Commit 546828de authored by studer_a1's avatar studer_a1

Initial import

parent 74312d76
Pipeline #1059 failed with stages
\NeedsTeXFormat{LaTeX2e}
\documentclass[11pt,a4paper]{article}
\usepackage{a4,latexsym}
\usepackage{epsfig}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{listings}
\usepackage{verbatim}
\usepackage{amssymb}
\author{alain.studer@psi.ch}
\begin{document}
\begin{equation}
\int_A p(x) dx = \int_{\varphi(A)} c(x) dx
\end{equation}
\begin{equation}
\int_A p(x) dx =
\int_{\varphi(A)} c(x) dx =
\int_A c(\varphi(x)) |det D\varphi(x)| dx
\end{equation}
\begin{equation}
p(x) =
c(\varphi(x)) \cdot |det D\varphi(x)|
\end{equation}
\begin{equation}
p(x) =
c(\varphi(x)) \cdot |det D\varphi(x)|
= c(x) |det \mathbf{1}| = c(x)
\end{equation}
\begin{equation}
\varphi* = \underset{ \varphi}{argmin} \int_{\Omega} |x - \varphi(x)| p(x) dx
\end{equation}
\begin{equation}
\int_{\Omega} \Phi(x, y) dx = c(y)
\quad \int_{\Omega} \Phi(x, y) dy = p(x)
\end{equation}
\begin{equation}
\Phi^* = \underset{ \Phi}{argmin} \int_{\Omega \times \Omega} |x - y| \Phi(x, y) dx dy
\end{equation}
\end{document}
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