diff --git a/elegantnote.cls b/elegantnote.cls new file mode 100644 index 0000000..4c25365 --- /dev/null +++ b/elegantnote.cls @@ -0,0 +1,427 @@ +%% start of file `elegantnote.cls'. +%% Copyright 2013-2019 ddswhu (ddswhu@gmail.com). +% +% % !Mode:: "TeX:UTF-8" +\NeedsTeXFormat{LaTeX2e} +\ProvidesClass{elegantnote}[2013/07/18 v1.00 elegant note document class] + +\RequirePackage{color,xcolor} + +\newcommand*{\base}[1]{ + \def\@base{\includegraphics[scale=0.3]{#1} + } +} + +\DeclareOption{green}{ + \definecolor{main}{RGB}{210,168,75} + \definecolor{seco}{RGB}{9,80,3} + \definecolor{thid}{RGB}{0,175,152} + \base{greenbase.pdf} +} + +\DeclareOption{cyan}{ + \definecolor{main}{RGB}{239,126,30} + \definecolor{seco}{RGB}{0,175,152} + \definecolor{thid}{RGB}{236,74,53} + \base{cyanbase.pdf} +} + +\DeclareOption{blue}{ + \definecolor{main}{RGB}{127,191,51} + \definecolor{seco}{RGB}{0,145,215} + \definecolor{thid}{RGB}{180,27,131} + \base{bluebase} +} + +\DeclareOption{times}{ + \AtBeginDocument{ + \RequirePackage{times} + } +} + +\DeclareOption{mtpro}{ + \AtBeginDocument{ + \RequirePackage{mtpro2} + } +} + + +%%载入基础类 +\DeclareOption*{% + \PassOptionsToClass{\CurrentOption}{book} +} + +\ExecuteOptions{green} + +\ProcessOptions\relax + +\LoadClass[12pt,a4paper,openany]{book} + + +\newtoks\zhtitle +\newtoks\entitle +\newtoks\email +\newtoks\version + +%%数学字体宏包 + +%% 常用宏包 +\RequirePackage{graphicx} +\RequirePackage{enumerate} +\RequirePackage{amsmath,mathrsfs,amsfonts} +\RequirePackage{booktabs} +\linespread{1.3} + +\graphicspath{{./figure/}{./figures/}{./image/}{./graphics/}{./graphic/}{./pictures/}{./picture/}} + +\newcommand*{\myquote}[1]{\def\@myquote{#1}} + +\newcommand*{\logo}[1]{ + \def\@logo{\includegraphics[height=5.8cm]{#1} + } +} + +%\newcommand*{\base}[1]{ +% \def\@base{\includegraphics[scale=0.3]{#1} +% } +%} + +% +%\newsavebox{\mylogo} +%\sbox{\mylogo}{% +%\centering +%\includegraphics[scale=0.3]{base.pdf}} + +\newcommand*{\cover}[1]{\def\@cover{ + \ThisTileWallPaper{\paperwidth}{\paperheight}{#1} + } +} + + +%% 页面设置 +\RequirePackage{hyperref} + +\hypersetup{ + breaklinks, + baseurl =http://, + unicode, + bookmarksnumbered =true, + bookmarksopen =true, + pdfauthor =\@author, + pdftitle =\@title note, + pdfsubject =\@author \@title note, + pdfkeywords ={notes}, + pdfcreator ={XeLaTeX with elegantnote class}, + colorlinks, + linkcolor =seco, + plainpages =false, + pdfstartview =FitH, + pdfborder={0 0 0}, + linktocpage + } + +\RequirePackage{geometry} +\geometry{ + a4paper, + left=27mm, %% or inner=23mm + right=27mm, %% or outer=18mm + top=25.4mm, bottom=25.4mm, + headheight=2.17cm, + headsep=4mm, + footskip=12mm +} + +%%% base +%\newsavebox{\mylogo} +%\sbox{\mylogo}{% +%\centering +%\includegraphics[scale=0.3]{base.pdf}} %需要修改尺寸和文件名 + +\RequirePackage{wallpaper} + +%% 章节设置 +\RequirePackage[center,pagestyles]{titlesec} +\renewcommand{\chaptername}{第 \thechapter 章} + +\titleformat{\chapter}[display]{\normalfont} +{\bfseries\filcenter\LARGE\enspace \color{seco}\chaptername\enspace}{1pt}{\color{seco}\LARGE\bfseries\filcenter}[\@base] + +\titleformat{\section}[hang]{\sffamily} +{\hspace{-2.45em}\Large\bfseries{\color{seco}\thesection}\enspace}{1pt}{\color{seco}\Large\bfseries\filright} + +\titleformat{\subsection}[hang]{\sffamily} +{\large\bfseries\color{seco}\thesubsection\enspace}{1pt}{\color{seco}\large\bfseries\filright} + +\titlespacing{\chapter}{0pt}{0pt}{1.5\baselineskip} +%\titlespacing{\subsection}{0pt}{0.5\baselineskip}{-\baselineskip} + + +%%中文结构名字 +\renewcommand{\contentsname}{\bfseries 目\hspace{2em}录} +\renewcommand{\figurename}{\textbf{图}} +\renewcommand{\tablename}{\text{表}} +\renewcommand{\partname}{部分} +\renewcommand{\listfigurename}{\bfseries 插图目录} +\renewcommand{\listtablename}{\bfseries 表格目录} +\renewcommand{\bibname}{\bfseries 参考文献} +\renewcommand{\appendixname}{\bfseries 附\hspace{2em}录} +\renewcommand{\indexname}{\bfseries 索\hspace{2em}引} + + + +%%字体设置 +%\RequirePackage{lmodern,fix-cm,type1cm} +\RequirePackage{fontenc} +\RequirePackage[no-math,cm-default]{fontspec} +\defaultfontfeatures{Mapping=tex-text} +\RequirePackage{xunicode} +\RequirePackage{xltxtra} +\setmainfont[Ligatures=TeX]{Minion Pro} % (\textrm) +\setsansfont{Myriad Pro} % (\textsf) +\setmonofont{Adobe Garamond Pro}%Palatino Linotype +%-中文字体设置-% +\RequirePackage{xeCJK} +\setCJKmainfont[BoldFont={黑体},ItalicFont={楷体}]{华文中宋}%方正书宋_GBK Adobe Song Std L +\setCJKsansfont[BoldFont={黑体}]{方正中等线简体} +\setCJKmonofont{方正启体简体} +\XeTeXlinebreaklocale "zh" +\XeTeXlinebreakskip = 0pt plus 1pt + +\setCJKfamilyfont{new}{方正苏新诗柳楷简体} + +%% 定理\引理\定义样式设置 +\RequirePackage{environ} +\RequirePackage{tikz} +\usetikzlibrary{shapes,decorations} + +%define the main and seco color in document +%\definecolor{main}{RGB}{210,168,75} +%\definecolor{seco}{RGB}{9,80,3} +%\definecolor{thid}{RGB}{0,175,152} + + +%\definecolor{main}{RGB}{239,126,30} +%\definecolor{seco}{RGB}{0,175,152} +%\definecolor{thid}{RGB}{236,74,53} + +%\definecolor{main}{RGB}{127,191,51} +%\definecolor{seco}{RGB}{0,145,215} +%\definecolor{thid}{RGB}{180,27,131} + + + + + +\definecolor{bule}{RGB}{18,29,57} +\definecolor{bablue}{RGB}{248,248,248} + +%define the style of tikz newthemsty + +\tikzstyle{newthemsty} + =[draw=seco, fill=blue!10,very thick,rectangle, + rounded corners, inner sep=10pt, inner ysep=20pt] +\tikzstyle{newthemstytitle} + =[fill=seco, text=blue!10] + +\tikzstyle{newdefinitionsty} + =[draw=main, fill=yellow!20,very thick,rectangle, + rounded corners, inner sep=10pt, inner ysep=20pt, + text=black,fill opacity=0.9] +\tikzstyle{newdefinitionstytitle} + =[fill=main, text=white] + +\tikzstyle{newpropositionsty} + =[draw=thid, 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] + +%%define the "newthem" environment +\newcounter{Newthem}[chapter] +\renewcommand{\theNewthem}{\thechapter.\arabic{Newthem}} +\NewEnviron{newthem}[1][{}]{% +\noindent\centering +\begin{tikzpicture} +\node[newthemsty] (box){ + \begin{minipage}{0.93\columnwidth} + \sffamily\BODY + \end{minipage}}; +\node[newthemstytitle,right=10pt] at (box.north west){ + \bf\textsf{Theorem \stepcounter{Newthem}\theNewthem\; #1}}; +\node[newthemstytitle, rounded corners] at (box.east) {$\clubsuit$}; +\end{tikzpicture} +}[\par\vspace{.5\baselineskip}] + +%%define the "newlemma" environment +\newcounter{Newlemma}[chapter] +\renewcommand{\theNewlemma}{\arabic{Newlemma}} +\NewEnviron{newlemma}[1][{}]{% +\noindent\centering +\begin{tikzpicture} +\node[newthemsty] (box){ + \begin{minipage}{0.93\columnwidth} + \sffamily\BODY + \end{minipage}}; +\node[newthemstytitle,right=10pt] at (box.north west){ + \bf\textsf{Lemma \stepcounter{Newlemma}\theNewlemma\; #1}}; +\node[newthemstytitle, rounded corners] at (box.east) {$\clubsuit$}; +\end{tikzpicture} +}[\par\vspace{.5\baselineskip}] + +%%define the "newcorol" environment +\newcounter{Newcorol}[chapter] +\renewcommand{\theNewcorol}{\arabic{Newcorol}} +\NewEnviron{newcorol}[1][{}]{% +\noindent\centering +\begin{tikzpicture} +\node[newthemsty] (box){ + \begin{minipage}{0.93\columnwidth} + \sffamily\BODY + \end{minipage}}; +\node[newthemstytitle,right=10pt] at (box.north west){ + \bf\textsf{Corollary \stepcounter{Newcorol}\theNewcorol\; #1}}; +\node[newthemstytitle, rounded corners] at (box.east) {$\clubsuit$}; +\end{tikzpicture} +}[\par\vspace{.5\baselineskip}] + +%% define the "proposition" environment +\newcounter{Newprop}[chapter] +\renewcommand{\theNewprop}{\thechapter.\arabic{Newprop}} +\NewEnviron{newprop}[1][{}]{% +\noindent\centering +\begin{tikzpicture} +\node[newpropositionsty] (box){ + \begin{minipage}{0.93\columnwidth} + \sffamily\BODY + \end{minipage}}; +\node[newpropositionstytitle,right=10pt] at (box.north west){ + \bf\textsf{Proposition \stepcounter{Newprop}\theNewprop\; #1}}; +\node[newpropositionstytitle, rounded corners] at (box.east) {$\spadesuit$}; +\end{tikzpicture} +}[\par\vspace{.5\baselineskip}] + + +%%define the "newdef" environment +\newcounter{Newdefinition}[chapter] +\renewcommand{\theNewdefinition}{\thechapter.\arabic{Newdefinition}} +\NewEnviron{newdef}[1][{}]{% +\noindent\centering +\begin{tikzpicture} +\node [newdefinitionsty] (dbox){\begin{minipage}{0.93\textwidth}\itshape\BODY\end{minipage}}; +\node[newdefinitionstytitle, right=10pt] at (dbox.north west) {\bf\textsf{Definition \stepcounter{Newdefinition}\theNewdefinition\; #1}}; +\node[newdefinitionstytitle, rounded corners] at (dbox.east) {$\heartsuit$}; +\end{tikzpicture} +}[\par\vspace{.5\baselineskip}] + + + +%%define the note and newproof environment +\RequirePackage{pifont,manfnt} +\newenvironment{note}{\par\ttfamily\itshape\noindent{\makebox[0pt][r]{\scriptsize\color{red!90}\textdbend\quad}\textbf{Note:}}}{\par\vspace{.5\baselineskip}} + +\newenvironment{example}{\par\noindent\textbf{Example: }\color{black!90}}{\par\vspace{.5\baselineskip}} + +\newenvironment{assumption}{\par\noindent\textbf{Assumptions: }\color{black!90}}{\par\vspace{.5\baselineskip}} + +\newenvironment{conclusion}{\par\noindent\textbf{Conclusions: }\color{black!90}}{\par\vspace{.5\baselineskip}} + +\newenvironment{newproof}{\par\noindent{\makebox[0pt][r]{\color{seco}\ding{43}\;\;}\textbf{Proof:}}\color{black!90}\small}{\hfill$\Box$\quad\par\vspace{.5\baselineskip}} + +%页眉页脚 + +\RequirePackage{fancyhdr} +\RequirePackage{lastpage} +\fancyhf{} +\fancyhead[EL,OR]{\color{seco}--\thepage/\pageref{LastPage}--} +\fancyhead[ER]{\color{seco}\em\nouppercase\leftmark{}} +\fancyhead[OL]{\color{seco}\em\nouppercase\rightmark} +\fancyfoot[c]{\@base} +\renewcommand{\headrule}{\color{seco}\hrule width\textwidth} +\pagestyle{fancy} + +\fancypagestyle{plain}{\renewcommand{\headrulewidth}{0pt}\fancyhf{}\renewcommand{\headrule}{}} +\renewcommand{\sectionmark}[1]{\markright{\thesection\; #1}{} } +\renewcommand{\chaptermark}[1]{\markboth{\chaptername \; #1\;}{}} + + +%\let\origdoublepage\cleardoublepage +%\newcommand{\clearemptydoublepage}{% +% \clearpage +% {\pagestyle{empty}\origdoublepage}% +%} +%\let\cleardoublepage\clearemptydoublepage + +%\RequirePackage{nextpage} +%\cleartooddpage[\thispagestyle{empty}] +%\cleartoevenpage[\thispagestyle{empty}] +%%封面 + +\def\maketitle{% +\thispagestyle{empty} +\@cover +\vfill +\vspace*{2cm} +\begin{center} +\color{main} +\rule{0.8\textwidth}{2pt}\\ +\Huge {\color{seco} \bfseries \the\entitle } {\color{main} \bfseries Note}\\ +{\Huge \CJKfamily{new}{\color{seco} \the\zhtitle } 笔记}\\ +\rule{0.8\textwidth}{2pt} +\end{center} +\vskip3ex +\begin{figure}[htp] +\centering +\@logo +\end{figure} +\begin{center} +\begin{minipage}{0.65\textwidth} +\Eindent\color{bule}\@myquote +\end{minipage} +\end{center} +\vfill +\vspace{2cm} +\begin{flushright} +\color{main} +\rule{0.45\textwidth}{1pt}\\ +整理:{\color{seco}\@author}\\ +整理时间:{\color{seco}\today}\\ +Email: \hyperlink{\the\email}{\the\email}\\ +\rule{0.45\textwidth}{1pt} +\end{flushright} +\vfill +\begin{center} +\color{main} Version: \the\version +\end{center} +\vfil\eject +} + + +%%中文两个字符缩进 +%----字宽/缩进----- +%----CJK字符宽度 +%\f@size = 当前字符大小数值(pt/pt) +%\p@ = 1pt +\def\elegant@CJKChar@size{\hskip \f@size \p@} +%----定义字宽 +%字宽 = 字符宽度 + 字符间距 = 相邻字符中心的间距 +\newdimen\elegant@CJKChar@size@dimen +\settowidth\elegant@CJKChar@size@dimen{\elegant@CJKChar@size\CJKglue} +%----用户接口 +%负责刷新字宽和段落缩进 +\newcommand{\CJKsetfontspace}{% +%刷新字宽 +\settowidth\elegant@CJKChar@size@dimen{\elegant@CJKChar@size\CJKglue}% +%刷新段落缩进 +%判断段落缩进是否被设置为0(如果是表示要求不缩进) +\ifdim\parindent=0pt% +\relax% +\else% +\parindent2\elegant@CJKChar@size@dimen% +\fi% +} +\newcommand{\Eindent}{\CJKsetfontspace\parindent2\elegant@CJKChar@size@dimen} +\newcommand{\Enoindent}{\parident\z@} +%----自动执行 +\AtBeginDocument{\Eindent} + diff --git a/figure/bluebase.pdf b/figure/bluebase.pdf new file mode 100644 index 0000000..e71f961 Binary files /dev/null and b/figure/bluebase.pdf differ diff --git a/figure/cover.pdf b/figure/cover.pdf new file mode 100644 index 0000000..ef841fc Binary files /dev/null and b/figure/cover.pdf differ diff --git a/figure/cyanbase.pdf b/figure/cyanbase.pdf new file mode 100644 index 0000000..baa246e Binary files /dev/null and b/figure/cyanbase.pdf differ diff --git a/figure/greenbase.pdf b/figure/greenbase.pdf new file mode 100644 index 0000000..05b43b1 Binary files /dev/null and b/figure/greenbase.pdf differ diff --git a/figure/logo.pdf b/figure/logo.pdf new file mode 100644 index 0000000..5775d07 Binary files /dev/null and b/figure/logo.pdf differ diff --git a/guide.pdf b/guide.pdf new file mode 100644 index 0000000..9db551c Binary files /dev/null and b/guide.pdf differ diff --git a/guide.tex b/guide.tex new file mode 100644 index 0000000..3507122 --- /dev/null +++ b/guide.tex @@ -0,0 +1,201 @@ +\documentclass[cyan]{elegantnote} + +\author{ddswhu \& 小L} +\email{ddswhu@gmail.com} +\zhtitle{优美的\LaTeX{}模板} +\entitle{Elegant \LaTeX{}} +\version{1.00} +\myquote{Victory won\rq t come to us unless we go to it.} +\logo{logo.pdf} +\cover{cover.pdf} + +%green color + \definecolor{main1}{RGB}{210,168,75} + \definecolor{seco1}{RGB}{9,80,3} + \definecolor{thid1}{RGB}{0,175,152} +%cyan color + \definecolor{main2}{RGB}{239,126,30} + \definecolor{seco2}{RGB}{0,175,152} + \definecolor{thid2}{RGB}{236,74,53} +%cyan color + \definecolor{main3}{RGB}{127,191,51} + \definecolor{seco3}{RGB}{0,145,215} + \definecolor{thid3}{RGB}{180,27,131} + +\usepackage{makecell} +\usepackage{lipsum} + + + + + +\begin{document} +\maketitle +\tableofcontents +\chapter{Elegant Note模板的由来} + +只有当自己想去做一件事的时候才能把事情做好! + +\section{长长的历史,长长的期待} + +写这个模板的初衷是为了简化我在写笔记中的工作,因为我不会写类文件和包文件,所以,最当初是想拜托小L做出一个简洁,清爽的\LaTeX{}模板,最好是类文件,而且因为这样可以简化导言区复杂的内容。后来,和小L一拍即合,遂开始一起做Elegant\LaTeX{}的设计。 + +在学校的时候,搞定了定理环境样式的代码。因为不想重复 ChinaTeX 那个经典的页眉页脚,我找到了计量书上的一个图案,小L拿 Ti\emph{k}Z 一点一点把那个画出来了,不过我最后还是用的截取的方式得到的图案。然后慢慢地,我们把初步的样子做出来了。 + +2013年的暑假开始后,我对那个初步的模板做了一点改动,然后用它写了Dynamic Programing 的笔记,并且,在写的过程中,对模板加了封面,也就是模板现在的封面。至此,模板的大致样子终于出来了,不过也在写笔记的过程中知道了某些不足,比如 +\begin{enumerate} +\item 定理类的环境在我们这个模板中不能浮动,也不能跨页,在我们这个1.00版本中,这个功能仍然没有得到解决。 +\item 某些环境不足,比如例子、假设、性质、结论等环境,在1.00版本中已经增加了这几个环境。 +\item 一些我们不可预知的错误将会不期而遇。 +\item 一些我们目前没有需求,但是可以继续改进的地方,比如表格样式,比如抄录样式等。 +\end{enumerate} + +写完那个笔记之后越发让我对Elegant\LaTeX{}模板的制作更有激情,在和小L相互讨论的几天里,我们终于得到了现在这个版本的ElegantNote模板。 + + + + +\section{一张白纸折腾出一个模板} + +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moderncv.cls文件、武汉大学黄正华老师的论文模板,以及 +各大\LaTeX{}疑问解答网站。 + +{\color{thid}这章还有这么大空间,忍不住插个图!} + +\begin{figure}[!hbtp] +\includegraphics[width=0.8\textwidth]{happy.jpg} +\caption{Happiness,We have it!\label{figur:happy}} +\end{figure} + +\chapter{Elegant Note开服说明} + +\section{关于字体} + +首先呢?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 +\begin{itemize} +\itemsep=3pt +\parskip=0pt +\item Adobe Garamond Pro +\item Minion Pro \& Myriad Pro +\item 方正字体 +\item 华文中宋 +\end{itemize} + +并且,如果系统内安装了Adobe字体,建议大家把模板中的黑体,楷体,宋体等字替换成Adobe字体,这样可以达到最佳效果。 + +\begin{note} +需要特别注意的是,如果笔记需要使用到抄录环境的,请重新修改字体,此版本并未为抄录环境设置合适字体,本note环境的字体即为抄录环境使用到的字体。 +\end{note} + +\section{文档说明} +\subsection{编译方式} +本模板基于book文类,所以book的选项对于本模板也是有效的。但是,只支持 \XeLaTeX{},编码为 UTF-8,推荐使用 \TeX{}live编译。作者编写环境为Win8(64bit)+\TeX{}live 2013。 + +本文特殊选项设置共有2类,分为{\color{main}颜色}和{\color{main}数学字体}。 + +\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green(default),cyan,blue。默认为green颜色主题。需要改变颜色的话请自行到elegantnote.cls文件内对颜色的RGB值进行修改。 + +第二类为{\color{main}数学字体}设置,有两个可选项,分别是computer modern 和 mtpro2字体,默认使用cm字体,无需在类文件前加选项,调用mtpro2字体的方法为\verb|\documentclass[mtpro]{elegantnote}| + +\begin{table}[htp] +\centering +\begin{tabular}{ccccc} +\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}}}& newdef\\ + +seco &\makecell{ {\color{seco1}\rule{1cm}{1cm}}}& \makecell{{\color{seco2}\rule{1cm}{1cm}}}&\makecell{ {\color{seco3}\rule{1cm}{1cm}}}&newthem \ newlemma \ newcorol\\ + +thid &\makecell{ {\color{thid1}\rule{1cm}{1cm}}}& \makecell{{\color{thid2}\rule{1cm}{1cm}}}&\makecell{ {\color{thid3}\rule{1cm}{1cm}}}&newprop\\ +\bottomrule +\end{tabular} +\caption{Elegant note 模板中的三套颜色主题\label{tab:color thm}} +\end{table} + +\subsection{数学环境简介} +在我们这个模板中,定义了三大类环境 +\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} newdef} 环境,含有一个可选项,编号以章节为单位; +\item {\color{main}newthem、newlemma、newcorol} 环境,三者颜色一致,但是定理环境编号以章节为单位,引理和推论为全文编号; +\item newprop 环境,含有可选项,编号以章节为单位。 +\end{itemize} +\item 证明类环境,有{\color{main}newproof、note} 环境,特点是,有引导符和引导词,并且证明环境有结束标志。 +\item 示例环境,有{\color{main} example、assumption、conclusion} 环境,三者均以粗体的引导词为开头,字体以灰色,和普通段落格式一致。 +\end{enumerate} + +\subsection{可编辑的字段} +在模板中,可以编辑的字段分别为作者\verb|\author|、\verb|\email|、\verb|\zhtitle|、\verb|\entitle|、\verb|\version|。并且,可以根据自己的喜好把封面水印效果的\verb|cover.pdf|替换掉,以及封面中用到的\verb|logo.pdf|。 + +\chapter{笔记写作示例} + +\section{灵魂不随便出卖,代码也不随便瞎写} +\lipsum[3] +考虑如下的随机动态规划问题 +\begin{align*} +&\max(\min)\quad \mathbb{E}\int_{t_0}^{t_1}f(t,x,u)\,dt\\ +&\quad\mbox{s.t.} \quad dx=g(t,x,u)dt+\sigma(t,x,u)dz\\ +&\quad \hspace{2.em} k(0)=k_0\;\text{given} +\end{align*} + +where $z$ is stochastic process or white noise or wiener process. + +\begin{newdef}[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} + +\lipsum[1-2] + +\begin{newthem}[勾股定理] +勾股定理的数学表达为 +\[a^2+b^2=c^2\] +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} + +\begin{note} +因为引理,推论的样式和定理的样式一致,仅仅只有计数器的设置不一样,在这里,我们就不写引理和推论的例子了。 +\end{note} + + +\lipsum[4] + +\begin{newprop}[最优性原理] +如果$u^*$在$[s,T]$上为最优解,则$u^*$在$[s,T]$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} + +\lipsum[5-6] +\begin{newcorol} +假设$V(\cdot,\cdot)$为值函数,则跟据最大值原理,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} + +\begin{newproof} +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\}\\ +&=\ln(zk^\alpha-\alpha\beta zk^\alpha)+\beta\mathbb{E}\Big[\frac{\alpha}{1-\alpha\beta}\ln y+\frac{1}{1-\alpha\beta}\ln z^\prime+\Delta\Big]\\ +&=\ln(1-\alpha\beta)zk^\alpha+\beta\Big\{\mathbb{E}\big[\frac{\alpha}{1-\alpha\beta}\ln \alpha\beta z k^\alpha\big]+\frac{1}{1-\alpha\beta}\mathbb{E}[\ln z^\prime]+\Delta\Big\} +\end{align*} +利用$\mathbb{E}[\ln z^\prime]=0$,并将对数展开得 +\begin{align*} +\text{右边}&=\ln (1-\alpha\beta)+\ln z+\alpha\ln k+\frac{\alpha\beta}{1-\alpha\beta}\big[\ln \alpha\beta+\ln z+\alpha\ln k\big]+\frac{\beta}{1-\alpha\beta}\mu+\beta \Delta\\ +&=\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} + + + + +\begin{conclusion} +今天看到一则小幽默,是这样说的:{\color{main} 别人都关心你飞的有多高,只有我关心你的翅膀好不好吃!}说多了都是泪啊! +\end{conclusion} + +最后祝大家\LaTeX{}的学习之路快乐精彩! + +\end{document} diff --git a/image/happy.jpg b/image/happy.jpg new file mode 100644 index 0000000..407dc43 Binary files /dev/null and b/image/happy.jpg differ