L─Fuzzy拓扑空间中几种正则及关系

本文我们将介绍三种不同于文献［１］中的正则．分别记作［正则］１、［正则］２、［正则］３。并讨论它们之间以及与［１］中正则的关系，我们将证明［正则］２不仅拓宽了原正则［１］。而且还具有相应好的性质。同时还将证明［正则］３在可拓扑生成条件下与［１］中正则是等价的。     

有理样条不可约解的行列式表示

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陈贻源［１］和张文修［２］分别引入了Ｆｕｚｚｙ弱自反关系的定义和有关的证明。本文在［１］和［２］给出Ｆｕｚｚｙ弱自反关系定义的基础上，对［１］和［２］的有关Ｆｕｚｚｙ弱自反关系证明提出了异议，并给出了新的证明。     

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也谈费马─斯坦勒尔问题

也谈费马─斯坦勒尔问题刘凯年（重庆师范学院数学系６３００４７）文献［１］（见本刊１９９４年第３期）、［２］、［３］用不同方法解决了费马一斯坦勒尔问题．但［３］为实验解，未给出严格的数学证明，［１］、［２］的方法又比较繁难，且［１］的方法很难为中学生所...     

求加权广义逆的矩阵方法

本文给出了应用矩阵方法求矩阵Ａ的加权广义逆Ａ＾［１，２，Ｗ３］，Ａ＾［１，２，ｗ３］和Ａ＾［１，２］［ｗ，ｗ］的充要条件。     

也谈对数大小的比较

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关于“华罗庚-王中烈型不等式”一文的注记

指出了［１］的定理２中的一个错误,推广了［１］中定理１给出的华罗庚－王中烈型不等式,避开控制不等式与动态规划模型等专门工具,改用较为初等的平均值不等式证明之,使改正后的［１］中的定理２成其推论     

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

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有约束错误指定模型下的优化问题

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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].