Related papers: Solutions to a Romanoff type problem
In this article, we establish a $L^1$ estimate for solutions to Poisson equation with mixed boundary condition, on complete noncompact manifolds with nonnegative Ricci curvature and compact manifolds with positive Ricci curvature…
We prove some general recursions for the numbers of representations of positive integers as a sum x+y, x in X, y in Y, where X,Y are increasing sequences. In particular, we obtain recursions for the number of the Goldbach, Lemoine-Levy,…
We introduce and discuss L\'evy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic…
In Diophantine approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that…
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
The present paper is written in response to the comment of M. R. Hadizadeh et. al on our original paper "Solution of the Specific Model of Five-body Problem to Investigate the Effective Alpha-Nucleon Interaction in a Partial-Wave analysis"…
In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell…
We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.
The article is devoted to introduce and investigation of new numeral systems. These representations are generalizations of classical representations of real numbers. The main properties of investigating representations are described. The…
In this paper, we consider the Yamabe equation on a complete noncompact Riemannian manifold and find some geometric conditions on the manifold such that the Yamabe problem admits a bounded positive solution.
The $L_p$ Aleksandrov integral curvature and its corresponding characterization problem---the $L_p$ Aleksandrov problem---were recently introduced by Huang, Lutwak, Yang, and Zhang. The current work presents a solution to the $L_p$…
We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…
Two fractional Stefan problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0,1)$ such that in the limit case ($\alpha =1$) both problems coincide with the same classical Stefan problem. For the one…
We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.
In a recent comment [arXiv:1405.2978v1 (2014)] Romanenko and Grassellino made unsubstantiated statements about our work [Appl. Phys. Lett. 104, 092601 (2014)] and ascribed to us wrong points which we had not made. Here we show that the…
A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…
We define natural classes of rational and polynomial representations of the Yangian of the general linear Lie algebra. We also present the classification and explicit realizations of all irreducible rational representations of the Yangian.
In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is…
A direct proof is given of the fact that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation.
The aim of this paper is to prove various ill-posedness and well-posedness results on the Cauchy problem associated to a class of fractional Kadomtsev-Petviashvili (KP) equations including the KP version of the Benjamin-Ono and Intermediate…