具有与任意图正交的(g,f)-因子分解的子图

设ｇ和ｆ分别是定义在图Ｇ的顶点集合Ｖ（Ｇ）上的整数位函数且对每个ｘ∈Ｖ（Ｇ）有０≤ｇ（ｘ）≤ｆ（ｘ）．证明了：若Ｇ是一个（ｍｇ＋ｋ,ｍｆ－ｋ）－图,１≤ｋ＜ｍ,Ｈ是Ｇ中一个给定的有ｋ条边的子图,则Ｇ有一个子图Ｌ使得Ｌ有一个（ｇ,ｆ）－因子分解与Ｈ正交．     

图的(g,f)-因子分解

设Ｇ是一个图，ｇ（ｘ）和ｆ（ｘ）是定义在图Ｇ的顶点集上的两个整数值函数且ｇ≤ｆ．图Ｇ的一个（ｇ，ｆ）－因子是Ｇ的一个支撑子图Ｆ使对任意的ｘ∈Ｖ（Ｆ），有ｇ（ｘ）≤ｄＦ（ｘ）≤ｆ（ｘ）．如果图Ｇ的边集能划分为若干个边不相交的（ｇ，ｆ）－因子，则说图Ｇ是（ｇ，ｆ）－可因子化的．本文研究了图的（ｇ，ｆ）－可因子化的问题，给出了一个图Ｇ是（ｇ，ｆ）－可因子化的若干充分条件．     

图的（g，f）－因子和因子分解

设Ｇ是一个图，ｇ，ｆ是定义在图Ｇ的顶点集上的两个整数值函数且图Ｇ的一个（ｇ，ｆ）－因子是Ｇ的一个支撑子图Ｆ使对任意的ｘ∈Ｖ（Ｆ）有本文给出了一个图（ｇ，ｆ）－可因子化的若干充分条件和一个图是（ｇ，ｆ）－消去图的充分必要条件，并研究了这些条件的应用。     

图的（g，f）－因子和因子分解

设Ｇ是一个图，ｇ，ｆ是定义在图Ｇ的顶点集上的两个整数值函数且图Ｇ的一个（ｇ，ｆ）－因子是Ｇ的一个支撑子图Ｆ使对任意的ｘ∈Ｖ（Ｆ）有本文给出了一个图（ｇ，ｆ）－可因子化的若干充分条件和一个图是（ｇ，ｆ）－消去图的充分必要条件，并研究了这些条件的应用。     

与任意图(m,r)-正交的(g,f)-因子分解

设ｇ和ｆ是定义在图Ｇ的顶点集Ｖ（Ｇ）上的整值函数．证明了如下结果：设ｒ是一个正整数,Ｇ是一个（ｍｇ＋（ｍ－１）ｒ,ｍｆ－（ｍ－１）ｒ）－图,且ｇ（ｘ）≥—１,对ｘ∈Ｖ（Ｇ）．则 Ｇ是一个随机（ｍ,ｒ）－正交的（ｇ,ｆ）－可因子化图．     

关于可重构的局部子图

一个图Ｇ在一顶点ｘ处的局部子图Ｌ｛ｘ｝是由Ｇ的给定性质定义的包含ｘ的子图Ｌ１，并以ｘ为根，例如在点ｘ处的ｋ－局部子图是以ｘ为根，以所有到ｘ距离不超过ｋ的顶点集合｛ｕ∈Ｖ（Ｇ）：ｄＧ（ｖ，ｘ）≤ｋ｝为顶点集；以｛ｕｖ∈Ｅ（Ｇ）：ｄＧ（ｕ，ｘ）〈ｋ，或ｄＧ（ｖ，ｘ）〈ｋ｝为边集的带根子图。本文证明了：对于Ｇ的局部子图Ｌ｛ｘ｝，如果每个Ｌ｛ｘ｝，ｘ∈Ｖ（Ｇ），的顶点数（或边数）都小于Ｇ的顶点数（边数）减     

一类泛连通无爪图

本文证明了如果Ｇ是３连通无爪图，且Ｇ的每个导出子图Ａ，Ａ＋都满足（ａ１，ａ２），则Ｇ是泛连通图（除了当ｕ，ｖ∈Ｖ（Ｇ），ｄ（ｕ，ｖ）＝１时，Ｇ中可能不存在（ｕ，ｖ）－ｋ路外，这里２≤ｋ≤４）．     

几类凝聚图的轮廓

设Ｇ是个图，｜Ｖ（Ｇ）＝ｎ｜对Ｇ上的任一个标号ｆ：Ｖ（Ｇ）→｛１，…，ｎ｝记，且当ｊ≠ｉ时，Ｇ中有边以ｆ（－１）（ｊ）及ｆ（－１）（ｉ）为两端点｝）．称Ｐ（Ｇ）＝ｍｉｎ｛Ｐ（ｆ）：ｆ是Ｇ上的标号｝为图Ｇ的轮廓．对以Ｗ表示Ｇ中Ｗ的边界．本文证明：ｉ）若Ｇ是凝聚图，ｆ及ｆ是Ｇ上一对互逆标号，则Ｐ（Ｇ）＝Ｐ（ｆ）的充要条件是ｆ为凝聚标号，且此时若Ｇ，Ｈ均是凝聚图，则存在阶梯标号。使得路、回、完全留之间的下列乘积图也是凝聚图，且其轮廓为     

图的（g＜f）－因子

设Ｇ是一个图，ｇ和ｆ是定义在图Ｇ的顶点集上的两个整数值函数且ｇ＜ｆ．本文给出了过图的每条边有一个（ｇ，ｆ）－因子的新的简单的判断准则，并研究了它的应用。从而得到了一些关于图有（ｇ，ｆ）－因子的新的充分条件，推广了若干已有的结果．     

新题征展(3)

题组新编１．（１）设Ｍ＝｛ｘ｜ｆ（ｘ）＝０｝、Ｎ＝｛ｘ｜ｇ（ｘ）＝０｝,则｛ｘ｜ｆ（ｘ）·ｇ（ｘ）＝０｝为（　　）;（Ａ）Ｍ　（Ｂ）Ｎ　（Ｃ）Ｍ∪Ｎ　（Ｄ）以上都不对（２）设ｆ（ｘ）＝ｘ－１ｘ＋３,ｇ（ｘ）＝ｘ＋３ｘ－１,则集合｛ｘ｜ｆ（ｘ）·ｇ（ｘ）＝０｝＝　　;（３）设函数ｆ（ｘ）、ｇ（ｘ）的定义域依次是Ｆ、Ｇ,且Ｍ＝｛ｘ｜ｆ（ｘ）＝０｝、Ｎ＝｛ｘ｜ｇ（ｘ）＝０｝,则｛ｘ｜ｆ（ｘ）·ｇ（ｘ）＝０｝＝　　．２．（１）设ｍ、ｋ∈Ｎ,则Ｃｎｎ＋Ｃｎｎ＋１＋Ｃｎｎ＋２＋…＋Ｃｎｎ＋ｋ＝　　;（２）求…     

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

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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].