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．     

（mg＋m—1,mf—m＋1）—图的（g,f）—因子

本文证明了（ｍｇ＋ｍ－１,ｍｆ－ｍ＋１）－图具有一些特殊的（ｇ,ｆ）－因子,从而推广到了关于（ｇ,ｆ）－覆盖图和（ｇ,ｆ）－消去图的有关结果,有助于进一步研究（ｍｇ＋ｍ－１,ｍｆ－ｍ＋１）－图的正交因子分解问题。     

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     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

(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).     

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.     

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.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in