基于连续值逻辑上的不分明化环

给出基于连续值逻辑上的不分明化环的概念,从一个新的方向讨论了环的某些代数性质。     

不分明化PCK—代数

在BCK－代数中定义了不分明化子代数和不分明化理想的概念,讨论了它们的性质及彼此间的关系。     

不分明化sp-拓扑空间及范畴FSPTop的拓扑性

基于连续逻辑值语义,研究了不分明化sp-拓扑空间,讨论了不分明化的sp-开集,sp-邻域,sp-闭包及sp-内部等性质,给出了不分明化sp-连续映射的概念,引入了范畴FSPTop,证明了范畴FSPTop是范畴Set上的拓扑范畴。     

不分明化scp-拓扑空间若干性质的研究

本文研究了不分明化scp-拓扑空间中的scp-开集、scp-邻域、scp-闭包以及scp-内部等性质,并给出了不分明化scp-连续映射的概念。     

L-不分明化一致空间和L-不分明化一致拓扑

通过应用完全剩余格值逻辑语义的方法把不分明化一致空间和不分明化一致拓扑推广为L-不分明化一致空间和L-不分明化一致拓扑。并且讨论了L-不分明化一致空间和L-不分明化一致拓扑的一些基本性质。     

关于零元L-不分明化邻域基的研究北大核心

本文研究了L-不分明化拓扑线性空间中零元L-不分明化邻域基的相关性质,并证明了满足这些性质的集值映射Bθ可生成一个L-不分明化拓扑线性空间(X,τBθ),而且Bθ恰为其零元L-不分明化邻域基。     

基于L~*-格值逻辑上的BCK-代数中直觉不分明化理想

在L~*-格值逻辑的语义框架下,以L~*-格值上的Lukasiewicz蕴涵算子为工具定义了L~*-格值逻辑上的直觉不分明化BCK-代数的概念,将用集论所刻画的BCK-代数中理想、正定蕴涵理想和蕴涵理想等概念在L~*-格值谓词演算下给予了新的刻画,讨论了它们的性质及其关系,研究了这些理想与其同态象、同态原象之间关系,获得了同类理想之积仍为该类理想.     

不分明化拓扑群的一致结构

本文引入了不分明化拓扑群的左、右、双一致结构，讨论了此类一致结构在一致连续下的一些性质，给出了此类结构在其子群上的相对结构和在其乘积上的来积结构。     

L—不分明拓扑空间的T1化

本文借助ａ－超闭滤与ａ－有限交性质对良紧性的刻画，构造性地给出了具Ｔ１分离性的不分明拓扑空间的Ｔ１紧化，所得结果以分明拓扑的Ｗａｌｌｍａｎ紧化为特款。     

基于L*-格值逻辑上的BCH-代数中的直觉不分明化理想

在L*-格值逻辑的语义框架下,以L*-格值上的Lukasiewicz蕴涵算子为工具定义了L*-格值逻辑上的直觉不分明化BCH-代数的概念,将用集论所刻画的BCH-代数与理想的概念在L*-格值谓词演算下给予了新的刻画,讨论了直觉不分明化BCH-代数中的理想、闭理想及q理想的有关性质.     

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.     

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     

(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 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].