MV-代数上的广义微分

在MV-代数上引入了广义微分的概念,研究了MV-代数广义微分的相关性质。进一步引入了保序广义微分的概念。给出了MV-代数上的保序广义微分的若干等价条件。进一步,在MV-代数M上引入了广义微分D的不动点集FixD(M),得到若D是保序广义微分,则FixD(M)是M的理想与格理想。进而通过广义微分的不动点集刻画了布尔代数和线性布尔代数。     

MV-代数的广义导子

借助于MV-代数的自同态引入并研究了MV-代数上的广义(→,⊕)-导子,得到了其等价刻画.此外,给出了MV-代数的广义中心主导子的概念,在此基础之上讨论了广义(→,⊕)-导子与MV-代数其它导子之间的关系,并利用强主中心广义导子的不动点集给出MV-代数成为Boole代数的等价刻画.所得结论推广了MV-代数上的导子,并借助导子深入刻画了MV-代数的结构理论.     

态BL-代数上的微分

在态BL-代数(A,σ)上引入(⊙,∨)-微分,研究了态BL-代数(A,σ)上(⊙,∨)-微分的性质。定义并研究了态BL-代数(A,σ)上正则微分和强微分,给出了正则强微分成为保序微分的等价条件。给出态BL-代数上的主微分的概念,讨论了全体主微分的代数结构,并利用Galois联结给出主微分的微分伴随。最后在态BL-代数(A,σ)上引入了不动点集A_(dσ),得到若d为正则保序的强微分时,A_(dσ)为A的格理想。我们的研究思路旨在将BL-代数上的态结构与微分结构紧密融合,以此来研究BL-代数的结构。     

MV-代数上的度量结构及其在多值逻辑中的应用

设M是一个MV-代数,Ω是从MV-代数M到MV-单位区间的全体赋值之集,μ是Ω上的概率测度.本文基于μ在M中引入了元素的尺寸和元素对之间的相似度概念,并由此在M上建立了度量结构.给出了MV-代数上的度量结构在多值逻辑中的一些应用.     

BL-代数上的⊙-导子

本文引入了BL-代数的⊙-导子并研究了BL-代数上⊙-导子的相关问题.利用导子的保序性,不动点集和BL-代数的格理想,讨论了BL-代数上的保序∧-导子和保序⊙-导子的关系,并给出了Gdel代数和线性Gdel代数的刻画.这些结果丰富了逻辑代数上的导子理论.     

MV-代数的Fuzzy拓扑表现定理

以ΩM记MV-代数M到MV-单位区间[0,1]的全体Lukasiewicz赋值之集．本文证明了格完备的MV-代数是正则的,从而可通过一种自然的方法在ΩM上引入fuzzy拓扑δ,建立了MV-代数的fuzzy拓扑表现定理,并给出了fuzzy拓扑δ的一些性质．     

MV-代数的素滤子MV-拓扑空间

在MV-方体[0,1]X的子集Ω上引进MV-拓扑结构,并套论MV-拓扑空间的紧性、Hausdorff分离性等拓扑性质.细致地讨论MV-代数的素滤子集上的MV-拓扑空间(M,ΩM),证明素滤子MV-拓扑空间是紧Hausdorff MV-空间,并且它还是良紧空间.作为应用,证明一个σ-完备格M是MV-代数当且仅当M同构于某个Stone MV-空间的MV-开闭集格.     

余剩余格及其应用

在偏序集上引入了余伴随对（＋,-）的概念,并研究了它在格上的若干性质,提出了余剩余格理论,最后在此基础上给出了MV-代数的一个等价刻画。     

格序代数的商及其代数性质

研究了格序代数的商及其一些重要的代数性质.给出了格序代数的商的概念,定义了商f-代数、商几乎f-代数和商d-代数,并给出其等价刻画.讨论了这三类格序代数的商的半素性和交换性质,得到了这些性质的若干刻画.     

Fuzzy蕴涵代数的MP滤子

给出了Fuzzy蕴涵代数(简称FI代数)上的MP滤子的等价刻画和由非空子集生成的MP滤子的表示定理; 探讨了FI代数的MP滤子与偏序滤子之间的关系; 证明了一个FI代数上全体MP滤子之集在集合包含序下构成一个分配连续(代数)格,从而构成一个Frame.     

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.     

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].     

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.