L—构造

Fuzzy 拓扑学把经典拓扑学作为它的特殊情况。但从经典拓扑学的观点来看,Fuzzy拓扑是对一个在 X 上定义,在〔0.1〕上取值(或某个格上取值)的函数空间,给与适当的拓扑结构,并研究它的拓扑性质。因此 Fuzzy 拓扑也可看成是经典拓扑的具体化。对于如此一个比较具体的对象,如何从实际出发构造它的拓扑,并研究它的性质,这在文献〔1〕     

完全分配格的谱论与拓扑分子格

本文借助于完全分配格的谱理论是首先证明分子格范畴同构于某连续偏序集范畴子范畴,然后利用上述同构,证明分子格上余拓扑同构于其中分子之集上。与分子序密切相关的某分明拓扑,从而就给“重域”“远域”这两个基本概念以合理解释,并证明许多拓扑分子格性质的研究可以化为相应的拓扑空间性质的研究.“重域”概念的引入,使 fuzzy 拓扑学的研究发生了根本变化,导致了有点派的兴起。而“远域”的引入,则导致因更广的拓扑分子格理论的产生,从而把 Fuzzy 拓扑为学纳入了拓扑格的范畴.本文中我们首先建立分子格范畴与连续偏序集范畴某子范畴的同构,从而把二者的研究紧密结合起来,然后借助上述同构把拓扑分子格中的问题的研究化为连续偏序集中问题去考虑,通过这种转化,我们将会看到,“重域”,“远域”等基本概念确为 fuzzy 拓扑学,拓扑分子格中唯一合理的点与集合的邻属关系,而择一原理这条fuzzy 拓扑学中的基本原理成立的原因也就变得很清楚。本文中凡未定义的概念请参看[4].     

拓扑分子格范畴的乘积与上积

本文在樊太和关于分子格范畴的积运算的基础上,研究了以拓扑分子格(TML)为对象,连续的广义序同态(CGOH)为态射的范畴中的乘积与上积,它们是一般拓扑学、Fuzzy拓扑学中积(和)空间概念的推广。     

拓扑分子格的上层空间

本文就拓扑分子格引进了上层空间的框架,借助于这种框架,从代数学范畴论的角度,分析了拓扑分子格与通常拓扑空间之间的自然关系。并指出,拓扑分子格理论有颇多的工作是一般拓扑学的“自然推广”。     

locale范畴中的逆极限

给出locale范畴中逆极限结构的明确描述 .借助于引入的一种新的极限形式———集体拉回 ,详细讨论了逆极限的性质 ,特别地 ,不用选择公理证明了locale形式的Steenrod定理 ,并且证明了紧空间式locale的逆极限一般不是空间式的 .作为在拓扑空间范畴中的应用 ,改进了经典拓扑学中的Steenrod定理     

拓扑分子格范畴中的积运算

文[1,2]以近年来发展起来的Fuzzy拓扑学中的工作为基础,建立了完全分配格上的点式拓扑理论。在文[1—3]的基础上,文[4]证明了分子格范畴对乘积运算封闭,并给出了其具体构造。本文进一步证明拓扑分子格范畴也对乘积运算封闭,同时给出了拓扑分子格范畴中的乘积结构。本文还证明这种乘积具有良好的性质,比如:连通性是可乘的最后,给出了这种乘积与L-Fuzzy拓扑空间乘积的关系。     

软拓扑空间的分离性质

研究了软拓扑空间的相关性质.采用经典拓扑学的定义方法,定义了新的软点和软连续,证明了软拓扑空间及乘积拓扑空间有关的分离性质,通过例子说明了各种分离性质之间的关系,进一步推广了软拓扑空间.     

L—fuzzyLocale理论与分配格的L—fuzzy拓扑表示

首先文中引入了Ｌ—ｆｕｚｚｙｌｏｃａｌｅ范畴，并证明了该范畴与满层Ｌ—ｆｕｚｚｙ拓扑空间范畴的关系类似于ｌｏｃａｌｅ与拓扑空间的联系．其次，文中建立了分配格的ｌｏｃａｌｅ式ｆｕｚｚｙＳｔｏｎｅ表示，并且与经典结果一致，任一分配格的Ｌ—ｆｕｚｚｙｌｏｃａｌｅ表示的点空间就是它的Ｌ—ｆｕｚｚｙ谱空间．     

L-fuzzy Locale理论与分配格的L-fuzzy拓扑表示

首先文中引入了Ｌ-ｆｕｚｚｙｌｏｃａｌｅ范畴，并证明了该范畴与满层Ｌ-ｆｕｚｚｙ拓扑空间范畴的关系类似于ｌｏｃａｌｅ与拓扑空间的联系．其次，文中建立了分配格的ｌｏｃａｌｅ式ｆｕｚｚｙＳｔｏｎｅ表示，并且与经典结果一致，任一分配格的Ｌ-ｆｕｚｚｙｌｏｃａｌｅ表示的点空间就是它的Ｌ-ｆｕｚｚｙ谱空间．     

不分明拓扑空间中紧性与Тихонов定理

<正> 紧性是经典拓扑学中最基本的一个性质;关于乘积空间的紧性的定理则被认为一般拓扑学中最重要定理之一([1,页143]).把紧性概念及定理推广到不分明拓扑空间,国外的尝试已有不少.正如[2]所指出的,有关工作[3]-[8]中,所定义的几种不分明紧性概念或者不能看作经典拓扑学中紧性概念的推广,或者定理不再一般地成立;总之都显得有相当局限.[2]提出一种称作α-紧性的不分明紧性概     

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.     

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].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].