Related papers: A note on the Lee-Yang circle theorem

We give a sketch for an alternative proof of a recent result by J. Tseng.

In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.

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…

In this note we briefly survey and propose some open problems related to isoparametric theory.

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…

In this note, we provide with a simple example to show a defect in the definition of the geometric mixing scale, and then introduce an improved scale, called as the strong geometric mixing scale. The main theorem in this note is the…

We give a brief proof of a recent result of Avron, Seiler and Simon.

An observation on Hall-Littlewood polynomials.

In this short note, we improve the famous Reid Inequality related to linear operators.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

With this short note, we close a gap in the linear stability theory of block predictor-corrector Runge-Kutta schemes originally proposed for the parallel solution of ODEs.

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

The note clarifies a gap in the proof of the minimum distance for Projective Reed-Muller Codes. The gap was identified by S.Ghorpade and R.Ludhani in a recent article. Here the original thoughts are explained and the gap closed.

Remarks on mathematical proof and the practice of mathematics.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…