Related papers: Wilson's and Wolstenholme's Theorems
Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or…
We present a strengthening of the proof of the St\'ephanois theorem. We follow the modular version by Waldschmidt, which is based in a suggestion by Daniel Bertrand, but it also applies to the original proof. The improvement is not in the…
In this paper, by studying the famous theorem of Pang and Zalcman, we find a normal family and obtain a result, which is an improvement of Pang and Zalcman's theorem in some sense. Meanwhile, several examples are provided to show that our…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
It is known that the duals of transversal matroids are precisely the strict gammoids. The purpose of this short note is to show how the Lindstrom-Gessel-Viennot lemma gives a simple proof of this result.
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
We demonstrate that many Naturalness tests of particle theories discussed in the literature can be reformulated as straightforward algorithmic finetuning assessments in the matching of Wilsonian effective theories above and below particle…
This technical report presents a direct proof of Theorem~1 in [1] and some consequences that also account for (20) in [1]. This direct proof exploits a state space change of basis which replaces the coupled difference equations (10) in [1]…
This expository paper focuses on free Lie $K$-algebras and the basic PBW theorem. We argue in various ways that the basic PBW theorem is a quite close consequence of the Magnus-Witt theorems concerning free Lie algebras.
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…
Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…
We provide a short proof for the Figiel, Lindenstrauss and Milman inequality regarding the number of vertices and faces of certain polytope, with an explicit bound on the universal constant involved. The proof is completely elementary and…
As an extension of positive and almost positive diagrams and links, we study two classes of links we call successively almost positive and weakly successively almost positive links. We prove various properties of polynomial invariants and…
Two well known facts from elementary number theory are proven by using Bergman spaces.
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
We give a large sieve type inequality for functions supported on primes. As application we prove a conjecture by Elliott, and give bounds for short character sums over primes. The proves uses a combination of the large sieve and the Selberg…