关于图与圈之并图的圈唯一性

Farrell[1]引进图 G 的圈多项式 c(G;■).文[6]猜测:轮形图 W_8是圈唯一的.本文中我们证明上述猜测为真且讨论了某些图与圈之并图的圈唯一性.     

三次平面图中包含六点二边集的圈

得到了３－连通三次平面图具包含其给定六点二边集的圈的一个充分必要条件。并且列出一些悬而未决的研究问题。     

超图的路和圈

超图是离散数学中最一般最复杂的结构 .无圈超图已被证明在数据库设计中非常有用 .从关系数据的结构出发 ,建立了关于超图的路、连通性和圈的新的公理系统 .该系统与特殊情形———图是符合的 .引入了虚圈和实圈的概念 ,这是一对相关联的概念 .虚圈在特殊情形———图中不存在 ,退化掉了 .定义了超图圈的相关性和独立性 ,给出了超图中最大独立实圈数目的计数公式 ,对特殊情形———图 ,这个公式就是Euler公式 .     

两个不交图的联图的最小圈基长度

这篇文章中,我们分两种情形分别给出了计算两个不交图的联图的最小圈基长度的公式.作为它们的应用,我们给出了计算n个相同的图的联图以及完全r-部图等图的最小圈基长度的公式.     

拟阵的可去圈

本首先用拟阵语言将图论的新概念定义成了拟阵的新概念，然后用拟阵语言将Goddyn和Heuevl所得的图论上的新结果平移成了拟阵的新结果，最后用拟阵的方法对它们给出了新的证明。     

一类线图的泛圈性

本文的主要结果是:设G是n≥3阶简单图,ε≥2,且不含3度的边,若GC_4,C_5及C_4∪K_1且对任意无公共顶点的两边e_1和e_2,有d(e_1) d(e_2)≥2n-3,则G的线圈L(G)是泛圈图。     

由圈长分布确定的偶图

阶为n的图G的圈长分布是序列(C1，C2，…，Cn)，其中ci是图G中长为i的圈数．本文得到如下结果：设A∈_E(Kn,r)，|A|≤1，且n≤r≤min{n 6，2n-3)，则G=Kn,r，r-A是由它的圈长分布确定的．     

Bondy的泛圈图定理的改进

记G=(V,E)是简单图,1971年Bondy得到O re条件下的泛圈图的著名结果:若2连通n阶图G的不相邻的任两点x、y均有d(x) d(y)≥n,则G是泛圈图或G=Kn/2,n/2.这里进一步研究条件d(x) d(y)≥n-1,得到:若2连通n阶图G的不相邻的任两点x、y均有d(x) d(y)≥n-1,则G是泛圈图或G∈{K(Cn 1)/2∨G(n-1)/2,Kn/2,n/2}.本文作者得知最近国际著名权威专家Ho lton等人也得到完全相同的结果,但本证明更简捷.     

具有两个同阶轨道的双轨道图的圈边连通度

一个边割被称为圈边割,如果该边割能分离图的两个不同圈.如果一个图有圈边割,称该图为圈边可分离的.一个圈边可分离图G的最小圈边割的阶数被称为圈边连通度,记作cλ（G）.定义：ζ（G）=min{w（X）｜X导出G的最短圈},其中w（X）为端点分别在X和V（G）-X中的边的数目.如果一个圈边可分离图G使得cλ（G）=ζ（G）成立,称该图是圈边最优的.Tian和Meng在文章[11]以及Yang et al在文章[15]中研究了两种不同的双轨道图的圈边最优性.本文我们将研究具有两个同阶轨道的双轨道图的圈边连通度.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].