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\documentclass[11pt]{scrartcl}
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\usepackage[utf8]{inputenc}
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\usepackage[ngerman]{babel}
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\usepackage{amsmath}
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%\usepackage{amssymb}
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\usepackage{multicol}
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%\usepackage{booktabs}
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%\usepackage{pstricks}
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%\usepackage{pst-node}
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\usepackage{listings}
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\lstset{
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language=Java,
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basicstyle=\ttfamily,
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keywordstyle=\color{red},
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commentstyle=\color{blue},
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stringstyle=\color{darkgreen},
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backgroundcolor=\color{lightgray},
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morecomment=[s][\color{blue}]{/*}{*/},
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emphstyle=\textbf,
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frame=single,
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showstringspaces=true,
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breaklines=true,
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numberstyle=\textcolor{grey},
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numbers=left,
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morekeywords={Merge,ExtractMinimum,Union,NIL,return,and},
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tabsize=4,
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captionpos=b
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}
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\usepackage[paper=a4paper,left=30mm,right=20mm,top=20mm,bottom =25mm]{geometry}
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\usepackage[
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pdftitle={Uebungsblatt 1: Priority Queues - AlgoDS2},
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pdfsubject={Algorithmen und Datenstrukturen 2; Uebungsblatt 1: Priority Queues},
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pdfauthor={Thomas Battermann},
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pdfkeywords={Uebungsblatt 1: Priority Queues - AlgoDS2},
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pdfborder={0 0 0}
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]{hyperref}
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\usepackage{tabularx}
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\usepackage{graphicx}
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\usepackage[usenames,dvipsnames]{color}
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\definecolor{grey}{rgb}{0.5,0.5,0.5}
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\definecolor{lightgray}{rgb}{0.9,0.9,0.9}
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\definecolor{darkgreen}{rgb}{0.0,0.4,0.0}
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\usepackage{lastpage}
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\usepackage{fancyhdr}
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\setlength{\parindent}{0ex}
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\setlength{\parskip}{2ex}
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\setcounter{secnumdepth}{4}
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\setcounter{tocdepth}{4}
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\definecolor{darkgreen}{rgb}{0,0.5,0}
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\definecolor{darkblue}{rgb}{0,0,0.5}
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\pagestyle{fancy} %eigener Seitenstil
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\fancyhf{} %alle Kopf- und Fußzeilenfelder bereinigen
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\fancyhead[L]{Übungsblatt 1\\Priority Queues} %Kopfzeile links
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\fancyhead[C]{} %zentrierte Kopfzeile
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\fancyhead[R]{\textsc{Algorithmen \& Datenstrukturen 2}\\14. November 2011} %Kopfzeile rechts
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\renewcommand{\headrulewidth}{0.4pt} %obere Trennlinie
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\fancyfoot[C]{Seite \thepage\ von \pageref{LastPage}}
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\renewcommand{\footrulewidth}{0.4pt} %untere Trennlinie
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\newcommand{\spa}{\hspace*{4mm}}
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\newcommand{\defin}{\textcolor{darkgreen}{\textbf{Def.: }}}
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\newcommand{\rrfloor}{\right\rfloor}
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\newcommand{\llfloor}{\left\lfloor}
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\title{Übung Priority Queues -- AlgoDS2}
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\author{Thomas Battermann}
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\date{14. November 2011}
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\begin{document}
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\pagestyle{fancy}
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\section*{Aufgabe 1}
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\addcontentsline{toc}{section}{Aufgabe 1}
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%\includegraphics{bilder/aufgabe_1.eps}
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\begin{lstlisting}[frame=single]
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Merge(H1,H2):
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head = NIL
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l1 = head(H1)
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l2 = head(H2)
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while ( l1 != NIL and l2 != NIL ) do
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if ( degree(l1) < degree(l2) ) then
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y = l1
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h = sibling(l1)
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else
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y = l2
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l2 = sibling(l2)
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if ( head == NIL ) then
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head = y
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x = y
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if ( l1 != NIL ) then
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if ( head == NIL ) then
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head = l1
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else
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sibling(x) = h
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if ( l2 != NIL ) then
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if ( head != NIL ) then
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head = l2
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else
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sibling(x) = l2
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return head;
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\end{lstlisting}
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\newpage
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\section*{Aufgabe 2}
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\addcontentsline{toc}{section}{Aufgabe 2}
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\begin{lstlisting}[frame=single]
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ExtractMinimum(H):
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x = head(H)
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prev_x = NIL
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min = x
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prev_min = NIL
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if ( x == NIL ) then
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return NIL
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prev_x = x
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x = sibling(x)
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while ( x != NIL ) do
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if ( key(x) < key(min) ) then
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min = x
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prev_min = prev_x
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prev_x = x
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x = sibling(x)
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if ( prev_min != NIL ) then
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sibling(prev_min) = sibling(min)
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else
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head = sibling(min)
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if ( child(min) != NIL ) then
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H2 = InvertChildren(min)
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Union(head,H2)
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sibling(min) = NIL
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parent(min) = NIL
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child(min) = NIL
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return min;
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\end{lstlisting}
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\section*{Aufgabe 3}
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\addcontentsline{toc}{section}{Aufgabe 3}
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Leider keine Lösung vorhanden :-(
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\end{document}
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@ -0,0 +1,159 @@
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\documentclass[11pt]{scrartcl}
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\usepackage[utf8]{inputenc}
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\usepackage[ngerman]{babel}
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\usepackage{ulem} % \sout
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\usepackage{marvosym} % \Lightning
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\usepackage{mathtools}
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\usepackage{multicol}
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\usepackage[paper=a4paper,left=30mm,right=20mm,top=20mm,bottom =25mm]{geometry}
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\usepackage[
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pdftitle={Uebungsblatt 2: Hashing - AlgoDS2},
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pdfsubject={Algorithmen und Datenstrukturen 2; Uebungsblatt 2: Hashing},
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pdfauthor={Thomas Battermann},
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pdfkeywords={Uebungsblatt 2: Hashing - AlgoDS2},
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pdfborder={0 0 0}
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]{hyperref}
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\usepackage{tabularx}
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\usepackage{graphicx}
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\usepackage[usenames,dvipsnames]{color}
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\usepackage{lastpage}
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\usepackage{fancyhdr}
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\setlength{\parindent}{0ex}
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\setlength{\parskip}{2ex}
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\pagestyle{fancy} %eigener Seitenstil
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\fancyhf{} %alle Kopf- und Fußzeilenfelder bereinigen
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\fancyhead[L]{Übungsblatt 2\\Hashing}%Kopfzeile links
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\fancyhead[C]{} %zentrierte Kopfzeile
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\fancyhead[R]{\textsc{Algorithmen \& Datenstrukturen 2}\\1. Dezember 2011} %Kopfzeile rechts
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\renewcommand{\headrulewidth}{0.4pt} %obere Trennlinie
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\fancyfoot[C]{Seite \thepage\ von \pageref{LastPage}}
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\renewcommand{\footrulewidth}{0.4pt} %untere Trennlinie
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\title{Übung Hashing -- AlgoDS2}
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\author{Thomas Battermann}
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\date{1. Dezember 2011}
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\begin{document}
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\pagestyle{fancy}
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\section*{Aufgabe 1}
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\addcontentsline{toc}{section}{Aufgabe 1}
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\subsection*{Mit der Formel}
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\addcontentsline{toc}{subsection}{Mit der Formel}
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\( m = 2^{12} = 4096; \quad A = \frac{\pi-2}{3} \)
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\subsubsection*{a)}
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\addcontentsline{toc}{subsubsection}{a)}
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\begin{align*}
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k &= 1000\\[4mm]
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h &= \left( 1000 * \frac{\pi-2}{3} - \lfloor 1000 * \frac{\pi-2}{3} \rfloor \right) * 4096\\
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&= 2174
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\end{align*}
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\subsubsection*{b)}
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\addcontentsline{toc}{subsubsection}{b)}
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\begin{align*}
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k &= 2500\\[4mm]
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h &= \left( 2500 * \frac{\pi-2}{3} - \lfloor 2500 * \frac{\pi-2}{3} \rfloor \right) * 4096\\
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&= 1340
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\end{align*}
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\subsection*{Mit Ganzzahlarithmetik}
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\addcontentsline{toc}{subsection}{Mit Ganzzahlarithmetik}
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\textbf{Approximation}
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\begin{align*}
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&\left| \frac{S}{2^{16}} - A \right| &\text{ minimal}\\
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&\frac{S}{2^{16}} - A = 0\\
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&S = \lceil A * 2^{16} \rceil = 24939
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\end{align*}
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\subsubsection*{a)}
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\addcontentsline{toc}{subsubsection}{a)}
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\begin{align*}
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k &= 1000\\[4mm]
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r &= s * k \mod 2^{16}\\
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&= 2493900 \mod 65536\\
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&= 35320\\[4mm]
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&\Rightarrow \underbracket{1000\,1001\,1111}\,1000\\
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h(1000) &= 2207 = \lfloor \frac{35320}{2^4} \rfloor
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\end{align*}
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\subsubsection*{b)}
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\addcontentsline{toc}{subsubsection}{b)}
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\begin{align*}
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k &= 2500\\[4mm]
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r &= s * k \mod 2^{16}\\
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&= 62347500 \mod 65536\\
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&= 22764\\[4mm]
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&\Rightarrow \underbracket{0101\,1000\,1110}\,1100\\
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H(2500) &= 1422 = \lfloor \frac{22764}{2^4} \rfloor
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\end{align*}
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\section*{Aufgabe 2}
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\addcontentsline{toc}{section}{Aufgabe 2}
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\subsection*{a)}
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\addcontentsline{toc}{subsection}{a)}
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\includegraphics{bilder/aufgabe_2a.eps}
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\subsection*{b)}
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\addcontentsline{toc}{subsection}{b)}
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\includegraphics{bilder/aufgabe_2b.eps}
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\subsection*{c)}
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\addcontentsline{toc}{subsection}{c)}
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\includegraphics{bilder/aufgabe_2c.eps}
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\begin{align*}
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h(k,i) &= (k+\frac12i+\frac12i^2) \mod 16
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\end{align*}
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\subsection*{d)}
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\addcontentsline{toc}{subsection}{d)}
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\includegraphics{bilder/aufgabe_2d.eps}
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\begin{align*}
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h_1(k) &= k \mod 11\\
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h_2(k) &= 1 + ( k \mod 10 )\\
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h(k,i) &= \Big( h_1(k) + i * h_2(k) \Big) \mod 11
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\end{align*}
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\textbf{Sondierungsfrequenz für k=31}
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\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|c}
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$i$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\\
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\hline
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$h(k,i)$ & 9 & 0 & 2 & 4 & 6 & 8 & 10 & 1 & 3 & 5 & 7
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\end{tabular}
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$<9,0,2,4,6,8,10,1,3,5,7>$
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\section*{Aufgabe 3}
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\addcontentsline{toc}{section}{Aufgabe 3}
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Für alle $ 0 \le j < m $ gilt:\\
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\[ \frac{n-j}{m-j} \le \frac n m \]
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Annahme: Es gibt ein $j$ mit:\\
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\begin{align*}
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\frac{n-j}{m-j} &> \frac n m & | * (m-j) * m \\
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(n-j)*m &> n * (m-j) \\
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\sout{n*m} -j * m &> \sout{n*m} - j * m &| *\frac{1}{-j}\\[4mm]
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m &< n & \text{\huge\color{Red}\Lightning}
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\end{align*}
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\end{document}
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@ -0,0 +1,506 @@
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<?xml version="1.0"?>
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<!DOCTYPE ipe SYSTEM "ipe.dtd">
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<ipe version="70005" creator="Ipe 7.1.1">
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<info created="D:20111224213616" modified="D:20111224213616"/>
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<ipestyle name="basic">
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<symbol name="arrow/arc(spx)">
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<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
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0 0 m
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-1 0.333 l
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-1 -0.333 l
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h
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</path>
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</symbol>
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<symbol name="arrow/farc(spx)">
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<path stroke="sym-stroke" fill="white" pen="sym-pen">
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0 0 m
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-1 0.333 l
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-1 -0.333 l
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h
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</path>
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</symbol>
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<symbol name="mark/circle(sx)" transformations="translations">
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<path fill="sym-stroke">
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0.6 0 0 0.6 0 0 e
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0.4 0 0 0.4 0 0 e
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</path>
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</symbol>
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<symbol name="mark/disk(sx)" transformations="translations">
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<path fill="sym-stroke">
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0.6 0 0 0.6 0 0 e
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</path>
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</symbol>
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<symbol name="mark/fdisk(sfx)" transformations="translations">
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<group>
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<path fill="sym-fill">
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0.5 0 0 0.5 0 0 e
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</path>
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<path fill="sym-stroke" fillrule="eofill">
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0.6 0 0 0.6 0 0 e
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0.4 0 0 0.4 0 0 e
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</path>
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</group>
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</symbol>
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<symbol name="mark/box(sx)" transformations="translations">
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<path fill="sym-stroke" fillrule="eofill">
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-0.6 -0.6 m
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0.6 -0.6 l
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0.6 0.6 l
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-0.6 0.6 l
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h
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-0.4 -0.4 m
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0.4 -0.4 l
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0.4 0.4 l
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-0.4 0.4 l
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h
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</path>
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</symbol>
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<symbol name="mark/square(sx)" transformations="translations">
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<path fill="sym-stroke">
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-0.6 -0.6 m
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0.6 -0.6 l
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0.6 0.6 l
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-0.6 0.6 l
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h
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</path>
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</symbol>
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||||||
|
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0.5 -0.5 l
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0.6 0.6 l
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h
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0.4 -0.4 l
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0.4 0.4 l
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0.57 0.43 l
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0.43 0.57 l
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h
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0.57 -0.43 l
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0.43 -0.57 l
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-0.57 0.43 l
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h
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0 0 m
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-1 0.333 l
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-1 -0.333 l
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h
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0 0 m
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-1 0.333 l
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-0.8 0 l
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-1 -0.333 l
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h
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<symbol name="arrow/fpointed(spx)">
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0 0 m
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-1 0.333 l
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-0.8 0 l
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-1 -0.333 l
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h
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</symbol>
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-1 0.333 m
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0 0 l
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-1 -0.333 l
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<symbol name="arrow/fdouble(spx)">
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0 0 m
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-1 0.333 l
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-1 -0.333 l
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h
|
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-1 0 m
|
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-2 0.333 l
|
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-2 -0.333 l
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h
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<symbol name="arrow/double(spx)">
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0 0 m
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-1 0.333 l
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-1 -0.333 l
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h
|
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|
-1 0 m
|
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|
-2 0.333 l
|
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|
-2 -0.333 l
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h
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<pen name="heavier" value="0.8"/>
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<pen name="fat" value="1.2"/>
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<color name="darkred" value="0.545 0 0"/>
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<color name="lightgreen" value="0.565 0.933 0.565"/>
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<textsize name="Large" value="\Large"/>
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<textsize name="LARGE" value="\LARGE"/>
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<textsize name="huge" value="\huge"/>
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<textsize name="Huge" value="\Huge"/>
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<textsize name="small" value="\small"/>
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<textsize name="footnote" value="\footnotesize"/>
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<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
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<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
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|
<gridsize name="4 pts" value="4"/>
|
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|
<gridsize name="8 pts (~3 mm)" value="8"/>
|
||||||
|
<gridsize name="16 pts (~6 mm)" value="16"/>
|
||||||
|
<gridsize name="32 pts (~12 mm)" value="32"/>
|
||||||
|
<gridsize name="10 pts (~3.5 mm)" value="10"/>
|
||||||
|
<gridsize name="20 pts (~7 mm)" value="20"/>
|
||||||
|
<gridsize name="14 pts (~5 mm)" value="14"/>
|
||||||
|
<gridsize name="28 pts (~10 mm)" value="28"/>
|
||||||
|
<gridsize name="56 pts (~20 mm)" value="56"/>
|
||||||
|
<anglesize name="90 deg" value="90"/>
|
||||||
|
<anglesize name="60 deg" value="60"/>
|
||||||
|
<anglesize name="45 deg" value="45"/>
|
||||||
|
<anglesize name="30 deg" value="30"/>
|
||||||
|
<anglesize name="22.5 deg" value="22.5"/>
|
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|
<tiling name="falling" angle="-60" step="4" width="1"/>
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|
<tiling name="rising" angle="30" step="4" width="1"/>
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|
</ipestyle>
|
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<page>
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|
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|
<layer name="beta"/>
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<path layer="alpha" stroke="black">
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64 768 m
|
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|
64 608 l
|
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80 608 l
|
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|
80 768 l
|
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h
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|
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|
64 752 m
|
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|
80 752 l
|
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|
</path>
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<path stroke="black">
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|
64 736 m
|
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|
80 736 l
|
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|
</path>
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|
64 720 m
|
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|
80 720 l
|
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|
</path>
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<path stroke="black">
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|
64 704 m
|
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|
80 704 l
|
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|
80 704 l
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|
</path>
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|
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|
64 688 m
|
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|
80 688 l
|
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|
</path>
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|
64 672 m
|
||||||
|
80 672 l
|
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|
</path>
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<path stroke="black">
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|
64 656 m
|
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|
80 656 l
|
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|
</path>
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|
64 640 m
|
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|
80 640 l
|
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|
</path>
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<path stroke="black">
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|
64 624 m
|
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|
80 624 l
|
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|
</path>
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|
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|
<text transformations="translations" pos="72 744" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$2$</text>
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<text transformations="translations" pos="72 728" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$3$</text>
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|
<text transformations="translations" pos="72 712" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$4$</text>
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|
<text transformations="translations" pos="72 696" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$5$</text>
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|
<text transformations="translations" pos="72 680" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$6$</text>
|
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|
<text transformations="translations" pos="72 664" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$7$</text>
|
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|
<text transformations="translations" pos="72 648" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$8$</text>
|
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|
<text transformations="translations" pos="72 632" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$9$</text>
|
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|
<text transformations="translations" pos="72 616" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$10$</text>
|
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|
<text transformations="translations" pos="72 776" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$0$</text>
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|
<path layer="alpha" stroke="black">
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|
80 768 m
|
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|
80 784 l
|
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|
64 784 l
|
||||||
|
64 768 l
|
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|
</path>
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|
<path layer="beta" stroke="black">
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|
128 720 m
|
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|
128 704 l
|
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|
160 704 l
|
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|
160 720 l
|
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|
h
|
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|
</path>
|
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|
<path stroke="black">
|
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|
192 720 m
|
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|
192 704 l
|
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|
224 704 l
|
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|
224 720 l
|
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|
h
|
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|
</path>
|
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|
<path stroke="black">
|
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|
256 720 m
|
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|
256 704 l
|
||||||
|
288 704 l
|
||||||
|
288 720 l
|
||||||
|
h
|
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|
</path>
|
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|
<path stroke="black">
|
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|
192 784 m
|
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|
192 768 l
|
||||||
|
224 768 l
|
||||||
|
224 784 l
|
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|
h
|
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|
</path>
|
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|
<path stroke="black">
|
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|
256 784 m
|
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|
256 768 l
|
||||||
|
288 768 l
|
||||||
|
288 784 l
|
||||||
|
h
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
192 688 m
|
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|
192 672 l
|
||||||
|
224 672 l
|
||||||
|
224 688 l
|
||||||
|
h
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
256 688 m
|
||||||
|
256 672 l
|
||||||
|
288 672 l
|
||||||
|
288 688 l
|
||||||
|
h
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
256 624 m
|
||||||
|
256 640 l
|
||||||
|
288 640 l
|
||||||
|
288 624 l
|
||||||
|
h
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
256 624 m
|
||||||
|
256 608 l
|
||||||
|
288 608 l
|
||||||
|
288 624 l
|
||||||
|
h
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
216 784 m
|
||||||
|
216 768 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
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|
280 784 m
|
||||||
|
280 768 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
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|
216 720 m
|
||||||
|
216 704 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
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|
152 720 m
|
||||||
|
152 704 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
216 688 m
|
||||||
|
216 672 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
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|
280 688 m
|
||||||
|
280 672 l
|
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|
</path>
|
||||||
|
<path stroke="black">
|
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|
280 720 m
|
||||||
|
280 704 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
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|
280 640 m
|
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|
280 624 l
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
280 624 m
|
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|
280 608 l
|
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|
</path>
|
||||||
|
<text transformations="translations" pos="204 776" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$88$</text>
|
||||||
|
<text transformations="translations" pos="268 776" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$22$</text>
|
||||||
|
<text transformations="translations" pos="140 712" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$59$</text>
|
||||||
|
<text transformations="translations" pos="204 712" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$15$</text>
|
||||||
|
<text transformations="translations" pos="268 712" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$4$</text>
|
||||||
|
<text transformations="translations" pos="204 680" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$17$</text>
|
||||||
|
<text transformations="translations" pos="268 680" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$28$</text>
|
||||||
|
<text transformations="translations" pos="268 632" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$31$</text>
|
||||||
|
<text transformations="translations" pos="268 616" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$10$</text>
|
||||||
|
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|
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|
<use name="mark/disk(sx)" pos="220 776" size="normal" stroke="black"/>
|
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|
<use name="mark/disk(sx)" pos="284 776" size="normal" stroke="black"/>
|
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|
<use name="mark/disk(sx)" pos="220 712" size="normal" stroke="black"/>
|
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|
<use name="mark/disk(sx)" pos="220 680" size="normal" stroke="black"/>
|
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|
<use name="mark/disk(sx)" pos="284 712" size="normal" stroke="black"/>
|
||||||
|
<use name="mark/disk(sx)" pos="284 680" size="normal" stroke="black"/>
|
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|
<use name="mark/disk(sx)" pos="284 632" size="normal" stroke="black"/>
|
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|
<use name="mark/disk(sx)" pos="284 616" size="normal" stroke="black"/>
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|
<path stroke="black">
|
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|
156 712 m
|
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|
192 712 l
|
||||||
|
192 712 l
|
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|
</path>
|
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|
<path stroke="black">
|
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|
220 712 m
|
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|
256 712 l
|
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|
</path>
|
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|
<path stroke="black">
|
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|
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128 712 l
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192 680 l
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256 632 l
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256 616 l
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300 632 l
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300 632 l
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296 636 l
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296 628 l
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300 628 l
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300 616 l
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300 616 l
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296 620 l
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296 612 l
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300 612 l
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284 680 m
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300 680 l
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300 680 l
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296 684 l
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296 676 l
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300 676 l
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284 712 m
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300 712 l
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296 708 l
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300 708 l
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300 776 l
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296 772 l
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300 772 l
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</ipe>
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@ -0,0 +1,338 @@
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h
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h
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-2 -0.333 l
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h
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h
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-2 -0.333 l
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<gridsize name="16 pts (~6 mm)" value="16"/>
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|
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64 768 m
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|
64 752 l
|
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|
240 752 l
|
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|
240 768 l
|
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h
|
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80 768 m
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80 752 l
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96 768 m
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96 752 l
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112 768 m
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112 752 l
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128 768 m
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|
128 752 l
|
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|
</path>
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144 768 m
|
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|
144 752 l
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</path>
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160 768 m
|
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|
160 752 l
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176 768 m
|
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|
176 752 l
|
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|
</path>
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<path stroke="black">
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192 768 m
|
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|
192 752 l
|
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|
</path>
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<path stroke="black">
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|
208 768 m
|
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|
208 752 l
|
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</path>
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<path stroke="black">
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224 768 m
|
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|
224 752 l
|
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</path>
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|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="72 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$0$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="88 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$1$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="104 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$2$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="120 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$3$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="136 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$4$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="152 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$5$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="168 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$6$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="184 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$7$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="200 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$8$</text>
|
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|
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<text matrix="1 0 0 1 0 12" transformations="translations" pos="232 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$10$</text>
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72 752 m
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80 736
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88 752 s
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<path stroke="darkorange" arrow="normal/normal">
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136 752 m
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144 736
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152 752 s
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<path stroke="brown" arrow="normal/normal">
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168 752 m
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176 736
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184 752 s
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136 736 m
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144 720
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152 736 s
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152 736 m
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160 720
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168 736 s
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<path stroke="red" arrow="normal/normal">
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168 736 m
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176 720
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184 736 s
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<path stroke="red" arrow="normal/normal">
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184 736 m
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192 720
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|
200 736 s
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</ipe>
|
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@ -0,0 +1,334 @@
|
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<ipe version="70005" creator="Ipe 7.1.1">
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-1 -0.333 l
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h
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0.5 0 0 0.5 0 0 e
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0.6 0.6 l
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h
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h
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-0.6 -0.6 m
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0.6 -0.6 l
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0.6 0.6 l
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-0.6 0.6 l
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h
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-0.4 -0.4 m
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0.4 -0.4 l
|
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|
0.4 0.4 l
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-0.4 0.4 l
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h
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-0.43 -0.57 m
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0.57 0.43 l
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0.43 0.57 l
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-0.57 -0.43 l
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h
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-0.43 0.57 m
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0.57 -0.43 l
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0.43 -0.57 l
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|
-0.57 0.43 l
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h
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0 0 m
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|
-1 -0.333 l
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|
h
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|
</path>
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<symbol name="arrow/pointed(spx)">
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0 0 m
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-0.8 0 l
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-1 -0.333 l
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h
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</path>
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<symbol name="arrow/fpointed(spx)">
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<path stroke="sym-stroke" fill="white" pen="sym-pen">
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|
0 0 m
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|
-1 0.333 l
|
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|
-0.8 0 l
|
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|
-1 -0.333 l
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|
h
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|
</path>
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</symbol>
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|
<symbol name="arrow/linear(spx)">
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|
<path stroke="sym-stroke" pen="sym-pen">
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|
-1 0.333 m
|
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|
0 0 l
|
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|
-1 -0.333 l
|
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|
</path>
|
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|
</symbol>
|
||||||
|
<symbol name="arrow/fdouble(spx)">
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|
<path stroke="sym-stroke" fill="white" pen="sym-pen">
|
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|
0 0 m
|
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|
-1 0.333 l
|
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|
-1 -0.333 l
|
||||||
|
h
|
||||||
|
-1 0 m
|
||||||
|
-2 0.333 l
|
||||||
|
-2 -0.333 l
|
||||||
|
h
|
||||||
|
</path>
|
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|
</symbol>
|
||||||
|
<symbol name="arrow/double(spx)">
|
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|
<path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen">
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|
0 0 m
|
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|
-1 0.333 l
|
||||||
|
-1 -0.333 l
|
||||||
|
h
|
||||||
|
-1 0 m
|
||||||
|
-2 0.333 l
|
||||||
|
-2 -0.333 l
|
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|
h
|
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|
</path>
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<pen name="heavier" value="0.8"/>
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|
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|
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|
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|
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|
<color name="violet" value="0.933 0.51 0.933"/>
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|
<color name="darkblue" value="0 0 0.545"/>
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|
<color name="darkcyan" value="0 0.545 0.545"/>
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|
<color name="darkgray" value="0.663"/>
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|
<color name="darkgreen" value="0 0.392 0"/>
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|
<color name="darkred" value="0.545 0 0"/>
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|
<color name="lightcyan" value="0.878 1 1"/>
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
<textsize name="small" value="\small"/>
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|
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|
<textstyle name="itemize" begin="\begin{itemize}" end="\end{itemize}"/>
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|
<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
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|
<gridsize name="4 pts" value="4"/>
|
||||||
|
<gridsize name="8 pts (~3 mm)" value="8"/>
|
||||||
|
<gridsize name="16 pts (~6 mm)" value="16"/>
|
||||||
|
<gridsize name="32 pts (~12 mm)" value="32"/>
|
||||||
|
<gridsize name="10 pts (~3.5 mm)" value="10"/>
|
||||||
|
<gridsize name="20 pts (~7 mm)" value="20"/>
|
||||||
|
<gridsize name="14 pts (~5 mm)" value="14"/>
|
||||||
|
<gridsize name="28 pts (~10 mm)" value="28"/>
|
||||||
|
<gridsize name="56 pts (~20 mm)" value="56"/>
|
||||||
|
<anglesize name="90 deg" value="90"/>
|
||||||
|
<anglesize name="60 deg" value="60"/>
|
||||||
|
<anglesize name="45 deg" value="45"/>
|
||||||
|
<anglesize name="30 deg" value="30"/>
|
||||||
|
<anglesize name="22.5 deg" value="22.5"/>
|
||||||
|
<tiling name="falling" angle="-60" step="4" width="1"/>
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|
<tiling name="rising" angle="30" step="4" width="1"/>
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|
</ipestyle>
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<page>
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|
<layer name="alpha"/>
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<view layers="alpha" active="alpha"/>
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|
80 768 m
|
||||||
|
80 752 l
|
||||||
|
</path>
|
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|
<path stroke="black">
|
||||||
|
96 768 m
|
||||||
|
96 752 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
112 768 m
|
||||||
|
112 752 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
128 768 m
|
||||||
|
128 752 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
144 768 m
|
||||||
|
144 752 l
|
||||||
|
</path>
|
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|
<path stroke="black">
|
||||||
|
160 768 m
|
||||||
|
160 752 l
|
||||||
|
</path>
|
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|
<path stroke="black">
|
||||||
|
176 768 m
|
||||||
|
176 752 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
192 768 m
|
||||||
|
192 752 l
|
||||||
|
</path>
|
||||||
|
<path stroke="black">
|
||||||
|
208 768 m
|
||||||
|
208 752 l
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
224 768 m
|
||||||
|
224 752 l
|
||||||
|
</path>
|
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|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="72 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$0$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="88 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$1$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="104 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$2$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="120 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$3$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="136 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$4$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="152 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$5$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="168 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$6$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="184 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$7$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="200 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$8$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="216 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$9$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="232 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$10$</text>
|
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304 736
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80 736
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72 752 s
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@ -0,0 +1,342 @@
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h
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-2 -0.333 l
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h
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h
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-2 -0.333 l
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h
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|
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<textstyle name="item" begin="\begin{itemize}\item{}" end="\end{itemize}"/>
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|
<gridsize name="4 pts" value="4"/>
|
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|
<gridsize name="8 pts (~3 mm)" value="8"/>
|
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|
<gridsize name="16 pts (~6 mm)" value="16"/>
|
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|
<gridsize name="32 pts (~12 mm)" value="32"/>
|
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|
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|
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|
<gridsize name="20 pts (~7 mm)" value="20"/>
|
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|
<gridsize name="14 pts (~5 mm)" value="14"/>
|
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|
<gridsize name="28 pts (~10 mm)" value="28"/>
|
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|
<gridsize name="56 pts (~20 mm)" value="56"/>
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|
<anglesize name="90 deg" value="90"/>
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|
<anglesize name="60 deg" value="60"/>
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|
<anglesize name="45 deg" value="45"/>
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|
<anglesize name="30 deg" value="30"/>
|
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|
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|
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<page>
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|
64 768 m
|
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|
64 752 l
|
||||||
|
240 752 l
|
||||||
|
240 768 l
|
||||||
|
h
|
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|
</path>
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<path stroke="black">
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80 768 m
|
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|
80 752 l
|
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|
</path>
|
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<path stroke="black">
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|
96 768 m
|
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|
96 752 l
|
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|
</path>
|
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|
112 768 m
|
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|
112 752 l
|
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|
</path>
|
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|
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|
128 768 m
|
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|
128 752 l
|
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|
</path>
|
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|
<path stroke="black">
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|
144 768 m
|
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|
144 752 l
|
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|
</path>
|
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|
<path stroke="black">
|
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|
160 768 m
|
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|
160 752 l
|
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|
</path>
|
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|
<path stroke="black">
|
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|
176 768 m
|
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|
176 752 l
|
||||||
|
</path>
|
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|
<path stroke="black">
|
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|
192 768 m
|
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|
192 752 l
|
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|
</path>
|
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|
<path stroke="black">
|
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|
208 768 m
|
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|
208 752 l
|
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|
</path>
|
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|
<path stroke="black">
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|
224 768 m
|
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|
224 752 l
|
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|
</path>
|
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|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="72 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$0$</text>
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|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="88 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$1$</text>
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|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="104 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$2$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="120 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$3$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="136 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$4$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="152 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$5$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="168 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$6$</text>
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||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="184 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$7$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="200 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$8$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="216 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">$9$</text>
|
||||||
|
<text matrix="1 0 0 1 0 12" transformations="translations" pos="232 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">$10$</text>
|
||||||
|
<text transformations="translations" pos="72 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">22</text>
|
||||||
|
<text transformations="translations" pos="104 760" stroke="red" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">59</text>
|
||||||
|
<text transformations="translations" pos="120 760" stroke="darkorange" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">17</text>
|
||||||
|
<text transformations="translations" pos="136 760" stroke="black" type="label" width="4.981" height="6.42" depth="0" halign="center" valign="center">4</text>
|
||||||
|
<text transformations="translations" pos="152 760" stroke="turquoise" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">15</text>
|
||||||
|
<text transformations="translations" pos="168 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">28</text>
|
||||||
|
<text transformations="translations" pos="184 760" stroke="seagreen" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">88</text>
|
||||||
|
<text transformations="translations" pos="216 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">31</text>
|
||||||
|
<text transformations="translations" pos="232 760" stroke="black" type="label" width="9.963" height="6.42" depth="0" halign="center" valign="center">10</text>
|
||||||
|
<path stroke="darkorange" arrow="normal/normal">
|
||||||
|
168 752 m
|
||||||
|
152 736
|
||||||
|
136 736
|
||||||
|
120 752 s
|
||||||
|
</path>
|
||||||
|
<path stroke="seagreen" arrow="normal/normal">
|
||||||
|
216 752 m
|
||||||
|
200 728
|
||||||
|
184 752 s
|
||||||
|
</path>
|
||||||
|
<path stroke="seagreen" arrow="normal/normal">
|
||||||
|
72 752 m
|
||||||
|
88 720
|
||||||
|
204 720
|
||||||
|
220 752 s
|
||||||
|
</path>
|
||||||
|
<path stroke="turquoise" arrow="normal/normal">
|
||||||
|
136 752 m
|
||||||
|
152 736
|
||||||
|
216 736
|
||||||
|
232 752 s
|
||||||
|
</path>
|
||||||
|
<path matrix="1 0 0 1 0 -8" stroke="turquoise" arrow="normal/normal">
|
||||||
|
232 784 m
|
||||||
|
216 800
|
||||||
|
168 800
|
||||||
|
152 784 s
|
||||||
|
</path>
|
||||||
|
<path stroke="red" arrow="normal/normal">
|
||||||
|
136 776 m
|
||||||
|
128 792
|
||||||
|
120 776 s
|
||||||
|
</path>
|
||||||
|
<path stroke="red" arrow="normal/normal">
|
||||||
|
120 776 m
|
||||||
|
112 792
|
||||||
|
104 776 s
|
||||||
|
</path>
|
||||||
|
</page>
|
||||||
|
</ipe>
|
||||||
Loading…
Reference in new issue