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-rw-r--r--buch/papers/reedsolomon/.gitignor24
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.aux65
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.bbl0
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.log714
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.nav43
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.out5
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.pdfbin53965 -> 135643 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.snm1
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.synctex.gzbin3637 -> 22450 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.tex150
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.toc5
-rw-r--r--buch/papers/reedsolomon/RS presentation/Thumbs.dbbin89088 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig1.pdfbin3071 -> 11898 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig1.pdf_tex81
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig1.pngbin27373 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig2.pdfbin0 -> 13901 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig2.pngbin30489 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig3.pdfbin0 -> 13099 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig3.pngbin16007 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig4.pdfbin0 -> 14995 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig4.pngbin27548 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig5.pdfbin0 -> 13298 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig5.pngbin30167 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig6.pdfbin0 -> 13688 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig6.pngbin22604 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig7.pdfbin0 -> 13278 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/fig7.pngbin28677 -> 0 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom1.aux1
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom1.log747
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom1.pdfbin0 -> 5938 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom1.synctex.gzbin0 -> 2399 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom1.tex59
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom2.aux1
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom2.log747
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom2.pdfbin0 -> 6995 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom2.synctex.gzbin0 -> 2410 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/images/polynom2.tex57
-rw-r--r--buch/papers/reedsolomon/experiments/f.m61
-rw-r--r--buch/papers/spannung/main.tex2
39 files changed, 2397 insertions, 366 deletions
diff --git a/buch/papers/reedsolomon/.gitignor b/buch/papers/reedsolomon/.gitignor
new file mode 100644
index 0000000..52a02ac
--- /dev/null
+++ b/buch/papers/reedsolomon/.gitignor
@@ -0,0 +1,24 @@
+RS.aux
+RS.bbl
+RS.bib
+RS.blg
+RS.idx
+RS.ilg
+RS.ind
+RS.log
+RS.out
+RS.pdf
+RS.run.xml
+RS.toc
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+.*.lb
diff --git a/buch/papers/reedsolomon/RS presentation/RS.aux b/buch/papers/reedsolomon/RS presentation/RS.aux
index 17ce46b..005172f 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.aux
+++ b/buch/papers/reedsolomon/RS presentation/RS.aux
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.bbl b/buch/papers/reedsolomon/RS presentation/RS.bbl
deleted file mode 100644
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.log b/buch/papers/reedsolomon/RS presentation/RS.log
index f7dc931..4e1c806 100644
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.nav b/buch/papers/reedsolomon/RS presentation/RS.nav
index 9033d8b..1d67391 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.nav
+++ b/buch/papers/reedsolomon/RS presentation/RS.nav
@@ -1,9 +1,40 @@
\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}
\headcommand {\beamer@framepages {1}{1}}
-\headcommand {\slideentry {0}{0}{2}{2/2}{}{0}}
+\headcommand {\beamer@sectionpages {1}{1}}
+\headcommand {\beamer@subsectionpages {1}{1}}
+\headcommand {\sectionentry {1}{Einführung}{2}{Einführung}{0}}
+\headcommand {\slideentry {1}{0}{1}{2/2}{}{0}}
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-\headcommand {\beamer@partpages {1}{2}}
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-\headcommand {\gdef \inserttotalframenumber {2}}
+\headcommand {\beamer@sectionpages {2}{2}}
+\headcommand {\beamer@subsectionpages {2}{2}}
+\headcommand {\sectionentry {2}{Polynom Ansatz}{3}{Polynom Ansatz}{0}}
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+\headcommand {\beamer@subsectionpages {3}{6}}
+\headcommand {\sectionentry {3}{Fourier Transformation}{7}{Fourier Transformation}{0}}
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+\headcommand {\beamer@subsectionpages {7}{14}}
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.out b/buch/papers/reedsolomon/RS presentation/RS.out
index e69de29..32b9a2c 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.out
+++ b/buch/papers/reedsolomon/RS presentation/RS.out
@@ -0,0 +1,5 @@
+\BOOKMARK [2][]{Outline0.1}{Einführung}{}% 1
+\BOOKMARK [2][]{Outline0.2}{Polynom\040Ansatz}{}% 2
+\BOOKMARK [2][]{Outline0.3}{Fourier\040Transformation}{}% 3
+\BOOKMARK [2][]{Outline0.4}{Diskrete\040Fourier\040Transformation}{}% 4
+\BOOKMARK [2][]{Outline0.5}{Probleme\040und\040Fragen}{}% 5
diff --git a/buch/papers/reedsolomon/RS presentation/RS.pdf b/buch/papers/reedsolomon/RS presentation/RS.pdf
index 459d7e8..913bc42 100644
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index e69de29..6607ea8 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.snm
+++ b/buch/papers/reedsolomon/RS presentation/RS.snm
@@ -0,0 +1 @@
+\beamer@slide {ft_discrete}{15}
diff --git a/buch/papers/reedsolomon/RS presentation/RS.synctex.gz b/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
index fe8adf5..001b5c8 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
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diff --git a/buch/papers/reedsolomon/RS presentation/RS.tex b/buch/papers/reedsolomon/RS presentation/RS.tex
index 400e654..eecd66b 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.tex
+++ b/buch/papers/reedsolomon/RS presentation/RS.tex
@@ -3,7 +3,9 @@
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[ngerman]{babel}
+\usepackage{tikz}
\usetheme{Hannover}
+
\begin{document}
\author{Joshua Bär und Michael Steiner}
\title{Reed-Solomon-Code}
@@ -17,13 +19,152 @@
\begin{frame}[plain]
\maketitle
\end{frame}
-%-------------------------------------------------------------------------------
+ \section{Einführung}
+ \begin{frame}
+ \frametitle{Einführung}
+ \begin{itemize}
+ \item Reed-Solomon-Code beschäftigt sich mit der Übertragung von Daten
+ und deren Fehler Erkennung.
+ \end{itemize}
+ \end{frame}
+\section{Polynom Ansatz}
\begin{frame}
- \frametitle{Test}
- Ich mag Züge.
+ Beispiel 2, 1, 5 Versenden und auf 2 Fehler absichern.
+ \end{frame}
+ \begin{frame}
+ Übertragen von
+ ${f}_2=$\textcolor{blue}{2}, ${f}_1$\textcolor{blue}{1}, ${f}_0$\textcolor{blue}{5}
+ als $ p(w) = \textcolor{blue}{2}w^2 + \textcolor{blue}{1}w + \textcolor{blue}{5} $.
+
+ \only<1>{
+ Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
+ \textcolor{green}{15}, \textcolor{green}{26},
+ \textcolor{green}{ 41}, \textcolor{green}{60},
+ \textcolor{green}{83}, \textcolor{green}{110})$
+ \includegraphics[scale = 1.2]{images/polynom1.pdf}}
+ \only<2>{
+ Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
+ \textcolor{red}{50}, \textcolor{red}{37},
+ \textcolor{green}{ 41}, \textcolor{green}{60},
+ \textcolor{green}{83}, \textcolor{green}{110})$
+ \includegraphics[scale = 1.2]{images/polynom2.pdf}
+ \textcolor{green}{7} Zahlen versenden, um \textcolor{blue}{3} Zahlen gegen \textcolor{red}{2} Fehlern abzusichern.}
\end{frame}
\begin{frame}
+ \frametitle{Parameter}
+ \begin{center}
+ \begin{tabular}{ c c c }
+ \hline
+ "Nutzlast" & Fehler & Versenden \\
+ \hline
+ 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\
+ 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\
+ 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\
+ &&\\
+ k & t & k+2t Werte eines Polynoms vom Grad k-1 \\
+ \hline
+ &&\\
+ &&\\
+ &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 Idee mit Fourier Transformieren und dann senden.
+ \item Danach Empfangen und 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}
+ Die Diskrete Fourier Transformation ist so gegeben:
+ \[
+ \label{ft_discrete}
+ \hat{c}_{k}
+ = \frac{1}{N} \sum_{n=0}^{N-1}
+ {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn}
+ \].
+
+ \[
+ w = e^{-\frac{2\pi j}{N} k}
+ \]
+ 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{frame}
+
+
+ \begin{frame}
+ \frametitle{Diskrete Fourier Transformation}
+ \[
+ \begin{pmatrix}
+ \hat{c}_1 \\\hat{c}_2 \\\hat{c}_3 \\ \vdots \\\hat{c}_n
+ \end{pmatrix}
+ =
+ \begin{pmatrix}
+ w^0 & w^0 & w^0 & \dots &w^0 \\
+ w^0 & w^1 &w^2 & \dots &w^N \\
+ w^0 & w^2 &w^4 & \dots &w^{2N} \\
+ \vdots & \vdots &\vdots &\ddots &\vdots \\
+ w^0 & w^{1(N-1)}&w^{2(N-1)}& \dots &w^{(N-1)(N-1)} \\
+ \end{pmatrix}
+ \begin{pmatrix}
+ \textcolor{blue}{f_0} \\
+ \textcolor{blue}{f_1} \\
+ \textcolor{blue}{f_2} \\
+ \vdots \\
+ 0 \\
+ \end{pmatrix}
+ \]
+ \end{frame}
+
+\section{Probleme und Fragen}
+ \begin{frame}
+ \frametitle{Probleme und Fragen}
+
+ Wie wird der Fehler lokalisiert?
+ \only<2>{
+ \newline
+ Indem in einem Endlichen Körper gerechnet wird.
+ }
+ \end{frame}
+
+ \begin{frame}
\frametitle{Reed-Solomon in Endlichen Körpern}
\begin{itemize}
@@ -728,4 +869,5 @@
\end{frame}
%-------------------------------------------------------------------------------
-\end{document} \ No newline at end of file
+
+\end{document}
diff --git a/buch/papers/reedsolomon/RS presentation/RS.toc b/buch/papers/reedsolomon/RS presentation/RS.toc
index 4cd1c86..44c06ab 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.toc
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@@ -1 +1,6 @@
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+\beamer@sectionintoc {2}{Polynom Ansatz}{3}{0}{2}
+\beamer@sectionintoc {3}{Fourier Transformation}{7}{0}{3}
+\beamer@sectionintoc {4}{Diskrete Fourier Transformation}{15}{0}{4}
+\beamer@sectionintoc {5}{Probleme und Fragen}{17}{0}{5}
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diff --git a/buch/papers/reedsolomon/RS presentation/images/polynom1.tex b/buch/papers/reedsolomon/RS presentation/images/polynom1.tex
new file mode 100644
index 0000000..db83daa
--- /dev/null
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+% polynome1
+%-------------------
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
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+\usepackage{pgfplots}
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+\usetikzlibrary{arrows,intersections,math}
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+\begin{document}
+ %Übertragen von den Zahlen
+ %\textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5}
+ %als $ p(x) = \textcolor{blue}{2}x^2 + \textcolor{blue}{1}x + \textcolor{blue}{5} $.\newline
+ %Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
+ % \textcolor{green}{15}, \textcolor{green}{26},
+ % \textcolor{green}{ 41}, \textcolor{green}{60},
+ % \textcolor{green}{83}, \textcolor{green}{110})$
+
+
+\begin{tikzpicture}[>=latex,thick]
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+\draw[color=blue, line width=1.4pt]
+plot[domain=0:8, samples=100]
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+ \fill[color=green] #1 circle[radius=0.08];
+ \draw #1 circle[radius=0.07];
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+%\draw[color=gray,line width=1pt,dashed]
+%plot[domain=0.5:7, samples=100]
+%({\x},{(0.1958*\x^2-1.2875*\x+3.0417)});
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+
+
+
+\end{tikzpicture}
+\end{document}
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diff --git a/buch/papers/reedsolomon/RS presentation/images/polynom2.pdf b/buch/papers/reedsolomon/RS presentation/images/polynom2.pdf
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diff --git a/buch/papers/reedsolomon/RS presentation/images/polynom2.tex b/buch/papers/reedsolomon/RS presentation/images/polynom2.tex
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@@ -0,0 +1,57 @@
+% polynome2
+%-------------------
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\newcommand{\teiler}{40}
+\begin{document}
+ %Übertragen von den Zahlen
+ %\textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5}
+ %als $ p(x) = \textcolor{blue}{2}x^2 + \textcolor{blue}{1}x + \textcolor{blue}{5} $.\newline
+ %Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
+ % \textcolor{green}{15}, \textcolor{green}{26},
+ % \textcolor{green}{ 41}, \textcolor{green}{60},
+ % \textcolor{green}{83}, \textcolor{green}{110})$
+
+
+ \begin{tikzpicture}[>=latex,thick]
+
+ \draw[color=blue, line width=1.4pt]
+ plot[domain=0:8, samples=100]
+ ({\x},{(2*\x^2+1*\x+5)/\teiler});
+ \draw[->] (-0.2,0) -- (8,0) coordinate[label={$x$}];
+ \draw[->] (0,-0.2) -- (0,150/\teiler) coordinate[label={right:$p(x)$}];
+ \def\punkt#1{
+ \fill[color=green] #1 circle[radius=0.08];
+ \draw #1 circle[radius=0.07];
+ }
+ \punkt{(1,8/\teiler)}
+ %\punkt{(2,15/\teiler)}
+ %\punkt{(3,26/\teiler)}
+ \punkt{(4,41/\teiler)}
+ \punkt{(5,60/\teiler)}
+ \punkt{(6,83/\teiler)}
+ \punkt{(7,110/\teiler)}
+ \draw[color=gray,line width=1pt,dashed]
+ plot[domain=0.5:7, samples=100]
+ ({\x},{(0.1958*\x^2-1.2875*\x+3.0417)});
+ \def\erpunkt#1{
+ \fill[color=red] #1 circle[radius=0.08];
+ \draw #1 circle[radius=0.07];
+ }
+ \erpunkt{(2,50/\teiler)}
+ \erpunkt{(3,0.9414)}
+
+
+ \draw(0,100/\teiler) -- (-0.1,100/\teiler) coordinate[label={left:$100$}];
+ \draw(1,0) -- (1,-0.1) coordinate[label={below:$1$}];
+
+
+
+
+ \end{tikzpicture}
+\end{document}
diff --git a/buch/papers/reedsolomon/experiments/f.m b/buch/papers/reedsolomon/experiments/f.m
new file mode 100644
index 0000000..6bdc741
--- /dev/null
+++ b/buch/papers/reedsolomon/experiments/f.m
@@ -0,0 +1,61 @@
+#
+# f.m -- Reed-Solomon-Visualisierung mit FFT
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+N = 64;
+b = 32;
+l = N + b;
+
+signal = zeros(l,1);
+signal(1:N,1) = round(10 * rand(N,1));
+signal
+
+plot(abs(signal));
+xlim([1, l]);
+title("Signal");
+pause()
+
+codiert = fft(signal)
+
+plot(abs(codiert));
+xlim([1, l]);
+title("Codiert");
+pause()
+
+fehler = zeros(l,1);
+fehler(21,1) = 2;
+fehler(75,1) = 1;
+fehler(7,1) = 2;
+
+plot(fehler);
+xlim([1, l]);
+title("Fehler");
+pause()
+
+empfangen = codiert + fehler;
+
+plot(abs(empfangen));
+xlim([1, l]);
+title("Empfangen");
+pause()
+
+decodiert = ifft(empfangen)
+plot(abs(decodiert));
+xlim([1, l]);
+title("Decodiert");
+pause()
+
+syndrom = decodiert;
+syndrom(1:N,1) = zeros(N,1)
+plot(abs(syndrom));
+xlim([1, l]);
+title("Syndrom");
+pause()
+
+locator = abs(fft(syndrom))
+
+plot(locator);
+xlim([1, l]);
+title("Locator");
+pause()
diff --git a/buch/papers/spannung/main.tex b/buch/papers/spannung/main.tex
index b87a4d0..585a423 100644
--- a/buch/papers/spannung/main.tex
+++ b/buch/papers/spannung/main.tex
@@ -6,7 +6,7 @@
\chapter{Thema\label{chapter:spannung}}
\lhead{Thema}
\begin{refsection}
-\chapterauthor{Hans Muster}
+\chapterauthor{Adrian Schuler und Thomas Reichlin}
Ein paar Hinweise für die korrekte Formatierung des Textes
\begin{itemize}