Related papers: On common energies and sumsets
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a general construction of polynomial weakly admissible meshes on…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might…
The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…
We are discussing the theorem about the volume of a set $A$ of $Z^n$ having a small doubling property $|2A| < Ck, k=|A|$ and oher problems of Structure Theory of Set Addition (Additive Combinatorics).
This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are…
We extend and generalize the results of Scheiderer (2006) on the representation of polynomials nonnegative on two-dimensional basic closed semialgebraic sets. Our extension covers some situations where the defining polynomials do not…
We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum,…
We give a simple recursive formula to obtain the general sum of the first $N$ natural numbers to the $r$th power. Our method allows one to obtain the general formula for the $(r+1)$th power once one knows the general formula for the $r$th…
An observation on Hall-Littlewood polynomials.
We establish an inequality of different metrics for algebraic polynomials.
Let $a,b$ and $n$ be positive integers with $a>b$. In this note, we prove that $$(2bn+1)(2bn+3){2bn \choose bn}\bigg|3(a-b)(3a-b){2an \choose an}{an\choose bn}.$$ This confirms a recent conjecture of Amdeberhan and Moll.
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…
In this Communication, we provide numerical evidence indicating that the standard single-reference coupled-cluster (CC) energies can be calculated alternatively to its copybook definition. We demonstrate that the CC energies can be…
We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…
In this paper some generalizations of the sum of powers of natural numbers is considered. In particular, the class of sums whose generating function is the power of the generating function for the classical sums of powers is studying. The…
Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one can efficiently recognize whether a given set $S$ is a sumset, i.e. whether there is a set $A$ such that $A+A=S$. Granville suggested an algorithm…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…