Related papers: On three problems of Y.--G. Chen

In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel…

In this paper, using Pesin theory and Liao theory, we give a positive solution to a conjecture of A. Katok.

We solve two conjectures of Ceken-Palmieri-Wang-Zhang concerning discriminants and give some applications.

For relatively prime integers $a$ and $b$ both greater than one and odd integer $c$, there are at most two solutions in positive integers $(x,y,z)$ to the equation $a^x + b^y = c^z$. There are an infinite number of $(a,b,c)$ giving exactly…

Reply to the recent comment by I.Ispolatov and M.Karttunen, cond-mat/0303564

We answer a question of Sean Keel in the affirmative in the case of ruled surfaces

This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via a minimization argument we prove existence of a positive…

Three problems related to the longest chains in an equivalence relation are formulated. Their relevance in estimating the cardinal of quotient spaces, and in particular, of reduced powers and ultrapowers, is indicated.

We study relationship among versions of the Knapsack Problem where variables take values in Z and the number of them is fixed. In particular, we construct a finitely presented group where the problem of solvability of exponential equations…

Let $X$ be an asymptotically hyperbolic manifold and $M$ its conformal infinity. This paper is devoted to deduce several existence results of the fractional Yamabe problem on $M$ under various geometric assumptions on $X$ and $M$: Firstly,…

We extend the methods of Lewicka - Pakzad, Sz\'ekelyhidi - Cao and Li - Qiu to study the notion of very weak solutions to the complex $\sigma_2$ equation in domains in $\mathbb C^n,\ n\geq 2$. As a by-product we sharpen the regularity…

We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem} (are all but finitely many terms of a…

We show two results of mean value problem, Smale's mean value problem is comprehensively solved in this paper.

In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.

This work is a continuation of what was done in a previous paper and strongly connected to the recent work of U. Abel and I. Rasa [arXiv:1707.00127]

We prove an improved form of an expectation of Polya and discuss several related questions

The calculations of Guang-Wen Ma's recent Letter [Phys.Lett. A239, (1998) 209] contain an easily detectable error which makes his conclusions irrelevant.

We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.