一类多项式系统极限环的研究

讨论了系统dxdt=(-y y2-dx)(1-y)a-x2(1-y)a-1dydt=x[(1-y)a (ax)a]极限环的存在性和唯一性,其中α为正数.     

求矩阵最小多项式的初等变换方法

分别给出计算矩阵的最小多项式和向量关于矩阵的最小多项式的初等变换方法 .     

Legendre-Fourier级数部分和 对有界变差函数的逼近

本文讨论了Legendre-Fourier级数部分和对有界变差函数逼近的间题，发展了文献【1]R. Bojanic和M. Vuilleumier的结果.     

On a class of Szász-Mirakyan type operators

The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.     

Bandwidth choice for local polynomial estimation of smooth boundaries

Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.     

Omega polynomial in twisted/chiral polyhex tori

The newly proposed Omega counting polynomial is investigated in case of twisted/chiral polyhex tori. Basic definition and properties are given. A factorization procedure is proposed for finding analytical relationships in families of polyhex toroidal nanostructures. Numerical data are also given. Dedicated to Professor Haruo Hosoya, Ochanomizu University, Tokyo, Japan, for his bright contribution to Chemical Graph Theory.     

一类特殊矩阵可对角化的判别及特征向量的求法

讨论了仅有两个互异的特征根的n阶方阵的可对角化的问题及特征向量的一种简单求法.     

需要安装时间的两台多功能机排序问题的计算复杂性

提出需要安装时间的多功能机排序问题,一般情况下,这是NP-困难的;主要研究只有两台机器时一些特殊情况下的计算复杂性.根据加工集合为机器全集的工件组数的不同,分别给出多项式时间算法和分枝定界算法.对各工件组的工件数和加工时间都相等的情况,给出一个多项式时间的最优算法-奇偶算法,从而证明此问题是多项式时间可解的.     

Variation of the Alexander-Conway polynomial under Dehn surgery

Let ε₁ and ε₂ belong to {±1}. When the ε₁-surgery along a knot K₁ in S³ produces the same homology sphere as the ε₂-surgery along a knot K₂ in S³, then the Casson surgery formula implies that ε₁Δ_K1″(1)=ε₂Δ_K2″(1), where Δ(t) denotes the symmetric Alexander polynomial. For any pair (Λ₁(t),Λ₂(t)) of possible knot Alexander polynomials such that ε₁Λ₁″(1)=ε₂Λ₂″(1), we exhibit a pair (K₁,K₂) of knots in S³ such that Δ_K1(t)=Λ₁(t), Δ_K2(t)=Λ₂(t) and the ε₁-surgery along K₁ produces the same homology sphere as the ε₂-surgery along K₂.     

A Note on a Remez-Type Inequality for Trigonometric Polynomials

We obtain sharp bounds, in the uniform norm along the unit circle , of exponentials of logarithmic potentials, if the logarithmic capacity of the subset of , where they are at most 1, is known.