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框架内小页面内容重叠

tag-icon • tag-icon minipage
框架内小页面内容重叠

我为我的框架使用了 minipage 环境。但即使我为我的框架使用了 minipage 环境，内容也会重叠，并且不会缩小[shrink]。我该如何修复这个问题？

梅威瑟：

\documentclass{beamer}

\usepackage{amsmath}

\begin{document}
\frame[shrink]{
  \begin{minipage}[shrink]{0.48\textwidth}
    Applying the model iteratively:
    $$y^{(t)}= V^{(t-1)}y^{(1)}$$
    where
    $$V^{(t-1)} = (AW)^{(t-1)}+ [\sum^{(t-2)}_{(k=0)}(AW)^{(k)}](I-A)$$
    for $t=2,3,\dots,$
    Assume that at equilibrium, $\underset{t \to \infty}{\lim}=y^{(\infty)}$ exist, in long run behaviour:
    $$y^{(\infty)} = Vy^{(1)}$$
    where $V=(I-AW)^{(-1)}(I-A)$ for $t=1,2,\ldots,$
  \end{minipage}
  \begin{minipage}[shrink]{0.48\textwidth}
    \begin{itemize}
    \item $V$: reduced-form matrix of coefficients to describe the total  interpersonal effects that transform the initial opinions into final opinions
    \item coefficients in $V=[v_{ij}]$ are non-negative, i.e. $0\leq v_{ij}\leq 1$
    \item $\sum_j v_{ij}=1$: sums for each row of $V$ is equal to 1
    \item $v_{ij}$ provides the relative weight of the initial opinion of individual $j$ to determine the final opinion of individual $i$
    \end{itemize}
  \end{minipage}
}
\end{document}

答案1

或者（另一种选择：将长方程分成两行：

在此处输入图片描述

对如何在不改变字体大小的情况下编写方程式、极限和矩阵进行了一些更改：

\documentclass{beamer}

    \begin{document}
\begin{frame}
    \begin{minipage}{0.45\textwidth}
Applying the model iteratively:
\[
y^{(t)}= \mathbf{V}^{(t-1)}y^{(1)}
\]
where
\begin{multline*}
V^{(t-1)} = (\mathbf{AW})^{(t-1)} + \\
    \left[\sum^{(t-2)}_{(k=0)}(\mathbf{AW})^{(k)}\right](\mathbf{I-A})
\end{multline*}
for $t=2,3,\dots,$. Assume that at equilibrium, $\lim\limits_{t \to \infty}=y^{(\infty)}$     exist, in long run behaviour:
\[
y^{(\infty)} = \mathbf{V}y^{(1)}
\]
where $\mathbf{V}=(\mathbf{I-AW})^{(-1)}(\mathbf{I-A})$ for $t=1,2,\ldots$
\end{minipage}\hfill
\begin{minipage}{0.52\textwidth}
    \begin{itemize}
\item $\mathbf{V}$: reduced-form matrix of coefficients to describe the total  interpersonal effects that transform the initial opinions into final opinions
\item coefficients in $\mathbf{V}=[v_{ij}]$ are non-negative, i.e. $0\leq v_{ij}\leq 1$
\item $\sum_j v_{ij}=1$: sums for each row of $\mathbf{V}$ is equal to 1
\item $v_{ij}$ provides the relative weight of the initial opinion of individual $j$ to determine the final opinion of individual $i$
    \end{itemize}
\end{minipage}
\end{frame}
    \end{document}

答案2

使用较小的字体大小，例如\small：

\documentclass{beamer}
\begin{document}

\frame{%
\small
\begin{minipage}{0.54\textwidth}
        Applying the model iteratively:
        $$y^{(t)}= V^{(t-1)}y^{(1)}$$
        where
        $$V^{(t-1)} = (AW)^{(t-1)}+ [\sum^{(t-2)}_{(k=0)}(AW)^{(k)}](I-A)$$
        for $t=2,3,\dots,$
        Assume that at equilibrium, $\underset{t \to \infty}{\lim}=y^{(\infty)}$     
        exist, in long run behaviour:
        $$y^{(\infty)} = Vy^{(1)}$$
        where $V=(I-AW)^{(-1)}(I-A)$ for $t=1,2,\ldots,$
\end{minipage}\hfill
\begin{minipage}{0.45\textwidth}
        \begin{itemize}
            \item $V$: reduced-form matrix of coefficients to describe the total  
            interpersonal effects that transform the initial opinions into final opinions
            \item coefficients in $V=[v_{ij}]$ are non-negative, i.e. $0\leq v_{ij}\leq 1$
            \item $\sum_j v_{ij}=1$: sums for each row of $V$ is equal to 1
            \item $v_{ij}$ provides the relative weight of the initial opinion of 
            individual $j$ to determine the final opinion of individual $i$
        \end{itemize}
\end{minipage}%
}
\end{document}

在此处输入图片描述

如果您需要更多空间使用：

\frame[plain]{%        
    \small\hspace*{-7mm}\abovedisplayskip=0.5\abovedisplayskip
    \abovedisplayshortskip=0pt
    [...]

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