Related papers: A note on the Lee-Yang circle theorem
The purpose of this short note, is to rewrite Morozov's formula for correlation functions over the unitary group, in a much simpler form, involving the computation of a single determinant.
This note shows that the three theorems presented in J. Math. Anal. Appl. 556 (2026), 130199, whose proofs, in their present formulation, are purely formal, follow from elementary calculus.
In this note we shall give a new proof to a quadrature formulae due to Newton.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…
In this note we prove that the centers of a closed chain of circles for which every two consecutive members meet in the points of two given circles form a tangent polygon of a conic.
This is a short note on the log canonical inversion of adjunction.
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We improve constants in the Rademacher-Menchov inequality.
In this paper we provide an application to the Neumann problem of a recent three critical points theorem.
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
This short note contains elementary evaluations of some Euler sums.
We discuss the (twisted) weak positivity theorem. We also treat some applications.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.