多列溢出

多列溢出

我正在整理一本数学教科书(Mörters 和 Peres 的《布朗运动》)中的定理和定义列表。文档中的每一项(例如定义、定理、注释)都以标题或简洁的描述开头。此截图演示中,评论 1.4 的标题溢出到相邻列。为什么会发生这种情况?页面上的其他项目的标题同样长,但它们却能正确换行。以下是从文档开头到(包括)“泼妇”项目的代码列表。

\title{Brownian Motion}
\date{}

\documentclass[8pt]{article}

\usepackage[margin=0.2in]{geometry}
\usepackage{amsmath}    % needed for subequations
\usepackage{amsfonts}   % needed for $\mathbb{R}$
\usepackage{dsfont} % needed for $\mathds{1}$
\usepackage{graphicx}   % needed for figures
\usepackage{color}      % needed if color is used in text
\usepackage{hyperref}   % needed for hypertext links, including those to external documents and URLs
\usepackage{multicol}   % needed for the multicols environment

\usepackage{amsthm}
\newtheorem{definition}{Definition}[section]
\newtheorem{theorem}[definition]{Theorem}
\newtheorem{theonition}[definition]{Theorem and Definition}
\newtheorem{proposition}[definition]{Proposition}
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{example}[definition]{Example}
\newtheorem{counterexample}[definition]{Counterexample}
\newtheorem{comment}[definition]{Comment}
\newtheorem{assumption}[definition]{Assumption}
\newtheorem{corollary}[definition]{Corollary}
\newtheorem{notation}[definition]{Notation}

\begin{document}
\maketitle

\begin{abstract}
A list of definitions, theorems and examples taught in the course ``Brownian Motion''.
\end{abstract}

\begin{multicols}{3}

\begin{comment}
  Lecture No. 1
\end{comment}

\section{Chapter 1. Brownian motion as a random function}

\subsection{Stochastic processes}

\begin{definition}[Stochastic process; p. 7]
  A \em{stochastic process} is a family $\left\{B\left(t\right) : t \geq 0\right\}$ of (uncountably many) random variables $\omega \mapsto B\left(t,\omega\right)$, defined on a single probability space $\left(\Omega,\mathcal{A},P\right)$.
\end{definition}

\begin{comment}[Sample path interpretation of a stochastic process; p. 7]
  A stochastic process can be interpreted as a random function with the sample functions defined by $t \mapsto B\left(t,\omega\right)$.
\end{comment}

\begin{definition}[Finite-dimensional distributions of a stochastic process; p. 8]
  By the \em{finite-dimensional distributions} of a stochastic process $\left\{B\left(t\right) : t \geq 0\right\}$ we mean the laws of all the finite dimensional random vectors $\left(B\left(t_1\right), B\left(t_2\right), \dots, B\left(t_n\right)\right)$ for all $0\leq t_1\leq t_2\leq \dots \leq t_n$.
\end{definition}

\begin{comment}[Finite-dimensional distributions; p. 8]
  \begin{enumerate}
  \item To describe these joint laws it suffices to describe the joint law of $B\left(0\right)$ and the increments
    \begin{multline*}
    \left(B\left(t_1\right) - B\left(0\right), \dots,\right. \\
      \left.B\left(t_n\right) - B\left(t_{n - 1}\right)\right)
    \end{multline*}
    for all $0 \leq t_1\leq \dots \leq t_n$.
    \item The set
      $$
      \left\{\omega \in \Omega : t\mapsto B\left(t,\omega\right)\textrm{ continuous}\right\}
      $$
      is in general not in the $\sigma$-algebra generated by the random vectors $\left(B\left(t_1\right), B\left(t_2\right),\dots,B\left(t_n\right)\right),\ n\in\mathbb{N}_1$.
  \end{enumerate}
\end{comment}
\end{multicols}
\end{document}

答案1

当项目只包含enumerate环境而没有其他内容时,就会出现此问题。一旦我在枚举前添加几个文字,标题就会开始正确换行。我不明白为什么会发生这种情况,但至少我设法解决了这个问题。

答案2

我遇到了类似的问题多色,您的评论帮助我解决了这个问题。当每行的第一个元素位于格式化指令内时,就会出现问题,例如:

\normalsize{\emph{{\textbf{Isoetes schweinfurthii}}} A.Braun ex Baker}
\linebreak

在开头添加额外的文本而不进行格式化是一种可能的解决方法。但是,在我的情况下,问题发生的原因是太空跳跃在文档级别定义的指令与多色

\spaceskip 0.5 em \relax

删除此指令,并使用\raggedright反而解决了这个问题。

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