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\documentclass{article}
\usepackage{epic}
\usepackage{amsmath}
\newtheorem{defi}{Definition}
\parindent=0pt
\begin{document}
\unitlength=1mm
\begin{defi}
Let $f$ be continuous on the half-open interval $[a, b)$ and suppose
$\lim_{x\rightarrow b^-}|f(x)|=\infty$. Then,
\[
\int_a^bf(x)dx=\lim_{t\rightarrow b^-}\int_a^tf(x)dx
\]
provided this limit exists and is finite, in which case we say the
integral converges. Otherwise, we say it diverges.
\end{defi}
\begin{picture}(80, 60)
\multiput(5, 0)(5, 0){15}{\line(0, 1){60}} % 畫 15 條直線,每隔 5mm 一條
\multiput(0, 5)(0, 5){11}{\line(1, 0){80}} % 畫 11 條橫線,每隔 5mm 一條
\thicklines
\put(0, 0){\vector(0, 1){60}} % 畫 y 軸
\put(0, 0){\vector(1, 0){80}} % 畫 x 軸
\put(0, 0){\circle*{1}} % 畫圓點,實心粗點
\put(-5, -5){$O(0, 0)$} % 標上原點的座標
\put(-5, 60){$y$} % 標上 y 軸字樣
\put(80, -5){$x$} % 標上 x 軸字樣
\end{picture}
\[
\frac{\frac{\displaystyle a}{\displaystyle x-y}+
\frac{\displaystyle b}{\displaystyle x+y}}
{\frac{\displaystyle x-y}{\displaystyle x+y}+
\frac{\displaystyle a-b}{\displaystyle a+b}}
\]
\[
\lim_{n \to \infty}\sum_{i=1}^n{\frac{1}{n}}\sin\frac{k}{n}
\]
\[
g(x,y) = \left\{\begin{array}{ll}
f(x,y), & \mbox{if $x<y$} \\ % 文字的部份要用 \mbox
f(y,x), & \mbox{if $x>y$} \\ % 包住,讓他使用正常字體
0, & \mbox{otherwise.}
\end{array} \right.
\]
\[
A =
\begin{pmatrix} % 使用小括號
t_{11} & t_{12} & t_{13} \\
t_{21} & t_{22} & t_{23} \\
t_{31} & t_{32} & t_{33}
\end{pmatrix}
\]
\begin{subequations} % 讓編號同數,但以英文小寫為子編號
\begin{align} % 韓信點兵,同餘方程式
x & \equiv 2 \pmod 3 \\ % 三三數之剩二
x & \equiv 3 \pmod 5 \\ % 五五數之剩三
x & \equiv 2 \pmod 7 % 七七數之剩二
\end{align}
\end{subequations}
aaaaaaaaaaaaaaa\cite{brumley:2011}
aaaaaaaaaaaaaaa\cite{cha:2010:nsdi}
helloworld\cite{jang:2012}
% bbbbbbbbbbbbbbb\cite[1986]{KDEm}
%\begin{thebibliography}{KDE} % 參考文獻中印出的編號最寬為三個字母寬
%\bibitem{KDEt} Knuth, D.E., \textit{The \TeX},
%Reading, Massachusetts: Addison-Wesley, 1989.
%\bibitem[KDE]{KDEm} Knuth, D.E., \textit{The MFbook},
%Reading, Massachusetts: Addison-Wesley, 1986.
%\end{thebibliography}
%\begin{thebibliography}{}
\bibliographystyle{plain}
\bibliography{djb-security}{}
\newblock Gde3: the third evolution step of generalized differential evolution.
\newblock In {\em IEEE Congress on Evolutionary Computation}, pages 443--450,
2005.
%\end{thebibliography}
\end{document}