关于一元多项式的除法

着重介绍一种由两个一元多项式的系数变换进行多项式整除性的研究方法 ,在进行多项式整除性的研究时 ,这种方法简单、实用、易懂 ,这种方法还可进一步推广用之于求一元多项式的最大公因式以及一元多项式互素等方面的研究 .     

Study of upper bound problem of heilbronn type

A set of n points in the plane determines a total Cn^2 distances (some of them may be the same). Let rn be the ratio of the maximum distance to the minimum distance, and Rn be the greatest lower bound for rn.By using the mathematical software Mathematica,the author gets the following results in this paper.R12≤2.99496…,R13≤cscπ/10.     

On the invertibility of Hilbert space idempotents

This note is to present some results on the group invertibility of linear combinations of idempotents when the difference of two idempotents is group invertible.     

非负矩阵最大特征值的估计法

通过构造一个新的矩阵,从而得到一个非负矩阵最大特征值的估计法,该方法将适用范围推广到一般非负矩阵,并通过实例验证了这种新方法精确度更高.     

一个向量场的Shannon信息熵函数的最大值怪异定理

给出一个定义在开直角梯形内的8维向量场,它的Shannon信息熵函数在这个开直角梯形内连续可微,但在其唯一的最大点处的梯度不等于零向量.     

Matrices over a commutative ring as sums of three idempotents or three involutions

Motivated by Hirano-Tominaga’s work on rings for which every element is a sum of two idempotents and by de Seguins Pazzis’s results on decomposing every matrix over a field of positive characteristic as a sum of idempotent matrices, we address decomposing every matrix over a commutative ring as a sum of three idempotent matrices and, respectively, as a sum of three involutive matrices.     

一类新的华氏宏观经济数学模型

提出了一类新的有消费的华氏宏观经济数学模型，给出了相应此模型的一套数学理论（包括主产系统失去和不失去平衡的条件、最大最小原则和正特征矢量法）及有关经济解释。这些内容推广和发展了华罗庚教授生前所做的有关工作。     

具有正规中间幂等元的富足半群的构造

本文研究富足半群上中间幂等元的若干性质，并给出了具有正规中间幂等元的富半群的构造。作为推论，我们得到Ｂｌｙｔｈ和ＭｃＦａｄｄｅｎ［１］及Ｅ１－Ｑａｌｌａｌｉ［２］中相应结果。     

Pseudo 1-homogeneous distance-regular graphs

Let Γ be a distance-regular graph of diameter d≥2 and a ₁≠0. Let θ be a real number. A pseudo cosine sequence for θ is a sequence of real numbers σ ₀,…,σ _d such that σ ₀=1 and c _i σ _i−1+a _i σ _i +b _i σ _i+1=θ σ _i for all i∈{0,…,d−1}. Furthermore, a pseudo primitive idempotent for θ is E _θ =s ∑ _i=0 ^d σ _i A _i , where s is any nonzero scalar. Let be the characteristic vector of a vertex v∈VΓ. For an edge xy of Γ and the characteristic vector w of the set of common neighbours of x and y, we say that the edge xy is tight with respect to θ whenever θ≠k and a nontrivial linear combination of vectors , and Ew is contained in . When an edge of Γ is tight with respect to two distinct real numbers, a parameterization with d+1 parameters of the members of the intersection array of Γ is given (using the pseudo cosines σ ₁,…,σ _d , and an auxiliary parameter ε). Let S be the set of all the vertices of Γ that are not at distance d from both vertices x and y that are adjacent. The graph Γ is pseudo 1-homogeneous with respect to xy whenever the distance partition of S corresponding to the distances from x and y is equitable in the subgraph induced on S. We show Γ is pseudo 1-homogeneous with respect to the edge xy if and only if the edge xy is tight with respect to two distinct real numbers. Finally, let us fix a vertex x of Γ. Then the graph Γ is pseudo 1-homogeneous with respect to any edge xy, and the local graph of x is connected if and only if there is the above parameterization with d+1 parameters σ ₁,…,σ _d ,ε and the local graph of x is strongly regular with nontrivial eigenvalues a ₁ σ/(1+σ) and (σ ₂−1)/(σ−σ ₂).     

一个关于高斯整数的最小正整数问题

主要讨论了高斯整数多项式所表整数的计算,利用初等数论基本理论和方法,获得了一个含有n(n≥1)个高斯整数常量和变量的线性多项式虚部所表整数中最小正整数的精确显式表达,并进一步获得了该多项式虚部所表整数的全体.