THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

For two rational quadratic B-spline curves with same control vertexes, the cross ratio of four eollinear points are represented; which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the twocurves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Beeier curves, the value is generally related with the loeation of the ray, and the necessary and sufficient condition o5 the ratio being independent of the ray‘s loeation is showed. Alsn another cross ratio o5 the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initlal vertex intersects respectivdy with the curve segmentt the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only whh the ray‘s location, butnot with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.     

在曲面上图嵌入的唯一性

在本文中，证明了图嵌入在一个已知曲面上的唯一性充分条件，这个条件比「４」中要弱些。     

超线性奇异边值问题解的全局结构

本文讨论一类具有奇异性的超线性边值问题.我们证明,解集存在无界连通分支.作为推论,我们在一定程度上改进了文[1]的主要结果,去掉了其主要条件.     

具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.     

带圆周约束的Steiner树问题

本文首先考虑了带圆周约束的Steiner树问题．设欧氏平面上有一圆，平面上有n个点，所成点集为N，该问题是要在圆周上找一点P，使NU{P}这n 1个点的Steiner树之长度达到最短．本文对干n=2的情形给出解．另一方面，鉴干问题的复杂性为NP-C，作者提出了一个近似解，并证明了近似解的性能比为（3的平方根）／2。     

有序拓扑向量空间中有效点的存在性定理

1980年,H.W.Cordy引进K-半紧概念,深入地讨论了Banach空间中有效点的存在性.本文将K-半紧性推广到K-仿紧性,从而在较弱条件下获得一般有序拓扑向量空间中的有效点存在性定理.     

格点定模SU(2)-Higgs模型的解析计算

对格点上基础表示的定模Higgs场与SU(2)规范场耦合系统的相图进行解析计算至累积展开的第四级,用扫瞄确定变分参数的方法,得到与Monte Carlo模拟很好符合的相图.计算了N_τ=1的有限温度情形下SU(2)-Higgs系统和纯SU(2)模型的Polyakov线,对后者得到迄今最佳的近似解析结果β_c.     

Halin-图的点强全染色

图G(V,E)的一个k-正常全染色f叫做一个k-点强全染色当且仅当对任意v∈V(G), N[v]中的元素被染不同色,其中N[v]={u|uv∈V(G)}∪{v}．χTvs(G)=min{k|存在图G的k- 点强全染色}叫做图G的点强全色数．对3-连通平面图G(V,E),如果删去面fo边界上的所有点后的图为一个树图,则G(V,E)叫做一个Halin-图．本文确定了最大度不小于6的Halin- 图和一些特殊图的的点强全色数XTvs(G),并提出了如下猜想:设G(V,E)为每一连通分支的阶不小于6的图,则χTvs(G)≤△(G) 2,其中△(G)为图G(V,E)的最大度．     

一类二阶三点边值问题单调正解的存在性

利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．     

QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS

This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.