Related papers: A note on a recent attempt to prove Sendov's conje…

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

We recall the history of the proof of Seifert fibre space conjecture, as well as it motivations and its several generalisations.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

Simon argued that the semi-classical theory of gravity, unless with some of its solutions excluded, is unacceptable for reasons of both self-consistency and experiment, and that it has to be replaced by a constrained semi-classical theory.…

In this note, we disprove two Romanov type conjectures posed by Chen.

We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We study analogues of Sidorenko's conjecture and the forcing conjecture in oriented graphs, showing that natural variants of these conjectures in directed graphs are equivalent to the asymmetric, undirected analogues of the conjectures.

We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erd\"os-Simonovits and…

The Sendovs conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a critical point of p(z) within unit distance of each zero. The conjecture has been proved to be true for many special…

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…

In a recent work Brevik \emph{et al.} have offered formal proofs of two results which figure prominently in calculations of the Casimir pressure on a sphere. It is shown by means of simple counterexamples that each of those proofs is…

We attempt to prove the Razumov-Stroganov conjecture using a bijectional approach. We have been unsuccessful but we believe the techniques we present can be used to prove the conjecture.

In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3);…