This commit is contained in:
EthanDeng
2019-01-15 15:11:24 +08:00
parent 775f3fe3d5
commit 2866196be5
5 changed files with 117 additions and 119 deletions

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@@ -1,11 +1,11 @@
%%%%%%%%%%%%%%%%%%%%%%
%% start of file `elegantbook.cls'.
%% Copyright 2013-2019 ElegantLaTeX (ElegantLaTeX2e@gmail.com)
%% Copyright 2013-2019 ElegantLaTeX (ddswhu@126.com)
%%
%% This work may be distributed and/or modified freely
%% available at https://ddswhu.me/resource/
% %
%% Last Modification 2018-9-11
%% Last Modification 2018-12-02
%%%%%%%%%%%%%%%%%%%%%
% % !Mode:: "TeX:UTF-8"
\NeedsTeXFormat{LaTeX2e}
@@ -44,22 +44,22 @@
\RequirePackage{xcolor}
\ifdefstring{\ELEGANT@color}{green}{
\definecolor{main}{RGB}{0,120,2}%
\definecolor{seco}{RGB}{230,90,7}%
\definecolor{thid}{RGB}{0,160,152}%
\definecolor{second}{RGB}{230,90,7}%
\definecolor{third}{RGB}{0,160,152}%
% \base{greenbase.pdf}%
}{\relax}
\ifdefstring{\ELEGANT@color}{cyan}{
\definecolor{main}{RGB}{0,175,152}%
\definecolor{seco}{RGB}{239,126,30}%
\definecolor{thid}{RGB}{120,8,13}%
\definecolor{second}{RGB}{239,126,30}%
\definecolor{third}{RGB}{120,8,13}%
% \base{cyanbase.pdf}%
}{\relax}
\ifdefstring{\ELEGANT@color}{blue}{
\definecolor{main}{RGB}{20,50,104}%
\definecolor{seco}{RGB}{180,50,131}%
\definecolor{thid}{RGB}{7,127,128}%
\definecolor{second}{RGB}{180,50,131}%
\definecolor{third}{RGB}{7,127,128}%
% \base{bluebase.pdf}%
}{\relax}
@@ -112,7 +112,7 @@
\newcommand*{\myquote}[1]{\def\@myquote{#1}}
\newcommand*{\logo}[1]{
\def\@logo{\includegraphics[height=5.8cm]{#1}
\def\@logo{\includegraphics[width=0.5\textwidth]{#1}
}
}
@@ -202,20 +202,18 @@
\defaultfontfeatures{Mapping=tex-text}
\RequirePackage{xunicode}
\RequirePackage{xltxtra}
\setmainfont[Ligatures=TeX]{Minion Pro} % (\textrm)
\setsansfont{Myriad Pro} % (\textsf)
\setmonofont{Inconsolata}%Palatino Linotype
\setmainfont[Ligatures=TeX]{Times New Roman} % (\textrm)
\setsansfont{Arial} % (\textsf)
\setmonofont{Courier New}%Palatino Linotype
%--%
\RequirePackage{xeCJK}
\setCJKmainfont[BoldFont={},ItalicFont={}]{}%_GBK Adobe Song Std L
\setCJKsansfont[BoldFont={}]{}
\setCJKsansfont[BoldFont={},ItalicFont={}]{}
\setCJKmonofont{}
\XeTeXlinebreaklocale "zh"
\XeTeXlinebreakskip = 0pt plus 1pt
\setCJKfamilyfont{new}{}
\setCJKfamilyfont{note}{}
\newfontfamily\gara{Adobe Garamond Pro}
%% \\
\RequirePackage{environ}
@@ -225,123 +223,123 @@
\definecolor{bule}{RGB}{18,29,57}
\definecolor{bablue}{RGB}{248,248,248}
%define the style of tikz newthemsty
\tikzstyle{newthemsty}
%define the style of tikz etheoremsty
\tikzstyle{etheoremsty}
=[draw=main, fill=blue!10,very thick,rectangle,
rounded corners, inner sep=10pt, inner ysep=20pt]
\tikzstyle{newthemstytitle}
\tikzstyle{etheoremstytitle}
=[fill=main, text=blue!10]
\tikzstyle{newdefinitionsty}
=[draw=seco, fill=yellow!20,very thick,rectangle,
\tikzstyle{edefinitionsty}
=[draw=second, fill=yellow!20,very thick,rectangle,
rounded corners, inner sep=10pt, inner ysep=20pt,
text=black,fill opacity=0.9]
\tikzstyle{newdefinitionstytitle}
=[fill=seco, text=white]
\tikzstyle{edefinitionstytitle}
=[fill=second, text=white]
\tikzstyle{newpropositionsty}
=[draw=thid, fill=bablue,very thick,rectangle,
\tikzstyle{epropositionositionsty}
=[draw=third, fill=bablue,very thick,rectangle,
rounded corners, inner sep=10pt, inner ysep=20pt,
text=black,fill opacity=0.9]
\tikzstyle{newpropositionstytitle}
=[fill=thid, text=white]
\tikzstyle{epropositionositionstytitle}
=[fill=third, text=white]
%%define the "newthem" environment
\newcounter{Newthem}[chapter]
\renewcommand{\theNewthem}{\thechapter.\arabic{Newthem}}
\NewEnviron{newthem}[1][{}]{%
%%define the "etheorem" environment
\newcounter{etheorem}[chapter]
\renewcommand{\theetheorem}{\thechapter.\arabic{etheorem}}
\NewEnviron{etheorem}[1][{}]{%
\begin{figure}[!htb]
\noindent\centering
\begin{tikzpicture}
\node[newthemsty] (box){
\node[etheoremsty] (box){
\begin{minipage}{0.93\columnwidth}
\sffamily\refstepcounter{Newthem}\BODY
\sffamily\refstepcounter{etheorem}\BODY
\end{minipage}};
\node[newthemstytitle,right=10pt] at (box.north west){
\bf\textsf{Theorem \theNewthem\; #1}};
\node[newthemstytitle, rounded corners] at (box.east) {$\clubsuit$};
\node[etheoremstytitle,right=10pt] at (box.north west){
\bf\textsf{Theorem \theetheorem\; #1}};
\node[etheoremstytitle, rounded corners] at (box.east) {$\clubsuit$};
\end{tikzpicture}
\end{figure}}
%%define the "newlemma" environment
\newcounter{Newlemma}[chapter]
\renewcommand{\theNewlemma}{\thechapter.\arabic{Newlemma}}
\NewEnviron{newlemma}[1][{}]{%
%%define the "elemma" environment
\newcounter{elemma}[chapter]
\renewcommand{\theelemma}{\thechapter.\arabic{elemma}}
\NewEnviron{elemma}[1][{}]{%
\begin{figure}[!htb]
\noindent\centering
\begin{tikzpicture}
\node[newthemsty] (box){
\node[etheoremsty] (box){
\begin{minipage}{0.93\columnwidth}
\sffamily\refstepcounter{Newlemma}\BODY
\sffamily\refstepcounter{elemma}\BODY
\end{minipage}};
\node[newthemstytitle,right=10pt] at (box.north west){
\bf\textsf{Lemma \theNewlemma\; #1}};
\node[newthemstytitle, rounded corners] at (box.east) {$\clubsuit$};
\node[etheoremstytitle,right=10pt] at (box.north west){
\bf\textsf{Lemma \theelemma\; #1}};
\node[etheoremstytitle, rounded corners] at (box.east) {$\clubsuit$};
\end{tikzpicture}
\end{figure}}
%%define the "newcorol" environment
\newcounter{Newcorol}[chapter]
\renewcommand{\theNewcorol}{\thechapter.\arabic{Newcorol}}
\NewEnviron{newcorol}[1][{}]{%
%%define the "ecorollary" environment
\newcounter{ecorollary}[chapter]
\renewcommand{\theecorollary}{\thechapter.\arabic{ecorollary}}
\NewEnviron{ecorollary}[1][{}]{%
\begin{figure}[!htb]
\noindent\centering
\begin{tikzpicture}
\node[newthemsty] (box){
\node[etheoremsty] (box){
\begin{minipage}{0.93\columnwidth}
\sffamily\refstepcounter{Newcorol}\BODY
\sffamily\refstepcounter{ecorollary}\BODY
\end{minipage}};
\node[newthemstytitle,right=10pt] at (box.north west){
\bf\textsf{Corollary \theNewcorol\; #1}};
\node[newthemstytitle, rounded corners] at (box.east) {$\clubsuit$};
\node[etheoremstytitle,right=10pt] at (box.north west){
\bf\textsf{Corollary \theecorollary\; #1}};
\node[etheoremstytitle, rounded corners] at (box.east) {$\clubsuit$};
\end{tikzpicture}
\end{figure}}
%% define the "proposition" environment
\newcounter{Newprop}[chapter]
\renewcommand{\theNewprop}{\thechapter.\arabic{Newprop}}
\NewEnviron{newprop}[1][{}]{%
\newcounter{eproposition}[chapter]
\renewcommand{\theeproposition}{\thechapter.\arabic{eproposition}}
\NewEnviron{eproposition}[1][{}]{%
\begin{figure}[!htb]\noindent\centering
\begin{tikzpicture}
\node[newpropositionsty] (box){
\node[epropositionositionsty] (box){
\begin{minipage}{0.93\columnwidth}
\sffamily\refstepcounter{Newprop}\BODY
\sffamily\refstepcounter{eproposition}\BODY
\end{minipage}};
\node[newpropositionstytitle,right=10pt] at (box.north west){
\bf\textsf{Proposition \theNewprop\; #1}};
\node[newpropositionstytitle, rounded corners] at (box.east) {$\spadesuit$};
\node[epropositionositionstytitle,right=10pt] at (box.north west){
\bf\textsf{Proposition \theeproposition\; #1}};
\node[epropositionositionstytitle, rounded corners] at (box.east) {$\spadesuit$};
\end{tikzpicture}
\end{figure}}
%%define the "newdef" environment
\newcounter{Newdefinition}[chapter]
\renewcommand{\theNewdefinition}{\thechapter.\arabic{Newdefinition}}
\NewEnviron{newdef}[1][{}]{%
%%define the "edefinition" environment
\newcounter{edefinition}[chapter]
\renewcommand{\theedefinition}{\thechapter.\arabic{edefinition}}
\NewEnviron{edefinition}[1][{}]{%
\begin{figure}[!htb]\noindent\centering
\begin{tikzpicture}
\node [newdefinitionsty] (dbox){\begin{minipage}{0.93\textwidth}\itshape\refstepcounter{Newdefinition}\BODY\end{minipage}};
\node[newdefinitionstytitle, right=10pt] at (dbox.north west) {\bf\textsf{Definition \theNewdefinition\; #1}};
\node[newdefinitionstytitle, rounded corners] at (dbox.east) {$\heartsuit$};
\node [edefinitionsty] (dbox){\begin{minipage}{0.93\textwidth}\itshape\refstepcounter{edefinition}\BODY\end{minipage}};
\node[edefinitionstytitle, right=10pt] at (dbox.north west) {\bf\textsf{Definition \theedefinition\; #1}};
\node[edefinitionstytitle, rounded corners] at (dbox.east) {$\heartsuit$};
\end{tikzpicture}
\end{figure}}
%% Example with counter
\newcounter{Newexam}[chapter]
\renewcommand{\theNewexam}{\thechapter.\arabic{Newexam}}
\newenvironment{example}{\par\noindent\textbf{Example\,\stepcounter{Newexam}\theNewexam: }\color{black!90}}{\par}
\newcounter{example}[chapter]
\renewcommand{\theexample}{\thechapter.\arabic{example}}
\newenvironment{example}{\par\noindent\textbf{Example\,\stepcounter{example}\theexample: }\color{black!90}}{\par}
%% Exercise with counter
\newcounter{Newexer}[chapter]
\renewcommand{\theNewexer}{\thechapter.\arabic{Newexer}}
\newenvironment{exercise}{\par\noindent{\makebox[0pt][r]{\color{main}\ding{50}\;\;}}\textbf{Exercise\,\stepcounter{Newexer}\theNewexer: }}{\par}
\newcounter{exercise}[chapter]
\renewcommand{\theexercise}{\thechapter.\arabic{exercise}}
\newenvironment{exercise}{\par\noindent{\makebox[0pt][r]{\color{main}\ding{50}\;\;}}\textbf{Exercise\,\stepcounter{exercise}\theexercise: }}{\par}
%%define the note and newproof environment
%%define the note and eproof environment
\RequirePackage{pifont,manfnt}
\newenvironment{note}{\par\itshape\CJKfamily{note}\gara\noindent{\makebox[0pt][r]{\scriptsize\color{red!90}\textdbend\quad}\textbf{Note:}}}{\par}
\newenvironment{note}{\par\itshape\noindent{\makebox[0pt][r]{\scriptsize\color{red!90}\textdbend\quad}\textbf{Note:}}}{\par}
\newenvironment{remark}{\par\itshape\CJKfamily{note}\gara\noindent{\makebox[0pt][r]{\color{red!90}\ding{96}\quad}\textbf{Remarks:}}}{\par}
\newenvironment{remark}{\par\itshape\noindent{\makebox[0pt][r]{\color{red!90}\ding{96}\quad}\textbf{Remarks:}}}{\par}
\newenvironment{assumption}{\par\noindent\textbf{Assumptions: }\color{black!90}}{\par}
@@ -350,7 +348,7 @@
\newenvironment{property}{\par\noindent\textbf{Properties: }}{\par}
\newenvironment{newproof}{\par\noindent{\makebox[0pt][r]{\color{main}\ding{43}\;\;}\textbf{Proof:}}\color{black!90}\small}{\hfill$\Box$\quad\par}
\newenvironment{eproof}{\par\noindent{\makebox[0pt][r]{\color{main}\ding{43}\;\;}\textbf{Proof:}}\color{black!90}\small}{\hfill$\Box$\quad\par}
\newenvironment{solution}{\par\noindent{\makebox[0pt][r]{\color{main}\ding{46}\;\;}\textbf{Solution:}}\small}{\hfill$\Box$\quad\par}
@@ -391,10 +389,10 @@
\vfill
\vspace*{2cm}
\begin{center}
\color{seco}
\color{second}
\rule{0.8\textwidth}{2pt}\\
\Huge {\color{main} \bfseries \the\entitle } {\color{seco} \bfseries \the\enend}\\
{\Huge \CJKfamily{new}{\color{main} \the\zhtitle } \the\zhend}\\
\Huge {\color{main} \bfseries \the\entitle } {\color{second} \bfseries \the\enend}\\
{\Huge \bfseries{\color{main} \the\zhtitle } \the\zhend}\\
\rule{0.8\textwidth}{2pt}
\end{center}
\vskip3ex
@@ -410,16 +408,16 @@
\vfill
\vspace{2cm}
\begin{flushright}
\color{seco}
\color{second}
\rule{0.45\textwidth}{1pt}\\
{\color{main}\@author}\\
{\color{main}\today}\\
Email: \hyperlink{\the\email}{\the\email}\\
{\color{main}\@author}\\
{\color{main}\today}\\
: \hyperlink{\the\email}{\the\email}\\
\rule{0.45\textwidth}{1pt}
\end{flushright}
\vfill
\begin{center}
\color{seco} Version: \the\version
\color{second} Version: \the\version
\end{center}
\vfil\eject
}

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@@ -8,23 +8,23 @@
\zhend{模板}
\entitle{Elegant\LaTeX{} Book}
\enend{Template}
\version{2.30}
\version{2.40}
\myquote{Victory won\rq t come to us unless we go to it.}
\logo{logo.pdf}
\logo{logo.png}
\cover{cover.pdf}
%green color
\definecolor{main1}{RGB}{0,120,2}
\definecolor{seco1}{RGB}{230,90,7}
\definecolor{thid1}{RGB}{0,160,152}
\definecolor{second1}{RGB}{230,90,7}
\definecolor{third1}{RGB}{0,160,152}
%cyan color
\definecolor{main2}{RGB}{0,175,152}
\definecolor{seco2}{RGB}{239,126,30}
\definecolor{thid2}{RGB}{120,8,13}
\definecolor{second2}{RGB}{239,126,30}
\definecolor{third2}{RGB}{120,8,13}
%blue color
\definecolor{main3}{RGB}{20,50,104}
\definecolor{seco3}{RGB}{180,50,131}
\definecolor{thid3}{RGB}{7,127,128}
\definecolor{second3}{RGB}{180,50,131}
\definecolor{third3}{RGB}{7,127,128}
\usepackage{makecell}
\usepackage{lipsum}
@@ -64,7 +64,7 @@
我以前从未写过类文件,所以,写这个模板的过程必然是折腾的过程,在写模板的过程中,最主要参考了《写给\LaTeXe{} 类与宏包的作者》\cite{packagewriter}、moderncv.cls 文件、\href{http://aff.whu.edu.cn/huangzh/}{武汉大学黄正华老师的论文模板}、《\LaTeXe{} 完全学习手册》\cite{complete}{\itshape The Not So Short Introduction to \LaTeXe{}}\cite{oetiker2010not}以及各大\LaTeX{} 疑问解答网站,在此为无私奉献的组织和个人表示感谢!
{\color{thid}忍不住插个图!}
{\color{third}忍不住插个图!}
\begin{figure}[!hbtp]
\includegraphics[width=0.8\textwidth]{happy.jpg}
@@ -79,7 +79,7 @@
如果您在使用此模板,方便的话,是否可以把您使用此模板制作的成品发一份给我们,谢谢!
\section{关于字体}
\section{关于字体(已删除)}
基于本模板追求视觉上的美观的角度,强烈建议使用者安装./fonts/文件夹下的字体。出于版权的考虑,务必不能将此模板用于涉及盈利目的的商业行为,否则,后果自负,本模板带的字体仅供学习使用,如果您喜欢某种字体,请自行购买正版。本文主要使用的字体如下
@@ -104,11 +104,11 @@
本文特殊选项设置共有3类分为{\color{main}颜色}{\color{main} 数学字体 }以及{\color{main} 章标题显示风格}
\subsection{选项设置}
第一类为{\color{main}颜色}主题设置,内置 3 组颜色主题,分别为 \verb|green|(默认),\verb|cyan|\verb|blue|,另外还有一个自定义的选项 \verb|nocolor|,用户\textbf{必须}在使用模板的时候选择某个颜色主题或选择 \verb|nocolor|选项。调用颜色主题 \verb|green| 的方法为\verb|\documentclass[green]{elegantbook}|或者使用\verb|\documentclass[color=green]{elegantbook}|。需要改变颜色的话请选择 \verb|nocolor|选项或者使用 \verb|color=none|然后在导言区定义main、seco、thid颜色具体的方法如下
第一类为{\color{main}颜色}主题设置,内置 3 组颜色主题,分别为 \verb|green|(默认),\verb|cyan|\verb|blue|,另外还有一个自定义的选项 \verb|nocolor|,用户\textbf{必须}在使用模板的时候选择某个颜色主题或选择 \verb|nocolor|选项。调用颜色主题 \verb|green| 的方法为\verb|\documentclass[green]{elegantbook}|或者使用\verb|\documentclass[color=green]{elegantbook}|。需要改变颜色的话请选择 \verb|nocolor|选项或者使用 \verb|color=none|然后在导言区定义main、second、third颜色具体的方法如下
\begin{verbatim}
\definecolor{main}{RGB}{70,70,70} %定义main颜色值
\definecolor{seco}{RGB}{115,45,2} %定义seco颜色值
\definecolor{thid}{RGB}{0,80,80} %定义thid颜色值
\definecolor{second}{RGB}{115,45,2} %定义second颜色值
\definecolor{third}{RGB}{0,80,80} %定义third颜色值
\end{verbatim}
第二类为{\color{main}数学字体}设置,有两个可选项,分别是 mathpazo默认 和 mtpro2 字体调用mathpazo 字体使用 \verb|\documentclass[mathpazo]{elegantbook}|,调用 mtpro2 字体时需要把 \verb|mathpazo|换成 \verb|mtpro|mathpazo 不需要用户自己安装字体mtpro2 的字体需要自己安装。
@@ -119,11 +119,11 @@
\toprule
& green & cyan & blue & 主要使用的环境\\
\midrule
main & \makecell{{\color{main1}\rule{1cm}{1cm}}}& \makecell{{\color{main2}\rule{1cm}{1cm}}}&\makecell{ {\color{main3}\rule{1cm}{1cm}}}& newthem \ newlemma \ newcorol\\
main & \makecell{{\color{main1}\rule{1cm}{1cm}}}& \makecell{{\color{main2}\rule{1cm}{1cm}}}&\makecell{ {\color{main3}\rule{1cm}{1cm}}}& etheorem \ elemma \ ecorollary\\
seco &\makecell{ {\color{seco1}\rule{1cm}{1cm}}}& \makecell{{\color{seco2}\rule{1cm}{1cm}}}&\makecell{ {\color{seco3}\rule{1cm}{1cm}}}&newdef\\
second &\makecell{ {\color{second1}\rule{1cm}{1cm}}}& \makecell{{\color{second2}\rule{1cm}{1cm}}}&\makecell{ {\color{second3}\rule{1cm}{1cm}}}&edefinition\\
thid &\makecell{ {\color{thid1}\rule{1cm}{1cm}}}& \makecell{{\color{thid2}\rule{1cm}{1cm}}}&\makecell{ {\color{thid3}\rule{1cm}{1cm}}}&newprop\\
third &\makecell{ {\color{third1}\rule{1cm}{1cm}}}& \makecell{{\color{third2}\rule{1cm}{1cm}}}&\makecell{ {\color{third3}\rule{1cm}{1cm}}}&eproposition\\
\bottomrule
\end{tabular}
\caption{ElegantBook 模板中的三套颜色主题\label{tab:color thm}}
@@ -138,11 +138,11 @@ thid &\makecell{ {\color{thid1}\rule{1cm}{1cm}}}& \makecell{{\color{thid2}\rule{
\begin{enumerate}
\item 定理类环境包含标题和内容两部分。根据格式的不同分为3种
\begin{itemize}
\item {\color{main} newthem、newlemma、newcorol} 环境颜色为主颜色main三者编号均以章节为单位
\item {\color{main} newdef} 环境含有一个可选项编号以章节为单位颜色为seco
\item {\color{main} newprop} 环境含有一个可选项编号以章节为单位颜色为thid。
\item {\color{main} etheorem、elemma、ecorollary} 环境颜色为主颜色main三者编号均以章节为单位
\item {\color{main} edefinition} 环境含有一个可选项编号以章节为单位颜色为second
\item {\color{main} eproposition} 环境含有一个可选项编号以章节为单位颜色为third。
\end{itemize}
\item 证明类环境,有 {\color{main} newproof、note、remark、solution} 环境,特点是,有引导符和引导词,并且 newproof、solution 环境有结束标志。
\item 证明类环境,有 {\color{main} eproof、note、remark、solution} 环境,特点是,有引导符和引导词,并且 eproof、solution 环境有结束标志。
\item 结论类环境,有 {\color{main} conclusion、assumption、property} 环境,三者均以粗体的引导词为开头,和普通段落格式一致。
\item 示例类环境--- {\color{main} example、exercise}环境编号以章节为单位其中exercise环境有引导符。
\item 自定义环境--- {\color{main} custom}带一个必选参数格式与conclusion 环境很类似。
@@ -164,9 +164,9 @@ thid &\makecell{ {\color{thid1}\rule{1cm}{1cm}}}& \makecell{{\color{thid2}\rule{
where $z$ is stochastic process or white noise or wiener process.
\begin{newdef}[Wiener Process]
\begin{edefinition}[Wiener Process]
If $z$ is wiener process, then for any partition $t_0,t_1,t_2,\ldots$ of time interval, the random variables $z(t_1)-z(t_0),z(t_2)-z(t_1),\ldots$ are independently and normally distributed with zero means and variance $t_1-t_0,t_2-t_1,\ldots$
\end{newdef}
\end{edefinition}
\lipsum[5]
@@ -178,11 +178,11 @@ $E$ and $F$ be two events such that $\mbf{P}(E)=\mbf{P}(F)=1/2$, and $\mbf{P}(E\
let $S=l^\infty=\big\{(x_n)\mid \exists\, M \text{ such that } \forall n, |x_n|\leq M,x_n\in \mathbb{R}\big\}$, $\rho_{\infty}(x,y)=\sup\limits_{n\geq 1}|x_n-y_n|$, show that $\big(l^\infty,\rho_{\infty}\big)$ is complete.
\end{exercise}
\begin{newthem}[勾股定理]\label{thm:31}
\begin{etheorem}[勾股定理]\label{thm:31}
勾股定理的数学表达Expression
\[a^2+b^2=c^2\]
其中$a,b$为直角三角形的两条直角边长,$c$为直角三角形斜边长。
\end{newthem}
\end{etheorem}
\begin{note}
在本模板中引理lemma推论corollary )的样式和定理的样式一致,包括颜色,仅仅只有计数器的设置不一样。在这个例稿中,我们将不给出引理推论的例子。
@@ -191,19 +191,19 @@ let $S=l^\infty=\big\{(x_n)\mid \exists\, M \text{ such that } \forall n, |x_n|\
\lipsum[4]
\begin{newprop}[最优性原理]
\begin{eproposition}[最优性原理]
如果$u^*$$[s,T]$上为最优解,则$u^*$$[s,T]$任意子区间都是最优解,假设区间为$[t_0,t_1]$的最优解为$u^*$,则$u(t_0)=u^{*}(t_0)$,即初始条件必须还是在$u^*$上。
\end{newprop}
\end{eproposition}
\lipsum[5-6]
\begin{newcorol}
\begin{ecorollary}
假设$V(\cdot,\cdot)$为值函数,则跟据最大值原理~\ref{thm:31},有如下推论
\[
V(k,z)=\max\Big\{u\big(zf(k)-y\big)+\beta \mathbb{E}V(y,z^\prime)\Big\}
\]
\end{newcorol}
\end{ecorollary}
\begin{newproof}
\begin{eproof}
因为 $y^*=\alpha\beta z k^\alpha$$V(k,z)=\alpha/1-\alpha\beta\ln k_0+1/1-\alpha\beta \ln z_0+\Delta$
\begin{align*}
\text{右边}&=\Big\{u\big(zf(k)-y\big)+\beta \mathbb{E}V(y,z^\prime)\Big\}\\
@@ -216,7 +216,7 @@ V(k,z)=\max\Big\{u\big(zf(k)-y\big)+\beta \mathbb{E}V(y,z^\prime)\Big\}
&=\frac{\alpha}{1-\alpha\beta}\ln k+\frac{1}{1-\alpha\beta}\ln z+\Delta
\end{align*}
所以$\text{左边}=\text{右边}$,证毕。
\end{newproof}
\end{eproof}
@@ -237,13 +237,13 @@ This is one example of the custom environment, the key word is given by the opti
\lipsum[6]
\begin{newdef}[Contraction mapping]
\begin{edefinition}[Contraction mapping]
$(S,\rho)$ is the metric space, $T: S\to S$, If there exists $\alpha\in(0,1)$ such that for any $x$ and $y\in S$, the distance
\begin{equation}
\rho(Tx,Ty)\leq \alpha\rho(x,y)
\end{equation}
Then $T$ is a {\color{main} contraction mapping}.
\end{newdef}
\end{edefinition}
\begin{remark}
\begin{enumerate}