Related papers: Introducing the discussion paper by Sz\'{e}kely an…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
The paper presents a counterexample to the Hodge conjecture.
I reply to the four points raised by S. A. Hayward, R. Di Criscienzo, M. Nadalini, L. Vanzo, S. Zerbini (arXiv:0909.2956v1) against my comment (arXiv:0907.2020v1) to their previous article. I maintain my position on the wrongness of their…
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
This is a comment to a letter by D. Mandal, K. Klymko and M. R. DeWeese published as Phys. Rev. Lett. 119, 258001 (2017).
The aim of the present text is to provide some basics around Reshetnyak's theory of subharmonic distances, together with an overview of the main results. This text is intended to be a complement to the English translation of \cite{R1954},…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
Some of the conclusions of an improved JWKB method by Eleuch H., Rostovtsev Y. V. and Scully M. O., EPL, 89 (2010) 50004 are clarified. The degree of approximation to exact solutions is quantitatively assessed. The improved JWKB method is…
We reply to a comment of Van Enter, Kuelske and Maes (cond-mat/0005176) on our letter "Critical Behavior of the Randomly Spin-Diluted 2-d Ising Model - A Grand Ensemble Approach", Phys. Rev. Lett. {\bf 73}, 2268-2271 (1994).
This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.
This paper examines Shavgulidze's postings to the ArXiv and publications which concern his argument that Thompson's group F is amenable. In particular I list specific places where there are errors in each of the postings and publications…
This article proposes a fresh and direct reading of foundational texts of philosophy and aims at bringing back the inflamed debates that are contemporaneous with the birth of Greek axiomatics, and indeed at understanding what is timeless in…
Comment on the paper Schiavoni et al., Phys. Rev. Lett. 90, 094101 (2003).
Sury's 2014 proof of an identity for Fibonacci and Lucas numbers (Identity 236 of Benjamin and Quinn's 2003 book: {\em Proofs that count: The art of combinatorial proof}) has excited a lot of comment. We give an alternate, telescoping,…
In this talk I explain in brief the motivations behind undertaking a study of the LHC-ILC interplay. I will give information about the activities of the LHC-LC study group as well as the study group document. I will illustrate the scope of…
This is a collection of questions that I am considering submitting to the next edition of the Kourovka Notebook of open questions in group theory. Most are questions I raised in papers between 1981 and the present; a few are new. I welcome…
This is a survey paper with some original results of the author on refined versions of the Azuma-Hoeffding inequality with some examples that are related to information theory. This work has evolved to the joint paper with Maxim Raginsky in…
Theory of $n$-complements with applications is presented.
We comment on the paper "Teleportation with a uniformly accelerated partner" (quant-ph/0302179).
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.