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\section{The four vertex theorem}
The classic 4-vertex theorem states that {\it the curvature of a smooth closed convex planar curve has at least four critical points}, see Figure \ref{ellipse} for an illustration.
\begin{figure}[hbtp]
\centering
\includegraphics[height=2in]{ellipse}
\caption{An ellipse and its evolu... | {'timestamp': '2018-06-18T02:10:56', 'yymm': '1805', 'arxiv_id': '1805.12065', 'language': 'en', 'url': 'https://arxiv.org/abs/1805.12065'} | ArXiv |
\section{Introduction}
This paper considers the question of determining the number of covers
between genus-$0$ curves with fixed ramification in positive
characteristic. More concretely, we consider covers $f:{\mathbb P}^1\to
{\mathbb P}^1$ branched at $r$ ordered points $Q_1, \ldots, Q_r$ of fixed {\em
ramification ... | {'timestamp': '2009-06-09T19:52:34', 'yymm': '0906', 'arxiv_id': '0906.1793', 'language': 'en', 'url': 'https://arxiv.org/abs/0906.1793'} | ArXiv |
\section{Introduction and main results}
In this note we are interested in the existence versus non-existence of stable sub- and super-solutions of equations of the form
\begin{equation} \label{eq1}
-div( \omega_1(x) \nabla u ) = \omega_2(x) f(u) \qquad \mbox{in $ {\mathbb{R}}^N$,}
\end{equation} where $f(u)$ is one o... | {'timestamp': '2011-08-17T02:00:55', 'yymm': '1108', 'arxiv_id': '1108.3118', 'language': 'en', 'url': 'https://arxiv.org/abs/1108.3118'} | ArXiv |
\section{Introduction}
\label{sec:intro}
\begin{figure}
\centering
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\begin{minipage}[c]{0.3\linewidth}
\includegraphics[width=\linewidth, height=1.4\linewidth]{res/img/example/2.jpg}
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\includegraphics[width=\linewid... | {'timestamp': '2020-08-13T02:11:53', 'yymm': '2008', 'arxiv_id': '2008.05156', 'language': 'en', 'url': 'https://arxiv.org/abs/2008.05156'} | ArXiv |
"\\section{Introduction}\n\nDynamic contrast enhanced MRI (DCE-MRI) in the liver is widely used for (...TRUNCATED) | "{'timestamp': '2018-10-04T02:05:48', 'yymm': '1807', 'arxiv_id': '1807.06956', 'language': 'en', 'u(...TRUNCATED) | ArXiv |
"Abstract: Motion artifacts are a primary source of magnetic resonance (MR) image quality deteriorat(...TRUNCATED) | "{'timestamp': '2019-04-22T22:38:06Z', 'url': 'https://arxiv.org/abs/1809.06276', 'language': 'en', (...TRUNCATED) | ArXiv |
"\\section{Introduction}\n\\label{sec:intro}\n\nLet $G$ be a simply-connected, simple compact Lie gr(...TRUNCATED) | "{'timestamp': '2019-09-12T02:11:50', 'yymm': '1909', 'arxiv_id': '1909.04643', 'language': 'en', 'u(...TRUNCATED) | ArXiv |
"\n\\section{Global Meshing by Labatut~et~al.}\n\\label{sec:base_method}\n\nOur base method is a glo(...TRUNCATED) | "{'timestamp': '2017-05-03T02:06:05', 'yymm': '1705', 'arxiv_id': '1705.00949', 'language': 'en', 'u(...TRUNCATED) | ArXiv |
"\\section{Introduction}\nCoronal lines are collisionally excited forbidden transitions within\nlow-(...TRUNCATED) | "{'timestamp': '2005-09-07T17:03:32', 'yymm': '0509', 'arxiv_id': 'astro-ph/0509181', 'language': 'e(...TRUNCATED) | ArXiv |
"\\section{Introduction}\n\\label{sec1}\n\\IEEEPARstart{W}{ith} the development of the internet of v(...TRUNCATED) | "{'timestamp': '2022-08-03T02:06:56', 'yymm': '2208', 'arxiv_id': '2208.01219', 'language': 'en', 'u(...TRUNCATED) | ArXiv |
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