summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/math-e/01-00-3.ltx
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/math-e/01-00-3.ltx')
-rw-r--r--Master/texmf-dist/doc/latex/math-e/01-00-3.ltx48
1 files changed, 48 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/math-e/01-00-3.ltx b/Master/texmf-dist/doc/latex/math-e/01-00-3.ltx
new file mode 100644
index 00000000000..be601182531
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/math-e/01-00-3.ltx
@@ -0,0 +1,48 @@
+%%
+%% An UIT Edition example
+%%
+%% Example 01-00-3 on page 4.
+%%
+%% Copyright (C) 2010 Herbert Voss
+%%
+%% It may be distributed and/or modified under the conditions
+%% of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%%
+%% See http://www.latex-project.org/lppl.txt for details.
+%%
+%%
+%% ====
+% Show page(s) 1
+%%
+\documentclass[]{exaarticle}
+\pagestyle{empty}
+\setlength\textwidth{375.57637pt}
+\setlength\parindent{0pt}
+\setcounter{equation}{3}
+\renewcommand\theequation{1.\arabic{equation}}
+\StartShownPreambleCommands
+\usepackage{amsmath,esint}
+\newcommand\abs[1]{\left\lvert#1\right\rvert}
+\newcommand*\diff{\mathop{}\!\mathrm{d}}
+\StopShownPreambleCommands
+\begin{document}
+\setlength\jot{15pt}
+\begin{align*}
+\begin{split}\abs{I_1} &= \left\lvert \int_\Omega gRu\diff\Omega\right\rvert\\
+ & \le C_3\left[\int_\Omega\left(\int_{a}^x g(\xi,t)\diff\xi\right)^2\diff\Omega\right]^{1/2}
+ \times\left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+ \left(\int_{a}^x cu_t\diff\xi\right)^2\right\}\diff\Omega\right]^{1/2}\\
+ & \le C_4\left\lvert \left\lvert f\left\lvert \widetilde{S}^{-1,0}_{a,-}W_2(\Omega,\Gamma_l)
+ \right\rvert\right\rvert\left\lvert \abs{u}\overset{\circ}\to W_2^{\widetilde{A}}
+ (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\\
+\begin{split}\abs{I_2} &= \left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+ -\int_{\gamma(t)}^a\frac{\diff\theta}{k(\theta,t)}
+ \int_{a}^\theta c(\xi)u_t(\xi,t)\diff\xi\right\}\diff t\right\rvert\\
+ & \le C_6\left\lvert \left\lvert f\int_\Omega\left\lvert \widetilde{S}^{-1,0}_{a,-}
+ W_2(\Omega,\Gamma_l)\right\rvert\right\rvert\left\lvert \abs{u}\overset{\circ}
+ \to W_2^{\widetilde{A}}(\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\tag{\theequation$'$}
+\end{align*}
+\end{document}