线性Ce^＊—半范数的次可乘性

证明了具有单位元的*-代数上的任何线性Ce^*-半范数（或具有自伴核的线性Ce0^*-半范数）一定是C^*-半范数。     

PrO-C*-代数的顺从性和核性

研究了Pro—C^*-代数的顺从性和核性．主要证明了(1)顺从Pro—C^*代数的闭理想是顺从的；(2)核Pro—C^*代数类对归纳极限封闭；(3)交换σ-C^*-代数和核C^*-代数都是核，σ-C^*-代数并且核σ-C^*-代数类对于商运算、张量积运算和可数逆向极限封闭．进一步得到核，σ-C^*-代数的扩张保持核性的条件。     

C^＊—代数KK—理论中的Puppe列

在C~*-代数K-理论中,K-群的计算问题是一个基本问题,解决这一问题的一个重要途径就是建立一系列相应群的正合列。在本文中,我们考虑两个C~*-代数和映射锥的KK—群之间的关系,证明其间存在一个六项Puppe列。设A、B为分层C~*—代数,φ:A→B为分层*-同态,其映射锥记为C_φ即     

具有Q-正则*-断面的正则半群上的*-同余格

文中给出了一个具有正则*-断面正则半群的例子,该半群同时存在非平凡*-同余和非平凡的非*-同余;证明了正则*-断面上的每个*-同余都能扩张成整个半群上的*-同余;刻划了*-同余和*-同余格;定义了*-同余格上的两个完全同余T*FS和T*S*;研究了*-同余格上的完全同余T*S*, T*, T*l, Tr, U*和V*, 给出了这些同余的类中的极值同余(除U*, V*外).     

R0-代数中一种混合运算的性质及L*系统的完备性

研究了王国俊教授建立的模糊命题演算的形式演绎系统L*及与之在语义上相关的R0-代数,讨论了R0-代数中混合运算():a()b= (a→()b)的性质,并以此为工具利用Petr Hajek证明Lukasiewicz模糊命题演算系统关于语义ΩL完备性的方法证明了L*系统关于语义ΩW的完备性.     

不同分布ρ--混合随机场的完全收敛性

讨论了不同分布ρ^--混合随机场的部分和的完全收敛性，建立了一个定理，此结果的获得推广了ρ^*-混合随机场和NA序列的相应的结果．     

分组ρ~*-混合随机场的强极限定理

利用求和法,在矩条件下,给出分组ρ*-混合随机场的强极限定理。它是经典结果的推广。     

关于Araki Elliott的定理1

在c~*-代数的定义中,要求范数是次乘的。但是这一点可以从其他条件推出来。 Araki-Elliott的定理1 设(A,||·||)是Banach空间,A并且是复数城上的*代数,及满足     

Hilben C*-模之间的同构定理

获得了Hilbert C^*-模之间的两个同构定理．作为推论，证明了C^*-代数上每个可数生成的Hilbert C^*-模均稳定酉等价于A。     

关于Gelfand-Mazur型的两个定理

证明了两个Gelfand-Mazur型的定理，其一是：设A是一单位C^*- wa ovt ,AH≌R，且h∈AK时，e^h具有凸谱集。则A≌C。这一结果回答了Bhatt等人的问题，给出了他们的结果在实情形中的结论。其二，部分地回答了Bhatt等人的另一个问题。结果是：设A是一复单位厄米Banach^*- 代数，假设（i)对任意x∈AH，谱集σA(x)的内部是空集，且C\σA（x)是连通的，（ii)A没有非零零因子，则A同构到C。     

STRONG UNIQUE CONTINUATION FOR THE LAMÉ SYSTEM OF ELASTICITY*

We prove quantitative estimates of unique continuation for the solutions of the Lamé system of the form of three–spheres–inequalities and of doubling inequalities.

     

随机变量的截尾与一类强偏差定理

通过极限相对对数似然比，利用随机变量截尾的方法并结合鞅这一工具研究相依连续型和离散型随机变量序列的性质，得到一类用不等式表示的强偏差定理．     

一类强极限定理与矩母函数方法

本文利用似然比的概念，研究离散随机变量序列的极限性质，得到了一类用不等式表示的强极限定理．证明中结合区间剖分法，提出了将矩母函数的工具应用于强极限定理的研究的一种途径．     

一类涉及两个单形的三角不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间En中涉及两个n维单形的几何不等式问题,建立了涉及两个单形的一类三角不等式.作为其应用,获得了涉及两个单形及其内点的几何不等式,特别,获得了n维单形与其垂足单形的体积的一类关系式,改进了关于垂足单形体积的几类几何不等式.     

On the relative strength of split,triangle and quadrilateral cuts

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in a well defined sense, triangle inequalities provide a good approximation of the integer hull. The same statement holds for quadrilateral inequalities. On the other hand, the approximation produced by split inequalities may be arbitrarily bad.     

渐近负相关随机域强定律的收敛率

In this paper,a notion of negative side ρ-mixing (ρ--mixing) which can be regarded as asymptotic negative association is defined,and some Rosenthal type inequalities for ρ--mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ--mixing random fields. The results obtained extend those for negatively associated sequences and ρ*-mixing random fields.     

两个新的Bonnesen型不等式

本文研究了Bonnesen型不等式.利用积分几何方法,得到了两个新的Bonnesen型不等式.     

关于正定矩阵的两个不等式

通过Hermite矩阵的谱分解及一个改进的Young不等式,得到了关于正定矩阵的两个不等式,所得结果是对一些经典的矩阵不等式的进一步推广.最后,作为应用,给出了著名的Holder不等式和Minkowsi不等式的一种反向形式.     

Capacitated facility location: Separation algorithms and computational experience

We consider the polyhedral approach to solving the capacitated facility location problem. The valid inequalities considered are the knapsack cover, flow cover, effective capacity, single depot, and combinatorial inequalities. The flow cover, effective capacity and single depot inequalities form subfamilies of the general family of submodular inequalities. The separation problem based on the family of submodular inequalities is NP-hard in general. For the well known subclass of flow cover inequalities, however, we show that if the client set is fixed, and if all capacities are equal, then the separation problem can be solved in polynomial time. For the flow cover inequalities based on an arbitrary client set and general capacities, and for the effective capacity and single depot inequalities we develop separation heuristics. An important part of these heuristics is based on the result that two specific conditions are necessary for the effective cover inequalities to be facet defining. The way these results are stated indicates precisely how structures that violate the two conditions can be modified to produce stronger inequalities. The family of combinatorial inequalities was originally developed for the uncapacitated facility location problem, but is also valid for the capacitated problem. No computational experience using the combinatorial inequalities has been reported so far. Here we suggest how partial output from the heuristic identifying violated submodular inequalities can be used as input to a heuristic identifying violated combinatorial inequalities. We report on computational results from solving 60 medium size problems. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Comparative and restrictive inequalities

Inequalities are an important topic in school mathematics, yet the body of research exploring students’ meanings for inequalities largely points to difficulties they experience. Thus, there is a need to further explore students’ meanings for inequalities. Addressing this need, we conducted an exploratory teaching experiment with two seventh-grade students to investigate their developing meanings for inequalities. We distinguish between two types of inequalities in student thinking: comparative and restrictive inequalities. Whereas a student reasoning about a comparative inequality compares two quantities’ values or magnitudes, reasoning about a restrictive inequality entails reasoning about a range of one quantity’s magnitudes or values. We realized a complexity arose in our interactions with students due to our conceiving the use of inequality symbols across the two types of inequalities as polysemous, whereas the students did not. Attending to these two types of inequalities has important implications for the teaching and learning of inequality.