Related papers: Solutions to a Romanoff type problem

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

Let $\mathcal{P}$ and $\mathbb{N}$ be the sets of all primes and natural numbers, respectively. In this article, it is proved that there has a positive lower density of the natural numbers which can be represented by the form…

We obtain some results related to Romanoff's theorem.

In this short note, we answer two questions of Chen and Ruzsa negatively and answer a problem of Ma and Chen affirmatively.

In this note, three 2003 problems of Nathanson and two 2007 problems of Chen on unique representation bases for the integers are resolved.

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

In this paper, we have found that some certain Fermat-type shift and difference equations have the meromorphic solutions generated by Riccati type functions. Also we have solved the open problems posed by Liu and Yang (A note on meromorphic…

In this paper, we give a first negative answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3): 943-968, 2012). Meanwhile we also give a second positive answer to the Li-Lin's open problem. The first positive answer was…

In 2014, Chen and Singer solved the summability problem of bivariate rational functions. Later an algorithmic proof was presented by Hou and the author. In this paper, the algorithm will be simplified and adapted to the $q$-case.

In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].

Exact solutions of the relativistic many-body problem are presented

Existence of solutions to the Lp Minkowski problem is proved for all p less than 0. For the cirtical case of p=-n, which is known as the centro-affine Minkowski problem, this paper contains the main result in [71] as a special case.

This is an English translation of the following paper, published several years ago: Nikonorov Yu.G., Nikonorova Yu.V. Generalized Popoviciu's problem (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 229-232 (2000), Zbl. 0958.51021. All inserted…

In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and…

We obtain some new inequalities of Chebyshev Type.

In this paper, we study the form type Calabi-Yau equation. We define the astheno-Ricci curvature and prove that there exists a solution for the form type Calabi-Yau equation if the astheno-Ricci curvature is non-positive.

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.

In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…

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.

Sharp reverse affine isoperimetric inequalities for asymmetric Wulff shapes and their polars are established, along with the characterization of all extremals. These new inequalities have as special cases previously obtained simplex…