路或圈的笛卡尔乘积图的支撑树数

设G是路或圈的笛卡尔乘积图，t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式，并考虑了t(G)的线性递归关系及渐近性态.     

图的可定向嵌入的标根可数性

给定一族图G,可定向曲面上存在多少个以其中某个图为基础图的标根地图？采用图的自同构群对图在可定向曲面上的嵌入集合进行分类，该文解决了这个问题，同时得到了求解计数函数f^r(M)的一种新的方法。     

Herstein定理的推广

1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使[x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.     

一类齐次对称多项式上的切比雪夫不等式

本文借助于控制不等式及数学归纳法，将著名的切比雪夫不等式推广到m次一般齐次对称多项式上(如文中定理及引理7)，并将此结果用于对称平均等．旨在展示证明解析不等式的一些有效的方法和技巧，同时为数学研究特别是高维几何研究提供一些新的有趣而有用的解析不等式．     

Piecewise quadratic trigonometric polynomial curves

Analogous to the quadratic B-spline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has continuity, while the quadratic B-spline curve has continuity. The quadratic trigonometric polynomial curve is closer to the given control polygon than the quadratic B-spline curve.

     

On the Bochner theorem on orthogonal operators

We prove the following theorem. Any isometric operator , that acts from the Hilbert space with nonnegative weight to the Hilbert space with nonnegative weight , allows for the integral representation

where the kernels and satisfy certain conditions that are necessary and sufficient for these kernels to generate the corresponding isometric operators.

     

On bifurcation points of a complex polynomial

Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.

     

Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .

     

空间有理参数多项式曲线的整数级绘制算法

讨论了空间有理曲线中心投影后导数上界的估计，基于曲线各阶差分的递推计算，给出了空间有理参数多项式曲线的快速绘制算法．算法只用到整数的加减法，效率高．     

Some computational methods for systems of nonlinear equations and systems of polynomial equations

This paper gives a brief survey and assessment of computational methods for finding solutions to systems of nonlinear equations and systems of polynomial equations. Starting from methods which converge locally and which find one solution, we progress to methods which are globally convergent and find an a priori determinable number of solutions. We will concentrate on simplicial algorithms and homotopy methods. Enhancements of published methods are included and further developments are discussed.