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@@ -1,10 +1,11 @@ | ||
%!TEX program = xelatex | ||
\documentclass[color=green,mathpazo,titlestyle=hang,11pt]{elegantbook} | ||
\documentclass[color=blue,mathpazo,titlestyle=hang,11pt]{elegantbook} | ||
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\author{ddswhu \& LiamHuang0205} | ||
\email{[email protected]} | ||
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\zhtitle{优美的\LaTeX{} 书籍} | ||
\zhend{} | ||
\zhend{模板} | ||
\entitle{Elegant\LaTeX{} Book} | ||
\enend{Template} | ||
\version{2.10} | ||
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@@ -174,7 +175,7 @@ \section{灵魂不随便出卖,代码也不随便瞎写} | |
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} | ||
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\begin{newthem}[勾股定理] | ||
\begin{newthem}[勾股定理]\label{them} | ||
勾股定理的数学表达(Expression)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。 | ||
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@@ -187,7 +188,7 @@ \section{灵魂不随便出卖,代码也不随便瞎写} | |
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\lipsum[4] | ||
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\begin{newprop}[最优性原理] | ||
\begin{newprop}[最优性原理]\label{thm} | ||
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} | ||
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@@ -233,14 +234,17 @@ \section{灵魂不随便出卖,代码也不随便瞎写} | |
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\lipsum[6] | ||
\begin{newdef}[Contraction mapping] | ||
\begin{newdef}[Contraction mapping]\label{def:2.3} | ||
$(S,\rho)$ 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} | ||
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\ref{def:2.3} | ||
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\ref{them} | ||
\begin{remark} | ||
\begin{enumerate} | ||
\parskip=0pt \itemsep=0pt | ||
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