二级传递性与二级传递模糊矩阵

推广传递性概念,给出二级传递性的定义;研究二级传递模糊矩阵的性质,给出其若干等价刻画;证明二级传递模糊矩阵或者收敛或者周期为2,指数不大于n 1;讨论二级传递与强传递、k-传递和泛传递等概念之间的关系,指出二级传递是传递性概念的一种新的推广形式。     

可控阵的k—泛传递刻画

研究k-泛传递的性质及其图的特征，证明acyclicity阵是可控阵，实现对可控阵的传递性刻画，得到可控阵的图的特征。     

-可分解Fuzy关系及其*-传递性

对［０，１］上一般的算子‘＊’引入＊－紧Ｆｕｚｚｙ关系及其○＊－可分解Ｆｕｚｙ关系的概念，证明了有单位元１的保序算子‘＊’及有单位元０的保序算子‘＊－’所定义的○＊－可分解和○＊－－可分解Ｆｕｚｚｙ关系在某种意义上构成了新的可传递Ｆｕｚｚｙ关系类，并且还给出了这些类在不同类型的传递性之间的一种位置关系，特别地，对二元○∨－可分解Ｆｕｚｚｙ关系，该文还得到了一个关于其传递性的完全刻画．     

模糊关系的对偶合成及其在传递性中的应用

引入了模糊关系的一种新的合成：对偶合成。这种新的合成使我们十分容易地刻画反向传递性。利用合成和对偶合成,我们建立了传递性、反向传递性、半传递性和Ferrers性质的若干有趣的等价条件。     

模糊互补判断矩阵的一致性检验及修正

利用模糊互补判断矩阵进行决策时,指出既要保持元素间两两比较序的传递性又要保持整体偏差的可接受性,定义了严格及弱序传递、满意一致性矩阵等概念;提出一种新的修正算法并证明了其收敛性;最后给出一算例.     

软泛代数及其整体结构性质

提出了软泛代数概念,将已有的软群、软环等概念统一纳入这一框架中,从整体上研究了软泛代数的序结构性质,证明了固定指标集和T-代数后,相应的软T-代数全体以点式序形成代数格.引入了Scott连续软泛代数概念,证明了从代数紧拓扑空间到给定T-代数的Scott连续软T-代数的全体以点式序形成代数格.     

直觉模糊度量空间上的半群作用

讨论在直觉模糊度量空间上的拓扑半群作用,引入诸如拓扑传递性,点传递性及点稠传递性等概念.考虑非敏感性与传递性,等度连续等动力学性质的相互关系.     

拟半序意义下随机选择过程中的极大元定理

本文首先分析、比较半序、偏好与拟半序三者之间的关系,然后,在比半序、偏好更一般的拟半序意义下提出并论证了随机选择过程中的极大元定理,本文定理将统一和改进若干已知结果.     

序同态的NC－连续性

本文在ＬＦ拓扑空间上利用良紧性作为背景引进了序同态的ＮＣ－连续性、分子网和理想的ＮＣ－收敛性及ＮＣ－闭包算子等概念，系统地讨论了这些概念之间的关系以及ＮＣ－连续序同态的特性，得到了若干重要的结果。     

偏序半群的最大自然序半格同态象

引进了自然序半格，偏序半群的自然序半格同态象和二次主根基等概念，利用二次主根基构造出了任意偏序半群的最大自然序半格同态象。     

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     

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.     

(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].