HG98fdzx7naGY/GVFz87ELsqmjAnN9Na7XhUVbbjHeXleLF+TvQGIrgicsm4SSXu8ePfLkZ//l6S5vnSDSm4sMVe/DvLzdjT3UTTh3TC/+6aIKrDZjSqkac/O/v8OPRPfHk5ZNafa6sthl/nbkeM1fvw9AeeXjogvGYMthdsvzXT9ajctH/8Kj/SeCWpUB3d/1F7Y57467IvfbO+iJS+PiXwPL/Aretpd5gN2ybA7x2LnDZW+w8WMI5+1YBRQPkbBjQc4QP714D5eJXDQVapqc4/gBghKIoQxRFCQC4FMDHVr9ZURScMb4PvvrNCTj3sH54cs42XP78YpTVmY90NaIxFMGv316JXgVZuPXEtv9jHt4zH/+8aALuP28ctpc34IoXFmPhNnuHMSbz2DdbsXJ3Ne45Y3SbQ0JzAz5cf9xQfPWbE3DhpP54cs423P7ealuHMSazu7IRj3+zBdPH9G4jzgBtfOwx+PVJI/Hp2v048eFv2zQqW0VVVdw/ewPqgxHcdVrb860Ksv345Ykj8PYNRyISZWeKvDDP2nkpeny7uRwfrdyLm6YNa9PU6fd6cNq4Pvji18fjiiMG4oX5O3DZ84vSjv01oqyuGX+buR6HD+6CK48Y1ObzRTl+3HPmoXjmysnYXt6AMx+fn6i7d8LL3+/Enuom/OGM0W125Dzx0tTPbzsehw3sgns+XIsbX1vmeKTrjoMNePCzTThhZA+cOqbtbmb/Lrn473VT8fvph2DWmn04/6kFKKmwd/CpRiQawy/+txzN4RgevGB8Gze6T1EO/n7uOMy69Th0yQ3gqpcW45XvdziKBQBfrmeNv7edPLJN6YLHo+CqIwdhzu+m4dKpbI1c+PRCx8+RSDSGv81ajz5F2bq9N72LsvHGz47E76cfgi/XH8Apj3yHBducvdcA4Kk5W7FsVxXuPG10GzHUszAbN/9oOD6/7XiM7FWAG15bajgpzgob99fiqblbcd5h/do8R7weBRdM7o9vfncC7pg+Cl9tKMN5Ty3A9vJ6x9f2l0/WAwDuPr3tc6RnYTaeuHwSXrn2cISjMVz2/CK888Nux7FW7a7GKwt2YNLweMIdcv5z2+LeIuCDn8uJRfAhfpB54k/CGdp7TMZ9jIaBNy4F9iwTH0s2qgo8ezzw37Mz/ZMQdkiz7jMq0FRVjQC4BcDnADYAeEdV1XV2X6c4N4B/XTQBT17OznA4+/Hvsbq02vbPc//sDdhR0YB/XTzB9LyKy48YiDd+diQ8ioLLnl+En7y0pNU0HSss3FaBx7/Zggsm9TedlFSQ7cdDF47HbSeNwHvLSvGz/y7F/hp7iaOqqrj343XwKAr+dJZx70FuwIdfnTQC7990NLrk+nHtyz/gs7X7bcUCmKh4Z2kpfn7CMBzS29hhnDK4K2b/6jhMO6Qn/j6LnZdi9z7urW7CbW+twIie+bjJ5MDVgmw//n7uODxx+WHYsK8WZzw2H4u32xfXf/pwHZojMfzjgvGmJQzTx/bGx788Fr0Ls3HNy0vwn6+2pD3nI5WSikY8NWcrThrdE0cPM3aPBnRlwumeM0bjqw0HcNEzC22PdA1HY/jdu6vg9yp48ALjs5E8HgW/mDYcL19zOPZWN+HUR7/Dawt32ooFAK8t2oWlu6rwwPnmLvTIXgX46JZjcOKoXrj3k/W49+N1uqNxzahuDOEvn6zHyF75uPqotqJao0dBFu4/bxyevWoytpXX45JnF6U9m0iP5+Ztx9o9tfjDGaORE9B34bzx+/jxLceiKMeHq15cgv8uND+bSI9F2yvwyFebcc7EvrhgkvFzpEdBFt664UicNaEvHv1qC654YbHlw0g1ItEY7nhvNQqz/aY9TFk+L26aNgz/++kRqGwI4Zwnv8ecTWWGX2/El+sP4Mv1B/Crk0aYlu9OO6QnZv7yOBw5tBt+P2M17p+9wfZ7rayuGTf9bxl6FWbj/KPifRUykkbt973qTfGxOjsbZwMLn5QTKxTfmJKxRkKNwJr3gAxWOwkjqAk0CZshVTuBzZ8CM34mPpZstPu3f01mf47OwJYvgbUz5MRqzwINAFRVna2q6khVVYepqnqfm9c6Y3wfvHcTm3J00TML8eGKPZa/94t1+/G/RSW4/tghpsmwxiG9CzD39mnxMasHcc3LP1gWF5UNIdz29goM6ZaHv54zJu3XK4qC204aifvOG4vvt1bg5H9/a/kUewB464fd+HpjGX5z8khLUwYnDCjGOzcehTH9CnHT68vwj083JsYLp+ObjQfw91nrceqYXvidhTN9inMDeO6qybj3rEPx7eZyXPniEtQ0WbuPsZiKO2asRjASw3MWT5Y/c3xffHjzMSjM9uHyFxbjxfk7LCfFn67Zh8/W7cevTxppafzqkO55+OAXx+C8if3wyFebcd2rP6Q91FVjV0UDLn1uIbxexdKIXo9HwfXHDcVL1xyOkspGnPvk91ie5sBODVVV8ccP12LZrir87dyxlkZUTzukJ2bdehyOGNoVf/xoHe79eJ3poZbJbD5Qh4c+24TjR/bAORPTj07PDfjwzJWTcM3Rg/HKgp04/T/zsG6vtdKKWEzFr99eibK6Zjx04QRLUxRPHdMbr/10Kg7WBXH2E/Px1foDlmIBwFfrD+Bfn2/C6eN644xx6fuXRvcpxIc3H4NpI3vgTx+twz0frrXsbh2sD+LWN1dgcLc83HfeuLSlrbkBH/5z6WH498UTsKq0Gmc9Ph9r91gvUXnsm61YVVqDe8+2NqzgqGHMlR/QJRfXvfIDHv1qs2Vxvae6CXfMWI1RvQtw3THpD5MtyvHj5WsOx9VHDcJz323HzW8st/xeaw5HceNry1DZGMLzV09Bfn4x+0RQQtIoy6X7/8BblwGf3y0nVsL50T//iitz7gNm/BTYPkd8LNlo91HGe02NP1cjzioj2jVN1v5fT1jg9QuB966TEyvN8z/jAo03Y/oW4eNbjsHEAcW47e2VuH/2hrQlX/O2lOOXb67AuH5F+N2p1g8KzfZ7cf1xQ/H4ZYdh1e5qXPb8olbn2+gRi6m4/d1VqGoI4/HLD2tT2mjGFUcMwpe/OR5De+bj5/9bjgc+Tb9T/NL8Hbjr/TW2D4Eszg3g9euPwKWHD8Az327DuU9+n7ZUaeP+WvzyjRU4tG8hHrlkouUmWe28lKeumIT1e2tw7pPf4+sN5kmxqqq4b/YGzNtyEHedPtrWBLSRvQrw4S3H4MRRPfG3mevxq7dWojFkvkaW7arE3R+swdh+hfjZcekTRo2cADsv5b7zxmLB1gqc+fj8NtMYU9l5sAGXPrcITeEo3rj+SFvXNu2QnnjvpqPg93pw8TML8dTcrabXFoup+PeXm/HWD7tx84+G2Tr3ZkDXXLz4k8Nx3TFD8MqCnbjxtaUoS1M6WlrViGtf/gF5WT7860Jjpy4Vn9eDe88eg//99Ag0hqK45NlF+HydubsbjERxz0drMWdTOf505qG2Bu1MHtQVM35xNHoUZOP6/y7FHe+tNjz4VEN7jozpW4R/XTTB8rUVZPvx3NVT8PMThuH1xSW45LlF2LCv1vR7GoIR/PTVpahpCuOJyych38Zz5PxJ/THjpqPhUYCLnlloySV/b1kpHvt6Cy6c3B9njrc+OKN/l1zMuOlonBN37i55dmFa4bT5QB2ueH4RwpEYnrh8kuV+UZ/Xg7+eMxZ/OH00vlh/ACc/8h3mpnHuovFNnhUl1Xjk4olscp12CLcM8dSofwiycGLOSlxtse5D4PM/iI+TCcISHTRtjdToH1DMnf1rgDcvAyL2HHZHyCxx1GJ1RoEm8zkSsbbxxY2d85mD3Blp7w6aCLrlZ+F/1x+R2E094v6v8cK87W12plVVxazV+/DTV5ZiSPc8vHrdVEeDAU4b1wfPXz0FO8obcOoj3+GB2RtaHQ4KsER4wdaD+MnLS/D1xjL84YzRjkaxD+qWh3dvPApXHDEQz367HTe8tkzXTdhX04Rb31yBv85kbtYLP5li+yiC3IAPD5w/Hs9fPQX7a5tx3lML8NqiXbo7/Au2HcRVLy5BfrYPL1x9uKPhEaeM6Y1Xr50Kn0fBT19digueXoD5W9r25uypbsIfP1qLF+fvwDVHD8aVRwy0Hasw249nrpyM2089BDNX78XJ//4On6za2+baahrD+M9XW3DZc4tRlOPHE5dNsn0fFUXBFUcMwrs/PwoAcN5T3+Mvn6xDMNLWTVi7pwaXPrcIwUgMb/zsSEeTSUf1LsSsXx6HH4/qiYc+24Rp/5yLj1ftbeMUqqqKP3+8Do9/sxUXTu6P355sfXNCw+thZbOaA3rCP+fi319u1t0U+Wr9AZz1+HzUNofx8jWHo6eDcdjHjuiOD24+GkN75OHG15bh7g/W6PYT7qpowIVPL8Qbi0tw4/FDceWRxqWNRozsVYAPbz4aN00bhneX7cZp//kOC7Ye1L2PL83fgateXIJ+XXLw4jVTbK9/r0fBnaeNwr8vnoDt5fU48/H5+PvM9bqisLSqETe8thRrSqvx+GWHOVojY/oW4cNbjsHI3gX4+f+W4cbXluqKwpqmMO79eB3umLEaxw7vjvstOHWp5AS8ePTSw/DMlZOwYV8dTnn0O3y2dl+b+xiLqXj5+x048/H5qGuO4JXrpmJ4T/sTNX92/FB8csux6JYXwDUv/4A/f7S21ZEpGs3hKG55Yzk+WrkXt596CE7THE/t8G0ZSWNThhIrGc7Puz8BFj4BBCXEko3MHrScYvZnU7X4WADw5uXAptlAxdb0X+uWoEQnUvtdyRCeGjF75fiO0Rw0L//R8G1I3riSsdHzyhnMQZZR4iu7jDjN8yOjUxztkjrF0QrLdlXi8W+2Yu6mcgzrkYdLDh+AvCwfFm+vxLJdVdhT3YSJA4rxyrWHozjX3fkRJRWN+MdnG/D5ugNQVRUnju6F6WN6Y0tZPT5duw+7KhpRmO3D7acegiuPHORq2p6qqnhlwU7cN2sDIjEVY/sVYly/IozsVYCyuiBe/n4HYjHg5h8Nxy0/Hu76SICSikb86u0VWFFSjZG98jHtkJ7IDXhRVhfE7spGzN96EEO65+GZKydjpIvJlgBzPp6asw0frdyDnRWNOHJoV5xyaG9k+T34YUclPlu3H6FIDJdNHYi/uTxZHmAT9+79ZD027KtF17wALpjUD0N75GPV7mp8s7EMZXVBnDiqJx6+eILrNVLTFMa/v9iEVxfuQkG2D0cP64aeBdkY1acAy3ZW4YOVe9AtLwv/u34qRvV2NxJdVVUs3VWFv36yHmv21OCood1w+OAuCEZiqG4M45tNZSivC+KG44firtNGuR4vu6uiAQ99tgmz1uxD9/wAjhjaDaN7F0BRFHy94QCWl1Tj0D6FeOLyw1yPsg9Gonjos014ZcFOeD0KpgzqgqE92CHv28rr8d6yUmT5vPjXRRO4nHmzdGclfvPOKpRUNmJcvyKM7VeI/l1y4fWwa/thZxVOObQX/nPpYYZ9Z1apagjhoc834s0lu9El148LJ/fHsB75qGuOYOmuSnyzsQwKFNx//jhcONndGTvN4Sie+GYr/rtwJ2qbIxjVuwCnj+uDcf2LsKKkGq98vwP1wQguP2Ig7jxttC2nTo+1e2rw+/dWY/2+WgzpnocTRvbAmL6FKMrx49WFO/H91gqcOKon/nHBeNfn0DSH2Rp56fsdyPF7cdGU/uiaF0C234uDdUHMXL0P+2ub2x6k3FQFPDgYOPUB4KhfuPoZ0rL1K+B/F7C/i56I1lgJPBR3/3+9Dijifz5TK/7eG4g0AVd9AAz7sdhY4Wbgvvj7/J5ywMf/vLBWPDIWqNkNnPkIMEVwOdQ3fwe++ydw7K+Bk+4VGwtomdB3w7dA34liY316B7D4GXYPz3xEbKxNnwJvXgp4/MCfnA9lsswblwCbPwOunAEMP0lsrLUzWFleoAC4W7DTWr0beHQs+/udJUA2//PyWqGtx1uWAd2Hi41VXw78Kx5DxoTKBwZAubu0fY7Zt4sTgQawRPWL9Qfw2NdbsG4v2yXuXZiNsf0KccqY3jhrfF/XSVUye6ub8PriXXhzyW5UNoTg8yiYOqQrLp4yANPH9uZ6GHRlQwgzlpXim41l2LC/FtWNrH/rrAl98ftTD+F+0O+s1fvwwvztWLenFqFoDN3yAuhdlI1jhnfHbSeNcDV2PZWmUBSvLtyJ1xbuSpSOds0L4OTRvfDLE4e7Gl+fSjSm4sv1B/Du0t2Yu5mdHVWQ5cPkwV3wm5NHuj4GIJUFWw/iveWlWL6rCmV1QTSGosj2e3DFEYNw64kjTIfU2CUaU/H64l14cs5WHKgNIsvnQV6WD1MGdcGpY3rjvMP6cT2zZUVJFZ6euw3r9tYmfm9DuuclDnrnuf5LKhrx0vc7sKq0GlvL6lHXHEHA58F5E/vh1jTDJezSFIri/RWleHNJSauDT0f0zMdlUwfiJ0cP5nqQ5oqSKjz33XZ8sf5Aor+vf5ccnDiqJ248YZilflKrVDWE8P6KPfhs7T4s3VWV2Eg85dBeuO2kkdzOmATYQJoPVuzBJ6v24oedlWgOs13YvIAX95x5KC49fADXs2i2HKjDv7/cjK83liV6ab0eBSeM7IGfHD0YJ4zs0fobomHgb92BH/0BOOH33H4OXVa/C7x/Pfu76IQgObG6aSHQi/9h1a147kfA3uXACXcCP7pLbKzKHcBjE9nfZZxN9uAQ5n6e/DfgmFvFxvr8D8yJnHAZcN4zYmNFI8DfurG/XzMLGHys2Hgf3Qys+B8w7mLggufFxpL5XgNahMVpDwFH3Cg21g8vALN+C+R0Be5wPu3YEuWbgCfjRyfJOGbi/n7MtTv3aWDi5WJj7V0JPHcC+/sfKwAvv3y2DaoK/LUrlHurDQWawOjtB0VRcOqY3jh1TG+U1wVR0xTGsB55wg6k61ucg9tPHYVfnzQSmw7UYVC3PNc7z0Z0zQvgZ8cPxc+OHwpVVXGwPoSYqqKXg/IxK5wxvg/OGN8nkei4OU8sHTkBL35+wjDccNxQVDWG0BSOok9RjpDT5L0eBdPH9sb0sb0Rjsawr7oZPQqyuAr3ZI4e3h1Hxw8Ebw5HUdUYQo/8LNvlk1bwxsfxX33UYMRiqvADNA8b2AXPXc2eN9pQiCyfR8j7bWC3XNx7Nhu0o6oqyuuDyPJ6UZTLT+Bq5AS8uOKIQbgifrxCfTCC5nAU3fPFlJUcNrALnr5yMmqawmgIRpDt97o6L82MLnkB/PTYIfjpsUNQUR/EjoMN6FOcw1Xgavi9Hlw8ZQAunjIAoUgM+2qacLA+hFG9C2z15FplRK8CPH3lZABssyIYicLv9RgPjPH6WamQjB40mSWOyeU0QfMeRy4o8fu7b5X4WHVJQ7NCDeIFmswSRy1GrfWhZ46p2NI2rkiCGehBk0E0qTRdSi+rVuIo2DkGWl+PjPLlwn7AwU1A6VLxAq12b8vfww2AV6A7GGluGVxjwP8LgZZMj4Is16UzVvF5PY76zJyiKIq0axMpzFLxeBR0E5QE6+H3ejCwG1/n0Yxsvxd9ivgnwnqIFmep8HTL0qEoCnoWiNmY0CM/yyds4yWZohw/V0c1Hd3ys6S93wI+DwZ1y8OgbtYH4bjB61GsufyBPLkDIBQJ75Pk62mWINC0eDLEYHJiJfr3Fo0A0Xgfk4zkW7ueGgkCLXnYhJRrkzhmP3ldRMNsI0YU4aRYUnpZ4wItKmGAh+yNnnB88F699WnKjkneBAk1iC3ftLAuOuWQEIIgCIJwTCBfzuhvzUFTo+Kno7Xa+ZYo0GQk33VJk0hFx2uVfEsUFskiVBThpOFmUh00yQJN9NTDkOT7qD1HZJ3LpyFlo0fiGkl14kVi4XpIoBEEQRBEMln58sfsi44ne+db5gj15OsRfh8lJ9+J8fBNzPmREQuQew6g7BLHxgrBsSSL+ISDFpS8RmRu9EjcMADEl2+Sg0YQBEEQNpFV4pjcgyZ8xzZTJY6S3RGZ91FmD5qMeNKvTeJB1cnXI7r3M1nEyCxxTI0tApkbPdFwSzlxZ36OGEACjSAIgiCSkSXQghITOZk738mJlWx3ROZ9lOGOtCo7lJh8y7i2TJU4djahm+z2dKaNnkxtGMiIRyWOBEEQBGGTgKQSx1BDy+GyspJvxSOvfEe7j6KP8wk1AH7tgHHRPWhxweTxyysD9MQHWshKGv15koeESEq+Pb7WcUWhrRFftsRrk7RGwhIdNO1aPH55z+NA/IxWmZshBpBAIwiCIIhkpAm0eiC/V8vfhcaKJwT5veTtsuf3BKC2TGITGS+/J/u7aNEk8z5q8Qp6x/8uob9O8QK53eRMw4w0sw2KWBiIBMXGCzW0vNeEr5H46+f3lDOKPvnaZDxHvAEgq0jec6SgtzyBpj1HqMSRIAiCINoZskocQw1AgcSk0ZfNRkfLctASSaME50daYpWUfMtaIzLFZyBPzpAc7fULZK4RWbEyIeJlPUcysEbye7IjBGRMus2XtRlCJY4EQRAEYQ+ZAk1m0hjIi7uDksqgEqJJRtKYL6c0T+auvuYyyRS6gTw56z8h0PqwP2VsGkgT8fESRxkCTfoaiZcTB/LkutVA6/JKUfHye7SOLTJWGkigEQRBEEQyWQUs6YlGxMWIRdno9ERiJSFBlZZ8y3bQMnRtovvrwhm8j6KTb+31ZYrP7GJWUin8vSbRZW2zGSJLxEvY6El9jsgQhIk1Qj1oBEEQBNG+CEgYOJGJMsBAvpz+ulBq0ijJQZMh0DSnp6A3EIuw0itRtFkjgoVFuFFi8q05aFpJmSTxmSVJWCieeC+fYBGf7NYBct5rWdp7TVaJYyfd6NEGkhhAAo0gCIIgkkkINIH/k9ZeO687+7NT9o5ITBqlXVsDmyqX06Xl38Jiacm3xMEF0kR86hrpZA6ydh9FD8lpsxkieoMi7qBlFWRgo0fgtalqizsoRcTXt/x/xgASaARBEASRjIxRy1oCkFUor1xIVvlaxkocJQkL7T5q/xYZC5A4JKQe8OdKciIlOmhan5YmmkT3u4UbUtaISBGfCZepIEPPEYHxwk0A1JbniIyeSBJoBEEQBGEDKQIt/tqJXX1ZZYAye0ck7Hxrh2LLKnEMNTD3QEuuRCapCRFfwISTLCdSZvmaJtBE3ketTytL4vr358rf6PHlyOmvy1QPmoz7KPM5QgKNIAiCIGwgs8RRuvOTz4aTiByAInNXv9V9lNSDFshjLkJyfBFITxobWSwZQ3I0h0LGWPM2a0Si0E2OLyoWIHGN1MsV8d6ApHLi1A0zST3BJpBAIwiCIIhkOmVildSnBYgdWd2mT0tW8i2rVDRfboljpso3ha4RiSWOGXmv5Ut6jsgWFvEhIVkFbKhMLCo2lrRy4kw8R8hBIwiCIAjrZMXdEaHla0mJVVaBvCEhssRnII8djK145TqRwntHZPagZShplLVGFA+Q0xWAIvY+amtC5nAL7XcGyFsjWQVif2exaHzSpyTxqcXSNpVklBNL2wwhgUYQBEEQ9pDujgguF9LOXEtMloP4ZCeQDyhKXDTJvI+SetC0pFGW8yN6QmUkBMTCQCBXzhoJxku8PB7x4jO1xFHKZkhuBkqlBT9HWjmRkvp0A3msny85vqhYQJLLKqkn2AQSaARBEASRTGfrQUuNBYiPp91DaUljPEGNhZnYEEWiBy0Dg2SkCF1Z5Zt1LfcwkCfW+ZTdp5jJEkdpmyGSNij8uYDHK35IjvQ1QmP2CYIgCMIefpkOmoS+mNTkIzm+qHiB3JaYMoUuIEd8yirxUrxsUILo+xiOn7kmK/kO1re4kKLPnWr1XitgUz+jYXHxEmP2Ja1Hj0/OGkmeKpooOxQsrDOy0ZMvfkgOlTgSBEEQhE28vvjIatGJlR/wBcT3oKWWyiV/TFS8ZHdEqLBIGQABSBBo+fGyK0Viqajg/iJdES+hT1GL2ek2KCTH0sqJZbp1WnyR8RLPEZkiXvCQnEgIiIZIoBEEQRCEbWQkja1cpnpAVQXFkl2alFS+I7O/SLT4jEZaevlkJcStRIxItyK+RvwSyzcTybfgwR1S10iYJd/+PMCfAzYARXQZYPJ7TXDfIJChUulO9BxJ3lQygQQaQRAEQaQiWqAF65E4SyuQD0BtKTPjjZ6D0FlLk5I/xpvkA4+1mFJ7+RoEinjJLlOwvmVaqtThFoKdn+T7KEXE16WsR1nHFchy4mU+RxRWOSF6SE7yGjGBBBpBEARBpCJj+mByYgVISBozlVhJKE3ySxAWyQ6C9qes+5iVD8QizJ0REiupB01KGWzqkBDB7zVvFuD1y0++pYj4pDJAkf11yWWA0nrQkvoUhZcT58Wnigp+jpBAIwiCIAiHiB5rnloGqH1MVCxAcl9M8gAIwbG8AdbLJ1PoAvKTb0CgsEhKvrWSOdEJsbQhIQ0S32t6Ak3iZggg/jmSJcGJjMXkb/S0uY+iniNJ7zUTSKARBEEQRCpSEqukBBWQs6svemS1qsrvQUtNvoXdR+3AY+33Jnpwh17SKGGNeH3skHHRJY6t1oisfjdZybckYZFaKgqIiyezBy3SBEDN0HNEYhmsCSTQCIIgCCIV0e5IUGbSqOf8iOrTSk2sRA9A0XGZRIuYjPSgCS47TKwRCccjJIatJPVghhqYayICmW518nEFgFwRL7o0VXtdf3yjR+Sk2zZOZD7EDslJfq/F1yWVOBIEQRBEO0P4WPPkHjTRCYHOrr5wty5JxKgxdq6QkHgSS5P0etCElgE2Jgkm0cIiKfnW4ol2mVr1YKpx10REvAYdEdNZetBklkrXMVHm9bF/i+wLSy0DFD4kJ4MbZgaQQCMIgiCIVKQmVhLK17TDbAGx4jOss/Ot/QwiCDXEzyRDy5/SnEgZZVepSaPANaL18gFiyw71km9A7KZBpvqLZJZKy7yPWjxZZYCBPMFDcjLQy0cOGkEQBEHYpLP1oGljvwEIPVMrUQaVVCoHCEx2GltieDzMARLpIAByBFpqL5+M8rU2ybcklylLQkmZ9jsTPQBFm4bpl1AqGouykkqZzk9Wkusj8vw6vRJHoJOIeCpxJAiCIAhnBPLZbm1EwI5tNMJK/tr0TolMvpMSK5FT8/RKHJM/zj1evc61SS5fE1F2FQkCarRt0ig0QU1OvgUKC+0a2gy3EOhYaMJCuIjX652S1RMp+DkSrNdZI5JcVhmlqVosr58dyyD69+YngUYQBEEQ9hCZELTpwdFiiXK16tHGHRHeO5KBnW8trsweNDUqpr+ujdCV0KeouT6AYBGv40QCkt1BySWOIkS8kcskco2kbobIPE8u+ePc46U8I4Wu/3o2JVXr5TOABBpBEARBpCIyIUgVMb4A4PFLTFAF9qBJTxolJ9/+XDbBDkgqzZOwRoQnqI0p91Fg8h002qDoJOWbHl9SL1+8dyoSFBDLoJdPloiR2oPWmUR8SiwDSKARBEEQRCoiy670pniJ3o2WVpoke+c79doEl5Sl3kdA8BqJx/DnAIpHstCVNOkz0YMpwEFO7dPS4gkbktPYunRNpLAwFGiy1oiMHjQJVQaREBAL62xQCOzTJYFGEARBEA4ICHRHgimJlfZ3qTvfgnqnZO7qpw7S0OLJvI+AmHiJ87Ti91FRJKwRST1obUocRbrVOgMZRCbfwfqUQRoSRbzos8mSD8UGBPd7SnSQU59ZWjxZ7zUDSKARBEEQRCpCE6uUEi9AgvOT0l8hamS1zBLH1EOxtXginUi95FtEPO1+JfeFiXa1AsmxCoBoEIiG+ccyLHGUIGK0eDKFbvLPwRPdjR7JGxRBURs9DQAU5hxrsRIfFxELEtcIOWgEQRAE4QyZPWja36WVJgkc3GE4Zr8TJFbBupRkWODgDt1rEzzcRVr5Zj0r1/RLOIRbr5xYtIhJ3XhJ/jl4xwJaxxM9oTXV9Vejgvrr4rESR4MILIM1eq+RQCMIgiCIdoYMERNIKhcSnhDoJY2Crs2fx8aZA/EdcKWTCl0Z4lNSGWxq+Zroa0tOvkUOydFdIwLd6qBRGWwHdwcjQf0+LUDctaW6/trHRcQCMtfLagAJNIIgCIJIReSYfW0XuFUCUiBGDBr1aQECk++kWCJ7p7T7mCosOkP5mkxhEYsBYaMBKIJ+b6kOgqghOUYDeYQm37KErkGJo0iXKbUHDRAXL3mN+DrTRk992/WvAwk0giAIgkhFhjuS2s8ks08LELjzndv6Y1n5YqavGSWosbDYsiuNrAyUOMrqidSuTVR/XaqDIErEm5U4CumdqjN4r8kq8RW0QaG3qSRzo8fjEbj+qcSRIAiCIDoGfgk736njuGWO9E/+OXjHa5N8i0oaNWGRvKsvePpmpib0AeL6i4yEbvLneJJ6H7V4QkV8SvIt6mwymWskWAd4swCvPymeaKEra6NHx2WS+owsYAfQRyNi4pFAIwiCIAgHeDxMQMno0wLEiRijBBUQ6I6kJlairi1lXLsWS/s5eKJXKurLjp9NJuj35stpORQbEDckRE/oii7Nk+6gpZzflfw53vGklcE26Ahd0SI+eY1I7EEDMvOMDHOOF4u1PSvPABJoBEEQBKGHqJIa3R4cQTu2pjvfEkqTtHhCHTQJCXGkmU2sS06+tf46IUK3sW2pqLDkW0/oClwjqQNJAIHJt0H5GsD/vR2NAJGm1vdRqBNvJGIElsHqDe4Q1TsoTaCZrRHO8fTKiQ0ggUYQBEEQeohMCPRKvAD+yZXRsAkRsYAMJY0ShIVeGZT2b2n3MR6Ld++UrtDV7qOIssO6tvdR1JAcmeWbmtuSfB+FOvH1rR0tQHyflozNEO01pa0R7WgQCUeR6K1HA0igEQRBEIQewtwRvT4tUcJCpzSps/Wg6SXfvCfLGe18iyy70ruPUFmJFO9YgLzSPMMeNEEixuNno/w1RI1s11uPgNhr0xPx0RAQ4XwIfVBvo0fkkByjUmlBsXzZgNfXOpb2OZ7olRMbQAKNIAiCIPQQNY7bMPmGuIRAZu+UzB40X05KYiU6+ZZYdqU3il77HE/aRQ+aQOdHT8RoPwfXWJLXSOqZa0DLGuHdOyV7kIzsEkfDNcL7PuqUExtAAo0gCIIg9BDpjqQ6CKJGtus5P0J7p/SSHUGlSUZOjPZz8ESvTwWQX+IICFgjOkmjx8vEr5A+rWadHjSBQ0L0+t0AceVrUq9N1vrXEWi+LMDj438fI6G2h2IDkkW8oPuoV05sAAk0giAIgtBD5s63qKQx4fzoJY28k+8wEA0auyO8e6eMpgFqn+MaSxMxKfdRmMva0HbSm+g10mbTQICIN3IQAvmChuQYlAECkl1WieXE2ud4x1I8gD+n5WOKIuYZadSnFSiQ6OiKdllJoBEEQRCEM4S6I5J70GT0/Bi6THlsAiLvc6eMpgEm/yy8MLs2UeWbeiPUk38WbrHq48l36tRIAddmJga1n4UnGSlxlNWnqDMNVtS1BeMiRlFS4hXIfY4I2egxc9CoB40gCIIg2hfCBJrkHVuPD/AGWn9cxKHHiWloOuPhkz/Pi2Bd20RHiy0ssZI4AEWWiDdMvkWsERMRA4hZk7KS78SkQ51NA2nDhgSWb+odrixko8fEiVRjQLiJczyJJY7Ug0YQBEEQLtGSb547ttqBx7LG7MtMvrXJiYauloByudREx+MRJCxMxuyLGg9vuEZ4T6jUuY9aPFkOgsgNitRr8+eIGZKjrX+9Mw65n8sXYtMapTnxOmIQEFMGa1SWnSXogHGZFQ3Ug0YQBEEQLgnkAbEI39K8cBPbBTaaviZi51uvnCaQJ3AUfWHbWMmf54XekBAtnoxBGtq/eZddJZJvnX43QEzSqHsfBTjIZvcRkFPiKGpIjqmIl3Xsg8AyWEMHTZDLJG2DQufavD427VbEhoFeObEOJNAIgiAIQg8RO7ZGSZxfVEmNjoOgxeee6NeyP40mVAopuzISaCKGJHjZ5LrUWFD5ll2ZTQMEOvZ9NCsVTf48L/QEGiBIfMZfLzX5zipgooKniDfr00r+WXjG010jAnrQjM6TE/YcMVojgta/XkWDDiTQCIIgCEIPEcmOkYPg8TCRJqTEUVLviFH5WiKx4rzzrTckBBCXWGXplYoKWCNBIwdBc0dE3EdJIt6oB02kOyhTfAby2Xs5mayCeO8UxwPGzfq0AEH9nrLc6jTuIHc30kSgiZhiaqH/DCCBRhAEQRD6iEh2EoMEJCY7erFE9MUEDcRnQqDV8osVi7HDeI129YUkcQb3EeAs4g1EjC8AeLMEOWhGQld2DxrHNWm6RgS914z6tAC+azLhoMnq9zQQMVJ70OKl0zyvLRYFIk0mVQaSyrJ1IIFGEARBEHqI6IsxOisJEDdZ0cxBiMU4xjLoQRMpYgyFroC+GKNddoBvPCMHTfsYdyfSwB2Reg6agP4izbHSfa8JODzdqE9Lez/wjGc0kMTjZSWWssSnzB40EULXaFNJ+5isknMdSKARBEEQhB4iBJrRzjcgpqTGsMQrH6x3iqewSNeDxtNBMDnwVVQPmlEs7fO8MHIQgLjzKTH5joXZ0BJeBOPHPrTp5RPgoBn1aQFxgSbAZTVyqwG+DrJRnyIgef0XMAeK5wHjwfp4v2d264+LfI7ILpW2AAk0giAIgtBDSImjwc43IKbhXu/AY0BMw32wnp23ZpR8c935NkusRDmRBsMmkn8eLrFMHDQR5ZtmPWgAf+dT99gHAUNCzER8VgFfwQSk2QyBGOdHhoMci5lPcQT4rxHdfs8Ofh8B43JiHUigEQRBEIQeQpJGyT1oRkmjiN3ooEEDvMfLBqBw3fk2K03KEzRIw0AMJv88vGIlv3YyvJ2faBiIBo0dXYB/ia/efRRRmpfOQZNxLp8WCxBTKp1aTgzw36DQSkWNymAB/g6y7noUWHJueB8llRPrQAKNIAiCIPQQmVgZDRPgmehEQqxEzdRB41wupJd8a/FkOWjafeQ61tyov0iAE2lWdsW7B83UQRBRdmgyxY63Y2Em0IScTZauxJHn7y3u/hltUAgZSGLiIPOedKt3H7VD6GXdRyE9wdSDRhAEQRDuEFLimKZ3SmaJF8DZ+amTKNDSlCbFIuywZ17InNAn00EzXY+C3BEjB4G3g2x05iDA7mM0xPcQeqMjLURthnj8bcuJAf4OWmKNSHS1jESMqPVPPWgEQRAE0UHw5QBQ+Cc7Hj8bmZ5KgPPoe7MJZaJKHA0FGuedb9nCwrAHTcSEyrp4L5/eGuE8+tvo4GhAXH+RoYPGef0bnRUGiJmsaNRfJPK9pnfgMXeha3IfRfUOGop4yQ5ypJnfABSzcmIdSKARBEEQhB4ej5hdfVMHoY5faZ7pKHpBDfeydr4TiZVJ7xSveLEo68PRi+X1MSHP20GT7SCY9aDxHiRjtv6FXJvBkRYAv0EhsZjxe9uXzSZXchdoRmukkP/vDJDcg2ay/qX1oMXXDa9Jt2ZiUAcSaARBEARhhAjHwqwHR42xXVsemI30F+UgGDpohYJ29SU4aGY9OIAYd9Aw+S5gYjEW5RPL9Mw1zR3k7GoZOQi8e37MRDzv/tJwIwBVf40oigDnp15fVAACRLxJqaioSZ+ynPh056Alf41bzJ5ZOpBAIwiCIAgjuA8uSLM7DPATTUaH2QL8HQQtnmlpEs9Y9YDiAfw5bT/Hu6TMzIkBBIl4k14+QE7SKOLwaNM1wvm9ZjpIhvd9NBExAP8NimBtGpe1lqMTb3Y0iIgeNDMnnrM7GKoDvFn65cS814iZE6kDCTSCIAiCMEKIQDNK9Dn3/JiVOPqyWGLSYXf14yJGrwcn4Q7yTr7NBqBImGIH8E+ITcvXOG8YqGqaHjTeQreWlRd6/TqxJApdQMz6N3OZoApwkE1EPO81YnRtInrQjN5r2byfIyblxDpkTKApivJPRVE2KoqyWlGUDxRFKc7Uz0IQBEEQuogoF0qbfEtIrAC+5UKxKOvVSJeg8trVN+tlSggLTo6dmROpxZPZg5b8M7nFLGn05zKXklesSJBN1zRb/9JK5Xi7I2n6i7J4O8hmPWii3EGzg6o5PbPSrRHeB4wbncsHJG30cH6OdAAH7UsAY1VVHQ9gM4C7MvizEARBEERbRCQEZj1oAH93REbDvdm4au3jsQi/seZm52mJSlBNhYWsHjTOvYNmSaOi8BWf6RwE7ZgJbiI+zbEP2tfwwJKDJuHAb6Bljch4jvA+YDyxGWLWp8h5jaQrJ27m9PzvKD1oqqp+oaqqNrtyEYD+mfpZCIIgCEKXrEIBpXlphAU30ZRuV59j8p2uv0JEP4c0ByFND5qI5NssQQX4bRqYnacF8F3/VlwmNcpPxJv2MnEeAGHW76Z9nPvE1HTik+MaMTr2AeDrfFp5ZsUiHAcpWXHQ/n/3oF0H4FO9TyiKcoOiKEsVRVlaXl4u+cciCIIg/l+TVcBvBxWw1oPGzR2pBxQv68PRjcdToJlMzEv+OM+k0ayXKflnch0rXQ+a5CmO2tfwIN3BuTwd5HQOAu8SX7OeSH8e2BmHvJ1Ig3g8e6e0cmKZ7qDRMwtocT55kNb15+0g12Zgo6cd9KApivKVoihrdf47J+lr/gAgAuB1vddQVfU5VVWnqKo6pUePHiJ/XIIgCIJoTXYh394p2T1oWfn6gzQAQcm3xJ4fowTV4+GbEMuc4mhlkAbAOfk2SRhluqy8p0YGa+WtEe19ZObG8F6P0gRaQ5o1wvF4BLPBRkDS+ufVF5ZmIAmUjPWg+fhE1UdV1ZPMPq8oyjUAzgRwoqry+r8fQRAEQXAiqwCIhVlJjd5IdztE46U5aR0Ejn1hZv0OWQVAxVY+sdIlqCKmDxrF0n4OnkkcYN4Xpp1N5vG6ixVuZGfhSSsVNRk2ocVrrOQTK20PGm8HzcK1cU++TURTuIHPGkmX6PMW8cG6NA4axw2KoMWNHhnPSI+Hfw+mWTlxang+Ue2jKMp0AL8HcLaqqo2Z+jkIgiAIwhCefQihdEkcbxFj0oOj/RwdtQfNbEiIFo93iaPf5KBqgE88K4Ndkr/OLVZEvKwetISw4HhtaUU8x/ea4jXexOH53k7b7ybgmAkzocvVrbbQpwjIceIB/hs9Ft0zILM9aE8AKADwpaIoKxVFeSaDPwtBEARBtIVnspNul90bADw+zgmqWfLNs8QrnfgU0HCf1h3hmDT6sgGvQdERT3cwXfma189+FllJo5ApjmmSb54bFKbJN+cSxyyDc/kAvhsUViYdaj8TD0IN5g4az2mwMjcoYlHmWKcTaDynOFrsPwMElziaoarq8EzFJgiCIAhLJEYt17h/rXQiRlHi5UIce9BM3ZFCINLESi+NxIflWBJ70CJBVnaazvnhVgaV7j5yTBoTyXcax4JniVdhX5NYmehB47D+o/Gy5HT9dVzFoMGAEC0WwGeNpHPieR9CH6oH8nsaf563iAFM1ogAoWsq0DhPMe0gDhpBEARBtG+yJTpoAF+BZnbmWvLPwWMoQ6IHTUJpUroSL+1zsnpweIrPdAmqFo+rE5nmPmq9U26x3IPGUejKXCOm72sRwkKi82n2HMnmKWKs9qBxfK9JK5VOcx9TIIFGEARBEEbwHA+fbhQ3wIQAryl2IQtDEpJ/LjcEtbOSDBrg/bmA4uHby5fOHeSZfGeb/c40YcGzBy1daR7Hc6csuYOchIVZqaiIMsB0ool3iaMRXJ8jVjcoOJYdmm5QaE582H2sdOXEXDd6rIr4/389aARBEATRvuHag5Zm0qH2OWm7+pyTHbNYisLv2qwc+BrI5zuhL6vI+PNcy9esOGicxKeqWutBA/i5g1bEII9yOdkuk5VhEwBfd1DG8Qiqav3aeL23zdaIdn4dl3JiC0KXpztIDhpBEARBcELmkBDtc7wSq+ZaiX0xFpKPrEK+gzSslCbxOMEnrTsiYFc/bQ8aj16+ZkCNSnTQ0ojBRO8UB4GWbtiK9jlua8TCQBLt69ySbtIhwO85ovV7mjnIvEW82XXxPL/O0oYZ5/JNs1gpkEAjCIIgCCOE7Oqn2bHlESvcxJLvdMlH8s/lhnRDEgB+rpbVEi81xqa0uY5nsb+I6xRHCcm3pfvI85gJC1PssgvllRNn5bP3SLiJTzyZ7zWzcmKAX2mepfvIuXwz3RrJKpDbgxaq59SDmaacOAUSaARBEARhhC/Ab6x5sA6AYnyeFsAx+Y7/vJZ2vjldW7r+Cl7Xlm6KXfLnZJRv8nRHNHGetgdNVi8f7/towWXluf4tDcnhVHZoqZxYQiyA/3NEpohPu0Z4OWgWpzgmf61TrJQTp0ACjSAIgiDM4LkbnVXAynQMYxXJdRCSv9ZtPGlJo8UhIclf65REqajJtfmymKPB69oC6dYIpwEQVnr5eE/NS1sGy2lku0x3MBqJn6dl8l7jutFjoVSOu0Aze45wdgetrBFZPWi8NiislBOnQAKNIAiCIMzguaufLrHKLuRTUtNsJbHiXJqXNrHiNH3QjrBwmxBb6cEB+J1NFqy1EKug5fw6N1gt8QLk9KAB/IYyWD3SAnC/Rqw4ulo8niLeDF4CrdmKg8ZzjVhZ/5wdNEvr3+UasSIGUyCBRhAEQRBm8HR+rOwOa1/rKpaFEkeZUxwBjiWOVkbR87qPFpxILR4P8dlcYy0W4N7VkukgANYHyfB0kGUcMG5FDGqf57UZYiVWNMg2GNygXZusUul0g420eFzuYx0bSuMLGH8Nr3MwrZQTp0ACjSAIgiDM4DW4w5KI0RICtzu2Fna+PV7WD8fNHbFwbTLO0wL4C12Z5ZvpHASZ18bdQZO0RjQxaFoqymmDwo5A4+bEWxC6gBzxqa1XLs9ICw4az/ea5ecxr80QEmgEQRAEwQeewsJKiSPgPtmxUuII8Omvi0WBcINFB6EOiMXcxbNaTgnIc0d4jb63UgbL7dosrBFeIl5VJfegWbmPvJJv2QLNgtDldXi6lTXC6xD6cDMQDcl5ZgHWSm4TU3xr3MWyUk6cAgk0giAIgjCD95CQdLG0r3UbK/n1zOK5TfStJh/a58MN7uI1W9ll55V8S3bQrJZ4AZLXiNs+rQYAqsUetFr3Z5PZKSd2LWLslMF20FJpszXC6xD6RDmlyaHwQLwHrZ7DGrHyXuPtoFEPGkEQBEHwgWdfTNqEIJ6ccCtxlJA0Wk0+eAoLyyLG7X20KmJ4DUCxOCQEcC8smmsBxQsETI59APisEasiPqsQgOq+x8iOy9TRRLzsjR5vlvmZawCfKgM795HH+XXNtenFIK/7SD1oBEEQBMEZLbHisasvq8QxWMdKj8z6tABwOVMoIWIk7uqnu4+8Rt9bdUe4TXG0Iz453UdFSR9Ptojnsf7TrUf//7H33XGSHNX9356ZzfH2dvdyjro76SSdcs4SCIFEMDmDjDFgDBjb2D/ANhhswGAbMIgsRBZBOYdTOp0u6XLOu3ebc57Qvz9e10zPTPdMV3VV3d1S389Hn9Xtzsybrn796r3vC1VBAaquTKSM6YPJBE3w1FW+GSRbDcjJsrIywsBDciSU+BZ9rquc8k1ZUxxNgGZgYGBgYCAH5bWAnXLKtASRSnEy3xKcnWLOByCH+WaOkq7AIgjzzeRpm+IoYR0TE3ReUlFZEodbBNIRGesY0PmWNTUvyLWlS/POoCmOQUf6S81WByjLk5lB0zkkp9i1ySrfND1oBgYGBgYGkiHDIYizHhxdUxwDTAMEMoM7Qslyvqu2vhidgUXAsqvyOnLCwpxNxu2ghnT2ubIjEoJqgKN3UMLZZIECC1lBvBWsfDMxRoG4sCzecmIJpdKBnzWNg40AjdlBGcGnKXE0MDAwMDCQCxlOY1CWvaQCiMQklHgFYIfZ9znjetD69TrfkZLiPTjlMnQkoINaKjODoMtBDep8SyQogjjDUggKJxgsNNIfyGQ+w2TRgjr6TJaUUlFdz1rAIF5G76Bt8xE9Yac4jg3Q9y5Wcu6CCdAMDAwMDAwKQUY/R9AATeZEtCDOB+uLCdNfp7MHjTlWQZjvUkmZnyB9WqzkMowjFzTLFI0BsQo5mc/Azrek7EjQ7GCYwCLtfGsMLILKAsLJC1pOXFotZ/S91mw1xzRMIFygGx+hQSPayjcDlpy7YAI0AwMDAwODQpBxFk5Q54O9RoZDHNRpTCWAxLi4rMBOoyQH1U4FW8fy2kzvkyh4enAASRm0IPIkDJzgLXEMFcQHzKDJ6EFLjJFOB1lHGYM7eIJB9nphWWwdi5AhlkVrLSPzE0RHyiUEMTpLHIMSBkxe6GvrD9Y364IJ0AwMDAwMDApBhtPI43yX18opcQzqfAByri1o2VWYzE/QTCTgOKiaevlkZtACZyw0TLFjssIOyRkLqP8yAt208x10kIyEISFBg0H2emFZHOdplUsgegJnB2spKxW2BzPQ5FmZga7G/rogdsQFE6AZGBgYGBgUghSHIGAZIACU1ektTQJCZn6GaKR9rLTw62JldKaSLua7vC58BiHoOsoI0NIH9XKUpoZB0MBCVn9daQ0QiRZ+XWk1ACukjjj3QOekT54sq44eNCC8/vP2aQEhA+uAZYAyAl2eIF5GdjAoGeKCCdAMDAwMDAwKQUr5GgfzXVYTrjQvlSQnkMuxCslGB3U+wjrEaeY7iGNVR68PW5rHE8SEydjxXFtZbcgenDEgOcGZHQzpfAeRFYk4QxlCygJOwwBNZql0EHl14daRq09Lkh0JRE5UAbBCBro85cSmxNHAwMDAwOD0g9QMWsB+jlCOPo8TJ6Hhnsf5KKuWFMQECZrqnNK8kI5cUFmApBLHoD1oGiZGApmAMdS1cQxJCOsQ8wZoE0N0TqGwvIFMf2UhsO8T5r5N8JQ4hsygidiRsDYyiI7IGKTEpf+sfDMuLs+UOBoYGBgYGEhGJEplNTKCpkCjv0P2jgQdVw3Ia7gP6nyUhyzf5CpxZFmtkE6qtiEh/UCsvHipKCDBQeUhDGSUbwY8XJx9pzAZ5KCHYgPO82g75xSKygt4bbLWMVYOREsCyAtpR7h6+ST06fLYkbD9pVxDQkJem22bEkcDAwMDAwMlCNsozhwrHudbtDSPx/mWMVmRJ4MWmtXnYL5l9YUFkRWJ0lrqkAVIzDJxrGNYZz+w8625xBEQX8tkgrJaQWSlzzgMoyNDwQgDQHMGTdIgpaD6r9OOhNWRBCsnNiWOBgYGBgYGciEjYxHYsaqlMeHxUTFZXKVyMoaEcGRHdDqNYXunEuPkWPHct7AljjyZyLH+EEE8T6DLMpF9YrKYvMDOd8ihDDoDtHGOLJNlydH/IFl4AOnzu0TLN4WCmJBBvNbg0wp+mDkgfm082ToXTIBmYGBgYGBQDKHLDjkdK0BcHo/TmHY+Qvag6WK+xwYQ2LEKm0HjyUQyeWFZfR4HNZWg3hghWSKBrqbgM+yzNjYAREooY1UMYYN4nkwkkxcmOzjBmUGDHd6OTEaihwWDkQBhkKwgPsjwHxdMgGZgYGBgYFAMMkrKeHpwgBAOAYfzLaPsiuvaZAQxtcEcq/J6+ikqj71PJ6vPEwwCIa6Ng9WPldMxCmGHu+gs3yyvpYxVMaR1pE9cFsD3bIcOLDh1RDhA4wniQ04xTcaJbOC5tlB9ipwZXUBcJ3l1xIEJ0AwMDAwMDIoh7GTFsT6goj64LCA8qx90IlqYwII5VjzMd3xYfCIaT6kou/7QGTQOebr6tMIGnzzZQcsKF1jwjPQHJDxrnD2RADDaJy7L/TlB5IUK0PoE7IiGIL6kkrKWooEuzxmAgIR17BewI5qyrA5MgGZgYGBgYFAMYVn90b6MU11UFmNsNQUW5fUhMggc5ZTu14Vho3kcfUDjOsrIDmoKLHjK15i80KVyHCWOidEQQTxHqRwLdoQDC85rC7OOgFjwKRpYpCfPBtARRvSE1kfOUlHh/rpBvqE1gD79d2ACNAMDAwMDg2IoCzsenqcMkB1oG8IhsCLOga4BUFEfwrHiyNYBLqdRVB5HaVKsDIhVhMgg9NHPwA6xjPI1jqAaCFe+WVIZbFw7EC74FMkyud8nIk+XPnJfW0gdESF6hLOsA0BJFRCNBXt9Rb0EoofnvtnARIi+MB7CADAljgYGBgYGBqcdymrIGUgl+d9r25ylSRIc1PK6YD04TJ42B1XC4I6gQQyTJyqLBa08921sQGyyYipF+hXUQU1nfnStY4jAYow3O1LvvC+k/gcBC+K1lTjWhywnHtYb6PKU5YW5NpEMGhBOJ4NeW0kFYEXNFEcDAwMDA4PTDsyZnRCYdhgfdXpw6oO9PmzZFQ/LDoRzrISYb+hxrJi80Bm0+mCvL6sF7CQwIXDo8YTAxEggnEPMU3IVZvogy7LyBp/CQRNHiSOTFzr45CgVjY+IlW8yWbxEj3Bg0cdnR8Jk4kXWEQip/wFlWVa4vsh0RUPAKb4OTIBmYGBgYGBQDGEGd/Cy7KXVxNiGYfV5HVRtGQQJZVdcgUUIx2q0D4ClJ2jiDXTT5Wt9/LKYPG2BLm+fYr3zvl5BeZz6H6oH0ymnjEQDygrRF8Zbchu2xHG0L3gwCIRbR56jQdyvC5VB5tD/MAOAmI4ErWhwYAI0AwMDAwODYgjTKM6clqDOjmWF7OfoE3OsRErzToljpanEcayP3h9kpD+TBYTTkaAZi1gp9ZDpWscwUxxFy9dESAPeMkAmLwxBwevoA2LPtoiOhOnB5M7EhxkSojGDnJgAEmN6CQrO8kbABGgGBgYGBgbFEYb5Zk4Lb9lhqAwajyzn0GOR0jyekf5MFiC2jrodK+4MQoiMRVpHNGV+uDOR9TRZMTHBL4s3OximxDc9rl1TiSPPxEggXBAvpCMhCQoe/WfrKEL08F5bmABN5ODoUCW+HNNZXTABmoGBgYGBQTGEOdCWN4PGXhuqB43TQQUEr60fXGWApTX0eq2OVZgMWj2HLOe1YcrXuAJCjax+mMBifACAFWxcOxBuSAhbR97gM0yJo0iAJnRtAtMAy0OU5on0stpJsT7dsT7KCMdKA8qSEaDpysRz6ogDE6AZGBgYGBgUQ3pwgUBfTNqxqg/+HtEMGu/ESCYLEO+dKqsJXgYYiYhPBBRxrFjviCirz7OOYXp+hLKsIUvKeHv5AD06UlIOxMrFrk0oiKkDRsME8brW0XmPjiA+maDBNbykEiB233iDwTDPmshUxTDn15kSRwMDAwMDA0VgzoOo8+H+jCAQzaAlxpyJkQIZNFGHmJcdFnUaRR2rpFMayS2vjz9gYu8TkQVocr7jzkh/TlmAeGDNeUiv8NEPvANJAFrzccFDj3knRuocEgI4vYNhBhvVB39PWP3n0f1ojDKyoYgezt5B4TJYzj5FByZAMzAwMDAwKIbyOlBpXh//e0UcK9EMmmgmBhDs+RF1vkNkEHjHw7vfyytPpAdNtL/IigQvAwTEe6fSmZgpwd8Tdh15Mwii+p8OLDhLHGFnjgPglaezxDFSQqWAPPLClIqKZOJ1ZNCA8HZEJIMmcg6mKXE0MDAwMDBQhEiUNnRRp7G0hljfoBBtuBcq8aqnn7oyaGWC5UKsvLSyIfh7RB1i2+Z3GmPlQLRU3CHmmRgJiDuobB15ArSyEMEn76RDIHzwKRI08ep/KsVPUITpwWS9pTzj2kV70ESz/oC4/vMEg4AE/eexI0z/B/lk2Ta9x5Q4GhgYGBgYKILoMAHeoR1Mlp3kdwhEB5IAIbIjmkocR3voJ5djVU8/ecu84iNAKs63jpYl3hfGO3kTcLH6nKV5IgFa2BJHkQya8NAaCA7J4by2iSHATvHJikTEz9TizegCIbJMTEc45IUZpKQzg6ZT/5mOmBJHAwMDAwMDRaioFxwS0sfvWIlOVkw7qDzZkTDlmyLla2Edq3oOWYLDBEQyCAA5faIOKrfzXU/O3wRnEM+ujbffDRDP/PA4w4D44em8EyMB8cCC9wzAtLwQZYcispITQJyzBzNMBk2UoBAKPgVkjfYBkRhQWhX8PaIZZJFySgcmQDMwMDAwMAiCMH0x3Oyw83peeSJnJTFW/3QfEjLaSwfvllTwyQIEAl3n9dyBdQMw0sP3HiZPJIMACASfAhmE0mpQEC9YmsqT9QRCDAlxyil5S0UBfv0Xdb7D9E5xlxMLHowtov/p8k1OWWxipM4MWsUUzlJR0Wetj37yEhQwAZqBgYGBgUEwhMmO8DpWYTNo3IGFgENs2+JDQkQa7pljxSsL0JtBEx2SIJJBAPQEaKLHIyTjdK+571s9BYO85ZsiQYxoiaNIOSXgrKNgiaOIPrL38kBE/yMRsRJfUZsVNkDjlQUIrKNAWbYDE6AZGBgYGBgEgWjZlVADvPN6bmfHeb1IzxuvLJEeHCDzet5yIZFSOe0ZtCniZbC6M2g6Mp9Mp3gGuwDOuttiOiKqj9w6ornEUYjocZ4X3qzuWB8NvSkp55RXLxDo9tFPoQyaYA8mtx0RLJVm624yaAYGBgYGBopQXk+bO+9kRZEGeNEM2mgfUFIFREv45XE7VgLnkgEuh5jX+RZwrEoqgGhZiFLRer73VTbwB2jpiZGCmR+RIL6sjiaT8qBMJEATdFBF+8JGe4FKTlml1YAVFc/8lGkI0GxbrE+LrTuvTorYLEBsuItITyTgPC82fw+mCBkivI6O/vMSFDABmoGBgYGBQTBU1NNkv/hI8Pck40B8WGMGTezMHSHHSuRcMiAcG83rfANih34LZ9Dq6X4nxoO/R2RiJBAug8YrCxAbkiNSTgmI94WN9vDLsixBgkKwxLGslv/MNaYjohm0UYEMmoiOCJU4hsjoAoL6z6kjZXUUxPNmIkVG+jswAZqBgYGBgUEQiARNwk5cDTkEIoGFNsfKeb22fg4BxwoQ6wsb7QNg8WdHRJh20Wyd7nWsbOB39EVLvEQzyCM9Qs6w0FASFmTxZpAr6p3SPI4ezLQdqeeTxTI3Ihk0oWetXjyDpk3/+/ivLRKh94x0871vpIcOFuctFYUJ0AwMDAwMDIIh3XDfF/w9os6H6JlaIoMEADHHStT5Tge6HE6jbYsHFkLZwT5yvHmmAQKZ4IDn2kSzdWWCmUjhQFdgQqVoiVe6xJHj2piOCJSTCfVgjvbRVNFYGd/7KhoA2HzXFiZbZ0X5AzSRMkBAbB3DZKsBvmsTHVoDAJVT+QkK0WcNJkAzMDAwMDAIBhGHQHRCGXuPCBstWuKYGOM7L4mtA/cACIEsU3wUSI6Ls/q6enBEhjKIBvGRKGX4hLIjnLKATH8dTw+maImXSH/d+AAd7i6c+REpuZ0qICtElpX3vlmWk/nhDSwE+t0AsXUU7vd01p7n2sLY40oBgkI0owsToBkYGBgYGASDUIkj66+oF5MnkkETdazY+4NCdACESNmVaC8T4KyjwGQ5oXUUcL5FMwiA4zRyll2FyaDZST4dGemhQ4HLOA6OBsQmK4bo96EyWF7nu1ssWycSxItm0Jg8nRm05DgRKjyyRCZGpgM0Dv0PcS4ZKqeKPWsifbMwAZqBgYGBgUEwiPTFiDLf7D1CpXmCGTSAz0kd7QUiJc4hxhwoqQSipfyyAL19MSIOqlDw2Uc/ReRVNfI5jWFKRdPXxnnfeA8FBsQmK44IllMCjvMtUL4pJCtEGaxoVpdHVirplAGKyHLew6v/QtflrCNXgBbGjohkIk0GzcDAwMDAQC3S2ZG+4O9hzkNlI7883gwac6xEHX2AzwEZ6RFzvi2LnBYuJ078PCFUTKF1SSaCvyd0Bo0nO9LnvFdAHi+rPz4YogyQOcSc901ElshkxTA6UjmV7gOPjox0hyxx5HnWmB0RDAi59FFwIAkgWHbYJ6b7sVLqsdMVoLFnjafEd0RQ/2ECNAMDAwMDg2AorQGsCF82ZqQbgKUngxaqv4I5Vl3B3yM6kAHg7+cIU74mMnBClNUvraaSPu4+RYGJkQB/gDYaouRWOIMmqCO8w13S2WrBDBrAHzTp6kEb7iK9Es6g9QV/ffpZE5AlWnYocl1Mnjb9n0pHHUwMBXt9mKE1MAGagYGBgYFBMEQizmRFDsdqpJscJN5DgYFMBi0oYxumT0XIsRKfUCbuNAqWOALBnX3bFne+hbKDfWITI4FMD1pgHemjn6EyaDxBTEgd4c3oAuHKDoPqfzLh9HsKjvSHxWlHukgfebPVAP/0zTAltyJ2RDSDxuTxygLClfgGlZceWmMCNAMDAwMDA7XgLTsUdfQBcghsp2wxCMKWeAGaAzRNPWi8w13G+mjdqwTKUgH+wEJ0IANApbOJseCHp4cq8RLJoAn2aTF5IjqiI7BITzAVeLYjUQrSeINPUTtSMYXv8HTRoxEAQTsieDQIkyeUQQtDYgW8b2EIA5gAzcDAwMDAIDh4yw7DBGi8GYthpzxRpN8tVkYlnMMczk6IEdLcgwtGe4FoGVBSwS+LN7BIO1YhHGLeDFqYDALAH1gIBbpO5oe3NFU4iG/g73crqwOiMX5Z7JkJvI7hnO/0kQVBMdwVgujh7J1N25EQ5Zu8EyrD6D+PzRrtFdcRXnschjCDCdAMDAwMDAyCg7c0LwzzzRtYMMeqKoQ87gxafQhZPcFL80QHkgCZ9R8O2F8XZrAL4DjffcFfP9obLoMABL+2MP1FkahzplxAfYw7mT3RAI33YOCRHuGR5tyBbpihHQB/BnmkK1xGF+AgKJgdEZAXLaEAKOg6ppLAeJgMmojNEsieAfx9imH6ZmECNAMDAwMDg+DgdqwEz0oC+KfmpR2rJjF5VY3Bh4TER4HEaLhr4zkvKUwmhq1H0GtLZxA0ZQdDlcFyll2FOQcK4OtnEj3InKFyCg1kCFyaF0JHePuLQmdZOQOL4S5xwoB3KMlINx2fUVYrJo8naArTNwvQ+idGgYmgJb59GnUknP6bAM3AwMDAwCAoKhuDl9SEGTYB8LP6w11UBsh7LplbXlBZQx30s6pZUBanszPaJ+7ol9XQuWvDncFen86OhClx5AziRbMjVbyleb3OocACpaIAX19YyBIvoZIy0ZJbVuIbuL/IWW9ReVVNwe1IMk5l1TpLpUUHkgB8mU+2jjr1X1Qfy+toii9vGazJoBkYGBgYGChGdROV5MTHir92YghITugrcWSOvrBj1cjf7yacrXPeFzRoCuNYWRafQxymxAtwhjKMBNORZCKc880d6IqfywSAL4M2Es5BFeodFA3imTzuMljB+1bdBAx3BCvxZZmv0CWOHBk0UVkAH9ETpt/N/T4dAVokSqWYvBlkweygCdAMDAwMDAyCgqdcLqwTxzuUIcwgAYDPQR12MmjVmgK0kW7xfjfAGSbAIStWDpRUisliDmCQYTJhpgEC1O9jRYOXbw51hnS+OYZbhBlIAgiUb4Zwvpk8nkA3VgGUCupIVRORN0HO5gsdxLBAN+B9G+4KGehO5c9Ehg7QOHowRfvdmDyeMthywYEkMAGagYGBgYFBcLCSPlbiVwhhnQ/eoQxhBgkAfP0cLNgJm0ELso6plHNtguWUTF5QJ26kh7KJoplInkl2YYdNRCJ8PT/DHeHWkasHLeSkwwqODFoqKX4uGQOv8x0miGH3IAghEjajmz48nSNoEu13A/j0Mey18QTxyYSTHRS0WQB/iW8IfTQBmoGBgYGBQVCkMz8BHKvhkAEawOcQhxkkAPD1c6R70ASdnWrmoAYI0Mb6gFQi8x4RVDUGz6CFziBwBBbMQQ3lEPP0DnaGW8dKjjO1ZJU4BtH/sX4AtoQMmqZySpZ5DqL/YTNolsU3uCY00dNAJb6BiJ6Q+s9T4jjSDcAOqf/6dMQEaAYGBgYGBkHB41iFzY4A/P0cYTNoQLBM03AXDVUQHTZRUuGcuxZAVthgkL03cA9aiMEuQMbZDJQdkRDEBx1cY9tOBi3EOvIMnBjpBkqqxMsA07KCON8hs3WAM8WUQ0fCZOt4Mshhj30AghM9yTgFu6H0kWMc/Ug3ZfhKysVkldcHH9wx1E4/q6eJyQI4ezDD6YgJ0AwMDAwMDIKCp3dKivMd0CGIj1JmQ4ZjFcTZGe4Q7z9jqGoM5qCGLacE6Nriw8DEcPHXhs0gpDORugK0gCVlY/3U9xQqg8ARNA2H7HcrKadR70EC3ZAT8wA4mZ/hYEc/jIY43xBwlTjy2JEQ1xY0gxb2+AD3e4NmtcLIikSCH1mQ7psNqf8j3cGGuwyHy1abAM3AwMDAwCAoSqtoeETQ7IgVFT/jBwh+NtlwyF4OwJX5Cep8hwzQqpsDlnhJyqABAe9bSOc7fXh00LIr6MmypgPdkD1oQLDsSNgADSAdYZmPQkiXU4YscXR/VkF5YbOsUwFYwQK04S7KFEVLxOUFzQ6G7QkDOImekIONmDyeTHzYEsfkOE3oLQTbJnkmQDMwMDAwMNCEqqbgpUlhzhNisoY7aVBGQVkyepk4siNDEgK0qib6nGJgzlfYHjSgeLCbGAfGB8KtY7SEgvJAgXU3lXrGysTlsXOniunIUMjJmwBfX5iUIH5asAAtHXxqKPFNJcOdywfQZL/KhoB2JGRGFwhus8L2u7nfGyjQlXBtQfvCmB6FIShqptPPwSI6OdoLpOKhZJkAzcDAwMDAgAcsaCqGsCw7QBt8KlF8ZDvL1oRxdsrrnZHtp1kGbaiD+kxk9PwUY9pl9DIxeYGyI+FYdpLVCNipADoiIYPG+neCZn5CZ9CCBmiSsiNAcf0f7QNgy3m2g65jaFlNdF3JROHXyeh34wnQhkNOjASCl/gOdVJPZFm1uCym/0NthV/H7qvJoBkYGBgYGGhCdUDHKmypHJMFFJcnI4OWHtleJIhh46pDBxZNtEbFnMbhTrquSAiXJV12WCxAk9ATBjiDOwKWXYUZWgAEDywkOI10/EAUGDhR+HW2LTGDFiSI7ww3tAYIHliwdQ5DGADOYdVBiR4JpaKwi5emjkgietyf5QemI6F7WZsCEj3t4W1WOoNWJEBLDyQ5gwM0y7I+bVmWbVlWSO0zMDAwMDDQgKAj20e6JWRiWF9YEXnpHjQJ/RxFMwg9AGw5JY6wgwUWMoJB9lmFIKMHh70/CKs/2Bb+2lhgUSyQYZnIsEMZaqYXd1DZ0QgysqzjA8VHtstw9IMG8YMn6Sdz1kVR1Ry8VDrscx10aiS79jC9fNEYBWnF9H+sn/q5whIUNdNJVmKi8OtkZKvTGbQiWd305NkzNECzLGsOgJsAHDuV38PAwMDAwCAwqprJkSnaFyapxBEo7liNdNFhtIy9FkWQke0yxt4Dwc9CG+oIHzCVVgGx8uLZQWkZNI7BBTIcVKD4Og530PeKREPKm5EJUnxlsUBXQgYNCHZtYWVVTHFGtgcM0GpnhpNX1VRcR2xbTgYtMEHRHX4gCRCM6JEQxADI6H+QoClsgFYxBYiWBcighS+5PdUZtG8C+CyAAPMqDQwMDAwMTgNUNQF2svDY6lSSMk0yptgBwTJolY3hBpIAwbKDMsbeA8GDz+HO8E6cZQVziIcl9OAAmQxaoSA+PgqM9wM1IQM0FsQUG1wwJGEdASeDVixAkzC0A3BlLIoF8RLKKSNRuu/FHH1W3hk2g1bdBEwMFh7rP9IjLxMJBMsgh71ngBOgFXnWJJQBAiDCwP15heSFJUMsK1hf5HAHECkJlYk8ZQGaZVlvANBq2/bWIq+707KsjZZlbezsDFBSYmBgYGBgoBLVAdjo4U4a3BDWIWCsfpAATYZjFcj5kNDLBARn9WWUOALBslrp/qIQJV4ABULFgngZB+cC1AsViQVzGsOWAQLBMmjpiXmSAotiGQsZ5WuAo/9F9HHwJFBWR1nZMAhCULBhFGGDeJ5S6bDZY4C+bzHCID3YRRZBUUAnExP0LEojKAJk0KqbQxFmSgM0y7KetCxrh8d/bwDwOQCfL/YZtm3fZdv2BbZtX9DUJMGwGBgYGBgYhEE6sCjkWDnOSViWPc3qByhxlOFYBen5kZYdCRCgTQwD8RE5wWeQyYrDHU4ZUyycrHTZVQFHbkiSgxqJBOtnGuqQ46DWzqD+oUI6wpxzlt0QRZCen2SCMk0yri3IuWuDJ2kNwiLIZNF0EB/SjpTXU0anqB3pCZ89BpwgXn0ZYFoWUFieLFIJoOAzSDllSHJCaYBm2/YNtm2vyv0PwCEACwBstSzrCIDZADZblhVSAw0MDAwMDBQjSOZnUFJ2hH1GUadRwoQyIFg/05BTvhO2362slvo5CmYQJPWpAE75ZrH+ojagJmRvEeByGguw+syhlKIjzcFGf0vREVZSVij4bKOsXthJh1WNlEEupCMjXQBsOdnB6gCB7sDJ8IEn4CIoCsgblET0BC3NG2qXQ4bUTKfy3UJB/FC7HDtS5UwWLRSgySqnBChYDjLFMaSsU1LiaNv2dtu2m23bnm/b9nwALQDOt227yBUbGBgYGBicYqRLkwoEaLLK1wBi6wuNNU+lgMETQO2s8LKC9PwMd1GQGrbfzbKKH1kga9gEQE7jUHvhvrDBtvDOMJPFPs8PMnWEXZsfxoecTKSkdQQoUPHDoNPvE+ZoBIAyyFVNha+NBcFhs0xA5mw+u8BohEFJARpPiaMMHambBQy0+v89MU7BbtjhJ0DmXhTLIFc3y9GR6uaAGTQZz9o0mlIaHyss70wM0AwMDAwMDM5YVExxen6KZBAASQHazMKZmOFOGiRQNzu8LOZUFHKIhySMhmeoKlK+me5TkRBY1M4CUvEimc82Oc53OkArcN8GTpAeyQiaimV+ZBzkzMAyjIWubahNju4Dxa+NBYoyyg6rpwHJCf9Dv1NJ0hEpsgI8a4PtQGl1uMOVGWpnAv0FAjQW4EjV/yIEhQzdZ/IK2mPJGTT3Z+YilZIy2Oi0CNCcTFqAebQGBgYGBganGJEIOamFnJ2hDqC8DigpDy+vZiZt+H7n/DBWXArzzRruCzg7/a1ygkGgeK+KrJH+QCbDONDi/fdUkpwuGRm0WBmV9xW6toETdG/DZhAAum/Dnf6HfrNsr6whCUDhaxuUtI5A8dK8QSe7rCODPNxJw19kBDGxMtLrQlktmYFurZNB88sOyjo+AAjWF9bfcgrsiET999PJ0V4izELet9MiQDMwMDAwMDijUKxcaFCmY1Wk50dmgFbVVLznZ0BSOSVADlq/T8AEyC1xrGMBmk+56HCX43xLCiyKOY0DrXLuGZNlp/z7mdI6IiGwKK8DYhUaM2hFArSBE9SDJENH0gc6+8iTGcSwzylUviwz0K2dBSTG/CeLpo8P0JBBs20nQJsTXhZAOlJQH9tp8qYMwqzY1EhJWX8ToBkYGBgYGPCiWGAh48wdBlZS5tfzwxyrWglsdHpqpI9jNT5Izf/SHNRZ9Hnjg95/H2il6ZSxMjmyAP/MJ3O4pAVoRc4LGzghbx1ZJsLv2piuyshYWBYFen7Xlpig4wqkZdCcEke/3sGBkyQr7AHcQOZ++D5rTEckBDGAk9UqFKCdlGdHGEHhZ7dkBp/pA519rm20F5gYAuolBWg1M0jn/KoM+lsz1x9aFgs+fYJ4Sb2lJkAzMDAwMDDgBXOs/JxGmeU7LOvhl7EbaAWipXLG7APkyPg5cQMSy8mAAIHFcXnrWDmVnEa/dZTZgwMUHu5i23IDtHRg4XffWmlqZnmdHHmFsoPps7tkBWjTqXfQry9sUEWge8xfFiBRR2b662MqRToizY44n+OnkwMn6PkIewYgQEF83Wyg77j33/ud30srcSxSdijVjjhTI/1ILEnlxCZAMzAwMDAw4EXdbP+BE8k4sdGyyneKjWzvb6XXyOhlAuh7+wZojjMpi41OO8Q+8mSWQVlWYYeYBTeynO+6ORTEJMbz/zbaCyRG5WYiAX/nu79FXlANFM4OMqdc1n1jBEW/j7M/cELePSupIAfcL7AYOEnOuawhObUznWySxzj6kS4gOS5vHdMZNJ9rY+e7hZ3OyjBlHtB31Ptv6YyuLBtZpKRSJmEWiTgllUXKYEMeLm4CNAMDAwMDA14UGjgx0Er9QLLKdyqmAKU1QK+Ps9N3lJwhWaibQw6q1zCBfon9bkDhdbRt+h6ynDigMKvfe4QyCLKc/fq5AGzv4DOdiZS0jhVTgJJKPZlIgNZo4KS3jvQ52ad6STrZsIh+dh/M/5vsTCRAz22hMsDqaXLKKYGM/nsFu+kgRlJgXdVM+u0XNMl+1urnZnTBSxZ7jQwUOhh+YhgY7ZGr/7Uz/ImevqOUqQ6ZrTYBmoGBgYGBAS8KZX5kZxAsC2iYD/Qe9v577xF5zjBADmpiFBjpyf/bQCsAS14QUzODhpJ4BRajvUB8WF6gCwANC/zXsecwBboyM5GAd8aCOa51khzUYtlBmRkEgK4tMep98Lfs8rWGhfTTK0Ab6aZepinz5cgCnP7SIlkmWWCBpZc8mX2DAOn1lHn6iJ76eXR/xoc8ZB2jQTOyyrILTY1ktkXWswZQYOmnI71HpdhjE6AZGBgYGBjwgjkyvUfy/5bOIEh0CKYsAHoO5f9+YpjKLGVn0ADvPpzeo+QMyRjaAQDRGA1B8WLaZTv6AK3jcKf3UJLeI/R3WWD33+vaWJDYIFFerc9k0fgoOcqyMjFA5nt7Bbt9R6lvTMbEPAAoraT+qe4D+X/rceTLvG91cyk48swgt0jO1hXQEdllgAAFDl42a2KE+rfq58uTxWySn/5PmS+vnLKykc4U9CrxZXZMph2pn0tEnFcPsqRA1wRoBgYGBgYGvCivo7IyL2dHRWDRsICCo1Qy+/fpYHC+PFkFs4OSWXaAHDXPQFdyJhJwBRY58mybfic1YJpJ2UEvB7XnMI39ljGQgaF+jo8z7GRMZGZZWUDU4xWgHZOb9QSAqYt8AjSHtGBZNhmomw3ER/IzyKmkoyMSZdXOpp42r6zWQCtlmWTqyJT53rKY3sjMRDJ98yqp7Dks91mLRCho8iQMmB2RSFDUz6X+wNxjLWzb0X8ToBkYGBgYGJwaTFngHVjIzjIxWal4foaEOVtSHau52Z+dJe+IXEcfcMo3j+T/vscpaZPpyLF1yg0shrvkl8pFSyir5ZdBaJgvL4MAUOAw1J5fUsbWVnp20PLPIMvMHgMUoPV4lDj2HqbvIZM0YPqWK6//OJCcyPTEyUA0RoGDVxDTd5SCRZk6MmUeHWuRexYaky9zHdNBfE7mP5WSH+gC9HleZbA9h2jKrcwhOfU+2cGhdjprToIdMQGagYGBgYGBCPwyP117gcYlcmU1+Dg7KhyrygagogHo3p/9+8Q4lRDJDGIA+ryhtvxJdl376eBgqRkEn9K8dDAo22lc4F+aJ3sd2XfPvTYV5ZQl5ZQhzJUVH6OMhcxgEACmLqagIjer1XOYHG+ZZMhU59nNvW/M+Z8qMUADnLJDjwCt6wBdt0z4ERQqsqxVU8mOdO3L/v1QG/UvStf/RXRduaWpPYdIH2UNdgEyWf3cAE3iOpoAzcDAwMDAQART5tMGnUxkfmfbQOc+oGm5XFmNy+hnZ46z07mXSuWqmiTLW0oBkhv9LQBsBSWOjjOfm0XoPpBxlmWhop4GE+ReW8du+in7vjWvADr2ZPeqpJKkN7KDGBag5QbxPYdpCqisgQwMU+bnO/rd+wE7CUxbIVcWC1Ryg6aeg3IDT8AZFBPL15F0OaWCAC1X91NJktcoOUBjz1PutXUfAEqr5R0fwNC0zGMdFRAGAOn/xGD+0Sc9h+QTL6yEN5egYMGohCDeBGgGBgYGBgYiaFgApBLZ07wGTpCT0LhUrqya6UB5PdCxM/v3HbuB5rPklkEBlAHMZb6ZMyK7xJEx6bnZyK798h1UgIKmzj3Zv+vYDZRUye13Y7Liw0Dfkczveo9Quar07IhPllVFOSVA379rX3bGon0X/WxeKV8WkB2gpVIkr1lyMBgtobXMzSB3HyAdkXUAN8OUeVQaFx/N/K7vGPU4ybYjUxdR8Nm5O/v3bduAaav02BF2D2UHTSwocut/KkUBoeysZ2kV9Q/mEmZde+koA1PiaGBgYGBgcIrAHMN2V9DEHH/ZmRjLAqatzGR6AHKMO3ZRgCYbjUuJiXaXlDHnW/a1MUfN7ciN9tJBvbIzaICT1dqdndXq3A00L5c3Yp9hmhOosLUDMvdQ9n0rr6VMam4fTs9h+dk6gPRgtCc7Y9GxC4iUKCgDnEuBhTtA6z1Mwe/0VXJlAU5gkZOt69xDhIGKIIZ9PgO7Ttn6Hy2hYLfDJSuVAtp2ANPPlisL8LEjOyhbJ3OwEZAJ4t02cvAklVPKDgYBshe5gW7nXrpmCeWUJkAzMDAwMDAQQfMKmtLXti3zuw5FQQxADn3H7kzGYrANGOuTn0EAMsy9O2hq20b9PlWSS+UqGyhzdXJr5ncnnTVVcW3NZ9FAEHfms2MP0KQg0G1aDsAip5QhHcQvUyOvbXvm3xPDVAaoRB+dz3Q7xB27SHeiJXJlRUsoK+EO0NiaTlMQoDUtI1nxMZe8XcA0BUHM9HPop/u+sedOdi8rQLrgDgZ7D1PWf8Y5amQB2STWSSdbJ5sMmTKfet5aNmZ+x65TdrYacNZxX/Zk3c490p5rE6AZGBgYGBiIoLSSGO6TrgDt+HoqAayW3BMGUDZmfCBTCsjKHZsVON+zzqefx17O/O7ktowzKRszVmcHaMfWAbCAORfKl8WCPhZMD5ygcdnTJJflAUBZNTlsuU5j3RygrEa+vFlrKHBhgcXJrYCdAmZfIF8WC2iZE5xKAS0bgFnnyZcFUB9mmyvQbdtBBImKDPLsi6gM9cQW+vdQhzodmbKAMkruAO3EFjofsKpRvrzms8iGTAzTv0++Sj9VZNBmraGfLa/Qz1SK9FOFLMsCZl9IOshwYjP9nHmufHnNK6gMlfXUjQ/SgBwToBkYGBgYGJxizDgnk0GzbeDYemDuJWpkzbmYfrKgqWUTAAuYca58WdXN5BAffZH+PTFCPTkqWHaAArTuA8DYAP376EtUulZeJ1/WtJV09lTrpowsQOF9u4icRlZS2bFbTUYLoEAslcjoJLvGmefLl1Uzne4PC3S791Np6txL5csCgHmXUTaQHUZ8bB05ySUV8mXNuYh+Hl9PP1kGSEWAFolQRslN9LRsUBNUA44u2BndOPIiBYgqMpGVDWRHjjnr2HuYstcqAjSACJ2uvZljBFo3E4mmwo4wYqDNIZYOPw/AztjpkDABmoGBgYGBgSjmXExnk3UfJOdjuEPaBp2HprNoUAgLmlpeISehvFaNvPlXAEfX0ZTKYy9RJmaWKqfRybq0bqRhCS0bgLmXqZFVVk2B5tF19O9j62j4g6rs4JyLqRS1ez+dt9a+k5h+FWD3hwUWx9dT/5aKjK5l0bUdfo7+zYiDOYoC3QVX0s/DzxNhcHw9sOhaNbKqGqks7pijIyzLpCJAAyjTdPJVysIMdVKGS5WOsKw0C5qOPE/Br+yyVIa5F9O9SqWAIy84v1OkI/OuoJ8HnybCrHVTphpANqafTdNRDz9P/z7wBAW6kggKE6AZGBgYGBiIYvH19PPg08Ceh+j/F16jRlYkQo7UkeedcrKN6lh2AFh8A/WmHHgC2PsoEKvIOMmyMe9yoKSS1nDfY0B8BFj+WjWyAAr+WjbQ2W6HnyOnNRpTJMtx2PY9Chx4EoANLL1JjazaGZQJ2fF7Gsyw73FgiSJZALD4Rpqa132Q7lv1dPkDQhimnU1n4h18ikiK5ASwUFGABtC1HXya1nHvo+SQqyg5BICzbqMDjvc9RjIBdQFaxRTKPB5bRyV5XfuA+YqeawBYcDURFC0bgEPPADUz5E+nZJhzEVDVDOy6n0oph9rVEWbREiKxDq8lO7L3EbrWWKmUjzcBmoGBgYGBgSgaFtJ/W+4BNv+cmHBVDioALL2F2PVn/52cnnmXq5O15Eagehrw0reB3Q9QtkJFORlA/XyLbyA5G35ITpZSp/FK6h954vPkoK64XZ2sqYsoINzwI2D7vXRt01erk3feu6iH6YFP0DVe8AF1spbcQD/XfYcC0HPfLn/KIUMkAix/HQXxr/yAytbmKcqyAsC576AgcO1/UAZo+W3qZM25mAKX574OrP0qBVCqAguAAokjzwOP/SOV+654gzpZS26kyZ7bfwscWksEljIdiVKwu/cR4JF/AKKlwMo71MgC6Fp6DgE/v4MmRl70IWkfbQI0AwMDAwODMLjib6k8qWsvsOb9amWtehOV1Tz3NZpatvKN6mRFS4DLPg4cfQEY6wcu+4Q6WQBw0Yepd+TI87SmEkZV+2LJTVTSuP57VN549pvVyQKASz9KhxEfeIKuU/YEOzdWv410Y/cDwOp3qCvLA4icWHIzsPFHdED1+e9VJwsAzn4L9TDtf4wCT1WEAUBlsItvJB2JldGzpwqRCHD9F2hse88h+n+VOnLJX1HwufsBYPXb5R8+70Z5HZE7G35IxzKc9251sgDgyk/TAJ6jL1BwVtmgTta576Az/46+SLoiMaNr2e4DBk9zXHDBBfbGjRuLv9DAwMDAwEAndt1PToFKdphh893AgacoeFJZ4shwdB31balq7HejfScdH8BKR1WibQew6afA8lvV9TK58dK3qXztbb9QG1gA1Me0/3HgnLeqK91k6DkM3P9x4PJPZjJqqpBKAo/9E52t9Zr/UFdyyJAYBzb9DFh0nZpD03Ox634KlmYozLAybPoZnTV48Ufo4GWV6G8FnvwCXddlH1crC6BjM7r3U9BUUq5W1nA3TdSddzk3qWRZ1ibbtj2NuAnQDAwMDAwMDAwMDAwMNKJQgGZKHA0MDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNIEJ0AwMDAwMDAwMDAwMDE4TWLZtn+rvEBiWZXUCOHqqv4fBaY1GAF2n+ksYnNYwOmJQDEZHDIrB6IhBMRgdMSiGebZtN3n94YwK0AwMisGyrI22bV9wqr+HwekLoyMGxWB0xKAYjI4YFIPREYMwMCWOBgYGBgYGBgYGBgYGpwlMgGZgYGBgYGBgYGBgYHCawARoBpMNd53qL2Bw2sPoiEExGB0xKAajIwbFYHTEQBimB83AwMDAwMDAwMDAwOA0gcmgGRgYGBgYGBgYGBgYnCYwAZqBgYGBgYGBgYGBgcFpAhOgGRgYGBgYGBgYGBgYnCYwAZqBgYGBgYGBgYGBgcFpAhOgGRgYGBgYGBgYGBgYnCYwAZqBgYGBgYGBgYGBgcFpgtip/gI8aGxstOfPn3+qv4aBgYGBgYGBgYGBgYEwNm3a1GXbdpPX386oAG3+/PnYuHHjqf4aBgYGBgYGBgYGBgYGwrAs66jf30yJo4GBgYGBgYGBgYGBwWkCE6AZGBgYGBgYGBgYGBicJjgjAjTLsm6zLOuu/v7+U/1VDAwMDAwMDAwMDAwMlOGMCNBs237Atu076+rqTvVXMTAwMDAwMDAwMDAwUIYzIkAzMDAwMDAwMDAwMDD4c4AJ0AwMDAwMDAwMDAwMDE4TmADNwMDAwMDAwMDAwMDgNMEZEaCZISEGBgYGBgYGBgYGBn8OOCMCNDMkxMDAwMDAwMDAwMDgzwFnRIBmYGBgYGBgYGBgYGDw5wAToBkYGBgYGBgYGBgYGJwmMAGagYGBgYGBgYGBgYHBaQIToBkYGBgYGBgYGBgYGJwmMAGagYGBgYGBgYGBgYHBaYIzIkAzY/YNDAwMDAwMDAwMDP4ccEYEaMJj9m0b6NwHtGwCUkk1X86NsX6gYw8wMaJeVmICaNsODHerlwUAXfuBE68CyYR6WWP9QOtmYOCEelmpFNC5l/5LpdTLGzgBHN8AjA+ql5WYIFkdu+lZUI3+FrpviXH1ssaHgBNbgNFe9bJSKdL9jj161nGoE2jdpEdHkgm6rv4W9bJsG+g5BLTv0vOsjfaR/uvSka799J8OHRk4ARx5ARjpUS8rlQS6DpCOqL422wb6jtM6atmzB4Bj64GBk+pl2TbtMy0b9VzbaC89azrscXwUOPqSHjsC0HUdW6/HH5kYIV9Ll450HQB6j+ixI71HaR/VoSMTw8DRdUD3QfWyANpH23cC8TH1shT5/jGpn3Y6ofco8PsPAi0b6N9TlwBv/TnQfJZ8WckE8OQXgPXfB1JxoKQKuPZzwGUfky8LAPY+Atz/cWC4E4AFnPU64PX/C1RMkS9rpAf400eBfY/Qv2tmAm+8C1hwpXxZALDlHuDRzwHjTrZ0zfuB134NiJbIl9W+E/j9h4GOnfTv6ecAb/oh0LRMvqz4GPDwp+n6AKC8Drj5K8B575QvCwAOPg3c9zFgoJX+veRmum8V9fJlDXWQPu57lP5dPY30cenN8mXZNvDCN4G1/wEkxoBoKXDxXwI3/AsQicqX17Eb+O17gK599O9ZFwBv/jEwZZ58WckE8NQXgXXfBewk2ZHXfk2djux5GHjgb4DhDvr3ijfQfStXcN7kYBvw2/cCx1+mf09dDNzxfWD2BfJlAcBL3wae+TIQHwEiJcAVnwSu+RwQUcBJdh0A7n0fOXEAMPN8siNTF8mXlUoBa78KPP9ftNdES4Eb/w245CPyZQHA4edJR3ocp2rRdXTfqpvlyxruAv5wJ3DwKfr31MXA678NzLtUviwA2PgT4NF/IDsSiQGXfRy47v+psSO9R4DffyjjjzQuJTsy/Wz5shLjdF2bfkZ2pLyOdF+Vjux+ELj/Yxki5Oy/AG77FlBaJV/WaC9w/yeA3ffTv6fMB+64C5h7sXxZtg1s+CHw1L/l+CNfB6IKXOeWjeRrde2lf09bRXZEhc+amCB/ZPPd9O+qJtprVt4hXxYAHFoL/PEvgUEnyF3xBuAN3wXKquXLGukBHvwksOs++nf1dOD27wCLb5AvK5UCnvkS8MK36FkrrQYu/ghw9d8DsdLQH39GZNC40d8K/PgWcqpe8zV6gMcHgJ/dBvQdkyvLtoE/fBhY921g9VuBN/4AWHAV8Pg/Aeu+I1cWQI73b94F1MwA3vhD4MpPAfseA372evmZu/gY8Is304Z53f8D3vQjeqDueSOxZbLx0v8C9/01MOMc4K33AJd8FNj0EzLIstmkrv3AT28FRrqB2/4beN03yXj8+GbaTGUilSLjtOUe4NKPAW/7JRnf+z5KG4BsHHwa+MVbgLJa4C0/BW74Iv3uV2+Tz5SN9QM/eQ0Z4Gv/CXjzT8h5+827iC2Tjee+Djz1L8CSG4G3/Aw4+y2kNw99Sr6O9B6haxsbAG7/P9qYu/YDP30dMNguV5ZtA7//AF3Lee8i/Z91PukIC+plYveDwG/eCdTOAG7/Hm0oex4C7r6dNm+ZGBsA7n4DBTA3f4Wc7uQEreOJLXJlAbRZPv5PwMJrgLf+Alj1RuC5r5HeyEZ/C/Cz11FG69ZvkI70HgF+dCPQc1i+vMf/iciJVW8E3vV7YNH1wKN/D2z4kXxZB56i+2ZZwG3/A1z/eXqm775dfnZ3YoQ+9+iLJOe2/6Es089uI9slG1vuISdu3mXA238DnPM2In4e+rR8O9J33PFH9rv8kUHg52+Un3GybeB37wM2/hi48IPkj8y+kHTkxf+WKwsgu//b9wBTFtC+dsWngB330rXJzlwk48A9byKC+rp/Jn8EAO5+PXDsZbmyANprHv4MMHsN7WvMH3n4M/Jlte8Efn4HZSJf9y3Sk+Eu4CevJf2RCdumgHrz3eSPvPknQP080hsWsMnEwWfovpXVkj2+5nO0//z6HXRPZWKkh561vY8CV36afOTKqcAv36bGH3nmS8Dz3yA/5I0/AJbcBDz/dSK1ZNgR27bPmP/WrFljF0Uyads/utm2vzzLtk9uy/y+Y49t//ts2/7xa2w7lSr+OUHxyg9t+wu1tv3c17O/w6/fadv/0mDbrVvkyRrtt+2vL7Ptb19M/8+w5xHb/kKdbT/wSXmybNu2H/snurad92V+N9xt2/+zxrb/c7Ftj/TKk9Wy0ba/OMW2f/0u207EM79/+t/pO2z7nTxZyYRt33WdbX91nm13H8r8vusA6ciPbparI5t+Rtfwwreyv8M9byEdadshT9ZQF13Xdy6x7dG+zO+3/Y6+wxNfkCfLtm37D39J9+3Qc5nfDXfb9n+fa9vfOEuyjmyy7S/W2/a9H8q+P49/nq5t62/kyWI68pU5pBcMrZtt+0vTbfvuOyTbkR/QNTz/X5nfxcdt+6e3kbzug/JkDXaQjnz/atseH8r8fscf6Ts8+a/yZNm2bf/pr0lHDj7r+g7ttv1fq2z7m6uyv0NYHF1HOvLb95Edtm26Tw98kq5t3+PyZKVSpAdfnmnbbTszv+/cT3rzvatIj2SB3Z+HP5vRvUTctu95s2NHdhZ8OxeGu237PxY6dsS11+x/kvaaR/5Bnizbzuw17vsz0kN73X8uIrsmCx17bftfm2z7Z6+37cRE5vfMjrz6a3mykgnb/v41tv3vc7LtfMce0pufvV6uHdnwY7qGdd91fYck7av/MlWujoz2kT/yvxdm68j2e+k7PPQZebJsm+zSF2pte8cfMr8b6rLt/z7Ptr++PHu/C4uj60jP7/1Qxo7YdkZHdv5JniymI/+52Lb7WjK/79xPfqxsn3XzPXQNz3w187v4ONky2XZkqNO2/2MBPcduX2Dzz+k7rP1PebJs27bv/SBdg9sfGemx7W+dY9vfPNu2x4flyTq2nq7hvo9l3x9OnxXARtsn5jnlQRfPf4ECtFd/RYuz6e78v238qVxHbmyQNo+f3Jr/AA130wMn8+F6/PNkNI5vzP/bw39Pjomsh6ttJzlV9308/2+tm0nWw38vR1YqZds/vInWK9fIJhO2fde1tv21JfIeri2/9N+ImY5sv1eOrLEBMlBeQd9wN/3thzfK05EHP0X3rX1X/t/+9FG6bx175cg68arj0P9L/t9aNjoB4RflyEqlbPsHN9j215Z66EiSNrivL5Pn7G/8ib+OrL/L0ZHfy5E13E0OvZez1t9Km/Qv3y5Hlm3b9v1/Q85ax578v/3+Ttv+18Zs4iIMWjbRWj32z/l/O/yC3IAwmaSg6BtnkW12Y2LUtr99EQWE8TE58nY/SN//5e/l/2377+lvG34sR9bYINnH712ZTWDZdoaU+fFr5dkRtp+c3J7/twc+SX/r3C9HVtcBZ6/5WP7f2nbQ3x76OzmyUinar78yl0gCN5IJsjFfnS+PWNp0t+Nz/Db/b4yUkWVHxgYpqPbSg6Euuua775Ajy7Zt+5F/JD1o2ZT/t4c+4/gjksjH4xvp8/740fy/tWwiHZHlj6TtyIp8O5KYoGfwGyvk2RHmj3jpyIYf0d92PSBH1kgv6fcPb8oOPG07Y0d+cqscWbZNPse/NHj7I799L+01PUfkyGI+x1Nfyv/b4eedgPBrcmSlUuSXfn1Zvo4kE0R+fm1pIJ+1UIA2uUocUylKS08/BzjXo2/jvHdTadna/5TTpLvlHuoDu/7zVAbiRmUDcNVnqGTj8HPhZQ11UI/b2W+mlHsurv4s1b8+//XwsgAqoymppPK4XMw8j9Z344/lNM4eXku9Kdf8Q37/SyQK3PQlYKgd2CihjCeVpB6OGaspLZ2L894FNK8EnvmKnEEGr9xFZZQ3fdlbR677Z+D4etKTsOhvpb6DNe/1rlu/4V+AWAVdvww89zW6X5f/Tf7fZq0BVr0ZWP89OYMMDj4NtLwCXPP3HjoSAW7+MpWoyigHTEwAa78GzL4IOOcv8v9+wQeBpuWOHZGgI+u+Q2WAt3w1X0dqZ1L/1N6HaOBFWPQeBbb8nHTEq9fyhi8CVgR48VvhZQFkRyqmkH3KxfzLgRW30zMyJmFC796HgZOvkj3O7W0oKadnsO+YnDKeVAp4+kvUJ3XBB/P/vvIOYM7FVP4iY5DBpp9Qr6BX/0vVVCovPvoC2dKwGO4i237uO4Dpq/L/fs0/ArFyurcy8OxXgVgZcO0/5/9t2krg/PeQ7R9sCy/r8FrgyPPUI57bRxeJArd+HRjtoesPi2SC9uNZa2jfzsWa9wONy2gdZdiRDT8ERrqAG/8l345UTSV/5OBTckq9Btvonqx+O5Vi5+Kaf6Qe2he+GV4W4Ow19cBrPPauWecD576dnhEZpecHniQ7ct0/59uRaAnZyIEWsqNhkUoCz/0n9SJ66ch576H5CWv/Q07J3MvfJf1+7X/m9+NWTaVS9yPPy2lh6TkEbPkFcNFfevsjN30ZsKLUKywDz32d9prLP5H/t/lXAMtupTJfGeXZB5+mQV7X/EO+jkSi1Bc81Abs+lMoMZMrQNv/ONC9nxxGr2bwSISMVPd+qmMOA9sGNv+MGsLnXOT9mvPfS82XL/9fOFkAyUqMAld5ODoAOftr3gvs/FP4muXeI9RgefGd9LleuPLTQCpBzlVYvPw9oLLRO6gGqE9g/pUkK2xgvf9xur4rP+2jI1F6wLv3A4efDScrmaCgetH13kE1QBtc5VQ5OvLydwE7BVz+Se+/VzUCF36AdCTshMz+FupZuuAD/kMlrvw0DWnY/LNwsgAKYmpmFNaRORfTcIiwOrLzj7QBX/V3+Y4OQHpz5aeBzt3AoWfCyYqPkWOx7LX+zeCX/BVQVkfBblhs+gnpyBV/6/332hkUlG79TfjAunMvDY655KNAWY33a678FPUHywiaXvpfoH4uEQNeWHw9DXlZ//3wzs7htUDHLtIRr4EBlkVDJ/qPU+AYBqkkDY6Zf2WBveY9NMBJhkO8+W4gOQ5c+nHvv1c3U3Cx8w/hHeLBdnre1rwPqJnm/ZrLPk57jSwdqZlBe7MXZqymQSjrvx8+sN7zIO01V/ytjx2Jkj/SuSd8n10qSX2I86/0H7xzwQcpyHnl++FkARQMJsbp+3uhsgE4/92OLQ2513QfpCFlF33Y345c8Sn6Ppt+Gk4WQIFX5VRg1Zu8/77wWrIj674bPrDe/zgFMld+xltHojHg0o8CbduAYyED6/go+VrLX0d67oXz30vXLmN+wsvfywzf8ULdLPIfdvyeEhBh0HuEfPoLC+gI22te/WU4WQDNnKiZSf6bF+ZfQYOANv4klJgzIkALfA7aq/dQQLTiDf6vWX4bUDsrfDamdRNt0Gt8DD1ArO2a95OT0ntUXFYqSZmRBVcDTUv9X3fRneR8bf2VuCwA2Ppr+rnm/f6vaVhADs/WX4dziAfbgP2P0TqWlPu/7sIPEvsddiPb8CPahSCmiQABAABJREFUoJfd6v+alXdQwBiWRd3/OGX+LvyQ/2tKKihrt/eRcEYqGad7sfzWwhMGL/gATRvaHJL92/xzcnIL6ci0FeQwbPxxOIe45xAxv2veR0y7Hy7+S6D/GI0fD4MtP6em9yU3+r9mxRuIrXv1F+Fk7X2YMqwXFdCR0irKZuy6j7IbokjGidFccjNQN9v/dRfdSWTQ9nvFZQG0jpEY3Tc/zFhNGYZXfxlORzr3Uhb+ojv9J6xZFtmR7v3hdWTjj8mRKTT1bOlraK8JqyMHnwYGT5CD6odYGdnQQ2vDDcKybbpv864Ampf7v+6CD1DQFDaLsOVumkbplYVkmLqInOLNd4dziPuO0eCT899TeK+54APEfocl6Lb+iu7/stf6v2bF7eSzhB0WdeBJsn2FdKS0kvaaXfeH22tYILT0FqBhof/rLvwQ6ci234jLAkjHrCjdFz9MXQQsvJp8wDA6MtxNe/E5b/OfwmdZRJr1HAzvj2z8MU0ZXF7AHznnbUTQhSUodj9I0ygv/kv/15RWUtCx77FwBF0yAWz/HbDi9UT6+eGC98uxI5t+SpUfhfaa2RdQYL3hR+H2mt4jdN/XvNffH7Es+i4tr9AAGEGcEQGaHeQctJEemtxy9l8UHskejZGBPvh0OGZn008phe/HsjCc9y4ANrGNoji2jpjY899T+HX1c4F5lwPbfiuugLZNBnXBVUD9nMKvXf12chzClHBuv5eCSj8mgmHZrUBFQzhjP9xF93312wqPyY2VURZh32PhzlDa+kugqpkm+xTC6ndQ0LT9d+KyDj1L5S2r31b4dQ0L6d5u+004Hdn+Wzpqodi4+XPfSY5Ry0YxWQCw7XcArOL6v/Q1VOYbZh37jlOJx7nv9GY0GWJlVCK7+8FwJRM7fk/HEiy4uvDrzn83ObJhSiYOr6UyufPeVfh1088Gpp0NbPu1uKxUkuzQkpuLj2Rf/XYiu9iYehFs/x1t0F5ly26svIPs9o4Qwedon8uJK0AYRGO0Pxx4Mpyzs/VXZPuWvqbw61a/HYBN2U9RtG4iQuTcIva4cbGz14S0I9t+S5/TuLjwa1e/nfbAllfEZAEkC7Z/Fp5hyU1UFbDtt+KyRnrovq96U+Gx/bFSeh73Px5OR7bfS4RRMR0579201+z8o7isg89Qa8cFBcg5gIKm2ReRPorqSCpFxOPiG4Ca6YVfe967aa8Jk2na/juys8WONjnr9aQjYezIYDvpyHnvLOyzllYCK99AgfXEsLi8rb9yfMQrCr/unLfSGoTRkWPrqJSyULIEABqXAHMvBbb/XlxWKkX6v/h6ysoVwnnvomMMTr4qLu/VXwGwiu+jq98ORMtCZXXPiAAtEPY/QUp1dpGACciwnnseEpMVHwN2/IE+xy+dyjBlHo25DaOAO35P/WDLihhfgOqYu/cD7TvEZHXsog161RuLv3bZa+h77XlQTBZA1zbjXHpQCyFWCpx1GzlG8VExWbvvp81pZYBrO+etNAp81/1isiZGgP1PEoNU7MyU5uXkFO9+QEwWQI57WW2wsz5W3E7sX+ceMVknX3V0xKeUzI3lr6WzmsIQFLvuIyNeO7Pw60orqXxj9wPi5UnMJgTR/5V3UCnY/ifEZI0P0XtX3F787KXmFdT3FsqO/DG4jpzzF46zLjgq/vgrlD0Oao+tSDj93/lHytYWc+JKKoClN9F9Fs38732Y9ppi5BxA9jiVEL+2xASw73Fi2IudqzNlHjnEe0KuY7SMbG0xnP1mOspGdK9p207v9+q9ycXy11L/7I4Q+r/7AWLQi5FKMef69z4qfuTE3ofpvgfRkRW3074k7I+MkryzXl9cR5qXE/kShsTa8wDZkYXXFn/tOX9BpeBd+8VktW6i3uJixAtAGb1omfg6AkSqzjiXeh8LIVZK1Vh7HhI/TmDXn4icPtujzzkX57wViA9nzhrlxWgfEXQr7yh+FuT0s6m3Noxft+dB6lMNstesvIPOou3cKyarZQORN0H8kZV3kI5sC6H/O/9IpFKhKhSAynyX3UL+i2BWd/IEaPseJSZ6xnnFX9u4NJwCHn2BHpaVtwd7/YrbgfbtYmWOtk0s/ZKbgh38uPxWAJZ4j93uB+n9xZg4gJydxdfTgbciCjjYDpzYTAdtB8HK24GJIWLwRLDnYcogBTkcdMZqoG4uMZsiOPg0lYkFcXQAyhAeXy9WwpZKkRO3+IbCjD4D0xFRp3HvI+RQB7m28jrq6dj7sBiL2n2QjPeK1wd7/fJbgbE+cRZ13yOOfQhwyPCci6k8SXQdD6+lAC/IOloWbS7H1okx7ckE2btlrylc3sXAnklRh2DPgxSYLy5QJspQ1UgBuGivVvdBoPtA4TIhN856PWUAjgtmY3Y/ANTN8R6OkIvp5wC1s8XtyNEXgYnBwmVybiy/FTi5VbwP+cBTNLwlyGHlZ72BSs/YgbC82POQY0eKsOwAEaGLriV9FLEj/S1ELAXda5a9lsrBjgkOS9j7CN13v14fN2aspsyGqD9yaC3ti8WyFQwr3kBOrUiZYypJ++jSm4MdxLv0Fvopakf2PUI6tiSAo19WTWWOex8S05GhDnp2gu41K95APU2iA7523U/EW6FSYoa5l1Lbhahfd+BJIgyWB9B/yyL9P/y82PAm5rMuui6Yz3qWs96igfXu+2mvCZLAqKinyp/9j4nJ6thNGbigvv+yW4moPCl23ufkCNCSCdpYltxYnB0ASAGX3kKTakQOdz7wFLED84ukihlYidvBp/hldeyisqRC/TBuVDdTra3og7z/cXq/X8N2LpbdSmWOIiwqc1qYES+GeZdTeZJI3Xd8jPpOFt9QuHSNwbJoUzj0rBiLeuBJoLSGvnMQLLuF2DSRbMyJLaQjQQwUQFmGGavF6+f3P0FZYb8BMrlYciPVbYuwqOw7FisTZVh0HTFkIs7++BBw5EVyPoIgEqUSvoNPi2Vj9j1GOjL3kmCvX3Q9AJt0khcnNlPgGvRZa1gINJ0lHjTtf5xKactrg71+2WvJhogEFgeepJ9BbeSiaykwENH/ZJwcFy47cmM4OxIto0O3g4AFcgcE7MjACcp2LLou2OurptJecUBgXwPo2matoc8JgiU3UgmbiB055Ey3XBLw2V54De3xewUCi/gYkYhLbw6uI4tvpP1J5ODe/Y/RvhjYH3GCHZH7dvJVKl0Lakfq59Dk7H2CDvG+xyk4qZgS7PVLb6a9pucQvyymI0EygwCtd7RMzI6MD1LPbNB9LRKlNd//uKCOPE4B3iyfATK5WH4rVQmIkOEnttCQrSDBIEA9as0rxFtl9j9BflbQvWbxjUToiegI81mDkoFLbqS9RsSOYLIEaCe3EtsVdGMByAAnJ+gh4cXBp2lqXElFsNc3LnGyMU/yy2LOWNANGqBN6MRmfqZ9fJAermL9MG4suIp+HnmeTxZA61gzgwx4EMTKyCiKGMTjL1NGa9H1wd+z+EZiJo+v55d36FliogvVlrsxfTUNHRAZk83ew6P/i64lFpW3f2q4i3QrSGaEgW1CIlmEQ88Su1yoGd2Nsmp6Ng8JrOPx9bQp8TxrC6+mwIe3f8q2yUFadE1wHZl5HmU2RPT/wJO0UfBc29KbaCQ3L4k12Ealazx2hOmuiP4ffIb0I6iOVEyhwEBkAmfrZspocdljx46I9E8dWgvMvZjKd4OgcQkNHTgiwOozZyyogwqQPT2xhYYr8GCkh8rXgpRAMTCbIxJ8HltHEwybAmQrAGL+514i5jS2bqQKG55rW3AV6cgJTqbdtslBXXRtsOoJgPaaquYMscEDpiM8z/biG8i28vZPjfRQ5dGia4K/Z4HzWhES69AzZBuCZD0BeibnXSa2joefp4zWYg5/ZOlNlNFq3cwny7Yp+F9wZbAEBkD2sbRazK878CSoCitgEA+Q/h97mQbQ8KD3CGW0gga6QIbIEyEoDj5DNqRYuwVDZQNNehfRR0yWAO2IY0TnXxn8PXMvpQljvAs31Em9OywwCQLLIiNz9EX+UsDDz1E5ZrF6VzcYk8Zb5nXsZaqFD8rEAdSU2bCQfyqabVMGc97lwVhGhkXXUv9UfwufvMPPU6kEz7XNuwyAxV/C0HcM6D3Mt4lFIvTdDj/PX55x9CUyGlWNwd+z8BraIHjPO2FrweOgsgCLV1YqSeux8Bo+HZl/BZVF8jqNR18kHZkTMKMFZGwOb2DRd4xYRh4dicZInsgEwkPP0kYRNOsJkKxUnD+wYN+P51lrPoucRl57nEpRGRqPLICCkNZNdP4cDw6vBWDx2f95l9N7eIOm4W5yUHn3mvmXky7z2pGDT9M9KNZ/48aiawHY/I7c0RfpfVx2ZI7YXgPQ3jb3kuAOKkD6L2JHjrwIwHL2Dw5ZgIAdOUr9NzzrGImQTonoyKFnqYetuin4exZcRXbkGCcZzvYaHr9u6iKanMm7jrZNzveCq4v3A7ux8BryB3lbEw6vpf79ORcHfw+rxuEtu+09DAy08tnIaAn5yCIExdEXyYYEzYwDpCOJUf5hYocdu8NDTjcspMQAr38cH6P38BBYAJG4rZuEholNjgDt8PNUjlNsWpgbZdXEEvAaDXZTg5auMcy5mJj2bo7yDNsm5iloCRTDrPMp9c7rEBx5AYiU8BkNgB583uCz5xCNMubZxAAyGgB/Vuv4euo9yz1UsBAq6oEZ5/A7BOwg0AUcGwtARmqghS/1nkqSDvOu4+yLKKPCaxCPrqNm/aAsI8OcS+ge8DgEnXsoMz6X89rYRsQbWB95kZ4dHh2pnUEHifIGn8yOMH0OirmX0IbL0z+SGCdmfh6nrDkXk47w2pGjL9IQAR4dsZygh5eg6NhFrDKvjsy7lEqKWzfxve/4egomeQLdinqyPdxBDAt0OQI0gPamwZOkJ0GRSlEGYdF1fGTIjHNpr2nhPET9+Hp638wAPeNuzLuMnjWevWa4i/Zd3n2UBQZHee3/C3TAd0V98PdUTSWS7Rjnvsb2Gu599BLSEZ4jGZIJel547cjcS8iv4HX2j7xIe83MAL2eDJbl+CPr+OxI135q1eAJdIHMuYQi+j9rTfCsJ0AEbOMyAVLVeX2x6Y25WHAlVULwnHWYjFNvL7d/7Dyb3H7dy5T1bCxw/FQuLIv2XV4dObkVSIzxk4ELrqLEh8Dh32d+gJZKkZPJa3wBqsc9uZWvpvfoS46Dei6fLBb08Chg9wEa884bMMXKqEeIl2lp2UiORNByGoY5F5OTxBN8iga601YR88SzkbGNhXcdATJqLRv4Uu8tG6gnoHkFnyzmrPMETR27qOSK19EvrSSHgHfc7LGXqO8kSIO4G3MvoWMAug8Gfw9bB7/Def0w83zqH+EhXxITFMSI6Mici+ie8xj7oy/R2Ta8OiJiR05uo3Lu2ZzrWF5LQy54mcbWTRTo8jDRAOnIUBtfdjxtRzj1f9YFACy+QSGpFHB8A78+ArSpt2zg60Nr2UDN7zPP5ZPFdKSFI/js2Enn8S3iZIdjpRSI8wa6x9ZTcMbjoAJkj8f6yO4FlsXIEM4gZuZ5FETy6EgyQXaLd18DaM9u2cAXfB57ySnd9Dnk3g9sv+CxkZ27gfhI8D4mhtIqWkteMrzlFSeI4dxrZl9IPdn9HP2sLHPPq/8zz6NKLB4dmRgmmyxiR+ZdSuvIoyMtG6k0nieIATJBUyuHP3JyG+kIrz2umkqVYryB7rH1ZO94MuMAERqDJ/gIihNOaemsNXyyZl9ElTm814bJEKD1HCKWPchErVzMXkMRMc9Bcq2bnI2F02hMXUxn2fA4Vuy1vI4VQNfWtiN4YJFKkoM6m9P4AhmDzRNYtG4mlp3XaERj9IDw9A627yCjIWIQ51xIOtKxO/h7WjeKOahNyymwY4YgCFjPAq/RAEiPT2wJHlhMjFCvlQgZknYaOTaylg3EjgXtLWKIlRLRwLOOHbtooqKQHbmQnFuezGfrJnrWeDeWGasdp1HAjojo/6w1RGIFdQjijj3lYb0ZmO3h2chaN9Mkzfoio9NzUV5LwTHPOnbto71GyB5f4NgRjsCiZRMFyLxBTNNyIrF4gibW1zL7Qj5ZAF3biS3Bic7EOBFDIvo417EjPNd27GUnW3cunywWfPISZvERsXWccxEFnz2cJNaci/jtSPNZNKCIyx476yDkI6wB2rYFP/4kMU57zWyBfY3thTz3rWUDlb1Nmc8nq6SC9hoem3ViC2VURMjAWRfQ5EjevWbm+QJ7zTmU+eSyx4xUFbi22RfxVdmM9FBSQMSOMB3m6fls3Uw6UujgbS+UVtJew0ti4QwJ0CzLus2yrLv6+z1GfjInTMQhYA9yUIYglSSjwWvoAUqrzjyXGIagOLGFjChvEAPQeqTiwacrduymxmZedgyg71dWy8e0nNhCmx+v0QDo4WrfFZyNPrmVfoo439PPyf6MYoiPORuLwDpGoqQjvI5VeR1/EANQgDbcSfXpQdC+k8rCeLPHAA0vKKkKvo4AXdusNXwlVwwssAjqEDBDLWJHeMtc4qP0vPGWdwHkrE9bybeOJ1+lvoxiZ4R5Yea5fA5B23bqbRQhDKatoswnj2N18lVaRxEdmX0BPWtBHQK214g82+xeB3UIkgm6NhFZ0Rg9ozx25OSrlNEVsSOz1vCRWJ17KKMrov9TFtD35NH/Y+v4y8kYZq2htQkafLI1FyV6gOB2ZGKE1lLEHkeiFFi0cUxfbt0kRpgBdK/jIzTQIQjadpCOiNqRaBmn/m8VW0eAru3kNg47EpJUdX9GMcRHad8WkVVSQaW6XMT7JhpSFHSIhhuzLyCisy/gcVRtji8tsmc3r6DMZxuPP75ZbB0BYNZ55M9w9nyeEQGabdsP2LZ9Z12dx9ksJ7ZQyWHQ6Uxu1M8jgxM0aOraT42MvP03DNPPJoMaNLBo30nOmEgQw/sghzEakQjJCzpdKDFBgaPIBg2QAU7FidEOgrbtFOjWz+eXNWUBBZ9BH+SOXeSghjX2QR2CE1vEHVT2HYPqSJvjFInoP3MIgjpWiQnazFmAzIuZ55NDEPQw7hObKcPNy6ACmYxF0Gtr20EMqgjRAziO1fbgxr5tR7Cz/7zAdCRoKWw60BV4tqMlpFtBM58Tw3R/Re3IjHMoYxG0FKptO+01Uxfzy5qygErRgj5rXXudcjJRh+B8foJi5moxO8J0KygZyCaeijzblkX3LeizlkyIZ2IA/sxn6ybHjizgl9W4lAiKoEFTxy6HMAvhj7TvCJ4db9tO90yIMHOc6KD6nw50Be5brJQCi6A6Mj5EvkQYezzeH7xcrn0nBTE8Q70YmpaTjgTes9leI2gjZznZ8aA60rpJ3GYxexBU/8PYkViZ0+IR0K8bH6KWI9FnbdYaJzvON9r/jAjQCqJtOwUx0Rj/ey2LnP2gGwt74EWdxunnECsUhEWybXqQpwccQZ+L+rk0tj3og9yxm5yPBoGNBcgEn0HOg+rc7TCo54rJYmP5g5amtm2ndRQJdCMRvsCCbeTCDvFqKrXrPlD8tck4yRPeoFdRbfSJV4O9/uQ2IjR4Joq6MWM1fUYQY9+1jwJdnolybjDdCjr+ngUxIs5HJEolQ0FlsWAnTGAx2hss85kYp7UMepRFLprPIjY6aIDWvoN0RIRBBeh+t+8KFny27RDP6AI0bhzg0BFnr+EtXQYyFRQ8jhUgbkemrSI7EqRcLhknWyq6jg2L+AKLth1EaIjuNTNWk54FCT67D9BeMy2EPQaC7zUnt9J9DmNHeP2RGaL+yCoa7R9kmEwyQT6CqD42LHIqKAI6xO3byX+pnSUmj/l1gezIdgB2CDvCAouAdqR9h7hfF405/sirwWUBIezIStKRICTW2AA9b8LE+woAFof+byP94JkW6cb0s4MT74zoFfVH2PrzlLjjTA/QbJsueBpno70b01aR4QkSWLTvoKZtkZJDwFUuF0Ap+o9TaZGoQlgWpXE7A5YUdOykE+1FnA+AZCXGgjEEHY6yNwte29TFdB/aAxjEVMoxiIKbGOAY+4BOY/tOCnRFMjFAZmhEEIeg5xA5H7yDJhhKKui9gZ3GEAwqQI5EfDiYjrDrF9X/hoVUPx8kg5ZK0etEZQH8DkHFFHHng8eOdO4hBlXYISghe9cRMBPZsZuea1EdaV5BbHSQ4DNNhgheG3MIgqyjbTv6L+joAKQjXfv49hqRbB2Q2RODOATMjojqfzRG9y2IPQbCBboArWPQvYY5e6LXNmUB3Ycg65hK0v0VtceAQ1BwEI/l9UDdHDFZPJnP7gMU8IvqfyQCNC0LXtHQvpPWUdSOTD/bIbFOFH9th7PeonakeQVNuw0SoCXj5JOF2Wuaz+Jbx9IaIuxFwL5nEP0PG8SUVtG+zUOYhbHH088GhtqDHZHAnhHRZ5tV+PHMMsCZHqANd1LNahiDOH0VlZL0BGCRuvY7wYFAtg6gMzqiZZRBKoa0gypoNADHIO4N5jR27A65sXAEFl17KXMjUssO0Po3LQ8mq/84MUBhgvjm5RRYBJku176TDKio89G4lGqjgxhE9rCLlPcyzFwdbFCIbZPzEUYWmzQWJIPcsZMCLFEHNVpCfW9BNrK+I2QDmjknobnB4xB07ad1DBPEABnHohDaHT0Ka0eCZv07dockzJzNvT2gQ1BSBdQKZnRLq0hHgjgEA61UoiLqxAG0jomxYKVQ7Tvp9UEPMc9F4zJyGoOsoww7Mn1V8AxaZ8i9pskhSINMDW7fSfZUlFSNxmgtgxAUvUfo/oaxI9NW0bTbIMdoMHssakcal9HPICRuOtANof/NZwWTlUrReoclzIBgPkLnXgpiRAmz0kryZYLY43RGN8Q6Ni4jvzfI+XwsgSGqI+nAgiNAaw5pR4IQBsk4Pf9h7AiX/u+ig7t5h1ExlFYRaf9nlUFjD18og8gYgoCBhaihB8hpn7oI6ApQvsb6q5qWictrWk5ZuMGThV833E1MQph1bFpODkGgB3kvGTTeSZi58roCbNBsE5+6RFwWz4McNqMbK6XvGtixssLp5LSzgdEeIjsKYfAkBbqNYdbRCbaC9A52Os+aqIMKkI4ECdDYWodlvoFg+h/WjpRVU1ASVP8jMbGeGIamZRRUTAwXfl3fMTryIcw6MhsUxB537iFnXaR0maFxaTBHn+lsYwh7zOUQ7BQvywOAknIqKwtqj8PakablZEdGegq/bribnMsw+xqz5UHsSMcup7crxF7TfFYw5jsd6IbYR5s5Mp9d+zM2VQSllUDd3ID2eA+RqqF0ZBkdozHaW/h1fUeIEA0VoDHCOICz37mHvptoEAPQs83j14VdR/dn+cG26frD2OPyWtKRQP7IHqoeEg1iAHp2eo/SsLVC6D1KLRBh/BFG9AQijHc5xHuIvaZ5RfBKFAdndoCWjthDKCAz9sV6fhLjxJCFebAAyggEMYhd+4CqZprQJ4qmgA4BU9AwDGqJU9YXxPno2hdugwboPvQfL+40MqMZ6kF21qWYsz/WT4FOmGAQcJjGAA5B525ac95z69xgGapi+s+CgTDrWF5HzdGBAosD4ZwPgO5b71GadlYInRIyCGk7UqTnhzmoYe1I09Jgz1r3AadMSzDrDwR3CNKkUoh1rJhCOhKkB7NzbzhnGCB97jlcfCiPFDvi3PMgdmSoLbyNDFoK1bkbmDJPjx2RQZiV1wa3I137wz9rzcuBgRbqsSmEdIAWJohnwWeRaxvto7O+wu41TUuD+SPdB0hHwpKqANBZRF6HBL+uvA6onhbs3M3OveFsFuDYkYPF+yLZfRWtDAEy+lwssBjqIFsShngHgldQdO6hdRCtHgIc/beL984yOxNmHWtnUy9sMX0E5NiRpuVk/zjOXT6zA7TugzRhr6pJ/DPKqh2HoIhC9ByihvSwN6lxqVMKUWSSoyyFAIo7cuzapy4KJ2/q4uIPVjJOaxl6HQM6xN37aSxzGB2pmgpUNhY3UqwnIvQ6LqJsRFEdORDeiWPftWiAJoH5A+i+FXMIknF6RsIYXyYLdvFele5DQM1MsgWiqGokW1RM/9NkiASComt/8dLU7oPh9TGoY5XW/5D3rWFh8ZLzsX7K6jaFJcyW0ETY3iKjnbv3UxlU9TRxWSz4LKb/Mu1I75HiTmPnvnCZQYCD6GF2JGRg0bikeBAjy46w9xcbptG9n5y+MHakZgaVUhUNdBlhIMEf6dpffHBT1wEJ9pgFFpr0v2FRcXs82kvVQzLscXKi+Ij47gPh95q6OZSpKmaP00GMBDvSc7j4XhO2BQIITlB0Swh0IxHHjhTx68aHiDATbclhmLqIsn4cB6if2QFa72HKIIRJTQN0k4s5+jIyCOz9dpI2jmLywmYQqprI2BfbWHoOUhlUnWAjKUPDInJ2Cz3I/cdJScMajcaAZS5d+0lWWB1pXFq8hIHpUEPYjWUhkQGFHmTbJh0KU7oGUPNwtDRYBq20mhyIMGhcShtLIR3pO0Y6EnodnbUpqv+HxCfKMVgWfUZRwkAC8wfQOsaHCw/TSKWcAC2krCnzAVgBHNSDFMSIjI92o2Fh8aCaBXBSgngUL3Nk9jisHQkSfEqzI8whKNDzxuxIWOejfi7tIcUcq6591IctOrSAIQjR03uU9trQ+u/YhmL3reewHDsydVGAdZToj8RHituRnoPhs3V1s6lMslgQ03OIyIyKKeHkTQ1gR7olkUrp4DPAfQvr+0QipGdB/DpADmE2MVS4LzIxTj36Mkh+INg6VjQAlQ3h5AUpTZW1jsyOFPP9XTizAzQZBhEgpSrmoLJFFZ3Ol5YVoKRyuJvq+cMaRMui71tMIboP0uvClEEBtI7xYWCwzf81staxYREAKwDTIsFBBai8I8jGAki4toXZn+eF4U5a67D6H3GGtRQLLHqPyCFDGhbSlL5CfQiygpigjlWvJDsShLHtPUpOiujkNYbGAHZk8ASd2xh204yVUQN9UQfVCXRD68gCp+exQPmyNHsc0CHoPhDeHgN67Ug6O17IjnSRHQkrK1pCz1vRzM9Bur9hyqAA+r5jfZRJ9ZUlKYPA1qaYQ8wI47CYuqQ4YdB7GIAVrt8HyJAAha5t8AQFcWHXMVpCQVoxf6TnUHjiEaBrG2oHxgf9X8OexSkh1zFIf7Vt030NG1QDAf26A0S+ht1rgvgjfccA2OH1v7SKvm+QLKsUv24+lS8XKjuUVWGWtiNHAr/lzA3QUklSChkP8tTFNDlptM//NX1Hqa65oj6cLHaTCm3SzFiGZTWZvCAGMSxbCwQrl5PlWJWUFzf2iQnaXGRsmvXzaEJfYtz/Nd0HyZEN08sBBAss2N9kXFvDouIBWt+x8M4AkNkIC+m/LINYUU8sbCEdmRimTVyKHQlQmtp3FKibFZ4MYfeiUGle2tGXcG2B7YgEm8U+o5A89rewOlnZQKPKC+ljYoLYYRlB/JT5+uwIs+mFSANZDioQLDvYd0yePQYK678soqe8ls7kKnRt44NEmsnQkcYlQN/xwoMSeo+SjoTpCQMymcxCk0Vl2WOA9EyXHWHft2Bg4ehP2IxuxRTyDwutIyMUZFxb/TwnQ1ygEqX7INn+sGRIOkArYEdk+XWAkx08Uvg1fUflyJoyr3i1ErvusPetZgYFzEEmxjs4cwO0/hbqHZDCfAdIPfYeDf8QA+QQlFQV3liYstSHZD6AjGPlV2NuOz06MoxvEIeg9wgpadhSOYDuRyGDONBKD5+M+zZlHgC78Kh9GSWHAFDdTDpSaGNJG0QJ8urnks75GXvbdgI0CesYxLHqO0bllJWCB1C6MWV+YXaYGUspdiRAaWrvUTmBbu0sp1yogP4zXZVx3xrmF7aPyQRtmlLsiLMRFiINeo9QiUt5bXh5Re1ICwBbzn2rd+xIXyGHQJKDWt3s9DNpcqzq5xYvp5RlR4IQPb1HqP84bBkUQHa2kB2RbY9hFy477JPkj9TOounLhfSf/U0KQTe/OKnaf1wu0VPIIe47RnakrCa8PLaP+so6nnldWEyZR5nvkQKj9mX0HwP0fa2oPjtSV2Qdkwmgv1WfP9JzmHqHS6vCyYpEnMD6SPC3hJN4CiHTINY55+gUNYgSDJRlFS9zYQ9y2NQ0QA9MYoyyBF4Y6aHyBWlOY6R4EFM/NzyrA9D6FDSIbGOR+SAf8X9Nf4ucoJr1MxUkDFiJi4xrm0M15n5lh6O9tBnocqz6jzv9CiFL5QCyD4U26FNhR2RkK6IxysQVdKycZ0P0fB83psynRmm/iZiDJ6jfSUoQ4+hZUTJkfnhZTF6hgEmmHUnr/xH/1/S3yJFlOSVwBQkD53tIsSNzKUPgV3Y41kfHvuhyrGTZY4Dscc8R/7/LJHrYvl9Q/yXZkVgpDa0oSPQcB2DJsyPDnTR4wU+WnZLk6Aewx7KId4B0MkigK8uvA/x9BNumtZRxbdESuvcF1/EIECsPN0SJoW42tcn4VaIMtFJvqRR7PJ9+FvTHJZFKTF6xUmkXztwAjSkLewjDoJhBZMyfNIegyIPcf5wmwoUtpwSKZwfZOtbODC8rGiOmob/IgyxtHedQuZDflLJ+yYwV4P8gJxPkpMrQR6C4Qew7BtRMp1LPsEjrv48jJ6sMBHDKhKcUzyDL2MQAum/9Lf4ZZLbGsthowN+OxEeJKJERxACOHSmyjtXT5OgIC2D95LFnvk6CE1cxhaaUFXMIpAZox/wzyEqIHj87Eqf+OxnOMED3o1igW9UUnh0GMsGQX7Arcx0rptAeWVD/W+Ta48ET/nYkvddIeLbZd/a7b4lx0hFpdqRIBrnvGPkHYcspgcx39pM3cIJ+yrhv5fWUQS6k/zKd72J2RKY/UowwHusn0lWWHamdmbk3Xug9Qt9JBqlaPwcFM8gy7UjtTCBSUtwfkUX01M0uvI45OPMDNBmBReVUiv79HNShDspCyTKIU4rUD/e3yHNQa4uwSOl1lOgQFHKs+lvlbZr1c4lJKfQgWxE511Yzgx5kv41l8CQxf9IcgpmF13GgVY7uAxnj47eRyTSIQIDAQrJjlYpTj6kXBlqp5FZGOWU6QPPTR4lOHPucYkSPrHVMB/HF7IgEeZZVOLCwnc1bRjAI0LXFh/0zyH3HqMRHmh2J+V/b4EkAtrxrq51V2CEYkGyPAX+dlGlHWHawKNEj044kCtiREzSdMuzkQcCx65a/jvQ7JbcyMmhAgABNImHG9qxBH52U6Y9YFt1/P79OZpYJoM8pVInSd4zO3ZKx19QXIVVlJjAAoHZGcX9E2l7DCAoNRE8kWniWQSrl+Kyy9H8WlaUWO4ibfT05UtXCsqzbLMu6q7/fVToxcJJqh0sqZAhwHmQfgzggkR0GaGOZGCzwIEvcWGqm00+/yYoyA12gcOYnMUEbnIz+MyBA5ucYlW/IYP4iUfreAye9/y7TQQWKP8gDJ+Wvoy/zzUpuZTlyc/xlTTh19bIYK6bXvgTFCXqNDOavpJwOl/fTR+aUSAus55JD76cjUokeR9f81pHZTqmBhY+s0V46c6hG4joC/qRB3zH6PmEHuwDUh1A93b/kvF+FHekqYkckrSM7psXXHksmKOpm+Tv644NUUinTQQX8g93Bk/QaGXYkVkaZb79+Pra+sp7t+rn0rPlWohyTZ4/ZnlV0H5W0t9UWIHpGe4l4l0ZOs320gB2pmyNHR8pq6EgTP7+uX3aANovumV9SYbBNgV9XiDC25Ol/3WyHGPPAUDsRvLL9ET+7lYMzIkCzbfsB27bvrKury/xy4IS8Bwugm+TnNLKHgAU7YZF2Gn1uksyUankdsTZ+Cjhwghjd6mY58upmk3HwepCZUyJrHYsxtv0t8hxGgDYNvwcr7aDKYpGc7+0nb/CkPEe/ciqVlPkGFicpwyyDHQbIkA8V21hkB2h+961Vvh3xzY5I1n+mI15radtyM5HVjOgp4FiV1clptgcydsQL7DtIsyMBCApZ9hig711oHQGJ2cFiduSEPGe4qpHsiG/5Wiv9XZodmR7AQdVkR2QGukARO8L8EVlBzAyq/hj2OOcqlaRrlrWO7DsX8kfK6+WU3AJ67Ug68+NHYum0I47uyCxxTIx6JxWSCfLtZAbVgL89Hmglf1UG8Q44xHsBXxwIf0YwQ9qO+Ny3HJwRAZonBlrlKQRQ2CAOSTaIzCB4OVbxUWL+ZMmyrCIP8gmn7EbC0A6AHi6/B1n2xpI29j6b9FC7nKZVtzy/Byv9IEs0iIC34RgfomZ7mTpSUP+ddZTB/AGkj2P9pOu56Jecrasp5lhJLBUFCpfmseddlk6mgyaPbIxsdjhWSr1KBQNdietYO5PWy4vVTztWku2IX1ZrqE2eEwcUCSwUOFaAt9M4MULPoUw7UjvTf68ZPEnXLsuOVE+nc9y8zjCSTZjVFGG+ZQa6QMAATZIdKRQ0DbVTaaesdSwpp8onPx2R2QIBUGA53OGdQZZuR5hf52NHZGaZAKfssMA6WlF5diud+fTQ/+FOCvBlySopByobC2e1pPp1jj32SiqkB7tIbF0BAvehncEB2gnJDsEsuvGeDkEbAIvKl2SAKZeXY8VOa5eqgDMLlxTIdqwA781FNmNVWkmN4n4n3A+1S3asZhQOdGVmEAr1M7HvIPO+VU8jQ+uFQdkOaoHAWnaWtaqJMsReBjGVkpuJBAr3/Ay2UzZblo4wB82L6Emvo2SCohBjKzVbPYs2fa9rk13RUDmVelV97UiHfKKnYCayVs7xAYCrB9lDJ5XYkWb/dRxsl+ug1kwHYHvLY4GULHnVzeTweu2jti235Byga/NdxzYafiHNjhQgemTbY8Dpr9bsj3gF1syOyAqsKxsBWN4BWipJ+6t0f6RA64ps4h3wtluyA12A7G0h/Ze9jslxn6SCZBtZrOUiB2dmgBYfo7p6maVJVU0AbO9zJQZPkoGW0YMAFM6gKQnQCmTQZCs7U0DPTVNyBg1wHAKvTOQYscOySjcBMuQTQ8DYQP7fhjuB6iaJsgo8yAOSnQ+AvrtvBkEyY5UmKArovywyJBJxCAqPDXqkm3qZZNuRiUHv7OBQm9xMZKEMmux1BDJ9CF4YbFPjWHnJk030RKJ037z0f3yInnmZdqRmunN0hQerL5tUYs6np4OqwrEqFKCdlEwYaNxHI1H/fXS0lxw8mfpf1URVEp460ibZHhcoX1ZhR2oKtAqwih5ZYM/tsMdwF3a91ZKet2iM7pvXvsayTCqIHq/Mj3S/rkAPshI70uRdcgvI90fSNtJH/6Nl1CokA2U1RMD5+eM5ODMDNLaRyrxJVY5z7aUUg5INYkkFZVsKMVayHQK/FO5wp1zjW9WY+dxcDJ4kFrKyUZ686une6zisItBlbJzHwzXcldEhGSitIpbUbx0B+Rm0Ib8MmoJMJOBvEEsqgbJqefL8JmLKLjkEijgEktexciplB3URPX6TvFIpR/9l2hHnWfKamjfYRn0qMgZEMfgFFkrsCCup9HLkFNiRkkpvfRxQ4VhNK0z0SM+gwd8hLquVc8SEW54X0aOEMGN2xMsfkbyOVU2UQS5EmMkmOr2Il6QzJVO2jQT89b9iimQd8cn8yM76A6QDqbh3UmG4U+49S/vHBQJdHXZEVSYS8PHrnHWURaoyeZO6xJEppMyNjCmz58MluXwBcB5kr41FhUF0GjzH+rJ/n4wT+1clMWBKP8hegYXD6kQkql2Nz4M8qCCILzTJa7hL7joCtLl4GUQVm2ZVEzDen8/Yxkfp97IzuoD3fRvukHtdgMPGeegjW1sl+u9hR2Qz35EIBUXaiJ6ZwGgPncPkxlgfHXeh047IJCcAf4dgUBFhBvgEFirsSGNhx0pm71RVM+lDro6MDzqZSBWZH5/AQvY6VjX5O8OAZMK4mD8iUVY05tgRnx40QLL+z6A1y20nGe2hnzIJ3KL+iGS/rtrHr1NFmAH+gYVM/S+poKmRnnakjQJ82f74UEd+UkFJJrKYHZF4XQDdFy874oEzO0CTcZ4EQ1Uh5ltyuhjwr7FNlxRIVIq0kcpRihFmECWuY2k1TfzzdIgVKLufY6Uiy1pomMBwp6IH2UMfR7rpTLYySX0qQGadcgMLFcxfxRQqG/DLoMnMxAD+DmrajqhwCDRk0AB/omeoXW5pBpDZ8HM3F/asS7VZBTLxKpxvX3vM7IjE+1aoxHe4U64+AkDVVG87MtxJOiLVjrB9NOe+pSeYasr8yK4MAei+eDlWKvwRVi6fq5O27ZR4ybYj0/33tbJaudnqykYAdj5hnCbMZPp1zGZ5EZ2SCTPAv6JHSbUG60HOkaeiogEoYEe6aPCLrBYggK4tMUbEjhsq/TqvrK4KwtiPePfAmRmgqWC+q32Y71SKDLCKwMJvSELlVCBaIk8W2zhyHy4VjpVl0ef5OcQqHKuJIeoVcUPFg1zZQD9ZYMuQStK1yXasCgUWlVPlpt39MsgqHFTLcvTfp3dKtkGsaiR2NpXK/n06E68gQMtdx/go9aZJtyN+DkGH/NIMv3KhtB3RxNiqeNaqm0nXcxlbFcw3W8fRHDuSTNDvZOuIrx3pUWBHfJzGdBmU5MxP5VSfbHWH3J5ggOz/cJcHq6/CH/EhzMYHgfiI3HUE/PvrhtoVOKhsH80ljJ11lPlsl1Q4rQI+gYXsZ61mGt2z3L1GRUUPW6dcf2S016lokE0Y+1SiMH9EJtJ2JJcwVjC0JuaQVJ5BvORMJGAyaEIoqyU2MVchxvoopcqMiiwUyqBJZ/58HKsRBRsL+zztD3KOQzDUAZq8KfHayuqohy5vY+kBYKvJoBVyrKTK8gksVDgfAD1PuQ4qoIixaqRnOHdK03AXAEveuUyAf0lNOlst2474NFOrWEedGTQmz8tGjvaoscepeL6ODLU7fbMS5fkRPex50OUQKLHHzI7k6L8Kwgyg75+7joCaDFpVIw0DmcghA0e6ocyO5K6jiqw/+zyvdVThj6Sz47lEj2Z/ZLRXkR1J5O9tQ6xvVmK/m1+gm26TURGg6fZHcv06BSW3AD27ecR7SlEmfqo3YeyBMzRA66LmeJnlO+nMT86DzDbsCskPcuUUID6cX6uvgvnzdayYQdTFtPSqcwi8gs+KermZyEiEHuRc46sigwA4zocHYzvSrWZjAfIN4qiiwKKyId8gJuP0O1UOQS5DNtJN91PWKGKAjn7wGu7C1lG2HalocBhTj8yPCmcY8Lcj0kvzPOxIKgmM9qlzCHLlDXc6w1gk6kisjHQkV/9VBbqspMbLjsgsJwMK2BFF+yjTfzeScXreVBA9gPdeU9kgX0fK6/LJFxVtCQDtlV5jxlVUNPjZEZXBZ+49S0zQlEzpfh3LjueSgQpaIMrrqcRXF2HmV5qn1Y4o0n8vwphlInURxh44QwM0BSVegDNq3M8gKthYgPybNKqAjfAtcVTpWOUaxHEq8ZK+QTusZW49+2ivXEaTwSuwGFEY6CYn8uuwRxQMEvDrnRpRGFh4btC2mtIkwMexkvysAd6MrTI7MoV0JD6SI09BEF9ZhOhRETTl3rPRPgC2Ggc1/flueQpYdsCxI36OlYJnOzEKTAxn/16F/qf3tVxnp8/5u2Sb7LmOquxxAf1XYkea9RJm8ZH8IVEqAoui/ojka/O0I71qZKXtSK5fp8CORCLe+6iKoxEAZ0iOH2GsIGAC8tdxpIf670slTnkGnHXMJcwUzIMACvdF5uDMDNCGFSgEkFFAN5Qxf1OyPz8tr4+YEZkoqQBKqrwDCysif9NkDqr7QVbloLK18jKIsu8Z4GS1NJZ4Ad6ZH9n6HyulcdxegW6khMZ1y4QXY6UqGKz0WcdhBT2RgE8mXlWg62dHFBAUFfUALO8eNNlN4oBPoOs8e7LXsbwA0SPbHgNO5ifXIVAdWGiwIyUVQLTUI9DtcQZIlcqVV5AwU5CJAbxJLNkkJ0DXNtafI0tBewfgbUdSKZLPgg5Z8M2gddGzJrPqBfAetqUq0C0v4NepIIy92iBUVkalEtk20rbV2BFmc73scWWD/ORMpUcmXll7R4GjH3JwZgZoqpjv8vp8g6iSsQKyNxfbmWwk2yAC3unpdPmOZDWodGr13ZkfVanp9MbSl/17VRk0r5KadGAhmx1mDoFrI0sm1JR4AaT/Xo6VEoM4lZ4196hl9uzJ1n8/5lvFxgI4ZbB9ObIUZtCAbJ2Mj9EELNn6GIn6Z35UBbojXdm1+qrssR/zPdanKBPvRfQoqmjwtCNxet5ky7IsZx/ty/69sooGZx3dZGDajsgmHn0yPyNd8ku8ACpxzAvQNNqR8QEAtnyCIlZGA4C8SnxlBxWAt44oC3Tr6aeuAM2rB1Ml8Q5k+5Fj/VQGKJ3oKadp4F7+uDK/LmcdldmRyZ5BUzENECCD6OdYSWejPUpBJoaJoVDB2FZ5OAQjPWqyTMxIuR+utEGUzVg5fYg6MggA9Q7mrqOywMLDIRjrg5ISL4C+f65jpUxHnM90y2P/L7O3FHAxVh6MrZJA18OxUpVB8yoFSa9jvVxZQKYv0g1V2eqKKVSrP+EielTZEV+ip09hqXSuHXFkq9J/916jqsQLcPqZ+rJ/p5IwS8WzyUD27KlaR88SR0X+iFcGzYrQwCqZ8PJHmD4qIYwbfDKRiuxxcoJIK7cs4MyuaAB87MgAUFajgHj3GEqiKtAFfPxxVZVRDR6EcV/me0iV5ZOJ98CZG6CpCizGB/IZWysi39nxepCVGkQPx2p8QL7yAZnP9AzQJD/IkShtVroYW1arnMvYxiqIGZSJdPlmX+Z3Sg1ivbeDqqoHB8hm/9KOVb1cWV5jdG3bcQgUXFu5lz72UZmxzClegLcdSZdl18uVBXhPexsfAMolnqXFwD5zbCDzO1X6n7ZZfdm/V5r5yc3WDVAZoOxS0fQ6uuyxqr5BwDuDNqKI+fYKPlUFaKXVNOnZ7VilUs7RCJoCtFGHMJPtfHvakT7ne9TLlQV4TxZVRYZ4+SOqKnrK6wBY2ftoMu7032vKxI8PyA/gAVfZodseK1pHJs+vxFE2PAljRf5ImujxmJqagzMvQLNtUhBVgYWdyh6jO9JDN0gZG+FmNfuc71EvVxbgTDLyYVpkgx18Oq7pQa7IYVpSSad2XpFBTI5nD2UY61ekj/X0c9zDQVUSfNZ7GERVJQXOZ7o3F1WDBID84DM+QqUZqu7bWH9+D6aSjaWAY6WKsc1l/sYG5B52zOBJ9CiyI5EoXUOeYzWkjjAb7ycZDKrsiKc9Vkj0eE0EVDlsBci2I0xfZOukZVGw687WjQ+Qz6Biz2YBWm5pnop7VigTry2w6FdE9BQijGUP7og6mR9d9thZR3dSYUzROha0I4oSJp4ERb18Wb6EsSXfjsRKidAf7y/60jMvQIuPkmOlIrDwY1pUKF9JpdNMrSmDVjElX9mVMd8FHCtVpVBZ66iodhjwdwiUOPoeGQTmHChxCOq9S3x1M99KnP1cx8r5f1V2JJfoUR7oepSvKRluUX+K7Ug3ZTFKKuXLyw0sVDpWXvdtvF+d7gPZ66jS+fbqwVSZiQSys5Eq7UhZbbaDmrbHivQ/lcgmA1UTPV6EsQp/JHcdAYVET73z+Tn+SEklDbWRjTw7wioaFOm/ncx29pUlMDzsiMpryy1xZFUvqnxIIKcMvI+uWXZyBqDPHRso+rIzL0BjD7VSh6Av8ztVCmFZ+Y2JKjNoZdUO2+cuzdPIfI+zMkDJU7yA/FS4SqPhWZqqKECLltCaua9NZWCR63zbtjqCwpOx6qPmcdklXkC+Q8CMo5JSEB+CQgnRU0HN1LqY77KcQJdVNGizI47zIXtoDaDXjnhlx1XZkZJKOmx7zEP/leyj9fmT3pT1KfoQZsrsSI0P0aOR6FSRQStEGCvxR2ry7cj4oD6iRxVhAOQTxipLzpkfMO4iA1URPWUeAVpa/1VVovRl/h0fpeolnS0XKuwx4E1QeOAMDNBUGsR6+pnFNParebAAj8xPn/N7BfLKagDY2WfhKGe+c5hGFUEFUMAgqnBQPQyiyge5vC6HsWWBhYrMTz3VyrNG2fgINVcrZaxyMhbKDGKN98aiUv/d7N9YnxpHB9DvEEwMZkpqEmM0pEGXYzU+RGSTCuQOt1DtoAJ6ArR0aZ5H5kfFPlpRT7af6cj4ALH8KvuLdKwjkM98K7XHfoFFvXxZhQhjVXbEHaBNDDuVURqJHhWyAL3+CDsPLGtIjiK/rqQCiMR8/BEFNjmXMFY1aAvwLt9UuWdP2gxamvnW9CBPDMk/FI+hsiG7NENpBo05BM6DnHCmGqlgPjyZFo2OlY4AbUJXgFabQxgodAhyp2+m9VEFq++cq+YmDFSSIXkOKiuD0rCOgGL9z3UI+kC18yqebWe94s59U2qP6x0Zmuyxzgwa04UsokeRYwXQ/fEqlVaxluX1AOzMM6ZlHXOmOCplvk9hBm1iiLKDKpA7lGSsj87AVFFOXFZL/kdigv6tuzJqfEgtYazNjjjrpcMfsSxvOxItlT8gDcjoIyN6tBDvuuxIzWTNoOl4kDU5VqXV2SOkVTUlAi6GwJGnch1ZE2RuaZ4qg8gcK1a+qTKDUKr7QfZyrCz5B0cDLoe4j36y4EnFfYtEKEjL2lj61DFWk9mxyr22sT76Dipq53M3srQdURgM5mZ+lDlW9T49aPXyZel2CPIIigEqjVVRcp4+C6rPkaUwWx0rpynLuUSPrtIknf6IbZMdUeWPlFVnr+NoH91LFeXEuUSnbuJ9fFDdOpbXa6zoySEoWKmoquygVyZepV/nPmZFpR1hRFVW33ifOsI416/zgdYAzbKshZZl/ciyrHtdv7vdsqwfWJb1G8uybir6ITpKCtzZGJWOVWlVzsbSp96xYsquspEayC/NU838JSeoRpnJAtSww7lOo21rLnF0jK+KTTPXsUqvo4JgkH2u1kykqwdTZSZSt2OVa0dU9lfkBhYqHatoCQXxeY6VQocgq8TRkatCJ3MdAttWd+wJ4BxF4mFHVMCP6FFhRyyL9pU8okcT863UjtQ7Mhw9jI+Qw6oqg+zpj9SrkZW7j6YDXQXySsppsJAuO1JaBUy4BruoJANz7QgrFdWViZ9QmInM3UfTdkSB/pdUENGjrXVFcg+aZVk/tiyrw7KsHTm/v8WyrL2WZR2wLOsfCn2GbduHbNv+YM7v/mTb9ocBfATAW4t+EZ3MdyqlwbFyj2tXWeLix3wrZFryar5VGUTn/rBpV2xNVTgEuaVJ8VGnB0dTiaNqBxUAxhzGT6VBBPwZWyWyaug+scNKlfag1dNP5qAqd6wqc3pLFepIXiaeBTEKiR53Jl5liWNZDTWhsx5MlQRFrj2Oj9DEvknBfOdMn1VJmAHOACydjtVghuhRPQ0W8HBQVRFm1fkZBJWBLpBP9Ci1I5oqGkqrgMQoHffDZMXKaQS/bORm0MYVEmaAN2GskngH9BDGlpWv/0oJihzCzAc8qZqfArjF/QvLsqIAvgPgNQBWAHi7ZVkrLMs627KsB3P+ay7y+f/sfFZhqGSs2Fk4acZKsYNamuOgqnQ+cptJVQa6gGMQ3Q+y4kAXyKylyo2spAqA5dpYFLLsgEeJo8IgXuc6ss/Nmj6lsHG7LMdpTPfgKDwHkOkGu0alpdJuOzKs7p7lMt8qM2hAvmOl0o6wXhtm9+MjACxyrmTD10HVaEdUBWhsdHm6okGDHdGViS+rccqunGtKl5yrqNZwnqncUlGlmR+XHYmPKCynzCWMNVT06CI603ZkJPNTmT1mhBkrFVXsj+T5dYozkUBmHcdVV/S4ArTEBMlVOSQkPpwhA30QeA6tbdvPWZY1P+fXFwE4YNv2IQCwLOvXAN5g2/ZXALwuyOdalmUB+CqAR2zb3uzx9zsB3AkAc+fOVR9YuAM05Y6Vs7HYNkXw8RE1DbnAqWGsss74UfkgO2vGNpf4MJU0qGCsIpHsB1mHQdTFfKfXkWUiFTPf7nW0bbWBRXra2yBQM43WtKRKzSjuaIyuLc18s3VUuJHFcxwrVRtLHtGjmfkeH1SbiQRI/8vr6GdplZpy4lg5jb7PsyMqM2i6HNQcx0pn5ocd+6CyxAtwAtzqDKmkREdKaQADe7Z1lJy7CbOJETUj/YH8TLzODFq6T0vDPlpWQ/pfolD3AVfriuJ1dPvHAOl/9XQ1snIDNB0VPUz/JxT7/l5TIz0QttlpFoDjrn+3OL/zhGVZUy3L+h6A8yzL+kfn1x8HcAOAN1uW9ZHc99i2fZdt2xfYtn1BU1OTWscKoIcr4TB/Kll2gBTQTgKJcfp3fDTzcMuG35AQHYEuoCc76C5xVLWJAdl9CMozkWza1XhG3qRyrBwZyTg9CyoODgVcBAUjXxQ6cUA2G522IyozCO4M2ohCO5LLfGvQf5ZBSCbINqsulXYTParumWVlOwQ6MvG5pXmq7llpTgZBp2OVGANga8ggu/RfpR0pqfDIRGrKxMeH1RHG5br9kRpXye0wAFthJp7to65KFFX2mAXxTP/T66hr2JBKf8TxBfIIYw1ED3vmlOt/4QBNUZTjDdu2u0G9Zu7f/Q+A/wn8ISpLM4Acg8icD8WBxcQwNbJODAO1M9XIStcq55QmKXMIXMqedHp/VBlf9hC5G2WVB2iu3hFAXWCR7mcaAKqbSO6UeWpkpUuTdAVoVUDf0WyZyjLIOSWOYzrtCJuGqdAhSIxRABONOY6VJgdVZck5QDYynrNBKy9NcjlWqvQRyJ6+OaGYDCyvdUrzhjIEk+p11OlYjTg8sWrHKs+O9Cu2I5X5JV5Kn7Vh6r2PRBQTxh6l0lZUnY6UVALDnY5M1aWiufqv2B8prfYgzBRmfsYHMzqi8rgCL8I4UqJmpD+QTfTotiM+CJtBawUwx/Xv2c7v1EE5Y+VhEJWX1DClUFjiGCujsr9ch0DlJh3PGcigLNDNMYgqmT/A50FW0KcCeEy70lDzPXEKMmjpdVQV6OYytgozCEC2HdFR4gi4AguNGbSJIdpIVZQTA846apjOCng4Vooz8e5jVlTrf/q+MaZdYw/OxDBNSFPRywdkryOzJ7qYb5XrCNB1pPVRQyYeyK5E0dVywQgDFaWiAO3Pab9OQ2UU4NrbFK4j4JRRujPIUGhHqgHYmb1G5XEFua0rOgJdty8OaPBH1AZoGwAssSxrgWVZpQDeBuD+kJ+ZB8uybrMs667+/n49zHcu86dtuIVCxwpwmFNXYGFFaZS1CpRU5BtEXaVJOjNoCcVMS25WS2VgEYlSEO8OLKJl6nQkK9DVlEFzj3XWlUFTTlDkBNbxUXXrGC2hMw7ZOibG1JETgONYsXXUMGwFyC5xVE70sACNOVaqCDrHjiRG1ffgsEDMHaCVVqtzvj0JM9WBrjtAU0306Cpx1BhYlFRS0M4yCCoHaQCOPXaeMeXkdC5hprC9A8jx65xnLqZI/9Pky5hTGTWqvjIq146ogjsTqdyOSM6gWZb1KwDrACyzLKvFsqwP2radAPAxAI8B2A3gt7Zt7xT8yr6wbfsB27bvrKur0/AgV+Y7BMqYFi+HQGVgkeMQqFI+gAxEKk5lV6qZ77zSJB3MNzOIjtFXxQ4zQxsfo7G98WENgYUrQFO6jq4hOUymKoIiPdzC5cgptyMah60AZEfYWqpmbN12RJXuA96Brip77GlHNBFmCcWZePa58THnaJCEukqUSCRf/5XbEffkTajT/1wyRGUGAcghOnURFEPkfKfi6tbRsvTakVhF/mwBbSWOiu1IaXWGMIgrzqCxe5QY1TNVFHDZkUHFxLtXBk0x8c4ynj7gmeL4dp/fPwzg4eDfLCQSYxodVE3Mt1aHwJX5URmglbgYW10PsjvQVTVZCMjuHVGdCi/xMIhKWSTX2XzKGSvXkBzVjBVbx6QzbCUxpq6WHSDDPtRG/698PLCrVDo+ChqSoNiOMOYvMarHsbJtDfY4t1R6BKhqUiMLoGdr4IQjy9F/Vcx3TKM9BnIqUVSXJtXQdSUT6u2Iex0BJ1utOvOjq8SX7aND6gkzgO5b2h85BUSP8iEhmvS/rBoY6XZkqt5HXYQxGzikyo5ES4BITG8vn66Wi3SgWzhAC1viqB9aGVtdBnHYxVhpzPyocgaA7LNwlDc3e/ROqTaI7hIvQINDMJ6Z5Ki0pEwn812TkaOasYo6wRhjGHXov3bHati1jirvm6vKQHUm3s00KrfHrgwC+6mLMNNFUMTHMoSgyixrSVX2PqraHgN67Egsx47oIHp0lZy77ciEYuIRIJ1khFl8VPG+VkH3KpXS4I/kHvszorgyKicTH4mp0xF3Bk318B/AsSO6/LqazLAt5XZksgZoypmW3KZ0S+2QBMAxiKy+XOGmGSvLOPkJ1QaRlQuNqm9ujpbknBejqTTJXZqnrOabOVajmYdZOUGhi7FyM7aKHdRojDauhCbHyp2JHB8k/VB2NIhuO1Kek4nUZUcUl3jl9TxoKJXO7Z1SXSqdGKVDWFXKAhw74u4JVpyJB/TYkdzSpIQGgsId6Kosp3TbER1ET6zc5Y9oIowTY/pKpVnJua5WAUAD8ejhj6gkekorXbMFFPfyuc+U00mYFcAZEaBlDQlRzljl1HyrbG52j4dXXSoHOAbRnUFQ3NwPOA/yeEa+MnmuB1l1L1+sgkrzUglaRyuikLFybSw61tHdz6EtQBtWz1gBTrkcc6zG9Qa6Sh0rV6m0jnWMlmU7VqpZdoDsiOrRx7nj4VUz3yUue8xKRSOKtmR35kcH0VOaQ3SqDnQBPXYkWgrA0kf05BLG2ggzDf5ItDQn0FVcKs3kqL42d+9UYpyOt1BNmKXP0h3Rs45uvy5aqk5eVgZZ0z46PqR+r5lMGbSsISHKHYJKZ7hFnBwepTXYbgeVKYTKwCI3g6Z4HZmcdGChKWOhOrCIOQYpMe7oY6Xa8cAA6UdSwzrmnt+ldPqUa3CHasYKcPRfl2NVoc+xcjO27BlQqv+udYyPqndQmZykk/lR5RCw4RZscI3KA2YBCnST404mXkPpPpBD9Ch2rHT2jgCOHVHsfFsW3ae40/OWSmgolXYTZgr7BsvcmXgNPWhZgYUuwngkY0dU2S1W0ZNV0aBwH42WZa5JF2GW0ET05E4x1UFQxEfU25HJFKBlITGu3rECHAMcz/SuqEBWzbfm0qS44ub+rHVkjpXqAG2IyndSCfWOFUDXFR9RPyQByHasVK5jbs+D0gll7syPYsYKyDgEqaTT76lyI6siciKVcmyWQllZGQTWX6Q6E+9yCJTqv6vnQQfRw/Q/MQbAVqyPOXZE9T0DNDtWmgmz5ETGjqi0/yXlGXIOUEw8uvs9FZOqnoGu6paLnAyyKrjHwyfGAVhU8q5SXnxET79nzJWJjI+o3Wu8Mmiq9Z/5xuOKSxyz7LHiknPLcipRJluAFh/VN9wiMa6WZYxE6Vp0NDcD2Rk01cY+/SCP6GNsswyipgxafExxs71XD5rqQNfF2KreWABy9ic0BBbsTC0d6+ieYpqcUFcCC/j04CjWf3cGTUcmXhvR42R+VB/SDmT0L52J17ivAZp7WRVnEIBMoAtoKJV29+Ao1n823CI5ob6cDNDoj+S0XCgtzXMRPUmnvF1V1QuQqejRYkfKiZROpfQObdJJ9KRSTkWbwnWMuvwRFuiqKjkHsjPIPjgjArR0D1pfHwBbsWPlSnOqNoiAXofAHbHrGGsLZPc8KHWsqnMykYrXESBDr6vmW5tBdJXmJSbUPmtRD+ZbKfvHmG9NPZFAJrBQuY6xMjp0XmcmPl0qraGXD8gE1lZE3bAVIDPpdkID8x3NYWxV6z7gTCnTVHLOnHzV2cG0HYnTOloRtfs2IzpPBdGjkuRka5ZyH1egmjBmmXjVxLvLHicUryOTNzGkp+Q8rf/j6p81T6JHQ+tKUsOezUhUZo9V+nVAhjAugDMiQMv0oDn117oUUEeAFi3VyPy5M2gaevmAbOZbRypcVw8OQIZedaAbcZwNtrG45auAe6yt6syPV6moUsbKISjSwaCOUukRum8q7YhlZZ5tXXYkPcVRdQYtZ9iQSpIHcGXiddgRxtiOachEugkzTRm0iRHqr0vF1ep/2rEad9ZRYU8wkCGx4poyCIBL/1VW9ESo7C85oZHocQ1tUjpVOqeXW7UdKXXsiI5R9LmZeC0l5zozaMN6fMhcwljlHgpk++M+OCMCtDTYwXg6m9KVB2glxPxpCSwcg2jbGmq+XU25bGNRumk6ARo7QFQp0+JmrHQ8yBU5BlFDoGvb6vU/j7HSvY4q+zkmsR1xZ+LjGqbYAZmKBtXMt1aihzk74+oDtGgJZVndpXnKp685fdxMviq4HauJYbXrCGT2UV0VDYCj/4oDXQCIlGRXNCjvnWJDcnS2riiuaACQPgdQx17jDtBU76OnolR6YsRlR1T6I4wwjqvPRAKZUukCOMMCtBT91GUQdTzI6QyapuZ+O5UZD69liuOY46AqXseYM8komaB/q3QI3Bk0nalwLUMSKgA4G6adVF8qBOjZWJi8rCl2GgKLiWGHsdWQiU/FNTWll2UcK9WlSVmMreJySiATWGgleibUE2aAk/nR3DuievKm+7NZiaOWAG1cb4DGyry0VPTosiPlGf9AdeuK+xxALesYo3VM67+OSpRx9f6I+5gJXT3x7ioslYNd8jLxqu3IpMug6QjQdDPfzLHSVPMNOJuL6gxazpAQ1cx3pMRplHWYFqUPsiuDptpBBTQ7BE7GYKyffmphvjUxViUV+h2r9DRYhesIuIgeDYFFbi+flgPvR/QQPZEY2REdmZ8sgkIxYQY4901X70glABsYH6B/KyV63KVJI+qJntxhQ1r1X2Mm3oqo751l5Bygt3dKNfEeKckc1wToI4xVDxuyrEyJr65e7vhwRpYWoschzJTbEVe/vw/OsACNlTjqKinQwbSU5DAtKjcyZ90mhskJ0THWmfU8qHas8hgrnZkfHYGFu5dPg/6nAzQdBlEjY6VtiiMbNqTJIUjbkTgFGUp7+UpBzveg828dPWhjeogeto4pJxMf0RWg6SQoNDhW7LOZjuggzLRl4p1SaS09aLmleTr03zW0RmVbAjv2RzdhprqXD9BrR3KHhOggjNNDm6Jqhzaxqi8dZdnpMfu6MvGTJIPGpjgODTpsnFLGKqfmW7lBdJjvlMbSvLE+598K19GyyFCwQHcyMVZZwy00Md9Z0zA1BE2sxEUXY6WD+c7NRGphbIf19o6kEmqdYSBjN9J2RGdPsG47ojKwcJUmqWa+AZdjpSGDxnSQMcRaSxx1lUprHhKiM4OW0pD1j5WR882CeF3nAGrxR3Iz8YqDGCBDGmghejSVnEei9JMNbVLq17l74nX4I5OkB41NcayuclhpLQZxRA/TEmHMtxOgWVF1sphRGu2jnzoeZK0ZhIQm5tvF2KqeYgdkMmg6mG/mWE3oMIiuc0cSiodNAK7mfl29fNDfO5JKqNV9wBWgOVlW1cMtIrGM/mvJILhLpTX2sqpmvktcwy1UD23SGqDlOlY69rVTNSREQ098yrEjysuyGWHs2BFdw4Z0zhbQYkdOgT/CMmg6/DpAL9GjqzJqsmTQ0tDRg8YULj6mySC6mG8ron7MOKAngwaQUUxoYv7YeGCdzDd7kFWvYzqDNq6+pCCq0bFyj3XW4RDonL6WLpeY0Mx8JzKsoyrkEj3K9b9C33hsZo+1Th/U0NwPZNZRC/PN7AjLxGuqaNBC9ORk0JQPZYCT1R1XbyMjLv3XlYlP2xHFRI8Vcfw6XXZEc0XPmFNhpsMea8ug5RLGmjLxOtpyWEVDAZxZARo0BGhMIeykHoPoZlomE/MNZE8f1MG0pHT1oGnunUpn0MZOgWOlOrAo01iaV5bTO6KhxCuV0MvYahlIkkP0aGFsGfOtY9iQu3dEQ2nSxDDJ1DHcQleJVx7zrak0SQvRw3rQNAzkYRU1yQSUH3gPuIiepAZ/JNeOKG65SE9o1bCO6aFlGu1Ieh11DcnRVCoKaCpxdLVcpBJqiXDAsceTKoOmYUiI27HSYhBLnZKapB4HFdDHfLNUuI7ekWgpZVjT41g1MFbjg6DxwKoZqzJ9QxIiOY6Vap1MZ5CTast7AdLHVCJzeKhKxjZN9Dg6qTxocmfQNNkRbZl4V1O6FuY7oWc8NnuW0yVeOjLxujNoGjLxlpXdg6ncjuT28qn0R5xrSfcf6ySMVWfic3tZNU0x1TpmX8cUR+da0q0rGuwIyyBrsyM6M2jj+nq52XPtgzMsQHMyaCoVMB2gJYlp0eJYMeZbc3O/6geZ9dfpKDvJcwhUMlbOtUxoKN8BkHXA8mQyiECmDltnaZ6Ongd2LemGe42l0roz8ap1kvXX6SDMIrHsISE6iB5dgW6WYzWJmG/A1YOpg+gspwqbNNGjwR9J72s6CGNNPWh5PfEa9jZdFQ3pTLxGOzKuqcRR92wBQFOAxjLxuojOyRqg6WCsWAZNi0HUWOIFAKO9zr8VM1aRKG1kWkq8cjM/GlLhTJYuxlZLRldjzTf7fJ2OFaDHIT4lDuqEpkBXM2NrMTui8biC9FRdHceeMB1RXVLjcqx0nCcH6LHHQHYmXmfvlBVR+2xrLzl3ZX60ZeI1ET2RKJBKaTw+KZEZ/qYjg8YIY12BhU7CWMfQsqxMvIaKnskSoLEx+6Ojzk1SPR7eitImZic1OqgaetDypiZpcKxSST0GMV2apyGrlR4kw5wP1Q/yqcigaegdARz911hSAOjR/9x11FEqzcY66xi2ArjWUQPRk0rqG7NvJ10ljioz8ZqJnlOaQZtEmXjWcznaS2uqdRqmLqJHY8uFrgxymjDWpP/pDJqlVifTZ84yO6LYrU8PydHZg6ZJ/2NlLsJYA/FeBGdEgMbG7FeUOcqgw0lNO1Y6GCvNzF+aaVGsgMyx0poK1/AgR2IArIzzodyxcjZNXcc+ABoZW50OgYv5jpaqnZiq20HNKnHU5FixEi/lk+XcdkTDOgKaMvGM6NHEfLMgXkcPms5psOzzdU8xHevTE1QAmQyCFqKHEcaTiDADHMLYKXHUpY9ahjYxosfREdX6b0Uzh0dPtpaLaImL6NGk/wVwRgRoGdjqx4wDToCm2UHV0oPGxsM7aVUdARpjo3WM2Qf0OFaW5QzuYAZR8WOk0yDqdqxipbRhphLq19FdUqPDGQD0bSw6D6qO5mSQVTO2rMRR13hsQO/BqBO6HKuIPsJMZ08wkCEobB1ED8ug9ekL0LTZkZj+HrS0/qv261wVPcr3UVcmXtc0TF2EcSRKA/smG/EOaG45mmwBmp1S/2AB2Rk0rcyfJoVIP8gaHKtUUlNgodGxAshRjGvaWNKOlaYhCYCemm9Ar0FkpUljfRrWMQLAOgW9fJPQjqQzaJrG7AN6pphaVmayIqDRsdJR4qWxuZ99vvbSvH49gy0A1xRHXYSxTjuiqVWAnblpp/SW+ConJ3IDXdVEj6XPr9Peg1nqIno0ZeIL4AwL0Gz1yg7QjdHmWLmm/ehiWiY0Ola6hoTkOVaq17JUn2NlRQDYNCJYuUHU7ViV6WO+2bWMD6q/LsAhenSVJpXoK6lJM7aO0zhZM2iRmNr+IiCH6FG9jhF9w1Z0HjDLPj89Zl/1Ojo6kRjTVxkyodNBTWgqFc0lehQ/a1ZUb6kcQD6C8tkCsexrU+6PsIqeU5GJ16D/6Qoz1bFGcX0/swI0XdDqWJ1CxkrHg6xrSEjUtZFZUQ3lcuUamT9W5jI6CQ2ixtI85rjpmNAE5GTiJ2Fzv84MWkI3863BsQI0Ez3WKSiV1p2J16D/zLGyUxp0P3fYkC57rGNoWU7vlPK1jOgb2uQmOlXrPuC0XGjyR9JEzySb4giQTurMRBbBGRigKWZZAM2OlfP5iVE9dfqA5tIkh43TmUHTYRCjpRoZK0fn4yP6xuynSwo0OPuJcT1Bk+V2rNSKApBjR3SNh9c4HltXD5rWnmBXX5gWO1Kmb0gIY751nScHaByzr7HEN21HbCg3JOzZmpTDhnIzaBoIY22ZSI0ZNCDbH9ESoGnKoOk8B43J09W6MikzaKrT4IBex8odWOjYWLJ6HjRsLtpLCkY0Md86GSuWQRvToI+nIoOmafpaVgZNg+mLRPUc+8A+X7djldBV4qiR+Xaz+so3aND1aB8SMkntCDsaR1cm3tZgR9ixP+l9VEdFT5wqepSXSrNnTZMdyZrOrVH/dbTlxMr1DglJaTyuAHAFTRrK93VWNBTBGRGgsXPQxsfHoSeDFtXI2DqfP6EpsIiWUrYO0FOalx4PrLF3SodBdKfCdTioAJWKKr9nOZPltPSgaRprmy5NSkKPHdHoELDx2JNxrHMkeoocK81Ej5YhISnH+dY1bEVTaVKsTN++xmxHKnkKMvEaiJ6UJsKMPWvszEEtdkRjoAtQxk53qbSuDJqdVH9tWSXnMfWtK1H3OpoMWiCwc9DKykr1Z9C0nbszomFjQYZFZf+vVFZU4zq6apW1ZdA0jgcGnD5FxTqifRomK03SwXy7HStNRI/OYUMAsZo61tGKkD4CmuyILsfKdQ6gttIkVuKoaUiIrUH/3X2zgB6iU5uD6iqV1kb0aOqJzzquQ7H+pysaToEd0Xmeoo6BVO5hQzpKRZNx+n9dQXx8RNM6lugjHidLBi0bmgzihGamRRdja0UyD5eWkoJTsY46HmTNjBVAzKYOlh3QV5qaZv7syVWaBOTov85MvIYMshVxOVYanH1dB/Vm9bJqKk2a0OVYuRziSUf0lOhnvu2UPsJY5zRM1qeooycS0Begaa3oOQUljlrH7Mcz/68S2nuCdWbQiuPMC9C0ZdA0O1a6eh4iUdfDpWNIiCNL69QkTb0j2hgrVuIY13DPcg+G1FDimDaIqs0Ry6DpYr41jnV267+2AE0j0ZPQpY+nYIojW0ddDrEWO+Jivq2IhoBQ8zRMQGMGLaLRHmvcR937mvvfqhCJUjk9MPl64llpKqCn5SIdVOvKoGkctqK7VLoAzrwATZdjlQ4sJtmDzOqHAT2pcAblZ1zpfpDLANj0/7qGhMDWW1KgxbHSODUpnUHTMB4bcAILpwFe57QrLZn4qMbSJNfn6wp0J4b1ZOLdtkpbSY2twbHSXeJ1Cqav6cygTcZMPNN31hOs4xw0Bm2EmabKKPe90nXsD6CR6NFkj7PG7GtquSiAMy9A09U7wqCLaUlOaOpB0/lwuT5fubF3H1egI0BzXY+ug1F1yGJrl9IwSABwAhcW6Ooaj62rB811PboGdyTG9PWypokeDcw3g/KjSNyl0joqGtx2RKNjpe3sRl0ZhDLXAbOqA13np44x+4CjI46N1NbLqoHo1LmvAZrtsYvo1FIZpdGOuO+VLsI4pWGqKJAZtuWWfQpxZgVotiY5WQ+yJsYK0NeD5vX/SmTpzKCVeP+/KmQxVpqYRmByZStyZehivrWN2XfbEU09mIC+THz6/ydTJp4RZuN61lEn863T9rPrslP6HKtc2cpwCjJoDLoqenLlqgJ7tnWQSloJCraOtiZ/ROO1ZZH8mnpZAX2ZeAYzJIQXOhkrB7oYq1y5qpCV1dLIfCsPYtyOziR2rHQYDbZ+k82x0t474s78aDrwHtBvR3Q5+7n/r1rWpHOsNAbVfw6OlbZSaZ0VPW7CWFMvq/unDlmAeh9BN2F2qjJoOm2/tooeB6rXcVL2oOkucdR1MCpwCphvnRk0nQ6BDoPokjGZDCKQWT9dTbkMukpFT0WJo64etNz/VwWtm/QpysRPutIk9zpOMsdKK9Hjmgarg+g5Fb1TgCb9d65Nd6CrtaJH4zrm/v8ZL0szYXYqCOMCOPMCNO0ZNJ1My2TrQdPJfJ+ijSX3/1VAZ0kBkFk/3YyV1iEhk8yx0m5HdBI9GpnviG6iZ5KXOAL6pup6yVYC3ecpOtcTKVEvL4ug0Ej06NzXcv9fuSzdGbRJ1BOvnejR6UdOkgDNsqzbLMu6a2Ji4hQ0909m5ls1+6FxSMip7EGbTE25gCtA0zQeOFeuMlg+/68I6euxNGd+NE1xTP+/pkOPc/9fBXSv46kaEqJjFD2Todux0paJ13hQNaA+Cw9o7uVDRke0lDjqHDZkiB4p0F4qbTJo3LBt+wHbtu8sLS3F5OtB02wQtQ6cOEU9aFrGY7sNosYSL53DLbQYxFOQQcv9f1Vwr6Ny5lu3Y8XWT/N47ElH9OjMxLvukw6ih63fZCtN0j4khAW6mgkznT1oys/AhOaeeN1Ej07y5VQMW4Em/Xf7I6c+PDr134AXOg1iJKbB+dY9Ncn0jkiBznIJnVlPQLNjdYqmJum0I7qZb52ZeN3TMCddqfQkZb6B7NI81TglzLfmoWWqq3mAUzdsaNL1oGku8dUZNGmvwnKeMVPieLpDt0GcbAqByTskRHvviE7Gyn3PdDK2unvQNE5N0ppB0zy0RufIau3jsSdbBu0UDQmZbL2spyKDBkw+e3yqMvG6SxwnXQbtVJVKaxxaNtky8ZOlxDELGuzhKdtYdPegTaZpP6eyd2QyjdkHMus32RyCrM1kMjPfOuyIs37ax2NrnBo2me2Izl5u7Y6VzvOLdPag6bbHGntZtRAGOokezX7dpPZH/hx64r1x5gVoOjBpmT/o3aR1MlaWpfdBPmXnjmg0iGXV6mWdKsZqUjuok4z5/nMZj62T+dbqWE2yc9C0Z9Am6zpi8pZKay8VPVUljjrum7OWJVXqZek8B21SZtB0HjCro3fE7QRPunNHNE5xBKD1gOXJPCSErV/pZAvQdG8sjgzdpaKTrQdN65CQUu//V4U/h17WWLkGWZOZ6NE4JMRt83W2Ckw2O3IqD7yfbOeysmvTThibg6r5YGPyMd8llflyVeKUnTui0SGYdFOTTlFJQaluxkq1OTpVpUk6iJ5al1yN5ylONuY7EkVaNyZ1ieMkdqx02uPJVipdqpkwPlVTHJWfb2taLqQh7Y/osCMaM58mgyYInQbRspCZUqOz5nuSMVZuGdozaKof5FPU3F9Wo17WqTKIk21ISLk7QNOZQdOYQQD0lB2mm9I1T3HUeuC3xl5WHXYkNomHhOg8Ty6romeyZeJ1Th/UXSo9Sc9TBIBUnH5qIXqCHftj27YEYZMuQLNDGUTbtvGHzS34zO+2omd4wv+Fkhyro93DeOv31+HRHW2FX1hSkS1XEK8c7sFvNx7HD547hEQy5f0iSQZxaDyB/tE4UqkCiiqpd2QikaJr23AcHYNj/i9MZ9DCrWNL7wi+/thevHyo2/9FEhmr3ScHcP/WE+gfiXu/4FQ190tgrMYTSaRStr9Bk3gO2kQihfu3nsADW094v0ByadLOE/2479VW/2uTRPSsO9iNP21pxYsHugqso7xA99evHMON/7UWX3lkN5J+z7ckO9I7PIGvPbYH133jWbywv8tHljyiJ5my0TU0jomEj30EMs5VAQf1wW0n8MX7d+Kz927Fyf5R8S9UxI4kkim09o2ipXcEx3tGwjkGARzUFw904ZZvPYd3/2g9xuJJcVlAIDvywNYTeNcP1+Mrj+xGb6E9uRgCljgOjyfw5K52rDvYLb6WAYaE9I/GcddzB9E9NC4mw40AQ0I2He3F3/7m1cL2KAjcfT4F9rWOgTH81+N7seloj7gsIJAdSaZsPLu3A+OJJEYmEuKy2DpaEd+M3R+3tOCWbz2HP25pEZcD5Pg+3nbEtm384x+24x0/eBm/WH803H3j8Ef2tg0W9n+LIUAm/vGdbfj6Y3vlBDJxx+fzIXps28Z/PLoHKz//KP7xD9vCyQpQ4rjpaC+u/M9ncOlXnsLafZ3isgL4IBpCe9kQd6z+9+kD+K8n9gEARuNJfOMtq1Fe4nETJJQmdQ2N4z0/fgVHu0ew4UgPfvr+i3DV0ibvF5dUAPGRUM7Hs3s78L6fbEj/e2p1Kd54/uz8F0oYj712Xyc+9svNGBxLoDQWwT/fehbec+n8/BdKcKxs28aH7t6I55wHYfaUCvzhry5Dc61HX4OE6YNr93Xir+7ZhJGJJH694Rie+tQ1qKv0MLBuh1iQRRoci+M3G47jPx/bi4lECrPqK/CrD1+CuVMrs18o4YDZsXgSn79vB57d24mK0iim1Zbjy7evwpJpHkYv6RjvEIxVKmXjXx/chZ++dAQAcMd5s/DNt56b/0JJgcW9m1rwuT9sx4RDTJw9qw7zG3NLNOWUOL54oAuP7DiJX64/hpRNG95nb1me/0IJvSM7Wvvx9h+8nP73+y6bj8+/bgUikQLfP4S87zxzAF97bC8WNFbh+2sPYdm0msJ2JASDeqx7BG/63kvoGhrH1KoyfOjuDXjh769DY3WO3ZXQy/rC/i588YGdONQ5hJQNVJVGcdd7LsDlixvzXxyNAXH4ruNLB7rwsV9uSf97eDyJ77zzfKHvVYyN/rcHd+Fn646m/z17SgW+/+41WDmzLqSsfMdq98kBfOCnG2DbwJ62QXz47o34zjvPR225oD7ZThDs41itP9SNT/7mVVSWRrHuUDcOdw7jrvdcICariGM1nkjih88fxjce3wvGOXz6xqX4+PVLBIQVJnpSKRt/+5tX8fSeDnz76QO4eeV0/Nvtq7x9jSAoMmb/YOdQ2kb8cUsr9rUP4u9u9rBHgWS59MJH/x/f2YavPbYX+zuG8L/PHMB/vOkc/MUFcwTlFbYjbf1j+Oc/bceTuztQVRpFZVkMa//uGlSWCtgB9/m2Hli7rxOf+u1W2DbwuT/sQEk0gtedM5NfDpCtFz7r+OzeTvzqlWOIWMBLB7tRXRbDG86dJSivcNCUStn476f245m9HdjW0o+yWAT3fuQynD1bwI4UOT5pR2s/PvbLLZhIpvDYzjasnlOPj1y9CIubBf2JhBOglXrbkftePYH/e/YgYhELv95wHO+/fAGWevk1QVBkSI5tk1+TSNqoKovi7+/dhuc+ey1KYyJE5aTLoEGY+T7SNYxvPbkPbzh3Jv7m+iV4aNtJ3Po/z3tnLdIGUTxA++SvX0X7wBju+eDFWDqtBh//1RYc6x7xfnEsXAZt09FefPyXW7CwsQoPf+JKLGwi58qT/Q45HnvT0R58+GcbMXtKJT5941JcNL8Bn79vJ7777IH8F0twrJ7a3YHn9nXiE9cvwc8/eBE6B8fxuT9u92ZmRpyMF8tIciKRTOGL9+/EjLpyfP/da9A7Esft333RmwWVMDXpC/ftxJce2g0A+PIdq9A9PI7/W3uwsCzB+3b3uiP47cYWrJ5Tj2XTanCgYwif+PWr3pnWtEEUM6ijE0nc8d0X8dOXjuDaZU04Z3Yd/rilFRuOeLCtsfAZtB88dwifvXcrzptbj399w0qUl0Twtcf35r9QQiZyR2s/3vnD9bjn5WN420Vz8dYL5uC7zx70ZlxDEj22beMrj+xGfWUJHv3klfjA5Qvw05eO4F8f3FX4jYL6uPNEP77x+F68fvVMPPG3V+HsWXX4ryf2eetISDvSOTiOd/94PeLJFB742BX41Ycvxlg8hT9tafWQFY7osW0bX3poF0Ynkvjraxfji7etwMz6Cnz0F5t9Mhz+PWhbjvXiw3dvxMKmKuz615vxtzcsxUPbT2J9oWx7IRQold7TNoC7Xz6K5dNr8KXbV+FLt69CPJnCx3+1BeMJgexWVolj/n37/aYW2Dbw0j9eh/980zlYd7Abf/e7reIseMLJLHoEaBOJFD73x+2YVV+Bdf94PT56zSI8sbsdhzqHxGQVcKz6RiZwzdeexdce24sbV0zDzz5wEW5cMQ3fW3tQLGtn+f4DAPDdZw/g6T0d+IsLZuO65c24d3MLbv/Oi9h1YoBfFuDKxHsHaF9/bC9KIhae/+y1eOP5s/C9tYfQ2hciq5sr14Wtx/tw5883YWAsjrvevQYXzW/Alx/ajbhfxU4xFMigtQ+M4fXffgHP7e9CTVkMwxNJdA6O48GtJwVlFQ7QvvP0AcxrqMSzn7kG8xur8LFfbsHvN4XMpAGediSVoqzP3IZK7P63WzC3oRK/ePlYCBmu7GDO3jY0nsBHf7EZ//3UfqRsG5+4fgkqSqP41pP7xGQVyMSzAKa2ogRvv2gubACP7WjDm7/3Eva1D4rJg2N/fAjjn7x0BEunVWP9565HVWkM//D7beLZ/yKZ+FcO92Dr8T587LrF+PxtK9E2MIY/veqxZ0nCmRegCTLf31t7ELFoBP9061n45A1LcNe71+BYzwg+c6/HBhSyxHHT0R68cKALn7lpGa5Y0ojvv3sNbNvGX96zCaMTHorDAgoBecmUjc/euxVTqkpxz4cuxoqZtfjbG5Zib/sgfrfxeP4b0j1oYuv4w+cPo7Yihl99+GJ8/Pol+On7L8Rrz56Orz+2F52DOc5OyIOq48kU/v2R3VjYVIWPX7cYVy5pwidvWIond3dga0t//huYQ7DqTdyyAOCel4/icNcw/u7m5bh55XT89P0X4nDXMP7o5TSG7B15ek87/rClFbeeMwMPffwKvPPiebjtnJm479VWDI7lkAYha+fjyRR++PxhXLZoKn7wngtw13suwJdvX4XdJwfwLw/sytf/ROGSgmJYu4/uz+dftwI/ft+F+PWdl2BabRm+9NDu/JLYLIPIv44HOgbx5Yd348YV0/CT91+I91w6H3deuRAPbTuJrcf7sl8socTxq4/sQW15DBv+6Qb8+x1n48t3rMLZs+rw/bWH8l8ccjz2n15txYsHuvGpG5di+fRa/L/XnYV3XjwXd687ggMdHo4skyPQOxJPpvC5P2xHfWUp/u0NqxCLRvCx6xajpXcUT+5uz39DyBLH//enHWgfGMOP33chVs2qw5JpNTh3Tj3u9XKIQvZXbD7Whz1tg/jraxfj0zctw/suX4DvvvN8DI0n8L9PexBLDDm9I7Zt44v370RdRQl+9eFLUFkaw51XLcTMunJ86aHdYoFMgdKkX60/htJoBL+581K865J5eNcl8/Dvd5yNQ53DeHi7gJNqFSZ6nt7TgUsWTUVjdRn+4sI5+Owty/DYznbc9ZyHbgdBgdKkeze14GDnML5w2wpUl8Xw7kvnoSwWwTeeEHQaC5RK3/fqCZzsH8M/vGY5vvOO83H10iZ8+qalGJ5IeutbUfjbkYlECt9+5gBuWTkd//Gmc/Ctt52H779rDbqGJvDp3231LxkuhAJ25GT/KB7d2Yb3XT4f02rL8emblgEA7vIi+rjlZtuRsXgS//Sn7WisLsNTn74GN62cjg9fuRD9o3G8eMCnPLkY0kGTd/Z4aDyBP330cmz74k14+R+vx+Lmavzf2oPoH/VpByiEtF7k2/7h8QQ2H+vFLatmYH5jFR742OW4eEED/t99O8SD3XS5aP49f2DbCexpG8Snb1qKslgU77x4Ll450oNXc/esoEgHaPnr+I3H9+LxXW34p9eehQc+dgU+deNSvP+yBXhqTweO9/gkDQqhANG55XgfXjncg49ftxhfeePZePJTV+PBT1yBWCSCO+/eKKb/DB6E8e6TA9h6vA9vu3AuplaX4atvOhubj/Xhxm+uRcdAgXYYPxQhjH+x/hhqy2N40/mzcdWSRqycWYvvrT0odl2TckiIgGPVPxrHn15txZvOn4XmmnJYloWbVk7H3928DE/saseTuztyZIQbs/9/zx5CfWUJ3nHxXADAvKlV+O+3n4c9bQP4j0f35L+hxCnXE2CH79/aioOdw/jsLcsws54CvdedMwPnz63H97yMdAjHamQigWf3duKWVdNRX0mbRSwawSeuX4KUDTy6I8dpCNmD9vD2kzjUOYx/uGU5SqL0fd95yVyUl0Twmw0ewefKO4CzbgMaFnDLOto9jC8/vBvXLmvCTSumAQCuXNKEFTNqvZ2hED1oY/EkPv3brThrRi2+8ZbV6TLDd14yDyMTSfzp1ZweqpCB7iuHe9AxOI73XjY//btbVk3H+y+fj5+/fBTbW3OC3YQTaAtOcXxsZzvqK0vwnkvnwbIsVJbG8JmblmHr8T48uy/nWQs5Hvv7aw+hvCSCr7zxnHTZy51XL0J1WQy/3pDLSIYbEvL8/k68cKALf3PDUjTVkG2IRSP4iwtmY0/bIPa05TDkIQO07689hJUza/Gui+fRV7YsfOrGpSgvieL/nvV4tkP0sv70xSPY2tKPL92+Kl3Se8NZ0zCrvgI/efFI/htCDBva1tKHR3e24a+uXozz505J//5158zAnrbBfKchy47wy/v20/tRV1GC15+bKVdaMq0Gbzh3Ju7d1JKfIVx5hyMr20F96WA3trb04xPXL8E0p8S6ojSKv75uMba39nuTRsXgQ/TEkyk8sO0kblgxLavE+tplzVjYVIWfvXQU3ChA9BzoGMShrmFctyxThv+hKxbi1nNm4KuP7sF+EfbbJxOfSKbwvbUHsXp2Ha5b3gwAaK4px51XLfImVoKggB25d1MLVs2qxUeuXoSYs48sn16LFTNq8UjunhUEBXrQtrf2YSyewu3nzYTlvO6mldPx+dtWYPfJATwkElgXOPbn/ldPwLaBt6yhEsNZ9RV4x0Vz8bN1R/HELg9iRUSug28+sQ87Twzg3+9YheoyWuMrlzaipiyGP2wWzCL4jNkfiyfx1O4O3HHeLKyYWQvLsjC9rhxfun0VWnpH8F9eFRJFZfkPNtpwpAeJlI3LF08FQHb9629ZDdsGvnDfDjHy5T33AdXTgGkr8/704xePYFFTFW5zSijfeck8NFSV4muP7QlH9ORcW1v/GO55+SjeeuEcfPiqhWmdfOP5VEoppP8FqofWHaRKgttWZ2ztvKlV+MfXLMeR7hHsPimYRQY8iZ7fbDiO0mgEd5xH1/O6c2bi7g9chLb+MXzzyf38MnxaV2zbxrt/tB73bz2BN54/GxWlUViWhb+6ZhEOdQ7jmT0dHh9WDJMxQBPA/VtPYCyewtsvmpv1+w9cvgBNNWV4aFuOQxwig7avfRBP7m7Hey+dn1Unfe2yZtxx7iz8flNLfvqVjdrndKw6Bsfwxft3YfXsOrxm1Yz07y3Lwu3nzcKR7hEc7hrOflOI3pFHtrdhNJ7Ea12yAGDZtBosaa7Gg9tyHvaQpUmP72pHU00ZbjhrWvp3teUluPXsmfjTllacyGW23vJT4K33cMsB6EFP2cBX33ROVn/P61bPwOZjfdie63yFmOL4yuEe9I7E8dlblmX1JayeXYeVM2vxi5dzGoZDjsd+Ylc7ymIRXLUk43xZloX3X0aB7M7c0pu4s64CJY4HOgbx2M423HDWtLQzBAC3nzcL1WUxPLFLXoB2sn8Uf3q1FW+9YA4aqjKfU10Ww1VLG/HU7o7sjF3I8dg/efEIZtSV412XZNuR1549A5YFPL4zxyEKMX1tT9sA9rQN4q0XzsnSx6nVZXjT+bPxwLYT+Y3ejLHlnBqWStm4Z/1RXLSgAa89O/NsRyMW3nvZPKw/3JNfnhWC6Pn9phaUl0TwwSuziZRrHWf92dzG6xB9bjta+/HM3k58xAnas+Qta8bQeAI7cq/tdd8E3v4b4Lx3Zf36wW0nUVUaxe3nZfeJ3LZ6JvV0bPIgjYohq3w5c5+3Hu9Dz/AEbjsn29ZGIhbevGY2Xj3ex88QF5ji+LuNLYhGrKz7H4lY+Lc3rEJZLCKWRYt7lzg+sO0EjvWM4GPXLUk7jABw51ULUVMWw49eOMwvK8uxylxnx8AYtrf249az83uJXnv2dGw+1pe/jxSFP9Gz/jCVcV84vyHr9687ewbmNlTil+sFAusCvax/evUEzp1Tn9Vv+8+vOwvLp9fgi/fv9K7YCYoceY/vasc1S5tw08rp6d+VxaJ420Vz8OC2EziS62sEQbpUOtseP7evE6PxZJZfAwCXLJyKKxY3Yp1ISXHajuTb/qf3dKA0FsEF8zL3bU5DJf72xiV4cncHHhcJdudcCHxmHzD/iqxf72jtx9bjfXjHxfPStr26LIZPXLcYLx7oFgzive3wc/s6EU/aeN9l2bZ2TkMlzp5Vh4e2Fxlg54UC05BfOdyDpdOqs/ZjALhkEQW+G73aHIIix46MxZP4w+YW3LxqOqa45F21tAnvuGgufrvxOH8Js48/sqN1AM/v78LZs+rwkasXpX9/y8rpmFpV6l1lVQwBXJAzIkCzLOs2y7Luik9MQMSxum9LK5ZOq8bZs7IbImPRCC5e0ID1h3uyHeIQPWjfX3sIFSXRrGwFw5vXzMbgeCL/YY+JZdAe2nYS/aNxfO0tqxHNGRpwzVLH2dmbmx0Uc6wSyRT+9+n9OGtGLS5ZODX7Iy0L153VjM3HejE87pqyFCKIGU8k8dzeTly3rDlvIMInb1gCGza+LsKieSCZsvGHza24emlTmhlneNcl89BYXYovP5zT9xOi7OqFA10odXTPDcuy8MbzKRtzot/lfIUYa2vbNp7c3Y7LFzeiojT7vbOnVKC6LJbParEMmsCQkM/9cQcqS6P41I1Ls35fEo3g8sVTsXZvR/azFqIH7efrjiJlAx+6cmHe365fPg0dg+PYccIVWIcYsz8WT2LdwW7ctGIaymLZ6zi1ugxLm2uw8Whv9pvSzDd/gPbHza15DjPDuy6Zh4lEKp9YEsygrTvUjaPdI3j7RfmN/m+9gDLWv8h1LAXtSCpl47Gd7bh6aVNewLSwsQrzplbi2Vw2MsQZSQ9vP4loxPK8NmbHXjqYU55lWcCyW4CK+vSvkikbT+xqw7XLm/OGPRBpNAN/3NzKX3rlc6+2HOsDAFyQ4+gDSBMtL+Z+76KyvImeZMrG7ze34PrlzXnDlxqqSvGm82fj/q0nMDTOOUEvPR4727H64fOHsXx6Da53AnKG6rIY3nrhHDy0/SR/L5qPY/W8Mxn0qqX5w2DecO4sWBbwq1c4e38KlEpvONyDRU1VmJoz6CYSsfC2i+bg5UM9/GVlPtNg97YNYvfJgXT2gKEsFsUXbluJ1r5R/NarzaEYmBzXOrb2jeJw1zCucJF8DB++aiGiESvfRgSB5U0Yv3SwG5WlUVy8MF//z587Bfvah8SftZx7Np5I4r5XT+DmldPz9sj3X76A+sPWh+gPy8F/PbEPNWUxvOn87Pv27kvnY+XMWnz1kT3+U7j9wK4tJ/v28qFuTK0qxdJp+Xv5a86ejq3H+9DSy6mPPsf+JFM2Nh3tzSMnAMrszqwrx4bcPZIHOYTxozvaMDCWwNsvzLftbzx/NpIpG8/k+r/F4DNs6MHtJxCLWPj5By/C9LqMjYxFI7ht9Uw8sbsdD+UmKIpikmTQbNt+wLbtO0tKS7hLHNv6x7DxaC9uPXtmFlvHcNGCBpzsH0NLr4tFEyxNOtk/ivtebcXbLpqTxyAA5BBMrSrNT4eyDBqns/Pcvk4saKzynFgzd2olFjZV4Zm9Pmw0p6ytLX040j2Cj1y90HOC3JWLmxBP2lh/2MVsCQ63sG0bf3XPZgyOJ7JS5QxzGipxw1nT8MrhkCN+HTy/vxNtA2N4y5r8aXW15SV458WURRhw94aFGBLy3L5OnD+v3nMS1flz6wEA29xlPkWa+wth87E+tPSOejr6kYiF5dNrPAK0wlOT/NAxMIYNR3rwnkvnp8tt3bh2WTNO9I9hX7vL+YpEM9fHuY5P7+nAxQsaMKehMu9v1y5vRsQCnnSTISGGhGw80ovReNJ3Euua+VOw5Whvdi26oB0ZTyTxu00tuPGsafkTDQEsnVaNxurS/JK6UpaJ58v8/89T+9FcU5bHVgNAXWUJrl8+DY/tbMu5NrFe1q0tfWgbGMMtq6bn/c2yLFy7rBkvHuzKrjIIkUF7bGcbLlnYkC7JdqOppgxLmqux/lBxO7LrxAC6hiZw44ppnn//4JULMDyRxC95HTmfAG3zsV7Mbaj0vP8rZtSivrIkHXwEhk+J4+6TdG1eNgKg7Pd4IpX9LPHAFaD1j8Sx88QAXnfODM995C+vXoSKkqh3K0Ah+ARoLxzoQmN1Kc6aXpv3ljkNlbh++TT8cv0xPofYJxOfKuCgAkiXc27kHU3vU9Hzxy1E4tx6Tv59u3TRVJwzuw735FZjBEGaMM7IYz1mrATQjeaacly2qBFP7Grnl+VD9Gxt6cOqmXXp1gY31syjsugtxzidfZ/95fl9XegfjePNHvt/STSCG1dMw8uHusON+Hew++QAnt7TgY9euzjPJkUjFv72hqVo6R3Nr0YqhrTOZ9bftm28fKgbFy9s8PR9WSVU0WOgcuGTid/XPoih8QQumD/F403ka68/1F34aKZCyCGMf73hGOY2VOYlDACa4txcU8Zf5utjR9bu7cQlC6d67iMfvGIB5k+txMd/tZnvyJVJ2YPGmUFjvUq3npPvEACZUoRN7sg+wLkjXnhkexsSKRvv9Ro5D3KIL1vcmH+eEetBSwQvWRlPJLHuUDeuWuIxJtrBNUub8fKh7uwyB6YUnM7wxiO0Ppct8pZ3wfwpKItF8OIBV4Am6BAf6xnB03s68MkbluAKn+tbPr0GLb2j/KyuB+7d1IIplSW4/ixv5+viBQ2wbWCzl44AXMHn3rZB7GkbxE0rvPXxrBm1iEWsbOc7RObnvldbURqL4OaV3te2fEYN9pwczDaatqMvnBm0x3e1w7aBm1d6X9vVTn9LXlaXMbYcjnjn4Dj2tA16j0kHMf9r5k3J6S8VH7P/3P5OlEYjnpsBAFwwbwoGxxPZk6oEz0F7Zk8HeoYn8PaL53r+3bIsrJpVhx25vYNpoif4te1rH8T6wz2486qFvmPAb1k1HV1DE9nlKYJB9aM72hCLWLhuubc+XrOsCWPxVLpUjGSITfc80DGEg53DvvoIEBu/taWvqGPJJpBetMDb+V45sw7nzqnP78MthgIZtPMcsibvLRELVy9twtN7Ogqf55aLrJLzjB1h5z16ZSsAYM3cKZhRVy42mATIYr43O071+fO8nbimmjK885K5eHJ3RzYhVgw+B1VvPd6HNfOm+B5Lccd5s9A9PMHZP+idQTvQOYSBsUQ6gMjFkuYaVJVG09nRwPCYBjuRSOHeTcdx3fJmzyAeAN5x0Vzs7xjK7zEuhnRPfEZfNh7pQX1lCZY2e5N2N62chiPdI9jTxtmr6NGDFk+msOvEAM7xGQG/ek49ymIRPJU7O6AYfAakbTzai5KolVfRwnDd8mZMJFJ46YBAWWUOWKCbm/V0y5o3tRJ/4C2Z88igdQ9P4ET/WFafrxvzG6tw9qw6/Pzlo3xTYX2Id9Y7eu4cb3nXLGtG19AEvz4yuM7oO9w1jJcP9eS1AKS/omMj1/EGhB4ZtGFnX/d7ruc0VOKH77kQKRu4dyPP0KHJFqDZ4HI+uobG8b21B/GaVdOx2MewLGmuRlksku3sCDLfT+/pwOLmao/zlzK4fNFUdAyOZ09hY45VPHj0vaN1AGPxFC71CZgA4NrlTZhIpLDukItp9WnKLYZNR3sxf2plejhCLspLovnZGMFx36zR9HUezCADyxqKj24l0CGYnbhl1QzfsyzOnVuPaMTyDuIBLp3845ZWxCJW1sACN8pLolg+owbbWvpcny9W4jgwFscfNrfilpXTUeNzltG5c5zAosNjHTl70B7YegILG6s8yykAYEZdBZZPr8GzuVnd9PTB4I44K0u7widAA4Drz5qGXScH0MbKRUP08q3d24kLF0xBVZn3d2SO+0sH3RlksV7WJ3d3oK6iBJcv8g4GAWDVzDrs7xjKzjSl7UjwkhXGQl+XU27mBgusN3gFaJyZ8Ud3tuGyxY2oq/Bek0sWTkV5SSS7ykDQjjy2k5hhv6wXQM9230gcR/yOQHGw6WgvZtVXYEad/xEe1y5rxrbWfnTxHE7scW1dQ+NoGxjLK8l34/WrZ6JvJI7n93MclOqj/+sP92De1Erfa4tELFy2qBGbjvaKDTBwZdA2Hu1BNGLh3Dn1vi+/fvk0JFM2XuKZDOjhWA2NJ3Coa7jgmXGXLZoKy4L/Iele8BkSwvYHr7JUgDIkq+fU8wdoHr2sT+1uR9fQBN51yTzft920cjpVEfAGMiwQdNmtzcf6cN6cet9A95aV01FVGsV/8w5m8CB69rYNYjyRwjk+OlJVFsPNK6fjvldb+capp0mJ7Gt49XgvVsyo9SWo1sybgljEwibejJ0HXjrYjYWNVVllctlf0cJNK6Zh3cGu/GnOheDhFxx0fEzPs04dfObmZTjaPYJf8WT+fTLxW1v6UFsew/zcc1wdXLW0CZZFfrIQXKTSbzYcR9Tpx/XDBfOnoG8kjkM8vZEe57Jub+1HykZBmzV3aiUuXtDAl/n8c8+gsUbTv752se9rYtEIzppRm92rUuRgSC8Mjyew/nB3QUcHyKTnswYzxPgzaIyt8GNZAcoOlkQtvHLYZVjSjlXwdWSlG36sJ8PSaTXZ5WuCpUnrDnWjsboMi5r8A4TlTsnKXl7GLge7Tw5gaDyBS3zYYwCoLI1h5czabAdVkNV/8UAXLpzf4Mt6AsA5s+uxvaU/w/wUaO4vhN9uOI6h8QTuvCq/R4uBXffLBz3YQY4pji29I1h/uAd3nDfLs5yC4aqlTdh4tCeb+Y/xB2gvHuhCbXkMqwo4sZc5AU76vgmO2T/ZP4q97YO42u+geQCzp1BJcZbDXGD6mh9SKRvP7u3A1Uubsoas5GLVrDokU3Y2Yy1A9Gxt6UdNeQzzp/rf69ryEsxpqMButyyBAK19YBxHu0dwTYF1LC+J4rJFjdlZVkE78viudqyeXVcwqGKb7qvHCztfm48Vt3/XLm+CbdO+ExgeOs9s2lkz8svyGK5c0oSa8hhfCY+HY5VK2dhwpMc3e8Bw7tx6dA9PZLcCBIWL6Nl6vB/Lp9cUPGj4vLn1qCmL5RM5heAu63WeO0YWrpzpv45TqkqxamYdnuMJdH0yaBuP9GJqVamvgwpQxnaXs+cEhseQkC3H+1AaixQkcRqqSnH+3Cl4yuuYjEJg57I6+tI/EseBjiHfDAJAfbgfvmohHt3Z5n/eqxc8Wi62OdnM1QUOUX7LBbMxMJbg03+PHrRkysa2lv6Cznd5SRRLp9XkVyxwIpWy8crhnvTADD/ccNY0xJN2djVSMaT9ggyBwgKTRU3+tv3qpTSpmmswiU/LxZZjfVg9p953/2+oKsV5c+rzK2gE8MKBTly8oCFvZoAbTF838wTWbp/f0U3ma/tldBkuX9yIve2D3mcre2IyBmgcjtWGI72oKY9hRYGNDgBWzarFztaBjEMskEHb1tKPeNLGpT4lUAysX+aYu1F4+ir6We3P9OZia0sfpteW/3/2/jTIdi07DwO/DeCMOWfem3e+bx5rrnoszmSVSpSKLpYGymaQZrtb4lAm1bLCUrdkKaSWQ3bbdHdHu8OyBpoOUrQUIjUFQ2LRDMuUGCRLI6tk1vhevXrzu3PenM98DoDdPzY2gIMD4AAHe+28eWp/ERX33ay8ufMAGxtrre9b38rdoM2ajecuJw6WBXrQvnznBAe9Mb47R04JiARtvzuK3OUWqHwPJx5+69WH+K6nd3ID/etbLbTrduUE7XczXLeSeOmxbXzx1nGUWCzw2Uauh6/fP8X7b+Q/6B+4voHOyMXbB73ZtUrct3/+ygO8eGU9N4m5vtXGje3WtCuWDKhKfEYpN8liBiXec3UdE4/jzf1YIl+SQeOc41++to/veOrCjDlOHC9eWUe7bsekeYtJRWXAndV/JvE9z1zEv33zIJKLLHKO3DnBfnc8t9Dz3GVRFZ2yP//gj4g/d18svt7tY7z/+kZmZVzihcvr0+z4Agna14Ii2PvmvOg+/tzFaQfaBZ617sjFV24f5ybVgDizmjULX72Tbf/cHbm4dzLE85fzezLfe3UDF1brJROL2T0vr3PeenXHwodubpWbm5TSN/vqgw6O+xN86xP5760PBQHs7y1igR8EcZxzvHLvdO77uGZb+K5nLuC3v/GwOGNnWdG1DP78WvDey2PQAMGw/vt3joqbJWS8l2QSn/fe+rYnd+D5HJ8v0z+dIpV+9X4HT19czS3iACKR/9rd02nzrnmQBaWgYCwlaVnSNYlPBT2MU4qdeUg5R758+xib7RpupvQWS3zHUxdwbbOFf1Rmjl2Ki+NX75ygP/bmFl/ee20dX7t7uvjQdgB3T0RLxnvn7EeR5KCcJX2KxPGNvS6aNQtXcwpUAPD7g/0/4wqchZR5iv2xkAF+KCfRBYTK4Eu3T2Zn5paA73O8vtcNi/RZePLCKjZatenWlHmQe59Z4bn1jQddXFpvzBj/JPFS2YRw+Rg0jjIM2hfePsRLOfpzifdcFQHxLXlAp2i+50G+KD8wZ4M2azYurzenE7SP/Angj/+6mOFVYr0PzAn0AdEs+ZU7J9HBEh6IZYLvB7At0cCfh2cCaVsoO1yg8v3PvnY/aNiddeaJw7IYnr20Njt7qiQ+//Yhrm+1Uk0t4viWx7cwnPhhkLnIMOBv3O9i4nG8/9pm7ve9/7r4/2UlcZFB1b2Ri3//ztHcpAIQyeeXbsWS+J/+V8B//I8KrSPx8t1TbK/Uc1+qQJRYTCXWYYJW7LO9fdDH3ZMhvnNOwcCxLXzo5iZ+N+ifzJtflIff+cY+Lq038FyOVAQQFbvhxMebDxOJRYkE7TdfeQCLYW5icWOrhZrN8MbDmHzjhU8D/+UxsPNU5r+LYzjx8PV7nXC/5eH5K+t4e78X9bMulKCdgrF8ZggQQSUQSZ0XsfL/4rvH8DnwkTmFF9tieHxnJdc1ULruzdvblsXwPc9cxO+89rD44NKUBO3r9zu4uDY/IPjgjU1840GnuHlBisTx383pP5N47rJIZL9YSp43/Yw97I5w0BvPvf+A6EW8lzQUmodEL+s39rrYbNdwaT3/Osp+oH+anD+ZiVkGbb87wlv7vTBIy8JLj2+h7ljlBjunFHpee9DJlJLH8fyVBVoB5BzR4Dq+FRQKn9rNV1Q8vbuKnZV6IdOdENbsOfKl2yd437WN3ETXthh+8MPX8LnXHuKgqKQ4xdjoXwTn7XenuFPG8b5rGzgMeroWhSw4PZnDaAEiRryx1cYbZZxMUxi0Nx528cSF1bnx7yee34XPUVwuPaVEEet+9c4pfD4//pWjVH67jMrgT/8e8J/+TvjXO8cDDCd+GG9mwbIYPnxzc7o1ZR5SBn7fPx3MjQ+BqBWmtAlQ3q+j7CfpQsG46rg/xmt73Uw9eByyn+k1+TJYoHfki7eE61aae2MSN7fb0wkaY8Dj31mYHTzqjfHOQX9uRQsQUqiTwQS3DgNpygI9aL/16kN85OZWqoNNHDNV/QXssX/j5Qe4vN4M5Wl5eP7yGl6931m4qsW5kBx8tMAe+UjgTCTNUhaROMpKZF5vCSD6Ips1C1+SfWgL9E79u7cOMPH4XNYTEC/W+6fDSPO+9Tjw7B8otI7EK/dP8cKVtdyXKiCqWo7FKiVoUo72LRluUXF84LoIYl3PX0ji6Ho+PvfaQ3zvsxfnf7bgxRslaOUZtN98dQ8fvrk1NdclDY5t4fGdldmXeAmFwSv3TuH6PFdKJPHC5TX4HFHv7ALnyFfvnODxnZUZe/0kbm630a7bUVC5wLP2hXcOYbHIFTUPT11cze1TeCeQbD2WI12T+N7nLuK4PyneCJ+aoJ3OZesA4IM3NuBz5LJ/U0jpZf337x7j6kYT17fyP1vNtvC+axtzpaBT+M+/DPzEvwj/+sq9+dJNie8NxsSUkovK93VwTd962MPjOytzn9sb2218oIz0KsW0SVbp82SAgAi+P3Jza7pXdR4SpmWnwwnungzxbIE98nxaQWwe/tBfB/7w3wSuvB8A8O5BD3XHwqW1bLUOIMyLvvXJlLFFuf9oOkEbTjx840EHHyhQNPqupy+AcxRnkcNnLbp/v/HKHl56bHtu3CaLWOUKFNOQ74UnczwKJJ66uDJdfJuHlHPkzf3e3GQQEKqWVq2EeU0KEy/PhXnFvvdcXcfuWqPcYOftJ4ErHwj/+lrQL1+kQPGRx7bw2l63uOyQMfG+jl3P+ydDXMnoGYyjXXfw1MWVEkWlpWPQiiNs2J1zYAIiQAWECxOAhdzX5umY47ix3S4/CyUGGbgXYdAknR4yPyUr34Oxh5fvneJbnph/HS+vN7HWcKINukBg9dqDLt57bX1u1QcQCeFRf7IwXf7mfg8HvTG+ZU7/BSCshHdW6mE1caGg8e1DbK/UcWM7vxrj2BZevLIe9SlmuK/l4ffePYZtsUwHpzjk/i/1QojB8zlevd9JtbJOou5YePLiynRFt2QP2tfunKLuWHg6p0dR4vGdFXg+x93j4UKuol+6fYzToRsGjHl44oJM0BL7v6AbbHfk4mt3TzOdS5N46uJq2Ai+CCRDW4RBk8ZH7xwGe6TkOeL7HL936zhXbithWQzP7K6GL+JFJI6/+9Yhnru8nmmOE8dTF1dw67Cf6WQmz+rHtucHO1Iq/ZW4yU8eEp/N9Xx840G3YIImzAukGcpcpCQWb+/38PQcZjhabxNfvXta3Dly8yZw/aXwr18PJFsvXJm/3uWNJq5uNKP3VhEkpNJvH/TCZ3IevuWxLXzp9knBzzbLxH/t7ikshkL7+1se38LX75foQ5NnfvD5ZCE5y1ExjhtbothRyl2xuQ586EfDv75z0MfN7Xahd/K3PrGDO8eD4r2KiZaL1x504fk8t29Q4v3XBWNROLFInFXDiYdX7p3iO1JGByTxYpDEfL7CoOU3H3ax2nAyjdbieHp3FW8+7C7MxI9cD7cO+7l9/BKObeF91zeKy5dTCsZfun2Ca5utuZ9NjlIRA7RLznoLIPf/0xfn738Z//xemcKS3QivJ+cc906Gua1EcdzcXineg7l8EkegKIX2+beFdeo8yhUANlpCBhExaOWkSSf9Ce6dDPFigUMFEBXi+6fDcg5EMXzp1gkYm8/EAEJ2yBiipKmkPfZX757A83khto4xhmcureLVBSWOrufjrf0entot5h4oGbvS1r4BPl+w/0zi0noTe6eBxKFk0Mg5x798fT9wDZu/h5+9tIbXHgTsYIqkYB6+cucEz+yuzgzeTMMzskCxYLD/1n4PI9cvVBkH5MsnlgyW7EF7+Z5gGOb1XwDJns/yEsfffvUhLJbvFinRrju4stGc7Z0qeI68ev8UnGNuj4LEU7sreOewX85qPYYv3T7GhdVGoergTO9syQTta3dP8bAzyjUIiePp3bXoPC55jgzGHr7w9hG+q0DgBQBPXlyFzyOmLIl3D/tYbzrYaM9P9q5sNLG9Ui/OaiX2/NsH4n7O668ARNP9pz9wFX//d98tNrQ30dzPOcfbB71cU4s4PnRzC2PXL9cbE8Od4wE2WrW5SgyJZ5KmU/Ng1wEwwLIwGHu4dzLMNb+J4yOPic/2cpHPlsLEf/3+KR7fWcl0Aozjw49tweeJWZd5SDDx7wZFkjy36PCfBq0AVXq13z3s47E58l4JOYbk375ZkCFMxCOvPxS/59MFYoBW3cYLV9aKB98J1l8WXook8TXbwocf26w0e1UyWkXe/09dXMXI9XGnaKKbiEfeOejD5/kGIXF86OYmXr57UiwmTWm5+Pq908Lx78ef30UnaMFYBG8f9LCzUi90Hn/gxiYshnJ9aHYtvJ6dkYv+2Cv0jgSEyuKdw15BBnkZE7SCle8vvH2I913bKHRgAuJAeD2s2JarfMuEZF6PisTNnRY4x2KOWBB08jO7q4Wqw+26g5vb7VhfWLnAStpwF2UHpxKLkknMraMBxp5fiBkBEH5faKZREl+5Ixzsih5il9YbuB8maOUYtNf3utjrjAoF+oAITo76E+x3x6VNQjjn+Oqdk0IJPCAKBnXbihiLkghNDQpUxgHg2mYLd44H0SFWYg4a5xxfu3taqMIKRLK0dw57qQzCPPz2a/v44I3NQi8DQMgc39hPShyLMfEvB4xp0RfdYwE7WGo4Zgxfvn2C91/P7/WQWG042FmpR8x/yXPkn7/yAIxFPQjz8OylVex1RkKaUvIc+fzbhxh7fuaMvCQiaWp6MvDOYR+PFQz0GWN4z9X1hSWOsqe26LP0Ix+9id7YKxY4Tp0jNo77E3SG7tzeOonI8fK40Pcn8eB0OLcfLI5nL63ijTIsglMPP+M7YRJT7LNJaWKhoDFlUPWr9zthwXAePnSjpJlAMkE7EM/79a35fTFA0ArwYLFWAM453j3s42bBJP6Z3VVstWv4t0X70BJJ0+t7XdgWK/y8feD6Jr58+6TYZ0vMQZMFmaL7/6OP7+CV+6c47hc000jg1mG/8FrS2KZw8pl4d0plRREGDQDef20TE48XK9ImFD1j18fbB/1CkkMA+I6nd2AxlJP5xnD7aIDrBa/jSsPBC1fWy41IsKNz5EHQc3h5jtGKxGM7bQwnPvaKqLq+WRk06RZVRLoj8fTFVby+1w0Si3K9I2GCVvCAlg/pIjJHzjm+dPukkEZb4tlLaxGrldIom4cv3jrG9a351HV8rTCxKFn5lr1rRapngLD2tRgWljh+PZDlFQlQASG7uX8SrFUyQft80LuWNeg4iecuxfr5Strs3zsZYr87nuuWJ+HYFm7utPHWghLHV+6dwrFY4ft2bbOFkeuLPQKIilXMNSkP7x72cTKYzHVmk7i83kTdtgTzU1Li2B8LJ8CigT4gqrFvzUiliyV3L987xUarVrhady1oXL5zXD5B645cvPGwO9c6OI4b8d7Zkgna774lCmZFenSBKLB4c79bOkH7d28dwLFY5lDpJKR08d2M87hMYAUImds3HnSKDX9NJmj3OrBLPEvvubpe3PEtIU2Sha2iLNOVjSZ21xoVErRRYakQIAY7j1y/+Hsy1jvy9n5xdgQAdtebuLTeCJ0fC4Mx9Mcu3jnsF37/b7RreO7SWvEANWFa9u5hH5fXm4WLz89dXsNhb4yHZebzBTjojdEfe4X3v2UxfOjmVnFpasK07I29Hh7bbmfOJE3i2Utr6AzdYjFA4ll7R0qXC+7/73pG9Lx9rszMvACcczw4HeFywf3/4tV1rDWd4kxk4rPJ3uSi+18Wqd4qMjMscY68td+D53M8U0ByC4ixLe+9tpE+2qcAbh8NcL2AaYfERx7bwhffPS5e6ImdI/eCBK3oO1k+J1lqjGksXYLGCwVWDzsj9MZeoQZJiWtbLfTGHjojt3SC9o37Haw1ncI3MdVqvyBuHw1w2BsXkm5KPHdpLZCheaVdHL/47jE+VKCPSSLqZyofWMkewKLBiW0x7Kw2sHda/sXjB31TRSvVgOhDO+iNhHa6ZIL2yr1TrDWcQkYDQNQA++qDTmpzfx6knGWenXUc1zZb4WFUFq/cO8XTu6toOMXutzQkCBMLp1F4P0qmoGjwbVkM17dbgS68HIMmnanyZg0mcWOrjdOhKyRnJd1gX77XwYtXihcMZIJ297j8ffvK7RNwjlKFnpsLJmiC9Twp1J8jIQe5Pjgdli70vHq/gycurOTO2opjo13DetOJjJRi8HyO20fFGQRAMBauz4sFO4kz8s39Lh7bbhd+llYaDh7bbhdM0Kab+2UQUZRlYkwMmP69BQf27p0OsTvHaCIO6dL2WlHptV0LnzlpmV8msX7hynp5iSMY3tjrgfPiChpAuFR+/u3DYn1oiUJP2YJB2Apwr7xC4l5wtlwrERA/eWEFbx/0orFFeUicI68/7BZucQBi/gFF9kiCrXv3oIe1hoOtguqID97YxGa7Vm6MRoDOyMVg4hUuUNgWw7c+sV2CiZw+69582MOVjSZW5hgySYRKkyJqpAQTL9VZ81wV4/j2J3fwe7eOIlfggvB9jjvHg8LsMSAStN7YKy7zdaIE7b5k0AreN5nsF1J1fbMyaNLsoGj1AED44OydDkv3jry218Ezu6uFA6uLqw20avZCCZps5CwqOQTEw+f5XCQyJeagPTgd4u7JsNRa17Zk0Dgo5fAGiEP28nqzkHRTYnetsVBl8M6xmElSpNdD4vJGE5wHjF3J5PPle6d4oUTwfXGtgdWGg7f3e6VdHKMDs3jAcHWzKe7ZAvj6/U4hUwMJuUdCfX3CNSkPv/vWITbbtcIyWEAkTbePkvtx/n2IBlRuFl5rih2X6xU4R1zPL6XjB6IkpnCfQgxfDkwsyjBoN7fbuHs8DBwxiydot48GOB26hWWpQFSxvHcyLP2svbbXDZ15i+JG0lk3wL2TASYeLxUQlwsap/f9naNB+HwUxYtXiyYW070jkpma5+AYx4dubuHtgz6Ois5MCuD7HHudES5vFJc4yutY2CLerofvt3snQ7RqNjZaxd8lL15Zx+t73QLM53QP2t1AYlzmvn38+V1MPDHPcS7Cc0Rcu1tHfVyfYzQVh3zHLdKHJuXTecPek3ji4gqGEx/3TgsUjsJzhMH3Od496BdyOZSYMXjLXWt6Dto7gXSz6DvZthi+6+kL+NdvlGfQZO/6bgmJ77c+sYO39nvYLxLfJM7I+6fDQtbwEu26g921Bt4uwvzEr5dl4/W9LhgrLqcERNI08ThevleOsd7vjjB2/VIJmjQKKSxzjEkcZdG66H27sdVCs2YVLIYsW4LGUSjrjOZNFN8wMkF7cDoqXfm+dTgoLBMBRCVyxmq/IL747jEajlVYTgEAF4J5OvvdUanASrojlWEQ5FDERQKr1/e6hdkziYtrDex1yjMIL5fsmwIQ9k88OB2WYtB8PxjQWiJAZYwJt89kYlFABigHK5YJTq5utHDQG5c2rjnuj3HvZFjYIASIAplwMGyJBO3zbx/ipce2CzmKSVxeb4o9UtJm/4u3hbz3wpx5VHFIdvz2Ub8UE//2gTBaKcN6Nms2Lq41Fkqsvxy4bs2btRXHpY0mPJ+LgaYlbPal3Kmo+QkgDDDqtiV6PkswaIOxh3cP+6WquYBIPm+lDCqWjlxFTRIAEagwtmCCdjwoxVYAYoj4Owf9+WxMotDzoDPEZrtWWCoHxPrQirpUBjjojeH6vJTEca1Zw9WN5vQw9jzEAqu7xwNc3WwWDr4BwaC5foE+nASD9uBU9qkU/2wfeUzMQ/v3RWYmxc6Rkevh/ukQN0ok1dsrdVxeb5a+ZwDCnusyn00WxgtJ5uU5YtnY740w9vxSicXuWgNrDScyFCqyVnD/7pZkYgBR0Lp3MixdoHgQqHzK7H/ZolConzURa+13R7iwWny8CyBMZ94uJHGc7om/ezzA7lqj1DnynkBN8XJJVvf2cfliyPWtFnbXGsWNQuxa+Bnvnw5xYbVeWNHg2Bbee3UjGpGUh29WBu2t/S4ajoUrJR6GKEEbAk7w72rzD8Gx6+PuySAMzIpiUav9f/vmAT58cwu1Ag52EjvBg3rQLRdYvXJPDJYtEzS26ja22jURNJZIYjjneGOBBG13rbFQD9qXbh3DsVipzza1R0p8tncO++iPvVJrAaIac+uwX9okRDC65RgE+VIsK3N8ObTOLv7Z1ptCUhZKHGOBVR6O+2O8fdDHhx/bLPU7XloXe8Tj5SSOrz3olGJYAYSB063DQakE7WslDUIkrm62wgp+GXzpdrFB93FcCPrHRH9pcTfYr945hW2xUkUlxljQ81mu0PPGwy44x0IM2u3DwYwsSxbRypzvctBs2QRtOPGw3x2XT9CuSIZkDosWL+5YNvZOR3NnWyXx/usbsFj5eVAyiSkjcQSECqC4xDEq9IgErdx1lPtz/n2bPkfunwzhWAwXVooXO2q2hWcvrYaz4XIRkzge9SbgvBwTAwDf/cwFfG4Ba/N7J0PUbIadgr2jgJh1CYg4bC5iBWMppyzaKgKIc+Kp3dVyEscADzuj0vtRvg/KOkfLInKZBE32l371dpEEbToe2e+OSxUWAeDxnXZBBm2aib9/OixsoiFxdaOJjVYtNMYqCmmsd22z+HnMmBg3VNg10o5LHAelihOAcI786p2ThccIxHHOErRiTX5vPhTzT8pU2XfXJDsyAq5/C/BHfhZ47Dvm/jvhRlfuBQ6IrL6si+Nxf4xX7p8WNpqQkI35B71RlLUXCHreeNjF9a1WqcoIIOQQQuJY/N/dOxmiN/ZK6c8B8cLf746LN4AG+NLtYzx/Za3UZ0tlWQtA9oeUDb5vbAtpHp8KCPJ/X9/neO1BtzSDcHUzJk0tgTLDZ+O4uNaIpBtOsQRNVhLL9E0BwgDA56KKHyH/bPB94V72RMH+HImNdg1rTUewMc0gAWrN7+F8+d4p6rZVSiYCANc3W6UljgfdEW4fDUpJNwGEbJs4RyJp0jx87e5JMHy93Dlyeb2ZYOLnryXlcEUdxSRubLcx9mbdt9457MOxWOlg/+kFgsY7C1SHgehcmRvsJBi0vc6odKC/0nDw7KW14jOTAsgAtex6zwTXsdD5Hgus7hwPSye6V4v2dCaY+PunQ+yuNUrFG4BgPl+5dzrfgTCm6JHjFMqoIwDgEy/s4nTo4gtvl+sfvB/MgCrz2S6tixaOvOHvIWItF1JOWfZZe2Z3tZzEkQnnwaP+pLD5mYRU3Hx9XjEkAcmg7ZZYb61Zw5MXVvDlQgxaFI+4no+jfvkE7bGdFex3R6WZ+PsnQ1wu+VwzxvDClbVi0uwY9juSiSy33ocf28S7h30cFJGLxuag3TsZFu4/k/jAjU2MXL+ApHgZGbSCEscyBiGAePGsNZyAHbGAD/5IoaBRVljL9CgAImnqjtxSWfbvvnUIzoFvf6pcgrazIiWOY5TpQXvzYa90wAiIfqayEkdZJS3TWwSIQD+UXRWE73N8+VY5J0wA2G7XUbPFC7moMx8gAqcyzmwSN7ZaGEw8HPRjssM51/TO8QCDiVeaQbi2cIJ2igur9dIvuq12HUe9YHbTe/8Y8O1/au6/kYOVy5hNAPHiS2yPzNn/e50RhhMfN0tIlyVubAXs+OPfBXzmt4Dd5+f+mzf2enj8QnH3Mond9UYxS98Y5Au/TP8ZgFAyI6TSxc+Rr94tJ++VuLzRLG0S8o0HXdTs4jbdElfDnrfp/f8gCFDtksG3NEooHHwj6iUsm1hckdXoeWxMQpr0sDMq/dwCQvL+pVvHpWzb9zvi2SsToAKCCR25fiSHzkPAxI9cD/vdUam+KUCMktho1QqcgbMSx0slq+yASKwPeuP5CpCrHwRufjuwcWPhBE060RaSVMZw72RQitECRPD9xIWVco6AzA4T47LrPb27iodyJEcewmeNhcXBsvt/d62JC6v10rMAH5wOsdpwCpt2SLzv2ga+UpJBO+yNwTlwoeRnk9LUuUYh8RjEEjL0skkMINjIb9wvN/7hqD+GxYQKpwyeC5jPN4rIbmNmQw9Oh6UZNGkW9Ma8osE3o8Rx4vlB5bt8YCWCnXISr0UTtM3AOajQgNEAMol577VywU6rbmOlbguJY8EeNN/neHO/G8oVyuDqZqu0SchrC1a+5Qu/jMzxncM+OiO3dIJmWQy7a0HQWCL5fPneKZ6+WJ5BkKzsrXhFd841XZRBuBQ0798vKXF8JTA/KYvNdh1Hcp7Mkx8DvvvPzv03X759jMd32qWDk5D57MQTtPxzJLIgL/dcA+IcEcUQBlz9UKF/IwYGlz+zLq410B256I8LuMEFkExL2UQ3ZNDkZwPmJ7qnQzzsjEr1n0lc2RCFHl6CrXvtQQdPXlgtJQEHokAteY7s98alAx2gxDycWGB1d0EGTVaj5waNsXvFmYW9TjlXRYkXr27gZDCJZkIWgDRy2ikhAwQiZ7hCA6uDAbPyDLuyWf6zyRmNuUgyaAtU2YFILvfKvEr7xeeAH/vfgMbqwgnaWrOGi2uNgvbfEe6flJevAcK2vZSLacCgNRyr8CgOicgoZM51jL2z5XN+sSTLBIj7VlbiKOSU5dd63/VN3D8dzo9LY8+2fNYuluxBk06OckRFkbV6E47O0F1oj1wPCtCnw+LvrqP+GJvtemm2WhrPZM26nMLqLtDexnDi4ag/KV3okbnAu3OftWVM0Oa8pG8d9uH6HE8skFhcWm+WDlDffCj63co+fPKAPZ5X9Ynh1mEfF1brhe2j49hZbeCwN0LRHrR7p0MMJz6e2i0fNF7ZaOF06KJf/LnDq/c7uLDaKGVaAESBVZnE+u3QRKb8Z7u03ijdg1bWIERCBmr3pxKL/CQvZCJL9qA1HBtrDSchA8zHcCKsa4vOJItjq10rtfcB8dnK9oQBsQQtLm+Yc45E5hDl98h2PPksAC9wL1ukqCQDjP1O8fXe3u/h4lqjdBVyvemgblvTPWhzzpGXF5T3AqJ3duz6GHjFkkEA+MZep7S8F4h6o5KOsAfdUdh7VwaSeZ0bEMfOkUgGVT7Yf3p3tVTl+3joY+LxhYJGqXIoZMwQ4KA7xkrdRqterkhVysnx6d8PvPDp8DoukjSFxcU8JNxgy853k3jqYkHGIoZFEzQAeGJnpZj9dwx7CyYWT15Ywa3DPsbuHIVQrNBz92SIKxvljF2AEq6psUKPTNDKSm6BYPD3/U6ptoqj/rh04glEKoevzpM5xs4ROV90EYkjUMAiPhaDPOiI/VjGnVViN+6cXhBHvUnhsQhxXN1soe5YxYoG/8H/B/iPfrG0xb5Eq25jd60RztnLRIFtfv4StDmf6q0KwbfoiynnzvOvXz/AS49vlc7oN9viYT0ZFF/v1lG/lCVyHDurdRF8FwysZBKzSNAoTUmOBsUdAb/xoIPnLi8eWJWReckXYlkZFCCC/TI9aN2Ri3snw4WCRvkS7oxiL7k5zN03HnRKOzhKbK+WSyy+dvcErs9LuXxKbK2UW2vi+cKCeYHn+sJqHYzJAFg+p/MZNNF7VD7w2lqpl3L5uncywNjzF9qPIfPTLf6Se+egjycWWIsxJs6RbvFCjzyPy8p7AWCzJc6Rzlju//x71h+7uHU4KC3vBcSZxRhmZioedMfheVYGj4UDS+clTXFp0kgkwSVlroAoih31J/kurLF7tR8URxZJLEqNEQhw0BstxERKJ8dCa334PwH+wP8zlK+VDVAB4Npms8Dg92gfupyjO3IXCvQvrjXQrtvFgsYAVRK0x4qaQAQYjD30x95C+/+JiyvweYFZrzLYtyzsLSAnA8SYiLpjzZevxVwcZbywiMT3hSvrGLl+qft22JuEMV8ZiLmYkbw/E/EErbPY/l9tOAHLOi9Bi/b/Xmfxc+RS3PehIA57Y2wtcB1ti+HxnXYxiWNzA2hvh8ZGi3y2x3bahkFLQ5igLZBYXFhtFJs5EeD+yRCvPujge565WHqtzYUYtPJukRI7K41SPWjyJXW9hFtOtFa5BM33+UKzi4BsaVIe3j7oY6Vul7ahBYIE7aQ4gyadOhdhYuQ8uJNh7DrO2f+vL3gdAdEXVqaXLxzDUGJOnsRmu4aR6xceVPluwIwv0hPp2BZ2Vup4GLfan3Mdbx8JFzinpFQOEP2lvbFXeGSBlJQUHRgch3wJPyzDoB30Cg9MT2JntV5qXMc7B32sNpxSLnASG1IGPgwq1fNkqcF1XGSP1GwL2+36FIPGOcdBb1Sa1QcE+21bbH6AGiu4HPTGC60FRFXeXAVIPEHrCnnDIgHqhdU6Nlq1YsYMAQ6644X2ACCcHAvPQgOiBG2t/HrXtlroDF2cDnPey7F9OPbE3txeIGhkTPRKlpEdygStzKxQiccvrOBhZ4RekeHYCMyAgIXu2xOhk+O8YD86R476k9ISWEAE3ze2WvMD4tg7W8YLi6y3iFHIUW+M7ZXy92yl4eDJCyvzDYCmGDS5/8t/tsd32qUkjg96FRK0uCt2QRz1x9ha8Bx58sJqMWfRADIWWoT5vLm9UqA48QglaIyxJxljP88Y+8exr73AGPtZxtg/Zoz9dMGflPv/vvagi+2V+kLVip3VOvpjr3A/hxxY+F3PXCi9luxBK5qgeT7H3eMBbpTsT5DYWQkq3wXtse8eD8BY1JtUBtslE7Q7xwP0x17YXFkGrbqQ5pXqQTvo4bGdldJSCkAcKp2Ri964mLnLoj2KALBSt2Ex4DTOoM2ROL5z0F+olwmQe6R4oP+l2ye4utEMpQplIKtgRVm0N4PKV1mXT4n1Vi3QuheTy8k5SotAfraiz7aUlCzUNxsyaMX2f3/sYq8zwuMLrAWIgGaaic/fjzIZXORZk0Wsqf2fg7CotOAZeXGtMcWgnQ5dTDy+UIBasy1c22zNZywSzf2LBANAYrB3FmJ7/jgo+iwiF2KMCee8EhLH/e5iiS5Q0skRgkGw2GLBtzyn8+dBRXt55IrfaXOB6wgAT1xoF5s9FeB0MMFa0yltWgMgfC8UTQjlu2CR6ygZ+rkBcchq2TjuT8KiTFncyJhjOIVYcfphV8wAXIStfnp3FRYDvlGwD41zjsMqicXF1fmJbiyeu386RDvwHSiLx4rIYONS6aCPZRFWS7LOD0q0pxz1xwsVQwDB6r572Idb0JjvMIhNFlJQ7LRx/3Q4J5dQlKAxxn6BMbbHGPtq4uufZIy9yhh7nTH2F/J+Buf8Tc75jye+9grn/KcA/BCA75z7i3A+N+t89UFnoUAfiKrRRYPUL98+QbtuL9QXI+U7xwVNQu6dDOD6fGEGbbNdE2tZxSrf946HuLDaKDygLw55oB8Miz0I0o70mQXv28X1crPQ3jnoL8wgSK31g4Lr3aqQoDHGsNas4XSKQcu+b6fDCU4Gk4UD1O2SssPXHnTw/AIGIUAUGBZdTzoiLSJxBETFuTN0Y9cv/xxZZI6ShPxsRdnIt/d7aDhW6ZlUgLhnjBVnkGV1dGEGTSbxLJIL5a/XWzgZlEW2KEGbf8+A8jbdEhfXGlOJ7kEFqRwgArmvzzPuiCVoVVgm6SJ4/zRHnhc7O6RsdBEmBghMIEr0M4m5TIt9tmcvCyfHonNDH3ZFortIEvNckTlXUwya+HOjtdhne2xnBbeOigeNJ4PJQvJGsVZB2W2AkEFY4L5ttGvYatfmFyiCPcmZhZPBeOHPFjrn5iE2ruNk4C6UVACiX/viWqOwSU5/7GHs+osnFhdW8M5hf2ZG4xRiSdPdYNj9IkWxJy6sYK8zyk8spgo94ndab5b3RWjXHaw1nRlZeRY45zjqTbC5ABMJCFXdxOOFx1sdBnnAIsWXDwSqon/3Zo5rqkIG7RcBfHL6ZzMbwN8A8P0AXgTwI4yxFxlj72OM/Vrif7vZvyP7QwD+VwC/XuxXyf5QYgZUp9RA1Dhkw33RavSXbx/jPVfXF3oRrDUdMFbcxVFuqhsL9qCtt2oYuz4mfkEG4WTxAFUe6If9Ygzaqws6D0rsrhV33/R8jltH/YX6fYAosS5639497GO96SxcGVxrOtMMQg7zeftQMgiL7ZHtFdGnWMT21ve5GGdRMfguyjLdOuxjq10rbWwhsd50cDqYFHIfdD0f90/Lz1GSkJXS44LJp3RwLNvHCsTlm8XOLFmJXZRlFUzkpJDEceL5uH00WMgJE4ipDGSBYs4L7e7xAHXHWjjJubjWwMNY0CUNcxapoAJiXt/rD7v5c4XiCVpvsX43IC5xzNkHsbOjOxLP+NoCgRUgEouicjnf5zjsjRZOdGXB9dWCMsf97uJr3dxuo1Wz8fXckQUxBi1IrBZl0B7bbmPi8XzmM4YqCZoslBRNrOX+LzOAOw4h3yxmOOH6wMTjIWteFje2hTFZofcyY+gOJ1gtaXkfx+5as3Dfu0x0F2XQHt9Zwdj1cfckJ7GYcoMdLhy7FXJyZLFEd+hiteEs1AoAyJ7+Eomut3iiK4u7RXsHD/tjrDWchUiKb3tyGyt1G7/xyoOc71KUoHHOfwdAMhX8KIDXA2ZsDODvA/jDnPOvcM5/IPG/vZyf/auc8+8H8KOpH4GxzzDGvsAY+8Jkkv/w3TkeoDcuPwNKQr4cizBorufj5XuneN+1zYXWsiyG9WYNJwWDOFkdurG92IO3Hhx8IRlTROK1QMMuIKR5dcfCYUGJ4zcedHBts7VwNfdiicPy7vEAE48vHDTKOSa9UfHeqZsLrgWIeR+dqYA4J0E7qrZHtleEa16vQF/YneMBRq6PJxfo9wHKSxz3Oos5pUnMXsfsw/FBZwSfL87ESJnaYeEEbXFGFxAMT9EE7bW9DhhbrE8LEOdIZ+jCLyAVvX8yhOvzhfovgcgI4WRYjEG7E1SOF0l0gcgkShYoDha0hpd4/40NcI78OUaxpGlRpzdAnEvrTQf384K4OIM28mFbDO0FZFBAObnc8WACny/WywTErPYLSsqqJGi2xfDs5bX8/iKmTuJ4JThjirIxVRK01YaDC6sNvDOvxyiA3P+LMGhAuX6mUVA4XvQ6ysJ1LosWKzz2Rh5WGovtfSAoChdkfuQ7btHEQvYm517LxLiORd9d0XOdk8TEinNV9iMgXLGLFieqJrqyL3LufLLYeouu1XBsfPczF/E733i40L+XqNKDdg3ArdjfbwdfSwVjbIcx9rMAPsQY+4vB1z7GGPtrjLH/CRkMGuf85zjnL3HOX6rVarmB1Wt71ZgYeagXMQp5a7+H4cQvPZMsjlB2WAC3jkRPWNmZDBLyIZIvlLzAinNeqQrDGBNSqF6xXr5X73cWvmeAOCyLBqgyoFiUQZOHendUkEE76C8kb5RYazo4HbiFGAvJsi7KoMnDqIgD4ZtBFeqpBSWHkcSx2HXcOx0u1OsmsdZ0pnvQcoL9RQcGS4TJZ4HrWMViX2KzXSvsBvv6Xhc3ttql7c4l5DkyLsDEyxfvIs5sANCs2WjWLJyMipmEVOkbBEQSP/Z8jAJrcOnoW4VBA4Av3T7O/qbYZ/J8ju0Fk0FAvBvuHBfrQTsdeVhtOAvJoIBycrnDwGxi0WCnXXdwc7uNr5di0BZbCwBeuCxmymUrCWISR5mgLShxLNQ7GEPVgPjxnXZhq/3D3hgNx1qolwkQjN3dkwFGbk7BL2i5kHHJolJR2fqRP9A8in06IxerjcWv4+56s7BqR77jthaU5j1RhPmMFW4PemNcW/AcDBm0vMKLLCpZNk4Gk7D4vwgKzR0MINU2i7KswpuiVpxBq9ATDADPXV7DneNB9qiJR8kkhHN+wDn/Kc75U5zznwm+9luc8z/NOf9POed/o+oaMvheuAE+ONT3CwT70hp00SQGEButqMTr9mEfV9abCzW1ApFGeCBzppzA6qg/wWDihS+PRbC9Usd+gUFonHO8fdBbuKIPROYuRRwBwwHECzjmAcBacKh3CzBoni/0zov2DQIIetAmMTvi7JflraM+2nV7ocZ/IKpwF5mF9mbYE7bYfQsljgX7tB6cjkJb3kUgmJ9iEseqvUybYQ/a/Gf77rGw2F/0zAJE0nQ6KFYMeX2vu5DlfXwtABh58ws9khVYNEEDROBb1Gzo7vEQVxcsYAHRGSkd/OSfiwbE2yt1XFpvlLKjr5JY3Nhu5QeosSDudORXkngVCuQCdIJBtIvKkwFhFPJGwev4sLM4gwaIOVdH/Ul20S8WWA1dH3XHQrO22HtZPhu5zGcMJ4NJpetYxjVyP+iJXDSJf3xnBZwL9+lMBHtSvk6rM2g5a4UJN0N3NFlY3guIovBBb1yod1AW6hbtebu0JuK+XHYwERcs+u5aa9ZwYbWeb+4SU/OIvsHFr+P1rTYedkaFHI87o8UdTCUeLzELsGqCdm2rBc7znHVpE7Q7AG7E/n49+Botcg6LO0cDNGuL9yA0HBtrTacQg1bFglZio10vwaD1cb1CoC+DjIHM5nMCK0kBL+qYB8h+pvlBo5jd41dKdNeCQCO31yPAu4d91Bc0ZAAiBq1I78WD06GYb7WgxAsA1lvOtLnFHAbt+tZizcFAOQbt1uEA7QVHFQBAPajMFmHQPJ/jYXe00KwhibWGg+HEBy8gcbwTJmiL7ZGabWGt4RSSb0aMbjUZbJHeC9fz8eZ+D89UeK5lEhNu/5yCwV6FOTISm+1arActe++PXR8POsNQMrYI5ItfJhQng0kQfC8uhXpsu0AfTgxVAoIb2228e9jPZn6mmvv9SgGqDOSKOBDKc3m1wno3ttshs52HkethOPEXDvQBhMZHr2RJKhM2+5ut2sJn7lrDwUrdLsegVfhsjwfuckWKmYe90cLyRiDezzRfLjeomKBttGtYazr5BYqmGPqMGx+tLnFcb4BzFJqbW8WuHRDtMNc2W/n7PzH2p0o89eyltWImOQokjtLQrAiL1g+y+Cr37dJ6A/sFR9IcVUzQrgf3IHNPEjNonwfwDGPsCcZYHcAPA/jVCj8vE4yxTzPGfs514xKlWdwJtLeLHpaAqHIUCXaqPnSAYNCK96ANFjYIAeIJWnBtcgKrb4SmHYv18gEicS3CoFVlK4B4X9j89d7e7+Gx7fbCfSoyyCiaDAKLOThKrEsGrcBg4NtH1faIrMx2Ciafl9eblZ61zXa9kJHGYW8Mz+eVAn0ZjIah6xwGbatdQ7u+eEDZbtiFgqC3KljsS2y0iiVo90+HGLt+5bWAggzayRCtmr2Qw1d8veOI9s/8vgenQ3AevRQXwXpQCZYJ2unArcRWACJILTPnqsp6N7fb6I+9bAY8duafDr3Kn+3KRqtQ71Q3uJ5VGLtrmy10RvNNIKIgbvG1ng9MxrIdOKcZtCrJIGMMlzea+fPr5FoT4QZYKSDeLh4QnwwmC0s3gaifKZexCPbksKJUFAicHPOSmPUrwE/9K+BT/190h9UkjrLAW8TgQjLxVZifa5st3M67Z4kErQoT/56r6/j6/Q4mWewgm5Y4VtmPkTR1/n7sBc6SVZ7tndVGSK7kQczArM6gAci5b+ps9n8ZwL8B8Bxj7DZj7Mc55y6APwXgnwF4BcA/5Jx/rcjPKwvO+Wc5559xHHtu5XvRvhGJdt0uZJJw2BvDYlho3ppE0R40WR1e1PwBiExC+pP5DNprD7pYqdsLm4QA4iHqjue7Ad6tyFbItYBiSVNVyWHDsVGzmcYEzUF35EbMT56L41F/YYt9IEpiZECVhwenw0qMFiA0+UVYJvkS3F2Q9QQQ08nPt9mv0mQt0a476BeQbby930OztjijC4gkZhAEb3mQsuxLFZ7rMmZD90+HuLTeqJTEb7RqOBoEn+vSi5nfJwPOa5X2v2TQIonjegX5DiAStLm21TFUqQ7LcyZzQCqL+i87I68SgwaIILBIsCMLPlXWk/d1Hosmz+UqQdxmu44rG81w/MsMEiYhVZIKQBQnizBoMjmt0vMjJcD3CkgqO4FD36LYbNew3nTyCxTB+TGsaLYCCInvXKv9y+/FCA7Gno/VigwagELmZL2Ri1bNXsjtW+L61jwGbfqzVNn/77m6gbHrZ5tpKDQJkfFKkREaIRNfJUFbqeOwN84fWQBgMPEwcv2FZamAKGAxlnNmqWLQOOc/wjm/wjmvcc6vc85/Pvj6r3POnw36yv6bEr97BeRLHBc1SJBYbTiFmJiD3hhb7cVmrUhsBpXveZvloDcC59WkQrJaGuaDOYGV7FOpEli168UYBBUM2moJBk24AVZLLFYajkhinvmDwPdmj/+7ddiHbTFcqZB8rjVrQjo/R+J40p+gM3Qr7f8o0S3GxlyusB8BwVYXkTjKZuwq900G32EKQ1zoadVsDAoE5e8c9PDY9mIW+xIyYJOV2iw87MhEd/HrGDHx84079k6rOW8CYk8eThzg//xPgR/5+5nfJ1+ClaTSsgdtIBm0av0+QGRGlJk0AcDj343/44U/DwCVWFuZoOUGO8wCLBudij04gDDVKiIXkozkWgXGQj6P85gfWWWvEsQBYibn65lub9MMWhXJISBGJBRh0GSCViUgls/HvTwzmQDdkVtpjzDG8MSFOT0/TDJoQKOinPjGVhu3jwZzx8RIB+aqNvtAMQatO/IqJUyA2P/73ZxerQSDVuUcec9VIfH92p0MBjlIBjmzAjnx4knM7loTNZsVY9CC+G5R51lAJGg+nz9/WJ5ZVZ61umNhd62Rc2Y9QiYhypAREAwCaUcVBgEQAUGRQP+wW43+BEQPGufRZsiCfAlWaXyuOxZaNTvGoGVv8jcediuZdgBBgDrx4H/8LwM/+ZuZ33fvZFhpdhEQkzjOCYhdz8dBb4SLFdgKIJbE/+g/BD7+FzO/79ZhH1c2mqgtOCMEiILGyNY8/b7dCnTOVfZ/u2aDsfkMGudcBN8VmBiguMRR2hlXdXEEAI78HjTOOe4cVWfQWnUb/SISx/3ewoY1EqEd/ZyXjmTQqjCRcq1wi8xh0KoYhACxQs+THwPa25nfJws9VYyNZhk0txJbARScK/THfw2/d+0/BlCt8i2VAe/mMhY2wGx0hm4lyRUQyYXmBcTyPKnCDkYMWn6lXQbfVYI4ALiSlzQlBlWvVQy+r2wIR8B5hhMqErRL601R1S8gcVSxR+aaksQYtKrP2o3tNgYTb25fWCi5rfDZLqzWwVhxBq0KWwfE9n/WfUucw4s6bwJCbm9bDG9mGYXEhosD1Rhd2xIS3yKMrny2Vyokn9tBDH0wx2dCvgOq9M0CyO8dfJRcHNUh/UPdORaHQNXK92rDKSRfq+rwAkR2ocdzLLL3pSFJBV0xIA720FguY3O4no8Hp8NKUiEAaAUP0ejb/yxw7SOZ33cnmLdWha2Th9/cRLc7BufVGASxnlOoT+veSTVXOSA6IMLEIkPiGA4yryCntCyG1fr8z3bUn2Ds+ZVkeYDY/0UYNJlYXKxQoJBMSBRKpu+306GL3thTIpWel6B5Psetw0ElB0egeIK21xnCtlilYki7LqQ6gznjOjjngcSxeoI2r/ACiHPkwmqjUgVeJvHyHOkMJpX654DIXW5eQNxXUB1u1oSDa25fGLPAmRUE39UljhOPz3UQ7Y4maNXshYfZAqLy3axZ8xk0BTIoIDAT6I4ykqbo7Jj4HI0Kew4ALm+04HPg4Zyg8VRBglZ3LFxcbcwNiD2foztyKweoj++0cfuony2/Dmz2hx6rfM9kC8itOUl8JJVb/L45toWdlUaoSshDf+xWYrSAGINcINhvOFalZ82xLVzZaOasJX62H8QkVc/IiwXnePZGLtp1u5La5EJBp+qI9a9437bay8+gSZMQz81+EcgAtWpiUSSwAkTSpCJhAjDXal/a/l+oMCNHrtef4+K43x3DryinBIBWYDs8mNOH80BBlb3o8Og9BRIvoLgM9t5J9c/WqkVyAgCZ9006BVUuUDSduQzaAwX26YCYhXY6nMCbI/F90BliZ6W+8IgJII2JTP9ZKiS3gJQ4zt+PY8+vLMsOJY7zErTTES6uNiq94BhjoudtToJ23J9g7PrVz5G6cN+cJwMXstSKzHjdAWPJHrRqVf3Ndg3NmoV7c6V5HuqOVYltB8S5/SBvgK5lA5YFz+eV2ZFwbuicPjQVgT5jDFc3Wrg7RwrYU9CDBgi23ucZgVwsGHZ9LGyxL1F0FpoKBg0Qw7HnrSWLIpULFNtt+Dyn500OqvZ4JYYVKDisGvEErdp13F1r5D9rsfWqFwzEHpmXyLyx+pHKex8QSpxM2WGg4pFF46rJ5+5as1iCNnYrfzbpSnowh2UNEzQFDNq9k8Hc91cWzkWCJk1CbDvbJCRsEq8YWK3oZNDakkHLD6zkS+LCWrX11poOwvdNRmAVzi6qXPkWG3tec/xBd4ydCswIUNzFUYVUTq43by3OOe6fDCtJrgCEA4XFYcgy9//9kyGaNatSkzVQjEG+H9qnV7tvm4HEdy7zczrExYpJdSRxlAla+nVUYVoDBIWeSbH9WGW+G4BwDs18Bq3aqAKJ9aaDwUQmaOlB1YOOmnNESnXmFXruHg8qF+ckg3w6dME5V+LiyBjD1c0W7s5hLPpjt5IsSWJ3vZlf1WcWeHDPqiZNYYI2J7jqDN3KlWggSD7nJhbVZVBAtG/TZY6xBM3jlVhbID4LTU+CdnWjOZeJVBWgyuLTvGB/5FW/Z3PXCiB7rKsmhJfWG4WGVVe19Aci9dRhHvPzZ17Gz137mcryXkBcy+x7Jva/H8SQVQqnAHBxrTGXPQaC61jxs8mY/bBAUQlQIHHcamHi8XQp7DeVxPFoAMdilSu2kh3J09WPXR8ngwl2KjJaYYI2pw/noDtCq2ZXrlQ0azbGMpPPkMrJl0RVdqQZPEjzBhAe9MaVJFdAdLDPSyzkQ1I1sSgicTzsjTH2/MoJmrznftDcn4W9zgi7a9WkokDAoM35bA8V9DIBwsURwFwnR2HsUnE/SiaSF2PQVEh85zNocj9W+2xFGbQHp8PK9wwQe2Tk5V/H6Byp9qzJYCNP5sg5D6TS1e4ZIALSztDFyPUx9vzKLo6AKBrenWPK0B1Vl0EBItnPreozK6x8Vw12ZNA4t+dHAYMGiHfSPFv/iEGrGnznmEDEGTQONJ2K/W4lGbSqrNal9fmMRdiDU5Flkj3R2bOgpMSxOuvZqtu4sNoowKCJc7lq8rm71gyLbHnojaozP6sNB3XHymerN67haGJXZusAcd8edIbp0lTGps6RekXW/+JaA8f9CUZu/vtSxXXcbhc7szoKRiMA82ahLWOClsOgXd5oVnJVBMQh4XNgOMlu2H37oAfOq80uAoCNwJ53XuV7vzuuLKcEhBRjXmD1QMFwWUAYTgDIlYtOPDWJrm0xtGr2fAatMwRj1cxWgGISx3thgFpdKgcE0rwcQ4a9zrCydBMoxqDJl0TV6yjdn+YVKB4Edu1V0HAsWCwmccw4HG8fD1C3rcpy4iIupqHktuJnkyzP6dwezFFlJhIQAWlY6JlzjlRNCGUva961VDHsXmK9VUNnOAmT3aoMGiAC8Ltze9CqV9kBsZcedkfZsuGgBw1AZeZHPv/zrPZV9LsB4p20d5pvSqLCZl+sJT7bg9TKd7TnOVhlieNGq5gM9mQwwWrDqdRfBIh+PlGEyH6muooYtCtBTJbJxgRFx5HLlUjzbmy35vegDRVJHIM+xXkS/e7IrcwOMsZwYaU+V5rXH3vKGDQ+R5qqkkED5ssOuwoSNMe2sNWuYX+uSYiaXtbcQdzLwqCFPWiehzwGraqDIxA1juZVbOUg56d3qzkdhs3983rQuqPKMkAAaNTsuQNm758OUbOrGQkAUeU7N7CSw74VJJ8rDWeumcBeZ4Ttdr1yn0dos58DySBUZ9BkgmblOm+qkq+tFehB2++MsVK3Q/nlolhPmDKkwfM5Hipg0BgTSfw8m/27x0Nc2WxW6tMCpMTRyw0m905HSgoGzZqNum3l2uz7Psdhb1xpgKlEq25jPGcOWjhzTZHEMa/Qo4r1BMT+Px1OwmtZtQcNEP2MD7uj3Dl1PQVGAoC43l5wr1MRq3xXTSy22jUwNl/i2K04T0vi8noDY8/PlXn1xy5si6FRMWjcWW3AtliGpJJN/XfVRJcxhisbLdybww5WnTklIWOJo172eaFK4ujYFi6vN7NZrdDFsZpph8SNrTZuHc6XEwNAu+J6YZ/inGBfBfMDiDhp7loK+rSAqFUoT5oqz5Gqz5o0/5rniNlTJAMXfbr5z5qqBC0cVl1gjEAazkWCVrQH7dpmtWZ7IJKU5TEkrz3owmLVE7S6Y2Glbs91sjvojnFRBYPm2DEGLaN35ETIoKoGqFLimDesV9LMVZNBQBzu3XkmIQp6meRavbGX2/h5T5GRRmsqQct+XB+ejpTI11bqBRi07ggXFFzHhiOrp9mB60FvBF+B8yYg2BhewCREhVSuVbfBef5nU1UwAIBGzcIoh/U/HU7gc1QavCnRrMXPkYyeyNPqxi5AtP/zellDgygFDJpkkE8GagJUQAwH5jy/x6g/VsSgzZvPZNkhg9aoKM1zbAvb7Tr25ziiCZOE6olF2KuVE1zJPpWqUm/bYri42pgrceSonugCyHfNC3A6UMNEyj6cPBbhNJR4URtOBGZiLldSoLix3cLd40EuqyXbLqpKU+U7KU9S7Psc/YmnJPncWWnMdR/sj7zKbB0QFZazR01YoYtj5QQtuI7zZLd9BfPkAPHZ5kmlBetZbbg4IPKJtaaT/tmWhUGLwJHGoHk+x4PTYeXGfiA+rDcnQdvr4OZ2u3LlDADaDQeDeWYCnWHlKjsQBHEhg5a+OVQ4DwIR8zPMqXzLSqiKBK2IcYdgmap/Npl8jnPm1jw8HcJSwI6EEkfOMnvQBmMPnZGrhEEr4uK43x0p2Y/y+cnrU1Rl7AKIPenzfInj3ePqM9CAYhLfhx01BQNABNt5yaB81qoaGwFiT47lUlkM2kl1i30gbjZUgEFTcN/qjoWJy8M92VZwxl8Mnsu8RvieAhkUEEnzMs0LYtIkFYnFzmq9gElI9aHYwJy+sAAqZFDReo10iWPs7PAVMGgA8Pi8gc4Q56QK+Zpk0fOCfRn/VO3BAQSDnNlfF7o4VpelAqKlwPV5LtM0cn0wBtTsasG3TNDyjEIGEw+cq/lsO6vzJY7dkVuZGQQi2f2DAudI1SKcXOv+HCMlFW6YgNgj8wx5OsOJkr5ZQCjl0tuYli5BQ2picdQX1vBq2JH5lu1vPuxVZs8k6nZ+5XvkisGLKoLGpmPPHTB7+7ivRCraKhCgHiia7wYUc9/cOx2pYWJq8+WbD4NB5lUrMHItL4dBi8YHVA+I1xoOumM3lx3c746UJNWy8pa3/1X1RAJISBxnr+VEzgBUUOgp4mL64FRNwQAQ1zKvp0QasWwpuG/NmoXRHJt91YWevHPkzvEArZpd2cEUAOqOjbHnh3LEqsEHELGWeb2WgkFTwNbJeUlZpiRT0iQVwf78qn5PUV9M5HaYHXz3FUm8gBzXyCkGjSm5jk/srOC4P8ndI2PXV7IfpcQxz8lOlcQREFL2Tpb82op6rFWwTJcKsFoj10fDsSqzrPKdlCfNUzX2AZDPWn4PpnCDrb6WZH4yTVAsO8agVTTkWWvi0noD//L1/dzv6ykyUrqy0cR+d5zfgzmqPqRdYqNVS3+ul49BA9KyTknVVzWbACL3p7x+pqP+WMlagGS1sgNUVb1MgDQJCf6SEli5no+7x0M1CVoBe+yDUOKoJrHOY9B8n2O/qyZBkxXTvM+mimWyLNGEnmcSIl8QSkxCmg44ny9NVSFxlNcx76B8cKrus7XiDFrK4Xj3eACfA9crDPuOrwXkJ/F7nWFli32JRs2aw6CJAGlbgcSxVbMxlBLHzMHpago97QISR8F6VncwBUTBbOz64bVUk6BJt9JsKbsYZquArVttoO5YuT0/ftiDpiZBy5PKuZ4Pz69uRQ9E74m8xKKrSAYFBAlaKoMwnaCpYCLlsPq39rNZtJHrKUkGJYuex8Z0hpPQfKsq1po1dLOcsWNDj1XctyIs63DiKdv789bqKnIVBcR9G0783GJVb+wpYdCAOb1ajIWGW1XPSMti+OR7LuO3Xn2YGcP5PkdvrEYqKgs9eQ6cHUV9s4Bwa//mYdBSEAb6CpiYiEHLDgg6Q1eJ/TIQBQRZkPbMShi0mo0Jzw6s7p8O4fk8HPhYBUVYpsPeGLbFlDQ+rzSc3IPrsD+G63OlDFqeNE9VgibX83i2zX7omKdC4hj0imTJHF3Px1F/rEjiGDSI5zBokh1UwY4LBi07QXs3CGpvKkjQ5jE/ns+x3x0ruWdAIHHMuY7SkEcFy9Ss55sNnQwmOB26ShI0GbTNkzheU3BmASLYGLl+WDRQERAXcSvtKUosLIvh+larYIKmRuKYF+gPg3ebirXqjoVmzco1FeqP1BgJAELieNyfzJ7zMz1oChi0C2L/5skcR4oYtPWmg5rNcq3GeyMP7Vr1Xj5AsHA+j2bUTYFFPdZqJL5BgpYjOxxN/Mp9U4DYj9sr9TkMmpq5fEDUCpL1vE0C5n9VwVqAmAWYnaBFDJqKPfn7XriEkevjS7eOU/9/WTBrKeyvyxtrocp5FsiROC4Lgzbl4pjyoWQFT4VDWXtOgjbxRAVDFf3ZqOX3jkibU1UMmnyo0gIr6X50XUGwI6noeSzTVrte2ZAECCReBXqZVEjlijJoKgoGgLiWHlimscu9Y8myVg+I5Ysrq2hw2B+DcygxrYlMQvIZtAuraow0RA+a/NvsnnvnQAS1j+2oY9CyEovD3hiez5XIUoH5EsfDvtoetElOD5o0O1BxjhRhIoVBlJrrWLcZxq4X7n8Vgdx604FtMRxnMGiezzFQ1F8EiALDu1kJmmWFRQpVEsfuyM0sVskzWcVagBh7kOdWKuSU6hg0IKXSzpIMmgL3we02LAa89TA7QRt7ahI0xhh2Vhq5TORE0VpA1MeWKnMMzg9PEYN2YbUOxuZJHNUwaIBQduQxMVKJpYKNCQfDZ9y3fpAMthUxP7vrOTMVmSXaLlB9DhqA8PzOMhxSKTmXQ+gzRwhAShxVJmj57TdZOBcJ2pSLYwpkRUFFVV9W37J60GT1ruqwSImGbWGcE1jdO1EXfDdrdvhQpQVWcpjeje3qa9kWQ92xcivfKuZbSTQcK9e0Q9XMKaAY87PfUcMyASJI9TiynQdPBlip20r2ZE0maBnXUj5r2wpkqTWbwWJzGLTTIS4qSmLEdcxm0G4d9lG3LVxSsF5UoEg/mKO+QXX7P6/Qc9Qbo+5YSpKApmR0gdxzRInEcU4v63AS9OgqOB+BwCTE4+G1VJGgMcaw2aplDmSX8k0VVXZAWo3rYdBkUTTLgU0lgwYEYxBygp2R66GhaK0ibAwUSRwbjhiynJtYKGJ+AFGoyWM+VfW7AVEfWyrzGetBUyEDdGwLF1Yb2MuVOKq7jrvrzVyTkMjSX41JCAAcZty3XniOqJM47nWG6f3ozILPmRKzFSDq0z3MkEuPPHH+q9iTsiia5xrZV9TvBohRLaeDSYrEd0kYtBAcmQyaYzElQ0Vlpd7104OdjsL5OIDYcPkSxwG22rXKM6cAYRIS2YzP/rzbRwMwpiYZBIJelRyW6cFp9flWEnUn32wldANUEHzPkzj2Ri4GE0+pxNHNkTjeOx7iymZLUQ+O+BmTjAQtMpuovv8ZEw32uS6OnZGyJH6eSci7h31c324pYXTnSRzDvkFVBYo5TPxhb4ztdl3JHpmWiqYwaApdFR3bQt2xMnuCVc5AA4LzWLFJCABstGuZDJpk4puKAqsb2y2cDt30+ZosKtKp7MPJMgpRzqC18hm0ieejoaCiD0QJWrrjm9j/HNXt2iW22nUcD3KSJk9dYrGzmj8eQS2DJhO0bAaNgykrUFxazxiPEEBVLx8wn0GTxUc1cuL8wfDyHFERKwLis008nl5YssQ5Urerm60AQgbOGDJnHMrYTsWzvd5y4Fgsd57i2OPK9v9mq46x588qrpZF4hgh3Wb/IHDMUxFYOUGA6ma42J0O1NnPAvMr3/dPhrisKGFq1Kzcyvd+V8xlUrUx23U7t7lfZfA9z2ZcZS/TPHt4lZJbIMb8ZDrmDZRIYIGoQJGZoEmzCQVSOUA6Aua7OKpgtACxH70cm/13D/tK+s+A+S6mDxUWDICAQc5j0PoTJQ6OgPhsPGTiZ6/j7SPhqqhqj7TrdqbEUWWPLgDUbTuUHALqEoutdj2TQZMzm2oK3l9AJC2VifIUmJA42hZTIhuWCVoWY6EyQAWkxDH7nTJ2fSWfC5gzn0kmFlyNxBHIT+IB8dlU7ccLq/kSx7Gn7jrKWCn1vkmJI1cjcQSEK+A8F0dV+/HSegMPuyO4Ge9Llb2sO+H8uvRzxA36gh1LzWeTrFZ6/5SQOKqKFW2LYatdzyz0SEWPCnacMTa3d3bi+UqkmwBCj4XZ67h0CRpSA4KDnjpDBrm55WZPImTQFEkc5zFoh/2xskC/4eSbJBwPJthQYCIg0arZGGSwWhPPx0FvpEy+JivfWRa0e50R1puOkpfpPIfKMEFTJF8TDFp2gnb3ZKhM4jU3QZMMmgI3QEAku1mJruv52O+qS+Kb8R60lGt5/2SojD2WL66s6ygrvOrmoOX3oB30RthWwHoCwXXMYeLvnw5xZUONqyIgZI5Zia7KGWhAdN+kHEtVALLVrmW6OMp3TdWRHBJyT6W6KwaBlSomRspYb2UMIlYZoAKCjemkOqIJTDyOmqPmOuZK84K97SuSOALAZis/QRu5nrL9WEjiqChAXc+9jtLFUY3EEZgvOxxO1DFo17faYg5vhlwuZH4U3LdmzcZK3c41CQEikqEq8ve/cERWdY4AYk9msVqhokHRntxeaWQykYC4liqkm0BOgrZ8DBqQlnU+7I6VGTLYltDVZjJoQYKmikGrz+mdOuyNFQbDMZOQFLncSX+CTUXSTUAkMoMMBm2/OwLnUNqDBiCTjdlTOHNKSlqyeqeOFFqaA4JBcDMGVY9dkcRcUWSSIBO0sZu+/6UTnQo3QCCfQT7oBfMNFd23ds3J7EFzPR+H/bES8xMgJpXOKPTsdUbYaNWUVd/nuTjud0e4qKiI1XSs3F7W/Y66ghmQn8TL4c+qpKLypdwdTeBYTFnStNmu42QOg6YqsJL3OZX5sURgpWrfba/UsdZw8G6G+6A8I1X1hc2VOLo+6hm96mVRsy20anbGDC8pcVR3LfMkjpxzpUnTzmod/bGXyUyPPR72I1dFrklI8E7jgVxOBS6tN7DfHWcWx+QcNBWQBYrbGT2fKntZASFzzEosZMyqKrGI7lt6gcKFpSzRBYKigQaTEECom/LmN04UMshhgjZTfFnGBC2NQVNoaQ4AjsUyKWspcVRls9+Y0zt12BsrlJPl944cD8ahJbQK1GzRcJ+G0FVRocQLyDa32OsMlRkyNOtirSwGTQYQKsYHACLRdTNMQvY6Q3CuxuUTAOpOfg/aYW+Clbqt7GDOC76jPaLKbMWK9WBOX0vpTqmK9XTm9PKp3I9A/hw0zjkeKkyaWvX8c+Rhd6SMGQRE0czLKJgd98do1dTtR3mO9Ebq2ApgDoPmSwZNsTQvlUFj8GChqeizMcZwc6eNtw+yAtSgv05REjNP4jjyfGUMGhAwdjkMmhhUrYhBC/ZImgrE9Tl8ri7Qv7CS3880dj1lvXz5TEzk4qhKmid7B7NMIITEUR2DBsxnkFWtt7OazTLJmFXVdcztHbSEUZTKM3Inj0Hz1CZoeQwy5xwTj8NRtP9lMft4WRk0abPv+x6yetB2FCUxQH5AoJNBm3g+OkNXaYKWV/k+6k2UMSNAkOhmmK1IiZcqk5CQQctIdvc6aoZUA1F/UZat/+lArZFMq2bD9a1UOZmUxKhiWedJHI/7apP4Rs0Ond6SUL1HWnUnStAS58h+R50TLBBJMbKe7WOFPWFAvsSxN/YwnPhKJbdZiS4gAiPVCVqWouFkMFFWCAHiEseJUvnOZruOwcRLvUfyjHQUsXUrDQftup3ROyUMh1QFjADw+M5Kpq3/UKHECxBB49j1U4s6IrBSxzLJ9TqjbAZNKG7Usazis82eGaoZhHnDqlVKRdt1G7bFMkxCIhdHRXlFqMrJMgoREkc1i13dbIKxyLk2CZUSR0AMa8/qQZPFcD0SRwseVyc5BPRKHMWYifzrWKeWOC4LgyZt9q2UJ7g/DhzzFAYENSub+TkdumAMWFPU0Fq37cweNDlcVlUg16xZseb+2Wt5Mphgs6UuaHRslinxehj2aalZr57DoHHOA0MSRRLHOUO45YGmao5GWzJoabLUgVq2TlbfMhm0vjpGF8ifX/dA4WgEQPQy8YwezMjYRVUva2A2lLH/uyNX2RkC5Jvk7AeBujKJY06hZzjx0Bm6ShO0mm3lMGhqi0rxHjSV1eG8YEd1DxogWLQscwuPMzQUJmg3d9q4fdRPVZ0oZ9Ba0nBiNtj3fA6uOGhca9ZyGbSs0T+LQO7jNDMZlXP5gMiyPZtBU5foMsaw2shiIqMeNFXMjzReyjIKGbm+Msltw7Fxaa2J2xkM2tD1YFtMGRuzs1LHQYYVvSz0qDd3STcJcRWahADisx31x6lnvTxHVK23s1rPnN8oYx9V1zE8s5aVQZtCMrAKKt9KGTSbwctgfk4HE6w2HCWOkYCUJmUMs+2r/WxNJx5YTb9YJp6P7shVzKBZc90wVSUW4dDjlAfuZDDB2PWVBY0124JjsVyJY6tmK3vAa7YlbPZTHugwQVN036TEcZyRWBwpDoibOQza3ukIjKlLmlr1bOZHJmiq9ojsZc1KdDtDdYMwgcjFMU0e9VCxaY2QSqcnaA8VJ4PAfAZNFVMNRC9lqgRt5iWNmIujoootIK5/ZoKmUJYHiMHYE4/jfgpjoZpBWA+v42ywL4tzqnqngGDuWqqkUtwrVWwFIGSwAFKNQkYhg6bOxRHIY9DU9eAAOVJRSyZolkIGLRgwnmEUMlJoEgKIPrSsuYMqZ9cBolif5QYbuTiq2ZNyuHaWSYhHYBLCebprZFSgUCQVDWLqNBZNdYK21nDA2BIzaNNIJGg9tZVvQCQWk4yAoDN0lcxbk6gHfVppwwDl5lHpmJfVOyI3j9IEzc4OrDrDCWyLhXLBqsjrQYtmTqlh0ADZO5Xdp6iqRxEIJLdgqRJH1QxaKHHMSJqONTJoe50hdlYayg7Kqd6p5DmieDQCYyyXie+OXKwqTNBkMpHGokkGTeXYh6xE96HiRBcQAUdWwUy5xDHYa92RqzSIW89puFfdgwaI92FqD5olJY5qAysgK7FQ34MGpPfFTFyZ6Kr7bOvNWoY0T0oc1e2RjZa8jtkMmnKJY46kTG2BIus6RhJHVQzazkodtsWyJY4KGTQAuLzRzFxLpSEJIBLdice1MD+2JZjPVAattYUTrCndI9tBDJ82/mGkeP/LmXJpTreqCz1WMKM5z6E1898q+Q10IsEiyAqQapMQLyOwOhmMlVZs86R5MkFTFRA3HCvTZl++FFQGO3lmKyLRdZTp98MANSVpUi3xAkTAkcegqUziLcbwy+7HwT/6kzP/H1mClmkSos5VFBDXMUuaJwaZKzTSsC2ET/WMxHGMhmOFVUMVqNks8zp2hy5WG+r2SJ6LqWp2sBWXOCaCqpBBU9yDlpXoClm2+vO4O3KVS+WAbGkeoK7yDYjrn2qz/8Kn8a9r36a0B20zs8ciPgdNlcTRyVxLtZEAkMP8xHrQVCHTTADA2JPjCtR8tnbdRquW0acIcS1VX8e8OWg+LKi6lJbFsLvWwP2T2c8m3TBVFl8urGb3hakcig3MkUordoOV66Xu/x/6X/A/t39CucQRSGd1VUt8rwau12nSVFdxDxognu1vSpt9+RJSZbMP5DM/Bz21hiR5gdWR4gRtSpqUqPypNpsABBOZ1TvSGU6UGa0AMYljynWUL7wtRXOggGDAcl6CpjBotC2Gf+Z/FP4HfnTm/zsZTFCz1TGReQma53N0hq7SJL7pWJkujg9O1TodWhbL7kELXA5VFQwAwLGt1ALFcOJh7PlqJY7SuCZFLv2wI6SiqsY+iHEd+VJRpQUzO9u0icokpDt0lVbZ83vQxB5RGezvrNZx3J/M7r/v+M/wj51PhaNCVGAjR5o3nKhNLOT7KW2tMEFTHqCm9+AAAMuYTbkI8lgtmeiqCogZY7iy2QznCCahsgcNENLUdIljsA+ZpfTs3WzXU5N4GR+oZJAvrjUy+5lUDsUGonOkO5q9lhPFLo5yvdT9v7qLQ6+tXOIIpMsOVRdfHttZAQC8k+I+q5qJBEQBffkljhwpDJoICFTKrvLcB1Xa3gMxaV5KYiEPapUzp7ICK/nCUylxtHMYhFPFPTj1nOsoP5vKQK6Vx6ANXGWDzIEocEsLUo/7IkBVxkSG7oOza3UVm58A+fbwKo1dAHEdsySOR/2x0gQeEAd86nUcEVzHHAb5YXeM7XZdWaN608nuQYuMjeh7Wceuj/7YU3pmxaXSSgPUVrY0zyVg0DZCM43ZQG44USvxksZSWQGxbTFlwU5eECdl2Wp7p2oYTvzZ9xhLL/RUwc5KHYyl28PLAFVlQHx9q407GQnaRDGDJkxCshNdZQ1oAdaaDrop7ptRT6RKBk3syTTGWvSgKWTQGjnniKe+lzXTJAeSZVX32XZyChTyvqk6k1cbDi6s1vFOyvxGbQna8jFoHLMM2hhrDUepZCOvKf2wqzpBy6583zse4sKquh4cy2Kw7SAoTCZosgdNoYtjLec6dhTLACMmMt0kBFD72fLmd6lm0KzgQfZTDCBOVZskONJ9cDbQl/Isles1nfTr6HpiALfKvkFxHdMLFL2xh5W6uoQJEC/KtOuo2uUTmC9xVMloWRaLrl8yQetP0FY4Jw/I7kFTLe8Fpl/KKp0O13LMLaJB1QqTpna27HDkemoZtJaU5qUxP+oszQHRE2axdKfDCZHEEUhjPsU5whQmFo5tYWeljocp5haqe9AA4NpmC3cy3AfHrmqTkIxA/8oH8e8v/iC+gmeVrQUIY4Y0lknGByr35IWwnyklsXA9bUx8yKDpMHeBepZ1qwCDpvJaPrazgrdTErQxRS9rq5ZqEDUP5yJBi+ag+TNZp6h8qwu8gcA1L8MyuDNylUoc85ifuycDXAsm1avC0F7DhDWAtatTXw970FQyaJaVaTOu2sUul0EbjFF31DbG5zFoqo1k5DmRxqCp7sHJkzjKg1olO5jFoO13xeBolRLHKQYtcY70Rq7S/jNADmqf/WySiVTbg5Zd6NnvjpSNs5BgmQma2h5FICiYpZwjJ0FCQNETDKi1a1+tCycv3QxamuHEcKJWdtWsCbvtLAZNZfHUshi22unzkkZEDBqQct/YzH8owcW1JvZS7OFHintwAOE+eNAbp46LoehB647cWZfZehu/dvP/jpG1omwtAFhtOuE5G0ckcVTbgwZEve5xDBW7OK7mJWjSDVbhOZJp7gJxLVXukZptYa3ppCdoiuegAcBj2228myNxrCsceL/Zqi3voOq8OWhdxYE+kD2o+qgnLvC2wn63PJOQO0cDXNtUxyAAQNdaw//7fZ8Fnv7E1NeP+xNYCue7AQGDkDOuQG0PWjaDcNIXSYxKjXuznu7iyDkPPpu66ygZNC+FQVPdgyODxDRpXkfxkHYgGP3g85lERlokK5U4MpbpPtgbuVhRnqCxVDdYeR1VJoSysphWoFDNoAFAeBanSKVVSg6B7J7gyHlW4Xk8xaCpez1aoSNaGoOmvgdtI0d26PlcaZWdMSYkPBk9aCoDVCDbajwMrBQzCEAOg6bwnQKIIct7aRJHxTbjgGDQAODO8XSQKgZ+c+WJrudz9FOSQd/nsBXK8gBxtqYxaKp7IoFofEmqxFGxSUiei6mrmUETn03ts72zUk+VOI5dHxZT+9lu7rRx92Q4U9SklDhOFyiWJEGbxvSH6hBUvh073R5bDnUkMQlJBPucc9w5HoSHqCrYFsPAas+6OA7G2GzXlc13k2tlm4ToY9BOBuqDxixzi8HEg+tz5SYhAFJHMahO0BhjweiHNImjemmerGQmr6UcMqrSxTGvB6078ggSNCt1XEGHsgct1WZ/rDxBizf3x3FMwKBlmQ1JuaBKRjdeEW4ofEEDIrhKc3GcKJ5fBORLHH3OlTnmSaQ3watn0ABhdpM+vyhwX1MsqQRS3DcZTYK2u9ZInd9FIXG8Hqhzkk52FP1u89wHbcXXcTUjsaBg0GQ8mJ6gqbfZB/IH3qvtQcuXOKpO0LZX6qk2+6oZXSCy2k+eW2OiBM3zOXrxAsWyMGhTSHwoCgbNyUgsItt7dcFOFoN20Btj5Pq4SpCgZZlNqJTKAVLiNbuW73N0x67SJCZP4iWNNFQi6zrKh12txDHbJER1ggYEzE9aYkHAoEmWIplYyLkyqk1Cchm0utpAsmanm1uQmK1kuJj2Ri4GE095gsbCBG3WDValTBrINm2SFXKVBbqpBE0hgwYEVuM5PWhqGbTsBM3zecjKq8JmK33ODw2DVgvVLHFQVL7nMWgqTUIAYHetiYed0cxZT9E7FQ50TkgqJ0SBPpDO/PicK937gFACjVx/pmBLwaA1azbWGk5GD5raAoUsIqa6OPrq9/96s4ax52fOXVO5FiBi6yybfZXMOBAzUkqcydH+V5ugAcnzeBkTtJnKt6s0YAREQJDGIKieSwbEXPMSB4ls3lXOoLHsxEJ1YJWVxHRGLjhX38sEZNvsbyg0CAGEZCnNtCOUwSp0scuSOHLORe+U4gJFzUln0Ch60LKSz73TIRhTy1bbFlJt9j2fYzBRz6A5GS6mJBLHkImffpGqHsAtEfWgpfQEU5wjKYWeXhCkqLxv8SBAdUCQNfRYJvEUAUFa0sQ5lCol5HpZDJpKsxUgqLLnDHNWmVhkDhgPGTS1e2R3vQGfR2odCQoGbb2Vzg5S9PuE1zElsXA99QnaakYiQ3EdASG7Tev3VC0DrNkWWjU718VRJROfVaDgnMPnaotKgIib0uTLwmxF7Tki45jkuTUh2P/hjMOUz5aH85egJfZDZzghkDimJxYys1cqccyYX3TvRCRoNAza7NeP+mPlDNq8AFWpxNHO60EbK5c4WowhTb0pDxeVMq9I4jj99ZHrw/U52srdB9Pt4SkYNCcrQQvmkqnUnFvxHrTYQdIfq2digByTEMn8KJWKius0TOz/MEFTaLYCxBm06P74PsfJYKJe4pjRy9elSNDiJiGKg7isYb0UPWg128JK3dYncUwbxArBWDRVB8PtOo564xnDCapB1UAa80MncQRmWa0xRX9dQxrXJBmEINHVJM3zfIIELXhHJY1CZJFTZRIDiMHfaf11I8UjLYBs2SHFPMWs/S+PY9VMfLvupF9HAgYtq0AR7X+FhZ40Bm35JI7TNvucc3QJGATbslIDgsPeGLbF1A5GzWDQuiOxSVXLNy0r3a79uE8QWGUxaCETQzC/KKsHTbXEkaVfRwqW1c5g0ORBpjqxyOtBaziW0gAoZAcT++SwN1Y2WFnCthg4n5U49oJnjcQkJDXRdVF3LMVW9OLzJN1nH3bEfryoWuIoX5ax63g6nMDnak07gGwmPrxvCqWpUyYhCu8PIJKYNKtlChdHQNyHNAZNJGiqJY5ZDAINg+b6fCbZpTAJyXTNy3AxrQpZ/OolmJ9wfpdiR8zVuqOFQct0w4R4r6ne+/Kd2BmlJxaqE+tWPd3VWUh81e7/1aaTykROfI6azZR+tmju2vR6MvZRnDOhXU8fu0PR7xZJHNN70FQO/E5fa+kSNExlnSPXx8Tj6ivfGXN3DnpCvqNSHlLPaO6Xm7Sl+OWWKXEk6R0RPTjJSqccZqtyPWlukbyOY9dHb+wp79OyMq5jyKApTNCskEGbXk++xNvKe6eymU/lcmI7PUET0mX17qxpNvsRE0PQg5Z2HUdqB5kD2VJRKZVS3YO2Z1/Ba60PAlfeH35NJgOqJY6OlX4de2MXzZqllGWN/yzVDNpmK919kKIHDRBV2ySrJaVJqgPUC2t19MbeTGIhekfUriXNLd7en55hFEkcNUjKiExCQtOk5HuMIPkE5HymxD3TOk9OFChUS27lekkGTSYWqhnkVs1OHVeg2iQEyJ4p53q+0qRCrJV+3+R1VJ7o1mxMvFlX57FiS38gZgCUlDhKsyHqHrTlY9CAeNbZJXBDA7Ln7hz2RkqZESDbfU0maE3FwbdlsRkmZuL56IxcpYOcgWz52oPApeqyQgMIQFzLpFSUImECxMGUQqCFDJpKxi5rDppk0EjcBzMYtPWWYkY3OKSSZho0zDhDuMoUg0YjcXSsdKlod6jeeTYrQdsPGLQdxT1oY3sF/7/r/z2w/WT4NfmsKbfZz2DQugQOvnEoN7do19Afeym2zpJBU50Q1sJZcRLyzFLtmndpLTCcSFjEu776oPE9VzcAAF+9ezL1dYpB1UCWpIwqQRO/ezLYH008MKa2vw6Qn00Hg5ZjEuKrZ9DCBG002zsFqJfmpc1F5ZyTJGhipEW6i6mjfH+kM5/yHFF+HYN4N3ktKVwcZSyTxcSrlDhKVcm0omHZEjSO6cr3kK53JM197bA3JkvQktI8eUA3FdPjNmMzTEw0T0g1OxLIrhLr3T8RL/FdxQla3bFmruP9E5pk0M6Qih71xlhvOsp7p4BZiWNvTMWgWRi76dI89YY84jolryVF8D01By2GiIlULBV1WDqDNpwoTz7DYkjiOu53R9hs15S7bTkpRSwK6TIA2Blz0HojV/k9i+P6Vlvpz9sM3h3JeWFhDxpJ8K2HQdhdl71T0xbxrseV9jIBgkHbaNXw1TvTCdqYwH0NyEjQZBxCxKAlk/ixx1GzLOUJYdroB4pEd6XuwGKzjnlAYLOvOInPMgmRxzFFYpGWVABqZamAMI67lRiNAIhiiOq9L5MYXedImKDNFCjU96A1HBvNmpXCoKln4lfqNmyLLSeDxhj7NGPs5zhP9mnRJGhZPQ8HBAlaVuV76HqwLaa8YmZbs8GOzOopKt/AbIL24HSI1Yaj/L4JBo3erh3IkzhOtO2RPmnvVAqDNpgQSPPEn8lgn2J8hjVlsz/LxFMwaFkmIVLbrwpWFoNGMKQaSDdSonBVBKTNfnqCpnqtOD7+/EWlP0+y6keJBI2qB62V0s8hE3jVkrLQsj3BoE18HzXFazHG8L5rG/hKMkEjYH4AwSLMzq+jcXFsZcyF9HxfOTsCiAB8RuJIIBW1LIbNdrbEV3UvU1bvYJhYKF4vTeIoYxHVDNrN7TYOe+MZVsv1KJjIdCMNKpMQuf+T13LsqTdbAUSBYmYOGsH+Z4ylON0uSYLGOf8s5/wzonoUfSj58CmvRmcEqBQMmmQQksHOYOyjVbOVV8xsa5ZBky52K4qr0fKFkmQR9jpDpQOIJdIYtDBB21C7nrDZn/36UX+sXE4ZmoQkA2JCBi1t/x/1xwQGEGfEoMUljmO6HrQskxAyBi01QVN7zwBx39JkqQBFwUwMqk72soo9ovaeSWy0asrZua1Q5jIdpHoE9tiACHaSjmjyEip+rYTugw9SGDSKxOLp3VW8s9+f+ppWiSNxD1oyQHUJZIBA0M80ypA4Ekh8sxM0xfcsw9yCSuLYTmHQKIxdAOCxHcHsv3uY3P9cOYMWmq0k3TB92YOmdLkwlkmeWxRz0ICgBzOZ6Prqe9CAlFEkBS4eXfmRCiyeoAW234qr0Wk9D67n42QwUTqkGogqOTMJ2sRTOuBQwk7pQRsRHcjZDNpIOaMFZEgcT4ewLYYd1fctx8VRtZwyix0JGQsCm/20BG2/oz7YDxm02GfzfI7+2MMqAcvkp9jsSzdA9VLpLLMVGnYQSEvQxnjP1XWlawHpZySF7T2AkIHx/OlgvzfylPfWAcC//YufUJ6sA5FCIYtBU20Skia7Ct3XFEdWG60a6o6Fh0kGzeNK5d4Sm+0aOiN3yqJ9Ela+1csA7x4nJWU0CVorwyRE7H0KBiGFQSOQeAHB/LpeRoKmONBv1ixYLCo+S1AxP80Um/3I2EXtWje3gwTtoB/2YwJBvyeB4mq1MVug4JzmzAoLFEm5KIFJCCDOrZlB1UTnyNIyaNNIkSZR2OwnKt/Hgwk4VzsDTayV3jsymnhhw7BKpEnzxkRUfNiD5iUTtCFJgmax2eTzwekIu2sN5QeJmIOW3oNGxaAl1+tRmYQ4s+YWg7GH3thTLpezUxhkqufasTIYNKrEImcO2hqBDBBIMwmhkTja1mzy2SNyw5S9WclCD5XE8fJGU3mvJZA9rNT1fdiWWntsQAT7SakcVYDKGMPuWmOWQSOQOALpttVjzwdj6oNGnQyafAcn75tLMCsMEAxCZziZYqep4gExvy7FZt/nyo1kGGOpM7Xk+aj6UrZrDsauP3X+ekTmPzcDBu2dBINGIXEE0o1kKOegAbP7f+yp768DRIFiZlA10TmyCIN2/hI0Db0jNXvWZp9ivhWQ3V80mHjKLfbleslAn0rSYIcMWnQtOefYI2LQ0vpiHpwOlZuRAEGCljauYDBRb5KQ2YNGExDX7VlzCznwWPU8rTT5ZujOStBbmtaD1hu5YEz9SAvHnjXSoJrdmOaGOZx46IxcEoljOoPmoWYz5XN/spLP7sjFKqFJiGqEEsfBLINGEXynWVZTSZMAIXOccXEkYtDSbKtlEKc6acpzcVQ9B82yGOqONcMgeITBt8+jYh8QuYqSMGiZEkf1n00Mj9ZkD18P3Ddj980lGEAPCEZ3s13DrRmJI00So9NsSL6Dk4k1hQEKkC5xHAdSUdV7ZJZBm4/zl6Cl9KDpsNk/6AZ21Zr6iwYTL3S0Ub1eci3pGKU6sKqFPWjTwffY85VfRyD9sz04HeIyQb+bYNCmv+b5HL2xRyZfS2PQGFPv9JnG/DwMErQLa/QFCunOqpodsVh8Dlp09HVHHto1W7lxQt22QpmLxGDiwfM5gRtmsEdi11Em1TQmIbM9aFSMlm2lM/HUJiGq0a7bqNvWTB+O53ESlkm+P+LVaKoeHED0MyVd8yYejblFWoI2cTkaJAFqDYOJN30mhgya+vVaNTvsX5IgY9BSZkGNPbFflM8BbNdx1BvP9JJKBlk1VhpOKF+XCMdMKJcTi3Mo3jvoE8kAAZHsJofQuz5Nv2danyJdopsucfR9muso9sjsmUXR7/bNIXFk0wmaqNiq/RhpNvvH4YwfTS6OE0954A2InrfkDG6qHrQwsIp9NqrZXYA07pi+joc99a6KQLrNvjSbUF4wCJP46a/3Ry5JYpFmbrHfoQn2UxO04GVAMQcNqT1oNIG+k2IP3yEaDRKx1dF6kvXfoUjQUhi03shV3g8p1wKmmXg/KIZQmYRQgDGGjXZtxmafjEFLsaz2iQJUQEjikj3Ari/s4VUjnUHzlFv6Awida6dYBCKJIyD6p1JdHIlMQoDpzzZxJYOmdr3tlRpcn6OTtL7nNPsxj0GjYn7izxqVOyuQzsZMCAZVA/I6pie6ZHPQEvfNJdr/qw0ntaikeu8DQuJ+OphERdTlkzhyTPegTbDacEicDpPBhzxUVAffjDFYLI1B85UPqQaEHtpNZGhUdrC1lMCKqk8FyGAHJx5aNYJkMGUtqrl8WUYyvbGHNkFiIeagJSWOItgnS9BiyS5VEmMxxBi02Dkyphl4XLOF+2Cc1aJi/eU54qdcxw2FQ9Ml0nrQqAZHy6pwfP/3J3SFHkrsrNTDZ0mCygCildJwTxWgArMmTZzzGWMXVchi0GgCqzT3zSBBI7iQzZShx3Q9aHJYb+w6+jQmIaHEN9GH5lExaPVZBo3cHj4ucfRoRloAYv8fJ4bQux7N/k8bIUDXy5fuYkolg12pOxhO/KmWDiqp6M5KHT5HTOa7dAkaZgZVUzRz1ywWHlISVENYgQxnxYmHFoVJiMWQdP6magoOq/reLINGMWDWSkmsB1RmKxZD0iOEzLQmwySkP3axQpDE153Z4FvK5VS75kUMWjyJF3uEIolJ6x3pEzFo8pCPnyVdokIPMDvjkCrRBTIYtLFLUnhJc4OlMnahxsW1RvgsSVD2oAGJBC3sQVO/Xj0xh5KqlwnISNA8Iqc3ae6S0uBPIRVNM3ehMNIA0iWO8rlWvSelkiXZh+Z6dAzyDINGbg8frSff1xTMz2YKgyZYJoJCT8o8RZ9IKi0ZtL6mAoV8X8V7MMeu+nEFgDCfAoD7J4GR0vIxaNPoDGkqtrZlgfPpfo6oL4bI+l6XSQjDjLkFlUmIk+K+JgMr1bO7AJHIxJMY1/Ph+pxkXEGazT61fG1WUuaRJLppPWj73RHWmw6hAUT0tVDiSPBs8/BQjEscPZLnWlYz43JR6YaleoQAMDvjkDIZdAJ2MI7uyCPtQUt1+jxnCdqF1caMFb3r0ch3mtoljnYiQRP/TfHZ1tMSNKIkJn1+HY1JCCDmZg009aCtpcg3w8Ra8bWU7sZHCat9n9MYoKw07KnAW64F6LGHl3EPFYOWlEpPiGYOtlIY3VDiqPizNRwLjAHDJINGlMTL90e8D42q0CPN6vY6y5qgcWDKJGSkfp4QECUW8cp3ZzhBu26TSFHSpHmDMeEctBmTEMmgqQ6+ZWAVXceIQaP/bHKWDEWim2bpHwXE6ud3AbOjGETvFI0MNtmDdtSn6eWzwv66+LNGw0QCiA7FKZMQOokjMD2ovUskcQTEOeJOFZXoEl3Hmu2v61FJHOWcKy9NKn2+EjTJoMWNEqhkgGlyIUqJo+hBm5V4UbwzmzUbdcdKMD80ie5mS45HmGXQKJjIVmoPGs0ekYluXOIoz2Jb8XrSAfj+zCgGTpLEtOvOjFSOzh5+1pBHxiIkPWjtejgHUILK6bCZMvCe6hxhjKGVsp5HlsSnJ2gUUlE5H/fB6WjOd0Y4XwkaMGMSQpKgpRoX0AQfQHrSNCQaVJ02v4uMQQsDqxiDNqYLrJLyTXk4U82T4xxTgRZV8B1KHJM2+2Mq17xZtu50MCHpZYr6i6KvhUk8wf6PKt/RV3pjl4SJlIFp3MmRUnaYPEeoBkenrQVQujimn8cAjaKBEhdXGxi5/pRRgkvE/KQ5olG5rwEpEsewl4kgG8SsUQKVVC6aXzfrwEYhcWzWbIw0SbzyGDTVAfGVjSZsi+H20bQ9vO8TBd91O4w3wrXC/a92rVCaN55N0Cju20arBs4xNZ9s4tJcx3aqxFH8SSXxTe/BVH9GyvdHN5GgUZzHF9dEgWJ6VmT+9Tt/CVrCJISiB81OSSyokkG53myC5tPY7KcyaB4ciyk/SGSAOtXcP6Jj0ERfTBQgyEOlQZToApiy2qeS5mVKHMceiWueldITeTqchNVWpWuF87ui+yb3I0XlnUvmLDGomiKxqKeMmZCBOVkvqz+9VsOxSOQajkaTkFqqVFo82+dN4ihf0nGZI1UDfHoPmviTIrBqOGKshCxauUSDeiWSCZrP6azoGUtIHCWDZql/tzSd2QCVih1sODYaM0wkTYLm2BaubDRx+2gw9XXX52ERUiXaDSeMNySoxkykuTiGCRrBZ0vtwSRi0NLmKVIluoBIdtNMQmiSeMmgTc8BpCgq1WwLF1br0wnanAt4/hK0BINGKU1KBjurBEEVMGsS4vkcY88nsdlPS9DGLo3mNkp04xLHoPJNkVgwNsXEyASNZuC3+DPNNY9qCPGMScjIpevlS2HQKJKKcH5X7LONJr5yw5oIsz1oIrGgkYoC0/uftpfVmjEJ0VVU4pyTSW7TetDOs8QRmE7QqCykmzkSR4I4DnVb9G7LPRj2oOli0IiCOMtigWteygwjogB1mOxBI2IHASHJj0scpSSbYr3rW62ZBI1sUHXNxtjzp5xFI/dBGnOLtB40iv2/mZKgkbk4ap6nmGTQpBsshQw2lDiO44oGn6Q4DACX1psJieNSJWjTAUGXKACJ3Aene9DWKYOdWJU9TCzqNEnTjGMkUYJWS7HHlk27bZJAbloGKF9yFFJRlpI0hbIrxclnxKBNf703pjJlSGPQ3NCSWfVawDTLNHJ9EtYTQKwHLdqbw4lP4+LoyARt2iSkVSPqZbVmjY2oGKbkrMjhxIfPaRKmNBfH82wSAiQSNEIXO2A6sKJyXwMiibyUOcr7RSVxXG9OzzCiCuIAERBP96CJz0oxqDp9DhqNDBYQVvunw6TklpHIYG9stXHrcFriSNaD2UgbHi3+VM1qtdMMeUKJI6GzaH86sabq9wSmk0+PkIlPzl2j7OVLNwmhKfQAIkELXRwL4FwkaIyxTzPGfk6MQRMXbuQKhz4KI4E0SQ1lsGMnDCcGlMxPiiHJ2KVhLNKkov2xC8diJJPak4nF0KXtQQOmh353h8L2XnWwJS9VMmnqj2kYtLT+OioGzU5j0FyPkEGbljjKyhkJE5/CIHeJjI0AOeMw0TeriUGTZxZF32BawWy5GDS63hFgui8mmpFKI3EEop5mN3RxpHmWV5u1qd4pKhkUIGahHaVIHGmkovrmoAFCwnmaZCKJkurrW23sdUYzZhoU11GOoOmlWN+rzqul2qmfMqiaQuKYxqBNfLo5aIA+Jj5p7uKFa+kxCaEqGACiB/lhfMzKMkgcOeef5Zx/RrCB4gNJSp6mBy1F4kiZoNnTkrLI3IIg+LZm5WtjIlvRNKmosIa3SQIEi6VfR10SR6qAOEoGo7XGro+Jx7WYMgwnHkauT9KDZqewIyOiggGA2IEo/qQM9MM5aAmTEKqkybIS+5HwzEr2oI1cun7P3HEdVEwrETZbNdgWw2HMapxqULUMGvUNqhbryQQtmoNGE+ysNpypBM0lCvQBYRQSD4blTqRg0Fp1G6OExJEy+VxrJq6jR8fWXdtqAQDuxVgEKoc+yaDFZ5OF9vCK94llMTQcK9XFkcokBEhKHOnmoAH6zIbEeITphAmgZdC6sR40qusIiALdYW8ci+WWIEGbQrAhQsc8TbbOovJN1IOWsMcOGTSi/qJZiaOn3GIfiAff0z1oVFXvGQZtQpjoSokcp0/inZweHKpxBUD02aIh7XTJYDz5FD1oVIG3lDgGDBrldUxJLDojl+TMAmYZtM7IJZm3BswyaDKgpEisU/f/2MNK3SaTtFHBshi22rWpYb2u75MEcTJoTAusKKr6kcRRrOeGLo5E0rymM+ViR1n53spg0BhF76AjeqemLdQJGbRWogfN9wmvY8pgbI+ovyiVQaYrUGRK8wiupYxF4xJfl2oOWop8kyrRBQSDlspEkvTpWrDYrMSRqqh0YbUOz+fRWbIMDFoaKO2qnUTvlOdzerlQQk4G0Di9WRab6WUauz6J5FAOunS96cCKIhgGZuWbAw0JGo9dSyojGStF4kg6riAh35QvbxIGjc0mMSPXQ4NAlgpgpgetS+gGmDquY0jjPAukDaqe0Mkpgx40KYOlmqUIpLOsvZEbVsjPG7ba9alhvZTsSKtuTw19lc+0DonjhHAOGiCe2ZEbmUB4RFbcgKh8751G8+t4UOihuI5Skj/NxtAlTetNB6eD2R40CkSMBf167RSHPo+wBzNpbiELFDSjGERi0Y2PRyB0cQT0MfErDXtacujRJWiMMaw0nMR+pGPQLgQS9/2uPP+XKkHjkB8oGgpMyaCJjSGDYV0mIZK2ppg7ZVuzboDClIGgJyxkEGIM2ohm5hQwK98chSYhFD1o4s/4tRyOPTQJe/nin01WmCjcMJ0Eg0ZZMLBTjGRoJY7y59JLHJ2UAgWpVJqxqWeNWuIIRD1NY5eSQZN7ZFrRcN4MQiS2VupTEscJoUNfOzH0lVbimDAJCSqBNaLPJt/98hn2fA6iHAaX15sYuX7MlIEuQUszd6GaAwWIc70zpJfKAZHD8VTvIKf5bFEPJr3EEQjs4VOSGIrkMy2x8H2aJEYmaNNmQ+JPnQwaVdFgpe5MJYSuz5UPaZeQJlH7sg9t6Ri04APJA4WC1UpKaiJrbKLEIiE7pEzQHMuaarYHAhdHEgYtpfJNzKBNOcu5tL18wDSrRdXLZ6fIKUNpHoEbppVgfqTDF4mLI8tK0KhdHKcljjqYeIDWJMSOseOc07P+QFR8iXrQ9JgNUVn668B2uz7bg0YUfDQzgkaqOWhAlKCRM2hBwUgG+5RJzJWNJoCod4qHg6rpegeHCXt4qj3SrgsmUsYFlHLKtcasNE8wn+rXkmdRfHi6LHJSfLzk/C6XkPkBRHvP1HXknOxzAelDuClaPuWAcclWR718NM92sufN9ThZUWkmQVsuBg2QHyjqi6Gr6k+C4CN0KCNKLJyESUjIWBANBk54hJDZ7KdZqJP2oNlsitGiNAlJm0028WiYH0szgyaLR2GCRsmgpSS6tC6O0xJH0n7PlB5MSpMQOzaofRSYyFAzaPLZlkEQSaEnw2yIYu/rwNbKdD+TS2QSAoizL63yTRE01pMSR592Dprc252ROJ98wiTmUpCgTQ2ZBcAIgsZmSs8P5Ry0mjNdSPWI3ACBqKDeDQrscsYVRfAtz6L4HDRS5qfmpA+qpmJ+GtPMj89pBn6nuThSzkFrNxxwHo1J8giZSGDWlIdqXAEgXByBmIvvUjFoMZt9yjk4tQSDRtkAD5stXKwAAFVCSURBVMwyPycDSlOG6UAHkDb7FO5rgcQrnliMPJJgGJjtQaOcg5Zmsz/xaDTgaSyTFpOQkEEj7EGTa8XnoE1oJLcAIolj8CetucX0dfSDXlYqkxDRyyr+m3JIu1wLiJ5tShfHtB608yxx3F6p4ag/CQsuHtGgamC2LyZyX1O/VtiDJpkY6eJIJs2blstRma0A2Qyacr92IJTJJx0BqfaIvD+T2H2jSyrE+SDjN/lIU3y2ZMEAiIJ9iv3frNvoT2b73cj6+WJzADnn4JyqJzJb4khifZ8Yj0DZgwaIAuA4piqjGlcACBVS3bZiVvvLlKABSDJoFNXoSFKTkO8Qya5sa5r5ORlMsFKnGWZrpQwhHhMxFlGVPdr8+90RdlbqytcC0mcz1WxG8mCn2ewL9x86Bi2Ww0QMGoVJSGI2GaUhT5p8U4vEMThHKGWwycRCSpcpTUK8BOtPVQxJslp6Et3YHDRCJp4aW23h5DUtzaOrDvdThudSze8CgFGw98I5aORsTBTsU13Hi6sNWAy4fzIQXwgSMxoDiKweNJrPFo6xCF4wLpHZBCD2SN2x0BlFSTVAy+iOYvEH5xyMEfUO1qwpQx55NlI5za7GJI6UbF0712Zf+XKhR0F/NO0GS5agWdaUY7tH+KwxxnBhtY79znj+N+M8JmgxBq1Zs0gOkmTvCGUDPCA2XlwGeDqckPSfASIgTs5BozJlSM4vGk48nA5dXFpvKl8LmJVvDiceSeANRAd8PCEcu0QMWorEMXRxJBrFAESfjVQqajEwhgTz6ZEYuwCIMWjiM+qyh/d9jg/9178BgKaoBEwXKCjvmVwLiF6esgKpa+C96EE7nwnadlCgklb7pC6ONTsxYFb8SZFY1BMM2iRYjKoaLQsdUuLoEjKRjm1hd60524NGYcoQmoTEg0bazwZEklRKBg0IeqdkUh18RIr1Gvb0XD6ATgYIBOYWEz3zu4AgQRtOM5EUS8kY6r/99a/j5bunwXp0hR7JsoYMGrFUtOawqXfLhNAkBxBKpNCUZ6kkjjEXxw6hXbWVCFBDC2mioDHNJIRCTgbMWvoDgc0+YYAqk8+9U0HrXgysRlUjKd8cuXQJWmizH7uUwiSEgK3LMQmhZNDig6objkVWCUxKU/WYhAQMGuEohjiDFpe+UCWf8etIKe8FUnrQZKJLOKhafjbOOY77E2y2ac5IamzJBC0wChEBMVEPWj3Zgyar+urXSvb8hAwalSNgY5pBo5qnJbG73sBe0DsiTyuKQdWhSYgmF8da4lmm7IkEpqV5ITtCWTBI9KBRDTNv1mwMxtNMDKCnBy16rinUQtHP/PWv3ANAPwcNiNw3qV0ca/Y0g+YSzkEDxH2LVA1LlaAh5uJIOfB1WuJFOeMHEAFIPEClTNAsxsB5YjAwEYNmh+yIuH57HVF9JGPQEsnnYOwRMgjiz6RJCI3EUfyZNEkAaBgS+bKUn61P6LwJpAw9JjQJYQmb/ZHrw2I0h39cmidfpM9fXsPvf+GS8rWA6XOEWuKY7FOUMnAKk5Cw0BOs1Rm5cH2O7TaNVJoaW8HvfRwwaEJSprcHjUTimHDNc0MXRyoGTZqEBAkap2MiASH1CtnI4PpRzbgCpiVlVEOIgRiDFro40rF1QIL5IWTQ0hM0TiLLA+T+mLZrB+gStLjEkXIAfRzyfUI9Bw2IYhxyBs22phg0j7hA0a7HXCOXi0GL0BnS2lUDcYcy2YNGyKAlXBypJI7JGVcAHYMm15NSF1l93KVi0BLyzeHEJ2MrrBRWa0I0riBMmKZcHF206zZpxSwe7FMlunK9ODtCOgct0dwvZbAUPQnxc0T2G/30x54iZf7jrCdAJ3GsJQyAKFUG4ZkVBJDHPSEPOa8MWtQEHwUgVMxPMylxDGJVEoljgkGTkjm6fiYLNZuFzxZl7wggKvsyaYoGVRMwaCk9aJSfTRYHZJDqerSJ7mrDmelBo0g+bUv0n4+96R5MKgZNFkNm7eFpEzTphAnQsYNf/at/ELbFZnreKN6bSQYtlIoSFSjqCQZtQlygWKk7YX/d8jFosUHV1DN+QgYtkO9QJjFxJuZ0MCGxNAdm5WuASECpPhsLGDsgsigmS9CsaTfMAWEPWiRxTJiEEPbgTEkcxx7pwG8g2v+DMZ3zJjB93yaecKOikMoBmJE4UiaDcWmeZNCoikqAOEe82D0DCOWUCeOOEWGfrp3oZZW9W9tEZkPUaIU26pGEh27GVTqDRpEzJRmLkEEjbLiP99hRGmkAIgCPhh4HCRrBemGCFmN+KFmtqNgSzUGjCoYBcQZ2h9PBN1ViUbetGYkjpSGPz6OzMEzQiD7bSsOBz0UhOuxBI0wG12P3LZI4ql9Ljk/pjaLnWqxFV6CQCZrni/iDsgetHZ+7Nucjnb8ETZqEDOlslmctpGkljkmTkBNCBi2ZfI5d8XA3iT4bQ5TE7HVGqNkslPioRtJMo0doxR31KYq/c84xJpI4MiakolMMGuGgXjvx2QYT+gQtkhPTstUzNvuEfYrxc0RWHilnd1mxc2RAzKA5GWckjcRxei05Q2zznEocowpxjEEjrOpPPB4GIJH7GoHEUbo4Bs/wJHRxpAsz4v0j1Axas2aHvZ1hDxpBIBeahAT7w/c5aWKR7CcVBQPCHrS4+yCxFX3NZtokjq0E80kucWxGcwApB3DH10v2vJG4RjbkYOwEg0bVg2lbmEjWn9h5FggYtKXtQTsDk5CxBomj3PC+z9Ebe1glD77FescDGezQXEvGopfZg9OhsCsmNJsAokOfclZSsgdNykPqRA92clYeJYMmP1vcEZBS4ujEGDRKJgaIB6bSJISQQYu5OFKOBYnWi86RAaH5CZAuA284FkngH5kNBRLHIEHbOqcSR9nP2Y8F4JRVfSAKGimb+6VULmTQiF0cgWl5NKUbJiDumwwaQxdHih60xBw0+iQmOQeNuActbhLi0ZlbAEDdsadmXHFCk5CkHb18rinORABhjNgbeaQJk8RKPZKmUrrBhgxayIzT2uw7toWxNy1LpTyz2g07GjC+dD1o0iSEMPjONAkhkgs59myA2qKWrwVn1nFf9nPQVKOFKQkP19pepat6J+Wbok+RKvGc3iPy5UbVb5E0QOmPXRKLfQChW1hoEjLxyPYjEBQoNLHVMzb7mhg0eSBTDle2YonukNgkJDlCYzSh62MNA//gJXoY9KCdV4mjSGQjGSqluYXc2zJo9Agr7Ywx1B0rZhJC6+IIiPNW7kGXsJcPEM9SJBeVEkeK8TQWHIuFMxqjXiZaKbYbT3SJXewie3ja5LMR249yPaot0koUXlyfztIfAFYbIrbpDt3YAG5aaWqSQSMZ+F0T52N/NG0kQ9eDxqaGtAN0zxogEtCR6wfn47IlaBDBXHfkYl2bSQidfAeYDlAjaRKVFbf4Uz7QRz1ZjaYJdhiiaktv5JJKvJLyTcGy0koc5eEhH3CqIDVpgNIdeWgTs4Oh4cTYI9uPQIJBC/Y/VTEk6kGTVWpKBi3q0+pqSNAcK3aOEM9Bi9jBqAeNKqlmjE31CRz3x7AYyPp0qcEYQ7tmT0scCXvQgGg/ULo4AtMBsUyoqRk0mQj6xAxaK5A4+j6PMWhE4xFilu3UNuPyWZbPF/UcqGbAavk+J5cB1p3pHjRKOXFYDAmfa5/YtCaaFxa6YRImaCsxaSonPEcYY1ipO9oYtLhMOjI2or9v/Ym3jAya+GCc0w58BTDVF+NYjExLP9XcHwSodPK1pMSR1hEtbhLSH3ukw2Xj8k3OuVaJ45iYQRNSnujv/ZFLJoNNOlRSuzhaVhqDRiRxDCtWEYNGZUiS2oNGvP/dRKFH2xw0wtEIQOC0FeyNo/4Ym+06KVtCjVbdwWAScx8k7EEDYrIrQmkSIJ7bcUwqRynxAiL1CeecdFYYEJOLul7MxZHoOtbsiEHzaJMYGYy6nh4GTRYxJ75P7nSYZhJCXgwJ2Wq6pBqYjlMpzX8k4uMRZCxCKRdN9qBRnZE1x4r6L0NjI0IGLYgBIifHbJy/BA0Mp0FSQSVfmzEJIayyA4nm/mBTNonla2GC1tfRgxaZdlDO04rLNwcTDz5hEs8SSUzUg0bFsk7PXOuT9qBNm630x7QSx/QeNKJ9Ig9enQyaJxK0ms1IzxE7lugOA8khVeCTPCPHrk/HekK8RGWV86h3fodUS4gARFhyUwaNzQSDFla+iW5V3bZC12NKd0oJJ3h3ysSTkkFoxRiSkEEjupDNmhUzm6A1Lkj2oE08WrOV+DgGj5gdrMcKBoDY/2QSxxQGjbKIFDlJ09reS6TNXaP6eGIItx6zlZot9ogo8khZth7mc/kkjozhsEdrsxzJ16Kgkcz2G4nm/kDWQD1gOZQ4Bj1olBJHmVf0xsQSx5h8U1Z6yBi0hM2+rNLVHLqAeGpQNWUPGpsOvocaGDS5H0OJI7VJSMxmX4uLY+A6S/kCjY8roL5nMz1ohBJHIHqJAsLYaJPI5VYXZIJGHaAmGTSPWuJYi0wZJkSutnHYluhBo56VBEz3GMmTmCoAF3JKPYN65TWbxBi0GiGDEB/HQG6z7yQZNDqJo5MYV0A9OF3+aGkND9AWKFITNEI2Ut8ctOhdFjJoxC6OQMCgLZ3EEcBBkKDtECVoUe9IFHxTMSPAdGBFbY+dTD6P+xPUbYuM2WIxk5D+yAstVCkQBcQ+Toe0c6fC6xgcjNQmIXbSJISwB82KMWic83AoNhXivVPUhjwzJiETOmkeYyxMrHsjl1TeCEyPK6B33pztQaPqvwSkVEm6s3pk6gldaNXF/C6P0wbf7YSLI7XEUdynoPLtcdJeDkDI8zyfPtAHpm3UOaYLPaoRt/Sn7kGbnYPmh7MHKdcbe76G4DtF4kiVoFmziS4lExk3KvOImXFAsFqyqETpBguIJEYyaNRFrDiDHLHVtHPQgEeMQWOMPckY+3nG2D9OfH2FMfYFxtgPFPxJOOyNABAyaDMzfjxS+U6qSUidesBsJHHcaNfIKvsWEzb7nHP0xnQ9YcC0xLFLPBg4Xr0CYgyaBiOZsetj7PmELo6RfHPsiTl5lHPQLDYrcazbxIOqwx40OgYNiIovlK6zybUAPbPrgFgPGmGiC4hKuCyCUM4A1AVZIfaJezlkUtFPShyJ4sYpF0ffJw10gGjP65QmxQd/W4xmH8YHcJO7OKbMQatRShxlD5obNwmh+WxJiaPv081Bk0mmvF8usVRU/mzO6c1/gCiW6o1dcolju5HSg0bmYhrtR5lcU+7/kEEbu2oYNMbYLzDG9hhjX018/ZOMsVcZY68zxv5C3s/gnL/JOf/xlP/rvwDwD4v8HsGiOOgGDNpqo/A/K4M0m33K4GPKJCR0XyM2CQkljmPSeUIsmPE2CgZiU/VNATHmc0riSDQrL7FHyF0cYxJHuUeormV8DuAwkNxSJjGOHSWfoTU3UUWVJRi0IXFi4Viiwk85NF1iao9M6MYHAJEEVQbj1GdkfOCs6GWlvZbUaNUcDCZ+jEGjWSfpLKfDxVHep8GY9tkCgJolGvxDFztiF0dAShxlDxqVVNQKTUJ0MWhxq3FKs5VQ4uh55AYQaRJHuoHf09fRI1wLiJIjn/PYoGrCxCJ4f3WHLjkTP+3iSLxHwjEu9KY1AMLiomAI89cp+pb7RQB/HcDfkV9gjNkA/gaA7wNwG8DnGWO/CsAG8DOJf/9jnPO95A9ljH0fgJcBNAv+HgAYDnpj1GxGb7Ovqb/Csljo1CSdvaiq32kSR6oZaEDUgxa52NEyMQCCMQyit44qKJ612ac2CYmS+N6Y9lrG3aH6wX6klDjG3QcnxIMiox60KMGgZtAmgUkI9dwum0UJ2nDioUnI+m8EPWAngWHTWEMPmgx8emOPPNmlRrtuYzB2Yw59RHbtCYkjtftaPCDe745xcY2miCohGLRImkQZWDVjDJofujhSmYTY2A8K0R75oN7peMf1fVJpqnxHjty4pEyPSQilxDHNDZM2QYvaLKil0kAUS/VGEYNGlQ+263Y4By3c/xpMcqhbVYCosF6EQSv0luOc/w5j7PHElz8K4HXO+ZsAwBj7+wD+MOf8ZwAUlCviYwBWALwIYMAY+3XOuR//BsbYZwB8BgA+csUSJiHdMbbadUJZXtIkREOVXZtJSHQY+z7H7aMB3n99g2QtIOhBQ2QpSln5jss3O8Q9aEmbfR09aHI/9ogt26NxBfTztIDp3inq4bZRQKWTQePojz1c36KV5dn2NMtKec/WEwkatQxcBlqcc3I3WB0ITUJkYEUU6Kw1HdQdC2/u9wDEm/tp1qs7Vnj2PuyM8NhOm2ahAI7NMHS5lsp3cqacWI8uQYtcHGkZNHnWulMMGqXEMerVou4vasz0oFFKHKcdsl3yHjSE61FLpYEoQeuOXHLGbqUxy6Dp6UHTZxJShEGrcrpcA3Ar9vfbwddSwRjbYYz9LIAPMcb+IgBwzv8S5/w/B/BLAP7nZHIWfM/Pcc5f4py/FPwkHPTGpNVoJ8mgTWgtpC2NJiHxJOZffH0Pd44H+OR7L5OsBQQ2+0H/GQCyvilgWr5JPRg43qALxHvQaB5sYRIi/lseXFSOmDLm8Hwe64kk7tNKziGhOiBDiaMFNziQaRk04TI3cj00CRkmYJpBo55d16zZaNasWILmo0FYdZQM2ji4Z9SGK9QITUKIE4uGY+N7nrmA//1rD8A5Jx0wK9aLAuKH3RE5gyYLIDLRpR5UDUibfbHXqYrENZtFph3Ec9BC23svmidH2Tso+4vHrg9qC3WtLo7SJMTXMzg96kHj5D1hwLSsnVriGHdx9In3SE32RHpcyxy0ZuAvMSgwqFrbW45zfgDgpzL+v18s/IOYMAnZWaVL0OIudoDYkOuEts42i88vog2I7Vhi8U+/eAe7aw186n1XSNYCIoljf0w/qDfOfMoqLtUcNCuZoBEzaBaLzSUb0coO4xJHXQxaOE/Op72OcZt96qHYQOQyR13kAWYH3lMmngCw2aqHcxTHGlwc+2M3ZOIpCz060K7b6E+iBI1yXtIffM9l/PNX9vC1u6f0Lo6OsNmfeD4OezokjtZUYEV5HVsxiSMPldJEBTkWtT1QOx2GEkePfi4ZkLDZJw6IZ01C6JKYNLMVSkYrLnH0NUgc5ftLJGi0TPxKw8HE41NJPNmsvHDMBL3kFog7IHNQMmh3ANyI/f168DViiDlo2ysaKnMxdoRaBhUyaGMPtsVImRhAbI5bh308d3mNtFpmMQbOEVqmUvagxRm03thF3bHoJIczPWi0wX7cACJk0IiS3fiYCcmgUfdpxZ2v4r+DcsQYNJmg6XBxFFJK2qTCssSz5vscE482YQJEH9pxMEeReuZVzY56+QCQjZjQhXbdESY8wfNFGRC///omAOCt/V7Mjp5mLTGo2sN+VzgtUydoSZt9bQwalyYhVM5yLNYTRu1iFymGdEi8aqEpg0feOzhrs08/By00CfE56XWMm4ToGDMh319j1ydn4tvhzEGXvIg1JXGkjj8wfd/mfm+FdT4P4BnG2BOMsTqAHwbwqxV+XiYYY59mjP2c/PtBb0w2A00iLjuk7kGLM3b9oHeErL8uxo7cOR7i2maLZB0JxsRavZD1oWfQhKsXrbwg1H9r6kGLm4RINpKKQYuzg/IZoGwaty0rPIQnoYsj0XUM9wQLg2MdPWjULodyLUDsSY+4jwQANtq1UOI48ThpgiZt9vvE8l5dkMG+TDgpA6vdIEna64yiwIrQfXDs+XjYGQVrl/D/WgBSHq3DJCE+9Fu6OFIlTfG+XPI5UDH3QWq2AogzaPTvl1mJI71JiLxfwiSE7kyMt1mEzLiG+zZyPS0ujoAoRpP3YGo2CWEx5lOVzf4vA/g3AJ5jjN1mjP0459wF8KcA/DMArwD4h5zzr1X4vTPBOf8s5/wzgHB56wxdeukEmx6eS1mNjgdW1NIkyfwMxj72uyNcpU7QIOagUfdNAdPSPMqDOL6WDHgmwRDdGiGDFpmE0BquxFlWagkKIAwSvES1mCwhjNns62IHXU9PgmbF7xunLVAAwGYrStDGno+aQ1l1F4E/tYOpLsjiyulQXD/KxGKzXUPdtvCwM9IyqHrkRgkaPYMmejx1mIQ4toWGY+G4P4GsfVO5OMadbalZJstisJgobOo47xuhzT69rXndEfvjJGD6Oedksryk+7fnczLzH2C6XUVrD9rEJ19PDnPuj1zyPRIyujGzIUrmEwjmA3NFEkfO+Y9wzq9wzmuc8+uc858Pvv7rnPNnOedPcc7/m+q/9nx0g+B0V0PzsU6bfQCh5IXSoUweTreP+gBAn6AFc9BC1odU4ij+9IIXNmF+NqX/BoCRp8MkRCwWjhAg7q/zfE7exC1+thWTOGpycWQW3noonO1ubNM9A45lhYlgg7gnLG5u5PmctJoKiMBfShxdzycbMQFEUiVqB1NdkP1MsqeO1u2N4eJaA3udIbnEseHoTdCkPFqHxBEAPnB9E1945zBk0Mh60GJnoo7P5tgWJr4f9gBTBqhTJiEaetAA4AP/1f8OQBTByRi05Bw0n5MmuvFRP9Tz5ICYxDGWWFMpvaYYNOo9EmfQNJ0jVhAXz8nPKkkczwQyQaM++C1r2riDsvptxwJiantsucnfPZQJGq0EhQUUmmR9KOcXSTmBH7iV6RgS6fkcDzsj/I//4jUAxHPQfJmgeWAMaBM7fca17bQJGmISR1oGTb5QOICX752CMeC5y+skawHiusmkgpxBi50jHrHEFxA9aCeDibB55rSyEOniGLHH55tBk8GOZASp5agX1xoBg0YbWEkXR8kMUs0qlRC9iXEmhvYZ+86nL+Ard04wls6KVAyaNasqoNwjNSkV9WmDYQAh0z5136gkjokziVJZE2ciAfo5aPJjxBk0qucaiDNoHmT7FBmDVo8xaMRs3XQPGm2BWEIkaAClSYg2xHvQpGZfi31vMKG9P/ZIK7Zxanww8cKBmDRriT9vHQ0AANc3aefUMCaC4cGYPkiNz++iljjGe/l+5tdfwV5QMSadgyYZtKGLlbpDxpBEEkd6eQ0gDsN4L59tMboXTRBQ+bDw8t1TPL6zQlo0cGwW9k1p60ELmE/qoH+zXcdg4qEbOKbS96BFTPx5H1Qth4jLhJOy8g0Ixcne6SgMrCglZQDCPU+5J4CIQYuSGNLl8J1P74Bz4LAnElBKBi2UymmQHdaCHs+wB5iyl0na+rsxxo5ovVGs/wwIJI6Ej5oTu2+u79MWieMtHcHHpJ1fN+viSLWejLd7Yw+eTxsTRAkapx/zE0B6MyjpQTtrxHvQOqHEkZb5sYKDvz/R5z7ohwwaPS1+91gkaLvrxExkQOXKgJGywhOf3+URH8RxI424bJOqV9GeYtAmpAFqxMREBzGpq1HcxZGY+bFixZBX7p/ihStrZGsBAYMWFieI56DFe9B8Th70bwSjRx52ZXGCuActJnGkNBvSAdn3KD8PtRx1d11IHKl7R0JmcESftAMiINbJoMnC8Dh0lqNj0HyNDJoTjCvQ0YMzZbNP/NlknANE88IoC7eOzUIWxuO09yxyA4zb7JMtp3UOmoxv3jnokRcb6zFGN+qBp2fQ+LIwaHF0Rh4sBtJB1UDkvqaj5yFuEtKfuKTBh9zop4MJ6rZFPiuJQcxB84glh8B00ywnPojjNvs3tiIWkiq5sKzI0r838sj6z4DpQJ96SCoQPWsAvV277EHzOHDrsI8nL6ySrQWIzyb7jKjnoMngNEzQiKuAMkGTluqURko1hwUmIfQFMx0IEzQpcSRn0Jo46k8wnIhDhG4OmtgD3eA9TX3mh4OqNfaOAIAnbfbJJI7WlNkEQG9973p+KDEnlVOGg7GjHrQaUaL7p37f0+F/TzwezEGjfZdF942WQYvHO54GiaNjW7AthnGMQaNa7rGdNj76xDb+h3/xGg67Y9LnekriqEExBIjk2vOXhEGLozPysLPa0HABxYMmJZWkjEUsID7qTbDVJhzCHWyI7sglNeyQYIyBQ1QDqYOQeGJBfRAnbfajr9PJDuVanZFLK7kNgxA9wUG8v871aGfH3Nn5Nvwd9/vQ5S34HFgj7pHRyaBN2exr6EGT1+6wJ4ZVUybWjbAHzQVjtIPTdUBKHKUUkDqZfuLCCgDg/3j3CAB9gtYbueRVaEBcNzG/izbxDNcLZWXi71QSR/ns+j7H2KOflSfnrnkaGIS4xJG6B+3KRgt/4fufBxApayi3iOyVBcS7jNr8BxB7UbpJU8dYwqXVI5+DxhjDT3/vU+gMXXz9fofcnRWQNvu0BQMJK2xZWbIErTt0yR0cgcjWPGTQKFktOb/L59jvjnBhlS5Bkxu9E/QxUUNqbT1fQ1UiHqBSSxxjNvvyQKbElEnIcII10oKB+NOP93YQVx0jiSMtg9bbeA5/xf0T2O8FhRfiBM2xrKgHjZhBC/e/F0iKiV/Wa03BoB10afsv5c/mXMzAXG04pJViHWgmpIDU9+oTL+xiteHgt7/xEACtiyMgPhelq6dELWCapLqAunfESSRoVO+0eF+6dMS8QBj31KzpHjTq3qmaLRhxHXPX5M+e+D65eZgde5f5xKNO5I/mQXwlvka7/xs1S4vEEYjkxHudITGDJn722OORSQi5zT5Doraf/n2kv4UixE1Chq5PXvUGpElIZEqiwyTkdDDByPWxoyFB645cLU5oDAACjTRxfhYxP16gNdciL4icB/90TE6hGvEkpjfytPRESiYm/jUKxIfCTzyOGuFaMqm4fyp6E6jNJuIvbF0mIZNQpkG73kZLXLuDkEEjfIkG1+4rt0/w7CXavkEdSPagURev2nUHv/+F3fDv9BJHlzzIAaLna6JLmhSejcHfySSOkXzt3skQK3WbtCgneqciN0AdTIxg0HSYUAXJrkc/H1UwaFHvIGUMEnftDXtLiSN66dJKPa4DiNqY9joj2h40yaC5vpZ+T0Bct6U0CXF9oE4sFQKkcYGvyR5e3CTpBLizQlcpi2+8tgYnNCFx5OSWs8B0YsGpXRylxDGQ19gWw5/9A8+RrRfvSeiOXKw2aoRrRQe/DttlceiL58z1/FByQAFZ3LlzPJz6OxXilT9qiaMMBkYTGfSQLhdj0ESCRsmYSHbuK3dO8J6rdGMRdCF0cQzYVerKNwBsx94rVMvJPdAb65E4RkNmgz1PLXFkiQTNJhp1ElPVPDgd4vJGk7a/yLLg+jFmhPjWRa6Rema8AeLd4hNLHIVUND4HjbawCQQmIWHCRMygOTZGrh9KHCn3pEzQOLHZyrTNvj6TkKWUOLo+R11DZS5pEkI7YFl8ngenImgkZdBiD9SKBgbNYsEgRR0mITHdvufrkzi6Hn2/Ty3mDtUZTkgTi8gAhZP3CABCNjEMAqyJT9uDJpOKe8eSQaNLdIHpF4suBm3s6WHQ1oNrqaMHLW5A8t6rG2Tr6IJk0OTYAB1sk5w/ZTHCOWghM+jp6UGzImc58Xc9DJofmIQwYgbN8wSDdnmD1rW65lgYe1xL4A3EGTR6d2eZxLs+PYM2bRKiZxYrj5mEUO//uiN60HzipAkQZ6QkRkhHTCRMQhij/2xMzkFbBgYtDsGg0f/asuenp2HuTsigBQnahVVNDJqOHjQIBs33aV0VgWkGjVriGJcXTDxObydtCwaNc47eWJ/EUUePQNOxhTOULzTglA26MrG9dyKeNWqJYzzwbpK7OE6zCdRFg2bNgmOx0MWR1Jo79rNfXAIGLerV0segNYIzijIYDhm0kUsqeZWQe3wUjMOhTnSTJiFUjF38DH5wMsTl9RbJOhJiUHXEoFHfuXogldMxr1Em8a4n4xC6tRzLimz2ifuA46N+dPSEAeLcGk18LS0rQMSi0TJoUQ+ajvE0gEiu+bIyaHoqc/pt9qXEkTJBiwekOqyqGQts9jUcxPGkiVriGO9BE8YWxAyaxTDxfAwnoupIyfwwxoS5i8+19AhINmHk+uQujtIa/t6JYNDoXRyjs0qXi+MokItSz9ZijGGt6YQMmg6JIwA8eXGFbB1dYIyhWbO09aABUWFTsuKUa/RGLqlUWUKeFSPtEseAaSI6q+LFlgedES5v0BqjyR40QI9Uru5YGHmiB02H+gQQvbk+sZInuo6BxJHY/VisE5c4ki0HIGhHCBJ5HUZNMkGj3COMMaw2HJwOJsJcTsNZbDEmjI2WkkHTlKAJm30R7LQJbZ3lgyYljpQz3jZatfAh1sKgBVSuRzyXDJhurKaWOEplix+4OFIHI/Lg74wmAOjdB23Gphg0ysBHMkvDiRdIHJeIQdMocbRDNkEPgwYA661aJHGknIMW2xPnfUi1RLNmRzb7GoIdHcqTkBkc65E4RkUJXRJH8afsQaOSEcvPdeuoD8/nuLxBzKDZVpDAiL+TJ2i2FZoy0M/KizFoxImFY1uYxCSOpH3wsRjE1yRxbDg2RhM/mDNLuhQAYEcDgwYAF1br2O+ORL+bJgZtaXrQ4i6OE59redHYwZyC3sjFSt2mdQSMMWjrTYf081kWC+es6ehBCzq1xBw0ailDvKJEnBDG5QXUzoNAJHGMTGvoDSc8X7xkGKNlYySDNnS9QOJIt5ZMyO4FJiGUzDiQ7EGjvWcyINYVrAIi4T3q6+1BWxY0HTsaVK2DQdOQMMWLEFp6xe2ouAPQX8fIvEP289FcU3ne/om//XnYFsOHbmySrCPhWCyUAAJ0JjIS9YCJ0dG/7YQ9aPSJRS0wlxPrUdvsB9FVzG1ZC/PpeuTJp4QcTfPS49uk61xYbeCgOyaXwEqwoAC+FAxa0sVRt8RRVxB31Btjo01rWgAAW0FVQoeLo2UFEkcNTaXx+V3UzcBTEkcdDJol3KG6Q9kTSWxuEbgM6Rh4HDFo9BJHx7bQrtsYez7qjkUe+E8xaJp60KTEUUfQv96shVV3SpmvTC4o5d+60axZ6I/03Ssd7sfx50mHxDHa83qKEjODqokSNHludEcufup7n8R7r9Ea4zjBgGUpfiVP0Ox4D5qeM9j1OHliYVsMk2Ad6tjRisUgcqYWtTyv4URz0HQkaA9ORdvPf/iRa6TrXFhtYL870qL0AqK4eCkYtDgmPieXCgGBxMvngaU5bSIjE87uyA0HmFJCzj/TMwdNBvq+tpen60uTELq15DMsZvDQJhWAbD7m0Vw+4nsnCxQ6egflnhcSR9pB1UAkc6ScKyQRv3bUDIZuuRcw3cOnowftIuGwXt1o1uyY4yb9enokjtG5pNMkJDLGof2MjDEhTwoCK5voxuk286rZLHxvAuK9TbueSAg9Df3boc2+75Mra2q2MAl52BnB9TmubdFJU+OjfmRPJHkPWi0w9NIkcfyrf+g9+OmPPYUP39wiXefCWiRx1NGDJgvg8yoh507M72k0CRm5ogpCabEPRLKQk8GE3E4XiAJiLRJHJtqOdbjjxBu4fU67nnyBCpt9nzz4rtnCJETaclOzuhaLzASog55Q4jjxtEhe1ps1PDgdkffxAVEAWbct8oNfBiKho50mBk2C8lwee+IzLVOC1oj1Neuo2upImOLFUy09aAmJI/X8LkCc/dSMRTxB03HfZMKEsAeNdr26Y6Hfd7X0oEnJ/MTj5AG4EyS6d4IxLlc36RI0liJxpI6xJIPGNZlpvPfaBjl7DIjZw0f9CcaeryXxtKTN/rzvo/9V1MLneiqBkcTRwwpxBUsGqBOPa2HQpNRKl0mIcHGkr0yEM2p8+mZga0riqIFBCw5+OdiW2oEzzqDRV+UiiaMOwxXJ+lAz40BkIqCD9T8bBi2WoBF+RmmmcYOwIq0bzbgcUENmoWMPNmtxBk3/ntdxHS3GwAOGiWwOGosnaDquoxWaaAD0Dn2twCBHh4Q+GlTNyZkf2ct3N0jQrhEmaID0SkA4v446xorPQdNRVNKFC0Hhb78z0vK5WEGTkHPHoHEwfT1onGPkeths07kqAtPzkaj7VIBIhtIkdKaUYIhchqhvmzzoPZ9+3klcXjDxOXlg4FjW9OB04uRa7n9O7KoIJExCfE5eMZZJhY4ETSbuOp7r5Bw03RJHyvv2B168jP/s9z2Nz3zPk2Rr6Eb8/NXB/Oh0cQT0Shx19l3aFgP35Tr0DJqOXj6p0ODQI5VbaTjojfQwaFHrA33vlGNZcH0/TNCuECuipBugLpOQqAdNj8RRFy6uihj/QWekzWafcz73+Dh/CRpnGhk0wOU++Xpx3T610xsQJYSToP+BEvFeLWr6PWTQ5KBqwvXkrLAvvHOI04FLPoRYBjunA2GzT83qijkdHJwxbT1oo4lwcaROduXL7OZ2m3QdIAoOdDzXMlgduholjq2IQaOU+dYdC/+3P/Ac2c8/C8TPDD0ujvR70LJYGMSdyRw0Tf0joTqJeFA1AHKHYCBSaOhi0FYbNrojV8t5L9+d0iSE8qPJcTh3jwdYbzpTCgMKyDFG1IPTJRqOHZqE6JiDpgvSfEowaPTrhXPQloFBY4x9GsCnP3LFAoce+15hEiJchsgTtNiLmjrQByLmQEeCZgUSRx/0muXIZl+ahNCuxznwr14/AAB8+5M7pGvJYOd0KBK0FnH/oBNIHBnT6+I40SAX/ZGP3sS1zRb+8g+8QLoOEAVXGy16d9aoB0081zqkGtMM2rlTzJ8p4gyazkHV1GjWRBCnw9ZfBvc6+y4ti4F7+hg0XRLHiedHJiE6GLSxp6c9QM5BC2z2KZMYOU/uzvGQtP9MQjJo4X0j3ip1R7hver6eXi1dkO/no/5Yy7s6lDgug0kI5/yzAD770lX7Jzl0MmhiCDH1iyb+otZRaf9zf/A5cA78wPuvkq8lJY7QMABQvtQ8zuH7emRDEvQvGfHzTwYT1Gz6Z8AKJI7QMB5hyiTE91EjvnGfev8VfOr9V0jXkDgNxiJ8z7MXydcKHe2Cwgv1ngT0mYQsI+L9xssyqBoQ/UUng4mWZCluRw/o6bOzLXoGLc4q6XiOawHzE5mE0K650nCEZH/sku8TyaBNPA3jdywGz+M47o/DebOUsAOlSzioWoPEERCM9TL1oMlivutpstkPTUKWIEGLQ2sPms8x1lAJjL+odTBoO6sN/L/+w/eTrwMELo4cWhit0LgjOLAc6nJSDLos1E8GrhZzF9sKJI6gr0rPuDhqCEh04Y2HXQDA739hl3wtmUiHjnYaXjTrmnrQlhH6JY66GDSxDqVpjIQdS9CaNUuL7EokaPKz0awXr1HpcsOUNvQA1aeKIFU8JwMXLU3zISNlDd1aNZthEtjetzSchzLQl2IoHT1oADAYe8uVoIUD6H0thX0xB21JGLQ4ODS6OPIgQSNer2azMJHRwaDpBAvmPfhch5GG2Oy9sReYkug7QOhdHKNRDDrGI9iMwdOUWIcSR1e4OC4TE/OXP/Ui/ukX75DPcQHOxtFO9liIM2x5Xtg6MG0SooNB03N/5OfSInGUM0SHLloaTK8APT1oUwyahr0hbPajHjQdDBogeqrXGrRSQPk+ERJO2t4p4Yapb5CzlMrJxJr6yJejQQYTT6tCiRqSedR13ywWKJSWbVC1TgbN9wUtTr0eYyxk0XRINHSCITYHTYPN/rc8voVf/8o9uD7XGjBSN8RLduJkMEFbg/ugFTBonoa5ZA0nLnGkX08nnru8hj//yee1BOByD+p0cVxvib2oIxlcNsTnoOnY8zpMQoAoQdMtcdThSgxIBi34bFQ2+3EGTUNMUAslXuLsoH51rgZjYk4GE/JzShZP/+kX72K/S2sCEZqtaBhPAwTvaS7WAzQwaLE+52Vi0OIfRU9iHUgc56x1Lt+qWhg0xuD6vhYGDYhYhIaml4wusCBD8zT0MgHAf/Ltj+Odgz6+fPtEaxMrtdOWDIBPdTJogVTDJg6+bYuhZjMMJ34gcTyXx9KZw04waDrnoBl5Y3nEJY46ggJ9JiH6JI4y+D7VyKBZFqIEjcwkJDauQEPxIyzuaErQJIPWHbnaTEL+5ev7AGj7tOQcNB0FaSDoQeM8YGM09KAFz/ZgslwSx/i90hE32iyaXZeHcxgJMS3SCdsOetA8XQnacjJoljxAfF/LgfXcpbXwv3U03ktQJxVOzGaf2sERiExCdAwSBUQf5nDiYeL7JthfEGcxE0q6OOoK/pcJUyYhS+biCGiyh7ci1lgbg6bDZj/2c3WZhAAR+86Iu9BWYioQ8kHViZ9PKnGM9fLpZGJCaSq52kU8b/2xS57E60T8XukzCVlKiaM+Bm0Y2FXrsPWXG3/ZEjTGpMRRz8aPBzo6JY7UMtiQQRtOyGegAUJi4/tcyyBRQDDH/bELzo1cblGEM6EmsgdNT+9Kq2YvVd+gLsQLLcvk4ij3gh5zi+i66ShcAYHNPjmDFv1cPTb7QYIWMGjUR/BqLEGjVmgkE1zKOKRmsaCXT5cboGBidEkqo3aE5ZI4xregtgTNx3JIHBljn2aM/RygtwdtELih6WTQdFUBdYGBhQeIjhhON1UtQc36ODGrYB09aDaTDJoe5rNZs0Kr7GVycdSJcCaURokjIFg0k6CVh5QCMqbJJETTPZLBvhaJY+y66XBABiSDJnvQiExC7HiCpr9/VZdJCEBfSEqeTbQ9aNKQRE9h0wpaEXSZoslYeDjxtCqUqBH/LDrO4nAO2jIwaJzzz3LOPwOIBE2LxDGw2Qf0vNgaSypxFBsRQS+THk12+N86XRyJq4Dxl7SOHjQr2P+uphdNs2ajE8wMMxLHxSBvk06JIwCst2rmni0AKXHUFejoukdy3+lgcON7XJuLo6bAW0KHomBW4kiL1ZgKxNY0Q1SCMgCXe2Ps+loCfSsWX+lQDIU2+xNviSWOetbjy2gSIiSOeg9+HZXAppQ4LhuDFuj1BQWv4b7Z8QdNp8RRT6MzAD1z0KbGI+hh0HojmaCdu2PpkQBjDI7FYjb7hkF7lCHVEjoCOUCf5Fu+O3UoT+Jyb13qE0sHgxbbEzrinVqCQaPeKysNfQ6myYSaVOIoZeaur9XFkXM9hR4pcVw2k5D4GaxF4mgtEYMWh2DQNLjYxQ9IjQxac9kYNADg/EwYNJ3nB/0ctBiD1tDDoLmexh40x45JHJfrGdAJx2ZhD5quwP/yehOb7ZqWtZYJ0hFtmaRCQJxBo3+O11vRvtPFoDk2g6+xB03HdYykeXpcHB3bCtkY6s+XTDZJJY6hzFyPBFAyMZ6mHjRZdOGcvk9RJ+LXTg/zGZiELN+gaoaaDgYtduG09KAtKYMWUvA+13JgxV9sOiWO1AxC/OfraIZ3LIax62tzcbQZC6u3OtzflhWOZYUSR10M2n/9R94L15tvGWwwDZ3zwnRCfh4deadtMaw1HHQ0zkGbZtCo5qDFEjQdLo7SAdbT04MGCKOQkTvWvv8pP5sTk4rqkzgKt2Ud68VbcJaJQdPtXRDOQVs+Bk0Po2VpZtCW1WZfSBwDlyHNPQl6JY7ULo7xHjT6ukq77qA/9oIeNPo9yZhorAb0MT/LCDsmcdRVoLiw2sDljaaWtZYJsgdt2fa7PC9kDzc1JIumy8VxelA1PYOmxw0zYNBccc907Eh536h70JLQwaCNPV8bg+b5HFyTQqkRM+LR6ZJNDf02+yjEoJ3LbEC3O5QOBk0mZsvn4ijocI9rYtA0Shx//v/yEj76xDYAHbNc4j1o9HtktWGjN3aDgZvky8G2WCivWTbJl07UbP0JmsFikK6Dy3af5FmoO0E7kzloy2KzL5kfT7DvOoLUnZW6WHuJ9r+8VbokgJbFwvhKxz1rxGY3LtFtOxOTkKXsQdM2qFpzgrbMDJqQOOqpFMercdSB/ideuIQP3dgkXUNiugeNnkFbbTroDl24vq+lB0JWAoHlC1h1Iu4+a67jo43QJGTJChJy37maEjSZ6Oqy2bcsaDUJ0SNxTJqEkC+JC6sNAPrPKSnjpMBZMTE+17NePBZepkKqbuVVOAdt3veR/yaKoUviqLuCJV8uy5egBYMUNbkB2poPSF3BSNwlUgeDttJw0B258LmeF6iQOOoLDpYV8WTaDPx+tLGsPWjyvPA1JWgyHtBrs09rEhIvZta0mIREvVOAnjN4Z/VsGLTh2CP72bp74CUTo29Q9XL2oE2ZhBiJ4+KwmKWHidFtErK0g6oFPE1ugFOVEA27W75cqE0S4sG2DgZtreFg5PoYjD1t84xcw/xUxlSAsEQv0GXEskscdTFo0lhLV4JmxSWOGhg0HfPrQpt9jSYhkkHTjeGEjkHTzcQwxuD50Dao2rFYmMws0+uFMRZ+Hi3S1MB9sz/JLxacCxdHxtinAXz6I1cs2JosuHWbhMjKxLIxaLLC4+mag6b5gIwa4ukOfWBa5qIjEJFJ4Mlgoq0SKJPcZarM6UZ8n+huvjcoh8gkRN+aP/wtN8gLjk9dXAUAXNtqka4jETJoZ2ESQsWgxc5AHedvNKg6MAnRIXFcEwnayWBCv1gM0uWWAvrjD6FQ8nx9CWHDsZduDhoQtFlo6uWTc9AenI5yv+9cJGic888C+OxLV+2f1JWg6TYJeWxnBdsrdaw2z8UtKQwhcYQ2swndVLUMiD1OLXHUy6CtBmsMJp6mBA1wfT/8b4PF4BgG7dzAskQ/tc779N/9sfeTr/EfvXQdN3fa+NbAQIkauouajqWXQdPhlhd3HwT0moQc9/UmaKQM2lRiTbZMiFDiyLm2Qk/dsUSCtlxcAmzG4EFPgsbC+5a/1rnLBuIuMpRYjQXBOhi0H3j/FXz/ey8v3ZBexkTfoMf12OwzxkKjBB2Bvj6JY8wkRIuLY7T/9Wnpo/82WAzxkQjLJp1bRjRq1tLdJ8YYvu3JHW3ryQKq7J+ihsUY/LA7hN7FUQckgzaRPWga1pTD7bUnaIQMWjzG0RXv+DyQOGp6b8qCyLK9p0OJo4aPJSWO806sc5cN1DUlaLKBVaypYw4UW7rkDIhVCjQNqgaiKpbOuWvU/RZTNvuaXByjtfUkaGn/bVAO8X6VZTOfWEY0a/bSJWi6IQPGMaE7Xxz2FING887WPWPKSfSg6Vh/qx0waIMx+VpxDChNQs7IxVFXCwkQzUJbtve0PId1KYZ8zjFPeHXuMoKGpkbgeAOrDhfHZQUDADkHTVMgInMZHQfIZvCSoZYdnlUPGjDNylAhvsSySSd0wtZcwTWohmbNWrpARzd+6FtuAAC+86kLWtazNAyq1g1ZzNHppHt1U/Qofvy5XfrFYhgSMq26TZqkxFHMXdPFoMnxIFqW0wZ5v3QUJ6RiyJ/DVRuJYwZ0M2jLiqkDRNPLTLBNvpYD5I9+6BpOBhP86LfeJF1HJmgtTRX3tViCpmMOj2HQ1EAGWoY9Ox9oOoZBq4oP39zC2//dp7StJwI5WpMQ3QhdHF19PWgbrRp+7//xfeGgcV3ghP3iugtkdjBPS1dLBxC1/Czbe1qnxJExcc/8OanF+UvQNDFo2ytRgrZszoo6wRi026fLZXRJHH/8u54gX0fOwtExAw1IMmgmQTsv0CnTMKiOZs1eukr0ssO2GDq8hbHVQn1JziopjR65eo2atmJxlg785Hc/gf/Ttz1G9vOnXRzJlgnBGCKTEM0SR90yXGrIe6fFfZMxcM5jbrDpOHcJWl1TghZn6ozEcXEwRAYauoJGZwkrPFYwf6Td0GSSE+tB0yPViP/38tw33ZBnlUnQzgdaNRsT4hEdBmphMYa/530C28//AP7kkpxVToJBY0vCDEr8wh9/CWOX45PvvUy6ztR4BE1SOc/XnKAFhMWyqTTk9dNR2A8ljnPY3HOXoOmSOMZhgp3FYbFoALGuAyR80Jbstjm2hZW6nkc2vo4WBk3zgPFlhWHQzhe+/akdbeYWBmpgW8AATRyv0isndCGcgyZ70JbsDP59z1/Sso5uiaNlAXeOh7hzzKdUX5SQLOvzV9a0rKcLlkYGTc5Bm+ctd/4StNq5+5W/ucGiIc66Ki6S8Fy2OVA1i2mTONrBjKax5xsXx3ME04N2vvBnvu/Zs/4VDEpCmiYtUxFEugSHJiFn+cucY+geVG0xhncP+wCAC6t6ErSv3jkBAHxU05xDXbA1FvbleIR5EsdzVyc5CwbNYHEwsFDiqMtlSKcbj07YFtMypFpCzqmxtZiERP+9TIGPbhgGzcCAFrIAuExFkJBB02gSsoyYcnHUNKhawiM0P4ljEsRzH7qxpWU9XZC3TldLB+cc88bnnjs6SpdJCAA8f3kNX7/f0bbeMsJiCHssNMT5AKLEbNleMjXb0sagAcCzl9aw1xlpCUR0N1cvKxzTg2ZgQAr5XlmmZ4wxBttiWm32lxFnMQdN4mFnRL4eAPyPP/IhfP3+KVoaYxEdkASCPpv9+XPQzl+CppFB+5U/+R3ojeiGGn4zQNqJAvpeaDrtUnVCJGj6HtnnLq/hX76+H1ZVKRE/FJeN+dSJSOJ47sQRBgbnCsvEoAHi84wMg1YJ8WNXt/vxg1M9CdqnP3AVn/7AVS1r6YRO7wJpEjIvuzh/CZrGrL1dd7QGxMsIBhZS4rokjmGCtmQv0D/3B5/D4xdWtK333CXRBPzaXpd8rSmJowkOFkZoFWzyMwMDEsiqt71kD1ndtsIEzRzBi0F7D9qSxThnCZ3tAdF4hCWz2W865+5X/qbGVEVJ06kvLYKXrQr4xz5yXet6H3lcaMxvbLXJ19ItDVlWyHl5hkEzMKABh8jQlo5Bi/UgLJvNvi7E94Qeu3byJb5pIMMOXRJHzrEcLo6MsU8D+PRHrlhae9AMVEDvgQUsr8RRN566uIrf+DPfg8d26Fm7aYkj+XJLC2noYva+gQENIgZtuR4yJ+ZqsWQfTRvOYg6agRrodHG0gtafpUjQOOefBfDZl67aP2kStPOF+Pmhj0EL1jNvmcp45pKeWSdTLzZz3xaGrODWjdutgQEJZExFfU79xp/5HjQ1xjs1K14kM2fwItBtdmUSNHXQKXG0rCU1CWmanrBzhbOwT5cvF/OSOT+IWxKbl87ikM/YUxf19SoaGHwzgloRoqs4JmEYtOqYmuepqZcJANYaDv6XH/8o+XrLDJ3u30UljueuUcEwaOcL7CwkjnI985I5N5geVH2Gv8g5x2AsfKFevLp+xr+JgcFyQla9l+2YmupBM0WyhTA1B03DNZTrfc+zF/Hhm8s1l0w3ZH1Cx9a3pEnIvO+j/1XUwpiEnC/EN7u2pmo5cNBE+ucGTHPlcVkhHTdfuGISNAMDSixbDmOFypMz/kXOMeIxjk6b/bpz7kL5Rw6WZgbNLzCo+tzd1c2V+ln/CgYlMM2M6Dn5LSNxPHcwEkc1kMNKXzQJmoEBEURUtWxOh5LxWa5PpRfWVB8f/XpyjZpt7lpV6BxAz4I5aEthEhLHss0e+WaCth604E9DxJwf6Ha/Wlb8zR/9MP63r97H7lrjrH8VA4OlRChxXLJjKnI/XrIPphHxd5dOBq1mm7i4KuTt0iVxBABv2eagGZwvTLk4aj5DTKB/fmBs9tXgvdc28N5rG2f9axgYLC2WtQctHHJvDuCFYenuQTMSR2XQuf/lGktnErJ8x+Jy4ywljuZFc34QLzaaHjQDA4NHFXJQ9bK9XsL35ZJ9Lp2wpySOOuzaxZ91w6BVRihx1JKgiT/n5GfnMEFbtlNxyRG/W/ps9qf/NHj0YRuJo4GBwTlAxKAt1zllhQzCGf8i5xi6TUKYkTgqQ1TYp19L3jc+5ww5h3fVnB7nCWcxqDpcz7xpzg3irJm5bQYGBo8qwqr3kp1TYQ/Osn0wjZjqpdYQXctigZE4VoeMF7Uwn0uboJnq+rmC7sGNgN6BgwZqEL9Vxn3TwMDAQC90MgjLCt0SR88Xk7QMg1Yd8nbpKOwXvV3n8K6a0+NcYcokRK+Lo4nzzw90u18ZGBgYGEQIbfbNi3NhxF9dOhRDbuAyYRi06rA1SnwjBm3O99H/Kophzo5zhbhcQhejpbMSYqAG02YyZ/iLGBgYGORgWV0cTe92dTDGwrhDR/zhyQTNzEGrDJ3zc00PmsEjAessGDQzz+XcwUgcDQwMzgMiF8flOqeMzb4a2BpbLFxP7EUjcawOne7fkYvjsiVo5vA4V4jfLkebxNFo6c8bbM3uVwYGBgYLYUkZtIhBOONf5JxDWt/reI25QQ+akThWh8xxdeS6yytxNDhXOEuJo6kEnh8YiaOBgcF5gAyqlu31YhkGTQkkg6ZT4mgYtOo4CwZtXpnnHN5Vc3icJ5yJxDFc2+yV84KpQdXmvhkYGDyi+PjzuwCAF6+un/FvohaRzb5BFYSJroZ4xzUJmjLI+/Uo9aA55L+Japjg7XxB81yQ+JqWObPODabnoJln3MDA4NHEH/rAVXzi+V2sNM5f+JQHnSYJywxHIxMpGbSGkThWhrxfOvxWQonjHI3jObyr5vA4T4jfLW0SR83rGVSHkTgaGBicFyxbcgaYHjRVCF0cjUnIuYJMzHQwn8YkxOCRgDXFoJkeNIN0nIUU1sDAwMBAwGLTfxosBkujgkcyaI6x2a8MnQyyVVDieP4SNMOgnSvE97ph0AyyEL9XRmJjYGBgoBeyMMZMjFUJOuegSRfHmknQKsPSyHwWZem0JWiMsScZYz/PGPvHsa99jDH2OcbYzzLGPlbwBxH9hgYUOJs5aKYH7bwhclA641/EwMDA4JsQ5gxWA51ugNIkxDbBTmXYGvd/JHGc831Ffhhj7BcYY3uMsa8mvv5JxtirjLHXGWN/Ie9ncM7f5Jz/ePLLALoAmgBuF/ldDIN2vsDOQOIYSTXMXjkvsMIZJOaeGRgYGOiGThe7ZYaUG+ocVK1rxuwyI5pf9+hIHIt2uv4igL8O4O/ILzDGbAB/A8D3QSRXn2eM/SoAG8DPJP79j3HO91J+7uc457/NGLsE4L8H8KNzfxNzeJxb6JM4SqmGwXmBcRAzMDAwODuENvvmCK4EnXPQfC4ZNHPTqiLqHdRhsy/+nMegFUrQOOe/wxh7PPHljwJ4nXP+pliQ/X0Af5hz/jMAfqDgz/WD/zwC0Ej7HsbYZwB8BgA+csXQuOcNZ2ESIjFv8xs8OjDyGgMDA4Ozg61RmrfMiAZ+06818UQIbRi06tAZg0TPGJ1JyDUAt2J/vx18LRWMsR3G2M8C+BBj7C8GX/tBxtj/BODvQjB0M+Cc/xzn/CXO+UvBT6rwKxvoRvys1+3iOG/GhMGjg2gGiXm+DQwMDHSDhSqGM/5Fzjl0JrqRi6MhL6rCtvTdN9USx8rgnB8A+KnE134FwK+U+kHm9DhXiN8t/QmaydDOC2yN+m8DAwMDg2mY3m010Oni+G1P7uDtgz42WjXytZYdOucAFjUJqZKg3QFwI/b368HXiGEOj/OEKYmj5h40k56dHzCN+m8DAwMDg2lENvsGVaAzQfuv/vB78ZPf8yS2V+rkay075O3Scd9YQQatCi/6eQDPMMaeYIzVAfwwgF+t8PMywRj7NGPs54K/UCxhQISpOWiaWHgjcTx/MD1oBgYGBmcHI3FUg8gNk36tumPhqYur9At9E0CvxFH8qSRBY4z9MoB/A+A5xthtxtiPc85dAH8KwD8D8AqAf8g5/1qF3zkTnPPPcs4/E/w2FEsYaIA2Bi3c/CZDOy8wEkcDAwODs4M5g9VAzow2/dTnC0xjkbjoM1bUxfFHMr7+6wB+vfivpQBm058rnIWLYyhxNPnZuYGROBoYGBicHXT24CwzdEocDdRBZ4FC7g0lg6oNDBaF3OuM6ZtxVXTGhMGjAyNxNDAwMDg7RGewOYSrIOzlM9fxXEHn/o9iVLoeNG0wPWjnF/JunQXdb1wczw/MDB4DAwODs4M5e9XAMGjnE9Ggan1rLUWCNt2DZnCeEA5t1HhYrdSFctcckOcHxuLZwMDA4OxgetDUwMz0PJ84izlo89bSNgdNHcymP084Cwbtv/3B9+G5y2v4zqcuaFvToBqYxuqVgYGBgcE0TA+aGtgaXRwN1EFnkTi09J8zYPz8JWhm158vMP10//ZKHX/m+57Vtp5BdeisXhkYGBgYTIMZmbkS2GcQ8xhUh6UxBpHPmjMnQTuH9Wqz6c8TdA7/Mzi/CPeJCQ4MDAwMtEPGiuYIroawB81cyHMFnUZlUVy8BAmaMQk5v5CW9yZBM8iDGZJqYGBgcHaIJI7mEK4C+wz67g2qIzQq03DfwjXsRv73kf8mCmAGVZ9fyLPeyCYM8mCcrwwMDAzODmGCdsa/x3mHZTEzLuYcQmes6nrCYfwfbf147vediwQthNMA7NpZ/xYGJRBRuWf7exg82jAujgYGBgZnB3P2qoHNmCk0nkNEffD0aw0mLgCgVbNzv+98hc27LwJrl8/6tzAogVDiaA5/gxwYeY2BgYHB2UEWUc300GpwLGaS3XMIndLU/tgDAKw0lilBMzh/kMyIqSgZ5CCcHWNOJAMDAwPtCItj3KRoVWCZBO1c4ixcTHfXmrn/vwmHDEhhGctZgwKwzJBUAwMDgzODfEeb9KwajMTxfMLW6OL4/e+9gv/ik8/jz3/yudzvOxcJmnRxPDk5OetfxaAkzmJQtcH5g5E4GhgYGJwdLEOgKYExCTmf0NkHb1sMP/2xp9Cu54+iPhcJmnRx3NjYOOtfxaAkmJE4GhRAyLSabWJgYGCgHfIM5oZDq4RmzUJjjvmDwaMHnYOqiyI/fTMwqIgo8H50Nr3Bowfj4mhgYGBwdjBnrxr8xHc/iU++x5jZnTeEg6ofIdrKJGgGpJBnvtFkG+QhOhzNPjEwMDDQDSNxVINrmy1c22yd9a9hUBLSoOxRIhMeoVzRYJlhEjSDPOicQWJgYGBgMI3QJMQkaAbfhGg4QpZadx6dtOjR+U0MlhKGGTEoAmYkjgYGBgZnBhb2oBkYfPPh9z2/i7/5ox/GYzsrZ/2rhDgXCZpxcTy/CCWOJu42yIEZx2BgYGBwdogYNJOiGXzzoVmz8R+878pZ/xpTOBcJmnFxPL9gMIG3wXzI/WFs9g0MDAz0w7yiDQweLZyLBM3g/MK48xkUQSRxPNvfw8DAwOCbEaHNviHQDAweCZgEzYAUxsXRoAjMOAYDAwODs4OZg2Zg8GjBJGgGpGCmt8igAGRiZiSOBgYGBvoh5z8ZBs3A4NGASdAMSCHDbSNxNMhD6PZptomBgYGBdph3tIHBowWToBmQwjBoBkXA5JBIs08MDAwMtMMyNvsGBo8UTIJmQApjEmJQBHbIoJl9YmBgYKAbxmbfwODRgknQDEgh423HMCMGOTADzQ0MDAzODvLoNemZgcGjgXORoJlB1ecXZg6aQREYm30DAwODs0OoXjAZmoHBI4FzkaCZQdXnF2HgbSJvgxzIBN5IHA0MDAz0w/SgGRg8WjgXCZrB+UVoEmLiboMcWKYHzcDAwODMYHrQDAweLZgEzYAUoc2+YdAMcmAZiaOBgYHBmcHUxgwMHi2YBM2AFFbIoJnT3yAbjDEwZhg0AwMDg7OAkTgaGDxaMAmaASlkvG1MQgzmwWLMMK0GBgYGZ4BI4njGv4iBgQEAk6AZEMNIHA2KwmJG4mhgYGBwFohMHE2GZmDwKMAkaAakYEbiaFAQFmNG4mhgYGBwBpDvaMOgGRg8GjAJmgEpjMTRoCgsxsw+MTAwMDgDWEbiaGDwSMEkaAakCCWOhhkxmAOLGScxAwMDg7OAeUcbGDxacM76FygCxtinAXz66aefPutfxaAkZFXOMYPQDObgT378aXzrE9tn/WsYGBgYfNNBihfMHDQDg0cD5yJB45x/FsBnX3rppZ9M/n+TyQS3b9/GcDg8g9/sfKHZbOL69euo1Wra1jQMmkFR/F8/bgowBgYGBmeB0MXxjH8PAwMDgXORoOXh9u3bWFtbw+OPPx4aUhjMgnOOg4MD3L59G0888YS2daMeNG1LGhgYGBgYGJSAKaIaGDxaOPdh83A4xM7OjknO5oAxhp2dHe1Mo3FxNDAwMDAweLQR2uwbCs3A4JHAuU/QAJjkrCDO4jqZOWgGBgYGBgaPNiKJo8nQDAweBSxFgmbw6MIwaAYGBgYGBo82LDMHzcDgkYJJ0BRgMBjge7/3e+F5HgDgk5/8JDY3N/EDP/ADU9/HOcdf+kt/Cc8++yxeeOEF/LW/9tfm/uysn/Xd3/3d+OAHP4gPfvCDuHr1Kv7IH/kjAIBf+7Vfw1/5K39FzQdTAEmcGQbNwMDAwMDg0USYoJ3x72FgYCBgEjQF+IVf+AX84A/+IGzbBgD8uT/35/B3/+7fnfm+X/zFX8StW7fw9a9/Ha+88gp++Id/eO7PzvpZn/vc5/DFL34RX/ziF/Ht3/7t+MEf/EEAwKc+9Sl89rOfRb/fr/ip1IAFIkczgNjAwMDAwODRhGV60AwMHimcexfHOP7qZ7+Gl++eKv2ZL15dx3/56ffkfs/f+3t/D7/0S78U/v0Tn/gEfuu3fmvm+/7W3/pb+KVf+iVYlsiLd3d3566f9bMkTk9P8Zu/+Zv423/7bwMQksKPfexj+LVf+zX80A/90NyfT43QxdFIHA0MDAwMDB5JREVUk6EZGDwKMAxaRYzHY7z55pt4/PHH537vG2+8gX/wD/4BXnrpJXz/938/Xnvttcrr/5N/8k/wiU98Auvr6+HXXnrpJXzuc5+r/LNVgBmJo4GBgYGBwSMN04NmYPBoYakYtHlMFwX29/exublZ6HtHoxGazSa+8IUv4Fd+5VfwYz/2Y5UTqV/+5V/GT/zET0x9bXd3F3fv3q30c1UhlDia/MzAwMDAwOCRhGUGVRsYPFIwDFpFtFqtwrPFrl+/HvaK/dE/+kfx5S9/udLa+/v7+N3f/V186lOfmvr6cDhE6//f3v2FVnnfcRz/fOKfHlc6tbSmbmdMwYg4AwepBWHKAmLrsNQOnM2NlQy6i3gnjMgYG3QXZSJejG2wabE3SwxqmZvbXNVg9UZXoax1W5xsNou06rJb2TD77iLHzD8nPdGc5Pd7zt4vCHnO8+Q8+RB+PDlfft/n98ybN6VzN8p4iyNPqgYAIEs0uQB54VPzFC1cuFCjo6OTKtK2bNmigYEBSdKZM2e0fPlySdKFCxe0ffv2h/7dhw8f1ubNm1Uqle7Zf/nyZa1ateqhzzcdWlhmHwCArP2vxZE5NCAHFGgNsHHjRp07d2789bp167R161adOnVK5XJZJ06ckCT19PToyJEjam9v1+7du7V//35J0tDQ0IQzXhOdS5L6+vrU2dn5wHsGBgYemFVLZXwGjZEGAECWWGYfyEtT3YOWSnd3t/bt26cNGzZI0oT3lS1YsEDHjx9/YP/58+fV3d1d8z2fdo9ardUdr1+/rlu3bqm9vX0SyaffnXmzFmbQAADIEsvsA3kpRIFm+0VJLy5btix1lJpWr16tjo4OjY6Ojj8L7WHs2bOnYVmGhoa0d+/ehp1vqmyegwYAQM7u/I+mxRHIQyEazyLilxHx2vz581NHmVBXV9cjFWeNtmbNGlUqldQxxn123mzNarGefHxu6igAAKAG0+IIZKUQM2gorkVPlHT2Wx1aPL9U/4cBAMCMM8+pBrJCgYZp97kFeSz5DwAAJkZ9BuShEC2OAAAAmB7jE2jcgwZkgQKtAbq6urRo0aJ7nj22bds2VSoVVSoVLVmyJKv7wgAAAO74zNzZemx2i76zeWXqKABEi2ND7NixQzt37rznYdOHDh0a3961a5dyXuAEAAD8/5rVYg1+f1PqGACqKNAaYP369bp69WrNYxGh/v5+nT59emZDAQAAACic5irQftMjffJBY8/5TLu06Y1HfvvZs2fV2tqqtra2BoYCAAAA0Iy4B22a9fb2qrOzM3UMAAAAAAXQXDNoU5jpmg63b9/W0aNHdfHixdRRAAAAABQAM2jT6OTJk1qxYoXK5XLqKAAAAAAKgAKtATo7O7V27VoNDg6qXC7rwIEDkqS+vj7aGwEAAABMWnO1OCbS29tbc//BgwdnNggAAACAQmMGDQAAAAAyQYEGAAAAAJmgQAMAAACATDRFgRYRqSMUAn8nAAAAIG+FL9BKpZJGRkYoPuqICI2MjKhUKqWOAgAAAGAChV/FsVwua3h4WDdv3kwdJXulUolnsgEAAAAZK3yBNmfOHC1dujR1DAAAAACYssK3OAIAAABAs6BAAwAAAIBMUKABAAAAQCZcpNUPbd+U9FHqHMjaU5L+kToEssYYQT2MEdTDGEE9jBHU88WIeLrWgUIVaEA9tt+LiGdT50C+GCOohzGCehgjqIcxgqmgxREAAAAAMkGBBgAAAACZoEBDs/lp6gDIHmME9TBGUA9jBPUwRvDIuAcNAAAAADLBDBoAAAAAZIICDU3B9lbbl2z/x/az9x3bbfuK7UHbz6fKiHzY/p7ta7bfr359NXUm5MH2C9VrxRXbPanzID+2r9r+oHrteC91HqRn+03bN2x/eNe+J22/Y/sv1e8LU2ZEsVCgoVl8KOlrkt69e6ftlZJekfQlSS9I+rHtWTMfDxnaFxGV6tevU4dBetVrw48kbZK0UlJn9RoC3K+jeu1gGXVI0kGNfca4W4+kUxHRJulU9TUwKRRoaAoR8aeIGKxx6CVJfRHxr4j4m6Qrkp6b2XQACuI5SVci4q8R8W9JfRq7hgDAhCLiXUn/vG/3S5Leqm6/JWnLTGZCsVGgodl9XtLf73o9XN0H7LT9h2prCq0nkLheYHJC0u9sX7T9WuowyFZrRHxc3f5EUmvKMCiW2akDAJNl+6SkZ2oc+nZE/GKm8yBvnzZeJP1E0usa+6D1uqS9krpmLh2AAvtyRFyzvUjSO7b/XJ1BAWqKiLDNsumYNAo0FEZEbHiEt12T9IW7Xper+9DkJjtebP9M0q+mOQ6KgesF6oqIa9XvN2y/rbHWWAo03O+67cUR8bHtxZJupA6E4qDFEc3umKRXbD9me6mkNkkXEmdCYtV/lne8rLFFZoDfS2qzvdT2XI0tMHQscSZkxPbjtp+4sy1po7h+oLZjkl6tbr8qiU4fTBozaGgKtl+W9ENJT0s6bvv9iHg+Ii7Z7pf0R0m3JXVHxGjKrMjCD2xXNNbieFXSN5OmQRYi4rbtnZJOSJol6c2IuJQ4FvLSKult29LYZ6ifR8Rv00ZCarZ7JX1F0lO2hyV9V9Ibkvptf0PSR5K+ni4hisYRtMQCAAAAQA5ocQQAAACATFCgAQAAAEAmKNAAAAAAIBMUaAAAAACQCQo0AAAAAMgEBRoAAAAAZIICDQAAAAAyQYEGAAAAAJn4L6VEAYoCc2VzAAAAAElFTkSuQmCC", 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", 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", 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28X5HL5P8DDyVlcB4P8Opn6sQQniQ4z3ThRBCnH5lZWUnvd/LZDLh7z/8v4OH09rayqxZs6irqwNg/fr1PProo3zwwQcjGn+s16AoynED2unq4tgExB/287iDv/a1ptP5kZryc2bN/JiwsEXU1v2BTZvPpqX1HVTVdWpvnpQHP9kIs2+EbX+D52dD9Zphh4R76XlhQhIvjk+i2WrnnG0VPF7bgs11iucqhBBCCCGEh4qKiiI+Pp6KigoA1qxZQ3Z29glGfXmnK6BtBdIURRmnKIoX8C3gvdN07zPOYIhj4oRnmTb1Vby8wigt/Rnbtl1Kb9/2U3tjL18452H4wWrQG+A/l8C7N8Bg77DDlkUEUTgzk4sjgnmyro0l2yrZ1W85tXMVQgghhBDCQz377LN85zvfYdKkSezatYt7TrBv7WScijb7/wM2ARmKojQqivIDVVUdwI3AR0AZ8JqqqvvG+t5nQn2XZcTdGoOCcpme+zbZWY8zZG1l+/Yr2Lv3FgYHT3ExMX4GXL8e8n8Gu/4Hz82E8pXDDgnR6/hjdiL/njiOPoeT87ZX8tD+ZgadUk0TQgghhBDfLFOmTGHbtm2UlJTwzjvvEBwcfMruNeYBTVXVq1RVjVZVVa+qapyqqi8d/PWVqqqmq6qaoqrqw2N93zOhvX+Ic58p5IltQ1S0mkY0RlE0REdfyuxZn5CUdCMdnR+zecvZ7N//exwO86mbrN4HFv8SflQAxjB45Sp484dg7hp22NlhgXw6I5NvR4fyx/p2zt5WQXHvwKmbpxBCCCGEEN9gp2uJ49dSsNGLny/JoLbPxdJnCrn37T10DYzs0GedzkhK8m3MnvUJ4eHnUHfgeTZtPovmljdO7f60mCnwo7Ww4B7Y9w48NwP2ve3ubnMcATotT2TG89rkFKwulYt2VnN/VSNmp/PUzVMIIYQQQohvIAloJ0Gv1XBt3jgen+fL1bOTeGVrAwt+t44XCmuwOUYWsnx8Ypgw/ilyp72Oj08MZWV3sXXbxfT0DH/Y9EnRecGCu+D6TyEoHl6/Bl77Hpjahh02L8SfddMz+H5sGC80drKwuIKinpFVDoUQQgghhBAnJgFtDPh5KfzqwvF8dGs+05KCeXhlGUue+pSP9rWOeH9aYOBUcqe9zvjsp7DZutix8yr27LmRwcGGUzfxyPHwg0/grF9D5Wp3NW33K8NW04w6Lb9Nj+OdnFS0Cly2az93VjRgckg1TQghhBBCiJMlAW0MpUb484/vz+Af35+OTqvh+n9v59svbKG0uX9E4xVFQ1TUhcye9QnJ426ls2sdmzYvobr6cRyOU1Sp0uog71b4yQYIz4C3r4f/XgF9wzcumRXkx5rpmfwkPpz/NHcxv7icNV0je51CCCGEEEKIY5OAdgosyIjgw1vy+c1F4ylv7ef8Z9dz95sldJhGtj9NqzUwbtxNzJ79CZGR53Og/i9s3LSYpqZXUNVTVKkKS4Pvr4JzH3Mfcv38LNj+z2Grab5aDQ+kxrJiahp+Wi3fKanh5rID9Ngdp2aOQgghhBBCfM1JQDtFdFoNV89OYt3PF3Lt3HG8sb2RhU+s4/l11QzZRxayfLyjGJ/9BNNz38bXN4nyinsp3noh3d0bT82kNVqY9WP3AdfRk+H9m+FfF0FP3bDDpgYa+Xh6OrclRvJmWw/zi8tZ1dF7auYohBBCCCHEaVRRUcGUKVMO/QgICODpp58+ZfeTgHaKBfrquX9ZNqtvm8es5FAe/7CCs578lJV7Wka8Py0gYBLTpr7KhPF/wOEwsXPX99hdcj0WS+2pmXTIOLj6PVj2FDTtgOfnwJa/guv4jU+8NRruSo7mw2nphHvp+P7eOq7fV0enTappQgghhBDiqysjI4Ndu3axa9cutm/fjq+vL8uXLz9l95OAdpJGGrKSw/148f9yefmHM/Hz1vHTl3dw5V82s6exb0TjFUUhMvJ8Zs38mJTkn9PTs4nNW5ZSVfVb7PZTsPdLo4Hca+GnmyBxNqy6A/5xHnRWDztsor8vH07L4K5xUazs6GNecRnvtPWM+H0SQgghhBDCU61Zs4aUlBQSExNP2T10p+zK3wAOu53/3nMbuogYBnOnYfDzP+GYualhfHBzPq9ubeD3qyu48LkiLp0axx3nZBAZ4HPC8VqtN0lJPyE6+jJqap6kvuFvtLS+TfK4W4mJuRKNZoz/SIPi4TtvwO7/wYd3w5/nwsJ7YfYN7iWRx6DXKNyWFMXS8EBuLWvgx6UHeLe9l0fT44j01o/t/IQQQgghxDfC+tcq6WwYGPU4p9OJVnvsf7eGxfuRf0X6iK/1yiuvcNVVV416DqMhFbSTYDUPEBARRcu2jbxww7UUvvx3zL09Jxyn1Sh8e2YCa+9YwHXzknlvVzMLn1jHs2uqRrw/zds7nKysR5gx/V2MxjQqKn9J8dZldHWtP9mXdTRFgSnfhhuKIWUxfHw/vHQ2tJcNOyzTaGDF1DR+mRLD2u5+5hWX82pLt1TThBBCCCHEV47NZuO9997j8ssvP6X3Ub5K/1jOzc1Vt23bdqancZRVb76Os7GWyk1FaHU6JixawvQLLyEgLGJE4w90mXlkZTkf7mslJtCHu5ZmcuHkGBRFGdF4VVXp6FxNddWjDA7VExq6kLTUX2A0ppzMyzrezWDfW7DyDhjqh/l3udv0a4evjO23DHF7eQNb+swsDPHndxnxxPl4jf38hBDiJK1bt44FCxac6WkIIYQAysrKyMrKOqlrmEwm/P1PvNLtRN59912ee+45Vq9ePapxx3oNiqJsV1U191hfLxW0MWAIDWfZLXfy/af+RGbefEo+WcVLN1/HR3/+Az2tzSccnxhq5M/fm8Yr180i2OjFLa/s4tI/bWRn/YmrceDenxYRfg6zZn1Iaurd9PZuZUvxeVRU/ga7vfckX91RN4MJl7qradkXwtqH4IWF0LJ72GEpvj68nZPKw2mxbOkzs6C4nH81deL6Cn2DQAghhBBCfHP973//O+XLG0EqaGPii99t7e9oZ+v7b7KnYDUuh5OMOfnMvPhywhKSTngtp0vlze2N/G51BR0mKxdPieHOczOJCTKMeD42Wyc1NU/T1PwqOp0/yeNuITb222g0p2D/V9kK+OB2MHdC3m0w/07QeQ875MCglZ9XNLC+Z4C5QX48mRlPomH4MUIIcbpIBU0IITyHp1TQzGYzCQkJ1NTUEBgYOKqxo62gSUAbA8f7MDf39rBtxdvsXr0Su3WI1OmzmLn8SqJS0k54zQGrgz+tq+aF9bVoFLhuXgo/np+Mr9fIm4AMDFRQWfUQPT0b8fVNIS31F4SGLhjx0skRG+yBj+6FXS9DeCZc9BzEHfPv2yGqqvLflm5+Vd2EQ4V7kqO5Ni4M7VjPTQghRkkCmhBCeA5PCWgnQ5Y4ehBjUDDzv3stP3rub8y69CoaSvfw8j238cbD99NYunfYsX7eOu44J5M1t8/nrKxI/rCmioVPrOOtHY24XCML1X5+GeRM+ReTJv0VVXWyu+SH7Nr9fQYGKsfi5X3OEAwXPw/feROsA+4GIh/dCzbLcYcoisJ3YkL5dEYmc4L8uL+6iYt3VFNlHhrbuQkhhBBCCPEVIgHtNDD4BzD3iu/woz/+nfxvX0PHgVpe/fXdvPLAXdTt2j5sV8P4EF/++O2pvP7j2UQG+HD7a7tZ/vwGth/oHtG9FUUhPGwxs2auIi3tPvr7d1O8dRnlFQ9gs43sGiOWdpb73LRp18CmP7pb8tdtGHZIjI8X/5k0jj9mJVBlGeKsbRU8e6ANxwhDqBBCCCGEEF8nEtBOksvlGvHXevv6MuOiy/jhsy+y8Jrr6Oto481HHuDle26nausm1GGuNT0phHd+OpffXz6Z1v4hLv3TJm787w4ae45fpTqcRuNFQvz3mT1rDbEx36a5+X9s2ryI+vqXcLlsI34NJ+QTAMuegv97H1SX+3DrD37urqwdh6IoXBYVQuGMTM4KDeDhmhbO21FJ2cDg2M1LCCGEEEKIrwDZg3YS7HY7f/nLX/D19eWKK67Az89vVOMddjulhQUUv/s6fW2thMYlMHP5FWTMzkdznMP0ACw2B3/+tIa/Fu7HpcKP8sfxkwWp+HmPYn+auYrqqt/S1V2IwZBIWuovCAs7a2z3p9nMUPAQbP4TBMbDhX+AlIUnHPZ+ey93VzbS73ByS2IkNydG4KWR7yUIIU4P2YMmhBCe45u4B00C2kkYGBhg1apV7Nu3D51Ox7Rp05gzZ86oO7u4nE4qNhay5Z3X6WqsJygymhkXX072vIVodcfvvNjcO8jjH5bzzq5mwv29ueOcDC6bGodGM/KQ1dm1jqqqR7BYqgkOnk1a2n34+2WOav4nVL8F3r0Buqpg6tWw5CHwGf496rI5+GV1E2+29ZBt9OGprAQm+/uO7byEEOIYJKAJIYTnkIDm4TwtoH3mgw8+wGazUVJSgqIo5OTkMHfuXEJCQkZ1HdXlonrbZra8/RptNdX4h4aTe8ElTFy8BL3X8dvQ76zv4TcrStlZ38v4mADuX5bNrOTQEd/X5bLT1Pw/amqeweHoJybmcpKTb8fbK2xU8x+WfQjWPQIb/wB+Ue5lkBnnnnDY6s4+7qxopMNu54b4CG5PisJHK9U0IcSpIwFNCCE8hwQ0D+epAe2zD/Oenh42bNjAzp07cblcTJw4kby8PCIiIkZ1PVVVqdu9gy1vv0pTeSm+gUFMO/9ipiw5Dy/DsatIqqry3u5mHltVTnPfEEsnRPGLpVkkhI686mS391Fb9yyNjf9Go/FhXNJPiY+/Bo1mDM8oa9oO794I7aUw6Uo491HwHT7I9tkd/Gp/M/9r6SbN15unMhPIDTSO3ZyEEOIwEtCEEMJzeEpAe+qpp3jxxRdRFIWJEyfy97//HR8fnxGNlYB2Bhx1UHV/P5s2bWLbtm3Y7XaysrLIz88nJiZm1NduLN3L5rdf5UDJTnyMfuQsvYCcpRdi8Dv2X7JBm5MX19fw/Lr9OF0q389L4saFqfj7jPyQarO5hur9j9LZuQYfn3jSUu8mPPycsduf5rDB+t/D+ifcLfrP/z1kX3TCYeu6+/lZeQPNVjvXxYVzV3I0vlJNE0KMMQloQgjhOTwhoDU1NZGXl0dpaSkGg4ErrriC8847j2uuuWZE4+UcNA8QEBDAOeecw6233sq8efOoqanhr3/9K//5z3+or68f1bXisidw2b0P8p2HnyQ2awKb3vgfL9xwLYUv/x1zb89RX2/w0nLT4jTW3bGACybH8JdPa1jwu3X8d0s9zhG2rjcak5k86a9MmfJPtFoDe/bewI6d36bfNPzZbSOm84KFv4Dr1kFADLx2tfvHQPuwwxaEBPDpjEz+LzaMvzR2sGhrORt6TGMzJyGEEEIIIY7D4XAwODiIw+HAYrF8qcLLSEkFbQyc6LutQ0NDFBcXs3nzZiwWC0lJSeTn55OcnDzqqlRHfR1b3n6Nyk1FaHU6JixawvQLLyEg7NjLKEsae3lwRSlb63rIjPLn/mXZzE0d+d4yl8tBc8tr1NQ8hd3eQ3T0paQk/wxv79Et2zwup8O9L23dI+DlB0sfh4mXwQnel409A9xeUU/doI3/iwnl/pQY/HTH73wphBAjJRU0IYTwHIdXn9b+46+0H6gZ9TWcDifa4/w7MSIxmYXXXHfCazzzzDPce++9GAwGlixZwssvvzzi+0sFzQP5+Pgwb948br31Vs455xy6urr497//zYsvvkh5efmwB1V/UXhCEstuuZPvP/UnMvPmU/LJKl66+To++vMf6GltPurrJ8UF8dr1s3n+O1MZsDr4zotb+OE/t1HbaR7R/TQaHXGx32bO7AISEn5Ia+u7bNq8mNq653A6h0Y87+PS6iD/dvhxEYSmwFs/hP9dBf1Hv5bDzQn2o2B6JtfHh/Ov5i7mF5eztqv/5OcjhBBCCCHEYXp6enj33Xepra2lubkZs9nMf/7zn1N2P6mgjYHRfrfV4XCwa9cuioqK6O3tJSIigvz8fMaPH49mlOd99Xe0s/X9N9lTsBqXw0nGnHxmXnw5YQlJR33tkN3J3zbU8lxBNTani6tnJ3HzojQCfUe+P81iqaN6/2N0dKzGxzuGlNQ7iYxYNjb701xO2PIXWPMb0HrBOQ9DzndPWE3b1mfmtvJ6qixWrooO4VcpMQTqR34mnBBCHE4qaEII4Tk8YQ/a66+/zocffshLL70EwL/+9S82b97M888/P6LxUkH7CtDpdOTm5nLTTTexfPlyXC4Xb775Js899xw7d+7E6XSO+FoB4REsvvYn/OiPf2PasovZv72Yf95xI+8+8RCt+6uO+FofvZafLkhl7R0LuHRqHH/bUMuCJ9by7011OJyuEd3P1zeJSRP/xNScl9Hpg9i371a277iCvv7do3oPjkmjhdk/hZ9sgKiJ8N6N8O/l0Dv8vr3cQCMf52ZwS2Ikr7V2M6+4nI86+05+PkIIIYQQ4hsvISHh0FYlVVVZs2bNSYfG4UgFbQyc7HdbXS4XZWVlrF+/ntbWVgIDA5k7dy45OTno9SOvbgEMmvrZsep9dn74HlazmcRJOcxafiVx2ROO+tp9zX08uKKUzTXdpEX4cd+ybOanh4/4XqrqpKXlTfbX/B6brZOoqItJSf45Pj7Ro5rzMblcsP1v8PED7p+f9SvI/QGcoMJYYrJwa1k9peYhLokM5sHUWEK9pJomhBg5qaAJIYTn8IQKGsADDzzAq6++ik6nIycnhxdffBFv75EdRSVt9s+AsfowV1WVqqoqCgsLaWxsxM/Pj9mzZ5ObmzvivwCfsVos7P54Jds/eAdLXy+xmeOZtfwKEidPPWI5oqqqrC5t47cryzjQZWFBRjj3nZ9FasTI/xI7HCbqDvyZhoa/ARoSE68nMeFHaLWGUc35mHrr4f1bYH8BJM6FC59171Ubhs3l4tkD7Tx9oI0AnZZH0uO4IDxw7I4JEEJ8rUlAE0IIz+EpAe1kSEA7A8b6w1xVVerq6igsLKS2thaDwcDMmTOZOXMmBsPoQo/dOsSegtVsff8tBro6iUxOZebyK0jNnYVyWDXK6nDyz411PLumGovdyfdmJXLL4jSCjV4jvtfgYAPV+x+nvX0l3t5RpKTcQVTkhSjKSa6kVVXY9TJ8eA84bbDoPpj1E/eSyGGUDQxya3k9u02DnB8eyCNpcUR4j64iKYT45pGAJoQQnkMCmof7pgS0wzU0NLB+/XoqKyvx8vJixowZzJo1Cz8/v1Fdx+mws+/TAra++wa9bS2ExiUwc/kVZMzOR6P9POh0Dlh56uNK/ldcj7+PnlvPSuO7sxLRj+JA6J7erVRVPYTJtJeAgMmkp91HYODUUc33mPpbYMVtULkKYnPhoucgInPYIQ6Xyp8b2vldXSsGjYYH02K5LDJYqmlCiOOSgCaEEJ5DApqH+yYGtM+0trayfv169u3bh06nY9q0acyZM4fAwMBRXcfldFKxaT1b3n6NrsZ6giKjmX7RZYyfvwit7vPqUnlrPw+tKKOoupPkcCP3nZ/FwoyIEQcbVXXR2vo21fufwGZrJzJiGSkpd2IwxI5qvse4MOx9E1beAbYBmH8XzL0FtMNXxqotQ9xW1sDWfjOLQwL4XUYcMT4jrw4KIb45JKAJIYTnkIDm4TwxoJm6h9hesvm0fZh3dHRQVFRESUkJiqIwZcoU8vLyCAkJGdV1VJeL6m2b2fL2a7TVVOMfGk7uBZcwcfES9F7u/W6qqlJQ3s7DH5RR02kmPy2M+87PJiNqNPvTzByo/yv19S8AkBD/AxITf4xOZxzVfI8y0AGr7oB9b0PUJHc1LXrSsEOcqsrfmzp5eH8LOgUeSI3lO9EhUk0TQhxBApoQQngOCWgeztMC2pDZzj/u3oDez8XMc9NJmxGFt+H0dAzs6elhw4YN7Ny5E5fLxYQJE8jPzyciImJU11FVlbrdO9jy9qs0lZfiGxjEtPMvZsqS8/Ay+AJgc7j4z+YDPP1JJQNWB9+emcBtZ6UT6jfyxiVDQ81U7/8dbW3v4eUVQUrKz4iOuuTk96eVvgcf/AwGuyHvdpj3c9ANP68Dg1ZuL29gQ+8A+cF+PJERT6JhdE1YhBBfXxLQhBDCc0hA83CeFtDsViflm1oo/rCSoV7QeWlInRZBdl4sUckBp6UyYzKZ2LhxI9u2bcNut5OVlUV+fj4xMTGjvlZj6V42v/0qB0p24mP0I2fpBeQsvRCDn/svdI/ZxjNrqvj35gP4emm5eVEa/zcnCS/dyENWX98OKqsepr9/F/7+40lLvY/g4BmjnusRLN3w0T2w+38QnuWupsVNG3aIqqr8p6WLX1c341Th3pRoro0NQyPVNCG+8SSgCSGE55CA5uE8LaB9Zu3atWSPm0ZpUTNVW9uwW50ERxvJnhtN5qxofPxOfedAs9nMli1b2LJlC1arldTUVObNm0dCQsKor9VaXcnmt19j/7bN6H0MTD57KbnLlmMMCgagut3EQx+Usa6ig6RQX35xXhZLsiNHtT+trW0F1fsfw2ptJSJ8Kampd2EwxI96rkeoXO1uyT/QCrNvhIX3gH74rpdNQzbuqGigoNvEzEAjT2bGk+Lrc3LzEEJ8pUlAE0IIz+EpAe2pp57ixRdfRFEUJk6cyN///nd8fEb2b0YJaGfA4R/mtiEH1dvaKd3QTFttPxqdQsqUcLLzYohND0bRnNoKzdDQEMXFxYdOO09MTGTevHkkJyePuqLXUV9H8TuvU7FxPVqdjgmLljD9wksICHMvo1xX0c5DH5RR3T7A7ORQ7l+WTXZMwIiv73QOUl//InUH/oKqOkmI/z5JST9BpzuJ/4GG+mD1/bDjnxCS4q6mJc4edoiqqrzW2sMvq5uwulzcMS6a6+PC0Z3iPyshhGeSgCaEEJ7DEwJaU1MTeXl5lJaWYjAYuOKKKzjvvPO45pprRjReAtoZcLwP887GAUo3NFO5pRWrxUFAuMFdVZsdjTHw1O55stlsbN++nY0bN2IymYiNjSU/P5+MjIxRB7WeliaK332D0sICALLnLWLGRZcRHB2Lw+niv8X1PPVxJb2Ddq7MjednSzII9x/F/jRrK/v3P0Fr69vo9aGkJN9OTMzlKMrw55wNa/9aeP9m6G2AGdfBWQ+A1/CNSdqsdu6qbODDzn6m+PvyVGY8WX5jcNi2EOIrRQKaEEJ4Dk8JaLNmzWL37t0EBARw8cUXc/PNN7NkyZIRjZeAdgac6MPcYXOyf2cHpUXNNFf1omgUkiaGkp0XQ8L4UDSnsFLjcDjYtWsXRUVF9Pb2EhERQX5+PuPHj0ejGV2Djv7Odra+9xZ7Cj7C5XCSMSefmRdfTlhCEn0WO38oqOKfG+vw0Wv56cIUrp07Dh/9yENWf38JlVUP0de3HT+/TNJS7yUkZM5oX/LnrAOw5jdQ/BcISoQLn4Xk+cMOUVWVd9t7uaeqEZPDxW1JkdyUEIleqmlCfGNIQBNCCM9xeLjpfX8/tmbzqK/hdDrQao/dyM8rxkjQBSknvMYzzzzDvffei8FgYMmSJbz88ssjvr8EtDNgNB/mvW0WSouaKd/cwqDJjl+wN5lzosmeG4N/yKnb++R0Otm7dy/r16+ns7OT0NBQ8vLymDRpElrt6CpV5t4etq14m90fr8I+NEhK7ixmLb+CqNR0ajoG+O3Kcj4payMu2MA952WxdELUKPanqbS3r6R6/2MMDTURFnYWaal34+s77su8bLcDG+HdG6F7P0y7Bs7+DfgMf35cp83BfVWNvNPey3g/H57OTGCiv++Xn4MQ4itDApoQQngOTwhoPT09XHrppbz66qsEBQVx+eWXc9lll/Hd7353RPeXgHYGfJkPc6fDRe3uTko3NNNQ1g1AQnYI2XkxJE0KQ6s9yfbzx+FyuSgrK2P9+vW0trYSGBjI3LlzycnJQa8fXTOTwQETO1e9x45V72E1m0mclMOs5VcSlz2BDdWdPLiilPJWEzOSQrh/WTYT40Z+qLbTaaWh4W/UHfgTLpeN+LirSUq6Eb1+5HvcjmAfhLW/hU1/BP9ouOAZSDv7hMNWdfRyV2UjXXYHNyVEcltSJN6jrDwKIb5aJKAJIYTn8IQljq+//joffvghL730EgD/+te/2Lx5M88///yIxktAOwNO9sO8v3OQso0tlG1swdxrxRDgRdbsKLLmxhAUcWqqNqqqUlVVxfr162loaMDPz4/Zs2eTm5uLt/fo9sdZLRZ2f7yS7R+8g6Wvl9jMbHdQm5jDa9sa+f3qCrotNi6dGscd52QQGTDySqHV2kFNzZM0t7yOXh9M8rhbiYm5Eo3mS54317gd3r0BOspg8lVwzm/Bd/hDvnvtDh6obubV1m7SfL15JjOBqYEnedC2EMJjSUATQgjP4QkBbcuWLVx77bVs3boVg8HANddcQ25uLjfddNOIxktAO83s7RY27CtmwcIFJ30tl9NF/b5u9hU1c2BvF6pLJTYjiOy5MSTnhKMbxX6ukVJVlbq6OgoLC6mtrcVgMDBz5kxmzpyJwTC6Bhl26xB7Cj5m6/tvMtDVSWRyKjOXX0HEhGk8/2kNfy+qQ6dV+Mn8FH40L3lU+9NMpn1UVj1Mb+8WjMY00lLvJTQ0f7Qv181hhcInoOhJMITAsich64ITDivo6ueOigZarHauiw/nznHR+J6iSqcQ4syRgCaEEJ7DEwIawAMPPMCrr76KTqcjJyeHF198ccRFDQlop5HTbKflt1uwebsInz8O36mRaP29xuTa5l7rwapaM/2dQ3gbdWTMjCI7L4bQGL8xuccXNTY2UlhYSGVlJV5eXsyYMYNZs2bh5ze6+zkddvZ9WsDWd9+gt62F0LgEZi6/Ap/0aTz2USUf7mslJtCHu8/L4oJJ0aPan9bRsZrq6kcZHKonNHQhaam/wGg88cbOY2opcVfTWktg/HJY+jvwCx92iMnh5MH9zfyruYtxBi+ezExgdtCp+fMQQpwZEtCEEMJzeEpAOxkS0E4j1e7CsqeD5o8rMPQooFEwZIdgnBGNd2rQmJx5prpUGit6KC1qpmZXBy6nSlRyANl5MaROi0TvPfZVtdbWVtavX8++ffvQ6XRMmzaNOXPmEBg48j1kAC6nk4pN69ny9mt0NdYTFBnN9IsuwxQ/hYdXVVLa0s/UhCDuX5ZNTkLwyK/rstLQ8E9q657D5RoiNvY7JI+7Gb0+aJSvFHDaYcMz8Olj4O0PSx+HCZfCCUJjUY+Jn5U3cGDIxvdjw7gvORqjbuz/LIQQp58ENCGE8BwS0DycpwU0AOqKKNw/wOyJ8zBvbcWyow2X2YE2yBtjbiS+06PQjdGZZ4MmG+WbWyktaqa3zYLeR0v69Eiy82KISPySzTOG0dnZSVFRESUlJQBMmTKFvLw8QkKG37P1RarLRfW2zWx5+zXaaqrxCw1j6rJLqQoZz5Of1NA5YGV5Tix3nptBdODIl1XabJ3U1DxNU/Or6HT+JI+7hdjYb6PRjK7ZCQDt5e5qWtM2yDgfzv89BEQPO8TsdPJYTSsvNHYQ66PnyYwE5oWcuf/5hRBjQwKaEEJ4DgloHs7jApq5E36XilOjR5u6CDLOQ01ewmCDDvPWVqxVvaCAT0YIxulR+GSGoGjHoKqmqrRU91G6oZnq7e047S7C4v0YnxdD2owovA1fsoHGcfT09LBhwwZ27tyJy+ViwoQJ5OfnExERMep5H9i9g81vv0pTeSm+gUFkn3sxm7wy+dvmBjQKXD8vhevnJ+PrNfLXMDBQQWXVQ/T0bMTXN4W01F8QGrpg1Ady43LC5j9BwYOg84ZzHoEp3z5hNW1rn5nbyuuptlj5TnQID6TGEiDVNCG+siSgCSGE55CA5uE8LqA57XBgI41rXiDOvBt66wEF4nIhYymOqHMw1/hh3taGy2RD4++FcVokxumR6EJH14DjeKwWO5XFbewraqarcQCdXkPqtAiy82KISgkcfUgZhslkYuPGjWzbtg273U5WVhb5+fnExMSM+lqNpXvZ/ParHCjZibfRSPyii1nlSuHD0g6iAny489wMLp4SO+JDvFVVpbOrgKqq3zI4WEdISD5pqffg55c+6rnRtR/euwkObICUxe6W/EHxww4Zcrr4fV0rz9W3E+mt57H0OJaEjW5JqBDCM0hAE0IIzyEBzcN5XEA7aN26dSyYPx/aS6F8JVSshOYd7t8MHoeadj5Dvudirg1mqLIHVPBODcI4PQrD+FAU3cl3AlRVlfYDJkqLmqna2obd6iQ42kj23GgyZkVh8Bub5iUAZrOZLVu2sGXLFqxWK6mpqeTn55OYmDjqa7VWV7L57dfYv20zeh8DhjkX8s5gPPtazUyOC+SXF2QzLXHkSypdLhuNTS9TW/sHnE4zMTFXkTzuFry8RrcsE5cLtr0EHz/grqCd/RuY9n04wRlou/ot3FZeT5l5iMsig/lNWiwh+rGtaAohTi0JaEII4TkkoHk4jw5oX/ww72+Gyg/dga32U3DawBCMI3E5FvVczAcCcfba0fjq8J0aiXFGFPoxOvPMNuSgens7pUXNtNX2o9EpJE8JJzsvhrj04DFpXgIwNDTE1q1b2bRpExaLhcTERObNm0dycvKoK3cd9XUUv/M6FRvXo9HpMOVezPsDUbQP2Fk2KZq7l2YSFzzy98dm66a29g80Nf8XrdaXcUk3ERf3PTSaUQbVngPw/s1Qsw6S8uHCP0BI8vD3drl45kAbzxxoI0in49H0OJZFBI3uvkKIM0YCmhBCeA4JaB7uKxXQDmcdgP1roGKVO7QN9qBqvLGGfwez42wGW/zBBV6JARhnRGGYGIbGa2z2MHU1DbCvqJnKLa1YLQ4Cwg1kz40mc3Y0xjFqXmKz2di+fTsbN27EZDIRGxtLfn4+6enpaE5QcfqinpYmit99k9LCNdgVHQcmXMwacyguFH6UP46fLEjFz3sU+9PMVVRX/Zau7kIMhkTSUn9BWNhZowuQqgo7/w0f3ete1rr4lzDzetAM/2dUOjDIrWX1lAwMsiw8kEfS4wj3+hINTIQQp5UENCGE8ByeEtCeeeYZXnjhBVRV5Uc/+hG33nrriMdKQDsDRvVh7nRAwxb3MsiKldBdg1MNxGL8LmbrAhxmA4qPFt8pERhnROE1RmeeOWxO9u/soLSomeaqXhSNQtLEULLzYkgYHzrivV7D3sPhYNeuXRQVFdHb20tERAT5+fmMHz9+1EGtv7Odre+9xd6C1fSq3uxNX8bWwSDC/b2545wMLpsaN6o5d3ato6rqESyWaoKDZ5OWdh/+fpmje4H9zbDiNnfIjpsBFz0H4cPvcXO4VP7U0M4Tda34ajQ8lBbLJZHBY7o3UAgxtiSgCSGE5/CEgLZ3716+9a1vUVxcjJeXF+eeey5//vOfSU1NHdF4CWhnwJf+MFdV6Kx0B7XylagNW7Gp2Zg1l2Cx5YJLiz7WiHFGNL6Tw9H4jM1ept42C6VFzZRvbmHQZMcv2JvMOdFkz43BP8TnpK/vdDrZu3cv69evp7Ozk5CQEPLy8pg0aRI63eheg7m3h20r3mb3x6toUP0pTjiXAw4j42MCuH9ZNrOSQ0d8LZfLTlPz/6ipeQaHo5+YmMtJTr4db6+wkU9IVWHP67DqTrBZYMHdMOdm0A7/uirNQ9xeXs+2fgtnhwbweEYc0d5jty9QCDF2JKAJIYTn8ISA9vrrr/Phhx/y0ksvAfDggw/i7e3NnXfeOaLxEtDOgDH7MB9od1dnKlbhqi7GYp2F2XUedlcCis6FYUIoxjkJeMX7j0kFxulwUbu7k9INzTSUdQOQkB1Cdl4MSZPC0GpPrnmJy+WivLycwsJCWltbCQwMZO7cueTk5KDXj26p3+CAiZ2r3mP7qvfYSzRbIufRq3qzdEIUv1iaRULoyPen2e191NY9S2Pjv9FofBiX9FPi469BoxnFks+BdvjgZ1D2HkRPcVfToiYMO8SpqrzU2MEjNS3oFIVfp8ZyVXSIVNOE8DAS0IQQwnMcHm5WrVpFa2vrqK/hdDrRao+9NSUqKoqlS5eecA4XXXQRmzZtwmAwsHjxYnJzc3n22WdHdH8JaKeZqqp8+umnY/9hbrNAzTrU8pXYSyswm2dicc5DxYAuYAjjjGiMczLQ+I7Nnqb+zkHKNrZQtrEFc68VQ4AXWbOjyJoTQ1DkyTUvUVWVqqoq1q9fT0NDA0ajkTlz5pCbm4u39+j2wVktFnZ/vJLNH7zPRiWR7cG5oNFybV4yNy5Kxd9n5O+H2VxD9f5H6excg49PPGmpdxMefs7oAtO+d2Dlz2GwB/J/Dvk/A93wlbFai5XbK+rZ1GtmXrAfT2TEk2AYm/2AQoiTJwFNCCE8hycENICXXnqJ559/HqPRyPjx4/H29ubpp58e0f2/UgFNURQj8DxgA9apqvrycF/vaQFNtdvZv2wZ/dExpH77KvzmzkVjNI79jVxOaNqOa++HWHZ3YO6bgl1NB+wYonowzknAO3cayij3eR37Vi7q93Wzr6iZA3u7UF0qselBZOfFkJwTjk7/5ZuXqKpKXV0dhYWF1NbWYjAYmDlzJjNnzsRgGN25cHbrEHsKPqZgxQd8Qhrl/pkEeSvcsTSbb81IRDuK/Wld3UVUVT2M2VxJUNAM0tLuJcB/+GrYEcxd8OHdsOc1iBgPFz8HMTnDDnGpKv9q7uLB/c2owH3J0VwTG4ZGqmlCnHES0IQQwnN4whLHL7rnnnuIi4vjpz/96Yi+/owHNEVR/gYsA9pVVZ1w2K+fCzwDaIEXVVV9VFGU7wG9qqq+ryjKq6qqXjnctT0toDl6emh75BF6P1mDxmJB8fLCd/Ys/Bctxm/BAvSREafmxl37sRUXYN49gKU3ExU/dNo2jPEd+M5JQ5udD7qTr8iYe62UbWqhbEMz/Z1DeBt1ZMyMIjsvhtCTbF7S2NhIYWEhlZWVeHl5MX36dGbPno2f3+iu63TY2fdpAe++/wkryaDFJ5px/hp+c/k08tNH/v67XA6aW16jpuYp7PYeoqMvJSX5Z3h7j+LPsGKVu4nIQDvMvRnm3w364ff0NQzZuKO8gXU9JmYFGnkyM4FkX6mmCXEmSUATQgjP4SkBrb29nYiICOrr61myZAmbN28mKChoRGM9IaDNAwaAf30W0BRF0QKVwNlAI7AVuAq4CFilquouRVH+q6rqt4e7tqcFtM+sW7OG6X7+DBQUYCoowN7QAIDPxIn4L16E38JFeKennZK9RmpvB5a1GzHvtWIzRwMODLrtGBO78c6dhJKxBHxHeUjzF+/hUmms6KG0qJmaXR24nCqR4wLIzoshLTcSvfeXr6q1trayfv169u3bh06nY9q0acyZM4fAwMBRXcfldFK+sZC/v7ueD9U0TPoAZoQr/PY7c0iNChrxdRwOE7V1f6Sh4Z9oNHoSE39MQvwP0GpH2DxlsBdW3+duyx+a5t6bljBz2CGqqvJKazcPVDdhc6ncNS6a6+LD0Uo1TYgzQgKaEEJ4Dk8JaPn5+XR1daHX63nyySdZvHjxiMee8YB28IZJwIrDAtps4Feqqp5z8Oe/OPiljUCPqqorFEV5RVXVbw13XY8NaId9mKuqiq26GtOaAkxrCxjaXQKAPi4Ov0UL8V+0GN9pU1FG2SRjJOzNPZgLdmIpd+FyeKOlHaPuE3wTetBNyIPM8054yPKJDJpslG9upWxDMz2tFvQ+WtKnR5KdF0NEYsCXvm5nZydFRUWUlLjfrylTppCXl0dIyOjCpepyUbplE0+/u5V1rkScio7z4+FX311AaNDI/8e0WOqo3v8YHR2r8fGOITX1LiIizh95yN5fAO/dAn0NMOsnsOg+8Bp++Wur1c6dFQ2s7upnaoAvT2UmkGE8+a6aQojRkYAmhBCew1MC2snw1IB2GXCuqqo/PPjz7wEzgbuAPwJDQNGx9qApinIdcB1AZGTktFdeeWXM53uyBgYGjrs0T9PXh3fJHrxLSvAqK0NxOHD5GrCOn4B18mRs47NRR7n/6oRcYGxTCamz4t1nBFz4aLZj1H6E06+FrvDpdIXOoD8gDZQvt29NVVUsndCzX6W/AVQn+ARDcLJCYCJovb5c9WdwcJCGhgZaWlpQVZWIiAgSExMxjnJvn6qqNNbW80apmd3aBHxUK+cEdnP+tHi8fEYeelS1HJf6CtAApKJRrkRRRhZytQ4LyTX/JrZ5JYM+UVRk3EBv8KQT3A82oucfGBhE4VKGuAArOimmCXHaDPdMF0IIcXoFBgaO+Lyx4xmuScjpUF1dTV9f3xG/tnDhQs8MaKqq3jia634VKmjDcVksmDduxLSmgIF163D29IBej3HGjIPVtUXoo6PHdG6O7iHMW1sxb23GNeBEox3AqKzCqPkInb8LMs6FjPMheT7ov1xQtFrsVBa3sa+oma7GAXR6DanTIsjOiyEqJfBLLe00mUxs3LiRbdu2YbfbycrKIj8/n5iYmFFfa23RDh5aVc5+ZyChjl5+mKnjmm+dh8FvZN9JUVUnLS1vsr/m99hsnURFXUxK8s/x8Rnhn1XdBnjvRuiugdxr4axfg8/w1cYOm517q5p4r72XiX4GnsqMZ4L/yXXTFEKMjFTQhBDCc0gFbYyMdImjqqqPjOa6X/WAdjjV6WRw1y5MBQUMrCnAVlcHgHd2Fv6LFuO/aCHeWVljtm9NdaoMVXRj3trKUHk3qODt34zR8QYGV4F7yWXKIvcyyLRzwC989PdQVTrqTewraqaquA271UlwlC/ZeTFkzIrC4Df6g5ktFgubN29my5YtWK1WUlNTyc/PJzExcdRze23NTn5XUEeny5txQw1cN9HAhZdeiDEoeETXcDhM1B34Mw0NfwM0JCZeT2LCj9BqRxBsbRZY+zBsfh78Y+CCZyDtrBMO+6Cjl7srG+mxO7gpIZJbkyLxHoNunUKI45OAJoQQnkMC2hg5RkDT4W4Sshhowt0k5Nuqqu4bzXW/TgHti6w1tQysLcC0poDBnTtBVdFFR+O/cCF+ixZhnDEdxWv0AedYnH1WzNvaMG9rxdljReOt4hu2H+Pgf9BbtgEKxM+EjKWQcR6Ep4/6HrYhB9Xb2yktaqatth+NTiF5SjjZeTHEpQejjKINPsDQ0BBbt25l06ZNWCwWEhMTmTdvHsnJyaMKsVaHk+c+2MlfNzdjdSlMHijj+1MCWbh8OQFhI+vYODjYQPX+x2lvX4m3dxQpKXcQFXkhykiWizZshXdvgM4KmPIdOOdhMAwfEHvsDn5Z3cTrrT1kGH14KjOeqQGn4DgHIQQgAU0IITyJBLQxoCjK/4AFQBjQBjygqupLiqKcBzyNu83+31RVfXi01/a0gKaqKre+ugu9pYNL509jUlwgRm/dSV/X0d3NwNp1mNYWYN6wEXVwEI3RiHFePv6LFuE3bx7aUXY5POb8XSrW6l7MW1sZLO0Cp4pXtBZjWBmG/v+iaTv4XoemHgxr50P8DNCMbg1vV9MA+4qaqdzSitXiICDcQPbcaDJnR2MMHF1LeZvNxvbt29m4cSMmk4mYmBjmzZtHeno6mlFUljoHrDz67k7e3NOJl9PKrL7tXJkTyeyLLyM4OnZE1+jp3UpV1UOYTHsJCJhMetp9BAZOPfFAhxU+fRyKngJjGCx7CjLPP+GwT7r6ubOigVarnR/HR3DHuCgMWqmmCTHWJKAJIYTnkIDm4TwtoHUNWLn8z5uo6TQDoFEgIyqAnIQgcuKDyEkIJjnMiGaU1aLDuYaGMG/axEDBWkxr1+Ls7AStFt/cXHcL/0WL8IqLO+nX4hywYdnRjrm4FUfnIIqPFt9sX4xBJXi1vQ2168FlB99QSD/XHdhSFp2wM+HhHDYn+3d2UFrUTHNVL4pGIWliKNl5MSSMDx3V++RwONi1axdFRUX09vYSERFBfn4+48ePH1VQK2/t51dv72bzgX6C7b3kdW/inCmJzFp+OWEJSSccr6ouWlvfpnr/E9hs7URGLCMl5U4MhhGEvJbd8M4N0LYHJlwKSx93B7Zh9DucPLi/mX83d5Fs8OapzHhmBkkzAyHGkgQ0IYTwHBLQPJynBbTPrFi9FmPieHbW97KzvoddDb2YhhwABPjomJIQfDCwBZETH0yg75drsa+6XAzt2eNuMrK2AGtVNQDe6enuJiOLF+MzfjzKSexRUlUVW20/5q2tWPZ0gsOFPtYPY04Qvr670NSuhKqPYKgPtN6QvOBgdW0p+EeN+D69bRZKi5op39zCoMmOX7A3mXOiyZoTTUDoyJuVOJ1O9u7dy/r16+ns7CQkJIS8vDwmTZqETjeyaqaqqhSUt/Pg+3up6x4i0drE3I4iZkxOZ9byK4hKPfEST4fDzIH6v1Jf/wIACfE/IDHxx+h0JwiwTjsUPQ2fPuZuHHLe72D8JXCCZZvru03cXtFA45CNa2PDuCc5GqPuzHUnEuLrRAKaEEJ4Dk8JaNdeey0rVqwgIiKCvXv3AtDd3c2VV15JXV0dSUlJvPbaawQHH711RQLaGfDFD3OXS6Wmc4Ad9b2HQltlmwnXwbc6OdxITnywO7AlBJER6Y/uSyxVs9XXu5uMFKzFsn07OJ3owsPxW7gQ/8WL8J01C4336JYQHs5lsWPZ1YG5uBV7qxlFr8EwORzjtDC81L0olaug/APoPeAeEDvNvWct4zyIyDphyABwOlzUlXRSWtRMfVk3AAnZIWTnxZA0KQztCN8Xl8tFeXk5hYWFtLa2EhgYyNy5c8nJyUE/wjPnbA4X/9l8gKc/qcQ0ZGeypZLcjo1kTshi1vIricuecMJrDA01U73/d7S1vYeXVwQpKT8jOuqSE+9Payt1701r3gGZy+D8358w8JodTh6pbeGlxk7ifLx4MiOe/JAz990hIb4uJKAJIYTn8JSAVlhYiJ+fH1dfffWhgHbnnXcSEhLC3XffzaOPPkpPTw+PPfbYUWMloJ0BI/kwH7A6KGn8LLC5Q1uX2QaAr5eWSXGB5BystE1JCCLCf3QHFDt6ejCvX49pTQHm9etxWSwovr74zZ2L36JF+C2Yj+4YiX4kVFXF3jiAubgVy+52VJsLXaQvxulRGHPC0QxUQ8VK94+m7e5BwUkHw9pSSJgD2hNXs/o7Bynb2ELZxhbMvVYM/noyZ0eTPTeGoMiRtZhXVZWqqirWr19PQ0MDRqOROXPmkJubi/cIw2qP2cYza6r496YDeGtczDTtIqutmITMTGYuv5KkyVNP2Jikr28HlVUP09+/C3//8aSl3kdw8Izhb+x0uLs8rn0YdD5w7qMw+VsnDLpbege4vbyB/YNWvhcTyv0pMQRINU2IL00CmhBCeA5PCWgAdXV1LFu27FBAy8jIYN26dURHR9PS0sKCBQuoqKg4apwEtDPgS7XZV1UaewbZUd/jDmwNvZQ292F3uv884oINhwJbTkIQ2TEBeI/wH90umw3Lli2HqmuOtjbQaDBMzcF/4SL8Fy/CKylplK/y4LWtDiy7D1bVGgdAp2CYEIZxehTeyYEoA21Qscr9o2YdOK3gEwRpS9wt/FMWn/AMMJfTRf2+bko3NFO3pwvVpRKbHkR2XgzJOeHo9Cd+H1RVpa6ujvXr11NTU4OPjw+zZs1i5syZGEZ4MHh1u4mHPihjXUUH0QaVOV0biW4rISo5lZnLryA1d9awy0lV1UVb2wqq9z+G1dpKRPhSUlPvwmCIH/7GndXualrDZkg9Gy54GgKH32c46HTxRF0rf6pvJ8pbz+MZ8ZwVOvz7LIQ4NgloQgjhOQ4PN5WVD2IaKBv1NZxOB9rjFAv8/bJIT79/RNf5YkALCgqit7cXcP/bMzg4+NDPj/caPiMB7RQbqw/zIbuTfc397PwstNX30Nw3BICXVsP42IAjlkbGBhlOWMlRVZWhfaUMFBRgKijAWl7uvl5ysrvJyMJFGCZPQvkSp6vbmgfce9V2dqAOOdCF+uA7PQrjtEi0/l5gHYCatVC+Eio/hMFu0Ohh3LzP962dIHiYe62UbWqhbEMz/Z1DePvqyJgZRXZeDKGxI2uO0djYSGFhIZWVlXh5eTF9+nRmz56Nn9/Ixq+raOehD8qobh9gYrDCrOY1+LRWEBqXwMyLLydjzjw0w7x/Tucg9fUvUnfgL6iqk4T475OU9BN0umG+k+NywdYX4JNfgaKFJQ/CtGtOWE3b0W/mtvIGKsxDXB4VzG9SYwnWn3xnUSG+SSSgCSGE5/iqBDSA4OBgenp6jhonAe0MOJUf5q19Q+xq6Dm0NLKkqZchuwuAcH/vQ90icxKCmBQXiK/X8P8Ytzc1YSpYy8DaAszFW8HhQBsait+C+fgvWoRxzhw0I6wwfUa1O7Hs6cRc3Iqtrh80CoasEIwzovBOO3jmmcsJDcVQ8YE7sHXvdw+Onvz5vrWoiccNIKpLpbGih9INzdTs7MDlVIkcF0B2XgxpuZHovU8cMFtbW1m/fj379u1Dp9Mxbdo05syZQ+AIjixwOF38t7ieJz+upG/QzjlxOibUrMLaWE1QZDTTL7qU7HmL0Q2z323I2sr+/U/Q2vo2en0oKcm3ExNzOYoyzNy7a+H9m6G20B1sL/gDhIwbdq5Wl4un69p4tr6NYL2Ox9LjOC886ISvUQjhJgFNCCE8hyxx9HDfxID2RXani4pW0+dVtoZeag+2+ddqFDIi/Q9W2NyhbVzo8dv8O00mBgoLGShYy0BhIS6TCcXbG+OcOe7q2oIF6MKGb/t+1PzaLZi3tWLZ3obL7EAb5I0xNxLf6VHoDj/zrKPy831rDcWACoHxn1fWEvNAd+yDuQcHbFRsbqW0qJmeVgt6Hy1p0yMZnxdDeIL/CauKnZ2dFBUVUVJSAsCUKVPIy8sjJCTkhK+vz2LnDwVV/HNjHT56DVemeRG39wO6ayvwCw1j+gWXMHHREvTex99D2N9fQmXVQ/T1bcfPL5O01HsJCZlz/JuqKuz4J3x0H6hOWPwAzLgOTtCtc6/Jwm3lDewZGOTCiCAeTosl3OvLdRAV4ptEApoQQngOTw5od9xxB6GhoYeahHR3d/P4448fNU4C2hlwpj/Mu802dje4l0TubOhlV30vJqu7zX+gQc+Uz1r8JwQzJS7omG3+VZsNy/bt7hb+BQXYm5tBUTBMmoTf4sX4L1qIV0rKCcPPoes5XAyWdmHe2oq1qhcU8EkPxjgjCp/MEJTDuzMOdLiXQFasgv0F4BgE7wBIPctdWUs7GwxBR99DVWnZ30dpUTPV29tx2l2ExfuRPTeG9JlReBuGryb29vayYcMGduzYgcvlYsKECeTn5xMREXHC11fTMcBvV5bxSVk78cEGfpDtjffW92iu2IdvYBDTzr+YyWefh7fvsZubqKpKe/tKqvc/xtBQE2FhZ5GWeje+vsNUx/oa4f1bofpjiJ8FFz0HYanDztPuUnm+vp3f17Xip9PwcFocF0cEjfjPUYhvojP9TBdCCPE5TwloV111FevWraOzs5PIyEh+/etfc/HFF3PFFVdQX19PYmIir7322jG/4S8B7QzwtA9zl0tlf8fAwQqbu9JW0Wbisz/qlHDjoQpbTnww6ZF+R7T5V1UVa0XFoSYjQwe/S6BPTDjUZMSQk4MywnPGHN1DmLe1Yt7WhqvfhsZfj3FaFMbpkei+eOaZfdDdXKRiJVR8COZ20OggcQ5knO+urgUnHnUPq8VOZXEb+4qa6WocQKfXkDotguy8GKJSAocNJCaTiY0bN7Jt2zbsdjuZmZnMmzePmJiYE762oqpOHlxRSkWbiRlJIVw33ovewnc4ULITb6ORnHMvZOrSCzD4H7thh9M5REPD36k78CdcLhvxcVeTlHQjev1xGnyoKpS8CqvuAscQLLwHZt1wwi6ZFeYhbiuvZ0e/hXPCAngsPZ4ob6mmCXEsnvZMF0KIbzJPCWgnQwLaaaSqKvdtuA9tt5ZLZl1CVmgW3tovf+7YqWQasrOnsY+dn1Xa6nuP2+Y/JyGYcP/PX4e9tZWBdeswrSnAsnkzqt2ONigIv/nz8Vu0COPcuWj9TnAgM6A6VYYqujFvbWWovBtU8E4Nwjg9EsP4MBTdF5bsuVzutv2fLYXscDc4IWK8uyNkxlKIzjliqZ+qqnTUm9hX1ExVcRt2q5PgKF+y82LImBWFwe/YyyYBLBYLmzdvZsuWLVitVlJTU8nPzycx8ehAeDiH08Wr2xp4cnUl3RYbl06N4//S9dR8/BbVWzej9/Zh8pLzyF22HGPQsY86sFrb2V/zJC0tb6DXB5M87lZiYq5EozlO8DK1wQe3Q/kKiJnqrqZFZg87T6eq8kJDB4/WtuClUfh1aizfigqRapoQXyABTQghPIcENA/naQGta7CL76z8Dk0DTQDoNDoygzOZFD7p0I84vziP/Aewqqo0dA8eqrDtrO9hX3M/Dtfwbf6dA2bMRUUMrC1gYN2nOPv6UPR6fGfPwn+RuyukPvLESwSdfVbM29owb2vF2WNF46vDd2okxhlR6COOc+ZZ1/7PW/jXbwTVBf7RkH4uZJ4PSfmg/3zvl23IQfX2dkqLmmmr7UejU0ieEk52Xgxx6QeblxzD0NAQW7duZdOmTVgsFhITE8nPzyflBEs8+4fsPFdQzd821KLXavjJ/BSWj9Oye8WbVGxcj0anZeKiJUy/8FICwo79HplM+6isepje3i0YjWmkpd5LaGj+sW+oqrDvbVh5Bwz1wfw7Ie820A5fGauxWLm9vJ7NfWYWBPvzu8x44n2OH1yF+KaRgCaEEJ5DApqH87SA9pn31ryHX5ofJR0llHSWsLdzL4OOQQBCfEKYFPZ5YJsQNgGj/sTVpjPB3ea/74jDtI/V5n9qorvKFm3UMbhzJwMFazEVFGCvrwfAZ8IEd5ORRYvwTk8fNtSoLhXr/l7Mxa0MlnaBU8UrMQDjjCgME8PQeB2nw6GlG6pWuytr1WvANgB6I6QuPrhvbQkYQw99eVfTAKVFzVRsacVqcRAQ5kN2XgyZs6MxBh676mmz2dixYwcbNmzAZDIRExPDvHnzSE9PRzNMg44DXWYeWVnOh/taiQ0ycNfSTPIiVLa++yalhQWASva8Rcy46DKCo2OPfk9UlY6O1VRXP8rgUD2hoQtJS/0FRmPKsW9o7nQvedz7BkROhIv+CDFTjjs/AJeq8o+mTh6qaUEB7k+J4eqYUDQe+M0EIU43CWhCCOE5JKB5OE8NaF/8MHe4HOzv3c/ujt2HQlttXy0AGkVDalCqO7CFTWJy+GSSApPQKMN35DtThmvzH+Hv/XnHyLhAMmxdOAo/ZaCggMGSElBV9LGx+C1ahP+ihfjm5qIM04beOWDDsqMdc3Erjs5BFG8tvjkRGKdH4TXcmWf2Iagrcrfwr1gFphZQNJAw+2BXyPMg1B1uHDYn+3d2UFrUTHNVL4pGIWliKNl5MSSMDz1mx0uHw8GuXbsoKiqit7eXiIgI8vPzGT9+/LBBbdP+Lh5cUUppSz9TE4K4f1k2Kb52tr73FnsLVuN0OEifncfM5VcQnpB01HiXy0pDwz+prXsOl2uI2NjvkDzuZvT6oGPfsPwDWHE7mDsg71aYd+cRFcVjqR+08vOKBgp7BpgdZOTJjATG+XrmMl0hThcJaEII4TkkoHm4r0pAO5Y+ax97O/dS0lHC7k53cDPZTAD46/2ZGD7xUGibGDaRIJ+gUz/xL+GzNv87DjtMu67LArjb/GdGudv85/qrjD9Qgs/WjZg3bkS1WtH4++M3bx7+ixdhzM9He5z/UVRVxVbb7z4Ee08nOFzoY/0wzojCd3I4Gp9hGmKoKjTvPLgUciW0uRucEJZxcN/aeRCbCxoNvW0WSjc0U76phUGTHb9gbzLnRJM1J5qALzYvAZxOJ3v37mX9+vV0dnYSEhJCXl4ekyZNQnechilOl8qb2xt5/KMKOgesLM+J5c5zMwhQh9j+wTvsWr0S+9AgKbmzmLX8CqJS04+6hs3WSU3N0zQ1v4pO50/yuFuIjf02Gs0xwu5gj7sd/67/uF/zRc9B/PTjv18H3+//tXTzQHUTDlXl7uRofhgXjlaqaeIbSgKaEEJ4DgloHu6rHNC+yKW6qOuvc1fYDv6o6q3CpbqrU0kBSYcC26TwSaQFp6E7XsOIM6zbbDuiyraroZeBw9r8z4gysNBcR+b+XRh3bMLV0wM6HcYZ0/FbtBj/hQvQxx691A/AZbFj2dWBubgVe6sZRa/BMCkc44wovEZw5hk9B9wt/Ms/gAMbwOUAY7h731rGeZC8AKfGh7qSTkqLmqkv6wYgISuE7LwYkiaHodUeWSVzuVyUl5dTWFhIa2srAQEBzJ07l6lTp6I/ToVwwOrgT+uqeWF9LRoFrp+XwvXzk1Fsg+xc9T47V73HkHmAxEk5zFp+JXHZE46+xkAFlVUP0dOzEV/fFNJSf0Fo6IJjvwfVn8B7t0B/E8y+ARbeC17H2dt3UIvVxp0VjXzc1U9ugC9PZSaQZhy+AifE15EENCGE8BwS0Dzc1ymgHYvFbmFf177Pl0Z2lNA11AWAQWcgOzSbSeGTmBw2mUnhkwj3DT/pe54KzkNt/j8PbZXt7jb/GtXFYrWDs7rLSd+/C5+WBgC8s7LwX7gQv8WL8MnOPip0qKqKvXEAc3Erlt3tqDYXukhfjNOjME6NQHOMs92OMtjrDi4VK6HqY7D2g84AKQvdSyHTz6V/yJ+yTS2Ub2xhoMeKwV9P5uxosufGEBR5ZMBRVZXq6moKCwtpaGjAaDQyZ84ccnNz8fY+9jLBhm4Lj35YzgclLUQF+HDnuRlcPCUWh3WQXatXsv2Dd7D09RKbmc3M5VeSNHnqEe+Fqqp0dhVQVfVbBgfrCAnJJy31Hvz8jq68MdQPn/wKtr0EwePce9OS8oZ9i1RV5a22Hu6rasLicvHzpCh+Eh+B7jgNVYT4OpKAJoQQnsNTAtq1117LihUriIiIOHRQ9euvv86vfvUrysrKKC4uJjf3mHlLAtqZcKo+zFVVpdncfESVrbS7FIfLXZ2KNkYfUWXz9Db/JY19n4e2hl66zTZiBzqY117Ggq4y4pv3o6guNBGRBCxeiP+ixfjOnIHG68gOgy6rg8HdnQxsbcXeYAKdgmF8GMYZUXgnD3/m2SEOm7ui9tlSyL4GQIG46ZB5Hq60pdS3hVK6oYW6PV2oLpWYtCCy82JImRqOTv958xJVVTlw4ACFhYXU1NTg4+PDrFmzmDlzJgbD0UslAbbWdfPgilJKGvuYHBfILy/IZlpiCHablT1rVrP1/TcZ6OokMjmVmRdfQer0WSiH7XdzuWw0Nr1Mbe0fcDrNxMRcRfK4W/DyOvpwRGrXw3s3Qk8dTP8hnPUr8B7+IdVhs/OLykZWdPQxyd/A05kJZPsd+7UI8XUjAU0IITyHpwS0wsJC/Pz8uPrqqw8FtLKyMjQaDddffz1PPPGEBDRPcjo/zK1OK+Xd5UeEtmZzM+Bu858VknVEaIv1i/XYNv/13ZZD+9h2NvTSWNvM1OZSZrXuI7ejEm+HDYePAWXGbKKXLiFo4Xy0QUFHXMfWYsZc3IJlZwfqkANdqA++06MwTotE6z/C1vGq6t6rVn7wvLWWXe5fD0mBjKWYY8+j7EA0ZZta6e8cwttXR8bMKLLzYgj9QvOSxsZG1q9fT0VFBV5eXkyfPp3Zs2fj53d0kxOXS+XtnU08/lE5bf1Wlk2K5u6lmcQF++J02CktXEvxu6/T29pCaFwCMy++nIw589BoPw+HNls3tbV/oKn5v2i1voxLuom4uO+h0XzhtdvMUPAwbH4eAuPggmfcHS9P4P32Xn5R2Uivw8EtiZHckhiJ1zCNUYT4OpCAJoQQnsNTAhpAXV0dy5YtOxTQPrNgwQIJaJ7mTH+Yd1g6KOn8PLDt69p3ZJv/cHe3yElh7jb/vvrh9yKdKUN2J3ub3G3+S2rbsBUXk75/F7Na9hFiNeFUNHQlZ6HJm0/ShecSl516KHyqdieWvV2Yi1uw1faDRsGQFeKuqqUd/8yzY+prgsqD563VFoLTBoYQ1LRzaPS9gNIDsdSU9OByqkSOCyA7L4a03Ej03p8Hp9bWVtavX8++ffvQ6XRMmzaNOXPmEBgYeNTtLDYHf/60hr8W7selwo/yx/GTBan4eetwOZ1UbC5iy1uv0tVYT1BkNNMvupTseYvRHbbfbcBcRXXVb+nqLsRgSCQt9ReEhZ11dDhvKIZ3b4DOSsj5Lix5GAxBw74d3XYHv6xq4o22HrKMPjyVmcCUAM/8OyTEWDjTz3QhhBCfOzzc3F/VyN6BwVFfw+lwotUd++imCX4GHkyLG9F1JKAdgwS0kXG4HFT3Vrs7Rh7cz1bXXwd89dr8t/QNsquum7qN21E2FZJUvp3E/lYAGgOjaR4/Hd28+aTmTWdiQjC+XjrsHRZ3B8jt7bjMdrRB3hhzI/HNjUIXNMoloEP9sL/AXVmr/AiGekHrzWD8OVSoF1FaG0VPuw29j5a06ZGMz4sh/LDmJZ2dnRQVFVFSUgLAlClTyMvLIyTk6KWIzb2DPP5hOe/saibc35s7zsngsqlxaDQKqstF9fYtbHnrNdpqqvALDWP6BZcwcdES9N6fN/Lo7FpHVdUjWCzVBAfPJi3tPvz9Mo+8kX0IPn0UNvwB/CJg2VPuPXgnsLqzjzsrGmm32flpQgQ/T4rCR+uZf2+EOBme9kwXQohvMgloHk4C2pfXZ+1jT+eez5dGdh6/zf+k8EkEeh9d6fEEdqeL8u3lNK/6CO3mIqLqytGqLrq9/SmOHk9Tdi7G2bOYlBxJTmwAUe1WzFtbsVb3AuCTHoxxRhQ+mSEoow0XTgfUbzq4b+0D6KlDVaEl8CJKbRewvykUhx3C4v3InhtD+swovA3uzpu9vb1s2LCBHTt24HK5mDBhAvn5+URERBx1mx31Pfzm/VJ2NfQyITaA+8/PZmay+9BtVVU5sHsHm99+jabyfRgCApl2/sVMWXI+3r7uqpbLZaep+X/U1DyDw9FPTMzlJCffjrdX2JE3atoB794I7ftg4uVw7mNHHO59LH12B7/e38x/W7pJ9fXmqcwEpgd65sHrQnxZX4VnuhBCfFPIEkcPJwFt7Iymzf/kiMmkBqV6ZJt/Z28vrR8X0LbqY3Tbt6C3DjKk9WJHRDqbosZTMW4SqWlxzA33Z+aASsj+flSTHY2/HuO0KIzTI9Ed48yzE1JV6Ch3V9bKV0LTNqwuXyqViykdOofOvgB0eg2p0yLIyoshOsXdvMRkMrFp0ya2bt2K3W4nMzOTefPmERMT84XLq7y3u5nHVpXT3DfE0glR/GJpFgmhny8tbCzby5a3X6Nu9w68jUZyzr2QqUsvwOAfAIDd3kdt3bM0Nv4bjcaHcUk/JT7+GjSaw6qIDhsUPQmFvwOfIDj/CRi//IQv/9NuEz+rqKdpyM4P48K4Ozkao/bY35kS4qvmq/hMF0KIrysJaB5OAtqp9cU2/7s7dtM95D4XzKAzMD50vDu0HQxuntbm32WzYSneSv+aNfR9sgY62nEpCrWRKawLzWBT9ATa/MK5ONCPC/FiXJ8DBfBKDsRvZhSG8WEoui+5ZM/Udmjfmrp/HR1Dseyznk/VYB52p57gSB+y8+PImBWFwc8Li8XC5s2bKS4uZmhoiJSUFObNm0diYuIRlx20OXlhfQ1/Wrcfp0vl+3lJ3LgwFX+fz/efte6vYsvbr1K9dTN6bx8mLzmP3GXLMQYFA2A211Bd/QidXQX4+MSTlno34eHnHLk/rXWve29ayy7IuhDOewL8I4d9yQMOJw/XtPD3pk4Sfbz4fWY8ecFn7owRIcbK1+WZLoQQXweeEtCuuuoq1q1bR2dnJ5GRkfz6178mJCSEm266iY6ODoKCgpgyZQofffTRUWMloJ0BX9cP88Pb/H8W2sq6yw61+Y8xxnwe2MInkRWShZd2hJ0TTzFVVRkqLWWgYC2mtQVYS8sAMEfGsi9pMisD0qj1jWOp4s0FeBGFBqtewZwaSNS8eCLGBX35m9vMsH8tVKzCVl5AdXcWpYNLaLOno9GoJE/wJ3tRKnHpwVhtVrZu3cqmTZuwWCwkJiaSn59PSkrKEQGqtW+I331UwZs7Ggnz8+JnSzK4Ijce7WHNTzrr69jyzutUbFyPRqdl4qIlTL/wUgLC3Msou7qLqKp6GLO5kqCgGaSl3UuA/2EHYjsdsOlZWPuI+1Drcx+DSVfACbqAbuod4PbyemoHbVwdE8r9KTH4H2edtxBfBV/XZ7oQQnwVeUpAOxkS0M6Ab9KHudVppayr7NA+tpKOElrMLQDoNfrP2/wf/BFjjPGINv/25mZMa9cysKYA89atYLdDUDC9k2dQkjCJOm0S2b2Qhw49ChU6lf3RPvhMCGVycihZ0QF4fZnqmssJjVuh/AO6du+ktCWdisH5WFV/AoxDZM0IJuucHPS+Gnbs2MGGDRswmUzExMQwb9480tPT0RzW1r6ksZcHV5Syta6HzCh/frksmzmpR+4t62ltpvidNygtLABUsvIXMuOiywmJicXlctDc8ho1NU9ht/cQHX0pKck/w9v7sL1wHZXualpjMaSd424iEhg77Mu0OF08XtvCXxs6iPbW87uMeBaFBoz+/RLCA3yTnulCCOHpJKB5OAlonqnd0s6ejj3s7nRX2fZ17mPIOQRAqE/oobA2OXwy40PHn/E2/06TCfP69ZgK1jJQWIirvx/F2xufmbPonTSXbl0qIc1OwmwqA6h8jJ1VWgeGOH9y4oPISQgmJyGI6ECf0YfPziocpauo2VxLaWMSTbaJKDhJiuwge04kMfmz2FNWTlFRET09PURERJCfn8/48eMPBTVVVVm5p5XfriyjqXeQs7Mjuee8LMaFHdmso7+zg23vv8WeNR/hdDhIn53HzOVXEJ6QhN3eT92B52ho+CcajZ6kxJ8QH38tWu3BjpAuJxT/FT75NWj1sOQhmHr1Catp2/vM3FpeT5XFypVRIfw6NYYgveftXRRiON/0Z7oQQngSCWgeTgLaV4PD5aCqp+qIKtvhbf7TgtKOqLIlBZy5Nv+q3Y5l+3ZMBQUMrCnA3tQEgM/kSRjnLMPmlY6r0Y7GqdLgBW84hljlsmEBIgO8yYl3h7WchGAmxgZi8BrF0j5zJ71bP6F0QyvlTYkMugIxarvJim8gY24cBwxxrN+8nc7OTkJCQsjLy2PSpEnodO7AM2R38rcNtTxXUI3N6eL/Zidx0+I0Ag36I2/T28P2D95h1+qV2IcGScmdyczlVxCdmoHFUkf1/sfo6FiNj3cMqal3ERFx/ufBs7sG3rsZ6tZD8gK44A8QnMhwrC4XT9W18Wx9G6F6HY+nx3NuuGd2BRXiWOSZLoQQnkMCmoeTgPbV1TvU627zfzCw7enYg8l+sM2/l/+h9v6TwicxMWziGWnzr6oq1soqBgrWYCpYy9CePQDox6XjO3M5ilcqzn4VVafQEu3LWh8XK7tMHOi2AKDVKGRF+x8R2pJCfUdUZXMOmqlbs4HSzV3Ud7qbryR47yYrvpGh5HiKWnS0dnQTEBDA3LlzmTp1KvqDB1W3m4b4/UeVvLa9gSCDntvPTueqGQnovnCMwOCAiZ2r3mfnqvcYMg+QOCmHmcuvIC5rAj29m6mqepiBgTICA6eSlnYfgQGT3QNdLtjxD1j9S1BdcNavYPoPQTN8qN5jsnBreT37Boa4OCKIh9LiCPOSaprwfPJMF0IIzyEBzcNJQPv6cKku6vrq3M1HDoa26t7qo9r8Tw6fzKTwSWekzb+9rY2BteswFazBsmkzqt2OLm48hmkXgy4BnAq6SF+UyWGUhujZ3mZiZ0MPuxv6GLC6G6kE++qZctiyyMnxQQT46Ie9b3+HmbLVOynfZmJg0BuDppcMQwG+kd3s0KXT0A9Go5E5c+aQm5uLt7e7bf6+5j4eXFHK5ppu0iL8uG9ZNvPTj+60aRu0sGv1SrZ/8A6Wvl5iMrKZdcmVJE6aTGvrW+yv+T02WydRUReTkvxzfHyi3QN7G+D9W2D/GkiYAxf9EUJThn8PXSp/rG/jybo2/HUafpsWx0URQR6xL1GI45FnuhBCeA4JaB5OAtrXm9luZl/nPko6P+8aebw2/5PDJxNmCDvBFceOy2xmYMMGBtYUMLBuHU7zEPqEWXhnLUHRh4NWwTAhDOOMKHRJAezvMLOzvoed9b3sbOihqn0AVXVv4UoN9ztUYctJCCItwv+IboyH7ulSqd/XRWlBFXXlFlRVIdprL+HGTdQYgqh1ReLjpWXWzNnMmD0HX19fVFVldWkbv11ZxoEuCwszwrn3/GxSI/yOur7dZmVvwWq2vvcWpq4OIpNTmXnxFSTljOdAw19paPgboCEx8XoSE36EVmtwn/+2+3/w4d3gsMKi+2DWT0Ez/NLOsoFBbitvYJfJwtKwQB5NjyPSe/igKsSZIs90IYTwHBLQPJwEtG8WVVVpGmg6Yi+bJ7T5Vx0OBnfuxFSwFlPBGpw9TvSJeeiT5qJofdD4a/GbG49xWiRaf/d8+ofslDT0uUNbQy8763vosdgBMHppmRwf5A5t8cFMSQgizM/7iHuae62UbWqhbH0j/d02vHVWonw/pcunm1pNDF4aF9NTQpl99iX4RcRjdTj558Y6nl1TjcXu5HuzErllcRrBxqPfH6fDTmnhWorffZ3e1hZC4xKYefHlJOSMo6bu97S3r8TbO4qUlDuIirwQRdGAqRVW3A4VH0DsNLjoOYgY/uHpcKn8tbGDx2tb8NZo+E1qLFdEBUs1TXgceaYLIYTn8JSAdu2117JixQoiIiIOHVT9+uuv86tf/YqysjKKi4vloGpPIh/mp89I2/x/tjQy2hh9SgOAqqrYamrcTUYKPsXeqUefmIcuLB1woY/WELA4A5/scJTDqmSqqnKgy8LOhoNVtvpeSlv6cbrc/z8mhPgeDGzuSttnbf5Vl0pjZQ+lRc3U7OrA5VAJDGnGqi+hAQM6xclUvw7m5mQSOPkCOn3ieerjSv5XXI+/j55bz0rju7MS0WuP3j/mcjqp2FzElrdepauxnsDIKGZcdBkxkwOpqX0Uk2kvAQGTSU+7j8DAqe5q2r63YOUdYDXB/Dth7q3uro/D2G8Z4vbyBrb0mVkY4s8TGfHE+njG+XlCgDzThRDCk3hKQCssLMTPz4+rr776UEArKytDo9Fw/fXX88QTT0hA8yTyYX5mDdfmP8wQdkQDklPd5t/R2cnAunWY1m3D3uGDLmY6Gu8AUC14JWoIujAHr7hjL80ctDnZ29x3aGnkjvoe2vqtAHjpNEyMDWTqYUsjg7RaKja3UlrUTE+rBcXHgia0knZnH6gupiilzA3uJDR7PuVh5/DQdi1F1V0khxu57/wsFmZEHDO8qi4X1du3sOWt12irqcIvJJTcC5cTMWGIugPPYLO1ExmxjJSUOzEYYsHc6Q5p+96CqIlw0fMQPWnY98mlqvy9qZOHa1rQAA+kxvDd6FCppgmPIM90IYTwHJ4S0ADq6upYtmzZoYD2mQULFkhA8zTyYe5Z7C471T3Vh/axlXSWcKD/AOBu858enH5EaEsMSDwlbf5dg4MMbNiEqWAfji5fNEGp7t+wNeGd6k3gspl4J8YNe42WvsGDFTZ3aCtp6sPmcDdSiQrwISchiCnxgaRpvbBXmqjb2YHVaUGNaKaPJlRcTKCSfLYQblAoiLyah5tzqemH/LQw7l+WTXrksR9YqqpyoGQnm996labyfRgCApl6/lJCspppavkHAAnxPyAx8cfodEYoex8++BlYuiDvNph3B+i8j3ntzxwYtPKz8gaKegfIC/Lj95nxJBqGHyPEqSbPdCGE8ByHh5tfv7+P0ub+UV/D6XSi1R57v3x2TAAPXDB+RNc5XQFNel6Lrx29Rk9WaBZZoVl8K/NbgLvN/2dLIks6SlhZu5LXKl8DIMArgInhE5kc5l4WOSFswpi0+dcYDASctYiAsxahOp0MbNyFaW0VTkcQtgZ/2p7ahTrwCoZsP/zPzsNnwvijKkjRgQaiJxo4b6K7k6LN4aKspf+wvWy9rNrbCoBOozAxxZ8ZmjBC2gJRemKx+jezz1fHHjWDTJ2FeU3v8KHtGf7tdR7P1FzCuU918O2pEdx23mRCv7DvTVEUkiZPJWnyVBrL9rLl7dfY8L9X8DYamXLeDfinllF34HmaW94gJeVnRGdegpI4Fz66Fwp/5w5sFz0Hccd+WAEkGrx5fUoKL7d086vqJhYUV3BvSjTXxoahkWqaEEIIIb6BpII2BuS7rV89LtVFbV8tJR0lh1r9V/dUo+L+/2Fc4LhDVbbJ4ZNJCUoZszb/qlNlYH05pvUHcA4YUBQNjo4yXN0l+EwKJ+CsRfjOnInGa2T7sjoHrOw62C1yZ30vuxt6MVudRDoVpru8SLU5sfk0MWhsRlUcjIsMZkFIKwGNBTzdPZP/OM/CV2Pnlow+rl4yG6+oTHe7yWNo3V/FlrdfpXrrZvTePkw6fxKGxO0MWPbi7z+etNT7CA6eAVUfu1vym1pg9g2w8F7QG4Z9HU1DNu6saGRNdz8zAo08mRlPqq/PqN9fIU6WPNOFEMJzyBJHDycBTZxKZruZvZ17D1XZSjqPbPM/IWzCEUsjx6LNv7PPiqmoDnNxC6pVi2ozY6/fhKNtK745afgvXoRx3jx0wcEjv6ZLparddGhpZEldD7qmISbbIci7FYtvE6rWjo8xnLycRMIGq3l0h5Z1g8kkKa3cE/QJZ09ORslcCvGzQHt0MO2sr2PLO69TsXE9Gp2GiRckoI/Zit3eTkT4UlJT78KgBMLHv4Ttf4eQFPe5aYlzhp27qqq80dbD/VVNDLpc3JEUxY/jI9Ad4xgCIU4VeaYLIYTnkIDm4SSgidNJVVUaBxo/D2wdJZR3l+NQ3W3+Y/1ijwhsmSGZX7rNv+pSse7vZWBzM0OlXaAqOPsPYKsuwNG6E9/JE/FbtAj/xYvwSkgY9fX7Bu2UNPayc087nbs7MJjqsRsbcWltDDn96A9JxTc4gOIDvdQPejNbU8r9un+RbTRB2jmQsRRSF4P3kQ+3ntZmit95g9LCAhStk+wL/NGH70bFRUL890lK+gm6+u3w3s3QewBmXAeLHwDvo89lO1y71c7dlY2s7Oxjsr+BpzMTyPIbvgInxFiRZ7oQQngOTwloV111FevWraOzs5PIyEh+/etfExISwk033URHRwdBQUFMmTKFjz766KixEtDOAPkw/+YYcgxR3l1+RAOSVrN7D9hne98mhZ1cm3/ngA3LjnbMxa04OgdBceLs2sPQ7vdx9TXglZqC/0J3WPOZNAlFM/oGJ3abg02f1rNjwzb6HTW4dEM4Hb6U26PZRjCKRsGlqpznv59f8gJR9gbQesG4eZBxnjuwBcQcul5/Zwfb3n+LPWs+QvEaJON80AVXoteHkpLyM2JCz0Up+C1s+QsExcMFf4CUhcPOUVVV3uvo5Z7KJvodTm5NjOSmxAi8vsTrFWI05JkuhBCew1MC2smQgHYGyIf5N1ubuY09nXsO7Wcr7Sodkzb/qqpiq+vHXNyKZU8nOFwoPlacbdswb3wDrGa0YWH4L1yA38JFGOfMRuMz+j1b3S0DrF25ibIDO3FoLGidBgZ04/jQ5k+f0wWoJGo6uTlwPQtdmwixNrkHxuQcDGvnQeR4UBTMvT1s/+Addq1eic6/m9QlFrR+7fj5ZZGWdi8h/cB7N0JXNUy9GpY8BD7DN2TptDm4v6qRt9t7yTb68FRWApP9T91RCULIM10IITyHBDQPJwFNfBXYXXaqeqqO2Mv2WZt/raIlLTjtiNCWFJB0wiqby2LHsrsDc3Er9hYzil5BG2zF0bQJ86fv4hoYQPHxwTh3Lv6LFuK3YAG60NBRzdthd7L+o2K27tyMxdmHxumNzied9dpgynoH8dJpcLlcJLoaWaLdwVKvnUxQK9GgYjXGos06H132+ZA4l8HBIXauep+dq97FJ7KF+PxetD5mwsLOJi3xVnyL/wsbnwW/KLjgaUg/54Tz+7Cjj7sqG+i0O7ghPoLbk6LwOcaB20KcLHmmCyGE55CA5uEkoImvqp6hnkNVtpKOEvZ07mHAPgAc1uY/fDKTwyYzIXwCAV4Bx7yOqqrYGwcwb23FsqsD1eZEF2FAFz6EvWY9A+s+xtHSAoqCYcoU/Bcvwm/RIryTk0c8V1VVKdmxj3UFn9Jj7kBx6ulzpFDsHULjkJ3s6ADyUkNpM1k5cKCW9P6NnK3ZTr5mDz6KnUGtH51R8/AZv4yAzIWUFG1i+6o3MCbUEjWtB41OJT7+GpK98tCtuBM6ymDSt+DcR8A3ZNi59dod/Kq6mVdau0nz9eapzARyA40j/4MQYgTkmS6EEJ5DApqHk4Amvi5O1OY/OTD5UIVtUtgkUoNS0WqOPGDRZXUyuLuDga2t2BtMoFMwjA9DH2llaF8R5rUFDJWWAuCVlORuMrJoIYacHJTjHNZ4OFVVqa2t45MPC2hub0B16qgbSmGbLhCLqnJJTix3Ls1Eq1HYVd/LnroWXNUFJHUVMp/thCn92NFS6TOZjqgF9Dkiad9XSGBaOSEZfWgVf1KTbyauphml6CkwhMD5v4fsC084t7Vd/fy8ooFmq53r4sK5KzkaX6mmiTEiz3QhhPAcEtA8nAQ08XU2YBtgb9feI7pG9lh7AHeb/4lhEw8FtonhE49o829rMWPZ2op5RzvqkANdqA++06PwigNL8XoG1hRgLi4Gux1tcDB+8+fjt3gRfnPmoDGeuALV2NjIuoJPqa6pwu7Ss28olRLFD71W4doZidxyfiY+enfoc7pUqlp7adizHl3VKlK6C0lwNQKw15nIpsFJ2NV+YnNq8YuxoCOGSdE/IPjTl6C1BLIvhvOeAL/wYedkcjh5aH8z/2zuIsngxe8z4pkbfOYevuLrQ57pQgjhOSSgeTgJaOKbRFVVGk2N7O7cfSiwVXRXHNnm/+BB2pPC3G3+dS4Nlr1dmItbsNX2g0bBJysE44wo9NF6LBs3YFpTwMCnn+Lq70fx8sI4ezZ+ixbht3AB+oiIYefU2tpK0foi9u7bi8nlww5rKrWKgSCNhuunJHDtBel4G/RHjTM1ldGx7R28939EdP9uUF1s7k+k3BhM1LQ2vAPt9PelMNGeSUrF/1C8/GDp4zDxsuMemv2ZDT0mbi9v4MCQjf+LCeX+lBj8dCeuEApxPPJMF0IIzyEBzcNJQBPfdEOOIcq6yz5fGtlRQpulDQAvjZe7zf9nSyOVLHz3OrHsaMdltqMN8saYG4lvbiRaoxbL9h0MrC3AtKYAe6O7wuUzaZK7yciiRXinpR23eUlnZydFRUWUlJTQ7PBjmz2ZTlVPrFPD99OjueDsZCIS/Y893tyJWvkRlj0r8KpbS53JwJ7wEPwm9aPoXDSXJzCju48s134awuczcNbvSE1NQz/MEkaz08njNa38tbGDGG89v8+MZ0HIsffxCXEi8kwXQgjP4SkB7dprr2XFihVEREQcOqj6jjvu4P3338fLy4uUlBT+/ve/ExQUdNRYCWhngHyYizOp1dx6RAOSfV37sDqtAIQbwpkSOpnFQ7PJPBCLd4MLAJ/0YIzTo/DJCgGNgrWqioGCtZgKChgqKQFAHxfnbjKycBG+06ai6I+ujPX29rJhwwa2bd9BpT2YnY4ELKqWbJuWi4ICmTMvnvQZkXj7Hj0WAPsQ1Bailq9g/651lEeo+KRacNkUgkt8mDjYig09j7q+R1XMReQkhpATH0ROQjBRgUcfKbCtz8xt5fVUWaxcFR3Cr1JiCNTrxuidFt8U8kwXQgjP4SkBrbCwED8/P66++upDAW316tUsWrQInU7HXXfdBcBjjz121FgJaGeAfJgLT2J32ansqTxiL1u9qR6AaHs43xo6n7mdkzEOeaMaNfjnxuA3IwpdqME9vr2dgbXrGCgowLxpE6rNhiYwEL958/BftBBjfj5aP78j7mkymdi0aRMbirezYzCMUmc0CgozhnTMdnqRNS2S7LwYolMCj3+kgMsFzTvZX/QXqtSN6CMH0bYqTK4aIFgdpFKXzvWDN1DrdO9Niw70ISchiJz4YHISgpgQG4iPXsuQ08WTda0819BOmF7H4xnxnBM2/FlrQhxOnulCCOE5PCWgAdTV1bFs2bJDAe1wb7/9Nm+88QYvv/zyUb8nAe0MkA9z4ek+a/P/2bLIfR37yOpJ5NzeucwYmIAWLZ0RA5Djz7iZEwj0DQLAZTYzsHEjA2sKGFi3DmdvL+j1GGfMwG/xIvwXLkQfHX3oPhaLhS1btvDxxh1sNEdQ5wohUKswf9CLdItCSJSRrLkxZM6OwuDnddz5qqpKdfEfqOt4AY3BQmipiwmdvWgVMEdMY1P0d/nQkkVxk4WG7kEAdBqF7JiAQxU2nzAfHm/poNQ8xCWRwTyYGkuol1TTxInJM10IITzHEeFm1d3QumfU13A4Hei0x/k3QNREWProiK4zXEC74IILuPLKK/nud7971O9JQDsD5MNcfNU4XU53m//OEqobyvEvU8htzSTaHka/doBt4eV0ZFpJSE451OZfo8Lgrl3uJiNr1mA74D582zs7C/9Fi/FftBDvrCwURWFoaIitW7fyVuFuCgci6FKNjPPTcR7++DYOodEqJE8JJzsvhriMYBTNsatqLpeNir3P0tT6Ij62QVJ3W4n6f/beMzqu67y/3tMHU9B7750ACRKsAEmAklUoWZJrHKc4juM4LnGL7b9tJXbc4yK32ImT2IkTv44tOyqWRFWCDWAn0Uj0QrRBr9Pbve+HCwKE2ClAHFFnr8WlxeHM3Dtzlg7OD89z9vG7CEgqtHoD5N7FQsbdnDVs4eSEisbBOZqH53D5ggBEWfRYS6LpidBg0aj5Wm4y70qJveK1BIKLiDldIBAIQoc3QkD7+te/zunTp3niiSeu2CkkAtptQPwwF9wJ2D12eppb8Z+ZJWHIjEbWcD6slxciGzgT3UFefP6S5r8srgzL6DyOOkUy4m5qAllGm5SEtaYGy55azJWV+IHTZ87wi7pzHLXH4kLP9uQw3hEVz0zjDF5XgPBYI0U7kinanoQ5wnDFe/P5Zug4/00mpp8g0eYlv8+JRgaPJgKzNAuoIG0LFN5PMO8+uoKJNA7O0Tg4S+PQHF0uD/7SKOQIPRFzfu6R9exIi2JDehS5cRbUVwmIgjcnYk4XCASC0CHUWxz/67/+i5/97Gfs378fk8l0xdeJgHYbED/MBXcaQYcP59lx5o8Po5oJ4NMGOB3bweNh++g0XgAg1ZK6ZIws12aS1GzDdeAQzoYGZI8HtcWCuboKa+0ejNu3cbqnjx+93MFpRyQqFTxSFMEf52QxcGKSka45VGoVGaUxlFQlk14SjfoK1kaHs5v281/GM91AfruLhAUvs6oE5Jy7iHa0KueoAcTkQsH9yp+0zcx7Jc4OzvJvw5McUvmQAzLa9jnUo27CDVrWp0cutUauT4skynz19kvBnY+Y0wUCgSB0COWA9sILL/CpT32KQ4cOERd39fNbRUC7DYgf5oI7FVmW8V1YwHlyDFfrFAQk/PFqerPGecV6nFOzZ5hwTQCK5r84ppj1EcVUDulJaRolWH+c4NQ0aLWYNm3CXLObM/Fp/ODUJO0uC2Z1gPdtjOF9W8voPjFBx7FR3HY/5kgDRduTKNqRRPiivORSpqYP0tn+FSKGO8nvcqEJynToq4i+99MkBXugcx/0HwHJD6YYyL9XCWs5NfQENHyyfZBTCy5KtTrWzQTpGpinY8xOUFLmw6xY82JgU0JbQaL1mpp/wZ2FmNMFAoEgdAiVgPae97yHgwcPMjU1RUJCAv/4j//IN7/5TbxeLzExMQBs3bqVf/3Xf73stSKg3QbED3PBmwHJ5cfVPInz5Bj+UScqnZqwsji863S0GrppmWqhZaqFtum2Jc1/giGOPc4MKnsgqXEI9YURAPT5+TRsvZt/cScy6g8jTuvhw9sSeM+eSkba52mrtzHYNgNAelE0RTuSySqPRaNdDkmS5GfE9r8MtX+XnM4xEqa8jHvNNJsepOjtHyU1Kw1Vbx10Pg/dL4JnHjQGyN5NsOB+fhFZzTdGHGhVKr6cm8LDMeG0jiysaI2ctCufw6hTU5ZyMbApoS0h/HLNv+DOQMzpAoFAEDqESkB7LYiAdhsQP8wFbyZkWcY/7MB5agxX0ySyL4g2wYS5MhHThngkI3TNdinGyClF8z9kHwIgeVbNvcPRbOyWiO2eRJZkntm8l18nb2cBAzn6BT6yI4W9u7fgdUi0Hx2l4+gojlkvYVYdhVuTKK5KJjJhucfb75+jv//HeJv+g4LuBbR+iRNTaQxG38PmR95D5vqNqKQADB6Djn3Q+RzMKccOXMi4h09lfoijRFMdaeG7hWlkhBmWPufInHsxsM3RODTL+ZEFfEHlLLnkCCMb0qOWQltJsqL5F7zxEXO6QCAQhA4ioIU4IqAJBKGF5A3ibp7EeWoM35AdNCrCSmMxVyZiyI5YsjPOeGZonWxdCm3nps6hmnewoVdmW5+W/H41vy28h2fStxFUqVmnm+CDm5Oo2bMbozGMwfPTtNXbuNA6jSzJJOdFUlyVTM6GOLR6JRQ5nX30n/8yMadfIGnCyxwmnu3PQ07awNZH3k1u5VZUajXIMky0KW2Qnc8jjZzlV0kP8JWcjyCptXwxJshflGxErb38cG1vIEibbbHKNqRU2oZnFc2/TqOiOCl8ObSlRZEWHXb1c98EIYuY0wUCgSB0EAHtdUalUj0M7AXCgZ/LsvzStZ4vAppAELr4Rp24To3hPDuB7AmgiTFirkzEvDEBjXWldCMoBemb71MO0p5qoc3WhLGll8I+C63GhzgeW4YRPxs1Q+y1zvOWBx8htqQE57yXjmOjtNXbWJjyYDBpyd+SSElVMjEpyuHZ0zP1TDZ8mszWLgw+ifNyFvs7k4hIyWLzw++kcPtO1JpLKl0Lo9D1AsM99XxGv5UDUZVsWTjPY3ITOXnbIWcPGMOv+rkn7B6aLglsLcPzS5r/GLN+qSVyQ1okZWmRWAziLLZQR8zpAoFAEDqIgHYTqFSqXwAPABOyLJde8vi9wA8BDfAfsixf92ABlUoVBXxXluW/vNbzREATCEIf2R/EdW4a58lRfP0LoFZhLIrGvDkRY97Vzzyz++ycmzpHy0Qz5462caqvmDFtGlEqJ1tVF9g0cY7oaIjfs5v8bXvx2HS01dvoa5pECsgkZIVTXJVM7sZ4tHoYHfgl6pf/kSTbPK4wC4ftmzjfHSQiIZHND72D4p170OpWVslkj53Hz5/kH+YseIHP9v+cvx59Gk3mDii4TxGNRKRc8/MHghJd4w4ah2aX9rP1TjoBUKmgIMG6VGHbkB5JjtD8hxxiThcIBILQob29ncLCwtfUkXI7A5osy3R0dLxuAW0n4AD++2JAU6lUGqALuBsYBk4B70EJa9981Vu8X5blicXXfQ/4/2RZPnuta4qAJhC8sfBPunCeGsd1ZhzJ6UcTYcC0KQFzZQLayGtLNiRJ4n9OnecHz/cx69GSrp5hk3qQ8oFOUi60M5wOji3FRFbuIXaikOnGIHNjbnQGDXmVCRRXJROVLDNx4rPENPwOoyfIRFoZB/pLGekewhIdQ+WDb2PdnnvQGVbey7jXz+c6B3lh2s4GaYbv9zxG4egR5R+TyqFgrxLYEtcpqes6zLv8NA0vykcWQ9uCJwCAVWj+Qw4xpwsEAkHo0N/fj9VqJSYm5pZD2u0KaLIsMz09jd1uJysra8W/rVmLo0qlygSevSSgbQO+LMvyPYt///zizb06nF18vQr4FvCyLMuvXOU5HwQ+CJCQkLDxN7/5zS3f71rhcDiwWCy3+zYEgtBFAvMERAypCZtWHnLFwkKahDMOuIbB3heUeWnAzzO9fvxBmSLNGGUaGzkjFyg510aYc56WLBWNuRpc6VvIsFcRPpaKSlJjjITIHBUxqQPkDH2XNNsQbqOO5sS30NxkxTE6gtYYRkL5JuJK16PRLx+ULctwDB3/SRguVPyRb4IPjj9H4tQJwhc6USHjMcQxFbuZ6ZjNzEWWIKsv37d2xa9Dlhl3yvTOB+mdk+idkxiyS1ycjRNMKnIiNeREqsmJUJNqVaMVVbbXDTGnCwQCQeigUqkwm81oNLcu4pJl+bbtCQ8GgzidTl6duWpqal63gPYO4F5Zlj+w+Pc/BbbIsvzRq7z+b4E/R6m0NcmyfPnBAZcgKmgCwRufwIwH5+kxXKfHCS74UFt1mDcmYK5MRHuFM88uMmH38L0Xu3j89BAmHaxXD5HDGBlI5J0+SVzvALIKupPVnM4LYyJuE+nuaiIdSaCViCsxsLngFImn/wmjy8NERir2si/S9FInF5rOYDCb2XDvg1Tc91bCrMt7zqZ8Ab7YPczTE3OUWsL4fmEa61QO6HpRUfj31kHADYZwyL0LCvcq/w2LvKnvxekN0Doyv1RhOzs4x5RDaP5vB2JOFwgEgjuLUJzXX88K2k0FtJtFBDSB4M5BDsp4umZwnhzD0zkDEhiyIzBvTiSsJBaV7spltfO2eb7yTBsn+mdINqvYQB9xwSmyEhNZ73Zjra/He74NgIV4M2fy0xgJ30CsZxN6yYjPYuOu9J9SOnMer17N+Oa7Uad9grPPHKDn1DF0BiPlb7mfjXsfxhIVvXTdfZNz/L+uYab9AT6WnsAnMxMwqNXgc0H/Ieh4DrpeAOckqLWQsUPZs1ZwH0Rl3Pz3c1Oa/yhKksOF5n+VEHO6QCAQ3FmE4rwesi2ON4sIaALBnUlwwYvz9DjO0+MEZzyoTVpMG+Ixb05El2C+7PmyLPPi+XG+sa+dwRkX6+O1FHnbMXjnSE9PZ/u6dcR3d+M4cBDX8ePIfj++yCh6ynYxElaKxptEfFgTe2K/S7TfyUi8kVMlNVjN78DR0E3vsWOotRpKa97C5re+nfC4eABm/QG+1DPC42Oz5JuM/KAwjYqIS+5PkmDk9JLCn8kO5fGE0mXJSNJ6UF+jp/MaXFfznxyxuJctkor0KFKjhOb/VhBzukAgENxZhOK8/noGNC2KJGQPMILSuvjHsiyfv+WLXIIIaALBnY0syXh753CeGsN9fhqCMvqMcMyVCYSVxaHWr6wQeQNBfnn0Aj/e34PbH+SuTAPpC634HHMkJydTXV1NXmoqroaj2Ov24zh0GGl+HmdEGiPrHmRMn0VlxK9Zb9iHXw9ns8L5N60FjzePsr4o9B0zqGQoqq5hy8PvIjpZMTjun17gM51DjHn9fDAtjs9mJWHSXCF0TfcqQa1zn3JQtiyBNWk5rGVWg+61tSq+WvPfPDSP269o/mMtetanLR+mXZYqNP83gpjTBQKB4M4iFOf1tbI4/i+wG4gFxoEvybL8c5VKdT/wAxRz4y9kWf76LV3gCoiAJhC8eQg6fLjOTuA8NUZg0o3KoMG0Pg7z5iT0KSsFDlMOL4+93MVvTg5iNWp5e0EYlrFGFuZmiYuLY+fOnZSUlKCSJFxnzuKoq8NeV4dnZJTJ2PV4i4uoTPgfYlQ2xuP0nExP59ceLX3TXkr7wikYsqKWVagLEim6/x62lO9Bp43gq702/ts2TVaYnscK09kWeQ2xhGtmcd/aPujZD34n6C2QU6uEtfx7wBR99dffIBc1/2cvGiOHZulb1PyrVZCfYF1qjaxIjyQ7Vmj+X42Y0wUCgeDOIhTn9ZA9qPpmEQFNIHjzIcsyvgsLOE+N4WqZgoCELsWCuTIR0/o41MblilDH2AJfe7ad+p4psmPNvLckDHfvaaamJomOjqaqqoqysjK0Wq3yvj092OsOYK/bz0y3DfMGA3lpZwhqoSvXzKh1N86Et3BuvofZhhbiOnzogmoG412MlxnJLCwjzLqVpxyZjPrhL1JieTQ7CbP2OnvB/B64cGS5FdI+Cio1pG9b3rcWk7Nq3+Gcy0fT0NxSa2TTpZp/o5b1i4r/DYu6/0jTm1vzL+Z0gUAguLMIxXldBLQ1JhQHXSC4E5HcAVxNEzhPjuEfdaLSqQkri8O8ORF9uhWVSoUsy9R1TPD159rpm3JSnRfLe4uMDLQeZ3R0lPDwcHbs2EFFRQW6Sw6qDkxOYj9wAPfhp7AYGgi3zjERbaA9OwLHxL3k5H+EuKIoDj7zKwYO1CN7/EzGBzmdNclYDHii343DfBfhag8fSvDwx+lFJJoTb+BDSTDatBzWxs8pj8cWQOH9SmBL2XTL+9aufEmZvimnci7bYnDrHFtAWvxxkB1rVs5mS49iQ1okhYlWtFdq4bxDEXO6QCAQ3FmE4rwuAtoaE4qDLhDcyciyjH/YoVTVmiaRfUG08SbMmxMxbYhHY9bhC0j8z/EBfvhKFw5vgD/enM5DOVpaTx9jcHAQs9nMtm3bqKysxGAwrHh/yWHH9/svou//FUE1dOeFMRgez2zrg8QHKii6r5AR23lOP/skrvk5TJlJOCpiOBwu0aipJaBLxOg4QKb3FSpiCyiLLaMsrozimGKM2uvsOZu9AJ0vKIFtoAGkAJjjIP9eReGftQv0plX/Tp3eAC3D8zQOLR+mPeXwARCm07AuNWKxwhZFRXok8Xew5l/M6QKBQHBnEYrzughoa0woDrpA8GZB8gZxt0ziPDmGb8gOGhVhpbGYKxMxZEcw5/bzg1e6+NWJQUx6DR/fk8euZDjWUE9fXx9Go5EtW7awZcsWTKZXBZ/pXuSnP4Jq8BgzVgttRTrmXVmMN70bo81MTkYAKdVP65mj2KeniM/KYd1b385/WsN5fEomDDeJ9sexz+4HQKvSkh+dvxTYyuPKSbOmXd206J5V9qt1PAc9r4B3AbRhi/vW7lNCmyVuTb5XWZYZnnUvyUcaB+c4b5vHH1R+ZqREhilVtrQ7T/Mv5nSBQCC4swjFeV0EtDUmFAddIHgz4h9z4jw5hvPsBLIngCbGiLkyEfPGBPpcXr6+r52DnZNkxpj4wv1FFEcEOHLkCJ2dnej1eiorK9m2bRsWyyWyD0mCU/+B/MqXkQnSmxnBYGIA11A5o61/hDxnJsneQljiNBc8EyzMzxKdkkbEw+/hR4Y4OlxeHow18VbrKP0zzbRMttA61Yor4AIgyhBFWVzZ0p/SmFIs+ivIRgI+GKhftEI+D/NDgArSNi9aIfdCbB6soVbf4w/SNrqwVGFrHJxjZO7O0/yLOV0gEAjuLEJxXhcBbY0JxUEXCN7MyP4g7nPTOE6O4eufB7UKY1E05s2JHJf8fP35DnomHGzLjuHvHygmRuPmyJEjnD9/Ho1GQ0VFBdu3bycyMnL5TWcvwB/+FvoP4U7MoinDg8sA/sHdDJy+n0DAgnW+D7P9CDMRDhYCXsxxifQ88j5+o7EQqdXyrfxUHoiPJCgF6Z3vpWWyZelP73wvACpU5ETmUB5XroS22DKyI7NRqy7ZAybLMNa6GNaeg9Fm5fHonOV9a2lbQL32Fa2JBc/SPrbGwVlahq+u+S9PjcT8BtD8izldIBAI7ixCcV4XAW2NCcVBFwgECv5JF85T47jOjCM5/WgiDOgq4nlG6+eHDf3Mu/38UWUan7q7ALXPQX19Pc3NSuApLy+nqqqKmJgY5c1kGc7+N7z0KLLkZ6xkPW3WLnS6WHSeP6P3lULmF9SoAx6sUy/jpAuHQcVCUgYv3/9e+nQmHoiL4Jv5qcTpdSvuc8G3wLnJczRPNS+FtgXfAgAWnYXS2NKltsh1seuIMkYtv3h+ZFky0n8YJD+ERSstkAX3KS2RhmscAbCKBIISneP2xcD2xtT8izldIBAI7ixCcV4XAW2NCcVBFwgEK5EDEu72aZwnx/D2zAHgywnnl9oA/1/XOEadho/U5PIXOzLxOO00NDRw9uxZJEmipKSE6upqEhISlDebH4FnPwHdLxFILqUjP4JxqROLpYgY08cZOJ1C9+kxAn4Zo7uZgL2eBWOAs2VV1FfuwaJR8/XCdN6WGH3VFkBZlhlYGKBlarnK1jXbRVBWqlPp1vQVrZH5Ufno1DrwLEDvfiWsdb0InjnQGCB71+J5a/dCeNLaf+GX8GrNf+PgLPYraP4r0iNZHwKafzGnCwQCwZ1FKM7rIqCtMaE46AKB4OoEZjw4T4/hOj1OcMHHsEnNv4QFODTtIC06jM/fV8R9pYk4HA6OHTvGqVOn8Pv9FBYWUl1dTUpKilJNa3kcnv8sst+No/IRWixteHw24mLvJj31Mwy3Gjhfb2NqyAGBIVSuQwxbZV7Y/Qi2xHSqJm18M85MzrYtqI3XtyK6/C7aptuWQlvzZDNT7ikADBoDJTEly6EttowEYzQMHleqax3PwdyA8kbJFcutkPHFa7pv7UpcV/MfZ2bDJa2RBQmvr+ZfzOkCgUBwZxGK87oIaGtMKA66QCC4PnJQxtM1g/PkGJ7OGU5JAf5Z56fX76cyI4p/eLCEdakRuFwuTpw4wYkTJ/B4POTk5FBdXU1mZibYx2Hfp6H9GeSkcmyba+heeBJJ8pGW+mdkZn6UWRu01dvoOjWO12FDDpzgWF48RyrvQhcM8KE//JY/1kpYa2qx1OxGGxV1vVtX7l+WGXOOrWiLbJtuwy/5AUgwJSy1RZbFrqNI0mDsflmpro0szqWRGUpQK7xfOShbo7vGFdeOi5r/s4vykaahlZr/stSI5cO00yOJt66d5l/M6QKBQHBnEYrzughoa0woDrpAILg5ggtenGfGmT85xtOzdv4DL/PIvK0kkc89VEJ8uBGPx8Pp06c5duwYTqeT9PR0du7cSU5ODqq2p+G5T4NnnsD2v6Er0cPoxJPodFFkZ32C5OR3E/Sr6DkzTlu9DVt3H1P6dvZtL2MoOYvCC1187j9/SubUJGEbNmCtrcVSW4MhK+umPocv6KNzppOWKaXC1jLZwohjBFA0/wXRBUqFzZJB+fwkqf1HUfUdhKAXjBGQ9xYlsOXeBcbwNfimb4yLmv+Lga1xaI62V2n+N1w8TDs9kpLkcAza1ZGiiDldIBAI7ixCcV4XAW2NCcVBFwgEt4YsyXh75xg7buPf2mw8LvvQqVT8VXESH3pbCSazHp/Px9mzZzl69CgLCwskJSWxc+dOCtJiUb/4BWh9HBJKcd79KToW/o+5uROYzXnk5X6RmJhqAKZHHLQ12DjX0M6x+EkObFoHwNvOneR99XUY2zsA0GdlYd1Ti6W2lrDyclSamw8hU+4pWidbl1ojW6dacQcUPX6UIYqymGLK1GbKZm2U9p/A4pwGtQ6yqpWwVnAfRKSu0jd863j8Qc7bFpZaI5su0fzrNWqKk8OXQ1ta5C1r/sWcLhAIBHcWoTivi4C2xoTioAsEgtdO0OGj48gQ3z7WzyGflwTUfCI3nrfdk4chLZxAIEBzczP19fXMzs4SFxdHdXU1JbohNPs+DY4J5B0fZ7K4gp4Lj+H2DBITU0Ne7ucxm3MACPiD9DVOcvBIJ/+Z4KE/JYFUWz9/3tfBPdFWjGcacZ48CYEAmuhoLLt3Y91Ti3nbNtSvPlj7Rj+XFKRnrmeFgKRvvg9Y1PybkyiXdJTNDFM2PUy23486sQwK9yphLbHsdd+3djXGFzxLtsjGwTlahufw+CUAYi2GpZbIDWlRlKVG3JDmX8zpAoFAcGcRivO6CGhrTCgOukAgWD1kWebI0UG+/koXnW4f69DwydhINlelY1ofj6xTcf78eY4cOcLk5CRRUVHs2rKesrHHUTf9CmLzkR78PkO00X/hJ0iSh5SU95Kd9bfodJFL15kdc/LD4138Z1iAoAqqTr3M3dN2qh55mCT7NPb9dTgOH0ay21EZDJi3bcOypxbr7t1o4+Je02e8puZfrWNdQE3Z/ARlXi9l+lgi8+9TwlpmNWhvr3XxUvxBic4x+5Itsmlwjr6pZc1/QeJilW3RHJkda75M8y/mdIFAILizCMV5XQS0NSYUB10gEKw+QUnm8WMDfPelTqa9Ae5Bx4e0YWSUJ2DenIguzUJnZyeHDx9mdHSU8PBw7s83UND1U1QLI7D1w/iq/4a+oZ8xYvstWq2V7KyPk5Lyx6jVy3KOEZeXj53q5qgUIGl8mHsP/h9pUjgV972djfdsxtfciL3uAI79+/HbbKBSEVZWhqW2FuueWvQ5ObfU2ncpV9b8dxKUlepUhj9ImcdDWVBFWeJG8gofQZd/L4TdmODk9WTW6aNpePkw7aahuSXNf7hRy/rFlsiLlbbGkw1iThcIBII7iFBcq4uAtsaE4qALBIK1w+EN8NMDPfzHkT7UMvwxBt4j6bDGmzFvTiRsfRz9owMcOXKEwcFBIk1a3hXdRvLwcxCVBW/9MY64eLq6v8bs7FFMphzycj9PTMzupWAlyzJPTczx+c4hHP4A284cprKxDr02ibwte9n+jj1EJpjwdnVh378fR90BPOfOAaBLT8daU4NlTy2migpU2uu39d0ILr+L89PnlcA20UjL+Fmm/HYAjJJEsc9PuSGOspRtlJW+h/ikjaty3dVG0fw7ODu4HNq6xu1Lmv9Es4odBSm3TfMvEAgEgtUlFNfqIqCtMaE46AKBYO0ZmnHxrRc6eK5llIQwHR8Os1AzE0CtURNWGou5MpExzRxH6o/Q29tLnn6CR9T7MXnGYNNfIt/1ZaYcp+ju/gZu9wWio6vJy/0CFkv+0jUmfX6+0DXCM5NzZHo91L7wW2JGu1Fp4onLqqHywT3kViSg1Wvwj4/jOHAAe10drmPHkf1+NBERWHbvwlJTi7mqCo3FvGqfX5ZlRp2jtEw00XxhPy1jp2n3zeBfLN4lSirKzCmUpVZRnn0fRXElGDSGVbv+auLwBmhZrLK90tjDoFPDtPNyzX9FeiTr11jzLxAIBILVJRTX6iKgrTGhOOgCgeD149SFGb76bBstw/OUJVj5VFwUeT0OZE8ATYwRc2Ui8ylB6k8fo6/zHHepT7BZOo1sTUb90I+QsncyPPwr+i/8iGDQRXLye8jO+jh6ffTSNZ6dmOPz3cPM+gO8w2cn+/e/xD8/hkodjTFiGyW7dlO6M42YFAsAQYcTZ0MDjrr9OA4eIjg/j0qnw7R1K9baGiy1tegSElb9u/AFfXRc2E9L51O0TDTRElhgRKdU8LSoKDSnUpaynbKEDZTFlZFqSX3N7ZirzcGDB9m1a9c1Nf+pUWFLtsgN6ZEUr6LmXyAQCASrSyiu1UVAW2NCcdAFAsHriyTJPNk4wrdf7GB8wcuD6xL524x4Is7P4uufBzUYC2Nw5Ws5OdzC3LmXeYiXiWMab/E7MTz4HXwamf7+HzFi+zUajYmszL8lNfVPUKsVCceMP8A/dI/w+/FZCkwGPu6dZuZ3v2J+YhiVOgKNsZKkvK2U7kwnd1M8eqMSjORAAHdjI/b9ddjr6vAPDgJgLClRJCO1tRgKCtYmKLlmmGp7kpbup2mZbqNFq+KcwYB7UcwRbYikLG69cjZbXBmlsaWYdatX5bsVrjanr9D8L7ZG2uY9gKL5L0kJZ0Pa8mHaKZG3pvkXCAQCweoSimt1EdDWmFAcdIFAcHtw+QL866E+fnaoF4C/qs7mA6VJ0DyN68w4ktOPJsKAt8RIs7ud6Pafs4OT+LQR+O75NuGV78bh7Ka7++vMzBwhLCyTvNzPExu7Z2mx//LUPJ/tGmbc6+dDqXG8fXaIs0/8hon+HtRaK2rdRozh68nfnEpxVTLxGdYVe9t8vb2KZKSuDndzM8gyuuRkRTJSW4OpshKVTnfVz3jLBLzQf4RAx7P09r5Ic3CBFoOBFksE/SpF2qFCRW5ULmWxZZTHlVMWV0ZWRBZq1eu3B+xm5vSxeQ9NQxcD2xwtI8ua/zirYckWuSE9krLUCEz61dkPKBAIBIIbJxTX6iKgrTGhOOgCgeD2MjLn5tsvdPB0k404q4HP3FPA28uS8XbO4jw1hrd7FgB/toFBVT2Fwz8lgUkGI7ZgfOSHxGcWMTV9kO7ub+By9RIVtZ28vC9itRQCsBAI8pUeG78anSYnzMBjhWkkDHZz4onfMtx+Dq3ejFpXgUpXRmxaDMU7kinYkoDBtDJ4BSYncRw6hH1/Hc6jR5G9XtRWK5bqaix7arFUV6MJD1/9L0iWYbQJOp+Hjn3MT57jnMFAS1QyzeExtATt2AMuACw6C+ti1y1V2cpiy4g0Rq7+PS3yWub0Jc3/Ja2R/Zdo/gsTLzlMOz2SrJjLNf8CgUAgWF1Cca0uAtoaE4qDLhAIQoOzg7N85Zk2mobmKE0J5+/3FrMlO4bAjAfn6TFcp8cJLvjwmLwETP9NnuMZPBhoTHovWXs/SVJyAiO2/6Wv74cEAgskJ7+LnOxPotfHAnB4xs6nO4cY9vj4y9RYPp+dxGx3ByeefJwLTWfQ6sMIi9yEz1uK1mAmtyKe4qpkknIjLmu/k9xunEePYq+rw3HgIMGZGdBqMW+uxFKjVNd0KSlr80XNDSphrXMfXKhHkgIMhMfTklZGiyWKFt8sXfM9SBc1/+EZlMWWLYW2vKg8dOrVqfqt9pw+6/TRtHguW+PQHE2Dc9i9SsUwIkzH+ouK//Qo1qdGEmFag+qlQCAQvIkJxbW6CGhrTCgOukAgCB1kWeYPzTb+6fkObPMe7itN5PP3FZEeY0IOyni6ZnCeGsfTMY0k9xAe9n0ipQHayeVcxvuprNlLSkok/f0/ZnjkV6jVRrIyP0xa2vtQqw04A0G+3jfKL0amSDfqeawwjaooK+N9PRx/4rf0nDqGVm8gJm0rDnsxQX8YkQkminckU7gtkTDr5QdNy8Eg7uYWHAfqsO+vw9fXB4ChsHBRMrIHY0nx2uyx8sxD98tKYOt+GbzzoDXiytrJ+bT1tJgttMz30TzZzLRnGgCjxkhxTPFSW2RZXBnxpvhbuvxaz+mSJNM76VissCmVts5xOxd/HOfEmZcqbBvSoshPsAjNv0AgELwGQnGtLgLaGhOKgy4QCEIPty/Ivx/p418O9hKUZP6iKpOP1uRiNSoVk+CCF+eZcZwnbegX/j8idb/Gh5YX2MVs2j3s3LWLxCQVvT3fYmq6jjBjOrm5nyMu7h5UKhXH5xx8smOQfrePP02O4e9zkgnXapgaGuDkU7+jo+Ewaq2GlKIdSNJ6pkbUqDUqssrjKKlKJrUwCtVV2u28/f046g5gP1CH+2wjSBLahAQstTVYa2sxbdmCWn950HvNBHwweBQ69imBbX4QUEHqJuT8+xjN2ExL0EHzVAstUy20T7fjl/wAJJmTlloiy+LKKIopuiHN/+2Y0+0eP63D8zRerLQNzi1p/k36Zc3/xT1tcdbQPK5AIBAIQpFQXKuLgLbGhOKgCwSC0GVs3sN3Xuzk/84OE2vR8+m3FPCuTWloFsORLMl4e+dwN5wgrO9LGNUd9JHDU9RgTsxn566dxMVN0tP7TZzOLiIjN5OX90XCraW4ghLf6R/lZ0OTJBp0fKcgjT0xyh6yubFRTv7h95w/uB+Qya6oIixqG4NtEl5ngPBYI0XbkynanoQ58uoBIDAzg+PQYUXhX9+A7HajNpkwV1cr1bVdu9BERq7+FyfLMH5uuRXS1qg8Hp0NBfdDwf34kjfQMd+jHKY92ULzZDM2pw0ArVpLUXTRitCWYkm5rAoYCnO6LMsMzbiXKmyNg7Octy0QkITmXyAQCG6WUJjXX40IaGtMKA66QCAIfZqH5vjqs22cHpilMNHKPzxQzPbc2BXPCdo9+J/5Afqu7yPJcIAaGlQFxEbFUr27iqjo81y48EP8/lmSkt5OTvanMRjiOTvv5BMdQ3S5PLwzMYqv5KYQtXge2cLUJKeffYLWV14kEPCTv2UHSQV7GO7UMNI5h0qtIqM0huKqZDJKolFfo71O8npxHT+OfX8djgMHCExOgkaDqaJiSeGvT09fmy9wfgS6XlDCWv9hCPogLBry74GC+yCnFgxWJl2TtEy1LIW289PncQfcAEQboymLWzRGxpZRElvCqYZTITmnK5r/+SVjpND8CwQCwY0Rimt1EdDWmFAcdIFA8MZAlmWeax3lm/s6GJlzc3dxAl+4v4is2JVngckz/ciPfxj12FFm5SKelGsZVOuJNIWzY2cF4dENjIz8D2q1jsyMvyEt7f0EVHp+cGGcHw2OE63T8k/5qdwfF7n0ns65Wc7se5rml57D53aTvXEzJbseYtpmpv3YGO4FH+ZIA0XbkyjankR4bNi1P4sk4Tl3TpGM1B3A29UFgD43B2vtHqy1NRjLylCp12A/ldcOPfsX9629CO5Z0Ogha5cS1gruh/AkAAJSgJ65nqUKW8tkCxcWLgCgVqlJ1CayPWv7kuo/MyLzddX83wxC8y8QCATXJxTX6iKgrTGhOOgCgeCNhccf5Of1/fz0QA++oMSfb8vkY3vyiAi7xOgny3Dmv5BfehQCQS5o38VznnSm1A4sOhNbKjKxJu9nevoVjIZkcnM/R3z8Xs453HyyY4hzDjdvjY/k63kpxOmX39fjcND4wjOcff4PeBx20tetp/KhdxL0J9HWMMpgmyLiSCuKpnhHMlnlsWi01w8svqEhHAcOYN9fh+v0aQgG0cTGYq3ZjaW2FvO2baiNxtX+KiEYgKHjiwr/52C2X3k8eQMU7FUCW0IJXFJdmvfO0zrVSstkCwc7DzIsDWP32QGw6qysi1u3ojUywhCx+ve9ClxL869RqyhMtC7JRzakR5IVaxZVNoFAcMcTimt1EdDWmFAcdIFA8MZkwu7hey928fiZIaJMej55dz7vqUxbafGbH4ZnPgE9LyMlVNKhez+HhiYYV80RptKzqTAMU9rLuDydRERUkJf3KCZLGT8ZHOexC+NYtGq+kZfKQ/GRKxbnPreL5lde4PQzT+CanyM5v4gtb3sXsemldBwdpf3oKI5ZL2FWHQVbkyjekURUovnyD3EFgvPzOA4fxl5Xh/PwESSnE5XRiHnHDqy1tVh270IbE7PK3yZKqJ3shM7nlMA2fBqQITJ9cd/afZCxAzTLgfXgwYPs3LWTCwsXltoiWyZb6J7rXtL8Z4ZnrghseVF5aNWhWZ2acfpoXpSPnB2co2loDsclmv9LA1t5WuTKXwoIBALBHUAortVFQFtjQnHQBQLBG5tzI/N89dk2TvTPkJ9g4dG9xezMj1t+gixD82/ghc9BwItU/f/oclXRcPYUQ/4J9LKailwHYWkHCEgzJCY+TE7233EhGMkn24dotLu4Nzacb+WnkWhYuSD3+7ycO/Ayp/7wf9inJonPzGHL295FzsatDLXP0t4wSn/LFLIkk5wXSXFVMjkb4tDqb0xSIft8OE+ewlFXh72ujsDYGKhUhG3YsKTwN2RnrebXuYx9fHHf2vPQdwACHjBEQN7dSljLu5uDxxuvOKe7/C7OT59faotsnmxmxjMDQJg2jOKYYmU/W6yi+o8zxV32HqFAcEnzv9wa2TWxrPnPjbesaI3MT7AuCWwEAoHgjUgortVFQFtjQnHQBQLBGx9Zlnnx/Djf2NfO4IyL2sJ4vnB/EbnxluUn2cfguU9Dx7OQXAEP/YSBcT2H9h+kb34YozpIWdYAxuQTqDRaMjL+mtS0D/Bzm4N/6h/FoFbzj7nJvDsx+rJWt2DAT9uRA5x6+vfMjtqITkljy8PvpHDHLtyOAB3HRmlrGGVh0o3BpCV/cyLFVcnEplq4UWRZxtvejn1/HfYDdXjb2gHQZ2YuSUbC1q9HpVkDQ6HPCX0HFYV/1wvgmgK1lpmIEqK3/gkU3KtU2q5x7zanbUWVrW2mjYCkVKduVfN/O7B7/LQMz69ojZy5RPNfnnrJYdppkULzLxAI3lCE4lpdBLQ1JhQHXSAQ3Dl4A0F+efQCP97fg9sf5E+2ZvCJu/KINC2eOybLcP5J2Pd34FmAXZ+Fqk8yNjbJoX0H6BjpJszgpDSrDUN8B3p1PLkFn8MVfg+f7hzm+LyTmmgr3ylII9V4+VlmkhSk61g9J576HVODF4hISGTzW99B8a49aDRaRrpmaau30ds0iRSQic8Mp6QqmdxN8eiNN9f257fZsB84gKPuAM6TJ8HvRxMVhWX3biy1NVh27EBtMq3G1/qqDxlU2h87n8PZ+H+YXcPK44nrlhT+JJWv2Ld2JbxBLx0zHStC281q/kMBWZYZnHEt2SIbh+Zou0TznxYddokxMoripHD0N7AvUSAQCG4HobhWFwFtjQnFQRcIBHceUw4vj73cxW9ODmI16vjEXXn8ydYMdBf3pzmn4PnPwbnfQ8I6ePgnkFTO9PQ0h185SGvHOazWcYqym9CFj2OWi8jJf5RnVDl8rW8UFfAPOcn8aXIM6iuEBlmS6D17ihNP/Iax3m4s0TFseuBtlN11DzqDEY/DT+eJMc7X25gddaIzaMjbFE9xVQrxmdabDiJBux1nfb2i8D98GGlhAZVej3nbNix7arHs3o0uPn4VvtmVHDx4kN2lqYq+v/N5RTgiSxCeAvn3QuH9kFkN2hurIt2o5r88rpySmBJMujUIoKuAxx/k3Mii5n/RHDl6UfOvVVOaHL7UFrkhPYrkCGNIhk+BQPDmIxTX6iKgrTGhOOgCgeDOpWNsga892059zxTZcWYe3VtETUH88mK44zl49lPgnISqTyoVNa2Bubk5GuobaDx7hpi4bnIym9EYnEQ6dmJI/RRfUYVxeM7B9kgLjxWmkRl25QAiyzIDrU2cePK3DLedIyw8go33P8T6e/ZiMJmRZZmxvgXa6kfoOT1BwC8Rk2KhuCqZ/M0JGM03L6GQ/X5cZ84oCv/9dfhHRgAwlpUpkpHaGgx5easSCC6b051T0P2S8r321oHfBXor5O5RKmt5d4Mp+obf/3qa/7zIPKXKtvgnMzx0Nf+j826aFlsiGwdnaRmexxtQRCrxVsNSWNuQFsk6ofkXCAS3iVBcq4uAtsaE4qALBII7G1mWqeuY4OvPtdM35aQ6L5a/f6CY/ASr8gT3LLz4KDT9CmIL4OGfQqryc8But3Ps2DHOnjlGQmIjqantqFERbdvL6aT38W2DTACZz2cn8ZepcWiuEXqGO85z4snHudB0BoPJzIZ7H2DDfW/FFK5o6L3uAN0nlara1JADjU5NbkU8xVVJJOVG3lKgkmUZb1c3jgN12PfX4WltBUCXlqZIRmpqMW3aiEp7a2HgmnO63wP9h5ara45xUGkgY/vyeWvRNy84uaj5vxjYWidbsfsXNf9661JLZFlcGeti14W05r9j1L5UYWscnOXCtAsQmn+BQHD7CMW1ughoa0woDrpAIHhz4AtI/M/xAX74ShcOb4A/3pLOJ+/KJ8ayWP3qeQX+8HGw22Drh6Hmi6BXWuhcLhcnTpygsXE/ScnHiI+/gMobjrr/T/lpei2HzbDJauL7Renkma99Xtl4Xw8nnnyc7pNH0RmMlN19H5seeARL1HJlaXLQzvl6G10nx/B7gkQmmCjekUzhtkTCrJfvfbtR/OMTynlrB+pwHTuO7POhjojAsnMn1j21mKuq0FhuXFxyw3O6JIGtcTGs7YOJNuXxuCKlDbLgfkXccgsHc0uyxIX5C0pgW2yP7JnruUzzXx6nGCNzI3NDVvM/7fDSPDy3ZIy8VPMfadKxPk1o/gUCwdoSimt1EdDWmFAcdIFA8OZi1unjB6908asTg5j0Gj6+J48/25apiBs8C/DKl+D0LyA6G976z5C5Y+m1Ho+H06dP09LyJEnJ9YSHT6FypNE2/rf8OCMLt1bFpxJi+GhRKtrr6NanhgY4+dTv6Gg4jFqroXT33VS+9e1ExCcsPcfvDdJzZpy2ehtjfQuoNSqyyuMoqUomtTAK1WtQuktOJ46GBhx1B3AcPEhwbg50OsxbtmCprcFaW4suMfGa73HLc/pMv1JV69wHA0dBDoIlQdm3VnA/ZO8CXdgtfS4Ap9/J+anztEwtt0ZeqvkviSlZqrKVx5UTGxZ7y9daS4TmXyAQvN6E4lpdBLQ1JhQHXSAQvDnpHrfz9X3tHOycJDPGxBfuL+Lu4gSljaz/MPzhYzB7ASr/Cu76EhisS6/1+XycPXuGtvb/IjHxKAaDC4ejmv/1/hUHY80Uu+E7MTFs2JCM+jpnns2NjXLyD7/n/MH9gExRVQ2bH34H0cmpK543bXPQXj9Kx4lRvM4A4bFGirYnU7gtCUvUa1O5y4EA7qYmReFftx//wCAAxuJiLLW1WPfUYigsvKzFblXmdNeMUr3seA569oPPDjoT5NQqYS3/HjC/tgAlyzIjjhFFPrJYZWufaV/S/Cebk1fsZSuKLkKvufVK5VpyLc2/Wa+h7BLN/4b0SGItQvMvEAhunFBcq4uAtsaE4qALBII3Nwc6lf1pPRMOtufE8PcPFFOUFK6c/VX3NTj+LxCRBm/9oRIaLiEQCNDUdJKu7n8mNvY0KhU0Bj7If6prWdCo+MvBAB+JjCCqMgl9qvUqd6CwMDXJ6WefoHX/SwT8PvK3VrH1kXcRl7Fyn1bAH6SvaZK2ehsjnXOoVJCxLpbiqmQySqJRa16bJEOWZXz9/dj378dRdwB3UxPIMtrkJKw1imTEXFmJSq9f/Tk94IUL9cv71hZGQKWGtC2L+9b2QmzuqlzKG/TSPt2+IrSNOkcB0Kl1y5r/xT/J5uSQ3AN2Pc1/erRpcS+bEtqKhOZfIBBcg1Bcq4uAtsaE4qALBAKBPyjx6xODfP+VLhbcft5dmcan7i5QDhkePAFPfwSmu2HDn8JbvgZhkSteHwwGaWk5TH//Y0REtjHrj+O32kc5ok4l1yHxpVY3ZZYwzJsTMa2PR32NM89c83Ocee4pml56Dp/bTfbGzWx95N0k5RVc9ty5CRftDaO0HxvFveDDHKGnaEcyRduTCI+99RbBSwlMTeE4dAj7/jqcR48iezyoLRYsO6sZSkyk8kMfQhMevirXWoEsw2jzcivkWIvyeEyeEtYK90JqJahX72DuCdcErZOtNE8pbZHnp87jCSp6/BhjzIq2yDeS5v/swBxjC8ua/3UpEStaI5OE5l8gECwSimt1EdDWmFAcdIFAILjIvMvPD/d389/HLmDUafhobS5/sSMTg+yHQ9+Chh8qe6Ue+AEU3HvZ6yVJorX1GYaGv0dY2AjHfDX82vBB5tHz5xMyf9nswKhRE7YuFvPmRPQZ4VddGHscDhpfeIazz/8Bj8NOemk5W9/2blKL1132mmBQYqBlmvP1NgbbpgFIK4yiuCqFrPJYNKtUMZHcbpzHjmOv24/jwEGC09Og1WLatGlR4V+LPjVlVa51GXND0PWC0gp5oR4kP5hiF/et3Qc5NaA3r+ol/ZKfntmeFVW2N7Lmf6nKNjhH68iy5j8h3LDiMO11KRGEXac1VyAQ3JmE4lr9jglo0RlF8t1f+MXtvo3LmJubIzIy8nbfhkAgEFwTty/I4KyLOZcfg1ZNerSJKJOOHH83H5p/jIzABY4Ya/iviL/Bob5C9UiWKDLuZ1PCE0iGIL/wfoTjxq2Ee4L8ZbeXt48GMcowpoMTVjVnLCqcmisHNXXAS7ytkcTB4+h9TuwRqdgydjAfkwNXCHcGn0TidJCE6SBGv4xPC+PRWsZiNLiNqxceVLJERHcLGyd6KOxtJG5GaQ8cj02lI2c9ndkbGE3IQF6DwBImOVnvPc0mz3HWe09hkR340NNq2MBp41bOGLYwr7nx89ZuhgAO3Op+5Y+qD7e6H0mlHKatlk2ESVmEyVmYpGzCpCw0rG5oXC1kGVy+AA5vALtH+e/FwAZg0muwGrRYjFosBi1GnQhsAsGbgVBcqz/+oe0ioK0loTjoAoFAcDXm3X4Gpl24/UGsRi0Z0SbC9TKPOH7DI47f4FBb+UX4RzgRVn3F12tUPiosT7Au7kXOq0r4N/ljzGkiyJjx8fBggOp5iUwvBIBWs4oTVhU9RhXyFYKXKugnbrSZpIFjGLwLOC0J2DKrmI0ruGJQQ5aJWpBImg4QMy+hAubNakZjNUxFapBWwfZ36ZwePTtOQV8jBb1NpNu6UcsyC+ZIurLX05GzngtpRQS0q6+F18gBCn3n2OQ5zibvMeKD4wB06wo5bdzKacNWhrUZV/6OVgEZCZ9qHLe6D9diYPOqRkClrBn0UgJhcvZiYMvGICejIjTDTiAoKYHNG8CxGNoWt7KhUatWBDaLQSuMkQLBHUgortXvmIAmWhwFAoFgdQgEJX57eojvvdTFrMvHOypS+cw9BcS7euDpDyv7pIofgvu/C5b4K76H1ztB67mvMjp3gP+V/4w6zVuIlwN8ryCd3RozzpNjOBsnkN0BNDFGzJsSMW9MQBN+uUkwGPDTfuQgJ5/+HbOjNqJT0tjy8Dsp3LELtebKC3/nvJeOY6O0NYyyMOnGYNKSvzmR4qpkYlNv/NyzV3O1OT0wO4vj0CFF4V9fj+xyoTKZsFRVYamtwbJrF9qoqFu+7lWRZeWMtY7F89ZsZ5XHo7IUI2TBfZC+DTRrew7a9TT/pbGlKw7UDmXNf8/EJZr/oVm6JxzIspJ3c+MsK4yRefFC8y8QvNEJxbX6HdPiKAKaQCAQrC4LHj8/qevhFw396DRqPrw7hw/sSMd48idw8FvKodb3fRvWvfOq1Rq7/Tznzn+JMy4vP5M/yqQ6gd1+B9/dWExKeCTu81M4T47h7ZsHNRgLYzBvTsSYf/mZZ5IUpOtYPSee+h1TgxeIiE9g80PvpHjXHrS6K1eqZElmpGuWtnobvU2TSAGZ+MxwinckkVeZgP4a8pIrcSNzuuT14jpxAvv+Ohx1dQQmJ0GtxlRRsaTw12dk3NR1b5gFm7JvrfN56DsEQS8YIxV1f8H9kLtnxfEJa8VFzf/FsNYy2ULHTAcBWdH8p1hSVgS2wujCkNX8L3j8tAzNLxkjGwdnmXX5AUXzX562qPlPi2K90PwLBG84QnGtLgLaGhOKgy4QCAQ3w4UpJ998vp0Xz4+TEhnG5+4r5MGkBVR/+BgMn1SkFQ98H8KTr/h6WZaZnHyJls5/4v/z7+YFHsDic/O+gIMPbdtETEwM/ik3zlNjuM6MIzn8aCL0mDYlYq5MQBtpXPl+kkTv2VOceOI3jPV2Y4mOYdMDb6Nszz3ojMYr3gOAx+Gn88QY5+ttzI460Rk05G2Kp7gqhfhM6w1Z/W52TpclCc/5NkUyUncAb2cnAPqcnEXJSA1h5eWo1Gsg2vA6oLdOqax1vQDuWdDoIbMaCu+H/PsgYo0EJ1fAE/DQMdOxHNqmWhhzjgGLmv+YIspiFWNkWVwZSeakkDQtyrLMwLSLxqHlw7TbR4XmXyB4oxKKa3UR0NaYUBx0gUAguBWO9U7z1WfbaBtdYGNGFH9/fwHrbb+F/V8BjQ7u+bqi5b/KolqSvAwN/ZIX+57nX+W/xKZKpWiin7/QytxTtYOEhATkgIS7fQbnqTG83bMAGPKisGxOxFgUjeqSM89kWWagtYkTT/6W4bZzhFnD2bj3YdbfsxeD6eqiClmWGetboK1+hJ7TEwT8EjEpFoqrksnfnIDRfPV9Y691TvcND+OoO4C9rg7XqVMQDKKJicFSsxtrbS3mbdtQh63OcQErCAZg6MTieWv7YKZPeTxpvVJZK7wfEkrXbN/a1Rh3jtM61UrLpNIa2TbdtqT5jw2LXVFlC2XNv9sX5Jxt+TDts4OzjC94gStr/pMj12CMBQLBLRGKa3UR0NaYUBx0gUAguFWCkszvzwzxnRe7mHJ4eWRDCp/faiD+wGfgwhHI3g0P/giirt7C5/VN0dH7Q346quIZHsIUdFPV2co9MZHs3LmTlBSlqhOY9eA8PY7r9BjBeR9qiw7zxgRMlYnoXnXm2XDHeU48+TgXms5gMJnZcO8DbLjvrZjCI675ebzuAN2nxmmrtzE5aEejU5NbEU9xVRJJuZGXVXBWc04Pzs/jOFKPo24/jsNHkBwOVEYj5u3bse6pVfatxa7BXi1ZhqkuJah17IPhU4AMEemLh2PfBxk7QPv6txz6JT/ds91LbZEtUy0MLAwAoFFpyIvKWxHaMsIz3jCa/5aReXyL1sjEcOPiXjYltJUmC82/QHC7CMW1ughoa0woDrpAIBC8VhzeAD890MN/1PejVsFfV2fxkfAj6Ou+rASAu/8RNv0lXKN1z+7o4Pn2f+e79moGVZmULvSw8VwXJWmp7Ny5k8zMTEDZR+bpmsV5cgxPxzRIYMiOwLw5kbCSWFS65WuM9/Vw4snH6T55FJ3BSNnd97HpgUewRF1fQT85aOd8vY2uk2P4PUEiE0wU70imcFsiYVYlrKzVnC77fDhPnVqqrgVGR0GlIqy8HMueWqy1teizs9em5c8xsbxvrfcABNxgiIC8uxb3rd112UHlryezntmlKlvLZAutU604/A4AwvXhrItbR3ms0hZZGltKhOHaofx24QtIdIwtLIe2oTkGpl0AaNUqipLCl0NbWhQZMaaQbPEUCO40QnGtLgLaGhOKgy4QCASrxdCMi2+90MFzLaMkhhv58i4r9/R9C1XvfkjfDg/9M8TkXPX1siwzOrGfb3ed4nf+uzCpfNw12Ex8/wQZ6elUV1eTm5u7tFANLnhxnhnHeWqc4IwHtUmLaUM85s2J6BKW2xqnhgY4+dTv6Gg4jFqroXT33VS+9e1ExCdc9zP5vUF6zkzQVm9jrG8etUZFVnkcJVXJ9Iw3U1NT89q/uGsgyzLejg7sdXU49tfhaWsDQJ+RsSQZCVu/HpV2DcyMPhf0HVzet+acBLVWqagV7lX2G16jOvp6IMkS/fP9S22RLVMt9Mz2IKOsWbIispaqbOVx5eRE5qBVr63F8laZcnhpWrRFNg7O0Tw0h9MXBCDKpFNaIhdbI8vSIgg3rv6xDQLBm51QXKuLgLbGhOKgCwQCwWpz6sIMX322jZbhecpTwvlhUTuZp78GAS/UPgpbPwzqq7dwSZKPQ72/59FhI71ks5k+trT14Z90kJSUxM6dOykoKEC9WJGTJRlv3xzOk2O4z09DUEafbsVcmUhYeRzqxXaxubFRTv7h95w/uB+QKaqqYfPD7yA6OfWGPte0zUF7/SgdJ0bxOgPozFCxJ4vCbclYol4fW59/dBT7gQM46g7gPHEC/H40kZFYdu3CsqcWy44dqM1rcDi0FISRM9DxnFJdm1IEJySULiv8kze87vvWroTD5+D89PmlKlvzZDOzXmUP4xtN8989YV/RGtk9oVQLVSrIi7ewIS1qqTUyN94iNP8CwWskFNfqIqCtMaE46AKBQLAWSJLMk40jfPvFDsYXvLy3RM+j8r8T1vcipGyCh34C8YXXfA+Xd5pvn3ueny/ko8fH+7VdWBrnmJ1ZIC4ujurqakpKStBccv5Z0OnHdXYc58kxApNuVAYNpvVxmCsT0acqSnn79BSnn3mClv0vEvD7yN9axZaH30l8ZvYNfbaAP0hf0yRHn2nDOaEsljPWxVJclUxGSTRqzeuzDyrocOCsr1cU/ocOIS0soNLrMW3birWmFktNDbqEK59N95qZ7l2UjDwPg8dAlsCatLhvbS9kVYM2NBTzsiwz7Bhe3sv2Btb8z7v9tAzPrWiNnFvU/FsMWsrTIpZC2/q0SGKE5l8guClCca0uAtoaE4qDLhAIBGuJ0xvgZ4d6+dnhPkDmu0W9PDD8GCqfA3Z9FnZ8QrE+XoOWqU4+0dZDWzCFCnU7HzX66D9tZ3JyiqioKKqqqigvL0d7SZufLMv4BhaUqlrrFLJfQpdsxlyZiGlDPGqjFtf8HGeee4qml57D53aTvXEzWx95N0l5BTf02Q4ePMj64s20N4zSfmwU94IPc4Sewu1JFO9IJjz29bPzyX4/rrONOOr2Y99fh394GADjunWKZKSmFkN+3trsY3JOQ/dL0Pkc9NSB3wl6C+TUKq2QeW8B0/X3/b2eXEvzr1frFc3/YmArjy0n0ZwYknvAZFnmwrRrxWHa7aN2goua/4wY0wpjZGGi0PwLBNciFNfqIqCtMaE46AKBQPB6MDLn5tsvdPB0k40Ci4f/iPstaaMvQuI6eOinkFR2zddLssyPu47xmE2LSg7wV6Z6Hggr5cSJYWw2G+Hh4Wzfvp2Kigr0+pXVD8kdwNU0gfPkGP5RJyqdmrB1sZg3J6LPCMfrdNL4wjOcff4PeBx20kvL2fq2d5NavO6ai/JL5/RgUGKgZZrz9TYG26YBSCuMorgqhazyWDSv46JYlmW83d1LkhFPSwsAutRULLU1WGtrMW3ciOoqB3q/JvwexeB5sRXSMQYqDaRvU6prhfdD9I1VKl9vrqX5jwuLWwpsZbFlFMcUh7Tmv3VkpeZ/wq5o/g0XNf/py6EtKUJo/gWCi4TiWl0EtDUmFAddIBAIXk/ODMzy1WfbaBqa469iz/GZwL+h981B1adg599dty2u3+nkY61nOe22UiK38oX4IVJ1b6GhoYXBwUHMZjPbtm1j06ZNGF91ULUsy/hHHMoh2E2TyN4g2vgwpapWkUBQE6D55ec58+yTOOdmSc4vYsvb3kXW+k1XDGpXm9PtMx7aG2y0Hx3FMevFaNFRuDWR4qpkohLXYH/YdfBPTOA4eBDH/jqcx44h+3yow8Ox7NyJdU8t5upqNBbL6l9YkmC0UQlqHftg4rzyeFzhcitkysZr2j1vJ37JT9ds14rWyEH7IKBo/vOj8leEtozwjJCtso3Oe1a0RbZeQ/O/LiUCo05o/gVvTkJxrS4C2hoTioMuEAgErzeSJPNMi41vPd+Ba36Kn8X9nq32lyCuSNmblrrxmq+XZZlfDg/zld4xgnKQP1L9ng9l5oFcQ339CXp7ezEajWzZsoUtW7ZgMl1e6ZC8QdwtkzhPjeEbtINGRVhJDObNiWhSTZw/9Aon//B77FOTxGfmsOWRd5K3eTuqS8LE9eZ0SZIZapuhrd7GhZYpJEkmKTeCkqpkciri0d6Gs64klwtHQwOOugM4Dh4kODsLOh3mykpF4V9Tgy45eW0uPntBCWud++BCA8hBMMdDwb2KaCR7N+hCu5pzUfN/sTWydaoVp98JQIQhgnWx65baIkvjSgnXh9/mO74yvoBE++jCUmBrHJxjcEZo/gWCUFyrh3RAU6lUZuAQ8GVZlp+91nNFQBMIBILQx+0L8u9H+viXg71UyWf5nuk/sfqnUG37KNR84bqL9RGPj0+1dXFoPkC+3M7H9E+yK//9+Hyl1NfX09HRgU6no7Kykm3btmG1Wq/4Pv4xJ85TYzjPTiC7A2hijJg3JWJcH01X01FOPv07ZkdtRKekseXhd1K4Yxdqjeam5nTnvJeOY6O0NYyyMOnGYNKSv1mpqsWmrkH16gaQg0HcTU1LCn/fhQsAGIqLsNYoCn9DUdHaLMzds9D9ihLWel4B7wJow5R9awX3KQp/S9zqX3eVCUpBRfM/tWyM7J3rXdL8Z0dkr6iy5UbmormGwfR2ci3Nf7RZv7iXbVHznxqBVWj+BXcgobhWX5OAplKpfgE8AEzIslx6yeP3Aj8ENMB/yLL8reu8z1cAB9AmAppAIBDcOYzNe/j2ix28fLabfwz7LW+TX0aOzkH10E8gY9s1XyvLMr8bn+XRrgE8wQBvl/+X90SMUZj/BdyuOOrr6zl37hxqtZqKigp27NhBZGTkld/LL+E+P4Xz5BjevnlQg7EwBtOmOAZn2znx1ONMDV4gIj6Byre+g2m1jto9d93UZ5UlmZHuOdrqbfQ2TiAFZOIzwynekUReZQJ64+07o8vb169IRuoO4G5sBFlGm5iItbYGS+0ezJsrUenXwG4Y8MFAvdIG2fk8LAwDKkjbvKjwvx/i8lf/umuEw+fg3PS5Fa2RFzX/Jq1J0fwvBrayuDJiwmJu8x1fmetp/vPjrStaI3PjLKiF5l/wBicU1+prFdB2ogSr/74Y0FQqlQboAu4GhoFTwHtQwto3X/UW7wfKgRjACEyJgCYQCAR3Hs1Dc3z12Tb0Q0d4zPgfJEiTqDZ/EPb8AxiuXWUa9/r5XOcgL0zbyaGfv5J/xOakzeRkfxqHQ0N9fT3Nzc0AlJeXU1VVRUzM1RfG/im3slftzDiSw48mQo9pYwKThjFOvPQ4Yz1d6MwWdrz9PZTtuQfdq/a73Qgeh5/OE2Ocr7cxO+pEZ9CQtyme4qoU4jOtt7WlLDA9jePgIewH6nDWNyB7PKjNZsw7q7HW1mLZuRNNRMTqX1iWYax1UeG/D0aVMSMmd3Hf2v2QtuWa5+iFGrIsM2wfpnmqeSmwdc50rtT8Lx6kXRaraP511zGb3i4u1fyfXQxt825F8281aClfqrJFsj4timhzaB5XIBBcjVBcq69Zi6NKpcoEnr0koG1DaVW8Z/HvnweQZfnV4ezi678OmIFiwA08IsuydLXriYAmEAgEb0xkWea51lF+8Fwj73X+kj/XvkTQmorukX9W9ihd57V/mJzj851DLAQCPMzveVi1j9zMD5KW9n7sdg9Hjx7l7NmzBINBSkpKqK6uJiEh4ervGZBwt8/gPDWGt1upghjyonAluHnxlV9gtw0RZg1n496HWX/PXgymm5eAyLLMeP8C5+tt9JweJ+CTiEmxUFyVTP7mBIzm27tYlzwenMeO4airw37gIMGpKdBoMG3apFTX9uxBn3pjh33fNPPDy/vW+o+A5AdTDOTdoxghs2uuG95DEU/AQ/tM+1JbZMtkC+OuceCNp/nvn3IuKf4bB+foGFvW/GfGmJZskRvSoihMsqJ7nc4JFAhuhVBcq7+eAe0dwL2yLH9g8e9/CmyRZfmj13mf93GVCppKpfog8EGAhISEjb/5zW9u+X7XCofDgWUtTFkCgUBwh+ELyrx0wY+tv5Wvqf+dbPUoAwlvYTDvfQS11w5BC7KK/yKMo+hJl8f4IN8li3lUqneiohK/38/Q0BA2m41gMEhMTAwZGRmEh19b6KB1Q/iwCuuICp1HhV8nMRPpoGOsnrHBVjR6A3HrNpCwrgJt2K0p2IM+mflBmO2V8cwqhvrwVIjKUWGK4/Yv0iUJ3YULGFpaMDS3oB0dBcCfnIy3vAxvWTmBjPQ1MTNqAi6iZxqJnTpB9MxpdAEnkkrHbFQ5U7GbmY6pxGcIrfPWbobZwCwD3gEu+C7Q7+1nyDeEX1aqU+GacDL1mWQZssg0ZJKmT8OgDs1DqL0BmQsLEr1zQXrnJXrmJOa9yhpSp4asCDXZERpyItXkRqqJMorAJggdQnGtXlNTE9oB7UYRFTSBQCC4M5iwe/jh862ktfyQv9I+h8cYh/HhH6EpvPe6r31hcp7PdQ0x5fPziO4Qe33/SlxEGfl5jxIeXobL5eLkyZMcP34cj8dDdnY2O3fuJDMz85rvK0synq5ZBvadwzKlAglUSXr6HC2cbn0WtV5L+V33senBt2GJuvXAMDlop63eRtfJMXyeIJEJJop3JFO4LZEwa2i0jvkGBrAfOIBjfx2uM2dAktDGxWGpqcFSW4N52zbUhjUIEkE/DB5bVPg/B3MDyuMpG5cV/vFFymapNyg3qvkvjyunLK6MdGv67Q/wV0CWZWzznuXDtAdnOTeygC+oNEIlRRiXKmwb0iMpFZp/wW0kFNfqIdvieLOIgCYQCAR3FudG5vn1E0/y55PfoUA9zHjWIyS88zEwXTsAzfkDfLnHxm/GZsjSe/nL4GNkBU6TmPgwOTmfwWhIxOv1curUKY4dO4bT6SQ9PZ3q6mpyc3Ove1B1dcV2nGfGcZ4aIzjjAYOaKZ2N053P45BnKd19N5VvfTsR8Vdvo7wefm+QnjMTtNXbGOubR61RkVUeS3FVMmmF0ahCRMwQmJ3Fefgw9roDOI8cQXK5UJlMWHZsx1K7B8vuXWijolb/wrIME+3L+9ZGziiPR2ZA4V4lsKVvgxDd13UzzHhmODd17qqa/4vikbK4MtbFrsOqv7K59HbjDQRpH7Uvh7ahWYZm3ICi+S9ODl+0RiqhLT1aaP4Frw+huFZ/PQOaFkUSsgcYQZGE/LEsy+dv+SKXIAKaQCAQ3HnIssxLLUPYnvkaf+L/PS5NOK63fIekre+87msPTC/wd51D2Lx+3mUd4F77P2BUBcnI+Gsy0j+ARhOG3+/n7NmzNDQ0sLCwQFJSEtXV1RQWFqK+QsvepXO6LMl4++ZwnhzDfX4agjIug5PztnqGXB3k79jB5offSXTya9urNW1z0F4/SseJUbzOANYYI8U7kijclowlKnRa3iSfD9eJE4rCv+4AgfFxUKsJ27BBkYzU1mDIylqbi9vHFvetPQ99ByHoBWMk5L1FCWu5d4ExNM8nu1kuav6bJ5uXVP8XNf8qVCs1/3Fl5ETkhKzmf9LupWlo2RjZPDyHS2j+Ba8zobhWXyuL4/8Cu4FYYBz4kizLP1epVPcDP0AxN/5CluWv39IFroAIaAKBQHDn4g0EefbFFyk6+QWKVf2ci9xD2nt/TERcyjVfZw8E+VqvjV/apskwqPmY8RmS5n6BwZBIbs5nSUh4EJVKTSAQoKWlhfr6emZmZoiLi6O6upqSkhI0muXF7dXm9KDTj+vsBM5TowQm3ATVQQbsbfTMNxK3IZctj7yT+Mzs1/QdBPxB+pomaasfZaRzFpUKMkpjKK5KJqM0BnUIiRhkWcZzvm1J4e/t6ABAn529pPAPKy9DpVmD4OB1QN8BJax1vQCuaVDrIKt6UeF/H0SskeDkNmH32Tk3taj5Xwxtc945QNH8XzxM+2KVLZQ1/13jl2j+h+boEZp/wRoTimv1kD6o+mYQAU0gEAjufKbmHZz5339k9+gvcKnCaC79Ajse/mt02msv9Otn7Xy6Y4gBj4/3xAZ5yP1Ngo5GwsPXk5/3RSIiKgAIBoO0tbVx+PBhJicniYqKoqqqivLycrRa7XXndFmW8Q0s4Dw5hqtlEgIyc/5JeucbUeUa2PS2d5CcX/iav4e5CRftDaO0HxvFveDDHKGncHsSxTuSCY+99mHftwP/yAj2ugM4DtThPHkKAgE00dFYanZjra3FvH076rA1uG8pCEMnofM55cy1mV7l8cSy5VbIxLI39L61KyHLMkP2oaW2yJapFrpmupY0/6mW1GVjZFw5BVEFIa35bx6aW2GNFJp/wWoSimt1EdDWmFAcdIFAIHij09d2Gumpj5Dr66BBuxn2Psb29aXX3LPiDAb5p74x/n14kmSDji/GDxA39lV8vgkSEh4kN+ezGI3JAEiSRGdnJ0eOHMFmsxEeHs727dtxOp3s2bPnhu5RcgdwNU9gP24jOOYmIPsZcnTgjHNS/Pa3kFZa9pr32ASDEgMt07Q12Bg4Pw0ypBVFUVyVQlZ5LBpt6FTVLhJcWMBx5AiO/XU4Dh9GcjhQGQyYt2/HUluDtaYGbWzs2lx8smtx39rzMHQCkBVlZsF9isI/owq0d+YC3x1w0z7dvhTYmieamXBPAIrmvzimeEVoSzAlhOQeMKH5F6w2obhWFwFtjQnFQRcIBII7ATkYoPsP3yGj+TG8spbfxvwNu971CfITr73X6NS8k092DNLj8vLuhHD+Qv8ss8P/CkB6+gfISP9rtItaf1mW6e3t5fDhwwwODqLT6di5cyeVlZUYb+Kgat+wnYVjI7iaxlEH1cz7ppgyjpH24EaytlauykLYPuOh/ego7Q02HLNejBYdhVsTKa5KJirx5s9qez2QfT5cZ85g31+HvW4/AdsoqFSElZVh2bMHa20N+pyctQkKjknoflGprPXWQcANhnDI3aMYIfPugrA1EJyEEGPOsWVj5FQLbdNteINeAOLD4lfsZSuOKSZMG3rVWQCXL0Dr8DyNi/vZzg7OMWlXPodBq6YsNYKKi6EtPYqE8Js/ZF5w5xKKa3UR0NaYUBx0gUAguJPwTXQz/eu/JmnuDIelMk6Wfon37915zVYnT1DiexfG+OnQBHE6HV/LMpE5+0PGx59Br48nJ+fTJCW+DZVq+TfvAwMDPPXUU8zOzmI0GtmyZQtbtmzBZLrx888kbxBH4yjTdd3oFrQE5QBTjBJRlUb2fdtRX6dV84auIckMtc3QVm/jQssUkiSTlBtBSVUyORXxaPWhKYyQZRlvZ6ciGdlfh+e84hDTpacvSUZMFRWotNrVv7jfrchFOvdB5wvgnAC1FjK2L+9bi8pc/euGGP6govm/VEAyZB8C7izNf3KEcbnKlh5JSbLQ/L+ZCcW1ughoa0woDrpAIBDccUgSzqP/hrbuy/iDMt9X/QlJtX/Dn23PRn+NNr+mBRef7Bik3enhbQlRfCZhmqn+r7Ow0ITVWkpe3qNERVYuPf/gwYPk5eVx5MgROjo60Ol0VFZWsm3bNqzWm9Obe0YWGHn6DOqBIDqVAZdsR11gIuORLeiiVqdS4Zz30nl8jLZ6G/OTbgwmLfmbEymuSiI2NTR17Bfxj43hOHAAe90BXMePI/v9aCIisOzehaV2D+YdO9BY1qAyKEmKtv+iwn9SEZwQX6K0QRbcB0kb1uRg7lBkxjND62TrUmhrnWzFFXABEGmIvExAEuqa/7MDs0uVtuFZRfOv06goTgpf0RqZFh0WkuFTsPqE4lpdBLQ1JhQHXSAQCO5YZgdw/d9HMA0f4bhUxI/Nf8ufP1DL3cVX30/jkyR+NDDBDwbGiNBq+WZeMpvlI/T0fhuvd4z4uPvIzf0cYWFpK+b08fFx6uvrOXfuHGq1moqKCnbs2EFkZORN3XLQ66f/6WO4z0wQpUpAkiUCcRLx95ZgLo5blTPPZElmpHuOtnobvY0TSAGZ+AwrxVXJ5FUmoDeuQVVqFQk6nDjr63EcqMNx8BDB+XlUOh2mrVux7qnFUlODLuHWz527JtO9ywr/waMgS2BNgvx7lepa1k7QvXla5oJSkL75vhXGyCtp/i9W2bIjskNW8z9h99A0OLcU2FqG55c0/zFm/VJL5Ia0SMrSIrEYQvv/E8GtEYpr9TsnoGVGyKe/VHW7b+My5ubmbvqHtUAgEAheA7IMjnECswMEJPhO4N106Et5NP4YRcbpq76sTZfAJ2LfToshhb3Oc3xt5mnclkEGwqeRVZC+EEXUoJaY8JUHZU/7DdQvJNHsUNTlZeZpqiJGidV5b/q2+8aiGB8vJ16/DqPGTJAFwqNasEa1oNUt3Px3cQU8fiOd00W0TZQx445Fq/aRH9NBcXwr8eaxkBcaypKMa9iDo8eFvduJf04xExoTDVhyTVjzTBji9GtT/ZD84J5V1P3uWSWsqdTKXrWwaOUQdXVo2hDXEjsS5/DRgpcWlZcWfMyplHZCs6yiFD1lGCiXDaxDTzShGdhkZFy+IA5vAIcngN0bwOMPLv27SafBYtRiMWixGLWE6TSoCPH/YQTXJRTX6qr377szAlpslll+8EtFt/s2LiMQCKBdi355gUAgEFyTyECAP5ueYIPbSaOUzd/5/xpX+DjZcXXotc4rvkZCTX/4PfREvhWN5KVo9jfkeI6yIcJNjsWHO6CieT6MXqce+VULM03ASPh8DhZHOipZjctsYz6iB7/efnM3LoN1ykjF4AZKVJtIDMsClUxPWBeno47RYT2HtLj4fU3IYHakEzexhajpcjSSHpdplKn4E0zHNhLUul/7NdYaWSZmWia3O0Bud5AUm/K9zIer6MnT0J2nZThNjaRZi0W0rGj8g36QAkpYA2XvmkarBDXVm6MN8kp4kXEg4UDCiYwLmYv/yxhkMKPGghozKkyoQzbmyMgEpZV/Lq6OVYBGrVrxRwS2Nx6huFb/r784c4cEtPxY+cEfPXi7b+MyQjGVCwQCwZsGWWbr9BB/3N+CIRjkB4G38x/yvaRmdJGW2oNafeWg41BF0aq9izl1MnHBfkoCdaSqRlkvd5KkdzEjmTkTzGFcjrzstWqfmvDRcKzjVtSSGleUi/mUeXwW303fvmncT1azhlJnEVnWdZi14Th0bhoTuzmd1MWMaXWqahq/jujhTGIv5GGej0FSB5hNHmQysxtHzARvlDWnecFHzvk5cs/NkNE1j84v4zFq6CuOpKc0ir6iSHxha7QQ8zmUypprBnyLvwDQmZSqmikGDBbeMF/kGiDJEk6/E6fficPvwOl34peU88xUqDDrzJh1Ziw6C2adGb0mdI87cPuDODwBpdLmDeDyBbi4ZDbqNFgXK2wWgxaTXhvyVek3O6G4Vv+v+/7rzghoYg+aQCAQCK6KYwL2/R20Pc2APo8P2d+PI6qQL9xXxL2liVdshwvKMj8fnuSbfaNoVSq+nJtCUmcLJcUuenr/CY9nhLjYu8nN/X+YTJmXvd7lcnHy5EmOHz+Ox+MhOzubnTt3kpGRcdPtd+N9PZx44nEc58bIidhAclgOKlTosyKwbE4krDQWlW51qjWTg3ba6m10nRzD5wkSmWCiaEcShVuTMIWH7qL51UguF85jx7Dvr8Nx8CDBmRnQajFvrsRSuwdrzW50KSlrc/HZAeh6ATqeg4EGpcJmjoP8exSFf/Zu0N+4/fNORJZlxl3jy4dpTyqaf5+k/CIj3hSv7GOLXdb8G7WhudfP6Q3QOjK/ZIw8OzjHlENpcTbq1JSlLB+mLTT/oUcortXvnD1oIqAJBAKB4Hqcfwr2/R2Sa5Zf69/BP87fz4aseP7hgWJKUyKu+JILbi+f6hji6JyDdfj5+dYyUvQyQ0O/4MLAvyBJftJS/4zMzI+i011+BpvX6+XUqVMcO3YMp9NJWloaO3fuJDc396aD2vTwICee+h0Xjp8my7KOgtjN6AMGVGFazBviMW9ORLdKZ575vUF6zkzQVm9jrG8etUZFVnksxVXJpBVGr4q85PVCDgZxNzfjqKvDvr8OX38/AIbCwkWFfy3GkuK12bfmnoOeVxQjZPfL4F0AbRjk1ChGyPx7wRK/+td9A+IP+umc7VwR2oYdwwBoVVryo/OXAlt5XDlp1rSQNC3KsszInHsxsCkHap8Xmv+QJRTX6iKgrTGhOOgCgUDwpsY1Ay/8P2j5LXOWXD7i+gBH3em8oyKVz9xTQPwVfrstyTL/Y5vmS11DqDUavpidxF+kxOL3TdLb9xijo79Hp4siO/uTJCe9C7X68jY6v9/P2bNnaWhoYGFhgaSkJKqrqyksLER9k8r2ufExTj39e84dfIU4Qyrrs+4i0hMDEujTrZgrEwkrj0O9SmeeTdsctDeM0nl8DI/TjzXGSPGOJAq3JWOJMqzKNV5PvH39OA7UYa87gLuxESQJbUICltoarLW1mLZsQa1fg2phwKdU1DqfVwLb/BCggtRKJawV7oXYfERP3DLT7mlap1qXAlvr1ErNf1lc2VJoK40tDWnNf5ttYTGwCc1/KBGKa3UR0NaYUBx0gUAgEKAcSPzsJ5Ad4xxPfC8fGLwLWWPkw7tz+EB19hV/o/37A4f4v+hUDszY2Rph5rHCdLJNBhbs5+ju/jpzcycxm/PIy3uUmOgrm4UDgQAtLS3U19czMzNDXFwc1dXVlJSUoNHcXKCyT09x+pknaNn/IuqghsqSB0jV5sFsAJVBg6k8TqmqpVhWZbEX9Ev0NU1yvt7GSOcsKhVklMZQXJVMRmkMas0bT4oRmJnBcfCQovCvb0B2u1GbTJirqxWF/86daNZif4osw/g56Fg8b220SXk8OnvxcOz7IW2LIhwRLBGUgvTO9y4FtpbJFnrnewFlL1tOZM6K0PZG0vw3D83j9l9B858eSVmq0PyvFaG4VhcBbY0JxUEXCAQCwSLuOXj57+Hsf+OPzOEx88f5l95YUiLD+Nx9hTxYlrQi2Bw8eJBdu3bx27EZvtRjwytJfC4riQ+mxaEGJidforvnm3g8Q8TG1JKb+3nM5uwrXjoYDNLW1sbhw4eZnJwkKiqKqqoqysvLb9oo5pqf48xzT9H00nP43G7Kyu6iKGE7qgE/sl9Cl2TGvDkR04Z41Kt05tnchIv2hlHaj43iXvBhjtBTuD2J4h3JhMeuzkHbrzeSx4Pz+HEcdQewH6gjODkFGg2mjRuV6tqePejT0tbm4vMj0LV43lr/YQj6FHV//j1KdS1nz6JoRPBqFnwLnJs6txzaplqY984DYNaZKY0tpSxWaYtcF7eOaGP0dd7x9hAISnSNO2gcml3az9Y7qQhn1CrIT7AuBbaK9EiyYy2o30CtxqFKKK7VRUBbY0Jx0AUCgUDwKnrr4A8fh/khRgv/nA+PPUDjmI+NGVH8/QPFrE+LBFbO6WNeP5/rGuLFqQU2WE18vyiNQnMYkuRlaOiX9F/4CZLkITXlT8jK+hg6XeQVLy1JEp2dnRw5cgSbzYbVamXHjh1UVFSgv8k2O4/DQeOLz3B23x/wOOxklVSwqfRBDMMa/DYnKp2asHWxmDcnos8IX52qWlBioHWatnobg+enkWVIK4qiaEcy2evj0GjfeFU1AFmS8Jw7p0hG6urwdncDYMjLxVJTi3VPLcZ161DdZHvqDeG1Q89+pbLW9SJ45kCjh6xdUHg/5N8H4Umrf907BFmWGbQP0jLZsrSfrWu2i6CsVKfSrGlLVbby+HLyo/LRhej5dfMuP03Dc5wdmKVxaI6mwVkWPMrZf1ajlvVpkZe0RkYSaXrjiHxChVBcq4uAtsaE4qALBAKB4Ap4HbD/H+HkvyFHZXIw/+/5zJlIphxe3rYhhc/cW0Bn44kVc7osyzw9MccXuodxBCQ+lZnAR9IT0KlVeH1T9PV9H5vtcbTacLKz/paUlD9GfZWFoCzL9Pb2cuTIEQYGBjCZTGzbto3KykqMxpuzvvk8blpefp7Tzz6Jc26WpPxCtu16JxEL0bibJ5G9QbTxYZgrEzFVJKAxr87i1D7jof3oKO0NNhyzXowWHYVbEymuSiZqleQltwvf4CCOAwew1x3Adfo0BINo4mKx7q7BUluDeds21Dc5TjdEMABDxxdbIZ+D2QvK48kVi62Q90FCidi3dh3cATdt021LVbbmyWYm3ZMAGDQGSmJKlNC2GNwSzAm3+Y6vjCTJ9E05aRycXWyNnKNzbAFpccmeHWtm/cXWyLRIChOtaN+ArcevJ6G4VhcBbY0JxUEXCAQCwTW40AB/+CjM9OHb8D5+ovlT/uX4JGoV3Juh4Zt/toewV8k3Jn1+Hu0e4emJOUotYfygMI1Sq6JRtzs66O7+OrOzRzGZcsjL+wKxMbuveQsDAwMcPnyY3t5ejEYjW7ZsYcuWLZhMN6dmD/h8nDvwMif/8HvsU5PEZ+aw5cF3kKzPxXV6HN+gHTQqwkpiMG9OxJAduSp2RkmSGWqfoa3exoXmKSRJJik3gpKqZHIq4tGukrzkdhGcm8Nx5Aj2/XU4Dx9GcrlQhYVh3rEda00tlprdaKPXoI1OlmGyQ6msdeyDkcV1T2T68r61jO2gCc1qUChxqeb/YpWtfbp9SfOfYEpYskWWxZVRFF0U0pr/luH5Fa2RUw7lc4TpNKxLjViSj1SkR15RhPRmJhTX6iKgrTGhOOgCgUAguA4+Fxz8Bhz7CViTmdz9T3y5PZnnWkdJijDy2XsLeKg85bL9H/sm5/hc1zCz/gAfS0/gE5kJGNRqZFlmamo/3T3fxO2+QHR0NXm5X8Biyb/mbYyMjHDkyBE6OjrQ6XRUVlaybds2rNabM9UFAwHajxzg5NO/Y3bURnRyKpsffic5uZV4zk7iPDuB7A6giTZirkzAvDERzSqdeeac99J5fIy2ehvzk270YVoKNidQXJ1MbGpoGvduBsnnw3Xi5JIVMjA2BioVYRs2KJKRmloM2Vlrc3H7uHLeWuc+6DsIAQ8YIyDvLUplLfcu5e+CG8IX9NE500nL1HJr5IhjBFA0/wXRBUtVtvLYclKtqSFpWpRlmeFZ95J8pHFwjvO2efxBZV2fEhmmVNkW2yNLksPf1Jr/UFyri4C2xoTioAsEAoHgBhk+DU9/RKlarH8v/+m7hyfGY2gdmac8LZJ/eKCYjRlRK14y6w/wpZ4RHh+bJd9k5AeFaVREKO19kuRjePhX9F/4EcGgi+Tk95Cd9XH0+mtXW8bHx6mvr+fcuXOo1WoqKirYsWMHkTdpF5SkIF3HGzj55ONMDl4gIj6Byre+g+Idtfi75nGeHMPbNw9qMBYqVTVjftSqVNVkSWake462ehu9jRNIAZn4DCvFVcnkVSagXyV5ye1ElmU8bW049tdhP3AAb3s7APrMTCx7arHW1hK2fj2qm7R13hA+J/QeUCQjXS+AawrUOsisWm6FjFwjwckdzJR7itbJVlqmljX/7oCix48yRC23RcaVURpTikUfmiIXjz9I2+jCUoWtcXCOkblLNP/JEYuBLZKK9ChSo948mv9QXKuLgLbGhOKgCwQCgeAmCHjh8HfgyGN4deHoHvlnnnCt59svdDBh9/JgeTKfu7eA1KiV7Yf7pxf4TOcQY14/f50Wx2ezkghb3Avi883Q3/8jRmy/RqMxkZX5t6Sm/glq9bWrVtPT0zQ0NNDU1ARAWVkZVVVVxMbG3tRHkmWZvrMnOf7Ebxnr6cISFc2mB99G2Z57wSHjOjWG88w4ksOPJlyPaVMC5spEtFGr0xrlcfjpPDFGW4ONGZsTrUFD3qZ4iquSSchcHXlJKOC32bDXHcBRV4fz5EkIBNBERWHZvRvrnlrM27ejvsm21RtCCsLwqeVWyGlFcELiOijYq4S1pHKxb+0WCEpBeuZ6lgJby2QLffN9wLLm/2JbZFlsGdmR2ahVobkHbGLBs7SPrXFwlpbhZc1/rEXP+rTlw7TLUyMx36Ga/1Bcq4uAtsaE4qALBAKB4BYYbcbxqz/H4uyH0rfj3PMNfnZqnp8dVhZnf1Wdzd/szlmxiLEHgny118Z/26bJDjPwWGEaWyOXf8PucHbT3f11ZmaOEBaWSV7u54mN3XPdgDI/P09DQwNnz54lGAxSUlJCdXU1CQk3JzaQZZnB1mZOPPlbhtpaCbOGs3Hvw6y/Zy96Qxie9hkcJ8fwds8CYMiLUg7BLopGtQp2RlmWGe9f4Hy9jZ7T4wR8EjEpZoqrksnfnIhxleQloUDQbsd55IgS2A4dQrLbURkMmLdtw1Jbg2X3bnTx8Wtz8aluJax1Pg9DJ0CWIDxFCWoF90FmNWjfeAeOhwoLvgXOTZ6jeap5KbQt+BYAsOgsiuZ/cT/buth1RBmjrvOOt4dAUKJz3L4Y2OZoHJql702g+Q/FtboIaGtMKA66QCAQCG6NQ3WvsEvTCIf+CYzhcP93GEm5j2+/2MnTTTbirQY+c08Bb69IXbFwOTJj59OdQwx6fLw/JZYvZidh1i63uU1NH6S7+xu4XL1ERW0nL++LWC2F170fh8PBsWPHOHXqFD6fj4KCAqqrq0lNTb3pzzbS0caJJ39Lf9MZDCYz6+95gIr734opPILAnAfnqXFcp8cIzvtQW3SYNipVNd0qnXnmcwfoOjVOW72NyUE7Gq2anIo4iquSSc6LvGOqagCy34/rzBlF4b9/P36bDQBjeRnWRYW/Pjd3bT6zc0pR93fuU46X8LtAb4XcPVC4V9m3ZgrNc8LeKMiyzMDCwIoq26Wa/3Rr+orWyFDW/M+5fDRdrLJdQ/NfkR7J+jeo5j8U1+oioK0xoTjoAoFAILg1lub08TZlb5rtLBQ+AHu/x5kZA199to2moTlKU8L5+73FbMmOWXqtMxDkm/2j/Hx4ilSjnu8VpLEzelmSIUl+Rmz/S1/fDwkEFkhOfhc52Z9Er79++6LL5eLkyZMcP34cj8dDdnY2O3fuJCMj46YX+eN9PZx46nG6Tx5Dq9dTftd9bHrgESzRMciSjKdrFufJMTwd0yCBPisCy+ZEwkpjUelWp5VrctBOW72NrpNj+DxBIhNMFO1IonBrEqZVkpeECrIs4+3qwlGnSEY8ra0A6NLSsNbWYqmtxbSxAtVNHl5+Q/jdyqHYHc8p+9Yc46DSKCbIi/vWotdIcPImw+V3KZr/qWXN/5R7CrjDNP9xZjZc0hpZkBD6mv9QXKuLgLbGhOKgCwQCgeDWWDGnBwNw/Kdw4OtKe9i930Ja90c80zrKt57vYHTew/3rEvn8fUWkRS/vMzox5+BTHUP0ur28NymaL+WmEH5JNc3vn6O//8cMj/wKtdpIVuaHSUt7H2r19VvQvF4vp0+f5ujRozidTtLS0ti5cye5t1CNmR4e5MRTv6Oj4RBqtZrSmrupfOs7iIhXFo7BBR/OM+M4T40RnPGgCtNi3hCPeXMiulU688zvDdJzZoL2BhujvfOoNSqyymMprkomrTB6VeQloYZ/fBzHgYPY6/bjOnYc2e9HHRGBZddOrLW1mKuq0VjW4Ew5SVJ+4XCxFXKiTXk8vnixFXIvJG+AtTiY+02ILMuMOcdWtEW2Tbfhl/zASs1/eVw5hdGFIa/5P7soH2kaWqn5L0uNWHGYdqhp/kNxrS4C2hoTioMuEAgEglvjinP6VI9ybtrgMaU97IEf4DYl8+9H+viXg70EJZn3V2XxkZocrEaljckdlPjuhTH+ZXCCBIOOb+encnfsSh2609lHT883mZquI8yYTm7u54iLu+eGgpbf7+fs2bM0NDSwsLBAUlIS1dXVFBYWor7JBfbc+Binnv495w6+gixLFFfXsPnhdxKdrLRRypKMt28e56kx3OemICijT7cqe9XK4lAbVsdYOGNz0tZgo/P4GB6nH2u0kaIdSRRtT8YSdWfunwo6nDgbGnDU1eE4eJDg/DwqnQ7Tli2LCv8adImJa3PxmT7oXFT4DxwFOQiWRCi4V6muZe0E3eq0twoUrqn5V2spjCpc0RqZagltzf/FwNY4NEfbqzT/Gy4epp0eSUlyOAbt7dP8h+JaXQS0NSYUB10gEAgEt8ZV53RJglP/Aa98GVRqeMtXoOJ9jNl9fPvFDp44O0KsRc+n31LAuzaloVms/DQuuPhExyCdTg/vSIjiK3kpROtWtrJNz9TT3f01nM5uIiM3k5/3KFZryQ3dbyAQoKWlhfr6emZmZoiLi6OqqorS0lI0N6l6t09PcfqZJ2jZ/yIBv4/8LTvY8si7iM/MXnpO0OnHdXYC56lRAhNuVAYNpvI4paqWYlmVxWTQL9HXNMn5ehsjnbOoVJBRGkNxVTIZpTGoQ7yd6laRAwHcjY3Y6w5gr9uPf2AQAGNx8ZLC31BYuDYLdtcMdL+shLWeV8DnAJ0JcmqVsJZ/L5hjrv8+gpvmWpr/aGM0ZbGXaP5jSzHr1qC6ugp4/EHO2xaWWiObLtH86zVqipPDl0NbWuTrqvkPxbW6CGhrTCgOukAgEAhujevO6bMX4A8fU/b1ZFbDW38M0Vk0D83x1WfbOD0wS2GilX94oJjtucreMq8k8cOBcX40ME6UTsu38lPZGxe54m0lKYBt9HH6+r6P3z9LUtI7yMn+FAbDjVn/gsEgbW1tHDlyhImJCaKioqiqqqK8vBztTe5tcs3PcWbf0zS9+Cw+t5vsikq2PPJukvOXpSayLOMbWMB5ahx3yySyX0KXZMa8ORHT+njUYauzn2p+0kVbwygdR0dxLfgwR+gp3J5E8Y5kwldJXhKKyLKMr69PkYzU1eFubgZZRpuctCQZMW3ahEq/Bvv1Al64cERpg+x8HhZGlF9KpG1Z3Ld2P8Tmrv51BQAEpAC9c71LFbaWqRb65/sBRfOfG5VLWWzZkuo/KyIrZDX/4wueJVtk4+AcLcNzePwSALEWw9I+tg1pUZSlRqyZ5j8U1+oioK0xoTjoAoFAILg1bmhOl2U4+0t48VGlLWzPP8DmDyKr1DzXOso393UwMufm7uIEvnB/EVmxym+8z9ldfLJjiFaHmwfjIvlGfgpx+pVmN79/gQsX/pmh4f9GrdaTmfEh0tLej0ZzY3s6JEmiq6uLw4cPY7PZsFqt7Nixg4qKCvQ3uZj3OBw0vvgMZ/f9AY/DTnppGVse+SPSStat+M235AngaprAeXIMv82JSqcmbF0s5s2J6DNW58yzYFBioHWatnobg+enkWVILYyiuCqZ7PI4NKskLwlVAlNTOA4exF53AOfRo8geD2qLBcvOaiy1e7DsrEYTHr76F5ZlGG1e3Le2D8YUwQkxeVC4GNZSK0F9+9rX3gzMe+c5N3VOkY9MNdM62bpC878udt0KAUmkMfL23vBVCAQlOsbsi/KRWZoG5+ibWtb8FySGL+1j25AeRXaseVU0/6G4VhcBbY0JxUEXCAQCwa1xU3P6/DA8+0nofkmpLjz0E4jNw+MP8vP6fn56oAdfUOLPt2XysT15RITp8EsyPx2c4HsXxrBo1XwtL5VH4i9XzLtcF+jp+RaTUy9jNKaQm/NZ4uP33nDYkWWZ3t5ejhw5wsDAACaTiW3btlFZWYnReHMb+H0eNy0vP8/pZ5/EOTdLUn4hWx95N1kbNl12P75hO85TY7iaJpG9QbTxYZgrEzFVJKBZpTPP7DMe2o+O0t5gwzHrxWjRUbg1keKqZKJWSV4SykhuN85jx7Dv34/jwEGCMzOg1WKq3IS1RrFC6lNT1ubic0OLlbV9SpVNCoApVmmBLLgPcmpAf+ePwe1GkiVF878oH2mZUjT/kqxUpzLCM1a0RuZF5YWs5n/W6aNpePkw7aahOeyLmv9wo5b1iy2RG16D5j8U1+oioK0xoTjoAoFAILg1bnpOl2Vo+S08/zlFaV7zBdj2UdBombB7+N6LXTx+Zogok55P3p3PeyrT0GrUdDo9fLJjkLMLLt4SE84/FaSSZLh84TEze4zu7q/jcLQTEbGR/LxHCQ8vu6nPNDAwwOHDh+nt7cVoNLJ582a2bt2KyWS6/osvIeDzce7Ay5z8w++xT00Sl5nNloffRd6WbahfVUGRfEHcLZM4T47hG7SDRkVYSQzmykQMOZGrYmeUJJmh9hna6m1caJ5CkmSSciMorkompyIenf7Or+rIwSDu5hYcBxSFv6+3FwBDQQGW2hqstXswlhSjWgszo2de2a/WsU/Zv+adB60Rsncv71uzhqZK/k7E5Xdxfvr8Umhrnmxm2jMNgFFjpDimeKktsiyujHjTGh2a/hpRNP8Ozg4uh7aucftr0vyH4lpdBLQ1JhQHXSAQCAS3xi3P6fZxeO5T0PGsoip/6CeQoIg+zo3M89Vn2zjRP0N+goVH9xazMz+OoCzz70OTfKt/FL1axZdzU3hPYvRlVSlZDmIb/T29vd/D758mMfFhcnI+g9Fwc3a/kZERjhw5QkdHBzqdjsrKSrZt24bVar3+iy8hGAjQXn+Qk0/9jtnREaKTU9n88Dsp3LELzRX2u/nHnEpVrXECyRVAE23EXJmAeWMimlU688w576Xz+Bht9TbmJ93ow7QUbE6guDqZ2NSb+3xvZHwXLixJRtxnG0GS0MbHL4a1Wkxbt6Jei31rQb9iguzcpwS2+UFABamblhX+cQUQgkbCOxVZlhl1ji6FtZapFtqn25c0/4nmxKUqW3lcOUUxRRg0oWlLdXgDtCxV2ZTQNu28iuY/PZJ468ougVBcq4uAtsaE4qALBAKB4NZ4TXO6LEPbU/Dc3ynVhZ2fgapPglaPLMu8eH6Mb+zrYHDGRW1hPF+4v4jceAt9Li+f6hjk+LyTXVFWvluYRprx8kV0IGDnwsC/Mjj4C1QqDRkZf01G+gfQaG5OljE+Pk59fT3nzp1DrVZTUVHBjh07iIyMvKn3kaQgXccbOPnk40wOXiA8LoHND72Dkt13odVd3k4l+yXc56dwnhzD2zcPajAWRGPenIixYHXOPJNlmZGuOdrqbfQ1ThIMSMRnWCmuSiavMgG9cW0kBKFIYHYWx8FDisK/oQHZ5UJtMmGuqsK6pxbzzp1oo6JW/8KyDOPnF1shnwNbo/J4VJZSWSu8H9K2gubNMxahgi/oo2OmY0Vr5JtB8z/d08TdtTW3+a5XIgLaGiMCmkAgENw5rMqc7pyGFz4Hrb+DhFJ46J+VqhrgDQT5r4YL/LiuB48/yJ9szeATd+URHqbjl7ZpvtprQwU8mpPMnyfHoL7C4sjtHqKn99tMTOzDYEgkN+ezJCQ8iOomTW7T09M0NDTQ1NQEQFlZGVVVVcTGxt7U+8iyTN/Zkxx/4reM9XRhiYpm04Nvo2zPveiust/NP+XGdWoM55lxJIcfTbge06YEzJWJaKNW55Bbj8NP54kx2hpszNicaA0a8jbFU1yVTELm6shL3ihIXi+u48ex1x3AUVdHYHIS1GpMFRVY9uzBWluDPiNjbS6+YFs2QvYfgqAPwqIg7x6lupa7BwxvnipnqDHlnloR2M5NnbvjNP/bk7X8+m/vuc13uBIR0NYYEdAEAoHgzmFV5/SOfYpExDkJOz4Ouz4HOiV8TDm8PPZyF785OYjVqOOTd+Xx3q0ZjPr8fKZzmEOzdrZFmnmsIJ0s05XbjmbnTtHd/VXs9vOEh68nP++LRERU3PRtzs/P09DQwNmzZwkGgxQXF1NdXU3iTR6QLMsyg63NnHjytwy1tRJmDWfj3odZf89eDKYrL+rkoISnfQbHyTG83bMAGPKilEOwi6JRaV/73ilZlhnvX6Ct3kb36XECPomYFDPFVcnkb07EuErykjcKsiThOX9ekYzUHcDb1QWAPicHa20tltoawsrL12bfmtcOvXVKWOt6AdyzoNErh2IX3KdU2MKTV/+6ghvmWpp/tUpNTmTOkua/PK6czIjMkNf8D3Wf568e2XO7b2cFIqCtMSKgCQQCwZ3Dqs/p7jl46YvQ+CuIzVf2pqVtXvrnjrEFvvpsGw090+TEmXl0bzG78mP5zfgsX+4ZwS/J/L/sJD6QGofmChUfWZYYG3uSnt7v4vNNkJDwILk5n8VovPlFrsPh4NixY5w6dQqfz0dBQQHV1dWkpqbe9HuNdLZz4snf0t94GoPJzPp7HqDi/rdiCo+46msCcx6cp8ZxnR4jOO9DbdFhqkjAXJmALu7mhCZXw+cO0HVqnLZ6G5ODdjRaNTkVcRRXJZOcd7lN882Ab3gYR50iGXGdOgXBIJrYWCy7d2Gt3YN521bUYWtw5lwwAEMnFvetPQezSgggaT0U7lUCW0Kp2LcWArxa898y2YLdZwfA+v+zd9/hcdVXwse/UyXNqNeRLMnqzd1Wsa1iXAjGNsWEwCZvdrObzZvNbioECKEk2RBCQgiEtM3mTdmS3Q2ExRQDJrihZkuy3C3J6sUa9ZFGml7uff8YQgpG1sgz9tj8Ps+T54kd3TK6ztE9Or/fOZooViSteLfF/4rEFSHX5j8U39VFghZkofjQBUEQhMUJWkzvPgCvftHXmn/9P8GWR0DrSzpkWeZA+ziPv95O36SVmoIkHtlZTFRsGA+cv8BbU7Osi9bxTFEmBfqLL//zeKwMDP4rg4O/ACAz81MszfwH1Gr/lyPZbDaam5s5evQoDoeDnJwcampqWLp0qd8JzFhvN00vPU9X8xHUWi2rtt1M6a7dRMYnvO8xsiTj6JzG2jyKo2MKJNBmxxBZbiBieSKKAM08mxico63eSGfzKC6Hl9gUHcWVqRStT0UXoOYl1xqv2Yylto65gwew1tYhWa0owsPRV1YStWUzkTfcgDrh/Z/doskyTHb6ErXzb8CFFkCGmMx3Kms3Q1YVqD5Y1c5Q9adt/v9Qaeua6Xq3zX9WdNa7Cdsf2vyrlVdvz2EovquLBC3IQvGhC4IgCIsT1JjunIP934CWX/gaJtz6I8iufvd/dnkk/vPoAM/u78Tq8vKx8ky+tC2ft602Hu68gNUrcV+2gX/MSEbzPg01HA4j3T1PMjb2KlptMrm5XybVcIff+9MAnE4nx44do7GxEavVSkZGBjU1NeTl5fmdqE1dGKTppd/R0fA2SqWS5ZtvpOzWO4lJnr8Nu3fWhfX4GNaWUbxTDhQRavRrktGXG9AEaOaZ2+Wlp3WctnojIz1mlCoF2asSKalMI6M4MM1LrkWyy4W1ucVXXTt0CM/ICCgURKxe7esKuXUr2uzs4FQdLeO+JZAdr0PvIfA4ICwG8rf5lkHmbYOI2MBfV1i0P7T5f3dp5MTpd9v8R6gjKEko8XWMTPS1+k/SJV2xewvFd3WRoAVZKD50QRAEYXGuSEzvq4NXPgfT/VD693DjP/9ZkwST1cUP9nfyX02D6LQqvrg1nx3rlvD13hFenZhhZWQEzxRnsizy/Zedmc3H6ex6nNnZk0RFLSc//xHiYssWdbtut5vjx4/T0NDA7OwsqampVFdXU1RUhNLPfUozY6O0vPwC597ejyRJlFRvpvz2jxCfNv8ySlmScfaasbaMYj87CV4ZbUYU+nIDESuTUIYFZuaZyWilrcHI+aOjOKxuouLDKa5MpXhjKpEBal5yLZJlGWd7+7st/J1t7QBoly59t8lIxJo1KFRBmD3nskHvYV9HyPP7wDYJSrWvola4w1ddi80M/HWFyyLLMkar8Y8NSCZO02ZqwyP5hlCn6lP/rMoWzDb/ofiuft0kaCsTEuRXd+y82rfxHjMzM363JhYEQRBC05WK6QqFh9j4DqJievB6IpiaWI3D/ueDY/vV0fwkZjXN4aks8czxT+aTOJP1fK9yC7Nh4fztqWb+7lQTGkm66DVkZCw5E0yVDuDRu9D3JZB4LAuNZXGJhhfoiYridGwsc1oNsS4XK6dnyLZY8Lc+Z5clznvt9ElOvEC6UkuRMpzYhSyDUoahiMhHoS9CoYlDllzI9h5kawe4Jxfxyd7Li5JR1VIGNflMqdJAlkj2DpPp6STZewEl1877UzBILhfemWm80zNIc3O+JYoqFarYWFRxcahiolEog5CsIfsq0TYT2KZ8w+EBtHrQxYMuAbSRQbiuEAgSEja3DavbisVtweqy4pScAChQoNPoidTo0WsiidTo0arCCER9NhTf1bN+858iQQumUHzogiAIwuJc6ZiuDTORmHwCjdaCZTYT09RyZOnP99kcDTPw05jVDGhiWOsY4xP2NvaUrmVfXgm5pkkeqX+Tksmx972GpPIys3yY6RXDyEqZ2HNpxJ9OR+le3J4QCeiP1HMqNo6ZMC1RbjcrpmfIm5vD31dyhyzR5XXQIznwAKkKDUWqCBIWul9Fm4xCV4QiIheFUo3smkK2dSDbukF2+Xk3F2dVRDGkzmdInYdTqSNMspHh6SLD04VetgTkGtcy2evFazbjnZnBOzMDXi8oFCijo33JWmwsyovMxQsItx3s7yRrzncSRXUYRMT7ErbwGAjRDoOCj0tyY3VbfEmby4LVY0OSvQBolBr0Gj2Rmkj0mkj0Gj2qRTzPUHxXv24SNLHEURAEQQi2qxLT3Q54+7vQ8Czok2DXM75hvn/6JV6J/24a5Jn9ncza3dxdlsG6dal868I44y43/5iZzH1ZBiJU7//y4nCO0tPzFKOje9BoEsjN/TJpqXeiUCyu0iFJEp2dndTW1mI0GomKiqKyspK1a9ei1frXZMNhsXDizVc5/vorOCxzZC5fScXuu8lYtnJBe5wkhwfbyXGszaO4jVYUGiURKxLRlxvQLg3MzDOvV2LgzBRt9UYGz00hy5BeFEdJVRo5q5JQBah5ybVMdruxtR5n7uABLAcO4h72DUEOX7GCqK1biNy8hbCC/ODsW7NOQdebvq6Q3QfBbfVV0/K2+pZC5n/Il7QJIc0jeeie6f6zBiT9s/2Ar81/Xmzeu0sjF9rmPxTf1a+bJY4iQRMEQRCC7arGdOMJePlzMHYWVnwEtn8X9H/eMc9sc/PsgS7+40g/4RoVn9qUQ3+Kht+Oz5AbEcYzRRmUx86/xMs8e4qurm9hNh8nMrKY/PyHiY/bsOjblmWZnp4e6urqGBgYQKfTsWHDBsrKygh/n0HV78flsHP6rTc4tncP1plpUguKWL/7brLXlC74pd41bMHaPILt5ASy04s6KQJ9mQHd2mRUkYHpzjhnctBxZIS2BiMWk5PwSA2F6w0sq0ojLkDNS651sizj7Op6t4W/4/RpADTp6b4mI1u2olu3FkUwqmtuB/TV+pK182+AZRQUKsjc4PvlR+HNEJ8T+OsKQWF2mjkzeebPBmq/X5v/lUkriQn783EeofiuLhK0IAvFhy4IgiAszlWP6R4X1D8Dtd/zLc/a+RSU3P6eWVA9ExaeeL2d/e3jZMRHcFt1Fv8j2zA6Pfx9eiJfzUlFP0/DBlmWGR9/je6eJ3E4hklKvJG8vAfR6bIu6/YHBgaoq6uju7ub8PBwysvLWb9+PTqdf3PMPC4XZw/vp/nl3zE3OUFSVg4Vt99FfsUGlAvc2yS5vNhPT2BtHsU1OAcqBRHLEtCXGQjLjQ1Id0ZJkhlqN9FWb6T/1CSSJJOaF0NJVRq5a5PRaIOxD+va5B4bx3L4MHMHD2A7chTZ5UIZHU1kTQ1RW7egr65GFRmE/WOSBCMnfB0hz78B4+d8f59U9E6TkR2wZB0EYzC3EBSSLNE/2/9nDUjma/NvPG1k62YxqDooRIImCIIgBFvIxPSxc/DyZ31VteJbYMf3Ieq9Lenruib41t52zo/NUZoVR+LKRF5y2sgM1/J0UQZVcVEXOfkfeb0OhoZ+Rf/AvyBJbjIyPkF21udQq+c/7lKMRiO1tbV0dHSg0WgoKytjw4YNREX5d16vx0N7/WGaX/od0yPDxKelU377Ryiq3IRKvfA9dO5RK9aWUWwnxpFsHlTx4ejLUtCvM6AK0Mwz26zLV1WrN2KesKONUFNYnkJJdRqJ6Zf3/bzeSFYrlsZGLAcOYjl82Ld3TaNBX17+TnVtC5rU1OBc3NT3Tgv/12CgEWQv6JOhcDsU7oScTaAJwmBuIaj+ss3/qYlTmBwmAMr15fzyzl9e5Tv8cyJBC7KQ+WEuCIIgXLaQiuleDxz5MRz6tu+F8ebvwsq731NN83glftsyxNNvdTJtc1Gz3ED7Eg2DssRfpyXwtdw0otTzV3KcznF6ep9mhxt/JAAAmKFJREFUZOQFNJo4cnLuIS31LpSXOVx2fHycuro6zp49i1KpZO3atVRWVvq9YV+SvHQebaB5z/NMDPYTnZRC+W0fZtmmbaj92O8muyXs5yaxNo/i7DWDEsIL49GXGwgviEehuvyqmizLGDtnOFdvpPfEBF6PRPLSKEqq0sgvS0EbfvUG9oYi2evFfuIEcwcPYTlwANfAAABhJcVEbfG18A8rLg7OvjX7NHTt97Xw79oPrjlQR0DuFt9SyPybIPLKzesSAudP2/wPnx/mU9s/dbVv6c+IBC3IQuqHuSAIgnBZQjKmT3b5qmlDTb5GB7t+ADFL3vNlZrubnxzq5tcNfahVSopXJnM0VoFBp+V7hRlsTYi+5KVm587S1fU4MzPN6PX55Oc/QkJ81WV/hKmpKRoaGjh58iQAK1eupKqqisTERL/OI8syvcebaXrxeUa6z6OPi6fsljtYuXU7Gj/3u7kn7dhaRrG2jiFZ3KiitehKU9CXGVAHaOaZw+rm/NFR2hqMmIxW1GEq8kuTKalKIyUrMM1LrieyLOPq62PuwAEsBw9hP3kSZBl1aipRmzcTuWUL+vIyFH42oVkQjwv663zLIM+/AbMXAAVkVPj2rBXthMT8wF9XCLpQjOsiQQuyUHzogiAIwuKEbEyXvND8/+DAP/uG9H7oW7D2b95TTQPon7TyxBvtvHlujMToMOTCWIbjVNyVGs8/5y0hTjN/BUeWZSYmfk9X9xM4HEMkJmwhL++r6PWX31TBbDbT2NhIa2srHo+HZcuWUV1djcFg8Os8siwzePYUTS8+x1DbGSKiolm74zbWbN9FmM6/Jh2yV8LRbsLaMoqjcxqAsPw49GUpRBQnoFBf/t4kWZYZ65ulrd5I17ExPC6JhCV6iivTKKwwEK4PUhv6a5xnauqdfWuHsDY0IDscKPV69DXVRG3ZSmRNNaqYmEufyF+yDKOnfYlax2u+/w6QkPfHfWsZ5RCUWW9CoIViXBcJWpCF4kMXBEEQFifkY7qpD175vO83/dmb4NYfQlzWRb+0sWeSx/a20z4yiyFFz4VsHfFJOr5bkM7NSbGXvJQkORka+nf6+n+CJDlIX/JxsrM/j0Zz6WMvxWKxcOTIEVpaWnC5XBQUFFBTU0N6errf5xo+307TnufoO3GMMJ2e1TftYu2OW9FF+//i7plxYG0Zw3ZsDK/ZiTJSg25tCvqyFDRJ/jU6eT8uu4fOljHa6o1MDM6hUivJXZtESVUaafmxoqr2PiS7HeuRo1gOHWTu0GG8k5OgUqErLfW18N+yBe0i/v0siPnCO5W116GvDiS3byh2wXZfdS13i29YthCSQjGuiwQtyELxoQuCIAiLc03EdEmC4/8Gv/8ayBJs+waUfeqiXei8kswLrUN8781OJi1OIjMjmcyO5LbMBB7PTydRe+n9UE7XJL29z2A0Po9aHU1O9hdYsuRjKJWXX/Wx2+00NTVx9OhRHA4HOTk5VFdXk5WV5XeiMtbbTdNLz9PVfAS1Vsuqbdsp3XUHkfEJlz74L8iSjKNz2ldVa58CCbTZMUSWG4hYnoBCE5jKycTgHG31RjqbR3E5vMSm6CiuTKVofSq6ADUvuR7JkoTj9GnmDhxk7tBBXN09AIQVFPiajGzdSviyZSiC0ZnRMQvd+30JW9eb4DCDKgxybvDtWyvYDlH+VYSF4ArFuC4StCALxYcuCIIgLM41FdNnhmDvl3wvi5kb4NYfQ2LeRb90zuHmp4d7+GV9HxIyrqwo9PnRPFGUyW3JC6vazFk66Op6nOnpRnS6XPLzHyIx4YaAfBSn08mxY8dobGzEarWSkZFBTU0NeXl5fidqUxeGaH7pedob3kapVLJ8842U3XonMcnv7YK5EN45F9bWMawto3inHCgi1OjXJKMvN6AJ0Mwzt8tLT+s4bfVGRnrMKJUKslclUlKVRkZxfEBGAlzPXAMD7zYZsR0/DpKEOimJyM2bidq6Bd369SjDwgJ/Ya8bBo+808L/NZgZ9P39knV/XAqZXHzRpcjClROKcV0kaEEWig9dEARBWJxrLqbLMpz6H9j3IHicsPlh2PDZ990bM2Sy8Z03OnjtzAjqCDW2vChuXJHCk4WZpIRduiImyzKTkwfo6n4Cu72f+Phq8vMeIjKyICAfx+12c+LECRoaGjCbzaSmplJdXU1RURFKP6shM2OjtLz8Aufe3o8kSRRX3UD57R8hYUnGou5NlmScvWasLaPYz06CV0abEYW+3EDEyiSUYYGpqpmMVtoajJw/OorD6iYqPpziylSKN6YSGaDmJdczz/Q01tpa5g4cxFJfj2yzodDpiKysJHLLFiJv2IQ6Li7wF5ZlGG/743Ds4Vbf38dlvZOs3QyZG0ElunheaaEY10WCFmSh+NAFQRCExblmY/rcKOy91/db/CXr4Laf+H5z/z6a+0x8c+85zg7PQowGzbJ4HivL5m5D/IIqVpLk4sKF39DX/0O8XhtpaR8lJ/uLaLXxAfk4Ho+H06dPU19fj8lkIjExkerqapYvX45qngHcFzNnmuTYq3s4vX8fHreLgopKKnbfRXLW4pueeK1ubCfGsTaP4hm3odCq0K1OQl9mQJMeGZB9ZF63RO+pCdrqjVzomEahgMzlCZRUppG1IgGlSgxWvhTJ6cTW1MTcwYNYDh7CMz4OSiURa9cQtXkLUVu3oM3KCs7FZ0d889bOvw69b4PXCeGxvk6sRTsgdyuEX7qzqnD5QjGuiwQtyELxoQuCIAiLc03HdFmGcy/C6/f79sls+gpUfQlUF6+MSZLMiyeGeeKNdqYsLryGCMrK0/jh2hzSwxe2/8nlMtHX90OGjf+NSqUjO+sLpKd/HKUyMPunJEni3Llz1NXVMT4+TlxcHJWVlaxevRq1H4OqAWzmGVpff5mTb76Gy24jZ20ZFbvvIq3g/RPZS5FlGdfgHNbmUeynJ5DdEppUPfpyA7rVySgjAlMtMU/YaGsYoaNxBNusC12MluINqRRXphGTJIYqL4QsSTjOtfmajBw4iPP8eQC0OTm+JiObtxCxaiUKP38BsCBOC/Qe8i2F7NwHdhMoNZBd46usFe646OgMITBCMa6LBC3IQvGhC4IgCItzXcR066QvSTv3IhhW+Kppqave/8udHn72dg//8nYPHhkU2VF8dVsBn8pKRrnASpDF2kVX1+OYTHVERGSRn/dVEhO3BqwjoSRJdHZ2Ultbi9FoJCoqisrKStauXYvWz5lYDquFk/v20vr6yzgsc2QuX0nF7rvJWLbysu5XcniwnfRV1dxGKwqNkogViejLDWiXBmbmmdcrMXBmirYGI4Nnp5BlSC+Ko6QqjZxVSag0oqq2UK4Lw1gO+pqM2FqOgceDKiGByBs2EbV1K/oNG1BGBCH5lby+mYbnX/clbCZfgxNSV/1x35phhdi3FkChGNdFghZkofjQBUEQhMW5rmJ6+6vw2pd9CVvVPbDpAVC/f6OE4Rk7X3+tjf1nRpHDlGStSubX25eRo1v4vqfJqcN0dX0bm62HuLiN5Oc/TFRkUSA+DfDOoOreXmpraxkYGECn07FhwwbKysoI93NQtcth5/Rbb3Bs7x6sM9Ok5hey/o6/IntN6WUnU65hC9bmEWwnJ5CdXtRJEejLDOjWJqOKDEx1cc7koOPICG0NRiwmJ+GRGgrXG1hWlUZcgJqXfFB4Z2ex1NZhOXgQS20tksWCIiwM/caNvuraDTeg9nOo+oLIsm8Q/fnXfPvWhpoBGWIy3qms3QxLq0AtOnpejlCM6yJBC7JQfOiCIAjC4lx3Md1mgjcfhlP/DUlFvmpa+kXfCd7V2m/ii3vOcGHMAtEa/nprLt8oz0G1wKRFktwMG/+H3t5n8XhmSUu7i9yce9BqA/uCOzAwQF1dHd3d3YSFhVFRUcH69evR6fybV+ZxuTh7eD8tr7zA7MQ4SVk5VNx+F/kVG1Be5iBiyeXFfnoCa/MorsE5UCmIWJaAvsxAWG5sQLozSpLMULuJ9nojfacmkSSZ1LwYSqrSyF2bjEYrhin7Q3a5sB079m4Lf49xBBQKIlatInLLFqK2bEabmxuceXWWiXf2rb0BPQfBY4ewaMjb5qus5d8IEbGBv+51LhTjesgmaAqFQgk8BkQDx2RZ/vf5vl4kaIIgCEKwXbcxvestePWLMDcC6//J1+1R+/6JjCTJ/PuxQZ7Y14HL5iE6PZIf376SmvSFd79zu2fo6/sRF4Z/g1IZTnbWZ8nI+ARKZWDbnRuNRmpra+no6ECj0VBaWsrGjRuJiory6zxej4f2+sM0v/Q7pkeGiUtLp+L2j1BUuQmVn/vdLsY9ZsXaPIrtxDiSzYMqPhx9aQr60hRU0YH5nthmXe9W1czjdrQRagrKUyipSiMpw7/vh+Cr2Do7OnxNRg4cxNHWBoBmaea7TUYi1qxBEYB/H+/hskHf29Dxmi9ps06AUg1LN0LhTl91LW5p4K97HQrFuB6UBE2hUPwK2AWMy7K8/E/+fjvwLKACfiHL8nfmOcdu4HZgCnhNluUD811TJGiCIAhCsF3XMd0xC299DVp/DfE5vrlpWZXzHmJzevjSG+f4fcswsiRTvtrAz29ZQZxu4UuurNZeurufYHLqIBHhmeTlPUhS0ocCXoEYHx+nrq6Os2fPolQqWbt2LZWVlcTGxvp1Hkny0tXUSNOLzzEx2E90Ugrlt32YZZu2ofZzv9vFyG4J+7lJrM2jOHvNoITwwnj05QbCC+JRqC7/+yLLMsbOGc7VG+k9MYHXI5G8NIqSqjTyy1LQhotW74vhHh3FcugQcwcOYm1qArcbVWwskZs2+Vr4V1Wi1Adheakk+dr2/2Ep5ESH7++Tl/k6QhbeDKlrLjqsXgjNuB6sBK0GsAD/8YcETaFQqIBO4EbgAtACfBRfsvbEX5zik+/8Z1qW5X9VKBQvyLJ853zXFAmaIAiCEGwfiJje+za88nmYGYCy/wvbvgFhkfMecnZijk+9eIrRPjOqMBWf25bPFypzUPmxRG9qqo6u7sexWruIja2gIP9hoqKWXeaHudh1pmhoaODkyZMArFy5kqqqKhL93EMkyzK9x5tpevF5RrrPo4+Lp3TXblZtuxmNn/vd3o9n0o712CjWY2NIFjeqaC260hT0pQbU8YG5hsPq5vzRUdoajJiMVtRhKvJLkympTCMlOzDNSz6IvBYL1vp6X3Xt7VoksxmFRoNuw3qitvi6QmpSkoNz8akeX6J2/nXfoGxZgqhUKNgORTshqxo0YmbeH4RiXA/aEkeFQpEF7P2TBG0D8A1Zlm96589fBZBl+S+Tsz8c/3HAJcvy8wqF4jlZlu+e73oiQRMEQRCC7QMT011WOPAYNP3M15Dg1h9C7uZ5D5FlmR+fucAzb5xHmnaSmBDB07evoCY/acGXlSQPxpHn6e19Brd7mtTUO8nNuZewsMC/yJrNZhobG2ltbcXj8bBs2TKqq6sxGAx+nUeWZQbPnqJpz/MMnTtNRFQ0a3fcxuqbdhKunz+xXfA1vBKOdhPWllEcndMAhOXF+oZgFyegUF9+ZUSWZcb6ZmmrN9J1bAyPSyI+TU9JVRqFFQbC9ZceVC5cnOx2Yzt+wtcV8uBB3ENDAIQvX+5rMrJlC2EFBcFJhm0m6Pq9bylk9wFwW0Gjh7yt7+xb+xDoEwJ/3WtIKMb1K5mg3Qlsl2X5U+/8+a+BClmWP/c+x+uAHwE2oEOW5Z9c5Gs+DXwaICUlZd1vf/vbRd9vsFgsFiIjAxOgBUEQhKvrgxbTo83tFHX8EJ3diDH1Rnpy/w6vev4lWmYJfjCmpPe8DYXDS2Gymk8WakjRLzyJkGUbsvwqMgcANQrFThTciEIR+G51LpeLoaEhjEYjXq+XhIQEli5dSnS0/0OCLaPDjLQeZXawD6VWS/LytaSsXIs6wr/GJPNR2yH6goKoYQUahwKPVmZuicxsuow7QKvnvG4Z8wBM98g4pkGhhOgMiMtRoEtGVNUuhyyjGhkh7NQpwk6fRtvXD4A3IQHnypU4V63ElZ8PQZi3pvS6iJ05Q8JUM4mTzYS5TMgoMccUM5lYzlRCBXZdasCvG+pCMa5v3rw5NBM0f4kKmiAIghBsH8iY7rbD4e9A4w8h0gC7noHC7Zc87NURE/e92Y6jy4xKhk9szOJLW/OJiVh4JcZm66e7+ztMTL5FePgS8nIfIDl5Z1ASBLvdTlNTE01NTdjtdnJycqiuriYrK8vv64319dC853k6mxtRa7Ws2rad0l13EBkfuEqFLMk4uqaxNo/iaDeBJKPNjkZfnopueQIKTWBe8CcG52hrMNLZNIrL4SUmOYKSyjSKNqSiixbt3S+Xe3wcy+HDWA4ewtrYiOxyoYyKIrKmhqitW9BXV6Pys6HNgkgSjJz841LIsbO+v08sfGff2g5YUvqB2LcWinE9ZJc4+kskaIIgCEKwfaBj+nArvPw5GG+DlXfD9u+ALn7eQ8xuDw+eGeDVhkHUwzaiIjQ8cFMhHy3LQK1a+IufafoIXV2PY7G0ExOzjoL8R4iOXnm5n+iinE4nx44do7GxEavVSkZGBtXV1eTn5/udqE1dGKL5pedpb3gbpVLJshu2UX7bncQk+7eM8lK8cy6srWNYW0bxTjlQhKvRr01GX25AE6CZZ26Xl57WcdrqjYz0mFEqFWSvSqSkKo304niUARgJ8EEn2WxYGxuZO3AQy+HDeKenQa1GX15G5JatRG3ZjCYtLTgXnx74Y7I20ACSB/RJvn1rhTsg54Z5O7tey0Ixrl/JBE2Nr0nIVmAYX5OQj8myfG7RF/kTIkETBEEQgu0DH9M9Lqj7PtQ9BRFxsPP7UHLbJQ87bJrli03dTJ+eQjntIi85kq/tKqGmYOH702TZi3HkBXp6vo/bPYXBcDu5ufcTHhbYZOcP3G43J06coKGhAbPZjMFgoKamhqKiIpR+VhVmxkZpeeUFzh3ejyRJFFfdQPntHyFhSUZA71mWZJy9Zqwto9jPToJXRpsR5durtjIJZVhgqmqmESttDUbOHxnFYXUTFR9OcWUqxRtTiYwTzScCQfZ6sZ88+W4Lf1d/PwBhxcVEbd5M5NYthJeUBGe5qX0Guvf7krWut8A5C+oI3z7Uwh1QcBNEBqnByVUQinE9WF0c/we4AUgExoCvy7L8S4VCsQP4Ab7Ojb+SZfnxRV3gIkSCJgiCIASbiOnvGD0DL38WRk75ErQdT13yhc3i8fJYj5H/PHGBiM5ZvDYPW4qSeWhHMXnJC9//4fHM0T/wMwYHf4VCoWLp0n9gaeanUKkiLvdTvc/1PJw+fZr6+npMJhOJiYlUV1ezfPlyVH7uE5ozTXLs1T2c3r8Pj9tFQUUlFbvvIjkrJ+D37bW6sZ0Yx9o8imfchkKrQrc6CX2ZAU16ZEBe7L1uid5TE7TVG7nQMY1CAZnLEyipTCNrRQJKP6qkwvycvX1YDh1k7sBB7CdOgCyjNhiI3HwDUVu2oqsoRxmAMQ/v4XH5KmrnX/dV2MxDgALSy/64FDKxAK7hfYmhGNdDdlC1v0SCJgiCIASbiOl/wuvx7Us7/ARoI+HmJ2HFnZd8UWuctnBP2wAXzpuI6LOAV+bj65fypW35xPoxP81uH6K750nGx18nLMxAXu4DpKTcgkIRnKRAkiTOnTtHXV0d4+PjxMXFUVlZyerVq1H7OYjYNmvm+Osvc2LfXlx2Gzlry6jYfRdpBcUBv29ZlnENzmFtHsV+egLZLaFJ1aMvN6BbnYwyIjAzz8wTNtobRmg/MoLN7EIXo6V4QyrFlWnEJAUnef6g8phMWA4dZu7QQawNjch2O0q9Hn11NVFbNhNZU4PKz/l+CyLLvl/OnH/DN3Nt5JTv7+NzfbPWinZCejmorq05eqEY10WCFmSh+NAFQRCExREx/SImzvuqaRdaoOBm2PU0RM+/T8bmlfhu3wg/7x4lus+Ca9BCdLiGe7bl83/WL0XjR+VleqaFrq7HmJs7R3T0agryHyYmZu3lfqr3JUkSnZ2d1NbWYjQaiYqKYuPGjaxbtw6tnxUMh9XCyX17aX3jFRxzs2QsW8n6O+4mY9nKoCxdkxwebCcnsLaM4h62gFqJbkUi+nID2qzAzDyTvBL9Z6ZoazAyeHYKWYb0ojhKqtLIWZWESiOqaoEkORxYjxzBcvAQc4cO4Z2cBJUK3bp177bw12YEdintu8zD0PkGdLwOfbUguSEi3rcEsnAH5G655AzFUBCKcV0kaEEWig9dEARBWBwR09+H5IWmf4UD3wSVFm56HNZ8/JLVtGNmK/d0DNI9ZiG9z8rEiJXcJD2P7CzhhsKkBScMsiwxOrqH7p6ncLnGSUm5hbzcBwgPD1JDBd4ZVN3bS21tLQMDA+h0OjZs2EBZWRnhfg6qdjnsnN6/j2Ovvoh1ZprU/EIqdt9NztqyoLW0dw1bsDaPYDs5gez0ok6KQF9mQLc2GVVkYJbKWaYdtDeO0NZgxGJyEh6poXC9gZLKNOJTAzQTQHiXLEk4zpzxNRk5dBBnVzcAYfl57zYZCV+xAkUwOjM6ZqHngK+61vkmOGZAFQY5m3zVtYKbITo0W/iHYlwXCVqQheJDFwRBEBZHxPRLmOqBV74AA/WQs9k34Do2c95DHF6JZwbG+PHAKDEmN5Hdc4xPO6gpSOKRncUUpCy8xbjHY2Vg8F8ZHPwFAJmZn2Jp5j+gvsTstss1MDBAXV0d3d3dhIWFUVFRQUVFBXq9f9f1uFycPbyflldeYHZinKSsHCpuv4v8ig0olYGfiwUgubzYT09ibRnFNTALKgURyxLQlxkIy41FEYDujJIkM9Ruor3eSN+pSSRJJjUvhpLKNHLXJaPRBuezfdC5Bgd9TUYOHsLW2gpeL6qkRKJu8DUZ0a9fj9LPXyYsiNcNg0f/uBRyut/392lr/7hvLbkkZPathWJcv24StLyMEvl7X/rN1b6N95iZmSE2GOuABUEQhCtOxPQFkCWy3a+yzPmvAJwL+zR9mlt9047nMRgB/7FUwXA4ZHVYmLkwh0uW2RCuY7s+ikg/fuuv0EwQnvZfaOIbkNxxOI0fxW3aBAR3eZ3NO8O4qwuzZwQlKhI0WSRpc9Eo/XsJliUvlqnTzIzU4nZMoQlPJDa1msiElSiClKgBhHskkhxuEh0e1DI4lAomw9VMhqtxB6jhh+SVsM26sJpdeN0SCiVERGnRx4ShCVCXSeG9ZI8Hr9mMd3oar9nsq3orVaiio1HFxaGKjUGhXviMQr+4bWCbApsJnHO+v1OH+8Z06OIhPAa4eslaKMb1O+5bJxK0YArFhy4IgiAsjojpCxchjbLG8X1SvMeYVK3kePgDWJVL5j3Go4A3U+ANg4Jwu5fcM3N0m21oFQpu0kVSFaFH7cdv3VX684Qv+TdU+m68thwcF/4WrzXwjTj+ksM7y5irixnPMAqUxGsySdbmoVX6N0dKliWspjZmjG/jso+h1sYSm1ZNZOJqlMogvUwDClkmzuklyeEm2i0hAzNaFRPhasxaVcAqH067B5vZiX3ODYAmTIUuRosuShuQyp3wPmQJ7+wc3plpvNMzyG4XoEAZGYkqLhZVbFxwKmsAXhfYTb5kzT4DsgRKNejifPvXIuJ8f76CQjGuXzcJmljiKAiCIASbiOl+kmU4+V+w7yHfi9mWR2D9P8IlqkDtFjtf6hjk1JydTZpwFB0zHO2eIitBx8M7S9hWnOzX/rSxsVfp7nkSp3OU5OQd5OU+QEREkBon/AmTyUR9fT0nT54EYOXKlVRVVZGYmOjXeWRZpvd4C00vPsdI93n0cfGU7trNqm03ownWi/Q7PJN2rMdGsR4bQ7K4UUVr0ZWmoC81oI4PzLUdVjfnm0ZpqzdiMlpRh6nIX5dMSVUaKdmBaV4iXJwsyzjOtWE5eJC5gwdxdnQAoM3OJnLLZqK2biVi1SoUfo6UWBCXFXoO+Vr4d+7zVdmUGsiq8nWELNgOscH//2koxvXrZomjSNAEQRCEYBMxfZFmR2DvPb6Ob0tK4bafQHLRvId4JJmfDY3zvf5RIpRKPqbW8XbjED0TVirzEnhkZwnFqdELvgWv18bA4C8YGPg54CUj45NkLf0MavXC97gtltlsprGxkdbWVjweD8uWLaO6uhqDwb8h27IsM3j2FE17nmfo3GkioqJZu+M2Vt+0k3B9cLvlyV4JR7sJa8sojs5pAMLyYn1DsIsTUKgvfwmkLMuM9c3SVm+k69gYHpdEfJqekqo0CisMhOuDVzUUfNzDw8wdOozl4AGszS3g8aCKjyfyhhuI2rIZ/caNKHX+VYIXRPLCUPM789ZehylfgxMMK3171op2+P57EJL1UIzrIkELslB86IIgCMLiiJh+GWQZzv4vvH4/uCyw6StQ+UVQzf/S3W1zcE/7EC2zVm6IjWTDLPz67V5m7W7uLsvkyx8qIDEybMG34XCM0NP7FKOjL6HVJpKTcy9pqXeiUAR//5PFYuHo0aM0NzfjcrkoKCigpqaG9PR0v881fL6dpj3P0XfiGNoIHWu272LtjtvQRccE4c7/nGfGgbVlDNuxMbxmJ0q9Bt26ZN8Q7KTAvLy77B66jo3RVm9kfGAOlVpJzpokllWlkVYQK6pqV4B3bg5LbS2Wg4ew1NYizc2hCAtDv2GDr7q2eTPqpKTgXHyyy5eodbwOQ02ADNFLfB0hC3dAVjWoA9NtNBTjukjQgiwUH7ogCIKwOCKmB4BlAl6/D9pe8v1G/LafQOrKeQ/xyjK/Hp7k8Z4RVAq4Pz2Z0bNT/OfRAcI1Kj63JY+/q8wiTL3wJMs8e4qurm9hNh8nMrKY/PyHiY/bcJkfbmHsdjtNTU00NTVht9vJzs6mpqaGrKwsvxOPsb4emvc8T2dzI2qtllXbtlO66w4i4xOCdPd/JEsyjq5prM2jONpNIMlos6PRl6eiW56AQhOYpHdiaI62eiOdzWO47B5ikiMoqUyjaEMquujAvKQL85NdLmytrcwdPITlwAHcRiMA4atWEvVOC39tXl5wEmfrpK91//nXoeegr+mINgryt/mStfwbfXvXFikU47pI0IIsFB+6IAiCsDgipgdQ28vw2n2+hgFV90LNfaCevxI2YHdyb8cQDTMWqmIj+WJiPP92oIcDHeNkxuv46s1FbF9u8GN/msz4+Gt09zyJwzFMUuKN5OU9iE6XFYAPeGlOp5Njx47R2NiI1WolIyOD6upq8vPz/X7RnbowRPNLz9Pe8DZKpZJlN2yj/LY7iUn2bxnlYnnnXFhbx7C2jOKdcqAIV6Nfm4y+3IDGEJgxB26Xl57j47TVGxnpNqNUKshelUhJVRrpxfEoRWORK0KWZZydncwdOIDl4CEcZ88CoMnMJGrzZiK3bEG3bi0KdRCafbjt0Pv2O0sh3wDrOChUsHTjH5dCxmX5dcpQjOsiQQuyUHzogiAIwuKImB5gNhPs+yqc/i0kFfuqaenr5j1EkmV+Y5zimz1GvDI8nJtKvk3m2691cH5sjvLseL62q4TlSxa+1M/rdTA09Cv6B/4FSXKTkfEJsrM+d0X2pwG43W5OnDhBQ0MDZrMZg8FATU0NRUVFKP0cKjwzNkrLKy9w7vB+JEmiuOoGym//CAlLgt9sAXxVNWefGWvzKPazk+CV0WREEVlmIGJVEsoAtdI3jVhpazBy/sgoDqubqPhwiitTKd6YSmRccBunCH/OPTqK5fBh5g4cxHb0KLLbjTImhshNNURt2Yq+qgpVZBBmEUoSGI9Dx2u+ZG2i3ff3ySW+ZK1wB6StgUv8fygU47pI0IIsFB+6IAiCsDgipgdJ55vw6pfAMgobPgebHwJNxLyHXHC4uP/8EIdMc5TH6HmqYAnNZyd4+q1Opm0u7lybzv03FZIcvfCXdadznJ7epxkZeQGNJo6cnHtIS70L5RVq++3xeDhz5gx1dXWYTCYSExOprq5m+fLlqPzsojdnmuTYq3s4vX8fHreLgvKNVNxxN8lZOUG6+/fyWt3YToxjbR7FM25DoVWhW53k26uWHhmQ5XBet0TvqQna6o1c6JhGoYDM5QmUVKaRtSIBZYDmtwkL47VYsTY0YDl4AMvht/GazSg0GnTr1xO1xVdd06SkBOfipt53hmO/AQONIHsh0gCF233JWvYm0Lw3HoRiXBcJWpCF4kMXBEEQFkfE9CBymOH3j8Lxf4f4XF81ben8e8JkWeb50Wm+1j2MU5K4PzuVjybE8rO3e/h1Qx8alZLPbs7j76uyCfdjP9Ts3Fm6uh5nZqYZvT6f/PxHSIivutxPuGCSJHHu3Dnq6uoYHx8nNjaWqqoqVq9ejdrPZWO2WTPHX3+ZE/v24rLbyFlbRsXuu0grCP48uD+QZRnX4JyvqnZ6AtktoUnVoy8zoFuTjDIiMAmwecJGe8MI7UdGsJld6GK0FG1IpaQyjZik+RN+IfBkjwfb8eNYDh5i7uBB3IODAIQvW/ZuC/+wwsLg7FuzmaDrLTj/GnQf8DUm0ughd7OvhX/+TaD37dMMxbguErQgC8WHLgiCICyOiOlXQM8hePULMDME5Z+GbV8H7fzLo8acbr7SOcS+yVlWR+l4piiDCIfEE2+08+a5MZbERvDgzUXsWpnq1/60iYnf09X9BA7HEIkJW8jL+yp6/ZWrQEmSRGdnJ7W1tRiNRqKioti4cSPr1q1Dq/WvOYbDauHkvr20vvEKjrlZMpatZP0dd5OxbOUV7YgoOTzYTk5gbRnFPWwBtRLdikT05Qa0WYGZeSZ5JfrPTNHWYGTw7BSyDOlFcZRUpZGzKgmVRlTVrjRZlnH19LzbZMR++jTIMpq0NCK3bCFqy2Z0paUo/Px3vSAeJ/TX+TpCnn8D5oygUEJGBRTuoMmcRMWOjwb+updBJGhBJn6YC4IgXD9ETL9CnBY48E1o/leIXQq3/ghyNs17iCzLvDw+w0NdF5jzSNyTlcLnM1No6Zvisb3ttI/Msm5pHI/uKmF1RuyCb0WSnAwN/Tt9/T9BkhykL/k42dmfR6NZ+DkulyzL9Pb2Ultby8DAADqdjg0bNlBWVka4n4OqXQ47p/fv49jePVinTaTmF1Kx+25y1pZd8db1rmEL1pZRbCfGkZ1e1EkRvqra2mRUkYF5UbdMO2hvHKGtwYjF5CRcr6FwvYGSqjTiU4OwL0pYEM/EBHOHD2M5eAhrYyOy04kyKorI6moit2whsqYaVfTC5xwumCzDyElfotbxOoydYcSwjdTP/G/gr3UZRIIWZOKHuSAIwvVDxPQrbKARXv4cmHpg3d/Cjd+E8Pmbf0y6PDzSdYGXxmdYFhnOD4oyKdFH8ELrEN97s5NJi5M71izh/u2FpMYsfNmb0zVJb+8zGI3Po1ZHk5P9BZYs+RhK5ZUdnjwwMEBdXR3d3d2EhYVRUVFBRUUFer1/yYbH5eLs4f20vPICsxPjJC3NpmL3XeRXbESpDP5MuD8lubzYT09ibRnFNTALKgURJQnoyw2E5caiCEB3RkmSudBuoq3eSN+pSSRJJjU3hpKqNHLXJaPRXtnPLPyRZLNhPXKEuYMHsRw6jNdkArUaXVkpUVu2Erl5M9r0JcG5+MwgR480sv7mvwrO+RdJJGhBJn6YC4IgXD9ETL8K3HY49G048mOISoVbnvXNPbqENyZm+ErnBabcHj6fmcI9WSm4XF5+eriHX9b3oVTAZzbl8g81uUT48XI+Z+mgq+txpqcb0elyyc9/iMSEGy7jAy6O0Wikrq6O9vZ2NBoNpaWlbNy4kago/zpPej0eOhrepuml3zFtvEBcWjoVt3+EospNqILRJv0S3GNWrM2+qppk86CKD0dfmoJ+XQqqmIUPJJ+PbdZFxxFfVc08bkcboaagPIWSyjSSMq9M507h4mSvF/up01gOHmDu4CFcvb0AhBUWErV1C5GbtxC+fFlAq72hGNdFghZkofjQBUEQhMURMf0qutAKL3/W10p71Ufhpm+DLn7eQ2bcHr7ebeS5URP5ujCeLcpkbYyeIZON77zRwWtnRkiNCeeB7YXctmrJgudoybLM5OQBurqfwG7vJz6+mvy8h4iMLAjEJ/XL+Pg4dXV1nD17FqVSyZo1a6isrCQuzr/BvZLkpaupkaYXn2NisJ/opBTKb/swyzZtQx2MfUGXILsl7Od8VTVnjxkUEF4Uj77MQHhhPArV5b+gy7KMsWuGtnojPccn8HokkjKjKKlKo6AsBW2AmpcIi+fs6/M1GTl0EPvxEyBJqFNSiNx8A1Fbt6KrqEB5mf8+QzGuiwQtyELxoQuCIAiLI2L6VeZxQu1TUP80RMTDrqeh+JZLHnZwapb7zw8x4nTz6YwkHshORadS0txn4rG9bZwZNrMqI5av7Sph3dKFJzaS5OLChd/Q1/9DvF4baWkfJSf7i2i18yeOwWAymaivr+fkyZMArFy5kqqqKhITE/06jyzL9B5voenF5xjpPo8+Lp7SXbtZte1mNH7udwsUz6Qd67FRrMfGkCxuVNFadKUp6EsNqOMDc08Oq5vzTaO01RsxGa2ow1Tkr0umpCqNlOzANC8RLo/HZMLydq2vhX99A7LdjlKnQ19VRdTWLehralD7+YsJCM24LhK0IAvFhy4IgiAsjojpIWLktK+aNnoalu2Gm78HkUnzHjLn8fJYj5H/ME6RHaHl6aJMNsRGIkkyL54Y5sl9HYzPObl1VRpfubmIJbEL35/mcpno7XsWo/F/UKl0ZGd9gfT0j6NUXvnKk9lsprGxkdbWVjweD8uWLaO6uhqDweDXeWRZZvDsKZr2PM/QudOER0Wz7uZbWb19F+H6yCDd/SXuySvhaDdhbRnF0TkNQFheLPpyAxHFCSjUl9+dUZZlxvpnaas30nVsHI/TS3yanpKqNAorDITrr+yeQ+HiJKcT65Ej71bXvBOToFKhW7vW1xVy6xa0mZkLOlcoxnWRoAVZKD50QRAEYXFETA8hXjc0/ADefhLCouDmJ2H5h+ESlY766Tm+3DHEgMPF3y1J5OGcVCLVKqxODz97u4ef1/r2vHy6JofPbMpFH7bwZW4WSydd3d/GZKojIiLrnf1pW65K9cVisXD06FGam5txuVwUFBRQU1NDenq63+cydrbTtOd5eo+3oI3QsWb7LtbuuA1d9PwNW4LJM+PEdmwUa8sYXrMTpV6Dbl2ybwh2ki4g13DZPXQdG6Ot3sj4wBwqtZKcNUksq0ojrSBWVNVChCxJOM6e9TUZOXAQZ1cXANq8XKI2+5K18JUrUSgvnsCHYlwXCVqQheJDFwRBEBZHxPQQNN7uq6YNt0LhTtj5fYhOnfcQq9fLd3pH+MWFSZaEa/h+YSab4n3NIYZn7Hz3jQ5eOWUkOSqM+28q5MNr0/3anzY1dZiu7iew2XqIi9tIfv7DREUWXfZHXQy73U5TUxNNTU3Y7Xays7OpqakhKyvL7wRjrK+H5j3P09nciFqrZdW27ZTuuoPI+IQg3f2lyZKMo2saa/MojnYTSDLa7Gj05anolieg8GNA+XwmhuZoqzfS2TyGy+4hJjmCkso0ijakoou+8pVS4f25hoawHDzI3MFD2I4dA68XVWIiUZtvIHLzFvQbN6D8k+W6oRjXRYIWZKH40AVBEITFETE9REleOPpTOPgtUIfBTU/A6o9dsprWPGPhno4heuxOPpYaz9dz04jR+CpmrQPTPLa3jZNDM6xYEsOju0ooz1743jJJcjM8/N/09j2LxzNHWtpd5Obcg1br356wQHE6nRw7dowjR45gsVjIyMigurqa/Px8vxO1qQtDNL/0PO0Nb6NUKll2wzbKb7uTmGT/llEGmnfOhbV1DFvLKJ4pB4pwNbo1SejLU9EGaOaZ2+Wl5/g4bfVGRrrNKJUKslYlUlKVRkZx/IITeeHK8M7MYKmrY+7gQay1dUhWK4rwcPSVlURt2ULkDZuoP3Mm5OK6SNCCTPwwFwRBuH6ImB7ipnp8c9MGGyF3q68lf2zGvIfYvRLf7x/lp4PjJGs1PFmYzocSfUv3JEnmlVNGvruvgxGzgx0rDHz15mIy4he+hM7tnqGv70dcGP4NSmU42VmfJSPjEyiVgWkZ7y+3282JEydoaGjAbDZjMBiorq6muLgY5fssAXs/M2OjtLzyAucO70eSJIorN1F++10kpM//PQ82WZJx9pmxNo9iPzsJXhlNRhSRZQYiViWhDAtMVc00YqWtwcj5I6M4rG4i48MoqUyjeGMqkXFXp6GK8P4klwtbc8u7Lfw9o6OgUGDdsoXSn/z4at/enxEJWpCJH+aCIAjXDxHTrwGSBMd+CW993VdBu/GbsO7v4BLJx4lZG/d0DNJhdfDhlDgey19C/DvVNLvLy89re/nZ2z14JZlPVmXz2c25RIUvvGGE1dpLd/cTTE4dJCI8k7y8B0lK+tBV28fk8Xg4c+YMdXV1mEwmEhMTqa6uZvny5ahU/iUwc6ZJWvfu4dRb+/C4XRSUb6TijrtJzsoJ0t0vnNfqxnZiHGvLKJ4xGwqtCt2qJPTlBjTpkQH5/nvdEr2nJmirN3KhYxqFAjKXJVBSlcbSFQmoVJffvEQILFmWcbS1YTl4iG6Xiw1fvvdq39KfEQlakIkf5oIgCNcPEdOvIdMD8OoXoPcwZFXDrT+E+PkTBpck8ezAGM8OjBGrVvNEQTq3JMe++7+Pmh08+WYHLx4fJjFSy30fKuQjpRmo/FjWNjVVR1f341itXcTGVlCQ/zBRUcsW+SEvnyRJtLW1UVtby/j4OLGxsVRVVbF69WrUfg6qts2aOf76y5zYtxeX3UbO2jIqdt9FWkFxkO5+4WRZxjU456uqnZ5AdktoDHr05QZ0q5NQ6gLTndE8Yae9wUj7kRFsZhe6aC1FG1MpqUwlJkDNS4TACsW4LhK0IAvFhy4IgiAsjojp1xhZhhP/CW8+7Ov6uPVrUPEPoJy/QnTOYuee9kFOW+zsTIrhOwXpJGn/+AJ/amiGb+5to3VgmuLUaB7dVczG3IXvLZMkD8aR5+ntfQa3e5rU1DvJzbmXsLDkRX/UyyVJEp2dndTV1TE8PExUVBQbN25k3bp1aP0cBOywWji5by+tb7yCY26WjGUrqdh9F5nLV4VE50PJ4cF2cgJryyjuYQuolehWJKIvM6AN0MwzySvRf2aKtgYjg2enkGVIL4qjpDKNnNVJqDSiqhYqQjGuiwQtyELxoQuCIAiLI2L6Nco8DHvvga43Ib0cbvsJJBXMe4hHkvmXoXG+1zeKXqXksfwlfDgl7t2Xd1mWee3MCE+83sHwjJ0PlaTw0I5ishIX3ozC7Z6lv//HDF34D5RKLVlLP0NGxidRqa7e/iVZlunt7aW2tpaBgQF0Oh3r16+nvLyccD8HVbscdk7v38exvXuwTptIzS+kYvfd5KwtC4lEDcA1bMHaMortxDiy04s6KQJ9mQHd2mRUkYHpzmiZdtDeOEJ7wwhzJgfheg2F6w2UVKURH6DmJcLihWJcFwlakIXiQxcEQRAWR8T0a5gsw5nfwRsPgMsGNzwIG78AqvmX8XVaHdzTMUjrrI1tCdE8WZBOWvgfX9wdbi+/rO/jp4e6cXkl/nZjFp/bkk9MxMKXzNls/XR3f4eJybcID19CXu4DJCfvvOpJzODgILW1tXR3dxMWFkZFRQUVFRXo9f4lFR6Xi3Nv76f55ReYnRgnaWk2FbvvIr9iI8pLVDOvFMnlxX56EmvLKK6BWVApiChJQF9uICw3FkUAujNKksyFdhNt9Ub6Tk0iSTKpuTGUVKWRuy4ZjTY0vhcfNKEY10WCFmSh+NAFQRCExREx/TpgGYfXvgztr0Dqal81zbB83kO8sswvL0zwRO8IaoWCb+Qt4WOp8X+WQI3POnjq9+f5XesF4nRa7rmxgI+WZaD2o0GEafoIXV2PY7G0ExOzjoL8R4iOXrnYTxowRqORuro62tvb0Wg0lJaWsnHjRqKiovw6j9fjoaPhbZpe+h3TxgvEpaVTcftHKKrchMrP/W7B5B6zYm0Zw3Z8DMnmQRUfjr40Bf26FFQxgem+aZt10XF0hLZ6I+ZxO9oINQXlKZRUppGU6d/3Vbg8oRjXRYIWZKH40AVBEITFETH9OnLuJXj9PrBPQ/V9UP1lUM+/pK3P5uTe84McmbFSExfJU4UZZEb8+Qv72WEzj+1to6nPREFKJI/sLKGmIGnBtyXLXowjL9DT833c7ikMhtvJzb2f8LCrO2MMYHx8nPr6es6cOYNSqWTNmjVUVlYSFxfn13kkyUtXUyNNe55nYqCP6KQUym79MMtv2Ibaz/1uwSR7JOznJrE2j+LsMYMCwovi0ZcZCC+MR6G6/KqaLMsYu2ZoqzfSc3wCr0ciKTOKkqo0CspS0EaETuJ6vQrFuC4StCALxYcuCIIgLI6I6dcZ6xTsexDOPA/Jy+D2n0DamnkPkWSZ/zBO8ViPERl4OCeVv1uSiPJPqmmyLPPmuVG+/XoHgyYbW4qSeWhHMXnJkQu+NY9njv6BnzE4+CsUChVLl/4DSzM/hUoVsdhPGzAmk4n6+npOnjwJwIoVK6iuriYx0b8h3LIs03u8haY9zzHSdR59XDylu3azatvNaPzc7xZsnkk71mOjWI+NIVncKKO1vqpaqQF1fGDu1WF1c75plLZ6IyajFbVWSX5pCiVVaaQEqHmJ8F6hGNdFghZkofjQBUEQhMURMf06df4NXxMRyzhUfgE2PQia+V+6hxwu7u8Y4vD0HOtj9DxdlEmO7s+raU6Pl39r6OdHB7txuL18fP1SvrQtn1jdwqtEdvsQ3T1PMj7+OmFhBvJyHyAl5RYUiqvfBdBsNtPY2Ehraysej4dly5ZRXV2NweBftU+WZYbOneboi88xdO404VHRrLv5VlZv30W4fuFJ7ZUgeyUcHSaszaM4OqcBCMuLRV9mIKIkAYX68p+LLMuM9c/SVm+k69g4HqeX+DQ9JZVpFK43EK4PzEgAwScU47pI0IIsFB+6IAiCsDgipl/H7DPw+0d8bfkT8n170zIr5j1ElmV+O2ri693DuCSZr2Sn8umMJFR/UemYtDh5+q1Ofts8SFS4hnu25fN/1i9F48f+tOmZFrq6HmNu7hzR0aspyH+EmJj5q31XisVi4ejRozQ3N+NyuSgoKKC6upqMjAy/z2XsbKdpz/P0Hm9BG6FjzfZdrN1xG7romCDc+eXxzDixHRvF2jKG1+xEqdegW5eMvsyAJkAzz1x2D13HxmirNzI+MIdKrSRnTRLLqtJIK4gVVbUACMW4ft0kaMtS8+Tn/+6pq30b7+HxePwe9CgIgiCEJhHTr396xVnS1L9GwxQm6UbGvHciM39jiMkwFT8oTuBIko7iGSf3tU2SZXW/5+v6ZPh/sopTKElH5v8qvJQqFv6uJSNhTz2GJe8NpLBZwkfXENW1E5XTvz1gweLCQ7dyki7VBC6Fl2QpkmJvCklyJAr8SyQkScLrdiF5vKAAlVqDSq0JSDfFgJNBjQatHIYaLQoUeHDjUjhx48TPj/7+l5FkvB4ZySshy6BQgkqlRKlWIvK0xQvFuL78id0iQQumUHzogiAIwuKImP7BoMROsup3JKgO4JKTGPb8PTa5eN5jZOCQQc+PCuOxq5X8de8Md/ebUf/Fq5QsQxMKfimrMKJgLRKfUnhZ6scLtqRyYl16EOvSwwDoBzajH9iM0huYDoOXy4OXHuUUnapxHAoPCZKOYm8KBjna70RNliQ8bjeSxwOASq1GpdGgUF79JZ4Xo5CVaGUtGsJRoUJGwoULl8KBpPAG5iIyeL0SkldG8vr+gSlVClRqJUqlImAJ4QdFKMb16yZBE0scBUEQhGATMf0Dpr8BXvkcmHqh9JOw7Z8hPHreQyZcbh7uGuaV8RmWR0bwg6IMlke9d7mbyyPxH0f6efZAFzaXl4+VZ3LPjQXE6xe+P83hMNLd8yRjY6+i1SaTl3sfBsPukNifBuB2uzlx4gQNDQ2YzWYMBgPV1dUUFxej9DPBMo+P0vzyC5w7vB9Jkiiu3ET57XeRkO7/MsorQZZlnL1mrM2j2M9OgldGkxGFviwF3aoklGGBSQhMI1baGoycPzKKw+omMj6M4o1pFG9MJSpAzUuud6EY16+bJY4iQRMEQRCCTcT0DyCXDQ49Dkd+AtFL4JZnIX/bJQ97bWKGBzsvMO328PnMFL6UlULYRZISk9XFD/Z38l9Ng+i0Kr64NZ+/2ZCF1o9mEzPmVrq6Hmd29hRRUcspyH+U2NiLvttdFV6vl9OnT1NXV4fJZCIxMZHq6mqWL1+OSuXfcOY50ySte/dw6q19eNwuCso3Ur77LlKyc4N095fPa3VjOzGOtWUUz5gNhVaFblUS+nIDmvTIgOwj87olek9N0FZv5ELHNAoFZC5LoKQqjaUrElD5sd/xgyYU47pI0IIsFB+6IAiCsDgipn+ADbXAy5+FyfOw+v/ATY9DxPx7v0xuD1/rGuaFsWkK9eE8U5TB2mj9Rb+2a2yOx15rp7ZzguxEPQ/tKGZbcfKCX95lWWJs7FW6e57E6RwlOXkHebkPEBEROhUmSZJoa2ujtraW8fFxYmNjqaqqYvXq1X4vMbPNmjn++suc2LcXl91G9ppSKnbfzZLC+ZeiXk2yLOManPNV1U5PILslNAY9+nIDutVJKHWB6c5onrDT3mCk/cgINrMLXbSWoo2plFSmEhOg5iXXk1CM6yJBC7JQfOiCIAjC4oiY/gHndkDtk1D/A9Anwq5noGjnJQ97a9LMA50XGHO6+UxGMvdnG4h4n4rGofPjfGtvGz0TVirzEnhkZwnFqfMvq/xTXq+NgcFfMDDwc8BLRsYnyVr6GdTqqAWfI9gkSaKzs5O6ujqGh4eJiopi48aNrFu3Dq2fg6odVgsn33yN1tdfxjE3S8aylVTsvovM5atCusOh5PBgOzWBtXkU97AF1Ep0KxLRlxnQBmjmmeSVGDg7RVu9kYGzU8gypBfFUVKZRs7qJFQaUVWD0IzrIkELslB86IIgCMLiiJguAGA86aumjZ2F5R+Gm5/0JWzzmPV4+Wa3kd+MTJETEcYzRRlUxF58xpfbK/HfTYM8s7+TWbubu8sy+fKHCkiMXHgTEIdjhJ7epxgdfQmtNpGcnHtJS70ThcK/JYXBJMsyvb291NXV0d/fj06nY/369ZSXlxPu56Bqt8PBqf1vcGzvHqzTJlLzCqm4425y1paFdKIG4Bq2YG0ZxXZiHNnpRZ0Ugb7MgG5tMqpI/xLW92OZdtDeOEJ7wwhzJgfheg2F6w2UVKURn3rxqu4HRSjGdZGgBVkoPnRBEARhcURMF97lcUHDD+DtJ32NQ3Z8D5bdwaX6ndea5vjy+SEuOFx8ckkiD+WkoldfPGmasbl49kAX/3lkgHCNis9tyePvKrMIe5+vvxjz7Cm6ur6F2XycyMhi8vMfJj5ugz+f9IoYHByktraW7u5uwsLCqKiooKKiAr3ev+TB43Jx7u39NL/8ArMT4yQtzaZi913kV2xEqQyd5PRiJJcX++lJrC2juAZmQaUgoiQBfbmBsNzYgIwYkCWZoXYTbfVG+k5NIkkyqbkxlFSlkbsuGY02tL9HwRCKcV0kaEEWig9dEARBWBwR04X3GGvzVdOMx6FoF+z8PkQZ5j3E6vHy7d4Rfjk8SUa4lqcLM6iOf/8liD0TFr79WjsHOsbJjNfx1ZuL2L7c4Mf+NJnx8dfo7nkSh2OYpMQbyct7EJ0uy59PekUYjUbq6upob29Ho9FQWlrKhg0biI5e+DJPAK/HQ0fD2zS99DumjReIS0un4vaPUFS5CVWItVS/GPeYFWvLGLbjY0g2D6q4MPSlBvSlKahiAjNOwTbrouPoCG31RszjdrThKgrKfVW1pMzQWRIbbKEY10WCFmSh+NAFQRCExRExXbgorweO/gQOPg6aCNj+HVj1V5esph2dsXBvxxC9dicfT03ga3lpRM9THavrmuBbe9s5PzZHeXY8X9tVwvIlMQu/Ta+DoaFf0T/wL0iSm4yMT5Cd9bmQ2p/2B+Pj49TX13PmzBmUSiVr1qyhsrKSuDj/hnJLkpeupiM07XmOiYE+opNSKLv1wyy/YRtqP/e7XQ2yR8J+bhJr8yjOHjMoILwoHn2ZgfDCeBSqAFTVZBlj1wxt9UZ6jk/g9UgkZUZRUpVGQVkK2ojQT2gvRyjGdZGgBVkoPnRBEARhcURMF+Y12QUvfw6GjkLejXDLDyAmfd5D7F6J7/WN8rOhcVLCNDxZkM6Nie+fdHm8Er9tGeLptzqZtrm4c206999USHL0wvdsOZ3j9PQ+zcjIC2g0ceTk3ENa6l0olaH3Im4ymWhoaODEiRPIsszKlSuprq4mMXH+PX9/SZZl+k4c4+iLv2Wk6zz6uHhKd+1m1bab0fi53+1q8UzZsbaMYW0dRZpzo4zWol+Xgr7MgDpAM88cVjedzaO01RuZGrai1irJK01hWVUaKQFqXhJqQjGuiwQtyELxoQuCIAiLI2K6cEmSBC3/D/Z/AxQq+NBjsO5vL1lNOz5r5Z6OIc5bHdyZEsdj+UuI07x/wmS2u/nJoW5+3dCHRqXks5vz+PuqbMI1C99DNDt3lq6ux5mZaUavzyc//xES4qsWfPyVZDabaWxspLW1FY/HQ0lJCTU1NRgM8y8n/UuyLDN07jRHX3yOoXOnCY+KZt3Nt7J6+y7C9Rdv2hJqZK+Eo8OEtXkUR+c0AGF5sejLDESUJKDwY4be+15Dlhnrn6Wt3kjXsXE8Ti/xaXpKKtMoXG8gXB+YkQChIBTjukjQgiwUH7ogCIKwOCKmCwtm6oNXvwB9tZBdA7f8EOKz5z3EKUn8oH+MHw2OEadR852CdHYmxc57TP+klSfeaOfNc2MsiY3gwZuL2LUy1a/9aRMTv6er+wkcjiESE7aQl/dV9PqchX7SK8pisXD06FGam5txuVwUFBRQXV1NRob/896Mne007Xme3uMtaCN0rNm+i7U7bkMXvfBlo1ebZ8aJ7dgo1pYxvGYnSr0a3doU3xDsAM08czk8dLWM0VZvZHxgDpVaSc6aJEqq0lhSEHvNV9VCMa6LBC3IQvGhC4IgCIsjYrrgF1mG4/8Obz4Cshe2fh3KPw3K+SscZ+ds3NMxxBmLnVuSYvl2wRKStPNXLBp7JnlsbzvtI7OsWxrH13aVsCojdsG3KklOhob+nb7+nyBJDtKXfJzs7M+j0Sz8HFeS3W6nubmZo0ePYrfbyc7OpqamhqysLL8ThvH+Xpr2PE9nUwNqrZaVW7dTestuouL9W0Z5NcmSjLNr2jcEu90Ekow2K9o3BHtFIgo/KqvzmbwwR1udkfPNY7jsHmKSIiipSqNoQyq66NDf03cxoRjXRYIWZKH40AVBEITFETFdWBTzBXj1S9D9FmSsh9t+Aol58x7ilmR+OjjO9/tHiVQr+VZ+OruT569WeCWZ3x0b4qnfn2fS4uKONUt4YHsRhhg/9qe5JuntfQaj8XnU6mhycr7IkrSPolSG5pI2p9NJa2srjY2NWCwW0tPTqampIT8/3+9EberCEM0v/472+sMolUqW3bCN8tvuJCbZv2WUV5t3zoW1dQxbyyieKQeKcDW6NUnoy1PRBmjmmdvlpef4OG31Rka6zSiVCrJWJVJSlUZGcTzKAIwEuFJCMa6LBC3IQvGhC4IgCIsjYrqwaLIMp5+DN74CHgdsfgjWfxZU8zfmOG91cE/HIMdnbXwoIZrvFqaTGjZ/pWLO4eanh3v4ZV0fKqWCz2zK5dM1OUT4MeNqbq6dru7HmZ4+gk6XS37+QyQm3LDg4680t9vNiRMnaGhowGw2YzAYqK6upri4GOUlKpZ/yTw+Sssr/8vZQ28hSRLFlZsov/0uEtL9X0Z5NcmyjLPXjLVlFPvZSfDIaDKi0JeloFuVhDIsME1hpkettNUb6Tg6isPiJjI+jOKNaRRvTCUqQM1LgikU47pI0IIsFB+6IAiCsDgipguXbW4MXrsXOvZC2lpfNS2lZN5DvLLM/xua4Dt9I2iVCv45bwl/ZYi/ZIVoyGTjO2908NqZEVJjwvnK9iJuXZW24OqGLMtMTh6gq/vb2O0DJMTXkJf/EJH6/AV/3CvN6/Vy+vRp6urqMJlMJCYmUlVVxYoVK1Cp/FvmN2eapHXvHk7t34fH5aKgfCPlu+8iJTs3SHcfPF6rG9uJcawto3jGbCi0KnSrknx71dIjA7KPzOuW6D01QVu9kQsd0ygUkLksgZKqNJauSECluvzmJcEQinFdJGhBFooPXRAEQVgcEdOFgJBlOLcHXr8fHGbY9ABU3QOq+ZcR9tqc3NsxyFGzlRviovheUQYZ4Zfe99PcZ+Kbe89xdniW1RmxPLqrhHVLFz5PTJJcXLjwG/r6f4jXa2NJ2sfIzv4CWm38gs9xpUmSRFtbG3V1dYyNjREbG0tVVRWrV69G7eegatusmeOvv8KJfa/istvIXlNKxe67WVJYHKS7Dx5ZlnENzvmqaqcmkN0SGoPet1dtdRJKXWCWspon7LQ3GGk/MoLN7EIXraVoYyollanEBKh5SaCEYlwXCVqQheJDFwRBEBZHxHQhoKyTviWPZ1+AlBVw248hbfW8h0iyzL8NT/Kt3hEUwKO5afxNWgLKS1RAJEnmxRPDPLmvg/E5J7euSuMrNxexJDZiwbfrcpno7XsWo/F/UKn0ZGd9nvT0j6NUhm5zCFmW6ezspLa2luHhYaKioti4cSPr1q1D6+egaofVwsk3X6P19ZdxzM2SsWwlFbvvInP5qmuyk6Hk8GA7NYG1eRT3sAXUSnQrEtGXGdAGaOaZ5JUYODtFW72RgbNTyDIsKYxjWVUaOauTUGmuflUtFOO6SNCCLBQfuiAIgrA4IqYLQdHxGuy9F6wTUPUlqHkANPPv3Rm0O7nv/BC10xY2xOp5ujCTbF3YJS9ldXr42ds9/Ly2F4BP1+TwmU256P3Yj2SxdNLV/W1MpjoiIrLe2Z+2JaSTFFmW6e3tpa6ujv7+fnQ6HevXr6e8vJxwPwdVux0OTh/YR8urL2KdNpGaV0jFHXeRs7Y8pL8H83ENW7C2jGI7MY7s9KJOikBfZkC3NhlVZGAScMu0g/bGEdobRpgzOQjXayhcb6CkMo34tMA0L1mMUIzrIkELslB86IIgCMLiiJguBI192teO/+RvILHQtzcto2zeQ2RZ5n9GTHy9exiPLPNgTiqfSk9CtYAkYXjGznff6OCVU0aSo8K4/6ZCPrw23a/9aVNTh+nqfgKbrYe4uI3k5z9MVGTRgo6/mgYHB6mtraW7u5uwsDDKy8tZv349er1/SYLH5eLc2/tpfvl/mZ0YIykzi4o77ia/YiNKZWDa2l9pksuL/cwk1uZRXAOzoFIQUZKAvsxAWF4sigB0Z5QlmaEOE231RvpOTiJJMoacGEqq0sgrTUbjRzObQAjFuC4StCALxYcuCIIgLI6I6ULQde+HV74Is8Ow4bOw+WHQzr9nx+hw8UDnBfZPzbIuWsczRZkU6BdWFWodmOaxvW2cHJphxZIYHt1VQnn2wveWSZKb4eH/prfvWTyeOdLS7iI35x602tCfIWY0Gqmrq6O9vR2NRkNpaSkbNmwgOjrar/N4PR46Gt6m6aXfMW28QFxaOuW33Ulx1Q2o/NzvFkrcY1asLWPYjo8h2Tyo4sLQlxrQl6agirl0tXYhbLMuOo76qmozYza04SoKyg2UVKWRlBkVkGtcSijG9ZBN0BQKRSbwQ8AEdMqy/J35vl4kaIIgCEKwiZguXBGOWdj/DTj2S4jL9u1Ny6qa9xBZlnlxbJpHuoaxeiXuyzbwTxnJqBdQ8ZAkmVdOGfnuvg5GzA52rDDw1ZuLyYhfeDMHt3uGvr4fcWH4NyiV4WRnfZaMjE+gVAbmRT6YxsfHqa+v58yZMyiVStasWUNlZSVxcQtvpAIgSV66mo7QtOc5Jgb6iE5KpuzWO1l+wzbUfu53CyWyR8J+zldVc/aYQQHhhfHoyw2EF8ajUAWgqibLGLtmaGsw0tM6gdcjkZQZRUlVGgVlKWgjgpfohmJcD0qCplAofgXsAsZlWV7+J3+/HXgWUAG/mC/pUigUO4E4WZZ/o1AonpNl+e75rikSNEEQBCHYREwXrqi+Wnjl8zDdD2Wfgm3fgLD5qwoTLjcPdl7gtQkzKyMjeKY4k2WRC2sEYnd5+XltLz97uwevJPPJqmw+uzmXqPCFd/azWnvp7n6CyamDRIRnkpf3IElJH7om9maZTCYaGho4ceIEsiyzcuVKqqurSUz0rxooyzJ9J45x9MXfMtJ1Hn1cPKU7b2fljTejDV94U5ZQ5JmyY20Zw9o6ijTnRhmtRb8uBX2ZAXWAZp45rG46m0dpqzcyNWxFrVWSV5rCsqo0UgLUvORPhWJcD1aCVgNYgP/4Q4KmUChUQCdwI3ABaAE+ii9Ze+IvTvFJwAu8AMjAf8qy/Ov5rikSNEEQBCHYREwXrjiXFQ5+C47+C8Skwy3PQt7WSx726vgMX+28wIzHwxeWpvClpSloFziwedTs4Mk3O3jx+DCJkVru+1AhHynNQOXH/qOpqTq6uh/Hau0iNraCgvyHiYpatuDjryaz2UxjYyOtra14PB5KSkqorq4mNTXVr/PIsszQudM07XmOwbOnCY+KZt3Nt7J6+y7C9ZFBuvsrQ/ZKODpMWJtHcXROgwxh+bHoywxElCSgUF9+d0ZZlhnrn6W93kjnsXE8Ti/xaXpKKtMorDAQHhmYkQChGNeDtsRRoVBkAXv/JEHbAHxDluWb3vnzVwFkWf7L5OwPx98HNMuyXKtQKF6QZfnO+a4nEjRBEAQh2ERMF66awSZ4+bMw1QVrPg4fehwiYuc9ZMrl4Wvdw/zv2DRF+nB+UJTJ6uiFL1s8NTTDN/e20TowTXFqNI/uKmZj7sKrSZLkwTjyPL29z+B2T5Oaeie5OfcSFpa84HNcTRaLhaNHj9Lc3IzL5aKgoIDq6moyMjL8Ppexs52mPc/Te7wFbYSO1TftZN3O29FFxwThzq8sz4wT27FRrMfG8M44UerV6Nam+IZgB2jmmcvhoatljLZ6I+MDc6jUSnLWJFFSlcaSgtjLqqqFYly/kgnancB2WZY/9c6f/xqokGX5c+9z/HLgG8AkYJFl+b6LfM2ngU8DpKSkrPvtb3+76PsNFovFQmTktf1bEkEQBMFHxHThalJ6XSwd+C2Zg3twaWPpLPhHphLLL3lcq6zmF+iYQcEtOLkTB9oFvs/KskzLqJfnzruYcsisTVZxd6GWFP3CKySybEOWX0XmAKBGodiJghtRKK6NfVlut5vh4WEuXLiAx+MhNjaWpUuXEhvrf2Jgmxxn9PhRpns6UajVJJWsImVVKdrIK9MQI6hk0E1C9AUl+nFQyArscTKz6TIWg4wcoOaMjmmZ6V6ZmX6Q3KCNhNhcBXHZoA73P1ELxbi+efPm0EzQ/CUqaIIgCEKwiZguhITh4/Dy52D8HKz4CGz/LugT5j3E7Pbwzz1G/nvERJ4ujKcLMyiPXfhLqcPt5Zf1ffzkUDdur8Tfbszic1vyiYlY+DIzm62f7u7vMDH5FuHhS8jLfYDk5J3XxP40AKfTSWtrK42NjVgsFtLT06mpqSE/P9/vzzA1PETzS7+jvf4wSqWSZZu2UXbbncSmGIJ091eWd86F7fgY1uZRPFMOFOFqdGuSfEOw0wKTDHlcXnqOj3Ou3shItxmlUkHWqkRKKtPIKIlf8MiIUIzrIbvE0V8iQRMEQRCCTcR0IWR4XFD/NNR+D8JjYedTsGz3JQ972zTHl88PMuxw86n0RB7MSUWvWnhpY3zWwVO/P8/vWi8Qp9Ny740F/FVZBmrVwitqpukjdHU9jsXSTkzMOgryHyE6euWCj7/a3G43J06coKGhAbPZjMFgoLq6muLiYpQL3Of3B+bxUVpe+V/OHnoLSZIortxE+e13kZDu/zLKUCTLMs5eM9aWUexnJ8Ejo0mPRF9uQLcqCaUfA9LnMz1qpa3eSMfRURwWN5HxYRRvTKN4YypRl2heEopx/UomaGp8TUK2AsP4moR8TJblc4u+yJ8QCZogCIIQbCKmCyFn9Kxvb9rISSi+FXY8BVEp8x5i8Xh5vHeEXw9Pkhmu5emiDKri/Ftid3bYzDf3ttHcZ6IgJZJHd5VQnZ+04ONl2Ytx5AV6er6P2z2FwbCb3Nz7CA+7dipIXq+X06dPU19fz9TUFImJiVRVVbFixQpUfiS9AHOmSVr37uHU/n14XC7yyzdQsftuUrJzg3T3V55kc2M9Po61ZRTPmA2FVoluVbJvr1p6ZEAqqV63RO+pCdrqjVzomEahgMxlCZRUpbF0RQKqi/wiIRTjerC6OP4PcAOQCIwBX5dl+ZcKhWIH8AN8nRt/Jcvy44u6wEWIBE0QBEEINhHThZDk9cCRH8GhJ3xDrbd/F1beBZd44T0yY+HejkH67C7+Ji2BR3PTiFIvPLGQZZk3z43y+OvtDJnsbC1K5qGdxeQmLXwJm8czR3//vzA49GsUChVLl/4DSzM/hUp17bSjlySJtrY26urqGBsbIzY2lqqqKlavXo3az0HVtlkzx19/hRP7XsVlt5G9ppSK3XezpLA4SHd/5cmyjGtoDmvzKPZTE8huCY1Bh77MgG5NMkpdYLozzk7aaWsw0t44gs3sQhetpWhDKiVVqcT8SfOSUIzrITuo2l8iQRMEQRCCTcR0IaRNdPqqaReaIf8m2PUMxCyZ9xCbV+LJvhF+PjSBIUzD9woz2JoQ7ddlnR4v/9bQz48OduNwe/nrDUv54tZ8YnULbwJitw/S3f0k4xNvEBZmIC/3AVJSbkGhuPx27VeKLMt0dnZSW1vL8PAwUVFRbNy4kXXr1qH1c1C1w2rh5Juv0fr6yzjmZskoWUHFHXeTuXzVNbNnbyEkhwfbqQmszaO4hy2gVqJbkejbqxagmWeSV2Lg7BRt9UYGzk4hy7CkMI5lVWnkrE6irqE25OL6dZOgZWVlyV//+tev9m28x8zMDLGxsVf7NgRBEIQAEDFdCHUKWaJ4ro51M3uRUNEcdxtdkesvWU0bDNPxvwmZjGsjWGuZYqdpGJ3k9evaFo+CQ5ORnDCHE66U2ZRopTTWjsqPd+ywsAHi4t5CGzaK07mEadONuFzpft1HKHA4HMzMzOB0OlEqlURHRxMVFeX3HjVZkrDOmJidmkRye9BGRBCdlEz49dD18S/ILi/eWReSxY0syyjUSlTRWlSRWvz6RzQPr0fCNuvCZnbh9UgolArUETJJabEBOX+gfPKTnxQJWjCJH+aCIAjXDxHThWtFlHuSyqnfkursZji8gMaEu7Go5+/06EHBwVgDb8ekoPd6uM00xDKb2e9rjzlUvDkRRZ9NS6LWw4eSLORHuvw4g4xef5qY2EOo1Ras1mXMTG/B6732ZoY5nU7MZjN2ux2FQkF0dDTR0dH+J2qyjG1mmtmpCbwuN5rwcKISk66LOWrvIYNkdfuSNacHAJVegzJKizIiME1FAJw2D1azEwk3iamxATtvIFw3CZpY4igIgiAEm4jpwjVFkuD4v8HvvwayBNu+AWWfgkskB2fmbHypY5BzFge3JcfyeH46iVr/XoxlWWZ/+zjffr2dvkkrNQVJPLKzmIKUhVd+PB4rA4P/yuDgLwDIzPy/LM38NGq13q97CQVGo5G6ujra29vRaDSsW7eOjRs3Eh3t33JSr8dDR8PbNL/0O0zGC8SlLqH89o9QXHUDKj/3u10L3GNWrC1j2I6PIdk8qGLD0JcZ0JemoIoJC8g1QjGuXzdLHEWCJgiCIASbiOnCNWlmCF79IvQcgMyNcNuPIWH+7oBuSebHg2M83T9GlFrJt/PTuS3Z/8HMLo/Efxzp59kDXdhcXj5Wnsk9NxYQr1/4niyHw0h3z5OMjb2KVptMXu59GAy7r6n9aX8wMTFBXV0dZ86cQalUsmbNGiorK4mLi/PrPJLkpavpCE17nmNioI/opGTKbr2T5TdsQ+3nfrdrgeyRsJ+bwtoyirN7BhQQXhiPvtxAeGE8istYAhmKcV0kaEEWig9dEARBWBwR04VrlizDyf+GN78KHidseQTW/xMo5+/a2G6xc0/HECfnbNycGMN3CtJJCfO/y57J6uIH+zv5r6ZBdFoVX9yaz99syEKrXniSNWNupavrcWZnTxEVtZyC/EeJjb3oO2zIM5lMNDQ0cPLkSSRJYuXKlVRVVZGUtPBRBeCrVPadOMbRF3/LSNd59HHxlO68nZU33ow2/NrphOkPz5Qda8sY1tZRpDk3ymgt+nUp6MsMqC8x8+xiQjGuiwQtyELxoQuCIAiLI2K6cM2bHYHX7oXzr8OSdXDbTyB5/hbuHknmXy9M8GTfCOFKJd/MW8JdhrhFddjrGpvjsdfaqe2cIDtRz0M7itlWnLzgc8myxNjYq3T3PInTOUpy8g7ych8gIuLaHOw8OztLY2Mjx44dw+PxUFJSQnV1NampqX6dR5Zlhs6dpmnPcwyePU14VDRrb76FNdtvIVy/8LEH1xLZK+HomMbaMorjvAlkCMuPRV9mIKIkAcUCk/9QjOsiQQuyUHzogiAIwuKImC5cF2QZzv4vvH4/uCyw6QGo/BKo5q+Mddsc3NsxRLPZyub4KL5XmEF6+OKW0x06P8639rbRM2GlMi+BR3aWUJy68P1YXq+NgcFfMDDwc8BLRsYnyVr6GdTqa7O7ocVi4ejRo7S0tOB0OsnPz6empoaMDP8TT2NnB017nqP3eAvaCB2rb9rJup23X58NRd7hmXFiOzaK9dgY3hknSr0a3VpfVU2TrJv32FCM6yJBC7JQfOiCIAjC4oiYLlxXLBPwxgNw7kUwrIDbfgqpK+c9RJJlfjU8yeM9I6gU8LXcND6eloByEdU0t1fiv5sGeWZ/J7N2N3eXZfLlDxWQGLnw5g8Oxwg9vU8xOvoSWm0iOTn3kpZ6JwrFwgduhxK73U5zczNHjx7FbreTnZ1NdXU12dnZflcsx/t7adrzPJ1NDag1WlZu207pLbuJik8M0t1ffbIk4+zyVdXsbSaQZLRZ0ejLDehWJKLQvPffRSjGdZGgBVkoPnRBEARhcURMF65L7a/C3nvBboKqe6DmflDPnyQN2J18uWOI+hkLlbGRPF2UwdKIxXXVm7G5ePZAF/95ZIBwjYrPbcnj7yqzCFMvPMkyz56iq+tbmM3HiYwsJj//YeLjNizqfkKB0+mktbWVxsZGLBYL6enp1NTUkJ+f73eiNjU8RMvLL9BWdwilUsmyTdsou+1OYlMMQbr70OCdc2E7Poa1ZQzPpB1FuArdmmTfEOy0Py77DMW4LhK0IAvFhy4IgiAsjojpwnXLZoI3H4ZT/w1JRb69aenzN+CQZZn/GjHxje5hvDI8lJPKJ9MTUS2imgbQM2Hh26+1c6BjnMx4HQ/tKOKmZQY/9qfJjI+/RnfPkzgcwyQl3khe3oPodFmLup9Q4Ha7OXnyJPX19ZjNZgwGA9XV1RQXF/s9S808PkrLK//L2UNvIUkSRZWbqLj9IySkZwbp7kODLMs4e82+qtrZSfDIaNIjfVW1VUnUHqkPubguErQgEz/MBUEQrh8ipgvXva63fC3550Zgw2dh88Ogmb8b4LDDxf3nhzhomqMsWs/TRRnk6/3vpvcHtZ0TfOu1NjrHLFRkx/PorhKWL1n4/imv18HQ0K/oH/gXJMlNRsYnyM763DW7Pw3A6/Vy+vRp6uvrmZqaIjExkaqqKlasWIFK5d9yTotpimN793Bq/xt4XC7yyzdQsftuUrLnH71wPZBsbqwnxrE2j+IZs6HQKplc6mHV32+62rf2Z0SCFmTih7kgCML1Q8R04QPBMQtvfQ1afw3xub65aUs3znuILMu8MDbNo13D2CWJ+7IM/GNGMmrl4qppHq/Eb1uGePqtTqZtLj6yLp37PlRIcvTCEz+nc5ye3qcZGXkBjSaOnJx7SEu9C6Xy2h3oLEkSbW1t1NXVMTY2RmxsLJWVlaxevRqNxr/xB7ZZM8dff4UT+17FZbeRvaaUit13s6Rw/q6e1wNZlnENzWFtHqXfPsLavxYJWlCIBE0QBEEINhHThQ+U3sPwyhdgZgDKPw1bvw5h87dsH3e6ebDzAq9PmlkZFcGzRZkURy5+HpfZ7ubHB7v4t8Z+tCol/7Q5j7+vyib8Is0e3s/s3Fm6uh5nZqYZvb6A/PyHSYivWvQ9hQJZluns7KS2tpbh4WEiIyPZuHEjpaWlaP0cVO2wWjj55mu0vv4yjrlZMkpWULH7bjJXrFrUKIVrTSjGdZGgBVkoPnRBEARhcURMFz5wnBY4+Bg0/SvEZsAtP4TczfMeIssyr0zM8FDnMLMeL19cmsIXliaj9XPP1J/qn7Ty7dfb+X3bGEtiI3jw5iJ2rUz1a3/axMSbdHV/B4djiMSELeTlfRW9PmfR9xQKZFmmr6+P2tpa+vv70el0rF+/nvLycsLD/Vtm6nY4OH1gH8defRHLtAlDXgHr77ibnLXl13WiFopxXSRoQRaKD10QBEFYHBHThQ+sgSPwyudgqhvW/g186FsQPv++sEmXh0e7LrBnfIYSfTjPFGeyKmr+mVSX0tgzyWN722kfmaV0aRyP7iphVUbsgo/3ep1cuPBv9PX/FElykJ7+12RnfR6N5tqfETY4OEhdXR1dXV2EhYVRXl7O+vXr0ev1fp3H43Zz7vB+ml9+gdmJMZIysyjffRcF6ytRKq/N8QXzCcW4LhK0IAvFhy4IgiAsjojpwgea2w6Hn4DGH0GkAW75ARTcdMnD9k2Y+UrnEJNuD5/NSObeLAPhqsVX07ySzO+ODfHU788zaXFxx5olPLC9CEOMH/vTXJP09j6D0fg8anU0OTlfZEnaR1Eq/dvHFYqMRiN1dXW0t7ej0WhYt24dGzduJDp64YPAAbweDx0Nb9P80u8wGS8Ql7qE8ts/QnHVDajU1+4+vr8UinFdJGhBFooPXRAEQVgcEdMFARhuhZc+CxPtsPKvYPsToIuf95AZt4dvdBv57aiJfF0YzxRlUhrjX2XnL8053Pz0cA+/rOtDpVTwmU25fLomhwjtwqs8c3PtdHU/zvT0EXS6XPLzHyIx4YbLuq9QMTExQV1dHWfOnEGpVLJ69WqqqqqIi4vz6zyS5KWr6QhNe55jYqCP6KRkym75MMs334jaz/1uoSgU47pI0IIsFB+6IAiCsDgipgvCOzxOqPu+7z8R8bDz+1By6yUPOzQ1y33nhzA63Xw6PYmv5KSiu4xqGsCQycZ33ujgtTMjpMaE85XtRdy6Kg3lAjtIyrLM5OQBurq/jd0+QEJ8DXn5DxGpz7+s+woVJpOJhoYGTp48iSRJrFy5kqqqKpKSkvw6jyzL9J04xtE9zzHS2YE+No7SXbtZeePNaMMX3wjmagvFuC4StCALxYcuCIIgLI6I6YLwF0bPwEv/BKOnoeR22PEURM7/4j/n8fKtHiP/bpwiK0LL9wszqIy7/BllzX0mvrn3HGeHZ1mdEcuju0pYt3Th1SJJcnHhwm/o6/8hXq+NJWkfIzv7C2i181cHrxWzs7M0NjZy7NgxPB4PJSUlVFdXk5qa6td5ZFlm6NwZmvb8lsGzpwmPjGLtjltZs/0WwvXzd/kMRaEY10WCFmSh+NAFQRCExRExXRAuwuuGxh/C4e+ANhJufhJW3AmX6PzXMD3HvR1DDDhcfCItgUdz04hUX14TCkmSefHEME/u62B8zsmtq9L4ys1FLIldeIXH5TLR2/csRuP/oFLpyc76POnpH0epvPaX8wFYLBaOHj1KS0sLTqeT/Px8ampqyMjI8Ptcxs4OmvY8R+/xFrQROlbftJN1O29HF33tNF0JxbguErQgC8WHLgiCICyOiOmCMI+J8/DyZ+FCCxTcDLuehui0eQ+xer082TvKzy9MkBam4anCDDYn+NfM4qLndXr42ds9/Ly2F4BP1+TwmU256MMW3tzCYumkq/vbmEx1RERkvbM/bct103LebrfT3NzM0aNHsdvtZGVlUVNTQ3Z2tt+fcby/l6Y9z9PZ1IBao2Xl1psoveUOohISg3T3gROKcV0kaEEWig9dEARBWBwR0wXhEiQvHP0X3+w0VRjc9Dis+fglq2nHzFbu6Riky+bko6nxfCM3jRjN5XcKHJ6x8903OnjllJHkqDDuv6mQD69N92t/2tTUYbq6n8Bm6yEubiP5+Q8TFVl02fcWKpxOJ62trTQ2NmKxWEhPT6e6upqCggK/E7Wp4SFaXn6BtrpDKBRKlt+wjbLb7iQ2xRCku798oRjXRYIWZKH40AVBEITFETFdEBZoqgde+TwMNEDOZrj1hxCbOe8hDq/E9/tH+enQOIkaNU8WZnBTYmCWyrUOTPPY3jZODs2wYkkMj+4qoTx74XvLJMnN8PB/09v3LB7PHGlpd5Gbcw9abehXiBbK7XZz8uRJ6uvrMZvNGAwGqqurKS4uRunnkHHz+Cgtr/wvZw+9hSRJFFVuouL2j5CQPv+/gashFOO6SNCCLBQfuiAIgrA4IqYLgh8kCY79Et76uq+Ctu0bUPr3cImX/ZOzNu7pGKTd6uCOlDgey1tCgvbyq2mSJPPKKSPfeaOD0VkHO1ek8uDNRWTEL3x4tts9Q1/fj7gw/BuUynCysz5LRsYnUCrDLvv+QoXX6+X06dPU19czNTVFQkIC1dXVrFixApXKvz2CFtMUx/bu4dT+N/C4XOSXb6Bi992kZOcG6e79F4pxXSRoQRaKD10QBEFYHBHTBWERpgfg1S9C7yFYWuWrpiXM/4LukiR+ODDODwZGiVGreaIgnVuSYgKy/8vm8vDz2l7+9e1evLLM31dl80835BIVvvAh1VZrL93dTzA5dZCI8Ezy8h4kKelD183+NABJkmhra6Ouro6xsTFiY2OprKxk9erVaDT+DfS2zZo5/vornNj3Ki67jezV66jYfTdLikqCdPcLF4pxXSRoQRaKD10QBEFYHBHTBWGRZBlO/AbefBi8Ltj6KFR8BpTzV2TaLHa+1DHI6Tk7O5NieCI/neQw/5KD9zNitvO9fed58cQwiZFh3PehAj5SmoFqgfvTAKam6ujqfhyrtYvY2AoK8h8mKmpZQO4vVMiyTGdnJ7W1tQwPDxMZGcnGjRspLS1F6+egaqfNysk3X6P1tZewz82SUbKCit13k7li1VVLbkMxrosELchC8aELgiAIiyNiuiBcplkj7L0HOvdBehnc9hNIKpz3EI8k8y9D4zzVP0qEUslj+Uu4MyUuYC/0J4dmeGxvG60D0xSnRvPormI25i58b5kkeTCOPE9v7zO43dOkpt5Jbs69hIUlB+T+QoUsy/T19VFbW0t/fz86nY7169dTVlZGRIR/g6rdDgenD+zj2KsvYpk2YcgrYP0dd5OztvyKJ2qhGNdFghZkofjQBUEQhMURMV0QAkCW4cwL8Mb94LLCDQ/Cxi+Aav7KWJfVwT0dgxybtbE1PprvFaaTFh6Y2WSyLLP39AjfeaOD4Rk7HypJ4aEdxWQl6hd8Drd7lv7+HzN04T9QKrVkLf1HMjI+iUp1/exP+4PBwUHq6uro6uoiLCyM8vJy1q9fj16/8O8XgMft5tzh/TS//AKzE2MkZWZRvvsuCtZXorxEdTVQQjGuiwQtyELxoQuCIAiLI2K6IASQZRxevx/aXoLUVb5qmmHFvId4ZZlfXZjk271G1AoFX89bwv9JjQ9Y1cXh9vLL+j5+cqgbt1fi7yqz+dyWPKL92J9ms/XR3f1dJibfIjx8CXm5XyE5ecd1tT/tD0ZGRqirq6OtrQ2NRsO6devYuHEj0dH+zbLzejx0NLxN80u/w2S8QFzqEspvu5Pi6s2o1JffIGY+oRjXRYIWZKH40AVBEITFETFdEIKg7WV47ctgn4bqL0P1faCevzLWb3dyb8cQjTMWquMieaowg6URgatUjc86eOr35/ld6wXidFruvbGAvyrLQK1aeLt5k6mRru7HsVg6iIlZR0H+I0RHrwzYPYaSiYkJ6urqOHPmDEqlktWrV1NVVUVcXJxf55EkL93NRzi653km+nuJTkqm7JYPs3zzjaj93O+2UKEY10WCFmSh+NAFQRCExRExXRCCxGaCfV+F07+F5BK47cewZN28h0iyzG+MU3yzx4hXhodzU/nkkkSUAaxUnR028829bTT3mShIieTRXSVU5yct+HhZ9mIceYGenu/jdk9hMOwmN/c+wsNCd3Dz5TCZTDQ0NHDy5EkkSWLlypVUVVWRlLTw7xm8s9/txDGO7nmOkc4O9LFxlO7azcobb0Yb7t9+t0sJxbh+3SRoJSUJ8n/+5qarfRvvMTMzQ2xs7NW+DUEQBCEAREwXhOCKHhtj6amzaBwOxvJyMBYWIF9i9ta4FMWP7Ddx3JPDMtUQX4zYxxLVdMDuSZahaTiDfz+1hnFrFOtSL/CJVcdZEj3nxzk8OBxGnM5RQEF4eCphYakoFFdmn9WV5vV4MM/OMjc3hyzL6PU6YmJi0Gr9rXLKOK1WZifHcVqtKFUqIuMTiIxPROnnTLb3E4pxvXTd/4gELZhC8aELgiAIiyNiuiAEn9LtJr2tnaSBIRx6Pf2rV2JNiJ/3GFmGA+5l/Ny+FTcqPh7ewO3aFlSKwL3Lur1KXusq5IW2Fbi8KrbndfKRkjNEhbkWfA5JcmC3D+F2m1AoNEREZKLVJgDX3/408A29npudZXZuFkmS0UVEEBMbQ1hYuN/nctlszE6O47DMoVAqiYxPICo+EeVl7lELxbh+3SRoYomjIAiCEGwipgvCFdRzCF79AswM+WambX0UtPN3CRxzuvlK5xD7JmdZHaXjmaIMiiMDuyRuYs7J02918lzLINERGr60NZ//s34pGj/2p01PN9PV/S3m5s4RHb2agvxHiIlZE9D7DCV2u53m5maOHj2K3W4nKyuLmpoasrOz/W6eMt7fS9NLv6PzaD1qjZaVW2+i9JY7iEpY+GiEPxWKcf26WeIoEjRBEAQh2ERMF4QrzGmBA/8MzT+H2KVw648gZ9O8h8iyzMvjMzzUdYE5j8Q9WSl8PjMFjR8DqBeifWSWb73WRkP3FLlJeh7ZVcLmwoXPPpNliZHRF+np+T4u1zgpKbeQl/sA4eFpAb3PUOJ0OmltbaWxsRGLxUJ6ejrV1dUUFBT4nahNDQ/R8vILtNUdQqFQsvyGbZTddiexKf7t7wvFuC4StCALxYcuCIIgLI6I6YJwlQw0wsufBVMvrPs7uPGbED5/K/dJl4eHuy7w8vgMyyLD+UFRJiuidAG9LVmW2d8+zrdfb6dv0kpNQRKP7CymICVqwefweKwMDP4rg4O/ACAz8/+yNPPTqNX+zRS7lrjdbk6ePEl9fT1ms5mUlBSqq6spKSlBqVx4JRLAPD5Kyyv/y9lDbyFJEkWVm6i4/SMkpGcu6PhQjOsiQQuyUHzogiAIwuKImC4IV5HLBoe/DUd+AlGpcMuzkH/jJQ97fWKGBzsvMOX28PnMFO7JSiHMzyTgkrfmkfiPI/08e6ALm8vLx8ozuefGAuL1C28N73AY6e55krGxV9Fqk8nLvQ+DYTcKRWDvNZR4vV7OnDlDXV0dU1NTJCQkUF1dzYoVK1D52QTEYpri2N49nNr/Bh6Xi/zyDVTsvpuU7Nx5jwvFuC4StCALxYcuCIIgLI6I6YIQAi4c81XTJjpg1cfgpsdBN38TkWm3h693D/P86DT5ujCeLcpkbUzgK1Qmq4sf7O/kv5oG0WlVfHFrPn+zIQuteuFJ1oy5la6ux5mdPUVU1HIK8h8lNvai7+rXDUmSaGtro66ujrGxMWJjY6msrGT16tVoNAsfEg5gmzVz4o1XOLFvL06blezV66jYfTdLikou+vWhGNdFghZkofjQBUEQhMURMV0QQoTHCbXfg7qnQZ8IO5+G4l2XPOzA1Cz3nx9i1Onm0xlJPJCdis6P5h4L1Tk2x2N726jrmiQ7Uc/DO4rZWpy84H1WsiwxNvYq3T1P4nSOkpy8g7zcB4iIyAj4vYYSWZbp7OyktraW4eFhIiMj2bhxI6WlpWj9HFTttFk5+eZrtL72Eva5WTJKVlCx+24yV6z6s+fw/9u77/Aoq7z/4+8z6QmEEAIhhJAQSAihKhCK0osgWBZx7RVFFHUtrI9t17Wtoth4BGy4ytpFRUQURLqU0KWlASmQUENNz8z9+yM8v8fHNeMEMplJ/LyuK9fF3OF7z5eZXAc+nDnneOO4roDmZt74pouIyNnRmC7iZQq2wtxJcHAbdBoLF79YFdicOFVp5+nd+czOP0rbIH9eTmpD37BGtd6aZVksSz/MM9/uZPfhIi5o34zHRyfTMcr52rlfstuLycl9h5yctwA7MTG3Ehc7EV9f19e41UeWZbF3715WrFhBdnY2QUFB9OnTh5SUFIKCarYrZ0VpKT//+D0bvvmS08cKadk+kd5/uop2PVIwxnjluK6A5mbe+KaLiMjZ0Zgu4oXsFbDqVVg+pWrjkFEvQOcr4Hdmq1YWnuLB9DxyS8u5JTqCx+OjCPGt/YOjK+wOPlybwyuLMzlVWsFVvdrw4IhEIhq5fmhzaWkBu/dM5cCBufj7RxAf/wCtosY12IOufykvL48VK1aQmZlJQEAAKSkp9OnTh5CQmn1EtbKigh3LFrN+3hxOHDpIRJs4ev/pzxSUVjJ4yBA3dX92FNDcTH+Zi4g0HBrTRbzYoV0w9y7I3wQdRsOYl6Gx8y3XiyrtPLe3gFn7jhAd6MfLHdowINw9s1PHi8t57cdM/r0mhyA/H+4e0p6bL4gjoAah8MTJrWRmPsOJE5to1KgjCQmPEd60r1v69TYFBQWsXLmSnTt34ufnR48ePejXrx+hoa7PSAI47HbSflrOuq8+ozB/H+GJydzy9Atu6vrsKKC5mf4yFxFpODSmi3g5eyWsnQFLnwXfALjoOeh+7e/Opq07fpoH0vLYXVLGdVHhPNE+mlA3zKYB7D58mn9+u4sf0w7RJjyYRy9O4qJOLWuwPs3i0KFvycqaQmlZPs2bj6B9u4cJDo51S7/e5vDhw6xcuZJt27Zhs9no3r07F154IU2bNq3RfRwOO1mpa8jIzmXM1de6qduzo4DmZvrLXESk4dCYLlJPHMmCeXdD7hpoN7RqS/4w5xtslNgdTM0+wMzcQ0QG+DElsTUjIpq4rcUVGVXr0zIOnqZ323D+NiaZztGuP5/dXkpu3ixyct7A4aggJuYm2sbd3eDXp/2PwsJCfvrpJ7Zs2YLD4aBLly7079+f5s2b1+g+3jiuK6C5mTe+6SIicnY0povUIw4HrH8HFv+jagZt+FNVh1z/zhlom08Wc19aLulFpYyLbMpTCdGE+/m6pcVKu4NP1ufx8g8ZHCsu58oerZk8ogMtQgNdvkdZ2SF273mJgoIv8PNrSnz8/bSK+jM2m3t69jYnT55k9erVbNiwgcrKSpKTk+nfvz9RUVEu1XvjuK6A5mbe+KaLiMjZ0ZguUg8dy4Z598Le5RDXHy6dBuHxTkvKHA5eyznItJyDhPn68nxia8a0CHNbiydKKnh9SSbvrc7G38fGXYPbM/7CtgT6uf4xy5OntpOZ+SzHj6cSEpJIQsJjNAu/0G09e5uioiLWrl1LamoqZWVlJCQkMGDAAGJinM+ceuO4roDmZt74pouIyNnRmC5ST1kWbJoNix4HRyUM/TukTACb8wC043QJ9+3KZdvpEsY0b8Jzia1p7l+zg5NrIvtIEf9csItFOw8SHRbEw6OSGNM1qkbr0w4fXkhm1vOUluYR0WwI7ds/QkiI80DakJSUlJCamsratWspKSkhLi6OAQMG0LZt2998Hb1xXFdAczNvfNNFROTsaEwXqedO7If590HmIojpDZe+Ds0TnZZUOCxm5h1i6t4DhPjYeCYhmrGRTV0OTWdj9e4jPD1/F7sKTtIztil/G5NMt5gwl+vt9jL27XuPvdkzcDhKad36BtrG3YOfn/vW1HmbsrIyNm7cyOrVqzl9+jTR0dEMGDCAxMREHVRdVxTQRETE3TSmizQAlgU/fwbfPQQVJTD4Eeh7D/g4X7OVUVTK/Wm5bDxZzPBmobzQoTVRAf5ua9PusPh8Qx5TF6Vz5HQ5Y8+L5qGRSbRsUoP1aeVH2LPnFfLzP8PXN5T4+L8Q3eoabDb3zQJ6m4qKCrZs2cKqVas4ceIEkZGR9O/fn+TkZGw2m1eO6wpobuaNb7qIiJwdjekiDcipg7DgQdj1DUR1h8tnQGQnpyV2y+KdfYd5fk8BvsbwZPtorokKd+ts2qnSCmYs282slXvxsRkmDmzHhAHxBPm7vj7t1KldZGY9y7FjawgObkdCwqNENBvktp69kd1uZ9u2baxcuZKjR4/SrFkz+vfvT2FhIUPq0UHVzre4ERERERGprxpHwlUfwJXvw4l98OZAWPY8VJZXW+JjDHfEtGBJryQ6Nw7igfQ8rtq6m9ySMve1GejHf41M4scHBzIkqQWvLM5gyEvLmLt5Pw6Ha5MpjRt35Lzu/6ZrlzexrEq2bh3Pli23cLoo0219exsfHx+6d+/OpEmTGDduHL6+vsydO5f09HRPt1YjmkGrBfrfVhGRhkNjukgDVXQUvn8Ytn0GkZ3hsteh1XlOSxyWxez8ozy9Ox8LeDw+ipujI7C5cTYNIHVvIU/N38H2/SfpHhPG3y9J5vw2rh/S7HCUs2/fB+zNnobdXkx0q2tp2/Ze/P3D3di197Esi4yMDNLT07n00ks93c7/oRk0EREREfljC2kGV7wNV38MRUfg7aGw+EmoKK22xGYMN0dHsCwliZTQEB7N3M/YzVnsKXbfbBpASttw5k26kBfHdSX/eAljZ6zm3o83s/94iUv1Nps/bdrcSt8+S2jV6hr253/EmrVDyc19F4ej+tnDhsYYQ4cOHQgNDfV0KzWigCYiIiIifxxJF8OkddD9Glj1MrzZH/JSnZbEBPrzcbd4Xk6KYWdRCUPWpzEz9xB2N34SzWYzXNkzhqWTB3HPkPYs3HGAIVOX8fKidIrKKl26h79/OEkdniSl13xCQ7uRmfUsa9eN4vCRH6lPn6L7o1FAExEREZE/lqAwuGw6XP9l1S6Ps0bA949CeXG1JcYYro1qxvKUJPo3bcyTu/O5ZFMm6UXVz8DVhpAAXx4c0YElkwdxUaeWTFuSxeCpy5izcZ/L69MaNUqke7d/0a3rOxjjw88/T2Dzlhs5dTrNrb3L2amzgGaMiTfGzDLGzPnFtRBjzPvGmLeNMdfVVS8iIiIiIrQfCnetgV7jYe10mNkP9q50WhIV4M/sLm2ZkRzL3uIyhq9P57Xsg1S4GJbOVnRYENOuOY8v7uxLVFgQkz/fymXTf2J9dqFL9cYYIiIG0zvlWxIT/s6pUztITb2EXWmPUV5+xK29S824FNCMMe8aYw4ZY7b/6vpIY0y6MSbLGPOws3tYlrXHsqzxv7o8FphjWdbtgHet3BMRERGRhi+gMYx+CW7+turx+2Ng/gNQdqraEmMMYyObsqJ3EhdFNOG5vQVcvDGD7aeqn4GrLT1iw/nqzn68elV3Dp8q48o31jDpw03kFbr23DabHzExN9Gv7xJiWt9IQcEcVq8ZSk7OWzgc7l1bJ65xdQbtPWDkLy8YY3yA6cAoIBm4xhiTbIzpYoyZ/6uvFtXctzWQd+bX9pq3LyIiIiJSC+IuhDtXQ9+7YcO7MKMvZC12WtLc34+3O8fxTqc4CsoqGLkxgyl7CihzONzaqs1muPy8aJZMHsh9wxJYknaIoS8vZ8r3aZwqrXDpHn5+YSQm/o3eKQsIC+tF1u4prF07kkOHF2p9moe5FNAsy1oB/Hr+NAXIOjMzVg58AlxmWdY2y7LG/OrrUDW33kdVSHO5FxERERERt/APhouehfGLwC8IPrgC5k6CkmNOy8a0CGNF7yQub9GUV3IOMmJDBptOFrm93WB/X+4blsiSyQMZ0yWKmct2M3jqcj5JzcXu4kcuQ0La0b3bO3Tv9h42nwC2bbuLTZuv49SpHW7uXqrj8jloxpg4YL5lWZ3PPB4HjLQs67Yzj28AeluWdXc19c2AZ4HhwDuWZT1njAkBXgdKgVWWZX34G3UTgAkAkZGRPT755JOa/QnrwOnTp2nUqJGn2xARkVqgMV1EAGz2cmJzPqVN7peU+zchI/FOjkb0/t26TZYv7xDMMQxjKONKSvF377Fp/9+e43Y+Sisn67iDmMY2rk3yp2MzH5frLcuOxQosay5QhOECjBmLMU3c1nNd8MZxffDgwdWeg1ZnAa026KBqERFxN43pIvJ/5G+BryfBwe3QeRyMeqHqTDUnTlbaeSornw8KjhIfFMArSTH0DqubgGBZFvN/LuD579LYf7yEEcmRPHpxR+IiQly+R0XFSbKzXydv32xsNn/iYu8kJuZWfHwC3Ni5+3jjuO6ug6r3AzG/eNz6zDURERERkYahVXe4fSkMehR2fg3TU2D7l+BkkiPU14epSTF81q0dFZbF5ZuzeCxjH0WV7t9ywRjDJd1a8eODA/nrRR1YlXWE4a8s558LdnHS5fVpoSQkPEqf3t8R3rQfu/dMZe264Rw8+K3Wp9WBc5lB8wUygKFUBbP1wLWWZbntA6tBMR2sdvfNdNftz1plZSW+vr6ebkNERGqBxnQRqU6CPYenS1+nsyOLxb69eTrgDo7amjqtsYBSh4MKh4UBgnxs+Jo6+swj4HBYlBdVUFlqBwMBIX74BvlSkw4sqxK7owwsOxhffGwBVO0XWD9447i+Y/LQc5tBM8Z8DKwBOhhj9hljxluWVQncDSwEdgGfuTOciYiIiIh4UqZPLNcFP89L/jfSv3IT84ru5dKKpU5n0wwQZLMR7GPDGCi2OyhxOKireSibzRDY2J+gpgHYfG2Una6guLCUynLXZ/OM8cXXJwSbLQgsB3Z7EXZ7CRbu3a3yj8rlGTRvoDVoIiLibhrTRcQlRzKr1qblrYP2w+GSV6FJa6clxXYHL+4t4M28w7QM8OOFDjEMaxZaN/1StT5t4Y4DPLtgF3mFJQxNasGjozvSrrnr6+MqK0+RnT2T3Lx/YYwPsbF3ENvmNnx8gtzY+bnxxnHdXWvQRERERET+mCIS4JbvYOQUyPkJpveBDf9yOpsW7GPjifbRzD8/gUY+Plz/8x7u2ZXDsYrKOmnZGMPIzlEsfmAgD49KYt3eQi56ZQVPfrOD48XlLt3D17cx7ds/RN8+C4loNoi9e19lzdphHDjwNZalGbXaoIAmIiIiInI2bD7QZ2LVAdetusP8+2D2pXAs22nZ+U1C+KFXIvfHRvLlwWMMSE1jweHjddBwlQBfHyYObMfSyYO4smcM76/OZtDUZby/OpsKu2shKyioDV26vM75532Mv38zdux8gA0br+TEic1u7r7hU0ATERERETkX4W3hpm9gzKuwfzPM6Avr3gRH9WEnwGbjv+Kj+L5HIpH+fty6PZsJO7I5XO7aTou1oXnjAJ4b24X59/QnOSqUJ+btYOSrK1iafsjlezRtmkKvnnPp2HEKpaX5bNg4ju077qO0NN+NnTdsCmgiIiIiIufKGOh5C0xaC7EXwHcPwXsXw5Esp2VdGgfzXY9EHm7bku8Pn2BgahpfHTxWp9vZJ7cK5cPbevP2jT2xOyxu+dd6bno3lcyDp1yqN8ZGq6hx9O2zmLi4SRw+vIg1a4exe88rVFYWubn7hkcBTURERESktjRpDdd9DpfPhEM74Y0L4KfXwF79OjM/m+G+uJYs6pVIbGAAd+7M4ebtezlQVnezacYYhidHsuj+gTw+uiObco8x8rWV/P3r7RQWubo+LYR28Q/Qt89imjcfQXb266xZO4yCgi+0Pq0GFNBERERERGqTMdD9WpiUCu2Gwg9/h1nD4eBOp2VJIUHM75HA39u1YnnhKQak7uLjgqN1Opvm72vjtv7xLP/rYK5NacOH63IZ9OJS3lm5h/JK10JWYGArOnd6lR49PiMwMIqdux5i/YY/cfy49+3G7o0U0ERERERE3KFxS7j6Qxj3LhzPgTcHwPIXwF79zJiPMdzVpgU/9upAx5Ag7k/L45qte8grdW0Wq7aEh/jz9OWd+e4v/ekWE8Yz3+7ioldXsHjnQZcDY1iTHvTsMYdOyS9TXn6EjZuuYtv2eygpyXNz9/WbApqIiIiIiLsYA52vqJpNS74Ulj4Lbw2Ggq1Oy9oFB/LVee15NiGa1JNFDEpN4739R3DU8RnGiZGNmX1rCv+6uRc2A7fN3sD1s9axq+CkS/XG2GjZ8jL69vmBtm3/wpEjS1i7bgRZu6dSWXnazd3XTwpoIiIiIiLuFhJRNZN21YdQdKgqpP34NFSWVVtiM4bxrZuztFcHzg8N5uGMfYzbspvskupr3MEYw+CkFnx/3wD+cUky2/efZPS0lTzy5TaOnHatFx+fYOLb3kvfPotp0eJicnJmsmbtUPLzP8Oy7G7+E9QvCmgiIiIiInWl4xiYtA66XQ0rp8Ib/WGf87VZsUEBfNatHS91iGHbqWIGp6bxVt4h7HU8m+bnY+PmC9qy/K+DuKlfHJ9vyGPwi8t4c/luyipdC1mBgVF0Sn6Jnj2/JCgwhl1pj5C6/nKOHVvr5u7rDwU0EREREZG6FNQULp8B130B5UVVG4gsfAzKi6stMcZwXatmLE9Jol9YY/6elc9lmzLJLCqtw8arhAX788QlnVh4/wBS2obz3HdpDH95Bd9vL3B5fVqT0G706PE5nTu9RmXFcTZtvo6ft91JcXGOm7v3fgpoIiIiIiKekDAM7loDPW6GNa9Xbcmf/ZPTklaB/nzQtS2vd2xDVnEZwzak8985B6l01O1sGkC75o2YdXMvZt+aQqCfjYkfbOLqt9ayff8Jl+qNMURGjqFPnx+Ij3+AwsJVrF13EZlZz1FZ6doZbA2RApqIiIiIiKcEhsKYV+Cmb8ByVB1u/e1kKKs+oBhjGNcynBUpSQxrFsqzewq4eFMGO0+X1GHj/2tAYnMW3NufZy7vTOah01zy+ioemrOVQyddm93z8Qmkbdwk+vb5kZYtLyM3dxar1wxh3/6PcDiqPz+uoVJAExERERHxtLYD4M7V0OcuWP8OzOgHu5c4LWkR4Meszm15u1Mc+0srGLEhnRf3FlDuqPtDoX19bFzfJ5alkwdx24Vt+WrzfgZPXcb0pVmUVri2Pi0goAXJHafQq9dcQkLak57+N1LXX8LRwlVu7t67KKCJiIiIiHgD/xAY+RzcuhB8A+Dff4Kv74aS407LLmkRxoqUJC5r0ZSXsg9y0YYMtpysfj2bOzUJ8uOx0cn8cP9ALmgfwYsL0xn60nLm/5zv8vq00MadOf+8j+jSeTp2ewlbttzE1q23U1S0x83dewcFNBERERERb9KmN0xcBRfeD1s+hBl9IP17pyXN/H2ZnhzL7C5tOVZh5+KNGTyzO59Se93PpgHERYTw1o09+ei23jQO9OXujzZz5Rtr+HnfcZfqjTG0aDGSPr0X0r7dQxw7nsq61FFkZD5DRYVra9zqKwU0ERERERFv4xcIw/4Bt/0IQeHw8VXwxe1QXOi0bEREE5andODqqHBezz3EsA3prD9RVDc9/4Z+7SP49t7+PD+2C9lHi7j09Z944LMtHDjh6vq0AGJj76Bv3x+JihpHXt77rF4zhLx9s3E4KtzcvWcooImIiIiIeKvo82HCMhj4MOz4EqanwI65Tkua+PnyclIbPukWT4ndwaWbMvlb5j6K7J45ENrHZrg6pQ1LJw9i4sB2zN9awOCpy3htcSYl5S6uT/OPoGPSs6T0mkfjxh3JyHiSdamjOXJ0mXub9wAFNBERERERb+brD4MfgQnLIbQVfH4TfHoDnD7ktGxQeCjLU5K4KTqCt/cdYUhqOquOeW77+saBfjw8KonFDwxkcFJzXlmcwZCXljF3834cLh4T0LhxR87r/m+6dnkTy6pk69bxbNlyC6eLMt3cfd1RQBMRERERqQ9adobblsDQJyBjYdVs2s+fgZPNNxr5+vB8Ymu+7N4eY2Dclt08lJ7HqUrPzKYBtGkWzIzrevDphD40a+TPfZ9uYezM1WzKPeZSvTGG5s2H0af39yS0f4wTJzeTmjqa9PR/UF7u/COg9YECmoiIiIhIfeHjC/0fgIkroVl7+PJ2+PhqOJnvtKxf00Ys6ZXEHTHN+Xf+UQalprHk6Mk6avq39Y5vxrxJF/LiuK7kHy9h7IzV3PvxZvYfd+08N5vNnzZtbqVvnyW0anUN+/M/Ys3aoeTmvovDUe7m7t1HAU1EREREpL5p3qFqO/6LnoM9y2F6b9g02+lsWrCPjSfbRzP//ASCfWxc+/Me/rIrl+MVnjsM2mYzXNkzhqWTB3HPkPYs3HGAIVOX8fKidIrKXOvL3z+cpA5PktJrPqGh3cjMepa160Zx+MiPLm/t700U0ERERERE6iObD/S9C+78CVp2hXn3wL8vh2M5Tst6NAnhh54d+EtsJHMOFjIgNY3vD3t26/qQAF8eHNGBJZMHcVGnlkxbksXgqcuYs3Gfy+vTGjVKpHu3f9Gt6zsYY+PnnyewZctNWNY+N3dfuxTQRERERETqs2bt4KZvYPRLsG8DzOgLqW+Do/oz0AJ9bDwSH8V3PRKJ8PPl5u17mbgjmyPlnptNA4gOC2LaNefxxZ19iQoLYvLnW7ls+k+sz3ZtbZkxhoiIwfROWUBiwt85eWo7lrXYzV3XLgU0EREREZH6zmaDXrfBXWuqDrpeMBneGw1Hdzst69o4mO97JvLXuJZ8e/gEA1J3MffgMY9/NLBHbDhf3dmPV6/qzuFTZVz5xhomfbiJvMJil+ptNj9iYm6iX98lGHOFm7utXQpoIiIiIiINRVgbuP5LuGw6HNwBM/vB6v8GR/W7NvrbbDzYtiWLeiYSE+jPxJ053Lo9m4Nlnj0I2mYzXH5eNEsmD+S+YQksSTvE0JeXM+X7NE6Vutabn18YxjR2c6e1SwFNRERERKQhMQbOux4mrYP4wbDocZg1Ag6lOS3r2CiIb89P5PH4KJYUnmRAahqfFhR6fDYt2N+X+4YlsmTyQMZ0iWLmst0MnrqcT1Jzsbu4Pq0+UUATEREREWmIQqPgmo/hillQuAfe7A8rXgR79bNPvjbD3bGR/NirA4nBgfwlLZfrft7D/lLPb1sf1SSIl6/qztxJFxDbLJiHv9zGmP9exerdRzzdWq0ynk7ENdEzrom14YkLPd3Gfzh+/DhhYWGebkNERGqBxnQRaZDs5VUhrfgI+IVARAL4N3JaYmFxoKyCnNJyDBAbFECkvy8GUzc9/05vR4vKyT1aTLndQdNgf2KbBRPo6/Mfv9cbx3Vz64KNlmX1/K3vaQZNRERERKSh8/GH5klVX/ZyKNgCx3PAqn6nR4MhKsCf7o2DCfHxYU9xGTtPl1LqZHfIumIwRIQE0D0mjJimQZwoqWBr3nFyCouo9IL+zoWvpxuokYgEuOVbT3fxH7YsW8agQYM83YaIiNQCjeki0uAVF8LCR2Hrx1WzaJdNh9Y9qv3tgUAny+KDgqM8mZWP3YLH2kVxa3QENuPZ2TQbEA34nSzlxYXpzNm0j/Bif+4fnsjVvWLw9bF557h+a/Wvm2bQRERERET+SILD4U9vwLWfQ9lJmDUMFv0NKkqqLTHGcEOrCJanJNE3LITHM/dz+eYssopL67Dx6rUIDeTFK7vxzd0X0q5FIx6fu53R01axMvOwp1urMQU0EREREZE/osQRVeemnX8jrJ4GMy+AnDVOS6ID/fmwazzTOrYhvaiUoevTeT3nIJVespti5+gmfDqhDzOvO5/iikpumJXKBzvLPN1WjSigiYiIiIj8UQU2gUtegxu/BkcF/GsULHgIyk5XW2KM4c8tw1mRksSQ8FCe2VPA6E0Z7Dpd/QxcXTLGMKpLFD/cP5CHRyXRpfl/bhzizRTQRERERET+6OIHwZ1roPcdkPoWzOwLe5Y5LYkM8OPdznG82SmWvNJyRmzI4KW9Byj3kk06Av18mDiwHd2a169tNxTQREREREQEAhrBqClwy3dVuz7Ovgzm3QulJ6otMcZwWYumrEjpyJjmTXgx+wAjN2Sw9VRxHTbesCigiYiIiIjI/4rtCxNXwQV/gc3/hhl9IWOR05IIf19mdorjvc5tOVpRycUbM/jn7nxK7d4xm1afKKCJiIiIiMj/5RcEw5+C8YshIBQ+uhK+mli1Rb8TI5s3YXlKEldGhjMt9xDDN6Sz4URRHTXdMCigiYiIiIjIb2vdA+5YDgMegm2fw/TesOsbpyVhfr682rENH3WNp9ju4JJNmTyRuZ9izaa5RAFNRERERESq5xsAQx6D25dC45bw6fXw+c1w2vkZY0OahbIsJYkbWjXjzX2HGbI+jZ+OnaqbnusxBTQREREREfl9UV3h9iUw5G+Q9i1MT4Ftc8Cq/gy0xr4+vNAhhjnd22FZcMWW3fxXeh6nK+112Hj9ooAmIiIiIiKu8fGDAZPhjpUQHg9fjIdProWTBU7LLmzamCUpHZjQujmz848yMDWNZYUn66jp+kUBTUREREREaqZFEoxfBCOehd1Lqtambf7A6WxaiI8PTyVEM+/8BIJ8bFy9dQ/3p+VyoqKyDhv3fgpoIiIiIiJSczYf6Hc33LkaWnaGryfBB2PheK7Tsl5NQljcswP3tGnBpwWFDEhNY+GR6s9a+6NRQBMRERERkbPXrB3cNB8ungq566rOTVv/Djiq37Ux0MfGY+1asaBHIuF+vty0bS937czhaLlm0xTQRERERETk3NhskHI73LUGWveEbx+E9y+Bo7udlnUPDWZhz0QejItk3qFjDEhNY96h43XTs5dSQBMRERERkdrRNBZumAuX/jcc+BlmXgBrpoOj+l0b/W02/to2ikU9OxAd4MeEHdmM376XQ2UVdde3F1FAExERERGR2mMMnH8jTFoH8QNh4aPw7kVwON1pWXKjIBb0SOSx+CgWHz3JwNQ05hwoxHKy8UhDpIAmIiIiIiK1L7QVXPMJjH0bjmbBGxfCypfAXv06M1+b4Z7YSH7o2YF2wQHcvSuXG7btJb+0vA4b9ywFNBERERERcQ9joOufYVIqdBgFPz4F7wyBA9ucliWGBPL1+Qk81b4VPx07xcDUND7MP/qHmE1TQBMREREREfdq1AL+PBuufB9O5sNbg2DpP6Gy+pkxH2OYENOCpSlJdGkczIPpefx5625ySsrqrm8PUEATEREREZG60enyqtm0zlfA8inw1kDYv8lpSVxQAHO6t2NKYms2nSxm8Pp0Zu07jKOBzqYpoImIiIiISN0JDoexb8E1n0LJMXhnKPzwBFSUVltiM4aboiNYnpJE7yYhPJa5nz9tzmJ3cfU19ZUCmoiIiIiI1L0OI+GutdD9Ovjp1apNRHLXOS1pHejPR13jeTUphrSiUoauT2dG7iHsDWg2TQFNREREREQ8IygMLnsdbvgKKsuqtuP/7mEoL6q2xBjD1VHNWJ6SxMDwxjy1O58xGzNJKyqpu77dSAFNREREREQ8q90QuGs19LoN1s2Emf1g7wqnJS0D/Hivc1tmJseSU1rG8PUZvJJ9gApH/Z5Nq9OAZoyJN8bMMsbM+cW1y40xbxtjPjXGjKjLfkRERERExEsENIbRU+HmBWBs8P4lMP9+KD1ZbYkxhj9FNmV5ShKjmjdhyt4DjNqYwbZTxXXYeO1yOaAZY941xhwyxmz/1fWRxph0Y0yWMeZhZ/ewLGuPZVnjf3VtrmVZtwMTgatq0ryIiIiIiDQwcRfAxJ+g792w8T2Y0RcyFzstae7vx1ud4pjVOY6D5RWM3JjB83sKKHM46qbnWlSTGbT3gJG/vGCM8QGmA6OAZOAaY0yyMaaLMWb+r75a/M79Hz9zLxERERER+SPzD4aLnoVbF4F/CHx4Bcy9q2rXRydGNw9jRUoSYyOb8mrOQYavzyDT8qmjpmuHqclp3MaYOGC+ZVmdzzzuC/zDsqyLzjx+BMCyrOd+5z5zLMsad+bXBnge+MGyrP+IxsaYCcAEgMjIyB6ffPKJy/3WldOnT9OoUSNPtyEiIrVAY7qIiHcxjgrisj+lTe4XlPs3ISPxTo5G9P7dus2WL28TTNeKYib6V9ZBp64bPHjwRsuyev7W93zP8d7RQN4vHu8Dqn21jDHNgGeB84wxj5wJcvcAw4Amxpj2lmW98csay7LeAt4C6NmzpzVo0KBzbLn2LVu2DG/sS0REak5juoiINxoOBfcQMHcSXbb/s+qg61EvQEhEtRWDgPGVdn5aubJejevnGtBqxLKso1StNfvltWnAtLrsQ0RERERE6pmobjBhKax6FZZPgT3L4OIXodNYMOY3S0J9fQj67W95rXPdxXE/EPOLx63PXBMREREREaldPn4w8K9wxwoIi4U5t8Kn18OpA57urNaca0BbDyQYY9oaY/yBq4F5596WiIiIiIhINSKTYfwPMPxpyFoM01Ngy0dQg/01vFVNttn/GFgDdDDG7DPGjLcsqxK4G1gI7AI+syxrh3taFREREREROcPHFy64t2pL/hbJMPdO+HAcHM/7/Vov5vIaNMuyrqnm+gJgQa11JCIiIiIi4qqI9lWHW69/Bxb/o+rctBFPwfk3g+1cPzBY9+pfxyIiIiIiIr9ks0HvCXDXaog+D+bfD7MvhcK9nu6sxhTQRERERESkYWgaBzfOg0teg/wtMLMfrfZ/5+muakQBTUREREREGg5joMfNMGktxF2IsbzrkOrfo4AmIiIiIiINT5PWcO1n7I8e7elOakQBTUREREREGiZjwNSvyFO/uhUREREREWnAFNBERERERES8hAKaiIiIiIiIl1BAExERERER8RIKaCIiIiIiIl5CAU1ERERERMRLKKCJiIiIiIh4CQU0ERERERERL6GAJiIiIiIi4iUU0ERERERERLyEApqIiIiIiIiXUEATERERERHxEgpoIiIiIiIiXkIBTURERERExEsooImIiIiIiHgJBTQREREREREvoYAmIiIiIiLiJRTQREREREREvIQCmoiIiIiIiJdQQBMREREREfESCmgiIiIiIiJeQgFNRERERETESxjLsjzdg8uMMYeBHKAJcKKWblsb94oAjtRCL+IZtfnzVJ/V59fB23r3RD918Zzueg6N6VLbvG1M8JT6+jp4W9+e6kfjeu3dyxvH9VjLspr/1jfqVUD7H8aYtyzLmuAt9zLGbLAsq2dt9CN1rzZ/nuqz+vw6eFvvnuinLp7TXc+hMV1qm7eNCZ5SX18Hb+vbU/1oXK+9e9W3cb2+fsTxGy+9l9RP+hmoUp9fB2/r3RP91MVzuus5NKZLbdPPQZX6+jp4W9+e6kfjeu3fq16olzNo3qa+pXIREamexnQRkYalvo3r9XUGzdu85ekGRESk1mhMFxFpWOrVuK4ZNBERERERES+hGTQREREREREvoYAmIiIiIiLiJRTQREREREREvIQCWi0zxoQYY943xrxtjLnO0/2IiMi5McbEG2NmGWPmeLoXERE5d8aYy8/8W/1TY8wIT/fzawpoLjDGvGuMOWSM2f6r6yONMenGmCxjzMNnLo8F5liWdTtwaZ03KyIiv6sm47plWXssyxrvmU5FRMQVNRzX5575t/pE4CpP9OuMAppr3gNG/vKCMcYHmA6MApKBa4wxyUBrIO/Mb7PXYY8iIuK693B9XBcREe/3HjUf1x8/832vooDmAsuyVgCFv7qcAmSd+Z/VcuAT4DJgH1UhDfT6ioh4pRqO6yIi4uVqMq6bKlOA7yzL2lTXvf4eBYizF83/zpRBVTCLBr4ErjDGzAS+8URjIiJyVn5zXDfGNDPGvAGcZ4x5xDOtiYjIWaju3+v3AMOAccaYiZ5ozBlfTzfQ0FiWVQTc4uk+RESkdliWdZSqdQoiItIAWJY1DZjm6T6qoxm0s7cfiPnF49ZnromISP2kcV1EpGGpl+O6AtrZWw8kGGPaGmP8gauBeR7uSUREzp7GdRGRhqVejusKaC4wxnwMrAE6GGP2GWPGW5ZVCdwNLAR2AZ9ZlrXDk32KiIhrNK6LiDQsDWlcN5ZleboHERERERERQTNoIiIiIiIiXkMBTURERERExEsooImIiIiIiHgJBTQREREREREvoYAmIiIiIiLiJRTQREREREREvIQCmoiIiIiIiJdQQBMREREREfESCmgiIiIiIiJe4v8BszKEA6cVlZ8AAAAASUVORK5CYII=", - "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 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(-) (limited to 'buch') 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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", + "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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28X5HL5P8DDyVlcB4P8Opn6sQQniQ4z3ThRBCnH5lZWUnvd/LZDLh7z/8v4OH09rayqxZs6irqwNg/fr1PProo3zwwQcjGn+s16AoynED2unq4tgExB/287iDv/a1ptP5kZryc2bN/JiwsEXU1v2BTZvPpqX1HVTVdWpvnpQHP9kIs2+EbX+D52dD9Zphh4R76XlhQhIvjk+i2WrnnG0VPF7bgs11iucqhBBCCCGEh4qKiiI+Pp6KigoA1qxZQ3Z29glGfXmnK6BtBdIURRmnKIoX8C3gvdN07zPOYIhj4oRnmTb1Vby8wigt/Rnbtl1Kb9/2U3tjL18452H4wWrQG+A/l8C7N8Bg77DDlkUEUTgzk4sjgnmyro0l2yrZ1W85tXMVQgghhBDCQz377LN85zvfYdKkSezatYt7TrBv7WScijb7/wM2ARmKojQqivIDVVUdwI3AR0AZ8JqqqvvG+t5nQn2XZcTdGoOCcpme+zbZWY8zZG1l+/Yr2Lv3FgYHT3ExMX4GXL8e8n8Gu/4Hz82E8pXDDgnR6/hjdiL/njiOPoeT87ZX8tD+ZgadUk0TQgghhBDfLFOmTGHbtm2UlJTwzjvvEBwcfMruNeYBTVXVq1RVjVZVVa+qapyqqi8d/PWVqqqmq6qaoqrqw2N93zOhvX+Ic58p5IltQ1S0mkY0RlE0REdfyuxZn5CUdCMdnR+zecvZ7N//exwO86mbrN4HFv8SflQAxjB45Sp484dg7hp22NlhgXw6I5NvR4fyx/p2zt5WQXHvwKmbpxBCCCGEEN9gp2uJ49dSsNGLny/JoLbPxdJnCrn37T10DYzs0GedzkhK8m3MnvUJ4eHnUHfgeTZtPovmljdO7f60mCnwo7Ww4B7Y9w48NwP2ve3ubnMcATotT2TG89rkFKwulYt2VnN/VSNmp/PUzVMIIYQQQohvIAloJ0Gv1XBt3jgen+fL1bOTeGVrAwt+t44XCmuwOUYWsnx8Ypgw/ilyp72Oj08MZWV3sXXbxfT0DH/Y9EnRecGCu+D6TyEoHl6/Bl77Hpjahh02L8SfddMz+H5sGC80drKwuIKinpFVDoUQQgghhBAnJgFtDPh5KfzqwvF8dGs+05KCeXhlGUue+pSP9rWOeH9aYOBUcqe9zvjsp7DZutix8yr27LmRwcGGUzfxyPHwg0/grF9D5Wp3NW33K8NW04w6Lb9Nj+OdnFS0Cly2az93VjRgckg1TQghhBBCiJMlAW0MpUb484/vz+Af35+OTqvh+n9v59svbKG0uX9E4xVFQ1TUhcye9QnJ426ls2sdmzYvobr6cRyOU1Sp0uog71b4yQYIz4C3r4f/XgF9wzcumRXkx5rpmfwkPpz/NHcxv7icNV0je51CCCGEEEKIY5OAdgosyIjgw1vy+c1F4ylv7ef8Z9dz95sldJhGtj9NqzUwbtxNzJ79CZGR53Og/i9s3LSYpqZXUNVTVKkKS4Pvr4JzH3Mfcv38LNj+z2Grab5aDQ+kxrJiahp+Wi3fKanh5rID9Ngdp2aOQgghhBBCfM1JQDtFdFoNV89OYt3PF3Lt3HG8sb2RhU+s4/l11QzZRxayfLyjGJ/9BNNz38bXN4nyinsp3noh3d0bT82kNVqY9WP3AdfRk+H9m+FfF0FP3bDDpgYa+Xh6OrclRvJmWw/zi8tZ1dF7auYohBBCCCHEaVRRUcGUKVMO/QgICODpp58+ZfeTgHaKBfrquX9ZNqtvm8es5FAe/7CCs578lJV7Wka8Py0gYBLTpr7KhPF/wOEwsXPX99hdcj0WS+2pmXTIOLj6PVj2FDTtgOfnwJa/guv4jU+8NRruSo7mw2nphHvp+P7eOq7fV0enTappQgghhBDiqysjI4Ndu3axa9cutm/fjq+vL8uXLz9l95OAdpJGGrKSw/148f9yefmHM/Hz1vHTl3dw5V82s6exb0TjFUUhMvJ8Zs38mJTkn9PTs4nNW5ZSVfVb7PZTsPdLo4Hca+GnmyBxNqy6A/5xHnRWDztsor8vH07L4K5xUazs6GNecRnvtPWM+H0SQgghhBDCU61Zs4aUlBQSExNP2T10p+zK3wAOu53/3nMbuogYBnOnYfDzP+GYualhfHBzPq9ubeD3qyu48LkiLp0axx3nZBAZ4HPC8VqtN0lJPyE6+jJqap6kvuFvtLS+TfK4W4mJuRKNZoz/SIPi4TtvwO7/wYd3w5/nwsJ7YfYN7iWRx6DXKNyWFMXS8EBuLWvgx6UHeLe9l0fT44j01o/t/IQQQgghxDfC+tcq6WwYGPU4p9OJVnvsf7eGxfuRf0X6iK/1yiuvcNVVV416DqMhFbSTYDUPEBARRcu2jbxww7UUvvx3zL09Jxyn1Sh8e2YCa+9YwHXzknlvVzMLn1jHs2uqRrw/zds7nKysR5gx/V2MxjQqKn9J8dZldHWtP9mXdTRFgSnfhhuKIWUxfHw/vHQ2tJcNOyzTaGDF1DR+mRLD2u5+5hWX82pLt1TThBBCCCHEV47NZuO9997j8ssvP6X3Ub5K/1jOzc1Vt23bdqancZRVb76Os7GWyk1FaHU6JixawvQLLyEgLGJE4w90mXlkZTkf7mslJtCHu5ZmcuHkGBRFGdF4VVXp6FxNddWjDA7VExq6kLTUX2A0ppzMyzrezWDfW7DyDhjqh/l3udv0a4evjO23DHF7eQNb+swsDPHndxnxxPl4jf38hBDiJK1bt44FCxac6WkIIYQAysrKyMrKOqlrmEwm/P1PvNLtRN59912ee+45Vq9ePapxx3oNiqJsV1U191hfLxW0MWAIDWfZLXfy/af+RGbefEo+WcVLN1/HR3/+Az2tzSccnxhq5M/fm8Yr180i2OjFLa/s4tI/bWRn/YmrceDenxYRfg6zZn1Iaurd9PZuZUvxeVRU/ga7vfckX91RN4MJl7qradkXwtqH4IWF0LJ72GEpvj68nZPKw2mxbOkzs6C4nH81deL6Cn2DQAghhBBCfHP973//O+XLG0EqaGPii99t7e9oZ+v7b7KnYDUuh5OMOfnMvPhywhKSTngtp0vlze2N/G51BR0mKxdPieHOczOJCTKMeD42Wyc1NU/T1PwqOp0/yeNuITb222g0p2D/V9kK+OB2MHdC3m0w/07QeQ875MCglZ9XNLC+Z4C5QX48mRlPomH4MUIIcbpIBU0IITyHp1TQzGYzCQkJ1NTUEBgYOKqxo62gSUAbA8f7MDf39rBtxdvsXr0Su3WI1OmzmLn8SqJS0k54zQGrgz+tq+aF9bVoFLhuXgo/np+Mr9fIm4AMDFRQWfUQPT0b8fVNIS31F4SGLhjx0skRG+yBj+6FXS9DeCZc9BzEHfPv2yGqqvLflm5+Vd2EQ4V7kqO5Ni4M7VjPTQghRkkCmhBCeA5PCWgnQ5Y4ehBjUDDzv3stP3rub8y69CoaSvfw8j238cbD99NYunfYsX7eOu44J5M1t8/nrKxI/rCmioVPrOOtHY24XCML1X5+GeRM+ReTJv0VVXWyu+SH7Nr9fQYGKsfi5X3OEAwXPw/feROsA+4GIh/dCzbLcYcoisJ3YkL5dEYmc4L8uL+6iYt3VFNlHhrbuQkhhBBCCPEVIgHtNDD4BzD3iu/woz/+nfxvX0PHgVpe/fXdvPLAXdTt2j5sV8P4EF/++O2pvP7j2UQG+HD7a7tZ/vwGth/oHtG9FUUhPGwxs2auIi3tPvr7d1O8dRnlFQ9gs43sGiOWdpb73LRp18CmP7pb8tdtGHZIjI8X/5k0jj9mJVBlGeKsbRU8e6ANxwhDqBBCCCGEEF8nEtBOksvlGvHXevv6MuOiy/jhsy+y8Jrr6Oto481HHuDle26nausm1GGuNT0phHd+OpffXz6Z1v4hLv3TJm787w4ae45fpTqcRuNFQvz3mT1rDbEx36a5+X9s2ryI+vqXcLlsI34NJ+QTAMuegv97H1SX+3DrD37urqwdh6IoXBYVQuGMTM4KDeDhmhbO21FJ2cDg2M1LCCGEEEKIrwDZg3YS7HY7f/nLX/D19eWKK67Az89vVOMddjulhQUUv/s6fW2thMYlMHP5FWTMzkdznMP0ACw2B3/+tIa/Fu7HpcKP8sfxkwWp+HmPYn+auYrqqt/S1V2IwZBIWuovCAs7a2z3p9nMUPAQbP4TBMbDhX+AlIUnHPZ+ey93VzbS73ByS2IkNydG4KWR7yUIIU4P2YMmhBCe45u4B00C2kkYGBhg1apV7Nu3D51Ox7Rp05gzZ86oO7u4nE4qNhay5Z3X6WqsJygymhkXX072vIVodcfvvNjcO8jjH5bzzq5mwv29ueOcDC6bGodGM/KQ1dm1jqqqR7BYqgkOnk1a2n34+2WOav4nVL8F3r0Buqpg6tWw5CHwGf496rI5+GV1E2+29ZBt9OGprAQm+/uO7byEEOIYJKAJIYTnkIDm4TwtoH3mgw8+wGazUVJSgqIo5OTkMHfuXEJCQkZ1HdXlonrbZra8/RptNdX4h4aTe8ElTFy8BL3X8dvQ76zv4TcrStlZ38v4mADuX5bNrOTQEd/X5bLT1Pw/amqeweHoJybmcpKTb8fbK2xU8x+WfQjWPQIb/wB+Ue5lkBnnnnDY6s4+7qxopMNu54b4CG5PisJHK9U0IcSpIwFNCCE8hwQ0D+epAe2zD/Oenh42bNjAzp07cblcTJw4kby8PCIiIkZ1PVVVqdu9gy1vv0pTeSm+gUFMO/9ipiw5Dy/DsatIqqry3u5mHltVTnPfEEsnRPGLpVkkhI686mS391Fb9yyNjf9Go/FhXNJPiY+/Bo1mDM8oa9oO794I7aUw6Uo491HwHT7I9tkd/Gp/M/9r6SbN15unMhPIDTSO3ZyEEOIwEtCEEMJzeEpAe+qpp3jxxRdRFIWJEyfy97//HR8fnxGNlYB2Bhx1UHV/P5s2bWLbtm3Y7XaysrLIz88nJiZm1NduLN3L5rdf5UDJTnyMfuQsvYCcpRdi8Dv2X7JBm5MX19fw/Lr9OF0q389L4saFqfj7jPyQarO5hur9j9LZuQYfn3jSUu8mPPycsduf5rDB+t/D+ifcLfrP/z1kX3TCYeu6+/lZeQPNVjvXxYVzV3I0vlJNE0KMMQloQgjhOTwhoDU1NZGXl0dpaSkGg4ErrriC8847j2uuuWZE4+UcNA8QEBDAOeecw6233sq8efOoqanhr3/9K//5z3+or68f1bXisidw2b0P8p2HnyQ2awKb3vgfL9xwLYUv/x1zb89RX2/w0nLT4jTW3bGACybH8JdPa1jwu3X8d0s9zhG2rjcak5k86a9MmfJPtFoDe/bewI6d36bfNPzZbSOm84KFv4Dr1kFADLx2tfvHQPuwwxaEBPDpjEz+LzaMvzR2sGhrORt6TGMzJyGEEEIIIY7D4XAwODiIw+HAYrF8qcLLSEkFbQyc6LutQ0NDFBcXs3nzZiwWC0lJSeTn55OcnDzqqlRHfR1b3n6Nyk1FaHU6JixawvQLLyEg7NjLKEsae3lwRSlb63rIjPLn/mXZzE0d+d4yl8tBc8tr1NQ8hd3eQ3T0paQk/wxv79Et2zwup8O9L23dI+DlB0sfh4mXwQnel409A9xeUU/doI3/iwnl/pQY/HTH73wphBAjJRU0IYTwHIdXn9b+46+0H6gZ9TWcDifa4/w7MSIxmYXXXHfCazzzzDPce++9GAwGlixZwssvvzzi+0sFzQP5+Pgwb948br31Vs455xy6urr497//zYsvvkh5efmwB1V/UXhCEstuuZPvP/UnMvPmU/LJKl66+To++vMf6GltPurrJ8UF8dr1s3n+O1MZsDr4zotb+OE/t1HbaR7R/TQaHXGx32bO7AISEn5Ia+u7bNq8mNq653A6h0Y87+PS6iD/dvhxEYSmwFs/hP9dBf1Hv5bDzQn2o2B6JtfHh/Ov5i7mF5eztqv/5OcjhBBCCCHEYXp6enj33Xepra2lubkZs9nMf/7zn1N2P6mgjYHRfrfV4XCwa9cuioqK6O3tJSIigvz8fMaPH49mlOd99Xe0s/X9N9lTsBqXw0nGnHxmXnw5YQlJR33tkN3J3zbU8lxBNTani6tnJ3HzojQCfUe+P81iqaN6/2N0dKzGxzuGlNQ7iYxYNjb701xO2PIXWPMb0HrBOQ9DzndPWE3b1mfmtvJ6qixWrooO4VcpMQTqR34mnBBCHE4qaEII4Tk8YQ/a66+/zocffshLL70EwL/+9S82b97M888/P6LxUkH7CtDpdOTm5nLTTTexfPlyXC4Xb775Js899xw7d+7E6XSO+FoB4REsvvYn/OiPf2PasovZv72Yf95xI+8+8RCt+6uO+FofvZafLkhl7R0LuHRqHH/bUMuCJ9by7011OJyuEd3P1zeJSRP/xNScl9Hpg9i371a277iCvv7do3oPjkmjhdk/hZ9sgKiJ8N6N8O/l0Dv8vr3cQCMf52ZwS2Ikr7V2M6+4nI86+05+PkIIIYQQ4hsvISHh0FYlVVVZs2bNSYfG4UgFbQyc7HdbXS4XZWVlrF+/ntbWVgIDA5k7dy45OTno9SOvbgEMmvrZsep9dn74HlazmcRJOcxafiVx2ROO+tp9zX08uKKUzTXdpEX4cd+ybOanh4/4XqrqpKXlTfbX/B6brZOoqItJSf45Pj7Ro5rzMblcsP1v8PED7p+f9SvI/QGcoMJYYrJwa1k9peYhLokM5sHUWEK9pJomhBg5qaAJIYTn8IQKGsADDzzAq6++ik6nIycnhxdffBFv75EdRSVt9s+AsfowV1WVqqoqCgsLaWxsxM/Pj9mzZ5ObmzvivwCfsVos7P54Jds/eAdLXy+xmeOZtfwKEidPPWI5oqqqrC5t47cryzjQZWFBRjj3nZ9FasTI/xI7HCbqDvyZhoa/ARoSE68nMeFHaLWGUc35mHrr4f1bYH8BJM6FC59171Ubhs3l4tkD7Tx9oI0AnZZH0uO4IDxw7I4JEEJ8rUlAE0IIz+EpAe1kSEA7A8b6w1xVVerq6igsLKS2thaDwcDMmTOZOXMmBsPoQo/dOsSegtVsff8tBro6iUxOZebyK0jNnYVyWDXK6nDyz411PLumGovdyfdmJXLL4jSCjV4jvtfgYAPV+x+nvX0l3t5RpKTcQVTkhSjKSa6kVVXY9TJ8eA84bbDoPpj1E/eSyGGUDQxya3k9u02DnB8eyCNpcUR4j64iKYT45pGAJoQQnkMCmof7pgS0wzU0NLB+/XoqKyvx8vJixowZzJo1Cz8/v1Fdx+mws+/TAra++wa9bS2ExiUwc/kVZMzOR6P9POh0Dlh56uNK/ldcj7+PnlvPSuO7sxLRj+JA6J7erVRVPYTJtJeAgMmkp91HYODUUc33mPpbYMVtULkKYnPhoucgInPYIQ6Xyp8b2vldXSsGjYYH02K5LDJYqmlCiOOSgCaEEJ5DApqH+yYGtM+0trayfv169u3bh06nY9q0acyZM4fAwMBRXcfldFKxaT1b3n6NrsZ6giKjmX7RZYyfvwit7vPqUnlrPw+tKKOoupPkcCP3nZ/FwoyIEQcbVXXR2vo21fufwGZrJzJiGSkpd2IwxI5qvse4MOx9E1beAbYBmH8XzL0FtMNXxqotQ9xW1sDWfjOLQwL4XUYcMT4jrw4KIb45JKAJIYTnkIDm4TwxoJm6h9hesvm0fZh3dHRQVFRESUkJiqIwZcoU8vLyCAkJGdV1VJeL6m2b2fL2a7TVVOMfGk7uBZcwcfES9F7u/W6qqlJQ3s7DH5RR02kmPy2M+87PJiNqNPvTzByo/yv19S8AkBD/AxITf4xOZxzVfI8y0AGr7oB9b0PUJHc1LXrSsEOcqsrfmzp5eH8LOgUeSI3lO9EhUk0TQhxBApoQQngOCWgeztMC2pDZzj/u3oDez8XMc9NJmxGFt+H0dAzs6elhw4YN7Ny5E5fLxYQJE8jPzyciImJU11FVlbrdO9jy9qs0lZfiGxjEtPMvZsqS8/Ay+AJgc7j4z+YDPP1JJQNWB9+emcBtZ6UT6jfyxiVDQ81U7/8dbW3v4eUVQUrKz4iOuuTk96eVvgcf/AwGuyHvdpj3c9ANP68Dg1ZuL29gQ+8A+cF+PJERT6JhdE1YhBBfXxLQhBDCc0hA83CeFtDsViflm1oo/rCSoV7QeWlInRZBdl4sUckBp6UyYzKZ2LhxI9u2bcNut5OVlUV+fj4xMTGjvlZj6V42v/0qB0p24mP0I2fpBeQsvRCDn/svdI/ZxjNrqvj35gP4emm5eVEa/zcnCS/dyENWX98OKqsepr9/F/7+40lLvY/g4BmjnusRLN3w0T2w+38QnuWupsVNG3aIqqr8p6WLX1c341Th3pRoro0NQyPVNCG+8SSgCSGE55CA5uE8LaB9Zu3atWSPm0ZpUTNVW9uwW50ERxvJnhtN5qxofPxOfedAs9nMli1b2LJlC1arldTUVObNm0dCQsKor9VaXcnmt19j/7bN6H0MTD57KbnLlmMMCgagut3EQx+Usa6ig6RQX35xXhZLsiNHtT+trW0F1fsfw2ptJSJ8Kampd2EwxI96rkeoXO1uyT/QCrNvhIX3gH74rpdNQzbuqGigoNvEzEAjT2bGk+Lrc3LzEEJ8pUlAE0IIz+EpAe2pp57ixRdfRFEUJk6cyN///nd8fEb2b0YJaGfA4R/mtiEH1dvaKd3QTFttPxqdQsqUcLLzYohND0bRnNoKzdDQEMXFxYdOO09MTGTevHkkJyePuqLXUV9H8TuvU7FxPVqdjgmLljD9wksICHMvo1xX0c5DH5RR3T7A7ORQ7l+WTXZMwIiv73QOUl//InUH/oKqOkmI/z5JST9BpzuJ/4GG+mD1/bDjnxCS4q6mJc4edoiqqrzW2sMvq5uwulzcMS6a6+PC0Z3iPyshhGeSgCaEEJ7DEwJaU1MTeXl5lJaWYjAYuOKKKzjvvPO45pprRjReAtoZcLwP887GAUo3NFO5pRWrxUFAuMFdVZsdjTHw1O55stlsbN++nY0bN2IymYiNjSU/P5+MjIxRB7WeliaK332D0sICALLnLWLGRZcRHB2Lw+niv8X1PPVxJb2Ddq7MjednSzII9x/F/jRrK/v3P0Fr69vo9aGkJN9OTMzlKMrw55wNa/9aeP9m6G2AGdfBWQ+A1/CNSdqsdu6qbODDzn6m+PvyVGY8WX5jcNi2EOIrRQKaEEJ4Dk8JaLNmzWL37t0EBARw8cUXc/PNN7NkyZIRjZeAdgac6MPcYXOyf2cHpUXNNFf1omgUkiaGkp0XQ8L4UDSnsFLjcDjYtWsXRUVF9Pb2EhERQX5+PuPHj0ejGV2Djv7Odra+9xZ7Cj7C5XCSMSefmRdfTlhCEn0WO38oqOKfG+vw0Wv56cIUrp07Dh/9yENWf38JlVUP0de3HT+/TNJS7yUkZM5oX/LnrAOw5jdQ/BcISoQLn4Xk+cMOUVWVd9t7uaeqEZPDxW1JkdyUEIleqmlCfGNIQBNCCM9xeLjpfX8/tmbzqK/hdDrQao/dyM8rxkjQBSknvMYzzzzDvffei8FgYMmSJbz88ssjvr8EtDNgNB/mvW0WSouaKd/cwqDJjl+wN5lzosmeG4N/yKnb++R0Otm7dy/r16+ns7OT0NBQ8vLymDRpElrt6CpV5t4etq14m90fr8I+NEhK7ixmLb+CqNR0ajoG+O3Kcj4payMu2MA952WxdELUKPanqbS3r6R6/2MMDTURFnYWaal34+s77su8bLcDG+HdG6F7P0y7Bs7+DfgMf35cp83BfVWNvNPey3g/H57OTGCiv++Xn4MQ4itDApoQQngOTwhoPT09XHrppbz66qsEBQVx+eWXc9lll/Hd7353RPeXgHYGfJkPc6fDRe3uTko3NNNQ1g1AQnYI2XkxJE0KQ6s9yfbzx+FyuSgrK2P9+vW0trYSGBjI3LlzycnJQa8fXTOTwQETO1e9x45V72E1m0mclMOs5VcSlz2BDdWdPLiilPJWEzOSQrh/WTYT40Z+qLbTaaWh4W/UHfgTLpeN+LirSUq6Eb1+5HvcjmAfhLW/hU1/BP9ouOAZSDv7hMNWdfRyV2UjXXYHNyVEcltSJN6jrDwKIb5aJKAJIYTn8IQljq+//joffvghL730EgD/+te/2Lx5M88///yIxktAOwNO9sO8v3OQso0tlG1swdxrxRDgRdbsKLLmxhAUcWqqNqqqUlVVxfr162loaMDPz4/Zs2eTm5uLt/fo9sdZLRZ2f7yS7R+8g6Wvl9jMbHdQm5jDa9sa+f3qCrotNi6dGscd52QQGTDySqHV2kFNzZM0t7yOXh9M8rhbiYm5Eo3mS54317gd3r0BOspg8lVwzm/Bd/hDvnvtDh6obubV1m7SfL15JjOBqYEnedC2EMJjSUATQgjP4QkBbcuWLVx77bVs3boVg8HANddcQ25uLjfddNOIxktAO83s7RY27CtmwcIFJ30tl9NF/b5u9hU1c2BvF6pLJTYjiOy5MSTnhKMbxX6ukVJVlbq6OgoLC6mtrcVgMDBz5kxmzpyJwTC6Bhl26xB7Cj5m6/tvMtDVSWRyKjOXX0HEhGk8/2kNfy+qQ6dV+Mn8FH40L3lU+9NMpn1UVj1Mb+8WjMY00lLvJTQ0f7Qv181hhcInoOhJMITAsich64ITDivo6ueOigZarHauiw/nznHR+J6iSqcQ4syRgCaEEJ7DEwIawAMPPMCrr76KTqcjJyeHF198ccRFDQlop5HTbKflt1uwebsInz8O36mRaP29xuTa5l7rwapaM/2dQ3gbdWTMjCI7L4bQGL8xuccXNTY2UlhYSGVlJV5eXsyYMYNZs2bh5ze6+zkddvZ9WsDWd9+gt62F0LgEZi6/Ap/0aTz2USUf7mslJtCHu8/L4oJJ0aPan9bRsZrq6kcZHKonNHQhaam/wGg88cbOY2opcVfTWktg/HJY+jvwCx92iMnh5MH9zfyruYtxBi+ezExgdtCp+fMQQpwZEtCEEMJzeEpAOxkS0E4j1e7CsqeD5o8rMPQooFEwZIdgnBGNd2rQmJx5prpUGit6KC1qpmZXBy6nSlRyANl5MaROi0TvPfZVtdbWVtavX8++ffvQ6XRMmzaNOXPmEBg48j1kAC6nk4pN69ny9mt0NdYTFBnN9IsuwxQ/hYdXVVLa0s/UhCDuX5ZNTkLwyK/rstLQ8E9q657D5RoiNvY7JI+7Gb0+aJSvFHDaYcMz8Olj4O0PSx+HCZfCCUJjUY+Jn5U3cGDIxvdjw7gvORqjbuz/LIQQp58ENCGE8BwS0DycpwU0AOqKKNw/wOyJ8zBvbcWyow2X2YE2yBtjbiS+06PQjdGZZ4MmG+WbWyktaqa3zYLeR0v69Eiy82KISPySzTOG0dnZSVFRESUlJQBMmTKFvLw8QkKG37P1RarLRfW2zWx5+zXaaqrxCw1j6rJLqQoZz5Of1NA5YGV5Tix3nptBdODIl1XabJ3U1DxNU/Or6HT+JI+7hdjYb6PRjK7ZCQDt5e5qWtM2yDgfzv89BEQPO8TsdPJYTSsvNHYQ66PnyYwE5oWcuf/5hRBjQwKaEEJ4DgloHs7jApq5E36XilOjR5u6CDLOQ01ewmCDDvPWVqxVvaCAT0YIxulR+GSGoGjHoKqmqrRU91G6oZnq7e047S7C4v0YnxdD2owovA1fsoHGcfT09LBhwwZ27tyJy+ViwoQJ5OfnExERMep5H9i9g81vv0pTeSm+gUFkn3sxm7wy+dvmBjQKXD8vhevnJ+PrNfLXMDBQQWXVQ/T0bMTXN4W01F8QGrpg1Ady43LC5j9BwYOg84ZzHoEp3z5hNW1rn5nbyuuptlj5TnQID6TGEiDVNCG+siSgCSGE55CA5uE8LqA57XBgI41rXiDOvBt66wEF4nIhYymOqHMw1/hh3taGy2RD4++FcVokxumR6EJH14DjeKwWO5XFbewraqarcQCdXkPqtAiy82KISgkcfUgZhslkYuPGjWzbtg273U5WVhb5+fnExMSM+lqNpXvZ/ParHCjZibfRSPyii1nlSuHD0g6iAny489wMLp4SO+JDvFVVpbOrgKqq3zI4WEdISD5pqffg55c+6rnRtR/euwkObICUxe6W/EHxww4Zcrr4fV0rz9W3E+mt57H0OJaEjW5JqBDCM0hAE0IIzyEBzcN5XEA7aN26dSyYPx/aS6F8JVSshOYd7t8MHoeadj5Dvudirg1mqLIHVPBODcI4PQrD+FAU3cl3AlRVlfYDJkqLmqna2obd6iQ42kj23GgyZkVh8Bub5iUAZrOZLVu2sGXLFqxWK6mpqeTn55OYmDjqa7VWV7L57dfYv20zeh8DhjkX8s5gPPtazUyOC+SXF2QzLXHkSypdLhuNTS9TW/sHnE4zMTFXkTzuFry8RrcsE5cLtr0EHz/grqCd/RuY9n04wRlou/ot3FZeT5l5iMsig/lNWiwh+rGtaAohTi0JaEII4TkkoHk4jw5oX/ww72+Gyg/dga32U3DawBCMI3E5FvVczAcCcfba0fjq8J0aiXFGFPoxOvPMNuSgens7pUXNtNX2o9EpJE8JJzsvhrj04DFpXgIwNDTE1q1b2bRpExaLhcTERObNm0dycvKoK3cd9XUUv/M6FRvXo9HpMOVezPsDUbQP2Fk2KZq7l2YSFzzy98dm66a29g80Nf8XrdaXcUk3ERf3PTSaUQbVngPw/s1Qsw6S8uHCP0BI8vD3drl45kAbzxxoI0in49H0OJZFBI3uvkKIM0YCmhBCeA4JaB7uKxXQDmcdgP1roGKVO7QN9qBqvLGGfwez42wGW/zBBV6JARhnRGGYGIbGa2z2MHU1DbCvqJnKLa1YLQ4Cwg1kz40mc3Y0xjFqXmKz2di+fTsbN27EZDIRGxtLfn4+6enpaE5QcfqinpYmit99k9LCNdgVHQcmXMwacyguFH6UP46fLEjFz3sU+9PMVVRX/Zau7kIMhkTSUn9BWNhZowuQqgo7/w0f3ete1rr4lzDzetAM/2dUOjDIrWX1lAwMsiw8kEfS4wj3+hINTIQQp5UENCGE8ByeEtCeeeYZXnjhBVRV5Uc/+hG33nrriMdKQDsDRvVh7nRAwxb3MsiKldBdg1MNxGL8LmbrAhxmA4qPFt8pERhnROE1RmeeOWxO9u/soLSomeaqXhSNQtLEULLzYkgYHzrivV7D3sPhYNeuXRQVFdHb20tERAT5+fmMHz9+1EGtv7Odre+9xd6C1fSq3uxNX8bWwSDC/b2545wMLpsaN6o5d3ato6rqESyWaoKDZ5OWdh/+fpmje4H9zbDiNnfIjpsBFz0H4cPvcXO4VP7U0M4Tda34ajQ8lBbLJZHBY7o3UAgxtiSgCSGE5/CEgLZ3716+9a1vUVxcjJeXF+eeey5//vOfSU1NHdF4CWhnwJf+MFdV6Kx0B7XylagNW7Gp2Zg1l2Cx5YJLiz7WiHFGNL6Tw9H4jM1ept42C6VFzZRvbmHQZMcv2JvMOdFkz43BP8TnpK/vdDrZu3cv69evp7Ozk5CQEPLy8pg0aRI63eheg7m3h20r3mb3x6toUP0pTjiXAw4j42MCuH9ZNrOSQ0d8LZfLTlPz/6ipeQaHo5+YmMtJTr4db6+wkU9IVWHP67DqTrBZYMHdMOdm0A7/uirNQ9xeXs+2fgtnhwbweEYc0d5jty9QCDF2JKAJIYTn8ISA9vrrr/Phhx/y0ksvAfDggw/i7e3NnXfeOaLxEtDOgDH7MB9od1dnKlbhqi7GYp2F2XUedlcCis6FYUIoxjkJeMX7j0kFxulwUbu7k9INzTSUdQOQkB1Cdl4MSZPC0GpPrnmJy+WivLycwsJCWltbCQwMZO7cueTk5KDXj26p3+CAiZ2r3mP7qvfYSzRbIufRq3qzdEIUv1iaRULoyPen2e191NY9S2Pjv9FofBiX9FPi469BoxnFks+BdvjgZ1D2HkRPcVfToiYMO8SpqrzU2MEjNS3oFIVfp8ZyVXSIVNOE8DAS0IQQwnMcHm5WrVpFa2vrqK/hdDrRao+9NSUqKoqlS5eecA4XXXQRmzZtwmAwsHjxYnJzc3n22WdHdH8JaKeZqqp8+umnY/9hbrNAzTrU8pXYSyswm2dicc5DxYAuYAjjjGiMczLQ+I7Nnqb+zkHKNrZQtrEFc68VQ4AXWbOjyJoTQ1DkyTUvUVWVqqoq1q9fT0NDA0ajkTlz5pCbm4u39+j2wVktFnZ/vJLNH7zPRiWR7cG5oNFybV4yNy5Kxd9n5O+H2VxD9f5H6excg49PPGmpdxMefs7oAtO+d2Dlz2GwB/J/Dvk/A93wlbFai5XbK+rZ1GtmXrAfT2TEk2AYm/2AQoiTJwFNCCE8hycENICXXnqJ559/HqPRyPjx4/H29ubpp58e0f2/UgFNURQj8DxgA9apqvrycF/vaQFNtdvZv2wZ/dExpH77KvzmzkVjNI79jVxOaNqOa++HWHZ3YO6bgl1NB+wYonowzknAO3cayij3eR37Vi7q93Wzr6iZA3u7UF0qselBZOfFkJwTjk7/5ZuXqKpKXV0dhYWF1NbWYjAYmDlzJjNnzsRgGN25cHbrEHsKPqZgxQd8Qhrl/pkEeSvcsTSbb81IRDuK/Wld3UVUVT2M2VxJUNAM0tLuJcB/+GrYEcxd8OHdsOc1iBgPFz8HMTnDDnGpKv9q7uLB/c2owH3J0VwTG4ZGqmlCnHES0IQQwnN4whLHL7rnnnuIi4vjpz/96Yi+/owHNEVR/gYsA9pVVZ1w2K+fCzwDaIEXVVV9VFGU7wG9qqq+ryjKq6qqXjnctT0toDl6emh75BF6P1mDxmJB8fLCd/Ys/Bctxm/BAvSREafmxl37sRUXYN49gKU3ExU/dNo2jPEd+M5JQ5udD7qTr8iYe62UbWqhbEMz/Z1DeBt1ZMyMIjsvhtCTbF7S2NhIYWEhlZWVeHl5MX36dGbPno2f3+iu63TY2fdpAe++/wkryaDFJ5px/hp+c/k08tNH/v67XA6aW16jpuYp7PYeoqMvJSX5Z3h7j+LPsGKVu4nIQDvMvRnm3w364ff0NQzZuKO8gXU9JmYFGnkyM4FkX6mmCXEmSUATQgjP4SkBrb29nYiICOrr61myZAmbN28mKChoRGM9IaDNAwaAf30W0BRF0QKVwNlAI7AVuAq4CFilquouRVH+q6rqt4e7tqcFtM+sW7OG6X7+DBQUYCoowN7QAIDPxIn4L16E38JFeKennZK9RmpvB5a1GzHvtWIzRwMODLrtGBO78c6dhJKxBHxHeUjzF+/hUmms6KG0qJmaXR24nCqR4wLIzoshLTcSvfeXr6q1trayfv169u3bh06nY9q0acyZM4fAwMBRXcfldFK+sZC/v7ueD9U0TPoAZoQr/PY7c0iNChrxdRwOE7V1f6Sh4Z9oNHoSE39MQvwP0GpH2DxlsBdW3+duyx+a5t6bljBz2CGqqvJKazcPVDdhc6ncNS6a6+LD0Uo1TYgzQgKaEEJ4Dk8JaPn5+XR1daHX63nyySdZvHjxiMee8YB28IZJwIrDAtps4Feqqp5z8Oe/OPiljUCPqqorFEV5RVXVbw13XY8NaId9mKuqiq26GtOaAkxrCxjaXQKAPi4Ov0UL8V+0GN9pU1FG2SRjJOzNPZgLdmIpd+FyeKOlHaPuE3wTetBNyIPM8054yPKJDJpslG9upWxDMz2tFvQ+WtKnR5KdF0NEYsCXvm5nZydFRUWUlLjfrylTppCXl0dIyOjCpepyUbplE0+/u5V1rkScio7z4+FX311AaNDI/8e0WOqo3v8YHR2r8fGOITX1LiIizh95yN5fAO/dAn0NMOsnsOg+8Bp++Wur1c6dFQ2s7upnaoAvT2UmkGE8+a6aQojRkYAmhBCew1MC2snw1IB2GXCuqqo/PPjz7wEzgbuAPwJDQNGx9qApinIdcB1AZGTktFdeeWXM53uyBgYGjrs0T9PXh3fJHrxLSvAqK0NxOHD5GrCOn4B18mRs47NRR7n/6oRcYGxTCamz4t1nBFz4aLZj1H6E06+FrvDpdIXOoD8gDZQvt29NVVUsndCzX6W/AVQn+ARDcLJCYCJovb5c9WdwcJCGhgZaWlpQVZWIiAgSExMxjnJvn6qqNNbW80apmd3aBHxUK+cEdnP+tHi8fEYeelS1HJf6CtAApKJRrkRRRhZytQ4LyTX/JrZ5JYM+UVRk3EBv8KQT3A82oucfGBhE4VKGuAArOimmCXHaDPdMF0IIcXoFBgaO+Lyx4xmuScjpUF1dTV9f3xG/tnDhQs8MaKqq3jia634VKmjDcVksmDduxLSmgIF163D29IBej3HGjIPVtUXoo6PHdG6O7iHMW1sxb23GNeBEox3AqKzCqPkInb8LMs6FjPMheT7ov1xQtFrsVBa3sa+oma7GAXR6DanTIsjOiyEqJfBLLe00mUxs3LiRbdu2YbfbycrKIj8/n5iYmFFfa23RDh5aVc5+ZyChjl5+mKnjmm+dh8FvZN9JUVUnLS1vsr/m99hsnURFXUxK8s/x8Rnhn1XdBnjvRuiugdxr4axfg8/w1cYOm517q5p4r72XiX4GnsqMZ4L/yXXTFEKMjFTQhBDCc0gFbYyMdImjqqqPjOa6X/WAdjjV6WRw1y5MBQUMrCnAVlcHgHd2Fv6LFuO/aCHeWVljtm9NdaoMVXRj3trKUHk3qODt34zR8QYGV4F7yWXKIvcyyLRzwC989PdQVTrqTewraqaquA271UlwlC/ZeTFkzIrC4Df6g5ktFgubN29my5YtWK1WUlNTyc/PJzExcdRze23NTn5XUEeny5txQw1cN9HAhZdeiDEoeETXcDhM1B34Mw0NfwM0JCZeT2LCj9BqRxBsbRZY+zBsfh78Y+CCZyDtrBMO+6Cjl7srG+mxO7gpIZJbkyLxHoNunUKI45OAJoQQnkMC2hg5RkDT4W4Sshhowt0k5Nuqqu4bzXW/TgHti6w1tQysLcC0poDBnTtBVdFFR+O/cCF+ixZhnDEdxWv0AedYnH1WzNvaMG9rxdljReOt4hu2H+Pgf9BbtgEKxM+EjKWQcR6Ep4/6HrYhB9Xb2yktaqatth+NTiF5SjjZeTHEpQejjKINPsDQ0BBbt25l06ZNWCwWEhMTmTdvHsnJyaMKsVaHk+c+2MlfNzdjdSlMHijj+1MCWbh8OQFhI+vYODjYQPX+x2lvX4m3dxQpKXcQFXkhykiWizZshXdvgM4KmPIdOOdhMAwfEHvsDn5Z3cTrrT1kGH14KjOeqQGn4DgHIQQgAU0IITyJBLQxoCjK/4AFQBjQBjygqupLiqKcBzyNu83+31RVfXi01/a0gKaqKre+ugu9pYNL509jUlwgRm/dSV/X0d3NwNp1mNYWYN6wEXVwEI3RiHFePv6LFuE3bx7aUXY5POb8XSrW6l7MW1sZLO0Cp4pXtBZjWBmG/v+iaTv4XoemHgxr50P8DNCMbg1vV9MA+4qaqdzSitXiICDcQPbcaDJnR2MMHF1LeZvNxvbt29m4cSMmk4mYmBjmzZtHeno6mlFUljoHrDz67k7e3NOJl9PKrL7tXJkTyeyLLyM4OnZE1+jp3UpV1UOYTHsJCJhMetp9BAZOPfFAhxU+fRyKngJjGCx7CjLPP+GwT7r6ubOigVarnR/HR3DHuCgMWqmmCTHWJKAJIYTnkIDm4TwtoHUNWLn8z5uo6TQDoFEgIyqAnIQgcuKDyEkIJjnMiGaU1aLDuYaGMG/axEDBWkxr1+Ls7AStFt/cXHcL/0WL8IqLO+nX4hywYdnRjrm4FUfnIIqPFt9sX4xBJXi1vQ2168FlB99QSD/XHdhSFp2wM+HhHDYn+3d2UFrUTHNVL4pGIWliKNl5MSSMDx3V++RwONi1axdFRUX09vYSERFBfn4+48ePH1VQK2/t51dv72bzgX6C7b3kdW/inCmJzFp+OWEJSSccr6ouWlvfpnr/E9hs7URGLCMl5U4MhhGEvJbd8M4N0LYHJlwKSx93B7Zh9DucPLi/mX83d5Fs8OapzHhmBkkzAyHGkgQ0IYTwHBLQPJynBbTPrFi9FmPieHbW97KzvoddDb2YhhwABPjomJIQfDCwBZETH0yg75drsa+6XAzt2eNuMrK2AGtVNQDe6enuJiOLF+MzfjzKSexRUlUVW20/5q2tWPZ0gsOFPtYPY04Qvr670NSuhKqPYKgPtN6QvOBgdW0p+EeN+D69bRZKi5op39zCoMmOX7A3mXOiyZoTTUDoyJuVOJ1O9u7dy/r16+ns7CQkJIS8vDwmTZqETjeyaqaqqhSUt/Pg+3up6x4i0drE3I4iZkxOZ9byK4hKPfEST4fDzIH6v1Jf/wIACfE/IDHxx+h0JwiwTjsUPQ2fPuZuHHLe72D8JXCCZZvru03cXtFA45CNa2PDuCc5GqPuzHUnEuLrRAKaEEJ4Dk8JaNdeey0rVqwgIiKCvXv3AtDd3c2VV15JXV0dSUlJvPbaawQHH711RQLaGfDFD3OXS6Wmc4Ad9b2HQltlmwnXwbc6OdxITnywO7AlBJER6Y/uSyxVs9XXu5uMFKzFsn07OJ3owsPxW7gQ/8WL8J01C4336JYQHs5lsWPZ1YG5uBV7qxlFr8EwORzjtDC81L0olaug/APoPeAeEDvNvWct4zyIyDphyABwOlzUlXRSWtRMfVk3AAnZIWTnxZA0KQztCN8Xl8tFeXk5hYWFtLa2EhgYyNy5c8nJyUE/wjPnbA4X/9l8gKc/qcQ0ZGeypZLcjo1kTshi1vIricuecMJrDA01U73/d7S1vYeXVwQpKT8jOuqSE+9Payt1701r3gGZy+D8358w8JodTh6pbeGlxk7ifLx4MiOe/JAz990hIb4uJKAJIYTn8JSAVlhYiJ+fH1dfffWhgHbnnXcSEhLC3XffzaOPPkpPTw+PPfbYUWMloJ0BI/kwH7A6KGn8LLC5Q1uX2QaAr5eWSXGB5BystE1JCCLCf3QHFDt6ejCvX49pTQHm9etxWSwovr74zZ2L36JF+C2Yj+4YiX4kVFXF3jiAubgVy+52VJsLXaQvxulRGHPC0QxUQ8VK94+m7e5BwUkHw9pSSJgD2hNXs/o7Bynb2ELZxhbMvVYM/noyZ0eTPTeGoMiRtZhXVZWqqirWr19PQ0MDRqOROXPmkJubi/cIw2qP2cYza6r496YDeGtczDTtIqutmITMTGYuv5KkyVNP2Jikr28HlVUP09+/C3//8aSl3kdw8Izhb+x0uLs8rn0YdD5w7qMw+VsnDLpbege4vbyB/YNWvhcTyv0pMQRINU2IL00CmhBCeA5PCWgAdXV1LFu27FBAy8jIYN26dURHR9PS0sKCBQuoqKg4apwEtDPgS7XZV1UaewbZUd/jDmwNvZQ292F3uv884oINhwJbTkIQ2TEBeI/wH90umw3Lli2HqmuOtjbQaDBMzcF/4SL8Fy/CKylplK/y4LWtDiy7D1bVGgdAp2CYEIZxehTeyYEoA21Qscr9o2YdOK3gEwRpS9wt/FMWn/AMMJfTRf2+bko3NFO3pwvVpRKbHkR2XgzJOeHo9Cd+H1RVpa6ujvXr11NTU4OPjw+zZs1i5syZGEZ4MHh1u4mHPihjXUUH0QaVOV0biW4rISo5lZnLryA1d9awy0lV1UVb2wqq9z+G1dpKRPhSUlPvwmCIH/7GndXualrDZkg9Gy54GgKH32c46HTxRF0rf6pvJ8pbz+MZ8ZwVOvz7LIQ4NgloQgjhOQ4PN5WVD2IaKBv1NZxOB9rjFAv8/bJIT79/RNf5YkALCgqit7cXcP/bMzg4+NDPj/caPiMB7RQbqw/zIbuTfc397PwstNX30Nw3BICXVsP42IAjlkbGBhlOWMlRVZWhfaUMFBRgKijAWl7uvl5ysrvJyMJFGCZPQvkSp6vbmgfce9V2dqAOOdCF+uA7PQrjtEi0/l5gHYCatVC+Eio/hMFu0Ohh3LzP962dIHiYe62UbWqhbEMz/Z1DePvqyJgZRXZeDKGxI2uO0djYSGFhIZWVlXh5eTF9+nRmz56Nn9/Ixq+raOehD8qobh9gYrDCrOY1+LRWEBqXwMyLLydjzjw0w7x/Tucg9fUvUnfgL6iqk4T475OU9BN0umG+k+NywdYX4JNfgaKFJQ/CtGtOWE3b0W/mtvIGKsxDXB4VzG9SYwnWn3xnUSG+SSSgCSGE5/iqBDSA4OBgenp6jhonAe0MOJUf5q19Q+xq6Dm0NLKkqZchuwuAcH/vQ90icxKCmBQXiK/X8P8Ytzc1YSpYy8DaAszFW8HhQBsait+C+fgvWoRxzhw0I6wwfUa1O7Hs6cRc3Iqtrh80CoasEIwzovBOO3jmmcsJDcVQ8YE7sHXvdw+Onvz5vrWoiccNIKpLpbGih9INzdTs7MDlVIkcF0B2XgxpuZHovU8cMFtbW1m/fj379u1Dp9Mxbdo05syZQ+AIjixwOF38t7ieJz+upG/QzjlxOibUrMLaWE1QZDTTL7qU7HmL0Q2z323I2sr+/U/Q2vo2en0oKcm3ExNzOYoyzNy7a+H9m6G20B1sL/gDhIwbdq5Wl4un69p4tr6NYL2Ox9LjOC886ISvUQjhJgFNCCE8hyxx9HDfxID2RXani4pW0+dVtoZeag+2+ddqFDIi/Q9W2NyhbVzo8dv8O00mBgoLGShYy0BhIS6TCcXbG+OcOe7q2oIF6MKGb/t+1PzaLZi3tWLZ3obL7EAb5I0xNxLf6VHoDj/zrKPy831rDcWACoHxn1fWEvNAd+yDuQcHbFRsbqW0qJmeVgt6Hy1p0yMZnxdDeIL/CauKnZ2dFBUVUVJSAsCUKVPIy8sjJCTkhK+vz2LnDwVV/HNjHT56DVemeRG39wO6ayvwCw1j+gWXMHHREvTex99D2N9fQmXVQ/T1bcfPL5O01HsJCZlz/JuqKuz4J3x0H6hOWPwAzLgOTtCtc6/Jwm3lDewZGOTCiCAeTosl3OvLdRAV4ptEApoQQngOTw5od9xxB6GhoYeahHR3d/P4448fNU4C2hlwpj/Mu802dje4l0TubOhlV30vJqu7zX+gQc+Uz1r8JwQzJS7omG3+VZsNy/bt7hb+BQXYm5tBUTBMmoTf4sX4L1qIV0rKCcPPoes5XAyWdmHe2oq1qhcU8EkPxjgjCp/MEJTDuzMOdLiXQFasgv0F4BgE7wBIPctdWUs7GwxBR99DVWnZ30dpUTPV29tx2l2ExfuRPTeG9JlReBuGryb29vayYcMGduzYgcvlYsKECeTn5xMREXHC11fTMcBvV5bxSVk78cEGfpDtjffW92iu2IdvYBDTzr+YyWefh7fvsZubqKpKe/tKqvc/xtBQE2FhZ5GWeje+vsNUx/oa4f1bofpjiJ8FFz0HYanDztPuUnm+vp3f17Xip9PwcFocF0cEjfjPUYhvojP9TBdCCPE5TwloV111FevWraOzs5PIyEh+/etfc/HFF3PFFVdQX19PYmIir7322jG/4S8B7QzwtA9zl0tlf8fAwQqbu9JW0Wbisz/qlHDjoQpbTnww6ZF+R7T5V1UVa0XFoSYjQwe/S6BPTDjUZMSQk4MywnPGHN1DmLe1Yt7WhqvfhsZfj3FaFMbpkei+eOaZfdDdXKRiJVR8COZ20OggcQ5knO+urgUnHnUPq8VOZXEb+4qa6WocQKfXkDotguy8GKJSAocNJCaTiY0bN7Jt2zbsdjuZmZnMmzePmJiYE762oqpOHlxRSkWbiRlJIVw33ovewnc4ULITb6ORnHMvZOrSCzD4H7thh9M5REPD36k78CdcLhvxcVeTlHQjev1xGnyoKpS8CqvuAscQLLwHZt1wwi6ZFeYhbiuvZ0e/hXPCAngsPZ4ob6mmCXEsnvZMF0KIbzJPCWgnQwLaaaSqKvdtuA9tt5ZLZl1CVmgW3tovf+7YqWQasrOnsY+dn1Xa6nuP2+Y/JyGYcP/PX4e9tZWBdeswrSnAsnkzqt2ONigIv/nz8Vu0COPcuWj9TnAgM6A6VYYqujFvbWWovBtU8E4Nwjg9EsP4MBTdF5bsuVzutv2fLYXscDc4IWK8uyNkxlKIzjliqZ+qqnTUm9hX1ExVcRt2q5PgKF+y82LImBWFwe/YyyYBLBYLmzdvZsuWLVitVlJTU8nPzycx8ehAeDiH08Wr2xp4cnUl3RYbl06N4//S9dR8/BbVWzej9/Zh8pLzyF22HGPQsY86sFrb2V/zJC0tb6DXB5M87lZiYq5EozlO8DK1wQe3Q/kKiJnqrqZFZg87T6eq8kJDB4/WtuClUfh1aizfigqRapoQXyABTQghPIcENA/naQGta7CL76z8Dk0DTQDoNDoygzOZFD7p0I84vziP/Aewqqo0dA8eqrDtrO9hX3M/Dtfwbf6dA2bMRUUMrC1gYN2nOPv6UPR6fGfPwn+RuyukPvLESwSdfVbM29owb2vF2WNF46vDd2okxhlR6COOc+ZZ1/7PW/jXbwTVBf7RkH4uZJ4PSfmg/3zvl23IQfX2dkqLmmmr7UejU0ieEk52Xgxx6QeblxzD0NAQW7duZdOmTVgsFhITE8nPzyflBEs8+4fsPFdQzd821KLXavjJ/BSWj9Oye8WbVGxcj0anZeKiJUy/8FICwo79HplM+6isepje3i0YjWmkpd5LaGj+sW+oqrDvbVh5Bwz1wfw7Ie820A5fGauxWLm9vJ7NfWYWBPvzu8x44n2OH1yF+KaRgCaEEJ5DApqH87SA9pn31ryHX5ofJR0llHSWsLdzL4OOQQBCfEKYFPZ5YJsQNgGj/sTVpjPB3ea/74jDtI/V5n9qorvKFm3UMbhzJwMFazEVFGCvrwfAZ8IEd5ORRYvwTk8fNtSoLhXr/l7Mxa0MlnaBU8UrMQDjjCgME8PQeB2nw6GlG6pWuytr1WvANgB6I6QuPrhvbQkYQw99eVfTAKVFzVRsacVqcRAQ5kN2XgyZs6MxBh676mmz2dixYwcbNmzAZDIRExPDvHnzSE9PRzNMg44DXWYeWVnOh/taiQ0ycNfSTPIiVLa++yalhQWASva8Rcy46DKCo2OPfk9UlY6O1VRXP8rgUD2hoQtJS/0FRmPKsW9o7nQvedz7BkROhIv+CDFTjjs/AJeq8o+mTh6qaUEB7k+J4eqYUDQe+M0EIU43CWhCCOE5JKB5OE8NaF/8MHe4HOzv3c/ujt2HQlttXy0AGkVDalCqO7CFTWJy+GSSApPQKMN35DtThmvzH+Hv/XnHyLhAMmxdOAo/ZaCggMGSElBV9LGx+C1ahP+ihfjm5qIM04beOWDDsqMdc3Erjs5BFG8tvjkRGKdH4TXcmWf2Iagrcrfwr1gFphZQNJAw+2BXyPMg1B1uHDYn+3d2UFrUTHNVL4pGIWliKNl5MSSMDz1mx0uHw8GuXbsoKiqit7eXiIgI8vPzGT9+/LBBbdP+Lh5cUUppSz9TE4K4f1k2Kb52tr73FnsLVuN0OEifncfM5VcQnpB01HiXy0pDwz+prXsOl2uI2NjvkDzuZvT6oGPfsPwDWHE7mDsg71aYd+cRFcVjqR+08vOKBgp7BpgdZOTJjATG+XrmMl0hThcJaEII4TkkoHm4r0pAO5Y+ax97O/dS0lHC7k53cDPZTAD46/2ZGD7xUGibGDaRIJ+gUz/xL+GzNv87DjtMu67LArjb/GdGudv85/qrjD9Qgs/WjZg3bkS1WtH4++M3bx7+ixdhzM9He5z/UVRVxVbb7z4Ee08nOFzoY/0wzojCd3I4Gp9hGmKoKjTvPLgUciW0uRucEJZxcN/aeRCbCxoNvW0WSjc0U76phUGTHb9gbzLnRJM1J5qALzYvAZxOJ3v37mX9+vV0dnYSEhJCXl4ekyZNQnechilOl8qb2xt5/KMKOgesLM+J5c5zMwhQh9j+wTvsWr0S+9AgKbmzmLX8CqJS04+6hs3WSU3N0zQ1v4pO50/yuFuIjf02Gs0xwu5gj7sd/67/uF/zRc9B/PTjv18H3+//tXTzQHUTDlXl7uRofhgXjlaqaeIbSgKaEEJ4DgloHu6rHNC+yKW6qOuvc1fYDv6o6q3CpbqrU0kBSYcC26TwSaQFp6E7XsOIM6zbbDuiyraroZeBw9r8z4gysNBcR+b+XRh3bMLV0wM6HcYZ0/FbtBj/hQvQxx691A/AZbFj2dWBubgVe6sZRa/BMCkc44wovEZw5hk9B9wt/Ms/gAMbwOUAY7h731rGeZC8AKfGh7qSTkqLmqkv6wYgISuE7LwYkiaHodUeWSVzuVyUl5dTWFhIa2srAQEBzJ07l6lTp6I/ToVwwOrgT+uqeWF9LRoFrp+XwvXzk1Fsg+xc9T47V73HkHmAxEk5zFp+JXHZE46+xkAFlVUP0dOzEV/fFNJSf0Fo6IJjvwfVn8B7t0B/E8y+ARbeC17H2dt3UIvVxp0VjXzc1U9ugC9PZSaQZhy+AifE15EENCGE8BwS0Dzc1ymgHYvFbmFf177Pl0Z2lNA11AWAQWcgOzSbSeGTmBw2mUnhkwj3DT/pe54KzkNt/j8PbZXt7jb/GtXFYrWDs7rLSd+/C5+WBgC8s7LwX7gQv8WL8MnOPip0qKqKvXEAc3Erlt3tqDYXukhfjNOjME6NQHOMs92OMtjrDi4VK6HqY7D2g84AKQvdSyHTz6V/yJ+yTS2Ub2xhoMeKwV9P5uxosufGEBR5ZMBRVZXq6moKCwtpaGjAaDQyZ84ccnNz8fY+9jLBhm4Lj35YzgclLUQF+HDnuRlcPCUWh3WQXatXsv2Dd7D09RKbmc3M5VeSNHnqEe+Fqqp0dhVQVfVbBgfrCAnJJy31Hvz8jq68MdQPn/wKtr0EwePce9OS8oZ9i1RV5a22Hu6rasLicvHzpCh+Eh+B7jgNVYT4OpKAJoQQnsNTAtq1117LihUriIiIOHRQ9euvv86vfvUrysrKKC4uJjf3mHlLAtqZcKo+zFVVpdncfESVrbS7FIfLXZ2KNkYfUWXz9Db/JY19n4e2hl66zTZiBzqY117Ggq4y4pv3o6guNBGRBCxeiP+ixfjOnIHG68gOgy6rg8HdnQxsbcXeYAKdgmF8GMYZUXgnD3/m2SEOm7ui9tlSyL4GQIG46ZB5Hq60pdS3hVK6oYW6PV2oLpWYtCCy82JImRqOTv958xJVVTlw4ACFhYXU1NTg4+PDrFmzmDlzJgbD0UslAbbWdfPgilJKGvuYHBfILy/IZlpiCHablT1rVrP1/TcZ6OokMjmVmRdfQer0WSiH7XdzuWw0Nr1Mbe0fcDrNxMRcRfK4W/DyOvpwRGrXw3s3Qk8dTP8hnPUr8B7+IdVhs/OLykZWdPQxyd/A05kJZPsd+7UI8XUjAU0IITyHpwS0wsJC/Pz8uPrqqw8FtLKyMjQaDddffz1PPPGEBDRPcjo/zK1OK+Xd5UeEtmZzM+Bu858VknVEaIv1i/XYNv/13ZZD+9h2NvTSWNvM1OZSZrXuI7ejEm+HDYePAWXGbKKXLiFo4Xy0QUFHXMfWYsZc3IJlZwfqkANdqA++06MwTotE6z/C1vGq6t6rVn7wvLWWXe5fD0mBjKWYY8+j7EA0ZZta6e8cwttXR8bMKLLzYgj9QvOSxsZG1q9fT0VFBV5eXkyfPp3Zs2fj53d0kxOXS+XtnU08/lE5bf1Wlk2K5u6lmcQF++J02CktXEvxu6/T29pCaFwCMy++nIw589BoPw+HNls3tbV/oKn5v2i1voxLuom4uO+h0XzhtdvMUPAwbH4eAuPggmfcHS9P4P32Xn5R2Uivw8EtiZHckhiJ1zCNUYT4OpCAJoQQnsNTAhpAXV0dy5YtOxTQPrNgwQIJaJ7mTH+Yd1g6KOn8PLDt69p3ZJv/cHe3yElh7jb/vvrh9yKdKUN2J3ub3G3+S2rbsBUXk75/F7Na9hFiNeFUNHQlZ6HJm0/ShecSl516KHyqdieWvV2Yi1uw1faDRsGQFeKuqqUd/8yzY+prgsqD563VFoLTBoYQ1LRzaPS9gNIDsdSU9OByqkSOCyA7L4a03Ej03p8Hp9bWVtavX8++ffvQ6XRMmzaNOXPmEBgYeNTtLDYHf/60hr8W7selwo/yx/GTBan4eetwOZ1UbC5iy1uv0tVYT1BkNNMvupTseYvRHbbfbcBcRXXVb+nqLsRgSCQt9ReEhZ11dDhvKIZ3b4DOSsj5Lix5GAxBw74d3XYHv6xq4o22HrKMPjyVmcCUAM/8OyTEWDjTz3QhhBCfOzzc3F/VyN6BwVFfw+lwotUd++imCX4GHkyLG9F1JKAdgwS0kXG4HFT3Vrs7Rh7cz1bXXwd89dr8t/QNsquum7qN21E2FZJUvp3E/lYAGgOjaR4/Hd28+aTmTWdiQjC+XjrsHRZ3B8jt7bjMdrRB3hhzI/HNjUIXNMoloEP9sL/AXVmr/AiGekHrzWD8OVSoF1FaG0VPuw29j5a06ZGMz4sh/LDmJZ2dnRQVFVFSUgLAlClTyMvLIyTk6KWIzb2DPP5hOe/saibc35s7zsngsqlxaDQKqstF9fYtbHnrNdpqqvALDWP6BZcwcdES9N6fN/Lo7FpHVdUjWCzVBAfPJi3tPvz9Mo+8kX0IPn0UNvwB/CJg2VPuPXgnsLqzjzsrGmm32flpQgQ/T4rCR+uZf2+EOBme9kwXQohvMgloHk4C2pfXZ+1jT+eez5dGdh6/zf+k8EkEeh9d6fEEdqeL8u3lNK/6CO3mIqLqytGqLrq9/SmOHk9Tdi7G2bOYlBxJTmwAUe1WzFtbsVb3AuCTHoxxRhQ+mSEoow0XTgfUbzq4b+0D6KlDVaEl8CJKbRewvykUhx3C4v3InhtD+swovA3uzpu9vb1s2LCBHTt24HK5mDBhAvn5+URERBx1mx31Pfzm/VJ2NfQyITaA+8/PZmay+9BtVVU5sHsHm99+jabyfRgCApl2/sVMWXI+3r7uqpbLZaep+X/U1DyDw9FPTMzlJCffjrdX2JE3atoB794I7ftg4uVw7mNHHO59LH12B7/e38x/W7pJ9fXmqcwEpgd65sHrQnxZX4VnuhBCfFPIEkcPJwFt7Iymzf/kiMmkBqV6ZJt/Z28vrR8X0LbqY3Tbt6C3DjKk9WJHRDqbosZTMW4SqWlxzA33Z+aASsj+flSTHY2/HuO0KIzTI9Ed48yzE1JV6Ch3V9bKV0LTNqwuXyqViykdOofOvgB0eg2p0yLIyoshOsXdvMRkMrFp0ya2bt2K3W4nMzOTefPmERMT84XLq7y3u5nHVpXT3DfE0glR/GJpFgmhny8tbCzby5a3X6Nu9w68jUZyzr2QqUsvwOAfAIDd3kdt3bM0Nv4bjcaHcUk/JT7+GjSaw6qIDhsUPQmFvwOfIDj/CRi//IQv/9NuEz+rqKdpyM4P48K4Ozkao/bY35kS4qvmq/hMF0KIrysJaB5OAtqp9cU2/7s7dtM95D4XzKAzMD50vDu0HQxuntbm32WzYSneSv+aNfR9sgY62nEpCrWRKawLzWBT9ATa/MK5ONCPC/FiXJ8DBfBKDsRvZhSG8WEoui+5ZM/Udmjfmrp/HR1Dseyznk/VYB52p57gSB+y8+PImBWFwc8Li8XC5s2bKS4uZmhoiJSUFObNm0diYuIRlx20OXlhfQ1/Wrcfp0vl+3lJ3LgwFX+fz/efte6vYsvbr1K9dTN6bx8mLzmP3GXLMQYFA2A211Bd/QidXQX4+MSTlno34eHnHLk/rXWve29ayy7IuhDOewL8I4d9yQMOJw/XtPD3pk4Sfbz4fWY8ecFn7owRIcbK1+WZLoQQXweeEtCuuuoq1q1bR2dnJ5GRkfz6178mJCSEm266iY6ODoKCgpgyZQofffTRUWMloJ0BX9cP88Pb/H8W2sq6yw61+Y8xxnwe2MInkRWShZd2hJ0TTzFVVRkqLWWgYC2mtQVYS8sAMEfGsi9pMisD0qj1jWOp4s0FeBGFBqtewZwaSNS8eCLGBX35m9vMsH8tVKzCVl5AdXcWpYNLaLOno9GoJE/wJ3tRKnHpwVhtVrZu3cqmTZuwWCwkJiaSn59PSkrKEQGqtW+I331UwZs7Ggnz8+JnSzK4Ijce7WHNTzrr69jyzutUbFyPRqdl4qIlTL/wUgLC3Msou7qLqKp6GLO5kqCgGaSl3UuA/2EHYjsdsOlZWPuI+1Drcx+DSVfACbqAbuod4PbyemoHbVwdE8r9KTH4H2edtxBfBV/XZ7oQQnwVeUpAOxkS0M6Ab9KHudVppayr7NA+tpKOElrMLQDoNfrP2/wf/BFjjPGINv/25mZMa9cysKYA89atYLdDUDC9k2dQkjCJOm0S2b2Qhw49ChU6lf3RPvhMCGVycihZ0QF4fZnqmssJjVuh/AO6du+ktCWdisH5WFV/AoxDZM0IJuucHPS+Gnbs2MGGDRswmUzExMQwb9480tPT0RzW1r6ksZcHV5Syta6HzCh/frksmzmpR+4t62ltpvidNygtLABUsvIXMuOiywmJicXlctDc8ho1NU9ht/cQHX0pKck/w9v7sL1wHZXualpjMaSd424iEhg77Mu0OF08XtvCXxs6iPbW87uMeBaFBoz+/RLCA3yTnulCCOHpJKB5OAlonqnd0s6ejj3s7nRX2fZ17mPIOQRAqE/oobA2OXwy40PHn/E2/06TCfP69ZgK1jJQWIirvx/F2xufmbPonTSXbl0qIc1OwmwqA6h8jJ1VWgeGOH9y4oPISQgmJyGI6ECf0YfPziocpauo2VxLaWMSTbaJKDhJiuwge04kMfmz2FNWTlFRET09PURERJCfn8/48eMPBTVVVVm5p5XfriyjqXeQs7Mjuee8LMaFHdmso7+zg23vv8WeNR/hdDhIn53HzOVXEJ6QhN3eT92B52ho+CcajZ6kxJ8QH38tWu3BjpAuJxT/FT75NWj1sOQhmHr1Catp2/vM3FpeT5XFypVRIfw6NYYgveftXRRiON/0Z7oQQngSCWgeTgLaV4PD5aCqp+qIKtvhbf7TgtKOqLIlBZy5Nv+q3Y5l+3ZMBQUMrCnA3tQEgM/kSRjnLMPmlY6r0Y7GqdLgBW84hljlsmEBIgO8yYl3h7WchGAmxgZi8BrF0j5zJ71bP6F0QyvlTYkMugIxarvJim8gY24cBwxxrN+8nc7OTkJCQsjLy2PSpEnodO7AM2R38rcNtTxXUI3N6eL/Zidx0+I0Ag36I2/T28P2D95h1+qV2IcGScmdyczlVxCdmoHFUkf1/sfo6FiNj3cMqal3ERFx/ufBs7sG3rsZ6tZD8gK44A8QnMhwrC4XT9W18Wx9G6F6HY+nx3NuuGd2BRXiWOSZLoQQnkMCmoeTgPbV1TvU627zfzCw7enYg8l+sM2/l/+h9v6TwicxMWziGWnzr6oq1soqBgrWYCpYy9CePQDox6XjO3M5ilcqzn4VVafQEu3LWh8XK7tMHOi2AKDVKGRF+x8R2pJCfUdUZXMOmqlbs4HSzV3Ud7qbryR47yYrvpGh5HiKWnS0dnQTEBDA3LlzmTp1KvqDB1W3m4b4/UeVvLa9gSCDntvPTueqGQnovnCMwOCAiZ2r3mfnqvcYMg+QOCmHmcuvIC5rAj29m6mqepiBgTICA6eSlnYfgQGT3QNdLtjxD1j9S1BdcNavYPoPQTN8qN5jsnBreT37Boa4OCKIh9LiCPOSaprwfPJMF0IIzyEBzcNJQPv6cKku6vrq3M1HDoa26t7qo9r8Tw6fzKTwSWekzb+9rY2BteswFazBsmkzqt2OLm48hmkXgy4BnAq6SF+UyWGUhujZ3mZiZ0MPuxv6GLC6G6kE++qZctiyyMnxQQT46Ie9b3+HmbLVOynfZmJg0BuDppcMQwG+kd3s0KXT0A9Go5E5c+aQm5uLt7e7bf6+5j4eXFHK5ppu0iL8uG9ZNvPTj+60aRu0sGv1SrZ/8A6Wvl5iMrKZdcmVJE6aTGvrW+yv+T02WydRUReTkvxzfHyi3QN7G+D9W2D/GkiYAxf9EUJThn8PXSp/rG/jybo2/HUafpsWx0URQR6xL1GI45FnuhBCeA4JaB5OAtrXm9luZl/nPko6P+8aebw2/5PDJxNmCDvBFceOy2xmYMMGBtYUMLBuHU7zEPqEWXhnLUHRh4NWwTAhDOOMKHRJAezvMLOzvoed9b3sbOihqn0AVXVv4UoN9ztUYctJCCItwv+IboyH7ulSqd/XRWlBFXXlFlRVIdprL+HGTdQYgqh1ReLjpWXWzNnMmD0HX19fVFVldWkbv11ZxoEuCwszwrn3/GxSI/yOur7dZmVvwWq2vvcWpq4OIpNTmXnxFSTljOdAw19paPgboCEx8XoSE36EVmtwn/+2+3/w4d3gsMKi+2DWT0Ez/NLOsoFBbitvYJfJwtKwQB5NjyPSe/igKsSZIs90IYTwHBLQPJwEtG8WVVVpGmg6Yi+bJ7T5Vx0OBnfuxFSwFlPBGpw9TvSJeeiT5qJofdD4a/GbG49xWiRaf/d8+ofslDT0uUNbQy8763vosdgBMHppmRwf5A5t8cFMSQgizM/7iHuae62UbWqhbH0j/d02vHVWonw/pcunm1pNDF4aF9NTQpl99iX4RcRjdTj558Y6nl1TjcXu5HuzErllcRrBxqPfH6fDTmnhWorffZ3e1hZC4xKYefHlJOSMo6bu97S3r8TbO4qUlDuIirwQRdGAqRVW3A4VH0DsNLjoOYgY/uHpcKn8tbGDx2tb8NZo+E1qLFdEBUs1TXgceaYLIYTn8JSAdu2117JixQoiIiIOHVT9+uuv86tf/YqysjKKi4vloGpPIh/mp89I2/x/tjQy2hh9SgOAqqrYamrcTUYKPsXeqUefmIcuLB1woY/WELA4A5/scJTDqmSqqnKgy8LOhoNVtvpeSlv6cbrc/z8mhPgeDGzuSttnbf5Vl0pjZQ+lRc3U7OrA5VAJDGnGqi+hAQM6xclUvw7m5mQSOPkCOn3ieerjSv5XXI+/j55bz0rju7MS0WuP3j/mcjqp2FzElrdepauxnsDIKGZcdBkxkwOpqX0Uk2kvAQGTSU+7j8DAqe5q2r63YOUdYDXB/Dth7q3uro/D2G8Z4vbyBrb0mVkY4s8TGfHE+njG+XlCgDzThRDCk3hKQCssLMTPz4+rr776UEArKytDo9Fw/fXX88QTT0hA8yTyYX5mDdfmP8wQdkQDklPd5t/R2cnAunWY1m3D3uGDLmY6Gu8AUC14JWoIujAHr7hjL80ctDnZ29x3aGnkjvoe2vqtAHjpNEyMDWTqYUsjg7RaKja3UlrUTE+rBcXHgia0knZnH6gupiilzA3uJDR7PuVh5/DQdi1F1V0khxu57/wsFmZEHDO8qi4X1du3sOWt12irqcIvJJTcC5cTMWGIugPPYLO1ExmxjJSUOzEYYsHc6Q5p+96CqIlw0fMQPWnY98mlqvy9qZOHa1rQAA+kxvDd6FCppgmPIM90IYTwHJ4S0ADq6upYtmzZoYD2mQULFkhA8zTyYe5Z7C471T3Vh/axlXSWcKD/AOBu858enH5EaEsMSDwlbf5dg4MMbNiEqWAfji5fNEGp7t+wNeGd6k3gspl4J8YNe42WvsGDFTZ3aCtp6sPmcDdSiQrwISchiCnxgaRpvbBXmqjb2YHVaUGNaKaPJlRcTKCSfLYQblAoiLyah5tzqemH/LQw7l+WTXrksR9YqqpyoGQnm996labyfRgCApl6/lJCspppavkHAAnxPyAx8cfodEYoex8++BlYuiDvNph3B+i8j3ntzxwYtPKz8gaKegfIC/Lj95nxJBqGHyPEqSbPdCGE8ByHh5tfv7+P0ub+UV/D6XSi1R57v3x2TAAPXDB+RNc5XQFNel6Lrx29Rk9WaBZZoVl8K/NbgLvN/2dLIks6SlhZu5LXKl8DIMArgInhE5kc5l4WOSFswpi0+dcYDASctYiAsxahOp0MbNyFaW0VTkcQtgZ/2p7ahTrwCoZsP/zPzsNnwvijKkjRgQaiJxo4b6K7k6LN4aKspf+wvWy9rNrbCoBOozAxxZ8ZmjBC2gJRemKx+jezz1fHHjWDTJ2FeU3v8KHtGf7tdR7P1FzCuU918O2pEdx23mRCv7DvTVEUkiZPJWnyVBrL9rLl7dfY8L9X8DYamXLeDfinllF34HmaW94gJeVnRGdegpI4Fz66Fwp/5w5sFz0Hccd+WAEkGrx5fUoKL7d086vqJhYUV3BvSjTXxoahkWqaEEIIIb6BpII2BuS7rV89LtVFbV8tJR0lh1r9V/dUo+L+/2Fc4LhDVbbJ4ZNJCUoZszb/qlNlYH05pvUHcA4YUBQNjo4yXN0l+EwKJ+CsRfjOnInGa2T7sjoHrOw62C1yZ30vuxt6MVudRDoVpru8SLU5sfk0MWhsRlUcjIsMZkFIKwGNBTzdPZP/OM/CV2Pnlow+rl4yG6+oTHe7yWNo3V/FlrdfpXrrZvTePkw6fxKGxO0MWPbi7z+etNT7CA6eAVUfu1vym1pg9g2w8F7QG4Z9HU1DNu6saGRNdz8zAo08mRlPqq/PqN9fIU6WPNOFEMJzyBJHDycBTZxKZruZvZ17D1XZSjqPbPM/IWzCEUsjx6LNv7PPiqmoDnNxC6pVi2ozY6/fhKNtK745afgvXoRx3jx0wcEjv6ZLparddGhpZEldD7qmISbbIci7FYtvE6rWjo8xnLycRMIGq3l0h5Z1g8kkKa3cE/QJZ09ORslcCvGzQHt0MO2sr2PLO69TsXE9Gp2GiRckoI/Zit3eTkT4UlJT78KgBMLHv4Ttf4eQFPe5aYlzhp27qqq80dbD/VVNDLpc3JEUxY/jI9Ad4xgCIU4VeaYLIYTnkIDm4SSgidNJVVUaBxo/D2wdJZR3l+NQ3W3+Y/1ijwhsmSGZX7rNv+pSse7vZWBzM0OlXaAqOPsPYKsuwNG6E9/JE/FbtAj/xYvwSkgY9fX7Bu2UNPayc087nbs7MJjqsRsbcWltDDn96A9JxTc4gOIDvdQPejNbU8r9un+RbTRB2jmQsRRSF4P3kQ+3ntZmit95g9LCAhStk+wL/NGH70bFRUL890lK+gm6+u3w3s3QewBmXAeLHwDvo89lO1y71c7dlY2s7Oxjsr+BpzMTyPIbvgInxFiRZ7oQQngOTwloV111FevWraOzs5PIyEh+/etfExISwk033URHRwdBQUFMmTKFjz766KixEtDOAPkw/+YYcgxR3l1+RAOSVrN7D9hne98mhZ1cm3/ngA3LjnbMxa04OgdBceLs2sPQ7vdx9TXglZqC/0J3WPOZNAlFM/oGJ3abg02f1rNjwzb6HTW4dEM4Hb6U26PZRjCKRsGlqpznv59f8gJR9gbQesG4eZBxnjuwBcQcul5/Zwfb3n+LPWs+QvEaJON80AVXoteHkpLyM2JCz0Up+C1s+QsExcMFf4CUhcPOUVVV3uvo5Z7KJvodTm5NjOSmxAi8vsTrFWI05JkuhBCew1MC2smQgHYGyIf5N1ubuY09nXsO7Wcr7Sodkzb/qqpiq+vHXNyKZU8nOFwoPlacbdswb3wDrGa0YWH4L1yA38JFGOfMRuMz+j1b3S0DrF25ibIDO3FoLGidBgZ04/jQ5k+f0wWoJGo6uTlwPQtdmwixNrkHxuQcDGvnQeR4UBTMvT1s/+Addq1eic6/m9QlFrR+7fj5ZZGWdi8h/cB7N0JXNUy9GpY8BD7DN2TptDm4v6qRt9t7yTb68FRWApP9T91RCULIM10IITyHBDQPJwFNfBXYXXaqeqqO2Mv2WZt/raIlLTjtiNCWFJB0wiqby2LHsrsDc3Er9hYzil5BG2zF0bQJ86fv4hoYQPHxwTh3Lv6LFuK3YAG60NBRzdthd7L+o2K27tyMxdmHxumNzied9dpgynoH8dJpcLlcJLoaWaLdwVKvnUxQK9GgYjXGos06H132+ZA4l8HBIXauep+dq97FJ7KF+PxetD5mwsLOJi3xVnyL/wsbnwW/KLjgaUg/54Tz+7Cjj7sqG+i0O7ghPoLbk6LwOcaB20KcLHmmCyGE55CA5uEkoImvqp6hnkNVtpKOEvZ07mHAPgAc1uY/fDKTwyYzIXwCAV4Bx7yOqqrYGwcwb23FsqsD1eZEF2FAFz6EvWY9A+s+xtHSAoqCYcoU/Bcvwm/RIryTk0c8V1VVKdmxj3UFn9Jj7kBx6ulzpFDsHULjkJ3s6ADyUkNpM1k5cKCW9P6NnK3ZTr5mDz6KnUGtH51R8/AZv4yAzIWUFG1i+6o3MCbUEjWtB41OJT7+GpK98tCtuBM6ymDSt+DcR8A3ZNi59dod/Kq6mVdau0nz9eapzARyA40j/4MQYgTkmS6EEJ5DApqHk4Amvi5O1OY/OTD5UIVtUtgkUoNS0WqOPGDRZXUyuLuDga2t2BtMoFMwjA9DH2llaF8R5rUFDJWWAuCVlORuMrJoIYacHJTjHNZ4OFVVqa2t45MPC2hub0B16qgbSmGbLhCLqnJJTix3Ls1Eq1HYVd/LnroWXNUFJHUVMp/thCn92NFS6TOZjqgF9Dkiad9XSGBaOSEZfWgVf1KTbyauphml6CkwhMD5v4fsC084t7Vd/fy8ooFmq53r4sK5KzkaX6mmiTEiz3QhhPAcEtA8nAQ08XU2YBtgb9feI7pG9lh7AHeb/4lhEw8FtonhE49o829rMWPZ2op5RzvqkANdqA++06PwigNL8XoG1hRgLi4Gux1tcDB+8+fjt3gRfnPmoDGeuALV2NjIuoJPqa6pwu7Ss28olRLFD71W4doZidxyfiY+enfoc7pUqlp7adizHl3VKlK6C0lwNQKw15nIpsFJ2NV+YnNq8YuxoCOGSdE/IPjTl6C1BLIvhvOeAL/wYedkcjh5aH8z/2zuIsngxe8z4pkbfOYevuLrQ57pQgjhOSSgeTgJaOKbRFVVGk2N7O7cfSiwVXRXHNnm/+BB2pPC3G3+dS4Nlr1dmItbsNX2g0bBJysE44wo9NF6LBs3YFpTwMCnn+Lq70fx8sI4ezZ+ixbht3AB+oiIYefU2tpK0foi9u7bi8nlww5rKrWKgSCNhuunJHDtBel4G/RHjTM1ldGx7R28939EdP9uUF1s7k+k3BhM1LQ2vAPt9PelMNGeSUrF/1C8/GDp4zDxsuMemv2ZDT0mbi9v4MCQjf+LCeX+lBj8dCeuEApxPPJMF0IIzyEBzcNJQBPfdEOOIcq6yz5fGtlRQpulDQAvjZe7zf9nSyOVLHz3OrHsaMdltqMN8saYG4lvbiRaoxbL9h0MrC3AtKYAe6O7wuUzaZK7yciiRXinpR23eUlnZydFRUWUlJTQ7PBjmz2ZTlVPrFPD99OjueDsZCIS/Y893tyJWvkRlj0r8KpbS53JwJ7wEPwm9aPoXDSXJzCju48s134awuczcNbvSE1NQz/MEkaz08njNa38tbGDGG89v8+MZ0HIsffxCXEi8kwXQgjP4SkB7dprr2XFihVEREQcOqj6jjvu4P3338fLy4uUlBT+/ve/ExQUdNRYCWhngHyYizOp1dx6RAOSfV37sDqtAIQbwpkSOpnFQ7PJPBCLd4MLAJ/0YIzTo/DJCgGNgrWqioGCtZgKChgqKQFAHxfnbjKycBG+06ai6I+ujPX29rJhwwa2bd9BpT2YnY4ELKqWbJuWi4ICmTMvnvQZkXj7Hj0WAPsQ1Bailq9g/651lEeo+KRacNkUgkt8mDjYig09j7q+R1XMReQkhpATH0ROQjBRgUcfKbCtz8xt5fVUWaxcFR3Cr1JiCNTrxuidFt8U8kwXQgjP4SkBrbCwED8/P66++upDAW316tUsWrQInU7HXXfdBcBjjz121FgJaGeAfJgLT2J32ansqTxiL1u9qR6AaHs43xo6n7mdkzEOeaMaNfjnxuA3IwpdqME9vr2dgbXrGCgowLxpE6rNhiYwEL958/BftBBjfj5aP78j7mkymdi0aRMbirezYzCMUmc0CgozhnTMdnqRNS2S7LwYolMCj3+kgMsFzTvZX/QXqtSN6CMH0bYqTK4aIFgdpFKXzvWDN1DrdO9Niw70ISchiJz4YHISgpgQG4iPXsuQ08WTda0819BOmF7H4xnxnBM2/FlrQhxOnulCCOE5PCWgAdTV1bFs2bJDAe1wb7/9Nm+88QYvv/zyUb8nAe0MkA9z4ek+a/P/2bLIfR37yOpJ5NzeucwYmIAWLZ0RA5Djz7iZEwj0DQLAZTYzsHEjA2sKGFi3DmdvL+j1GGfMwG/xIvwXLkQfHX3oPhaLhS1btvDxxh1sNEdQ5wohUKswf9CLdItCSJSRrLkxZM6OwuDnddz5qqpKdfEfqOt4AY3BQmipiwmdvWgVMEdMY1P0d/nQkkVxk4WG7kEAdBqF7JiAQxU2nzAfHm/poNQ8xCWRwTyYGkuol1TTxInJM10IITzHEeFm1d3QumfU13A4Hei0x/k3QNREWProiK4zXEC74IILuPLKK/nud7971O9JQDsD5MNcfNU4XU53m//OEqobyvEvU8htzSTaHka/doBt4eV0ZFpJSE451OZfo8Lgrl3uJiNr1mA74D582zs7C/9Fi/FftBDvrCwURWFoaIitW7fyVuFuCgci6FKNjPPTcR7++DYOodEqJE8JJzsvhriMYBTNsatqLpeNir3P0tT6Ij62QVJ3W4n6f/beMzqu67y/3tMHU9B7750ACRKsAEmAklUoWZJrHKc4juM4LnGL7b9tJXbc4yK32ImT2IkTv44tOyqWRFWCDWAn0Uj0QrRBr9Pbve+HCwKE2ClAHFFnr8WlxeHM3Dtzlg7OD89z9vG7CEgqtHoD5N7FQsbdnDVs4eSEisbBOZqH53D5ggBEWfRYS6LpidBg0aj5Wm4y70qJveK1BIKLiDldIBAIQoc3QkD7+te/zunTp3niiSeu2CkkAtptQPwwF9wJ2D12eppb8Z+ZJWHIjEbWcD6slxciGzgT3UFefP6S5r8srgzL6DyOOkUy4m5qAllGm5SEtaYGy55azJWV+IHTZ87wi7pzHLXH4kLP9uQw3hEVz0zjDF5XgPBYI0U7kinanoQ5wnDFe/P5Zug4/00mpp8g0eYlv8+JRgaPJgKzNAuoIG0LFN5PMO8+uoKJNA7O0Tg4S+PQHF0uD/7SKOQIPRFzfu6R9exIi2JDehS5cRbUVwmIgjcnYk4XCASC0CHUWxz/67/+i5/97Gfs378fk8l0xdeJgHYbED/MBXcaQYcP59lx5o8Po5oJ4NMGOB3bweNh++g0XgAg1ZK6ZIws12aS1GzDdeAQzoYGZI8HtcWCuboKa+0ejNu3cbqnjx+93MFpRyQqFTxSFMEf52QxcGKSka45VGoVGaUxlFQlk14SjfoK1kaHs5v281/GM91AfruLhAUvs6oE5Jy7iHa0KueoAcTkQsH9yp+0zcx7Jc4OzvJvw5McUvmQAzLa9jnUo27CDVrWp0cutUauT4skynz19kvBnY+Y0wUCgSB0COWA9sILL/CpT32KQ4cOERd39fNbRUC7DYgf5oI7FVmW8V1YwHlyDFfrFAQk/PFqerPGecV6nFOzZ5hwTQCK5r84ppj1EcVUDulJaRolWH+c4NQ0aLWYNm3CXLObM/Fp/ODUJO0uC2Z1gPdtjOF9W8voPjFBx7FR3HY/5kgDRduTKNqRRPiivORSpqYP0tn+FSKGO8nvcqEJynToq4i+99MkBXugcx/0HwHJD6YYyL9XCWs5NfQENHyyfZBTCy5KtTrWzQTpGpinY8xOUFLmw6xY82JgU0JbQaL1mpp/wZ2FmNMFAoEgdAiVgPae97yHgwcPMjU1RUJCAv/4j//IN7/5TbxeLzExMQBs3bqVf/3Xf73stSKg3QbED3PBmwHJ5cfVPInz5Bj+UScqnZqwsji863S0GrppmWqhZaqFtum2Jc1/giGOPc4MKnsgqXEI9YURAPT5+TRsvZt/cScy6g8jTuvhw9sSeM+eSkba52mrtzHYNgNAelE0RTuSySqPRaNdDkmS5GfE9r8MtX+XnM4xEqa8jHvNNJsepOjtHyU1Kw1Vbx10Pg/dL4JnHjQGyN5NsOB+fhFZzTdGHGhVKr6cm8LDMeG0jiysaI2ctCufw6hTU5ZyMbApoS0h/HLNv+DOQMzpAoFAEDqESkB7LYiAdhsQP8wFbyZkWcY/7MB5agxX0ySyL4g2wYS5MhHThngkI3TNdinGyClF8z9kHwIgeVbNvcPRbOyWiO2eRJZkntm8l18nb2cBAzn6BT6yI4W9u7fgdUi0Hx2l4+gojlkvYVYdhVuTKK5KJjJhucfb75+jv//HeJv+g4LuBbR+iRNTaQxG38PmR95D5vqNqKQADB6Djn3Q+RzMKccOXMi4h09lfoijRFMdaeG7hWlkhBmWPufInHsxsM3RODTL+ZEFfEHlLLnkCCMb0qOWQltJsqL5F7zxEXO6QCAQhA4ioIU4IqAJBKGF5A3ibp7EeWoM35AdNCrCSmMxVyZiyI5YsjPOeGZonWxdCm3nps6hmnewoVdmW5+W/H41vy28h2fStxFUqVmnm+CDm5Oo2bMbozGMwfPTtNXbuNA6jSzJJOdFUlyVTM6GOLR6JRQ5nX30n/8yMadfIGnCyxwmnu3PQ07awNZH3k1u5VZUajXIMky0KW2Qnc8jjZzlV0kP8JWcjyCptXwxJshflGxErb38cG1vIEibbbHKNqRU2oZnFc2/TqOiOCl8ObSlRZEWHXb1c98EIYuY0wUCgSB0EAHtdUalUj0M7AXCgZ/LsvzStZ4vAppAELr4Rp24To3hPDuB7AmgiTFirkzEvDEBjXWldCMoBemb71MO0p5qoc3WhLGll8I+C63GhzgeW4YRPxs1Q+y1zvOWBx8htqQE57yXjmOjtNXbWJjyYDBpyd+SSElVMjEpyuHZ0zP1TDZ8mszWLgw+ifNyFvs7k4hIyWLzw++kcPtO1JpLKl0Lo9D1AsM99XxGv5UDUZVsWTjPY3ITOXnbIWcPGMOv+rkn7B6aLglsLcPzS5r/GLN+qSVyQ1okZWmRWAziLLZQR8zpAoFAEDqIgHYTqFSqXwAPABOyLJde8vi9wA8BDfAfsixf92ABlUoVBXxXluW/vNbzREATCEIf2R/EdW4a58lRfP0LoFZhLIrGvDkRY97Vzzyz++ycmzpHy0Qz5462caqvmDFtGlEqJ1tVF9g0cY7oaIjfs5v8bXvx2HS01dvoa5pECsgkZIVTXJVM7sZ4tHoYHfgl6pf/kSTbPK4wC4ftmzjfHSQiIZHND72D4p170OpWVslkj53Hz5/kH+YseIHP9v+cvx59Gk3mDii4TxGNRKRc8/MHghJd4w4ah2aX9rP1TjoBUKmgIMG6VGHbkB5JjtD8hxxiThcIBILQob29ncLCwtfUkXI7A5osy3R0dLxuAW0n4AD++2JAU6lUGqALuBsYBk4B70EJa9981Vu8X5blicXXfQ/4/2RZPnuta4qAJhC8sfBPunCeGsd1ZhzJ6UcTYcC0KQFzZQLayGtLNiRJ4n9OnecHz/cx69GSrp5hk3qQ8oFOUi60M5wOji3FRFbuIXaikOnGIHNjbnQGDXmVCRRXJROVLDNx4rPENPwOoyfIRFoZB/pLGekewhIdQ+WDb2PdnnvQGVbey7jXz+c6B3lh2s4GaYbv9zxG4egR5R+TyqFgrxLYEtcpqes6zLv8NA0vykcWQ9uCJwCAVWj+Qw4xpwsEAkHo0N/fj9VqJSYm5pZD2u0KaLIsMz09jd1uJysra8W/rVmLo0qlygSevSSgbQO+LMvyPYt///zizb06nF18vQr4FvCyLMuvXOU5HwQ+CJCQkLDxN7/5zS3f71rhcDiwWCy3+zYEgtBFAvMERAypCZtWHnLFwkKahDMOuIbB3heUeWnAzzO9fvxBmSLNGGUaGzkjFyg510aYc56WLBWNuRpc6VvIsFcRPpaKSlJjjITIHBUxqQPkDH2XNNsQbqOO5sS30NxkxTE6gtYYRkL5JuJK16PRLx+ULctwDB3/SRguVPyRb4IPjj9H4tQJwhc6USHjMcQxFbuZ6ZjNzEWWIKsv37d2xa9Dlhl3yvTOB+mdk+idkxiyS1ycjRNMKnIiNeREqsmJUJNqVaMVVbbXDTGnCwQCQeigUqkwm81oNLcu4pJl+bbtCQ8GgzidTl6duWpqal63gPYO4F5Zlj+w+Pc/BbbIsvzRq7z+b4E/R6m0NcmyfPnBAZcgKmgCwRufwIwH5+kxXKfHCS74UFt1mDcmYK5MRHuFM88uMmH38L0Xu3j89BAmHaxXD5HDGBlI5J0+SVzvALIKupPVnM4LYyJuE+nuaiIdSaCViCsxsLngFImn/wmjy8NERir2si/S9FInF5rOYDCb2XDvg1Tc91bCrMt7zqZ8Ab7YPczTE3OUWsL4fmEa61QO6HpRUfj31kHADYZwyL0LCvcq/w2LvKnvxekN0Doyv1RhOzs4x5RDaP5vB2JOFwgEgjuLUJzXX88K2k0FtJtFBDSB4M5BDsp4umZwnhzD0zkDEhiyIzBvTiSsJBaV7spltfO2eb7yTBsn+mdINqvYQB9xwSmyEhNZ73Zjra/He74NgIV4M2fy0xgJ30CsZxN6yYjPYuOu9J9SOnMer17N+Oa7Uad9grPPHKDn1DF0BiPlb7mfjXsfxhIVvXTdfZNz/L+uYab9AT6WnsAnMxMwqNXgc0H/Ieh4DrpeAOckqLWQsUPZs1ZwH0Rl3Pz3c1Oa/yhKksOF5n+VEHO6QCAQ3FmE4rwesi2ON4sIaALBnUlwwYvz9DjO0+MEZzyoTVpMG+Ixb05El2C+7PmyLPPi+XG+sa+dwRkX6+O1FHnbMXjnSE9PZ/u6dcR3d+M4cBDX8ePIfj++yCh6ynYxElaKxptEfFgTe2K/S7TfyUi8kVMlNVjN78DR0E3vsWOotRpKa97C5re+nfC4eABm/QG+1DPC42Oz5JuM/KAwjYqIS+5PkmDk9JLCn8kO5fGE0mXJSNJ6UF+jp/MaXFfznxyxuJctkor0KFKjhOb/VhBzukAgENxZhOK8/noGNC2KJGQPMILSuvjHsiyfv+WLXIIIaALBnY0syXh753CeGsN9fhqCMvqMcMyVCYSVxaHWr6wQeQNBfnn0Aj/e34PbH+SuTAPpC634HHMkJydTXV1NXmoqroaj2Ov24zh0GGl+HmdEGiPrHmRMn0VlxK9Zb9iHXw9ns8L5N60FjzePsr4o9B0zqGQoqq5hy8PvIjpZMTjun17gM51DjHn9fDAtjs9mJWHSXCF0TfcqQa1zn3JQtiyBNWk5rGVWg+61tSq+WvPfPDSP269o/mMtetanLR+mXZYqNP83gpjTBQKB4M4iFOf1tbI4/i+wG4gFxoEvybL8c5VKdT/wAxRz4y9kWf76LV3gCoiAJhC8eQg6fLjOTuA8NUZg0o3KoMG0Pg7z5iT0KSsFDlMOL4+93MVvTg5iNWp5e0EYlrFGFuZmiYuLY+fOnZSUlKCSJFxnzuKoq8NeV4dnZJTJ2PV4i4uoTPgfYlQ2xuP0nExP59ceLX3TXkr7wikYsqKWVagLEim6/x62lO9Bp43gq702/ts2TVaYnscK09kWeQ2xhGtmcd/aPujZD34n6C2QU6uEtfx7wBR99dffIBc1/2cvGiOHZulb1PyrVZCfYF1qjaxIjyQ7Vmj+X42Y0wUCgeDOIhTn9ZA9qPpmEQFNIHjzIcsyvgsLOE+N4WqZgoCELsWCuTIR0/o41MblilDH2AJfe7ad+p4psmPNvLckDHfvaaamJomOjqaqqoqysjK0Wq3yvj092OsOYK/bz0y3DfMGA3lpZwhqoSvXzKh1N86Et3BuvofZhhbiOnzogmoG412MlxnJLCwjzLqVpxyZjPrhL1JieTQ7CbP2OnvB/B64cGS5FdI+Cio1pG9b3rcWk7Nq3+Gcy0fT0NxSa2TTpZp/o5b1i4r/DYu6/0jTm1vzL+Z0gUAguLMIxXldBLQ1JhQHXSC4E5HcAVxNEzhPjuEfdaLSqQkri8O8ORF9uhWVSoUsy9R1TPD159rpm3JSnRfLe4uMDLQeZ3R0lPDwcHbs2EFFRQW6Sw6qDkxOYj9wAPfhp7AYGgi3zjERbaA9OwLHxL3k5H+EuKIoDj7zKwYO1CN7/EzGBzmdNclYDHii343DfBfhag8fSvDwx+lFJJoTb+BDSTDatBzWxs8pj8cWQOH9SmBL2XTL+9aufEmZvimnci7bYnDrHFtAWvxxkB1rVs5mS49iQ1okhYlWtFdq4bxDEXO6QCAQ3FmE4rwuAtoaE4qDLhDcyciyjH/YoVTVmiaRfUG08SbMmxMxbYhHY9bhC0j8z/EBfvhKFw5vgD/enM5DOVpaTx9jcHAQs9nMtm3bqKysxGAwrHh/yWHH9/svou//FUE1dOeFMRgez2zrg8QHKii6r5AR23lOP/skrvk5TJlJOCpiOBwu0aipJaBLxOg4QKb3FSpiCyiLLaMsrozimGKM2uvsOZu9AJ0vKIFtoAGkAJjjIP9eReGftQv0plX/Tp3eAC3D8zQOLR+mPeXwARCm07AuNWKxwhZFRXok8Xew5l/M6QKBQHBnEYrzughoa0woDrpA8GZB8gZxt0ziPDmGb8gOGhVhpbGYKxMxZEcw5/bzg1e6+NWJQUx6DR/fk8euZDjWUE9fXx9Go5EtW7awZcsWTKZXBZ/pXuSnP4Jq8BgzVgttRTrmXVmMN70bo81MTkYAKdVP65mj2KeniM/KYd1b385/WsN5fEomDDeJ9sexz+4HQKvSkh+dvxTYyuPKSbOmXd206J5V9qt1PAc9r4B3AbRhi/vW7lNCmyVuTb5XWZYZnnUvyUcaB+c4b5vHH1R+ZqREhilVtrQ7T/Mv5nSBQCC4swjFeV0EtDUmFAddIHgz4h9z4jw5hvPsBLIngCbGiLkyEfPGBPpcXr6+r52DnZNkxpj4wv1FFEcEOHLkCJ2dnej1eiorK9m2bRsWyyWyD0mCU/+B/MqXkQnSmxnBYGIA11A5o61/hDxnJsneQljiNBc8EyzMzxKdkkbEw+/hR4Y4OlxeHow18VbrKP0zzbRMttA61Yor4AIgyhBFWVzZ0p/SmFIs+ivIRgI+GKhftEI+D/NDgArSNi9aIfdCbB6soVbf4w/SNrqwVGFrHJxjZO7O0/yLOV0gEAjuLEJxXhcBbY0JxUEXCN7MyP4g7nPTOE6O4eufB7UKY1E05s2JHJf8fP35DnomHGzLjuHvHygmRuPmyJEjnD9/Ho1GQ0VFBdu3bycyMnL5TWcvwB/+FvoP4U7MoinDg8sA/sHdDJy+n0DAgnW+D7P9CDMRDhYCXsxxifQ88j5+o7EQqdXyrfxUHoiPJCgF6Z3vpWWyZelP73wvACpU5ETmUB5XroS22DKyI7NRqy7ZAybLMNa6GNaeg9Fm5fHonOV9a2lbQL32Fa2JBc/SPrbGwVlahq+u+S9PjcT8BtD8izldIBAI7ixCcV4XAW2NCcVBFwgECv5JF85T47jOjCM5/WgiDOgq4nlG6+eHDf3Mu/38UWUan7q7ALXPQX19Pc3NSuApLy+nqqqKmJgY5c1kGc7+N7z0KLLkZ6xkPW3WLnS6WHSeP6P3lULmF9SoAx6sUy/jpAuHQcVCUgYv3/9e+nQmHoiL4Jv5qcTpdSvuc8G3wLnJczRPNS+FtgXfAgAWnYXS2NKltsh1seuIMkYtv3h+ZFky0n8YJD+ERSstkAX3KS2RhmscAbCKBIISneP2xcD2xtT8izldIBAI7ixCcV4XAW2NCcVBFwgEK5EDEu72aZwnx/D2zAHgywnnl9oA/1/XOEadho/U5PIXOzLxOO00NDRw9uxZJEmipKSE6upqEhISlDebH4FnPwHdLxFILqUjP4JxqROLpYgY08cZOJ1C9+kxAn4Zo7uZgL2eBWOAs2VV1FfuwaJR8/XCdN6WGH3VFkBZlhlYGKBlarnK1jXbRVBWqlPp1vQVrZH5Ufno1DrwLEDvfiWsdb0InjnQGCB71+J5a/dCeNLaf+GX8GrNf+PgLPYraP4r0iNZHwKafzGnCwQCwZ1FKM7rIqCtMaE46AKB4OoEZjw4T4/hOj1OcMHHsEnNv4QFODTtIC06jM/fV8R9pYk4HA6OHTvGqVOn8Pv9FBYWUl1dTUpKilJNa3kcnv8sst+No/IRWixteHw24mLvJj31Mwy3Gjhfb2NqyAGBIVSuQwxbZV7Y/Qi2xHSqJm18M85MzrYtqI3XtyK6/C7aptuWQlvzZDNT7ikADBoDJTEly6EttowEYzQMHleqax3PwdyA8kbJFcutkPHFa7pv7UpcV/MfZ2bDJa2RBQmvr+ZfzOkCgUBwZxGK87oIaGtMKA66QCC4PnJQxtM1g/PkGJ7OGU5JAf5Z56fX76cyI4p/eLCEdakRuFwuTpw4wYkTJ/B4POTk5FBdXU1mZibYx2Hfp6H9GeSkcmyba+heeBJJ8pGW+mdkZn6UWRu01dvoOjWO12FDDpzgWF48RyrvQhcM8KE//JY/1kpYa2qx1OxGGxV1vVtX7l+WGXOOrWiLbJtuwy/5AUgwJSy1RZbFrqNI0mDsflmpro0szqWRGUpQK7xfOShbo7vGFdeOi5r/s4vykaahlZr/stSI5cO00yOJt66d5l/M6QKBQHBnEYrzughoa0woDrpAILg5ggtenGfGmT85xtOzdv4DL/PIvK0kkc89VEJ8uBGPx8Pp06c5duwYTqeT9PR0du7cSU5ODqq2p+G5T4NnnsD2v6Er0cPoxJPodFFkZ32C5OR3E/Sr6DkzTlu9DVt3H1P6dvZtL2MoOYvCC1187j9/SubUJGEbNmCtrcVSW4MhK+umPocv6KNzppOWKaXC1jLZwohjBFA0/wXRBUqFzZJB+fwkqf1HUfUdhKAXjBGQ9xYlsOXeBcbwNfimb4yLmv+Lga1xaI62V2n+N1w8TDs9kpLkcAza1ZGiiDldIBAI7ixCcV4XAW2NCcVBFwgEt4YsyXh75xg7buPf2mw8LvvQqVT8VXESH3pbCSazHp/Px9mzZzl69CgLCwskJSWxc+dOCtJiUb/4BWh9HBJKcd79KToW/o+5uROYzXnk5X6RmJhqAKZHHLQ12DjX0M6x+EkObFoHwNvOneR99XUY2zsA0GdlYd1Ti6W2lrDyclSamw8hU+4pWidbl1ojW6dacQcUPX6UIYqymGLK1GbKZm2U9p/A4pwGtQ6yqpWwVnAfRKSu0jd863j8Qc7bFpZaI5su0fzrNWqKk8OXQ1ta5C1r/sWcLhAIBHcWoTivi4C2xoTioAsEgtdO0OGj48gQ3z7WzyGflwTUfCI3nrfdk4chLZxAIEBzczP19fXMzs4SFxdHdXU1JbohNPs+DY4J5B0fZ7K4gp4Lj+H2DBITU0Ne7ucxm3MACPiD9DVOcvBIJ/+Z4KE/JYFUWz9/3tfBPdFWjGcacZ48CYEAmuhoLLt3Y91Ti3nbNtSvPlj7Rj+XFKRnrmeFgKRvvg9Y1PybkyiXdJTNDFM2PUy23486sQwK9yphLbHsdd+3djXGFzxLtsjGwTlahufw+CUAYi2GpZbIDWlRlKVG3JDmX8zpAoFAcGcRivO6CGhrTCgOukAgWD1kWebI0UG+/koXnW4f69DwydhINlelY1ofj6xTcf78eY4cOcLk5CRRUVHs2rKesrHHUTf9CmLzkR78PkO00X/hJ0iSh5SU95Kd9bfodJFL15kdc/LD4138Z1iAoAqqTr3M3dN2qh55mCT7NPb9dTgOH0ay21EZDJi3bcOypxbr7t1o4+Je02e8puZfrWNdQE3Z/ARlXi9l+lgi8+9TwlpmNWhvr3XxUvxBic4x+5Itsmlwjr6pZc1/QeJilW3RHJkda75M8y/mdIFAILizCMV5XQS0NSYUB10gEKw+QUnm8WMDfPelTqa9Ae5Bx4e0YWSUJ2DenIguzUJnZyeHDx9mdHSU8PBw7s83UND1U1QLI7D1w/iq/4a+oZ8xYvstWq2V7KyPk5Lyx6jVy3KOEZeXj53q5qgUIGl8mHsP/h9pUjgV972djfdsxtfciL3uAI79+/HbbKBSEVZWhqW2FuueWvQ5ObfU2ncpV9b8dxKUlepUhj9ImcdDWVBFWeJG8gofQZd/L4TdmODk9WTW6aNpePkw7aahuSXNf7hRy/rFlsiLlbbGkw1iThcIBII7iFBcq4uAtsaE4qALBIK1w+EN8NMDPfzHkT7UMvwxBt4j6bDGmzFvTiRsfRz9owMcOXKEwcFBIk1a3hXdRvLwcxCVBW/9MY64eLq6v8bs7FFMphzycj9PTMzupWAlyzJPTczx+c4hHP4A284cprKxDr02ibwte9n+jj1EJpjwdnVh378fR90BPOfOAaBLT8daU4NlTy2migpU2uu39d0ILr+L89PnlcA20UjL+Fmm/HYAjJJEsc9PuSGOspRtlJW+h/ikjaty3dVG0fw7ODu4HNq6xu1Lmv9Es4odBSm3TfMvEAgEgtUlFNfqIqCtMaE46AKBYO0ZmnHxrRc6eK5llIQwHR8Os1AzE0CtURNWGou5MpExzRxH6o/Q29tLnn6CR9T7MXnGYNNfIt/1ZaYcp+ju/gZu9wWio6vJy/0CFkv+0jUmfX6+0DXCM5NzZHo91L7wW2JGu1Fp4onLqqHywT3kViSg1Wvwj4/jOHAAe10drmPHkf1+NBERWHbvwlJTi7mqCo3FvGqfX5ZlRp2jtEw00XxhPy1jp2n3zeBfLN4lSirKzCmUpVZRnn0fRXElGDSGVbv+auLwBmhZrLK90tjDoFPDtPNyzX9FeiTr11jzLxAIBILVJRTX6iKgrTGhOOgCgeD149SFGb76bBstw/OUJVj5VFwUeT0OZE8ATYwRc2Ui8ylB6k8fo6/zHHepT7BZOo1sTUb90I+QsncyPPwr+i/8iGDQRXLye8jO+jh6ffTSNZ6dmOPz3cPM+gO8w2cn+/e/xD8/hkodjTFiGyW7dlO6M42YFAsAQYcTZ0MDjrr9OA4eIjg/j0qnw7R1K9baGiy1tegSElb9u/AFfXRc2E9L51O0TDTRElhgRKdU8LSoKDSnUpaynbKEDZTFlZFqSX3N7ZirzcGDB9m1a9c1Nf+pUWFLtsgN6ZEUr6LmXyAQCASrSyiu1UVAW2NCcdAFAsHriyTJPNk4wrdf7GB8wcuD6xL524x4Is7P4uufBzUYC2Nw5Ws5OdzC3LmXeYiXiWMab/E7MTz4HXwamf7+HzFi+zUajYmszL8lNfVPUKsVCceMP8A/dI/w+/FZCkwGPu6dZuZ3v2J+YhiVOgKNsZKkvK2U7kwnd1M8eqMSjORAAHdjI/b9ddjr6vAPDgJgLClRJCO1tRgKCtYmKLlmmGp7kpbup2mZbqNFq+KcwYB7UcwRbYikLG69cjZbXBmlsaWYdatX5bsVrjanr9D8L7ZG2uY9gKL5L0kJZ0Pa8mHaKZG3pvkXCAQCweoSimt1EdDWmFAcdIFAcHtw+QL866E+fnaoF4C/qs7mA6VJ0DyN68w4ktOPJsKAt8RIs7ud6Pafs4OT+LQR+O75NuGV78bh7Ka7++vMzBwhLCyTvNzPExu7Z2mx//LUPJ/tGmbc6+dDqXG8fXaIs0/8hon+HtRaK2rdRozh68nfnEpxVTLxGdYVe9t8vb2KZKSuDndzM8gyuuRkRTJSW4OpshKVTnfVz3jLBLzQf4RAx7P09r5Ic3CBFoOBFksE/SpF2qFCRW5ULmWxZZTHlVMWV0ZWRBZq1eu3B+xm5vSxeQ9NQxcD2xwtI8ua/zirYckWuSE9krLUCEz61dkPKBAIBIIbJxTX6iKgrTGhOOgCgeD2MjLn5tsvdPB0k404q4HP3FPA28uS8XbO4jw1hrd7FgB/toFBVT2Fwz8lgUkGI7ZgfOSHxGcWMTV9kO7ub+By9RIVtZ28vC9itRQCsBAI8pUeG78anSYnzMBjhWkkDHZz4onfMtx+Dq3ejFpXgUpXRmxaDMU7kinYkoDBtDJ4BSYncRw6hH1/Hc6jR5G9XtRWK5bqaix7arFUV6MJD1/9L0iWYbQJOp+Hjn3MT57jnMFAS1QyzeExtATt2AMuACw6C+ti1y1V2cpiy4g0Rq7+PS3yWub0Jc3/Ja2R/Zdo/gsTLzlMOz2SrJjLNf8CgUAgWF1Cca0uAtoaE4qDLhAIQoOzg7N85Zk2mobmKE0J5+/3FrMlO4bAjAfn6TFcp8cJLvjwmLwETP9NnuMZPBhoTHovWXs/SVJyAiO2/6Wv74cEAgskJ7+LnOxPotfHAnB4xs6nO4cY9vj4y9RYPp+dxGx3ByeefJwLTWfQ6sMIi9yEz1uK1mAmtyKe4qpkknIjLmu/k9xunEePYq+rw3HgIMGZGdBqMW+uxFKjVNd0KSlr80XNDSphrXMfXKhHkgIMhMfTklZGiyWKFt8sXfM9SBc1/+EZlMWWLYW2vKg8dOrVqfqt9pw+6/TRtHguW+PQHE2Dc9i9SsUwIkzH+ouK//Qo1qdGEmFag+qlQCAQvIkJxbW6CGhrTCgOukAgCB1kWeYPzTb+6fkObPMe7itN5PP3FZEeY0IOyni6ZnCeGsfTMY0k9xAe9n0ipQHayeVcxvuprNlLSkok/f0/ZnjkV6jVRrIyP0xa2vtQqw04A0G+3jfKL0amSDfqeawwjaooK+N9PRx/4rf0nDqGVm8gJm0rDnsxQX8YkQkminckU7gtkTDr5QdNy8Eg7uYWHAfqsO+vw9fXB4ChsHBRMrIHY0nx2uyx8sxD98tKYOt+GbzzoDXiytrJ+bT1tJgttMz30TzZzLRnGgCjxkhxTPFSW2RZXBnxpvhbuvxaz+mSJNM76VissCmVts5xOxd/HOfEmZcqbBvSoshPsAjNv0AgELwGQnGtLgLaGhOKgy4QCEIPty/Ivx/p418O9hKUZP6iKpOP1uRiNSoVk+CCF+eZcZwnbegX/j8idb/Gh5YX2MVs2j3s3LWLxCQVvT3fYmq6jjBjOrm5nyMu7h5UKhXH5xx8smOQfrePP02O4e9zkgnXapgaGuDkU7+jo+Ewaq2GlKIdSNJ6pkbUqDUqssrjKKlKJrUwCtVV2u28/f046g5gP1CH+2wjSBLahAQstTVYa2sxbdmCWn950HvNBHwweBQ69imBbX4QUEHqJuT8+xjN2ExL0EHzVAstUy20T7fjl/wAJJmTlloiy+LKKIopuiHN/+2Y0+0eP63D8zRerLQNzi1p/k36Zc3/xT1tcdbQPK5AIBAIQpFQXKuLgLbGhOKgCwSC0GVs3sN3Xuzk/84OE2vR8+m3FPCuTWloFsORLMl4e+dwN5wgrO9LGNUd9JHDU9RgTsxn566dxMVN0tP7TZzOLiIjN5OX90XCraW4ghLf6R/lZ0OTJBp0fKcgjT0xyh6yubFRTv7h95w/uB+Qya6oIixqG4NtEl5ngPBYI0XbkynanoQ58uoBIDAzg+PQYUXhX9+A7HajNpkwV1cr1bVdu9BERq7+FyfLMH5uuRXS1qg8Hp0NBfdDwf34kjfQMd+jHKY92ULzZDM2pw0ArVpLUXTRitCWYkm5rAoYCnO6LMsMzbiXKmyNg7Octy0QkITmXyAQCG6WUJjXX40IaGtMKA66QCAIfZqH5vjqs22cHpilMNHKPzxQzPbc2BXPCdo9+J/5Afqu7yPJcIAaGlQFxEbFUr27iqjo81y48EP8/lmSkt5OTvanMRjiOTvv5BMdQ3S5PLwzMYqv5KYQtXge2cLUJKeffYLWV14kEPCTv2UHSQV7GO7UMNI5h0qtIqM0huKqZDJKolFfo71O8npxHT+OfX8djgMHCExOgkaDqaJiSeGvT09fmy9wfgS6XlDCWv9hCPogLBry74GC+yCnFgxWJl2TtEy1LIW289PncQfcAEQboymLWzRGxpZRElvCqYZTITmnK5r/+SVjpND8CwQCwY0Rimt1EdDWmFAcdIFA8MZAlmWeax3lm/s6GJlzc3dxAl+4v4is2JVngckz/ciPfxj12FFm5SKelGsZVOuJNIWzY2cF4dENjIz8D2q1jsyMvyEt7f0EVHp+cGGcHw2OE63T8k/5qdwfF7n0ns65Wc7se5rml57D53aTvXEzJbseYtpmpv3YGO4FH+ZIA0XbkyjankR4bNi1P4sk4Tl3TpGM1B3A29UFgD43B2vtHqy1NRjLylCp12A/ldcOPfsX9629CO5Z0Ogha5cS1gruh/AkAAJSgJ65nqUKW8tkCxcWLgCgVqlJ1CayPWv7kuo/MyLzddX83wxC8y8QCATXJxTX6iKgrTGhOOgCgeCNhccf5Of1/fz0QA++oMSfb8vkY3vyiAi7xOgny3Dmv5BfehQCQS5o38VznnSm1A4sOhNbKjKxJu9nevoVjIZkcnM/R3z8Xs453HyyY4hzDjdvjY/k63kpxOmX39fjcND4wjOcff4PeBx20tetp/KhdxL0J9HWMMpgmyLiSCuKpnhHMlnlsWi01w8svqEhHAcOYN9fh+v0aQgG0cTGYq3ZjaW2FvO2baiNxtX+KiEYgKHjiwr/52C2X3k8eQMU7FUCW0IJXFJdmvfO0zrVSstkCwc7DzIsDWP32QGw6qysi1u3ojUywhCx+ve9ClxL869RqyhMtC7JRzakR5IVaxZVNoFAcMcTimt1EdDWmFAcdIFA8MZkwu7hey928fiZIaJMej55dz7vqUxbafGbH4ZnPgE9LyMlVNKhez+HhiYYV80RptKzqTAMU9rLuDydRERUkJf3KCZLGT8ZHOexC+NYtGq+kZfKQ/GRKxbnPreL5lde4PQzT+CanyM5v4gtb3sXsemldBwdpf3oKI5ZL2FWHQVbkyjekURUovnyD3EFgvPzOA4fxl5Xh/PwESSnE5XRiHnHDqy1tVh270IbE7PK3yZKqJ3shM7nlMA2fBqQITJ9cd/afZCxAzTLgfXgwYPs3LWTCwsXltoiWyZb6J7rXtL8Z4ZnrghseVF5aNWhWZ2acfpoXpSPnB2co2loDsclmv9LA1t5WuTKXwoIBALBHUAortVFQFtjQnHQBQLBG5tzI/N89dk2TvTPkJ9g4dG9xezMj1t+gixD82/ghc9BwItU/f/oclXRcPYUQ/4J9LKailwHYWkHCEgzJCY+TE7233EhGMkn24dotLu4Nzacb+WnkWhYuSD3+7ycO/Ayp/7wf9inJonPzGHL295FzsatDLXP0t4wSn/LFLIkk5wXSXFVMjkb4tDqb0xSIft8OE+ewlFXh72ujsDYGKhUhG3YsKTwN2RnrebXuYx9fHHf2vPQdwACHjBEQN7dSljLu5uDxxuvOKe7/C7OT59faotsnmxmxjMDQJg2jOKYYmU/W6yi+o8zxV32HqFAcEnzv9wa2TWxrPnPjbesaI3MT7AuCWwEAoHgjUgortVFQFtjQnHQBQLBGx9Zlnnx/Djf2NfO4IyL2sJ4vnB/EbnxluUn2cfguU9Dx7OQXAEP/YSBcT2H9h+kb34YozpIWdYAxuQTqDRaMjL+mtS0D/Bzm4N/6h/FoFbzj7nJvDsx+rJWt2DAT9uRA5x6+vfMjtqITkljy8PvpHDHLtyOAB3HRmlrGGVh0o3BpCV/cyLFVcnEplq4UWRZxtvejn1/HfYDdXjb2gHQZ2YuSUbC1q9HpVkDQ6HPCX0HFYV/1wvgmgK1lpmIEqK3/gkU3KtU2q5x7zanbUWVrW2mjYCkVKduVfN/O7B7/LQMz69ojZy5RPNfnnrJYdppkULzLxAI3lCE4lpdBLQ1JhQHXSAQ3Dl4A0F+efQCP97fg9sf5E+2ZvCJu/KINC2eOybLcP5J2Pd34FmAXZ+Fqk8yNjbJoX0H6BjpJszgpDSrDUN8B3p1PLkFn8MVfg+f7hzm+LyTmmgr3ylII9V4+VlmkhSk61g9J576HVODF4hISGTzW99B8a49aDRaRrpmaau30ds0iRSQic8Mp6QqmdxN8eiNN9f257fZsB84gKPuAM6TJ8HvRxMVhWX3biy1NVh27EBtMq3G1/qqDxlU2h87n8PZ+H+YXcPK44nrlhT+JJWv2Ld2JbxBLx0zHStC281q/kMBWZYZnHEt2SIbh+Zou0TznxYddokxMoripHD0N7AvUSAQCG4HobhWFwFtjQnFQRcIBHceUw4vj73cxW9ODmI16vjEXXn8ydYMdBf3pzmn4PnPwbnfQ8I6ePgnkFTO9PQ0h185SGvHOazWcYqym9CFj2OWi8jJf5RnVDl8rW8UFfAPOcn8aXIM6iuEBlmS6D17ihNP/Iax3m4s0TFseuBtlN11DzqDEY/DT+eJMc7X25gddaIzaMjbFE9xVQrxmdabDiJBux1nfb2i8D98GGlhAZVej3nbNix7arHs3o0uPn4VvtmVHDx4kN2lqYq+v/N5RTgiSxCeAvn3QuH9kFkN2hurIt2o5r88rpySmBJMujUIoKuAxx/k3Mii5n/RHDl6UfOvVVOaHL7UFrkhPYrkCGNIhk+BQPDmIxTX6iKgrTGhOOgCgeDOpWNsga892059zxTZcWYe3VtETUH88mK44zl49lPgnISqTyoVNa2Bubk5GuobaDx7hpi4bnIym9EYnEQ6dmJI/RRfUYVxeM7B9kgLjxWmkRl25QAiyzIDrU2cePK3DLedIyw8go33P8T6e/ZiMJmRZZmxvgXa6kfoOT1BwC8Rk2KhuCqZ/M0JGM03L6GQ/X5cZ84oCv/9dfhHRgAwlpUpkpHaGgx5easSCC6b051T0P2S8r321oHfBXor5O5RKmt5d4Mp+obf/3qa/7zIPKXKtvgnMzx0Nf+j826aFlsiGwdnaRmexxtQRCrxVsNSWNuQFsk6ofkXCAS3iVBcq4uAtsaE4qALBII7G1mWqeuY4OvPtdM35aQ6L5a/f6CY/ASr8gT3LLz4KDT9CmIL4OGfQqryc8But3Ps2DHOnjlGQmIjqantqFERbdvL6aT38W2DTACZz2cn8ZepcWiuEXqGO85z4snHudB0BoPJzIZ7H2DDfW/FFK5o6L3uAN0nlara1JADjU5NbkU8xVVJJOVG3lKgkmUZb1c3jgN12PfX4WltBUCXlqZIRmpqMW3aiEp7a2HgmnO63wP9h5ara45xUGkgY/vyeWvRNy84uaj5vxjYWidbsfsXNf9661JLZFlcGeti14W05r9j1L5UYWscnOXCtAsQmn+BQHD7CMW1ughoa0woDrpAIHhz4AtI/M/xAX74ShcOb4A/3pLOJ+/KJ8ayWP3qeQX+8HGw22Drh6Hmi6BXWuhcLhcnTpygsXE/ScnHiI+/gMobjrr/T/lpei2HzbDJauL7Renkma99Xtl4Xw8nnnyc7pNH0RmMlN19H5seeARL1HJlaXLQzvl6G10nx/B7gkQmmCjekUzhtkTCrJfvfbtR/OMTynlrB+pwHTuO7POhjojAsnMn1j21mKuq0FhuXFxyw3O6JIGtcTGs7YOJNuXxuCKlDbLgfkXccgsHc0uyxIX5C0pgW2yP7JnruUzzXx6nGCNzI3NDVvM/7fDSPDy3ZIy8VPMfadKxPk1o/gUCwdoSimt1EdDWmFAcdIFA8OZi1unjB6908asTg5j0Gj6+J48/25apiBs8C/DKl+D0LyA6G976z5C5Y+m1Ho+H06dP09LyJEnJ9YSHT6FypNE2/rf8OCMLt1bFpxJi+GhRKtrr6NanhgY4+dTv6Gg4jFqroXT33VS+9e1ExCcsPcfvDdJzZpy2ehtjfQuoNSqyyuMoqUomtTAK1WtQuktOJ46GBhx1B3AcPEhwbg50OsxbtmCprcFaW4suMfGa73HLc/pMv1JV69wHA0dBDoIlQdm3VnA/ZO8CXdgtfS4Ap9/J+anztEwtt0ZeqvkviSlZqrKVx5UTGxZ7y9daS4TmXyAQvN6E4lpdBLQ1JhQHXSAQvDnpHrfz9X3tHOycJDPGxBfuL+Lu4gSljaz/MPzhYzB7ASr/Cu76EhisS6/1+XycPXuGtvb/IjHxKAaDC4ejmv/1/hUHY80Uu+E7MTFs2JCM+jpnns2NjXLyD7/n/MH9gExRVQ2bH34H0cmpK543bXPQXj9Kx4lRvM4A4bFGirYnU7gtCUvUa1O5y4EA7qYmReFftx//wCAAxuJiLLW1WPfUYigsvKzFblXmdNeMUr3seA569oPPDjoT5NQqYS3/HjC/tgAlyzIjjhFFPrJYZWufaV/S/Cebk1fsZSuKLkKvufVK5VpyLc2/Wa+h7BLN/4b0SGItQvMvEAhunFBcq4uAtsaE4qALBII3Nwc6lf1pPRMOtufE8PcPFFOUFK6c/VX3NTj+LxCRBm/9oRIaLiEQCNDUdJKu7n8mNvY0KhU0Bj7If6prWdCo+MvBAB+JjCCqMgl9qvUqd6CwMDXJ6WefoHX/SwT8PvK3VrH1kXcRl7Fyn1bAH6SvaZK2ehsjnXOoVJCxLpbiqmQySqJRa16bJEOWZXz9/dj378dRdwB3UxPIMtrkJKw1imTEXFmJSq9f/Tk94IUL9cv71hZGQKWGtC2L+9b2QmzuqlzKG/TSPt2+IrSNOkcB0Kl1y5r/xT/J5uSQ3AN2Pc1/erRpcS+bEtqKhOZfIBBcg1Bcq4uAtsaE4qALBAKBPyjx6xODfP+VLhbcft5dmcan7i5QDhkePAFPfwSmu2HDn8JbvgZhkSteHwwGaWk5TH//Y0REtjHrj+O32kc5ok4l1yHxpVY3ZZYwzJsTMa2PR32NM89c83Ocee4pml56Dp/bTfbGzWx95N0k5RVc9ty5CRftDaO0HxvFveDDHKGnaEcyRduTCI+99RbBSwlMTeE4dAj7/jqcR48iezyoLRYsO6sZSkyk8kMfQhMevirXWoEsw2jzcivkWIvyeEyeEtYK90JqJahX72DuCdcErZOtNE8pbZHnp87jCSp6/BhjzIq2yDeS5v/swBxjC8ua/3UpEStaI5OE5l8gECwSimt1EdDWmFAcdIFAILjIvMvPD/d389/HLmDUafhobS5/sSMTg+yHQ9+Chh8qe6Ue+AEU3HvZ6yVJorX1GYaGv0dY2AjHfDX82vBB5tHz5xMyf9nswKhRE7YuFvPmRPQZ4VddGHscDhpfeIazz/8Bj8NOemk5W9/2blKL1132mmBQYqBlmvP1NgbbpgFIK4yiuCqFrPJYNKtUMZHcbpzHjmOv24/jwEGC09Og1WLatGlR4V+LPjVlVa51GXND0PWC0gp5oR4kP5hiF/et3Qc5NaA3r+ol/ZKfntmeFVW2N7Lmf6nKNjhH68iy5j8h3LDiMO11KRGEXac1VyAQ3JmE4lr9jglo0RlF8t1f+MXtvo3LmJubIzIy8nbfhkAgEFwTty/I4KyLOZcfg1ZNerSJKJOOHH83H5p/jIzABY4Ya/iviL/Bob5C9UiWKDLuZ1PCE0iGIL/wfoTjxq2Ee4L8ZbeXt48GMcowpoMTVjVnLCqcmisHNXXAS7ytkcTB4+h9TuwRqdgydjAfkwNXCHcGn0TidJCE6SBGv4xPC+PRWsZiNLiNqxceVLJERHcLGyd6KOxtJG5GaQ8cj02lI2c9ndkbGE3IQF6DwBImOVnvPc0mz3HWe09hkR340NNq2MBp41bOGLYwr7nx89ZuhgAO3Op+5Y+qD7e6H0mlHKatlk2ESVmEyVmYpGzCpCw0rG5oXC1kGVy+AA5vALtH+e/FwAZg0muwGrRYjFosBi1GnQhsAsGbgVBcqz/+oe0ioK0loTjoAoFAcDXm3X4Gpl24/UGsRi0Z0SbC9TKPOH7DI47f4FBb+UX4RzgRVn3F12tUPiosT7Au7kXOq0r4N/ljzGkiyJjx8fBggOp5iUwvBIBWs4oTVhU9RhXyFYKXKugnbrSZpIFjGLwLOC0J2DKrmI0ruGJQQ5aJWpBImg4QMy+hAubNakZjNUxFapBWwfZ36ZwePTtOQV8jBb1NpNu6UcsyC+ZIurLX05GzngtpRQS0q6+F18gBCn3n2OQ5zibvMeKD4wB06wo5bdzKacNWhrUZV/6OVgEZCZ9qHLe6D9diYPOqRkClrBn0UgJhcvZiYMvGICejIjTDTiAoKYHNG8CxGNoWt7KhUatWBDaLQSuMkQLBHUgortXvmIAmWhwFAoFgdQgEJX57eojvvdTFrMvHOypS+cw9BcS7euDpDyv7pIofgvu/C5b4K76H1ztB67mvMjp3gP+V/4w6zVuIlwN8ryCd3RozzpNjOBsnkN0BNDFGzJsSMW9MQBN+uUkwGPDTfuQgJ5/+HbOjNqJT0tjy8Dsp3LELtebKC3/nvJeOY6O0NYyyMOnGYNKSvzmR4qpkYlNv/NyzV3O1OT0wO4vj0CFF4V9fj+xyoTKZsFRVYamtwbJrF9qoqFu+7lWRZeWMtY7F89ZsZ5XHo7IUI2TBfZC+DTRrew7a9TT/pbGlKw7UDmXNf8/EJZr/oVm6JxzIspJ3c+MsK4yRefFC8y8QvNEJxbX6HdPiKAKaQCAQrC4LHj8/qevhFw396DRqPrw7hw/sSMd48idw8FvKodb3fRvWvfOq1Rq7/Tznzn+JMy4vP5M/yqQ6gd1+B9/dWExKeCTu81M4T47h7ZsHNRgLYzBvTsSYf/mZZ5IUpOtYPSee+h1TgxeIiE9g80PvpHjXHrS6K1eqZElmpGuWtnobvU2TSAGZ+MxwinckkVeZgP4a8pIrcSNzuuT14jpxAvv+Ohx1dQQmJ0GtxlRRsaTw12dk3NR1b5gFm7JvrfN56DsEQS8YIxV1f8H9kLtnxfEJa8VFzf/FsNYy2ULHTAcBWdH8p1hSVgS2wujCkNX8L3j8tAzNLxkjGwdnmXX5AUXzX562qPlPi2K90PwLBG84QnGtLgLaGhOKgy4QCAQ3w4UpJ998vp0Xz4+TEhnG5+4r5MGkBVR/+BgMn1SkFQ98H8KTr/h6WZaZnHyJls5/4v/z7+YFHsDic/O+gIMPbdtETEwM/ik3zlNjuM6MIzn8aCL0mDYlYq5MQBtpXPl+kkTv2VOceOI3jPV2Y4mOYdMDb6Nszz3ojMYr3gOAx+Gn88QY5+ttzI460Rk05G2Kp7gqhfhM6w1Z/W52TpclCc/5NkUyUncAb2cnAPqcnEXJSA1h5eWo1Gsg2vA6oLdOqax1vQDuWdDoIbMaCu+H/PsgYo0EJ1fAE/DQMdOxHNqmWhhzjgGLmv+YIspiFWNkWVwZSeakkDQtyrLMwLSLxqHlw7TbR4XmXyB4oxKKa3UR0NaYUBx0gUAguBWO9U7z1WfbaBtdYGNGFH9/fwHrbb+F/V8BjQ7u+bqi5b/KolqSvAwN/ZIX+57nX+W/xKZKpWiin7/QytxTtYOEhATkgIS7fQbnqTG83bMAGPKisGxOxFgUjeqSM89kWWagtYkTT/6W4bZzhFnD2bj3YdbfsxeD6eqiClmWGetboK1+hJ7TEwT8EjEpFoqrksnfnIDRfPV9Y691TvcND+OoO4C9rg7XqVMQDKKJicFSsxtrbS3mbdtQh63OcQErCAZg6MTieWv7YKZPeTxpvVJZK7wfEkrXbN/a1Rh3jtM61UrLpNIa2TbdtqT5jw2LXVFlC2XNv9sX5Jxt+TDts4OzjC94gStr/pMj12CMBQLBLRGKa3UR0NaYUBx0gUAguFWCkszvzwzxnRe7mHJ4eWRDCp/faiD+wGfgwhHI3g0P/giirt7C5/VN0dH7Q346quIZHsIUdFPV2co9MZHs3LmTlBSlqhOY9eA8PY7r9BjBeR9qiw7zxgRMlYnoXnXm2XDHeU48+TgXms5gMJnZcO8DbLjvrZjCI675ebzuAN2nxmmrtzE5aEejU5NbEU9xVRJJuZGXVXBWc04Pzs/jOFKPo24/jsNHkBwOVEYj5u3bse6pVfatxa7BXi1ZhqkuJah17IPhU4AMEemLh2PfBxk7QPv6txz6JT/ds91LbZEtUy0MLAwAoFFpyIvKWxHaMsIz3jCa/5aReXyL1sjEcOPiXjYltJUmC82/QHC7CMW1ughoa0woDrpAIBC8VhzeAD890MN/1PejVsFfV2fxkfAj6Ou+rASAu/8RNv0lXKN1z+7o4Pn2f+e79moGVZmULvSw8VwXJWmp7Ny5k8zMTEDZR+bpmsV5cgxPxzRIYMiOwLw5kbCSWFS65WuM9/Vw4snH6T55FJ3BSNnd97HpgUewRF1fQT85aOd8vY2uk2P4PUEiE0wU70imcFsiYVYlrKzVnC77fDhPnVqqrgVGR0GlIqy8HMueWqy1teizs9em5c8xsbxvrfcABNxgiIC8uxb3rd112UHlryezntmlKlvLZAutU604/A4AwvXhrItbR3ms0hZZGltKhOHaofx24QtIdIwtLIe2oTkGpl0AaNUqipLCl0NbWhQZMaaQbPEUCO40QnGtLgLaGhOKgy4QCASrxdCMi2+90MFzLaMkhhv58i4r9/R9C1XvfkjfDg/9M8TkXPX1siwzOrGfb3ed4nf+uzCpfNw12Ex8/wQZ6elUV1eTm5u7tFANLnhxnhnHeWqc4IwHtUmLaUM85s2J6BKW2xqnhgY4+dTv6Gg4jFqroXT33VS+9e1ExCdc9zP5vUF6zkzQVm9jrG8etUZFVnkcJVXJ9Iw3U1NT89q/uGsgyzLejg7sdXU49tfhaWsDQJ+RsSQZCVu/HpV2DcyMPhf0HVzet+acBLVWqagV7lX2G16jOvp6IMkS/fP9S22RLVMt9Mz2IKOsWbIispaqbOVx5eRE5qBVr63F8laZcnhpWrRFNg7O0Tw0h9MXBCDKpFNaIhdbI8vSIgg3rv6xDQLBm51QXKuLgLbGhOKgCwQCwWpz6sIMX322jZbhecpTwvlhUTuZp78GAS/UPgpbPwzqq7dwSZKPQ72/59FhI71ks5k+trT14Z90kJSUxM6dOykoKEC9WJGTJRlv3xzOk2O4z09DUEafbsVcmUhYeRzqxXaxubFRTv7h95w/uB+QKaqqYfPD7yA6OfWGPte0zUF7/SgdJ0bxOgPozFCxJ4vCbclYol4fW59/dBT7gQM46g7gPHEC/H40kZFYdu3CsqcWy44dqM1rcDi0FISRM9DxnFJdm1IEJySULiv8kze87vvWroTD5+D89PmlKlvzZDOzXmUP4xtN8989YV/RGtk9oVQLVSrIi7ewIS1qqTUyN94iNP8CwWskFNfqIqCtMaE46AKBQLAWSJLMk40jfPvFDsYXvLy3RM+j8r8T1vcipGyCh34C8YXXfA+Xd5pvn3ueny/ko8fH+7VdWBrnmJ1ZIC4ujurqakpKStBccv5Z0OnHdXYc58kxApNuVAYNpvVxmCsT0acqSnn79BSnn3mClv0vEvD7yN9axZaH30l8ZvYNfbaAP0hf0yRHn2nDOaEsljPWxVJclUxGSTRqzeuzDyrocOCsr1cU/ocOIS0soNLrMW3birWmFktNDbqEK59N95qZ7l2UjDwPg8dAlsCatLhvbS9kVYM2NBTzsiwz7Bhe3sv2Btb8z7v9tAzPrWiNnFvU/FsMWsrTIpZC2/q0SGKE5l8guClCca0uAtoaE4qDLhAIBGuJ0xvgZ4d6+dnhPkDmu0W9PDD8GCqfA3Z9FnZ8QrE+XoOWqU4+0dZDWzCFCnU7HzX66D9tZ3JyiqioKKqqqigvL0d7SZufLMv4BhaUqlrrFLJfQpdsxlyZiGlDPGqjFtf8HGeee4qml57D53aTvXEzWx95N0l5BTf02Q4ePMj64s20N4zSfmwU94IPc4Sewu1JFO9IJjz29bPzyX4/rrONOOr2Y99fh394GADjunWKZKSmFkN+3trsY3JOQ/dL0Pkc9NSB3wl6C+TUKq2QeW8B0/X3/b2eXEvzr1frFc3/YmArjy0n0ZwYknvAZFnmwrRrxWHa7aN2goua/4wY0wpjZGGi0PwLBNciFNfqIqCtMaE46AKBQPB6MDLn5tsvdPB0k40Ci4f/iPstaaMvQuI6eOinkFR2zddLssyPu47xmE2LSg7wV6Z6Hggr5cSJYWw2G+Hh4Wzfvp2Kigr0+pXVD8kdwNU0gfPkGP5RJyqdmrB1sZg3J6LPCMfrdNL4wjOcff4PeBx20kvL2fq2d5NavO6ai/JL5/RgUGKgZZrz9TYG26YBSCuMorgqhazyWDSv46JYlmW83d1LkhFPSwsAutRULLU1WGtrMW3ciOoqB3q/JvwexeB5sRXSMQYqDaRvU6prhfdD9I1VKl9vrqX5jwuLWwpsZbFlFMcUh7Tmv3VkpeZ/wq5o/g0XNf/py6EtKUJo/gWCi4TiWl0EtDUmFAddIBAIXk/ODMzy1WfbaBqa469iz/GZwL+h981B1adg599dty2u3+nkY61nOe22UiK38oX4IVJ1b6GhoYXBwUHMZjPbtm1j06ZNGF91ULUsy/hHHMoh2E2TyN4g2vgwpapWkUBQE6D55ec58+yTOOdmSc4vYsvb3kXW+k1XDGpXm9PtMx7aG2y0Hx3FMevFaNFRuDWR4qpkohLXYH/YdfBPTOA4eBDH/jqcx44h+3yow8Ox7NyJdU8t5upqNBbL6l9YkmC0UQlqHftg4rzyeFzhcitkysZr2j1vJ37JT9ds14rWyEH7IKBo/vOj8leEtozwjJCtso3Oe1a0RbZeQ/O/LiUCo05o/gVvTkJxrS4C2hoTioMuEAgErzeSJPNMi41vPd+Ba36Kn8X9nq32lyCuSNmblrrxmq+XZZlfDg/zld4xgnKQP1L9ng9l5oFcQ339CXp7ezEajWzZsoUtW7ZgMl1e6ZC8QdwtkzhPjeEbtINGRVhJDObNiWhSTZw/9Aon//B77FOTxGfmsOWRd5K3eTuqS8LE9eZ0SZIZapuhrd7GhZYpJEkmKTeCkqpkciri0d6Gs64klwtHQwOOugM4Dh4kODsLOh3mykpF4V9Tgy45eW0uPntBCWud++BCA8hBMMdDwb2KaCR7N+hCu5pzUfN/sTWydaoVp98JQIQhgnWx65baIkvjSgnXh9/mO74yvoBE++jCUmBrHJxjcEZo/gWCUFyrh3RAU6lUZuAQ8GVZlp+91nNFQBMIBILQx+0L8u9H+viXg71UyWf5nuk/sfqnUG37KNR84bqL9RGPj0+1dXFoPkC+3M7H9E+yK//9+Hyl1NfX09HRgU6no7Kykm3btmG1Wq/4Pv4xJ85TYzjPTiC7A2hijJg3JWJcH01X01FOPv07ZkdtRKekseXhd1K4Yxdqjeam5nTnvJeOY6O0NYyyMOnGYNKSv1mpqsWmrkH16gaQg0HcTU1LCn/fhQsAGIqLsNYoCn9DUdHaLMzds9D9ihLWel4B7wJow5R9awX3KQp/S9zqX3eVCUpBRfM/tWyM7J3rXdL8Z0dkr6iy5UbmormGwfR2ci3Nf7RZv7iXbVHznxqBVWj+BXcgobhWX5OAplKpfgE8AEzIslx6yeP3Aj8ENMB/yLL8reu8z1cAB9AmAppAIBDcOYzNe/j2ix28fLabfwz7LW+TX0aOzkH10E8gY9s1XyvLMr8bn+XRrgE8wQBvl/+X90SMUZj/BdyuOOrr6zl37hxqtZqKigp27NhBZGTkld/LL+E+P4Xz5BjevnlQg7EwBtOmOAZn2znx1ONMDV4gIj6Byre+g2m1jto9d93UZ5UlmZHuOdrqbfQ2TiAFZOIzwynekUReZQJ64+07o8vb169IRuoO4G5sBFlGm5iItbYGS+0ezJsrUenXwG4Y8MFAvdIG2fk8LAwDKkjbvKjwvx/i8lf/umuEw+fg3PS5Fa2RFzX/Jq1J0fwvBrayuDJiwmJu8x1fmetp/vPjrStaI3PjLKiF5l/wBicU1+prFdB2ogSr/74Y0FQqlQboAu4GhoFTwHtQwto3X/UW7wfKgRjACEyJgCYQCAR3Hs1Dc3z12Tb0Q0d4zPgfJEiTqDZ/EPb8AxiuXWUa9/r5XOcgL0zbyaGfv5J/xOakzeRkfxqHQ0N9fT3Nzc0AlJeXU1VVRUzM1RfG/im3slftzDiSw48mQo9pYwKThjFOvPQ4Yz1d6MwWdrz9PZTtuQfdq/a73Qgeh5/OE2Ocr7cxO+pEZ9CQtyme4qoU4jOtt7WlLDA9jePgIewH6nDWNyB7PKjNZsw7q7HW1mLZuRNNRMTqX1iWYax1UeG/D0aVMSMmd3Hf2v2QtuWa5+iFGrIsM2wfpnmqeSmwdc50rtT8Lx6kXRaraP511zGb3i4u1fyfXQxt825F8281aClfqrJFsj4timhzaB5XIBBcjVBcq69Zi6NKpcoEnr0koG1DaVW8Z/HvnweQZfnV4ezi678OmIFiwA08IsuydLXriYAmEAgEb0xkWea51lF+8Fwj73X+kj/XvkTQmorukX9W9ihd57V/mJzj851DLAQCPMzveVi1j9zMD5KW9n7sdg9Hjx7l7NmzBINBSkpKqK6uJiEh4ervGZBwt8/gPDWGt1upghjyonAluHnxlV9gtw0RZg1n496HWX/PXgymm5eAyLLMeP8C5+tt9JweJ+CTiEmxUFyVTP7mBIzm27tYlzwenMeO4airw37gIMGpKdBoMG3apFTX9uxBn3pjh33fNPPDy/vW+o+A5AdTDOTdoxghs2uuG95DEU/AQ/tM+1JbZMtkC+OuceCNp/nvn3IuKf4bB+foGFvW/GfGmJZskRvSoihMsqJ7nc4JFAhuhVBcq7+eAe0dwL2yLH9g8e9/CmyRZfmj13mf93GVCppKpfog8EGAhISEjb/5zW9u+X7XCofDgWUtTFkCgUBwh+ELyrx0wY+tv5Wvqf+dbPUoAwlvYTDvfQS11w5BC7KK/yKMo+hJl8f4IN8li3lUqneiohK/38/Q0BA2m41gMEhMTAwZGRmEh19b6KB1Q/iwCuuICp1HhV8nMRPpoGOsnrHBVjR6A3HrNpCwrgJt2K0p2IM+mflBmO2V8cwqhvrwVIjKUWGK4/Yv0iUJ3YULGFpaMDS3oB0dBcCfnIy3vAxvWTmBjPQ1MTNqAi6iZxqJnTpB9MxpdAEnkkrHbFQ5U7GbmY6pxGcIrfPWbobZwCwD3gEu+C7Q7+1nyDeEX1aqU+GacDL1mWQZssg0ZJKmT8OgDs1DqL0BmQsLEr1zQXrnJXrmJOa9yhpSp4asCDXZERpyItXkRqqJMorAJggdQnGtXlNTE9oB7UYRFTSBQCC4M5iwe/jh862ktfyQv9I+h8cYh/HhH6EpvPe6r31hcp7PdQ0x5fPziO4Qe33/SlxEGfl5jxIeXobL5eLkyZMcP34cj8dDdnY2O3fuJDMz85rvK0synq5ZBvadwzKlAglUSXr6HC2cbn0WtV5L+V33senBt2GJuvXAMDlop63eRtfJMXyeIJEJJop3JFO4LZEwa2i0jvkGBrAfOIBjfx2uM2dAktDGxWGpqcFSW4N52zbUhjUIEkE/DB5bVPg/B3MDyuMpG5cV/vFFymapNyg3qvkvjyunLK6MdGv67Q/wV0CWZWzznuXDtAdnOTeygC+oNEIlRRiXKmwb0iMpFZp/wW0kFNfqIdvieLOIgCYQCAR3FudG5vn1E0/y55PfoUA9zHjWIyS88zEwXTsAzfkDfLnHxm/GZsjSe/nL4GNkBU6TmPgwOTmfwWhIxOv1curUKY4dO4bT6SQ9PZ3q6mpyc3Ove1B1dcV2nGfGcZ4aIzjjAYOaKZ2N053P45BnKd19N5VvfTsR8Vdvo7wefm+QnjMTtNXbGOubR61RkVUeS3FVMmmF0ahCRMwQmJ3Fefgw9roDOI8cQXK5UJlMWHZsx1K7B8vuXWijolb/wrIME+3L+9ZGziiPR2ZA4V4lsKVvgxDd13UzzHhmODd17qqa/4vikbK4MtbFrsOqv7K59HbjDQRpH7Uvh7ahWYZm3ICi+S9ODl+0RiqhLT1aaP4Frw+huFZ/PQOaFkUSsgcYQZGE/LEsy+dv+SKXIAKaQCAQ3HnIssxLLUPYnvkaf+L/PS5NOK63fIekre+87msPTC/wd51D2Lx+3mUd4F77P2BUBcnI+Gsy0j+ARhOG3+/n7NmzNDQ0sLCwQFJSEtXV1RQWFqK+QsvepXO6LMl4++ZwnhzDfX4agjIug5PztnqGXB3k79jB5offSXTya9urNW1z0F4/SseJUbzOANYYI8U7kijclowlKnRa3iSfD9eJE4rCv+4AgfFxUKsJ27BBkYzU1mDIylqbi9vHFvetPQ99ByHoBWMk5L1FCWu5d4ExNM8nu1kuav6bJ5uXVP8XNf8qVCs1/3Fl5ETkhKzmf9LupWlo2RjZPDyHS2j+Ba8zobhWXyuL4/8Cu4FYYBz4kizLP1epVPcDP0AxN/5CluWv39IFroAIaAKBQHDn4g0EefbFFyk6+QWKVf2ci9xD2nt/TERcyjVfZw8E+VqvjV/apskwqPmY8RmS5n6BwZBIbs5nSUh4EJVKTSAQoKWlhfr6emZmZoiLi6O6upqSkhI0muXF7dXm9KDTj+vsBM5TowQm3ATVQQbsbfTMNxK3IZctj7yT+Mzs1/QdBPxB+pomaasfZaRzFpUKMkpjKK5KJqM0BnUIiRhkWcZzvm1J4e/t6ABAn529pPAPKy9DpVmD4OB1QN8BJax1vQCuaVDrIKt6UeF/H0SskeDkNmH32Tk3taj5Xwxtc945QNH8XzxM+2KVLZQ1/13jl2j+h+boEZp/wRoTimv1kD6o+mYQAU0gEAjufKbmHZz5339k9+gvcKnCaC79Ajse/mt02msv9Otn7Xy6Y4gBj4/3xAZ5yP1Ngo5GwsPXk5/3RSIiKgAIBoO0tbVx+PBhJicniYqKoqqqivLycrRa7XXndFmW8Q0s4Dw5hqtlEgIyc/5JeucbUeUa2PS2d5CcX/iav4e5CRftDaO0HxvFveDDHKGncHsSxTuSCY+99mHftwP/yAj2ugM4DtThPHkKAgE00dFYanZjra3FvH076rA1uG8pCEMnofM55cy1mV7l8cSy5VbIxLI39L61KyHLMkP2oaW2yJapFrpmupY0/6mW1GVjZFw5BVEFIa35bx6aW2GNFJp/wWoSimt1EdDWmFAcdIFAIHij09d2Gumpj5Dr66BBuxn2Psb29aXX3LPiDAb5p74x/n14kmSDji/GDxA39lV8vgkSEh4kN+ezGI3JAEiSRGdnJ0eOHMFmsxEeHs727dtxOp3s2bPnhu5RcgdwNU9gP24jOOYmIPsZcnTgjHNS/Pa3kFZa9pr32ASDEgMt07Q12Bg4Pw0ypBVFUVyVQlZ5LBpt6FTVLhJcWMBx5AiO/XU4Dh9GcjhQGQyYt2/HUluDtaYGbWzs2lx8smtx39rzMHQCkBVlZsF9isI/owq0d+YC3x1w0z7dvhTYmieamXBPAIrmvzimeEVoSzAlhOQeMKH5F6w2obhWFwFtjQnFQRcIBII7ATkYoPsP3yGj+TG8spbfxvwNu971CfITr73X6NS8k092DNLj8vLuhHD+Qv8ss8P/CkB6+gfISP9rtItaf1mW6e3t5fDhwwwODqLT6di5cyeVlZUYb+Kgat+wnYVjI7iaxlEH1cz7ppgyjpH24EaytlauykLYPuOh/ego7Q02HLNejBYdhVsTKa5KJirx5s9qez2QfT5cZ85g31+HvW4/AdsoqFSElZVh2bMHa20N+pyctQkKjknoflGprPXWQcANhnDI3aMYIfPugrA1EJyEEGPOsWVj5FQLbdNteINeAOLD4lfsZSuOKSZMG3rVWQCXL0Dr8DyNi/vZzg7OMWlXPodBq6YsNYKKi6EtPYqE8Js/ZF5w5xKKa3UR0NaYUBx0gUAguJPwTXQz/eu/JmnuDIelMk6Wfon37915zVYnT1DiexfG+OnQBHE6HV/LMpE5+0PGx59Br48nJ+fTJCW+DZVq+TfvAwMDPPXUU8zOzmI0GtmyZQtbtmzBZLrx888kbxBH4yjTdd3oFrQE5QBTjBJRlUb2fdtRX6dV84auIckMtc3QVm/jQssUkiSTlBtBSVUyORXxaPWhKYyQZRlvZ6ciGdlfh+e84hDTpacvSUZMFRWotNrVv7jfrchFOvdB5wvgnAC1FjK2L+9bi8pc/euGGP6govm/VEAyZB8C7izNf3KEcbnKlh5JSbLQ/L+ZCcW1ughoa0woDrpAIBDccUgSzqP/hrbuy/iDMt9X/QlJtX/Dn23PRn+NNr+mBRef7Bik3enhbQlRfCZhmqn+r7Ow0ITVWkpe3qNERVYuPf/gwYPk5eVx5MgROjo60Ol0VFZWsm3bNqzWm9Obe0YWGHn6DOqBIDqVAZdsR11gIuORLeiiVqdS4Zz30nl8jLZ6G/OTbgwmLfmbEymuSiI2NTR17Bfxj43hOHAAe90BXMePI/v9aCIisOzehaV2D+YdO9BY1qAyKEmKtv+iwn9SEZwQX6K0QRbcB0kb1uRg7lBkxjND62TrUmhrnWzFFXABEGmIvExAEuqa/7MDs0uVtuFZRfOv06goTgpf0RqZFh0WkuFTsPqE4lpdBLQ1JhQHXSAQCO5YZgdw/d9HMA0f4bhUxI/Nf8ufP1DL3cVX30/jkyR+NDDBDwbGiNBq+WZeMpvlI/T0fhuvd4z4uPvIzf0cYWFpK+b08fFx6uvrOXfuHGq1moqKCnbs2EFkZORN3XLQ66f/6WO4z0wQpUpAkiUCcRLx95ZgLo5blTPPZElmpHuOtnobvY0TSAGZ+AwrxVXJ5FUmoDeuQVVqFQk6nDjr63EcqMNx8BDB+XlUOh2mrVux7qnFUlODLuHWz527JtO9ywr/waMgS2BNgvx7lepa1k7QvXla5oJSkL75vhXGyCtp/i9W2bIjskNW8z9h99A0OLcU2FqG55c0/zFm/VJL5Ia0SMrSIrEYQvv/E8GtEYpr9TsnoGVGyKe/VHW7b+My5ubmbvqHtUAgEAheA7IMjnECswMEJPhO4N106Et5NP4YRcbpq76sTZfAJ2LfToshhb3Oc3xt5mnclkEGwqeRVZC+EEXUoJaY8JUHZU/7DdQvJNHsUNTlZeZpqiJGidV5b/q2+8aiGB8vJ16/DqPGTJAFwqNasEa1oNUt3Px3cQU8fiOd00W0TZQx445Fq/aRH9NBcXwr8eaxkBcaypKMa9iDo8eFvduJf04xExoTDVhyTVjzTBji9GtT/ZD84J5V1P3uWSWsqdTKXrWwaOUQdXVo2hDXEjsS5/DRgpcWlZcWfMyplHZCs6yiFD1lGCiXDaxDTzShGdhkZFy+IA5vAIcngN0bwOMPLv27SafBYtRiMWixGLWE6TSoCPH/YQTXJRTX6qr377szAlpslll+8EtFt/s2LiMQCKBdi355gUAgEFyTyECAP5ueYIPbSaOUzd/5/xpX+DjZcXXotc4rvkZCTX/4PfREvhWN5KVo9jfkeI6yIcJNjsWHO6CieT6MXqce+VULM03ASPh8DhZHOipZjctsYz6iB7/efnM3LoN1ykjF4AZKVJtIDMsClUxPWBeno47RYT2HtLj4fU3IYHakEzexhajpcjSSHpdplKn4E0zHNhLUul/7NdYaWSZmWia3O0Bud5AUm/K9zIer6MnT0J2nZThNjaRZi0W0rGj8g36QAkpYA2XvmkarBDXVm6MN8kp4kXEg4UDCiYwLmYv/yxhkMKPGghozKkyoQzbmyMgEpZV/Lq6OVYBGrVrxRwS2Nx6huFb/r784c4cEtPxY+cEfPXi7b+MyQjGVCwQCwZsGWWbr9BB/3N+CIRjkB4G38x/yvaRmdJGW2oNafeWg41BF0aq9izl1MnHBfkoCdaSqRlkvd5KkdzEjmTkTzGFcjrzstWqfmvDRcKzjVtSSGleUi/mUeXwW303fvmncT1azhlJnEVnWdZi14Th0bhoTuzmd1MWMaXWqahq/jujhTGIv5GGej0FSB5hNHmQysxtHzARvlDWnecFHzvk5cs/NkNE1j84v4zFq6CuOpKc0ir6iSHxha7QQ8zmUypprBnyLvwDQmZSqmikGDBbeMF/kGiDJEk6/E6fficPvwOl34peU88xUqDDrzJh1Ziw6C2adGb0mdI87cPuDODwBpdLmDeDyBbi4ZDbqNFgXK2wWgxaTXhvyVek3O6G4Vv+v+/7rzghoYg+aQCAQCK6KYwL2/R20Pc2APo8P2d+PI6qQL9xXxL2liVdshwvKMj8fnuSbfaNoVSq+nJtCUmcLJcUuenr/CY9nhLjYu8nN/X+YTJmXvd7lcnHy5EmOHz+Ox+MhOzubnTt3kpGRcdPtd+N9PZx44nEc58bIidhAclgOKlTosyKwbE4krDQWlW51qjWTg3ba6m10nRzD5wkSmWCiaEcShVuTMIWH7qL51UguF85jx7Dvr8Nx8CDBmRnQajFvrsRSuwdrzW50KSlrc/HZAeh6ATqeg4EGpcJmjoP8exSFf/Zu0N+4/fNORJZlxl3jy4dpTyqaf5+k/CIj3hSv7GOLXdb8G7WhudfP6Q3QOjK/ZIw8OzjHlENpcTbq1JSlLB+mLTT/oUcortXvnD1oIqAJBAKB4Hqcfwr2/R2Sa5Zf69/BP87fz4aseP7hgWJKUyKu+JILbi+f6hji6JyDdfj5+dYyUvQyQ0O/4MLAvyBJftJS/4zMzI+i011+BpvX6+XUqVMcO3YMp9NJWloaO3fuJDc396aD2vTwICee+h0Xjp8my7KOgtjN6AMGVGFazBviMW9ORLdKZ575vUF6zkzQVm9jrG8etUZFVnksxVXJpBVGr4q85PVCDgZxNzfjqKvDvr8OX38/AIbCwkWFfy3GkuK12bfmnoOeVxQjZPfL4F0AbRjk1ChGyPx7wRK/+td9A+IP+umc7VwR2oYdwwBoVVryo/OXAlt5XDlp1rSQNC3KsszInHsxsCkHap8Xmv+QJRTX6iKgrTGhOOgCgUDwpsY1Ay/8P2j5LXOWXD7i+gBH3em8oyKVz9xTQPwVfrstyTL/Y5vmS11DqDUavpidxF+kxOL3TdLb9xijo79Hp4siO/uTJCe9C7X68jY6v9/P2bNnaWhoYGFhgaSkJKqrqyksLER9k8r2ufExTj39e84dfIU4Qyrrs+4i0hMDEujTrZgrEwkrj0O9SmeeTdsctDeM0nl8DI/TjzXGSPGOJAq3JWOJMqzKNV5PvH39OA7UYa87gLuxESQJbUICltoarLW1mLZsQa1fg2phwKdU1DqfVwLb/BCggtRKJawV7oXYfERP3DLT7mlap1qXAlvr1ErNf1lc2VJoK40tDWnNf5ttYTGwCc1/KBGKa3UR0NaYUBx0gUAgEKAcSPzsJ5Ad4xxPfC8fGLwLWWPkw7tz+EB19hV/o/37A4f4v+hUDszY2Rph5rHCdLJNBhbs5+ju/jpzcycxm/PIy3uUmOgrm4UDgQAtLS3U19czMzNDXFwc1dXVlJSUoNHcXKCyT09x+pknaNn/IuqghsqSB0jV5sFsAJVBg6k8TqmqpVhWZbEX9Ev0NU1yvt7GSOcsKhVklMZQXJVMRmkMas0bT4oRmJnBcfCQovCvb0B2u1GbTJirqxWF/86daNZif4osw/g56Fg8b220SXk8OnvxcOz7IW2LIhwRLBGUgvTO9y4FtpbJFnrnewFlL1tOZM6K0PZG0vw3D83j9l9B858eSVmq0PyvFaG4VhcBbY0JxUEXCAQCwSLuOXj57+Hsf+OPzOEx88f5l95YUiLD+Nx9hTxYlrQi2Bw8eJBdu3bx27EZvtRjwytJfC4riQ+mxaEGJidforvnm3g8Q8TG1JKb+3nM5uwrXjoYDNLW1sbhw4eZnJwkKiqKqqoqysvLb9oo5pqf48xzT9H00nP43G7Kyu6iKGE7qgE/sl9Cl2TGvDkR04Z41Kt05tnchIv2hlHaj43iXvBhjtBTuD2J4h3JhMeuzkHbrzeSx4Pz+HEcdQewH6gjODkFGg2mjRuV6tqePejT0tbm4vMj0LV43lr/YQj6FHV//j1KdS1nz6JoRPBqFnwLnJs6txzaplqY984DYNaZKY0tpSxWaYtcF7eOaGP0dd7x9hAISnSNO2gcml3az9Y7qQhn1CrIT7AuBbaK9EiyYy2o30CtxqFKKK7VRUBbY0Jx0AUCgUDwKnrr4A8fh/khRgv/nA+PPUDjmI+NGVH8/QPFrE+LBFbO6WNeP5/rGuLFqQU2WE18vyiNQnMYkuRlaOiX9F/4CZLkITXlT8jK+hg6XeQVLy1JEp2dnRw5cgSbzYbVamXHjh1UVFSgv8k2O4/DQeOLz3B23x/wOOxklVSwqfRBDMMa/DYnKp2asHWxmDcnos8IX52qWlBioHWatnobg+enkWVIK4qiaEcy2evj0GjfeFU1AFmS8Jw7p0hG6urwdncDYMjLxVJTi3VPLcZ161DdZHvqDeG1Q89+pbLW9SJ45kCjh6xdUHg/5N8H4Umrf907BFmWGbQP0jLZsrSfrWu2i6CsVKfSrGlLVbby+HLyo/LRhej5dfMuP03Dc5wdmKVxaI6mwVkWPMrZf1ajlvVpkZe0RkYSaXrjiHxChVBcq4uAtsaE4qALBAKB4Ap4HbD/H+HkvyFHZXIw/+/5zJlIphxe3rYhhc/cW0Bn44kVc7osyzw9MccXuodxBCQ+lZnAR9IT0KlVeH1T9PV9H5vtcbTacLKz/paUlD9GfZWFoCzL9Pb2cuTIEQYGBjCZTGzbto3KykqMxpuzvvk8blpefp7Tzz6Jc26WpPxCtu16JxEL0bibJ5G9QbTxYZgrEzFVJKAxr87i1D7jof3oKO0NNhyzXowWHYVbEymuSiZqleQltwvf4CCOAwew1x3Adfo0BINo4mKx7q7BUluDeds21Dc5TjdEMABDxxdbIZ+D2QvK48kVi62Q90FCidi3dh3cATdt021LVbbmyWYm3ZMAGDQGSmJKlNC2GNwSzAm3+Y6vjCTJ9E05aRycXWyNnKNzbAFpccmeHWtm/cXWyLRIChOtaN+ArcevJ6G4VhcBbY0JxUEXCAQCwTW40AB/+CjM9OHb8D5+ovlT/uX4JGoV3Juh4Zt/toewV8k3Jn1+Hu0e4emJOUotYfygMI1Sq6JRtzs66O7+OrOzRzGZcsjL+wKxMbuveQsDAwMcPnyY3t5ejEYjW7ZsYcuWLZhMN6dmD/h8nDvwMif/8HvsU5PEZ+aw5cF3kKzPxXV6HN+gHTQqwkpiMG9OxJAduSp2RkmSGWqfoa3exoXmKSRJJik3gpKqZHIq4tGukrzkdhGcm8Nx5Aj2/XU4Dx9GcrlQhYVh3rEda00tlprdaKPXoI1OlmGyQ6msdeyDkcV1T2T68r61jO2gCc1qUChxqeb/YpWtfbp9SfOfYEpYskWWxZVRFF0U0pr/luH5Fa2RUw7lc4TpNKxLjViSj1SkR15RhPRmJhTX6iKgrTGhOOgCgUAguA4+Fxz8Bhz7CViTmdz9T3y5PZnnWkdJijDy2XsLeKg85bL9H/sm5/hc1zCz/gAfS0/gE5kJGNRqZFlmamo/3T3fxO2+QHR0NXm5X8Biyb/mbYyMjHDkyBE6OjrQ6XRUVlaybds2rNabM9UFAwHajxzg5NO/Y3bURnRyKpsffic5uZV4zk7iPDuB7A6giTZirkzAvDERzSqdeeac99J5fIy2ehvzk270YVoKNidQXJ1MbGpoGvduBsnnw3Xi5JIVMjA2BioVYRs2KJKRmloM2Vlrc3H7uHLeWuc+6DsIAQ8YIyDvLUplLfcu5e+CG8IX9NE500nL1HJr5IhjBFA0/wXRBUtVtvLYclKtqSFpWpRlmeFZ95J8pHFwjvO2efxBZV2fEhmmVNkW2yNLksPf1Jr/UFyri4C2xoTioAsEAoHgBhk+DU9/RKlarH8v/+m7hyfGY2gdmac8LZJ/eKCYjRlRK14y6w/wpZ4RHh+bJd9k5AeFaVREKO19kuRjePhX9F/4EcGgi+Tk95Cd9XH0+mtXW8bHx6mvr+fcuXOo1WoqKirYsWMHkTdpF5SkIF3HGzj55ONMDl4gIj6Byre+g+Idtfi75nGeHMPbNw9qMBYqVTVjftSqVNVkSWake462ehu9jRNIAZn4DCvFVcnkVSagXyV5ye1ElmU8bW049tdhP3AAb3s7APrMTCx7arHW1hK2fj2qm7R13hA+J/QeUCQjXS+AawrUOsisWm6FjFwjwckdzJR7itbJVlqmljX/7oCix48yRC23RcaVURpTikUfmiIXjz9I2+jCUoWtcXCOkblLNP/JEYuBLZKK9ChSo948mv9QXKuLgLbGhOKgCwQCgeAmCHjh8HfgyGN4deHoHvlnnnCt59svdDBh9/JgeTKfu7eA1KiV7Yf7pxf4TOcQY14/f50Wx2ezkghb3Avi883Q3/8jRmy/RqMxkZX5t6Sm/glq9bWrVtPT0zQ0NNDU1ARAWVkZVVVVxMbG3tRHkmWZvrMnOf7Ebxnr6cISFc2mB99G2Z57wSHjOjWG88w4ksOPJlyPaVMC5spEtFGr0xrlcfjpPDFGW4ONGZsTrUFD3qZ4iquSSchcHXlJKOC32bDXHcBRV4fz5EkIBNBERWHZvRvrnlrM27ejvsm21RtCCsLwqeVWyGlFcELiOijYq4S1pHKxb+0WCEpBeuZ6lgJby2QLffN9wLLm/2JbZFlsGdmR2ahVobkHbGLBs7SPrXFwlpbhZc1/rEXP+rTlw7TLUyMx36Ga/1Bcq4uAtsaE4qALBAKB4BYYbcbxqz/H4uyH0rfj3PMNfnZqnp8dVhZnf1Wdzd/szlmxiLEHgny118Z/26bJDjPwWGEaWyOXf8PucHbT3f11ZmaOEBaWSV7u54mN3XPdgDI/P09DQwNnz54lGAxSUlJCdXU1CQk3JzaQZZnB1mZOPPlbhtpaCbOGs3Hvw6y/Zy96Qxie9hkcJ8fwds8CYMiLUg7BLopGtQp2RlmWGe9f4Hy9jZ7T4wR8EjEpZoqrksnfnIhxleQloUDQbsd55IgS2A4dQrLbURkMmLdtw1Jbg2X3bnTx8Wtz8aluJax1Pg9DJ0CWIDxFCWoF90FmNWjfeAeOhwoLvgXOTZ6jeap5KbQt+BYAsOgsiuZ/cT/buth1RBmjrvOOt4dAUKJz3L4Y2OZoHJql702g+Q/FtboIaGtMKA66QCAQCG6NQ3WvsEvTCIf+CYzhcP93GEm5j2+/2MnTTTbirQY+c08Bb69IXbFwOTJj59OdQwx6fLw/JZYvZidh1i63uU1NH6S7+xu4XL1ERW0nL++LWC2F170fh8PBsWPHOHXqFD6fj4KCAqqrq0lNTb3pzzbS0caJJ39Lf9MZDCYz6+95gIr734opPILAnAfnqXFcp8cIzvtQW3SYNipVNd0qnXnmcwfoOjVOW72NyUE7Gq2anIo4iquSSc6LvGOqagCy34/rzBlF4b9/P36bDQBjeRnWRYW/Pjd3bT6zc0pR93fuU46X8LtAb4XcPVC4V9m3ZgrNc8LeKMiyzMDCwIoq26Wa/3Rr+orWyFDW/M+5fDRdrLJdQ/NfkR7J+jeo5j8U1+oioK0xoTjoAoFAILg1lub08TZlb5rtLBQ+AHu/x5kZA199to2moTlKU8L5+73FbMmOWXqtMxDkm/2j/Hx4ilSjnu8VpLEzelmSIUl+Rmz/S1/fDwkEFkhOfhc52Z9Er79++6LL5eLkyZMcP34cj8dDdnY2O3fuJCMj46YX+eN9PZx46nG6Tx5Dq9dTftd9bHrgESzRMciSjKdrFufJMTwd0yCBPisCy+ZEwkpjUelWp5VrctBOW72NrpNj+DxBIhNMFO1IonBrEqZVkpeECrIs4+3qwlGnSEY8ra0A6NLSsNbWYqmtxbSxAtVNHl5+Q/jdyqHYHc8p+9Yc46DSKCbIi/vWotdIcPImw+V3KZr/qWXN/5R7CrjDNP9xZjZc0hpZkBD6mv9QXKuLgLbGhOKgCwQCgeDWWDGnBwNw/Kdw4OtKe9i930Ja90c80zrKt57vYHTew/3rEvn8fUWkRS/vMzox5+BTHUP0ur28NymaL+WmEH5JNc3vn6O//8cMj/wKtdpIVuaHSUt7H2r19VvQvF4vp0+f5ujRozidTtLS0ti5cye5t1CNmR4e5MRTv6Oj4RBqtZrSmrupfOs7iIhXFo7BBR/OM+M4T40RnPGgCtNi3hCPeXMiulU688zvDdJzZoL2BhujvfOoNSqyymMprkomrTB6VeQloYZ/fBzHgYPY6/bjOnYc2e9HHRGBZddOrLW1mKuq0VjW4Ew5SVJ+4XCxFXKiTXk8vnixFXIvJG+AtTiY+02ILMuMOcdWtEW2Tbfhl/zASs1/eVw5hdGFIa/5P7soH2kaWqn5L0uNWHGYdqhp/kNxrS4C2hoTioMuEAgEglvjinP6VI9ybtrgMaU97IEf4DYl8+9H+viXg70EJZn3V2XxkZocrEaljckdlPjuhTH+ZXCCBIOOb+encnfsSh2609lHT883mZquI8yYTm7u54iLu+eGgpbf7+fs2bM0NDSwsLBAUlIS1dXVFBYWor7JBfbc+Binnv495w6+gixLFFfXsPnhdxKdrLRRypKMt28e56kx3OemICijT7cqe9XK4lAbVsdYOGNz0tZgo/P4GB6nH2u0kaIdSRRtT8YSdWfunwo6nDgbGnDU1eE4eJDg/DwqnQ7Tli2LCv8adImJa3PxmT7oXFT4DxwFOQiWRCi4V6muZe0E3eq0twoUrqn5V2spjCpc0RqZagltzf/FwNY4NEfbqzT/Gy4epp0eSUlyOAbt7dP8h+JaXQS0NSYUB10gEAgEt8ZV53RJglP/Aa98GVRqeMtXoOJ9jNl9fPvFDp44O0KsRc+n31LAuzaloVms/DQuuPhExyCdTg/vSIjiK3kpROtWtrJNz9TT3f01nM5uIiM3k5/3KFZryQ3dbyAQoKWlhfr6emZmZoiLi6OqqorS0lI0N6l6t09PcfqZJ2jZ/yIBv4/8LTvY8si7iM/MXnpO0OnHdXYC56lRAhNuVAYNpvI4paqWYlmVxWTQL9HXNMn5ehsjnbOoVJBRGkNxVTIZpTGoQ7yd6laRAwHcjY3Y6w5gr9uPf2AQAGNx8ZLC31BYuDYLdtcMdL+shLWeV8DnAJ0JcmqVsJZ/L5hjrv8+gpvmWpr/aGM0ZbGXaP5jSzHr1qC6ugp4/EHO2xaWWiObLtH86zVqipPDl0NbWuTrqvkPxbW6CGhrTCgOukAgEAhujevO6bMX4A8fU/b1ZFbDW38M0Vk0D83x1WfbOD0wS2GilX94oJjtucreMq8k8cOBcX40ME6UTsu38lPZGxe54m0lKYBt9HH6+r6P3z9LUtI7yMn+FAbDjVn/gsEgbW1tHDlyhImJCaKioqiqqqK8vBztTe5tcs3PcWbf0zS9+Cw+t5vsikq2PPJukvOXpSayLOMbWMB5ahx3yySyX0KXZMa8ORHT+njUYauzn2p+0kVbwygdR0dxLfgwR+gp3J5E8Y5kwldJXhKKyLKMr69PkYzU1eFubgZZRpuctCQZMW3ahEq/Bvv1Al64cERpg+x8HhZGlF9KpG1Z3Ld2P8Tmrv51BQAEpAC9c71LFbaWqRb65/sBRfOfG5VLWWzZkuo/KyIrZDX/4wueJVtk4+AcLcNzePwSALEWw9I+tg1pUZSlRqyZ5j8U1+oioK0xoTjoAoFAILg1bmhOl2U4+0t48VGlLWzPP8DmDyKr1DzXOso393UwMufm7uIEvnB/EVmxym+8z9ldfLJjiFaHmwfjIvlGfgpx+pVmN79/gQsX/pmh4f9GrdaTmfEh0tLej0ZzY3s6JEmiq6uLw4cPY7PZsFqt7Nixg4qKCvQ3uZj3OBw0vvgMZ/f9AY/DTnppGVse+SPSStat+M235AngaprAeXIMv82JSqcmbF0s5s2J6DNW58yzYFBioHWatnobg+enkWVILYyiuCqZ7PI4NKskLwlVAlNTOA4exF53AOfRo8geD2qLBcvOaiy1e7DsrEYTHr76F5ZlGG1e3Le2D8YUwQkxeVC4GNZSK0F9+9rX3gzMe+c5N3VOkY9MNdM62bpC878udt0KAUmkMfL23vBVCAQlOsbsi/KRWZoG5+ibWtb8FySGL+1j25AeRXaseVU0/6G4VhcBbY0JxUEXCAQCwa1xU3P6/DA8+0nofkmpLjz0E4jNw+MP8vP6fn56oAdfUOLPt2XysT15RITp8EsyPx2c4HsXxrBo1XwtL5VH4i9XzLtcF+jp+RaTUy9jNKaQm/NZ4uP33nDYkWWZ3t5ejhw5wsDAACaTiW3btlFZWYnReHMb+H0eNy0vP8/pZ5/EOTdLUn4hWx95N1kbNl12P75hO85TY7iaJpG9QbTxYZgrEzFVJKBZpTPP7DMe2o+O0t5gwzHrxWjRUbg1keKqZKJWSV4SykhuN85jx7Dv34/jwEGCMzOg1WKq3IS1RrFC6lNT1ubic0OLlbV9SpVNCoApVmmBLLgPcmpAf+ePwe1GkiVF878oH2mZUjT/kqxUpzLCM1a0RuZF5YWs5n/W6aNpePkw7aahOeyLmv9wo5b1iy2RG16D5j8U1+oioK0xoTjoAoFAILg1bnpOl2Vo+S08/zlFaV7zBdj2UdBombB7+N6LXTx+Zogok55P3p3PeyrT0GrUdDo9fLJjkLMLLt4SE84/FaSSZLh84TEze4zu7q/jcLQTEbGR/LxHCQ8vu6nPNDAwwOHDh+nt7cVoNLJ582a2bt2KyWS6/osvIeDzce7Ay5z8w++xT00Sl5nNloffRd6WbahfVUGRfEHcLZM4T47hG7SDRkVYSQzmykQMOZGrYmeUJJmh9hna6m1caJ5CkmSSciMorkompyIenf7Or+rIwSDu5hYcBxSFv6+3FwBDQQGW2hqstXswlhSjWgszo2de2a/WsU/Zv+adB60Rsncv71uzhqZK/k7E5Xdxfvr8Umhrnmxm2jMNgFFjpDimeKktsiyujHjTGh2a/hpRNP8Ozg4uh7aucftr0vyH4lpdBLQ1JhQHXSAQCAS3xi3P6fZxeO5T0PGsoip/6CeQoIg+zo3M89Vn2zjRP0N+goVH9xazMz+OoCzz70OTfKt/FL1axZdzU3hPYvRlVSlZDmIb/T29vd/D758mMfFhcnI+g9Fwc3a/kZERjhw5QkdHBzqdjsrKSrZt24bVar3+iy8hGAjQXn+Qk0/9jtnREaKTU9n88Dsp3LELzRX2u/nHnEpVrXECyRVAE23EXJmAeWMimlU688w576Xz+Bht9TbmJ93ow7QUbE6guDqZ2NSb+3xvZHwXLixJRtxnG0GS0MbHL4a1Wkxbt6Jei31rQb9iguzcpwS2+UFABamblhX+cQUQgkbCOxVZlhl1ji6FtZapFtqn25c0/4nmxKUqW3lcOUUxRRg0oWlLdXgDtCxV2ZTQNu28iuY/PZJ468ougVBcq4uAtsaE4qALBAKB4NZ4TXO6LEPbU/Dc3ynVhZ2fgapPglaPLMu8eH6Mb+zrYHDGRW1hPF+4v4jceAt9Li+f6hjk+LyTXVFWvluYRprx8kV0IGDnwsC/Mjj4C1QqDRkZf01G+gfQaG5OljE+Pk59fT3nzp1DrVZTUVHBjh07iIyMvKn3kaQgXccbOPnk40wOXiA8LoHND72Dkt13odVd3k4l+yXc56dwnhzD2zcPajAWRGPenIixYHXOPJNlmZGuOdrqbfQ1ThIMSMRnWCmuSiavMgG9cW0kBKFIYHYWx8FDisK/oQHZ5UJtMmGuqsK6pxbzzp1oo6JW/8KyDOPnF1shnwNbo/J4VJZSWSu8H9K2gubNMxahgi/oo2OmY0Vr5JtB8z/d08TdtTW3+a5XIgLaGiMCmkAgENw5rMqc7pyGFz4Hrb+DhFJ46J+VqhrgDQT5r4YL/LiuB48/yJ9szeATd+URHqbjl7ZpvtprQwU8mpPMnyfHoL7C4sjtHqKn99tMTOzDYEgkN+ezJCQ8iOomTW7T09M0NDTQ1NQEQFlZGVVVVcTGxt7U+8iyTN/Zkxx/4reM9XRhiYpm04Nvo2zPveiust/NP+XGdWoM55lxJIcfTbge06YEzJWJaKNW55Bbj8NP54kx2hpszNicaA0a8jbFU1yVTELm6shL3ihIXi+u48ex1x3AUVdHYHIS1GpMFRVY9uzBWluDPiNjbS6+YFs2QvYfgqAPwqIg7x6lupa7BwxvnipnqDHlnloR2M5NnbvjNP/bk7X8+m/vuc13uBIR0NYYEdAEAoHgzmFV5/SOfYpExDkJOz4Ouz4HOiV8TDm8PPZyF785OYjVqOOTd+Xx3q0ZjPr8fKZzmEOzdrZFmnmsIJ0s05XbjmbnTtHd/VXs9vOEh68nP++LRERU3PRtzs/P09DQwNmzZwkGgxQXF1NdXU3iTR6QLMsyg63NnHjytwy1tRJmDWfj3odZf89eDKYrL+rkoISnfQbHyTG83bMAGPKilEOwi6JRaV/73ilZlhnvX6Ct3kb36XECPomYFDPFVcnkb07EuErykjcKsiThOX9ekYzUHcDb1QWAPicHa20tltoawsrL12bfmtcOvXVKWOt6AdyzoNErh2IX3KdU2MKTV/+6ghvmWpp/tUpNTmTOkua/PK6czIjMkNf8D3Wf568e2XO7b2cFIqCtMSKgCQQCwZ3Dqs/p7jl46YvQ+CuIzVf2pqVtXvrnjrEFvvpsGw090+TEmXl0bzG78mP5zfgsX+4ZwS/J/L/sJD6QGofmChUfWZYYG3uSnt7v4vNNkJDwILk5n8VovPlFrsPh4NixY5w6dQqfz0dBQQHV1dWkpqbe9HuNdLZz4snf0t94GoPJzPp7HqDi/rdiCo+46msCcx6cp8ZxnR4jOO9DbdFhqkjAXJmALu7mhCZXw+cO0HVqnLZ6G5ODdjRaNTkVcRRXJZOcd7lN882Ab3gYR50iGXGdOgXBIJrYWCy7d2Gt3YN521bUYWtw5lwwAEMnFvetPQezSgggaT0U7lUCW0Kp2LcWArxa898y2YLdZwfA+v+zd9/hcdVXwse/UyXNqNeRLMnqzd1Wsa1iXAjGNsWEwCZvdrObzZvNbioECKEk2RBCQgiEtM3mTdmS3Q2ExRQDJrihZkuy3C3J6sUa9ZFGml7uff8YQgpG1sgz9tj8Ps+T54kd3TK6ztE9Or/fOZooViSteLfF/4rEFSHX5j8U39VFghZkofjQBUEQhMUJWkzvPgCvftHXmn/9P8GWR0DrSzpkWeZA+ziPv95O36SVmoIkHtlZTFRsGA+cv8BbU7Osi9bxTFEmBfqLL//zeKwMDP4rg4O/ACAz81MszfwH1Gr/lyPZbDaam5s5evQoDoeDnJwcampqWLp0qd8JzFhvN00vPU9X8xHUWi2rtt1M6a7dRMYnvO8xsiTj6JzG2jyKo2MKJNBmxxBZbiBieSKKAM08mxico63eSGfzKC6Hl9gUHcWVqRStT0UXoOYl1xqv2Yylto65gwew1tYhWa0owsPRV1YStWUzkTfcgDrh/Z/doskyTHb6ErXzb8CFFkCGmMx3Kms3Q1YVqD5Y1c5Q9adt/v9Qaeua6Xq3zX9WdNa7Cdsf2vyrlVdvz2EovquLBC3IQvGhC4IgCIsT1JjunIP934CWX/gaJtz6I8iufvd/dnkk/vPoAM/u78Tq8vKx8ky+tC2ft602Hu68gNUrcV+2gX/MSEbzPg01HA4j3T1PMjb2KlptMrm5XybVcIff+9MAnE4nx44do7GxEavVSkZGBjU1NeTl5fmdqE1dGKTppd/R0fA2SqWS5ZtvpOzWO4lJnr8Nu3fWhfX4GNaWUbxTDhQRavRrktGXG9AEaOaZ2+Wlp3WctnojIz1mlCoF2asSKalMI6M4MM1LrkWyy4W1ucVXXTt0CM/ICCgURKxe7esKuXUr2uzs4FQdLeO+JZAdr0PvIfA4ICwG8rf5lkHmbYOI2MBfV1i0P7T5f3dp5MTpd9v8R6gjKEko8XWMTPS1+k/SJV2xewvFd3WRoAVZKD50QRAEYXGuSEzvq4NXPgfT/VD693DjP/9ZkwST1cUP9nfyX02D6LQqvrg1nx3rlvD13hFenZhhZWQEzxRnsizy/Zedmc3H6ex6nNnZk0RFLSc//xHiYssWdbtut5vjx4/T0NDA7OwsqampVFdXU1RUhNLPfUozY6O0vPwC597ejyRJlFRvpvz2jxCfNv8ySlmScfaasbaMYj87CV4ZbUYU+nIDESuTUIYFZuaZyWilrcHI+aOjOKxuouLDKa5MpXhjKpEBal5yLZJlGWd7+7st/J1t7QBoly59t8lIxJo1KFRBmD3nskHvYV9HyPP7wDYJSrWvola4w1ddi80M/HWFyyLLMkar8Y8NSCZO02ZqwyP5hlCn6lP/rMoWzDb/ofiuft0kaCsTEuRXd+y82rfxHjMzM363JhYEQRBC05WK6QqFh9j4DqJievB6IpiaWI3D/ueDY/vV0fwkZjXN4aks8czxT+aTOJP1fK9yC7Nh4fztqWb+7lQTGkm66DVkZCw5E0yVDuDRu9D3JZB4LAuNZXGJhhfoiYridGwsc1oNsS4XK6dnyLZY8Lc+Z5clznvt9ElOvEC6UkuRMpzYhSyDUoahiMhHoS9CoYlDllzI9h5kawe4Jxfxyd7Li5JR1VIGNflMqdJAlkj2DpPp6STZewEl1877UzBILhfemWm80zNIc3O+JYoqFarYWFRxcahiolEog5CsIfsq0TYT2KZ8w+EBtHrQxYMuAbSRQbiuEAgSEja3DavbisVtweqy4pScAChQoNPoidTo0WsiidTo0arCCER9NhTf1bN+858iQQumUHzogiAIwuJc6ZiuDTORmHwCjdaCZTYT09RyZOnP99kcDTPw05jVDGhiWOsY4xP2NvaUrmVfXgm5pkkeqX+Tksmx972GpPIys3yY6RXDyEqZ2HNpxJ9OR+le3J4QCeiP1HMqNo6ZMC1RbjcrpmfIm5vD31dyhyzR5XXQIznwAKkKDUWqCBIWul9Fm4xCV4QiIheFUo3smkK2dSDbukF2+Xk3F2dVRDGkzmdInYdTqSNMspHh6SLD04VetgTkGtcy2evFazbjnZnBOzMDXi8oFCijo33JWmwsyovMxQsItx3s7yRrzncSRXUYRMT7ErbwGAjRDoOCj0tyY3VbfEmby4LVY0OSvQBolBr0Gj2Rmkj0mkj0Gj2qRTzPUHxXv24SNLHEURAEQQi2qxLT3Q54+7vQ8Czok2DXM75hvn/6JV6J/24a5Jn9ncza3dxdlsG6dal868I44y43/5iZzH1ZBiJU7//y4nCO0tPzFKOje9BoEsjN/TJpqXeiUCyu0iFJEp2dndTW1mI0GomKiqKyspK1a9ei1frXZMNhsXDizVc5/vorOCxzZC5fScXuu8lYtnJBe5wkhwfbyXGszaO4jVYUGiURKxLRlxvQLg3MzDOvV2LgzBRt9UYGz00hy5BeFEdJVRo5q5JQBah5ybVMdruxtR5n7uABLAcO4h72DUEOX7GCqK1biNy8hbCC/ODsW7NOQdebvq6Q3QfBbfVV0/K2+pZC5n/Il7QJIc0jeeie6f6zBiT9s/2Ar81/Xmzeu0sjF9rmPxTf1a+bJY4iQRMEQRCC7arGdOMJePlzMHYWVnwEtn8X9H/eMc9sc/PsgS7+40g/4RoVn9qUQ3+Kht+Oz5AbEcYzRRmUx86/xMs8e4qurm9hNh8nMrKY/PyHiY/bsOjblmWZnp4e6urqGBgYQKfTsWHDBsrKygh/n0HV78flsHP6rTc4tncP1plpUguKWL/7brLXlC74pd41bMHaPILt5ASy04s6KQJ9mQHd2mRUkYHpzjhnctBxZIS2BiMWk5PwSA2F6w0sq0ojLkDNS651sizj7Op6t4W/4/RpADTp6b4mI1u2olu3FkUwqmtuB/TV+pK182+AZRQUKsjc4PvlR+HNEJ8T+OsKQWF2mjkzeebPBmq/X5v/lUkriQn783EeofiuLhK0IAvFhy4IgiAszlWP6R4X1D8Dtd/zLc/a+RSU3P6eWVA9ExaeeL2d/e3jZMRHcFt1Fv8j2zA6Pfx9eiJfzUlFP0/DBlmWGR9/je6eJ3E4hklKvJG8vAfR6bIu6/YHBgaoq6uju7ub8PBwysvLWb9+PTqdf3PMPC4XZw/vp/nl3zE3OUFSVg4Vt99FfsUGlAvc2yS5vNhPT2BtHsU1OAcqBRHLEtCXGQjLjQ1Id0ZJkhlqN9FWb6T/1CSSJJOaF0NJVRq5a5PRaIOxD+va5B4bx3L4MHMHD2A7chTZ5UIZHU1kTQ1RW7egr65GFRmE/WOSBCMnfB0hz78B4+d8f59U9E6TkR2wZB0EYzC3EBSSLNE/2/9nDUjma/NvPG1k62YxqDooRIImCIIgBFvIxPSxc/DyZ31VteJbYMf3Ieq9Lenruib41t52zo/NUZoVR+LKRF5y2sgM1/J0UQZVcVEXOfkfeb0OhoZ+Rf/AvyBJbjIyPkF21udQq+c/7lKMRiO1tbV0dHSg0WgoKytjw4YNREX5d16vx0N7/WGaX/od0yPDxKelU377Ryiq3IRKvfA9dO5RK9aWUWwnxpFsHlTx4ejLUtCvM6AK0Mwz26zLV1WrN2KesKONUFNYnkJJdRqJ6Zf3/bzeSFYrlsZGLAcOYjl82Ld3TaNBX17+TnVtC5rU1OBc3NT3Tgv/12CgEWQv6JOhcDsU7oScTaAJwmBuIaj+ss3/qYlTmBwmAMr15fzyzl9e5Tv8cyJBC7KQ+WEuCIIgXLaQiuleDxz5MRz6tu+F8ebvwsq731NN83glftsyxNNvdTJtc1Gz3ED7Eg2DssRfpyXwtdw0otTzV3KcznF6ep9mhxt/JAAAmKFJREFUZOQFNJo4cnLuIS31LpSXOVx2fHycuro6zp49i1KpZO3atVRWVvq9YV+SvHQebaB5z/NMDPYTnZRC+W0fZtmmbaj92O8muyXs5yaxNo/i7DWDEsIL49GXGwgviEehuvyqmizLGDtnOFdvpPfEBF6PRPLSKEqq0sgvS0EbfvUG9oYi2evFfuIEcwcPYTlwANfAAABhJcVEbfG18A8rLg7OvjX7NHTt97Xw79oPrjlQR0DuFt9SyPybIPLKzesSAudP2/wPnx/mU9s/dbVv6c+IBC3IQuqHuSAIgnBZQjKmT3b5qmlDTb5GB7t+ADFL3vNlZrubnxzq5tcNfahVSopXJnM0VoFBp+V7hRlsTYi+5KVm587S1fU4MzPN6PX55Oc/QkJ81WV/hKmpKRoaGjh58iQAK1eupKqqisTERL/OI8syvcebaXrxeUa6z6OPi6fsljtYuXU7Gj/3u7kn7dhaRrG2jiFZ3KiitehKU9CXGVAHaOaZw+rm/NFR2hqMmIxW1GEq8kuTKalKIyUrMM1LrieyLOPq62PuwAEsBw9hP3kSZBl1aipRmzcTuWUL+vIyFH42oVkQjwv663zLIM+/AbMXAAVkVPj2rBXthMT8wF9XCLpQjOsiQQuyUHzogiAIwuKEbEyXvND8/+DAP/uG9H7oW7D2b95TTQPon7TyxBvtvHlujMToMOTCWIbjVNyVGs8/5y0hTjN/BUeWZSYmfk9X9xM4HEMkJmwhL++r6PWX31TBbDbT2NhIa2srHo+HZcuWUV1djcFg8Os8siwzePYUTS8+x1DbGSKiolm74zbWbN9FmM6/Jh2yV8LRbsLaMoqjcxqAsPw49GUpRBQnoFBf/t4kWZYZ65ulrd5I17ExPC6JhCV6iivTKKwwEK4PUhv6a5xnauqdfWuHsDY0IDscKPV69DXVRG3ZSmRNNaqYmEufyF+yDKOnfYlax2u+/w6QkPfHfWsZ5RCUWW9CoIViXBcJWpCF4kMXBEEQFifkY7qpD175vO83/dmb4NYfQlzWRb+0sWeSx/a20z4yiyFFz4VsHfFJOr5bkM7NSbGXvJQkORka+nf6+n+CJDlIX/JxsrM/j0Zz6WMvxWKxcOTIEVpaWnC5XBQUFFBTU0N6errf5xo+307TnufoO3GMMJ2e1TftYu2OW9FF+//i7plxYG0Zw3ZsDK/ZiTJSg25tCvqyFDRJ/jU6eT8uu4fOljHa6o1MDM6hUivJXZtESVUaafmxoqr2PiS7HeuRo1gOHWTu0GG8k5OgUqErLfW18N+yBe0i/v0siPnCO5W116GvDiS3byh2wXZfdS13i29YthCSQjGuiwQtyELxoQuCIAiLc03EdEmC4/8Gv/8ayBJs+waUfeqiXei8kswLrUN8781OJi1OIjMjmcyO5LbMBB7PTydRe+n9UE7XJL29z2A0Po9aHU1O9hdYsuRjKJWXX/Wx2+00NTVx9OhRHA4HOTk5VFdXk5WV5XeiMtbbTdNLz9PVfAS1Vsuqbdsp3XUHkfEJlz74L8iSjKNz2ldVa58CCbTZMUSWG4hYnoBCE5jKycTgHG31RjqbR3E5vMSm6CiuTKVofSq6ADUvuR7JkoTj9GnmDhxk7tBBXN09AIQVFPiajGzdSviyZSiC0ZnRMQvd+30JW9eb4DCDKgxybvDtWyvYDlH+VYSF4ArFuC4StCALxYcuCIIgLM41FdNnhmDvl3wvi5kb4NYfQ2LeRb90zuHmp4d7+GV9HxIyrqwo9PnRPFGUyW3JC6vazFk66Op6nOnpRnS6XPLzHyIx4YaAfBSn08mxY8dobGzEarWSkZFBTU0NeXl5fidqUxeGaH7pedob3kapVLJ8842U3XonMcnv7YK5EN45F9bWMawto3inHCgi1OjXJKMvN6AJ0Mwzt8tLT+s4bfVGRnrMKJUKslclUlKVRkZxfEBGAlzPXAMD7zYZsR0/DpKEOimJyM2bidq6Bd369SjDwgJ/Ya8bBo+808L/NZgZ9P39knV/XAqZXHzRpcjClROKcV0kaEEWig9dEARBWJxrLqbLMpz6H9j3IHicsPlh2PDZ990bM2Sy8Z03OnjtzAjqCDW2vChuXJHCk4WZpIRduiImyzKTkwfo6n4Cu72f+Phq8vMeIjKyICAfx+12c+LECRoaGjCbzaSmplJdXU1RURFKP6shM2OjtLz8Aufe3o8kSRRX3UD57R8hYUnGou5NlmScvWasLaPYz06CV0abEYW+3EDEyiSUYYGpqpmMVtoajJw/OorD6iYqPpziylSKN6YSGaDmJdczz/Q01tpa5g4cxFJfj2yzodDpiKysJHLLFiJv2IQ6Li7wF5ZlGG/743Ds4Vbf38dlvZOs3QyZG0ElunheaaEY10WCFmSh+NAFQRCExblmY/rcKOy91/db/CXr4Laf+H5z/z6a+0x8c+85zg7PQowGzbJ4HivL5m5D/IIqVpLk4sKF39DX/0O8XhtpaR8lJ/uLaLXxAfk4Ho+H06dPU19fj8lkIjExkerqapYvX45qngHcFzNnmuTYq3s4vX8fHreLgopKKnbfRXLW4pueeK1ubCfGsTaP4hm3odCq0K1OQl9mQJMeGZB9ZF63RO+pCdrqjVzomEahgMzlCZRUppG1IgGlSgxWvhTJ6cTW1MTcwYNYDh7CMz4OSiURa9cQtXkLUVu3oM3KCs7FZ0d889bOvw69b4PXCeGxvk6sRTsgdyuEX7qzqnD5QjGuiwQtyELxoQuCIAiLc03HdFmGcy/C6/f79sls+gpUfQlUF6+MSZLMiyeGeeKNdqYsLryGCMrK0/jh2hzSwxe2/8nlMtHX90OGjf+NSqUjO+sLpKd/HKUyMPunJEni3Llz1NXVMT4+TlxcHJWVlaxevRq1H4OqAWzmGVpff5mTb76Gy24jZ20ZFbvvIq3g/RPZS5FlGdfgHNbmUeynJ5DdEppUPfpyA7rVySgjAlMtMU/YaGsYoaNxBNusC12MluINqRRXphGTJIYqL4QsSTjOtfmajBw4iPP8eQC0OTm+JiObtxCxaiUKP38BsCBOC/Qe8i2F7NwHdhMoNZBd46usFe646OgMITBCMa6LBC3IQvGhC4IgCItzXcR066QvSTv3IhhW+Kppqave/8udHn72dg//8nYPHhkU2VF8dVsBn8pKRrnASpDF2kVX1+OYTHVERGSRn/dVEhO3BqwjoSRJdHZ2Ultbi9FoJCoqisrKStauXYvWz5lYDquFk/v20vr6yzgsc2QuX0nF7rvJWLbysu5XcniwnfRV1dxGKwqNkogViejLDWiXBmbmmdcrMXBmirYGI4Nnp5BlSC+Ko6QqjZxVSag0oqq2UK4Lw1gO+pqM2FqOgceDKiGByBs2EbV1K/oNG1BGBCH5lby+mYbnX/clbCZfgxNSV/1x35phhdi3FkChGNdFghZkofjQBUEQhMW5rmJ6+6vw2pd9CVvVPbDpAVC/f6OE4Rk7X3+tjf1nRpHDlGStSubX25eRo1v4vqfJqcN0dX0bm62HuLiN5Oc/TFRkUSA+DfDOoOreXmpraxkYGECn07FhwwbKysoI93NQtcth5/Rbb3Bs7x6sM9Ok5hey/o6/IntN6WUnU65hC9bmEWwnJ5CdXtRJEejLDOjWJqOKDEx1cc7koOPICG0NRiwmJ+GRGgrXG1hWlUZcgJqXfFB4Z2ex1NZhOXgQS20tksWCIiwM/caNvuraDTeg9nOo+oLIsm8Q/fnXfPvWhpoBGWIy3qms3QxLq0AtOnpejlCM6yJBC7JQfOiCIAjC4lx3Md1mgjcfhlP/DUlFvmpa+kXfCd7V2m/ii3vOcGHMAtEa/nprLt8oz0G1wKRFktwMG/+H3t5n8XhmSUu7i9yce9BqA/uCOzAwQF1dHd3d3YSFhVFRUcH69evR6fybV+ZxuTh7eD8tr7zA7MQ4SVk5VNx+F/kVG1Be5iBiyeXFfnoCa/MorsE5UCmIWJaAvsxAWG5sQLozSpLMULuJ9nojfacmkSSZ1LwYSqrSyF2bjEYrhin7Q3a5sB079m4Lf49xBBQKIlatInLLFqK2bEabmxuceXWWiXf2rb0BPQfBY4ewaMjb5qus5d8IEbGBv+51LhTjesgmaAqFQgk8BkQDx2RZ/vf5vl4kaIIgCEKwXbcxvestePWLMDcC6//J1+1R+/6JjCTJ/PuxQZ7Y14HL5iE6PZIf376SmvSFd79zu2fo6/sRF4Z/g1IZTnbWZ8nI+ARKZWDbnRuNRmpra+no6ECj0VBaWsrGjRuJiory6zxej4f2+sM0v/Q7pkeGiUtLp+L2j1BUuQmVn/vdLsY9ZsXaPIrtxDiSzYMqPhx9aQr60hRU0YH5nthmXe9W1czjdrQRagrKUyipSiMpw7/vh+Cr2Do7OnxNRg4cxNHWBoBmaea7TUYi1qxBEYB/H+/hskHf29Dxmi9ps06AUg1LN0LhTl91LW5p4K97HQrFuB6UBE2hUPwK2AWMy7K8/E/+fjvwLKACfiHL8nfmOcdu4HZgCnhNluUD811TJGiCIAhCsF3XMd0xC299DVp/DfE5vrlpWZXzHmJzevjSG+f4fcswsiRTvtrAz29ZQZxu4UuurNZeurufYHLqIBHhmeTlPUhS0ocCXoEYHx+nrq6Os2fPolQqWbt2LZWVlcTGxvp1Hkny0tXUSNOLzzEx2E90Ugrlt32YZZu2ofZzv9vFyG4J+7lJrM2jOHvNoITwwnj05QbCC+JRqC7/+yLLMsbOGc7VG+k9MYHXI5G8NIqSqjTyy1LQhotW74vhHh3FcugQcwcOYm1qArcbVWwskZs2+Vr4V1Wi1Adheakk+dr2/2Ep5ESH7++Tl/k6QhbeDKlrLjqsXgjNuB6sBK0GsAD/8YcETaFQqIBO4EbgAtACfBRfsvbEX5zik+/8Z1qW5X9VKBQvyLJ853zXFAmaIAiCEGwfiJje+za88nmYGYCy/wvbvgFhkfMecnZijk+9eIrRPjOqMBWf25bPFypzUPmxRG9qqo6u7sexWruIja2gIP9hoqKWXeaHudh1pmhoaODkyZMArFy5kqqqKhL93EMkyzK9x5tpevF5RrrPo4+Lp3TXblZtuxmNn/vd3o9n0o712CjWY2NIFjeqaC260hT0pQbU8YG5hsPq5vzRUdoajJiMVtRhKvJLkympTCMlOzDNSz6IvBYL1vp6X3Xt7VoksxmFRoNuw3qitvi6QmpSkoNz8akeX6J2/nXfoGxZgqhUKNgORTshqxo0YmbeH4RiXA/aEkeFQpEF7P2TBG0D8A1Zlm96589fBZBl+S+Tsz8c/3HAJcvy8wqF4jlZlu+e73oiQRMEQRCC7QMT011WOPAYNP3M15Dg1h9C7uZ5D5FlmR+fucAzb5xHmnaSmBDB07evoCY/acGXlSQPxpHn6e19Brd7mtTUO8nNuZewsMC/yJrNZhobG2ltbcXj8bBs2TKqq6sxGAx+nUeWZQbPnqJpz/MMnTtNRFQ0a3fcxuqbdhKunz+xXfA1vBKOdhPWllEcndMAhOXF+oZgFyegUF9+ZUSWZcb6ZmmrN9J1bAyPSyI+TU9JVRqFFQbC9ZceVC5cnOx2Yzt+wtcV8uBB3ENDAIQvX+5rMrJlC2EFBcFJhm0m6Pq9bylk9wFwW0Gjh7yt7+xb+xDoEwJ/3WtIKMb1K5mg3Qlsl2X5U+/8+a+BClmWP/c+x+uAHwE2oEOW5Z9c5Gs+DXwaICUlZd1vf/vbRd9vsFgsFiIjAxOgBUEQhKvrgxbTo83tFHX8EJ3diDH1Rnpy/w6vev4lWmYJfjCmpPe8DYXDS2Gymk8WakjRLzyJkGUbsvwqMgcANQrFThTciEIR+G51LpeLoaEhjEYjXq+XhIQEli5dSnS0/0OCLaPDjLQeZXawD6VWS/LytaSsXIs6wr/GJPNR2yH6goKoYQUahwKPVmZuicxsuow7QKvnvG4Z8wBM98g4pkGhhOgMiMtRoEtGVNUuhyyjGhkh7NQpwk6fRtvXD4A3IQHnypU4V63ElZ8PQZi3pvS6iJ05Q8JUM4mTzYS5TMgoMccUM5lYzlRCBXZdasCvG+pCMa5v3rw5NBM0f4kKmiAIghBsH8iY7rbD4e9A4w8h0gC7noHC7Zc87NURE/e92Y6jy4xKhk9szOJLW/OJiVh4JcZm66e7+ztMTL5FePgS8nIfIDl5Z1ASBLvdTlNTE01NTdjtdnJycqiuriYrK8vv64319dC853k6mxtRa7Ws2rad0l13EBkfuEqFLMk4uqaxNo/iaDeBJKPNjkZfnopueQIKTWBe8CcG52hrMNLZNIrL4SUmOYKSyjSKNqSiixbt3S+Xe3wcy+HDWA4ewtrYiOxyoYyKIrKmhqitW9BXV6Pys6HNgkgSjJz841LIsbO+v08sfGff2g5YUvqB2LcWinE9ZJc4+kskaIIgCEKwfaBj+nArvPw5GG+DlXfD9u+ALn7eQ8xuDw+eGeDVhkHUwzaiIjQ8cFMhHy3LQK1a+IufafoIXV2PY7G0ExOzjoL8R4iOXnm5n+iinE4nx44do7GxEavVSkZGBtXV1eTn5/udqE1dGKL5pedpb3gbpVLJshu2UX7bncQk+7eM8lK8cy6srWNYW0bxTjlQhKvRr01GX25AE6CZZ26Xl57WcdrqjYz0mFEqFWSvSqSkKo304niUARgJ8EEn2WxYGxuZO3AQy+HDeKenQa1GX15G5JatRG3ZjCYtLTgXnx74Y7I20ACSB/RJvn1rhTsg54Z5O7tey0Ixrl/JBE2Nr0nIVmAYX5OQj8myfG7RF/kTIkETBEEQgu0DH9M9Lqj7PtQ9BRFxsPP7UHLbJQ87bJrli03dTJ+eQjntIi85kq/tKqGmYOH702TZi3HkBXp6vo/bPYXBcDu5ufcTHhbYZOcP3G43J06coKGhAbPZjMFgoKamhqKiIpR+VhVmxkZpeeUFzh3ejyRJFFfdQPntHyFhSUZA71mWZJy9Zqwto9jPToJXRpsR5durtjIJZVhgqmqmESttDUbOHxnFYXUTFR9OcWUqxRtTiYwTzScCQfZ6sZ88+W4Lf1d/PwBhxcVEbd5M5NYthJeUBGe5qX0Guvf7krWut8A5C+oI3z7Uwh1QcBNEBqnByVUQinE9WF0c/we4AUgExoCvy7L8S4VCsQP4Ab7Ojb+SZfnxRV3gIkSCJgiCIASbiOnvGD0DL38WRk75ErQdT13yhc3i8fJYj5H/PHGBiM5ZvDYPW4qSeWhHMXnJC9//4fHM0T/wMwYHf4VCoWLp0n9gaeanUKkiLvdTvc/1PJw+fZr6+npMJhOJiYlUV1ezfPlyVH7uE5ozTXLs1T2c3r8Pj9tFQUUlFbvvIjkrJ+D37bW6sZ0Yx9o8imfchkKrQrc6CX2ZAU16ZEBe7L1uid5TE7TVG7nQMY1CAZnLEyipTCNrRQJKP6qkwvycvX1YDh1k7sBB7CdOgCyjNhiI3HwDUVu2oqsoRxmAMQ/v4XH5KmrnX/dV2MxDgALSy/64FDKxAK7hfYmhGNdDdlC1v0SCJgiCIASbiOl/wuvx7Us7/ARoI+HmJ2HFnZd8UWuctnBP2wAXzpuI6LOAV+bj65fypW35xPoxP81uH6K750nGx18nLMxAXu4DpKTcgkIRnKRAkiTOnTtHXV0d4+PjxMXFUVlZyerVq1H7OYjYNmvm+Osvc2LfXlx2Gzlry6jYfRdpBcUBv29ZlnENzmFtHsV+egLZLaFJ1aMvN6BbnYwyIjAzz8wTNtobRmg/MoLN7EIXo6V4QyrFlWnEJAUnef6g8phMWA4dZu7QQawNjch2O0q9Hn11NVFbNhNZU4PKz/l+CyLLvl/OnH/DN3Nt5JTv7+NzfbPWinZCejmorq05eqEY10WCFmSh+NAFQRCExREx/SImzvuqaRdaoOBm2PU0RM+/T8bmlfhu3wg/7x4lus+Ca9BCdLiGe7bl83/WL0XjR+VleqaFrq7HmJs7R3T0agryHyYmZu3lfqr3JUkSnZ2d1NbWYjQaiYqKYuPGjaxbtw6tnxUMh9XCyX17aX3jFRxzs2QsW8n6O+4mY9nKoCxdkxwebCcnsLaM4h62gFqJbkUi+nID2qzAzDyTvBL9Z6ZoazAyeHYKWYb0ojhKqtLIWZWESiOqaoEkORxYjxzBcvAQc4cO4Z2cBJUK3bp177bw12YEdintu8zD0PkGdLwOfbUguSEi3rcEsnAH5G655AzFUBCKcV0kaEEWig9dEARBWBwR09+H5IWmf4UD3wSVFm56HNZ8/JLVtGNmK/d0DNI9ZiG9z8rEiJXcJD2P7CzhhsKkBScMsiwxOrqH7p6ncLnGSUm5hbzcBwgPD1JDBd4ZVN3bS21tLQMDA+h0OjZs2EBZWRnhfg6qdjnsnN6/j2Ovvoh1ZprU/EIqdt9NztqyoLW0dw1bsDaPYDs5gez0ok6KQF9mQLc2GVVkYJbKWaYdtDeO0NZgxGJyEh6poXC9gZLKNOJTAzQTQHiXLEk4zpzxNRk5dBBnVzcAYfl57zYZCV+xAkUwOjM6ZqHngK+61vkmOGZAFQY5m3zVtYKbITo0W/iHYlwXCVqQheJDFwRBEBZHxPRLmOqBV74AA/WQs9k34Do2c95DHF6JZwbG+PHAKDEmN5Hdc4xPO6gpSOKRncUUpCy8xbjHY2Vg8F8ZHPwFAJmZn2Jp5j+gvsTstss1MDBAXV0d3d3dhIWFUVFRQUVFBXq9f9f1uFycPbyflldeYHZinKSsHCpuv4v8ig0olYGfiwUgubzYT09ibRnFNTALKgURyxLQlxkIy41FEYDujJIkM9Ruor3eSN+pSSRJJjUvhpLKNHLXJaPRBuezfdC5Bgd9TUYOHsLW2gpeL6qkRKJu8DUZ0a9fj9LPXyYsiNcNg0f/uBRyut/392lr/7hvLbkkZPathWJcv24StLyMEvl7X/rN1b6N95iZmSE2GOuABUEQhCtOxPQFkCWy3a+yzPmvAJwL+zR9mlt9047nMRgB/7FUwXA4ZHVYmLkwh0uW2RCuY7s+ikg/fuuv0EwQnvZfaOIbkNxxOI0fxW3aBAR3eZ3NO8O4qwuzZwQlKhI0WSRpc9Eo/XsJliUvlqnTzIzU4nZMoQlPJDa1msiElSiClKgBhHskkhxuEh0e1DI4lAomw9VMhqtxB6jhh+SVsM26sJpdeN0SCiVERGnRx4ShCVCXSeG9ZI8Hr9mMd3oar9nsq3orVaiio1HFxaGKjUGhXviMQr+4bWCbApsJnHO+v1OH+8Z06OIhPAa4eslaKMb1O+5bJxK0YArFhy4IgiAsjojpCxchjbLG8X1SvMeYVK3kePgDWJVL5j3Go4A3U+ANg4Jwu5fcM3N0m21oFQpu0kVSFaFH7cdv3VX684Qv+TdU+m68thwcF/4WrzXwjTj+ksM7y5irixnPMAqUxGsySdbmoVX6N0dKliWspjZmjG/jso+h1sYSm1ZNZOJqlMogvUwDClkmzuklyeEm2i0hAzNaFRPhasxaVcAqH067B5vZiX3ODYAmTIUuRosuShuQyp3wPmQJ7+wc3plpvNMzyG4XoEAZGYkqLhZVbFxwKmsAXhfYTb5kzT4DsgRKNejifPvXIuJ8f76CQjGuXzcJmljiKAiCIASbiOl+kmU4+V+w7yHfi9mWR2D9P8IlqkDtFjtf6hjk1JydTZpwFB0zHO2eIitBx8M7S9hWnOzX/rSxsVfp7nkSp3OU5OQd5OU+QEREkBon/AmTyUR9fT0nT54EYOXKlVRVVZGYmOjXeWRZpvd4C00vPsdI93n0cfGU7trNqm03ownWi/Q7PJN2rMdGsR4bQ7K4UUVr0ZWmoC81oI4PzLUdVjfnm0ZpqzdiMlpRh6nIX5dMSVUaKdmBaV4iXJwsyzjOtWE5eJC5gwdxdnQAoM3OJnLLZqK2biVi1SoUfo6UWBCXFXoO+Vr4d+7zVdmUGsiq8nWELNgOscH//2koxvXrZomjSNAEQRCEYBMxfZFmR2DvPb6Ob0tK4bafQHLRvId4JJmfDY3zvf5RIpRKPqbW8XbjED0TVirzEnhkZwnFqdELvgWv18bA4C8YGPg54CUj45NkLf0MavXC97gtltlsprGxkdbWVjweD8uWLaO6uhqDwb8h27IsM3j2FE17nmfo3GkioqJZu+M2Vt+0k3B9cLvlyV4JR7sJa8sojs5pAMLyYn1DsIsTUKgvfwmkLMuM9c3SVm+k69gYHpdEfJqekqo0CisMhOuDVzUUfNzDw8wdOozl4AGszS3g8aCKjyfyhhuI2rIZ/caNKHX+VYIXRPLCUPM789ZehylfgxMMK3171op2+P57EJL1UIzrIkELslB86IIgCMLiiJh+GWQZzv4vvH4/uCyw6StQ+UVQzf/S3W1zcE/7EC2zVm6IjWTDLPz67V5m7W7uLsvkyx8qIDEybMG34XCM0NP7FKOjL6HVJpKTcy9pqXeiUAR//5PFYuHo0aM0NzfjcrkoKCigpqaG9PR0v881fL6dpj3P0XfiGNoIHWu272LtjtvQRccE4c7/nGfGgbVlDNuxMbxmJ0q9Bt26ZN8Q7KTAvLy77B66jo3RVm9kfGAOlVpJzpokllWlkVYQK6pqV4B3bg5LbS2Wg4ew1NYizc2hCAtDv2GDr7q2eTPqpKTgXHyyy5eodbwOQ02ADNFLfB0hC3dAVjWoA9NtNBTjukjQgiwUH7ogCIKwOCKmB4BlAl6/D9pe8v1G/LafQOrKeQ/xyjK/Hp7k8Z4RVAq4Pz2Z0bNT/OfRAcI1Kj63JY+/q8wiTL3wJMs8e4qurm9hNh8nMrKY/PyHiY/bcJkfbmHsdjtNTU00NTVht9vJzs6mpqaGrKwsvxOPsb4emvc8T2dzI2qtllXbtlO66w4i4xOCdPd/JEsyjq5prM2jONpNIMlos6PRl6eiW56AQhOYpHdiaI62eiOdzWO47B5ikiMoqUyjaEMquujAvKQL85NdLmytrcwdPITlwAHcRiMA4atWEvVOC39tXl5wEmfrpK91//nXoeegr+mINgryt/mStfwbfXvXFikU47pI0IIsFB+6IAiCsDgipgdQ28vw2n2+hgFV90LNfaCevxI2YHdyb8cQDTMWqmIj+WJiPP92oIcDHeNkxuv46s1FbF9u8GN/msz4+Gt09zyJwzFMUuKN5OU9iE6XFYAPeGlOp5Njx47R2NiI1WolIyOD6upq8vPz/X7RnbowRPNLz9Pe8DZKpZJlN2yj/LY7iUn2bxnlYnnnXFhbx7C2jOKdcqAIV6Nfm4y+3IDGEJgxB26Xl57j47TVGxnpNqNUKshelUhJVRrpxfEoRWORK0KWZZydncwdOIDl4CEcZ88CoMnMJGrzZiK3bEG3bi0KdRCafbjt0Pv2O0sh3wDrOChUsHTjH5dCxmX5dcpQjOsiQQuyUHzogiAIwuKImB5gNhPs+yqc/i0kFfuqaenr5j1EkmV+Y5zimz1GvDI8nJtKvk3m2691cH5sjvLseL62q4TlSxa+1M/rdTA09Cv6B/4FSXKTkfEJsrM+d0X2pwG43W5OnDhBQ0MDZrMZg8FATU0NRUVFKP0cKjwzNkrLKy9w7vB+JEmiuOoGym//CAlLgt9sAXxVNWefGWvzKPazk+CV0WREEVlmIGJVEsoAtdI3jVhpazBy/sgoDqubqPhwiitTKd6YSmRccBunCH/OPTqK5fBh5g4cxHb0KLLbjTImhshNNURt2Yq+qgpVZBBmEUoSGI9Dx2u+ZG2i3ff3ySW+ZK1wB6StgUv8fygU47pI0IIsFB+6IAiCsDgipgdJ55vw6pfAMgobPgebHwJNxLyHXHC4uP/8EIdMc5TH6HmqYAnNZyd4+q1Opm0u7lybzv03FZIcvfCXdadznJ7epxkZeQGNJo6cnHtIS70L5RVq++3xeDhz5gx1dXWYTCYSExOprq5m+fLlqPzsojdnmuTYq3s4vX8fHreLgvKNVNxxN8lZOUG6+/fyWt3YToxjbR7FM25DoVWhW53k26uWHhmQ5XBet0TvqQna6o1c6JhGoYDM5QmUVKaRtSIBZYDmtwkL47VYsTY0YDl4AMvht/GazSg0GnTr1xO1xVdd06SkBOfipt53hmO/AQONIHsh0gCF233JWvYm0Lw3HoRiXBcJWpCF4kMXBEEQFkfE9CBymOH3j8Lxf4f4XF81ben8e8JkWeb50Wm+1j2MU5K4PzuVjybE8rO3e/h1Qx8alZLPbs7j76uyCfdjP9Ts3Fm6uh5nZqYZvT6f/PxHSIivutxPuGCSJHHu3Dnq6uoYHx8nNjaWqqoqVq9ejdrPZWO2WTPHX3+ZE/v24rLbyFlbRsXuu0grCP48uD+QZRnX4JyvqnZ6AtktoUnVoy8zoFuTjDIiMAmwecJGe8MI7UdGsJld6GK0FG1IpaQyjZik+RN+IfBkjwfb8eNYDh5i7uBB3IODAIQvW/ZuC/+wwsLg7FuzmaDrLTj/GnQf8DUm0ughd7OvhX/+TaD37dMMxbguErQgC8WHLgiCICyOiOlXQM8hePULMDME5Z+GbV8H7fzLo8acbr7SOcS+yVlWR+l4piiDCIfEE2+08+a5MZbERvDgzUXsWpnq1/60iYnf09X9BA7HEIkJW8jL+yp6/ZWrQEmSRGdnJ7W1tRiNRqKioti4cSPr1q1Dq/WvOYbDauHkvr20vvEKjrlZMpatZP0dd5OxbOUV7YgoOTzYTk5gbRnFPWwBtRLdikT05Qa0WYGZeSZ5JfrPTNHWYGTw7BSyDOlFcZRUpZGzKgmVRlTVrjRZlnH19LzbZMR++jTIMpq0NCK3bCFqy2Z0paUo/Px3vSAeJ/TX+TpCnn8D5oygUEJGBRTuoMmcRMWOjwb+updBJGhBJn6YC4IgXD9ETL9CnBY48E1o/leIXQq3/ghyNs17iCzLvDw+w0NdF5jzSNyTlcLnM1No6Zvisb3ttI/Msm5pHI/uKmF1RuyCb0WSnAwN/Tt9/T9BkhykL/k42dmfR6NZ+DkulyzL9Pb2Ultby8DAADqdjg0bNlBWVka4n4OqXQ47p/fv49jePVinTaTmF1Kx+25y1pZd8db1rmEL1pZRbCfGkZ1e1EkRvqra2mRUkYF5UbdMO2hvHKGtwYjF5CRcr6FwvYGSqjTiU4OwL0pYEM/EBHOHD2M5eAhrYyOy04kyKorI6moit2whsqYaVfTC5xwumCzDyElfotbxOoydYcSwjdTP/G/gr3UZRIIWZOKHuSAIwvVDxPQrbKARXv4cmHpg3d/Cjd+E8Pmbf0y6PDzSdYGXxmdYFhnOD4oyKdFH8ELrEN97s5NJi5M71izh/u2FpMYsfNmb0zVJb+8zGI3Po1ZHk5P9BZYs+RhK5ZUdnjwwMEBdXR3d3d2EhYVRUVFBRUUFer1/yYbH5eLs4f20vPICsxPjJC3NpmL3XeRXbESpDP5MuD8lubzYT09ibRnFNTALKgURJQnoyw2E5caiCEB3RkmSudBuoq3eSN+pSSRJJjU3hpKqNHLXJaPRXtnPLPyRZLNhPXKEuYMHsRw6jNdkArUaXVkpUVu2Erl5M9r0JcG5+MwgR480sv7mvwrO+RdJJGhBJn6YC4IgXD9ETL8K3HY49G048mOISoVbnvXNPbqENyZm+ErnBabcHj6fmcI9WSm4XF5+eriHX9b3oVTAZzbl8g81uUT48XI+Z+mgq+txpqcb0elyyc9/iMSEGy7jAy6O0Wikrq6O9vZ2NBoNpaWlbNy4kago/zpPej0eOhrepuml3zFtvEBcWjoVt3+EospNqILRJv0S3GNWrM2+qppk86CKD0dfmoJ+XQqqmIUPJJ+PbdZFxxFfVc08bkcboaagPIWSyjSSMq9M507h4mSvF/up01gOHmDu4CFcvb0AhBUWErV1C5GbtxC+fFlAq72hGNdFghZkofjQBUEQhMURMf0qutAKL3/W10p71Ufhpm+DLn7eQ2bcHr7ebeS5URP5ujCeLcpkbYyeIZON77zRwWtnRkiNCeeB7YXctmrJgudoybLM5OQBurqfwG7vJz6+mvy8h4iMLAjEJ/XL+Pg4dXV1nD17FqVSyZo1a6isrCQuzr/BvZLkpaupkaYXn2NisJ/opBTKb/swyzZtQx2MfUGXILsl7Od8VTVnjxkUEF4Uj77MQHhhPArV5b+gy7KMsWuGtnojPccn8HokkjKjKKlKo6AsBW2AmpcIi+fs6/M1GTl0EPvxEyBJqFNSiNx8A1Fbt6KrqEB5mf8+QzGuiwQtyELxoQuCIAiLI2L6VeZxQu1TUP80RMTDrqeh+JZLHnZwapb7zw8x4nTz6YwkHshORadS0txn4rG9bZwZNrMqI5av7Sph3dKFJzaS5OLChd/Q1/9DvF4baWkfJSf7i2i18yeOwWAymaivr+fkyZMArFy5kqqqKhITE/06jyzL9B5voenF5xjpPo8+Lp7SXbtZte1mNH7udwsUz6Qd67FRrMfGkCxuVNFadKUp6EsNqOMDc08Oq5vzTaO01RsxGa2ow1Tkr0umpCqNlOzANC8RLo/HZMLydq2vhX99A7LdjlKnQ19VRdTWLehralD7+YsJCM24LhK0IAvFhy4IgiAsjojpIWLktK+aNnoalu2Gm78HkUnzHjLn8fJYj5H/ME6RHaHl6aJMNsRGIkkyL54Y5sl9HYzPObl1VRpfubmIJbEL35/mcpno7XsWo/F/UKl0ZGd9gfT0j6NUXvnKk9lsprGxkdbWVjweD8uWLaO6uhqDweDXeWRZZvDsKZr2PM/QudOER0Wz7uZbWb19F+H6yCDd/SXuySvhaDdhbRnF0TkNQFheLPpyAxHFCSjUl9+dUZZlxvpnaas30nVsHI/TS3yanpKqNAorDITrr+yeQ+HiJKcT65Ej71bXvBOToFKhW7vW1xVy6xa0mZkLOlcoxnWRoAVZKD50QRAEYXFETA8hXjc0/ADefhLCouDmJ2H5h+ESlY766Tm+3DHEgMPF3y1J5OGcVCLVKqxODz97u4ef1/r2vHy6JofPbMpFH7bwZW4WSydd3d/GZKojIiLrnf1pW65K9cVisXD06FGam5txuVwUFBRQU1NDenq63+cydrbTtOd5eo+3oI3QsWb7LtbuuA1d9PwNW4LJM+PEdmwUa8sYXrMTpV6Dbl2ybwh2ki4g13DZPXQdG6Ot3sj4wBwqtZKcNUksq0ojrSBWVNVChCxJOM6e9TUZOXAQZ1cXANq8XKI2+5K18JUrUSgvnsCHYlwXCVqQheJDFwRBEBZHxPQQNN7uq6YNt0LhTtj5fYhOnfcQq9fLd3pH+MWFSZaEa/h+YSab4n3NIYZn7Hz3jQ5eOWUkOSqM+28q5MNr0/3anzY1dZiu7iew2XqIi9tIfv7DREUWXfZHXQy73U5TUxNNTU3Y7Xays7OpqakhKyvL7wRjrK+H5j3P09nciFqrZdW27ZTuuoPI+IQg3f2lyZKMo2saa/MojnYTSDLa7Gj05anolieg8GNA+XwmhuZoqzfS2TyGy+4hJjmCkso0ijakoou+8pVS4f25hoawHDzI3MFD2I4dA68XVWIiUZtvIHLzFvQbN6D8k+W6oRjXRYIWZKH40AVBEITFETE9REleOPpTOPgtUIfBTU/A6o9dsprWPGPhno4heuxOPpYaz9dz04jR+CpmrQPTPLa3jZNDM6xYEsOju0ooz1743jJJcjM8/N/09j2LxzNHWtpd5Obcg1br356wQHE6nRw7dowjR45gsVjIyMigurqa/Px8vxO1qQtDNL/0PO0Nb6NUKll2wzbKb7uTmGT/llEGmnfOhbV1DFvLKJ4pB4pwNbo1SejLU9EGaOaZ2+Wl5/g4bfVGRrrNKJUKslYlUlKVRkZx/IITeeHK8M7MYKmrY+7gQay1dUhWK4rwcPSVlURt2ULkDZuoP3Mm5OK6SNCCTPwwFwRBuH6ImB7ipnp8c9MGGyF3q68lf2zGvIfYvRLf7x/lp4PjJGs1PFmYzocSfUv3JEnmlVNGvruvgxGzgx0rDHz15mIy4he+hM7tnqGv70dcGP4NSmU42VmfJSPjEyiVgWkZ7y+3282JEydoaGjAbDZjMBiorq6muLgY5fssAXs/M2OjtLzyAucO70eSJIorN1F++10kpM//PQ82WZJx9pmxNo9iPzsJXhlNRhSRZQYiViWhDAtMVc00YqWtwcj5I6M4rG4i48MoqUyjeGMqkXFXp6GK8P4klwtbc8u7Lfw9o6OgUGDdsoXSn/z4at/enxEJWpCJH+aCIAjXDxHTrwGSBMd+CW993VdBu/GbsO7v4BLJx4lZG/d0DNJhdfDhlDgey19C/DvVNLvLy89re/nZ2z14JZlPVmXz2c25RIUvvGGE1dpLd/cTTE4dJCI8k7y8B0lK+tBV28fk8Xg4c+YMdXV1mEwmEhMTqa6uZvny5ahU/iUwc6ZJWvfu4dRb+/C4XRSUb6TijrtJzsoJ0t0vnNfqxnZiHGvLKJ4xGwqtCt2qJPTlBjTpkQH5/nvdEr2nJmirN3KhYxqFAjKXJVBSlcbSFQmoVJffvEQILFmWcbS1YTl4iG6Xiw1fvvdq39KfEQlakIkf5oIgCNcPEdOvIdMD8OoXoPcwZFXDrT+E+PkTBpck8ezAGM8OjBGrVvNEQTq3JMe++7+Pmh08+WYHLx4fJjFSy30fKuQjpRmo/FjWNjVVR1f341itXcTGVlCQ/zBRUcsW+SEvnyRJtLW1UVtby/j4OLGxsVRVVbF69WrUfg6qts2aOf76y5zYtxeX3UbO2jIqdt9FWkFxkO5+4WRZxjU456uqnZ5AdktoDHr05QZ0q5NQ6gLTndE8Yae9wUj7kRFsZhe6aC1FG1MpqUwlJkDNS4TACsW4LhK0IAvFhy4IgiAsjojp1xhZhhP/CW8+7Ov6uPVrUPEPoJy/QnTOYuee9kFOW+zsTIrhOwXpJGn/+AJ/amiGb+5to3VgmuLUaB7dVczG3IXvLZMkD8aR5+ntfQa3e5rU1DvJzbmXsLDkRX/UyyVJEp2dndTV1TE8PExUVBQbN25k3bp1aP0cBOywWji5by+tb7yCY26WjGUrqdh9F5nLV4VE50PJ4cF2cgJryyjuYQuolehWJKIvM6AN0MwzySvRf2aKtgYjg2enkGVIL4qjpDKNnNVJqDSiqhYqQjGuiwQtyELxoQuCIAiLI2L6Nco8DHvvga43Ib0cbvsJJBXMe4hHkvmXoXG+1zeKXqXksfwlfDgl7t2Xd1mWee3MCE+83sHwjJ0PlaTw0I5ishIX3ozC7Z6lv//HDF34D5RKLVlLP0NGxidRqa7e/iVZlunt7aW2tpaBgQF0Oh3r16+nvLyccD8HVbscdk7v38exvXuwTptIzS+kYvfd5KwtC4lEDcA1bMHaMortxDiy04s6KQJ9mQHd2mRUkYHpzmiZdtDeOEJ7wwhzJgfheg2F6w2UVKURH6DmJcLihWJcFwlakIXiQxcEQRAWR8T0a5gsw5nfwRsPgMsGNzwIG78AqvmX8XVaHdzTMUjrrI1tCdE8WZBOWvgfX9wdbi+/rO/jp4e6cXkl/nZjFp/bkk9MxMKXzNls/XR3f4eJybcID19CXu4DJCfvvOpJzODgILW1tXR3dxMWFkZFRQUVFRXo9f4lFR6Xi3Nv76f55ReYnRgnaWk2FbvvIr9iI8pLVDOvFMnlxX56EmvLKK6BWVApiChJQF9uICw3FkUAujNKksyFdhNt9Ub6Tk0iSTKpuTGUVKWRuy4ZjTY0vhcfNKEY10WCFmSh+NAFQRCExREx/TpgGYfXvgztr0Dqal81zbB83kO8sswvL0zwRO8IaoWCb+Qt4WOp8X+WQI3POnjq9+f5XesF4nRa7rmxgI+WZaD2o0GEafoIXV2PY7G0ExOzjoL8R4iOXrnYTxowRqORuro62tvb0Wg0lJaWsnHjRqKiovw6j9fjoaPhbZpe+h3TxgvEpaVTcftHKKrchMrP/W7B5B6zYm0Zw3Z8DMnmQRUfjr40Bf26FFQxgem+aZt10XF0hLZ6I+ZxO9oINQXlKZRUppGU6d/3Vbg8oRjXRYIWZKH40AVBEITFETH9OnLuJXj9PrBPQ/V9UP1lUM+/pK3P5uTe84McmbFSExfJU4UZZEb8+Qv72WEzj+1to6nPREFKJI/sLKGmIGnBtyXLXowjL9DT833c7ikMhtvJzb2f8LCrO2MMYHx8nPr6es6cOYNSqWTNmjVUVlYSFxfn13kkyUtXUyNNe55nYqCP6KQUym79MMtv2Ibaz/1uwSR7JOznJrE2j+LsMYMCwovi0ZcZCC+MR6G6/KqaLMsYu2ZoqzfSc3wCr0ciKTOKkqo0CspS0EaETuJ6vQrFuC4StCALxYcuCIIgLI6I6dcZ6xTsexDOPA/Jy+D2n0DamnkPkWSZ/zBO8ViPERl4OCeVv1uSiPJPqmmyLPPmuVG+/XoHgyYbW4qSeWhHMXnJkQu+NY9njv6BnzE4+CsUChVLl/4DSzM/hUoVsdhPGzAmk4n6+npOnjwJwIoVK6iuriYx0b8h3LIs03u8haY9zzHSdR59XDylu3azatvNaPzc7xZsnkk71mOjWI+NIVncKKO1vqpaqQF1fGDu1WF1c75plLZ6IyajFbVWSX5pCiVVaaQEqHmJ8F6hGNdFghZkofjQBUEQhMURMf06df4NXxMRyzhUfgE2PQia+V+6hxwu7u8Y4vD0HOtj9DxdlEmO7s+raU6Pl39r6OdHB7txuL18fP1SvrQtn1jdwqtEdvsQ3T1PMj7+OmFhBvJyHyAl5RYUiqvfBdBsNtPY2Ehraysej4dly5ZRXV2NweBftU+WZYbOneboi88xdO404VHRrLv5VlZv30W4fuFJ7ZUgeyUcHSaszaM4OqcBCMuLRV9mIKIkAYX68p+LLMuM9c/SVm+k69g4HqeX+DQ9JZVpFK43EK4PzEgAwScU47pI0IIsFB+6IAiCsDgipl/H7DPw+0d8bfkT8n170zIr5j1ElmV+O2ri693DuCSZr2Sn8umMJFR/UemYtDh5+q1Ofts8SFS4hnu25fN/1i9F48f+tOmZFrq6HmNu7hzR0aspyH+EmJj5q31XisVi4ejRozQ3N+NyuSgoKKC6upqMjAy/z2XsbKdpz/P0Hm9BG6FjzfZdrN1xG7romCDc+eXxzDixHRvF2jKG1+xEqdegW5eMvsyAJkAzz1x2D13HxmirNzI+MIdKrSRnTRLLqtJIK4gVVbUACMW4ft0kaMtS8+Tn/+6pq30b7+HxePwe9CgIgiCEJhHTr396xVnS1L9GwxQm6UbGvHciM39jiMkwFT8oTuBIko7iGSf3tU2SZXW/5+v6ZPh/sopTKElH5v8qvJQqFv6uJSNhTz2GJe8NpLBZwkfXENW1E5XTvz1gweLCQ7dyki7VBC6Fl2QpkmJvCklyJAr8SyQkScLrdiF5vKAAlVqDSq0JSDfFgJNBjQatHIYaLQoUeHDjUjhx48TPj/7+l5FkvB4ZySshy6BQgkqlRKlWIvK0xQvFuL78id0iQQumUHzogiAIwuKImP7BoMROsup3JKgO4JKTGPb8PTa5eN5jZOCQQc+PCuOxq5X8de8Md/ebUf/Fq5QsQxMKfimrMKJgLRKfUnhZ6scLtqRyYl16EOvSwwDoBzajH9iM0huYDoOXy4OXHuUUnapxHAoPCZKOYm8KBjna70RNliQ8bjeSxwOASq1GpdGgUF79JZ4Xo5CVaGUtGsJRoUJGwoULl8KBpPAG5iIyeL0SkldG8vr+gSlVClRqJUqlImAJ4QdFKMb16yZBE0scBUEQhGATMf0Dpr8BXvkcmHqh9JOw7Z8hPHreQyZcbh7uGuaV8RmWR0bwg6IMlke9d7mbyyPxH0f6efZAFzaXl4+VZ3LPjQXE6xe+P83hMNLd8yRjY6+i1SaTl3sfBsPukNifBuB2uzlx4gQNDQ2YzWYMBgPV1dUUFxej9DPBMo+P0vzyC5w7vB9Jkiiu3ET57XeRkO7/MsorQZZlnL1mrM2j2M9OgldGkxGFviwF3aoklGGBSQhMI1baGoycPzKKw+omMj6M4o1pFG9MJSpAzUuud6EY16+bJY4iQRMEQRCCTcT0DyCXDQ49Dkd+AtFL4JZnIX/bJQ97bWKGBzsvMO328PnMFL6UlULYRZISk9XFD/Z38l9Ng+i0Kr64NZ+/2ZCF1o9mEzPmVrq6Hmd29hRRUcspyH+U2NiLvttdFV6vl9OnT1NXV4fJZCIxMZHq6mqWL1+OSuXfcOY50ySte/dw6q19eNwuCso3Ur77LlKyc4N095fPa3VjOzGOtWUUz5gNhVaFblUS+nIDmvTIgOwj87olek9N0FZv5ELHNAoFZC5LoKQqjaUrElD5sd/xgyYU47pI0IIsFB+6IAiCsDgipn+ADbXAy5+FyfOw+v/ATY9DxPx7v0xuD1/rGuaFsWkK9eE8U5TB2mj9Rb+2a2yOx15rp7ZzguxEPQ/tKGZbcfKCX95lWWJs7FW6e57E6RwlOXkHebkPEBEROhUmSZJoa2ujtraW8fFxYmNjqaqqYvXq1X4vMbPNmjn++suc2LcXl91G9ppSKnbfzZLC+ZeiXk2yLOManPNV1U5PILslNAY9+nIDutVJKHWB6c5onrDT3mCk/cgINrMLXbSWoo2plFSmEhOg5iXXk1CM6yJBC7JQfOiCIAjC4oiY/gHndkDtk1D/A9Anwq5noGjnJQ97a9LMA50XGHO6+UxGMvdnG4h4n4rGofPjfGtvGz0TVirzEnhkZwnFqfMvq/xTXq+NgcFfMDDwc8BLRsYnyVr6GdTqqAWfI9gkSaKzs5O6ujqGh4eJiopi48aNrFu3Dq2fg6odVgsn33yN1tdfxjE3S8aylVTsvovM5atCusOh5PBgOzWBtXkU97AF1Ep0KxLRlxnQBmjmmeSVGDg7RVu9kYGzU8gypBfFUVKZRs7qJFQaUVWD0IzrIkELslB86IIgCMLiiJguAGA86aumjZ2F5R+Gm5/0JWzzmPV4+Wa3kd+MTJETEcYzRRlUxF58xpfbK/HfTYM8s7+TWbubu8sy+fKHCkiMXHgTEIdjhJ7epxgdfQmtNpGcnHtJS70ThcK/JYXBJMsyvb291NXV0d/fj06nY/369ZSXlxPu56Bqt8PBqf1vcGzvHqzTJlLzCqm4425y1paFdKIG4Bq2YG0ZxXZiHNnpRZ0Ugb7MgG5tMqpI/xLW92OZdtDeOEJ7wwhzJgfheg2F6w2UVKURn3rxqu4HRSjGdZGgBVkoPnRBEARhcURMF97lcUHDD+DtJ32NQ3Z8D5bdwaX6ndea5vjy+SEuOFx8ckkiD+WkoldfPGmasbl49kAX/3lkgHCNis9tyePvKrMIe5+vvxjz7Cm6ur6F2XycyMhi8vMfJj5ugz+f9IoYHByktraW7u5uwsLCqKiooKKiAr3ev+TB43Jx7u39NL/8ArMT4yQtzaZi913kV2xEqQyd5PRiJJcX++lJrC2juAZmQaUgoiQBfbmBsNzYgIwYkCWZoXYTbfVG+k5NIkkyqbkxlFSlkbsuGY02tL9HwRCKcV0kaEEWig9dEARBWBwR04X3GGvzVdOMx6FoF+z8PkQZ5j3E6vHy7d4Rfjk8SUa4lqcLM6iOf/8liD0TFr79WjsHOsbJjNfx1ZuL2L7c4Mf+NJnx8dfo7nkSh2OYpMQbyct7EJ0uy59PekUYjUbq6upob29Ho9FQWlrKhg0biI5e+DJPAK/HQ0fD2zS99DumjReIS0un4vaPUFS5CVWItVS/GPeYFWvLGLbjY0g2D6q4MPSlBvSlKahiAjNOwTbrouPoCG31RszjdrThKgrKfVW1pMzQWRIbbKEY10WCFmSh+NAFQRCExRExXbgorweO/gQOPg6aCNj+HVj1V5esph2dsXBvxxC9dicfT03ga3lpRM9THavrmuBbe9s5PzZHeXY8X9tVwvIlMQu/Ta+DoaFf0T/wL0iSm4yMT5Cd9bmQ2p/2B+Pj49TX13PmzBmUSiVr1qyhsrKSuDj/hnJLkpeupiM07XmOiYE+opNSKLv1wyy/YRtqP/e7XQ2yR8J+bhJr8yjOHjMoILwoHn2ZgfDCeBSqAFTVZBlj1wxt9UZ6jk/g9UgkZUZRUpVGQVkK2ojQT2gvRyjGdZGgBVkoPnRBEARhcURMF+Y12QUvfw6GjkLejXDLDyAmfd5D7F6J7/WN8rOhcVLCNDxZkM6Nie+fdHm8Er9tGeLptzqZtrm4c206999USHL0wvdsOZ3j9PQ+zcjIC2g0ceTk3ENa6l0olaH3Im4ymWhoaODEiRPIsszKlSuprq4mMXH+PX9/SZZl+k4c4+iLv2Wk6zz6uHhKd+1m1bab0fi53+1q8UzZsbaMYW0dRZpzo4zWol+Xgr7MgDpAM88cVjedzaO01RuZGrai1irJK01hWVUaKQFqXhJqQjGuiwQtyELxoQuCIAiLI2K6cEmSBC3/D/Z/AxQq+NBjsO5vL1lNOz5r5Z6OIc5bHdyZEsdj+UuI07x/wmS2u/nJoW5+3dCHRqXks5vz+PuqbMI1C99DNDt3lq6ux5mZaUavzyc//xES4qsWfPyVZDabaWxspLW1FY/HQ0lJCTU1NRgM8y8n/UuyLDN07jRHX3yOoXOnCY+KZt3Nt7J6+y7C9Rdv2hJqZK+Eo8OEtXkUR+c0AGF5sejLDESUJKDwY4be+15Dlhnrn6Wt3kjXsXE8Ti/xaXpKKtMoXG8gXB+YkQChIBTjukjQgiwUH7ogCIKwOCKmCwtm6oNXvwB9tZBdA7f8EOKz5z3EKUn8oH+MHw2OEadR852CdHYmxc57TP+klSfeaOfNc2MsiY3gwZuL2LUy1a/9aRMTv6er+wkcjiESE7aQl/dV9PqchX7SK8pisXD06FGam5txuVwUFBRQXV1NRob/896Mne007Xme3uMtaCN0rNm+i7U7bkMXvfBlo1ebZ8aJ7dgo1pYxvGYnSr0a3doU3xDsAM08czk8dLWM0VZvZHxgDpVaSc6aJEqq0lhSEHvNV9VCMa6LBC3IQvGhC4IgCIsjYrrgF1mG4/8Obz4Cshe2fh3KPw3K+SscZ+ds3NMxxBmLnVuSYvl2wRKStPNXLBp7JnlsbzvtI7OsWxrH13aVsCojdsG3KklOhob+nb7+nyBJDtKXfJzs7M+j0Sz8HFeS3W6nubmZo0ePYrfbyc7OpqamhqysLL8ThvH+Xpr2PE9nUwNqrZaVW7dTestuouL9W0Z5NcmSjLNr2jcEu90Ekow2K9o3BHtFIgo/KqvzmbwwR1udkfPNY7jsHmKSIiipSqNoQyq66NDf03cxoRjXRYIWZKH40AVBEITFETFdWBTzBXj1S9D9FmSsh9t+Aol58x7ilmR+OjjO9/tHiVQr+VZ+OruT569WeCWZ3x0b4qnfn2fS4uKONUt4YHsRhhg/9qe5JuntfQaj8XnU6mhycr7IkrSPolSG5pI2p9NJa2srjY2NWCwW0tPTqampIT8/3+9EberCEM0v/472+sMolUqW3bCN8tvuJCbZv2WUV5t3zoW1dQxbyyieKQeKcDW6NUnoy1PRBmjmmdvlpef4OG31Rka6zSiVCrJWJVJSlUZGcTzKAIwEuFJCMa6LBC3IQvGhC4IgCIsjYrqwaLIMp5+DN74CHgdsfgjWfxZU8zfmOG91cE/HIMdnbXwoIZrvFqaTGjZ/pWLO4eanh3v4ZV0fKqWCz2zK5dM1OUT4MeNqbq6dru7HmZ4+gk6XS37+QyQm3LDg4680t9vNiRMnaGhowGw2YzAYqK6upri4GOUlKpZ/yTw+Sssr/8vZQ28hSRLFlZsov/0uEtL9X0Z5NcmyjLPXjLVlFPvZSfDIaDKi0JeloFuVhDIsME1hpkettNUb6Tg6isPiJjI+jOKNaRRvTCUqQM1LgikU47pI0IIsFB+6IAiCsDgipguXbW4MXrsXOvZC2lpfNS2lZN5DvLLM/xua4Dt9I2iVCv45bwl/ZYi/ZIVoyGTjO2908NqZEVJjwvnK9iJuXZW24OqGLMtMTh6gq/vb2O0DJMTXkJf/EJH6/AV/3CvN6/Vy+vRp6urqMJlMJCYmUlVVxYoVK1Cp/FvmN2eapHXvHk7t34fH5aKgfCPlu+8iJTs3SHcfPF6rG9uJcawto3jGbCi0KnSrknx71dIjA7KPzOuW6D01QVu9kQsd0ygUkLksgZKqNJauSECluvzmJcEQinFdJGhBFooPXRAEQVgcEdOFgJBlOLcHXr8fHGbY9ABU3QOq+ZcR9tqc3NsxyFGzlRviovheUQYZ4Zfe99PcZ+Kbe89xdniW1RmxPLqrhHVLFz5PTJJcXLjwG/r6f4jXa2NJ2sfIzv4CWm38gs9xpUmSRFtbG3V1dYyNjREbG0tVVRWrV69G7eegatusmeOvv8KJfa/istvIXlNKxe67WVJYHKS7Dx5ZlnENzvmqaqcmkN0SGoPet1dtdRJKXWCWspon7LQ3GGk/MoLN7EIXraVoYyollanEBKh5SaCEYlwXCVqQheJDFwRBEBZHxHQhoKyTviWPZ1+AlBVw248hbfW8h0iyzL8NT/Kt3hEUwKO5afxNWgLKS1RAJEnmxRPDPLmvg/E5J7euSuMrNxexJDZiwbfrcpno7XsWo/F/UKn0ZGd9nvT0j6NUhm5zCFmW6ezspLa2luHhYaKioti4cSPr1q1D6+egaofVwsk3X6P19ZdxzM2SsWwlFbvvInP5qmuyk6Hk8GA7NYG1eRT3sAXUSnQrEtGXGdAGaOaZ5JUYODtFW72RgbNTyDIsKYxjWVUaOauTUGmuflUtFOO6SNCCLBQfuiAIgrA4IqYLQdHxGuy9F6wTUPUlqHkANPPv3Rm0O7nv/BC10xY2xOp5ujCTbF3YJS9ldXr42ds9/Ly2F4BP1+TwmU256P3Yj2SxdNLV/W1MpjoiIrLe2Z+2JaSTFFmW6e3tpa6ujv7+fnQ6HevXr6e8vJxwPwdVux0OTh/YR8urL2KdNpGaV0jFHXeRs7Y8pL8H83ENW7C2jGI7MY7s9KJOikBfZkC3NhlVZGAScMu0g/bGEdobRpgzOQjXayhcb6CkMo34tMA0L1mMUIzrIkELslB86IIgCMLiiJguBI192teO/+RvILHQtzcto2zeQ2RZ5n9GTHy9exiPLPNgTiqfSk9CtYAkYXjGznff6OCVU0aSo8K4/6ZCPrw23a/9aVNTh+nqfgKbrYe4uI3k5z9MVGTRgo6/mgYHB6mtraW7u5uwsDDKy8tZv349er1/SYLH5eLc2/tpfvl/mZ0YIykzi4o77ia/YiNKZWDa2l9pksuL/cwk1uZRXAOzoFIQUZKAvsxAWF4sigB0Z5QlmaEOE231RvpOTiJJMoacGEqq0sgrTUbjRzObQAjFuC4StCALxYcuCIIgLI6I6ULQde+HV74Is8Ow4bOw+WHQzr9nx+hw8UDnBfZPzbIuWsczRZkU6BdWFWodmOaxvW2cHJphxZIYHt1VQnn2wveWSZKb4eH/prfvWTyeOdLS7iI35x602tCfIWY0Gqmrq6O9vR2NRkNpaSkbNmwgOjrar/N4PR46Gt6m6aXfMW28QFxaOuW33Ulx1Q2o/NzvFkrcY1asLWPYjo8h2Tyo4sLQlxrQl6agirl0tXYhbLMuOo76qmozYza04SoKyg2UVKWRlBkVkGtcSijG9ZBN0BQKRSbwQ8AEdMqy/J35vl4kaIIgCEKwiZguXBGOWdj/DTj2S4jL9u1Ny6qa9xBZlnlxbJpHuoaxeiXuyzbwTxnJqBdQ8ZAkmVdOGfnuvg5GzA52rDDw1ZuLyYhfeDMHt3uGvr4fcWH4NyiV4WRnfZaMjE+gVAbmRT6YxsfHqa+v58yZMyiVStasWUNlZSVxcQtvpAIgSV66mo7QtOc5Jgb6iE5KpuzWO1l+wzbUfu53CyWyR8J+zldVc/aYQQHhhfHoyw2EF8ajUAWgqibLGLtmaGsw0tM6gdcjkZQZRUlVGgVlKWgjgpfohmJcD0qCplAofgXsAsZlWV7+J3+/HXgWUAG/mC/pUigUO4E4WZZ/o1AonpNl+e75rikSNEEQBCHYREwXrqi+Wnjl8zDdD2Wfgm3fgLD5qwoTLjcPdl7gtQkzKyMjeKY4k2WRC2sEYnd5+XltLz97uwevJPPJqmw+uzmXqPCFd/azWnvp7n6CyamDRIRnkpf3IElJH7om9maZTCYaGho4ceIEsiyzcuVKqqurSUz0rxooyzJ9J45x9MXfMtJ1Hn1cPKU7b2fljTejDV94U5ZQ5JmyY20Zw9o6ijTnRhmtRb8uBX2ZAXWAZp45rG46m0dpqzcyNWxFrVWSV5rCsqo0UgLUvORPhWJcD1aCVgNYgP/4Q4KmUChUQCdwI3ABaAE+ii9Ze+IvTvFJwAu8AMjAf8qy/Ov5rikSNEEQBCHYREwXrjiXFQ5+C47+C8Skwy3PQt7WSx726vgMX+28wIzHwxeWpvClpSloFziwedTs4Mk3O3jx+DCJkVru+1AhHynNQOXH/qOpqTq6uh/Hau0iNraCgvyHiYpatuDjryaz2UxjYyOtra14PB5KSkqorq4mNTXVr/PIsszQudM07XmOwbOnCY+KZt3Nt7J6+y7C9ZFBuvsrQ/ZKODpMWJtHcXROgwxh+bHoywxElCSgUF9+d0ZZlhnrn6W93kjnsXE8Ti/xaXpKKtMorDAQHhmYkQChGNeDtsRRoVBkAXv/JEHbAHxDluWb3vnzVwFkWf7L5OwPx98HNMuyXKtQKF6QZfnO+a4nEjRBEAQh2ERMF66awSZ4+bMw1QVrPg4fehwiYuc9ZMrl4Wvdw/zv2DRF+nB+UJTJ6uiFL1s8NTTDN/e20TowTXFqNI/uKmZj7sKrSZLkwTjyPL29z+B2T5Oaeie5OfcSFpa84HNcTRaLhaNHj9Lc3IzL5aKgoIDq6moyMjL8Ppexs52mPc/Te7wFbYSO1TftZN3O29FFxwThzq8sz4wT27FRrMfG8M44UerV6Nam+IZgB2jmmcvhoatljLZ6I+MDc6jUSnLWJFFSlcaSgtjLqqqFYly/kgnancB2WZY/9c6f/xqokGX5c+9z/HLgG8AkYJFl+b6LfM2ngU8DpKSkrPvtb3+76PsNFovFQmTktf1bEkEQBMFHxHThalJ6XSwd+C2Zg3twaWPpLPhHphLLL3lcq6zmF+iYQcEtOLkTB9oFvs/KskzLqJfnzruYcsisTVZxd6GWFP3CKySybEOWX0XmAKBGodiJghtRKK6NfVlut5vh4WEuXLiAx+MhNjaWpUuXEhvrf2Jgmxxn9PhRpns6UajVJJWsImVVKdrIK9MQI6hk0E1C9AUl+nFQyArscTKz6TIWg4wcoOaMjmmZ6V6ZmX6Q3KCNhNhcBXHZoA73P1ELxbi+efPm0EzQ/CUqaIIgCEKwiZguhITh4/Dy52D8HKz4CGz/LugT5j3E7Pbwzz1G/nvERJ4ujKcLMyiPXfhLqcPt5Zf1ffzkUDdur8Tfbszic1vyiYlY+DIzm62f7u7vMDH5FuHhS8jLfYDk5J3XxP40AKfTSWtrK42NjVgsFtLT06mpqSE/P9/vzzA1PETzS7+jvf4wSqWSZZu2UXbbncSmGIJ091eWd86F7fgY1uZRPFMOFOFqdGuSfEOw0wKTDHlcXnqOj3Ou3shItxmlUkHWqkRKKtPIKIlf8MiIUIzrIbvE0V8iQRMEQRCCTcR0IWR4XFD/NNR+D8JjYedTsGz3JQ972zTHl88PMuxw86n0RB7MSUWvWnhpY3zWwVO/P8/vWi8Qp9Ny740F/FVZBmrVwitqpukjdHU9jsXSTkzMOgryHyE6euWCj7/a3G43J06coKGhAbPZjMFgoLq6muLiYpQL3Of3B+bxUVpe+V/OHnoLSZIortxE+e13kZDu/zLKUCTLMs5eM9aWUexnJ8Ejo0mPRF9uQLcqCaUfA9LnMz1qpa3eSMfRURwWN5HxYRRvTKN4YypRl2heEopx/UomaGp8TUK2AsP4moR8TJblc4u+yJ8QCZogCIIQbCKmCyFn9Kxvb9rISSi+FXY8BVEp8x5i8Xh5vHeEXw9Pkhmu5emiDKri/Ftid3bYzDf3ttHcZ6IgJZJHd5VQnZ+04ONl2Ytx5AV6er6P2z2FwbCb3Nz7CA+7dipIXq+X06dPU19fz9TUFImJiVRVVbFixQpUfiS9AHOmSVr37uHU/n14XC7yyzdQsftuUrJzg3T3V55kc2M9Po61ZRTPmA2FVoluVbJvr1p6ZEAqqV63RO+pCdrqjVzomEahgMxlCZRUpbF0RQKqi/wiIRTjerC6OP4PcAOQCIwBX5dl+ZcKhWIH8AN8nRt/Jcvy44u6wEWIBE0QBEEINhHThZDk9cCRH8GhJ3xDrbd/F1beBZd44T0yY+HejkH67C7+Ji2BR3PTiFIvPLGQZZk3z43y+OvtDJnsbC1K5qGdxeQmLXwJm8czR3//vzA49GsUChVLl/4DSzM/hUp17bSjlySJtrY26urqGBsbIzY2lqqqKlavXo3az0HVtlkzx19/hRP7XsVlt5G9ppSK3XezpLA4SHd/5cmyjGtoDmvzKPZTE8huCY1Bh77MgG5NMkpdYLozzk7aaWsw0t44gs3sQhetpWhDKiVVqcT8SfOSUIzrITuo2l8iQRMEQRCCTcR0IaRNdPqqaReaIf8m2PUMxCyZ9xCbV+LJvhF+PjSBIUzD9woz2JoQ7ddlnR4v/9bQz48OduNwe/nrDUv54tZ8YnULbwJitw/S3f0k4xNvEBZmIC/3AVJSbkGhuPx27VeKLMt0dnZSW1vL8PAwUVFRbNy4kXXr1qH1c1C1w2rh5Juv0fr6yzjmZskoWUHFHXeTuXzVNbNnbyEkhwfbqQmszaO4hy2gVqJbkejbqxagmWeSV2Lg7BRt9UYGzk4hy7CkMI5lVWnkrE6irqE25OL6dZOgZWVlyV//+tev9m28x8zMDLGxsVf7NgRBEIQAEDFdCHUKWaJ4ro51M3uRUNEcdxtdkesvWU0bDNPxvwmZjGsjWGuZYqdpGJ3k9evaFo+CQ5ORnDCHE66U2ZRopTTWjsqPd+ywsAHi4t5CGzaK07mEadONuFzpft1HKHA4HMzMzOB0OlEqlURHRxMVFeX3HjVZkrDOmJidmkRye9BGRBCdlEz49dD18S/ILi/eWReSxY0syyjUSlTRWlSRWvz6RzQPr0fCNuvCZnbh9UgolArUETJJabEBOX+gfPKTnxQJWjCJH+aCIAjXDxHThWtFlHuSyqnfkursZji8gMaEu7Go5+/06EHBwVgDb8ekoPd6uM00xDKb2e9rjzlUvDkRRZ9NS6LWw4eSLORHuvw4g4xef5qY2EOo1Ras1mXMTG/B6732ZoY5nU7MZjN2ux2FQkF0dDTR0dH+J2qyjG1mmtmpCbwuN5rwcKISk66LOWrvIYNkdfuSNacHAJVegzJKizIiME1FAJw2D1azEwk3iamxATtvIFw3CZpY4igIgiAEm4jpwjVFkuD4v8HvvwayBNu+AWWfgkskB2fmbHypY5BzFge3JcfyeH46iVr/XoxlWWZ/+zjffr2dvkkrNQVJPLKzmIKUhVd+PB4rA4P/yuDgLwDIzPy/LM38NGq13q97CQVGo5G6ujra29vRaDSsW7eOjRs3Eh3t33JSr8dDR8PbNL/0O0zGC8SlLqH89o9QXHUDKj/3u10L3GNWrC1j2I6PIdk8qGLD0JcZ0JemoIoJC8g1QjGuXzdLHEWCJgiCIASbiOnCNWlmCF79IvQcgMyNcNuPIWH+7oBuSebHg2M83T9GlFrJt/PTuS3Z/8HMLo/Efxzp59kDXdhcXj5Wnsk9NxYQr1/4niyHw0h3z5OMjb2KVptMXu59GAy7r6n9aX8wMTFBXV0dZ86cQalUsmbNGiorK4mLi/PrPJLkpavpCE17nmNioI/opGTKbr2T5TdsQ+3nfrdrgeyRsJ+bwtoyirN7BhQQXhiPvtxAeGE8istYAhmKcV0kaEEWig9dEARBWBwR04VrlizDyf+GN78KHidseQTW/xMo5+/a2G6xc0/HECfnbNycGMN3CtJJCfO/y57J6uIH+zv5r6ZBdFoVX9yaz99syEKrXniSNWNupavrcWZnTxEVtZyC/EeJjb3oO2zIM5lMNDQ0cPLkSSRJYuXKlVRVVZGUtPBRBeCrVPadOMbRF3/LSNd59HHxlO68nZU33ow2/NrphOkPz5Qda8sY1tZRpDk3ymgt+nUp6MsMqC8x8+xiQjGuiwQtyELxoQuCIAiLI2K6cM2bHYHX7oXzr8OSdXDbTyB5/hbuHknmXy9M8GTfCOFKJd/MW8JdhrhFddjrGpvjsdfaqe2cIDtRz0M7itlWnLzgc8myxNjYq3T3PInTOUpy8g7ych8gIuLaHOw8OztLY2Mjx44dw+PxUFJSQnV1NampqX6dR5Zlhs6dpmnPcwyePU14VDRrb76FNdtvIVy/8LEH1xLZK+HomMbaMorjvAlkCMuPRV9mIKIkAcUCk/9QjOsiQQuyUHzogiAIwuKImC5cF2QZzv4vvH4/uCyw6QGo/BKo5q+Mddsc3NsxRLPZyub4KL5XmEF6+OKW0x06P8639rbRM2GlMi+BR3aWUJy68P1YXq+NgcFfMDDwc8BLRsYnyVr6GdTqa7O7ocVi4ejRo7S0tOB0OsnPz6empoaMDP8TT2NnB017nqP3eAvaCB2rb9rJup23X58NRd7hmXFiOzaK9dgY3hknSr0a3VpfVU2TrJv32FCM6yJBC7JQfOiCIAjC4oiYLlxXLBPwxgNw7kUwrIDbfgqpK+c9RJJlfjU8yeM9I6gU8LXcND6eloByEdU0t1fiv5sGeWZ/J7N2N3eXZfLlDxWQGLnw5g8Oxwg9vU8xOvoSWm0iOTn3kpZ6JwrFwgduhxK73U5zczNHjx7FbreTnZ1NdXU12dnZflcsx/t7adrzPJ1NDag1WlZu207pLbuJik8M0t1ffbIk4+zyVdXsbSaQZLRZ0ejLDehWJKLQvPffRSjGdZGgBVkoPnRBEARhcURMF65L7a/C3nvBboKqe6DmflDPnyQN2J18uWOI+hkLlbGRPF2UwdKIxXXVm7G5ePZAF/95ZIBwjYrPbcnj7yqzCFMvPMkyz56iq+tbmM3HiYwsJj//YeLjNizqfkKB0+mktbWVxsZGLBYL6enp1NTUkJ+f73eiNjU8RMvLL9BWdwilUsmyTdsou+1OYlMMQbr70OCdc2E7Poa1ZQzPpB1FuArdmmTfEOy0Py77DMW4LhK0IAvFhy4IgiAsjojpwnXLZoI3H4ZT/w1JRb69aenzN+CQZZn/GjHxje5hvDI8lJPKJ9MTUS2imgbQM2Hh26+1c6BjnMx4HQ/tKOKmZQY/9qfJjI+/RnfPkzgcwyQl3khe3oPodFmLup9Q4Ha7OXnyJPX19ZjNZgwGA9XV1RQXF/s9S808PkrLK//L2UNvIUkSRZWbqLj9IySkZwbp7kODLMs4e82+qtrZSfDIaNIjfVW1VUnUHqkPubguErQgEz/MBUEQrh8ipgvXva63fC3550Zgw2dh88Ogmb8b4LDDxf3nhzhomqMsWs/TRRnk6/3vpvcHtZ0TfOu1NjrHLFRkx/PorhKWL1n4/imv18HQ0K/oH/gXJMlNRsYnyM763DW7Pw3A6/Vy+vRp6uvrmZqaIjExkaqqKlasWIFK5d9yTotpimN793Bq/xt4XC7yyzdQsftuUrLnH71wPZBsbqwnxrE2j+IZs6HQKplc6mHV32+62rf2Z0SCFmTih7kgCML1Q8R04QPBMQtvfQ1afw3xub65aUs3znuILMu8MDbNo13D2CWJ+7IM/GNGMmrl4qppHq/Eb1uGePqtTqZtLj6yLp37PlRIcvTCEz+nc5ye3qcZGXkBjSaOnJx7SEu9C6Xy2h3oLEkSbW1t1NXVMTY2RmxsLJWVlaxevRqNxr/xB7ZZM8dff4UT+17FZbeRvaaUit13s6Rw/q6e1wNZlnENzWFtHqXfPsLavxYJWlCIBE0QBEEINhHThQ+U3sPwyhdgZgDKPw1bvw5h87dsH3e6ebDzAq9PmlkZFcGzRZkURy5+HpfZ7ubHB7v4t8Z+tCol/7Q5j7+vyib8Is0e3s/s3Fm6uh5nZqYZvb6A/PyHSYivWvQ9hQJZluns7KS2tpbh4WEiIyPZuHEjpaWlaP0cVO2wWjj55mu0vv4yjrlZMkpWULH7bjJXrFrUKIVrTSjGdZGgBVkoPnRBEARhcURMFz5wnBY4+Bg0/SvEZsAtP4TczfMeIssyr0zM8FDnMLMeL19cmsIXliaj9XPP1J/qn7Ty7dfb+X3bGEtiI3jw5iJ2rUz1a3/axMSbdHV/B4djiMSELeTlfRW9PmfR9xQKZFmmr6+P2tpa+vv70el0rF+/nvLycsLD/Vtm6nY4OH1gH8defRHLtAlDXgHr77ibnLXl13WiFopxXSRoQRaKD10QBEFYHBHThQ+sgSPwyudgqhvW/g186FsQPv++sEmXh0e7LrBnfIYSfTjPFGeyKmr+mVSX0tgzyWN722kfmaV0aRyP7iphVUbsgo/3ep1cuPBv9PX/FElykJ7+12RnfR6N5tqfETY4OEhdXR1dXV2EhYVRXl7O+vXr0ev1fp3H43Zz7vB+ml9+gdmJMZIysyjffRcF6ytRKq/N8QXzCcW4LhK0IAvFhy4IgiAsjojpwgea2w6Hn4DGH0GkAW75ARTcdMnD9k2Y+UrnEJNuD5/NSObeLAPhqsVX07ySzO+ODfHU788zaXFxx5olPLC9CEOMH/vTXJP09j6D0fg8anU0OTlfZEnaR1Eq/dvHFYqMRiN1dXW0t7ej0WhYt24dGzduJDp64YPAAbweDx0Nb9P80u8wGS8Ql7qE8ts/QnHVDajU1+4+vr8UinFdJGhBFooPXRAEQVgcEdMFARhuhZc+CxPtsPKvYPsToIuf95AZt4dvdBv57aiJfF0YzxRlUhrjX2XnL8053Pz0cA+/rOtDpVTwmU25fLomhwjtwqs8c3PtdHU/zvT0EXS6XPLzHyIx4YbLuq9QMTExQV1dHWfOnEGpVLJ69WqqqqqIi4vz6zyS5KWr6QhNe55jYqCP6KRkym75MMs334jaz/1uoSgU47pI0IIsFB+6IAiCsDgipgvCOzxOqPu+7z8R8bDz+1By6yUPOzQ1y33nhzA63Xw6PYmv5KSiu4xqGsCQycZ33ujgtTMjpMaE85XtRdy6Kg3lAjtIyrLM5OQBurq/jd0+QEJ8DXn5DxGpz7+s+woVJpOJhoYGTp48iSRJrFy5kqqqKpKSkvw6jyzL9J04xtE9zzHS2YE+No7SXbtZeePNaMMX3wjmagvFuC4StCALxYcuCIIgLI6I6YLwF0bPwEv/BKOnoeR22PEURM7/4j/n8fKtHiP/bpwiK0LL9wszqIy7/BllzX0mvrn3HGeHZ1mdEcuju0pYt3Th1SJJcnHhwm/o6/8hXq+NJWkfIzv7C2i181cHrxWzs7M0NjZy7NgxPB4PJSUlVFdXk5qa6td5ZFlm6NwZmvb8lsGzpwmPjGLtjltZs/0WwvXzd/kMRaEY10WCFmSh+NAFQRCExRExXRAuwuuGxh/C4e+ANhJufhJW3AmX6PzXMD3HvR1DDDhcfCItgUdz04hUX14TCkmSefHEME/u62B8zsmtq9L4ys1FLIldeIXH5TLR2/csRuP/oFLpyc76POnpH0epvPaX8wFYLBaOHj1KS0sLTqeT/Px8ampqyMjI8Ptcxs4OmvY8R+/xFrQROlbftJN1O29HF33tNF0JxbguErQgC8WHLgiCICyOiOmCMI+J8/DyZ+FCCxTcDLuehui0eQ+xer082TvKzy9MkBam4anCDDYn+NfM4qLndXr42ds9/Ly2F4BP1+TwmU256MMW3tzCYumkq/vbmEx1RERkvbM/bct103LebrfT3NzM0aNHsdvtZGVlUVNTQ3Z2tt+fcby/l6Y9z9PZ1IBao2Xl1psoveUOohISg3T3gROKcV0kaEEWig9dEARBWBwR0wXhEiQvHP0X3+w0VRjc9Dis+fglq2nHzFbu6Riky+bko6nxfCM3jRjN5XcKHJ6x8903OnjllJHkqDDuv6mQD69N92t/2tTUYbq6n8Bm6yEubiP5+Q8TFVl02fcWKpxOJ62trTQ2NmKxWEhPT6e6upqCggK/E7Wp4SFaXn6BtrpDKBRKlt+wjbLb7iQ2xRCku798oRjXRYIWZKH40AVBEITFETFdEBZoqgde+TwMNEDOZrj1hxCbOe8hDq/E9/tH+enQOIkaNU8WZnBTYmCWyrUOTPPY3jZODs2wYkkMj+4qoTx74XvLJMnN8PB/09v3LB7PHGlpd5Gbcw9abehXiBbK7XZz8uRJ6uvrMZvNGAwGqqurKS4uRunnkHHz+Cgtr/wvZw+9hSRJFFVuouL2j5CQPv+/gashFOO6SNCCLBQfuiAIgrA4IqYLgh8kCY79Et76uq+Ctu0bUPr3cImX/ZOzNu7pGKTd6uCOlDgey1tCgvbyq2mSJPPKKSPfeaOD0VkHO1ek8uDNRWTEL3x4tts9Q1/fj7gw/BuUynCysz5LRsYnUCrDLvv+QoXX6+X06dPU19czNTVFQkIC1dXVrFixApXKvz2CFtMUx/bu4dT+N/C4XOSXb6Bi992kZOcG6e79F4pxXSRoQRaKD10QBEFYHBHTBWERpgfg1S9C7yFYWuWrpiXM/4LukiR+ODDODwZGiVGreaIgnVuSYgKy/8vm8vDz2l7+9e1evLLM31dl80835BIVvvAh1VZrL93dTzA5dZCI8Ezy8h4kKelD183+NABJkmhra6Ouro6xsTFiY2OprKxk9erVaDT+DfS2zZo5/vornNj3Ki67jezV66jYfTdLikqCdPcLF4pxXSRoQRaKD10QBEFYHBHTBWGRZBlO/AbefBi8Ltj6KFR8BpTzV2TaLHa+1DHI6Tk7O5NieCI/neQw/5KD9zNitvO9fed58cQwiZFh3PehAj5SmoFqgfvTAKam6ujqfhyrtYvY2AoK8h8mKmpZQO4vVMiyTGdnJ7W1tQwPDxMZGcnGjRspLS1F6+egaqfNysk3X6P1tZewz82SUbKCit13k7li1VVLbkMxrosELchC8aELgiAIiyNiuiBcplkj7L0HOvdBehnc9hNIKpz3EI8k8y9D4zzVP0qEUslj+Uu4MyUuYC/0J4dmeGxvG60D0xSnRvPormI25i58b5kkeTCOPE9v7zO43dOkpt5Jbs69hIUlB+T+QoUsy/T19VFbW0t/fz86nY7169dTVlZGRIR/g6rdDgenD+zj2KsvYpk2YcgrYP0dd5OztvyKJ2qhGNdFghZkofjQBUEQhMURMV0QAkCW4cwL8Mb94LLCDQ/Cxi+Aav7KWJfVwT0dgxybtbE1PprvFaaTFh6Y2WSyLLP39AjfeaOD4Rk7HypJ4aEdxWQl6hd8Drd7lv7+HzN04T9QKrVkLf1HMjI+iUp1/exP+4PBwUHq6uro6uoiLCyM8vJy1q9fj16/8O8XgMft5tzh/TS//AKzE2MkZWZRvvsuCtZXorxEdTVQQjGuiwQtyELxoQuCIAiLI2K6IASQZRxevx/aXoLUVb5qmmHFvId4ZZlfXZjk271G1AoFX89bwv9JjQ9Y1cXh9vLL+j5+cqgbt1fi7yqz+dyWPKL92J9ms/XR3f1dJibfIjx8CXm5XyE5ecd1tT/tD0ZGRqirq6OtrQ2NRsO6devYuHEj0dH+zbLzejx0NLxN80u/w2S8QFzqEspvu5Pi6s2o1JffIGY+oRjXRYIWZKH40AVBEITFETFdEIKg7WV47ctgn4bqL0P1faCevzLWb3dyb8cQjTMWquMieaowg6URgatUjc86eOr35/ld6wXidFruvbGAvyrLQK1aeLt5k6mRru7HsVg6iIlZR0H+I0RHrwzYPYaSiYkJ6urqOHPmDEqlktWrV1NVVUVcXJxf55EkL93NRzi653km+nuJTkqm7JYPs3zzjaj93O+2UKEY10WCFmSh+NAFQRCExRExXRCCxGaCfV+F07+F5BK47cewZN28h0iyzG+MU3yzx4hXhodzU/nkkkSUAaxUnR028829bTT3mShIieTRXSVU5yct+HhZ9mIceYGenu/jdk9hMOwmN/c+wsNCd3Dz5TCZTDQ0NHDy5EkkSWLlypVUVVWRlLTw7xm8s9/txDGO7nmOkc4O9LFxlO7azcobb0Yb7t9+t0sJxbh+3SRoJSUJ8n/+5qarfRvvMTMzQ2xs7NW+DUEQBCEAREwXhOCKHhtj6amzaBwOxvJyMBYWIF9i9ta4FMWP7Ddx3JPDMtUQX4zYxxLVdMDuSZahaTiDfz+1hnFrFOtSL/CJVcdZEj3nxzk8OBxGnM5RQEF4eCphYakoFFdmn9WV5vV4MM/OMjc3hyzL6PU6YmJi0Gr9rXLKOK1WZifHcVqtKFUqIuMTiIxPROnnTLb3E4pxvXTd/4gELZhC8aELgiAIiyNiuiAEn9LtJr2tnaSBIRx6Pf2rV2JNiJ/3GFmGA+5l/Ny+FTcqPh7ewO3aFlSKwL3Lur1KXusq5IW2Fbi8KrbndfKRkjNEhbkWfA5JcmC3D+F2m1AoNEREZKLVJgDX3/408A29npudZXZuFkmS0UVEEBMbQ1hYuN/nctlszE6O47DMoVAqiYxPICo+EeVl7lELxbh+3SRoYomjIAiCEGwipgvCFdRzCF79AswM+WambX0UtPN3CRxzuvlK5xD7JmdZHaXjmaIMiiMDuyRuYs7J02918lzLINERGr60NZ//s34pGj/2p01PN9PV/S3m5s4RHb2agvxHiIlZE9D7DCV2u53m5maOHj2K3W4nKyuLmpoasrOz/W6eMt7fS9NLv6PzaD1qjZaVW2+i9JY7iEpY+GiEPxWKcf26WeIoEjRBEAQh2ERMF4QrzGmBA/8MzT+H2KVw648gZ9O8h8iyzMvjMzzUdYE5j8Q9WSl8PjMFjR8DqBeifWSWb73WRkP3FLlJeh7ZVcLmwoXPPpNliZHRF+np+T4u1zgpKbeQl/sA4eFpAb3PUOJ0OmltbaWxsRGLxUJ6ejrV1dUUFBT4nahNDQ/R8vILtNUdQqFQsvyGbZTddiexKf7t7wvFuC4StCALxYcuCIIgLI6I6YJwlQw0wsufBVMvrPs7uPGbED5/K/dJl4eHuy7w8vgMyyLD+UFRJiuidAG9LVmW2d8+zrdfb6dv0kpNQRKP7CymICVqwefweKwMDP4rg4O/ACAz8/+yNPPTqNX+zRS7lrjdbk6ePEl9fT1ms5mUlBSqq6spKSlBqVx4JRLAPD5Kyyv/y9lDbyFJEkWVm6i4/SMkpGcu6PhQjOsiQQuyUHzogiAIwuKImC4IV5HLBoe/DUd+AlGpcMuzkH/jJQ97fWKGBzsvMOX28PnMFO7JSiHMzyTgkrfmkfiPI/08e6ALm8vLx8ozuefGAuL1C28N73AY6e55krGxV9Fqk8nLvQ+DYTcKRWDvNZR4vV7OnDlDXV0dU1NTJCQkUF1dzYoVK1D52QTEYpri2N49nNr/Bh6Xi/zyDVTsvpuU7Nx5jwvFuC4StCALxYcuCIIgLI6I6YIQAi4c81XTJjpg1cfgpsdBN38TkWm3h693D/P86DT5ujCeLcpkbUzgK1Qmq4sf7O/kv5oG0WlVfHFrPn+zIQuteuFJ1oy5la6ux5mdPUVU1HIK8h8lNvai7+rXDUmSaGtro66ujrGxMWJjY6msrGT16tVoNAsfEg5gmzVz4o1XOLFvL06blezV66jYfTdLikou+vWhGNdFghZkofjQBUEQhMURMV0QQoTHCbXfg7qnQZ8IO5+G4l2XPOzA1Cz3nx9i1Onm0xlJPJCdis6P5h4L1Tk2x2N726jrmiQ7Uc/DO4rZWpy84H1WsiwxNvYq3T1P4nSOkpy8g7zcB4iIyAj4vYYSWZbp7OyktraW4eFhIiMj2bhxI6WlpWj9HFTttFk5+eZrtL72Eva5WTJKVlCx+24yV6z6s+fw/9u77/Aoq7z/4+8z6QmEEAIhhJAQSAihKhCK0osgWBZx7RVFFHUtrI9t17Wtoth4BGy4ytpFRUQURLqU0KWlASmQUENNz8z9+yM8v8fHNeMEMplJ/LyuK9fF3OF7z5eZXAc+nDnneOO4roDmZt74pouIyNnRmC7iZQq2wtxJcHAbdBoLF79YFdicOFVp5+nd+czOP0rbIH9eTmpD37BGtd6aZVksSz/MM9/uZPfhIi5o34zHRyfTMcr52rlfstuLycl9h5yctwA7MTG3Ehc7EV9f19e41UeWZbF3715WrFhBdnY2QUFB9OnTh5SUFIKCarYrZ0VpKT//+D0bvvmS08cKadk+kd5/uop2PVIwxnjluK6A5mbe+KaLiMjZ0Zgu4oXsFbDqVVg+pWrjkFEvQOcr4Hdmq1YWnuLB9DxyS8u5JTqCx+OjCPGt/YOjK+wOPlybwyuLMzlVWsFVvdrw4IhEIhq5fmhzaWkBu/dM5cCBufj7RxAf/wCtosY12IOufykvL48VK1aQmZlJQEAAKSkp9OnTh5CQmn1EtbKigh3LFrN+3hxOHDpIRJs4ev/pzxSUVjJ4yBA3dX92FNDcTH+Zi4g0HBrTRbzYoV0w9y7I3wQdRsOYl6Gx8y3XiyrtPLe3gFn7jhAd6MfLHdowINw9s1PHi8t57cdM/r0mhyA/H+4e0p6bL4gjoAah8MTJrWRmPsOJE5to1KgjCQmPEd60r1v69TYFBQWsXLmSnTt34ufnR48ePejXrx+hoa7PSAI47HbSflrOuq8+ozB/H+GJydzy9Atu6vrsKKC5mf4yFxFpODSmi3g5eyWsnQFLnwXfALjoOeh+7e/Opq07fpoH0vLYXVLGdVHhPNE+mlA3zKYB7D58mn9+u4sf0w7RJjyYRy9O4qJOLWuwPs3i0KFvycqaQmlZPs2bj6B9u4cJDo51S7/e5vDhw6xcuZJt27Zhs9no3r07F154IU2bNq3RfRwOO1mpa8jIzmXM1de6qduzo4DmZvrLXESk4dCYLlJPHMmCeXdD7hpoN7RqS/4w5xtslNgdTM0+wMzcQ0QG+DElsTUjIpq4rcUVGVXr0zIOnqZ323D+NiaZztGuP5/dXkpu3ixyct7A4aggJuYm2sbd3eDXp/2PwsJCfvrpJ7Zs2YLD4aBLly7079+f5s2b1+g+3jiuK6C5mTe+6SIicnY0povUIw4HrH8HFv+jagZt+FNVh1z/zhlom08Wc19aLulFpYyLbMpTCdGE+/m6pcVKu4NP1ufx8g8ZHCsu58oerZk8ogMtQgNdvkdZ2SF273mJgoIv8PNrSnz8/bSK+jM2m3t69jYnT55k9erVbNiwgcrKSpKTk+nfvz9RUVEu1XvjuK6A5mbe+KaLiMjZ0ZguUg8dy4Z598Le5RDXHy6dBuHxTkvKHA5eyznItJyDhPn68nxia8a0CHNbiydKKnh9SSbvrc7G38fGXYPbM/7CtgT6uf4xy5OntpOZ+SzHj6cSEpJIQsJjNAu/0G09e5uioiLWrl1LamoqZWVlJCQkMGDAAGJinM+ceuO4roDmZt74pouIyNnRmC5ST1kWbJoNix4HRyUM/TukTACb8wC043QJ9+3KZdvpEsY0b8Jzia1p7l+zg5NrIvtIEf9csItFOw8SHRbEw6OSGNM1qkbr0w4fXkhm1vOUluYR0WwI7ds/QkiI80DakJSUlJCamsratWspKSkhLi6OAQMG0LZt2998Hb1xXFdAczNvfNNFROTsaEwXqedO7If590HmIojpDZe+Ds0TnZZUOCxm5h1i6t4DhPjYeCYhmrGRTV0OTWdj9e4jPD1/F7sKTtIztil/G5NMt5gwl+vt9jL27XuPvdkzcDhKad36BtrG3YOfn/vW1HmbsrIyNm7cyOrVqzl9+jTR0dEMGDCAxMREHVRdVxTQRETE3TSmizQAlgU/fwbfPQQVJTD4Eeh7D/g4X7OVUVTK/Wm5bDxZzPBmobzQoTVRAf5ua9PusPh8Qx5TF6Vz5HQ5Y8+L5qGRSbRsUoP1aeVH2LPnFfLzP8PXN5T4+L8Q3eoabDb3zQJ6m4qKCrZs2cKqVas4ceIEkZGR9O/fn+TkZGw2m1eO6wpobuaNb7qIiJwdjekiDcipg7DgQdj1DUR1h8tnQGQnpyV2y+KdfYd5fk8BvsbwZPtorokKd+ts2qnSCmYs282slXvxsRkmDmzHhAHxBPm7vj7t1KldZGY9y7FjawgObkdCwqNENBvktp69kd1uZ9u2baxcuZKjR4/SrFkz+vfvT2FhIUPq0UHVzre4ERERERGprxpHwlUfwJXvw4l98OZAWPY8VJZXW+JjDHfEtGBJryQ6Nw7igfQ8rtq6m9ySMve1GejHf41M4scHBzIkqQWvLM5gyEvLmLt5Pw6Ha5MpjRt35Lzu/6ZrlzexrEq2bh3Pli23cLoo0219exsfHx+6d+/OpEmTGDduHL6+vsydO5f09HRPt1YjmkGrBfrfVhGRhkNjukgDVXQUvn8Ytn0GkZ3hsteh1XlOSxyWxez8ozy9Ox8LeDw+ipujI7C5cTYNIHVvIU/N38H2/SfpHhPG3y9J5vw2rh/S7HCUs2/fB+zNnobdXkx0q2tp2/Ze/P3D3di197Esi4yMDNLT07n00ks93c7/oRk0EREREfljC2kGV7wNV38MRUfg7aGw+EmoKK22xGYMN0dHsCwliZTQEB7N3M/YzVnsKXbfbBpASttw5k26kBfHdSX/eAljZ6zm3o83s/94iUv1Nps/bdrcSt8+S2jV6hr253/EmrVDyc19F4ej+tnDhsYYQ4cOHQgNDfV0KzWigCYiIiIifxxJF8OkddD9Glj1MrzZH/JSnZbEBPrzcbd4Xk6KYWdRCUPWpzEz9xB2N34SzWYzXNkzhqWTB3HPkPYs3HGAIVOX8fKidIrKKl26h79/OEkdniSl13xCQ7uRmfUsa9eN4vCRH6lPn6L7o1FAExEREZE/lqAwuGw6XP9l1S6Ps0bA949CeXG1JcYYro1qxvKUJPo3bcyTu/O5ZFMm6UXVz8DVhpAAXx4c0YElkwdxUaeWTFuSxeCpy5izcZ/L69MaNUqke7d/0a3rOxjjw88/T2Dzlhs5dTrNrb3L2amzgGaMiTfGzDLGzPnFtRBjzPvGmLeNMdfVVS8iIiIiIrQfCnetgV7jYe10mNkP9q50WhIV4M/sLm2ZkRzL3uIyhq9P57Xsg1S4GJbOVnRYENOuOY8v7uxLVFgQkz/fymXTf2J9dqFL9cYYIiIG0zvlWxIT/s6pUztITb2EXWmPUV5+xK29S824FNCMMe8aYw4ZY7b/6vpIY0y6MSbLGPOws3tYlrXHsqzxv7o8FphjWdbtgHet3BMRERGRhi+gMYx+CW7+turx+2Ng/gNQdqraEmMMYyObsqJ3EhdFNOG5vQVcvDGD7aeqn4GrLT1iw/nqzn68elV3Dp8q48o31jDpw03kFbr23DabHzExN9Gv7xJiWt9IQcEcVq8ZSk7OWzgc7l1bJ65xdQbtPWDkLy8YY3yA6cAoIBm4xhiTbIzpYoyZ/6uvFtXctzWQd+bX9pq3LyIiIiJSC+IuhDtXQ9+7YcO7MKMvZC12WtLc34+3O8fxTqc4CsoqGLkxgyl7CihzONzaqs1muPy8aJZMHsh9wxJYknaIoS8vZ8r3aZwqrXDpHn5+YSQm/o3eKQsIC+tF1u4prF07kkOHF2p9moe5FNAsy1oB/Hr+NAXIOjMzVg58AlxmWdY2y7LG/OrrUDW33kdVSHO5FxERERERt/APhouehfGLwC8IPrgC5k6CkmNOy8a0CGNF7yQub9GUV3IOMmJDBptOFrm93WB/X+4blsiSyQMZ0yWKmct2M3jqcj5JzcXu4kcuQ0La0b3bO3Tv9h42nwC2bbuLTZuv49SpHW7uXqrj8jloxpg4YL5lWZ3PPB4HjLQs67Yzj28AeluWdXc19c2AZ4HhwDuWZT1njAkBXgdKgVWWZX34G3UTgAkAkZGRPT755JOa/QnrwOnTp2nUqJGn2xARkVqgMV1EAGz2cmJzPqVN7peU+zchI/FOjkb0/t26TZYv7xDMMQxjKONKSvF377Fp/9+e43Y+Sisn67iDmMY2rk3yp2MzH5frLcuOxQosay5QhOECjBmLMU3c1nNd8MZxffDgwdWeg1ZnAa026KBqERFxN43pIvJ/5G+BryfBwe3QeRyMeqHqTDUnTlbaeSornw8KjhIfFMArSTH0DqubgGBZFvN/LuD579LYf7yEEcmRPHpxR+IiQly+R0XFSbKzXydv32xsNn/iYu8kJuZWfHwC3Ni5+3jjuO6ug6r3AzG/eNz6zDURERERkYahVXe4fSkMehR2fg3TU2D7l+BkkiPU14epSTF81q0dFZbF5ZuzeCxjH0WV7t9ywRjDJd1a8eODA/nrRR1YlXWE4a8s558LdnHS5fVpoSQkPEqf3t8R3rQfu/dMZe264Rw8+K3Wp9WBc5lB8wUygKFUBbP1wLWWZbntA6tBMR2sdvfNdNftz1plZSW+vr6ebkNERGqBxnQRqU6CPYenS1+nsyOLxb69eTrgDo7amjqtsYBSh4MKh4UBgnxs+Jo6+swj4HBYlBdVUFlqBwMBIX74BvlSkw4sqxK7owwsOxhffGwBVO0XWD9447i+Y/LQc5tBM8Z8DKwBOhhj9hljxluWVQncDSwEdgGfuTOciYiIiIh4UqZPLNcFP89L/jfSv3IT84ru5dKKpU5n0wwQZLMR7GPDGCi2OyhxOKireSibzRDY2J+gpgHYfG2Una6guLCUynLXZ/OM8cXXJwSbLQgsB3Z7EXZ7CRbu3a3yj8rlGTRvoDVoIiLibhrTRcQlRzKr1qblrYP2w+GSV6FJa6clxXYHL+4t4M28w7QM8OOFDjEMaxZaN/1StT5t4Y4DPLtgF3mFJQxNasGjozvSrrnr6+MqK0+RnT2T3Lx/YYwPsbF3ENvmNnx8gtzY+bnxxnHdXWvQRERERET+mCIS4JbvYOQUyPkJpveBDf9yOpsW7GPjifbRzD8/gUY+Plz/8x7u2ZXDsYrKOmnZGMPIzlEsfmAgD49KYt3eQi56ZQVPfrOD48XlLt3D17cx7ds/RN8+C4loNoi9e19lzdphHDjwNZalGbXaoIAmIiIiInI2bD7QZ2LVAdetusP8+2D2pXAs22nZ+U1C+KFXIvfHRvLlwWMMSE1jweHjddBwlQBfHyYObMfSyYO4smcM76/OZtDUZby/OpsKu2shKyioDV26vM75532Mv38zdux8gA0br+TEic1u7r7hU0ATERERETkX4W3hpm9gzKuwfzPM6Avr3gRH9WEnwGbjv+Kj+L5HIpH+fty6PZsJO7I5XO7aTou1oXnjAJ4b24X59/QnOSqUJ+btYOSrK1iafsjlezRtmkKvnnPp2HEKpaX5bNg4ju077qO0NN+NnTdsCmgiIiIiIufKGOh5C0xaC7EXwHcPwXsXw5Esp2VdGgfzXY9EHm7bku8Pn2BgahpfHTxWp9vZJ7cK5cPbevP2jT2xOyxu+dd6bno3lcyDp1yqN8ZGq6hx9O2zmLi4SRw+vIg1a4exe88rVFYWubn7hkcBTURERESktjRpDdd9DpfPhEM74Y0L4KfXwF79OjM/m+G+uJYs6pVIbGAAd+7M4ebtezlQVnezacYYhidHsuj+gTw+uiObco8x8rWV/P3r7RQWubo+LYR28Q/Qt89imjcfQXb266xZO4yCgi+0Pq0GFNBERERERGqTMdD9WpiUCu2Gwg9/h1nD4eBOp2VJIUHM75HA39u1YnnhKQak7uLjgqN1Opvm72vjtv7xLP/rYK5NacOH63IZ9OJS3lm5h/JK10JWYGArOnd6lR49PiMwMIqdux5i/YY/cfy49+3G7o0U0ERERERE3KFxS7j6Qxj3LhzPgTcHwPIXwF79zJiPMdzVpgU/9upAx5Ag7k/L45qte8grdW0Wq7aEh/jz9OWd+e4v/ekWE8Yz3+7ioldXsHjnQZcDY1iTHvTsMYdOyS9TXn6EjZuuYtv2eygpyXNz9/WbApqIiIiIiLsYA52vqJpNS74Ulj4Lbw2Ggq1Oy9oFB/LVee15NiGa1JNFDEpN4739R3DU8RnGiZGNmX1rCv+6uRc2A7fN3sD1s9axq+CkS/XG2GjZ8jL69vmBtm3/wpEjS1i7bgRZu6dSWXnazd3XTwpoIiIiIiLuFhJRNZN21YdQdKgqpP34NFSWVVtiM4bxrZuztFcHzg8N5uGMfYzbspvskupr3MEYw+CkFnx/3wD+cUky2/efZPS0lTzy5TaOnHatFx+fYOLb3kvfPotp0eJicnJmsmbtUPLzP8Oy7G7+E9QvCmgiIiIiInWl4xiYtA66XQ0rp8Ib/WGf87VZsUEBfNatHS91iGHbqWIGp6bxVt4h7HU8m+bnY+PmC9qy/K+DuKlfHJ9vyGPwi8t4c/luyipdC1mBgVF0Sn6Jnj2/JCgwhl1pj5C6/nKOHVvr5u7rDwU0EREREZG6FNQULp8B130B5UVVG4gsfAzKi6stMcZwXatmLE9Jol9YY/6elc9lmzLJLCqtw8arhAX788QlnVh4/wBS2obz3HdpDH95Bd9vL3B5fVqT0G706PE5nTu9RmXFcTZtvo6ft91JcXGOm7v3fgpoIiIiIiKekDAM7loDPW6GNa9Xbcmf/ZPTklaB/nzQtS2vd2xDVnEZwzak8985B6l01O1sGkC75o2YdXMvZt+aQqCfjYkfbOLqt9ayff8Jl+qNMURGjqFPnx+Ij3+AwsJVrF13EZlZz1FZ6doZbA2RApqIiIiIiKcEhsKYV+Cmb8ByVB1u/e1kKKs+oBhjGNcynBUpSQxrFsqzewq4eFMGO0+X1GHj/2tAYnMW3NufZy7vTOah01zy+ioemrOVQyddm93z8Qmkbdwk+vb5kZYtLyM3dxar1wxh3/6PcDiqPz+uoVJAExERERHxtLYD4M7V0OcuWP8OzOgHu5c4LWkR4Meszm15u1Mc+0srGLEhnRf3FlDuqPtDoX19bFzfJ5alkwdx24Vt+WrzfgZPXcb0pVmUVri2Pi0goAXJHafQq9dcQkLak57+N1LXX8LRwlVu7t67KKCJiIiIiHgD/xAY+RzcuhB8A+Dff4Kv74aS407LLmkRxoqUJC5r0ZSXsg9y0YYMtpysfj2bOzUJ8uOx0cn8cP9ALmgfwYsL0xn60nLm/5zv8vq00MadOf+8j+jSeTp2ewlbttzE1q23U1S0x83dewcFNBERERERb9KmN0xcBRfeD1s+hBl9IP17pyXN/H2ZnhzL7C5tOVZh5+KNGTyzO59Se93PpgHERYTw1o09+ei23jQO9OXujzZz5Rtr+HnfcZfqjTG0aDGSPr0X0r7dQxw7nsq61FFkZD5DRYVra9zqKwU0ERERERFv4xcIw/4Bt/0IQeHw8VXwxe1QXOi0bEREE5andODqqHBezz3EsA3prD9RVDc9/4Z+7SP49t7+PD+2C9lHi7j09Z944LMtHDjh6vq0AGJj76Bv3x+JihpHXt77rF4zhLx9s3E4KtzcvWcooImIiIiIeKvo82HCMhj4MOz4EqanwI65Tkua+PnyclIbPukWT4ndwaWbMvlb5j6K7J45ENrHZrg6pQ1LJw9i4sB2zN9awOCpy3htcSYl5S6uT/OPoGPSs6T0mkfjxh3JyHiSdamjOXJ0mXub9wAFNBERERERb+brD4MfgQnLIbQVfH4TfHoDnD7ktGxQeCjLU5K4KTqCt/cdYUhqOquOeW77+saBfjw8KonFDwxkcFJzXlmcwZCXljF3834cLh4T0LhxR87r/m+6dnkTy6pk69bxbNlyC6eLMt3cfd1RQBMRERERqQ9adobblsDQJyBjYdVs2s+fgZPNNxr5+vB8Ymu+7N4eY2Dclt08lJ7HqUrPzKYBtGkWzIzrevDphD40a+TPfZ9uYezM1WzKPeZSvTGG5s2H0af39yS0f4wTJzeTmjqa9PR/UF7u/COg9YECmoiIiIhIfeHjC/0fgIkroVl7+PJ2+PhqOJnvtKxf00Ys6ZXEHTHN+Xf+UQalprHk6Mk6avq39Y5vxrxJF/LiuK7kHy9h7IzV3PvxZvYfd+08N5vNnzZtbqVvnyW0anUN+/M/Ys3aoeTmvovDUe7m7t1HAU1EREREpL5p3qFqO/6LnoM9y2F6b9g02+lsWrCPjSfbRzP//ASCfWxc+/Me/rIrl+MVnjsM2mYzXNkzhqWTB3HPkPYs3HGAIVOX8fKidIrKXOvL3z+cpA5PktJrPqGh3cjMepa160Zx+MiPLm/t700U0ERERERE6iObD/S9C+78CVp2hXn3wL8vh2M5Tst6NAnhh54d+EtsJHMOFjIgNY3vD3t26/qQAF8eHNGBJZMHcVGnlkxbksXgqcuYs3Gfy+vTGjVKpHu3f9Gt6zsYY+PnnyewZctNWNY+N3dfuxTQRERERETqs2bt4KZvYPRLsG8DzOgLqW+Do/oz0AJ9bDwSH8V3PRKJ8PPl5u17mbgjmyPlnptNA4gOC2LaNefxxZ19iQoLYvLnW7ls+k+sz3ZtbZkxhoiIwfROWUBiwt85eWo7lrXYzV3XLgU0EREREZH6zmaDXrfBXWuqDrpeMBneGw1Hdzst69o4mO97JvLXuJZ8e/gEA1J3MffgMY9/NLBHbDhf3dmPV6/qzuFTZVz5xhomfbiJvMJil+ptNj9iYm6iX98lGHOFm7utXQpoIiIiIiINRVgbuP5LuGw6HNwBM/vB6v8GR/W7NvrbbDzYtiWLeiYSE+jPxJ053Lo9m4Nlnj0I2mYzXH5eNEsmD+S+YQksSTvE0JeXM+X7NE6Vutabn18YxjR2c6e1SwFNRERERKQhMQbOux4mrYP4wbDocZg1Ag6lOS3r2CiIb89P5PH4KJYUnmRAahqfFhR6fDYt2N+X+4YlsmTyQMZ0iWLmst0MnrqcT1Jzsbu4Pq0+UUATEREREWmIQqPgmo/hillQuAfe7A8rXgR79bNPvjbD3bGR/NirA4nBgfwlLZfrft7D/lLPb1sf1SSIl6/qztxJFxDbLJiHv9zGmP9exerdRzzdWq0ynk7ENdEzrom14YkLPd3Gfzh+/DhhYWGebkNERGqBxnQRaZDs5VUhrfgI+IVARAL4N3JaYmFxoKyCnNJyDBAbFECkvy8GUzc9/05vR4vKyT1aTLndQdNgf2KbBRPo6/Mfv9cbx3Vz64KNlmX1/K3vaQZNRERERKSh8/GH5klVX/ZyKNgCx3PAqn6nR4MhKsCf7o2DCfHxYU9xGTtPl1LqZHfIumIwRIQE0D0mjJimQZwoqWBr3nFyCouo9IL+zoWvpxuokYgEuOVbT3fxH7YsW8agQYM83YaIiNQCjeki0uAVF8LCR2Hrx1WzaJdNh9Y9qv3tgUAny+KDgqM8mZWP3YLH2kVxa3QENuPZ2TQbEA34nSzlxYXpzNm0j/Bif+4fnsjVvWLw9bF557h+a/Wvm2bQRERERET+SILD4U9vwLWfQ9lJmDUMFv0NKkqqLTHGcEOrCJanJNE3LITHM/dz+eYssopL67Dx6rUIDeTFK7vxzd0X0q5FIx6fu53R01axMvOwp1urMQU0EREREZE/osQRVeemnX8jrJ4GMy+AnDVOS6ID/fmwazzTOrYhvaiUoevTeT3nIJVespti5+gmfDqhDzOvO5/iikpumJXKBzvLPN1WjSigiYiIiIj8UQU2gUtegxu/BkcF/GsULHgIyk5XW2KM4c8tw1mRksSQ8FCe2VPA6E0Z7Dpd/QxcXTLGMKpLFD/cP5CHRyXRpfl/bhzizRTQRERERET+6OIHwZ1roPcdkPoWzOwLe5Y5LYkM8OPdznG82SmWvNJyRmzI4KW9Byj3kk06Av18mDiwHd2a169tNxTQREREREQEAhrBqClwy3dVuz7Ovgzm3QulJ6otMcZwWYumrEjpyJjmTXgx+wAjN2Sw9VRxHTbesCigiYiIiIjI/4rtCxNXwQV/gc3/hhl9IWOR05IIf19mdorjvc5tOVpRycUbM/jn7nxK7d4xm1afKKCJiIiIiMj/5RcEw5+C8YshIBQ+uhK+mli1Rb8TI5s3YXlKEldGhjMt9xDDN6Sz4URRHTXdMCigiYiIiIjIb2vdA+5YDgMegm2fw/TesOsbpyVhfr682rENH3WNp9ju4JJNmTyRuZ9izaa5RAFNRERERESq5xsAQx6D25dC45bw6fXw+c1w2vkZY0OahbIsJYkbWjXjzX2HGbI+jZ+OnaqbnusxBTQREREREfl9UV3h9iUw5G+Q9i1MT4Ftc8Cq/gy0xr4+vNAhhjnd22FZcMWW3fxXeh6nK+112Hj9ooAmIiIiIiKu8fGDAZPhjpUQHg9fjIdProWTBU7LLmzamCUpHZjQujmz848yMDWNZYUn66jp+kUBTUREREREaqZFEoxfBCOehd1Lqtambf7A6WxaiI8PTyVEM+/8BIJ8bFy9dQ/3p+VyoqKyDhv3fgpoIiIiIiJSczYf6Hc33LkaWnaGryfBB2PheK7Tsl5NQljcswP3tGnBpwWFDEhNY+GR6s9a+6NRQBMRERERkbPXrB3cNB8ungq566rOTVv/Djiq37Ux0MfGY+1asaBHIuF+vty0bS937czhaLlm0xTQRERERETk3NhskHI73LUGWveEbx+E9y+Bo7udlnUPDWZhz0QejItk3qFjDEhNY96h43XTs5dSQBMRERERkdrRNBZumAuX/jcc+BlmXgBrpoOj+l0b/W02/to2ikU9OxAd4MeEHdmM376XQ2UVdde3F1FAExERERGR2mMMnH8jTFoH8QNh4aPw7kVwON1pWXKjIBb0SOSx+CgWHz3JwNQ05hwoxHKy8UhDpIAmIiIiIiK1L7QVXPMJjH0bjmbBGxfCypfAXv06M1+b4Z7YSH7o2YF2wQHcvSuXG7btJb+0vA4b9ywFNBERERERcQ9joOufYVIqdBgFPz4F7wyBA9ucliWGBPL1+Qk81b4VPx07xcDUND7MP/qHmE1TQBMREREREfdq1AL+PBuufB9O5sNbg2DpP6Gy+pkxH2OYENOCpSlJdGkczIPpefx5625ySsrqrm8PUEATEREREZG60enyqtm0zlfA8inw1kDYv8lpSVxQAHO6t2NKYms2nSxm8Pp0Zu07jKOBzqYpoImIiIiISN0JDoexb8E1n0LJMXhnKPzwBFSUVltiM4aboiNYnpJE7yYhPJa5nz9tzmJ3cfU19ZUCmoiIiIiI1L0OI+GutdD9Ovjp1apNRHLXOS1pHejPR13jeTUphrSiUoauT2dG7iHsDWg2TQFNREREREQ8IygMLnsdbvgKKsuqtuP/7mEoL6q2xBjD1VHNWJ6SxMDwxjy1O58xGzNJKyqpu77dSAFNREREREQ8q90QuGs19LoN1s2Emf1g7wqnJS0D/Hivc1tmJseSU1rG8PUZvJJ9gApH/Z5Nq9OAZoyJN8bMMsbM+cW1y40xbxtjPjXGjKjLfkRERERExEsENIbRU+HmBWBs8P4lMP9+KD1ZbYkxhj9FNmV5ShKjmjdhyt4DjNqYwbZTxXXYeO1yOaAZY941xhwyxmz/1fWRxph0Y0yWMeZhZ/ewLGuPZVnjf3VtrmVZtwMTgatq0ryIiIiIiDQwcRfAxJ+g792w8T2Y0RcyFzstae7vx1ud4pjVOY6D5RWM3JjB83sKKHM46qbnWlSTGbT3gJG/vGCM8QGmA6OAZOAaY0yyMaaLMWb+r75a/M79Hz9zLxERERER+SPzD4aLnoVbF4F/CHx4Bcy9q2rXRydGNw9jRUoSYyOb8mrOQYavzyDT8qmjpmuHqclp3MaYOGC+ZVmdzzzuC/zDsqyLzjx+BMCyrOd+5z5zLMsad+bXBnge+MGyrP+IxsaYCcAEgMjIyB6ffPKJy/3WldOnT9OoUSNPtyEiIrVAY7qIiHcxjgrisj+lTe4XlPs3ISPxTo5G9P7dus2WL28TTNeKYib6V9ZBp64bPHjwRsuyev7W93zP8d7RQN4vHu8Dqn21jDHNgGeB84wxj5wJcvcAw4Amxpj2lmW98csay7LeAt4C6NmzpzVo0KBzbLn2LVu2DG/sS0REak5juoiINxoOBfcQMHcSXbb/s+qg61EvQEhEtRWDgPGVdn5aubJejevnGtBqxLKso1StNfvltWnAtLrsQ0RERERE6pmobjBhKax6FZZPgT3L4OIXodNYMOY3S0J9fQj67W95rXPdxXE/EPOLx63PXBMREREREaldPn4w8K9wxwoIi4U5t8Kn18OpA57urNaca0BbDyQYY9oaY/yBq4F5596WiIiIiIhINSKTYfwPMPxpyFoM01Ngy0dQg/01vFVNttn/GFgDdDDG7DPGjLcsqxK4G1gI7AI+syxrh3taFREREREROcPHFy64t2pL/hbJMPdO+HAcHM/7/Vov5vIaNMuyrqnm+gJgQa11JCIiIiIi4qqI9lWHW69/Bxb/o+rctBFPwfk3g+1cPzBY9+pfxyIiIiIiIr9ks0HvCXDXaog+D+bfD7MvhcK9nu6sxhTQRERERESkYWgaBzfOg0teg/wtMLMfrfZ/5+muakQBTUREREREGg5joMfNMGktxF2IsbzrkOrfo4AmIiIiIiINT5PWcO1n7I8e7elOakQBTUREREREGiZjwNSvyFO/uhUREREREWnAFNBERERERES8hAKaiIiIiIiIl1BAExERERER8RIKaCIiIiIiIl5CAU1ERERERMRLKKCJiIiIiIh4CQU0ERERERERL6GAJiIiIiIi4iUU0ERERERERLyEApqIiIiIiIiXUEATERERERHxEgpoIiIiIiIiXkIBTURERERExEsooImIiIiIiHgJBTQREREREREvoYAmIiIiIiLiJRTQREREREREvIQCmoiIiIiIiJdQQBMREREREfESCmgiIiIiIiJeQgFNRERERETESxjLsjzdg8uMMYeBHKAJcKKWblsb94oAjtRCL+IZtfnzVJ/V59fB23r3RD918Zzueg6N6VLbvG1M8JT6+jp4W9+e6kfjeu3dyxvH9VjLspr/1jfqVUD7H8aYtyzLmuAt9zLGbLAsq2dt9CN1rzZ/nuqz+vw6eFvvnuinLp7TXc+hMV1qm7eNCZ5SX18Hb+vbU/1oXK+9e9W3cb2+fsTxGy+9l9RP+hmoUp9fB2/r3RP91MVzuus5NKZLbdPPQZX6+jp4W9+e6kfjeu3fq16olzNo3qa+pXIREamexnQRkYalvo3r9XUGzdu85ekGRESk1mhMFxFpWOrVuK4ZNBERERERES+hGTQREREREREvoYAmIiIiIiLiJRTQREREREREvIQCWi0zxoQYY943xrxtjLnO0/2IiMi5McbEG2NmGWPmeLoXERE5d8aYy8/8W/1TY8wIT/fzawpoLjDGvGuMOWSM2f6r6yONMenGmCxjzMNnLo8F5liWdTtwaZ03KyIiv6sm47plWXssyxrvmU5FRMQVNRzX5575t/pE4CpP9OuMAppr3gNG/vKCMcYHmA6MApKBa4wxyUBrIO/Mb7PXYY8iIuK693B9XBcREe/3HjUf1x8/832vooDmAsuyVgCFv7qcAmSd+Z/VcuAT4DJgH1UhDfT6ioh4pRqO6yIi4uVqMq6bKlOA7yzL2lTXvf4eBYizF83/zpRBVTCLBr4ErjDGzAS+8URjIiJyVn5zXDfGNDPGvAGcZ4x5xDOtiYjIWaju3+v3AMOAccaYiZ5ozBlfTzfQ0FiWVQTc4uk+RESkdliWdZSqdQoiItIAWJY1DZjm6T6qoxm0s7cfiPnF49ZnromISP2kcV1EpGGpl+O6AtrZWw8kGGPaGmP8gauBeR7uSUREzp7GdRGRhqVejusKaC4wxnwMrAE6GGP2GWPGW5ZVCdwNLAR2AZ9ZlrXDk32KiIhrNK6LiDQsDWlcN5ZleboHERERERERQTNoIiIiIiIiXkMBTURERERExEsooImIiIiIiHgJBTQREREREREvoYAmIiIiIiLiJRTQREREREREvIQCmoiIiIiIiJdQQBMREREREfESCmgiIiIiIiJe4v8BszKEA6cVlZ8AAAAASUVORK5CYII=", + "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 (limited to 'buch') 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(-) (limited to 'buch') 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(+) (limited to 'buch') 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 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(+) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 e0fb3e7b5861b9199eb2d361311cd1b768f8bed4 Mon Sep 17 00:00:00 2001 From: Andrea Mozzini Vellen Date: Thu, 9 Jun 2022 15:53:28 +0200 Subject: Korrektur Feedback --- buch/papers/kreismembran/main.tex | 4 +- buch/papers/kreismembran/references.bib | 24 ++++++- buch/papers/kreismembran/teil1.tex | 95 +++++++++++++++++----------- buch/papers/kreismembran/teil2.tex | 107 ++++++++++++++++---------------- buch/papers/kreismembran/teil3.tex | 40 +++++++----- 5 files changed, 161 insertions(+), 109 deletions(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/main.tex b/buch/papers/kreismembran/main.tex index e63a118..e19c64a 100644 --- a/buch/papers/kreismembran/main.tex +++ b/buch/papers/kreismembran/main.tex @@ -3,8 +3,8 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Schwingungen einer kreisförmligen Membran\label{chapter:kreismembran}} -\lhead{Schwingungen einer kreisförmligen Membran} +\chapter{Schwingungen einer kreisförmigen Membran\label{chapter:kreismembran}} +\lhead{Schwingungen einer kreisförmigen Membran} \begin{refsection} \chapterauthor{Andrea Mozzini Vellen und Tim Tönz} diff --git a/buch/papers/kreismembran/references.bib b/buch/papers/kreismembran/references.bib index 0b6a683..1aef90b 100644 --- a/buch/papers/kreismembran/references.bib +++ b/buch/papers/kreismembran/references.bib @@ -24,7 +24,7 @@ } @article{kreismembran:mendezmueller, - author = { Tabea Méndez and Andreas Müller }, + author = { Tabea Méndez and Andreas Müller }, title = { Noncommutative harmonic analysis and image registration }, journal = { Appl. Comput. Harmon. Anal.}, year = 2019, @@ -33,3 +33,25 @@ url = {https://doi.org/10.1016/j.acha.2017.11.004} } +@book{lokenath_debnath_integral_2015, + edition = {Third Edition}, + title = {Integral Tansforms and Their Applications}, + publisher = {{CRC} Press}, + author = {{Lokenath Debnath} and Dambaru Bhatta}, + date = {2015}, +} + +@thesis{nishanth_p_vibrations_2018, + title = {Vibrations of a Circular Membrane - Some Undergraduadte Exercises}, + type = {phdthesis}, + author = {{Nishanth P.} and {Udayanandan K. M.}}, + date = {2018}, +} + +@thesis{prof_dr_horst_knorrer_kreisformige_2013, + title = {Kreisförmige Membranen}, + institution = {{ETHZ}}, + type = {phdthesis}, + author = {{Prof. Dr. Horst Knörrer}}, + date = {2013}, +} \ No newline at end of file diff --git a/buch/papers/kreismembran/teil1.tex b/buch/papers/kreismembran/teil1.tex index aef5b79..38bcfe4 100644 --- a/buch/papers/kreismembran/teil1.tex +++ b/buch/papers/kreismembran/teil1.tex @@ -7,13 +7,14 @@ \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. +An diesem Punkt bleibt also nur noch die Lösung der partiellen Differentialgleichung. In diesem Kapitel wird sie mit Hilfe der Separationsmethode gelöst. +\subsection{Aufgabestellung\label{sub:aufgabestellung}} 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 + \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: +Da es sich um eine Kreisscheibe handelt, werden Polarkoordinaten verwendet, so dass sich der Laplaceoperator \begin{equation*} \Delta = @@ -23,78 +24,98 @@ Da es sich um eine Kreisscheibe handelt, werden Polarkoordinaten verwendet, so d \frac{\partial}{\partial r} + \frac{1}{r 2} - \frac{\partial^2}{\partial\varphi^2}. + \frac{\partial^2}{\partial\varphi^2} \label{buch:pde:kreis:laplace} \end{equation*} +ergibt. -Es wird eine runde elastische Membran berücksichtigt, die den Gebietbereich $\Omega$ abdeckt und am Rand $\Gamma$ befestigt ist. +Es wird eine runde elastische Membran berücksichtigt, die das Gebiet $\Omega$ 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. +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 eingespannten homogenen schwingenden Membran. Daher ist die Membranabweichung im Punkt $(r,\varphi)$ $\in$ $\overline{\rm \Omega}$ zum Zeitpunkt $t$: \begin{align*} u: \overline{\rm \Omega} \times \mathbb{R}_{\geq 0} &\longrightarrow \mathbb{R}\\ (r,\varphi,t) &\longmapsto u(r,\varphi,t) \end{align*} -Da die Membran am Rand befestigt ist, kann es keine Schwingungen geben, so dass die \textit{Dirichlet-Randbedingung} gilt: +Da die Membran am Rand befestigt ist, kann es keine Schwingungen geben, so dass die \textit{Dirichlet-Randbedingung} \cite{prof_dr_horst_knorrer_kreisformige_2013} \begin{equation*} - u\big|_{\Gamma} = 0 + u\big|_{\Gamma} = 0 \quad \text{für} \quad 0 \leq \varphi \leq 2\pi,\quad t \geq 0 \end{equation*} +gilt. + 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) + u_t(r,\varphi, 0) &= g(r,\varphi). \end{align*} + +\subsection{Lösung\label{sub:lösung1}} +\subsubsection{Ansatz der Separation der Variablen\label{subsub:ansatz_separation}} 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: +Dank der Randbedingungen kann also gefordert werden, dass $F(R)=0$ ist, und natürlich, dass $G(\varphi)$ $2\pi$ periodisch ist. Eingesetzt in der Differenzialgleichung ergibt sich: \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)} + \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*} +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 Gründen 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{align*} + 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{align*} 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{align*} + r^2F''(r) + rF'(r) + (\kappa^2 r^2 - \nu)F(r) &= 0 \\ + G''(\varphi) &= \nu G(\varphi). +\end{align*} + +\subsubsection{Lösung für $G(\varphi)$\label{subsub:lösung_G}} +Da für die Zweite Gelichung Lösungen von Schwingungen erwartet werden, für die $G''(\varphi)=-\omega^2 G(\varphi)$ gilt, schreibt die gemeinsame Konstante als $-\nu^2$, was die Formeln später vereinfacht. Also: \begin{equation*} G(\varphi) = C_n \cos(\varphi) + D_n \sin(\varphi) + \label{eq:cos_sin_überlagerung} \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 + +\subsubsection{Lösung für $F(r)$\label{subsub:lösung_F}} +Die Gleichung für $F$ hat die Gestalt +\begin{align} + r^2F''(r) + rF'(r) + (\kappa^2 r^2 - n^2)F(r) = 0 + \label{eq:2nd_degree_PDE} +\end{align} +Wir bereits in Kapitel \ref{buch:differntialgleichungen:section:bessel} 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" +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 +Die Funktionen $F(r) = J_n(\kappa r)$ lösen also die Differentialgleichung \eqref{eq:2nd_degree_PDE}. 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 +haben, und dass $\underset{\substack{m\to\infty}}{\text{lim}} \alpha_{mn}=\infty$. Somit ergibt 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} + F(r) = J_n (\kappa_{mn}r) \quad \text{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} - 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. -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. +\subsubsection{Lösung für $T(t)$\label{subsub:lösung_T}} +Die Differenzialgleichung $T''(t) + c^2\kappa^2T(t) = 0$, wird auf ähnliche Weise gelöst wie $G(\varphi)$. + +\subsubsection{Zusammenfassung der Lösungen\label{subsub:zusammenfassung_lösungen}} +Durch Überlagerung aller Ergebnisse erhält man die Lösung +\begin{align} + u(r, \varphi, t) = \displaystyle\sum_{m=1}^{\infty}\displaystyle\sum_{n=0}^{\infty} J_n (k_{mn}r)[a_{mn}\cos(n\varphi) + b_{mn}\sin(n\varphi)](n\varphi)[c_{mn}\cos(c \kappa_{mn} t)+d_{mn}\sin(c \kappa_{mn} t)] + \label{eq:lösung_endliche_generelle} +\end{align} + +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 $\kappa mn$ die Wellenzahl und $r$ der Radius ist. $a_{mn}$ und $b_{mn}$ sind die zu bestimmenden Konstanten. + + +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 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 8afe817..6efda49 100644 --- a/buch/papers/kreismembran/teil2.tex +++ b/buch/papers/kreismembran/teil2.tex @@ -5,95 +5,98 @@ \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: +Hermann Hankel (1839--1873) war ein deutscher Mathematiker, der für seinen Beitrag zur mathematischen Analysis und insbesondere für die nach ihm benannte Transformation bekannt ist. +Diese Transformation tritt bei der Untersuchung von Funktionen auf, die nur von der Entfernung des Ursprungs abhängen. +Er studierte auch Funktionen, jetzt Hankel- oder Bessel- Funktionen genannt, der dritten Art. +Die Hankel-Transformation, die die Bessel-Funktion enthält, taucht natürlich bei achsensymmetrischen Problemen auf, die in zylindrischen Polarkoordinaten formuliert sind. +In diesem Abschnitt werden die Theorie der Transformation und einige Eigenschaften der Grundoperationen erläutert. + +\subsubsection{Hankel-Transformation \label{subsub:hankel_tansformation}} +Wir führen die Definition der Hankel-Transformation \cite{lokenath_debnath_integral_2015} 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} + \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: +wo $\mathbf{r}=(x,y)$ und $\bm{\kappa}=(k,l)$. Polarkoordinaten sind für diese Art von Problemen am besten geeignet, 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. + 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, + 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 +Unter Verwendung der Integraldarstellung der Besselfunktion vom Ordnung $n$ \eqref{buch:fourier:eqn:bessel-integraldarstellung} +\begin{equation*} + 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} +\end{equation*} \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} \\ + F(k,\phi)&=e^{in(\phi-\frac{\pi}{2})}\int_{0}^{\infty}rJ_n(\kappa r) f(r) \; dr \nonumber \\ &=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: +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. + \mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)=\int_{0}^{\infty}rJ_n(\kappa r) f(r) \; dr. \label{equation:hankel} \end{align} +\subsubsection{Inverse Hankel-Transformation \label{subsub:inverse_hankel_tansformation}} 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} +\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} +\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 \\ + &= e^{in\theta}\int_{0}^{\infty}\kappa J_n(\kappa r) \tilde{f}_n(\kappa) \; d\kappa, +\end{align*} -Also, die inverse \textit{Hankel Transformation} ist so definiert: +von \eqref{equation:bessel_n_ordnung} also ist, die inverse \textit{Hankel-Transformation} 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. + \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. +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, +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, +\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. +\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. -\subsubsection{Theorem 1: Skalierung \label{subsub:skalierung}} -Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: +\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. -\begin{equation*} - \mathscr{H}_n\{f(ar)\}=\frac{1}{a^{2}}\tilde{f}_n \left(\frac{\kappa}{a}\right), \quad a>0. -\end{equation*} +\begin{satz}{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*} +\end{satz} -\subsubsection{Theorem 2: Persevalsche Relation \label{subsub:perseval}} +\begin{satz}{Persevalsche Relation (Skalarprodukt bleibt erhalten):} Wenn $\tilde{f}(\kappa)=\mathscr{H}_n\{f(r)\}$ und $\tilde{g}(\kappa)=\mathscr{H}_n\{g(r)\}$, dann: \begin{equation*} - \int_{0}^{\infty}rf(r) dr = \int_{0}^{\infty}\kappa\tilde{f}(\kappa)\tilde{g}(\kappa) d\kappa. + \int_{0}^{\infty}rf(r)g(r) \; dr = \int_{0}^{\infty}\kappa\tilde{f}(\kappa)\tilde{g}(\kappa) \; d\kappa. \end{equation*} +\end{satz} -\subsubsection{Theorem 3: Hankel Transformationen von Ableitungen \label{subsub:ableitungen}} +\begin{satz}{Hankel-Transformationen von Ableitungen:} Wenn $\tilde{f}_n(\kappa)=\mathscr{H}_n\{f(r)\}$, dann: \begin{align*} @@ -101,13 +104,13 @@ Wenn $\tilde{f}_n(\kappa)=\mathscr{H}_n\{f(r)\}$, dann: &\mathscr{H}_1\{f'(r)\}=-\kappa \tilde{f}_0(\kappa), \end{align*} bereitgestellt dass $[rf(r)]$ verschwindet als $r\to0$ und $r\to\infty$. +\end{satz} -\subsubsection{Theorem 4 \label{subsub:thorem4}} +\begin{satz} Wenn $\mathscr{H}_n\{f(r)\}=\tilde{f}_n(\kappa)$, dann: \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 $r\to\infty$. - - +bereitgestellt dass $rf'(r)$ und $rf(r)$ verschwinden für $r\to0$ und $r\to\infty$. +\end{satz} diff --git a/buch/papers/kreismembran/teil3.tex b/buch/papers/kreismembran/teil3.tex index bef8b5f..10338e7 100644 --- a/buch/papers/kreismembran/teil3.tex +++ b/buch/papers/kreismembran/teil3.tex @@ -6,7 +6,10 @@ \section{Lösungsmethode 2: Transformationsmethode \label{kreismembran:section:teil3}} \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: +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. + +\subsubsection{Transformation und Reduktion auf eine algebraische Gleichung\label{subsub:transf_reduktion}} +Führt man also das Konzept einer unendlichen und achsensymmetrischen Membran ein: \begin{equation*} \frac{\partial^2u}{\partial t^2} = @@ -18,16 +21,15 @@ Die Hankel-Transformation wird dann zur Lösung der Differentialgleichung verwen \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: 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 (limited to 'buch') 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 + 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buch/papers/nav/images/position/position2.pdf | Bin 0 -> 90563 bytes buch/papers/nav/images/position/position2.pov | 70 ++++++ buch/papers/nav/images/position/position2.tex | 53 ++++ buch/papers/nav/images/position/position3.pdf | Bin 0 -> 85020 bytes buch/papers/nav/images/position/position3.pov | 48 ++++ buch/papers/nav/images/position/position3.tex | 51 ++++ buch/papers/nav/images/position/position4.pdf | Bin 0 -> 86376 bytes buch/papers/nav/images/position/position4.pov | 69 ++++++ buch/papers/nav/images/position/position4.tex | 50 ++++ buch/papers/nav/images/position/position5.pdf | Bin 0 -> 91680 bytes buch/papers/nav/images/position/position5.pov | 69 ++++++ buch/papers/nav/images/position/position5.tex | 50 ++++ 36 files changed, 1087 insertions(+), 164 deletions(-) create mode 100644 buch/papers/nav/images/macros.inc create mode 100644 buch/papers/nav/images/position/Makefile create mode 100644 buch/papers/nav/images/position/common.inc create mode 100644 buch/papers/nav/images/position/common.tex create mode 100644 buch/papers/nav/images/position/position1.pdf create mode 100644 buch/papers/nav/images/position/position1.pov create mode 100644 buch/papers/nav/images/position/position1.tex create mode 100644 buch/papers/nav/images/position/position2.pdf create mode 100644 buch/papers/nav/images/position/position2.pov create mode 100644 buch/papers/nav/images/position/position2.tex create mode 100644 buch/papers/nav/images/position/position3.pdf 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 (limited to 'buch') 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 .../nav/images/beispiele/2k_earth_daymap.png | Bin 0 -> 1473323 bytes buch/papers/nav/images/beispiele/Makefile | 30 ++++++++ buch/papers/nav/images/beispiele/beispiele1.pdf | Bin 0 -> 399907 bytes buch/papers/nav/images/beispiele/beispiele1.pov | 12 ++++ buch/papers/nav/images/beispiele/beispiele1.tex | 49 +++++++++++++ buch/papers/nav/images/beispiele/beispiele2.pdf | Bin 0 -> 404679 bytes buch/papers/nav/images/beispiele/beispiele2.pov | 12 ++++ buch/papers/nav/images/beispiele/beispiele2.tex | 50 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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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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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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/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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 \[ -- cgit v1.2.1 From c982d50db43bc3254f3b158e17c679d5ef3253e2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 21 Jun 2022 08:34:19 +0200 Subject: typos --- buch/chapters/050-differential/bessel.tex | 11 +++- .../050-differential/potenzreihenmethode.tex | 61 ++++++++++++++-------- 2 files changed, 49 insertions(+), 23 deletions(-) (limited to 'buch') diff --git a/buch/chapters/050-differential/bessel.tex b/buch/chapters/050-differential/bessel.tex index a3237fe..cf271e3 100644 --- a/buch/chapters/050-differential/bessel.tex +++ b/buch/chapters/050-differential/bessel.tex @@ -316,10 +316,14 @@ J_{-\alpha}(x) y_2(x). \end{align*} +% +% Ganzzahlige Ordnung +% +\subsubsection{Besselfunktionen ganzzahliger Ordnung} Man beachte, dass diese Definition für beliebige ganzzahlige $\alpha$ funktioniert. Ist $\alpha=-n<0$, $n\in\mathbb{N}$, dann hat der Nenner Pole -an den Stellen $k=0,1,\dots,n-$. +an den Stellen $k=0,1,\dots,n-1$. Die Summe beginnt also erst bei $k=n$ oder \begin{align*} J_{-n}(x) @@ -340,6 +344,9 @@ J_{n}(x). Insbesondere unterscheiden sich $J_n(x)$ und $J_{-n}(x)$ nur durch ein Vorzeichen. +% +% Erzeugende Funktione +% \subsubsection{Erzeugende Funktion} \begin{figure} \centering @@ -754,6 +761,6 @@ BJ_{\frac12}(x) \biggl(\frac12\biggr)^2 J_{\frac12}(x). \end{align*} Dies zeigt, dass $J_{\frac12}(x)$ tatsächlich eine Eigenfunktion -des Bessel-Operators zum Eigenwert $\alpha^2 = \frac14$. +des Bessel-Operators zum Eigenwert $\alpha^2 = \frac14$ ist. Analog kann man die Lösung $y_2(x)$ für $-\frac12$ verifizieren. diff --git a/buch/chapters/050-differential/potenzreihenmethode.tex b/buch/chapters/050-differential/potenzreihenmethode.tex index 84c52c2..d046f06 100644 --- a/buch/chapters/050-differential/potenzreihenmethode.tex +++ b/buch/chapters/050-differential/potenzreihenmethode.tex @@ -290,7 +290,7 @@ Für ganzzahliges $\alpha$ wird daraus die binomische Formel \] % -% 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(+) (limited to 'buch') 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 (limited to 'buch') 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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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=", - "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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", 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", - "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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(+) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 (limited to 'buch') 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 (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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(-) (limited to 'buch') 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 35d08feb3fdcae56cad97ab48822b0f8c2ab4aa1 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Tue, 19 Jul 2022 19:38:35 +0200 Subject: Added analysis of reaching target --- buch/papers/lambertw/main.tex | 2 +- buch/papers/lambertw/teil0.tex | 18 ++-- buch/papers/lambertw/teil1.tex | 204 +++++++++++++++-------------------------- 3 files changed, 83 insertions(+), 141 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/main.tex b/buch/papers/lambertw/main.tex index 68b7a5d..a347608 100644 --- a/buch/papers/lambertw/main.tex +++ b/buch/papers/lambertw/main.tex @@ -28,10 +28,10 @@ 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/teil4.tex} +\input{papers/lambertw/teil1.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 73fe187..50d2255 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -4,7 +4,7 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Was sind Verfolgungskurven? -\label{lambertw:section:teil0}} +\label{lambertw:section:Was_sind_Verfolgungskurven}} \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. @@ -31,17 +31,17 @@ Wie bereits erwähnt, wird der Verfolger durch seine Verfolgungsstrategie defini \hline \end{tabular} \caption{mögliche Verfolgungsstrategien} - \label{lambertw:Strategien} + \label{lambertw:table:Strategien} \end{table} -%\begin{figure} -% \centering -% \includegraphics{.\papers\lambertw\Bilder\pursuerDGL2.pdf} -% \label{pursuer:pursuerDGL2} -%\end{figure} +\begin{figure} + \centering + \includegraphics[scale=0.2]{./papers/lambertw/Bilder/pursuerDGL2.pdf} + \label{lambertw:grafic:pursuerDGL2} +\end{figure} In der Tabelle \eqref{lambertw:Strategien} sind drei mögliche Strategien aufgezählt. Folgend wird nur noch auf die Strategie 1 eingegangen. @@ -67,7 +67,7 @@ Aus dem Verfolgungsproblem ist auch ersichtlich, dass die Punkte $V$ und $Z$ nic 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{align} - \label{pursuer:pursuerDGL} + \label{lambertw:pursuerDGL} \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot \overrightarrow{\dot{V}} &= @@ -87,7 +87,7 @@ Wie der Verfolger wird auch unser Ziel sich strikt an eine Fluchtstrategie halte 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) + \vec{Z}(t) = \begin{Bmatrix} 0\\ diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index cc4a62a..3415c45 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -3,160 +3,102 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Ziel +\section{Wird das Ziel erreicht? \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|} +Sehr oft kommt es vor, dass bei Verfolgungsproblemen die Frage auftaucht, ob das Ziel überhaupt erreicht wird. +Wenn zum Beispiel die Geschwindigkeit des Verfolgers kleiner ist als diejenige des Ziels, gibt es Anfangsbedingungen bei denen das Ziel nie erreicht wird. +Sobald diese Frage beantwortet wurde stellt sich meist die Frage, wie lange es dauert bis das Ziel erreicht wird. +Diese beiden Fragen werden in diesem Kapitel behandelt und an einem Beispiel betrachtet. + +\subsection{Ziel erreichen (überarbeiten) +\label{lambertw:subsection:ZielErreichen}} +Für diese Betrachtung wird das Beispiel aus \eqref{lambertw:section:teil4} zur Hilfe genommen. +Wir verwenden die Hergeleiteten Gleichungen +\begin{align*} + x\left(t\right) + &= + \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ + y(x) + &= + \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) \\ + \chi + &= + \frac{r_0+y_0}{r_0-y_0}; \cdot\chi \\ + \eta + &= + \left(\frac{x}{x_0}\right)^2 + \:;\: + r_0 = - \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. + \sqrt{x_0^2+y_0^2} \\ +\end{align*} +Wir definieren einen Treffer wenn die Koordinaten des Verfolgers mit denen des Ziels übereinstimmen bei einem diskreten Zeitpunkt $t_1$. Aus dem vorangegangenem Beispiel, sind die Gleichungen zu den x- und y-Koordinaten des Verfolgers bekannt. Die Des Ziels sind -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}|} + \overrightarrow{Z}(t) + = + \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) = - 1 + \left( \begin{array}{c} 0 \\ t \end{array} \right) + ;\quad + \overrightarrow{V}(t) + = + \left( \begin{array}{c} x(t) \\ y(t) \end{array} \right) + \label{lambertw:Anfangspunkte} \end{equation} -Diese DGL ist der Kern des Verfolgungsproblems, insofern sich der Verfolger immer direkt auf sein Ziel zubewegt. +Somit gilt es -\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. +\begin{equation*} + \overrightarrow{Z}(t_1)=\overrightarrow{V}(t_1) +\end{equation*} -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. +zu lösen. Da die $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. -\begin{align} - v_P^2 +\begin{align*} + 0 &= - \dot{P}\cdot\dot{P} + x(t) = - 1 - \\[5pt] - v_A - &= - 1 - \\[5pt] - A + \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} + \\ + v \cdot t &= - \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. + y(t) + = + \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) + \\ +\end{align*} + +Zuerst wird die Bedingung der x-Koordinate betrachtet. Diese kann durch quadrieren und anschliessendes multiplizieren von $\chi$ vereinfacht werden. \begin{equation} - \dfrac{-x\cdot\dot{x}+(t-y)\cdot\dot{y}}{\sqrt{x^2+(t-y)^2}} = 1 + 0 + = + W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) \end{equation} +Dies entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei +\begin{equation*} + W(0)=0 +\end{equation*} +besitzt. Kann die Bedingung weiter vereinfacht werden zu - - - - - - -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{lambertw:equation1} + 0 + = + \chi\cdot e^{\chi-\frac{4t}{r_0-y_0}} \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{lambertw: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{lambertw: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{lambertw: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. + +Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingung unmöglich zu erfüllen. +Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. +Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Treffer möglich wäre. +Somit kann nach den Gestellten Bedingungen das Ziel nie getroffen werden. +Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. +Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. -- cgit v1.2.1 From 429b93e4fff7d907b66ce65a1cf2d81b702df12f Mon Sep 17 00:00:00 2001 From: tim30b Date: Wed, 20 Jul 2022 17:52:10 +0200 Subject: Write citations --- buch/papers/kreismembran/references.bib | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) (limited to 'buch') diff --git a/buch/papers/kreismembran/references.bib b/buch/papers/kreismembran/references.bib index 1aef90b..f642aa8 100644 --- a/buch/papers/kreismembran/references.bib +++ b/buch/papers/kreismembran/references.bib @@ -4,6 +4,25 @@ % (c) 2020 Autor, Hochschule Rapperswil % +@online{kreismembran:Duden:Membrane, + title = {Duden:Membrane}, + url = {https://www.duden.de/rechtschreibung/Membrane}, + date = {2022-07-20}, + year = {2022}, + month = {7}, + day = {20} +} + +@online{kreismembran:wellengleichung_herleitung, + title = {Derivation of the 2D Wave Equation}, + author = {Dr. Christopher Lum}, + url = {https://www.youtube.com/watch?v=KAS7JBztw8E&t=0s}, + date = {2022-07-20}, + year = {2022}, + month = {7}, + day = {20} +} + @online{kreismembran:bibtex, title = {BibTeX}, url = {https://de.wikipedia.org/wiki/BibTeX}, -- cgit v1.2.1 From 8e792d7a9df5de84e24147758a4875e280426d3c Mon Sep 17 00:00:00 2001 From: tim30b Date: Wed, 20 Jul 2022 18:23:51 +0200 Subject: Begin writing intro, Einleitung & Annahmen --- buch/papers/kreismembran/teil0.tex | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/teil0.tex b/buch/papers/kreismembran/teil0.tex index 1552259..804640e 100644 --- a/buch/papers/kreismembran/teil0.tex +++ b/buch/papers/kreismembran/teil0.tex @@ -5,6 +5,23 @@ % \section{Einleitung\label{kreismembran:section:teil0}} \rhead{Einleitung} +Eine naheliegende kreisförmige Membrane ist eine Runde Trommel. +Der Zusammenhang zwischen rund und kreisförmig wird hier nicht erläutert, was in diesem Kapitel als Membrane verstanden wird sollte jedoch erwähnt sein. +Eine Membrane, Membran oder selten ein Schwingblatt ist laut Duden \cite{kreismembran:Duden:Membrane} ein "dünnes Blättchen aus Metall, Papier o. Ä., das durch seine Schwingungsfähigkeit geeignet ist, Schallwellen zu übertragen". +Um zu verstehen wie sich eine Kreisförmige Membrane oder eben eine Trommel verhaltet, wird das Verhalten eines infinitesimal kleines Stück einer Membrane untersucht. - +\paragraph{Annahmen} Für die Herleitung einer Differentialgleichung mit überschaubarer Komplexität werden gebräuchliche Annahmen zur Modellierung einer Membrane \cite{kreismembran:wellengleichung_herleitung} getroffen: +\begin{enumerate}[i] + \item Die Membrane ist homogen. + Dies bedeutet, dass die Membrane über die ganze Fläche die selbe Dichte $ \rho $ und Elastizität hat. + Durch die konstante Elastizität ist die ganze Membrane unter gleichmässiger Spannung $ T $. + \item Die Membrane ist perfekt flexibel. + Daraus folgt, dass die Membrane ohne Kraftaufwand verbogen werden kann. + Die Membrane ist dadurch nicht alleine schwing-fähig, hierzu muss sie gespannt werden mit der Kraft $ T $. + \item Die Membrane kann sich nur in Richtung ihrer Normalen in kleinem Ausmass Auslenken. + Auslenkungen in der ebene der Membrane sind nicht möglich. + \item Die Membrane erfährt keine Art von Dämpfung. + Neben der perfekten Flexibilität wird die Membrane auch nicht durch ihr umliegendes Medium aus gebremst. + Dadurch entsteht kein dämpfender Term abhängig von der Geschwindigkeit der Membrane in der Differenzialgleichung. +\end{enumerate} -- cgit v1.2.1 From 741a16165ff886bd411445a23b5963750c636a30 Mon Sep 17 00:00:00 2001 From: tim30b Date: Wed, 20 Jul 2022 18:58:36 +0200 Subject: Einleitung verbesserungen schreiben --- buch/papers/kreismembran/teil0.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/teil0.tex b/buch/papers/kreismembran/teil0.tex index 804640e..6f5e907 100644 --- a/buch/papers/kreismembran/teil0.tex +++ b/buch/papers/kreismembran/teil0.tex @@ -4,11 +4,11 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Einleitung\label{kreismembran:section:teil0}} -\rhead{Einleitung} -Eine naheliegende kreisförmige Membrane ist eine Runde Trommel. +\rhead{Membrane} +Eine naheliegendes Beispiel einer kreisförmigen Membrane ist eine Runde Trommel. Der Zusammenhang zwischen rund und kreisförmig wird hier nicht erläutert, was in diesem Kapitel als Membrane verstanden wird sollte jedoch erwähnt sein. -Eine Membrane, Membran oder selten ein Schwingblatt ist laut Duden \cite{kreismembran:Duden:Membrane} ein "dünnes Blättchen aus Metall, Papier o. Ä., das durch seine Schwingungsfähigkeit geeignet ist, Schallwellen zu übertragen". -Um zu verstehen wie sich eine Kreisförmige Membrane oder eben eine Trommel verhaltet, wird das Verhalten eines infinitesimal kleines Stück einer Membrane untersucht. +Eine Membrane, Membran oder selten ein Schwingblatt ist laut Duden \cite{kreismembran:Duden:Membrane} ein "dünnes Blättchen aus Metall, Papier o. Ä., ...". +Um zu verstehen wie sich eine Kreisförmige Membrane oder eben eine Trommel verhaltet, wird vorerst das Verhalten eines infinitesimal kleines Stück einer Membrane untersucht. \paragraph{Annahmen} Für die Herleitung einer Differentialgleichung mit überschaubarer Komplexität werden gebräuchliche Annahmen zur Modellierung einer Membrane \cite{kreismembran:wellengleichung_herleitung} getroffen: \begin{enumerate}[i] -- cgit v1.2.1 From 6dd01e88ff8b1d93decb31fabef8edb95b361e87 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 20 Jul 2022 20:16:26 +0200 Subject: made some adjustments --- buch/papers/lambertw/Bilder/pursuerDGL2.ggb | Bin 17954 -> 21894 bytes buch/papers/lambertw/Bilder/pursuerDGL2.pdf | Bin 17941 -> 21894 bytes buch/papers/lambertw/main.tex | 38 ++++++++-------- buch/papers/lambertw/teil0.tex | 65 ++++++++++++++++------------ 4 files changed, 56 insertions(+), 47 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/pursuerDGL2.ggb b/buch/papers/lambertw/Bilder/pursuerDGL2.ggb index 0bd39b2..3c4500b 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 index 284dd7d..932d9d9 100644 Binary files a/buch/papers/lambertw/Bilder/pursuerDGL2.pdf and b/buch/papers/lambertw/Bilder/pursuerDGL2.pdf differ diff --git a/buch/papers/lambertw/main.tex b/buch/papers/lambertw/main.tex index a347608..9e6d04f 100644 --- a/buch/papers/lambertw/main.tex +++ b/buch/papers/lambertw/main.tex @@ -4,28 +4,28 @@ % (c) 2020 Hochschule Rapperswil % \chapter{Verfolgungskurven\label{chapter:lambertw}} -\lhead{Thema} +\lhead{Verfolgungskurven} \begin{refsection} \chapterauthor{David Hugentobler und Yanik Kuster} -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} +%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/lambertw/teil0.tex} %\input{papers/lambertw/teil2.tex} diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 50d2255..2905605 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -5,14 +5,26 @@ % \section{Was sind Verfolgungskurven? \label{lambertw:section:Was_sind_Verfolgungskurven}} -\rhead{Teil 0} +\rhead{Was sind Verfolgungskurven?} -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 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 verfolgt sein Ziel, das versucht zu entkommen. +Der Pfad, der der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. +Um diese Kurve zu bestimmen, kann das Verfolgungsproblem als Differentialgleichung formuliert werden. +Diese Differentialgleichung entspringt der Verfolgungsstrategie des Verfolgers. \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. +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{table} \centering @@ -39,46 +51,46 @@ Wie bereits erwähnt, wird der Verfolger durch seine Verfolgungsstrategie defini \begin{figure} \centering - \includegraphics[scale=0.2]{./papers/lambertw/Bilder/pursuerDGL2.pdf} + \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.pdf} + \caption{Vektordarstellung Strategie 1} \label{lambertw:grafic: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. +In der Tabelle \eqref{lambertw:table:Strategien} sind drei mögliche Strategien aufgezählt. +Im 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 zu. +In der Abbildung \eqref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, +wobei $\vec{V}$ der Ortsvektor des Verfolgers, $\vec{Z}$ der Ortsvektor des Ziels und $\dot{\vec{V}}$ der Geschwindigkeitsvektor des Verfolgers ist. Die konstante Geschwindigkeit kann man mit der Gleichung \begin{equation} - |\overrightarrow{\dot{V}}| - = konst = A - \quad|A\in\mathbb{R}>0 + |\dot{\vec{V}}| + = const = A + \quad A\in\mathbb{R}>0 \end{equation} darstellen. Der Geschwindigkeitsvektor wiederum kann mit der Gleichung \begin{equation} - \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot|\overrightarrow{\dot{V}}| + \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot|\dot{\vec{V}}| = - \overrightarrow{\dot{V}} + \dot{\vec{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. +Die Differenz der Ortsvektoren $\vec{V}$ und $\vec{Z}$ ist ein Vektor der vom Punkt $V$ auf $Z$ zeigt. +Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den 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. +Nun wird die Gleichung mit $\dot{\vec{V}}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. \begin{align} \label{lambertw:pursuerDGL} - \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot - \overrightarrow{\dot{V}} + \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot + \dot{\vec{V}} &= - |\overrightarrow{\dot{V}}|^2 + |\dot{\vec{V}}|^2 \\ - \frac{\overrightarrow{Z}-\overrightarrow{V}}{|\overrightarrow{Z}-\overrightarrow{V}|}\cdot \frac{\overrightarrow{\dot{V}}}{|\overrightarrow{\dot{V}}|} + \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot \frac{\dot{\vec{V}}}{|\dot{\vec{V}}|} &= 1 \end{align} -Diese DGL ist der Kern des Verfolgungsproblems, insofern der Verfolger die Strategie 1 verwendet. - +Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Strategie 1 verwendet. \subsection{Ziel \label{lambertw:subsection:Ziel}} @@ -89,14 +101,11 @@ Zum Beispiel könnte ein Ziel auf einer Geraden flüchten, welches auf einer Ebe \begin{equation} \vec{Z}(t) = - \begin{Bmatrix} - 0\\ - t - \end{Bmatrix} + \left( \begin{array}{c} 0 \\ t \end{array} \right) \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. +Die Fluchtkurve kann eine beliebige Form haben, jedoch wird die zu lösende Differentialgleichung immer komplexer. -- cgit v1.2.1 From 8d63b7cdea0c9bed2fed397a7dd35cf9c53aae8b Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 20 Jul 2022 22:04:39 +0200 Subject: adjusted chapter --- buch/papers/lambertw/main.log | 692 +++-------------------------------------- buch/papers/lambertw/teil1.tex | 21 +- 2 files changed, 56 insertions(+), 657 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/main.log b/buch/papers/lambertw/main.log index 4b0af4d..754563d 100644 --- a/buch/papers/lambertw/main.log +++ b/buch/papers/lambertw/main.log @@ -1,14 +1,12 @@ -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 +This is pdfTeX, Version 3.141592653-2.6-1.40.23 (MiKTeX 21.8) (preloaded format=pdflatex 2021.9.21) 20 JUL 2022 18:38 entering extended mode - restricted \write18 enabled. - %&-line parsing enabled. -**main.tex -(./main.tex -LaTeX2e <2021-11-15> -L3 programming layer <2021-11-12> +**./main.tex +(main.tex +LaTeX2e <2021-06-01> patch level 1 +L3 programming layer <2021-08-27> ! 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==> Fatal error occurred, no output PDF file produced! diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 3415c45..2f71f43 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -25,7 +25,7 @@ Wir verwenden die Hergeleiteten Gleichungen \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) \\ \chi &= - \frac{r_0+y_0}{r_0-y_0}; \cdot\chi \\ + \frac{r_0+y_0}{r_0-y_0}\\ \eta &= \left(\frac{x}{x_0}\right)^2 @@ -37,13 +37,13 @@ Wir verwenden die Hergeleiteten Gleichungen Wir definieren einen Treffer wenn die Koordinaten des Verfolgers mit denen des Ziels übereinstimmen bei einem diskreten Zeitpunkt $t_1$. Aus dem vorangegangenem Beispiel, sind die Gleichungen zu den x- und y-Koordinaten des Verfolgers bekannt. Die Des Ziels sind \begin{equation} - \overrightarrow{Z}(t) + \vec{Z}(t) = \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) = \left( \begin{array}{c} 0 \\ t \end{array} \right) ;\quad - \overrightarrow{V}(t) + \vec{V}(t) = \left( \begin{array}{c} x(t) \\ y(t) \end{array} \right) \label{lambertw:Anfangspunkte} @@ -52,7 +52,7 @@ Wir definieren einen Treffer wenn die Koordinaten des Verfolgers mit denen des Z Somit gilt es \begin{equation*} - \overrightarrow{Z}(t_1)=\overrightarrow{V}(t_1) + \vec{Z}(t_1)=\vec{V}(t_1) \end{equation*} zu lösen. Da die $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. @@ -72,7 +72,10 @@ zu lösen. Da die $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei \\ \end{align*} -Zuerst wird die Bedingung der x-Koordinate betrachtet. Diese kann durch quadrieren und anschliessendes multiplizieren von $\chi$ vereinfacht werden. +Zuerst wird die Bedingung der x-Koordinate betrachtet. +Diese kann durch quadrieren und anschliessendes multiplizieren von $\chi$ vereinfacht werden. +Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. +Die Gleichung \begin{equation} 0 @@ -80,7 +83,8 @@ Zuerst wird die Bedingung der x-Koordinate betrachtet. Diese kann durch quadrier W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) \end{equation} -Dies entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei + +entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei \begin{equation*} W(0)=0 @@ -100,5 +104,10 @@ Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Treffe Somit kann nach den Gestellten Bedingungen das Ziel nie getroffen werden. Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. +Dies kann mathematisch mit + +\begin{equation} + |\vec{V}-\vec{Z]|0 +\end{equation} -- cgit v1.2.1 From a7da84afe5d97069c243f103bb1438a459764cd3 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 20 Jul 2022 22:07:21 +0200 Subject: further adjustment --- buch/papers/lambertw/teil1.tex | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 2f71f43..eb43b3e 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -104,10 +104,20 @@ Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Treffe Somit kann nach den Gestellten Bedingungen das Ziel nie getroffen werden. Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. -Dies kann mathematisch mit +Somit wird in einer nächsten Betrachtung untersucht, ob der Verfolger dem Ziel näher kommt als ein definierter Trefferradius. +Falls dies stattfinden sollte, wird dies als Treffer interpretiert. +Mathematisch kann dies mit \begin{equation} |\vec{V}-\vec{Z]|0 \end{equation} +beschrieben werden, wobei $a_min$ dem Trefferradius entspricht. +Diese Gleichung wird noch quadriert, um die Wurzeln des Betrages loszuwerden. +Da sowohl der Betrag als auch $a_min$ grösser null sind, bleibt die Aussage unverändert. + +\begin{equation} + |\vec{V}-\vec{Z]|^20 +\end{equation} + -- cgit v1.2.1 From 1504ba1daa40a4ea1057a767dab89a210a9f4ae4 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Thu, 21 Jul 2022 12:07:31 +0200 Subject: Corrected writing Error --- buch/papers/lambertw/teil1.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index eb43b3e..aa7f226 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -29,9 +29,9 @@ Wir verwenden die Hergeleiteten Gleichungen \eta &= \left(\frac{x}{x_0}\right)^2 - \:;\: + \\ r_0 - = + &= \sqrt{x_0^2+y_0^2} \\ \end{align*} Wir definieren einen Treffer wenn die Koordinaten des Verfolgers mit denen des Ziels übereinstimmen bei einem diskreten Zeitpunkt $t_1$. Aus dem vorangegangenem Beispiel, sind die Gleichungen zu den x- und y-Koordinaten des Verfolgers bekannt. Die Des Ziels sind @@ -55,7 +55,7 @@ Somit gilt es \vec{Z}(t_1)=\vec{V}(t_1) \end{equation*} -zu lösen. Da die $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. +zu lösen. Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. \begin{align*} 0 -- cgit v1.2.1 From 0a60dc01038a4c9444043f6675877e1d52cd12d6 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Thu, 21 Jul 2022 12:29:12 +0200 Subject: corrected a typo --- buch/papers/lambertw/teil1.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index aa7f226..e8171fd 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -109,7 +109,7 @@ Falls dies stattfinden sollte, wird dies als Treffer interpretiert. Mathematisch kann dies mit \begin{equation} - |\vec{V}-\vec{Z]|0 + |\vec{V}-\vec{Z}|0 \end{equation} beschrieben werden, wobei $a_min$ dem Trefferradius entspricht. @@ -117,7 +117,7 @@ Diese Gleichung wird noch quadriert, um die Wurzeln des Betrages loszuwerden. Da sowohl der Betrag als auch $a_min$ grösser null sind, bleibt die Aussage unverändert. \begin{equation} - |\vec{V}-\vec{Z]|^20 + |\vec{V}-\vec{Z}|^2 0 \end{equation} -- cgit v1.2.1 From b5e57cde49a8cf16d39ad198b2c3e41136c74d4a Mon Sep 17 00:00:00 2001 From: daHugen Date: Thu, 21 Jul 2022 23:45:02 +0200 Subject: made some changes and added some things --- .../papers/lambertw/Bilder/VerfolgungskurveBsp.png | Bin 124329 -> 297455 bytes buch/papers/lambertw/teil4.tex | 70 +++++++++++++++------ 2 files changed, 51 insertions(+), 19 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png index 53eb2f9..90758cd 100644 Binary files a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png and b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png differ diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 6184369..bc1bf4d 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -3,45 +3,60 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Beispiel Verfolgungskurve +\section{Beispiel einer Verfolgungskurve \label{lambertw:section:teil4}} -\rhead{Beispiel Verfolgungskurve} -In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie 1 beschreiben. +\rhead{Beispiel einer Verfolgungskurve} +In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie 1 beschreiben. Dafür werden zuerst Bewegungsraum, Anfangspositionen und Bewegungsverhalten definiert, in einem nächsten Schritt soll eine Differentialgleichung dafür aufgestellt werden und anschliessend gelöst 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: +\subsection{Anfangsbedingungen definieren und einsetzen + \label{lambertw:subsection:Anfangsbedingungen}} +Das zu verfolgende Ziel \(\vec{Z}\) bewegt sich entlang der \(y\)-Achse mit konstanter Geschwindigkeit \(v = 1\), beginnend beim Ursprung des Kartesischen Koordinatensystems. Der Verfolger \(\vec{V}\) startet auf einem beliebigen Punkt im ersten Quadranten und bewegt sich auch mit konstanter Geschwindigkeit \(|\dot{V}| = 1\) in Richtung Ziel. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: \begin{equation} - \overrightarrow{Z} + \vec{Z} = \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) = \left( \begin{array}{c} 0 \\ t \end{array} \right) - ; - \overrightarrow{V} + ,\: + \vec{V} = \left( \begin{array}{c} x \\ y \end{array} \right) - \label{lambertw:Anfangspunkte} + \:\text{und}\:\: + \bigl| \dot{V} \bigl| + = + 1. + \label{lambertw:Anfangsbed} \end{equation} -Wenn man diese Startpunkte in die Gleichung der Verfolgungskurve \eqref{lambertw:pursuerDGL} einfügt ergibt sich folgender Ausdruck: +Wir haben nun die Anfangsbedingungen definiert, jetzt fehlt nur noch eine DGL, welche die fortlaufende Änderung der Position und Bewegungsrichtung des Verfolgers beschreibt. +Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} definiert, und zwar Gleichung \eqref{lambertw:pursuerDGL}. Wenn man die Startpunkte 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 + \cdot \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) = - 1 - \label{lambertw:eqMitAnfangspunkte} + 1. + \label{lambertw:eqMitAnfangsbed} \end{equation} -Macht man den linken Term Bruchfrei und löst das Skalarprodukt auf, dann ergibt sich folgende DGL: + +\subsection{DGL vereinfachen + \label{lambertw:subsection:DGLvereinfach}} +Nun haben wir eine Gleichung, es stellt sich aber die Frage ob es überhaupt eine geschlossene Lösung dafür gibt. Eine Funktion welche die Beziehung \(y(x)\) beschreibt oder sogar \(x(t)\) und \(y(t)\) liefert. Zum jetzigen Zeitpunkt mag es nicht trivial scheinen, aber mit den gewählten Anfangsbedingungen \eqref{lambertw:Anfangsbed} ist es möglich eine geschlossene Lösung für die Gleichung \eqref{lambertw:eqMitAnfangsbed} zu finden. +Auf dem Weg dahin muss die definierte DGL zuerst wesentlich vereinfacht werden, sei es mittels algebraische Umformungen oder mit den Tools aus der Analysis. Also legen wir los! + +Zuerst müssen wir den Bruch in \eqref{lambertw:eqMitAnfangsbed} los werden, der sieht so nicht handlich aus. Dafür multiplizieren wir beidseitig mit dem Nenner: \[ \left( \begin{array}{c} 0-x \\ t-y \end{array} \right) - \circ + \cdot \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) - = \sqrt{x^2 + (t-y)^2}\\ + = \sqrt{x^2 + (t-y)^2},\\ \] +In einem weiteren Schritt, lösen wir das Skalarprodukt auf und erhalten folgende Gleichung \eqref{lambertw:eqOhneSkalarprod} ohne vektorielle Grössen: \begin{equation} -x \cdot \dot{x} + (t-y) \cdot \dot{y} = \sqrt{x^2 + (t-y)^2} - \label{lambertw:eq1BspVerfolgKurve} + \label{lambertw:eqOhneSkalarprod} \end{equation} +Ist es nicht schön? Wir sind die 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 @@ -71,7 +86,10 @@ 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:eq1BspVerfolgKurve} eine wesentlich einfachere DGL: + +\subsection{Zeitabhängigkeit loswerden + \label{lambertw:subsection:ZeitabhLoswerden}} +Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} eine wesentlich einfachere DGL: \begin{equation} x \dot{y} + (t-y) \dot{x} = 0 @@ -112,6 +130,9 @@ Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambert xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} &= 0 \end{align*} + +\subsection{DGL lösen + \label{lambertw:subsection:DGLloes}} Mittels der Substitution \(y^{\prime} = u\) kann vorherige DGL in eine erster Ordnung umgewandelt werden: \begin{equation*} xu^{\prime} - \sqrt{1+u^2} @@ -149,6 +170,8 @@ Diese kann mit den selben Methoden gelöst werden, diesmal in Kombination mit de C_1 + C_2 x^2 - \frac{ln(x)}{8 \cdot C_2} \end{align*} +\subsection{Lösung analysieren + \label{lambertw:subsection:LoesAnalys}} \begin{figure} \centering \includegraphics{papers/lambertw/Bilder/VerfolgungskurveBsp.png} @@ -173,7 +196,11 @@ 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, siehe \ref{lambertw:BildFunkLoes}. 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. + +\subsection{Allgemeine Lösung + \label{lambertw:subsection:AllgLoes}} +Dies wird durch das Einsetzen folgender Anfangsbedingungen erreicht: \begin{equation} y(x)\big \vert_{t=0} = @@ -215,7 +242,12 @@ Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfang \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) \\ + \left(y_0+r_0\right)\left(\eta-1\right)+\left(r_0-y_0\right)ln\left(\eta\right) +\end{align*} + +\subsection{Funktion nach der Zeit + \label{lambertw:subsection:FunkNachT}} +\begin{align*} -4t+\left(y_0+r_0\right) &= \left(y_0+r_0\right)\eta+\left(r_0-y_0\right)ln\left(\eta\right) \\ -- cgit v1.2.1 From 137e7755104042841230d40f0e6f1132d9d430db Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Fri, 22 Jul 2022 15:26:31 +0200 Subject: Polished some sentences. Corrected missing amount in formula. Added new information in chapter Wird das Ziel erreicht? --- buch/papers/lambertw/teil0.tex | 14 ++--- buch/papers/lambertw/teil1.tex | 116 ++++++++++++++++++++++++++++------------- 2 files changed, 86 insertions(+), 44 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 2905605..30c4b60 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -46,9 +46,6 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um \label{lambertw:table:Strategien} \end{table} - - - \begin{figure} \centering \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.pdf} @@ -57,14 +54,14 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um \end{figure} In der Tabelle \eqref{lambertw:table:Strategien} sind drei mögliche Strategien aufgezählt. -Im Folgend wird nur noch auf die Strategie 1 eingegangen. +Im Folgenden 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 zu. In der Abbildung \eqref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, wobei $\vec{V}$ der Ortsvektor des Verfolgers, $\vec{Z}$ der Ortsvektor des Ziels und $\dot{\vec{V}}$ der Geschwindigkeitsvektor des Verfolgers ist. Die konstante Geschwindigkeit kann man mit der Gleichung \begin{equation} |\dot{\vec{V}}| - = const = A + = \operatorname{const} = A \quad A\in\mathbb{R}>0 \end{equation} darstellen. Der Geschwindigkeitsvektor wiederum kann mit der Gleichung @@ -80,12 +77,11 @@ Aus dem Verfolgungsproblem ist auch ersichtlich, dass die Punkte $V$ und $Z$ nic Wenn die Punkte $V$ und $Z$ trotzdem am gleichen Ort starten, ist die Lösung trivial. Nun wird die Gleichung mit $\dot{\vec{V}}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. \begin{align} - \label{lambertw:pursuerDGL} - \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot - \dot{\vec{V}} + \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot|\dot{\vec{V}}|\cdot\dot{\vec{V}} &= |\dot{\vec{V}}|^2 \\ + \label{lambertw:pursuerDGL} \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot \frac{\dot{\vec{V}}}{|\dot{\vec{V}}|} &= 1 @@ -105,7 +101,7 @@ Zum Beispiel könnte ein Ziel auf einer Geraden flüchten, welches auf einer Ebe \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 Differentialgleichung immer komplexer. +Die Fluchtkurve kann eine beliebige Form haben, jedoch wird die zu lösende Differentialgleichung für die Verfolgungskurve immer komplexer. diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index e8171fd..819658a 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -4,18 +4,18 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Wird das Ziel erreicht? -\label{lambertw:section:teil1}} -\rhead{Problemstellung} +\label{lambertw:section:Wird_das_Ziel_erreicht}} +\rhead{Wird das Ziel erreicht?} Sehr oft kommt es vor, dass bei Verfolgungsproblemen die Frage auftaucht, ob das Ziel überhaupt erreicht wird. Wenn zum Beispiel die Geschwindigkeit des Verfolgers kleiner ist als diejenige des Ziels, gibt es Anfangsbedingungen bei denen das Ziel nie erreicht wird. -Sobald diese Frage beantwortet wurde stellt sich meist die Frage, wie lange es dauert bis das Ziel erreicht wird. +Im Anschluss dieser Frage stellt sich meist die nächste Frage, wie lange es dauert bis das Ziel erreicht wird. Diese beiden Fragen werden in diesem Kapitel behandelt und an einem Beispiel betrachtet. - -\subsection{Ziel erreichen (überarbeiten) -\label{lambertw:subsection:ZielErreichen}} +% +%\subsection{Ziel erreichen (überarbeiten) +%\label{lambertw:subsection:ZielErreichen}} Für diese Betrachtung wird das Beispiel aus \eqref{lambertw:section:teil4} zur Hilfe genommen. -Wir verwenden die Hergeleiteten Gleichungen +Wir verwenden die Hergeleiteten Gleichungen für Startbedingung im ersten Quadranten \begin{align*} x\left(t\right) &= @@ -32,30 +32,36 @@ Wir verwenden die Hergeleiteten Gleichungen \\ r_0 &= - \sqrt{x_0^2+y_0^2} \\ + \sqrt{x_0^2+y_0^2} \text{.}\\ \end{align*} -Wir definieren einen Treffer wenn die Koordinaten des Verfolgers mit denen des Ziels übereinstimmen bei einem diskreten Zeitpunkt $t_1$. Aus dem vorangegangenem Beispiel, sind die Gleichungen zu den x- und y-Koordinaten des Verfolgers bekannt. Die Des Ziels sind +% +Das Ziel wird erreicht, wenn die Koordinaten des Verfolgers mit denen des Ziels bei einem diskreten Zeitpunkt $t_1$ übereinstimmen. +Somit gilt es + +\begin{equation*} + \vec{Z}(t_1)=\vec{V}(t_1) +\end{equation*} +% +zu lösen. +Aus dem vorangegangenem Beispiel, ist die Parametrisierung des Verfolgers und des Ziels bekannt. +Das Ziel wird parametrisiert durch \begin{equation} \vec{Z}(t) = - \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) - = \left( \begin{array}{c} 0 \\ t \end{array} \right) - ;\quad +\end{equation} +% +und der Verfolger durch + +\begin{equation} \vec{V}(t) = \left( \begin{array}{c} x(t) \\ y(t) \end{array} \right) - \label{lambertw:Anfangspunkte} + \text{.} \end{equation} - -Somit gilt es - -\begin{equation*} - \vec{Z}(t_1)=\vec{V}(t_1) -\end{equation*} - -zu lösen. Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. +% + Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. Es entstehen daher folgende Bedingungen \begin{align*} 0 @@ -71,7 +77,8 @@ zu lösen. Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einz \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) \\ \end{align*} - +% +, welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. Zuerst wird die Bedingung der x-Koordinate betrachtet. Diese kann durch quadrieren und anschliessendes multiplizieren von $\chi$ vereinfacht werden. Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. @@ -82,26 +89,62 @@ Die Gleichung = W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) \end{equation} - - +% entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei \begin{equation*} W(0)=0 \end{equation*} - -besitzt. Kann die Bedingung weiter vereinfacht werden zu +% +besitzt, kann die Bedingung weiter vereinfacht werden zu \begin{equation} 0 = \chi\cdot e^{\chi-\frac{4t}{r_0-y_0}} + \text{.} \end{equation} - +% Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingung unmöglich zu erfüllen. Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. -Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Treffer möglich wäre. -Somit kann nach den Gestellten Bedingungen das Ziel nie getroffen werden. +Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Einholen möglich wäre. +Somit kann nach den Gestellten Bedingungen das Ziel nie erreicht werden. +Aus der Symmetrie des Problems an der y-Achse können auch alle Anfangspunkte im zweiten Quadranten die Bedingungen nicht erfüllen. +Bei allen Anfangspunkten mit $y_0<0$ ist ein Einholen unmöglich, da die Geschwindigkeit des Verfolgers und Ziels übereinstimmen und der Verfolger dem Ziel bereits am Anfang nachgeht. +Wenn die Wertemenge der Anfangsbedingung um die positive y-Achse erweitert wird, kann das Ziel wiederum erreicht werden. +Sobald der Verfolger auf der positiven y-Achse startet, bewegen sich Verfolger und Ziel aufeinander zu, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel Zeigt und der Verfolger sich auf der Fluchtgeraden befindet. +Dies führt zwingend dazu, dass der Verfolger das Ziel erreichen wird. +Die Verfolgungskurve kann in diesem Fall mit + +\begin{equation} + \vec{V}(t) + = + \left( \begin{array}{c} 0 \\ y_0-t \end{array} \right) +\end{equation} +% +parametrisiert werden. +Nun kann der Abstand zwischen Verfolger und Ziel leicht bestimmt und nach 0 aufgelöst werden. +Daraus folgt + +\begin{equation} + 0 + = + |\vec{V}(t_1)-\vec{Z}(t_1)| + = + y_0-2t_1 +\end{equation} +% +, was aufgelöst zu + +\begin{equation} + t_1 + = + \frac{y_0}{2} +\end{equation} +% +führt. +Nun ist klar, dass lediglich Anfangspunkte auf der positiven y-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. +Bei allen anderen Anfangspunkten wird der Verfolger das Ziel nie erreichen. Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. Somit wird in einer nächsten Betrachtung untersucht, ob der Verfolger dem Ziel näher kommt als ein definierter Trefferradius. @@ -109,15 +152,18 @@ Falls dies stattfinden sollte, wird dies als Treffer interpretiert. Mathematisch kann dies mit \begin{equation} - |\vec{V}-\vec{Z}|0 + |\vec{V}-\vec{Z}|0 \end{equation} - -beschrieben werden, wobei $a_min$ dem Trefferradius entspricht. -Diese Gleichung wird noch quadriert, um die Wurzeln des Betrages loszuwerden. -Da sowohl der Betrag als auch $a_min$ grösser null sind, bleibt die Aussage unverändert. +% +beschrieben werden, wobei $a_{min}$ dem Trefferradius entspricht. +Durch quadrieren verschwindet die Wurzel des Betrages, womit \begin{equation} - |\vec{V}-\vec{Z}|^2 0 + |\vec{V}-\vec{Z}|^2 0 \end{equation} +% +die neue Bedingung ist. +Da sowohl der Betrag als auch $a_{min}$ grösser null sind, bleibt die Aussage unverändert. + -- cgit v1.2.1 From 7152877683f6ee147a404b5ab5f00a10a9a80c16 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Fri, 22 Jul 2022 15:36:14 +0200 Subject: polished sentence in chapter Verfolger und Verfolgungsstrategie --- buch/papers/lambertw/teil0.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 2905605..41257e6 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -78,7 +78,7 @@ Die Differenz der Ortsvektoren $\vec{V}$ und $\vec{Z}$ ist ein Vektor der vom Pu Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den 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 $\dot{\vec{V}}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. +Nun wird die Gleichung mit $\dot{\vec{V}}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergeben sich \begin{align} \label{lambertw:pursuerDGL} \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot @@ -88,7 +88,7 @@ Nun wird die Gleichung mit $\dot{\vec{V}}$ skalar multipliziert, um das Gleichun \\ \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot \frac{\dot{\vec{V}}}{|\dot{\vec{V}}|} &= - 1 + 1 \text{.} \end{align} Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Strategie 1 verwendet. @@ -98,11 +98,13 @@ 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{Z}(t) = \left( \begin{array}{c} 0 \\ t \end{array} \right) \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 Differentialgleichung immer komplexer. -- cgit v1.2.1 From df7209b60ecfb28b0f32a674920357cec038d6a0 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Fri, 22 Jul 2022 15:58:02 +0200 Subject: Corrected typos --- buch/papers/lambertw/teil1.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 819658a..b46ed12 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -15,7 +15,7 @@ Diese beiden Fragen werden in diesem Kapitel behandelt und an einem Beispiel bet %\subsection{Ziel erreichen (überarbeiten) %\label{lambertw:subsection:ZielErreichen}} Für diese Betrachtung wird das Beispiel aus \eqref{lambertw:section:teil4} zur Hilfe genommen. -Wir verwenden die Hergeleiteten Gleichungen für Startbedingung im ersten Quadranten +Wir verwenden die hergeleiteten Gleichungen für Startbedingung im ersten Quadranten \begin{align*} x\left(t\right) &= @@ -112,7 +112,7 @@ Somit kann nach den Gestellten Bedingungen das Ziel nie erreicht werden. Aus der Symmetrie des Problems an der y-Achse können auch alle Anfangspunkte im zweiten Quadranten die Bedingungen nicht erfüllen. Bei allen Anfangspunkten mit $y_0<0$ ist ein Einholen unmöglich, da die Geschwindigkeit des Verfolgers und Ziels übereinstimmen und der Verfolger dem Ziel bereits am Anfang nachgeht. Wenn die Wertemenge der Anfangsbedingung um die positive y-Achse erweitert wird, kann das Ziel wiederum erreicht werden. -Sobald der Verfolger auf der positiven y-Achse startet, bewegen sich Verfolger und Ziel aufeinander zu, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel Zeigt und der Verfolger sich auf der Fluchtgeraden befindet. +Sobald der Verfolger auf der positiven y-Achse startet, bewegen sich Verfolger und Ziel aufeinander zu, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel zeigt und der Verfolger sich auf der Fluchtgeraden befindet. Dies führt zwingend dazu, dass der Verfolger das Ziel erreichen wird. Die Verfolgungskurve kann in diesem Fall mit -- cgit v1.2.1 From f3ced170faef47bcdf76f96eabf0534a58fd348e Mon Sep 17 00:00:00 2001 From: Fabian <@> Date: Fri, 22 Jul 2022 16:31:41 +0200 Subject: 0f1, struktur --- buch/papers/0f1/images/airy.pdf | Bin 0 -> 25568 bytes buch/papers/0f1/images/konvergenzAiry.pdf | Bin 0 -> 15137 bytes buch/papers/0f1/images/konvergenzNegativ.pdf | Bin 0 -> 16312 bytes buch/papers/0f1/images/konvergenzPositiv.pdf | Bin 0 -> 18924 bytes buch/papers/0f1/images/stabilitaet.pdf | Bin 0 -> 20944 bytes buch/papers/0f1/listings/kettenbruchIterativ.c | 45 ++++++++++++++++++++++++ buch/papers/0f1/listings/kettenbruchRekursion.c | 19 ++++++++++ buch/papers/0f1/listings/potenzreihe.c | 13 +++++++ 8 files changed, 77 insertions(+) create mode 100644 buch/papers/0f1/images/airy.pdf create mode 100644 buch/papers/0f1/images/konvergenzAiry.pdf create mode 100644 buch/papers/0f1/images/konvergenzNegativ.pdf create mode 100644 buch/papers/0f1/images/konvergenzPositiv.pdf create mode 100644 buch/papers/0f1/images/stabilitaet.pdf create mode 100644 buch/papers/0f1/listings/kettenbruchIterativ.c create mode 100644 buch/papers/0f1/listings/kettenbruchRekursion.c create mode 100644 buch/papers/0f1/listings/potenzreihe.c (limited to 'buch') diff --git a/buch/papers/0f1/images/airy.pdf b/buch/papers/0f1/images/airy.pdf new file mode 100644 index 0000000..672d789 Binary files /dev/null and b/buch/papers/0f1/images/airy.pdf differ diff --git a/buch/papers/0f1/images/konvergenzAiry.pdf b/buch/papers/0f1/images/konvergenzAiry.pdf new file mode 100644 index 0000000..2e635ea Binary files /dev/null and b/buch/papers/0f1/images/konvergenzAiry.pdf differ diff --git a/buch/papers/0f1/images/konvergenzNegativ.pdf b/buch/papers/0f1/images/konvergenzNegativ.pdf new file mode 100644 index 0000000..3b58be4 Binary files /dev/null and b/buch/papers/0f1/images/konvergenzNegativ.pdf differ diff --git a/buch/papers/0f1/images/konvergenzPositiv.pdf b/buch/papers/0f1/images/konvergenzPositiv.pdf new file mode 100644 index 0000000..24e3fd5 Binary files /dev/null and b/buch/papers/0f1/images/konvergenzPositiv.pdf differ diff --git a/buch/papers/0f1/images/stabilitaet.pdf b/buch/papers/0f1/images/stabilitaet.pdf new file mode 100644 index 0000000..be4af42 Binary files /dev/null and b/buch/papers/0f1/images/stabilitaet.pdf differ diff --git a/buch/papers/0f1/listings/kettenbruchIterativ.c b/buch/papers/0f1/listings/kettenbruchIterativ.c new file mode 100644 index 0000000..befea8e --- /dev/null +++ b/buch/papers/0f1/listings/kettenbruchIterativ.c @@ -0,0 +1,45 @@ +static double fractionRekursion0f1(const double c, const double x, unsigned int n) +{ + double a = 0.0; + double b = 0.0; + double Ak = 0.0; + double Bk = 0.0; + double Ak_1 = 0.0; + double Bk_1 = 0.0; + double Ak_2 = 0.0; + double Bk_2 = 0.0; + + for (unsigned int k = 0; k <= n; ++k) + { + if (k == 0) + { + a = 1.0; //a0 + //recursion fomula for A0, B0 + Ak = a; + Bk = 1.0; + } + else if (k == 1) + { + a = 1.0; //a1 + b = x/c; //b1 + //recursion fomula for A1, B1 + Ak = a * Ak_1 + b * 1.0; + Bk = a * Bk_1; + } + else + { + a = 1 + (x / (k * ((k - 1) + c)));//ak + b = -(x / (k * ((k - 1) + c))); //bk + //recursion fomula for Ak, Bk + Ak = a * Ak_1 + b * Ak_2; + Bk = a * Bk_1 + b * Bk_2; + } + //save old values + Ak_2 = Ak_1; + Bk_2 = Bk_1; + Ak_1 = Ak; + Bk_1 = Bk; + } + //approximation fraction + return Ak/Bk; +} diff --git a/buch/papers/0f1/listings/kettenbruchRekursion.c b/buch/papers/0f1/listings/kettenbruchRekursion.c new file mode 100644 index 0000000..958d4e1 --- /dev/null +++ b/buch/papers/0f1/listings/kettenbruchRekursion.c @@ -0,0 +1,19 @@ +static double fractionIter0f1(const double b0, const double z, unsigned int n) +{ + double a = 0.0; + double b = 0.0; + double abn = 0.0; + double temp = 0.0; + + for (; n > 0; --n) + { + abn = z / (n * ((n - 1) + b0)); //abn = ak, bk + + a = n > 1 ? (1 + abn) : 1; //a0, a1 + b = n > 1 ? -abn : abn; //b1 + + temp = b / (a + temp); + } + + return a + temp; //a0 + temp +} \ No newline at end of file diff --git a/buch/papers/0f1/listings/potenzreihe.c b/buch/papers/0f1/listings/potenzreihe.c new file mode 100644 index 0000000..bfaa0e3 --- /dev/null +++ b/buch/papers/0f1/listings/potenzreihe.c @@ -0,0 +1,13 @@ +#include + +static double powerseries(const double b, const double z, unsigned int n) +{ + double temp = 0.0; + + for (unsigned int k = 0; k < n; ++k) + { + temp += pow(z, k) / (factorial(k) * pochhammer(b, k)); + } + + return temp; +} \ No newline at end of file -- cgit v1.2.1 From 4e98fc86feda32c0f2c20b879fe357ff64ee1441 Mon Sep 17 00:00:00 2001 From: daHugen Date: Fri, 22 Jul 2022 21:37:40 +0200 Subject: made some changes and added some things --- buch/papers/lambertw/teil4.tex | 239 ++++++++++++++++++++++++----------------- 1 file changed, 141 insertions(+), 98 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index bc1bf4d..78314a1 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -44,134 +44,137 @@ Nun haben wir eine Gleichung, es stellt sich aber die Frage ob es überhaupt ein Auf dem Weg dahin muss die definierte DGL zuerst wesentlich vereinfacht werden, sei es mittels algebraische Umformungen oder mit den Tools aus der Analysis. Also legen wir los! Zuerst müssen wir den Bruch in \eqref{lambertw:eqMitAnfangsbed} los werden, der sieht so nicht handlich aus. Dafür multiplizieren wir beidseitig mit dem Nenner: -\[ +\begin{equation} \left( \begin{array}{c} 0-x \\ t-y \end{array} \right) \cdot \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) - = \sqrt{x^2 + (t-y)^2},\\ -\] + = \sqrt{x^2 + (t-y)^2}. + \label{lambertw:eqOhneBruch} +\end{equation} In einem weiteren Schritt, lösen wir das Skalarprodukt auf und erhalten folgende Gleichung \eqref{lambertw:eqOhneSkalarprod} ohne vektorielle Grössen: \begin{equation} -x \cdot \dot{x} + (t-y) \cdot \dot{y} - = \sqrt{x^2 + (t-y)^2} + = \sqrt{x^2 + (t-y)^2}. \label{lambertw:eqOhneSkalarprod} \end{equation} -Ist es nicht schön? Wir sind die -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, anschliessend wird die Gleichung mit \(-1\) multipliziert: -\[ - \underbrace{(\dot{x}^2 - 1)}_{\mathclap{-\dot{y}^2}} \cdot x^2 - 2x(t-y) \dot{x} \dot{y} + \underbrace{(\dot{y}^2 - 1)}_{\mathclap{-\dot{x}^2}} \cdot (t-y)^2 - = 0 -\] -\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 \\ +Im letzten Schritt, fällt die Nützlichkeit des Skalarproduktes in der Verfolgungsgleichung \eqref{lambertw:pursuerDGL} markant auf. Meiner Meinung ziemlich elegant und nicht selbstverständlich in der Lage zu sein, das Problem auf eine einzige Gleichung reduzieren zu können. + +Die nächsten Schritte sind sehr algebralastig und würden das lesen dieses Papers einfach nur mühsam machen, also werde ich diese auslassen. Hingegen werden ich die algebraische Hauptschritte erwähnen, die notwendig wären falls man es trotzdem selber ausprobieren möchte: +\begin{itemize} + \item + Quadrieren und erweitern. + \item + Gruppieren. + \item + Substitution von einzelnen Thermen mittels der Beziehung \(\dot{x}^2 + \dot{y}^2 = 1\). + \item + Und das erkennen des Musters einer Binomischen Formel. +\end{itemize} +Das Resultat aller dieser Vereinfachungen führen zu folgender Gleichung \eqref{lambertw:eqAlgVerinfacht}, die viel handhabbarer ist als zuvor: +\begin{equation} (x \dot{y} + (t-y) \dot{x})^2 - &= 0 -\end{align*} + = 0. + \label{lambertw:eqAlgVerinfacht} +\end{equation} +Da der linke Term gleich Null ist, muss auch der Inhalt des Quadrates gleich Null sein, somit folgt eine weitere Vereinfachung, welche zu einer im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} wesentlich einfachere DGL führt: +\begin{equation} + x \dot{y} + (t-y) \dot{x} + = 0. + \label{lambertw:eqGanzVerinfacht} +\end{equation} +Kompakt, ohne Wurzelterme und Quadrate, nur elementare Operationen und Ableitungen. Nun stellt sich die Frage wie es weiter gehen soll, bei der Gleichung \eqref{lambertw:eqGanzVerinfacht} scheinen keine weiteren Vereinfachungen möglich zu sein. Wir brauchen einen neuen Ansatz um unser Ziel einer möglichen Lösung zu verfolgen. \subsection{Zeitabhängigkeit loswerden \label{lambertw:subsection:ZeitabhLoswerden}} -Wenn man nun beidseitig die Quadratwurzel zieht, dann ergibt sich im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} eine wesentlich einfachere DGL: +Der nächste logischer Schritt schient irgendwie die Zeitabhängigkeit in der Gleichung \eqref{lambertw:eqGanzVerinfacht} loszuwerden, aber wieso? Nun, wie am Anfang von Abschnitt \ref{lambertw:subsection:DGLvereinfach} beschrieben, suchen wir eine Lösung der Art \(y(x)\), dies ist natürlich erst möglich wenn wir die Abhängigkeit nach \(t\) eliminieren können. + +Der erste Schritt auf dem Weg dahin, ist es die zeitlichen Ableitung los zu werden, dafür wird \eqref{lambertw:eqGanzVerinfacht} beidseitig mit \(\dot{x}\) dividiert, was erlaubt ist, weil diese Änderung ungleich Null ist: \begin{equation} - x \dot{y} + (t-y) \dot{x} - = 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 und Vereinfachen ergibt sich folgende DGL: + = 0. + \label{lambertw:eqVorKeineZeitAbleit} +\end{equation} +Der Grund dafür ist, dass +\begin{equation} + \frac{\displaystyle\dot{y}}{\displaystyle\dot{x}} + = \frac{\displaystyle\frac{dy}{dt}}{\displaystyle\frac{dx}{dt}} + = \frac{dy}{dx} + = y^{\prime}, + \label{lambertw:eqQuotZeitAbleit} +\end{equation} +und somit kann der Quotient dieser zeitlichen Ableitungen in eine Ableitung nach \(x\) umgewandelt werden. +Nach dem diese Eigenschaft \eqref{lambertw:eqQuotZeitAbleit} in \eqref{lambertw:eqVorKeineZeitAbleit} eingesetzt wird und vereinfacht wurde, entsteht folgende neue Gleichung: \begin{equation} x y^{\prime} + t - y - = 0 + = 0. \label{lambertw:DGLmitT} \end{equation} -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: +Hier wäre es natürlich passend wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen muss man auf die Definition der Bogenlänge aus der Analysis zurückgreifen, wobei die Strecke \(s\) folgendem entspricht: \begin{equation} s = v \cdot t = + 1 \cdot t + = t = - \int_{x_0}^{x_{end}}\sqrt{1+y^{\prime\, 2}} \: dx + \int_{\displaystyle x_0}^{\displaystyle x_{\text{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 + = 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*} +Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambertw:DGLohneT} nach \(x\) ab und erhaltet folgende DGL \eqref{lambertw:DGLohneInt}: +\begin{align} y^{\prime}+ xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} - y^{\prime} - &= 0 \\ + &= 0, \\ xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} - &= 0 -\end{align*} + &= 0. + \label{lambertw:DGLohneInt} +\end{align} +Nun sind wir unserem Ziel eine weiteren Schritt näher. Die Gleichung \eqref{lambertw:DGLohneInt} mag auf den ersten Blick nicht gerade einfach sein, aber im Nächsten Abschnitt werden wir sehen, dass sie relativ einfach zu lösen ist. \subsection{DGL lösen \label{lambertw:subsection:DGLloes}} -Mittels der Substitution \(y^{\prime} = u\) kann vorherige DGL in eine erster Ordnung umgewandelt werden: -\begin{equation*} +Die Gleichung \eqref{lambertw:DGLohneInt} ist eine DGL zweiter Ordnung und kann +mittels der Substitution \(y^{\prime} = u\) in eine DGL erster Ordnung umgewandelt werden: +\begin{equation} xu^{\prime} - \sqrt{1+u^2} - = 0 + = 0. \label{lambertw:DGLmitU} -\end{equation*} -Welche mittels Separation gelöst werden kann: -\begin{align*} - arsinh(u) + C_L - &= - ln(x) + C_R \\ - arsinh(u) +\end{equation} +Diese \eqref{lambertw:DGLmitU} zu lösen ist ziemlich einfach da sie separierbar ist, also werde ich direkt zur Lösung \eqref{lambertw:loesDGLmitU} übergehen: +\begin{align} + \operatorname{arsinh}(u) &= - ln(x) + C \\ + \operatorname{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: + \operatorname{sinh}(\operatorname{ln}(x) + C). + \label{lambertw:loesDGLmitU} +\end{align} +Indem man die Substitution rückgängig macht, erhält man eine weitere DGL erster Ordnung die bereits separiert ist und erhält folgende Lösung: \begin{equation} y^{\prime} = - sinh(ln(x) + C) + \operatorname{sinh}(\operatorname{ln}(x) + C). + \label{lambertw:loesDGLmitY} \end{equation} -Diese kann mit den selben Methoden gelöst werden, diesmal in Kombination mit der exponentiellen Definition der \(sinh\)-Funktion: -\begin{align*} +Diese \eqref{lambertw:loesDGLmitY} kann mit den selben Methoden gelöst werden wie \eqref{lambertw:DGLmitU}, diesmal aber in Kombination mit der exponentiellen Definition der \(\operatorname{sinh}\)-Funktion: +\begin{equation} y - &= - \int sinh(ln(x) + C) \\ - &= - \int \frac{1}{2} (e^{ln(x)+C} - e^{-(ln(x)+C)}) \\ - &= - \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*} + = + C_1 + C_2 x^2 - \frac{\operatorname{ln}(x)}{8 \cdot C_2}. +\end{equation} +Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die Frage ob sie überhaupt plausibel ist. Dieser Frage werden wir in nächsten Abschnitt \ref{lambertw:subsection:LoesAnalys} nachgehen. \subsection{Lösung analysieren \label{lambertw:subsection:LoesAnalys}} + \begin{figure} \centering \includegraphics{papers/lambertw/Bilder/VerfolgungskurveBsp.png} @@ -184,47 +187,87 @@ Das Resultat, wie ersichtlich, ist folgende Funktion \eqref{lambertw:funkLoes} w \begin{equation} {\color{red}{y(x)}} = - C_1 + C_2 {\color{darkgreen}{x^2}} {\color{blue}{-}} \frac{\color{blue}{ln(x)}}{8 \cdot C_2} + C_1 + C_2 {\color{darkgreen}{x^2}} {\color{blue}{-}} \frac{\color{blue}{\operatorname{ln}(x)}}{8 \cdot C_2}. \label{lambertw:funkLoes} \end{equation} -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: +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 \(y(x)\) 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. + Für grosse \(x\)-Werte, welche in der Regel in der Nähe von \(x_0\) sein sollten, ist der quadratisch Term in der Funktion \eqref{lambertw:funkLoes} dominant. + \item + 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. Irgendwann werden Verfolger und Ziel auf gleicher Höhe sein. \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 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. + Aufgrund des Monotoniewechsels in der Kurve \eqref{lambertw:funkLoes} muss diese auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? + + Eine Abschätzung darüber kann 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 des Verfolgers, somit auch sein Vorzeichen und dadurch entsteht auch das Minimum. \end{itemize} -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. +Alle diese Eigenschafte stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde, welche durch die Grafik \ref{lambertw:BildFunkLoes} repräsentiert wurde. Nun stellt sich die Frage wie die Kurve wirklich aussieht. Dies wird im folgenden Abschnitt \ref{lambertw:subsection:AllgLoes} behandelt. -\subsection{Allgemeine Lösung +-------------------------------Ab hier muss im Kapitel 12.2 noch einiges bearbeitet werden----------------- +\subsection{Anfangswertproblem \label{lambertw:subsection:AllgLoes}} -Dies wird durch das Einsetzen folgender Anfangsbedingungen erreicht: +Wie üblich bei der Suche nach einer exakten Lösung, kommt ein Anfangswertproblem auf. Um dies zu lösen, müssen wir zuerst die Anfangswerte definieren. Da wir hier das Problem allgemein lösen, ergeben sich folgende zwei Anfangswerte: \begin{equation} y(x)\big \vert_{t=0} = y(x_0) = y_0 - \:;\: + \label{lambertw:eq1Anfangswert} +\end{equation} +und +\begin{equation} \frac{dy}{dx}\bigg \vert_{t=0} = y^{\prime}(x_0) = - \frac{y_0}{x_0} + \frac{y_0}{x_0}. + \label{lambertw:eq2Anfangswert} \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} +Der zweite Anfangswert \eqref{lambertw:eq2Anfangswert} mag nicht grade offensichtlich sein. Die Erklärung dafür ist aber simpel: Der Verfolger wird zum Zeitpunkt \(t=0\) in Richtung Koordinatenursprung bewegen wollen, wo sich das Ziel befindet. Somit entsteht das Steigungsdreieck \(\Delta x = x_0\) und \(\Delta y = y_0\). + +Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches ich nicht unbedingt eingehen möchte. Zur Vollständigkeit und Nachvollziehbarkeit werde ich aber das Gleichungssystem \eqref{lambertw:eqGleichungssystem} präsentieren, welches notwendig ist um das Anfangswertproblem zu lösen, sowie auch die allgemeine Lösung \eqref{lambertw:eqAllgLoes} die sich nach dem einsetzen der Koeffizienten \(C_1\) und \(C_2\) ergibt. + +\begin{itemize} + \item + Gleichungssystem: + \begin{subequations} + \begin{align} + y_0 + &= + C_1 + C_2 x^2_0 - \frac{\operatorname{ln}(x_0)}{8 \cdot C_2}, \\ + \frac{y_0}{x_0} + &= + 2 \cdot C_2 x_0 - \frac{1}{8 \cdot C_2 \cdot x_0}. + \end{align} + \label{lambertw:eqGleichungssystem} + \end{subequations} + \item + Allgemeine Funktion: + \begin{equation} + -4t + = + \left(y_0+r_0\right)\left(\eta-1\right)+\left(r_0-y_0\right)ln\left(\eta\right). + \label{lambertw:eqAllgLoes} + \end{equation} + Wobei aus Übersichtlichkeitsgründen \(\eta\) und \(r_0\) wie folgt definiert wurden: + \begin{equation} + \eta + = + \left(\frac{x}{x_0}\right)^2 + \:\:\text{und}\:\: + r_0 + = + \sqrt{x_0^2+y_0^2}. + \end{equation} +\end{itemize} + + + +Leitet man die Funktion \eqref{lambertw:funkLoes} nach \(x\) ab und setzt die Anfangsbedingungen ein, dann ergibt sich folgendes Gleichungssystem: + ... Mit folgenden Formeln geht es weiter: \begin{align*} \eta -- cgit v1.2.1 From f56d6490331812f1228bacee54845d7778d8fe10 Mon Sep 17 00:00:00 2001 From: Alain Date: Fri, 22 Jul 2022 22:52:37 +0200 Subject: gitgnore --- buch/papers/parzyl/.gitignore | 1 + 1 file changed, 1 insertion(+) create mode 100644 buch/papers/parzyl/.gitignore (limited to 'buch') diff --git a/buch/papers/parzyl/.gitignore b/buch/papers/parzyl/.gitignore new file mode 100644 index 0000000..75ec3f0 --- /dev/null +++ b/buch/papers/parzyl/.gitignore @@ -0,0 +1 @@ +.vscode/* \ No newline at end of file -- cgit v1.2.1 From 330b5694c49f16cd21ae30446aec261fe114d2b3 Mon Sep 17 00:00:00 2001 From: Alain Date: Fri, 22 Jul 2022 22:54:00 +0200 Subject: aller anfang ist schwer --- buch/papers/parzyl/.gitignore | 2 +- buch/papers/parzyl/main.tex | 22 ++++------------------ buch/papers/parzyl/teil0.tex | 2 +- buch/papers/parzyl/teil1.tex | 33 ++++++++++++++++++--------------- buch/papers/parzyl/teil2.tex | 2 +- 5 files changed, 25 insertions(+), 36 deletions(-) (limited to 'buch') diff --git a/buch/papers/parzyl/.gitignore b/buch/papers/parzyl/.gitignore index 75ec3f0..dbe9c82 100644 --- a/buch/papers/parzyl/.gitignore +++ b/buch/papers/parzyl/.gitignore @@ -1 +1 @@ -.vscode/* \ No newline at end of file +.vscode/ \ No newline at end of file diff --git a/buch/papers/parzyl/main.tex b/buch/papers/parzyl/main.tex index ff21c9f..01a8d59 100644 --- a/buch/papers/parzyl/main.tex +++ b/buch/papers/parzyl/main.tex @@ -8,24 +8,10 @@ \begin{refsection} \chapterauthor{Thierry Schwaller, Alain Keller} -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 Laplace-Gleichung ist eine wichtige Gleichung in der Physik. +Mit ihr lässt sich zum Beispiel das elektrische Feld in einem ladungsfreien Raum bestimmen. +In diesem Kapitel wird die Lösung der Laplace-Gliechung im +parabolischen Zyplinderkoordinatensystem genauer untersucht. \input{papers/parzyl/teil0.tex} \input{papers/parzyl/teil1.tex} diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index 09b4024..5f5b22f 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -3,7 +3,7 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 0\label{parzyl:section:teil0}} +\section{Elektrisches feld\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 diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex index 9ea60e2..6027f71 100644 --- a/buch/papers/parzyl/teil1.tex +++ b/buch/papers/parzyl/teil1.tex @@ -3,16 +3,10 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 1 +\section{Parabolische Zylinderfunktion \label{parzyl: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 +Die Parabolischen Zylinderfunktion sind spezielle funktionen \begin{equation} \int_a^b x^2\, dx = @@ -31,14 +25,23 @@ 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 +\subsection{Parabolische Zylinderkoordinaten \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 -provident, similique sunt in culpa qui officia deserunt mollitia -animi, id est laborum et dolorum fuga \eqref{000tempmlate:equation1}. - +Im parabloischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koordinatenflächen. +Die Koordinate $(\sigma, \tau, z)$ sind in kartesischen Koordinaten ausgedrückt mit +\begin{align} + x & = \sigma \tau \\ + y & = \frac{1}{2}\left(\tau^2 - \sigma^2\right) \\ + z & = z. +\end{align} +Wird $\tau$ oder $\sigma$ konstant gesetzt reultieren die Parabeln +\begin{equation} + y = \frac{1}{2} \left( \frac{x^2}{\sigma^2} - \sigma^2 \right) +\end{equation} +und +\begin{equation} + y = \frac{1}{2} \left( -\frac{x^2}{\tau^2} + \tau^2 \right). +\end{equation} Et harum quidem rerum facilis est et expedita distinctio \ref{parzyl:section:loesung}. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex index 75ba259..8bba905 100644 --- a/buch/papers/parzyl/teil2.tex +++ b/buch/papers/parzyl/teil2.tex @@ -3,7 +3,7 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Teil 2 +\section{Parabolische Zylinderfunkltion \label{parzyl:section:teil2}} \rhead{Teil 2} Sed ut perspiciatis unde omnis iste natus error sit voluptatem -- cgit v1.2.1 From 94fdbadada6397bba2e155abce7bdb855342045b Mon Sep 17 00:00:00 2001 From: Alain Date: Fri, 22 Jul 2022 22:58:20 +0200 Subject: ok --- buch/papers/parzyl/.gitignore | 1 - 1 file changed, 1 deletion(-) delete mode 100644 buch/papers/parzyl/.gitignore (limited to 'buch') diff --git a/buch/papers/parzyl/.gitignore b/buch/papers/parzyl/.gitignore deleted file mode 100644 index dbe9c82..0000000 --- a/buch/papers/parzyl/.gitignore +++ /dev/null @@ -1 +0,0 @@ -.vscode/ \ No newline at end of file -- cgit v1.2.1 From 585150092dfc7fe9f3043a2dd0966e1a597e9258 Mon Sep 17 00:00:00 2001 From: Alain Date: Sat, 23 Jul 2022 12:09:19 +0200 Subject: umstelung struktur --- buch/papers/parzyl/teil0.tex | 24 +++++++++++++++++++++++- buch/papers/parzyl/teil1.tex | 21 ++------------------- buch/papers/parzyl/teil2.tex | 2 +- 3 files changed, 26 insertions(+), 21 deletions(-) (limited to 'buch') diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index 5f5b22f..ff927b7 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -3,8 +3,30 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Elektrisches feld\label{parzyl:section:teil0}} +\section{Problem\label{parzyl:section:teil0}} \rhead{Teil 0} + +\subsection{Laplace Gleichung} + +\subsection{Parabolische Zylinderkoordinaten +\label{parzyl:subsection:finibus}} +Im parabloischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koordinatenflächen. +Die Koordinate $(\sigma, \tau, z)$ sind in kartesischen Koordinaten ausgedrückt mit +\begin{align} + x & = \sigma \tau \\ + y & = \frac{1}{2}\left(\tau^2 - \sigma^2\right) \\ + z & = z. +\end{align} +Wird $\tau$ oder $\sigma$ konstant gesetzt reultieren die Parabeln +\begin{equation} + y = \frac{1}{2} \left( \frac{x^2}{\sigma^2} - \sigma^2 \right) +\end{equation} +und +\begin{equation} + y = \frac{1}{2} \left( -\frac{x^2}{\tau^2} + \tau^2 \right). +\end{equation} + +\subsection{Differnetialgleichung} 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{parzyl:bibtex}. diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex index 6027f71..7d5c1a4 100644 --- a/buch/papers/parzyl/teil1.tex +++ b/buch/papers/parzyl/teil1.tex @@ -3,10 +3,9 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Parabolische Zylinderfunktion +\section{Lösung \label{parzyl:section:teil1}} \rhead{Problemstellung} -Die Parabolischen Zylinderfunktion sind spezielle funktionen \begin{equation} \int_a^b x^2\, dx = @@ -25,23 +24,7 @@ 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{Parabolische Zylinderkoordinaten -\label{parzyl:subsection:finibus}} -Im parabloischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koordinatenflächen. -Die Koordinate $(\sigma, \tau, z)$ sind in kartesischen Koordinaten ausgedrückt mit -\begin{align} - x & = \sigma \tau \\ - y & = \frac{1}{2}\left(\tau^2 - \sigma^2\right) \\ - z & = z. -\end{align} -Wird $\tau$ oder $\sigma$ konstant gesetzt reultieren die Parabeln -\begin{equation} - y = \frac{1}{2} \left( \frac{x^2}{\sigma^2} - \sigma^2 \right) -\end{equation} -und -\begin{equation} - y = \frac{1}{2} \left( -\frac{x^2}{\tau^2} + \tau^2 \right). -\end{equation} + Et harum quidem rerum facilis est et expedita distinctio \ref{parzyl:section:loesung}. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex index 8bba905..c1bd723 100644 --- a/buch/papers/parzyl/teil2.tex +++ b/buch/papers/parzyl/teil2.tex @@ -3,7 +3,7 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Parabolische Zylinderfunkltion +\section{Physik sache \label{parzyl:section:teil2}} \rhead{Teil 2} Sed ut perspiciatis unde omnis iste natus error sit voluptatem -- 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 (limited to 'buch') 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 From 92f8c87eec2b11e6900c09c252bea77cb35f4f25 Mon Sep 17 00:00:00 2001 From: daHugen Date: Sat, 23 Jul 2022 18:12:37 +0200 Subject: made some changes, now the document is ready for a second pull-request --- buch/papers/lambertw/teil4.tex | 167 +++++++++++++++++++++++++---------------- 1 file changed, 104 insertions(+), 63 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 78314a1..fe7ed49 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -136,7 +136,7 @@ Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambert &= 0. \label{lambertw:DGLohneInt} \end{align} -Nun sind wir unserem Ziel eine weiteren Schritt näher. Die Gleichung \eqref{lambertw:DGLohneInt} mag auf den ersten Blick nicht gerade einfach sein, aber im Nächsten Abschnitt werden wir sehen, dass sie relativ einfach zu lösen ist. +Nun sind wir unserem Ziel einen weiteren Schritt näher. Die Gleichung \eqref{lambertw:DGLohneInt} mag auf den ersten Blick nicht gerade einfach sein, aber im Nächsten Abschnitt werden wir sehen, dass sie relativ einfach zu lösen ist. \subsection{DGL lösen \label{lambertw:subsection:DGLloes}} @@ -147,7 +147,7 @@ mittels der Substitution \(y^{\prime} = u\) in eine DGL erster Ordnung umgewande = 0. \label{lambertw:DGLmitU} \end{equation} -Diese \eqref{lambertw:DGLmitU} zu lösen ist ziemlich einfach da sie separierbar ist, also werde ich direkt zur Lösung \eqref{lambertw:loesDGLmitU} übergehen: +Diese \eqref{lambertw:DGLmitU} zu lösen ist ziemlich einfach da sie separierbar ist, aus diesem Grund werde ich direkt zur Lösung \eqref{lambertw:loesDGLmitU} übergehen: \begin{align} \operatorname{arsinh}(u) &= @@ -157,7 +157,7 @@ Diese \eqref{lambertw:DGLmitU} zu lösen ist ziemlich einfach da sie separierbar \operatorname{sinh}(\operatorname{ln}(x) + C). \label{lambertw:loesDGLmitU} \end{align} -Indem man die Substitution rückgängig macht, erhält man eine weitere DGL erster Ordnung die bereits separiert ist und erhält folgende Lösung: +Indem man die Substitution rückgängig macht, erhält man eine weitere DGL erster Ordnung die bereits separiert ist und erhält folgende Gleichung: \begin{equation} y^{\prime} = @@ -205,10 +205,9 @@ Für die Koeffizienten \(C_1\) und \(C_2\) ergibt sich ein Anfangswertproblem, w \end{itemize} Alle diese Eigenschafte stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde, welche durch die Grafik \ref{lambertw:BildFunkLoes} repräsentiert wurde. Nun stellt sich die Frage wie die Kurve wirklich aussieht. Dies wird im folgenden Abschnitt \ref{lambertw:subsection:AllgLoes} behandelt. --------------------------------Ab hier muss im Kapitel 12.2 noch einiges bearbeitet werden----------------- \subsection{Anfangswertproblem \label{lambertw:subsection:AllgLoes}} -Wie üblich bei der Suche nach einer exakten Lösung, kommt ein Anfangswertproblem auf. Um dies zu lösen, müssen wir zuerst die Anfangswerte definieren. Da wir hier das Problem allgemein lösen, ergeben sich folgende zwei Anfangswerte: +Wie üblich bei der Suche nach einer exakten Lösung, kommt ein Anfangswertproblem vor. Um dieses zu lösen, müssen wir zuerst die Anfangswerte definieren. Da wir das Problem allgemein lösen wollen, ergeben sich folgende zwei Anfangswerte: \begin{equation} y(x)\big \vert_{t=0} = @@ -226,9 +225,9 @@ und \frac{y_0}{x_0}. \label{lambertw:eq2Anfangswert} \end{equation} -Der zweite Anfangswert \eqref{lambertw:eq2Anfangswert} mag nicht grade offensichtlich sein. Die Erklärung dafür ist aber simpel: Der Verfolger wird zum Zeitpunkt \(t=0\) in Richtung Koordinatenursprung bewegen wollen, wo sich das Ziel befindet. Somit entsteht das Steigungsdreieck \(\Delta x = x_0\) und \(\Delta y = y_0\). +Der zweite Anfangswert \eqref{lambertw:eq2Anfangswert} mag nicht grade offensichtlich sein. Die Erklärung dafür ist aber simpel: Der Verfolger wird sich zum Zeitpunkt \(t=0\) in Richtung Koordinatenursprung bewegen wollen, wo sich das Ziel befindet. Somit entsteht das Steigungsdreieck mit \(\Delta x = x_0\) und \(\Delta y = y_0\). -Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches ich nicht unbedingt eingehen möchte. Zur Vollständigkeit und Nachvollziehbarkeit werde ich aber das Gleichungssystem \eqref{lambertw:eqGleichungssystem} präsentieren, welches notwendig ist um das Anfangswertproblem zu lösen, sowie auch die allgemeine Lösung \eqref{lambertw:eqAllgLoes} die sich nach dem einsetzen der Koeffizienten \(C_1\) und \(C_2\) ergibt. +Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches ich nicht unbedingt eingehen möchte. Zur Vollständigkeit und Nachvollziehbarkeit, werde ich aber das Gleichungssystem \eqref{lambertw:eqGleichungssystem} präsentieren, welches notwendig ist um das Anfangswertproblem zu lösen, sowie auch die allgemeine Lösung \eqref{lambertw:eqAllgLoes} die sich nach dem einsetzen der Koeffizienten \(C_1\) und \(C_2\) in die Funktion \eqref{lambertw:funkLoes} ergibt. \begin{itemize} \item @@ -245,83 +244,125 @@ Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches \label{lambertw:eqGleichungssystem} \end{subequations} \item - Allgemeine Funktion: + Die allgemeine Funktion: \begin{equation} - -4t + y(x) = - \left(y_0+r_0\right)\left(\eta-1\right)+\left(r_0-y_0\right)ln\left(\eta\right). + \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right) \label{lambertw:eqAllgLoes} \end{equation} - Wobei aus Übersichtlichkeitsgründen \(\eta\) und \(r_0\) wie folgt definiert wurden: + Damit die Funkion \eqref{lambertw:eqAllgLoes} trotzdem noch übersichtlich bleibt, wurden \(\eta\) und \(r_0\) wie folgt definiert: \begin{equation} \eta = - \left(\frac{x}{x_0}\right)^2 + \left(\frac{x}{x_0}\right)^2 \:\:\text{und}\:\: r_0 = \sqrt{x_0^2+y_0^2}. \end{equation} \end{itemize} +Diese neue allgemein Funktion \eqref{lambertw:eqAllgLoes} weist immer noch die selbe Struktur wie die vorherig hergeleitete Funktion \eqref{lambertw:funkLoes} auf, einerseits einen quadratischen Teil der in \(\eta\) enthalten ist, anderseits den \(\operatorname{ln}\)-Teil. Aus dieser Ähnlichkeit kann geschlossen werden, dass sich \eqref{lambertw:eqAllgLoes} auf eine ähnliche Art verhalten wird. - - -Leitet man die Funktion \eqref{lambertw:funkLoes} nach \(x\) ab und setzt die Anfangsbedingungen ein, dann ergibt sich folgendes Gleichungssystem: - -... 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) -\end{align*} +Nun sind wir soweit, dass wir eine \(y(x)\)-Beziehung für beliebige Anfangswerte darstellen können, unser erstes Ziel wurde erreicht. Ist das alles? Nein, wir können einen Schritt weiter gehen und uns Fragen: Ist es analytisch möglich herauszufinden, wo sich Verfolger und Ziel zu jedem Zeitpunkt befinden? Dieser Frage werden wir im nächsten Abschnitt nachgehen. \subsection{Funktion nach der Zeit \label{lambertw:subsection:FunkNachT}} -\begin{align*} +Lieber Leser sei mir nicht böse, aber in diesem Abschnitt werde ich ein wenig mehr bei den algebraischen Umformungen ins Detail gehen. Dies hat auch einen bestimmten Grund, ich möchte den Einsatz einer speziellen Funktion aufzeigen, sowie auch wann und wieso diese vorkommt. Welche spezielle Funktion? Fragst du dich wahrscheinlich in diesem Moment. Nun, um diese Frage zu kurz zu beantworten, es ist "YouTube's favorite special function" laut dem Mathematiker Michael Penn, die Lambert-W-Funktion \(W(x)\) welche übrigens im Kapitel \ref{buch:section:lambertw} bereits beschrieben wurde. + +Also fangen wir an. Der erste Schritt ist es herauszufinden, wie die Zeitabhängigkeit wieder hinein gebracht werden kann. Dafür greifen wir auf die letzte Gleichung zu, in welcher \(t\) noch enthalten war, und zwar DGL \eqref{lambertw:DGLmitT}, welche zur Übersichtlichkeit hier nochmals aufgeführt wird: +\begin{equation} + x y^{\prime} + t - y + = 0. + \label{lambertw:eqDGLmitTnochmals} +\end{equation} +Wie in \eqref{lambertw:eqDGLmitTnochmals} zu sehen ist, werden \(y\) und deren Ableitung \(y^{\prime}\) benötigt, diese sind: +\begin{subequations} + \begin{align} + y + &= + \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right), \\ + \label{lambertw:eqFunkUndAbleit1} + 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). + \end{align} + \label{lambertw:eqFunkUndAbleit} +\end{subequations} +Wenn man diese Gleichungen \ref{lambertw:eqFunkUndAbleit} in die DGL \label{lambertw:eqDGLmitTnochmals} einfügt, vereinfacht und nach \(t\) auflöst, dann ergibt sich folgenden Ausdruck: +\begin{equation} + -4t + = + \left(y_0+r_0\right)\left(\eta-1\right)+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right). + \label{lambertw:eqFunkUndAbleitEingefuegt} +\end{equation} +In einem nächsten Schritt wird alles mit \(x\) auf die eine Seite gebracht, der Rest auf die andere Seite und anschliessend beidseitig exponentiert, was wie folgt aussieht: +\begin{align} -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)} + \left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right), \\ + e^{\displaystyle -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\ \\ + e^{\displaystyle \left(y_0+r_0\right)\eta}\cdot\eta^{\displaystyle \left(r_0-y_0\right)}. + \label{lambertw:eqMitExp} +\end{align} +Auf dem rechten Term von \eqref{lambertw:eqMitExp} beginnen wir langsam eine ähnliche Struktur wie \(\eta e^\eta\) zu erkennen, dies schreit nach der Struktur die benötigt wird um \(\eta\) mittels der Lambert-W-Funktion \(W(x)\) zu erhalten. Dies macht durchaus Sinn, wenn wir die Funktion \(x(t)\) finden wollen und \(W(x)\) die Umkehrfunktion von \(x e^x\) ist. + +Die erste Sache die uns in \eqref{lambertw:eqMitExp} stört ist, dass \(\eta\) als Potenz da steht. Dieses Problem können wir loswerden, indem wir beidseitig mit \(\:\displaystyle \frac{1}{r_0-y_0}\:\) potenzieren: +\begin{equation} + e^{\displaystyle \frac{-4t}{r_0-y_0}+\frac{y_0+r_0}{r_0-y_0}} + = + \eta\cdot e^{\displaystyle \frac{y_0+r_0}{r_0-y_0}\eta} . + \label{lambertw:eqOhnePotenz} +\end{equation} +Das nächste Problem auf welches wir in \eqref{lambertw:eqOhnePotenz} treffen ist, dass \(\eta\) nicht alleine im Exponent steht. Dies kann elegant mit folgender Substitution gelöst werden: +\begin{equation} \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 \\ - \frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi} - &= - \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*} + = + \frac{y_0+r_0}{r_0-y_0}. + \label{lambertw:eqChiSubst} +\end{equation} +Es gäbe natürlich andere Substitutionen wie z.B. +\[\displaystyle \chi=\frac{y_0+r_0}{r_0-y_0}\cdot\eta,\] +die auf das selbe Ergebnis führen würden, aber \eqref{lambertw:eqChiSubst} liefert in einem Schritt die kompakteste Lösung. Also fahren wir mit der Substitution \eqref{lambertw:eqChiSubst} weiter, setzen diese in die Gleichung \eqref{lambertw:eqOhnePotenz} ein und multiplizieren beidseitig mit \(\chi\). Daraus erhalten wir folgende Gleichung: +\begin{equation} + \chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}} + = + \chi\eta\cdot e^{\displaystyle \chi\eta}. + \label{lambertw:eqNachSubst} +\end{equation} +Schön oder? Nun sind wir endlich soweit, dass wir die angedeutete Lambert-W-Funktion \(W(x)\)einsetzen können. Wenn wir beidseitig \(W(x)\) anwenden, dann erhalten wir folgenden Ausdruck: \begin{equation} - y(t) + W\left(\chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}}\right) = - \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} + \chi\eta \end{equation} +Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir die gesuchte \(x(t)\)-Funktion \eqref{lambertw:eqFunkXNachT}. Dieses \(x(t)\) in Kombination mit \eqref{lambertw:eqFunkUndAbleit1} liefert die Position des Verfolgers zu jedem Zeitpunkt. Das Gleichungspaar \eqref{lambertw:eqFunktionenNachT}, besteht aus folgenden Gleichungen: +\begin{subequations} + \begin{align} + \label{lambertw:eqFunkXNachT} + x(t) + &= + x_0\cdot\sqrt{\frac{W\left(\chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}}\right)}{\chi}}, \\ + \label{lambertw:eqFunkYNachT} + y(x(t)) + = + y(t) + &= + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right) + \end{align} + \label{lambertw:eqFunktionenNachT} +\end{subequations} +Nun haben wir unser letztes Ziel erreicht und sind in der Lage eine Verfolgung rechnerisch sowie graphisch zu repräsentieren. + +Wir sind aber noch nicht ganz fertig, ich muss gestehen, dass ich in diesem Abschnitt einen wichtigen Teil verschwiegen habe. Und zwar wieso, dass ich schon bei der Gleichung \eqref{lambertw:eqFunkUndAbleitEingefuegt} wusste, dass man nach einigen Umformungen die Lambert-W-Funktion eingesetzt werden kann. +Der Grund dafür ist die Struktur +\begin{equation} + y + = + p(x) +\operatorname{ln}(x), + \label{lambertw:eqEinsatzLambW} +\end{equation} +bei welcher \(p(x)\) eine beliebige Potenz von \(x\) darstellt. + +Jedes mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oftmals vorkommt, was die Lambert-W-Funktion so wichtig macht. \ No newline at end of file -- cgit v1.2.1 From 07b8e7dcf04243e04d7bc1e7b92846fb6a26278e Mon Sep 17 00:00:00 2001 From: daHugen Date: Sat, 23 Jul 2022 18:24:01 +0200 Subject: corrected something --- buch/papers/lambertw/teil4.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index fe7ed49..84a0ec7 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -335,7 +335,7 @@ Schön oder? Nun sind wir endlich soweit, dass wir die angedeutete Lambert-W-Fun \begin{equation} W\left(\chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}}\right) = - \chi\eta + \chi\eta. \end{equation} Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir die gesuchte \(x(t)\)-Funktion \eqref{lambertw:eqFunkXNachT}. Dieses \(x(t)\) in Kombination mit \eqref{lambertw:eqFunkUndAbleit1} liefert die Position des Verfolgers zu jedem Zeitpunkt. Das Gleichungspaar \eqref{lambertw:eqFunktionenNachT}, besteht aus folgenden Gleichungen: \begin{subequations} @@ -349,7 +349,7 @@ Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir di = y(t) &= - \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right) + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right). \end{align} \label{lambertw:eqFunktionenNachT} \end{subequations} -- cgit v1.2.1 From f203a63e8310dac852efccd3ed957362b0ed0761 Mon Sep 17 00:00:00 2001 From: Yanik Kuster Date: Sat, 23 Jul 2022 19:39:26 +0200 Subject: Adjusted x(t), due to earlier error --- buch/papers/lambertw/teil1.tex | 34 +++++++++++++++++----------------- 1 file changed, 17 insertions(+), 17 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index b46ed12..fa7deb1 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -15,21 +15,20 @@ Diese beiden Fragen werden in diesem Kapitel behandelt und an einem Beispiel bet %\subsection{Ziel erreichen (überarbeiten) %\label{lambertw:subsection:ZielErreichen}} Für diese Betrachtung wird das Beispiel aus \eqref{lambertw:section:teil4} zur Hilfe genommen. -Wir verwenden die hergeleiteten Gleichungen für Startbedingung im ersten Quadranten +Wir verwenden die hergeleiteten Gleichungen \eqref{lambertw:eqFunkXNachT} für Startbedingung im ersten Quadranten \begin{align*} x\left(t\right) &= - \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ - y(x) + x_0\cdot\sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ + y(t) &= - \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) \\ + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\\ \chi &= \frac{r_0+y_0}{r_0-y_0}\\ \eta &= - \left(\frac{x}{x_0}\right)^2 - \\ + \left(\frac{x}{x_0}\right)^2\\ r_0 &= \sqrt{x_0^2+y_0^2} \text{.}\\ @@ -68,29 +67,28 @@ und der Verfolger durch &= x(t) = - \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} + x_0\sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ - v \cdot t + t &= y(t) = - \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) + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right) \\ \end{align*} % , welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. Zuerst wird die Bedingung der x-Koordinate betrachtet. -Diese kann durch quadrieren und anschliessendes multiplizieren von $\chi$ vereinfacht werden. -Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. -Die Gleichung - +Diese kann durch dividieren durch $x_0$, anschliessendes quadrieren und multiplizieren von $\chi$ vereinfacht werden. Daraus folgt \begin{equation} - 0 - = - W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) + 0 + = + W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) + \text{.} \end{equation} % -entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei +Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. +Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei \begin{equation*} W(0)=0 @@ -167,3 +165,5 @@ Da sowohl der Betrag als auch $a_{min}$ grösser null sind, bleibt die Aussage u + + -- cgit v1.2.1 From 68df1dfae4ea68c42fd97860280fac5ef3d672fb Mon Sep 17 00:00:00 2001 From: Alain Date: Sun, 24 Jul 2022 22:11:37 +0200 Subject: =?UTF-8?q?wenig=20isch=20besser=20als=20n=C3=BCt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/parzyl/teil0.tex | 31 ++++++++++++++++++++++++++++++- 1 file changed, 30 insertions(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index ff927b7..2fc8737 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -7,7 +7,36 @@ \rhead{Teil 0} \subsection{Laplace Gleichung} - +Die partielle Differentialgleichung +\begin{equation} + \Delta f = 0 +\end{equation} +ist als Laplace Gleichung bekannt. +Sie ist eine spezielle Form der poisson Gleichung +\begin{equation} + \Delta f = g +\end{equation} +mit g als beliebige Funktion. +In der Physik hat die Laplace Gleichung in verschieden Gebieten +verwendet, zum Beispiel im Elektromagnetismus. +Das Gaussche Gesetz in den Maxwellgleichungen +\begin{equation} + \nabla \cdot E = \frac{\varrho}{\epsilon_0} +\label{parzyl:eq:max1} +\end{equation} +besagt das die Divergenz eines Elektrischen Feldes an einem +Punkt gleich der Ladung an diesem Punkt ist. +Das elektrische Feld ist hierbei der Gradient des elektrischen +Potentials +\begin{equation} + \nabla \phi = E. +\end{equation} +Eingesetzt in \eqref{parzyl:eq:max1} resultiert +\begin{equation} + \nabla \cdot \nabla \phi = \Delta \phi = \frac{\varrho}{\epsilon_0}, +\end{equation} +was eine Possion gleichung ist. +An Ladungsfreien Stellen, ist der rechte Teil der Gleichung $0$. \subsection{Parabolische Zylinderkoordinaten \label{parzyl:subsection:finibus}} Im parabloischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koordinatenflächen. -- cgit v1.2.1 From bed0b6e09967200014ab83444a8b4316f285781a Mon Sep 17 00:00:00 2001 From: Fabian <@> Date: Mon, 25 Jul 2022 00:27:05 +0200 Subject: 0f1, inhalt struktur --- buch/papers/0f1/main.tex | 32 ++++-------- buch/papers/0f1/teil0.tex | 31 +++++------- buch/papers/0f1/teil1.tex | 121 ++++++++++++++++++++++++++++------------------ buch/papers/0f1/teil2.tex | 103 ++++++++++++++++++++++++++------------- buch/papers/0f1/teil3.tex | 85 +++++++++++++++++++------------- 5 files changed, 215 insertions(+), 157 deletions(-) (limited to 'buch') diff --git a/buch/papers/0f1/main.tex b/buch/papers/0f1/main.tex index 264ad56..b8cdc21 100644 --- a/buch/papers/0f1/main.tex +++ b/buch/papers/0f1/main.tex @@ -3,29 +3,17 @@ % % (c) 2020 Hochschule Rapperswil % -\chapter{Thema\label{chapter:0f1}} -\lhead{Thema} +% + + + +\chapter{Algorithmus zur Berechnung von $\mathstrut_0F_1$\label{chapter:0f1}} +\lhead{Algorithmus zur Berechnung von $\mathstrut_0F_1$} \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{Fabian Dünki} + + + \input{papers/0f1/teil0.tex} \input{papers/0f1/teil1.tex} diff --git a/buch/papers/0f1/teil0.tex b/buch/papers/0f1/teil0.tex index 9087808..bfc265f 100644 --- a/buch/papers/0f1/teil0.tex +++ b/buch/papers/0f1/teil0.tex @@ -1,22 +1,15 @@ % -% einleitung.tex -- Beispiel-File für die Einleitung +% einleitung.tex -- Einleitung % -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% (c) 2022 Fabian Dünki, Hochschule Rapperswil % -\section{Teil 0\label{0f1: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{0f1: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. - - +\section{Ausgangslage\label{0f1:section:ausgangslage}} +\rhead{Ausgangslage} +Die Hypergeometrische Funktion $\mathstrut_0F_1$ wird in vielen Funktionen als Basisfunktion benutzt, +zum Beispiel um die Airy Funktion zu berechnen. +In der GNU Scientific Library \cite{library-gsl} +ist die Funktion $\mathstrut_0F_1$ vorhanden. +Allerdings wirft die Funktion, bei negativen Übergabenwerten wie zum Beispiel \verb+gsl_sf_hyperg_0F1(1, -1)+, eine Exception. +Bei genauerer Untersuchung hat sich gezeigt, dass die Funktion je nach Betriebssystem funktioniert oder eben nicht. +So kann die Funktion unter Windows fehlerfrei aufgerufen werden, beim Mac OS und Linux sind negative Übergabeparameter im Moment nicht möglich. +Ziel dieser Arbeit war es zu evaluieren, ob es mit einfachen mathematischen Operationen möglich ist, die Hypergeometrische Funktion $\mathstrut_0F_1$ zu implementieren. diff --git a/buch/papers/0f1/teil1.tex b/buch/papers/0f1/teil1.tex index aca84d2..910e8bb 100644 --- a/buch/papers/0f1/teil1.tex +++ b/buch/papers/0f1/teil1.tex @@ -1,55 +1,80 @@ % -% teil1.tex -- Beispiel-File für das Paper +% teil1.tex -- Mathematischer Hintergrund % -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% (c) 2022 Fabian Dünki, Hochschule Rapperswil % -\section{Teil 1 -\label{0f1: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 +\section{Mathematischer Hintergrund +\label{0f1:section:mathHintergrund}} +\rhead{Mathematischer Hintergrund} + +\subsection{Hypergeometrische Funktion $\mathstrut_0F_1$ +\label{0f1:subsection:0f1}} +Wie in Kapitel \ref{buch:rekursion:section:hypergeometrische-funktion} beschrieben, +wird die Funktion $\mathstrut_0F_1$ folgendermassen definiert. +\begin{definition} + \label{0f1:rekursion:hypergeometrisch:def} + Die hypergeometrische Funktion + $\mathstrut_0F_1$ ist definiert durch die Reihe + \[ + \mathstrut_0F_1 + \biggl( + \begin{matrix} + \\ + b_1 + \end{matrix} + ; + x + \biggr) + = + \mathstrut_0F_1(;b_1;x) + = + \sum_{k=0}^\infty + \frac{1}{(b_1)_k}\frac{x^k}{k!}. + \] +\end{definition} + + +\subsection{Airy Funktion +\label{0f1:subsection:airy}} +Wie in \ref{buch:differentialgleichungen:section:hypergeometrisch} dargestellt, ist die Airy-Differentialgleichung +folgendermassen definiert. +\begin{definition} + y'' - xy = 0 + \label{0f1:airy:eq:differentialgleichung} +\end{definition} + +Daraus ergibt sich wie in Aufgabe~\ref{503} gefundenen Lösungen der +Airy-Differentialgleichung als hypergeometrische Funktionen. + + +\begin{align*} +y_1(x) += +\sum_{k=0}^\infty +\frac{1}{(\frac23)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k += +\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac23\end{matrix};\frac{x^3}{9} +\biggr). +\\ +y_2(x) = -\left[ \frac13 x^3 \right]_a^b +\sum_{k=0}^\infty +\frac{1}{(\frac43)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k = -\frac{b^3-a^3}3. -\label{0f1: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{0f1: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{0f1: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{0f1: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. +x\cdot\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac43\end{matrix}; +\frac{x^3}{9} +\biggr). +\qedhere +\end{align*} +\begin{figure} + \centering + \includegraphics{papers/0f1/images/airy.pdf} + \caption{Plot der Lösungen der Airy-Differentialgleichung $y''-xy=0$ + zu den Anfangsbedingungen $y(0)=1$ und $y'(0)=0$ in {\color{red}rot} + und $y(0)=0$ und $y'(0)=1$ in {\color{blue}blau}. + \label{0f1:airy:plot:vorgabe}} +\end{figure} \ No newline at end of file diff --git a/buch/papers/0f1/teil2.tex b/buch/papers/0f1/teil2.tex index 804d11b..07e17c0 100644 --- a/buch/papers/0f1/teil2.tex +++ b/buch/papers/0f1/teil2.tex @@ -1,40 +1,75 @@ % -% teil2.tex -- Beispiel-File für teil2 +% teil2.tex -- Umsetzung in C Programmen % -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% (c) 2022 Fabian Dünki, Hochschule Rapperswil % -\section{Teil 2 +\section{Umsetzung \label{0f1: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{0f1: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. +\rhead{Umsetzung} +Zur Umsetzung wurden drei Ansätze gewählt und +Die Unterprogramme wurde jeweils, wie die GNU Scientific Library, in C geschrieben. +\subsection{Potenzreihe +\label{0f1:subsection:potenzreihe}} +Die naheliegendste Lösung ist die Programmierung der Potenzreihe. +\begin{equation} + \label{0f1:rekursion:hypergeometrisch:eq} + \mathstrut_0F_1(;b;z) + = + \sum_{k=0}^\infty + \frac{z^k}{(b)_k \cdot k!} +\end{equation} + +\lstinputlisting[style=C,float,caption={Rekursivformel für Kettenbruch.},label={0f1:listing:potenzreihe}]{papers/0f1/listings/potenzreihe.c} + +\subsection{Kettenbruch +\label{0f1:subsection:kettenbruch}} +Ein endlicher Kettenbruch ist ein Bruch der Form +\begin{equation} +a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{n-1}}{a_{n-1} + \cfrac{b_n}{a_n}}}}} +\end{equation} +in welchem $a_0, a_1,\dots,a_n$ und $b_1,b_2,\dots,b_n$ ganze Zahlen +darstellen. + +{\color{red}TODO: Bessere Beschreibung mit Verknüpfung zur Potenzreihe} + +%Gauss hat durch + +\lstinputlisting[style=C,float,caption={Rekursivformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}]{papers/0f1/listings/kettenbruchIterativ.c} +\subsection{Rekursionsformel +\label{0f1:subsection:rekursionsformel}} +Wesentlich effizienter zur Berechnung eines Kettenbruches ist die Rekursionsformel. + +\begin{align*} +\frac{A_n}{B_n} += +a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{n-1}}{a_{n-1} + \cfrac{b_n}{a_n}}}}} +\end{align*} + +Die Berechnung von $A_n, B_n$ kann man auch ohne die Matrizenschreibweise +aufschreiben: +\begin{itemize} +\item Start: +\begin{align*} +A_{-1} &= 0 & A_0 &= a_0 \\ +B_{-1} &= 1 & B_0 &= 1 +\end{align*} +$\rightarrow$ 0-te Näherung: $\displaystyle\frac{A_0}{B_0} = a_0$ +\item Schritt $k\to k+1$: +\[ +\begin{aligned} +k &\rightarrow k + 1: +& +A_{k+1} &= A_{k-1} \cdot b_k + A_k \cdot a_k \\ +&& +B_{k+1} &= B_{k-1} \cdot b_k + B_k \cdot a_k +\end{aligned} +\] +\item +Näherungsbruch $n$: \qquad$\displaystyle\frac{A_n}{B_n}$ +\end{itemize} +{\color{red}TODO: Verweis Numerik} + + +\lstinputlisting[style=C,float,caption={Rekursivformel für Kettenbruch.},label={0f1:listing:kettenbruchRekursion}]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file diff --git a/buch/papers/0f1/teil3.tex b/buch/papers/0f1/teil3.tex index 25472cb..dca61f8 100644 --- a/buch/papers/0f1/teil3.tex +++ b/buch/papers/0f1/teil3.tex @@ -1,40 +1,57 @@ % -% teil3.tex -- Beispiel-File für Teil 3 +% teil3.tex -- Resultate und Ausblick % -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% (c) 2022 Fabian Dünki, Hochschule Rapperswil % -\section{Teil 3 +\section{Resultate \label{0f1: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{0f1: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{Resultate} +Im Verlauf des Seminares hat sich gezeigt, +das ein einfacher mathematischer Algorithmus zu implementieren gar nicht so einfach ist. +So haben alle drei umgesetzten Ansätze Probleme mit grossen negativen x in der Funktion $\mathstrut_0F_1(;b;x)$. +Ebenso wird, je grösser der Wert x wird $\mathstrut_0F_1(;b;x)$, desto mehr weichen die berechneten Resultate +von den erwarteten ab. +{\color{red}TODO cite wolfram alpha rechner} + +\subsection{Auswertung +\label{0f1:subsection:auswertung}} +\begin{figure} + \centering + \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzAiry.pdf} + \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion}. + \label{0f1:ausblick:plot:airy:konvergenz}} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzPositiv.pdf} + \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat}. + \label{0f1:ausblick:plot:konvergenz:positiv}} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzNegativ.pdf} + \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat}. + \label{0f1:ausblick:plot:konvergenz:negativ}} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=1\textwidth]{papers/0f1/images/stabilitaet.pdf} + \caption{Stabilität der 3 Algorithmen verglichen mit der GNU Scientific Library}. + \label{0f1:ausblick:plot:airy:stabilitaet}} +\end{figure} + +\begin{itemize} + \item Negative Zahlen sind sowohl für die Potenzreihe als auch für den Kettenbruch ein Problem. + \item Die Potenzreihe hat das Problem, je tiefer die Rekursionstiefe, desto mehr machen die Brüche ein Problem. Also der Nenner mit der Fakultät und dem Pochhammer Symbol. + \item Die Rekursionformel liefert für sehr grosse positive Werte die genausten Ergebnisse, verglichen mit der GNU Scientific Library. +\end{itemize} + + +\subsection{Ausblick +\label{0f1:subsection:ausblick}} + -- cgit v1.2.1 From c558a668bcc6d820c489dad980dc0f8f83acdbde Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Mon, 25 Jul 2022 08:33:08 +0200 Subject: fix brace-problem --- buch/papers/0f1/teil3.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) (limited to 'buch') diff --git a/buch/papers/0f1/teil3.tex b/buch/papers/0f1/teil3.tex index dca61f8..44a4600 100644 --- a/buch/papers/0f1/teil3.tex +++ b/buch/papers/0f1/teil3.tex @@ -18,28 +18,28 @@ von den erwarteten ab. \begin{figure} \centering \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzAiry.pdf} - \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion}. + \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion. \label{0f1:ausblick:plot:airy:konvergenz}} \end{figure} \begin{figure} \centering \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzPositiv.pdf} - \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat}. + \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat. \label{0f1:ausblick:plot:konvergenz:positiv}} \end{figure} \begin{figure} \centering \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzNegativ.pdf} - \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat}. + \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat. \label{0f1:ausblick:plot:konvergenz:negativ}} \end{figure} \begin{figure} \centering \includegraphics[width=1\textwidth]{papers/0f1/images/stabilitaet.pdf} - \caption{Stabilität der 3 Algorithmen verglichen mit der GNU Scientific Library}. + \caption{Stabilität der 3 Algorithmen verglichen mit der GNU Scientific Library. \label{0f1:ausblick:plot:airy:stabilitaet}} \end{figure} -- cgit v1.2.1 From 7d01dd49954a2f6c1c2b662af1c01f3928ddb827 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Mon, 25 Jul 2022 10:06:45 +0200 Subject: Add missing explanations, correct typos, mention sign change of LP earlier --- buch/papers/laguerre/definition.tex | 36 ++++----- buch/papers/laguerre/eigenschaften.tex | 3 +- buch/papers/laguerre/gamma.tex | 89 ++++++++++++---------- buch/papers/laguerre/main.tex | 21 ++--- .../presentation/sections/gamma_approx.tex | 2 +- buch/papers/laguerre/quadratur.tex | 19 +++-- 6 files changed, 93 insertions(+), 77 deletions(-) (limited to 'buch') diff --git a/buch/papers/laguerre/definition.tex b/buch/papers/laguerre/definition.tex index e2062d2..61549e0 100644 --- a/buch/papers/laguerre/definition.tex +++ b/buch/papers/laguerre/definition.tex @@ -4,15 +4,14 @@ % (c) 2022 Patrik Müller, Ostschweizer Fachhochschule % \section{Herleitung% -% \section{Einleitung -% \section{Definition -\label{laguerre:section:definition}} + % \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. +Zudem werden wir die Lösung auf die assoziierten Laguerre-Polynome ausweiten. +Im Anschluss soll dann noch die Orthogonalität dieser Polynome bewiesen werden. \subsection{Assoziierte Laguerre-Differentialgleichung} Die assoziierte Laguerre-Differentialgleichung ist gegeben durch @@ -32,14 +31,14 @@ zuerst von Yacovlevich Sonine (1849 - 1915) beschrieben, aber aufgrund ihrer Ähnlichkeit nach Laguerre benannt. Die klassische Laguerre-Diffentialgleichung erhält man, wenn $\nu = 0$. -{\subsection{Potenzreihenansatz} +\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. Wir stellen die Vermutung auf, dass die Lösungen orthogonale Polynome sind. -Die Orthogonalität der Lösung werden wir im +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. @@ -49,7 +48,7 @@ Der Potenzreihenansatz ist gegeben als % erscheint dieser Ansatz sinnvoll. \begin{align*} y(x) -& = + & = \sum_{k=0}^\infty a_k x^k % \\ . @@ -57,13 +56,13 @@ y(x) 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} @@ -71,7 +70,7 @@ y''(x) \end{align*} \subsection{Lösen der Laguerre-Differentialgleichung} -Setzt man nun den Potenzreihenansatz in +Setzt man nun den Potenzreihenansatz in \eqref{laguerre:dgl} %die Differentialgleichung ein, @@ -106,7 +105,8 @@ denn für $k=n$ wird $a_{n+1} = 0$ und damit auch $a_{n+2}=a_{n+3}=\ldots=0$. 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 $a_1, a_2, a_3$ +Wählen wir nun $a_0 = 1$, dann folgt für die Koeffizienten +% $a_1, a_2, a_3$ \begin{align*} a_1 = @@ -136,8 +136,10 @@ k & >n: & a_k & = -0. +0 +. \end{align*} +Die Koeffizienten wechseln also für $k \leq n$ das Vorzeichen. Somit erhalten wir für $\nu = 0$ die Laguerre-Polynome \begin{align} L_n(x) @@ -174,11 +176,11 @@ 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} +Abschnitt \ref{buch:funktionentheorie:subsection:dglsing} im ersten Teil des Buches finden. -Nach einigen aufwändigen Rechnungen, +Nach einigen aufwändigen Rechnungen, % die am besten ein Computeralgebrasystem übernimmt, -die den Rahmen dieses Kapitel sprengen würden, +die den Rahmen dieses Kapitels sprengen würden, erhalten wir \begin{align*} \Xi_n diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 55d2276..6ba9135 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -90,6 +90,7 @@ S & = 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 @@ -133,7 +134,7 @@ deshalb ist die Laguerre-Gewichtsfunktion nur geeignet für den Definitionsbereich $(0, \infty)$. \subsubsection{Randbedingungen} -Bleibt nur noch sicherzustellen, dass die Randbedingungen, +Bleibt nur noch sicherzustellen, dass die Randbedingungen \begin{align} k_0 y(0) + h_0 p(0)y'(0) & = diff --git a/buch/papers/laguerre/gamma.tex b/buch/papers/laguerre/gamma.tex index e40d8ca..0cf17b9 100644 --- a/buch/papers/laguerre/gamma.tex +++ b/buch/papers/laguerre/gamma.tex @@ -25,7 +25,7 @@ markant verbessern können. % wenden wir dann die Gauss-Laguerre-Quadratur auf die Gamma-Funktion und % erweitern die Methode -{\subsection{Gamma-Funktion} +\subsection{Gamma-Funktion% \label{laguerre:subsection:gamma}} Die Gamma-Funktion ist eine Erweiterung der Fakultät auf die reale und komplexe Zahlenmenge. @@ -44,11 +44,11 @@ Integral der Form . \end{align} Der Term $e^{-x}$ im Integranden und der Integrationsbereich erfüllen -genau die Bedingungen der Laguerre-Integration. +genau die Bedingungen der Gauss-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 assoziierte Laguerre-Integration die -Gewichtsfunktion $x^\nu e^{-x}$ exakt dem Integranden +Weiter zu erwähnen ist, dass für die assoziierte Gauss-Laguerre-Integration die +Gewichtsfunktion $x^\nu e^{-x}$ exakt dem Integranden für $\nu = z - 1$ entspricht. \subsubsection{Funktionalgleichung} @@ -84,10 +84,11 @@ 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 +dass sich die Gamma-Funktion bestens für die Gauss-Laguerre-Quadratur \begin{align*} \int_0^\infty x^{z-1} e^{-x} \, dx = @@ -169,16 +170,6 @@ Somit entscheiden wir uns aufgrund der vorherigen Punkte, 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 -\begin{align} -\Gamma(z) -\approx -\sum_{i=1}^n x_i^{z-1} A_i. -\label{laguerre:naive_lag} -\end{align} % \begin{figure} \centering @@ -186,10 +177,22 @@ ergibt sich \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} +für verschiedene reelle Werte von $z$ und Grade $n$ der +Laguerre-Polynome}% \label{laguerre:fig:rel_error_simple} \end{figure} -% +%. +Wenden wir also die Gauss-Laguerre-Quadratur aus +\eqref{laguerre:laguerrequadratur} auf die Gamma-Funktion +\eqref{laguerre:gamma} an, +ergibt sich +\begin{align} +\Gamma(z) +\approx +\sum_{i=1}^n x_i^{z-1} A_i +\label{laguerre:naive_lag} +. +\end{align} 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 @@ -220,8 +223,8 @@ 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 direkt die Gauss-Laguerre-Quadratur auf die Gamma-Funktion -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 $L_n$. @@ -229,18 +232,17 @@ 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 $z \leq 2n$. -Laut der Theorie der Gauss-Quadratur auch ist das zu erwarten, +Laut der Theorie der Gauss-Quadratur ist das auch 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. +exakt ist für zu integrierende Polynome mit Grad $\leq 2n-1$ und +der Integrand $x^{z-1}$ wird für $z \in \mathbb{N} \setminus \{0\}$ +zu einem Polynom . +% Hinzukommt, dass zudem von $z$ noch $1$ abgezogen wird im Exponenten. Es ist ersichtlich, 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 verwenden. \begin{figure} \centering @@ -248,10 +250,12 @@ könnten wir die Reflektionsformel der Gamma-Funktion verwenden. \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} +für verschiedene reelle Werte von $z$ und Grade $n$ der Laguerre-Polynome} \label{laguerre:fig:rel_error_mirror} \end{figure} +Um die linke Hälfte in den Griff zu bekommen, +könnten wir die Reflektionsformel der Gamma-Funktion verwenden. 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}. @@ -269,9 +273,10 @@ 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, -damit wir ihn besser verstehen und -dadurch geeignete Gegenmassnahmen zu entwickeln können. +Darum möchten wir ihn jetzt analysieren, +damit wir ihn besser verstehen können. +Dies sollte es uns ermöglichen, +anschliessend geeignete Gegenmassnahmen zu entwickeln. % Dieser Abschnitt soll eine grafisches Verständnis dafür schaffen, % wieso der Integrand so problematisch ist. @@ -311,16 +316,17 @@ dass kleine Exponenten um $0$ genauere Resultate liefern sollten. 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 $x^{z-1} e^{-x}$ +und erhalten so wieder den kompletten Integranden $x^{z} e^{-x}$ 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 $e^{-x}$, +Um $x = 1$ wächst der Term $x^z$ für positive $z$ +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. +Kleine positive $z$ scheinen nun aber auch zulässig zu sein. Damit formulieren wir die Vermutung, dass $a(n)$, welches das Intervall $[a(n), a(n) + 1]$ definiert, @@ -416,7 +422,8 @@ können die Intervalle $[a(n), a(n)+1]$ empirisch gesucht werden. Wir bestimmen nun die optimalen Verschiebungsterme empirisch 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. +reicht es, +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. In $n$-Richtung lässt sich eine klare lineare Abhängigkeit erkennen und @@ -481,7 +488,7 @@ dann beim Übergang auf die orange Linie wechselt. \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 $m$. +für verschiedene reelle 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} @@ -520,7 +527,7 @@ Abbildung~\ref{laguerre:fig:rel_error_range}. \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 Laguerre-Polynome vom Grad $n$} +für verschiedene reelle Werte von $z$ und Laguerre-Polynome vom Grad $n$} \label{laguerre:fig:rel_error_range} \end{figure} @@ -569,14 +576,14 @@ 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 eine Genauigkeit von $13$ -korrekten, signifikanten Stellen für reele Argumente. +korrekten, signifikanten Stellen für reelle Argumente. Zum Vergleich: die vorgestellte Methode erreicht für $n = 7$ eine minimale Genauigkeit von $6$ korrekten, signifikanten Stellen -für reele Argumente. +für reelle Argumente. \subsubsection{Fazit} % Das Resultat ist etwas enttäuschend, -Die Genauigkeit der vorgestellten Methode schneidet somit schlechter ab, +Die Genauigkeit der vorgestellten Methode schneidet somit schlechter ab als die Lanczos-Methode. Dieser Erkenntnis kommt nicht ganz unerwartet, % aber nicht unerwartet, @@ -595,6 +602,6 @@ nur $n$ Funktionsevaluationen und wenige zusätzliche Multiplikationen und Additionen. Demzufolge könnte diese Methode Anwendung in Systemen mit wenig Rechenleistung und/oder knappen Energieressourcen finden. -Die vorgestellte Methode ist ein weiteres Beispiel dafür, -wie Verfahren durch die Kenntnis der Eigenschaften einer Funktion +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/main.tex b/buch/papers/laguerre/main.tex index 91c1475..133d686 100644 --- a/buch/papers/laguerre/main.tex +++ b/buch/papers/laguerre/main.tex @@ -8,24 +8,27 @@ \begin{refsection} \chapterauthor{Patrik Müller} -{\parindent0pt Die} Laguerre\--Polynome, +{\parindent0pt Die} Laguerre\--Polynome, 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 +sind Lösungen der ebenfalls nach %Laguerre +ihm +benannten Differentialgleichung. +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, +Darum möchten wir uns in diesem Kapitel, ganz im Sinne des Entdeckers, -den Laguerre-Polynomen für Approximationen von Integralen mit -exponentiell-abfallenden Funktionen widmen. +den Laguerre-Polynomen für Approximationen von Integralen mit +exponentiell abfallenden Funktionen widmen. Namentlich werden wir versuchen, mittels Laguerre-Polynomen und -der Gauss-Quadratur eine geeignete Approximation für die Gamma-Funktion zu finden. +der Gauss-Quadratur eine geeignete Approximation für die Gamma-Funktion zu +finden. -Laguerre-Polynome tauchen zudem auch in der Quantenmechanik im radialen Anteil +Laguerre-Polynome tauchen zudem auch in der Quantenmechanik im radialen Anteil der Lösung für die Schrödinger-Gleichung eines Wasserstoffatoms auf. \input{papers/laguerre/definition} diff --git a/buch/papers/laguerre/presentation/sections/gamma_approx.tex b/buch/papers/laguerre/presentation/sections/gamma_approx.tex index 811fbfa..b5e1131 100644 --- a/buch/papers/laguerre/presentation/sections/gamma_approx.tex +++ b/buch/papers/laguerre/presentation/sections/gamma_approx.tex @@ -51,7 +51,7 @@ R_n(\xi) % \scalebox{0.91}{\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 +\caption{Relativer Fehler des einfachen Ansatzes für verschiedene reelle Werte von $z$ und Grade $n$ der Laguerre-Polynome} \end{figure} diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex index 841bc20..0e32012 100644 --- a/buch/papers/laguerre/quadratur.tex +++ b/buch/papers/laguerre/quadratur.tex @@ -16,7 +16,7 @@ verwendet. Stellt man also sicher, dass ein Verfahren gut für Polynome funktioniert, sollte es auch für andere Funktionen angemessene Resultate liefern. -Es wird ein Polynom verwendet, +Es wird ein Interpolationspolynom 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 @@ -66,10 +66,11 @@ gegen $0$ konvergiert als jedes Polynom. % $L_n$ ausweiten. % Diese sind orthogonal im Intervall $(0, \infty)$ bezüglich % der Gewichtsfunktion $e^{-x}$. -Um also das Integral einer Funktion $g(x)$ im Intervall~$(0,\infty)$ zu berechen, +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 g(x) \, dx = \int_0^\infty f(x) e^{-x} \, dx \end{align*} @@ -77,7 +78,7 @@ 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 +Die Gleichung~\eqref{laguerre:gaussquadratur} wird also für die Gauss-Laguerre-Quadratur zu \begin{align} \int_{0}^{\infty} f(x) e^{-x} dx @@ -89,8 +90,8 @@ für die Gauss-Laguerre-Quadratur zu \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 +des Approximationspolynoms genommen werden. +Für das Laguerre-Polynom $L_n(x)$ müssen demnach dessen Nullstellen $x_i$ und als Gewichte $A_i$ die Integrale von $l_i(x) e^{-x}$ verwendet werden. Dabei sind \begin{align*} @@ -104,7 +105,7 @@ l_i(x_j) \end{cases} % . \end{align*} -die Lagrangschen Interpolationspolynome. +die Lagrangeschen Interpolationspolynome. Laut \cite{laguerre:hildebrand2013introduction} können die Gewichte mit \begin{align*} A_i @@ -122,7 +123,9 @@ des orthogonalen Polynoms $\phi_n(x)$, $\forall i =0,\ldots,n$ und dem Normalisierungsfaktor. Wir setzen nun $\phi_n(x) = L_n(x)$ und -nutzen den Vorzeichenwechsel der Laguerre-Koeffizienten aus, +nutzen den Vorzeichenwechsel der Laguerre-Koeffizienten +(ersichtlich am Term $(-1)^k$ in \eqref{laguerre:polynom}) +aus, damit erhalten wir \begin{align*} A_i -- cgit v1.2.1 From 02fad480aad27d6d2fa1192eeab5c6654557b884 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 26 Jul 2022 09:31:35 +0200 Subject: svae between --- buch/papers/fm/01_AM-FM.tex | 37 ++++++++++++++++++++++--------------- buch/papers/fm/main.tex | 2 +- buch/papers/fm/references.bib | 11 +++++++++++ 3 files changed, 34 insertions(+), 16 deletions(-) (limited to 'buch') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index ef55d55..2267d39 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -7,30 +7,37 @@ \rhead{AM- FM} Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot cos(\omega_c(t)+\varphi)\). +\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). 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. +Jedoch ist das für die Vielfalt 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. +mit der Ableitung der Phase\cite{fm:NAT}. +Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, +die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): \newline \newline -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. - +To do: Bilder jeder Modulationsart +\subsection{AM - Amplitudenmodulation} +Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideeen in FM. +Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal +\[ + x_c(t) = A_c \cdot \cos(\omega_ct). +\] +Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt +und das Trägersignal nur zwei komplexe Schwingungen besitzt. +Dies sieht man besonders in der Eulerischen Formel +\[ + x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. +\] +Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +\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 fcf4d1a..6af3386 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -27,7 +27,7 @@ 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. +Nun zur Modulation im nächsten Abschnitt.\cite{fm:NAT} \input{papers/fm/01_AM-FM.tex} \input{papers/fm/02_frequenzyspectrum.tex} diff --git a/buch/papers/fm/references.bib b/buch/papers/fm/references.bib index 76eb265..21b910b 100644 --- a/buch/papers/fm/references.bib +++ b/buch/papers/fm/references.bib @@ -23,6 +23,17 @@ volume = {2} } +@book{fm:NAT, + title = {Nachrichtentechnik 1 + 2}, + author = {Thomas Kneubühler}, + publisher = {None}, + year = {2021}, + isbn = {}, + inseries = {Script for students}, + volume = {} +} + + @article{fm:mendezmueller, author = { Tabea Méndez and Andreas Müller }, title = { Noncommutative harmonic analysis and image registration }, -- cgit v1.2.1 From a5b1d13fd6d9d5df3d7289093e57cf67ae5cb81c Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Tue, 26 Jul 2022 15:04:22 +0200 Subject: Kapitel TODOs --- buch/papers/fm/01_AM-FM.tex | 4 +++ buch/papers/fm/02_frequenzyspectrum.tex | 2 ++ buch/papers/fm/03_bessel.tex | 24 ++++++---------- buch/papers/fm/04_fazit.tex | 32 ++------------------- buch/papers/fm/FM presentation/A2-14.pdf | Bin 0 -> 259673 bytes buch/papers/fm/FM presentation/FM_presentation.pdf | Bin 0 -> 357597 bytes ...quency modulation (FM) and Bessel functions.pdf | Bin 0 -> 159598 bytes ...l2022_Book_H\303\266hereMathematikImAlltag.pdf" | Bin 0 -> 4118379 bytes 8 files changed, 17 insertions(+), 45 deletions(-) create mode 100644 buch/papers/fm/FM presentation/A2-14.pdf create mode 100644 buch/papers/fm/FM presentation/FM_presentation.pdf create mode 100644 buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf create mode 100644 "buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" (limited to 'buch') diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex index 2267d39..163c792 100644 --- a/buch/papers/fm/01_AM-FM.tex +++ b/buch/papers/fm/01_AM-FM.tex @@ -38,6 +38,10 @@ Dies sieht man besonders in der Eulerischen Formel x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. \] Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. +\newline \newline TODO: Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] +so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). +Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] diff --git a/buch/papers/fm/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex index 1c6044d..80e1c65 100644 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ b/buch/papers/fm/02_frequenzyspectrum.tex @@ -7,7 +7,9 @@ \label{fm:section:teil1}} \rhead{Problemstellung} +TODO Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. +Somit auch die Herleitung des Frequenzspektrum. %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 diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index fdaa0d1..aed084e 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -7,22 +7,16 @@ \label{fm:section:teil2}} \rhead{Teil 2} + +TODO 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? -% +\begin{itemize} + \item Zuerest einmal die Herleitung von FM zu der Besselfunktion + \item Im Frequenzspektrum darstellen mit Farben, ersichtlich machen. + \item Parameter tuing der Trägerfrequenz, Modulierende frequenz und Beta. +\end{itemize} + + %\subsection{De finibus bonorum et malorum %\label{fm:subsection:bonorum}} diff --git a/buch/papers/fm/04_fazit.tex b/buch/papers/fm/04_fazit.tex index 8c6c002..8d5eca4 100644 --- a/buch/papers/fm/04_fazit.tex +++ b/buch/papers/fm/04_fazit.tex @@ -6,35 +6,7 @@ \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. + +TODO Anwendungen erklären und Sinn des Ganzen. diff --git a/buch/papers/fm/FM presentation/A2-14.pdf b/buch/papers/fm/FM presentation/A2-14.pdf new file mode 100644 index 0000000..7348cca Binary files /dev/null and b/buch/papers/fm/FM presentation/A2-14.pdf differ diff --git a/buch/papers/fm/FM presentation/FM_presentation.pdf b/buch/papers/fm/FM presentation/FM_presentation.pdf new file mode 100644 index 0000000..496e35e Binary files /dev/null and b/buch/papers/fm/FM presentation/FM_presentation.pdf differ diff --git a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf new file mode 100644 index 0000000..a6e701c Binary files /dev/null and b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel 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Fachhochschule} + \date{16.5.2022} + \subject{Mathematisches Seminar - Spezielle Funktionen} + %\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/FM presentation/Frequency modulation (FM) and Bessel functions.pdf b/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf deleted file mode 100644 index a6e701c..0000000 Binary files a/buch/papers/fm/FM presentation/Frequency modulation (FM) and Bessel functions.pdf and /dev/null differ diff --git a/buch/papers/fm/FM presentation/README.txt b/buch/papers/fm/FM presentation/README.txt new file mode 100644 index 0000000..65f390d --- /dev/null +++ b/buch/papers/fm/FM presentation/README.txt @@ -0,0 +1 @@ +Dies ist die Presentation des FM - Bessel \ No newline at end of file diff --git "a/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" "b/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" deleted file mode 100644 index 2a0bddd..0000000 Binary files "a/buch/papers/fm/FM presentation/Seydel2022_Book_H\303\266hereMathematikImAlltag.pdf" and 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\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 deleted file mode 100644 index a6e701c..0000000 Binary files a/buch/papers/fm/RS presentation/Frequency modulation (FM) and Bessel functions.pdf and /dev/null differ diff --git a/buch/papers/fm/RS presentation/README.txt b/buch/papers/fm/RS presentation/README.txt deleted file mode 100644 index 4d0620f..0000000 --- a/buch/papers/fm/RS presentation/README.txt +++ /dev/null @@ -1 +0,0 @@ -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 deleted file mode 100644 index 8a67619..0000000 --- a/buch/papers/fm/RS presentation/RS.tex +++ /dev/null @@ -1,123 +0,0 @@ -%% !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- Spezielle Funktionen} - %\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(\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} - -%------------------------------------------------------------------------------- -\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[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\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 presentation/images/100HZ.png deleted file mode 100644 index 371b9bf..0000000 Binary files a/buch/papers/fm/RS presentation/images/100HZ.png and 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files changed, 255 insertions(+), 85 deletions(-) (limited to 'buch') diff --git a/buch/papers/0f1/references.bib b/buch/papers/0f1/references.bib index fb9cd8b..2d3f874 100644 --- a/buch/papers/0f1/references.bib +++ b/buch/papers/0f1/references.bib @@ -4,32 +4,78 @@ % (c) 2020 Autor, Hochschule Rapperswil % -@online{0f1:bibtex, - title = {BibTeX}, - url = {https://de.wikipedia.org/wiki/BibTeX}, - date = {2020-02-06}, - year = {2020}, - month = {2}, - day = {6} +@online{0f1:library-gsl, + title = {GNU Scientific Library}, + url ={https://www.gnu.org/software/gsl/}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {19} } -@book{0f1: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} +@online{0f1:wiki-airyFunktion, + title = {Airy-Funktion}, + url ={https://de.wikipedia.org/wiki/Airy-Funktion}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {25} } -@article{0f1: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{0f1:wiki-kettenbruch, + title = {Kettenbruch}, + url ={https://de.wikipedia.org/wiki/Kettenbruch}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {25} } +@online{0f1:double, + title = {C - Data Types}, + url ={https://www.tutorialspoint.com/cprogramming/c_data_types.htm}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {25} +} + +@online{0f1:wolfram-0f1, + title = {Hypergeometric 0F1}, + url ={https://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=Hypergeometric0F1}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {25} +} + +@online{0f1:wiki-fraction, + title = {Gauss continued fraction}, + url ={https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {25} +} + +@book{0f1:SeminarNumerik, + title = {Mathematisches Seminar Numerik}, + author = {Andreas Müller, Benjamin Bouhafs-Keller, Daniel Bucher, Manuel Cattaneo +Patrick Elsener, Reto Fritsche, Niccolò Galliani, Tobias Grab +Thomas Kistler, Fabio Marti, Joël Rechsteiner, Cédric Renda +Michael Schmid, Mike Schmid, Michael Schneeberger +Martin Stypinski, Manuel Tischhauser, Nicolas Tobler +Raphael Unterer, Severin Weiss}, + publisher = {Andreas Müller}, + year = {2022}, +} + +@article{0f1:kettenbrueche, + author = { Benjamin Bouhafs-Keller }, + title = { Kettenbrüche }, + journal = { Mathematisches Seminar Numerik }, + year = 2020, + volume = 13, + pages = {363--376}, + url = {https://github.com/AndreasFMueller/SeminarNumerik} +} \ No newline at end of file diff --git a/buch/papers/0f1/teil0.tex b/buch/papers/0f1/teil0.tex index bfc265f..780d432 100644 --- a/buch/papers/0f1/teil0.tex +++ b/buch/papers/0f1/teil0.tex @@ -7,7 +7,7 @@ \rhead{Ausgangslage} Die Hypergeometrische Funktion $\mathstrut_0F_1$ wird in vielen Funktionen als Basisfunktion benutzt, zum Beispiel um die Airy Funktion zu berechnen. -In der GNU Scientific Library \cite{library-gsl} +In der GNU Scientific Library \cite{0f1:library-gsl} ist die Funktion $\mathstrut_0F_1$ vorhanden. Allerdings wirft die Funktion, bei negativen Übergabenwerten wie zum Beispiel \verb+gsl_sf_hyperg_0F1(1, -1)+, eine Exception. Bei genauerer Untersuchung hat sich gezeigt, dass die Funktion je nach Betriebssystem funktioniert oder eben nicht. diff --git a/buch/papers/0f1/teil1.tex b/buch/papers/0f1/teil1.tex index 910e8bb..2a60737 100644 --- a/buch/papers/0f1/teil1.tex +++ b/buch/papers/0f1/teil1.tex @@ -6,16 +6,40 @@ \section{Mathematischer Hintergrund \label{0f1:section:mathHintergrund}} \rhead{Mathematischer Hintergrund} +Basierend auf den Herleitungen des vorhergehenden Kapitels \ref{buch:rekursion:section:hypergeometrische-funktion} +und dem Seminarbuch Numerik \cite{0f1:kettenbrueche}, werden im nachfolgenden Abschnitt nochmals die Resultate +beschrieben. + +\subsection{Hypergeometrische Funktion +\label{0f1:subsection:hypergeometrisch}} +Als Grundlage der umgesetzten Algorithmen dient die Hypergeometrische Funktion $\mathstrut_0F_1$. Diese ist eine Unterfunktion der allgemein definierten Funktion $\mathstrut_pF_q$. -\subsection{Hypergeometrische Funktion $\mathstrut_0F_1$ -\label{0f1:subsection:0f1}} -Wie in Kapitel \ref{buch:rekursion:section:hypergeometrische-funktion} beschrieben, -wird die Funktion $\mathstrut_0F_1$ folgendermassen definiert. \begin{definition} - \label{0f1:rekursion:hypergeometrisch:def} - Die hypergeometrische Funktion - $\mathstrut_0F_1$ ist definiert durch die Reihe - \[ + \label{0f1:math:qFp:def} + Die hypergeometrische Funktion + $\mathstrut_pF_q$ ist definiert durch die Reihe + \[ + \mathstrut_pF_q + \biggl( + \begin{matrix} + a_1,\dots,a_p\\ + b_1,\dots,b_q + \end{matrix} + ; + x + \biggr) + = + \mathstrut_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;x) + = + \sum_{k=0}^\infty + \frac{(a_1)_k\cdots(a_p)_k}{(b_1)_k\cdots(b_q)_k}\frac{x^k}{k!}. + \] +\end{definition} + +Angewendet auf die Funktion $\mathstrut_pF_q$ ergibt sich für $\mathstrut_0F_1$: + +\begin{equation} + \label{0f1:math:0f1:eq} \mathstrut_0F_1 \biggl( \begin{matrix} @@ -29,26 +53,29 @@ wird die Funktion $\mathstrut_0F_1$ folgendermassen definiert. \mathstrut_0F_1(;b_1;x) = \sum_{k=0}^\infty - \frac{1}{(b_1)_k}\frac{x^k}{k!}. - \] -\end{definition} + \frac{x^k}{(b_1)_k \cdot k!}. +\end{equation} + + \subsection{Airy Funktion \label{0f1:subsection:airy}} -Wie in \ref{buch:differentialgleichungen:section:hypergeometrisch} dargestellt, ist die Airy-Differentialgleichung -folgendermassen definiert. +Die Airy-Funktion $Ai(x)$ und die verwandte Funktion $Bi(x)$ werden als Airy-Funktion bezeichnet. Sie werden zur Lösung verschiedener physikalischer Probleme benutzt, wie zum Beispiel zur Lösung der Schrödinger-Gleichung. \cite{0f1:wiki-airyFunktion} + \begin{definition} - y'' - xy = 0 - \label{0f1:airy:eq:differentialgleichung} + \label{0f1:airy:differentialgleichung:def} + Die Differentialgleichung + $y'' - xy = 0$ + heisst die {\em Airy-Differentialgleichung}. \cite{0f1:wiki-airyFunktion} \end{definition} -Daraus ergibt sich wie in Aufgabe~\ref{503} gefundenen Lösungen der -Airy-Differentialgleichung als hypergeometrische Funktionen. +Die Airy Funktion lässt sich auf verschiedene Arten darstellen. \cite{0f1:wiki-airyFunktion} +Als hypergeometrische Funktion berechnet, ergibt sich wie in Kapitel \ref{buch:differentialgleichungen:section:hypergeometrisch} hergeleitet, folgende Lösungen der Airy-Differentialgleichung zu den Anfangsbedingungen $A(0)=1$ und $A'(0)=0$, sowie $B(0)=0$ und $B'(0)=0$. - -\begin{align*} -y_1(x) +\begin{align} +\label{0f1:airy:hypergeometrisch:eq} +Ai(x) = \sum_{k=0}^\infty \frac{1}{(\frac23)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k @@ -57,7 +84,7 @@ y_1(x) \begin{matrix}\text{---}\\\frac23\end{matrix};\frac{x^3}{9} \biggr). \\ -y_2(x) +Bi(x) = \sum_{k=0}^\infty \frac{1}{(\frac43)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k @@ -67,14 +94,9 @@ x\cdot\mathstrut_0F_1\biggl( \frac{x^3}{9} \biggr). \qedhere -\end{align*} +\end{align} + +In diesem speziellem Fall wird die Airy Funktion $Ai(x)$ \eqref{0f1:airy:hypergeometrisch:eq} +benutzt, um die Stabilität der Algorithmen zu $\mathstrut_0F_1$ zu überprüfen. -\begin{figure} - \centering - \includegraphics{papers/0f1/images/airy.pdf} - \caption{Plot der Lösungen der Airy-Differentialgleichung $y''-xy=0$ - zu den Anfangsbedingungen $y(0)=1$ und $y'(0)=0$ in {\color{red}rot} - und $y(0)=0$ und $y'(0)=1$ in {\color{blue}blau}. - \label{0f1:airy:plot:vorgabe}} -\end{figure} \ No newline at end of file diff --git a/buch/papers/0f1/teil2.tex b/buch/papers/0f1/teil2.tex index 07e17c0..446bc93 100644 --- a/buch/papers/0f1/teil2.tex +++ b/buch/papers/0f1/teil2.tex @@ -6,56 +6,158 @@ \section{Umsetzung \label{0f1:section:teil2}} \rhead{Umsetzung} -Zur Umsetzung wurden drei Ansätze gewählt und -Die Unterprogramme wurde jeweils, wie die GNU Scientific Library, in C geschrieben. +Zur Umsetzung wurden drei verschiedene Ansätze gewählt. Dabei wurde der Schwerpunkt auf die Funktionalität und eine gute Lesbarkeit des Codes gelegt. +Die Unterprogramme wurde jeweils, wie die GNU Scientific Library, in C geschrieben. Die Zwischenresultate wurden vom Hauptprogramm in einem CSV-File gespeichert. Anschliessen wurde mit der Matplot-Libray in Python die Resultate geplottet. \subsection{Potenzreihe \label{0f1:subsection:potenzreihe}} -Die naheliegendste Lösung ist die Programmierung der Potenzreihe. +Die naheliegendste Lösung ist die Programmierung der Potenzreihe. Allerdings ist ein Problem dieser Umsetzung \ref{0f1:listing:potenzreihe}, dass die Fakultät im Nenner schnell grosse Werte annimmt und so der Bruch gegen Null strebt. Spätesten ab $k=167$ stösst diese Umsetzung \eqref{0f1:umsetzung:0f1:eq} an ihre Grenzen, da die Fakultät von $168$ eine Bereichsüberschreitung des \textit{double} Bereiches darstellt. \cite{0f1:double} -\begin{equation} - \label{0f1:rekursion:hypergeometrisch:eq} +\begin{align} + \label{0f1:umsetzung:0f1:eq} \mathstrut_0F_1(;b;z) - = + &= \sum_{k=0}^\infty \frac{z^k}{(b)_k \cdot k!} -\end{equation} + &= + \frac{1}{b} + +\frac{z^1}{(1+b) \cdot 1} + + \cdots + + \frac{z^{20}}{(20+b) \cdot 2.4 \cdot 10^{18}} +\end{align} -\lstinputlisting[style=C,float,caption={Rekursivformel für Kettenbruch.},label={0f1:listing:potenzreihe}]{papers/0f1/listings/potenzreihe.c} +\lstinputlisting[style=C,float,caption={Potenzreihe.},label={0f1:listing:potenzreihe}]{papers/0f1/listings/potenzreihe.c} \subsection{Kettenbruch \label{0f1:subsection:kettenbruch}} Ein endlicher Kettenbruch ist ein Bruch der Form +\begin{equation*} +a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{b_3}{a_3+\cdots}}} +\end{equation*} +in welchem $a_0, a_1,\dots,a_n$ und $b_1,b_2,\dots,b_n$ ganze Zahlen darstellen. + +Die Kurzschreibweise für einen allgemeinen Kettenbruch ist +\begin{equation*} + a_0 + \frac{a_1|}{|b_1} + \frac{a_2|}{|b_2} + \frac{a_3|}{|b_3} + \cdots +\end{equation*} +und ist somit verknüpfbar mit der Potenzreihe. +\cite{0f1:wiki-kettenbruch} + +Angewendet auf die Funktion $\mathstrut_0F_1$ bedeutet dies: +\begin{equation*} + \mathstrut_0F_1(;b;z) = 1 + \frac{z}{a1!} + \frac{z^2}{a(a+1)2!} + \frac{z^3}{a(a+1)(a+2)3!} + \cdots +\end{equation*} +\cite{0f1:wiki-fraction} + +Nach allen Umformungen ergibt sich folgender, irregulärer Kettenbruch \eqref{0f1:math:kettenbruch:0f1:eq} \begin{equation} -a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{n-1}}{a_{n-1} + \cfrac{b_n}{a_n}}}}} + \label{0f1:math:kettenbruch:0f1:eq} + \mathstrut_0F_1(;b;z) = 1 + \cfrac{\cfrac{z}{b}}{1+\cfrac{-\cfrac{z}{2(1+b)}}{1+\cfrac{z}{2(1+b)}+\cfrac{-\cfrac{z}{3(2+b)}}{1+\cfrac{z}{5(4+b)} + \cdots}}}, \end{equation} -in welchem $a_0, a_1,\dots,a_n$ und $b_1,b_2,\dots,b_n$ ganze Zahlen -darstellen. +der als Code \ref{0f1:listing:kettenbruchIterativ} umgesetzt wurde. +\cite{0f1:wolfram-0f1} -{\color{red}TODO: Bessere Beschreibung mit Verknüpfung zur Potenzreihe} +\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}]{papers/0f1/listings/kettenbruchIterativ.c} -%Gauss hat durch - -\lstinputlisting[style=C,float,caption={Rekursivformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}]{papers/0f1/listings/kettenbruchIterativ.c} \subsection{Rekursionsformel \label{0f1:subsection:rekursionsformel}} -Wesentlich effizienter zur Berechnung eines Kettenbruches ist die Rekursionsformel. +Wesentlich stabiler zur Berechnung eines Kettenbruches ist die Rekursionsformel. Nachfolgend wird die verkürzte Herleitung vom Kettenbruch zur Rekursionsformel aufgezeigt. Eine vollständige Schritt für Schritt Herleitung ist im Seminarbuch Numerik, im Kapitel Kettenbrüche zu finden. \cite{0f1:kettenbrueche}) + +\subsubsection{Verkürzte Herleitung} +Ein Näherungsbruch in der Form +\begin{align*} + \cfrac{A_k}{B_k} = a_k + \cfrac{b_{k + 1}}{a_{k + 1} + \cfrac{p}{q}} +\end{align*} +lässt sich zu +\begin{align*} + \cfrac{A_k}{B_k} = \cfrac{b_{k+1}}{a_{k+1} + \cfrac{p}{q}} = \frac{b_{k+1} \cdot q}{a_{k+1} \cdot q + p} +\end{align*} +umformen. +Dies lässt sich auch durch die folgende Matrizenschreibweise ausdrücken: +\begin{equation*} + \begin{pmatrix} + A_k\\ + B_k + \end{pmatrix} + = \begin{pmatrix} + b_{k+1} \cdot q\\ + a_{k+1} \cdot q + p + \end{pmatrix} + =\begin{pmatrix} + 0& b_{k+1}\\ + 1& a_{k+1} + \end{pmatrix} + \begin{pmatrix} + p \\ + q + \end{pmatrix}. + %\label{0f1:math:rekursionsformel:herleitung} +\end{equation*} + +Wendet man dies nun auf den Kettenbruch in der Form +\begin{equation*} + \frac{A_k}{B_k} = a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{k-1}}{a_{k-1} + \cfrac{b_k}{a_k}}}}} +\end{equation*} +an, ergibt sich folgende Matrixdarstellungen: \begin{align*} -\frac{A_n}{B_n} -= -a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{n-1}}{a_{n-1} + \cfrac{b_n}{a_n}}}}} + \begin{pmatrix} + A_k\\ + B_k + \end{pmatrix} + &= + \begin{pmatrix} + 1& a_0\\ + 0& 1 + \end{pmatrix} + \begin{pmatrix} + 0& b_1\\ + 1& a_1 + \end{pmatrix} + \cdots + \begin{pmatrix} + 0& b_{k-1}\\ + 1& a_{k-1} + \end{pmatrix} + \begin{pmatrix} + b_k\\ + a_k + \end{pmatrix} \end{align*} -Die Berechnung von $A_n, B_n$ kann man auch ohne die Matrizenschreibweise -aufschreiben: +Nach vollständiger Induktion ergibt sich für den Schritt $k$, die Matrix +\begin{equation} + \label{0f1:math:matrix:ende:eq} + \begin{pmatrix} + A_{k}\\ + B_{k} + \end{pmatrix} + = + \begin{pmatrix} + A_{k-2}& A_{k-1}\\ + B_{k-2}& B_{k-1} + \end{pmatrix} + \begin{pmatrix} + b_k\\ + a_k + \end{pmatrix}. +\end{equation} + +Und Schlussendlich kann der Näherungsbruch +\[ +\frac{Ak}{Bk} +\] +berechnet werden. + + +\subsubsection{Lösung} +Die Berechnung von $A_k, B_k$ \eqref{0f1:math:matrix:ende:eq} kann man auch ohne die Matrizenschreibweise aufschreiben: \cite{0f1:wiki-fraction} \begin{itemize} -\item Start: +\item Startbedingungen: \begin{align*} A_{-1} &= 0 & A_0 &= a_0 \\ B_{-1} &= 1 & B_0 &= 1 \end{align*} -$\rightarrow$ 0-te Näherung: $\displaystyle\frac{A_0}{B_0} = a_0$ \item Schritt $k\to k+1$: \[ \begin{aligned} @@ -67,9 +169,10 @@ B_{k+1} &= B_{k-1} \cdot b_k + B_k \cdot a_k \end{aligned} \] \item -Näherungsbruch $n$: \qquad$\displaystyle\frac{A_n}{B_n}$ +Näherungsbruch: \qquad$\displaystyle\frac{A_k}{B_k}$ \end{itemize} -{\color{red}TODO: Verweis Numerik} +Ein grosser Vorteil dieser Umsetzung \ref{0f1:listing:kettenbruchRekursion} ist, dass im Vergleich zum Code \ref{0f1:listing:kettenbruchIterativ} eine Division gespart werden kann und somit weniger Folgefehler entstehen können. -\lstinputlisting[style=C,float,caption={Rekursivformel für Kettenbruch.},label={0f1:listing:kettenbruchRekursion}]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file +%Code +\lstinputlisting[style=C,float,caption={Iterativ umgesetzter Kettenbruch.},label={0f1:listing:kettenbruchRekursion}]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file diff --git a/buch/papers/0f1/teil3.tex b/buch/papers/0f1/teil3.tex index 44a4600..76d6e32 100644 --- a/buch/papers/0f1/teil3.tex +++ b/buch/papers/0f1/teil3.tex @@ -10,15 +10,14 @@ Im Verlauf des Seminares hat sich gezeigt, das ein einfacher mathematischer Algorithmus zu implementieren gar nicht so einfach ist. So haben alle drei umgesetzten Ansätze Probleme mit grossen negativen x in der Funktion $\mathstrut_0F_1(;b;x)$. Ebenso wird, je grösser der Wert x wird $\mathstrut_0F_1(;b;x)$, desto mehr weichen die berechneten Resultate -von den erwarteten ab. -{\color{red}TODO cite wolfram alpha rechner} +von den Erwarteten ab. \cite{0f1:wolfram-0f1} \subsection{Auswertung \label{0f1:subsection:auswertung}} \begin{figure} \centering \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzAiry.pdf} - \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion. + \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion zu den Anfangsbedingungen $y(0)=1$ und $y'(0)=0$. \label{0f1:ausblick:plot:airy:konvergenz}} \end{figure} @@ -52,6 +51,6 @@ von den erwarteten ab. \subsection{Ausblick \label{0f1:subsection:ausblick}} - - +Eine mögliche Lösung zum Problem ist \cite{0f1:SeminarNumerik} +{\color{red} TODO beschreiben Lösung} -- cgit v1.2.1 From 336251607dae5947b3690bbc91e4c57036910d7b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Tue, 26 Jul 2022 18:53:07 +0200 Subject: fix references.bib --- buch/papers/0f1/references.bib | 9 ++------- 1 file changed, 2 insertions(+), 7 deletions(-) (limited to 'buch') diff --git a/buch/papers/0f1/references.bib b/buch/papers/0f1/references.bib index 2d3f874..ce9b8da 100644 --- a/buch/papers/0f1/references.bib +++ b/buch/papers/0f1/references.bib @@ -60,12 +60,7 @@ @book{0f1:SeminarNumerik, title = {Mathematisches Seminar Numerik}, - author = {Andreas Müller, Benjamin Bouhafs-Keller, Daniel Bucher, Manuel Cattaneo -Patrick Elsener, Reto Fritsche, Niccolò Galliani, Tobias Grab -Thomas Kistler, Fabio Marti, Joël Rechsteiner, Cédric Renda -Michael Schmid, Mike Schmid, Michael Schneeberger -Martin Stypinski, Manuel Tischhauser, Nicolas Tobler -Raphael Unterer, Severin Weiss}, + author = {Andreas Müller et al}, publisher = {Andreas Müller}, year = {2022}, } @@ -78,4 +73,4 @@ Raphael Unterer, Severin Weiss}, volume = 13, pages = {363--376}, url = {https://github.com/AndreasFMueller/SeminarNumerik} -} \ No newline at end of file +} -- cgit v1.2.1 From c53e9fe25866376d1b3086579c01725444a04702 Mon Sep 17 00:00:00 2001 From: Fabian <@> Date: Tue, 26 Jul 2022 21:27:23 +0200 Subject: 0f1, Code ueberarbeitet --- buch/papers/0f1/listings/kettenbruchIterativ.c | 16 +++++-- buch/papers/0f1/listings/kettenbruchRekursion.c | 22 ++++++---- buch/papers/0f1/listings/potenzreihe.c | 56 +++++++++++++++++++++++++ buch/papers/0f1/teil2.tex | 6 +-- 4 files changed, 86 insertions(+), 14 deletions(-) (limited to 'buch') diff --git a/buch/papers/0f1/listings/kettenbruchIterativ.c b/buch/papers/0f1/listings/kettenbruchIterativ.c index befea8e..d897b8f 100644 --- a/buch/papers/0f1/listings/kettenbruchIterativ.c +++ b/buch/papers/0f1/listings/kettenbruchIterativ.c @@ -1,5 +1,13 @@ -static double fractionRekursion0f1(const double c, const double x, unsigned int n) +/** + * @brief Calculates the Hypergeometric Function 0F1(;b;z) + * @param b0 in 0F1(;b0;z) + * @param z in 0F1(;b0;z) + * @param n number of itertions (precision) + * @return Result + */ +static double fractionRekursion0f1(const double c, const double z, unsigned int n) { + //declaration double a = 0.0; double b = 0.0; double Ak = 0.0; @@ -21,15 +29,15 @@ static double fractionRekursion0f1(const double c, const double x, unsigned int else if (k == 1) { a = 1.0; //a1 - b = x/c; //b1 + b = z/c; //b1 //recursion fomula for A1, B1 Ak = a * Ak_1 + b * 1.0; Bk = a * Bk_1; } else { - a = 1 + (x / (k * ((k - 1) + c)));//ak - b = -(x / (k * ((k - 1) + c))); //bk + a = 1 + (z / (k * ((k - 1) + c)));//ak + b = -(z / (k * ((k - 1) + c))); //bk //recursion fomula for Ak, Bk Ak = a * Ak_1 + b * Ak_2; Bk = a * Bk_1 + b * Bk_2; diff --git a/buch/papers/0f1/listings/kettenbruchRekursion.c b/buch/papers/0f1/listings/kettenbruchRekursion.c index 958d4e1..143683f 100644 --- a/buch/papers/0f1/listings/kettenbruchRekursion.c +++ b/buch/papers/0f1/listings/kettenbruchRekursion.c @@ -1,18 +1,26 @@ -static double fractionIter0f1(const double b0, const double z, unsigned int n) +/** + * @brief Calculates the Hypergeometric Function 0F1(;c;z) + * @param c in 0F1(;c;z) + * @param z in 0F1(;c;z) + * @param k number of itertions (precision) + * @return Result + */ +static double fractionIter0f1(const double c, const double z, unsigned int k) { + //declaration double a = 0.0; double b = 0.0; - double abn = 0.0; + double abk = 0.0; double temp = 0.0; - for (; n > 0; --n) + for (; k > 0; --k) { - abn = z / (n * ((n - 1) + b0)); //abn = ak, bk + abk = z / (k * ((k - 1) + c)); //abk = ak, bk - a = n > 1 ? (1 + abn) : 1; //a0, a1 - b = n > 1 ? -abn : abn; //b1 + a = k > 1 ? (1 + abk) : 1; //a0, a1 + b = k > 1 ? -abk : abk; //b1 - temp = b / (a + temp); + temp = b / (a + temp); ////bk / (ak + last result) } return a + temp; //a0 + temp diff --git a/buch/papers/0f1/listings/potenzreihe.c b/buch/papers/0f1/listings/potenzreihe.c index bfaa0e3..3eb9b86 100644 --- a/buch/papers/0f1/listings/potenzreihe.c +++ b/buch/papers/0f1/listings/potenzreihe.c @@ -1,5 +1,61 @@ #include +/** + * @brief Calculates pochhammer + * @param (a+n-1)! + * @return Result + */ +static double pochhammer(const double x, double n) +{ + double temp = x; + + if (n > 0) + { + while (n > 1) + { + temp *= (x + n - 1); + --n; + } + + return temp; + } + else + { + return 1; + } +} + +/** + * @brief Calculates the Factorial + * @param n! + * @return Result + */ +static double fac(int n) +{ + double temp = n; + + if (n > 0) + { + while (n > 1) + { + --n; + temp *= n; + } + return temp; + } + else + { + return 1; + } +} + +/** + * @brief Calculates the Hypergeometric Function 0F1(;b;z) + * @param b0 in 0F1(;b0;z) + * @param z in 0F1(;b0;z) + * @param n number of itertions (precision) + * @return Result + */ static double powerseries(const double b, const double z, unsigned int n) { double temp = 0.0; diff --git a/buch/papers/0f1/teil2.tex b/buch/papers/0f1/teil2.tex index 446bc93..ca48e6e 100644 --- a/buch/papers/0f1/teil2.tex +++ b/buch/papers/0f1/teil2.tex @@ -26,7 +26,7 @@ Die naheliegendste Lösung ist die Programmierung der Potenzreihe. Allerdings is + \frac{z^{20}}{(20+b) \cdot 2.4 \cdot 10^{18}} \end{align} -\lstinputlisting[style=C,float,caption={Potenzreihe.},label={0f1:listing:potenzreihe}]{papers/0f1/listings/potenzreihe.c} +\lstinputlisting[style=C,float,caption={Potenzreihe.},label={0f1:listing:potenzreihe}, firstline=59]{papers/0f1/listings/potenzreihe.c} \subsection{Kettenbruch \label{0f1:subsection:kettenbruch}} @@ -57,7 +57,7 @@ Nach allen Umformungen ergibt sich folgender, irregulärer Kettenbruch \eqref{0f der als Code \ref{0f1:listing:kettenbruchIterativ} umgesetzt wurde. \cite{0f1:wolfram-0f1} -\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}]{papers/0f1/listings/kettenbruchIterativ.c} +\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}, firstline=8]{papers/0f1/listings/kettenbruchIterativ.c} \subsection{Rekursionsformel \label{0f1:subsection:rekursionsformel}} @@ -175,4 +175,4 @@ Näherungsbruch: \qquad$\displaystyle\frac{A_k}{B_k}$ Ein grosser Vorteil dieser Umsetzung \ref{0f1:listing:kettenbruchRekursion} ist, dass im Vergleich zum Code \ref{0f1:listing:kettenbruchIterativ} eine Division gespart werden kann und somit weniger Folgefehler entstehen können. %Code -\lstinputlisting[style=C,float,caption={Iterativ umgesetzter Kettenbruch.},label={0f1:listing:kettenbruchRekursion}]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file +\lstinputlisting[style=C,float,caption={Iterativ umgesetzter Kettenbruch.},label={0f1:listing:kettenbruchRekursion}, firstline=8]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file -- cgit v1.2.1 From 7a1207f6d66f245cda06e06ecbae1ec0d6a99b02 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 27 Jul 2022 00:14:54 +0200 Subject: eqref->ref, Improved some sentences --- buch/papers/lambertw/teil0.tex | 48 ++++++++++++++++++++++-------------------- buch/papers/lambertw/teil1.tex | 30 +++++++++++++------------- 2 files changed, 40 insertions(+), 38 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 36ef7c3..6ab0bae 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -7,10 +7,10 @@ \label{lambertw:section:Was_sind_Verfolgungskurven}} \rhead{Was sind Verfolgungskurven?} -Verfolgungskurven tauchen oft auf bei Fragen wie welchen Pfad begeht ein Hund während er einer Katze nachrennt. +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 verfolgt sein Ziel, das versucht zu entkommen. -Der Pfad, der der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. +Der Pfad, den der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. Um diese Kurve zu bestimmen, kann das Verfolgungsproblem als Differentialgleichung formuliert werden. Diese Differentialgleichung entspringt der Verfolgungsstrategie des Verfolgers. @@ -30,64 +30,66 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um \centering \begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} \hline - \text{}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ + \text{Strategie}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ \hline - \text{Strategie 1} + \text{Jagd} & \text{konstant} & \text{-} & \text{direkt auf Ziel hinzu}\\ - \text{Strategie 2} + \text{Beschattung} & \text{-} & \text{konstant} & \text{direkt auf Ziel hinzu}\\ - \text{Strategie 3} + \text{Vorhalt} & \text{konstant} & \text{-} & \text{etwas voraus Zielen}\\ \hline \end{tabular} \caption{mögliche Verfolgungsstrategien} \label{lambertw:table:Strategien} \end{table} - +% \begin{figure} \centering \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.pdf} \caption{Vektordarstellung Strategie 1} \label{lambertw:grafic:pursuerDGL2} \end{figure} - -In der Tabelle \eqref{lambertw:table:Strategien} sind drei mögliche Strategien aufgezählt. +% +In der Tabelle \ref{lambertw:table:Strategien} sind drei mögliche Strategien aufgezählt. Im Folgenden 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 zu. -In der Abbildung \eqref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, -wobei $\vec{V}$ der Ortsvektor des Verfolgers, $\vec{Z}$ der Ortsvektor des Ziels und $\dot{\vec{V}}$ der Geschwindigkeitsvektor des Verfolgers ist. +Der Verfolger und sein Ziel werden als Punkte $V$ und $Z$ modelliert. + +In der Abbildung \ref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, +wobei $v$ der Ortsvektor des Verfolgers, $z$ der Ortsvektor des Ziels und $\dot{v}$ der Geschwindigkeitsvektor des Verfolgers ist. Die konstante Geschwindigkeit kann man mit der Gleichung \begin{equation} - |\dot{\vec{V}}| + |\dot{v}| = \operatorname{const} = A \quad A\in\mathbb{R}>0 \end{equation} darstellen. Der Geschwindigkeitsvektor wiederum kann mit der Gleichung \begin{equation} - \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot|\dot{\vec{V}}| + \frac{z-v}{|z-v|}\cdot|\dot{v}| = - \dot{\vec{V}} + \dot{v} \end{equation} beschrieben werden. -Die Differenz der Ortsvektoren $\vec{V}$ und $\vec{Z}$ ist ein Vektor der vom Punkt $V$ auf $Z$ zeigt. +Die Differenz der Ortsvektoren $v$ und $z$ ist ein Vektor der vom Punkt $V$ auf $Z$ zeigt. Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den 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 $\dot{\vec{V}}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergeben sich +Nun wird die Gleichung mit $\dot{v}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergeben sich \begin{align} - \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot|\dot{\vec{V}}|\cdot\dot{\vec{V}} + \frac{z-v}{|z-v|}\cdot|\dot{v}|\cdot\dot{v} &= - |\dot{\vec{V}}|^2 + |\dot{v}|^2 \\ \label{lambertw:pursuerDGL} - \frac{\vec{Z}-\vec{V}}{|\vec{Z}-\vec{V}|}\cdot \frac{\dot{\vec{V}}}{|\dot{\vec{V}}|} + \frac{z-v}{|z-v|}\cdot \frac{\dot{v}}{|\dot{v}|} &= 1 \text{.} \end{align} Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Strategie 1 verwendet. - +% \subsection{Ziel \label{lambertw:subsection:Ziel}} Als nächstes gehen wir auf das Ziel ein. @@ -96,14 +98,14 @@ Diese Strategie kann als Parameterdarstellung der Position nach der Zeit beschri Zum Beispiel könnte ein Ziel auf einer Geraden flüchten, welches auf einer Ebene mit der Parametrisierung \begin{equation} - \vec{Z}(t) + z(t) = \left( \begin{array}{c} 0 \\ t \end{array} \right) \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 Differentialgleichung für die Verfolgungskurve immer komplexer. +Für die Fluchtkurve kann eine beliebige Form gewählt werden, jedoch wird die zu lösende Differentialgleichung für die Verfolgungskurve komplexer. diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index fa7deb1..2e75a19 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -15,7 +15,7 @@ Diese beiden Fragen werden in diesem Kapitel behandelt und an einem Beispiel bet %\subsection{Ziel erreichen (überarbeiten) %\label{lambertw:subsection:ZielErreichen}} Für diese Betrachtung wird das Beispiel aus \eqref{lambertw:section:teil4} zur Hilfe genommen. -Wir verwenden die hergeleiteten Gleichungen \eqref{lambertw:eqFunkXNachT} für Startbedingung im ersten Quadranten +Dazu werden die hergeleiteten Gleichungen \eqref{lambertw:eqFunkXNachT} mit Startbedingung im ersten Quadranten verwendet, welche \begin{align*} x\left(t\right) &= @@ -25,15 +25,16 @@ Wir verwenden die hergeleiteten Gleichungen \eqref{lambertw:eqFunkXNachT} für S \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\\ \chi &= - \frac{r_0+y_0}{r_0-y_0}\\ + \frac{r_0+y_0}{r_0-y_0}, \quad \eta - &= - \left(\frac{x}{x_0}\right)^2\\ + = + \left(\frac{x}{x_0}\right)^2,\quad r_0 - &= - \sqrt{x_0^2+y_0^2} \text{.}\\ + = + \sqrt{x_0^2+y_0^2} \end{align*} % +sind. Das Ziel wird erreicht, wenn die Koordinaten des Verfolgers mit denen des Ziels bei einem diskreten Zeitpunkt $t_1$ übereinstimmen. Somit gilt es @@ -60,7 +61,7 @@ und der Verfolger durch \text{.} \end{equation} % - Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der x- und y-Koordinaten einzeln überprüft werden. Es entstehen daher folgende Bedingungen + Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der $x$- und $y$-Koordinaten einzeln überprüft werden. Es entstehen daher folgende Bedingungen \begin{align*} 0 @@ -73,12 +74,11 @@ und der Verfolger durch &= y(t) = - \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right) - \\ + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\text{,} \end{align*} % -, welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. -Zuerst wird die Bedingung der x-Koordinate betrachtet. +welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. +Zuerst wird die Bedingung der $x$-Koordinate betrachtet. Diese kann durch dividieren durch $x_0$, anschliessendes quadrieren und multiplizieren von $\chi$ vereinfacht werden. Daraus folgt \begin{equation} 0 @@ -107,10 +107,10 @@ Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingu Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Einholen möglich wäre. Somit kann nach den Gestellten Bedingungen das Ziel nie erreicht werden. -Aus der Symmetrie des Problems an der y-Achse können auch alle Anfangspunkte im zweiten Quadranten die Bedingungen nicht erfüllen. +Aus der Symmetrie des Problems an der $y$-Achse können auch alle Anfangspunkte im zweiten Quadranten die Bedingungen nicht erfüllen. Bei allen Anfangspunkten mit $y_0<0$ ist ein Einholen unmöglich, da die Geschwindigkeit des Verfolgers und Ziels übereinstimmen und der Verfolger dem Ziel bereits am Anfang nachgeht. -Wenn die Wertemenge der Anfangsbedingung um die positive y-Achse erweitert wird, kann das Ziel wiederum erreicht werden. -Sobald der Verfolger auf der positiven y-Achse startet, bewegen sich Verfolger und Ziel aufeinander zu, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel zeigt und der Verfolger sich auf der Fluchtgeraden befindet. +Wenn die Wertemenge der Anfangsbedingung um die positive $y$-Achse erweitert wird, kann das Ziel wiederum erreicht werden. +Sobald der Verfolger auf der positiven $y$-Achse startet, bewegen sich Verfolger und Ziel aufeinander zu, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel zeigt und der Verfolger sich auf der Fluchtgeraden befindet. Dies führt zwingend dazu, dass der Verfolger das Ziel erreichen wird. Die Verfolgungskurve kann in diesem Fall mit @@ -141,7 +141,7 @@ Daraus folgt \end{equation} % führt. -Nun ist klar, dass lediglich Anfangspunkte auf der positiven y-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. +Nun ist klar, dass lediglich Anfangspunkte auf der positiven $y$-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. Bei allen anderen Anfangspunkten wird der Verfolger das Ziel nie erreichen. Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. -- cgit v1.2.1 From 220b382cf4b7019b199c3023ddab73ba2658e27a Mon Sep 17 00:00:00 2001 From: Fabian <@> Date: Wed, 27 Jul 2022 13:08:39 +0200 Subject: 0f1, bilder --- buch/papers/0f1/images/airy.pdf | Bin 25568 -> 0 bytes buch/papers/0f1/images/konvergenzAiry.pdf | Bin 15137 -> 15785 bytes buch/papers/0f1/images/konvergenzNegativ.pdf | Bin 16312 -> 18155 bytes buch/papers/0f1/images/konvergenzPositiv.pdf | Bin 18924 -> 18581 bytes buch/papers/0f1/images/stabilitaet.pdf | Bin 20944 -> 19612 bytes buch/papers/0f1/listings/kettenbruchRekursion.c | 8 +- buch/papers/0f1/listings/potenzreihe.c | 8 +- buch/papers/0f1/main.tex | 48 ++-- buch/papers/0f1/teil0.tex | 30 +- buch/papers/0f1/teil1.tex | 204 +++++++------- buch/papers/0f1/teil2.tex | 354 ++++++++++++------------ buch/papers/0f1/teil3.tex | 112 ++++---- 12 files changed, 382 insertions(+), 382 deletions(-) delete mode 100644 buch/papers/0f1/images/airy.pdf (limited to 'buch') diff --git a/buch/papers/0f1/images/airy.pdf b/buch/papers/0f1/images/airy.pdf deleted file mode 100644 index 672d789..0000000 Binary files a/buch/papers/0f1/images/airy.pdf and /dev/null differ diff --git a/buch/papers/0f1/images/konvergenzAiry.pdf b/buch/papers/0f1/images/konvergenzAiry.pdf index 2e635ea..206cd3a 100644 Binary files a/buch/papers/0f1/images/konvergenzAiry.pdf and b/buch/papers/0f1/images/konvergenzAiry.pdf differ diff --git a/buch/papers/0f1/images/konvergenzNegativ.pdf b/buch/papers/0f1/images/konvergenzNegativ.pdf index 3b58be4..03b2ba1 100644 Binary files a/buch/papers/0f1/images/konvergenzNegativ.pdf and b/buch/papers/0f1/images/konvergenzNegativ.pdf differ diff --git a/buch/papers/0f1/images/konvergenzPositiv.pdf b/buch/papers/0f1/images/konvergenzPositiv.pdf index 24e3fd5..2e45129 100644 Binary files a/buch/papers/0f1/images/konvergenzPositiv.pdf and b/buch/papers/0f1/images/konvergenzPositiv.pdf differ diff --git a/buch/papers/0f1/images/stabilitaet.pdf b/buch/papers/0f1/images/stabilitaet.pdf index be4af42..13dea39 100644 Binary files a/buch/papers/0f1/images/stabilitaet.pdf and b/buch/papers/0f1/images/stabilitaet.pdf differ diff --git a/buch/papers/0f1/listings/kettenbruchRekursion.c b/buch/papers/0f1/listings/kettenbruchRekursion.c index 143683f..3caaf43 100644 --- a/buch/papers/0f1/listings/kettenbruchRekursion.c +++ b/buch/papers/0f1/listings/kettenbruchRekursion.c @@ -17,11 +17,11 @@ static double fractionIter0f1(const double c, const double z, unsigned int k) { abk = z / (k * ((k - 1) + c)); //abk = ak, bk - a = k > 1 ? (1 + abk) : 1; //a0, a1 - b = k > 1 ? -abk : abk; //b1 + a = k > 1 ? (1 + abk) : 1; //a0, a1 + b = k > 1 ? -abk : abk; //b1 - temp = b / (a + temp); ////bk / (ak + last result) + temp = b / (a + temp); //bk / (ak + last result) } - return a + temp; //a0 + temp + return a + temp; //a0 + temp } \ No newline at end of file diff --git a/buch/papers/0f1/listings/potenzreihe.c b/buch/papers/0f1/listings/potenzreihe.c index 3eb9b86..23fdfea 100644 --- a/buch/papers/0f1/listings/potenzreihe.c +++ b/buch/papers/0f1/listings/potenzreihe.c @@ -51,18 +51,18 @@ static double fac(int n) /** * @brief Calculates the Hypergeometric Function 0F1(;b;z) - * @param b0 in 0F1(;b0;z) - * @param z in 0F1(;b0;z) + * @param c in 0F1(;c;z) + * @param z in 0F1(;c;z) * @param n number of itertions (precision) * @return Result */ -static double powerseries(const double b, const double z, unsigned int n) +static double powerseries(const double c, const double z, unsigned int n) { double temp = 0.0; for (unsigned int k = 0; k < n; ++k) { - temp += pow(z, k) / (factorial(k) * pochhammer(b, k)); + temp += pow(z, k) / (factorial(k) * pochhammer(c, k)); } return temp; diff --git a/buch/papers/0f1/main.tex b/buch/papers/0f1/main.tex index b8cdc21..0b1020f 100644 --- a/buch/papers/0f1/main.tex +++ b/buch/papers/0f1/main.tex @@ -1,24 +1,24 @@ -% -% main.tex -- Paper zum Thema <0f1> -% -% (c) 2020 Hochschule Rapperswil -% -% - - - -\chapter{Algorithmus zur Berechnung von $\mathstrut_0F_1$\label{chapter:0f1}} -\lhead{Algorithmus zur Berechnung von $\mathstrut_0F_1$} -\begin{refsection} -\chapterauthor{Fabian Dünki} - - - - -\input{papers/0f1/teil0.tex} -\input{papers/0f1/teil1.tex} -\input{papers/0f1/teil2.tex} -\input{papers/0f1/teil3.tex} - -\printbibliography[heading=subbibliography] -\end{refsection} +% +% main.tex -- Paper zum Thema <0f1> +% +% (c) 2020 Hochschule Rapperswil +% +% + + + +\chapter{Algorithmus zur Berechnung von $\mathstrut_0F_1$\label{chapter:0f1}} +\lhead{Algorithmus zur Berechnung von $\mathstrut_0F_1$} +\begin{refsection} +\chapterauthor{Fabian Dünki} + + + + +\input{papers/0f1/teil0.tex} +\input{papers/0f1/teil1.tex} +\input{papers/0f1/teil2.tex} +\input{papers/0f1/teil3.tex} + +\printbibliography[heading=subbibliography] +\end{refsection} diff --git a/buch/papers/0f1/teil0.tex b/buch/papers/0f1/teil0.tex index 780d432..adccac7 100644 --- a/buch/papers/0f1/teil0.tex +++ b/buch/papers/0f1/teil0.tex @@ -1,15 +1,15 @@ -% -% einleitung.tex -- Einleitung -% -% (c) 2022 Fabian Dünki, Hochschule Rapperswil -% -\section{Ausgangslage\label{0f1:section:ausgangslage}} -\rhead{Ausgangslage} -Die Hypergeometrische Funktion $\mathstrut_0F_1$ wird in vielen Funktionen als Basisfunktion benutzt, -zum Beispiel um die Airy Funktion zu berechnen. -In der GNU Scientific Library \cite{0f1:library-gsl} -ist die Funktion $\mathstrut_0F_1$ vorhanden. -Allerdings wirft die Funktion, bei negativen Übergabenwerten wie zum Beispiel \verb+gsl_sf_hyperg_0F1(1, -1)+, eine Exception. -Bei genauerer Untersuchung hat sich gezeigt, dass die Funktion je nach Betriebssystem funktioniert oder eben nicht. -So kann die Funktion unter Windows fehlerfrei aufgerufen werden, beim Mac OS und Linux sind negative Übergabeparameter im Moment nicht möglich. -Ziel dieser Arbeit war es zu evaluieren, ob es mit einfachen mathematischen Operationen möglich ist, die Hypergeometrische Funktion $\mathstrut_0F_1$ zu implementieren. +% +% einleitung.tex -- Einleitung +% +% (c) 2022 Fabian Dünki, Hochschule Rapperswil +% +\section{Ausgangslage\label{0f1:section:ausgangslage}} +\rhead{Ausgangslage} +Die Hypergeometrische Funktion $\mathstrut_0F_1$ wird in vielen Funktionen als Basisfunktion benutzt, +zum Beispiel um die Airy Funktion zu berechnen. +In der GNU Scientific Library \cite{0f1:library-gsl} +ist die Funktion $\mathstrut_0F_1$ vorhanden. +Allerdings wirft die Funktion, bei negativen Übergabenwerten wie zum Beispiel \verb+gsl_sf_hyperg_0F1(1, -1)+, eine Exception. +Bei genauerer Untersuchung hat sich gezeigt, dass die Funktion je nach Betriebssystem funktioniert oder eben nicht. +So kann die Funktion unter Windows fehlerfrei aufgerufen werden, beim Mac OS und Linux sind negative Übergabeparameter im Moment nicht möglich. +Ziel dieser Arbeit war es zu evaluieren, ob es mit einfachen mathematischen Operationen möglich ist, die Hypergeometrische Funktion $\mathstrut_0F_1$ zu implementieren. diff --git a/buch/papers/0f1/teil1.tex b/buch/papers/0f1/teil1.tex index 2a60737..f8d70a8 100644 --- a/buch/papers/0f1/teil1.tex +++ b/buch/papers/0f1/teil1.tex @@ -1,102 +1,102 @@ -% -% teil1.tex -- Mathematischer Hintergrund -% -% (c) 2022 Fabian Dünki, Hochschule Rapperswil -% -\section{Mathematischer Hintergrund -\label{0f1:section:mathHintergrund}} -\rhead{Mathematischer Hintergrund} -Basierend auf den Herleitungen des vorhergehenden Kapitels \ref{buch:rekursion:section:hypergeometrische-funktion} -und dem Seminarbuch Numerik \cite{0f1:kettenbrueche}, werden im nachfolgenden Abschnitt nochmals die Resultate -beschrieben. - -\subsection{Hypergeometrische Funktion -\label{0f1:subsection:hypergeometrisch}} -Als Grundlage der umgesetzten Algorithmen dient die Hypergeometrische Funktion $\mathstrut_0F_1$. Diese ist eine Unterfunktion der allgemein definierten Funktion $\mathstrut_pF_q$. - -\begin{definition} - \label{0f1:math:qFp:def} - Die hypergeometrische Funktion - $\mathstrut_pF_q$ ist definiert durch die Reihe - \[ - \mathstrut_pF_q - \biggl( - \begin{matrix} - a_1,\dots,a_p\\ - b_1,\dots,b_q - \end{matrix} - ; - x - \biggr) - = - \mathstrut_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;x) - = - \sum_{k=0}^\infty - \frac{(a_1)_k\cdots(a_p)_k}{(b_1)_k\cdots(b_q)_k}\frac{x^k}{k!}. - \] -\end{definition} - -Angewendet auf die Funktion $\mathstrut_pF_q$ ergibt sich für $\mathstrut_0F_1$: - -\begin{equation} - \label{0f1:math:0f1:eq} - \mathstrut_0F_1 - \biggl( - \begin{matrix} - \\ - b_1 - \end{matrix} - ; - x - \biggr) - = - \mathstrut_0F_1(;b_1;x) - = - \sum_{k=0}^\infty - \frac{x^k}{(b_1)_k \cdot k!}. -\end{equation} - - - - -\subsection{Airy Funktion -\label{0f1:subsection:airy}} -Die Airy-Funktion $Ai(x)$ und die verwandte Funktion $Bi(x)$ werden als Airy-Funktion bezeichnet. Sie werden zur Lösung verschiedener physikalischer Probleme benutzt, wie zum Beispiel zur Lösung der Schrödinger-Gleichung. \cite{0f1:wiki-airyFunktion} - -\begin{definition} - \label{0f1:airy:differentialgleichung:def} - Die Differentialgleichung - $y'' - xy = 0$ - heisst die {\em Airy-Differentialgleichung}. \cite{0f1:wiki-airyFunktion} -\end{definition} - -Die Airy Funktion lässt sich auf verschiedene Arten darstellen. \cite{0f1:wiki-airyFunktion} -Als hypergeometrische Funktion berechnet, ergibt sich wie in Kapitel \ref{buch:differentialgleichungen:section:hypergeometrisch} hergeleitet, folgende Lösungen der Airy-Differentialgleichung zu den Anfangsbedingungen $A(0)=1$ und $A'(0)=0$, sowie $B(0)=0$ und $B'(0)=0$. - -\begin{align} -\label{0f1:airy:hypergeometrisch:eq} -Ai(x) -= -\sum_{k=0}^\infty -\frac{1}{(\frac23)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k -= -\mathstrut_0F_1\biggl( -\begin{matrix}\text{---}\\\frac23\end{matrix};\frac{x^3}{9} -\biggr). -\\ -Bi(x) -= -\sum_{k=0}^\infty -\frac{1}{(\frac43)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k -= -x\cdot\mathstrut_0F_1\biggl( -\begin{matrix}\text{---}\\\frac43\end{matrix}; -\frac{x^3}{9} -\biggr). -\qedhere -\end{align} - -In diesem speziellem Fall wird die Airy Funktion $Ai(x)$ \eqref{0f1:airy:hypergeometrisch:eq} -benutzt, um die Stabilität der Algorithmen zu $\mathstrut_0F_1$ zu überprüfen. - - +% +% teil1.tex -- Mathematischer Hintergrund +% +% (c) 2022 Fabian Dünki, Hochschule Rapperswil +% +\section{Mathematischer Hintergrund +\label{0f1:section:mathHintergrund}} +\rhead{Mathematischer Hintergrund} +Basierend auf den Herleitungen des vorhergehenden Kapitels \ref{buch:rekursion:section:hypergeometrische-funktion} +und dem Seminarbuch Numerik \cite{0f1:kettenbrueche}, werden im nachfolgenden Abschnitt nochmals die Resultate +beschrieben. + +\subsection{Hypergeometrische Funktion +\label{0f1:subsection:hypergeometrisch}} +Als Grundlage der umgesetzten Algorithmen dient die Hypergeometrische Funktion $\mathstrut_0F_1$. Diese ist eine Unterfunktion der allgemein definierten Funktion $\mathstrut_pF_q$. + +\begin{definition} + \label{0f1:math:qFp:def} + Die hypergeometrische Funktion + $\mathstrut_pF_q$ ist definiert durch die Reihe + \[ + \mathstrut_pF_q + \biggl( + \begin{matrix} + a_1,\dots,a_p\\ + b_1,\dots,b_q + \end{matrix} + ; + x + \biggr) + = + \mathstrut_pF_q(a_1,\dots,a_p;b_1,\dots,b_q;x) + = + \sum_{k=0}^\infty + \frac{(a_1)_k\cdots(a_p)_k}{(b_1)_k\cdots(b_q)_k}\frac{x^k}{k!}. + \] +\end{definition} + +Angewendet auf die Funktion $\mathstrut_pF_q$ ergibt sich für $\mathstrut_0F_1$: + +\begin{equation} + \label{0f1:math:0f1:eq} + \mathstrut_0F_1 + \biggl( + \begin{matrix} + \\ + b_1 + \end{matrix} + ; + x + \biggr) + = + \mathstrut_0F_1(;b_1;x) + = + \sum_{k=0}^\infty + \frac{x^k}{(b_1)_k \cdot k!}. +\end{equation} + + + + +\subsection{Airy Funktion +\label{0f1:subsection:airy}} +Die Airy-Funktion $Ai(x)$ und die verwandte Funktion $Bi(x)$ werden als Airy-Funktion bezeichnet. Sie werden zur Lösung verschiedener physikalischer Probleme benutzt, wie zum Beispiel zur Lösung der Schrödinger-Gleichung. \cite{0f1:wiki-airyFunktion} + +\begin{definition} + \label{0f1:airy:differentialgleichung:def} + Die Differentialgleichung + $y'' - xy = 0$ + heisst die {\em Airy-Differentialgleichung}. \cite{0f1:wiki-airyFunktion} +\end{definition} + +Die Airy Funktion lässt sich auf verschiedene Arten darstellen. \cite{0f1:wiki-airyFunktion} +Als hypergeometrische Funktion berechnet, ergibt sich wie in Kapitel \ref{buch:differentialgleichungen:section:hypergeometrisch} hergeleitet, folgende Lösungen der Airy-Differentialgleichung zu den Anfangsbedingungen $A(0)=1$ und $A'(0)=0$, sowie $B(0)=0$ und $B'(0)=0$. + +\begin{align} +\label{0f1:airy:hypergeometrisch:eq} +Ai(x) += +\sum_{k=0}^\infty +\frac{1}{(\frac23)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k += +\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac23\end{matrix};\frac{x^3}{9} +\biggr). +\\ +Bi(x) += +\sum_{k=0}^\infty +\frac{1}{(\frac43)_k} \frac{1}{k!}\biggl(\frac{x^3}{9}\biggr)^k += +x\cdot\mathstrut_0F_1\biggl( +\begin{matrix}\text{---}\\\frac43\end{matrix}; +\frac{x^3}{9} +\biggr). +\qedhere +\end{align} + +In diesem speziellem Fall wird die Airy Funktion $Ai(x)$ \eqref{0f1:airy:hypergeometrisch:eq} +benutzt, um die Stabilität der Algorithmen zu $\mathstrut_0F_1$ zu überprüfen. + + diff --git a/buch/papers/0f1/teil2.tex b/buch/papers/0f1/teil2.tex index ca48e6e..3c2b5cd 100644 --- a/buch/papers/0f1/teil2.tex +++ b/buch/papers/0f1/teil2.tex @@ -1,178 +1,178 @@ -% -% teil2.tex -- Umsetzung in C Programmen -% -% (c) 2022 Fabian Dünki, Hochschule Rapperswil -% -\section{Umsetzung -\label{0f1:section:teil2}} -\rhead{Umsetzung} -Zur Umsetzung wurden drei verschiedene Ansätze gewählt. Dabei wurde der Schwerpunkt auf die Funktionalität und eine gute Lesbarkeit des Codes gelegt. -Die Unterprogramme wurde jeweils, wie die GNU Scientific Library, in C geschrieben. Die Zwischenresultate wurden vom Hauptprogramm in einem CSV-File gespeichert. Anschliessen wurde mit der Matplot-Libray in Python die Resultate geplottet. - -\subsection{Potenzreihe -\label{0f1:subsection:potenzreihe}} -Die naheliegendste Lösung ist die Programmierung der Potenzreihe. Allerdings ist ein Problem dieser Umsetzung \ref{0f1:listing:potenzreihe}, dass die Fakultät im Nenner schnell grosse Werte annimmt und so der Bruch gegen Null strebt. Spätesten ab $k=167$ stösst diese Umsetzung \eqref{0f1:umsetzung:0f1:eq} an ihre Grenzen, da die Fakultät von $168$ eine Bereichsüberschreitung des \textit{double} Bereiches darstellt. \cite{0f1:double} - -\begin{align} - \label{0f1:umsetzung:0f1:eq} - \mathstrut_0F_1(;b;z) - &= - \sum_{k=0}^\infty - \frac{z^k}{(b)_k \cdot k!} - &= - \frac{1}{b} - +\frac{z^1}{(1+b) \cdot 1} - + \cdots - + \frac{z^{20}}{(20+b) \cdot 2.4 \cdot 10^{18}} -\end{align} - -\lstinputlisting[style=C,float,caption={Potenzreihe.},label={0f1:listing:potenzreihe}, firstline=59]{papers/0f1/listings/potenzreihe.c} - -\subsection{Kettenbruch -\label{0f1:subsection:kettenbruch}} -Ein endlicher Kettenbruch ist ein Bruch der Form -\begin{equation*} -a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{b_3}{a_3+\cdots}}} -\end{equation*} -in welchem $a_0, a_1,\dots,a_n$ und $b_1,b_2,\dots,b_n$ ganze Zahlen darstellen. - -Die Kurzschreibweise für einen allgemeinen Kettenbruch ist -\begin{equation*} - a_0 + \frac{a_1|}{|b_1} + \frac{a_2|}{|b_2} + \frac{a_3|}{|b_3} + \cdots -\end{equation*} -und ist somit verknüpfbar mit der Potenzreihe. -\cite{0f1:wiki-kettenbruch} - -Angewendet auf die Funktion $\mathstrut_0F_1$ bedeutet dies: -\begin{equation*} - \mathstrut_0F_1(;b;z) = 1 + \frac{z}{a1!} + \frac{z^2}{a(a+1)2!} + \frac{z^3}{a(a+1)(a+2)3!} + \cdots -\end{equation*} -\cite{0f1:wiki-fraction} - -Nach allen Umformungen ergibt sich folgender, irregulärer Kettenbruch \eqref{0f1:math:kettenbruch:0f1:eq} -\begin{equation} - \label{0f1:math:kettenbruch:0f1:eq} - \mathstrut_0F_1(;b;z) = 1 + \cfrac{\cfrac{z}{b}}{1+\cfrac{-\cfrac{z}{2(1+b)}}{1+\cfrac{z}{2(1+b)}+\cfrac{-\cfrac{z}{3(2+b)}}{1+\cfrac{z}{5(4+b)} + \cdots}}}, -\end{equation} -der als Code \ref{0f1:listing:kettenbruchIterativ} umgesetzt wurde. -\cite{0f1:wolfram-0f1} - -\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}, firstline=8]{papers/0f1/listings/kettenbruchIterativ.c} - -\subsection{Rekursionsformel -\label{0f1:subsection:rekursionsformel}} -Wesentlich stabiler zur Berechnung eines Kettenbruches ist die Rekursionsformel. Nachfolgend wird die verkürzte Herleitung vom Kettenbruch zur Rekursionsformel aufgezeigt. Eine vollständige Schritt für Schritt Herleitung ist im Seminarbuch Numerik, im Kapitel Kettenbrüche zu finden. \cite{0f1:kettenbrueche}) - -\subsubsection{Verkürzte Herleitung} -Ein Näherungsbruch in der Form -\begin{align*} - \cfrac{A_k}{B_k} = a_k + \cfrac{b_{k + 1}}{a_{k + 1} + \cfrac{p}{q}} -\end{align*} -lässt sich zu -\begin{align*} - \cfrac{A_k}{B_k} = \cfrac{b_{k+1}}{a_{k+1} + \cfrac{p}{q}} = \frac{b_{k+1} \cdot q}{a_{k+1} \cdot q + p} -\end{align*} -umformen. -Dies lässt sich auch durch die folgende Matrizenschreibweise ausdrücken: -\begin{equation*} - \begin{pmatrix} - A_k\\ - B_k - \end{pmatrix} - = \begin{pmatrix} - b_{k+1} \cdot q\\ - a_{k+1} \cdot q + p - \end{pmatrix} - =\begin{pmatrix} - 0& b_{k+1}\\ - 1& a_{k+1} - \end{pmatrix} - \begin{pmatrix} - p \\ - q - \end{pmatrix}. - %\label{0f1:math:rekursionsformel:herleitung} -\end{equation*} - -Wendet man dies nun auf den Kettenbruch in der Form -\begin{equation*} - \frac{A_k}{B_k} = a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{k-1}}{a_{k-1} + \cfrac{b_k}{a_k}}}}} -\end{equation*} -an, ergibt sich folgende Matrixdarstellungen: - -\begin{align*} - \begin{pmatrix} - A_k\\ - B_k - \end{pmatrix} - &= - \begin{pmatrix} - 1& a_0\\ - 0& 1 - \end{pmatrix} - \begin{pmatrix} - 0& b_1\\ - 1& a_1 - \end{pmatrix} - \cdots - \begin{pmatrix} - 0& b_{k-1}\\ - 1& a_{k-1} - \end{pmatrix} - \begin{pmatrix} - b_k\\ - a_k - \end{pmatrix} -\end{align*} - -Nach vollständiger Induktion ergibt sich für den Schritt $k$, die Matrix -\begin{equation} - \label{0f1:math:matrix:ende:eq} - \begin{pmatrix} - A_{k}\\ - B_{k} - \end{pmatrix} - = - \begin{pmatrix} - A_{k-2}& A_{k-1}\\ - B_{k-2}& B_{k-1} - \end{pmatrix} - \begin{pmatrix} - b_k\\ - a_k - \end{pmatrix}. -\end{equation} - -Und Schlussendlich kann der Näherungsbruch -\[ -\frac{Ak}{Bk} -\] -berechnet werden. - - -\subsubsection{Lösung} -Die Berechnung von $A_k, B_k$ \eqref{0f1:math:matrix:ende:eq} kann man auch ohne die Matrizenschreibweise aufschreiben: \cite{0f1:wiki-fraction} -\begin{itemize} -\item Startbedingungen: -\begin{align*} -A_{-1} &= 0 & A_0 &= a_0 \\ -B_{-1} &= 1 & B_0 &= 1 -\end{align*} -\item Schritt $k\to k+1$: -\[ -\begin{aligned} -k &\rightarrow k + 1: -& -A_{k+1} &= A_{k-1} \cdot b_k + A_k \cdot a_k \\ -&& -B_{k+1} &= B_{k-1} \cdot b_k + B_k \cdot a_k -\end{aligned} -\] -\item -Näherungsbruch: \qquad$\displaystyle\frac{A_k}{B_k}$ -\end{itemize} - -Ein grosser Vorteil dieser Umsetzung \ref{0f1:listing:kettenbruchRekursion} ist, dass im Vergleich zum Code \ref{0f1:listing:kettenbruchIterativ} eine Division gespart werden kann und somit weniger Folgefehler entstehen können. - -%Code +% +% teil2.tex -- Umsetzung in C Programmen +% +% (c) 2022 Fabian Dünki, Hochschule Rapperswil +% +\section{Umsetzung +\label{0f1:section:teil2}} +\rhead{Umsetzung} +Zur Umsetzung wurden drei verschiedene Ansätze gewählt. Dabei wurde der Schwerpunkt auf die Funktionalität und eine gute Lesbarkeit des Codes gelegt. +Die Unterprogramme wurde jeweils, wie die GNU Scientific Library, in C geschrieben. Die Zwischenresultate wurden vom Hauptprogramm in einem CSV-File gespeichert. Anschliessen wurde mit der Matplot-Libray in Python die Resultate geplottet. + +\subsection{Potenzreihe +\label{0f1:subsection:potenzreihe}} +Die naheliegendste Lösung ist die Programmierung der Potenzreihe. Allerdings ist ein Problem dieser Umsetzung \ref{0f1:listing:potenzreihe}, dass die Fakultät im Nenner schnell grosse Werte annimmt und so der Bruch gegen Null strebt. Spätesten ab $k=167$ stösst diese Umsetzung \eqref{0f1:umsetzung:0f1:eq} an ihre Grenzen, da die Fakultät von $168$ eine Bereichsüberschreitung des \textit{double} Bereiches darstellt. \cite{0f1:double} + +\begin{align} + \label{0f1:umsetzung:0f1:eq} + \mathstrut_0F_1(;c;z) + &= + \sum_{k=0}^\infty + \frac{z^k}{(c)_k \cdot k!} + &= + \frac{1}{c} + +\frac{z^1}{(c+1) \cdot 1} + + \cdots + + \frac{z^{20}}{c(c+1)(c+2)\cdots(c+19) \cdot 2.4 \cdot 10^{18}} +\end{align} + +\lstinputlisting[style=C,float,caption={Potenzreihe.},label={0f1:listing:potenzreihe}, firstline=59]{papers/0f1/listings/potenzreihe.c} + +\subsection{Kettenbruch +\label{0f1:subsection:kettenbruch}} +Ein endlicher Kettenbruch ist ein Bruch der Form +\begin{equation*} +a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{b_3}{a_3+\cdots}}} +\end{equation*} +in welchem $a_0, a_1,\dots,a_n$ und $b_1,b_2,\dots,b_n$ ganze Zahlen darstellen. + +Die Kurzschreibweise für einen allgemeinen Kettenbruch ist +\begin{equation*} + a_0 + \frac{a_1|}{|b_1} + \frac{a_2|}{|b_2} + \frac{a_3|}{|b_3} + \cdots +\end{equation*} +und ist somit verknüpfbar mit der Potenzreihe. +\cite{0f1:wiki-kettenbruch} + +Angewendet auf die Funktion $\mathstrut_0F_1$ bedeutet dies: +\begin{equation*} + \mathstrut_0F_1(;c;z) = 1 + \frac{z}{c\cdot1!} + \frac{z^2}{c(c+1)\cdot2!} + \frac{z^3}{c(c+1)(c+2)\cdot3!} + \cdots +\end{equation*} +\cite{0f1:wiki-fraction} + +Nach allen Umformungen ergibt sich folgender, irregulärer Kettenbruch \eqref{0f1:math:kettenbruch:0f1:eq} +\begin{equation} + \label{0f1:math:kettenbruch:0f1:eq} + \mathstrut_0F_1(;c;z) = 1 + \cfrac{\cfrac{z}{c}}{1+\cfrac{-\cfrac{z}{2(c+1)}}{1+\cfrac{z}{2(c+1)}+\cfrac{-\cfrac{z}{3(c+2)}}{1+\cfrac{z}{5(c+4)} + \cdots}}}, +\end{equation} +der als Code \ref{0f1:listing:kettenbruchIterativ} umgesetzt wurde. +\cite{0f1:wolfram-0f1} + +\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}, firstline=8]{papers/0f1/listings/kettenbruchIterativ.c} + +\subsection{Rekursionsformel +\label{0f1:subsection:rekursionsformel}} +Wesentlich stabiler zur Berechnung eines Kettenbruches ist die Rekursionsformel. Nachfolgend wird die verkürzte Herleitung vom Kettenbruch zur Rekursionsformel aufgezeigt. Eine vollständige Schritt für Schritt Herleitung ist im Seminarbuch Numerik, im Kapitel Kettenbrüche zu finden. \cite{0f1:kettenbrueche}) + +\subsubsection{Verkürzte Herleitung} +Ein Näherungsbruch in der Form +\begin{align*} + \cfrac{A_k}{B_k} = a_k + \cfrac{b_{k + 1}}{a_{k + 1} + \cfrac{p}{q}} +\end{align*} +lässt sich zu +\begin{align*} + \cfrac{A_k}{B_k} = \cfrac{b_{k+1}}{a_{k+1} + \cfrac{p}{q}} = \frac{b_{k+1} \cdot q}{a_{k+1} \cdot q + p} +\end{align*} +umformen. +Dies lässt sich auch durch die folgende Matrizenschreibweise ausdrücken: +\begin{equation*} + \begin{pmatrix} + A_k\\ + B_k + \end{pmatrix} + = \begin{pmatrix} + b_{k+1} \cdot q\\ + a_{k+1} \cdot q + p + \end{pmatrix} + =\begin{pmatrix} + 0& b_{k+1}\\ + 1& a_{k+1} + \end{pmatrix} + \begin{pmatrix} + p \\ + q + \end{pmatrix}. + %\label{0f1:math:rekursionsformel:herleitung} +\end{equation*} + +Wendet man dies nun auf den Kettenbruch in der Form +\begin{equation*} + \frac{A_k}{B_k} = a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{k-1}}{a_{k-1} + \cfrac{b_k}{a_k}}}}} +\end{equation*} +an, ergibt sich folgende Matrixdarstellungen: + +\begin{align*} + \begin{pmatrix} + A_k\\ + B_k + \end{pmatrix} + &= + \begin{pmatrix} + 1& a_0\\ + 0& 1 + \end{pmatrix} + \begin{pmatrix} + 0& b_1\\ + 1& a_1 + \end{pmatrix} + \cdots + \begin{pmatrix} + 0& b_{k-1}\\ + 1& a_{k-1} + \end{pmatrix} + \begin{pmatrix} + b_k\\ + a_k + \end{pmatrix} +\end{align*} + +Nach vollständiger Induktion ergibt sich für den Schritt $k$, die Matrix +\begin{equation} + \label{0f1:math:matrix:ende:eq} + \begin{pmatrix} + A_{k}\\ + B_{k} + \end{pmatrix} + = + \begin{pmatrix} + A_{k-2}& A_{k-1}\\ + B_{k-2}& B_{k-1} + \end{pmatrix} + \begin{pmatrix} + b_k\\ + a_k + \end{pmatrix}. +\end{equation} + +Und Schlussendlich kann der Näherungsbruch +\[ +\frac{Ak}{Bk} +\] +berechnet werden. + + +\subsubsection{Lösung} +Die Berechnung von $A_k, B_k$ \eqref{0f1:math:matrix:ende:eq} kann man auch ohne die Matrizenschreibweise aufschreiben: \cite{0f1:wiki-fraction} +\begin{itemize} +\item Startbedingungen: +\begin{align*} +A_{-1} &= 0 & A_0 &= a_0 \\ +B_{-1} &= 1 & B_0 &= 1 +\end{align*} +\item Schritt $k\to k+1$: +\[ +\begin{aligned} +k &\rightarrow k + 1: +& +A_{k+1} &= A_{k-1} \cdot b_k + A_k \cdot a_k \\ +&& +B_{k+1} &= B_{k-1} \cdot b_k + B_k \cdot a_k +\end{aligned} +\] +\item +Näherungsbruch: \qquad$\displaystyle\frac{A_k}{B_k}$ +\end{itemize} + +Ein grosser Vorteil dieser Umsetzung \ref{0f1:listing:kettenbruchRekursion} ist, dass im Vergleich zum Code \ref{0f1:listing:kettenbruchIterativ} eine Division gespart werden kann und somit weniger Rundungsfehler entstehen können. + +%Code \lstinputlisting[style=C,float,caption={Iterativ umgesetzter Kettenbruch.},label={0f1:listing:kettenbruchRekursion}, firstline=8]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file diff --git a/buch/papers/0f1/teil3.tex b/buch/papers/0f1/teil3.tex index 76d6e32..355e1b7 100644 --- a/buch/papers/0f1/teil3.tex +++ b/buch/papers/0f1/teil3.tex @@ -1,56 +1,56 @@ -% -% teil3.tex -- Resultate und Ausblick -% -% (c) 2022 Fabian Dünki, Hochschule Rapperswil -% -\section{Resultate -\label{0f1:section:teil3}} -\rhead{Resultate} -Im Verlauf des Seminares hat sich gezeigt, -das ein einfacher mathematischer Algorithmus zu implementieren gar nicht so einfach ist. -So haben alle drei umgesetzten Ansätze Probleme mit grossen negativen x in der Funktion $\mathstrut_0F_1(;b;x)$. -Ebenso wird, je grösser der Wert x wird $\mathstrut_0F_1(;b;x)$, desto mehr weichen die berechneten Resultate -von den Erwarteten ab. \cite{0f1:wolfram-0f1} - -\subsection{Auswertung -\label{0f1:subsection:auswertung}} -\begin{figure} - \centering - \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzAiry.pdf} - \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion zu den Anfangsbedingungen $y(0)=1$ und $y'(0)=0$. - \label{0f1:ausblick:plot:airy:konvergenz}} -\end{figure} - -\begin{figure} - \centering - \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzPositiv.pdf} - \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat. - \label{0f1:ausblick:plot:konvergenz:positiv}} -\end{figure} - -\begin{figure} - \centering - \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzNegativ.pdf} - \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat. - \label{0f1:ausblick:plot:konvergenz:negativ}} -\end{figure} - -\begin{figure} - \centering - \includegraphics[width=1\textwidth]{papers/0f1/images/stabilitaet.pdf} - \caption{Stabilität der 3 Algorithmen verglichen mit der GNU Scientific Library. - \label{0f1:ausblick:plot:airy:stabilitaet}} -\end{figure} - -\begin{itemize} - \item Negative Zahlen sind sowohl für die Potenzreihe als auch für den Kettenbruch ein Problem. - \item Die Potenzreihe hat das Problem, je tiefer die Rekursionstiefe, desto mehr machen die Brüche ein Problem. Also der Nenner mit der Fakultät und dem Pochhammer Symbol. - \item Die Rekursionformel liefert für sehr grosse positive Werte die genausten Ergebnisse, verglichen mit der GNU Scientific Library. -\end{itemize} - - -\subsection{Ausblick -\label{0f1:subsection:ausblick}} -Eine mögliche Lösung zum Problem ist \cite{0f1:SeminarNumerik} -{\color{red} TODO beschreiben Lösung} - +% +% teil3.tex -- Resultate und Ausblick +% +% (c) 2022 Fabian Dünki, Hochschule Rapperswil +% +\section{Resultate +\label{0f1:section:teil3}} +\rhead{Resultate} +Im Verlauf des Seminares hat sich gezeigt, +das ein einfacher mathematischer Algorithmus zu implementieren gar nicht so einfach ist. +So haben alle drei umgesetzten Ansätze Probleme mit grossen negativen z in der Funktion $\mathstrut_0F_1(;c;z)$. +Ebenso wird, je grösser der Wert z wird $\mathstrut_0F_1(;c;z)$, desto mehr weichen die berechneten Resultate +von den Erwarteten ab. \cite{0f1:wolfram-0f1} + +\subsection{Auswertung +\label{0f1:subsection:auswertung}} +\begin{figure} + \centering + \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzAiry.pdf} + \caption{Konvergenz nach drei Iterationen, dargestellt anhand der Airy Funktion zu den Anfangsbedingungen $Ai(0)=1$ und $Ai'(0)=0$. + \label{0f1:ausblick:plot:airy:konvergenz}} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzPositiv.pdf} + \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat. + \label{0f1:ausblick:plot:konvergenz:positiv}} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzNegativ.pdf} + \caption{Konvergenz: Logarithmisch dargestellte Differenz vom erwarteten Endresultat. + \label{0f1:ausblick:plot:konvergenz:negativ}} +\end{figure} + +\begin{figure} + \centering + \includegraphics[width=1\textwidth]{papers/0f1/images/stabilitaet.pdf} + \caption{Stabilität der 3 Algorithmen verglichen mit der GNU Scientific Library. + \label{0f1:ausblick:plot:airy:stabilitaet}} +\end{figure} + +\begin{itemize} + \item Negative Zahlen sind sowohl für die Potenzreihe als auch für den Kettenbruch ein Problem. + \item Die Potenzreihe hat das Problem, je tiefer die Rekursionstiefe, desto mehr machen die Brüche ein Problem. Also der Nenner mit der Fakultät und dem Pochhammer Symbol. + \item Die Rekursionformel liefert für sehr grosse positive Werte die genausten Ergebnisse, verglichen mit der GNU Scientific Library. +\end{itemize} + + +\subsection{Ausblick +\label{0f1:subsection:ausblick}} +Eine mögliche Lösung zum Problem ist \cite{0f1:SeminarNumerik} +{\color{red} TODO beschreiben Lösung} + -- cgit v1.2.1 From 20f444f3f3782440539b51125dec4cb72777f793 Mon Sep 17 00:00:00 2001 From: daHugen Date: Wed, 27 Jul 2022 13:45:38 +0200 Subject: Update to next version, which includes changes in syntax and text structure --- buch/papers/lambertw/teil4.tex | 251 +++++++++++++++++++++++++---------------- 1 file changed, 153 insertions(+), 98 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 84a0ec7..c959715 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -6,19 +6,19 @@ \section{Beispiel einer Verfolgungskurve \label{lambertw:section:teil4}} \rhead{Beispiel einer Verfolgungskurve} -In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie 1 beschreiben. Dafür werden zuerst Bewegungsraum, Anfangspositionen und Bewegungsverhalten definiert, in einem nächsten Schritt soll eine Differentialgleichung dafür aufgestellt werden und anschliessend gelöst werden. +In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie 1 beschreiben. Dafür werden zuerst Bewegungsraum, Anfangspositionen und Bewegungsverhalten definiert, in einem nächsten Schritt soll eine Differentialgleichung dafür aufgestellt und anschliessend gelöst werden. \subsection{Anfangsbedingungen definieren und einsetzen \label{lambertw:subsection:Anfangsbedingungen}} -Das zu verfolgende Ziel \(\vec{Z}\) bewegt sich entlang der \(y\)-Achse mit konstanter Geschwindigkeit \(v = 1\), beginnend beim Ursprung des Kartesischen Koordinatensystems. Der Verfolger \(\vec{V}\) startet auf einem beliebigen Punkt im ersten Quadranten und bewegt sich auch mit konstanter Geschwindigkeit \(|\dot{V}| = 1\) in Richtung Ziel. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: +Das zu verfolgende Ziel \(Z\) bewegt sich entlang der \(y\)-Achse mit konstanter Geschwindigkeit \(v = 1\), beginnend beim Ursprung des Kartesischen Koordinatensystems. Der Verfolger \(V\) startet auf einem beliebigen Punkt im ersten Quadranten und bewegt sich auch mit konstanter Geschwindigkeit \(|\dot{V}| = 1\) in Richtung Ziel. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: \begin{equation} - \vec{Z} + Z = \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) = \left( \begin{array}{c} 0 \\ t \end{array} \right) ,\: - \vec{V} + V = \left( \begin{array}{c} x \\ y \end{array} \right) \:\text{und}\:\: @@ -28,7 +28,7 @@ Das zu verfolgende Ziel \(\vec{Z}\) bewegt sich entlang der \(y\)-Achse mit kons \label{lambertw:Anfangsbed} \end{equation} Wir haben nun die Anfangsbedingungen definiert, jetzt fehlt nur noch eine DGL, welche die fortlaufende Änderung der Position und Bewegungsrichtung des Verfolgers beschreibt. -Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} definiert, und zwar Gleichung \eqref{lambertw:pursuerDGL}. Wenn man die Startpunkte einfügt ergibt sich folgender Ausdruck: +Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} definiert, und zwar Gleichung \eqref{lambertw:pursuerDGL}. Wenn man die Startpunkte 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}} \cdot @@ -38,57 +38,71 @@ Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} defin \label{lambertw:eqMitAnfangsbed} \end{equation} -\subsection{DGL vereinfachen +\subsection{Differentialgleichung vereinfachen \label{lambertw:subsection:DGLvereinfach}} -Nun haben wir eine Gleichung, es stellt sich aber die Frage ob es überhaupt eine geschlossene Lösung dafür gibt. Eine Funktion welche die Beziehung \(y(x)\) beschreibt oder sogar \(x(t)\) und \(y(t)\) liefert. Zum jetzigen Zeitpunkt mag es nicht trivial scheinen, aber mit den gewählten Anfangsbedingungen \eqref{lambertw:Anfangsbed} ist es möglich eine geschlossene Lösung für die Gleichung \eqref{lambertw:eqMitAnfangsbed} zu finden. -Auf dem Weg dahin muss die definierte DGL zuerst wesentlich vereinfacht werden, sei es mittels algebraische Umformungen oder mit den Tools aus der Analysis. Also legen wir los! +Nun haben wir eine Gleichung, es stellt sich aber die Frage, ob es überhaupt eine geschlossene Lösung dafür gibt. Eine Funktion welche die Beziehung \(y(x)\) beschreibt oder sogar \(x(t)\) und \(y(t)\) liefert. Zum jetzigen Zeitpunkt mag es nicht trivial scheinen, aber mit den gewählten Anfangsbedingungen \eqref{lambertw:Anfangsbed} ist es möglich eine geschlossene Lösung für die Gleichung \eqref{lambertw:eqMitAnfangsbed} zu finden. -Zuerst müssen wir den Bruch in \eqref{lambertw:eqMitAnfangsbed} los werden, der sieht so nicht handlich aus. Dafür multiplizieren wir beidseitig mit dem Nenner: -\begin{equation} - \left( \begin{array}{c} 0-x \\ t-y \end{array} \right) - \cdot - \left(\begin{array}{c} \dot{x} \\ \dot{y} \end{array}\right) - = \sqrt{x^2 + (t-y)^2}. - \label{lambertw:eqOhneBruch} -\end{equation} -In einem weiteren Schritt, lösen wir das Skalarprodukt auf und erhalten folgende Gleichung \eqref{lambertw:eqOhneSkalarprod} ohne vektorielle Grössen: +Auf dem Weg dahin muss die definierte DGL zuerst wesentlich vereinfacht werden, sei es mittels algebraischer Umformungen oder mit den Tools aus der Analysis. Da die nächsten Schritte sehr algebralastig sind und sie das Lesen dieses Papers einfach nur mühsam machen würden, werden wir uns hier nur die wesentlichsten Schritte konzentrieren, welche notwendig sind, um den Lösungsweg nachvollziehen zu können. + +\subsubsection{Skalarprodukt auflösen + \label{lambertw:subsubsection:SkalProdAufl}} +Zuerst müssen wir den Bruch und das Skalarprodukt in \eqref{lambertw:eqMitAnfangsbed} wegbringen, damit wir eine. Dies führt zu: \begin{equation} -x \cdot \dot{x} + (t-y) \cdot \dot{y} = \sqrt{x^2 + (t-y)^2}. \label{lambertw:eqOhneSkalarprod} \end{equation} -Im letzten Schritt, fällt die Nützlichkeit des Skalarproduktes in der Verfolgungsgleichung \eqref{lambertw:pursuerDGL} markant auf. Meiner Meinung ziemlich elegant und nicht selbstverständlich in der Lage zu sein, das Problem auf eine einzige Gleichung reduzieren zu können. +Im letzten Schritt, fällt die Nützlichkeit des Skalarproduktes in der Verfolgungsgleichung \eqref{lambertw:pursuerDGL} markant auf. Anstatt zwei gekoppelte Differentialgleichungen zu erhalten, eine für die \(x\) und die andere für die \(y\)-Komponente, erhält man einen einzigen Ausdruck, was in der Regel mit weniger Lösungsaufwand verbunden ist. -Die nächsten Schritte sind sehr algebralastig und würden das lesen dieses Papers einfach nur mühsam machen, also werde ich diese auslassen. Hingegen werden ich die algebraische Hauptschritte erwähnen, die notwendig wären falls man es trotzdem selber ausprobieren möchte: -\begin{itemize} - \item - Quadrieren und erweitern. - \item - Gruppieren. - \item - Substitution von einzelnen Thermen mittels der Beziehung \(\dot{x}^2 + \dot{y}^2 = 1\). - \item - Und das erkennen des Musters einer Binomischen Formel. -\end{itemize} -Das Resultat aller dieser Vereinfachungen führen zu folgender Gleichung \eqref{lambertw:eqAlgVerinfacht}, die viel handhabbarer ist als zuvor: +\subsubsection{Quadrieren und Gruppieren + \label{lambertw:subsubsection:QuadUndGrup}} +Mit der Quadratwurzel in \ref{lambertw:eqOhneSkalarprod} kann man nichts anfangen, sie steht nur im Weg, also muss man sie loswerden. Wenn man dies macht, kann \eqref{lambertw:eqOhneSkalarprod} auf folgende Form gebracht werden: +\begin{equation} + \left(\dot{x}^2-1\right) \cdot x^2 -2x \left(t-y\right) \dot{x}\dot{y} + \left(\dot{y}^2-1\right) \cdot \left(t-y\right)^2 + =0. + \label{lambertw:eqOhneWurzel} +\end{equation} +Diese Form mag auf den ersten Blick nicht gerade nützlich sein, aber man kann sie mit einer Substitution weiter vereinfachen. + +\subsubsection{Wichtige Substitution + \label{lambertw:subsubsection:WichtSubst}} +Wenn man beachtet, dass die Geschwindigkeit des Verfolgers konstant und gleich 1 ist, dann kann man folgende Gleichung aufstellen: +\begin{equation} + \dot{x}^2 + \dot{y}^2 + = 1. + \label{lambertw:eqGeschwSubst} +\end{equation} +Umformungen der Gleichung \eqref{lambertw:eqGeschwSubst} können in \eqref{lambertw:eqOhneWurzel} erkannt werden. Ersetzt führen sie zu folgendem Ausdruck: +\begin{equation} + \dot{y}^2 \cdot x^2 +2x \left(t-y\right) \dot{x}\dot{y} + \dot{x}^2 \cdot \left(t-y\right)^2 + =0. + \label{lambertw:eqGeschwSubstituiert} +\end{equation} +Diese unscheinbare Substitution führt dazu, dass weitere Vereinfachungen durchgeführt werden können. + +\subsubsection{Binom erkennen und vereinfachen + \label{lambertw:subsubsection:BinomVereinfach}} +Versteckt im Ausdruck \eqref{lambertw:eqGeschwSubstituiert} befindet sich die erste binomische Formel, welche zu folgender Gleichung führt: \begin{equation} (x \dot{y} + (t-y) \dot{x})^2 = 0. \label{lambertw:eqAlgVerinfacht} \end{equation} -Da der linke Term gleich Null ist, muss auch der Inhalt des Quadrates gleich Null sein, somit folgt eine weitere Vereinfachung, welche zu einer im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} wesentlich einfachere DGL führt: +Da der linke Term gleich Null ist, muss auch der Inhalt des Quadrates gleich Null sein, somit folgt eine weitere Vereinfachung, welche zu einer im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} wesentlich einfacheren DGL führt: \begin{equation} x \dot{y} + (t-y) \dot{x} = 0. \label{lambertw:eqGanzVerinfacht} \end{equation} -Kompakt, ohne Wurzelterme und Quadrate, nur elementare Operationen und Ableitungen. Nun stellt sich die Frage wie es weiter gehen soll, bei der Gleichung \eqref{lambertw:eqGanzVerinfacht} scheinen keine weiteren Vereinfachungen möglich zu sein. Wir brauchen einen neuen Ansatz um unser Ziel einer möglichen Lösung zu verfolgen. +Kompakt, ohne Wurzelterme und Quadrate, nur elementare Operationen und Ableitungen. Nun stellt sich die Frage wie es weiter gehen soll, bei der Gleichung \eqref{lambertw:eqGanzVerinfacht} scheinen keine weiteren Vereinfachungen möglich zu sein. Wir brauchen einen neuen Ansatz, um unser Ziel einer möglichen Lösung zu verfolgen. \subsection{Zeitabhängigkeit loswerden \label{lambertw:subsection:ZeitabhLoswerden}} -Der nächste logischer Schritt schient irgendwie die Zeitabhängigkeit in der Gleichung \eqref{lambertw:eqGanzVerinfacht} loszuwerden, aber wieso? Nun, wie am Anfang von Abschnitt \ref{lambertw:subsection:DGLvereinfach} beschrieben, suchen wir eine Lösung der Art \(y(x)\), dies ist natürlich erst möglich wenn wir die Abhängigkeit nach \(t\) eliminieren können. +Der nächste logischer Schritt scheint irgendwie die Zeitabhängigkeit in der Gleichung \eqref{lambertw:eqGanzVerinfacht} loszuwerden, aber wieso? Nun, wie am Anfang von Abschnitt \ref{lambertw:subsection:DGLvereinfach} beschrieben, suchen wir eine Lösung der Art \(y(x)\), dies ist natürlich erst möglich wenn wir die Abhängigkeit nach \(t\) eliminieren können. -Der erste Schritt auf dem Weg dahin, ist es die zeitlichen Ableitung los zu werden, dafür wird \eqref{lambertw:eqGanzVerinfacht} beidseitig mit \(\dot{x}\) dividiert, was erlaubt ist, weil diese Änderung ungleich Null ist: +\subsubsection{Zeitliche Ableitungen loswerden + \label{lambertw:subsubsection:ZeitAbleit}} +Der erste Schritt auf dem Weg zur Funktion \(y(x)\), ist es die zeitlichen Ableitungen los zu werden, dafür wird \eqref{lambertw:eqGanzVerinfacht} beidseitig mit \(\dot{x}\) dividiert, was erlaubt ist, weil diese Änderung ungleich Null ist: \begin{equation} x \frac{\dot{y}}{\dot{x}} + (t-y) \frac{\dot{x}}{\dot{x}} = 0. @@ -103,13 +117,17 @@ Der Grund dafür ist, dass \label{lambertw:eqQuotZeitAbleit} \end{equation} und somit kann der Quotient dieser zeitlichen Ableitungen in eine Ableitung nach \(x\) umgewandelt werden. -Nach dem diese Eigenschaft \eqref{lambertw:eqQuotZeitAbleit} in \eqref{lambertw:eqVorKeineZeitAbleit} eingesetzt wird und vereinfacht wurde, entsteht folgende neue Gleichung: +Nach dem die Eigenschaft \eqref{lambertw:eqQuotZeitAbleit} in \eqref{lambertw:eqVorKeineZeitAbleit} eingesetzt wird und vereinfacht wurde, entsteht die neue Gleichung \begin{equation} x y^{\prime} + t - y = 0. \label{lambertw:DGLmitT} \end{equation} -Hier wäre es natürlich passend wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen muss man auf die Definition der Bogenlänge aus der Analysis zurückgreifen, wobei die Strecke \(s\) folgendem entspricht: + +\subsubsection{Variable \(t\) eliminieren + \label{lambertw:subsubsection:ZeitAbleit}} +Hier wäre es natürlich passend, wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen, muss man auf die Definition der Bogenlänge zurückgreifen. +Die Strecke \(s\) entspricht \begin{equation} s = @@ -122,13 +140,16 @@ Hier wäre es natürlich passend wenn man die Abhängigkeit nach \(t\) komplett \int_{\displaystyle x_0}^{\displaystyle x_{\text{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: + +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 und erhaltet folgende DGL \eqref{lambertw:DGLohneInt}: +Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambertw:DGLohneT} nach \(x\) ab und erhaltet folgende DGL zweiter Ordnung \eqref{lambertw:DGLohneInt}: \begin{align} y^{\prime}+ xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} - y^{\prime} &= 0, \\ @@ -138,16 +159,22 @@ Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambert \end{align} Nun sind wir unserem Ziel einen weiteren Schritt näher. Die Gleichung \eqref{lambertw:DGLohneInt} mag auf den ersten Blick nicht gerade einfach sein, aber im Nächsten Abschnitt werden wir sehen, dass sie relativ einfach zu lösen ist. -\subsection{DGL lösen +\subsection{Differentialgleichung lösen \label{lambertw:subsection:DGLloes}} -Die Gleichung \eqref{lambertw:DGLohneInt} ist eine DGL zweiter Ordnung und kann -mittels der Substitution \(y^{\prime} = u\) in eine DGL erster Ordnung umgewandelt werden: +Die Gleichung \eqref{lambertw:DGLohneInt} ist eine DGL zweiter Ordnung, in der \(y\) nicht vorkommt. Sie kann mittels der Substitution \(y^{\prime} = u\) in eine DGL erster Ordnung umgewandelt werden: \begin{equation} xu^{\prime} - \sqrt{1+u^2} = 0. \label{lambertw:DGLmitU} \end{equation} -Diese \eqref{lambertw:DGLmitU} zu lösen ist ziemlich einfach da sie separierbar ist, aus diesem Grund werde ich direkt zur Lösung \eqref{lambertw:loesDGLmitU} übergehen: +Diese Gleichung ist separierbar, was sie viel handlicher macht. In der separierten Form +\begin{equation} + \int{\frac{1}{\sqrt{1+u^2}}\:du} + = + \int{\frac{1}{x}\:dx}, +\end{equation} +lässt sich die Gleichung mittels einer Integrationstabelle sehr rasch lösen. +Mit dem Ergebnis: \begin{align} \operatorname{arsinh}(u) &= @@ -157,20 +184,20 @@ Diese \eqref{lambertw:DGLmitU} zu lösen ist ziemlich einfach da sie separierbar \operatorname{sinh}(\operatorname{ln}(x) + C). \label{lambertw:loesDGLmitU} \end{align} -Indem man die Substitution rückgängig macht, erhält man eine weitere DGL erster Ordnung die bereits separiert ist und erhält folgende Gleichung: +Wenn man in \eqref{lambertw:loesDGLmitU} die Substitution rückgängig macht, erhält man folgende DGL erster Ordnung, die bereits separiert ist: \begin{equation} y^{\prime} = \operatorname{sinh}(\operatorname{ln}(x) + C). \label{lambertw:loesDGLmitY} \end{equation} -Diese \eqref{lambertw:loesDGLmitY} kann mit den selben Methoden gelöst werden wie \eqref{lambertw:DGLmitU}, diesmal aber in Kombination mit der exponentiellen Definition der \(\operatorname{sinh}\)-Funktion: +Ersetzt man den \(\operatorname{sinh}\) mit seiner exponentiellen Definition \(\operatorname{sinh}(x)=\frac{1}{2}(e^x-e^{-x})\), so resultiert auf sehr einfache Art folgende Lösung für \eqref{lambertw:loesDGLmitY}: \begin{equation} y = C_1 + C_2 x^2 - \frac{\operatorname{ln}(x)}{8 \cdot C_2}. \end{equation} -Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die Frage ob sie überhaupt plausibel ist. Dieser Frage werden wir in nächsten Abschnitt \ref{lambertw:subsection:LoesAnalys} nachgehen. +Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die Frage, ob sie überhaupt plausibel ist. Dieser Frage werden wir im nächsten Abschnitt nachgehen. \subsection{Lösung analysieren \label{lambertw:subsection:LoesAnalys}} @@ -178,7 +205,7 @@ Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die \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. + \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{\operatorname{ln}(x)}-Teil entspricht. \label{lambertw:BildFunkLoes} } \end{figure} @@ -190,24 +217,30 @@ Das Resultat, wie ersichtlich, ist folgende Funktion \eqref{lambertw:funkLoes} w C_1 + C_2 {\color{darkgreen}{x^2}} {\color{blue}{-}} \frac{\color{blue}{\operatorname{ln}(x)}}{8 \cdot C_2}. \label{lambertw:funkLoes} \end{equation} -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 \(y(x)\) 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 \(y(x)\) 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 \eqref{lambertw:funkLoes} dominant. \item - 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. Irgendwann werden Verfolger und Ziel auf gleicher Höhe sein. + 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. Irgendwann werden Verfolger und Ziel auf gleicher Höhe sein, also gleiche \(y\) aber verschiedene \(x\)-Koordinate besitzen. \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. + 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 ihm nachgeht. \item Aufgrund des Monotoniewechsels in der Kurve \eqref{lambertw:funkLoes} muss diese auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? - Eine Abschätzung darüber kann 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 des Verfolgers, somit auch sein Vorzeichen und dadurch entsteht auch das Minimum. \end{itemize} -Alle diese Eigenschafte stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde, welche durch die Grafik \ref{lambertw:BildFunkLoes} repräsentiert wurde. Nun stellt sich die Frage wie die Kurve wirklich aussieht. Dies wird im folgenden Abschnitt \ref{lambertw:subsection:AllgLoes} behandelt. +Alle diese Eigenschaften stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde, welche durch die Grafik \ref{lambertw:BildFunkLoes} repräsentiert wurde. \subsection{Anfangswertproblem \label{lambertw:subsection:AllgLoes}} -Wie üblich bei der Suche nach einer exakten Lösung, kommt ein Anfangswertproblem vor. Um dieses zu lösen, müssen wir zuerst die Anfangswerte definieren. Da wir das Problem allgemein lösen wollen, ergeben sich folgende zwei Anfangswerte: +In diesem Abschnitt soll eine Parameterfunktion hergeleitet werden, bei der jeder beliebige Anfangspunkt im ersten Quadranten eingesetzt werden kann, ausser der Ursprung im Koordinatensystem. Diese Aufgabe erfordert ein Anfangswertproblem. + +Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches hier nicht explizit eingegangen wird. Zur Vollständigkeit und Nachvollziehbarkeit, wird aber das Gleichungssystem präsentiert, welches notwendig ist, um das Anfangswertproblem zu lösen. + +\subsubsection{Anfangswerte bestimmen + \label{lambertw:subsubsection:Anfangswerte}} +Der erste Schritt auf dem Weg zur gesuchten Parameterfunktion ist, die Anfangswerte \eqref{lambertw:eq1Anfangswert} zu definieren. +Die Anfangswerte sind: \begin{equation} y(x)\big \vert_{t=0} = @@ -227,50 +260,63 @@ und \end{equation} Der zweite Anfangswert \eqref{lambertw:eq2Anfangswert} mag nicht grade offensichtlich sein. Die Erklärung dafür ist aber simpel: Der Verfolger wird sich zum Zeitpunkt \(t=0\) in Richtung Koordinatenursprung bewegen wollen, wo sich das Ziel befindet. Somit entsteht das Steigungsdreieck mit \(\Delta x = x_0\) und \(\Delta y = y_0\). -Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches ich nicht unbedingt eingehen möchte. Zur Vollständigkeit und Nachvollziehbarkeit, werde ich aber das Gleichungssystem \eqref{lambertw:eqGleichungssystem} präsentieren, welches notwendig ist um das Anfangswertproblem zu lösen, sowie auch die allgemeine Lösung \eqref{lambertw:eqAllgLoes} die sich nach dem einsetzen der Koeffizienten \(C_1\) und \(C_2\) in die Funktion \eqref{lambertw:funkLoes} ergibt. - -\begin{itemize} - \item - Gleichungssystem: - \begin{subequations} - \begin{align} - y_0 - &= - C_1 + C_2 x^2_0 - \frac{\operatorname{ln}(x_0)}{8 \cdot C_2}, \\ - \frac{y_0}{x_0} - &= - 2 \cdot C_2 x_0 - \frac{1}{8 \cdot C_2 \cdot x_0}. - \end{align} - \label{lambertw:eqGleichungssystem} - \end{subequations} - \item - Die allgemeine Funktion: - \begin{equation} - y(x) - = - \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right) - \label{lambertw:eqAllgLoes} - \end{equation} - Damit die Funkion \eqref{lambertw:eqAllgLoes} trotzdem noch übersichtlich bleibt, wurden \(\eta\) und \(r_0\) wie folgt definiert: - \begin{equation} - \eta - = - \left(\frac{x}{x_0}\right)^2 - \:\:\text{und}\:\: - r_0 - = - \sqrt{x_0^2+y_0^2}. - \end{equation} -\end{itemize} -Diese neue allgemein Funktion \eqref{lambertw:eqAllgLoes} weist immer noch die selbe Struktur wie die vorherig hergeleitete Funktion \eqref{lambertw:funkLoes} auf, einerseits einen quadratischen Teil der in \(\eta\) enthalten ist, anderseits den \(\operatorname{ln}\)-Teil. Aus dieser Ähnlichkeit kann geschlossen werden, dass sich \eqref{lambertw:eqAllgLoes} auf eine ähnliche Art verhalten wird. +\subsubsection{Gleichungssystem aufstellen und lösen + \label{lambertw:subsubsection:GlSys}} +Wenn man die Anfangswerte \eqref{lambertw:eq1Anfangswert} und \eqref{lambertw:eq2Anfangswert} in die Gleichung \eqref{lambertw:funkLoes} und deren Ableitung \(y^{\prime}(x)\) einsetzt, dann ergibt sich folgendes Gleichungssystem: +\begin{subequations} + \begin{align} + y_0 + &= + C_1 + C_2 x^2_0 - \frac{\operatorname{ln}(x_0)}{8 \cdot C_2}, \\ + \frac{y_0}{x_0} + &= + 2 \cdot C_2 x_0 - \frac{1}{8 \cdot C_2 \cdot x_0}. + \end{align} + \label{lambertw:eqGleichungssystem} +\end{subequations} +Damit die gesuchte Funktion im ersten Quadranten bleibt, werden nur die positiven Lösungen des Gleichungssystems gewählt, welche wie folgt aussehen: +\begin{subequations} + \begin{align} + \label{lambertw:eqKoeff1} + C_1 + &= + \frac{2\cdot\operatorname{ln}(x_0)\left(\sqrt{x_0^2 + y_0^2} - y_0 \right) - \sqrt{x_0^2 + y_0^2} + 3 y_0}{4}, \\ + \label{lambertw:eqKoeff2} + C_2 + &= + \frac{\sqrt{x_0^2 + y_0^2} + y_0}{4x_0^2}. + \end{align} +\end{subequations} +\subsubsection{Gesuchte Parameterfunktion aufstellen + \label{lambertw:subsubsection:ParamFunk}} +Wenn man die Koeffizienten \eqref{lambertw:eqKoeff1} und \eqref{lambertw:eqKoeff2} in die Funktion \eqref{lambertw:funkLoes} einsetzt, dann ergibt sich nach dem Vereinfachen die gesuchte Parameterfunktion: +\begin{equation} + y(x) + = + \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right). + \label{lambertw:eqAllgLoes} +\end{equation} +Damit die Funktion \eqref{lambertw:eqAllgLoes} trotzdem übersichtlich bleibt, wurden Anfangssteigung \(\eta\) und Anfangsentfernung \(r_0\) wie folgt definiert: +\begin{equation} + \eta + = + \left(\frac{x}{x_0}\right)^2 + \:\:\text{und}\:\: + r_0 + = + \sqrt{x_0^2+y_0^2}. +\end{equation} +Diese neue allgemeine Funktion \eqref{lambertw:eqAllgLoes} weist immer noch die selbe Struktur wie die vorher hergeleitete Funktion \eqref{lambertw:funkLoes} auf. Sie enthält einerseits einen quadratischen Teil, der in \(\eta\) enthalten ist, anderseits den \(\operatorname{ln}\)-Teil. Aus dieser Ähnlichkeit kann geschlossen werden, dass sich \eqref{lambertw:eqAllgLoes} auf eine ähnliche Art verhalten wird. -Nun sind wir soweit, dass wir eine \(y(x)\)-Beziehung für beliebige Anfangswerte darstellen können, unser erstes Ziel wurde erreicht. Ist das alles? Nein, wir können einen Schritt weiter gehen und uns Fragen: Ist es analytisch möglich herauszufinden, wo sich Verfolger und Ziel zu jedem Zeitpunkt befinden? Dieser Frage werden wir im nächsten Abschnitt nachgehen. +Nun sind wir soweit, dass wir eine \(y(x)\)-Beziehung für beliebige Anfangswerte darstellen können, unser erstes Ziel wurde erreicht. Wir können aber einen Schritt weiter gehen und uns Fragen: Ist es analytisch möglich herauszufinden, wo sich Verfolger und Ziel zu jedem Zeitpunkt befinden? Dieser Frage werden wir im nächsten Abschnitt nachgehen. \subsection{Funktion nach der Zeit \label{lambertw:subsection:FunkNachT}} -Lieber Leser sei mir nicht böse, aber in diesem Abschnitt werde ich ein wenig mehr bei den algebraischen Umformungen ins Detail gehen. Dies hat auch einen bestimmten Grund, ich möchte den Einsatz einer speziellen Funktion aufzeigen, sowie auch wann und wieso diese vorkommt. Welche spezielle Funktion? Fragst du dich wahrscheinlich in diesem Moment. Nun, um diese Frage zu kurz zu beantworten, es ist "YouTube's favorite special function" laut dem Mathematiker Michael Penn, die Lambert-W-Funktion \(W(x)\) welche übrigens im Kapitel \ref{buch:section:lambertw} bereits beschrieben wurde. +In diesem Abschnitt werden algebraischen Umformungen ein wenig detaillierter als zuvor beschrieben. Dies hat auch einen bestimmten Grund: Den Einsatz einer speziellen Funktion aufzeigen, sowie auch wann und wieso diese vorkommt. Welche spezielle Funktion? Fragst du dich wahrscheinlich in diesem Moment. Nun, um diese Frage kurz zu beantworten, es ist ``YouTube's favorite special function'' laut dem Mathematiker Michael Penn, die Lambert-\(W\)-Funktion \(W(x)\) welche im Kapitel \ref{buch:section:lambertw} bereits beschrieben wurde. -Also fangen wir an. Der erste Schritt ist es herauszufinden, wie die Zeitabhängigkeit wieder hinein gebracht werden kann. Dafür greifen wir auf die letzte Gleichung zu, in welcher \(t\) noch enthalten war, und zwar DGL \eqref{lambertw:DGLmitT}, welche zur Übersichtlichkeit hier nochmals aufgeführt wird: +\subsubsection{Zeitabhängigkeit wiederherstellen + \label{lambertw:subsubsection:ZeitabhWiederherst}} +Der erste Schritt ist es herauszufinden, wie die Zeitabhängigkeit wieder hineingebracht werden kann. Dafür greifen wir auf die letzte Gleichung zu, in welcher \(t\) noch enthalten war, und zwar DGL \eqref{lambertw:DGLmitT}, welche zur Übersichtlichkeit hier nochmals aufgeführt wird: \begin{equation} x y^{\prime} + t - y = 0. @@ -289,6 +335,7 @@ Wie in \eqref{lambertw:eqDGLmitTnochmals} zu sehen ist, werden \(y\) und deren A \end{align} \label{lambertw:eqFunkUndAbleit} \end{subequations} + Wenn man diese Gleichungen \ref{lambertw:eqFunkUndAbleit} in die DGL \label{lambertw:eqDGLmitTnochmals} einfügt, vereinfacht und nach \(t\) auflöst, dann ergibt sich folgenden Ausdruck: \begin{equation} -4t @@ -296,6 +343,12 @@ Wenn man diese Gleichungen \ref{lambertw:eqFunkUndAbleit} in die DGL \label{lamb \left(y_0+r_0\right)\left(\eta-1\right)+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right). \label{lambertw:eqFunkUndAbleitEingefuegt} \end{equation} + +\subsubsection{Umformungen die zur Funktion nach der Zeit führen + \label{lambertw:subsubsection:UmformBisZumZiel}} +Mit dem Ausdruck \eqref{lambertw:eqFunkUndAbleitEingefuegt}, welcher Terme mit \(x\) und \(t\) verbindet, kann nun nach der gesuchten Variable \(x\) aufgelöst werden. + + In einem nächsten Schritt wird alles mit \(x\) auf die eine Seite gebracht, der Rest auf die andere Seite und anschliessend beidseitig exponentiert, was wie folgt aussieht: \begin{align} -4t+\left(y_0+r_0\right) @@ -306,7 +359,7 @@ In einem nächsten Schritt wird alles mit \(x\) auf die eine Seite gebracht, der e^{\displaystyle \left(y_0+r_0\right)\eta}\cdot\eta^{\displaystyle \left(r_0-y_0\right)}. \label{lambertw:eqMitExp} \end{align} -Auf dem rechten Term von \eqref{lambertw:eqMitExp} beginnen wir langsam eine ähnliche Struktur wie \(\eta e^\eta\) zu erkennen, dies schreit nach der Struktur die benötigt wird um \(\eta\) mittels der Lambert-W-Funktion \(W(x)\) zu erhalten. Dies macht durchaus Sinn, wenn wir die Funktion \(x(t)\) finden wollen und \(W(x)\) die Umkehrfunktion von \(x e^x\) ist. +Auf dem rechten Term von \eqref{lambertw:eqMitExp} beginnen wir langsam eine ähnliche Struktur wie \(\eta e^\eta\) zu erkennen, dies schreit nach der Struktur die benötigt wird um \(\eta\) mittels der Lambert-\(W\)-Funktion \(W(x)\) zu erhalten. Dies macht durchaus Sinn, wenn wir die Funktion \(x(t)\) finden wollen und \(W(x)\) die Umkehrfunktion von \(x e^x\) ist. Die erste Sache die uns in \eqref{lambertw:eqMitExp} stört ist, dass \(\eta\) als Potenz da steht. Dieses Problem können wir loswerden, indem wir beidseitig mit \(\:\displaystyle \frac{1}{r_0-y_0}\:\) potenzieren: \begin{equation} @@ -324,14 +377,14 @@ Das nächste Problem auf welches wir in \eqref{lambertw:eqOhnePotenz} treffen is \end{equation} Es gäbe natürlich andere Substitutionen wie z.B. \[\displaystyle \chi=\frac{y_0+r_0}{r_0-y_0}\cdot\eta,\] -die auf das selbe Ergebnis führen würden, aber \eqref{lambertw:eqChiSubst} liefert in einem Schritt die kompakteste Lösung. Also fahren wir mit der Substitution \eqref{lambertw:eqChiSubst} weiter, setzen diese in die Gleichung \eqref{lambertw:eqOhnePotenz} ein und multiplizieren beidseitig mit \(\chi\). Daraus erhalten wir folgende Gleichung: +die auf dasselbe Ergebnis führen würden, aber \eqref{lambertw:eqChiSubst} liefert in einem Schritt die kompakteste Lösung. Also fahren wir mit der Substitution \eqref{lambertw:eqChiSubst} weiter, setzen diese in die Gleichung \eqref{lambertw:eqOhnePotenz} ein und multiplizieren beidseitig mit \(\chi\). Daraus erhalten wir folgende Gleichung: \begin{equation} \chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}} = \chi\eta\cdot e^{\displaystyle \chi\eta}. \label{lambertw:eqNachSubst} \end{equation} -Schön oder? Nun sind wir endlich soweit, dass wir die angedeutete Lambert-W-Funktion \(W(x)\)einsetzen können. Wenn wir beidseitig \(W(x)\) anwenden, dann erhalten wir folgenden Ausdruck: +Nun sind wir endlich soweit, dass wir die angedeutete Lambert-\(W\)-Funktion \(W(x)\)einsetzen können. Wenn wir beidseitig \(W(x)\) anwenden, dann erhalten wir folgenden Ausdruck: \begin{equation} W\left(\chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}}\right) = @@ -354,9 +407,11 @@ Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir di \label{lambertw:eqFunktionenNachT} \end{subequations} Nun haben wir unser letztes Ziel erreicht und sind in der Lage eine Verfolgung rechnerisch sowie graphisch zu repräsentieren. - -Wir sind aber noch nicht ganz fertig, ich muss gestehen, dass ich in diesem Abschnitt einen wichtigen Teil verschwiegen habe. Und zwar wieso, dass ich schon bei der Gleichung \eqref{lambertw:eqFunkUndAbleitEingefuegt} wusste, dass man nach einigen Umformungen die Lambert-W-Funktion eingesetzt werden kann. -Der Grund dafür ist die Struktur + +\subsubsection{Hinweise zur Lambert-\(W\)-Funktion + \label{lambertw:subsubsection:HinwLambertW}} +Wir sind aber noch nicht ganz fertig, eine Frage muss noch beantwortet werden. Und zwar wieso, dass man schon bei der Gleichung \eqref{lambertw:eqFunkUndAbleitEingefuegt} weiss, dass die Lambert-\(W\)-Funktion zum Einsatz kommen wird. +Nun, der Grund dafür ist die Struktur \begin{equation} y = @@ -365,4 +420,4 @@ Der Grund dafür ist die Struktur \end{equation} bei welcher \(p(x)\) eine beliebige Potenz von \(x\) darstellt. -Jedes mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oftmals vorkommt, was die Lambert-W-Funktion so wichtig macht. \ No newline at end of file +Jedes Mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oftmals vorkommt, was die Lambert-\(W\)-Funktion so wichtig macht. \ No newline at end of file -- cgit v1.2.1 From 70c7a56a5b596a09cb63f5749eee342ab2086770 Mon Sep 17 00:00:00 2001 From: daHugen Date: Wed, 27 Jul 2022 14:06:50 +0200 Subject: made some changes --- buch/papers/lambertw/teil4.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index c959715..c79aa0c 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -363,9 +363,9 @@ Auf dem rechten Term von \eqref{lambertw:eqMitExp} beginnen wir langsam eine äh Die erste Sache die uns in \eqref{lambertw:eqMitExp} stört ist, dass \(\eta\) als Potenz da steht. Dieses Problem können wir loswerden, indem wir beidseitig mit \(\:\displaystyle \frac{1}{r_0-y_0}\:\) potenzieren: \begin{equation} - e^{\displaystyle \frac{-4t}{r_0-y_0}+\frac{y_0+r_0}{r_0-y_0}} + \operatorname{exp}\left(\displaystyle \frac{-4t}{r_0-y_0}+\frac{y_0+r_0}{r_0-y_0}\right) = - \eta\cdot e^{\displaystyle \frac{y_0+r_0}{r_0-y_0}\eta} . + \eta\cdot \operatorname{exp}\left(\displaystyle \frac{y_0+r_0}{r_0-y_0}\eta\right). \label{lambertw:eqOhnePotenz} \end{equation} Das nächste Problem auf welches wir in \eqref{lambertw:eqOhnePotenz} treffen ist, dass \(\eta\) nicht alleine im Exponent steht. Dies kann elegant mit folgender Substitution gelöst werden: @@ -379,14 +379,14 @@ Es gäbe natürlich andere Substitutionen wie z.B. \[\displaystyle \chi=\frac{y_0+r_0}{r_0-y_0}\cdot\eta,\] die auf dasselbe Ergebnis führen würden, aber \eqref{lambertw:eqChiSubst} liefert in einem Schritt die kompakteste Lösung. Also fahren wir mit der Substitution \eqref{lambertw:eqChiSubst} weiter, setzen diese in die Gleichung \eqref{lambertw:eqOhnePotenz} ein und multiplizieren beidseitig mit \(\chi\). Daraus erhalten wir folgende Gleichung: \begin{equation} - \chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}} + \chi\cdot \operatorname{exp}\left(\displaystyle \chi-\frac{4t}{r_0-y_0}\right) = \chi\eta\cdot e^{\displaystyle \chi\eta}. \label{lambertw:eqNachSubst} \end{equation} Nun sind wir endlich soweit, dass wir die angedeutete Lambert-\(W\)-Funktion \(W(x)\)einsetzen können. Wenn wir beidseitig \(W(x)\) anwenden, dann erhalten wir folgenden Ausdruck: \begin{equation} - W\left(\chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}}\right) + W\left(\chi\cdot \operatorname{exp}\left(\displaystyle \chi-\frac{4t}{r_0-y_0}\right)\right) = \chi\eta. \end{equation} @@ -396,7 +396,7 @@ Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir di \label{lambertw:eqFunkXNachT} x(t) &= - x_0\cdot\sqrt{\frac{W\left(\chi\cdot e^{\displaystyle \chi-\frac{4t}{r_0-y_0}}\right)}{\chi}}, \\ + x_0\cdot\sqrt{\frac{W\left(\chi\cdot \operatorname{exp}\left(\displaystyle \chi-\frac{4t}{r_0-y_0}\right)\right)}{\chi}}, \\ \label{lambertw:eqFunkYNachT} y(x(t)) = -- cgit v1.2.1 From e7f4d8d568bf62c76f4bf0ffdc0fe009134c184d Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 27 Jul 2022 17:45:10 +0200 Subject: Herleitung Kapitel Bessel --- buch/papers/fm/03_bessel.tex | 123 +++++++++++++++++++++++++++++++++++++++++-- buch/papers/fm/Makefile | 8 +-- buch/papers/fm/packages.tex | 2 +- 3 files changed, 126 insertions(+), 7 deletions(-) (limited to 'buch') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index aed084e..7a0e20e 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -4,9 +4,126 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{FM und Besselfunktion -\label{fm:section:teil2}} -\rhead{Teil 2} - +\label{fm:section:proof}} +\rhead{Herleitung} +Die momentane Trägerkreisfrequenz \(\omega_i\) wie schon in (ref) beschrieben ist, bringt die Vorigen Kapittel beschreiben. (Ableitung \(\frac{d \varphi(t)}{dt}\) mit sich). +Diese wiederum kann durch \(\beta\sin(\omega_mt)\) ausgedrückt werden, wobei es das Modulierende Signal \(m(t)\) ist. +Somit haben wir unser \(x_c\) welches +\[ +\cos(\omega_c t+\beta\sin(\omega_mt)) +\] +ist. +\subsection{Herleitung} +Das Ziel ist es Unser moduliertes Signal mit der Besselfunktion so auszudrücken: +\begin{align} + \cos(\omega_ct+\beta\sin(\omega_mt)) + &= + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) + \label{fm:eq:proof} +\end{align} +Doch dazu brauchen wir die Hilfe der Additionsthoerme +\begin{align} + \cos(A + B) + &= + \cos(A)\cos(B)-\sin(A)\sin(B) + \label{fm:eq:addth1} + \\ + 2\cos (A)\cos (B) + &= + \cos(A-B)+\cos(A+B) + \label{fm:eq:addth2} + \\ + 2\sin(A)\sin(B) + &= + \cos(A-B)-\cos(A+B) + \label{fm:eq:addth3} +\end{align} +und die drei Besselfunktions indentitäten, +\begin{align} + \cos(\beta\sin\phi) + &= + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\phi) + \label{fm:eq:besselid1} + \\ + \sin(\beta\sin\phi) + &= + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\phi) + \label{fm:eq:besselid2} + \\ + J_{-n}(\beta) &= (-1)^n J_n(\beta) + \label{fm:eq:besselid3} +\end{align} +welche man im Kapitel (ref), ref, ref findet. +\newline +Mit dem \refname{fm:eq:addth1} wird aus dem modulierten Signal +\[ +\cos(\omega_c t + \beta\sin(\omega_mt)) +\] +das Signal +\[ + \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). + \label{fm:eq:start} +\] +Zu beginn wird der erste Teil +\[ + \cos(\omega_c)\cos(\beta\sin(\omega_mt)) +\] +mit hilfe der Bessel indentität \ref{fm:eq:besselid1} zum +\[ + J_0(\beta)\cos(\omega_c) + \sum_{k=1}^\infty J_{2k}(\beta) 2\cos(\omega_c t)\cos(2k\omega_m t) +\] +\newline +TODO 2 und \(\cos( )\) in lime. +wobei mit dem \colorbox{lime}{Additionstheorem} \ref{fm:eq:addth2} zum +\[ + J_0(\beta)\dot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} +\] +wird. +Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term +\[ + \sum_{n\, gerade} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) + \label{fm:eq:gerade} +\] +\newline +nun zum zweiten Teil des Term \ref{fm:eq:start} +\[ + \sin(\omega_c)\sin(\beta\sin(\omega_m t)). +\] +Dieser wird mit der \ref{fm:eq:besselid2} Bessel indentität zu +\[ + J_0(\beta) \dot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) 2\sin(\omega_c t)\cos((2k+1)\omega_m t). +\] +Auch hier wird ein Additionstheorem \ref{fm:eq:addth3} gebraucht um aus dem Sumanden diesen Term +\[ + J_0(\beta) \dot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{Teil1} - \cos((\omega_c+(2k+1)\omega_m) t) \} +\]zu gewinnen. +Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. +Zusätzlich dabei noch die letzte Bessel indentität \ref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1 J_n(\beta)\). +Somit wird Teil1 zum negativen Term und die Summe vereinfacht sich zu +\[ + \sum_{n\, ungerade} -1 J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \label{fm:eq:ungerade} +\] +Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. +Beide Teile \ref{fm:eq:gerade} Gerade und \ref{fm:eq:ungerade} Ungerade ergeben zusammen +\[ + \cos(\omega_ct+\beta\sin(\omega_mt)) + = + \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t). +\] +Somit ist \ref{fm:eq:proof} bewiesen. +\newpage +\subsection{Bessel und Frequenzspektrum} +Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. +\begin{figure} + \centering + \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} + \caption{Bessle Funktion \(J_{k}(\beta)\)} + \label{fig:bessel} +\end{figure} +TODO Grafik einfügen, +\newline +Nun einmal das Modulierte FM signal im Frequenzspektrum mit den einzelen Summen dargestellt TODO Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. diff --git a/buch/papers/fm/Makefile b/buch/papers/fm/Makefile index c84963f..aee954f 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -16,15 +16,17 @@ SOURCES := \ #FIGURES := $(patsubst tikz/%.tex, figures/%.pdf, $(TIKZFIGURES)) -#.PHONY: images -#images: $(FIGURES) +all: images standalone + +.PHONY: images +images: $(FIGURES) #figures/%.pdf: tikz/%.tex # mkdir -p figures # pdflatex --output-directory=figures $< .PHONY: standalone -standalone: standalone.tex $(SOURCES) #$(FIGURES) +standalone: standalone.tex $(SOURCES) $(FIGURES) mkdir -p standalone cd ../..; \ pdflatex \ diff --git a/buch/papers/fm/packages.tex b/buch/papers/fm/packages.tex index 4cba2b6..f0ca8cc 100644 --- a/buch/papers/fm/packages.tex +++ b/buch/papers/fm/packages.tex @@ -7,4 +7,4 @@ % if your paper needs special packages, add package commands as in the % following example %\usepackage{packagename} - +\usepackage{xcolor} -- cgit v1.2.1 From 66adfe693cae143039fe70c473d3b0a6b7d64687 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 27 Jul 2022 18:07:36 +0200 Subject: Notation in Teil0 adjusted --- buch/papers/lambertw/teil0.tex | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 6ab0bae..1431faa 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -7,7 +7,7 @@ \label{lambertw:section:Was_sind_Verfolgungskurven}} \rhead{Was sind Verfolgungskurven?} -Verfolgungskurven tauchen oft auf bei Fragen wie "Welchen Pfad begeht ein Hund während er einer Katze nachrennt.". +Verfolgungskurven tauchen oft auf bei Fragen wie "Welchen Pfad begeht ein Hund während er einer Katze nachrennt?". Ein solches Problem hat im Kern immer ein Verfolger und sein Ziel. Der Verfolger verfolgt sein Ziel, das versucht zu entkommen. Der Pfad, den der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. @@ -25,7 +25,7 @@ Der Verfolger hat nur einen direkten Einfluss auf seinen Geschwindigkeitsvektor. Mit diesem kann er neben Richtung und Betrag auch den Abstand zwischen Verfolger und Ziel kontrollieren. Wenn zwei dieser drei Parameter durch die Strategie definiert werden, ist der dritte nicht mehr frei. Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um den Verfolger komplett zu beschreiben. - +% \begin{table} \centering \begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} @@ -64,7 +64,7 @@ Die konstante Geschwindigkeit kann man mit der Gleichung \begin{equation} |\dot{v}| = \operatorname{const} = A - \quad A\in\mathbb{R}>0 + \text{,}\quad A\in\mathbb{R}^+ \end{equation} darstellen. Der Geschwindigkeitsvektor wiederum kann mit der Gleichung \begin{equation} @@ -77,6 +77,7 @@ Die Differenz der Ortsvektoren $v$ und $z$ ist ein Vektor der vom Punkt $V$ auf Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den 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 $\dot{v}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergeben sich \begin{align} \frac{z-v}{|z-v|}\cdot|\dot{v}|\cdot\dot{v} -- cgit v1.2.1 From 141e6d40c59f7cc3eda4ae04b5b1b57e7c7f4075 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 27 Jul 2022 18:10:05 +0200 Subject: adjusted notation in Teil0 --- buch/papers/lambertw/teil0.tex | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 1431faa..f0589e5 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -49,32 +49,32 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um \begin{figure} \centering \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.pdf} - \caption{Vektordarstellung Strategie 1} + \caption{Vektordarstellung Jagdstrategie} \label{lambertw:grafic:pursuerDGL2} \end{figure} % In der Tabelle \ref{lambertw:table:Strategien} sind drei mögliche Strategien aufgezählt. -Im Folgenden wird nur noch auf die Strategie 1 eingegangen. +Im Folgenden wird nur noch auf die Jagdstrategie eingegangen. Bei dieser Strategie ist die Geschwindigkeit konstant und der Verfolger bewegt sich immer direkt auf sein Ziel zu. Der Verfolger und sein Ziel werden als Punkte $V$ und $Z$ modelliert. - In der Abbildung \ref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, wobei $v$ der Ortsvektor des Verfolgers, $z$ der Ortsvektor des Ziels und $\dot{v}$ der Geschwindigkeitsvektor des Verfolgers ist. +Der Geschwindigkeitsvektor entspricht dem Richtungsvektors des Verfolgers. Die konstante Geschwindigkeit kann man mit der Gleichung \begin{equation} |\dot{v}| = \operatorname{const} = A \text{,}\quad A\in\mathbb{R}^+ \end{equation} -darstellen. Der Geschwindigkeitsvektor wiederum kann mit der Gleichung +darstellen. Der Geschwindigkeitsvektor kann mit der Gleichung \begin{equation} \frac{z-v}{|z-v|}\cdot|\dot{v}| = \dot{v} \end{equation} -beschrieben werden. +beschrieben werden, wenn die Jagdstrategie verwendet wird. Die Differenz der Ortsvektoren $v$ und $z$ ist ein Vektor der vom Punkt $V$ auf $Z$ zeigt. -Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den Betrag, die Länge auf eins festgelegt. +Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den Betrag, ein Einheitsvektor erzeugt. 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. @@ -89,7 +89,7 @@ Nun wird die Gleichung mit $\dot{v}$ skalar multipliziert, um das Gleichungssyst &= 1 \text{.} \end{align} -Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Strategie 1 verwendet. +Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Jagdstrategie verwendet. % \subsection{Ziel \label{lambertw:subsection:Ziel}} -- cgit v1.2.1 From 18378909d070e684c0d7ee0b539be7baeee62cea Mon Sep 17 00:00:00 2001 From: Fabian <@> Date: Wed, 27 Jul 2022 18:45:06 +0200 Subject: 0f1, abgabe --- buch/papers/0f1/references.bib | 19 ++++++++++++----- buch/papers/0f1/teil1.tex | 3 +-- buch/papers/0f1/teil2.tex | 20 +++++++----------- buch/papers/0f1/teil3.tex | 46 +++++++++++++++++++++++++----------------- 4 files changed, 49 insertions(+), 39 deletions(-) (limited to 'buch') diff --git a/buch/papers/0f1/references.bib b/buch/papers/0f1/references.bib index 2d3f874..ca1b558 100644 --- a/buch/papers/0f1/references.bib +++ b/buch/papers/0f1/references.bib @@ -10,7 +10,7 @@ date = {2022-07-07}, year = {2022}, month = {7}, - day = {19} + day = {7} } @online{0f1:wiki-airyFunktion, @@ -19,7 +19,7 @@ date = {2022-07-07}, year = {2022}, month = {7}, - day = {25} + day = {7} } @online{0f1:wiki-kettenbruch, @@ -37,7 +37,7 @@ date = {2022-07-07}, year = {2022}, month = {7}, - day = {25} + day = {7} } @online{0f1:wolfram-0f1, @@ -46,7 +46,7 @@ date = {2022-07-07}, year = {2022}, month = {7}, - day = {25} + day = {7} } @online{0f1:wiki-fraction, @@ -55,7 +55,16 @@ date = {2022-07-07}, year = {2022}, month = {7}, - day = {25} + day = {7} +} + +@online{0f1:code, + title = {Vollständiger C-Code}, + url ={https://github.com/AndreasFMueller/SeminarSpezielleFunktionen/tree/master/buch/papers/0f1/listings}, + date = {2022-07-07}, + year = {2022}, + month = {7}, + day = {7} } @book{0f1:SeminarNumerik, diff --git a/buch/papers/0f1/teil1.tex b/buch/papers/0f1/teil1.tex index f8d70a8..2ca9647 100644 --- a/buch/papers/0f1/teil1.tex +++ b/buch/papers/0f1/teil1.tex @@ -6,8 +6,7 @@ \section{Mathematischer Hintergrund \label{0f1:section:mathHintergrund}} \rhead{Mathematischer Hintergrund} -Basierend auf den Herleitungen des vorhergehenden Kapitels \ref{buch:rekursion:section:hypergeometrische-funktion} -und dem Seminarbuch Numerik \cite{0f1:kettenbrueche}, werden im nachfolgenden Abschnitt nochmals die Resultate +Basierend auf den Herleitungen des vorhergehenden Kapitels \ref{buch:rekursion:section:hypergeometrische-funktion}, werden im nachfolgenden Abschnitt nochmals die Resultate beschrieben. \subsection{Hypergeometrische Funktion diff --git a/buch/papers/0f1/teil2.tex b/buch/papers/0f1/teil2.tex index 3c2b5cd..9269961 100644 --- a/buch/papers/0f1/teil2.tex +++ b/buch/papers/0f1/teil2.tex @@ -6,7 +6,7 @@ \section{Umsetzung \label{0f1:section:teil2}} \rhead{Umsetzung} -Zur Umsetzung wurden drei verschiedene Ansätze gewählt. Dabei wurde der Schwerpunkt auf die Funktionalität und eine gute Lesbarkeit des Codes gelegt. +Zur Umsetzung wurden drei verschiedene Ansätze gewählt.\cite{0f1:code} Dabei wurde der Schwerpunkt auf die Funktionalität und eine gute Lesbarkeit des Codes gelegt. Die Unterprogramme wurde jeweils, wie die GNU Scientific Library, in C geschrieben. Die Zwischenresultate wurden vom Hauptprogramm in einem CSV-File gespeichert. Anschliessen wurde mit der Matplot-Libray in Python die Resultate geplottet. \subsection{Potenzreihe @@ -35,20 +35,16 @@ Ein endlicher Kettenbruch ist ein Bruch der Form a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{b_3}{a_3+\cdots}}} \end{equation*} in welchem $a_0, a_1,\dots,a_n$ und $b_1,b_2,\dots,b_n$ ganze Zahlen darstellen. - Die Kurzschreibweise für einen allgemeinen Kettenbruch ist \begin{equation*} a_0 + \frac{a_1|}{|b_1} + \frac{a_2|}{|b_2} + \frac{a_3|}{|b_3} + \cdots \end{equation*} und ist somit verknüpfbar mit der Potenzreihe. \cite{0f1:wiki-kettenbruch} - -Angewendet auf die Funktion $\mathstrut_0F_1$ bedeutet dies: +Angewendet auf die Funktion $\mathstrut_0F_1$ bedeutet dies\cite{0f1:wiki-fraction}: \begin{equation*} \mathstrut_0F_1(;c;z) = 1 + \frac{z}{c\cdot1!} + \frac{z^2}{c(c+1)\cdot2!} + \frac{z^3}{c(c+1)(c+2)\cdot3!} + \cdots \end{equation*} -\cite{0f1:wiki-fraction} - Nach allen Umformungen ergibt sich folgender, irregulärer Kettenbruch \eqref{0f1:math:kettenbruch:0f1:eq} \begin{equation} \label{0f1:math:kettenbruch:0f1:eq} @@ -57,13 +53,13 @@ Nach allen Umformungen ergibt sich folgender, irregulärer Kettenbruch \eqref{0f der als Code \ref{0f1:listing:kettenbruchIterativ} umgesetzt wurde. \cite{0f1:wolfram-0f1} -\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchIterativ}, firstline=8]{papers/0f1/listings/kettenbruchIterativ.c} +\lstinputlisting[style=C,float,caption={Iterativ umgesetzter Kettenbruch.},label={0f1:listing:kettenbruchIterativ}, firstline=8]{papers/0f1/listings/kettenbruchIterativ.c} \subsection{Rekursionsformel \label{0f1:subsection:rekursionsformel}} -Wesentlich stabiler zur Berechnung eines Kettenbruches ist die Rekursionsformel. Nachfolgend wird die verkürzte Herleitung vom Kettenbruch zur Rekursionsformel aufgezeigt. Eine vollständige Schritt für Schritt Herleitung ist im Seminarbuch Numerik, im Kapitel Kettenbrüche zu finden. \cite{0f1:kettenbrueche}) +Wesentlich stabiler zur Berechnung eines Kettenbruches ist die Rekursionsformel. Nachfolgend wird die verkürzte Herleitung vom Kettenbruch zur Rekursionsformel aufgezeigt. Eine vollständige Schritt für Schritt Herleitung ist im Seminarbuch Numerik, im Kapitel Kettenbrüche zu finden. \cite{0f1:kettenbrueche} -\subsubsection{Verkürzte Herleitung} +\subsubsection{Herleitung} Ein Näherungsbruch in der Form \begin{align*} \cfrac{A_k}{B_k} = a_k + \cfrac{b_{k + 1}}{a_{k + 1} + \cfrac{p}{q}} @@ -93,7 +89,6 @@ Dies lässt sich auch durch die folgende Matrizenschreibweise ausdrücken: \end{pmatrix}. %\label{0f1:math:rekursionsformel:herleitung} \end{equation*} - Wendet man dies nun auf den Kettenbruch in der Form \begin{equation*} \frac{A_k}{B_k} = a_0 + \cfrac{b_1}{a_1+\cfrac{b_2}{a_2+\cfrac{\cdots}{\cdots+\cfrac{b_{k-1}}{a_{k-1} + \cfrac{b_k}{a_k}}}}} @@ -124,7 +119,6 @@ an, ergibt sich folgende Matrixdarstellungen: a_k \end{pmatrix} \end{align*} - Nach vollständiger Induktion ergibt sich für den Schritt $k$, die Matrix \begin{equation} \label{0f1:math:matrix:ende:eq} @@ -142,7 +136,6 @@ Nach vollständiger Induktion ergibt sich für den Schritt $k$, die Matrix a_k \end{pmatrix}. \end{equation} - Und Schlussendlich kann der Näherungsbruch \[ \frac{Ak}{Bk} @@ -161,6 +154,7 @@ B_{-1} &= 1 & B_0 &= 1 \item Schritt $k\to k+1$: \[ \begin{aligned} +\label{0f1:math:loesung:eq} k &\rightarrow k + 1: & A_{k+1} &= A_{k-1} \cdot b_k + A_k \cdot a_k \\ @@ -175,4 +169,4 @@ Näherungsbruch: \qquad$\displaystyle\frac{A_k}{B_k}$ Ein grosser Vorteil dieser Umsetzung \ref{0f1:listing:kettenbruchRekursion} ist, dass im Vergleich zum Code \ref{0f1:listing:kettenbruchIterativ} eine Division gespart werden kann und somit weniger Rundungsfehler entstehen können. %Code -\lstinputlisting[style=C,float,caption={Iterativ umgesetzter Kettenbruch.},label={0f1:listing:kettenbruchRekursion}, firstline=8]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file +\lstinputlisting[style=C,float,caption={Rekursionsformel für Kettenbruch.},label={0f1:listing:kettenbruchRekursion}, firstline=8]{papers/0f1/listings/kettenbruchRekursion.c} \ No newline at end of file diff --git a/buch/papers/0f1/teil3.tex b/buch/papers/0f1/teil3.tex index 355e1b7..2855e26 100644 --- a/buch/papers/0f1/teil3.tex +++ b/buch/papers/0f1/teil3.tex @@ -3,17 +3,37 @@ % % (c) 2022 Fabian Dünki, Hochschule Rapperswil % -\section{Resultate +\section{Auswertung \label{0f1:section:teil3}} \rhead{Resultate} Im Verlauf des Seminares hat sich gezeigt, das ein einfacher mathematischer Algorithmus zu implementieren gar nicht so einfach ist. -So haben alle drei umgesetzten Ansätze Probleme mit grossen negativen z in der Funktion $\mathstrut_0F_1(;c;z)$. -Ebenso wird, je grösser der Wert z wird $\mathstrut_0F_1(;c;z)$, desto mehr weichen die berechneten Resultate -von den Erwarteten ab. \cite{0f1:wolfram-0f1} +So haben alle drei umgesetzten Ansätze Probleme mit grossen negativen $z$ in der Funktion $\mathstrut_0F_1(;c;z)$. +Ebenso kann festgestellt werden,dass je grösser der Wert $z$ in $\mathstrut_0F_1(;c;z)$ wird, desto mehr weichen die berechneten Resultate von den Erwarteten ab. \cite{0f1:wolfram-0f1} + +\subsection{Konvergenz +\label{0f1:subsection:konvergenz}} +Es zeigt sich in Abbildung \ref{0f1:ausblick:plot:airy:konvergenz}, dass schon nach drei Iterationen ($k = 3$) die Funktionen schon genaue Resultate im Bereich von -2 bis 2 liefert. Ebenso kann festgestellt werden, dass der Kettenbruch schneller konvergiert und im positiven Bereich sogar mit der Referenzfunktion $Ai(x)$ übereinstimmt. Da die Rekursionsformel \ref{0f1:listing:kettenbruchRekursion} eine Abwandlung des Kettenbruches ist, verhalten sich die Funktionen in diesem Fall gleich. + +Erst wenn mehrere Durchläufe gemacht werden, um die Genauigkeit zu verbessern, ist der Kettenbruch den anderen zwei Algorithmen, bezüglich Konvergenz überlegen. +Interessant ist auch, dass die Rekursionsformel nahezu gleich schnell wie die Potenzreihe konvergiert, aber sich danach einschwingt. Dieses Verhalten ist auch bei grösseren $z$ zu beobachten, allerdings ist dann die Differenz zwischen dem ersten lokalen Minimum von k bis zum Abbruch kleiner. +\ref{0f1:ausblick:plot:konvergenz:positiv} +Dieses Phänomen ist auf die Lösung der Rekursionsformel zurück zu führen.\ref{0f1:math:loesung:eq} Da im Gegensatz die ganz kleinen Werte nicht zu einer Konvergenz wie beim Kettenbruch führen, sondern sich noch eine Zeit lang durch die Multiplikation aufschwingen. + +Ist $z$ negativ wie im Abbild \ref{0f1:ausblick:plot:konvergenz:negativ}, führt dies zu einer Gegenseitigen Kompensation von negativen und positiven Termen so bricht die Rekursionsformel hier zusammen mit der Potenzreihe ab. +Die ansteigende Differenz mit anschliessender, ist aufgrund der sich alternierenden Termen mit wechselnden Vorzeichens zu erklären. + +\subsection{Stabilität +\label{0f1:subsection:Stabilitaet}} +Verändert sich der Wert von z in $\mathstrut_0F_1(;c;z)$ gegen grössere positive Werte, wie zum Beispiel $c = 800$ liefert die Kettenbruch-Funktion \ref{0f1:listing:kettenbruchIterativ} \verb+inf+ zurück. Dies könnte durch ein Abbruchkriterien abgefangen werden. Allerdings würde das, bei grossen Werten zulasten der Genauigkeit gehen. Trotzdem könnte, je nach Anwendung, auf ein paar Nachkommastellen verzichtet werden. + +Wohingegen die Potenzreihe \ref{0f1:listing:potenzreihe} das Problem hat, dass je mehr Terme berechnet werden, desto schneller wächst die Fakultät und irgendwann gibt es eine Bereichsüberschreitung von \verb+double+. Schlussendlich gibt das Unterprogramm das Resultat \verb+-nan(ind)+ zurück. +Die Rekursionformel \ref{0f1:listing:kettenbruchRekursion} liefert für sehr grosse positive Werte die genausten Ergebnisse, verglichen mit der GNU Scientific Library. Wie schon vermutet ist die Rekursionsformel, im positivem Bereich, der stabilste Algorithmus. Um die Stabilität zu gewährleisten, muss wie in \ref{0f1:ausblick:plot:konvergenz:positiv} dargestellt, die Iterationstiefe $k$ genug gross gewählt werden. + +Im negativem Bereich sind alle gewählten und umgesetzten Ansätze instabil. Grund dafür ist die Fakultät im Nenner, was zum Phänomen der Auslöschung führt.\cite{0f1:SeminarNumerik} Schön zu beobachten ist dies in der Abbildung \ref{0f1:ausblick:plot:airy:stabilitaet} mit der Airy-Funktion als Test. So sind sowohl der Kettenbruch, als auch die Rekursionsformel bis ungefähr $\frac{-15^3}{9}$ stabil. Dies macht auch Sinn, da beide auf der gleichen mathematischen Grundlage basieren. Danach verhält sich allerdings die Instabilität unterschiedlich. Das unterschiedliche Verhalten kann damit erklärt werden, dass beim Kettenbruch jeweils eine zusätzliche Division stattfindet. Diese Unterschiede sind auch in Abbildung \ref{0f1:ausblick:plot:konvergenz:positiv} festzustellen. + + -\subsection{Auswertung -\label{0f1:subsection:auswertung}} \begin{figure} \centering \includegraphics[width=0.8\textwidth]{papers/0f1/images/konvergenzAiry.pdf} @@ -38,19 +58,7 @@ von den Erwarteten ab. \cite{0f1:wolfram-0f1} \begin{figure} \centering \includegraphics[width=1\textwidth]{papers/0f1/images/stabilitaet.pdf} - \caption{Stabilität der 3 Algorithmen verglichen mit der GNU Scientific Library. + \caption{Stabilität der 3 Algorithmen verglichen mit der Referenz Funktion $Ai(x)$. \label{0f1:ausblick:plot:airy:stabilitaet}} \end{figure} -\begin{itemize} - \item Negative Zahlen sind sowohl für die Potenzreihe als auch für den Kettenbruch ein Problem. - \item Die Potenzreihe hat das Problem, je tiefer die Rekursionstiefe, desto mehr machen die Brüche ein Problem. Also der Nenner mit der Fakultät und dem Pochhammer Symbol. - \item Die Rekursionformel liefert für sehr grosse positive Werte die genausten Ergebnisse, verglichen mit der GNU Scientific Library. -\end{itemize} - - -\subsection{Ausblick -\label{0f1:subsection:ausblick}} -Eine mögliche Lösung zum Problem ist \cite{0f1:SeminarNumerik} -{\color{red} TODO beschreiben Lösung} - -- cgit v1.2.1 From 166573a69495056cfeaf76624373a74326374170 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 27 Jul 2022 19:28:06 +0200 Subject: Reorganized Kapitel --- buch/papers/fm/00_modulation.tex | 28 ++++++++++++++++ buch/papers/fm/01_AM-FM.tex | 47 --------------------------- buch/papers/fm/01_AM.tex | 29 +++++++++++++++++ buch/papers/fm/02_FM.tex | 56 ++++++++++++++++++++++++++++++++ buch/papers/fm/02_frequenzyspectrum.tex | 57 --------------------------------- buch/papers/fm/Makefile | 5 +-- buch/papers/fm/Makefile.inc | 5 +-- buch/papers/fm/main.tex | 6 ++-- 8 files changed, 123 insertions(+), 110 deletions(-) create mode 100644 buch/papers/fm/00_modulation.tex delete mode 100644 buch/papers/fm/01_AM-FM.tex create mode 100644 buch/papers/fm/01_AM.tex create mode 100644 buch/papers/fm/02_FM.tex delete mode 100644 buch/papers/fm/02_frequenzyspectrum.tex (limited to 'buch') diff --git a/buch/papers/fm/00_modulation.tex b/buch/papers/fm/00_modulation.tex new file mode 100644 index 0000000..dc99b40 --- /dev/null +++ b/buch/papers/fm/00_modulation.tex @@ -0,0 +1,28 @@ +% +% teil3.tex -- Beispiel-File für Teil 3 +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\subsection{Modulationsarten\label{fm:section:modulation}} + +Das sinusförmige Trägersignal hat die übliche Form: +\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). +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 Vielfalt 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\cite{fm:NAT}. +Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, +die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): +\newline +\newline +To do: Bilder jeder Modulationsart + + + diff --git a/buch/papers/fm/01_AM-FM.tex b/buch/papers/fm/01_AM-FM.tex deleted file mode 100644 index 163c792..0000000 --- a/buch/papers/fm/01_AM-FM.tex +++ /dev/null @@ -1,47 +0,0 @@ -% -% einleitung.tex -- Beispiel-File für die Einleitung -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{AM - FM\label{fm:section:teil0}} -\rhead{AM- FM} - -Das sinusförmige Trägersignal hat die übliche Form: -\(x_c(t) = A_c \cdot \cos(\omega_c(t)+\varphi)\). -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 Vielfalt 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\cite{fm:NAT}. -Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, -die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): -\newline -\newline -To do: Bilder jeder Modulationsart - -\subsection{AM - Amplitudenmodulation} -Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideeen in FM. -Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal -\[ - x_c(t) = A_c \cdot \cos(\omega_ct). -\] -Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt -und das Trägersignal nur zwei komplexe Schwingungen besitzt. -Dies sieht man besonders in der Eulerischen Formel -\[ - x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. -\] -Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. -Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. -\newline -\newline -TODO: -Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] -so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). -Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] diff --git a/buch/papers/fm/01_AM.tex b/buch/papers/fm/01_AM.tex new file mode 100644 index 0000000..921fcf2 --- /dev/null +++ b/buch/papers/fm/01_AM.tex @@ -0,0 +1,29 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Amplitudenmodulation\label{fm:section:teil0}} +\rhead{AM} + +Das Ziel ist FM zu verstehen doch dazu wird zuerst AM erklärt welches einwenig einfacher zu verstehen ist und erst dann übertragen wir die Ideen in FM. +Nun zur Amplitudenmodulation verwenden wir das bevorzugte Trägersignal +\[ + x_c(t) = A_c \cdot \cos(\omega_ct). +\] +Dies bringt den grossen Vorteil das, dass modulierend Signal sämtliche Anteile im Frequenzspektrum inanspruch nimmt +und das Trägersignal nur zwei komplexe Schwingungen besitzt. +Dies sieht man besonders in der Eulerischen Formel +\[ + x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. +\] +Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. +Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. +\newline +\newline +TODO: +Hier beschrieib ich was AmplitudenModulation ist und mache dan den link zu Frequenzmodulation inkl Formel \[\cos( \cos x)\] +so wird beschrieben das daraus eigentlich \(x_c(t) = A_c \cdot \cos(\omega_i)\) wird und somit \(x_c(t) = A_c \cdot \cos(\omega_c + \frac{d \varphi(t)}{dt})\). +Da \(\sin \) abgeleitet \(\cos \) ergibt, so wird aus dem \(m(t)\) ein \( \frac{d \varphi(t)}{dt}\) in der momentan frequenz. \[ \Rightarrow \cos( \cos x) \] + +\subsection{Frequenzspektrum} \ No newline at end of file diff --git a/buch/papers/fm/02_FM.tex b/buch/papers/fm/02_FM.tex new file mode 100644 index 0000000..fedfaaa --- /dev/null +++ b/buch/papers/fm/02_FM.tex @@ -0,0 +1,56 @@ +% +% teil1.tex -- Beispiel-File für das Paper +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{FM +\label{fm:section:teil1}} +\rhead{FM} +\subsection{Frequenzspektrum} +TODO +Hier Beschreiben ich FM und FM im Frequenzspektrum. +%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/02_frequenzyspectrum.tex b/buch/papers/fm/02_frequenzyspectrum.tex deleted file mode 100644 index 80e1c65..0000000 --- a/buch/papers/fm/02_frequenzyspectrum.tex +++ /dev/null @@ -1,57 +0,0 @@ -% -% teil1.tex -- Beispiel-File für das Paper -% -% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil -% -\section{AM-FM im Frequenzspektrum -\label{fm:section:teil1}} -\rhead{Problemstellung} - -TODO -Hier Beschreiben ich das Frequenzspektrum und wie AM und FM aussehen und generiert werden. -Somit auch die Herleitung des Frequenzspektrum. -%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/Makefile b/buch/papers/fm/Makefile index aee954f..f30c4a9 100644 --- a/buch/papers/fm/Makefile +++ b/buch/papers/fm/Makefile @@ -5,8 +5,9 @@ # SOURCES := \ - 01_AM-FM.tex \ - 02_frequenzyspectrum.tex \ + 00_modulation.tex \ + 01_AM.tex \ + 02_FM.tex \ 03_bessel.tex \ 04_fazit.tex \ main.tex diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index e5cd9f6..b686b98 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,8 +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/01_modulation.tex \ + papers/fm/01_AM.tex \ + papers/fm/02_FM.tex \ papers/fm/03_bessel.tex \ papers/fm/04_fazit.tex \ papers/fm/references.bib diff --git a/buch/papers/fm/main.tex b/buch/papers/fm/main.tex index 6af3386..731f56f 100644 --- a/buch/papers/fm/main.tex +++ b/buch/papers/fm/main.tex @@ -29,8 +29,10 @@ Zuerst wird erklärt was \textit{FM-AM} ist, danach wie sich diese im Frequenzsp Erst dann erklär ich dir wie die Besselfunktion mit der Frequenzmodulation( acro?) zusammenhängt. Nun zur Modulation im nächsten Abschnitt.\cite{fm:NAT} -\input{papers/fm/01_AM-FM.tex} -\input{papers/fm/02_frequenzyspectrum.tex} + +\input{papers/fm/00_modulation.tex} +\input{papers/fm/01_AM.tex} +\input{papers/fm/02_FM.tex} \input{papers/fm/03_bessel.tex} \input{papers/fm/04_fazit.tex} -- cgit v1.2.1 From 8210e25cc561db3dea0464019dea50eb5dc482ed Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Wed, 27 Jul 2022 21:39:05 +0200 Subject: adjusted errors in teil1 and improved some sentences and structure --- buch/papers/lambertw/Bilder/pursuerDGL2.png | Bin 0 -> 48606 bytes buch/papers/lambertw/teil0.tex | 2 +- buch/papers/lambertw/teil1.tex | 97 ++++++++++++++++------------ 3 files changed, 58 insertions(+), 41 deletions(-) create mode 100644 buch/papers/lambertw/Bilder/pursuerDGL2.png (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/pursuerDGL2.png b/buch/papers/lambertw/Bilder/pursuerDGL2.png new file mode 100644 index 0000000..f41dffe Binary files /dev/null and b/buch/papers/lambertw/Bilder/pursuerDGL2.png differ diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index f0589e5..5007867 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -48,7 +48,7 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um % \begin{figure} \centering - \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.pdf} + \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.png} \caption{Vektordarstellung Jagdstrategie} \label{lambertw:grafic:pursuerDGL2} \end{figure} diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 2e75a19..a330838 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -10,16 +10,35 @@ Sehr oft kommt es vor, dass bei Verfolgungsproblemen die Frage auftaucht, ob das Ziel überhaupt erreicht wird. Wenn zum Beispiel die Geschwindigkeit des Verfolgers kleiner ist als diejenige des Ziels, gibt es Anfangsbedingungen bei denen das Ziel nie erreicht wird. Im Anschluss dieser Frage stellt sich meist die nächste Frage, wie lange es dauert bis das Ziel erreicht wird. -Diese beiden Fragen werden in diesem Kapitel behandelt und an einem Beispiel betrachtet. +Diese beiden Fragen werden in diesem Kapitel behandelt und am Beispiel aus \ref{lambertw:section:teil4} betrachtet. +Das Beispiel wird bei dieser Betrachtung noch etwas erweitert indem alle Punkte auf der gesamtem $xy$-Ebene als Startwerte zugelassen werden. + +Nun gilt es zu definieren, wann das Ziel erreicht wird. +Da sowohl Ziel und Verfolger als Punkte modelliert wurden, gilt das Ziel als erreicht, wenn die Koordinaten des Verfolgers mit denen des Ziels bei einem diskreten Zeitpunkt $t_1$ übereinstimmen. +Somit gilt es + +\begin{equation*} + z(t_1)=v(t_1) +\end{equation*} +% +zu lösen. +Die Parametrisierung von $z(t)$ ist im Beispiel definiert als +\begin{equation} + z(t) + = + \left( \begin{array}{c} 0 \\ t \end{array} \right)\text{.} +\end{equation} +% +Die Parametrisierung von $v(t)$ ist von den Startbedingungen abhängig. Deshalb wird die obige Bedingung jeweils für die unterschiedlichen Startbedingungen separat analysiert. + +\subsection{Anfangsbedingung im \RN{1}-Quadranten} % -%\subsection{Ziel erreichen (überarbeiten) -%\label{lambertw:subsection:ZielErreichen}} -Für diese Betrachtung wird das Beispiel aus \eqref{lambertw:section:teil4} zur Hilfe genommen. -Dazu werden die hergeleiteten Gleichungen \eqref{lambertw:eqFunkXNachT} mit Startbedingung im ersten Quadranten verwendet, welche +$ x_0$ $\boldsymbol{x}$ dd +Wenn der Verfolger im \RN{1}-Quadranten startet, dann kann $v(t)$ mit den Gleichungen aus \eqref{lambertw:eqFunkXNachT}, welche \begin{align*} x\left(t\right) &= - x_0\cdot\sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\ + x_0\cdot\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp(\chi-\frac{4t}{r_0-y_0})\right)} \\ y(t) &= \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\\ @@ -34,34 +53,16 @@ Dazu werden die hergeleiteten Gleichungen \eqref{lambertw:eqFunkXNachT} mit Star \sqrt{x_0^2+y_0^2} \end{align*} % -sind. -Das Ziel wird erreicht, wenn die Koordinaten des Verfolgers mit denen des Ziels bei einem diskreten Zeitpunkt $t_1$ übereinstimmen. -Somit gilt es - -\begin{equation*} - \vec{Z}(t_1)=\vec{V}(t_1) -\end{equation*} -% -zu lösen. -Aus dem vorangegangenem Beispiel, ist die Parametrisierung des Verfolgers und des Ziels bekannt. -Das Ziel wird parametrisiert durch - -\begin{equation} - \vec{Z}(t) - = - \left( \begin{array}{c} 0 \\ t \end{array} \right) -\end{equation} -% -und der Verfolger durch - +Der Folger ist durch \begin{equation} - \vec{V}(t) + v(t) = \left( \begin{array}{c} x(t) \\ y(t) \end{array} \right) \text{.} \end{equation} % - Da $y(t)$ viel komplexer ist als $x(t)$ wird das Problem in zwei einzelne Teilprobleme zerlegt. Wobei die Bedingung der $x$- und $y$-Koordinaten einzeln überprüft werden. Es entstehen daher folgende Bedingungen +parametrisiert, wobei $y(t)$ viel komplexer ist als $x(t)$. +Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Bedingung der $x$- und $y$-Koordinaten einzeln überprüft werden müssen. Es entstehen daher folgende Bedingungen \begin{align*} 0 @@ -107,27 +108,41 @@ Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingu Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Einholen möglich wäre. Somit kann nach den Gestellten Bedingungen das Ziel nie erreicht werden. -Aus der Symmetrie des Problems an der $y$-Achse können auch alle Anfangspunkte im zweiten Quadranten die Bedingungen nicht erfüllen. -Bei allen Anfangspunkten mit $y_0<0$ ist ein Einholen unmöglich, da die Geschwindigkeit des Verfolgers und Ziels übereinstimmen und der Verfolger dem Ziel bereits am Anfang nachgeht. -Wenn die Wertemenge der Anfangsbedingung um die positive $y$-Achse erweitert wird, kann das Ziel wiederum erreicht werden. -Sobald der Verfolger auf der positiven $y$-Achse startet, bewegen sich Verfolger und Ziel aufeinander zu, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel zeigt und der Verfolger sich auf der Fluchtgeraden befindet. -Dies führt zwingend dazu, dass der Verfolger das Ziel erreichen wird. -Die Verfolgungskurve kann in diesem Fall mit + +\subsection{Anfangsbedingung $y_0<0$} +Da die Geschwindigkeit des Verfolgers und des Ziels übereinstimmen, kann der Verfolgers niemals das Ziel einholen. +Dies kann veranschaulicht werden anhand + +\begin{equation} + v(t)\cdot \left( \begin{array}{c} 0 \\ 1 \end{array}\right) + \leq + z(t)\cdot \left( \begin{array}{c} 0 \\ 1 \end{array}\right) + = + 1\text{.} +\end{equation} +% +Da der $y$-Anteil der Geschwindigkeit des Ziels grösser-gleich der des Verfolgers ist, können die $y$-Koordinaten nie übereinstimmen. + +\subsection{Anfangsbedingung auf positiven $y$-Achse} +Wenn der Verfolger auf der positiven $y$-Achse startet, befindet er sich direkt auf der Fluchtgeraden des Ziels. +Dies führt dazu, dass der Verfolger und das Ziel sich direkt aufeinander zu bewegen, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel zeigt. +Die Folge ist, dass das Ziel zwingend erreicht wird. +Um $t_1$ zu bestimmen, kann die Verfolgungskurve in diesem Fall mit \begin{equation} - \vec{V}(t) + v(t) = \left( \begin{array}{c} 0 \\ y_0-t \end{array} \right) \end{equation} % parametrisiert werden. Nun kann der Abstand zwischen Verfolger und Ziel leicht bestimmt und nach 0 aufgelöst werden. -Daraus folgt +Woraus folgt \begin{equation} 0 = - |\vec{V}(t_1)-\vec{Z}(t_1)| + |v(t_1)-z(t_1)| = y_0-2t_1 \end{equation} @@ -141,7 +156,9 @@ Daraus folgt \end{equation} % führt. -Nun ist klar, dass lediglich Anfangspunkte auf der positiven $y$-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. +Somit wird das Ziel immer erreicht bei $t_1$, wenn der Verfolger auf der positiven $y$-Achse startet. +\subsection{Fazit} +Durch die Symmetrie der Fluchtkurve an der $y$-Achse führen die Anfangsbedingungen in den Quadranten \RN{1} und \RN{2} zu den gleichen Ergebnissen. Nun ist klar, dass lediglich Anfangspunkte auf der positiven $y$-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. Bei allen anderen Anfangspunkten wird der Verfolger das Ziel nie erreichen. Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. @@ -150,14 +167,14 @@ Falls dies stattfinden sollte, wird dies als Treffer interpretiert. Mathematisch kann dies mit \begin{equation} - |\vec{V}-\vec{Z}|0 + |v-z| 0 + |v-z|^2 Date: Wed, 27 Jul 2022 22:00:28 +0200 Subject: comment out bessel.png --- buch/papers/fm/03_bessel.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index 7a0e20e..edb932b 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -117,7 +117,7 @@ Somit ist \ref{fm:eq:proof} bewiesen. Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. \begin{figure} \centering - \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} +% \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} \caption{Bessle Funktion \(J_{k}(\beta)\)} \label{fig:bessel} \end{figure} -- cgit v1.2.1 From 1666b63c2f4d5e8392c40ab6f6c8e9e71f20f4a3 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 28 Jul 2022 07:14:37 +0200 Subject: Resolve error in orthogonality proof --- buch/papers/laguerre/eigenschaften.tex | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) (limited to 'buch') diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 6ba9135..1411f7c 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -97,38 +97,38 @@ 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 \begin{align*} \int \frac{dp}{p} & = --\int \frac{\nu + 1 - x}{x} \, dx +\int \frac{\nu + 1 - x}{x} \, dx = --\int \frac{\nu + 1}{x} \, dx - \int 1\, dx +\int \frac{\nu + 1}{x} \, dx - \int 1\, dx \\ \log p & = --(\nu + 1)\log x - x + c +(\nu + 1)\log x - x + c \\ p(x) & = --C x^{\nu + 1} e^{-x} +C x^{\nu + 1} e^{-x} . \end{align*} Eingefügt in Gleichung~\eqref{laguerre:sl-lag} ergibt sich \begin{align*} \frac{C}{w(x)} \left( -x^{\nu+1} e^{-x} \frac{d^2}{dx^2} + +-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 $\nu > -1$. +dass $w(x) = x^\nu e^{-x}$ und $C=-1$ mit $\nu \geq 0$. Die Gewichtsfunktion $w(x)$ wächst für $x\rightarrow-\infty$ sehr schnell an, deshalb ist die Laguerre-Gewichtsfunktion nur geeignet für den Definitionsbereich $(0, \infty)$. -- cgit v1.2.1 From 8daaabab904020da2111d6bee3ce26db3b4b6df0 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 28 Jul 2022 07:30:31 +0200 Subject: Redescribe why definition range of Laguerre is (0,\infty) --- buch/papers/laguerre/eigenschaften.tex | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) (limited to 'buch') diff --git a/buch/papers/laguerre/eigenschaften.tex b/buch/papers/laguerre/eigenschaften.tex index 1411f7c..b007c2d 100644 --- a/buch/papers/laguerre/eigenschaften.tex +++ b/buch/papers/laguerre/eigenschaften.tex @@ -128,10 +128,11 @@ Eingefügt in Gleichung~\eqref{laguerre:sl-lag} ergibt sich 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 $\nu \geq 0$. -Die Gewichtsfunktion $w(x)$ wächst für $x\rightarrow-\infty$ sehr schnell an, -deshalb ist die Laguerre-Gewichtsfunktion nur geeignet für den -Definitionsbereich $(0, \infty)$. +dass $w(x) = x^\nu e^{-x}$ und $C=-1$. %mit $\nu \geq 0$. +Die Gewichtsfunktion $w(x)$ wächst für $x\rightarrow-\infty$ sehr schnell an. +Ausserdem hat die Gewichtsfunktion $w(x)$ für negative $\nu$ einen Pol bei $x=0$, +daher ist die Laguerre-Gewichtsfunktion nur für den +Definitionsbereich $(0, \infty)$ geeignet. \subsubsection{Randbedingungen} Bleibt nur noch sicherzustellen, dass die Randbedingungen -- cgit v1.2.1 From b4c0297a9cf2e2bc38fcb9110f7b5c89ae0fe9fa Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Thu, 28 Jul 2022 17:49:24 +0200 Subject: Kapitel bessel unterteilt --- buch/papers/fm/03_bessel.tex | 87 ++++++++++++++++--------- buch/papers/fm/Python animation/Bessel-FM.ipynb | 26 ++++---- 2 files changed, 70 insertions(+), 43 deletions(-) (limited to 'buch') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index edb932b..bf485b1 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -13,14 +13,18 @@ Somit haben wir unser \(x_c\) welches \cos(\omega_c t+\beta\sin(\omega_mt)) \] ist. + \subsection{Herleitung} -Das Ziel ist es Unser moduliertes Signal mit der Besselfunktion so auszudrücken: +Das Ziel ist es unser moduliertes Signal mit der Besselfunktion so auszudrücken: \begin{align} + x_c(t) + = \cos(\omega_ct+\beta\sin(\omega_mt)) &= \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) \label{fm:eq:proof} \end{align} +\subsubsection{Hilfsmittel} Doch dazu brauchen wir die Hilfe der Additionsthoerme \begin{align} \cos(A + B) @@ -54,70 +58,89 @@ und die drei Besselfunktions indentitäten, \label{fm:eq:besselid3} \end{align} welche man im Kapitel (ref), ref, ref findet. -\newline -Mit dem \refname{fm:eq:addth1} wird aus dem modulierten Signal -\[ -\cos(\omega_c t + \beta\sin(\omega_mt)) -\] -das Signal + +\subsubsection{Anwenden des Additionstheorem} +Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal \[ + x_c(t) + = + \cos(\omega_c t + \beta\sin(\omega_mt)) + = \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). \label{fm:eq:start} \] -Zu beginn wird der erste Teil +\subsubsection{Cos-Teil} +Zu beginn wird der Cos-Teil \[ \cos(\omega_c)\cos(\beta\sin(\omega_mt)) \] -mit hilfe der Bessel indentität \ref{fm:eq:besselid1} zum -\[ - J_0(\beta)\cos(\omega_c) + \sum_{k=1}^\infty J_{2k}(\beta) 2\cos(\omega_c t)\cos(2k\omega_m t) -\] -\newline -TODO 2 und \(\cos( )\) in lime. -wobei mit dem \colorbox{lime}{Additionstheorem} \ref{fm:eq:addth2} zum +mit hilfe der Bessel indentität \eqref{fm:eq:besselid1} zum +\begin{align*} + \cos(\omega_c t) \cdot [\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\omega_m t)\, ] + &=\\ + J_0(\beta)\cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) + \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{Additionstheorem} +\end{align*} +wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum \[ - J_0(\beta)\dot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} + J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} \] wird. Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term \[ - \sum_{n\, gerade} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t), \label{fm:eq:gerade} \] -\newline -nun zum zweiten Teil des Term \ref{fm:eq:start} +dabei gehen nun die Terme von \(-\infty \to \infty\), dabei bleibt n Ganzzahlig. + +\subsubsection{Sin-Teil} +Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil \[ \sin(\omega_c)\sin(\beta\sin(\omega_m t)). \] -Dieser wird mit der \ref{fm:eq:besselid2} Bessel indentität zu +Dieser wird mit der \eqref{fm:eq:besselid2} Bessel indentität zu +\begin{align*} + \sin(\omega_c t) \cdot [J_0(\beta) \sin(\omega_c t) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\omega_m t)] + &=\\ + J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{Additionstheorem}. +\end{align*} +Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), +somit wird daraus \[ - J_0(\beta) \dot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) 2\sin(\omega_c t)\cos((2k+1)\omega_m t). -\] -Auch hier wird ein Additionstheorem \ref{fm:eq:addth3} gebraucht um aus dem Sumanden diesen Term -\[ - J_0(\beta) \dot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{Teil1} - \cos((\omega_c+(2k+1)\omega_m) t) \} -\]zu gewinnen. + J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{neg.Teil} - \cos((\omega_c+(2k+1)\omega_m) t) \} +\]dieser Term. Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. -Zusätzlich dabei noch die letzte Bessel indentität \ref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1 J_n(\beta)\). -Somit wird Teil1 zum negativen Term und die Summe vereinfacht sich zu +Zusätzlich dabei noch die letzte Bessel indentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). +Somit wird negTeil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\)und die Summe vereinfacht sich zu \[ - \sum_{n\, ungerade} -1 J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). \label{fm:eq:ungerade} \] Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. -Beide Teile \ref{fm:eq:gerade} Gerade und \ref{fm:eq:ungerade} Ungerade ergeben zusammen + +\subsubsection{Summe Zusammenführen} +Beide Teile \eqref{fm:eq:gerade} Gerade +\[ + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\]und \eqref{fm:eq:ungerade} Ungerade +\[ + \sum_{n\, \text{ungerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\] +ergeben zusammen \[ \cos(\omega_ct+\beta\sin(\omega_mt)) = \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t). \] -Somit ist \ref{fm:eq:proof} bewiesen. +Somit ist \eqref{fm:eq:proof} bewiesen. \newpage + +%---------------------------------------------------------------------------- \subsection{Bessel und Frequenzspektrum} Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. \begin{figure} \centering -% \includegraphics[width=0.5\textwidth]{/home/joshua/Documents/SeminarSpezielleFunktionen/buch/papers/fm/FM presentation/images/bessel.png} +% \input{./PyPython animation/bessel.pgf} \caption{Bessle Funktion \(J_{k}(\beta)\)} \label{fig:bessel} \end{figure} diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb index bfbb83d..6f099a7 100644 --- a/buch/papers/fm/Python animation/Bessel-FM.ipynb +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 117, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -11,6 +11,9 @@ "from scipy.fft import fft, ifft, fftfreq\n", "import scipy.special as sc\n", "import scipy.fftpack\n", + "import matplotlib as mpl\n", + "# Use the pgf backend (must be set before pyplot imported)\n", + "#mpl.use('pgf')\n", "import matplotlib.pyplot as plt\n", "from matplotlib.widgets import Slider\n", "def fm(beta):\n", @@ -94,12 +97,12 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 29, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -119,18 +122,19 @@ ], "source": [ "\n", - "for n in range (-4,4):\n", - " x = np.linspace(0,11,1000)\n", + "for n in range (-2,4):\n", + " x = np.linspace(-11,11,1000)\n", " y = sc.jv(n,x)\n", - " plt.plot(x, y, '-')\n", - "plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", - "plt.xlim(0,10)\n", + " plt.plot(x, y, '-',label='n='+str(n))\n", + "#plt.plot([1,1],[sc.jv(0,1),sc.jv(-1,1)],)\n", + "plt.xlim(-10,10)\n", "plt.grid(True)\n", - "plt.ylabel('Bessel J_n(b)')\n", - "plt.xlabel('b')\n", + "plt.ylabel('Bessel $J_n(\\\\beta)$')\n", + "plt.xlabel(' $ \\\\beta $ ')\n", "plt.plot(x, y)\n", + "plt.legend()\n", "plt.show()\n", - "\n", + "#plt.savefig('bessel.pgf', format='pgf')\n", "print(sc.jv(0,1))" ] }, -- cgit v1.2.1 From 795f274fd1343ad7ba7f24f2988cb9d22b60f85c Mon Sep 17 00:00:00 2001 From: tim30b Date: Thu, 28 Jul 2022 17:57:14 +0200 Subject: =?UTF-8?q?quelle=20hinzugef=C3=BCgt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/kreismembran/references.bib | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/references.bib b/buch/papers/kreismembran/references.bib index f642aa8..acf8f90 100644 --- a/buch/papers/kreismembran/references.bib +++ b/buch/papers/kreismembran/references.bib @@ -4,9 +4,9 @@ % (c) 2020 Autor, Hochschule Rapperswil % -@online{kreismembran:Duden:Membrane, - title = {Duden:Membrane}, - url = {https://www.duden.de/rechtschreibung/Membrane}, +@online{kreismembran:Duden:Membran, + title = {Duden:Membran}, + url = {https://www.duden.de/rechtschreibung/Membran}, date = {2022-07-20}, year = {2022}, month = {7}, @@ -73,4 +73,12 @@ type = {phdthesis}, author = {{Prof. Dr. Horst Knörrer}}, date = {2013}, +} + +@thesis{kreismembran:membrane_vs_thin_plate, + title = {Modeling and Control of SPIDER Satellite Components}, + institution = {{faculty of the Virginia Polytechnic Institute and State University}}, + type = {Dissertation}, + author = {{Eric John Ruggiero Doctor of Philosophy In Mechanical Engineering}}, + date = {2005}, } \ No newline at end of file -- cgit v1.2.1 From 74763d677a4612d8844332f21026e5d1306333ac Mon Sep 17 00:00:00 2001 From: tim30b Date: Thu, 28 Jul 2022 17:57:37 +0200 Subject: einleitung und herleitung DGL erste version fertig --- buch/papers/kreismembran/teil0.tex | 89 ++++++++++++++++++++++++++++++-------- 1 file changed, 72 insertions(+), 17 deletions(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/teil0.tex b/buch/papers/kreismembran/teil0.tex index 6f5e907..bb8188d 100644 --- a/buch/papers/kreismembran/teil0.tex +++ b/buch/papers/kreismembran/teil0.tex @@ -4,24 +4,79 @@ % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % \section{Einleitung\label{kreismembran:section:teil0}} -\rhead{Membrane} -Eine naheliegendes Beispiel einer kreisförmigen Membrane ist eine Runde Trommel. -Der Zusammenhang zwischen rund und kreisförmig wird hier nicht erläutert, was in diesem Kapitel als Membrane verstanden wird sollte jedoch erwähnt sein. -Eine Membrane, Membran oder selten ein Schwingblatt ist laut Duden \cite{kreismembran:Duden:Membrane} ein "dünnes Blättchen aus Metall, Papier o. Ä., ...". -Um zu verstehen wie sich eine Kreisförmige Membrane oder eben eine Trommel verhaltet, wird vorerst das Verhalten eines infinitesimal kleines Stück einer Membrane untersucht. +\rhead{Membran} +Eine Membran oder selten ein Schwingblatt ist laut Duden \cite{kreismembran:Duden:Membran} ein "dünnes Blättchen aus Metall, Papier o. Ä., das durch seine Schwingungsfähigkeit geeignet ist, Schallwellen zu übertragen ...". +Ein dünnes Blättchen aus Metall zeig jedoch nicht die selben dynamischen Eigenschaften auf, wie ein gespanntes Stück Papier. +Beschreibt man das dynamische Verhalten, muss zwischen einer dünnen Platte und einer Membrane unterschieden werden \cite{kreismembran:membrane_vs_thin_plate}. +Eine dünne Platte zum Beispiel aus Metall, wirkt selbst entgegen ihrer Deformation sobald sie gekrümmt wird. +Eine Membran auf der anderen Seite besteht aus einem Material welches sich ohne Kraftaufwand verbiegen lässt wie zum Beispiel Papier. +Bevor Papier als schwingende Membran betrachtet werden kann wird jedoch noch eine Spannung $ T $ benötigt welche das Material daran hindert aus der Ruhelage gebracht zu werden. -\paragraph{Annahmen} Für die Herleitung einer Differentialgleichung mit überschaubarer Komplexität werden gebräuchliche Annahmen zur Modellierung einer Membrane \cite{kreismembran:wellengleichung_herleitung} getroffen: +Ein geläufiges Beispiel einer Kreismembran ist eine runde Trommel. +Sie besteht herkömmlicher weise aus einem Leder (Fell), welches auf einen offenen Zylinder (Zargen) aufgespannt wird. +Das Leder alleine erzeugt nach einem Aufschlag keine hörbaren Schwingungen. +Sobald das Fell jedoch über den Zargen gespannt wird, kann das Fell auf verschiedensten weisen weiter schwingen, was für den Klang der Trommel verantwortlich ist. +Wie genau diese Schwingungen untersucht werden können wird in der Folgenden Arbeit Diskutiert. + + +\paragraph{Annahmen} +Um die Wellengleichung herzuleiten \cite{kreismembran:wellengleichung_herleitung}, muss ein Modell einer Membran definiert werden. +Das untersuchte Modell einer Membrane Erfüllt folgende Eigenschaften: \begin{enumerate}[i] - \item Die Membrane ist homogen. - Dies bedeutet, dass die Membrane über die ganze Fläche die selbe Dichte $ \rho $ und Elastizität hat. - Durch die konstante Elastizität ist die ganze Membrane unter gleichmässiger Spannung $ T $. - \item Die Membrane ist perfekt flexibel. - Daraus folgt, dass die Membrane ohne Kraftaufwand verbogen werden kann. - Die Membrane ist dadurch nicht alleine schwing-fähig, hierzu muss sie gespannt werden mit der Kraft $ T $. - \item Die Membrane kann sich nur in Richtung ihrer Normalen in kleinem Ausmass Auslenken. - Auslenkungen in der ebene der Membrane sind nicht möglich. - \item Die Membrane erfährt keine Art von Dämpfung. - Neben der perfekten Flexibilität wird die Membrane auch nicht durch ihr umliegendes Medium aus gebremst. - Dadurch entsteht kein dämpfender Term abhängig von der Geschwindigkeit der Membrane in der Differenzialgleichung. + \item Die Membran ist homogen. + Dies bedeutet, dass die Membran über die ganze Fläche die selbe Dichte $ \rho $ und Elastizität hat. + Durch die konstante Elastizität ist die ganze Membran unter gleichmässiger Spannung $ T $. + \item Die Membran ist perfekt flexibel. + Daraus folgt, dass die Membran ohne Kraftaufwand verbogen werden kann. + Die Membran ist dadurch nicht allein stehend schwing-fähig, hierzu muss sie gespannt werden mit einer Kraft $ T $. + \item Die Membran kann sich nur in Richtung ihrer Normalen in kleinem Ausmass Auslenken. + Auslenkungen in der ebene der Membran sind nicht möglich. + \item Die Membran erfährt keine Art von Dämpfung. + Die Membran wird also nicht durch ihr umliegendes Medium abgebremst noch erfährt sie Wärmeverluste durch Deformation. + Die resultierende Schwingung wird daher nicht gedämpft sein. + \end{enumerate} +\subsection{Wellengleichung} Um die Wellengleichung einer Membran herzuleiten wird vorerst eine schwingende Saite betrachtet. +Es lohnt sich das Verhalten einer Saite zu beschreiben da eine Saite das selbe Verhalten wie eine Membran aufweist mit dem Unterschied einer fehlenden Dimension. +Die Verbindung zwischen Membran und Saite ist intuitiv ersichtlich, stellt man sich einen Querschnitt einer Trommel vor. +%Wie analog zur Membran kann eine Saite erst unter Spannung schwingen. + +Abbildung \ref{TODO} ist ein infinitesimales Stück einer Saite mit Länge $ dx $ skizziert. +Wie für die Membran ist die Annahme iii gültig, keine Bewegung in die Richtung $ \hat{x} $. +Um dies zu erfüllen muss der Punkt $ P_1 $ gleich stark in Richtung $ -\hat{x} $ gezogen werden wie der Punkt $ P_2 $ in Richtung $ \hat{x} $ gezogen wird. Ist $ T_1 $ die Kraft welche mit Winkel $ \alpha $ auf Punkt $ P_1 $ wirkt sowie $ T_2 $ und $ \beta$ das analoge für Punkt $ P_2 $ ist, so können die Kräfte +\begin{equation}\label{kreismembran:eq:no_translation} + T_1 \cos \alpha = T_2 \cos \beta = T +\end{equation} +gleichgesetzt werden. +Das dynamische verhalten der senkrechten Auslenkung $ u(x,t) $ muss das newtonsche Gesetz +\begin{equation*} + \sum F = m \cdot a +\end{equation*} +befolgen. Die senkrecht wirkenden Kräfte werden mit $ T_1 $ und $ T_2 $ ausgedrückt, die Masse als Funktion der Dichte $ \rho $ und die Beschleunigung in Form der zweiten Ableitung als +\begin{equation*} + T_2 \sin \beta - T_1 \sin \alpha = \rho dx \frac{\partial^2 u}{\partial t^2} . +\end{equation*} +Die Gleichung wird durch $ T $ dividiert, wobei $ T $ nach \ref{kreismembran:eq:no_translation} geschickt gewählt wird. Somit kann +\begin{equation*} + \frac{T_2 \sin \beta}{T_2 \cos \beta} - \frac{T_1 \sin \alpha}{T_1 \cos \alpha} = \frac{\rho dx}{T} \frac{\partial^2 u}{\partial t^2} +\end{equation*} +vereinfacht als +\begin{equation*} + \tan \beta - \tan \alpha = \frac{\rho dx}{T} \frac{\partial^2 u}{\partial t^2} +\end{equation*} +geschrieben werden. +Der $ \tan \alpha $ entspricht der örtlichen Ableitung von $ u(x,t) $ an der Stelle $ x_0 $ und analog der $ \tan \beta $ für die Stelle $ x_0 + dx $. +Die Gleichung wird dadurch zu +\begin{equation*} + \frac{\partial u}{\partial x} \big\vert_{x_0 + dx} - \frac{\partial u}{\partial x} \big\vert_{x_0} = \frac{\rho dx}{T} \frac{\partial^2 u}{\partial t^2}. +\end{equation*} +Durch die Division mit $ dx $ entsteht +\begin{equation*} + \frac{1}{dx} \bigg[\frac{\partial u}{\partial x} \big\vert_{x_0 + dx} - \frac{\partial u}{\partial x} \big\vert_{x_0}\bigg] = \frac{\rho}{T}\frac{\partial^2 u}{\partial t^2}. +\end{equation*} +Auf der Linken Seite der Gleichung wird die Differenz der Steigungen durch die Intervall-Länge geteilt, in anderen Worten die zweite Ableitung von $ u(x,t) $ nach $ x $ berechnet. Der Term $ \frac{\rho}{T} $ wird mit $ c^2 $ ersetzt, da der Bruch für eine gegebene Membran eine positive Konstante sein muss. Somit resultiert die, in der Literatur gebräuchliche Form +\begin{equation} + \frac{1}{c^2}\frac{\partial^2u}{\partial t^2} = \Delta u. +\end{equation} +In dieser Form ist die Gleichung auch gültig für eine Membran. Für den Fall einer Membran muss lediglich die Ableitung in zwei Dimensionen gerechnet werden. \ No newline at end of file -- cgit v1.2.1 From 7aef721d37d440a7ac22b93aa3b998b8f15dbade Mon Sep 17 00:00:00 2001 From: tim30b Date: Thu, 28 Jul 2022 17:58:37 +0200 Subject: kapitel -> abschnitt --- buch/papers/kreismembran/teil1.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/teil1.tex b/buch/papers/kreismembran/teil1.tex index 38bcfe4..39ca598 100644 --- a/buch/papers/kreismembran/teil1.tex +++ b/buch/papers/kreismembran/teil1.tex @@ -10,7 +10,7 @@ An diesem Punkt bleibt also nur noch die Lösung der partiellen Differentialgleichung. In diesem Kapitel wird sie mit Hilfe der Separationsmethode gelöst. \subsection{Aufgabestellung\label{sub:aufgabestellung}} -Wie im vorherigen Kapitel gezeigt, lautet die partielle Differentialgleichung, die die Schwingungen einer Membran beschreibt: +Wie im vorherigen Abschnitt 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*} -- cgit v1.2.1 From 79731c7db599b675b38cdb637c1b00d323c1ccde Mon Sep 17 00:00:00 2001 From: tim30b Date: Thu, 28 Jul 2022 18:06:43 +0200 Subject: =?UTF-8?q?Struktur=20Anpassung=20f=C3=BCr=20Simulations-Teil?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- buch/papers/kreismembran/main.tex | 1 + buch/papers/kreismembran/teil3.tex | 2 +- buch/papers/kreismembran/teil4.tex | 8 ++++++++ 3 files changed, 10 insertions(+), 1 deletion(-) create mode 100644 buch/papers/kreismembran/teil4.tex (limited to 'buch') diff --git a/buch/papers/kreismembran/main.tex b/buch/papers/kreismembran/main.tex index e19c64a..f6000a1 100644 --- a/buch/papers/kreismembran/main.tex +++ b/buch/papers/kreismembran/main.tex @@ -12,6 +12,7 @@ \input{papers/kreismembran/teil1.tex} \input{papers/kreismembran/teil2.tex} \input{papers/kreismembran/teil3.tex} +\input{papers/kreismembran/teil4.tex} \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/kreismembran/teil3.tex b/buch/papers/kreismembran/teil3.tex index 10338e7..7d5648a 100644 --- a/buch/papers/kreismembran/teil3.tex +++ b/buch/papers/kreismembran/teil3.tex @@ -76,7 +76,7 @@ Nimmt man jedoch die allgemeine Lösung mit Summationen, \end{align} kann man die Lösungsmethoden 1 und 2 vergleichen. -\subsection{Vergleich der Lösungen +\subsection{Vergleich der Analytischen Lösungen \label{kreismembran:vergleich}} Bei der Analyse der Gleichungen \eqref{eq:lösung_endliche_generelle} und \eqref{eq:lösung_unendliche_generelle} fällt sofort auf, dass die Gleichung \eqref{eq:lösung_unendliche_generelle} nicht mehr von $m$ und $n$ abhängt, sondern nur noch von $n$ \cite{nishanth_p_vibrations_2018}. Das macht Sinn, denn $n$ beschreibt die Anzahl der Knotenlinien, und in einer unendlichen Membran gibt es keine. Tatsächlich werden $a_{m0}$, $b_{m0}$ und $\kappa_{m0}$ in $a_m$, $b_m$ bzw. $\kappa_m$ umbenannt. Die beiden Termen $\cos(n\varphi)$ und $\sin(n\varphi)$ verschwinden ebenfalls, da für $n=0$ der $\cos(n\varphi)$ gleich 1 und der $\sin(n \varphi)$ gleich 0 ist. Die Funktion hängt also nicht mehr von der Besselfunktionen $n$-ter Ordnung ab, sondern nur von der $0$-ter Ordnung. diff --git a/buch/papers/kreismembran/teil4.tex b/buch/papers/kreismembran/teil4.tex new file mode 100644 index 0000000..830bce7 --- /dev/null +++ b/buch/papers/kreismembran/teil4.tex @@ -0,0 +1,8 @@ +% +% einleitung.tex -- Beispiel-File für die Einleitung +% +% (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil +% +\section{Lösungsmethode 3: Simulation + \label{kreismembran:section:teil4}} +Needs to be written \ No newline at end of file -- cgit v1.2.1 From e2b1ed24b607291b6af86ba43c8f6f656a92b476 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Thu, 28 Jul 2022 18:09:00 +0200 Subject: minor cosmetic changes --- buch/papers/fm/03_bessel.tex | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) (limited to 'buch') diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index bf485b1..760cdc4 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -74,16 +74,16 @@ Zu beginn wird der Cos-Teil \[ \cos(\omega_c)\cos(\beta\sin(\omega_mt)) \] -mit hilfe der Bessel indentität \eqref{fm:eq:besselid1} zum +mit hilfe der Besselindentität \eqref{fm:eq:besselid1} zum \begin{align*} - \cos(\omega_c t) \cdot [\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\omega_m t)\, ] + \cos(\omega_c t) \cdot \bigg[\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] &=\\ J_0(\beta)\cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) - \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{Additionstheorem} + \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem}} \end{align*} wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum \[ - J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k\omega_m) t)+\cos((\omega_c + 2k\omega_m) t) \} + J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k \omega_m) t)+\cos((\omega_c + 2k \omega_m) t) \} \] wird. Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term @@ -98,20 +98,20 @@ Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil \[ \sin(\omega_c)\sin(\beta\sin(\omega_m t)). \] -Dieser wird mit der \eqref{fm:eq:besselid2} Bessel indentität zu +Dieser wird mit der \eqref{fm:eq:besselid2} Besselindentität zu \begin{align*} - \sin(\omega_c t) \cdot [J_0(\beta) \sin(\omega_c t) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\omega_m t)] + \sin(\omega_c t) \cdot \bigg[ J_0(\beta) + 2 \sum_{k=1}^\infty J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] &=\\ - J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{Additionstheorem}. + J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{\text{Additionstheorem}}. \end{align*} Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), somit wird daraus \[ - J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{neg.Teil} - \cos((\omega_c+(2k+1)\omega_m) t) \} + J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{\text{neg.Teil}} - \cos((\omega_c+(2k+1)\omega_m) t) \} \]dieser Term. Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. -Zusätzlich dabei noch die letzte Bessel indentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). -Somit wird negTeil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\)und die Summe vereinfacht sich zu +Zusätzlich dabei noch die letzte Besselindentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). +Somit wird neg.Teil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\) und die Summe vereinfacht sich zu \[ \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). \label{fm:eq:ungerade} -- cgit v1.2.1 From c01fed1273bc5994b49a5e554e8bc60294fb9519 Mon Sep 17 00:00:00 2001 From: tim30b Date: Thu, 28 Jul 2022 18:53:33 +0200 Subject: Anfang von numerik --- buch/papers/kreismembran/teil4.tex | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/teil4.tex b/buch/papers/kreismembran/teil4.tex index 830bce7..58fffc9 100644 --- a/buch/papers/kreismembran/teil4.tex +++ b/buch/papers/kreismembran/teil4.tex @@ -5,4 +5,10 @@ % \section{Lösungsmethode 3: Simulation \label{kreismembran:section:teil4}} -Needs to be written \ No newline at end of file +\paragraph{TODO Einleitung} + +Um numerisch das Verhalten einer Membran zu ermitteln, muss eine numerische Darstellung definiert werden. +Die Membran wird hier in Form der Matrix $ A $ digitalisiert. +Jedes Element $ A_{ij} $ steh für die Auslenkung der Membran $ u(x,y,t) $ an der Stelle $ {x,y}={i,j} $. +Die Auslenkung ist jedoch auch von der Zeit abhängig für dies wird ein Array $ X[] $ aus $ v \times A $ Matrizen erstellt. +s -- cgit v1.2.1 From 26301cab48f22b33ca56918c2787e5c67eb315a1 Mon Sep 17 00:00:00 2001 From: tim30b Date: Thu, 28 Jul 2022 20:53:12 +0200 Subject: numerik continues --- buch/papers/kreismembran/teil4.tex | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) (limited to 'buch') diff --git a/buch/papers/kreismembran/teil4.tex b/buch/papers/kreismembran/teil4.tex index 58fffc9..c124354 100644 --- a/buch/papers/kreismembran/teil4.tex +++ b/buch/papers/kreismembran/teil4.tex @@ -9,6 +9,8 @@ Um numerisch das Verhalten einer Membran zu ermitteln, muss eine numerische Darstellung definiert werden. Die Membran wird hier in Form der Matrix $ A $ digitalisiert. -Jedes Element $ A_{ij} $ steh für die Auslenkung der Membran $ u(x,y,t) $ an der Stelle $ {x,y}={i,j} $. -Die Auslenkung ist jedoch auch von der Zeit abhängig für dies wird ein Array $ X[] $ aus $ v \times A $ Matrizen erstellt. -s +Jedes Element $ A_{ij} $ steh für die Auslenkung der Membran $ u(x,y,t) $ an der Stelle $ \{x,y\}=\{i,j\} $. +Die zeitliche Dimension wird in Form des Array $ X[] $ aus $ v \times A $ Matrizen dargestellt. +Das Element auf Zeile $ i $, Spalte $ j $ der $ w $-ten Matrix von $ X[] $ also $ X[w]_{ij} $ entspricht der Auslenkung $ u(i,j,w) $. + +\paragraph{title} \ No newline at end of file -- cgit v1.2.1 From 54b20e3e34ccb7c11d2f78cbbdd0bbf951bb9cba Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Thu, 28 Jul 2022 21:01:15 +0200 Subject: typo korrigiert --- buch/papers/fm/Makefile.inc | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/fm/Makefile.inc b/buch/papers/fm/Makefile.inc index b686b98..40f23b1 100644 --- a/buch/papers/fm/Makefile.inc +++ b/buch/papers/fm/Makefile.inc @@ -6,7 +6,7 @@ dependencies-fm = \ papers/fm/packages.tex \ papers/fm/main.tex \ - papers/fm/01_modulation.tex \ + papers/fm/00_modulation.tex \ papers/fm/01_AM.tex \ papers/fm/02_FM.tex \ papers/fm/03_bessel.tex \ -- cgit v1.2.1 From 50f65a2a67b3574d5fbf162ee5951fc189f52319 Mon Sep 17 00:00:00 2001 From: tschwall <55748566+tschwall@users.noreply.github.com> Date: Fri, 29 Jul 2022 13:43:08 +0200 Subject: Let the pain begin --- buch/SeminarSpezielleFunktionen.pdf | Bin 0 -> 22090645 bytes buch/papers/parzyl/teil2.tex | 108 ++++++++++++++++++++++++++---------- buch/papers/parzyl/teil3.tex | 101 ++++++++++++++++++++++----------- 3 files changed, 149 insertions(+), 60 deletions(-) create mode 100644 buch/SeminarSpezielleFunktionen.pdf (limited to 'buch') diff --git a/buch/SeminarSpezielleFunktionen.pdf b/buch/SeminarSpezielleFunktionen.pdf new file mode 100644 index 0000000..d581f96 Binary files /dev/null and b/buch/SeminarSpezielleFunktionen.pdf differ diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex index c1bd723..1ffdeec 100644 --- a/buch/papers/parzyl/teil2.tex +++ b/buch/papers/parzyl/teil2.tex @@ -6,35 +6,85 @@ \section{Physik sache \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 -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 + + +\subsection{Elektrisches Feld einer semi-infiniten Platte \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 -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. +Die parabolischen Zylinderkoordinaten tauchen auf, wenn man das elektrische Feld einer semi-infiniten Platte finden will. Das dies so ist kann mit Hilfe von komplexen Funktionen gezeigt werden. Jede komplexe Funktion $F(z)$, wie in gezeigt, kann geschrieben werden als +\begin{equation} + F(z) = U(x,y) + iV(x,y) \qquad z = x + iy. +\end{equation} +Dabei muss gelten, falls die Funktion differenzierbar ist, dass +\begin{equation} + \frac{\partial U(x,y)}{\partial x} + = + \frac{\partial V(x,y)}{\partial y} + \qquad + \frac{\partial V(x,y)}{\partial x} + = + -\frac{\partial U(x,y)}{\partial y}. +\end{equation} +Aus dieser Bedingung folgt +\begin{equation} + \label{parzyl_e_feld_zweite_ab} + \underbrace{ + \frac{\partial^2 U(x,y)}{\partial x^2} + + + \frac{\partial^2 U(x,y)}{\partial y^2} + = + 0 + }_{\nabla^2U(x,y)=0} + \qquad + \underbrace{ + \frac{\partial^2 V(x,y)}{\partial x^2} + + + \frac{\partial^2 V(x,y)}{\partial y^2} + = + 0 + }_{\nabla^2V(x,y) = 0}. +\end{equation} +Zusätzlich zeigen diese Bedingungen auch, dass die zwei Funktionen $U(x,y)$ und $V(x,y)$ orthogonal zueinander sind. +Der Zusammenhang zum elektrischen Feld ist jetzt, dass das Potential an einem quellenfreien Punkt als +\begin{equation} + \nabla^2\phi(x,y) = 0. +\end{equation} +Da dies bei komplexen differenzierbaren Funktionen gilt, wie Gleichung \ref{parzyl_e_feld_zweite_ab} zeigt, kann entweder $U(x,y)$ oder $V(x,y)$ von einer solchen Funktion als das Potential angesehen werden. Im weiteren wird für dies $U(x,y)$ verwendet. +Da die Funktion, welche nicht das Potential beschreibt $V(x,y)$ orthogonal zum Potential ist, zeigt diese das Verhalten des elektrischen Feldes. +Um nun zu den parabolische Zylinderkoordinaten zu gelangen muss nur noch eine geeignete komplexe Funktion $F(z)$ gefunden werden, welche eine semi-infinite Platte beschreiben kann. Man könnte natürlich auch nach anderen Funktionen suchen, welche andere Bedingungen erfüllen und würde dann auf andere Koordinatensysteme stossen. Die gesuchte Funktion in diesem Fall ist +\begin{equation} + F(z) + = + \sqrt{z} + = + \sqrt{x + iy}. +\end{equation} +Dies kann umgeformt werden zu +\begin{equation} + F(z) + = + \underbrace{\sqrt{\frac{\sqrt{x^2+y^2} + x}{2}}}_{U(x,y)} + + + i\underbrace{\sqrt{\frac{\sqrt{x^2+y^2} - x}{2}}}_{V(x,y)} + . +\end{equation} +Die Äquipotentialflächen können nun betrachtet werden, indem man die Funktion welche das Potential beschreibt gleich eine Konstante setzt, +\begin{equation} + \sigma = U(x,y) = \sqrt{\frac{\sqrt{x^2+y^2} + x}{2}}, +\end{equation} +und die Flächen mit der gleichen elektrischen Feldstärke können als +\begin{equation} + \tau = V(x,y) = \sqrt{\frac{\sqrt{x^2+y^2} - x}{2}} +\end{equation} +beschrieben werden. Diese zwei Gleichungen zeigen nun wie man vom kartesischen Koordinatensystem ins parabolische Zylinderkoordinatensystem kommt. Werden diese Formeln nun nach x und y aufgelöst so beschreibe sie, wie man aus dem parabolischen Zylinderkoordinatensystem zurück ins kartesische rechnen kann +\begin{equation} + x = \sigma \tau, +\end{equation} +\begin{equation} + y = \frac{1}{2}\left ( \tau^2 - \sigma^2 \right ) +\end{equation} + + + + diff --git a/buch/papers/parzyl/teil3.tex b/buch/papers/parzyl/teil3.tex index 72c23ca..a143aa1 100644 --- a/buch/papers/parzyl/teil3.tex +++ b/buch/papers/parzyl/teil3.tex @@ -6,35 +6,74 @@ \section{Teil 3 \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 -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 +\subsection{Helmholtz Gleichung im parabolischen Zylinderkoordinatensystem \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 -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. - - +Die Differentialgleichungen, welche zu den parabolischen Zylinderfunktionen führen tauchen, wie bereits erwähnt, dann auf, wenn die Helmholtz Gleichung +\begin{equation} + \Delta f(x,y,z) = \lambda f(x,y,z) +\end{equation} +im parabolischen Zylinderkoordinatensystem +\begin{equation} + \Delta f(\sigma,\tau,z) = \lambda f(\sigma,\tau,z) +\end{equation} +gelöst wird. +Wobei der Laplace Operator $\Delta$ im parabolischen Zylinderkoordinatensystem gegeben ist als +\begin{equation} + \nabla + = + \frac{1}{\sigma^2 + \tau^2} + \left ( + \frac{\partial^2}{\partial \sigma^2} + + + \frac{\partial^2}{\partial \tau^2} + \right ) + + + \frac{\partial^2}{\partial z^2}. +\end{equation} +Die Helmholtz Gleichung würde also wie folgt lauten +\begin{equation} + \nabla f(\sigma, \tau, z) + = + \frac{1}{\sigma^2 + \tau^2} + \left ( + \frac{\partial^2 f(\sigma,\tau,z)}{\partial \sigma^2} + + + \frac{\partial^2 f(\sigma,\tau,z)}{\partial \tau^2} + \right ) + + + \frac{\partial^2 f(\sigma,\tau,z)}{\partial z^2} + = + \lambda f(\sigma,\tau,z) +\end{equation} +Diese partielle Differentialgleichung kann mit Hilfe von Separation gelöst werden, dazu wird +\begin{equation} + f(\sigma,\tau,z) = g(\sigma)h(\tau)i(z) +\end{equation} +gesetzt. +Was dann schlussendlich zu den Differentialgleichungen +\begin{equation} + h''(\tau) + - + \left ( + \lambda\tau^2 + - + \mu + \right ) + h(\tau) + = + 0 +\end{equation} +und +\begin{equation} + g''(\sigma) + - + \left ( + \lambda\sigma^2 + + + \mu + \right ) + g(\sigma) + = + 0 +\end{equation} +führt. -- cgit v1.2.1 From 3b98c68ff4e00bd55fd95b4affcaed3b521c32e4 Mon Sep 17 00:00:00 2001 From: Alain Date: Fri, 29 Jul 2022 13:49:54 +0200 Subject: ein bild --- buch/papers/parzyl/img/koordinaten.png | Bin 0 -> 159434 bytes buch/papers/parzyl/teil0.tex | 12 ++++++++++++ 2 files changed, 12 insertions(+) create mode 100644 buch/papers/parzyl/img/koordinaten.png (limited to 'buch') diff --git a/buch/papers/parzyl/img/koordinaten.png b/buch/papers/parzyl/img/koordinaten.png new file mode 100644 index 0000000..3ee582d Binary files /dev/null and b/buch/papers/parzyl/img/koordinaten.png differ diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index 2fc8737..ab3056b 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -55,6 +55,18 @@ und y = \frac{1}{2} \left( -\frac{x^2}{\tau^2} + \tau^2 \right). \end{equation} +\begin{figure} + \centering + \includegraphics[scale=0.4]{papers/parzyl/img/koordinaten.png} + \caption{Das parabolische Koordinatensystem. Die roten Parabeln haben ein + konstantes $\sigma$ und die grünen ein konstantes $\tau$.} + \label{fig:cordinates} +\end{figure} + +Abbildung \ref{fig:cordinates} zeigt das Parabolische Koordinatensystem. +Das parabolische Zylinderkoordinatensystem entsteht wenn die Parabeln aus der +Ebene gezogen werden. + \subsection{Differnetialgleichung} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam -- cgit v1.2.1 From 200d9ac2dd1173bb8e6d4e8389de7c6863b9d76d Mon Sep 17 00:00:00 2001 From: tschwall <55748566+tschwall@users.noreply.github.com> Date: Fri, 29 Jul 2022 14:41:08 +0200 Subject: Made stuff --- buch/SeminarSpezielleFunktionen.pdf | Bin 22090645 -> 22091943 bytes buch/papers/parzyl/teil2.tex | 13 ++++++------ buch/papers/parzyl/teil3.tex | 41 ++++++++++++++++++++++++++++++------ 3 files changed, 41 insertions(+), 13 deletions(-) (limited to 'buch') diff --git a/buch/SeminarSpezielleFunktionen.pdf b/buch/SeminarSpezielleFunktionen.pdf index d581f96..169dfd2 100644 Binary files a/buch/SeminarSpezielleFunktionen.pdf and b/buch/SeminarSpezielleFunktionen.pdf differ diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex index 1ffdeec..59f8b94 100644 --- a/buch/papers/parzyl/teil2.tex +++ b/buch/papers/parzyl/teil2.tex @@ -10,9 +10,11 @@ \subsection{Elektrisches Feld einer semi-infiniten Platte \label{parzyl:subsection:bonorum}} -Die parabolischen Zylinderkoordinaten tauchen auf, wenn man das elektrische Feld einer semi-infiniten Platte finden will. Das dies so ist kann mit Hilfe von komplexen Funktionen gezeigt werden. Jede komplexe Funktion $F(z)$, wie in gezeigt, kann geschrieben werden als +Die parabolischen Zylinderkoordinaten tauchen auf, wenn man das elektrische Feld einer semi-infiniten Platte finden will. +Das dies so ist kann im zwei Dimensionalen mit Hilfe von komplexen Funktionen gezeigt werden. Wobei die Platte dann nur eine Linie ist. +Jede komplexe Funktion $F(z)$ kann geschrieben werden als \begin{equation} - F(z) = U(x,y) + iV(x,y) \qquad z = x + iy. + F(z) = U(x,y) + iV(x,y) \qquad z \in \mathbb{C}; x,y \in \mathbb{R}. \end{equation} Dabei muss gelten, falls die Funktion differenzierbar ist, dass \begin{equation} @@ -44,12 +46,12 @@ Aus dieser Bedingung folgt }_{\nabla^2V(x,y) = 0}. \end{equation} Zusätzlich zeigen diese Bedingungen auch, dass die zwei Funktionen $U(x,y)$ und $V(x,y)$ orthogonal zueinander sind. -Der Zusammenhang zum elektrischen Feld ist jetzt, dass das Potential an einem quellenfreien Punkt als +Der Zusammenhang zum elektrischen Feld ist jetzt, dass das Potential an einem quellenfreien Punkt gegeben ist als \begin{equation} \nabla^2\phi(x,y) = 0. \end{equation} -Da dies bei komplexen differenzierbaren Funktionen gilt, wie Gleichung \ref{parzyl_e_feld_zweite_ab} zeigt, kann entweder $U(x,y)$ oder $V(x,y)$ von einer solchen Funktion als das Potential angesehen werden. Im weiteren wird für dies $U(x,y)$ verwendet. -Da die Funktion, welche nicht das Potential beschreibt $V(x,y)$ orthogonal zum Potential ist, zeigt diese das Verhalten des elektrischen Feldes. +Da dies bei komplexen differenzierbaren Funktionen gilt, wie Gleichung \ref{parzyl_e_feld_zweite_ab} zeigt, kann entweder $U(x,y)$ oder $V(x,y)$ von einer solchen Funktion als das Potential angesehen werden. Im weiteren wird für das Potential $U(x,y)$ verwendet. +Da die Funktion, welche nicht das Potential beschreibt, in weiteren angenommen als $V(x,y)$, orthogonal zum Potential ist, zeigt dies das Verhalten des elektrischen Feldes. Um nun zu den parabolische Zylinderkoordinaten zu gelangen muss nur noch eine geeignete komplexe Funktion $F(z)$ gefunden werden, welche eine semi-infinite Platte beschreiben kann. Man könnte natürlich auch nach anderen Funktionen suchen, welche andere Bedingungen erfüllen und würde dann auf andere Koordinatensysteme stossen. Die gesuchte Funktion in diesem Fall ist \begin{equation} F(z) @@ -87,4 +89,3 @@ beschrieben werden. Diese zwei Gleichungen zeigen nun wie man vom kartesischen K - diff --git a/buch/papers/parzyl/teil3.tex b/buch/papers/parzyl/teil3.tex index a143aa1..0364056 100644 --- a/buch/papers/parzyl/teil3.tex +++ b/buch/papers/parzyl/teil3.tex @@ -51,7 +51,19 @@ Diese partielle Differentialgleichung kann mit Hilfe von Separation gelöst werd \end{equation} gesetzt. Was dann schlussendlich zu den Differentialgleichungen -\begin{equation} +\begin{equation}\label{parzyl_sep_dgl_1} + g''(\sigma) + - + \left ( + \lambda\sigma^2 + + + \mu + \right ) + g(\sigma) + = + 0, +\end{equation} +\begin{equation}\label{parzyl_sep_dgl_2} h''(\tau) - \left ( @@ -63,17 +75,32 @@ Was dann schlussendlich zu den Differentialgleichungen = 0 \end{equation} -und -\begin{equation} - g''(\sigma) - - +und +\begin{equation}\label{parzyl_sep_dgl_3} + i''(z) + + \left ( - \lambda\sigma^2 + \lambda + \mu \right ) - g(\sigma) + i(\tau) = 0 \end{equation} führt. +Wobei die Lösung von \ref{parzyl_sep_dgl_3} +\begin{equation} + i(z) + = + A\cos{ + \left ( + \sqrt{\lambda + \mu}z + \right )} + + + B\sin{ + \left ( + \sqrt{\lambda + \mu}z + \right )} +\end{equation} +ist und \ref{parzyl_sep_dgl_1} und \ref{parzyl_sep_dgl_2} die sogenannten Weberschen Differentialgleichungen sind, welche die parabolischen Zylinder Funktionen als Lösung haben. -- cgit v1.2.1 From 0c3ae18ee42f7b3154642175faea29e957d8bba0 Mon Sep 17 00:00:00 2001 From: Alain Date: Fri, 29 Jul 2022 15:53:20 +0200 Subject: skalierungsfaktoren --- buch/papers/parzyl/teil0.tex | 77 +++++++++++++++++++++++++++++++++----------- buch/papers/parzyl/teil1.tex | 32 ------------------ 2 files changed, 59 insertions(+), 50 deletions(-) (limited to 'buch') diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index ab3056b..f6e63d4 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -43,8 +43,10 @@ Im parabloischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koor Die Koordinate $(\sigma, \tau, z)$ sind in kartesischen Koordinaten ausgedrückt mit \begin{align} x & = \sigma \tau \\ + \label{parzyl:coordRelationsa} y & = \frac{1}{2}\left(\tau^2 - \sigma^2\right) \\ z & = z. + \label{parzyl:coordRelationse} \end{align} Wird $\tau$ oder $\sigma$ konstant gesetzt reultieren die Parabeln \begin{equation} @@ -60,26 +62,65 @@ und \includegraphics[scale=0.4]{papers/parzyl/img/koordinaten.png} \caption{Das parabolische Koordinatensystem. Die roten Parabeln haben ein konstantes $\sigma$ und die grünen ein konstantes $\tau$.} - \label{fig:cordinates} + \label{parzyl:fig:cordinates} \end{figure} -Abbildung \ref{fig:cordinates} zeigt das Parabolische Koordinatensystem. +Abbildung \ref{parzyl:fig:cordinates} zeigt das Parabolische Koordinatensystem. Das parabolische Zylinderkoordinatensystem entsteht wenn die Parabeln aus der Ebene gezogen werden. -\subsection{Differnetialgleichung} -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{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. - -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. - - +Um in diesem Koordinatensystem integrieren und differenzieren zu +können braucht es die Skalierungsfaktoren $h_{\tau}$, $h_{\sigma}$ und $h_{z}$. +Der Skalierungsfaktor braucht es, damit die Distanzen zwischen zwei +Punkten unabhängig vom Koordinatensystem sind. +Wird eine infinitessimal kleine Distanz $ds$ zwischen zwei Punkten betrachtet +kann dies im kartesischen Koordinatensystem mit +\begin{equation} + \left(ds\right)^2 = \left(dx\right)^2 + \left(dy\right)^2 + + \left(dz\right)^2 + \label{parzyl:eq:ds} +\end{equation} +ausgedrückt werden. +Das Skalierungsfaktoren werden so bestimmt, dass +\begin{equation} + \left(ds\right)^2 = \left(h_{\sigma}d\sigma\right)^2 + + \left(h_{\tau}d\tau\right)^2 + \left(h_z dz\right)^2 +\label{parzyl:eq:dspara} +\end{equation} +gilt. +Dafür werden $dx$, $dy$, und $dz$ in \eqref{parzyl:eq:ds} mit den Beziehungen +von \eqref{parzyl:coordRelationsa} - \eqref{parzyl:coordRelationse} als +\begin{align} + dx &= \frac{\delta x }{\delta \sigma} d\sigma + + \frac{\delta x }{\delta \tau} d\tau + + \frac{\delta x }{\delta \tilde{z}} d \tilde{z} + = \tau d\sigma + \sigma d \tau \\ + dy &= \frac{\delta y }{\delta \sigma} d\sigma + + \frac{\delta y }{\delta \tau} d\tau + + \frac{\delta y }{\delta \tilde{z}} d \tilde{z} + = \tau d\tau - \sigma d \sigma \\ + dz &= \frac{\delta \tilde{z} }{\delta \sigma} d\sigma + + \frac{\delta \tilde{z} }{\delta \tau} d\tau + + \frac{\delta \tilde{z} }{\delta \tilde{z}} d \tilde{z} + = d \tilde{z} \\ +\end{align} +substituiert. +Wird diese gleichung in der Form von \eqref{parzyl:eq:dspara} +geschrieben, resultiert +\begin{equation} + \left(d s\right)^2 = + \left(\sigma^2 + \tau^2\right)\left(d\sigma\right)^2 + + \left(\sigma^2 + \tau^2\right)\left(d\tau\right)^2 + + \left(d \tilde{z}\right)^2. +\end{equation} +Daraus resultieren die Skalierungsfaktoren +\begin{align} + h_{\sigma} &= \sqrt{\sigma^2 + \tau^2}\\ + h_{\sigma} &= \sqrt{\sigma^2 + \tau^2}\\ + h_{z} &= 1. +\end{align} +\subsection{Differentialgleichung} +Möchte man eine Differentialgleichung im parabolischen +Zylinderkoordinatensystem lösen müssen die Skalierungsfaktoren +mitgerechnet werden. +\dots diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex index 7d5c1a4..b7e906c 100644 --- a/buch/papers/parzyl/teil1.tex +++ b/buch/papers/parzyl/teil1.tex @@ -6,36 +6,4 @@ \section{Lösung \label{parzyl:section:teil1}} \rhead{Problemstellung} -\begin{equation} -\int_a^b x^2\, dx -= -\left[ \frac13 x^3 \right]_a^b -= -\frac{b^3-a^3}3. -\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 -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? - - -Et harum quidem rerum facilis est et expedita distinctio -\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{parzyl: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. - -- cgit v1.2.1 From 3db5682b70a73baec580d839e5f9e1cc909bd5fb Mon Sep 17 00:00:00 2001 From: tschwall <55748566+tschwall@users.noreply.github.com> Date: Fri, 29 Jul 2022 16:39:19 +0200 Subject: Stuff added --- buch/papers/parzyl/main.tex | 1 - buch/papers/parzyl/teil0.tex | 108 ++++++++++++++++++++++++++++++++++++++----- buch/papers/parzyl/teil3.tex | 98 --------------------------------------- 3 files changed, 96 insertions(+), 111 deletions(-) (limited to 'buch') diff --git a/buch/papers/parzyl/main.tex b/buch/papers/parzyl/main.tex index 01a8d59..0996007 100644 --- a/buch/papers/parzyl/main.tex +++ b/buch/papers/parzyl/main.tex @@ -16,7 +16,6 @@ parabolischen Zyplinderkoordinatensystem genauer untersucht. \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/teil0.tex b/buch/papers/parzyl/teil0.tex index ab3056b..f4e8726 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -68,18 +68,102 @@ Das parabolische Zylinderkoordinatensystem entsteht wenn die Parabeln aus der Ebene gezogen werden. \subsection{Differnetialgleichung} -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{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. +Die Differentialgleichungen, welche zu den parabolischen Zylinderfunktionen führen tauchen, wie bereits erwähnt, dann auf, wenn die Helmholtz Gleichung +\begin{equation} + \Delta f(x,y,z) = \lambda f(x,y,z) +\end{equation} +im parabolischen Zylinderkoordinatensystem +\begin{equation} + \Delta f(\sigma,\tau,z) = \lambda f(\sigma,\tau,z) +\end{equation} +gelöst wird. +Wobei der Laplace Operator $\Delta$ im parabolischen Zylinderkoordinatensystem gegeben ist als +\begin{equation} + \nabla + = + \frac{1}{\sigma^2 + \tau^2} + \left ( + \frac{\partial^2}{\partial \sigma^2} + + + \frac{\partial^2}{\partial \tau^2} + \right ) + + + \frac{\partial^2}{\partial z^2}. +\end{equation} +Die Helmholtz Gleichung würde also wie folgt lauten +\begin{equation} + \nabla f(\sigma, \tau, z) + = + \frac{1}{\sigma^2 + \tau^2} + \left ( + \frac{\partial^2 f(\sigma,\tau,z)}{\partial \sigma^2} + + + \frac{\partial^2 f(\sigma,\tau,z)}{\partial \tau^2} + \right ) + + + \frac{\partial^2 f(\sigma,\tau,z)}{\partial z^2} + = + \lambda f(\sigma,\tau,z) +\end{equation} +Diese partielle Differentialgleichung kann mit Hilfe von Separation gelöst werden, dazu wird +\begin{equation} + f(\sigma,\tau,z) = g(\sigma)h(\tau)i(z) +\end{equation} +gesetzt. +Was dann schlussendlich zu den Differentialgleichungen +\begin{equation}\label{parzyl_sep_dgl_1} + g''(\sigma) + - + \left ( + \lambda\sigma^2 + + + \mu + \right ) + g(\sigma) + = + 0, +\end{equation} +\begin{equation}\label{parzyl_sep_dgl_2} + h''(\tau) + - + \left ( + \lambda\tau^2 + - + \mu + \right ) + h(\tau) + = + 0 +\end{equation} +und +\begin{equation}\label{parzyl_sep_dgl_3} + i''(z) + + + \left ( + \lambda + + + \mu + \right ) + i(\tau) + = + 0 +\end{equation} +führt. +Wobei die Lösung von \ref{parzyl_sep_dgl_3} +\begin{equation} + i(z) + = + A\cos{ + \left ( + \sqrt{\lambda + \mu}z + \right )} + + + B\sin{ + \left ( + \sqrt{\lambda + \mu}z + \right )} +\end{equation} +ist und \ref{parzyl_sep_dgl_1} und \ref{parzyl_sep_dgl_2} die sogenannten Weberschen Differentialgleichungen sind, welche die parabolischen Zylinder Funktionen als Lösung haben. -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/teil3.tex b/buch/papers/parzyl/teil3.tex index 0364056..4e44bd6 100644 --- a/buch/papers/parzyl/teil3.tex +++ b/buch/papers/parzyl/teil3.tex @@ -6,101 +6,3 @@ \section{Teil 3 \label{parzyl:section:teil3}} \rhead{Teil 3} -\subsection{Helmholtz Gleichung im parabolischen Zylinderkoordinatensystem -\label{parzyl:subsection:malorum}} -Die Differentialgleichungen, welche zu den parabolischen Zylinderfunktionen führen tauchen, wie bereits erwähnt, dann auf, wenn die Helmholtz Gleichung -\begin{equation} - \Delta f(x,y,z) = \lambda f(x,y,z) -\end{equation} -im parabolischen Zylinderkoordinatensystem -\begin{equation} - \Delta f(\sigma,\tau,z) = \lambda f(\sigma,\tau,z) -\end{equation} -gelöst wird. -Wobei der Laplace Operator $\Delta$ im parabolischen Zylinderkoordinatensystem gegeben ist als -\begin{equation} - \nabla - = - \frac{1}{\sigma^2 + \tau^2} - \left ( - \frac{\partial^2}{\partial \sigma^2} - + - \frac{\partial^2}{\partial \tau^2} - \right ) - + - \frac{\partial^2}{\partial z^2}. -\end{equation} -Die Helmholtz Gleichung würde also wie folgt lauten -\begin{equation} - \nabla f(\sigma, \tau, z) - = - \frac{1}{\sigma^2 + \tau^2} - \left ( - \frac{\partial^2 f(\sigma,\tau,z)}{\partial \sigma^2} - + - \frac{\partial^2 f(\sigma,\tau,z)}{\partial \tau^2} - \right ) - + - \frac{\partial^2 f(\sigma,\tau,z)}{\partial z^2} - = - \lambda f(\sigma,\tau,z) -\end{equation} -Diese partielle Differentialgleichung kann mit Hilfe von Separation gelöst werden, dazu wird -\begin{equation} - f(\sigma,\tau,z) = g(\sigma)h(\tau)i(z) -\end{equation} -gesetzt. -Was dann schlussendlich zu den Differentialgleichungen -\begin{equation}\label{parzyl_sep_dgl_1} - g''(\sigma) - - - \left ( - \lambda\sigma^2 - + - \mu - \right ) - g(\sigma) - = - 0, -\end{equation} -\begin{equation}\label{parzyl_sep_dgl_2} - h''(\tau) - - - \left ( - \lambda\tau^2 - - - \mu - \right ) - h(\tau) - = - 0 -\end{equation} -und -\begin{equation}\label{parzyl_sep_dgl_3} - i''(z) - + - \left ( - \lambda - + - \mu - \right ) - i(\tau) - = - 0 -\end{equation} -führt. -Wobei die Lösung von \ref{parzyl_sep_dgl_3} -\begin{equation} - i(z) - = - A\cos{ - \left ( - \sqrt{\lambda + \mu}z - \right )} - + - B\sin{ - \left ( - \sqrt{\lambda + \mu}z - \right )} -\end{equation} -ist und \ref{parzyl_sep_dgl_1} und \ref{parzyl_sep_dgl_2} die sogenannten Weberschen Differentialgleichungen sind, welche die parabolischen Zylinder Funktionen als Lösung haben. -- cgit v1.2.1 From 81b33c456132ec906ca12f48c78cca83fe1c6437 Mon Sep 17 00:00:00 2001 From: Alain Date: Fri, 29 Jul 2022 16:44:28 +0200 Subject: mehr sachen --- buch/papers/parzyl/teil0.tex | 2 +- buch/papers/parzyl/teil1.tex | 17 +++++++++++++++++ 2 files changed, 18 insertions(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index f6e63d4..650428f 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -113,7 +113,7 @@ geschrieben, resultiert \left(\sigma^2 + \tau^2\right)\left(d\tau\right)^2 + \left(d \tilde{z}\right)^2. \end{equation} -Daraus resultieren die Skalierungsfaktoren +Daraus ergeben sich die Skalierungsfaktoren \begin{align} h_{\sigma} &= \sqrt{\sigma^2 + \tau^2}\\ h_{\sigma} &= \sqrt{\sigma^2 + \tau^2}\\ diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex index b7e906c..1ae7bfd 100644 --- a/buch/papers/parzyl/teil1.tex +++ b/buch/papers/parzyl/teil1.tex @@ -6,4 +6,21 @@ \section{Lösung \label{parzyl:section:teil1}} \rhead{Problemstellung} +Die Differentialgleichung aus \dots kann mit einer Substitution +in die Whittaker Gleichung gelöst werden. +\begin{definition} + Die Funktion + \begin{equation*} + W_{k,m}(z) = + e^{-z/2} z^{m+1/2} \, + {}_{1} F_{1}(\frac{1}{2} + m - k, 1 + 2m; z) + \end{equation*} + heisst Whittaker Funktion und ist eine Lösung + von + \begin{equation} + \frac{d^2W}{d z^2} + + \left(-\frac{1}{4} + \frac{k}{z} + \frac{\frac{1}{4} - m^2}{z^2} \right) W = 0. + \end{equation} +\end{definition} + -- cgit v1.2.1 From 05ec2574b277820e0e07dc56392add19ecbc6565 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Fri, 29 Jul 2022 17:41:50 +0200 Subject: polished teil0 und teil1, created a new figure Strategie.pdf --- buch/papers/lambertw/Bilder/Strategie.pdf | Bin 0 -> 120904 bytes buch/papers/lambertw/Bilder/Strategie.py | 52 ++ buch/papers/lambertw/Bilder/Strategie.svg | 790 ++++++++++++++++++++++++++++++ buch/papers/lambertw/main.tex | 6 +- buch/papers/lambertw/teil0.tex | 15 +- buch/papers/lambertw/teil1.tex | 94 ++-- 6 files changed, 914 insertions(+), 43 deletions(-) create mode 100644 buch/papers/lambertw/Bilder/Strategie.pdf create mode 100644 buch/papers/lambertw/Bilder/Strategie.py create mode 100644 buch/papers/lambertw/Bilder/Strategie.svg (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/Strategie.pdf b/buch/papers/lambertw/Bilder/Strategie.pdf new file mode 100644 index 0000000..0de3001 Binary files /dev/null and b/buch/papers/lambertw/Bilder/Strategie.pdf differ diff --git a/buch/papers/lambertw/Bilder/Strategie.py b/buch/papers/lambertw/Bilder/Strategie.py new file mode 100644 index 0000000..b9b41bf --- /dev/null +++ b/buch/papers/lambertw/Bilder/Strategie.py @@ -0,0 +1,52 @@ +# -*- coding: utf-8 -*- +""" +Created on Fri Jul 29 09:40:11 2022 + +@author: yanik +""" +import pylatex + +import numpy as np +import matplotlib.pyplot as plt + +N = np.array([0, 0]) +V = np.array([1, 4]) +Z = np.array([5, 5]) +VZ = Z-V +vzScale = 0.4 + + +a = [N, N, V] +b = [V, Z, vzScale*VZ] + +X = np.array([i[0] for i in a]) +Y = np.array([i[1] for i in a]) +U = np.array([i[0] for i in b]) +W = np.array([i[1] for i in b]) + +xlim = 6 +ylim = 6 +fig, ax = plt.subplots(1,1) +ax.set_xlim([0, xlim]) #<-- set the x axis limits +ax.set_ylim([0, ylim]) #<-- set the y axis limits +#plt.figure(figsize=(xlim, ylim)) +ax.quiver(X, Y, U, W, angles='xy', scale_units='xy', scale=1, headwidth=5, headlength=7, headaxislength=5.5) + +ax.plot([V[0], (VZ+V)[0]], [V[1], (VZ+V)[1]], 'k--') +ax.plot(np.vstack([V, Z])[:, 0], np.vstack([V, Z])[:,1], 'bo', markersize=10) + + +ax.text(2.5, 4.5, "Visierlinie", size=20, rotation=10) + +plt.rcParams.update({ + "text.usetex": True, + "font.family": "serif", + "font.serif": ["New Century Schoolbook"], +}) + +ax.text(1.6, 4.3, r"$\vec{v}$", size=30) +ax.text(0.6, 3.9, r"$V$", size=30, c='b') +ax.text(5.1, 4.77, r"$Z$", size=30, c='b') + + + diff --git a/buch/papers/lambertw/Bilder/Strategie.svg b/buch/papers/lambertw/Bilder/Strategie.svg new file mode 100644 index 0000000..30f9f22 --- /dev/null +++ b/buch/papers/lambertw/Bilder/Strategie.svg @@ -0,0 +1,790 @@ + + + + + + + + + 2022-07-29T16:52:06.315252 + image/svg+xml + + + Matplotlib v3.3.2, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/buch/papers/lambertw/main.tex b/buch/papers/lambertw/main.tex index 9e6d04f..394963f 100644 --- a/buch/papers/lambertw/main.tex +++ b/buch/papers/lambertw/main.tex @@ -7,7 +7,7 @@ \lhead{Verfolgungskurven} \begin{refsection} \chapterauthor{David Hugentobler und Yanik Kuster} - +% %Ein paar Hinweise für die korrekte Formatierung des Textes %\begin{itemize} %\item @@ -26,12 +26,12 @@ %Bilden Sie auch für Formeln kurze Zeilen, einerseits der besseren %Übersicht wegen, aber auch um GIT die Arbeit zu erleichtern. %\end{itemize} - +% \input{papers/lambertw/teil0.tex} %\input{papers/lambertw/teil2.tex} %\input{papers/lambertw/teil3.tex} \input{papers/lambertw/teil4.tex} \input{papers/lambertw/teil1.tex} - +% \printbibliography[heading=subbibliography] \end{refsection} diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 5007867..8fa8f9b 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -6,15 +6,14 @@ \section{Was sind Verfolgungskurven? \label{lambertw:section:Was_sind_Verfolgungskurven}} \rhead{Was sind Verfolgungskurven?} - +% 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 verfolgt sein Ziel, das versucht zu entkommen. Der Pfad, den der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. Um diese Kurve zu bestimmen, kann das Verfolgungsproblem als Differentialgleichung formuliert werden. Diese Differentialgleichung entspringt der Verfolgungsstrategie des Verfolgers. - - +% \subsection{Verfolger und Verfolgungsstrategie \label{lambertw:subsection:Verfolger}} Wie bereits erwähnt, wird der Verfolger durch seine Verfolgungsstrategie definiert. @@ -48,7 +47,7 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um % \begin{figure} \centering - \includegraphics[scale=0.1]{./papers/lambertw/Bilder/pursuerDGL2.png} + \includegraphics[scale=0.6]{./papers/lambertw/Bilder/Strategie.pdf} \caption{Vektordarstellung Jagdstrategie} \label{lambertw:grafic:pursuerDGL2} \end{figure} @@ -61,23 +60,27 @@ In der Abbildung \ref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, wobei $v$ der Ortsvektor des Verfolgers, $z$ der Ortsvektor des Ziels und $\dot{v}$ der Geschwindigkeitsvektor des Verfolgers ist. Der Geschwindigkeitsvektor entspricht dem Richtungsvektors des Verfolgers. Die konstante Geschwindigkeit kann man mit der Gleichung +% \begin{equation} |\dot{v}| = \operatorname{const} = A \text{,}\quad A\in\mathbb{R}^+ \end{equation} +% darstellen. Der Geschwindigkeitsvektor kann mit der Gleichung +% \begin{equation} \frac{z-v}{|z-v|}\cdot|\dot{v}| = \dot{v} \end{equation} +% beschrieben werden, wenn die Jagdstrategie verwendet wird. Die Differenz der Ortsvektoren $v$ und $z$ ist ein Vektor der vom Punkt $V$ auf $Z$ zeigt. Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den Betrag, ein Einheitsvektor erzeugt. 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 $\dot{v}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergeben sich \begin{align} \frac{z-v}{|z-v|}\cdot|\dot{v}|\cdot\dot{v} @@ -97,7 +100,7 @@ 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} z(t) = diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index a330838..2733759 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -6,7 +6,7 @@ \section{Wird das Ziel erreicht? \label{lambertw:section:Wird_das_Ziel_erreicht}} \rhead{Wird das Ziel erreicht?} - +% Sehr oft kommt es vor, dass bei Verfolgungsproblemen die Frage auftaucht, ob das Ziel überhaupt erreicht wird. Wenn zum Beispiel die Geschwindigkeit des Verfolgers kleiner ist als diejenige des Ziels, gibt es Anfangsbedingungen bei denen das Ziel nie erreicht wird. Im Anschluss dieser Frage stellt sich meist die nächste Frage, wie lange es dauert bis das Ziel erreicht wird. @@ -16,7 +16,7 @@ Das Beispiel wird bei dieser Betrachtung noch etwas erweitert indem alle Punkte Nun gilt es zu definieren, wann das Ziel erreicht wird. Da sowohl Ziel und Verfolger als Punkte modelliert wurden, gilt das Ziel als erreicht, wenn die Koordinaten des Verfolgers mit denen des Ziels bei einem diskreten Zeitpunkt $t_1$ übereinstimmen. Somit gilt es - +% \begin{equation*} z(t_1)=v(t_1) \end{equation*} @@ -30,15 +30,14 @@ Die Parametrisierung von $z(t)$ ist im Beispiel definiert als \end{equation} % Die Parametrisierung von $v(t)$ ist von den Startbedingungen abhängig. Deshalb wird die obige Bedingung jeweils für die unterschiedlichen Startbedingungen separat analysiert. - +% \subsection{Anfangsbedingung im \RN{1}-Quadranten} % -$ x_0$ $\boldsymbol{x}$ dd Wenn der Verfolger im \RN{1}-Quadranten startet, dann kann $v(t)$ mit den Gleichungen aus \eqref{lambertw:eqFunkXNachT}, welche \begin{align*} x\left(t\right) &= - x_0\cdot\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp(\chi-\frac{4t}{r_0-y_0})\right)} \\ + x_0\cdot\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right) \right)} \\ y(t) &= \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\\ @@ -63,13 +62,13 @@ Der Folger ist durch % parametrisiert, wobei $y(t)$ viel komplexer ist als $x(t)$. Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Bedingung der $x$- und $y$-Koordinaten einzeln überprüft werden müssen. Es entstehen daher folgende Bedingungen - +% \begin{align*} 0 &= x(t) = - x_0\sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} + x_0\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right)\right)} \\ t &= @@ -80,39 +79,66 @@ Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Beding % welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. Zuerst wird die Bedingung der $x$-Koordinate betrachtet. -Diese kann durch dividieren durch $x_0$, anschliessendes quadrieren und multiplizieren von $\chi$ vereinfacht werden. Daraus folgt +Da $x_0 \neq 0$ und $\chi \neq 0$ mit \begin{equation} - 0 - = - W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right) - \text{.} + 0 + = + x_0\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right)\right)} \end{equation} -% -Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. -Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei - -\begin{equation*} - W(0)=0 -\end{equation*} -% -besitzt, kann die Bedingung weiter vereinfacht werden zu - +ist diese Bedingung genau dann erfüllt, wenn \begin{equation} 0 = - \chi\cdot e^{\chi-\frac{4t}{r_0-y_0}} + W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right)\right) \text{.} \end{equation} % +Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. +Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei +\begin{equation} + W(0)=0 +\end{equation} +% Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingung unmöglich zu erfüllen. Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Einholen möglich wäre. -Somit kann nach den Gestellten Bedingungen das Ziel nie erreicht werden. - +Somit kann nach den gestellten Bedingungen das Ziel nie erreicht werden. +% +% +% +%Diese kann durch dividieren durch $x_0$, anschliessendes quadrieren und multiplizieren von $\chi$ vereinfacht werden. Daraus folgt +%\begin{equation} +% 0 +% = +% W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right)\right) +% \text{.} +%5\end{equation} +% +%Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. +%Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei +% +%\begin{equation*} +% W(0)=0 +%\end{equation*} +% +%besitzt, kann die Bedingung weiter vereinfacht werden zu +% +%\begin{equation} +% 0 +% = +% \chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right) +% \text{.} +%\end{equation} +% +%Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingung unmöglich zu erfüllen. +%Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. +%Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Einholen möglich wäre. +%Somit kann nach den gestellten Bedingungen das Ziel nie erreicht werden. +% \subsection{Anfangsbedingung $y_0<0$} Da die Geschwindigkeit des Verfolgers und des Ziels übereinstimmen, kann der Verfolgers niemals das Ziel einholen. Dies kann veranschaulicht werden anhand - +% \begin{equation} v(t)\cdot \left( \begin{array}{c} 0 \\ 1 \end{array}\right) \leq @@ -122,13 +148,13 @@ Dies kann veranschaulicht werden anhand \end{equation} % Da der $y$-Anteil der Geschwindigkeit des Ziels grösser-gleich der des Verfolgers ist, können die $y$-Koordinaten nie übereinstimmen. - +% \subsection{Anfangsbedingung auf positiven $y$-Achse} Wenn der Verfolger auf der positiven $y$-Achse startet, befindet er sich direkt auf der Fluchtgeraden des Ziels. Dies führt dazu, dass der Verfolger und das Ziel sich direkt aufeinander zu bewegen, da der Geschwindigkeitsvektor des Verfolgers auf das Ziel zeigt. Die Folge ist, dass das Ziel zwingend erreicht wird. Um $t_1$ zu bestimmen, kann die Verfolgungskurve in diesem Fall mit - +% \begin{equation} v(t) = @@ -138,17 +164,17 @@ Um $t_1$ zu bestimmen, kann die Verfolgungskurve in diesem Fall mit parametrisiert werden. Nun kann der Abstand zwischen Verfolger und Ziel leicht bestimmt und nach 0 aufgelöst werden. Woraus folgt - +% \begin{equation} 0 = |v(t_1)-z(t_1)| = - y_0-2t_1 + y_0-2t_1\text{,} \end{equation} % -, was aufgelöst zu - +was aufgelöst zu +% \begin{equation} t_1 = @@ -165,14 +191,14 @@ Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumli Somit wird in einer nächsten Betrachtung untersucht, ob der Verfolger dem Ziel näher kommt als ein definierter Trefferradius. Falls dies stattfinden sollte, wird dies als Treffer interpretiert. Mathematisch kann dies mit - +% \begin{equation} |v-z| Date: Fri, 29 Jul 2022 18:20:55 +0200 Subject: verbesserungen --- buch/papers/parzyl/main.tex | 5 +- buch/papers/parzyl/teil0.tex | 110 +++++++++++++++++++++++++------------------ buch/papers/parzyl/teil1.tex | 4 +- buch/papers/parzyl/teil2.tex | 2 +- 4 files changed, 68 insertions(+), 53 deletions(-) (limited to 'buch') diff --git a/buch/papers/parzyl/main.tex b/buch/papers/parzyl/main.tex index 0996007..528a2e2 100644 --- a/buch/papers/parzyl/main.tex +++ b/buch/papers/parzyl/main.tex @@ -8,10 +8,7 @@ \begin{refsection} \chapterauthor{Thierry Schwaller, Alain Keller} -Die Laplace-Gleichung ist eine wichtige Gleichung in der Physik. -Mit ihr lässt sich zum Beispiel das elektrische Feld in einem ladungsfreien Raum bestimmen. -In diesem Kapitel wird die Lösung der Laplace-Gliechung im -parabolischen Zyplinderkoordinatensystem genauer untersucht. + \input{papers/parzyl/teil0.tex} \input{papers/parzyl/teil1.tex} diff --git a/buch/papers/parzyl/teil0.tex b/buch/papers/parzyl/teil0.tex index a77398d..4b251db 100644 --- a/buch/papers/parzyl/teil0.tex +++ b/buch/papers/parzyl/teil0.tex @@ -3,21 +3,24 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Problem\label{parzyl:section:teil0}} +\section{Einleitung\label{parzyl:section:teil0}} \rhead{Teil 0} - +Die Laplace-Gleichung ist eine wichtige Gleichung in der Physik. +Mit ihr lässt sich zum Beispiel das elektrische Feld in einem ladungsfreien Raum bestimmen. +In diesem Kapitel wird die Lösung der Laplace-Gleichung im +parabolischen Zylinderkoordinatensystem genauer untersucht. \subsection{Laplace Gleichung} Die partielle Differentialgleichung \begin{equation} \Delta f = 0 \end{equation} -ist als Laplace Gleichung bekannt. -Sie ist eine spezielle Form der poisson Gleichung +ist als Laplace-Gleichung bekannt. +Sie ist eine spezielle Form der Poisson-Gleichung \begin{equation} \Delta f = g \end{equation} mit g als beliebige Funktion. -In der Physik hat die Laplace Gleichung in verschieden Gebieten +In der Physik hat die Laplace-Gleichung in verschieden Gebieten verwendet, zum Beispiel im Elektromagnetismus. Das Gaussche Gesetz in den Maxwellgleichungen \begin{equation} @@ -35,11 +38,11 @@ Eingesetzt in \eqref{parzyl:eq:max1} resultiert \begin{equation} \nabla \cdot \nabla \phi = \Delta \phi = \frac{\varrho}{\epsilon_0}, \end{equation} -was eine Possion gleichung ist. +was eine Possion-Gleichung ist. An Ladungsfreien Stellen, ist der rechte Teil der Gleichung $0$. \subsection{Parabolische Zylinderkoordinaten \label{parzyl:subsection:finibus}} -Im parabloischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koordinatenflächen. +Im parabolischen Zylinderkoordinatensystem bilden parabolische Zylinder die Koordinatenflächen. Die Koordinate $(\sigma, \tau, z)$ sind in kartesischen Koordinaten ausgedrückt mit \begin{align} x & = \sigma \tau \\ @@ -48,7 +51,7 @@ Die Koordinate $(\sigma, \tau, z)$ sind in kartesischen Koordinaten ausgedrückt z & = z. \label{parzyl:coordRelationse} \end{align} -Wird $\tau$ oder $\sigma$ konstant gesetzt reultieren die Parabeln +Wird $\tau$ oder $\sigma$ konstant gesetzt resultieren die Parabeln \begin{equation} y = \frac{1}{2} \left( \frac{x^2}{\sigma^2} - \sigma^2 \right) \end{equation} @@ -68,10 +71,12 @@ und Abbildung \ref{parzyl:fig:cordinates} zeigt das Parabolische Koordinatensystem. Das parabolische Zylinderkoordinatensystem entsteht wenn die Parabeln aus der Ebene gezogen werden. + Um in diesem Koordinatensystem integrieren und differenzieren zu können braucht es die Skalierungsfaktoren $h_{\tau}$, $h_{\sigma}$ und $h_{z}$. -Der Skalierungsfaktor braucht es, damit die Distanzen zwischen zwei -Punkten unabhängig vom Koordinatensystem sind. + +\dots + Wird eine infinitessimal kleine Distanz $ds$ zwischen zwei Punkten betrachtet kann dies im kartesischen Koordinatensystem mit \begin{equation} @@ -90,21 +95,21 @@ gilt. Dafür werden $dx$, $dy$, und $dz$ in \eqref{parzyl:eq:ds} mit den Beziehungen von \eqref{parzyl:coordRelationsa} - \eqref{parzyl:coordRelationse} als \begin{align} - dx &= \frac{\delta x }{\delta \sigma} d\sigma + - \frac{\delta x }{\delta \tau} d\tau + - \frac{\delta x }{\delta \tilde{z}} d \tilde{z} + dx &= \frac{\partial x }{\partial \sigma} d\sigma + + \frac{\partial x }{\partial \tau} d\tau + + \frac{\partial x }{\partial \tilde{z}} d \tilde{z} = \tau d\sigma + \sigma d \tau \\ - dy &= \frac{\delta y }{\delta \sigma} d\sigma + - \frac{\delta y }{\delta \tau} d\tau + - \frac{\delta y }{\delta \tilde{z}} d \tilde{z} + dy &= \frac{\partial y }{\partial \sigma} d\sigma + + \frac{\partial y }{\partial \tau} d\tau + + \frac{\partial y }{\partial \tilde{z}} d \tilde{z} = \tau d\tau - \sigma d \sigma \\ - dz &= \frac{\delta \tilde{z} }{\delta \sigma} d\sigma + - \frac{\delta \tilde{z} }{\delta \tau} d\tau + - \frac{\delta \tilde{z} }{\delta \tilde{z}} d \tilde{z} + dz &= \frac{\partial \tilde{z} }{\partial \sigma} d\sigma + + \frac{\partial \tilde{z} }{\partial \tau} d\tau + + \frac{\partial \tilde{z} }{\partial \tilde{z}} d \tilde{z} = d \tilde{z} \\ \end{align} substituiert. -Wird diese gleichung in der Form von \eqref{parzyl:eq:dspara} +Wird diese Gleichung in der Form von \eqref{parzyl:eq:dspara} geschrieben, resultiert \begin{equation} \left(d s\right)^2 = @@ -120,11 +125,22 @@ Daraus ergeben sich die Skalierungsfaktoren \end{align} \subsection{Differentialgleichung} Möchte man eine Differentialgleichung im parabolischen -Zylinderkoordinatensystem lösen müssen die Skalierungsfaktoren -mitgerechnet werden. -\dots -\subsection{Lösung der Helmholtz Gleichung im parabolischen Zylinderfunktion} -Die Differentialgleichungen, welche zu den parabolischen Zylinderfunktionen führen tauchen, wie bereits erwähnt, dann auf, wenn die Helmholtz Gleichung +Zylinderkoordinatensystem aufstellen müssen die Skalierungsfaktoren +mitgerechnet werden. +Der Laplace Operator ist dadurch gegeben als +\begin{equation} + \Delta f = \frac{1}{\sigma^2 + \tau^2} + \left( + \frac{\partial^2 f}{\partial \sigma ^2} + + \frac{\partial^2 f}{\partial \tau ^2} + \right) + + \frac{\partial^2 f}{\partial z}. + \label{parzyl:eq:laplaceInParZylCor} +\end{equation} +\subsubsection{Lösung der Helmholtz-Gleichung im parabolischen Zylinderfunktion} +Die Differentialgleichungen, welche zu den parabolischen Zylinderfunktionen führen, tauchen +%, wie bereits erwähnt, +dann auf, wenn die Helmholtz-Gleichung \begin{equation} \Delta f(x,y,z) = \lambda f(x,y,z) \end{equation} @@ -133,22 +149,22 @@ im parabolischen Zylinderkoordinatensystem \Delta f(\sigma,\tau,z) = \lambda f(\sigma,\tau,z) \end{equation} gelöst wird. -Wobei der Laplace Operator $\Delta$ im parabolischen Zylinderkoordinatensystem gegeben ist als -\begin{equation} - \nabla - = - \frac{1}{\sigma^2 + \tau^2} - \left ( - \frac{\partial^2}{\partial \sigma^2} - + - \frac{\partial^2}{\partial \tau^2} - \right ) - + - \frac{\partial^2}{\partial z^2}. -\end{equation} -Die Helmholtz Gleichung würde also wie folgt lauten -\begin{equation} - \nabla f(\sigma, \tau, z) +%Wobei der Laplace Operator $\Delta$ im parabolischen Zylinderkoordinatensystem gegeben ist als +%\begin{equation} +% \Delta +% = +% \frac{1}{\sigma^2 + \tau^2} +% \left ( +% \frac{\partial^2}{\partial \sigma^2} +% + +% \frac{\partial^2}{\partial \tau^2} +% \right ) +% + +% \frac{\partial^2}{\partial z^2}. +%\end{equation} +Mit dem Laplace Operator aus \eqref{parzyl:eq:laplaceInParZylCor} lautet die Helmholtz Gleichung +\begin{equation} + \Delta f(\sigma, \tau, z) = \frac{1}{\sigma^2 + \tau^2} \left ( @@ -159,7 +175,7 @@ Die Helmholtz Gleichung würde also wie folgt lauten + \frac{\partial^2 f(\sigma,\tau,z)}{\partial z^2} = - \lambda f(\sigma,\tau,z) + \lambda f(\sigma,\tau,z). \end{equation} Diese partielle Differentialgleichung kann mit Hilfe von Separation gelöst werden, dazu wird \begin{equation} @@ -167,7 +183,7 @@ Diese partielle Differentialgleichung kann mit Hilfe von Separation gelöst werd \end{equation} gesetzt. Was dann schlussendlich zu den Differentialgleichungen -\begin{equation}\label{parzyl_sep_dgl_1} +\begin{equation}\label{parzyl:sep_dgl_1} g''(\sigma) - \left ( @@ -179,7 +195,7 @@ Was dann schlussendlich zu den Differentialgleichungen = 0, \end{equation} -\begin{equation}\label{parzyl_sep_dgl_2} +\begin{equation}\label{parzyl:sep_dgl_2} h''(\tau) - \left ( @@ -192,7 +208,7 @@ Was dann schlussendlich zu den Differentialgleichungen 0 \end{equation} und -\begin{equation}\label{parzyl_sep_dgl_3} +\begin{equation}\label{parzyl:sep_dgl_3} i''(z) + \left ( @@ -205,7 +221,7 @@ und 0 \end{equation} führt. -Wobei die Lösung von \ref{parzyl_sep_dgl_3} +Wobei die Lösung von \eqref{parzyl:sep_dgl_3} \begin{equation} i(z) = @@ -219,7 +235,7 @@ Wobei die Lösung von \ref{parzyl_sep_dgl_3} \sqrt{\lambda + \mu}z \right )} \end{equation} -ist und \ref{parzyl_sep_dgl_1} und \ref{parzyl_sep_dgl_2} die sogenannten Weberschen Differentialgleichungen sind, welche die parabolischen Zylinder Funktionen als Lösung haben. +ist und \eqref{parzyl:sep_dgl_1} und \eqref{parzyl:sep_dgl_2} die sogenannten Weberschen Differentialgleichungen sind, welche die parabolischen Zylinder Funktionen als Lösung haben. diff --git a/buch/papers/parzyl/teil1.tex b/buch/papers/parzyl/teil1.tex index 1ae7bfd..f297189 100644 --- a/buch/papers/parzyl/teil1.tex +++ b/buch/papers/parzyl/teil1.tex @@ -6,7 +6,7 @@ \section{Lösung \label{parzyl:section:teil1}} \rhead{Problemstellung} -Die Differentialgleichung aus \dots kann mit einer Substitution +Die Differentialgleichungen \eqref{parzyl:sep_dgl_1} und \eqref{parzyl:sep_dgl_2} können mit einer Substitution in die Whittaker Gleichung gelöst werden. \begin{definition} Die Funktion @@ -23,4 +23,6 @@ in die Whittaker Gleichung gelöst werden. \end{equation} \end{definition} +Lösung Folgt\dots + diff --git a/buch/papers/parzyl/teil2.tex b/buch/papers/parzyl/teil2.tex index 59f8b94..3f890d0 100644 --- a/buch/papers/parzyl/teil2.tex +++ b/buch/papers/parzyl/teil2.tex @@ -3,7 +3,7 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{Physik sache +\section{Anwendung in der Physik \label{parzyl:section:teil2}} \rhead{Teil 2} -- cgit v1.2.1 From 7415664f6b5ee3ccd54da3e71fca4d9478186125 Mon Sep 17 00:00:00 2001 From: LordMcFungus Date: Fri, 29 Jul 2022 18:23:03 +0200 Subject: Delete SeminarSpezielleFunktionen.pdf --- buch/SeminarSpezielleFunktionen.pdf | Bin 22225335 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 buch/SeminarSpezielleFunktionen.pdf (limited to 'buch') diff --git a/buch/SeminarSpezielleFunktionen.pdf b/buch/SeminarSpezielleFunktionen.pdf deleted file mode 100644 index 0502c88..0000000 Binary files a/buch/SeminarSpezielleFunktionen.pdf and /dev/null differ -- cgit v1.2.1 From 5c71b098ca50b4bb11f273f8c78279c8ce23ef02 Mon Sep 17 00:00:00 2001 From: daHugen Date: Sun, 31 Jul 2022 18:09:55 +0200 Subject: Update to next version includes changes in syntax and structure --- .../papers/lambertw/Bilder/VerfolgungskurveBsp.png | Bin 297455 -> 356399 bytes buch/papers/lambertw/teil4.tex | 168 +++++++++++---------- 2 files changed, 91 insertions(+), 77 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png index 90758cd..e6e7c1e 100644 Binary files a/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png and b/buch/papers/lambertw/Bilder/VerfolgungskurveBsp.png differ diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index c79aa0c..0050b61 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -6,15 +6,15 @@ \section{Beispiel einer Verfolgungskurve \label{lambertw:section:teil4}} \rhead{Beispiel einer Verfolgungskurve} -In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie 1 beschreiben. Dafür werden zuerst Bewegungsraum, Anfangspositionen und Bewegungsverhalten definiert, in einem nächsten Schritt soll eine Differentialgleichung dafür aufgestellt und anschliessend gelöst werden. +In diesem Abschnitt wird rechnerisch das Beispiel einer Verfolgungskurve mit der Verfolgungsstrategie ``Jagd'' beschreiben. Dafür werden zuerst Bewegungsraum, Anfangspositionen und Bewegungsverhalten definiert, in einem nächsten Schritt soll eine Differentialgleichung dafür aufgestellt und anschliessend gelöst werden. \subsection{Anfangsbedingungen definieren und einsetzen \label{lambertw:subsection:Anfangsbedingungen}} -Das zu verfolgende Ziel \(Z\) bewegt sich entlang der \(y\)-Achse mit konstanter Geschwindigkeit \(v = 1\), beginnend beim Ursprung des Kartesischen Koordinatensystems. Der Verfolger \(V\) startet auf einem beliebigen Punkt im ersten Quadranten und bewegt sich auch mit konstanter Geschwindigkeit \(|\dot{V}| = 1\) in Richtung Ziel. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: +Das zu verfolgende Ziel \(Z\) bewegt sich entlang der \(y\)-Achse mit konstanter Geschwindigkeit \(|\dot{z}| = 1\), beginnend beim Ursprung des Kartesischen Koordinatensystems. Der Verfolger \(V\) startet auf einem beliebigen Punkt im ersten Quadranten und bewegt sich auch mit konstanter Geschwindigkeit \(|\dot{v}| = 1\) in Richtung Ziel. Diese Anfangspunkte oder Anfangsbedingungen können wie folgt formuliert werden: \begin{equation} Z = - \left( \begin{array}{c} 0 \\ v \cdot t \end{array} \right) + \left( \begin{array}{c} 0 \\ |\dot{z}| \cdot t \end{array} \right) = \left( \begin{array}{c} 0 \\ t \end{array} \right) ,\: @@ -22,13 +22,13 @@ Das zu verfolgende Ziel \(Z\) bewegt sich entlang der \(y\)-Achse mit konstanter = \left( \begin{array}{c} x \\ y \end{array} \right) \:\text{und}\:\: - \bigl| \dot{V} \bigl| + |\dot{v}| = 1. \label{lambertw:Anfangsbed} \end{equation} Wir haben nun die Anfangsbedingungen definiert, jetzt fehlt nur noch eine DGL, welche die fortlaufende Änderung der Position und Bewegungsrichtung des Verfolgers beschreibt. -Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} definiert, und zwar Gleichung \eqref{lambertw:pursuerDGL}. Wenn man die Startpunkte einfügt, ergibt sich folgender Ausdruck: +Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} definiert, und zwar Gleichung \eqref{lambertw:pursuerDGL}. Wenn man die Startpunkte einfügt, ergibt sich der Ausdruck \begin{equation} \frac{\left( \begin{array}{c} 0-x \\ t-y \end{array} \right)}{\sqrt{x^2 + (t-y)^2}} \cdot @@ -42,37 +42,38 @@ Diese DGL haben wir bereits in Kapitel \ref{lambertw:subsection:Verfolger} defin \label{lambertw:subsection:DGLvereinfach}} Nun haben wir eine Gleichung, es stellt sich aber die Frage, ob es überhaupt eine geschlossene Lösung dafür gibt. Eine Funktion welche die Beziehung \(y(x)\) beschreibt oder sogar \(x(t)\) und \(y(t)\) liefert. Zum jetzigen Zeitpunkt mag es nicht trivial scheinen, aber mit den gewählten Anfangsbedingungen \eqref{lambertw:Anfangsbed} ist es möglich eine geschlossene Lösung für die Gleichung \eqref{lambertw:eqMitAnfangsbed} zu finden. -Auf dem Weg dahin muss die definierte DGL zuerst wesentlich vereinfacht werden, sei es mittels algebraischer Umformungen oder mit den Tools aus der Analysis. Da die nächsten Schritte sehr algebralastig sind und sie das Lesen dieses Papers einfach nur mühsam machen würden, werden wir uns hier nur die wesentlichsten Schritte konzentrieren, welche notwendig sind, um den Lösungsweg nachvollziehen zu können. +Auf dem Weg dahin muss die definierte DGL zuerst wesentlich vereinfacht werden, sei es mittels algebraischer Umformungen oder mit den Tools aus der Analysis. Da die nächsten Schritte sehr algebralastig sind und sie das Lesen dieses Papers träge machen würden, werden wir uns hier nur auf die wesentlichsten Schritte konzentrieren, welche notwendig sind, um den Lösungsweg nachvollziehen zu können. \subsubsection{Skalarprodukt auflösen \label{lambertw:subsubsection:SkalProdAufl}} -Zuerst müssen wir den Bruch und das Skalarprodukt in \eqref{lambertw:eqMitAnfangsbed} wegbringen, damit wir eine. Dies führt zu: +Zuerst müssen wir den Bruch und das Skalarprodukt in \eqref{lambertw:eqMitAnfangsbed} wegbringen, damit wir eine viel handlichere Differentialgleichung erhalten. Dies führt zu \begin{equation} -x \cdot \dot{x} + (t-y) \cdot \dot{y} = \sqrt{x^2 + (t-y)^2}. \label{lambertw:eqOhneSkalarprod} \end{equation} -Im letzten Schritt, fällt die Nützlichkeit des Skalarproduktes in der Verfolgungsgleichung \eqref{lambertw:pursuerDGL} markant auf. Anstatt zwei gekoppelte Differentialgleichungen zu erhalten, eine für die \(x\) und die andere für die \(y\)-Komponente, erhält man einen einzigen Ausdruck, was in der Regel mit weniger Lösungsaufwand verbunden ist. +Im letzten Schritt, fällt die Nützlichkeit des Skalarproduktes in der Verfolgungsgleichung \eqref{lambertw:pursuerDGL} markant auf. Anstatt zwei gekoppelte Differentialgleichungen zu erhalten, eine für die \(x\)- und die andere für die \(y\)-Komponente, erhält man einen einzigen Ausdruck, was in der Regel mit weniger Lösungsaufwand verbunden ist. \subsubsection{Quadrieren und Gruppieren \label{lambertw:subsubsection:QuadUndGrup}} -Mit der Quadratwurzel in \ref{lambertw:eqOhneSkalarprod} kann man nichts anfangen, sie steht nur im Weg, also muss man sie loswerden. Wenn man dies macht, kann \eqref{lambertw:eqOhneSkalarprod} auf folgende Form gebracht werden: +Mit der Quadratwurzel in \eqref{lambertw:eqOhneSkalarprod} kann man nichts anfangen, sie steht nur im Weg, also muss man sie loswerden. Wenn man dies macht, kann \eqref{lambertw:eqOhneSkalarprod} auf die Form \begin{equation} \left(\dot{x}^2-1\right) \cdot x^2 -2x \left(t-y\right) \dot{x}\dot{y} + \left(\dot{y}^2-1\right) \cdot \left(t-y\right)^2 - =0. + =0 \label{lambertw:eqOhneWurzel} \end{equation} +gebracht werden. Diese Form mag auf den ersten Blick nicht gerade nützlich sein, aber man kann sie mit einer Substitution weiter vereinfachen. \subsubsection{Wichtige Substitution \label{lambertw:subsubsection:WichtSubst}} -Wenn man beachtet, dass die Geschwindigkeit des Verfolgers konstant und gleich 1 ist, dann kann man folgende Gleichung aufstellen: +Wenn man beachtet, dass die Geschwindigkeit des Verfolgers konstant und gleich 1 ist, dann ergibt sich die Beziehung \begin{equation} \dot{x}^2 + \dot{y}^2 = 1. \label{lambertw:eqGeschwSubst} \end{equation} -Umformungen der Gleichung \eqref{lambertw:eqGeschwSubst} können in \eqref{lambertw:eqOhneWurzel} erkannt werden. Ersetzt führen sie zu folgendem Ausdruck: +Umformungen der Gleichung \eqref{lambertw:eqGeschwSubst} können in \eqref{lambertw:eqOhneWurzel} erkannt werden. Wenn man sie ersetzt, erhält man \begin{equation} \dot{y}^2 \cdot x^2 +2x \left(t-y\right) \dot{x}\dot{y} + \dot{x}^2 \cdot \left(t-y\right)^2 =0. @@ -82,27 +83,31 @@ Diese unscheinbare Substitution führt dazu, dass weitere Vereinfachungen durchg \subsubsection{Binom erkennen und vereinfachen \label{lambertw:subsubsection:BinomVereinfach}} -Versteckt im Ausdruck \eqref{lambertw:eqGeschwSubstituiert} befindet sich die erste binomische Formel, welche zu folgender Gleichung führt: +Versteckt im Ausdruck \eqref{lambertw:eqGeschwSubstituiert} befindet sich die erste binomische Formel, wobei \begin{equation} (x \dot{y} + (t-y) \dot{x})^2 - = 0. + = 0 \label{lambertw:eqAlgVerinfacht} \end{equation} -Da der linke Term gleich Null ist, muss auch der Inhalt des Quadrates gleich Null sein, somit folgt eine weitere Vereinfachung, welche zu einer im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} wesentlich einfacheren DGL führt: +die faktorisierte Darstellung davon ist. +Da der linke Term gleich Null ist, muss auch der Inhalt des Quadrates gleich Null sein. Es ergibt sich eine weitere Vereinfachung, welche zu der im Vergleich zu \eqref{lambertw:eqOhneSkalarprod} wesentlich einfacheren DGL \begin{equation} x \dot{y} + (t-y) \dot{x} - = 0. + = 0 \label{lambertw:eqGanzVerinfacht} \end{equation} -Kompakt, ohne Wurzelterme und Quadrate, nur elementare Operationen und Ableitungen. Nun stellt sich die Frage wie es weiter gehen soll, bei der Gleichung \eqref{lambertw:eqGanzVerinfacht} scheinen keine weiteren Vereinfachungen möglich zu sein. Wir brauchen einen neuen Ansatz, um unser Ziel einer möglichen Lösung zu verfolgen. +führt. +Kompakt, ohne Wurzelterme und Quadrate, nur elementare Operationen und Ableitungen. + +Nun stellt sich die Frage wie es weiter gehen soll, bei der Gleichung \eqref{lambertw:eqGanzVerinfacht} scheinen keine weiteren Vereinfachungen möglich zu sein. Wir brauchen einen neuen Ansatz, um unser Ziel einer möglichen Lösung zu verfolgen. \subsection{Zeitabhängigkeit loswerden \label{lambertw:subsection:ZeitabhLoswerden}} -Der nächste logischer Schritt scheint irgendwie die Zeitabhängigkeit in der Gleichung \eqref{lambertw:eqGanzVerinfacht} loszuwerden, aber wieso? Nun, wie am Anfang von Abschnitt \ref{lambertw:subsection:DGLvereinfach} beschrieben, suchen wir eine Lösung der Art \(y(x)\), dies ist natürlich erst möglich wenn wir die Abhängigkeit nach \(t\) eliminieren können. +Der nächste logische Schritt scheint irgendwie die Zeitabhängigkeit in der Gleichung \eqref{lambertw:eqGanzVerinfacht} loszuwerden, aber wieso? Nun, wie am Anfang von Abschnitt \ref{lambertw:subsection:DGLvereinfach} beschrieben, suchen wir eine Lösung der Art \(y(x)\), dies ist natürlich erst möglich wenn wir die Abhängigkeit nach \(t\) eliminieren können. \subsubsection{Zeitliche Ableitungen loswerden \label{lambertw:subsubsection:ZeitAbleit}} -Der erste Schritt auf dem Weg zur Funktion \(y(x)\), ist es die zeitlichen Ableitungen los zu werden, dafür wird \eqref{lambertw:eqGanzVerinfacht} beidseitig mit \(\dot{x}\) dividiert, was erlaubt ist, weil diese Änderung ungleich Null ist: +Der erste Schritt auf dem Weg zur Funktion \(y(x)\) ist, die zeitlichen Ableitungen los zu werden, dafür wird \eqref{lambertw:eqGanzVerinfacht} beidseitig durch \(\dot{x}\) dividiert, was erlaubt ist, weil diese Änderung ungleich Null ist: \begin{equation} x \frac{\dot{y}}{\dot{x}} + (t-y) \frac{\dot{x}}{\dot{x}} = 0. @@ -126,30 +131,31 @@ Nach dem die Eigenschaft \eqref{lambertw:eqQuotZeitAbleit} in \eqref{lambertw:eq \subsubsection{Variable \(t\) eliminieren \label{lambertw:subsubsection:ZeitAbleit}} -Hier wäre es natürlich passend, wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte. Um dies zu erreichen, muss man auf die Definition der Bogenlänge zurückgreifen. -Die Strecke \(s\) entspricht +Hier wäre es natürlich passend, wenn man die Abhängigkeit nach \(t\) komplett wegbringen könnte, aber wie? +Wir wissen, dass sich der Verfolger mit Geschwindigkeit 1 bewegt, also legt er in der Zeit \(t\) die Strecke \(1\cdot t = t\) zurück. Längen und Strecken können auch mit der Bogenlänge repräsentiert werden, somit kann Zeit und zurückgelegte Strecke in der Gleichung \begin{equation} s = - v \cdot t + |\dot{v}| \cdot t = 1 \cdot t = t = - \int_{\displaystyle x_0}^{\displaystyle x_{\text{end}}}\sqrt{1+y^{\prime\, 2}} \: dx. + \int_{\displaystyle x_0}^{\displaystyle x_{\text{end}}}\sqrt{1+y^{\prime\, 2}} \: dx \label{lambertw:eqZuBogenlaenge} \end{equation} - +verbunden werden. + 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: +Wenn man nun \eqref{lambertw:eqZuBogenlaenge} in die DGL \eqref{lambertw:DGLmitT} einfügt, dann ergibt sich der neue 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 und erhaltet folgende DGL zweiter Ordnung \eqref{lambertw:DGLohneInt}: +Um das Integral los zu werden, leitet man \eqref{lambertw:DGLohneT} nach \(x\) ab und erhält die DGL zweiter Ordnung \begin{align} y^{\prime}+ xy^{\prime\prime} - \sqrt{1+y^{\prime\, 2}} - y^{\prime} &= 0, \\ @@ -157,16 +163,17 @@ Um das Integral los zu werden, leitet man den vorherigen Ausdruck \eqref{lambert &= 0. \label{lambertw:DGLohneInt} \end{align} -Nun sind wir unserem Ziel einen weiteren Schritt näher. Die Gleichung \eqref{lambertw:DGLohneInt} mag auf den ersten Blick nicht gerade einfach sein, aber im Nächsten Abschnitt werden wir sehen, dass sie relativ einfach zu lösen ist. +Nun sind wir unserem Ziel einen weiteren Schritt näher. Die Gleichung \eqref{lambertw:DGLohneInt} mag auf den ersten Blick nicht gerade einfach sein, aber im nächsten Abschnitt werden wir sehen, dass sie relativ einfach zu lösen ist. \subsection{Differentialgleichung lösen \label{lambertw:subsection:DGLloes}} -Die Gleichung \eqref{lambertw:DGLohneInt} ist eine DGL zweiter Ordnung, in der \(y\) nicht vorkommt. Sie kann mittels der Substitution \(y^{\prime} = u\) in eine DGL erster Ordnung umgewandelt werden: +Die Gleichung \eqref{lambertw:DGLohneInt} ist eine DGL zweiter Ordnung, in der \(y\) nicht vorkommt. Sie kann mittels der Substitution \(y^{\prime} = u\) in die DGL \begin{equation} xu^{\prime} - \sqrt{1+u^2} - = 0. + = 0 \label{lambertw:DGLmitU} \end{equation} +erster Ordnung umgewandelt werden. Diese Gleichung ist separierbar, was sie viel handlicher macht. In der separierten Form \begin{equation} \int{\frac{1}{\sqrt{1+u^2}}\:du} @@ -174,7 +181,7 @@ Diese Gleichung ist separierbar, was sie viel handlicher macht. In der separiert \int{\frac{1}{x}\:dx}, \end{equation} lässt sich die Gleichung mittels einer Integrationstabelle sehr rasch lösen. -Mit dem Ergebnis: +Das Ergebnis ist \begin{align} \operatorname{arsinh}(u) &= @@ -184,20 +191,23 @@ Mit dem Ergebnis: \operatorname{sinh}(\operatorname{ln}(x) + C). \label{lambertw:loesDGLmitU} \end{align} -Wenn man in \eqref{lambertw:loesDGLmitU} die Substitution rückgängig macht, erhält man folgende DGL erster Ordnung, die bereits separiert ist: +Wenn man in \eqref{lambertw:loesDGLmitU} die Substitution rückgängig macht, erhält man die DGL \begin{equation} y^{\prime} = - \operatorname{sinh}(\operatorname{ln}(x) + C). + \operatorname{sinh}(\operatorname{ln}(x) + C) \label{lambertw:loesDGLmitY} \end{equation} -Ersetzt man den \(\operatorname{sinh}\) mit seiner exponentiellen Definition \(\operatorname{sinh}(x)=\frac{1}{2}(e^x-e^{-x})\), so resultiert auf sehr einfache Art folgende Lösung für \eqref{lambertw:loesDGLmitY}: +erster Ordnung, die bereits separiert ist. +Ersetzt man den \(\operatorname{sinh}\) durch seine exponentiellen Definition \(\operatorname{sinh}(x)=\frac{1}{2}(e^x-e^{-x})\), so resultiert auf sehr einfache Art die Lösung \begin{equation} y = - C_1 + C_2 x^2 - \frac{\operatorname{ln}(x)}{8 \cdot C_2}. + C_1 + C_2 x^2 - \frac{\operatorname{ln}(x)}{8 \cdot C_2} \end{equation} -Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die Frage, ob sie überhaupt plausibel ist. Dieser Frage werden wir im nächsten Abschnitt nachgehen. +für \eqref{lambertw:loesDGLmitY}. + +Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die Frage, ob sie überhaupt plausibel ist. \subsection{Lösung analysieren \label{lambertw:subsection:LoesAnalys}} @@ -210,37 +220,34 @@ Nun haben wir eine Lösung, aber wie es immer mit Lösungen ist, stellt sich die } \end{figure} -Das Resultat, wie ersichtlich, ist folgende Funktion \eqref{lambertw:funkLoes} welche mittels Anfangsbedingungen parametrisiert werden kann: +Das Resultat, wie ersichtlich, ist die Funktion \begin{equation} {\color{red}{y(x)}} = - C_1 + C_2 {\color{darkgreen}{x^2}} {\color{blue}{-}} \frac{\color{blue}{\operatorname{ln}(x)}}{8 \cdot C_2}. + C_1 + C_2 {\color{darkgreen}{x^2}} {\color{blue}{-}} \frac{\color{blue}{\operatorname{ln}(x)}}{8 \cdot C_2}, \label{lambertw:funkLoes} \end{equation} -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 \(y(x)\) geschaffen werden: +für welche die Koeffizienten \(C_1\) und \(C_2\) aus den Anfangsbedingungen bestimmt werden können. Zuerst soll aber eine qualitative Intuition oder Idee für das Aussehen der Funktion \(y(x)\) 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 \eqref{lambertw:funkLoes} dominant. \item - 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. Irgendwann werden Verfolger und Ziel auf gleicher Höhe sein, also gleiche \(y\) aber verschiedene \(x\)-Koordinate besitzen. + 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. Irgendwann werden Verfolger und Ziel auf gleicher Höhe sein, also gleiche \(y\)- aber verschiedene \(x\)-Koordinate besitzen. + In diesem Punkt findet ein Monotoniewechsel in der Kurve \eqref{lambertw:funkLoes} statt, was zu einem Minimum führt. \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 ihm nachgeht. - \item - Aufgrund des Monotoniewechsels in der Kurve \eqref{lambertw:funkLoes} muss diese auch ein Minimum aufweisen. Es stellt sich nun die Frage: Wo befindet sich dieser Punkt? - Eine Abschätzung darüber kann 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 des Verfolgers, somit auch sein Vorzeichen und dadurch entsteht auch das Minimum. \end{itemize} Alle diese Eigenschaften stimmen mit dem überein, was man von einer Kurve dieser Art erwarten würde, welche durch die Grafik \ref{lambertw:BildFunkLoes} repräsentiert wurde. \subsection{Anfangswertproblem \label{lambertw:subsection:AllgLoes}} -In diesem Abschnitt soll eine Parameterfunktion hergeleitet werden, bei der jeder beliebige Anfangspunkt im ersten Quadranten eingesetzt werden kann, ausser der Ursprung im Koordinatensystem. Diese Aufgabe erfordert ein Anfangswertproblem. +In diesem Abschnitt soll eine Parameterfunktion hergeleitet werden, bei der jeder beliebige Anfangspunkt im ersten Quadranten eingesetzt werden kann, ausser der Ursprung im Koordinatensystem. Diese Aufgabe ist ein Anfangswertproblem für \(y(x)\). -Das Lösen des Anfangswertproblems ist ein Problem aus der Algebra, auf welches hier nicht explizit eingegangen wird. Zur Vollständigkeit und Nachvollziehbarkeit, wird aber das Gleichungssystem präsentiert, welches notwendig ist, um das Anfangswertproblem zu lösen. +Das Lösen des Anfangswertproblems ist ein Problem aus der Analysis, auf welches hier nicht explizit eingegangen wird. Zur Vollständigkeit und Nachvollziehbarkeit, wird aber das Gleichungssystem präsentiert, welches notwendig ist, um das Anfangswertproblem zu lösen. \subsubsection{Anfangswerte bestimmen \label{lambertw:subsubsection:Anfangswerte}} -Der erste Schritt auf dem Weg zur gesuchten Parameterfunktion ist, die Anfangswerte \eqref{lambertw:eq1Anfangswert} zu definieren. -Die Anfangswerte sind: +Der erste Schritt auf dem Weg zur gesuchten Parameterfunktion ist, die Anfangswerte \begin{equation} y(x)\big \vert_{t=0} = @@ -255,15 +262,17 @@ und = y^{\prime}(x_0) = - \frac{y_0}{x_0}. + \frac{y_0}{x_0} \label{lambertw:eq2Anfangswert} \end{equation} +zu definieren. Der zweite Anfangswert \eqref{lambertw:eq2Anfangswert} mag nicht grade offensichtlich sein. Die Erklärung dafür ist aber simpel: Der Verfolger wird sich zum Zeitpunkt \(t=0\) in Richtung Koordinatenursprung bewegen wollen, wo sich das Ziel befindet. Somit entsteht das Steigungsdreieck mit \(\Delta x = x_0\) und \(\Delta y = y_0\). \subsubsection{Gleichungssystem aufstellen und lösen \label{lambertw:subsubsection:GlSys}} -Wenn man die Anfangswerte \eqref{lambertw:eq1Anfangswert} und \eqref{lambertw:eq2Anfangswert} in die Gleichung \eqref{lambertw:funkLoes} und deren Ableitung \(y^{\prime}(x)\) einsetzt, dann ergibt sich folgendes Gleichungssystem: +Wenn man die Anfangswerte \eqref{lambertw:eq1Anfangswert} und \eqref{lambertw:eq2Anfangswert} in die Gleichung \eqref{lambertw:funkLoes} und deren Ableitung \(y^{\prime}(x)\) einsetzt, dann ergibt sich das Gleichungssystem \begin{subequations} + \label{lambertw:eqGleichungssystem} \begin{align} y_0 &= @@ -272,9 +281,8 @@ Wenn man die Anfangswerte \eqref{lambertw:eq1Anfangswert} und \eqref{lambertw:eq &= 2 \cdot C_2 x_0 - \frac{1}{8 \cdot C_2 \cdot x_0}. \end{align} - \label{lambertw:eqGleichungssystem} \end{subequations} -Damit die gesuchte Funktion im ersten Quadranten bleibt, werden nur die positiven Lösungen des Gleichungssystems gewählt, welche wie folgt aussehen: +Damit die gesuchte Funktion im ersten Quadranten bleibt, werden nur die positiven Lösungen \begin{subequations} \begin{align} \label{lambertw:eqKoeff1} @@ -284,16 +292,17 @@ Damit die gesuchte Funktion im ersten Quadranten bleibt, werden nur die positive \label{lambertw:eqKoeff2} C_2 &= - \frac{\sqrt{x_0^2 + y_0^2} + y_0}{4x_0^2}. + \frac{\sqrt{x_0^2 + y_0^2} + y_0}{4x_0^2} \end{align} \end{subequations} +des Gleichungssystems gewählt. \subsubsection{Gesuchte Parameterfunktion aufstellen \label{lambertw:subsubsection:ParamFunk}} -Wenn man die Koeffizienten \eqref{lambertw:eqKoeff1} und \eqref{lambertw:eqKoeff2} in die Funktion \eqref{lambertw:funkLoes} einsetzt, dann ergibt sich nach dem Vereinfachen die gesuchte Parameterfunktion: +Wenn man die Koeffizienten \eqref{lambertw:eqKoeff1} und \eqref{lambertw:eqKoeff2} in die Funktion \eqref{lambertw:funkLoes} einsetzt, dann ergibt sich beim Vereinfachen die gesuchte Parameterfunktion \begin{equation} y(x) = - \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right). + \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(y_0-r_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right). \label{lambertw:eqAllgLoes} \end{equation} Damit die Funktion \eqref{lambertw:eqAllgLoes} trotzdem übersichtlich bleibt, wurden Anfangssteigung \(\eta\) und Anfangsentfernung \(r_0\) wie folgt definiert: @@ -316,27 +325,28 @@ In diesem Abschnitt werden algebraischen Umformungen ein wenig detaillierter als \subsubsection{Zeitabhängigkeit wiederherstellen \label{lambertw:subsubsection:ZeitabhWiederherst}} -Der erste Schritt ist es herauszufinden, wie die Zeitabhängigkeit wieder hineingebracht werden kann. Dafür greifen wir auf die letzte Gleichung zu, in welcher \(t\) noch enthalten war, und zwar DGL \eqref{lambertw:DGLmitT}, welche zur Übersichtlichkeit hier nochmals aufgeführt wird: +Der erste Schritt ist es herauszufinden, wie die Zeitabhängigkeit wieder hineingebracht werden kann. Dafür greifen wir auf die letzte Gleichung zu, in welcher \(t\) noch enthalten war, und zwar DGL \begin{equation} x y^{\prime} + t - y - = 0. + = 0 \label{lambertw:eqDGLmitTnochmals} \end{equation} +aus dem Abschnitt \eqref{lambertw:subsection:ZeitabhLoswerden}, welche zur Übersichtlichkeit hier nochmals aufgeführt wurde. Wie in \eqref{lambertw:eqDGLmitTnochmals} zu sehen ist, werden \(y\) und deren Ableitung \(y^{\prime}\) benötigt, diese sind: \begin{subequations} + \label{lambertw:eqFunkUndAbleit} \begin{align} + \label{lambertw:eqFunkUndAbleit1} y &= - \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right)-r_0+3y_0\right), \\ - \label{lambertw:eqFunkUndAbleit1} + \frac{1}{4}\left(\left(y_0+r_0\right)\eta+\left(y_0-r_0\right)\operatorname{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). + \frac{1}{2}\left(\left(y_0+r_0\right)\frac{x}{x_0^2}+\left(y_0-r_0\right)\frac{1}{x}\right). \end{align} - \label{lambertw:eqFunkUndAbleit} \end{subequations} -Wenn man diese Gleichungen \ref{lambertw:eqFunkUndAbleit} in die DGL \label{lambertw:eqDGLmitTnochmals} einfügt, vereinfacht und nach \(t\) auflöst, dann ergibt sich folgenden Ausdruck: +Wenn man diese Gleichungen \eqref{lambertw:eqFunkUndAbleit} in die DGL \eqref{lambertw:eqDGLmitTnochmals} einfügt, vereinfacht und nach \(t\) auflöst, dann ergibt sich der Ausdruck \begin{equation} -4t = @@ -348,17 +358,20 @@ Wenn man diese Gleichungen \ref{lambertw:eqFunkUndAbleit} in die DGL \label{lamb \label{lambertw:subsubsection:UmformBisZumZiel}} Mit dem Ausdruck \eqref{lambertw:eqFunkUndAbleitEingefuegt}, welcher Terme mit \(x\) und \(t\) verbindet, kann nun nach der gesuchten Variable \(x\) aufgelöst werden. - -In einem nächsten Schritt wird alles mit \(x\) auf die eine Seite gebracht, der Rest auf die andere Seite und anschliessend beidseitig exponentiert, was wie folgt aussieht: -\begin{align} +In einem nächsten Schritt wird alles mit \(x\) auf die eine Seite gebracht, der Rest auf die andere Seite und anschliessend beidseitig exponenziert, sodass man +\begin{equation} -4t+\left(y_0+r_0\right) - &= - \left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right), \\ + = + \left(y_0+r_0\right)\eta+\left(r_0-y_0\right)\operatorname{ln}\left(\eta\right) +\end{equation} +und anschliessend +\begin{equation} e^{\displaystyle -4t+\left(y_0+r_0\right)} - &= - e^{\displaystyle \left(y_0+r_0\right)\eta}\cdot\eta^{\displaystyle \left(r_0-y_0\right)}. + = + e^{\displaystyle \left(y_0+r_0\right)\eta}\cdot\eta^{\displaystyle \left(r_0-y_0\right)} \label{lambertw:eqMitExp} -\end{align} +\end{equation} +erhält. Auf dem rechten Term von \eqref{lambertw:eqMitExp} beginnen wir langsam eine ähnliche Struktur wie \(\eta e^\eta\) zu erkennen, dies schreit nach der Struktur die benötigt wird um \(\eta\) mittels der Lambert-\(W\)-Funktion \(W(x)\) zu erhalten. Dies macht durchaus Sinn, wenn wir die Funktion \(x(t)\) finden wollen und \(W(x)\) die Umkehrfunktion von \(x e^x\) ist. Die erste Sache die uns in \eqref{lambertw:eqMitExp} stört ist, dass \(\eta\) als Potenz da steht. Dieses Problem können wir loswerden, indem wir beidseitig mit \(\:\displaystyle \frac{1}{r_0-y_0}\:\) potenzieren: @@ -368,30 +381,32 @@ Die erste Sache die uns in \eqref{lambertw:eqMitExp} stört ist, dass \(\eta\) a \eta\cdot \operatorname{exp}\left(\displaystyle \frac{y_0+r_0}{r_0-y_0}\eta\right). \label{lambertw:eqOhnePotenz} \end{equation} -Das nächste Problem auf welches wir in \eqref{lambertw:eqOhnePotenz} treffen ist, dass \(\eta\) nicht alleine im Exponent steht. Dies kann elegant mit folgender Substitution gelöst werden: +Das nächste Problem auf welches wir in \eqref{lambertw:eqOhnePotenz} treffen ist, dass \(\eta\) nicht alleine im Exponent steht. Dies kann elegant mit der Substitution \begin{equation} \chi = - \frac{y_0+r_0}{r_0-y_0}. + \frac{y_0+r_0}{r_0-y_0} \label{lambertw:eqChiSubst} \end{equation} +gelöst werden. Es gäbe natürlich andere Substitutionen wie z.B. \[\displaystyle \chi=\frac{y_0+r_0}{r_0-y_0}\cdot\eta,\] -die auf dasselbe Ergebnis führen würden, aber \eqref{lambertw:eqChiSubst} liefert in einem Schritt die kompakteste Lösung. Also fahren wir mit der Substitution \eqref{lambertw:eqChiSubst} weiter, setzen diese in die Gleichung \eqref{lambertw:eqOhnePotenz} ein und multiplizieren beidseitig mit \(\chi\). Daraus erhalten wir folgende Gleichung: +die auf dasselbe Ergebnis führen würden, aber \eqref{lambertw:eqChiSubst} liefert in einem Schritt die kompakteste Lösung. Also fahren wir mit der Substitution \eqref{lambertw:eqChiSubst} weiter, setzen diese in die Gleichung \eqref{lambertw:eqOhnePotenz} ein und multiplizieren beidseitig mit \(\chi\). Daraus erhalten wir die Gleichung \begin{equation} \chi\cdot \operatorname{exp}\left(\displaystyle \chi-\frac{4t}{r_0-y_0}\right) = \chi\eta\cdot e^{\displaystyle \chi\eta}. \label{lambertw:eqNachSubst} \end{equation} -Nun sind wir endlich soweit, dass wir die angedeutete Lambert-\(W\)-Funktion \(W(x)\)einsetzen können. Wenn wir beidseitig \(W(x)\) anwenden, dann erhalten wir folgenden Ausdruck: +Nun sind wir endlich soweit, dass wir die angedeutete Lambert-\(W\)-Funktion \(W(x)\) einsetzen können. Wenn wir beidseitig \(W(x)\) anwenden, dann erhalten wir den Ausdruck \begin{equation} W\left(\chi\cdot \operatorname{exp}\left(\displaystyle \chi-\frac{4t}{r_0-y_0}\right)\right) = \chi\eta. \end{equation} -Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir die gesuchte \(x(t)\)-Funktion \eqref{lambertw:eqFunkXNachT}. Dieses \(x(t)\) in Kombination mit \eqref{lambertw:eqFunkUndAbleit1} liefert die Position des Verfolgers zu jedem Zeitpunkt. Das Gleichungspaar \eqref{lambertw:eqFunktionenNachT}, besteht aus folgenden Gleichungen: +Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir die gesuchte \(x(t)\)-Funktion \eqref{lambertw:eqFunkXNachT}. Dieses \(x(t)\) in Kombination mit \eqref{lambertw:eqFunkUndAbleit1} liefert die Position des Verfolgers zu jedem Zeitpunkt. Das Gleichungspaar besteht also aus den Gleichungen \begin{subequations} + \label{lambertw:eqFunktionenNachT} \begin{align} \label{lambertw:eqFunkXNachT} x(t) @@ -402,15 +417,14 @@ Nach dem Auflösen nach \(x\) welches in \(\eta\) enthalten ist, erhalten wir di = y(t) &= - \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right). + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(y_0-r_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right). \end{align} - \label{lambertw:eqFunktionenNachT} \end{subequations} Nun haben wir unser letztes Ziel erreicht und sind in der Lage eine Verfolgung rechnerisch sowie graphisch zu repräsentieren. \subsubsection{Hinweise zur Lambert-\(W\)-Funktion \label{lambertw:subsubsection:HinwLambertW}} -Wir sind aber noch nicht ganz fertig, eine Frage muss noch beantwortet werden. Und zwar wieso, dass man schon bei der Gleichung \eqref{lambertw:eqFunkUndAbleitEingefuegt} weiss, dass die Lambert-\(W\)-Funktion zum Einsatz kommen wird. +Wir sind aber noch nicht ganz fertig, eine Frage muss noch beantwortet werden. Und zwar wieso, man schon bei der Gleichung \eqref{lambertw:eqFunkUndAbleitEingefuegt} weiss, dass die Lambert-\(W\)-Funktion zum Einsatz kommen wird. Nun, der Grund dafür ist die Struktur \begin{equation} y @@ -420,4 +434,4 @@ Nun, der Grund dafür ist die Struktur \end{equation} bei welcher \(p(x)\) eine beliebige Potenz von \(x\) darstellt. -Jedes Mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oftmals vorkommt, was die Lambert-\(W\)-Funktion so wichtig macht. \ No newline at end of file +Jedes Mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oft vorkommt, was die Lambert-\(W\)-Funktion so wichtig macht. \ No newline at end of file -- cgit v1.2.1 From 435a9b21bad8244ea81f63cf4254d85212942436 Mon Sep 17 00:00:00 2001 From: daHugen Date: Sun, 31 Jul 2022 18:14:56 +0200 Subject: Update also includes some changes in the pursuitcurve-picture --- buch/papers/lambertw/teil4.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'buch') diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex index 0050b61..1053dd1 100644 --- a/buch/papers/lambertw/teil4.tex +++ b/buch/papers/lambertw/teil4.tex @@ -434,4 +434,4 @@ Nun, der Grund dafür ist die Struktur \end{equation} bei welcher \(p(x)\) eine beliebige Potenz von \(x\) darstellt. -Jedes Mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oft vorkommt, was die Lambert-\(W\)-Funktion so wichtig macht. \ No newline at end of file +Jedes Mal wenn \(x\) gesucht ist und in einer Struktur der Art \eqref{lambertw:eqEinsatzLambW} vorkommt, dann kann mit ein paar Umformungen die Struktur \(f(x)e^{f(x)}\) erzielt werden. Wie bereits in diesem Abschnitt \ref{lambertw:subsection:FunkNachT} gezeigt wurde, kann \(x\) nun mittels der \(W(x)\)-Funktion aufgelöst werden. Erstaunlicherweise ist \eqref{lambertw:eqEinsatzLambW} eine Struktur die oft vorkommt, was die Lambert-\(W\)-Funktion so wichtig macht. \ No newline at end of file -- cgit v1.2.1 From ca43e5660ccbd3f4beaaa2073ce7dda05a80eff6 Mon Sep 17 00:00:00 2001 From: Nao Pross Date: Mon, 1 Aug 2022 19:58:09 +0200 Subject: Kugel: Introduction and preliminaries (not spherical harmonics, yet) --- buch/common/macros.tex | 4 + buch/papers/kugel/applications.tex | 9 + buch/papers/kugel/introduction.tex | 35 +++ buch/papers/kugel/main.tex | 37 +--- buch/papers/kugel/preliminaries.tex | 346 ++++++++++++++++++++++++++++++ buch/papers/kugel/references.bib | 226 ++++++++++++++++--- buch/papers/kugel/spherical-harmonics.tex | 13 ++ 7 files changed, 609 insertions(+), 61 deletions(-) create mode 100644 buch/papers/kugel/applications.tex create mode 100644 buch/papers/kugel/introduction.tex create mode 100644 buch/papers/kugel/preliminaries.tex create mode 100644 buch/papers/kugel/spherical-harmonics.tex (limited to 'buch') diff --git a/buch/common/macros.tex b/buch/common/macros.tex index bb6e9b0..e37698e 100644 --- a/buch/common/macros.tex +++ b/buch/common/macros.tex @@ -111,6 +111,10 @@ \newtheorem{forderung}{Forderung}[chapter] \newtheorem{konsequenz}[satz]{Konsequenz} \newtheorem{algorithmus}[satz]{Algorithmus} + +% English variants +\newtheorem{theorem}[satz]{Theorem} + \renewcommand{\floatpagefraction}{0.7} \definecolor{darkgreen}{rgb}{0,0.6,0} diff --git a/buch/papers/kugel/applications.tex b/buch/papers/kugel/applications.tex new file mode 100644 index 0000000..b2f227e --- /dev/null +++ b/buch/papers/kugel/applications.tex @@ -0,0 +1,9 @@ +% vim:ts=2 sw=2 et spell: + +\section{Applications} + +\subsection{Electroencephalography (EEG)} + +\subsection{Measuring Gravitational Fields} + +\subsection{Quantisation of Angular Momentum} diff --git a/buch/papers/kugel/introduction.tex b/buch/papers/kugel/introduction.tex new file mode 100644 index 0000000..5b09e9c --- /dev/null +++ b/buch/papers/kugel/introduction.tex @@ -0,0 +1,35 @@ +% vim:ts=2 sw=2 et spell tw=78: + +\section{Introduction} + +This chapter of the book is devoted to the sef of functions called +\emph{spherical harmonics}. However, before we dive into the topic, we want to +make a few preliminary remarks to avoid ``upsetting'' a certain type of +reader. Specifically, we would like to specify that the authors of this +chapter not mathematicians but engineers, and therefore the text will not be +always complete with sound proofs after every claim. Instead we will go +through the topic in a more intuitive way including rigorous proofs only if +they are enlightening or when they are very short. Where no proofs are given +we will try to give an intuition for why it is true. + +That being said, when talking about spherical harmonics one could start by +describing their name. The latter may be a cause of some confusion because of +the misleading translations in other languages. In German the name for this +set of functions is ``Kugelfunktionen'', which puts the emphasis only on the +spherical context, whereas the English name ``spherical harmonics'' also +contains the \emph{harmonic} part hinting at Fourier theories and harmonic +analysis in general. + +The structure of this chapter is organized in the following way. First, we +will quickly go through some fundamental linear algebra and Fourier theory to +refresh a few important concepts. In principle, we could have written the +whole thing starting from a much more abstract level without much preparation, +but then we would have lost some of the beauty that comes from the +appreciation of the power of some surprisingly simple ideas. Then once the +basics are done, we can explore the main topic of spherical harmonics which as +we will see arises from the eigenfunctions of the Laplacian operator in +spherical coordinates. Finally, after studying what we think are the most +beautiful and interesting properties of the spherical harmonics, to conclude +this journey we will present a few real-world applications, which are of +course most of interest for engineers. + diff --git a/buch/papers/kugel/main.tex b/buch/papers/kugel/main.tex index 06368af..98d9cb2 100644 --- a/buch/papers/kugel/main.tex +++ b/buch/papers/kugel/main.tex @@ -1,39 +1,20 @@ -% +% vim:ts=2 sw=2 et: % main.tex -- Paper zum Thema % % (c) 2020 Hochschule Rapperswil % -\chapter{Recurrence Relations for Spherical Harmonics in Quantum Mechanics\label{chapter:kugel}} -\lhead{Recurrence Relations in Quantum Mechanics} +\begin{otherlanguage}{english} +\chapter{Spherical Harmonics\label{chapter:kugel}} +\lhead{Spherical Harmonics} \begin{refsection} \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} - +\input{papers/kugel/introduction} +\input{papers/kugel/preliminaries} +\input{papers/kugel/spherical-harmonics} +\input{papers/kugel/applications} \printbibliography[heading=subbibliography] \end{refsection} +\end{otherlanguage} diff --git a/buch/papers/kugel/preliminaries.tex b/buch/papers/kugel/preliminaries.tex new file mode 100644 index 0000000..03cd421 --- /dev/null +++ b/buch/papers/kugel/preliminaries.tex @@ -0,0 +1,346 @@ +% vim:ts=2 sw=2 et spell tw=78: + +\section{Preliminaries} + +The purpose of this section is to dust off some concepts that will become +important later on. This will enable us to be able to get a richer and more +general view of the topic than just liming ourselves to a specific example. + +\subsection{Vectors and inner product spaces} + +We shall start with a few fundamentals of linear algebra. We will mostly work +with complex numbers, but for the sake of generality we will do what most +textbook do, and write \(\mathbb{K}\) instead of \(\mathbb{C}\) since the +theory works the same when we replace \(\mathbb{K}\) with the real +numbers \(\mathbb{R}\). + +\begin{definition}[Vector space] + \label{kugel:def:vector-space} \nocite{axler_linear_2014} + A \emph{vector space} over a field \(\mathbb{K}\) is a set \(V\) with an + addition on \(V\) and a multiplication on \(V\) such that the following + properties hold: + \begin{enumerate}[(a)] + \item (Commutativity) \(u + v = v + u\) for all \(u, v \in V\); + \item (Associativity) \((u + v) + w = u + (v + w)\) and \((ab)v = a(bv)\) + for all \(u, v, w \in V\) and \(a, b \in \mathbb{K}\); + \item (Additive identity) There exists an element \(0 \in V\) such that + \(v + 0 = v\) for all \(v \in V\); + \item (Additive inverse) For every \(v \in V\), there exists a \(w \in V\) + such that \(v + w = 0\); + \item (Multiplicative identity) \(1 v = v\) for all \(v \in V\); + \item (Distributive properties) \(a(u + v) = au + av\) and \((a + b)v = av + + bv\) for all \(a, b \in \mathbb{K}\) and all \(u,v \in V\). + \end{enumerate} +\end{definition} + +\begin{definition}[Dot product] + \label{kugel:def:dot-product} + In the vector field \(\mathbb{K}^n\) the scalar or dot product between two + vectors \(u, v \in \mathbb{K}^n\) is + \( + u \cdot v + = u_1 \overline{v}_1 + u_2 \overline{v}_2 + \cdots + u_n \overline{v}_n + = \sum_{i=1}^n u_i \overline{v}_i. + \) +\end{definition} + +\texttt{TODO: Text here.} + +\begin{definition}[Span] +\end{definition} + +\texttt{TODO: Text here.} + +\begin{definition}[Linear independence] +\end{definition} + + +\texttt{TODO: Text here.} + +\begin{definition}[Basis] +\end{definition} + +\texttt{TODO: Text here.} + +\begin{definition}[Inner product] + \label{kugel:def:inner-product} \nocite{axler_linear_2014} + The \emph{inner product} on \(V\) is a function that takes each ordered pair + \((u, v)\) of elements of \(V\) to a number \(\langle u, v \rangle \in + \mathbb{K}\) and has the following properties: + \begin{enumerate}[(a)] + \item (Positivity) \(\langle v, v \rangle \geq 0\) for all \(v \in V\); + \item (Definiteness) \(\langle v, v \rangle = 0\) iff \(v = 0\); + \item (Additivity) \( + \langle u + v, w \rangle = + \langle u, w \rangle + \langle v, w \rangle + \) for all \(u, v, w \in V\); + \item (Homogeneity) \( + \langle \lambda u, v \rangle = + \lambda \langle u, v \rangle + \) for all \(\lambda \in \mathbb{K}\) and all \(u, v \in V\); + \item (Conjugate symmetry) + \(\langle u, v \rangle = \overline{\langle v, u \rangle}\) for all + \(u, v \in V\). + \end{enumerate} +\end{definition} + +This newly introduced inner product is thus a generalization of the scalar +product that does not explicitly depend on rows or columns of vectors. This +has the interesting consequence that anything that behaves according to the +rules given in definition \ref{kugel:def:inner-product} \emph{is} an inner +product. For example if we say that the vector space \(V = \mathbb{R}^n\), +then the dot product defined in definition \ref{kugel:def:dot-product} +\( + u \cdot v = u_1 \overline{v}_1 + u_2 \overline{v}_2 + \cdots + u_n \overline{v}_n +\) +is an inner product in \(V\), and the two are said to form an \emph{inner +product space}. + +\begin{definition}[Inner product space] + \nocite{axler_linear_2014} + An inner product space is a vector space \(V\) equipped with an inner + product on \(V\). +\end{definition} + +How about a more interesting example: the set of continuous complex valued +functions on the interval \([0; 1]\) can behave like vectors. Functions can +be added, subtracted, multiplied with scalars, are associative and there is +even the identity element (zero function \(f(x) = 0\)), so we can create an +inner product +\[ + \langle f, g \rangle = \int_0^1 f(x) \overline{g(x)} \, dx, +\] +which will indeed satisfy all of the rules for an inner product (in fact this +is called the Hermitian inner product\nocite{allard_mathematics_2009}). If +this last step sounds too good to be true, you are right, because it is not +quite so simple. The problem that we have swept under the rug here is +convergence, which any student who took an analysis class will know is a +rather hairy question. We will not need to go too much into the details since +formally discussing convergence is definitely beyond the scope of this text, +however, for our purposes we will still need to dig a little deeper for a few +more paragraph. + +\subsection{Convergence} + +In the last section we hinted that we can create ``infinite-dimensional'' +vector spaces using functions as vectors, and inner product spaces by +integrating the product of two functions of said vector space. However, there +is a problem with convergence which twofold: the obvious problem is that the +integral of the inner product may not always converge, while the second is a +bit more subtle and will be discussed later. The inner product that does +not converge is a problem because we want a \emph{norm}. + +\begin{definition}[\(L^2\) Norm] + \nocite{axler_linear_2014} + The norm of a vector \(v\) of an inner product space is a number + denoted as \(\| v \|\) that is computed by \(\| v \| = \sqrt{\langle v, v + \rangle}\). +\end{definition} + +In \(\mathbb{R}^n\) with the dot product (Euclidian space) the norm is the +geometric length of a vector, while in a more general inner product space the +norm can be thought of as a more abstract measure of ``length''. In any case +it is rather important that the expression \(\sqrt{\langle v, v \rangle}\), +which when using functions \(f: \mathbb{R} \to \mathbb{C}\) becomes +\[ + \sqrt{\langle f, f \rangle} = + \sqrt{\int_\mathbb{R} f(x) \overline{f(x)} \, dx} = + \sqrt{\int_\mathbb{R} |f(x)|^2 \, dx}, +\] +always exists. So, to fix this problems we do what mathematicians do best: +make up the solution. Since the integrand under the square root is always the +square of the magnitude, we can just specify that the functions must be +\emph{absolutely square integrable}. To be more compact it is common to just +write \(f \in L^2\), where \(L^2\) denotes the set of absolutely square +integrable functions. + +Now we can tackle the second (much more difficult) problem of convergence +mentioned at the beginning. Using the technical jargon, we need that our inner +product space is what is called a \emph{complete metric space}, which just +means that we can measure distances. For the more motivated readers although +not really necessary we can also give a more formal definition, the others can +skip to the next section. + +\begin{definition}[Metric space] + \nocite{tao_analysis_2016} + A metric space \((X, d)\) is a space \(X\) of objects (called points), + together with a distance function or metric \(d: X \times X \to [0, + +\infty)\), which associates to each pair \(x, y\) of points in \(X\) a + non-negative real number \(d(x, y) \geq 0\). Furthermore, the metric must + satisfy the following four axioms: + \begin{enumerate}[(a)] + \item For any \(x\in X\), we have \(d(x, x) = 0\). + \item (Positivity) For any \emph{distinct} \(x, y \in X\), we have + \(d(x,y) > 0\). + \item (Symmetry) For any \(x,y \in X\), we have \(d(x, y) = d(y, x)\). + \item (Triangle inequality) For any \(x, y, z \in X\) we have + \(d(x, z) \leq d(x, y) + d(y, z)\). + \end{enumerate} +\end{definition} + +As is seen in the definition metric spaces are a very abstract concept and +rely on rather weak statements, which makes them very general. Now, the more +intimidating part is the \emph{completeness} which is defined as follows. + +\begin{definition}[Complete metric space] + \label{kugel:def:complete-metric-space} + A metric space \((X, d)\) is said to be \emph{complete} iff every Cauchy + sequence in \((X, d)\) is convergent in \((X, d)\). +\end{definition} + +To fully explain definition \ref{kugel:def:complete-metric-space} it would +take a few more pages, which would get a bit too heavy. So instead we will +give an informal explanation through an counterexample to get a feeling of +what is actually happening. Cauchy sequences is a rather fancy name for a +sequence for example of numbers that keep changing, but in a such a way that +at some point the change keeps getting smaller (the infamous +\(\varepsilon-\delta\) definition). For example consider the sequence of +numbers +\[ + 1, + 1.4, + 1.41, + 1.414, + 1.4142, + 1.41421, + \ldots +\] +in the metric space \((\mathbb{Q}, d)\) with \(d(x, y) = |x - y|\). Each +element of this sequence can be written with some fraction in \(\mathbb{Q}\), +but in \(\mathbb{R}\) the sequence is converging towards the number +\(\sqrt{2}\). However, \(\sqrt{2} \notin \mathbb{Q}\). Since we can find a +sequence of fractions whose distance's limit is not in \(\mathbb{Q}\), the +metric space \((\mathbb{Q}, d)\) is \emph{not} complete. Conversely, +\((\mathbb{R}, d)\) is a complete metric space since \(\sqrt{2} \in +\mathbb{R}\). + +Of course the analogy above also applies to vectors, i.e. if in an inner +product space \(V\) over a field \(\mathbb{K}\) all sequences of vectors have +a distance that is always in \(\mathbb{K}\), then \(V\) is also a complete +metric space. In the jargon, this particular case is what is known as a +Hilbert space, after the incredibly influential German mathematician David +Hilbert. + +\begin{definition}[Hilbert space] + A Hilbert space is a vector space \(H\) with an inner product \(\langle f, g + \rangle\) and a norm \(\sqrt{\langle f, f \rangle}\) defined such that \(H\) + turns into a complete metric space. +\end{definition} + +\subsection{Orthogonal basis and Fourier series} + +Now we finally have almost everything we need to get into the domain of +Fourier theory from the perspective of linear algebra. However, we still need +to briefly discuss the matter of orthogonality\footnote{See chapter +\ref{buch:chapter:orthogonalitaet} for more on orthogonality.} and +periodicity. Both should be very straightforward and already well known. + +\begin{definition}[Orthogonality and orthonormality] + \label{kugel:def:orthogonality} + In an inner product space \(V\) two vectors \(u, v \in V\) are said to be + \emph{orthogonal} if \(\langle u, v \rangle = 0\). Further, if both \(u\) + and \(v\) are of unit length, i.e. \(\| u \| = 1\) and \(\| v \| = 1\), then + they are said to be ortho\emph{normal}. +\end{definition} + +\begin{definition}[1-periodic function and \(C(\mathbb{R}/\mathbb{Z}; \mathbb{C})\)] + A function is said to be 1-periodic if \(f(x + 1) = f(x)\). The set of + 1-periodic function from the real to the complex + numbers is denoted by \(C(\mathbb{R}/\mathbb{Z}; \mathbb{C})\). +\end{definition} + +In the definition above the notation \(\mathbb{R}/\mathbb{Z}\) was borrowed +from group theory, and is what is known as a quotient group; Not really +relevant for our discussion but still a ``good to know''. More importantly, it +is worth noting that we could have also defined more generally \(L\)-periodic +functions with \(L\in\mathbb{R}\), however, this would introduce a few ugly +\(L\)'s everywhere which are not really necessary (it will always be possible +to extend the theorems to \(\mathbb{R} / L\mathbb{Z}\)). Thus, we will +continue without the \(L\)'s, and to simplify the language unless specified +otherwise ``periodic'' will mean 1-periodic. Having said that, we can +officially begin with the Fourier theory. + +\begin{lemma} + The subset of absolutely square integrable functions in + \(C(\mathbb{R}/\mathbb{Z}; \mathbb{C})\) together with the Hermitian inner + product + \[ + \langle f, g \rangle = \int_{[0; 1)} f(x) \overline{g(x)} \, dx + \] + form a Hilbert space. +\end{lemma} +\begin{proof} + It is not too difficult to show that the functions in \(C(\mathbb{R} / + \mathbb{Z}; \mathbb{C})\) are well behaved and form a vector space. Thus, + what remains is that the norm needs to form a complete metric space. + However, this follows from the fact that we defined the functions to be + absolutely square integrable\footnote{For the curious on why, it is because + \(L^2\) is what is known as a \emph{compact metric space}, and compact + metric spaces are always complete (see \cite{eck_metric_2022, + tao_analysis_2016}). To explain compactness and the relationship between + compactness and completeness is definitely beyond the goals of this text.}. +\end{proof} + +This was probably not a very satisfactory proof since we brushed off a lot of +details by referencing other theorems. However, the main takeaway should be +that we have ``constructed'' this new Hilbert space of functions in a such a +way that from now on we will not have to worry about the details of +convergence. + +\begin{lemma} + \label{kugel:lemma:exp-1d} + The set of functions \(E_n(x) = e^{i2\pi nx}\) on the interval + \([0; 1)\) with \(n \in \mathbb{Z} \) are orthonormal. +\end{lemma} +\begin{proof} + We need to show that \(\langle E_m, E_n \rangle\) equals 1 when \(m = n\) + and zero otherwise. This is a straightforward computation: We start by + unpacking the notation to get + \[ + \langle E_m, E_n \rangle + = \int_0^1 e^{i2\pi mx} e^{- i2\pi nx} \, dx + = \int_0^1 e^{i2\pi (m - n)x} \, dx, + \] + then inside the integrand we can see that when \(m = n\) we have \(e^0 = 1\) and + thus \( \int_0^1 dx = 1, \) while when \(m \neq n\) we can just say that we + have a new non-zero integer + \(k := m - n\) and + \[ + \int_0^1 e^{i2\pi kx} \, dx + = \frac{e^{i2\pi k} - e^{0}}{i2\pi k} + = \frac{1 - 1}{i2\pi k} + = 0 + \] + as desired. \qedhere +\end{proof} + +\begin{definition}[Spectrum] +\end{definition} + +\begin{theorem}[Fourier Theorem] + \[ + \lim_{N \to \infty} \left \| + f(x) - \sum_{n = -N}^N \hat{f}(n) E_n(x) + \right \|_2 = 0 + \] +\end{theorem} + +\begin{lemma} + The set of functions \(E_{m, n}(\xi, \eta) = e^{i2\pi m\xi}e^{i2\pi n\eta}\) + on the square \([0; 1)^2\) with \(m, n \in \mathbb{Z} \) are orthonormal. +\end{lemma} +\begin{proof} + The proof is almost identical to lemma \ref{kugel:lemma:exp-1d}, with the + only difference that the inner product is given by + \[ + \langle E_{m,n}, E_{m', n'} \rangle + = \iint_{[0;1)^2} + E_{m, n}(\xi, \eta) \overline{E_{m', n'} (\xi, \eta)} + \, d\xi d\eta + .\qedhere + \] +\end{proof} + +\subsection{Laplacian operator} + +\subsection{Eigenvalue Problem} diff --git a/buch/papers/kugel/references.bib b/buch/papers/kugel/references.bib index 013da60..b74c5cd 100644 --- a/buch/papers/kugel/references.bib +++ b/buch/papers/kugel/references.bib @@ -1,35 +1,195 @@ -% -% references.bib -- Bibliography file for the paper kugel -% -% (c) 2020 Autor, Hochschule Rapperswil -% - -@online{kugel:bibtex, - title = {BibTeX}, - url = {https://de.wikipedia.org/wiki/BibTeX}, - date = {2020-02-06}, - year = {2020}, - month = {2}, - day = {6} -} - -@book{kugel: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{kugel: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} + +@article{carvalhaes_surface_2015, + title = {The surface Laplacian technique in {EEG}: Theory and methods}, + volume = {97}, + issn = {01678760}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0167876015001749}, + doi = {10.1016/j.ijpsycho.2015.04.023}, + shorttitle = {The surface Laplacian technique in {EEG}}, + pages = {174--188}, + number = {3}, + journaltitle = {International Journal of Psychophysiology}, + shortjournal = {International Journal of Psychophysiology}, + author = {Carvalhaes, Claudio and de Barros, J. Acacio}, + urldate = {2022-05-16}, + date = {2015-09}, + langid = {english}, + file = {Submitted Version:/Users/npross/Zotero/storage/SN4YUNQC/Carvalhaes and de Barros - 2015 - The surface Laplacian technique in EEG Theory and.pdf:application/pdf}, +} + +@video{minutephysics_better_2021, + title = {A Better Way To Picture Atoms}, + url = {https://www.youtube.com/watch?v=W2Xb2GFK2yc}, + abstract = {Thanks to Google for sponsoring a portion of this video! +Support {MinutePhysics} on Patreon: http://www.patreon.com/minutephysics + +This video is about using Bohmian trajectories to visualize the wavefunctions of hydrogen orbitals, rendered in 3D using custom python code in Blender. + +{REFERENCES} +A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I +David Bohm, Physical Review, Vol 85 No. 2, January 15, 1952 + +Speakable and Unspeakable in Quantum Mechanics +J. S. Bell + +Trajectory construction of Dirac evolution +Peter Holland + +The de Broglie-Bohm Causal Interpretation of Quantum Mechanics and its Application to some Simple Systems by Caroline Colijn + +Bohmian Trajectories as the Foundation of Quantum Mechanics +http://arxiv.org/abs/0912.2666v1 + +The Pilot-Wave Perspective on Quantum Scattering and Tunneling +http://arxiv.org/abs/1210.7265v2 + +A Quantum Potential Description of One-Dimensional Time-Dependent Scattering From Square Barriers and Square Wells +Dewdney, Foundations of Physics, {VoL} 12, No. 1, 1982 + +Link to Patreon Supporters: http://www.minutephysics.com/supporters/ + +{MinutePhysics} is on twitter - @minutephysics +And facebook - http://facebook.com/minutephysics + +Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! + +Created by Henry Reich}, + author = {{minutephysics}}, + urldate = {2022-05-19}, + date = {2021-05-19}, +} + +@article{ries_role_2013, + title = {Role of the lateral prefrontal cortex in speech monitoring}, + volume = {7}, + issn = {1662-5161}, + url = {http://journal.frontiersin.org/article/10.3389/fnhum.2013.00703/abstract}, + doi = {10.3389/fnhum.2013.00703}, + journaltitle = {Frontiers in Human Neuroscience}, + shortjournal = {Front. Hum. Neurosci.}, + author = {Riès, Stephanie K. and Xie, Kira and Haaland, Kathleen Y. and Dronkers, Nina F. and Knight, Robert T.}, + urldate = {2022-05-16}, + date = {2013}, + file = {Full Text:/Users/npross/Zotero/storage/W7KTJB8E/Riès et al. - 2013 - Role of the lateral prefrontal cortex in speech mo.pdf:application/pdf}, +} + +@online{saylor_academy_atomic_2012, + title = {Atomic Orbitals and Their Energies}, + url = {http://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s10-05-atomic-orbitals-and-their-ener.html}, + author = {{Saylor Academy}}, + urldate = {2022-05-30}, + date = {2012}, + file = {Atomic Orbitals and Their Energies:/Users/npross/Zotero/storage/LJ8DM3YI/s10-05-atomic-orbitals-and-their-ener.html:text/html}, +} + +@inproceedings{schmitz_using_2012, + location = {Santa Clara, {CA}, {USA}}, + title = {Using spherical harmonics for modeling antenna patterns}, + isbn = {978-1-4577-1155-8 978-1-4577-1153-4 978-1-4577-1154-1}, + url = {http://ieeexplore.ieee.org/document/6175298/}, + doi = {10.1109/RWS.2012.6175298}, + eventtitle = {2012 {IEEE} Radio and Wireless Symposium ({RWS})}, + pages = {155--158}, + booktitle = {2012 {IEEE} Radio and Wireless Symposium}, + publisher = {{IEEE}}, + author = {Schmitz, Arne and Karolski, Thomas and Kobbelt, Leif}, + urldate = {2022-05-16}, + date = {2012-01}, +} + +@online{allard_mathematics_2009, + title = {Mathematics 203-204 - Basic Analysis I-{II}}, + url = {https://services.math.duke.edu/~wka/math204/}, + author = {Allard, William K.}, + urldate = {2022-07-25}, + date = {2009}, + file = {Mathematics 203-204 - Basic Analysis I-II:/Users/npross/Zotero/storage/LJISXBCM/math204.html:text/html}, +} + +@book{olver_introduction_2013, + location = {New York, {NY}}, + title = {Introduction to partial differential equations}, + isbn = {978-3-319-02098-3}, + publisher = {Springer Science+Business Media, {LLC}}, + author = {Olver, Peter J.}, + date = {2013}, +} + +@book{miller_partial_2020, + location = {Mineola, New York}, + title = {Partial differential equations in engineering problems}, + isbn = {978-0-486-84329-2}, + abstract = {"Requiring only an elementary knowledge of ordinary differential equations, this concise text begins by deriving common partial differential equations associated with vibration, heat flow, electricity, and elasticity. The treatment discusses and applies the techniques of Fourier analysis to these equations and extends the discussion to the Fourier integral. Final chapters discuss Legendre, Bessel, and Mathieu functions and the general structure of differential operators"--}, + publisher = {Dover Publications, Inc}, + author = {Miller, Kenneth S.}, + date = {2020}, + keywords = {Differential equations, Partial}, +} + +@book{asmar_complex_2018, + location = {Cham}, + title = {Complex analysis with applications}, + isbn = {978-3-319-94062-5}, + series = {Undergraduate texts in mathematics}, + pagetotal = {494}, + publisher = {Springer}, + author = {Asmar, Nakhlé H. and Grafakos, Loukas}, + date = {2018}, + doi = {10.1007/978-3-319-94063-2}, + file = {Table of Contents PDF:/Users/npross/Zotero/storage/G2Q2RDFU/Asmar and Grafakos - 2018 - Complex analysis with applications.pdf:application/pdf}, +} + +@book{adkins_ordinary_2012, + location = {New York}, + title = {Ordinary differential equations}, + isbn = {978-1-4614-3617-1}, + series = {Undergraduate texts in mathematics}, + pagetotal = {799}, + publisher = {Springer}, + author = {Adkins, William A. and Davidson, Mark G.}, + date = {2012}, + keywords = {Differential equations}, +} + +@book{griffiths_introduction_2015, + title = {Introduction to electrodynamics}, + isbn = {978-93-325-5044-5}, + author = {Griffiths, David J}, + date = {2015}, + note = {{OCLC}: 965197645}, +} + +@book{tao_analysis_2016, + title = {Analysis 2}, + isbn = {978-981-10-1804-6}, + url = {https://doi.org/10.1007/978-981-10-1804-6}, + author = {Tao, Terence}, + urldate = {2022-07-25}, + date = {2016}, + note = {{OCLC}: 965325026}, +} + +@book{axler_linear_2015, + location = {Cham}, + title = {Linear Algebra Done Right}, + isbn = {978-3-319-11079-0 978-3-319-11080-6}, + url = {https://link.springer.com/10.1007/978-3-319-11080-6}, + series = {Undergraduate Texts in Mathematics}, + publisher = {Springer International Publishing}, + author = {Axler, Sheldon}, + urldate = {2022-07-25}, + date = {2015}, + langid = {english}, + doi = {10.1007/978-3-319-11080-6}, + file = {Submitted Version:/Users/npross/Zotero/storage/3Y8MX74N/Axler - 2015 - Linear Algebra Done Right.pdf:application/pdf}, } +@online{eck_metric_2022, + title = {Metric Spaces: Completeness}, + url = {https://math.hws.edu/eck/metric-spaces/completeness.html}, + titleaddon = {Math 331: Foundations of Analysis}, + author = {Eck, David J.}, + urldate = {2022-08-01}, + date = {2022}, + file = {Metric Spaces\: Completeness:/Users/npross/Zotero/storage/5JYEE8NF/completeness.html:text/html}, +} \ No newline at end of file diff --git a/buch/papers/kugel/spherical-harmonics.tex b/buch/papers/kugel/spherical-harmonics.tex new file mode 100644 index 0000000..6b23ce5 --- /dev/null +++ b/buch/papers/kugel/spherical-harmonics.tex @@ -0,0 +1,13 @@ +% vim:ts=2 sw=2 et spell: + +\section{Spherical Harmonics} + +\subsection{Eigenvalue Problem in Spherical Coordinates} + +\subsection{Properties} + +\subsection{Recurrence Relations} + +\section{Series Expansions in \(C(S^2)\)} + +\nocite{olver_introduction_2013} -- cgit v1.2.1 From 8dc531ac53ae1b085482c9f1bda6001ca803c164 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Tue, 2 Aug 2022 21:14:53 +0200 Subject: Created python files for graphics. Created addtional subsection verlockende Intuition --- buch/papers/lambertw/Bilder/Abstand.py | 18 +++++ buch/papers/lambertw/Bilder/Intuition.pdf | Bin 0 -> 186972 bytes buch/papers/lambertw/Bilder/Strategie.pdf | Bin 120904 -> 151640 bytes buch/papers/lambertw/Bilder/Strategie.py | 2 +- buch/papers/lambertw/Bilder/konvergenz.py | 20 ++++++ .../Bilder/lambertAbstandBauchgef\303\274hl.py" | 58 ++++++++++++++++ buch/papers/lambertw/teil1.tex | 76 ++++++++++++++++++++- 7 files changed, 170 insertions(+), 4 deletions(-) create mode 100644 buch/papers/lambertw/Bilder/Abstand.py create mode 100644 buch/papers/lambertw/Bilder/Intuition.pdf create mode 100644 buch/papers/lambertw/Bilder/konvergenz.py create mode 100644 "buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/Abstand.py b/buch/papers/lambertw/Bilder/Abstand.py new file mode 100644 index 0000000..d787c34 --- /dev/null +++ b/buch/papers/lambertw/Bilder/Abstand.py @@ -0,0 +1,18 @@ +# -*- coding: utf-8 -*- +""" +Created on Sat Jul 30 23:09:33 2022 + +@author: yanik +""" + +import numpy as np +import matplotlib.pyplot as plt + +phi = np.pi/2 +t = np.linspace(0, 10, 10**5) +x0 = 1 + +def D(t): + return np.sqrt(x0**2+2*x0*t*np.cos(phi)+2*t**2-2*t**2*np.sin(phi)) + +plt.plot(t, D(t)) diff --git a/buch/papers/lambertw/Bilder/Intuition.pdf b/buch/papers/lambertw/Bilder/Intuition.pdf new file mode 100644 index 0000000..236212a Binary files /dev/null and b/buch/papers/lambertw/Bilder/Intuition.pdf differ diff --git a/buch/papers/lambertw/Bilder/Strategie.pdf b/buch/papers/lambertw/Bilder/Strategie.pdf index 0de3001..91442cc 100644 Binary files a/buch/papers/lambertw/Bilder/Strategie.pdf and b/buch/papers/lambertw/Bilder/Strategie.pdf differ diff --git a/buch/papers/lambertw/Bilder/Strategie.py b/buch/papers/lambertw/Bilder/Strategie.py index b9b41bf..28f7bcd 100644 --- a/buch/papers/lambertw/Bilder/Strategie.py +++ b/buch/papers/lambertw/Bilder/Strategie.py @@ -44,7 +44,7 @@ plt.rcParams.update({ "font.serif": ["New Century Schoolbook"], }) -ax.text(1.6, 4.3, r"$\vec{v}$", size=30) +ax.text(1.6, 4.3, r"$\dot{v}$", size=30) ax.text(0.6, 3.9, r"$V$", size=30, c='b') ax.text(5.1, 4.77, r"$Z$", size=30, c='b') diff --git a/buch/papers/lambertw/Bilder/konvergenz.py b/buch/papers/lambertw/Bilder/konvergenz.py new file mode 100644 index 0000000..dac99a7 --- /dev/null +++ b/buch/papers/lambertw/Bilder/konvergenz.py @@ -0,0 +1,20 @@ +# -*- coding: utf-8 -*- +""" +Created on Sun Jul 31 14:34:13 2022 + +@author: yanik +""" + +import numpy as np +import matplotlib.pyplot as plt + +t = 0 +phi = np.linspace(np.pi/2, 3*np.pi/2, 10**5) +x0 = 1 +y0 = -2 + +def D(t): + return (x0+t*np.cos(phi))*np.cos(phi)+(y0+t*(np.sin(phi)-1))*(np.sin(phi)-1)/(np.sqrt((x0+t*np.cos(phi))**2+(y0+t*(np.sin(phi)-1))**2)) + + +plt.plot(phi, D(t)) \ No newline at end of file diff --git "a/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" "b/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" new file mode 100644 index 0000000..9031bfc --- /dev/null +++ "b/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" @@ -0,0 +1,58 @@ +# -*- coding: utf-8 -*- +""" +Created on Sun Jul 31 13:32:53 2022 + +@author: yanik +""" + +import numpy as np +import matplotlib.pyplot as plt +import scipy.special as sci + +W = sci.lambertw + + +t = np.linspace(0, 1.2, 1000) +x0 = 1 +y0 = 1 + +r0 = np.sqrt(x0**2+y0**2) +chi = (r0+y0)/(r0-y0) + +x = x0*np.sqrt(1/chi*W(chi*np.exp(chi-4*t/(r0-y0)))) +eta = (x/x0)**2 +y = 1/4*((y0+r0)*eta+(y0-r0)*np.log(eta)-r0+3*y0) + +ymin= (min(y)).real +xmin = (x[np.where(y == ymin)][0]).real + + +#Verfolger +plt.plot(x, y, 'r--') +plt.plot(xmin, ymin, 'bo', markersize=10) + +#Ziel +plt.plot(np.zeros_like(t), t, 'g--') +plt.plot(0, ymin, 'bo', markersize=10) + + +plt.plot([0, xmin], [ymin, ymin], 'k--') +#plt.xlim(-0.1, 1) +#plt.ylim(1, 2) +#plt.ylabel("y") +#plt.xlabel("x") +plt.grid(True) +plt.quiver(xmin, ymin, -0.2, 0, scale=1) + +plt.text(xmin+0.1, ymin-0.1, "Verfolgungskurve", size=20, rotation=20, color='r') +plt.text(0.01, 0.02, "Fluchtkurve", size=20, rotation=90, color='g') + +plt.rcParams.update({ + "text.usetex": True, + "font.family": "serif", + "font.serif": ["New Century Schoolbook"], +}) + +plt.text(xmin-0.11, ymin-0.12, r"$\dot{v}$", size=30) +plt.text(xmin-0.02, ymin+0.05, r"$V$", size=30, c='b') +plt.text(0.02, ymin+0.05, r"$Z$", size=30, c='b') \ No newline at end of file diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 2733759..2da07db 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -205,8 +205,78 @@ Durch quadrieren verschwindet die Wurzel des Betrages, womit % die neue Bedingung ist. Da sowohl der Betrag als auch $a_{min}$ grösser null sind, bleibt die Aussage unverändert. - - - +% +\subsection{verleitende/trügerisch/verführerisch Intuition} +In der Grafik \ref{lambertw:grafic:intuition} ist eine Mögliche Verfolgungskurve dargestellt, wobei für die Startbedingung der erste-Quadrant verwendet wurde. +Als erste Intuition bietet sich der tiefste Punkt der Verfolgungskurve an, bei dem der y-Anteil des Richtungsvektors null entspricht. +Wenn sich der Verfolger an diesem Punkt befindet, muss zwingend das Ziel auf gleicher Höhe sein. +Es lässt sich vermuten, dass bei diesem Punkt der Abstand zum Ziel minimal sein könnte. +\begin{figure} + \centering + \includegraphics[scale=0.4]{./papers/lambertw/Bilder/Intuition.pdf} + \caption{Intuition} + \label{lambertw:grafic:intuition} +\end{figure} +% +Dies kann leicht überprüft werden, indem wir lokal alle relevanten benachbarten Punkte betrachten und das Vorzeichen der Änderung des Abstandes prüfen. +Dafür wird ein Ausdruck benötigt, der den Abstand und die benachbarten Punkte beschreibt. +Der Richtungsvektor wird allgemein mit dem Winkel $\alpha \in[ 0, 2\pi)$ +Die Ortsvektoren der Punkte können wiederum mit +\begin{align} + v + &= + t\cdot\left(\begin{array}{c} \cos (\alpha) \\ \sin (\alpha) \end{array}\right) +\left(\begin{array}{c} x_0 \\ y_0 \end{array}\right) + \\ + z + &= + \left(\begin{array}{c} 0 \\ t \end{array}\right) +\end{align} +beschrieben werden. Der Verfolger wurde allgemein für jede Richtung $\alpha$ definiert, um alle unmittelbar benachbarten Punkte beschreiben zu können. +Da der Abstand +\begin{equation} + a + = + |v-z| + \geq + 0 +\end{equation} +ist, kann durch quadrieren ohne Informationsverlust die Rechnung vereinfacht werden zu +\begin{equation} + a^2 + = + |v-z|^2 + = + (t\cdot\cos(\alpha)+x_0)^2+t^2(\sin(\alpha)-1)^2 + \text{.} +\end{equation} +Der Abstand im Quadrat abgeleitet nach der Zeit ist +\begin{equation} + \frac{d a^2}{d t} + = + 2(t\cdot\cos (\alpha)+x_0)\cdot\cos(\alpha)(\alpha)+2t(\sin(\alpha)-1)^2 + \text{.} +\end{equation} +Da nur die unmittelbar benachbarten Punkten von Interesse sind, wird die Ableitung für $t=0$ untersucht. Dabei kann die Ableitung in +\begin{align} + \frac{d a^2}{d t} + &= + 2x_0\cos(\alpha) + \\ + \frac{d a^2}{d t} + &< + 0\Leftrightarrow\alpha\in\left( \frac{\pi}{2}, \frac{3\pi}{2}\right) + \\ + \frac{d a^2}{d t} + &> + 0\Leftrightarrow\alpha\in\left[0, \frac{\pi}{2}\right)\cup\left(\frac{3\pi}{2}, 2\pi\right) + \\ + \frac{d a^2}{d t} + &= + 0\Leftrightarrow\alpha\in\left\{ \frac{\pi}{2}, \frac{3\pi}{2}\right\} +\end{align} +unterteilt werden. +Von Interesse ist lediglich das Intervall $\alpha\in\left( \frac{\pi}{2}, \frac{3\pi}{2}\right)$, da der Verfolger sich stets in die negative $y$-Richtung bewegt. +In diesem Intervall ist die Ableitung negativ, woraus folgt, dass jeglicher unmittelbar benachbarte Punkt, den der Verfolger als nächstes begehen könnte, stets näher am Ziel ist als zuvor. +Dies bedeutet, dass der Scheitelpunkt der Verfolgungskurve nie ein lokales Minimum bezüglich des Abstandes sein kann. -- cgit v1.2.1 From f8ac7479589ae069c7a509cf9908f8e3dddd8451 Mon Sep 17 00:00:00 2001 From: Joshua Baer Date: Wed, 3 Aug 2022 19:45:04 +0200 Subject: bessel labeled --- buch/chapters/075-fourier/bessel.tex | 3 +- buch/papers/fm/03_bessel.tex | 65 +- buch/papers/fm/Python animation/Bessel-FM.ipynb | 50 +- buch/papers/fm/Python animation/bessel.pgf | 2057 +++++++++++++++++++++++ buch/papers/fm/packages.tex | 1 + 5 files changed, 2116 insertions(+), 60 deletions(-) create mode 100644 buch/papers/fm/Python animation/bessel.pgf (limited to 'buch') diff --git a/buch/chapters/075-fourier/bessel.tex b/buch/chapters/075-fourier/bessel.tex index 7e978f7..db7880b 100644 --- a/buch/chapters/075-fourier/bessel.tex +++ b/buch/chapters/075-fourier/bessel.tex @@ -454,7 +454,8 @@ Terme mit $\pm n$ können wegen \[ \left. \begin{aligned} -J_{-n}(\xi) &= (-1)^n J_n(\xi) +J_{-n}(\xi) &= (-1)^n J_n(\xi) +\label{buch:fourier:eqn:symetrie} \\ i^{-n}&=(-1)^n i^n \end{aligned} diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index 760cdc4..eec64f2 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -24,6 +24,7 @@ Das Ziel ist es unser moduliertes Signal mit der Besselfunktion so auszudrücken \sum_{k= -\infty}^\infty J_{k}(\beta) \cos((\omega_c+k\omega_m)t) \label{fm:eq:proof} \end{align} + \subsubsection{Hilfsmittel} Doch dazu brauchen wir die Hilfe der Additionsthoerme \begin{align} @@ -46,18 +47,18 @@ und die drei Besselfunktions indentitäten, \begin{align} \cos(\beta\sin\phi) &= - J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\phi) + J_0(\beta) + 2\sum_{k=1}^\infty(-1)^k \cdot J_{2k}(\beta) \cos(2k\phi) \label{fm:eq:besselid1} \\ \sin(\beta\sin\phi) &= - J_0(\beta) + 2\sum_{k=1}^\infty J_{2k+1}(\beta) \cos((2k+1)\phi) + 2\sum_{k=0}^\infty (-1)^k J_{2k+1}(\beta) \cos((2k+1)\phi) \label{fm:eq:besselid2} \\ J_{-n}(\beta) &= (-1)^n J_n(\beta) \label{fm:eq:besselid3} \end{align} -welche man im Kapitel (ref), ref, ref findet. +welche man im Kapitel \eqref{buch:fourier:eqn:expinphireal}, \eqref{buch:fourier:eqn:expinphiimaginary}, \eqref{buch:fourier:eqn:symetrie}. \subsubsection{Anwenden des Additionstheorem} Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal @@ -66,26 +67,31 @@ Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal = \cos(\omega_c t + \beta\sin(\omega_mt)) = - \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_c)\sin(\beta\sin(\omega_m t)). + \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_ct)\sin(\beta\sin(\omega_m t)). \label{fm:eq:start} \] + \subsubsection{Cos-Teil} Zu beginn wird der Cos-Teil \[ - \cos(\omega_c)\cos(\beta\sin(\omega_mt)) + \cos(\omega_c t)\cdot\cos(\beta\sin(\omega_mt)) \] mit hilfe der Besselindentität \eqref{fm:eq:besselid1} zum \begin{align*} - \cos(\omega_c t) \cdot \bigg[\, J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] - &=\\ - J_0(\beta)\cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) - \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem}} + \cos(\omega_c t) \cdot \bigg[ J_0(\beta) + 2\sum_{k=1}^\infty(-1)^k \cdot J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] + &= + (-1)^k \cdot \sum_{k=1}^\infty J_{2k}(\beta) \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem}} \end{align*} wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum -\[ - J_0(\beta)\cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \cos((\omega_c - 2k \omega_m) t)+\cos((\omega_c + 2k \omega_m) t) \} -\] -wird. +\begin{align*} + J_0(\beta) \cdot \cos(\omega_c t) +(-1)^k \cdot \sum_{k=1}^\infty J_{2k}(\beta) \{ \underbrace{\cos((\omega_c - 2k \omega_m) t)} \,+\, \cos((\omega_c + 2k \omega_m) t) \} + \\ + = + (-1)^k \cdot \sum_{k=-\infty}^{-1} J_{2k}(\beta) \overbrace{\cos((\omega_c +2k \omega_m) t)} + \,+\,J_0(\beta)\cdot \cos(\omega_c t+ 2\cdot0 \omega_m) + \,+\, (-1)^k \cdot\sum_{k=1}^\infty J_{2k}(\beta)\cos((\omega_c + 2k \omega_m) t) +\end{align*} + Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term \[ \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t), @@ -96,22 +102,32 @@ dabei gehen nun die Terme von \(-\infty \to \infty\), dabei bleibt n Ganzzahlig. \subsubsection{Sin-Teil} Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil \[ - \sin(\omega_c)\sin(\beta\sin(\omega_m t)). + -\sin(\omega_c t)\cdot\sin(\beta\sin(\omega_m t)). \] Dieser wird mit der \eqref{fm:eq:besselid2} Besselindentität zu \begin{align*} - \sin(\omega_c t) \cdot \bigg[ J_0(\beta) + 2 \sum_{k=1}^\infty J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] - &=\\ - J_0(\beta) \cdot \sin(\omega_c t) + \sum_{k=1}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{\text{Additionstheorem}}. + -\sin(\omega_c t) \cdot \bigg[ 2 \sum_{k=0}^\infty(-1)^k \cdot J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] + \\ + = + (-1)^k \cdot -\sum_{k=0}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{\text{Additionstheorem}}. \end{align*} Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), somit wird daraus -\[ - J_0(\beta) \cdot \sin(\omega_c) + \sum_{k=1}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c-(2k+1)\omega_m) t)}_{\text{neg.Teil}} - \cos((\omega_c+(2k+1)\omega_m) t) \} -\]dieser Term. -Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert. +\begin{align*} + (-1)^k \cdot -\sum_{k=0}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c - (2k+1)\omega_m) t)} \,-\, \cos((\omega_c+(2k+1)\omega_m) t) \} + \\ + = + (-1)^k \cdot -\sum_{k=- \infty}^{-1} J_{2k+1}(\beta) \overbrace{\cos((\omega_c + (2k+1)\omega_m) t)} + \,-\, (-1)^k \cdot -\sum_{k=0}^\infty J_{2k+1}(\beta) \cos((\omega_c + (2k+1)\omega_m) t) +\end{align*} +dieser Term. Zusätzlich dabei noch die letzte Besselindentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). -Somit wird neg.Teil zum Term \(-\cos((\omega_c+(2k+1)\omega_m) t)\) und die Summe vereinfacht sich zu +Somit wird neg.Teil zum Term +\[ + (-1)^k \cdot \sum_{k= \infty}^{1} -1 \cdot J_{2k+1}(\beta) \cos((\omega_c+(2k+1)\omega_m) t). +\] +TODO (jetzt habe ich zwei Summen die immer positiv sind? ) +Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert vereinfacht sich die Summe zu \[ \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). \label{fm:eq:ungerade} @@ -122,7 +138,8 @@ Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. Beide Teile \eqref{fm:eq:gerade} Gerade \[ \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) -\]und \eqref{fm:eq:ungerade} Ungerade +\] +und \eqref{fm:eq:ungerade} Ungerade \[ \sum_{n\, \text{ungerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t) \] @@ -140,7 +157,7 @@ Somit ist \eqref{fm:eq:proof} bewiesen. Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. \begin{figure} \centering -% \input{./PyPython animation/bessel.pgf} + \input{papers/fm/Python animation/bessel.pgf} \caption{Bessle Funktion \(J_{k}(\beta)\)} \label{fig:bessel} \end{figure} diff --git a/buch/papers/fm/Python animation/Bessel-FM.ipynb b/buch/papers/fm/Python animation/Bessel-FM.ipynb index 6f099a7..74f1011 100644 --- a/buch/papers/fm/Python animation/Bessel-FM.ipynb +++ b/buch/papers/fm/Python animation/Bessel-FM.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -13,7 +13,7 @@ "import scipy.fftpack\n", "import matplotlib as mpl\n", "# Use the pgf backend (must be set before pyplot imported)\n", - "#mpl.use('pgf')\n", + "mpl.use('pgf')\n", "import matplotlib.pyplot as plt\n", "from matplotlib.widgets import Slider\n", "def fm(beta):\n", @@ -70,39 +70,26 @@ "xf = fftfreq(N, 1 / 1000)\n", "plt.plot(xf, np.abs(yf_old))\n", "#plt.xlim(-150, 150)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 118, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "
" ] @@ -111,13 +98,6 @@ "needs_background": "light" }, "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.7651976865579666\n" - ] } ], "source": [ @@ -133,8 +113,8 @@ "plt.xlabel(' $ \\\\beta $ ')\n", "plt.plot(x, y)\n", "plt.legend()\n", - "plt.show()\n", - "#plt.savefig('bessel.pgf', format='pgf')\n", + "#plt.show()\n", + "plt.savefig('bessel.pgf', format='pgf')\n", "print(sc.jv(0,1))" ] }, diff --git a/buch/papers/fm/Python animation/bessel.pgf b/buch/papers/fm/Python animation/bessel.pgf new file mode 100644 index 0000000..cc7af1e --- /dev/null +++ b/buch/papers/fm/Python animation/bessel.pgf @@ -0,0 +1,2057 @@ +%% 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/joshua/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setsansfont{DejaVuSans.ttf}[Path=\detokenize{/home/joshua/.local/lib/python3.8/site-packages/matplotlib/mpl-data/fonts/ttf/}] +%% \setmonofont{DejaVuSansMono.ttf}[Path=\detokenize{/home/joshua/.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% +\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{6.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{6.000000in}{4.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{4.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{}% +\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{0.750000in}{0.500000in}}% +\pgfpathlineto{\pgfqpoint{5.400000in}{0.500000in}}% +\pgfpathlineto{\pgfqpoint{5.400000in}{3.520000in}}% +\pgfpathlineto{\pgfqpoint{0.750000in}{3.520000in}}% +\pgfpathlineto{\pgfqpoint{0.750000in}{0.500000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.750000in}{0.500000in}}{\pgfqpoint{4.650000in}{3.020000in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.750000in}{0.500000in}}% +\pgfpathlineto{\pgfqpoint{0.750000in}{3.520000in}}% +\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{0.750000in}{0.500000in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.750000in,y=0.402778in,,top]{\color{textcolor}\sffamily\fontsize{10.000000}{12.000000}\selectfont \ensuremath{-}10.0}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.750000in}{0.500000in}}{\pgfqpoint{4.650000in}{3.020000in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.690196,0.690196,0.690196}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.331250in}{0.500000in}}% +\pgfpathlineto{\pgfqpoint{1.331250in}{3.520000in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% 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+\endgroup% diff --git a/buch/papers/fm/packages.tex b/buch/papers/fm/packages.tex index f0ca8cc..7bbbe35 100644 --- a/buch/papers/fm/packages.tex +++ b/buch/papers/fm/packages.tex @@ -8,3 +8,4 @@ % following example %\usepackage{packagename} \usepackage{xcolor} +\usepackage{pgf} -- cgit v1.2.1 From 05b1350074c1c62340c7c32f240cb46078c152e7 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Thu, 4 Aug 2022 17:31:48 +0200 Subject: changed textsize in Strategie.pdf. Did minor changes in Teil0 and Teil1 --- buch/papers/lambertw/Bilder/Strategie.pdf | Bin 151640 -> 151684 bytes buch/papers/lambertw/Bilder/Strategie.py | 9 +++--- buch/papers/lambertw/teil0.tex | 47 ++++++++++++++++++++---------- buch/papers/lambertw/teil1.tex | 36 ++++++++++++----------- 4 files changed, 55 insertions(+), 37 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/Strategie.pdf b/buch/papers/lambertw/Bilder/Strategie.pdf index 91442cc..b5428f5 100644 Binary files a/buch/papers/lambertw/Bilder/Strategie.pdf and b/buch/papers/lambertw/Bilder/Strategie.pdf differ diff --git a/buch/papers/lambertw/Bilder/Strategie.py b/buch/papers/lambertw/Bilder/Strategie.py index 28f7bcd..d7d06cb 100644 --- a/buch/papers/lambertw/Bilder/Strategie.py +++ b/buch/papers/lambertw/Bilder/Strategie.py @@ -34,7 +34,8 @@ ax.quiver(X, Y, U, W, angles='xy', scale_units='xy', scale=1, headwidth=5, headl ax.plot([V[0], (VZ+V)[0]], [V[1], (VZ+V)[1]], 'k--') ax.plot(np.vstack([V, Z])[:, 0], np.vstack([V, Z])[:,1], 'bo', markersize=10) - +ax.set_xlabel("x") +ax.set_ylabel("y") ax.text(2.5, 4.5, "Visierlinie", size=20, rotation=10) @@ -44,9 +45,9 @@ plt.rcParams.update({ "font.serif": ["New Century Schoolbook"], }) -ax.text(1.6, 4.3, r"$\dot{v}$", size=30) -ax.text(0.6, 3.9, r"$V$", size=30, c='b') -ax.text(5.1, 4.77, r"$Z$", size=30, c='b') +ax.text(1.6, 4.3, r"$\dot{v}$", size=20) +ax.text(0.65, 3.9, r"$V$", size=20, c='b') +ax.text(5.15, 4.85, r"$Z$", size=20, c='b') diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 8fa8f9b..088cb7b 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -7,7 +7,7 @@ \label{lambertw:section:Was_sind_Verfolgungskurven}} \rhead{Was sind Verfolgungskurven?} % -Verfolgungskurven tauchen oft auf bei Fragen wie "Welchen Pfad begeht ein Hund während er einer Katze nachrennt?". +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 verfolgt sein Ziel, das versucht zu entkommen. Der Pfad, den der Verfolger während der Verfolgung begeht, wird Verfolgungskurve genannt. @@ -27,15 +27,15 @@ Daraus folgt, dass eine Strategie zwei dieser drei Parameter festlegen muss, um % \begin{table} \centering - \begin{tabular}{|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} + \begin{tabular}{|>{$}l<{$}|>{$}c<{$}|>{$}c<{$}|>{$}c<{$}|} \hline \text{Strategie}&\text{Geschwindigkeit}&\text{Abstand}&\text{Richtung}\\ \hline \text{Jagd} - & \text{konstant} & \text{-} & \text{direkt auf Ziel hinzu}\\ + & \text{konstant} & \text{-} & \text{direkt auf Ziel zu}\\ \text{Beschattung} - & \text{-} & \text{konstant} & \text{direkt auf Ziel hinzu}\\ + & \text{-} & \text{konstant} & \text{direkt auf Ziel zu}\\ \text{Vorhalt} & \text{konstant} & \text{-} & \text{etwas voraus Zielen}\\ @@ -59,7 +59,7 @@ Der Verfolger und sein Ziel werden als Punkte $V$ und $Z$ modelliert. In der Abbildung \ref{lambertw:grafic:pursuerDGL2} ist das Problem dargestellt, wobei $v$ der Ortsvektor des Verfolgers, $z$ der Ortsvektor des Ziels und $\dot{v}$ der Geschwindigkeitsvektor des Verfolgers ist. Der Geschwindigkeitsvektor entspricht dem Richtungsvektors des Verfolgers. -Die konstante Geschwindigkeit kann man mit der Gleichung +Die konstante Geschwindigkeit kann man mit % \begin{equation} |\dot{v}| @@ -67,38 +67,53 @@ Die konstante Geschwindigkeit kann man mit der Gleichung \text{,}\quad A\in\mathbb{R}^+ \end{equation} % -darstellen. Der Geschwindigkeitsvektor kann mit der Gleichung -% +darstellen. Der Geschwindigkeitsvektor muss auf das Ziel zeigen, woraus folgt +\begin{equation} + \dot{v} + \quad||\quad + z-v + \text{.} +\end{equation} +Um den Richtungsvektor zu konstruieren kann der Einheitsvektor parallel zu $z-v$ um $\dot{v}$ gestreckt werden, was zu \begin{equation} - \frac{z-v}{|z-v|}\cdot|\dot{v}| + \dot{v} = + |\dot{v}|\cdot e_{z-v} +\end{equation} +führt. Dies kann noch ausgeschrieben werden zu +\begin{equation} \dot{v} + = + |\dot{v}|\cdot\frac{z-v}{|z-v|} + \text{.} \end{equation} % -beschrieben werden, wenn die Jagdstrategie verwendet wird. -Die Differenz der Ortsvektoren $v$ und $z$ ist ein Vektor der vom Punkt $V$ auf $Z$ zeigt. -Da die Länge dieses Vektors beliebig sein kann, wird durch Division durch den Betrag, ein Einheitsvektor erzeugt. 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 $\dot{v}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergeben sich + +Nun wird die Gleichung mit $\dot{v}$ skalar multipliziert, um das Gleichungssystem von zwei auf eine Gleichung zu reduzieren. Somit ergibt sich \begin{align} \frac{z-v}{|z-v|}\cdot|\dot{v}|\cdot\dot{v} &= |\dot{v}|^2 - \\ +\end{align} +was algebraisch zu +\begin{align} \label{lambertw:pursuerDGL} \frac{z-v}{|z-v|}\cdot \frac{\dot{v}}{|\dot{v}|} &= - 1 \text{.} + 1 \end{align} +umgeformt werden kann. Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Jagdstrategie 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. +Als Strategie eignet sich eine definierte Fluchtkurve oder ähnlich wie beim Verfolger ein Verhalten, das vom Verfolger abhängig ist. +Ein vom Verfolger abhängiges Verhalten führt zu einem gekoppeltem DGL-System, das schwierig zu lösen sein wird. +Eine definierte Fluchtkurve kann mit einer 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} diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 2da07db..0fd0108 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -17,9 +17,10 @@ Nun gilt es zu definieren, wann das Ziel erreicht wird. Da sowohl Ziel und Verfolger als Punkte modelliert wurden, gilt das Ziel als erreicht, wenn die Koordinaten des Verfolgers mit denen des Ziels bei einem diskreten Zeitpunkt $t_1$ übereinstimmen. Somit gilt es % -\begin{equation*} +\begin{equation} z(t_1)=v(t_1) -\end{equation*} + \label{bedingung_treffer} +\end{equation} % zu lösen. Die Parametrisierung von $z(t)$ ist im Beispiel definiert als @@ -29,12 +30,12 @@ Die Parametrisierung von $z(t)$ ist im Beispiel definiert als \left( \begin{array}{c} 0 \\ t \end{array} \right)\text{.} \end{equation} % -Die Parametrisierung von $v(t)$ ist von den Startbedingungen abhängig. Deshalb wird die obige Bedingung jeweils für die unterschiedlichen Startbedingungen separat analysiert. +Die Parametrisierung von $v(t)$ ist von den Startbedingungen abhängig. Deshalb wird \eqref{bedingung_treffer} jeweils für die unterschiedlichen Startbedingungen separat analysiert. % -\subsection{Anfangsbedingung im \RN{1}-Quadranten} +\subsection{Anfangsbedingung im ersten Quadranten} % -Wenn der Verfolger im \RN{1}-Quadranten startet, dann kann $v(t)$ mit den Gleichungen aus \eqref{lambertw:eqFunkXNachT}, welche -\begin{align*} +Wenn der Verfolger im ersten Quadranten startet, dann kann $v(t)$ mit den Gleichungen aus \eqref{lambertw:eqFunkXNachT}, welche +\begin{align} x\left(t\right) &= x_0\cdot\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right) \right)} \\ @@ -50,7 +51,8 @@ Wenn der Verfolger im \RN{1}-Quadranten startet, dann kann $v(t)$ mit den Gleich r_0 = \sqrt{x_0^2+y_0^2} -\end{align*} + \text{.} +\end{align} % Der Folger ist durch \begin{equation} @@ -61,9 +63,9 @@ Der Folger ist durch \end{equation} % parametrisiert, wobei $y(t)$ viel komplexer ist als $x(t)$. -Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Bedingung der $x$- und $y$-Koordinaten einzeln überprüft werden müssen. Es entstehen daher folgende Bedingungen +Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Bedingung der $x$- und $y$-Koordinaten einzeln überprüft werden müssen. Es entstehen daher die Bedingungen % -\begin{align*} +\begin{align} 0 &= x(t) @@ -75,7 +77,7 @@ Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Beding y(t) = \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\text{,} -\end{align*} +\end{align} % welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. Zuerst wird die Bedingung der $x$-Koordinate betrachtet. @@ -101,7 +103,7 @@ Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Da die % Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingung unmöglich zu erfüllen. Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. -Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste damit ein Einholen möglich wäre. +Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste, damit ein Einholen möglich wäre. Somit kann nach den gestellten Bedingungen das Ziel nie erreicht werden. % % @@ -136,7 +138,7 @@ Somit kann nach den gestellten Bedingungen das Ziel nie erreicht werden. %Somit kann nach den gestellten Bedingungen das Ziel nie erreicht werden. % \subsection{Anfangsbedingung $y_0<0$} -Da die Geschwindigkeit des Verfolgers und des Ziels übereinstimmen, kann der Verfolgers niemals das Ziel einholen. +Da die Geschwindigkeit des Verfolgers und des Ziels übereinstimmen, kann der Verfolger niemals das Ziel einholen. Dies kann veranschaulicht werden anhand % \begin{equation} @@ -184,7 +186,7 @@ was aufgelöst zu führt. Somit wird das Ziel immer erreicht bei $t_1$, wenn der Verfolger auf der positiven $y$-Achse startet. \subsection{Fazit} -Durch die Symmetrie der Fluchtkurve an der $y$-Achse führen die Anfangsbedingungen in den Quadranten \RN{1} und \RN{2} zu den gleichen Ergebnissen. Nun ist klar, dass lediglich Anfangspunkte auf der positiven $y$-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. +Durch die Symmetrie der Fluchtkurve an der $y$-Achse führen die Anfangsbedingungen im ersten und zweiten Quadranten zu den gleichen Ergebnissen. Nun ist klar, dass lediglich Anfangspunkte auf der positiven $y$-Achse oder direkt auf dem Ziel dazu führen, dass der Verfolger das Ziel bei $t_1$ einholt. Bei allen anderen Anfangspunkten wird der Verfolger das Ziel nie erreichen. Dieses Resultat ist aber eher akademischer Natur, weil der Verfolger und das Ziel als Punkt betrachtet wurden. Wobei aber in Realität nicht von Punkten sondern von Objekten mit einer räumlichen Ausdehnung gesprochen werden kann. @@ -193,18 +195,18 @@ Falls dies stattfinden sollte, wird dies als Treffer interpretiert. Mathematisch kann dies mit % \begin{equation} - |v-z| Date: Thu, 4 Aug 2022 18:04:11 +0200 Subject: Herleitung fix --- buch/papers/fm/00_modulation.tex | 12 ++-- buch/papers/fm/01_AM.tex | 4 +- buch/papers/fm/03_bessel.tex | 135 ++++++++++++++++++++++++--------------- 3 files changed, 93 insertions(+), 58 deletions(-) (limited to 'buch') diff --git a/buch/papers/fm/00_modulation.tex b/buch/papers/fm/00_modulation.tex index dc99b40..e2ba39f 100644 --- a/buch/papers/fm/00_modulation.tex +++ b/buch/papers/fm/00_modulation.tex @@ -18,10 +18,14 @@ Mathematisch wird dann daraus \omega_i = \omega_c + \frac{d \varphi(t)}{dt} \] mit der Ableitung der Phase\cite{fm:NAT}. -Mit diesen drei parameter ergeben sich auch drei modulationsarten, die Amplitudenmodulation welche \(A_c\) benutzt, -die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): -\newline -\newline +Mit diesen drei Parameter ergeben sich auch drei Modulationsarten, die Amplitudenmodulation, welche \(A_c\) benutzt, +die Phasenmodulation \(\varphi\) und dann noch die Momentankreisfrequenz \(\omega_i\): +\begin{itemize} + \item AM + \item PM + \item FM +\end{itemize} + To do: Bilder jeder Modulationsart diff --git a/buch/papers/fm/01_AM.tex b/buch/papers/fm/01_AM.tex index 921fcf2..21927f5 100644 --- a/buch/papers/fm/01_AM.tex +++ b/buch/papers/fm/01_AM.tex @@ -17,8 +17,8 @@ Dies sieht man besonders in der Eulerischen Formel \[ x_c(t) = \frac{A_c}{2} \cdot e^{j\omega_ct}\;+\;\frac{A_c}{2} \cdot e^{-j\omega_ct}. \] -Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reelwertiges Trägersignal ergibt. -Nun wird der parameter \(A_c\) durch das Moduierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. +Dabei ist die negative Frequenz der zweiten komplexen Schwingung zwingend erforderlich, damit in der Summe immer ein reellwertiges Trägersignal ergibt. +Nun wird der Parameter \(A_c\) durch das Modulierende Signal \(m(t)\) ersetzt, wobei so \(m(t) \leqslant |1|\) normiert wurde. \newline \newline TODO: diff --git a/buch/papers/fm/03_bessel.tex b/buch/papers/fm/03_bessel.tex index eec64f2..5f85dc6 100644 --- a/buch/papers/fm/03_bessel.tex +++ b/buch/papers/fm/03_bessel.tex @@ -3,11 +3,11 @@ % % (c) 2020 Prof Dr Andreas Müller, Hochschule Rapperswil % -\section{FM und Besselfunktion +\section{FM und Bessel-Funktion \label{fm:section:proof}} \rhead{Herleitung} -Die momentane Trägerkreisfrequenz \(\omega_i\) wie schon in (ref) beschrieben ist, bringt die Vorigen Kapittel beschreiben. (Ableitung \(\frac{d \varphi(t)}{dt}\) mit sich). -Diese wiederum kann durch \(\beta\sin(\omega_mt)\) ausgedrückt werden, wobei es das Modulierende Signal \(m(t)\) ist. +Die momentane Trägerkreisfrequenz \(\omega_i\), wie schon in (ref) beschrieben ist, bringt die Ableitung \(\frac{d \varphi(t)}{dt}\) mit sich. +Diese wiederum kann durch \(\beta\sin(\omega_mt)\) ausgedrückt werden, wobei es das modulierende Signal \(m(t)\) ist. Somit haben wir unser \(x_c\) welches \[ \cos(\omega_c t+\beta\sin(\omega_mt)) @@ -15,7 +15,7 @@ Somit haben wir unser \(x_c\) welches ist. \subsection{Herleitung} -Das Ziel ist es unser moduliertes Signal mit der Besselfunktion so auszudrücken: +Das Ziel ist, unser moduliertes Signal mit der Bessel-Funktion so auszudrücken: \begin{align} x_c(t) = @@ -43,22 +43,22 @@ Doch dazu brauchen wir die Hilfe der Additionsthoerme \cos(A-B)-\cos(A+B) \label{fm:eq:addth3} \end{align} -und die drei Besselfunktions indentitäten, +und die drei Bessel-Funktionsindentitäten, \begin{align} \cos(\beta\sin\phi) &= - J_0(\beta) + 2\sum_{k=1}^\infty(-1)^k \cdot J_{2k}(\beta) \cos(2k\phi) + J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos(2k\phi) \label{fm:eq:besselid1} \\ \sin(\beta\sin\phi) &= - 2\sum_{k=0}^\infty (-1)^k J_{2k+1}(\beta) \cos((2k+1)\phi) + 2\sum_{k=0}^\infty J_{2k+1}(\beta) \cos((2k+1)\phi) \label{fm:eq:besselid2} \\ J_{-n}(\beta) &= (-1)^n J_n(\beta) \label{fm:eq:besselid3} \end{align} -welche man im Kapitel \eqref{buch:fourier:eqn:expinphireal}, \eqref{buch:fourier:eqn:expinphiimaginary}, \eqref{buch:fourier:eqn:symetrie}. +welche man im Kapitel \eqref{buch:fourier:eqn:expinphireal}, \eqref{buch:fourier:eqn:expinphiimaginary}, \eqref{buch:fourier:eqn:symetrie} findet. \subsubsection{Anwenden des Additionstheorem} Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal @@ -70,70 +70,102 @@ Mit dem \eqref{fm:eq:addth1} wird aus dem modulierten Signal \cos(\omega_c t)\cos(\beta\sin(\omega_m t))-\sin(\omega_ct)\sin(\beta\sin(\omega_m t)). \label{fm:eq:start} \] - +%----------------------------------------------------------------------------------------------------------- \subsubsection{Cos-Teil} Zu beginn wird der Cos-Teil -\[ +\begin{align*} + c(t) + &= \cos(\omega_c t)\cdot\cos(\beta\sin(\omega_mt)) -\] +\end{align*} mit hilfe der Besselindentität \eqref{fm:eq:besselid1} zum \begin{align*} - \cos(\omega_c t) \cdot \bigg[ J_0(\beta) + 2\sum_{k=1}^\infty(-1)^k \cdot J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] + c(t) &= - (-1)^k \cdot \sum_{k=1}^\infty J_{2k}(\beta) \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem}} + \cos(\omega_c t) \cdot \bigg[ J_0(\beta) + 2\sum_{k=1}^\infty J_{2k}(\beta) \cos( 2k \omega_m t)\, \bigg] + \\ + &= + J_0(\beta) \cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \underbrace{2\cos(\omega_c t)\cos(2k\omega_m t)}_{\text{Additionstheorem \eqref{fm:eq:addth2}}} \end{align*} -wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) zum +%intertext{} Funktioniert nicht. +wobei mit dem Additionstheorem \eqref{fm:eq:addth2} \(A = \omega_c t\) und \(B = 2k\omega_m t \) ersetzt wurden. \begin{align*} - J_0(\beta) \cdot \cos(\omega_c t) +(-1)^k \cdot \sum_{k=1}^\infty J_{2k}(\beta) \{ \underbrace{\cos((\omega_c - 2k \omega_m) t)} \,+\, \cos((\omega_c + 2k \omega_m) t) \} + c(t) + &= + J_0(\beta) \cdot \cos(\omega_c t) + \sum_{k=1}^\infty J_{2k}(\beta) \{ \underbrace{\cos((\omega_c - 2k \omega_m) t)} \,+\, \cos((\omega_c + 2k \omega_m) t) \} \\ - = - (-1)^k \cdot \sum_{k=-\infty}^{-1} J_{2k}(\beta) \overbrace{\cos((\omega_c +2k \omega_m) t)} + &= + \sum_{k=-\infty}^{-1} J_{2k}(\beta) \overbrace{\cos((\omega_c +2k \omega_m) t)} \,+\,J_0(\beta)\cdot \cos(\omega_c t+ 2\cdot0 \omega_m) - \,+\, (-1)^k \cdot\sum_{k=1}^\infty J_{2k}(\beta)\cos((\omega_c + 2k \omega_m) t) + \,+\, \sum_{k=1}^\infty J_{2k}(\beta)\cos((\omega_c + 2k \omega_m) t) \end{align*} - -Wenn dabei \(2k\) durch alle geraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert erhält man den vereinfachten Term -\[ - \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n\omega_m) t), +wird. +Das Minus im Ersten Term wird zur negativen Summe \(\sum_{-\infty}^{-1}\) ersetzt. +Da \(2k\) immer gerade ist, wird es durch alle negativen und positiven Ganzzahlen \(n\) ersetzt: +\begin{align*} + \sum_{n\, \text{gerade}} J_{n}(\beta) \cos((\omega_c + n \omega_m) t), \label{fm:eq:gerade} -\] -dabei gehen nun die Terme von \(-\infty \to \infty\), dabei bleibt n Ganzzahlig. - +\end{align*} +%---------------------------------------------------------------------------------------------------------------- \subsubsection{Sin-Teil} Nun zum zweiten Teil des Term \eqref{fm:eq:start}, den Sin-Teil -\[ +\begin{align*} + s(t) + &= -\sin(\omega_c t)\cdot\sin(\beta\sin(\omega_m t)). -\] +\end{align*} Dieser wird mit der \eqref{fm:eq:besselid2} Besselindentität zu \begin{align*} - -\sin(\omega_c t) \cdot \bigg[ 2 \sum_{k=0}^\infty(-1)^k \cdot J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] + s(t) + &= + -\sin(\omega_c t) \cdot \bigg[ 2 \sum_{k=0}^\infty J_{ 2k + 1}(\beta) \cos(( 2k + 1) \omega_m t) \bigg] \\ - = - (-1)^k \cdot -\sum_{k=0}^\infty J_{2k+1}(\beta) \underbrace{2\sin(\omega_c t)\cos((2k+1)\omega_m t)}_{\text{Additionstheorem}}. + &= + \sum_{k=0}^\infty -1 \cdot J_{2k+1}(\beta) 2\sin(\omega_c t)\cos((2k+1)\omega_m t). +\end{align*} +Da \(2k + 1\) alle ungeraden positiven Ganzzahlen entspricht wird es durch \(n\) ersetzt. +Wird die Besselindentität \eqref{fm:eq:besselid3} gebraucht, so ersetzten wird \(J_{-n}(\beta) = -1\cdot J_n(\beta)\) ersetzt: +\begin{align*} + s(t) + &= + \sum_{n=0}^\infty J_{-n}(\beta) \underbrace{2\sin(\omega_c t)\cos(n \omega_m t)}_{\text{Additionstheorem \eqref{fm:eq:addth3}}}. \end{align*} -Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = (2k+1)\omega_m t \), -somit wird daraus +Auch hier wird ein Additionstheorem \eqref{fm:eq:addth3} gebraucht, dabei ist \(A = \omega_c t\) und \(B = n \omega_m t \), +somit wird daraus: \begin{align*} - (-1)^k \cdot -\sum_{k=0}^\infty J_{2k+1}(\beta) \{ \underbrace{\cos((\omega_c - (2k+1)\omega_m) t)} \,-\, \cos((\omega_c+(2k+1)\omega_m) t) \} + s(t) + &= + \sum_{n=0}^\infty J_{-n}(\beta) \{ \underbrace{\cos((\omega_c - n\omega_m) t)} \,-\, \cos((\omega_c + n\omega_m) t) \} \\ - = - (-1)^k \cdot -\sum_{k=- \infty}^{-1} J_{2k+1}(\beta) \overbrace{\cos((\omega_c + (2k+1)\omega_m) t)} - \,-\, (-1)^k \cdot -\sum_{k=0}^\infty J_{2k+1}(\beta) \cos((\omega_c + (2k+1)\omega_m) t) + &= + \sum_{n=- \infty}^{0} J_{n}(\beta) \overbrace{\cos((\omega_c + n \omega_m) t)} + \,-\, \sum_{n=0}^\infty J_{-n}(\beta) \cos((\omega_c + n\omega_m) t) \end{align*} -dieser Term. -Zusätzlich dabei noch die letzte Besselindentität \eqref{fm:eq:besselid3} brauchen, ist bei allen ungeraden negativen \(n : J_{-n}(\beta) = -1\cdot J_n(\beta)\). -Somit wird neg.Teil zum Term -\[ - (-1)^k \cdot \sum_{k= \infty}^{1} -1 \cdot J_{2k+1}(\beta) \cos((\omega_c+(2k+1)\omega_m) t). -\] -TODO (jetzt habe ich zwei Summen die immer positiv sind? ) -Wenn dabei \(2k +1\) durch alle ungeraden Zahlen von \(-\infty \to \infty\) mit \(n\) substituiert vereinfacht sich die Summe zu +Auch hier wurde wieder eine zweite Summe \(\sum_{-\infty}^{-1}\) gebraucht um das Minus zu einem Plus zu wandeln. +Wenn \(n = 0 \) ist der Minuend gleich dem Subtrahend und somit dieser Teil \(=0\), das bedeutet \(n\) ended bei \(-1\) und started bei \(1\). +\begin{align*} + s(t) + &= + \sum_{n=- \infty}^{-1} J_{n}(\beta) \cos((\omega_c + n \omega_m) t) + \underbrace{\,-\, \sum_{n=1}^\infty J_{-n}(\beta)} \cos((\omega_c + n\omega_m) t) +\end{align*} +Um aus diesem Subtrahend eine Addition zu kreiernen, wird die Besselindentität \eqref{fm:eq:besselid3} gebraucht, +jedoch so \(-1 \cdot J_{-n}(\beta) = J_n(\beta)\) und daraus wird dann: +\begin{align*} + s(t) + &= + \sum_{n=- \infty}^{-1} J_{n}(\beta) \cos((\omega_c + n \omega_m) t) + \,+\, \sum_{n=1}^\infty J_{n}(\beta) \cos((\omega_c + n\omega_m) t) +\end{align*} +Da \(n\) immer ungerade ist und \(0\) nicht zu den ungeraden zahlen zählt, kann man dies so vereinfacht \[ - \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). - \label{fm:eq:ungerade} + s(t) + = + \sum_{n\, \text{ungerade}} -1 \cdot J_{n}(\beta) \cos((\omega_c + n\omega_m) t). + \label{fm:eq:ungerade} \] -Substituiert man nun noch \(n \text{mit} -n \) so fällt das \(-1\) weg. - +schreiben. +%------------------------------------------------------------------------------------------ \subsubsection{Summe Zusammenführen} Beide Teile \eqref{fm:eq:gerade} Gerade \[ @@ -151,10 +183,9 @@ ergeben zusammen \] Somit ist \eqref{fm:eq:proof} bewiesen. \newpage - -%---------------------------------------------------------------------------- +%----------------------------------------------------------------------------------------- \subsection{Bessel und Frequenzspektrum} -Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Besselfunktion \(J_{k}(\beta)\) in geplottet. +Um sich das ganze noch einwenig Bildlicher vorzustellenhier einmal die Bessel-Funktion \(J_{k}(\beta)\) in geplottet. \begin{figure} \centering \input{papers/fm/Python animation/bessel.pgf} @@ -168,7 +199,7 @@ Nun einmal das Modulierte FM signal im Frequenzspektrum mit den einzelen Summen TODO Hier wird beschrieben wie die Bessel Funktion der FM im Frequenzspektrum hilft, wieso diese gebrauch wird und ihre Vorteile. \begin{itemize} - \item Zuerest einmal die Herleitung von FM zu der Besselfunktion + \item Zuerest einmal die Herleitung von FM zu der Bessel-Funktion \item Im Frequenzspektrum darstellen mit Farben, ersichtlich machen. \item Parameter tuing der Trägerfrequenz, Modulierende frequenz und Beta. \end{itemize} -- cgit v1.2.1 From ded30e493c1b05f1f412f2e78636d7195ea054e0 Mon Sep 17 00:00:00 2001 From: Kuster Yanik Date: Thu, 4 Aug 2022 21:24:11 +0200 Subject: added new subsection wird das Ziel erreicht? --- buch/papers/lambertw/Bilder/Intuition.pdf | Bin 186972 -> 187016 bytes buch/papers/lambertw/Bilder/Strategie.py | 4 +- .../Bilder/lambertAbstandBauchgef\303\274hl.py" | 10 +- buch/papers/lambertw/teil0.tex | 5 +- buch/papers/lambertw/teil1.tex | 101 +++++++++++++++++---- 5 files changed, 93 insertions(+), 27 deletions(-) (limited to 'buch') diff --git a/buch/papers/lambertw/Bilder/Intuition.pdf b/buch/papers/lambertw/Bilder/Intuition.pdf index 236212a..739b02b 100644 Binary files a/buch/papers/lambertw/Bilder/Intuition.pdf and b/buch/papers/lambertw/Bilder/Intuition.pdf differ diff --git a/buch/papers/lambertw/Bilder/Strategie.py b/buch/papers/lambertw/Bilder/Strategie.py index d7d06cb..975e248 100644 --- a/buch/papers/lambertw/Bilder/Strategie.py +++ b/buch/papers/lambertw/Bilder/Strategie.py @@ -34,8 +34,8 @@ ax.quiver(X, Y, U, W, angles='xy', scale_units='xy', scale=1, headwidth=5, headl ax.plot([V[0], (VZ+V)[0]], [V[1], (VZ+V)[1]], 'k--') ax.plot(np.vstack([V, Z])[:, 0], np.vstack([V, Z])[:,1], 'bo', markersize=10) -ax.set_xlabel("x") -ax.set_ylabel("y") +ax.set_xlabel("x", size=20) +ax.set_ylabel("y", size=20) ax.text(2.5, 4.5, "Visierlinie", size=20, rotation=10) diff --git "a/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" "b/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" index 9031bfc..3a90afa 100644 --- "a/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" +++ "b/buch/papers/lambertw/Bilder/lambertAbstandBauchgef\303\274hl.py" @@ -39,8 +39,8 @@ plt.plot(0, ymin, 'bo', markersize=10) plt.plot([0, xmin], [ymin, ymin], 'k--') #plt.xlim(-0.1, 1) #plt.ylim(1, 2) -#plt.ylabel("y") -#plt.xlabel("x") +plt.ylabel("y") +plt.xlabel("x") plt.grid(True) plt.quiver(xmin, ymin, -0.2, 0, scale=1) @@ -53,6 +53,6 @@ plt.rcParams.update({ "font.serif": ["New Century Schoolbook"], }) -plt.text(xmin-0.11, ymin-0.12, r"$\dot{v}$", size=30) -plt.text(xmin-0.02, ymin+0.05, r"$V$", size=30, c='b') -plt.text(0.02, ymin+0.05, r"$Z$", size=30, c='b') \ No newline at end of file +plt.text(xmin-0.11, ymin-0.08, r"$\dot{v}$", size=20) +plt.text(xmin-0.02, ymin+0.05, r"$V$", size=20, c='b') +plt.text(0.02, ymin+0.05, r"$Z$", size=20, c='b') \ No newline at end of file diff --git a/buch/papers/lambertw/teil0.tex b/buch/papers/lambertw/teil0.tex index 088cb7b..6632eca 100644 --- a/buch/papers/lambertw/teil0.tex +++ b/buch/papers/lambertw/teil0.tex @@ -74,7 +74,7 @@ darstellen. Der Geschwindigkeitsvektor muss auf das Ziel zeigen, woraus folgt z-v \text{.} \end{equation} -Um den Richtungsvektor zu konstruieren kann der Einheitsvektor parallel zu $z-v$ um $\dot{v}$ gestreckt werden, was zu +Um den Richtungsvektor zu konstruieren kann der Einheitsvektor parallel zu $z-v$ um $|\dot{v}|$ gestreckt werden, was zu \begin{equation} \dot{v} = @@ -86,6 +86,7 @@ führt. Dies kann noch ausgeschrieben werden zu = |\dot{v}|\cdot\frac{z-v}{|z-v|} \text{.} + \label{lambertw:richtungsvektor} \end{equation} % 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. @@ -105,7 +106,7 @@ was algebraisch zu 1 \end{align} umgeformt werden kann. -Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, insofern der Verfolger die Jagdstrategie verwendet. +Die Lösungen dieser Differentialgleichung sind die gesuchten Verfolgungskurven, sofern der Verfolger die Jagdstrategie verwendet. % \subsection{Ziel \label{lambertw:subsection:Ziel}} diff --git a/buch/papers/lambertw/teil1.tex b/buch/papers/lambertw/teil1.tex index 0fd0108..e8eca2c 100644 --- a/buch/papers/lambertw/teil1.tex +++ b/buch/papers/lambertw/teil1.tex @@ -30,7 +30,7 @@ Die Parametrisierung von $z(t)$ ist im Beispiel definiert als \left( \begin{array}{c} 0 \\ t \end{array} \right)\text{.} \end{equation} % -Die Parametrisierung von $v(t)$ ist von den Startbedingungen abhängig. Deshalb wird \eqref{bedingung_treffer} jeweils für die unterschiedlichen Startbedingungen separat analysiert. +Die Parametrisierung von $v(t)$ ist von den Startbedingungen abhängig. Deshalb wird die Bedingung \eqref{bedingung_treffer} jeweils für die unterschiedlichen Startbedingungen separat analysiert. % \subsection{Anfangsbedingung im ersten Quadranten} % @@ -41,7 +41,7 @@ Wenn der Verfolger im ersten Quadranten startet, dann kann $v(t)$ mit den Gleich x_0\cdot\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right) \right)} \\ y(t) &= - \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\\ + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(y_0-r_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\\ \chi &= \frac{r_0+y_0}{r_0-y_0}, \quad @@ -54,7 +54,7 @@ Wenn der Verfolger im ersten Quadranten startet, dann kann $v(t)$ mit den Gleich \text{.} \end{align} % -Der Folger ist durch +Der Verfolger ist durch \begin{equation} v(t) = @@ -76,31 +76,37 @@ Daher wird das Problem in zwei einzelne Teilprobleme zerlegt, wodurch die Beding &= y(t) = - \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(r_0-y_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\text{,} + \frac{1}{4}\left(\left(y_0+r_0\right)\left(\frac{x(t)}{x_0}\right)^2+\left(y_0-r_0\right)\operatorname{ln}\left(\left(\frac{x(t)}{x_0}\right)^2\right)-r_0+3y_0\right)\text{,} \end{align} % -welche Beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. +welche beide gleichzeitig erfüllt sein müssen, damit das Ziel erreicht wurde. Zuerst wird die Bedingung der $x$-Koordinate betrachtet. -Da $x_0 \neq 0$ und $\chi \neq 0$ mit +Da $x_0 \neq 0$ und $\chi \neq 0$ kann \begin{equation} 0 = x_0\sqrt{\frac{1}{\chi}W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right)\right)} \end{equation} -ist diese Bedingung genau dann erfüllt, wenn +algebraisch zu \begin{equation} 0 = W\left(\chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right)\right) - \text{.} \end{equation} -% +umgeformt werden. Es ist zu beachten, dass $W(x)$ die Lambert W-Funktion ist, welche im Kapitel \eqref{buch:section:lambertw} behandelt wurde. -Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Da die Lambert W-Funktion genau eine Nullstelle bei -\begin{equation} +Diese Gleichung entspricht genau den Nullstellen der Lambert W-Funktion. Mit der einzigen Nullstelle der Lambert W-Funktion bei +\begin{equation*} W(0)=0 + \text{,} +\end{equation*} +kann die Bedingung weiter vereinfacht werden zu +\begin{equation} + 0 + = + \chi\cdot \exp\left( \chi-\frac{4t}{r_0-y_0}\right) + \text{.} \end{equation} -% Da $\chi\neq0$ und die Exponentialfunktion nie null sein kann, ist diese Bedingung unmöglich zu erfüllen. Beim Grenzwert für $t\rightarrow\infty$ geht die Exponentialfunktion gegen null. Dies nützt nicht viel, da unendlich viel Zeit vergehen müsste, damit ein Einholen möglich wäre. @@ -203,16 +209,18 @@ Durch quadrieren verschwindet die Wurzel des Betrages, womit % \begin{equation} |v-z|^2e_y\cdot v$. +Aus diesem Argument würde folgen, dass beim tiefsten Punkt der Verfolgungskurve im Beispiel den minimalen Abstand befindet. +% \begin{figure} \centering \includegraphics[scale=0.4]{./papers/lambertw/Bilder/Intuition.pdf} @@ -220,7 +228,8 @@ Es lässt sich vermuten, dass bei diesem Punkt der Abstand zum Ziel minimal sein \label{lambertw:grafic:intuition} \end{figure} % -Dies kann leicht überprüft werden, indem wir lokal alle relevanten benachbarten Punkte betrachten und das Vorzeichen der Änderung des Abstandes prüfen. + +Dieses Argument kann leicht überprüft werden, indem lokal alle relevanten benachbarten Punkte betrachtet und das Vorzeichen der Änderung des Abstandes überprüft wird. Dafür wird ein Ausdruck benötigt, der den Abstand und die benachbarten Punkte beschreibt. Der Richtungsvektor wird allgemein mit dem Winkel $\alpha \in[ 0, 2\pi)$ Die Ortsvektoren der Punkte können wiederum mit @@ -280,5 +289,61 @@ unterteilt werden. Von Interesse ist lediglich das Intervall $\alpha\in\left( \frac{\pi}{2}, \frac{3\pi}{2}\right)$, da der Verfolger sich stets in die negative $y$-Richtung bewegt. In diesem Intervall ist die Ableitung negativ, woraus folgt, dass jeglicher unmittelbar benachbarte Punkt, den der Verfolger als nächstes begehen könnte, stets näher am Ziel ist als zuvor. Dies bedeutet, dass der Scheitelpunkt der Verfolgungskurve nie ein lokales Minimum bezüglich des Abstandes sein kann. +% +\subsection{Wo ist der Abstand minimal?} +Damit der Verfolger das Ziel erreicht muss die Bedingung \eqref{lambertw:minimumAbstand} erfüllt sein. +Somit ist es ausreichend zu zeigen, dass +\begin{equation} + \operatorname{min}(|z-v|)