相关论文: A Short Proof of the Poincar\'e Conjecture

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

We expose here a short proof of Cramer's theorem in R based on convex duality.

"V - E + F = 2", the famous Euler's polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as the Euler-Poincar\'e Formula. We provide another short inductive proof of the general formula.…

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

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…

In this short note, we show that a result about words which coincide except in one position given as an exercise in Lothaire's Algebraic Combinatorics on Words is false. Moreover, we derive a modified statement which allows us to fix the…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

General considerations on the Equivalence conjectures and a review of few mathematical results.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We provide new sufficient conditions under which Ryser's conjecture holds.

We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

We present a conjecture about partitions, with a very elementary formulation.

A version of Woodin's HOD dichotomy is proved assuming the existence of just one strongly compact cardinal.

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.