完备分配格L上的S-幂零矩阵

利用完备分配格L上的s-模定义格L上的矩阵运算,给出这些运算的一些基本性质,并且定义格L上的s-幂零矩阵,给出一些全新的结果.     

Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic

The psi function ψ(x) is defined by ψ(x)=Γ^′(x)/Γ(x), where Γ(x) is the gamma function. We give necessary and sufficient conditions for the function ψ^″(x)+[ψ^′(x+α)]² or its negative to be completely monotonic on (−α,∞), where . We also prove that the function [ψ^′(x)]²+λψ^″(x) is completely monotonic on (0,∞) if and only if λ1. As an application of the latter conclusion, the monotonicity and convexity of the function e^pψ(x+1)−qx with respect to x(−1,∞) are thoroughly discussed for p≠0 and .     

Frequency and Magnitude Response Design Approximation Problems for Nonlinear-phase Nonrecursive Digital Filters

In this article special (possibly constrained) problems of linear and nonlinear complex approximation are studied with respect to the existence and uniqueness of solutions and the convergence of the approximation errors, where the errors are measured by an arbitrary L p and l p norm respectively. The problems arise in connection with the frequency and magnitude response approximation at the design of nonrecursive digital filters in the frequency domain. Two main results of the article concern the completeness of the functions exp ( m ik y ), k = 0,1,2,… , with respect to a certain space of continuous functions. These results imply that, under usual assumptions and with increasing number of approximating functions exp ( m ik y ), the errors in the frequency and magnitude response approximation problems converge to zero when the design region is not the total interval [0, ~ ] (in case of real coefficients) and not [ m ~ , ~ ] (in case of complex coefficients) which is given for the majority of filter design problems, but that the frequency response errors may not converge to zero when the design region equals [0, ~ ] or [ m ~ , ~ ] respectively.     

Binomial Edge Ideals of Complete Multipartite Graphs

In this article, we prove some results about the binomial edge ideal J _G of a complete r-partite graph G = K _{a 1,…, a r} : (1) characterization of unmixedness of J _G and Cohen–Macaulayness of the residue ring S/J _G , (2) F-purity of S/J _G , and (3) the equality of the symbolic and the ordinary powers of J _G .     

Complete Asymptotic Expansions for the Chlodovsky Polynomials

The purpose of this article is to study the local rate of convergence of the Chlodovsky operators (C_nf)(x). As the main results, we investigate their asymptotic behaviour and derive the complete asymptotic expansions of these operators. All the coefficients of n^?k (k = 1, 2,…) are calculated in terms of the Stirling numbers of first and second kind. We mention that analogous results for the Bernstein polynomials can be found in Lorentz [2 G. G. Lorentz ( 1953 ). Bernstein Polynomials . University of Toronto Press , Toronto . [Google Scholar]].     

The Bhattacharya Function of Complete Monomial Ideals in Two Variables

We give explicit formulas for the Bhattacharya function of 𝔪-primary complete monomial ideals in two variables in terms of the vertices of the Newton polyhedra or in terms of the decompositions of the ideals as products of simple ideals.