相关论文: Comments on a Theorem by Ancona
Withdrawn -- a revised version will appear in due course.
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
The note complements topological aspects of the theory of chiral algebras.
We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…
The Bernstein-type operator of Aldaz, Kounchev and Render (2009) is discussed. New direct results in terms of the classical second order modulus as well as in a modification following Marsden and Schoenberg are given.
A conjecture regarding the structure of expander graphs is discussed.
The article on the upper central series of infinite groups by M. de Falco, F. de Giovanni, C. Musella and Y.P. Sysak, proceedings of the american mathematical society, Volume 139, Number 2, February 2011, 385--389 consists of a quite long…
In this lecture we prove a converse to Cartan's Theorem B for real analytic sets, due to Fernando and Ghiloni [arXiv:2506.18347].
As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.
In 1962 P\'osa conjectured that every graph G on n vertices with minimum degree at least 2n/3 contains the square of a hamiltonian cycle. In 1996 Fan and Kierstead proved the path version of P\'osa's Conjecture. They also proved that it…
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…
This note is a reaction to Conant and Kruckman's recent preprint `Three surprising instance of dividing'. It mainly consists of an erratum to the author's paper `Forking, imaginaries and other features of ACFG', in light of the results of…
This paper deals with the notion of Gr\"obner $\delta$-base for some rings of linear differential operators by adapting the works of W. Trinks, A. Assi, M. Insa and F. Pauer. We compare this notion with the one of Gr\"obner base for such…
Gentzen's 1936 proof of the consistency of Peano Arithmetic was a significant result in the foundations of mathematics. We provide here a modified version of the proof, based on G\"{o}del's reformulation, and including additional details…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
As well known, the important hypothesis formulated by B.G. RIEMANN in 1859 states that all non-trivial zeroes of the Zeta function $Z(s)=\sum_{n=1}^{\infty } n^{-s}$ should fall on the Critical Line (C.L.) $Re(s)=\frac{1}{2}$.\\ Although…
The aim of these notes is to give a introduction to the ideas and techniques of handling rational curves on varieties. The main emphasis is on varieties with many rational curves which are the higher dimensional analogs of rational curves…
In this paper, we revise the BBM formula due to J. Bourgain, H. Brezis, and P. Mironescu in [1].
The article provides a counterexample to a conjecture by Blocki-Zwonek.
We present a short proof of Cantor's Theorem (circa 1870s): if $a_n \cos nx + b_n \sin nx \to 0$ for each $x$ in some (nonempty) open interval, where $a_n, b_n$ are sequences of complex numbers, then $a_n$ and $b_n$ converge to 0.