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BEARBEITEN:

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BEARBEITEN:

Ich habe folgendes:

\documentclass[11pt, a4paper]{report}
\usepackage{bm}
\usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}
\usepackage{color}
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}
\usepackage{parskip}
\usepackage{lipsum}
    \newtheorem{theorem}{Theorem}[section]
\newtheorem{example}[theorem]{Example}   

 \begin{document}
    \begin{example} 
    Consider a random walk on the $n$-cycle. Let $\Omega = \mathbb{Z}_n = \lbrace 0, 1, 2, \cdots, n-1 \rbrace$ be the set of remainders modulo $n$. Also consider the transition matrix:
    \[
    P(x,y) = 
    \begin{cases} 
    \frac{1}{2} & \text{if } y=x+1\;\; (mod\;n)\\
    \frac{1}{2} & \text{if } y=x-1\;\; (mod\;n)\\
    0 & \text{otherwise}
    \end{cases}
    \]

    The associated Markov chain $X_t$ is called a random walk on the $n$-cycle. The sates can be visualised as equally spaced nodes arranged in a circle(see figure 1.1)
    \end{example}

    \begin{figure}[htbp]
        \centering
        \begin{tikzpicture}
        \foreach \i in {90,54,...,-234} {
            \draw[ultra thick] (\i:2)--({\i-36}:2);
        }
        \foreach \i in {90,18,...,-198} {
            \draw[fill=black] (\i:2) circle (1.25mm);
        }
        \foreach \i in {54,-18,...,-234} {
            \draw[fill=white] (\i:2) circle (1.25mm);
        }
        \begin{scope}[xshift=5cm]
        \foreach \i in {90,50,...,-230} {
            \draw[ultra thick] (\i:2)--({\i-40}:2);
            \draw[fill=black] (\i:2) circle (1.25mm);
        }
        \end{scope}
        \end{tikzpicture}
        \caption{Random walk on $\mathbb{Z}_10$ is periodic, since every step
    goes from an even state to an odd state, or vice-versa. Random
    walk on $\mathbb{Z}_9$ is aperiodic.}
        \label{my:figure}
    \end{figure}
    \end{document}

nun möchte ich die Abstände in der Beschriftung in dem Sinne anpassen, dass ich diese "in die Mitte schieben" möchte, weiß aber nicht wie ich vorgehen soll.

BEARBEITEN: ähnliche Frage wie oben, aber die Überschrift sieht in diesem Fall furchtbar aus. Gibt es irgendwelche Korrekturen, um sie zu strecken:

\begin{example} Consider the graph $G$ following shown in figure 1.2. The transition matrix of a simple random walk $G$ is 

\begin{equation*}
P =
\begin{bmatrix}[1.25]
    0 & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} & 0 & 0 \\
    \frac{1}{4} & 0 & \frac{1}{4} & 0 & \frac{1}{4} & \frac{1}{4} \\
    \frac{1}{4} & \frac{1}{4} & 0 & \frac{1}{4} & \frac{1}{4} & 0 \\
    \frac{1}{3} & 0 & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\
    0 & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & 0 & \frac{1}{4} \\
    0 & \frac{1}{2} & 0 & 0 & \frac{1}{2} & 0 \\
\end{bmatrix}
\end{equation*}

\begin{figure}[htbp]
 \centering
 \ffigbox[1.1\FBwidth]{%
 \caption{An example of a vertex set $V = \lbrace 1, 2, 3, 4, 5, 6\rbrace$ with $10$ edges.}
 \label{my:figure}}%
 {\begin{tikzpicture}[bn/.style={circle,fill,draw,text=white,font=\sffamily,minimum
size=1mm},every node/.append style={bn}]
 \path node (1) {1} -- ++ (50:2.5) node (2) {2} -- ++(-95:1.75) node (3) {3}
 -- ++(-85:1.75) node (4) {4} -- ++(40:2.75) node (5) {5}
 -- ++ (0,1.75) node (6) {6} ;
 \draw[thick] (1)--(2)--(6)--(5)--(4)--(1)--(3)--(5)--(2)--(3)--(4);
\end{tikzpicture}}%
\end{figure}
\end{example}

gibt es eine Möglichkeit, dies auf höchstens 2 Zeilen zu strecken?

Antwort1

Wenn ich Sie richtig verstehe, können Sie die folgenden beiden Zeilen in Ihrer Präambel verwenden

\usepackage{caption} % <================================================
\captionsetup{width=0.8\textwidth} % <==================================

captionum die Beschriftung nur 80 % der Textbreite einnehmen zu lassen. Weitere Möglichkeiten, das Layout der Beschriftungen durch Tippen texdoc captionauf Ihrer Konsole/Ihrem Terminal zu ändern, finden Sie in der Paketdokumentation .

Der komplette Code

\documentclass[11pt, a4paper]{report}
\usepackage{bm}
\usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}
\usepackage{color}
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}
\usepackage{parskip}
\usepackage{lipsum}

\usepackage{caption} % <================================================
\captionsetup{width=0.8\textwidth} % <==================================

\newtheorem{theorem}{Theorem}[section]
\newtheorem{example}[theorem]{Example}   


\begin{document}

\begin{example} 
Consider a random walk on the $n$-cycle. 
Let $\Omega = \mathbb{Z}_n = \lbrace 0, 1, 2, \cdots, n-1 \rbrace$ be 
the set of remainders modulo $n$. Also consider the transition matrix:
\[
  P(x,y) = 
  \begin{cases} 
    \frac{1}{2} & \text{if } y=x+1\;\; (mod\;n)\\
    \frac{1}{2} & \text{if } y=x-1\;\; (mod\;n)\\
    0           & \text{otherwise}
  \end{cases}
\]

The associated Markov chain $X_t$ is called a random walk on the 
$n$-cycle. The sates can be visualised as equally spaced nodes arranged 
in a circle (see figure~\ref{my:figure}). % <==========================
\end{example}

\begin{figure}[htbp]
  \centering
  \begin{tikzpicture}
        \foreach \i in {90,54,...,-234} {
            \draw[ultra thick] (\i:2)--({\i-36}:2);
        }
        \foreach \i in {90,18,...,-198} {
            \draw[fill=black] (\i:2) circle (1.25mm);
        }
        \foreach \i in {54,-18,...,-234} {
            \draw[fill=white] (\i:2) circle (1.25mm);
        }
        \begin{scope}[xshift=5cm]
        \foreach \i in {90,50,...,-230} {
            \draw[ultra thick] (\i:2)--({\i-40}:2);
            \draw[fill=black] (\i:2) circle (1.25mm);
        }
        \end{scope}
  \end{tikzpicture}
  \caption{Random walk on $\mathbb{Z}_10$ is periodic, since every step
    goes from an even state to an odd state, or vice-versa. Random
    walk on $\mathbb{Z}_9$ is aperiodic.}
  \label{my:figure}
\end{figure}
Text after the figure.
\end{document}

gibt Ihnen das Ergebnis:

resultierendes PDF

BEARBEITEN:

Mit Ihrem zweiten Beispiel (nach dem Kommentieren \ffigbox, siehe Markierungen <======im Code)

\documentclass[11pt, a4paper]{report}
\usepackage{bm}
\usepackage{amsfonts, graphicx, verbatim, amsmath,amssymb, amsthm}
\usepackage{color}
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}
\usepackage{parskip}
\usepackage{lipsum}

\usepackage{floatrow}

\usepackage{caption} % <================================================
\captionsetup{width=0.8\textwidth} % <==================================

\newtheorem{theorem}{Theorem}[section]
\newtheorem{example}[theorem]{Example}   


\begin{document}

\begin{example} 
Consider a random walk on the $n$-cycle. 
Let $\Omega = \mathbb{Z}_n = \lbrace 0, 1, 2, \cdots, n-1 \rbrace$ be 
the set of remainders modulo $n$. Also consider the transition matrix:
\[
  P(x,y) = 
  \begin{cases} 
    \frac{1}{2} & \text{if } y=x+1\;\; (mod\;n)\\
    \frac{1}{2} & \text{if } y=x-1\;\; (mod\;n)\\
    0           & \text{otherwise}
  \end{cases}
\]

The associated Markov chain $X_t$ is called a random walk on the 
$n$-cycle. The sates can be visualised as equally spaced nodes arranged 
in a circle (see figure~\ref{my:figure}).
\end{example}

\begin{figure}[htbp]
  \centering
  \begin{tikzpicture}
        \foreach \i in {90,54,...,-234} {
            \draw[ultra thick] (\i:2)--({\i-36}:2);
        }
        \foreach \i in {90,18,...,-198} {
            \draw[fill=black] (\i:2) circle (1.25mm);
        }
        \foreach \i in {54,-18,...,-234} {
            \draw[fill=white] (\i:2) circle (1.25mm);
        }
        \begin{scope}[xshift=5cm]
        \foreach \i in {90,50,...,-230} {
            \draw[ultra thick] (\i:2)--({\i-40}:2);
            \draw[fill=black] (\i:2) circle (1.25mm);
        }
        \end{scope}
  \end{tikzpicture}
  \caption{Random walk on $\mathbb{Z}_10$ is periodic, since every step
    goes from an even state to an odd state, or vice-versa. Random
    walk on $\mathbb{Z}_9$ is aperiodic.}
  \label{my:figure}
\end{figure}
Text after the figure.

\clearpage
\begin{example} Consider the graph $G$ following shown in figure 1.2. The transition matrix of a simple random walk $G$ is 

\begin{equation*}
P =
\begin{bmatrix}[1.25]
    0 & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} & 0 & 0 \\
    \frac{1}{4} & 0 & \frac{1}{4} & 0 & \frac{1}{4} & \frac{1}{4} \\
    \frac{1}{4} & \frac{1}{4} & 0 & \frac{1}{4} & \frac{1}{4} & 0 \\
    \frac{1}{3} & 0 & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\
    0 & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & 0 & \frac{1}{4} \\
    0 & \frac{1}{2} & 0 & 0 & \frac{1}{2} & 0 \\
\end{bmatrix}
\end{equation*}

\begin{figure}[htbp]
 \centering
%\ffigbox[1.1\FBwidth]{% <==============================================
 \caption{An example of a vertex set $V = \lbrace 1, 2, 3, 4, 5, 6\rbrace$ with $10$ edges.}
 \label{my:figure}%
%}% <===================================================================
 {\begin{tikzpicture}[bn/.style={circle,fill,draw,text=white,font=\sffamily,minimum
size=1mm},every node/.append style={bn}]
 \path node (1) {1} -- ++ (50:2.5) node (2) {2} -- ++(-95:1.75) node (3) {3}
 -- ++(-85:1.75) node (4) {4} -- ++(40:2.75) node (5) {5}
 -- ++ (0,1.75) node (6) {6} ;
 \draw[thick] (1)--(2)--(6)--(5)--(4)--(1)--(3)--(5)--(2)--(3)--(4);
\end{tikzpicture}}%
\end{figure}
\end{example}
\end{document}

Sie erhalten die resultierende zweite Abbildung/Seite:

zweite Seite

Antwort2

Wenn ich richtig verstanden habe, was Sie möchten, ist dies ganz einfach mit dem \ffigboxBefehl von floatrow, der Ihnen die volle Kontrolle über die Breite der Überschrift gibt:

\documentclass[11pt, a4paper]{report}
\usepackage{bm}
\usepackage{graphicx, verbatim, amsmath,amssymb, amsthm}
\usepackage{color}
\usepackage{array}
\usepackage{setspace}% if you must (for double spacing thesis)
\usepackage{fancyhdr}
\usepackage{enumitem}
\usepackage{tikz}
\usepackage{parskip}
\usepackage{lipsum}
    \newtheorem{theorem}{Theorem}[section]
\newtheorem{example}[theorem]{Example}
\usepackage{floatrow}

 \begin{document}

    \begin{example}
    Consider a random walk on the $n$-cycle. Let $\Omega = \mathbb{Z}_n = \lbrace 0, 1, 2, \cdots, n-1 \rbrace$ be the set of remainders modulo $n$. Also consider the transition matrix:
    \[
    P(x,y) =
    \begin{cases}
    \frac{1}{2} & \text{if } y=x+1 \pmod n\\
    \frac{1}{2} & \text{if } y=x-1\pmod n\\
    0 & \text{otherwise}
    \end{cases}
    \]

    The associated Markov chain $X_t$ is called a random walk on the $n$-cycle. The states can be visualised as equally spaced nodes arranged in a circle(see figure 1.1)
    \end{example}

 \begin{figure}[htbp]
 \centering
 \ffigbox[1.1\FBwidth]{%
 \caption{Random walk on $\mathbb{Z}_10$ is periodic, since every step
 goes from an even state to an odd state, or vice-versa. Random
 walk on $\mathbb{Z}_9$ is aperiodic.}
 \label{my:figure}}%
 {\begin{tikzpicture}
 \foreach \i in {90,54,...,-234} {
 \draw[ultra thick] (\i:2)--({\i-36}:2);
 }
 \foreach \i in {90,18,...,-198} {
 \draw[fill=black] (\i:2) circle (1.25mm);
 }
 \foreach \i in {54,-18,...,-234} {
 \draw[fill=white] (\i:2) circle (1.25mm);
 }
 \begin{scope}[xshift=5cm]
 \foreach \i in {90,50,...,-230} {
 \draw[ultra thick] (\i:2)--({\i-40}:2);
 \draw[fill=black] (\i:2) circle (1.25mm);
 }
 \end{scope}
 \end{tikzpicture}}%
 \end{figure}

\end{document}

Bildbeschreibung hier eingeben

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