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

In this paper, we confirm two conjectures proposed by Georgiev, G\'{o}mez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$, thereby providing a complete solution to the de Bruin--Sharma problem. We further…

It is shown that a recent claim of equivalence between three Chern-Simons theories is not tenable.

In this paper, we proved a special case of the DDVV Conjecture.

A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

We prove Simon's conjecture for 3-manifolds.

In this paper the circulant Hadamard conjecture is proved.

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

In this short note, we expose some of the works on Serre intersection multiplicity conjecture. I provide a proof of the vanishing of Serre intersection multiplicity in non-proper intersection over a regular ring based on the intersection…

This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)

In the paper [Hong-Shi Zong, Wei-Min Sun, Phys. Lett. B 640 (2006) 196], the authors claim that our proof of the inconsistency of the ladder approximation to QCD [Phys. Lett. B 611 (2005) 129] was incorrect. However, their claim is based on…

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

We provide a new characterization of the logarithmic Sobolev inequality.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

It is shown that the arguments in the reply of Z.-D. Zhang (arXiv:0812.0194) to the comment arXiv:0811.1802 defending his conjectures in arXiv:0705.1045 are invalid. His conjectures have been thoroughly disproved.

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…

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…

In this short note, we will give the key point of the section conjecture of Grothendieck, that is reformulated by monodromy actions. Here, we will also give the result of the section conjecture for algebraic schemes over a number field.

Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler…