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| (12 dazwischenliegende Versionen von 2 Benutzern werden nicht angezeigt) |
| Zeile 6: |
Zeile 6: |
| : AltGr-K: æßðđŋħjĸł˝^ | | : AltGr-K: æßðđŋħjĸł˝^ |
| : AltGr-K: «»¢“”nµ─· | | : AltGr-K: «»¢“”nµ─· |
|
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|
| |
| === math ===
| |
| ''(s. http://de.wikipedia.org/wiki/Hilfe:TeX oder https://www.mediawiki.org/wiki/Extension:MathJax )''
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|
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| ==== Math 1 ====
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| <math>y=2*x^3-x+22</math>
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| <pre><nowiki> <#math>y=2*x^3-x+22</#math> </nowiki></pre>
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|
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| ==== Math 2 ====
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| <math>\sum_{n=0}^\infty \frac{x^n+1}{n!}</math>
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| <pre><nowiki> <#math>\sum_{n=0}^\infty \frac{x^n+1}{n!}</#math> </nowiki></pre>
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|
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| ==== Math 3 ====
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| ''(@see https://www.mediawiki.org/wiki/Extension:MathJax#Usage )''
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| <math>
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| <!-- some LaTeX macros we want to use: -->
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| $\newcommand{\Re}{\mathrm{Re}\,}
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| \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)}$
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|
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| We consider, for various values of $s$, the $n$-dimensional integral
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| \begin{align}
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| \label{def:Wns}
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| W_n (s)
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| &:=
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| \int_{[0, 1]^n}
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| \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x}
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| \end{align}
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| which occurs in the theory of uniform random walk integrals in the plane,
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| where at each step a unit-step is taken in a random direction. As such,
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| the integral \eqref{def:Wns} expresses the $s$-th moment of the distance
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| to the origin after $n$ steps.
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|
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| By experimentation and some sketchy arguments we quickly conjectured and
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| strongly believed that, for $k$ a nonnegative integer
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| \begin{align}
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| \label{eq:W3k}
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| W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}.
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| \end{align}
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| Appropriately defined, \eqref{eq:W3k} also holds for negative odd integers.
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| The reason for \eqref{eq:W3k} was long a mystery, but it will be explained
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| at the end of the paper.
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| </math>
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|
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|
| |
| === Handler ===
| |
| ''(display ogg-files)''
| |
|
| |
| {| border="1" align="center" width="70%"
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| ! Oggs
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| | valign="top" |
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| * Sound: [[Image:Sound.ogg|thumb]]
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| * Video: [[Image:Video.ogv|thumb]]
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| |-
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| ! mp3
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| | valign="top" |
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| * Sound: [[Image:Sound.mp3|thumb]]
| |
| |-
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| ! mp4
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| | valign="top" |
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| * Video: [[Image:Video.m4v|thumb]]
| |
| |-
| |
| ! Pdf
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| | valign="top" | [[Image:Test.pdf|thumb]]
| |
| |}
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|
| |
| === graphviz ===
| |
| Homepage...: http://www.graphviz.org
| |
| Demos......: http://www.graphviz.org/Gallery.php
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| MediaWiki..: https://www.mediawiki.org/wiki/Extension:GraphViz
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|
| |
|
| |
|
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| ==== einfach ====
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| <graphviz border='frame' format='png'>
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| digraph simple { Hello -> World }
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| </graphviz>
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|
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| <pre><nowiki>
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| <graphviz border='frame' format='png'>
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| digraph simple { Hello -> World }
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| </graphviz>
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| </nowiki></pre>
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|
| |
| ----
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|
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| <graphviz>
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| digraph test1 {
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| size ="4,4";
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| main [shape=box]; /* this is a comment */
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| main -> parse [weight=8];
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| parse -> execute;
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| main -> init [style=dotted];
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| main -> cleanup;
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| execute -> { make_string; printf}
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| init -> make_string;
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| edge [color=red]; // so is this
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| main -> printf [style=bold,label="100 times"];
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| make_string [label="make a\nstring"];
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| node [shape=box,style=filled,color=".7 .3 1.0"];
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| execute -> compare;
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| }
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| </graphviz>
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|
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| <pre><nowiki>
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| <graphviz>
| |
| digraph test1 {
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| size ="4,4";
| |
| main [shape=box]; /* this is a comment */
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| main -> parse [weight=8];
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| parse -> execute;
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| main -> init [style=dotted];
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| main -> cleanup;
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| execute -> { make_string; printf}
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| init -> make_string;
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| edge [color=red]; // so is this
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| main -> printf [style=bold,label="100 times"];
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| make_string [label="make a\nstring"];
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| node [shape=box,style=filled,color=".7 .3 1.0"];
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| execute -> compare;
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| }
| |
| </graphviz>
| |
| </nowiki></pre>
| |
|
| |
| ==== mit Verweisen ====
| |
| <graphviz>
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| digraph test2 {
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| Perl [URL="http://www.perl.org"];
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| Java [URL="http://java.sun.com"];
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| Perl -> Java
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| }
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| </graphviz>
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|
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| <pre><nowiki>
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| <graphviz>
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| digraph test2 {
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| Perl [URL="http://www.perl.org"];
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| Java [URL="http://java.sun.com"];
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| Perl -> Java
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| }
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| </graphviz>
| |
| </nowiki></pre>
| |
|
| |
| ==== etwas komplexer ====
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|
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| <graphviz>
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| graph test4
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| {
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| //rotate=90;
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| id[label="id"];
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| email[label="email"];
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| name[label="name"];
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| uname[label="Name"];
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| address[label="Address"];
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| node[shape=rectangle];
| |
| university[label="University Department"];
| |
| student[label="Student"];
| |
| StUnDe[shape=diamond];
| |
| university -- StUnDe [label="1", len=3];
| |
| StUnDe -- student [label="n", len=2];
| |
| student -- id;
| |
| student -- name;
| |
| student -- email;
| |
| university -- uname;
| |
| university -- address;
| |
| }
| |
| </graphviz>
| |
|
| |
| <pre><nowiki>
| |
| <graphviz>
| |
| graph test4
| |
| {
| |
| //rotate=90;
| |
| id[label="id"];
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| email[label="email"];
| |
| name[label="name"];
| |
| uname[label="Name"];
| |
| address[label="Address"];
| |
| node[shape=rectangle];
| |
| university[label="University Department"];
| |
| student[label="Student"];
| |
| StUnDe[shape=diamond];
| |
| university -- StUnDe [label="1", len=3];
| |
| StUnDe -- student [label="n", len=2];
| |
| student -- id;
| |
| student -- name;
| |
| student -- email;
| |
| university -- uname;
| |
| university -- address;
| |
| }
| |
| </graphviz>
| |
| </nowiki></pre>
| |
|
| |
| ----
| |
|
| |
| <graphviz>
| |
| graph test5
| |
| {
| |
| edge [len=2];
| |
| V1 -- V2 [label="20"];
| |
| V2 -- V3 [label="15"];
| |
| V3 -- V4 [label="3"];
| |
| V4 -- V5 [label="17"];
| |
| V5 -- V6 [label="28"];
| |
| V6 -- V1 [label="23"];
| |
| V7 -- V1 [label="1"];
| |
| V7 -- V2 [label="4"];
| |
| V7 -- V3 [label="9"];
| |
| V7 -- V4 [label="16"];
| |
| V7 -- V5 [label="25"];
| |
| V7 -- V6 [label="36"];
| |
| }
| |
| </graphviz>
| |
|
| |
| <pre><nowiki>
| |
| <graphviz>
| |
| graph test5
| |
| {
| |
| edge [len=2];
| |
| V1 -- V2 [label="20"];
| |
| V2 -- V3 [label="15"];
| |
| V3 -- V4 [label="3"];
| |
| V4 -- V5 [label="17"];
| |
| V5 -- V6 [label="28"];
| |
| V6 -- V1 [label="23"];
| |
| V7 -- V1 [label="1"];
| |
| V7 -- V2 [label="4"];
| |
| V7 -- V3 [label="9"];
| |
| V7 -- V4 [label="16"];
| |
| V7 -- V5 [label="25"];
| |
| V7 -- V6 [label="36"];
| |
| }
| |
| </graphviz>
| |
| </nowiki></pre>
| |
|
| |
| ----
| |
|
| |
| <graphviz>
| |
| digraph test6 {
| |
| graph [rankdir = "LR"];
| |
| node [fontsize = "16" shape = "ellipse"];
| |
| edge [];
| |
| "node0" [label = "<f0> 0x10ba8| <f1>" shape = "record" ];
| |
| "node1" [label = "<f0> 0xf7fc4380| <f1> | <f2> |-1" shape = "record"];
| |
| "node2" [label = "<f0> 0xf7fc44b8| | |2" shape = "record"];
| |
| "node3" [label = "<f0> 3.43322790286038071e-06|44.79998779296875|0" shape = "record"];
| |
| "node4" [label = "<f0> 0xf7fc4380| <f1> | <f2> |2" shape = "record"];
| |
| "node5" [label = "<f0> (nil)| | |-1" shape = "record"];
| |
| "node6" [label = "<f0> 0xf7fc4380| <f1> | <f2> |1" shape = "record"];
| |
| "node7" [label = "<f0> 0xf7fc4380| <f1> | <f2> |2" shape = "record"];
| |
| "node8" [label = "<f0> (nil)| | |-1" shape = "record"];
| |
| "node9" [label = "<f0> (nil)| | |-1" shape = "record"];
| |
| "node10" [label = "<f0> (nil)| <f1> | <f2> |-1" shape = "record"];
| |
| "node11" [label = "<f0> (nil)| <f1> | <f2> |-1" shape = "record"];
| |
| "node12" [label = "<f0> 0xf7fc43e0| | |1 "shape = "record"];
| |
| "node0":f0 -> "node1":f0 [id = 0];
| |
| "node0":f1 -> "node2":f0 [id = 1];
| |
| "node1":f0 -> "node3":f0 [id = 2];
| |
| "node1":f1 -> "node4":f0 [id = 3];
| |
| "node1":f2 -> "node5":f0 [id = 4];
| |
| "node4":f0 -> "node3":f0 [id = 5];
| |
| "node4":f1 -> "node6":f0 [id = 6];
| |
| "node4":f2 -> "node10":f0 [id = 7];
| |
| "node6":f0 -> "node3":f0 [id = 8];
| |
| "node6":f1 -> "node7":f0 [id = 9];
| |
| "node6":f2 -> "node9":f0 [id = 10];
| |
| "node7":f0 -> "node3":f0 [id = 11];
| |
| "node7":f1 -> "node1":f0 [id = 12];
| |
| "node7":f2 -> "node8":f0 [id = 13];
| |
| "node10":f1 -> "node11":f0 [id = 14];
| |
| "node10":f2 -> "node12":f0 [id = 15];
| |
| "node11":f2 -> "node1":f0 [id = 16];
| |
| }
| |
| </graphviz>
| |
|
| |
| <pre><nowiki>
| |
| <graphviz>
| |
| digraph test6 {
| |
| graph [rankdir = "LR"];
| |
| node [fontsize = "16" shape = "ellipse"];
| |
| edge [];
| |
| "node0" [label = "<f0> 0x10ba8| <f1>" shape = "record" ];
| |
| "node1" [label = "<f0> 0xf7fc4380| <f1> | <f2> |-1" shape = "record"];
| |
| "node2" [label = "<f0> 0xf7fc44b8| | |2" shape = "record"];
| |
| "node3" [label = "<f0> 3.43322790286038071e-06|44.79998779296875|0" shape = "record"];
| |
| "node4" [label = "<f0> 0xf7fc4380| <f1> | <f2> |2" shape = "record"];
| |
| "node5" [label = "<f0> (nil)| | |-1" shape = "record"];
| |
| "node6" [label = "<f0> 0xf7fc4380| <f1> | <f2> |1" shape = "record"];
| |
| "node7" [label = "<f0> 0xf7fc4380| <f1> | <f2> |2" shape = "record"];
| |
| "node8" [label = "<f0> (nil)| | |-1" shape = "record"];
| |
| "node9" [label = "<f0> (nil)| | |-1" shape = "record"];
| |
| "node10" [label = "<f0> (nil)| <f1> | <f2> |-1" shape = "record"];
| |
| "node11" [label = "<f0> (nil)| <f1> | <f2> |-1" shape = "record"];
| |
| "node12" [label = "<f0> 0xf7fc43e0| | |1 "shape = "record"];
| |
| "node0":f0 -> "node1":f0 [id = 0];
| |
| "node0":f1 -> "node2":f0 [id = 1];
| |
| "node1":f0 -> "node3":f0 [id = 2];
| |
| "node1":f1 -> "node4":f0 [id = 3];
| |
| "node1":f2 -> "node5":f0 [id = 4];
| |
| "node4":f0 -> "node3":f0 [id = 5];
| |
| "node4":f1 -> "node6":f0 [id = 6];
| |
| "node4":f2 -> "node10":f0 [id = 7];
| |
| "node6":f0 -> "node3":f0 [id = 8];
| |
| "node6":f1 -> "node7":f0 [id = 9];
| |
| "node6":f2 -> "node9":f0 [id = 10];
| |
| "node7":f0 -> "node3":f0 [id = 11];
| |
| "node7":f1 -> "node1":f0 [id = 12];
| |
| "node7":f2 -> "node8":f0 [id = 13];
| |
| "node10":f1 -> "node11":f0 [id = 14];
| |
| "node10":f2 -> "node12":f0 [id = 15];
| |
| "node11":f2 -> "node1":f0 [id = 16];
| |
| }
| |
| </graphviz>
| |
| </nowiki></pre>
| |
|
| |
|
| === Syntax-Highlighting === | | === Syntax-Highlighting === |
| Zeile 349: |
Zeile 35: |
| </syntaxhighlight> | | </syntaxhighlight> |
| |} | | |} |
| | |
| | |
| | === Handler === |
| | ''(display pdf-files)'' |
| | |
| | {| border="1" align="center" width="70%" |
| | |- |
| | ! Pdf |
| | | valign="top" | [[File:Test.pdf|thumb]] |
| | |} |
| | |
| | === math === |
| | ''(s. http://de.wikipedia.org/wiki/Hilfe:TeX oder https://www.mediawiki.org/wiki/Extension:MathJax )'' |
| | deaktiviert, da Extension nicht mehr gepflegt wird |
| | |
| | === graphviz === |
| | Homepage...: http://www.graphviz.org |
| | Demos......: http://www.graphviz.org/Gallery.php |
| | MediaWiki..: https://www.mediawiki.org/wiki/Extension:GraphViz |
| | |
| | deaktiviert, da Extension nicht mehr gepflegt wird |
