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

The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…

In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional $g$-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of…

The Halting Problem is ill-conceived and ill-defined.

In this work, we investigate a problem posed by Feng Qi and Bai-Ni Guo in their paper Complete monotonicities of functions involving the gamma and digamma functions.

We present a collection of easily stated open problems in wavelet theory and we survey the current status of answering them. This includes a problem of Larson on minimally supported frequency wavelets. We show that it has an affirmative…

This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…

This article gives explicit solutions to the Yang-Mills equations. The solutions have positive energy that can be made arbitrarily small by selection of a parameter showing that Yang-Mills field theories do not have a mass gap.

Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.

This note replies Dr. Jensen (2010) comments on Problem 2.3, which was left in Fuh (2010). In the following, we use the same notations and definitions in Fuh (2006) unless specified.

I argue that we must distinguish between: (0) the Three-Doors-Problem Problem [sic], which is to make sense of some real world question of a real person. (1) a large number of solutions to this meta-problem, i.e., many specific…

We present a solution of $3x+1$ problem. For a history of this problem we refer the reader to Lagarias, Jeffrey C.

In this paper, two new results and short proofs are given for the existence of positive entire large and bounded radial positive solutions for a nonlinear system with gradient term. Our results complete and improve a recently work published…

In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences.

We reply to the comment by Ying Zhang and S. Das Sarma on our PRL 94, 226405 (2005).

New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…

This work deals with the existence of at least two positive solutions for the class of quasilinear elliptic equations with cylindrical singularities and multiple critical nonlinearities that can be written in the form \begin{align*}…

New cases of the multiplicity conjecture are considered.

In this paper, we solve the gap equation of the Yang-Mills-Gribov-Zwanziger-Chern-Simon theory by considering the first order in the Chern-Simon topological mass term, $M$. As a result, we find three possible solutions to the gap equation,…

Taking a new approach towards analyzing the Collatz Problem, or, 3x+1 conjecture. Introducing some new functions, the Collatz-2 and Collatz-3 sequences, as well as deducing results related to Collatz-2 and Collatz-3 sequences.

We prove the total positivity of the Narayana triangles of type $A$ and type $B$, and thus affirmatively confirm a conjecture of Chen, Liang and Wang and a conjecture of Pan and Zeng. We also prove the strict total positivity of the…