匹配最大根小于等于2的图的匹配等价

给出了十六个匹配等价桥,证明了两个匹配最大根小于等于2的图匹配等价当且仅当它们之间可以由这十六个匹配等价桥进行等价转换,完整地刻画了这些图的补图的匹配等价图类,找到了这些图和它们的补图中的所有匹配唯一图．     

不含整数2的2-系整数组成的可重集的计数公式

为了更好地研究图的组合性质,就特殊图类的伴随等价图的计数问题做了讨论.通过讨论由2-系整数组成且不含整数2的可重集的色等价图的计数问题得到伴随等价图的计数方法.给出了伴随等价图及其补图的色等价图的个数的计算公式.本文提供了一种图的伴随等价计数的新方法,此方法比传统方法更为简洁.     

等价无穷小代换在极限运算中的推广

探讨了当自变量为等价无穷小时,函数为等价无穷小关系的一个充分条件,并给出了函数等价无穷小代换的若干结论,举例说明了具体应用.     

关于等价转化

关于等价转化肖东（江苏丰县宋楼中学２２１７３１）利用等价性原则（如充要条件、逆否命题与原命题等价、等价性法则规定等）对问题所施行的等价转化，能确保结果的正确无误．同样，在牢牢确立等价转化思想意识的前提下，恰如其分地利用某些非等价转化手段，也常使问题的...     

具有相同广义反射函数的微分系统的等价性

利用广义反射函数给出了微分系统等价的定义,研究了线性微分系统的相互等价性及其与非线性微分系统的等价性.     

树映射的链等价集与拓扑熵

本文讨论了树映射f的链等价集的性质,得到了f具有零拓扑熵的几个等价条件,并证明了:如果 f的一个链等价集是个无限集,那么这个链等价集的任何孤立点都是f的非周期的终于周期点.     

树映射的链等价集与拓扑熵

本文讨论了树映射f的链等价集的性质,得到了f具有零拓扑熵的几个等价条件,并证明了如果f的一个链等价集是个无限集,那么这个链等价集的任何孤立点都是f的非周期的终于周期点.     

拓扑空间的内部运算

讨论了拓扑空间上内部运算的性质,并对满足内部运算前三条性质的一类运算,引入一种等价关系,将这些运算进行等价分类,证明了每个等价类中的所有运算导出同一个拓扑,并进一步证明了每个等价类中仅有一个是内部运算且是等价类中的最小元.     

函子范畴的等价

本文建立了函子范畴等价的Ｍｏｒｉｔａ理论．考虑的主要问题是ｍｏｄＣ何时等价于ｍｏｄＣ′及这些等价条件．同时定义了函子范畴的双模和函子张量积，并刻画了等价函子．     

用等价无穷小代换求极限中的一些问题

学生用等价无穷小代换求极限的过程中出现许多我们认为是错误的方法,但有些错误的方法又能够得到正确的结论,如求极限时对复合函数的中间变量作等价无穷小代换;两非等价无穷小和差分别做等价无穷小代换等,这应该算对还是错？本文在理论上作了分析．     

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.     

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.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

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.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

CONTENTS OF VOLUME 30

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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].