Cubature Formula and Interpolation on the Cubic Domain

Several cubature formulas on the cubic domains are derived using the dis-crete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Cheby-shev weight functions and associated interpolation polynomials on [-1,1]2, as well as new results on [-1,1]3. In particular, compact formulas for the fundamental interpo-lation polynomials are derived, based on n3/4 + (n2) nodes of a cubature formula on [-1,1]3.     

Kac方程的解及其性质

研究Kac方程的初值问题．证明了该类方程存在唯一的全局分布解．并且使用一种新的线性化方法证明了该类方程的解具有相应的多项式衰减性．     

三次矩阵方程的解的判定

给定A∈Mn(F),g(x)=x3+ax2+bx+c∈F[x],本文讨论矩阵方程g(X)=A的解的存在性问题.在Li′s研究的基础上,当f(x)=p1(x)p2(x)…ps(x)时,我们给出g(X)=A有解的充要条件为对每一个pi(x),pi(g(x))在F[x]中存在ni次因式,ni=degpi(x).     

分析变换代数结构的途径与方法

在高中代数教学中,数学思想方法的发现往往在问题的深入中展开．而多项式是最常见的代数结构,本文试以多项式中常见的元素在学习、解题过程中的处理及意义出发,分析代数结构变换的一般思路与方法．     

图的无号Laplace矩阵的最大特征值

The signless Laplacian matrix of a graph is the sum of its diagonal matrix of vertex degrees and its adjacency matrix. Li and Feng gave some basic results on the largest eigenvalue and characteristic polynomial of adjacency matrix of a graph in 1979. In this paper, we translate these results into the signless Laplacian matrix of a graph and obtain the similar results.     

量子代数${\cal U}_q(f(K,H))$的量子伴随作用

Let H = uq（sl（2）） or u（sl（2））. By means of the standard basis of polynomial algebras, the Glebsch-Gordan formula and quantum Clebsch-Gordan formula are proved by a unified method, and the explicit formula of the decomposition of V（1）^n into the direct sum of simple modules is given in this paper.     

关于反中心对称矩阵的某些性质探讨

利用反中心对称矩阵的定义以及翻转矩阵等技巧,给出了反中心对称矩阵的伴随矩阵、特征值及特征向量的一些新结论.     

拟调和球的不存在性

证明了当N的万有覆盖上存在一个多项式增长的非负严格凸函数时,不存在从R~3到N的非平凡拟调和球.于是在dim M=3时推广了Eells-Sampson的定理.     

串联双路图的亏格分布

计算双路图的亏格分布是拓扑图论关注的一个问题,利用传递矩阵与向量积矩阵,给出了两类由双路图串联构建而成的两类闭链图的亏格分布.