Related papers: A simplified proof of a Lee-Yang type theorem
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
Based on the material in an old article of Wallach a short proof of the Harish-Chandra condition is given.
We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.
We generalize Thomas-Yau's uniqueness theorem in two ways. We prove a stronger statement for special Lagrangians and include minimal Lagrangians in K\"ahler-Einstein manifold or more generally J-minimal Lagrangians introduced by Lotay and…
In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].
This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
A type analysable in one-based types in a simple theory is itself one-based.
We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on $\R^n$. This is an application of small ball estimate and Chernoff's…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
A short proof is given of a necessary and sufficient condition for the normalized occupation measure of a L\'evy process in a metrizable compact group to be asymptotically uniform with probability one.
We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$
Using nonstandard analysis, a very short and elementary proof of the Doob-Meyer decomposition and the Dol{\'e}ans Dade theorems is provided.
We give a formal Laurent series proof of Andrews's $q$-Dyson Conjecture, first proved by Zeilberger and Bressoud.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
Inspired Yau's work (Comm. Anal. Geom., 1994), in this short note we provide a new version of Li-Yau gradient estimate for the linear heat equation, which generalizes some known results and gives new gradient estimates. Also we explain the…
We present a proof of Chow's theorem using two results of Errett Bishop retated to volumes and limits of analytic varieties. We think this approach suggested a long time ago in the beautiful book by Gabriel Stolzenberg, is very attractive…
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.