Related papers: The binary Goldbach problem with arithmetic weight…
The goal of the paper is to study a spectral problem corresponding to the mixed problem for a sixth order weak parabolic equation.
We study multiple sampling and interpolation problems with unbounded multiplicities in the weighted Bergman space, both in the hilbertian case p = 2 and the uniform case p = +$\infty$.
Using the variational approach and the critical point theory, we established several criteria for the existence of at least one nontrivial solution for a discrete elliptic boundary value problem with a weight $p(\cdot, \cdot)$ and depending…
The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…
It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifth-order algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order…
Let $\Sigma_{2n}$ be the set of all partitions of the even integers from the interval $(4,2n], n>2,$ into two odd prime parts. We select a partition from the set $\Sigma_{2n}$ uniformly at random. Let $2G_n$ be the number partitioned by…
A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the…
We present some questions and suggestion on the second part of the Hilbert 16th problem
This paper presents some considerations about the Goldbach's conjecture (GC). The work is based on elementary results of the number theory and it provides a constructive method that permits, given an even integer, to find at least a pair of…
We begin by considering a sequence of polynomials in three variables whose coefficients count restricted binary overpartitions with certain properties. We then concentrate on two specific subsequences that are closely related to the…
We consider the problem of evaluation of the weight enumerator of a binary linear code. We show that the exact evaluation is hard for polynomial hierarchy. More exactly, if WE is an oracle answering the solution of the evaluation problem…
We solve the Cauchy problem of the Ward equation with both continuous and discrete scattering data.
By means of a dynamical process we provide a characterization of the Goldbach Conjecture in an infinite set of even numbers that depends on time.
The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items. A new systemic viewpoint to bin packing problems…
We construct a countable inductive limit of weighted Banach spaces of holomorphic functions, which is not a topological subspace of the corresponding weighted inductive limit of spaces of continuous functions. The main step of our…
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…
Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure…
Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
We obtain a new solution to the star-triangle relation for an Ising-type model with two kinds of spin variables at each lattice site, taking continuous real values and arbitrary integer values, respectively. The Boltzmann weights are…