testing my sans math template

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2025-05-31 22:57:18 +08:00
parent 14c4303f03
commit 0fd4a3410e
5 changed files with 511 additions and 3 deletions

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@@ -1,5 +1,6 @@
\documentclass[11pt]{article}
\usepackage{chao}
% \usepackage{chao}
\usepackage[sans]{myctex}
% \usepackage{natbib}
@@ -64,7 +65,7 @@ For graphs with constant genus, \cite{lee_genus_2010} gives a $O(\sqrt{\log g})$
\section{Approximations}
Techniques for approximating \scut{}.
\subsection{LP $\Theta(\log n)$ - \nonuscut{}}
\subsection{LP \texorpdfstring{$\Theta(\log n)$}{θ(log n)} - \nonuscut{}}
\begin{minipage}{0.47\linewidth}
\begin{equation}\label{IP}
@@ -149,7 +150,7 @@ The gap can be improved to $\log k$ through a stronger metric embedding theorem
I believe the later method is more general and works for \nonuscut{}, while the former method is limited to \uscut{}. However, the proof in \cite{leighton_multicommodity_1999} may have connections with the proof of Bourgain's thm? Why does their method fail to work on \nonuscut{}?
\end{remark}
\subsection{SDP $O(\sqrt{\log n})$ - \uscut{}}
\subsection{SDP \texorpdfstring{$O(\sqrt{\log n})$}{O(√log n)} - \uscut{}}
This $O(\sqrt{\log n})$ approximation via SDP is developed in \cite{arora_expander_2004}. This is also described in \cite[section 15.4]{Williamson_Shmoys_2011}.
\begin{equation*}