M－连续格到Hilbert方体的嵌入

本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．     

L2空间中的Bernstein─Markov不等式及其最佳常数（Ⅱ）

继［１５］．本中考虑了带不同权函数L²[-1,1]空间中的Ｂｅｒｎｓｔｃｉｎ－Ｍａｒｋｏｖ不等式，给出了其最佳常数；最后还得到相应的反向Ｂｅｒｎｓｔｃｉｎ－Ｍａｒｋｏｖ不等式．     

态射的广义Moore—Penrose逆

本文定义了态射的广义Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆，给出了它存在的一些充要条件，确定了它的一些表达式，推广了关于态射的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆的相应结果。     

线性模型中回归参数的最佳逼近M－估计

本文首先提出了选取回归参数Ｍ－估计中函数ρ的一种新原则，然后利用ρ的最佳逼近函数定义了一种新估计－ＢＡＭＥ．并证明了其强相合性；讨论了其稳健性，较比通常的Ｍ－估计，ＢＡＭＥ有以下优点：（１）ρ的选取充分利用了误差的分布信息；（２）具有显式表达，其算法方便；（３）相合性的证明相当于ＬＳ－估计的复杂程度，比Ｍ－估计简单得多．     

Banach空间结构理论的重大进展--关于Gowers-Maurey系列成果

最近,ＧｏｗｅｒｓＷ．Ｔ．和ＭａｕｒｅｙＢ．构造出第一例遗传不可分解空间,否定地解决了无条件基序列问题,由此导致了Ｂａｎａｃｈ空间的结构理论研究中系列问题的解决,本综述介绍这一新动向,反映了Ｇ－Ｍ系列成果,全文分为七个部分,１个历史回顾与问题沿革;２．Ｇ－Ｍ空间ＸＧ１及其遗传不可分解性质,３．关于空间ＸＧ１上的算子构成;４个关于共轭空间ＸＧ１,５．关于Ｇ－Ｍ的系列成果,６．Ｇ－Ｍ型空间构造的     

一种特殊规划的分块超松驰组合牛顿——乘子算法

本文给出了分块的超松驰组合牛顿－乘子（ＢＳＯＲ－Ｎ－Ｍ）方法，来求解一类约束函数可分块的规划问题，证明了其收敛性，进一步给出与理论相应的数值结果。     

投影寻踪型Cramer—von Mises—Smirnov统计量

为了检验一个总体分布是否服从所给定的分布Ｆ（ｘ），Ｃｒａｍｅｒ－ｖｏｎ Ｍｉｓｅｓ－Ｓｍｉｒｎｏｖ统计量是一种常用的重要工具，对于一维分布，计算表明确切分布很快趋于极限分布。当样本量大于３时，确切分布与极限分布之差就很小，当总体分布是连续分布方法建立Ｃｒａｍｅｒ－ｖｏｎ Ｍｉｓｅｓ－Ｓｍｉｒｎｏｖ统计量，对此统计量尾部概率上界及极限分布，包括当样本很大，维数很高时的极限性质，自助法是否能逼近极限分     

词偏序集的Mobius函数的Cohen—Macaulay性质的推广

本文主要利用偏序集的同调方法，给出任意两个分层偏序集的等价分类映射概念；证明了该映射是保Ｃｏｈｅｎ－Ｍａｃａｕｌａｙ性质的。本文的结论部份回答了Ｂ．Ｓｔｅｃｈｉｎ＾［１］的问题，同时推广了词偏序集的Ｍｏｂｉｕｓ函数的符号交错性。     

具有紧豫解式的m──增生算子的连续扰动

本文在Ｂａｎａｃｈ空间中证明了具有紧豫解式的ｍ－增生算子的连续扰动的几个映射定理、它们分别改善和推广了Ｋａｒｔｓａｔｏｓ，Ｈｉｒａｎｏ和Ｍｏｒａｌｅｓ等人的一些结果。     

ψ—混合误差下非参数回归函数加权核估计的相合性

本文在ψ－混合误差下讨论Ｐｒｉｅｓｔｌｅｙ，Ｍ．Ｂ．和Ｃｈａｏ，Ｍ．Ｔ．［１］提出的一类非参数回归函数加权核估计的相合性。在较弱的条件下证明了它的完全收敛性和强相合性。这些结论改进了现有的独立情形和相依情形的相应结论。     

Further properties on M-continuity

The concept of M-open sets [1] can be applied in modifications of rough set approximations [2], [3] which is widely applied in many application fields. The aim of this paper is to introduce and investigate some new classes of topological mappings called M-continuous mappings via M-open sets. Also,M-irresolute mappings which are stronger than M-continuous mappings are studied and the relationships between these mappings are investigated. Several properties of these new notions have been discussed and the connections between them are studied.     

The free orthomodular lattice on countably many generators is a subalgebra of the free orthomodular lattice on three generators

We show every at most countable orthomodular lattice is a subalgebra of one generated by three elements. As a corollary we obtain that the free orthomodular lattice on countably many generators is a subalgebra of the free orthomodular lattice on three generators. This answers a question raised by Bruns in 1976 [2] and listed as Problem 15 in Kalmbach's book on orthomodular lattices [6]. Received April 12, 2001; accepted in final form May 6, 2002.     

Distributive Envelopes and Topological Duality for Lattices via Canonical Extensions

We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A positive consequence of the choice of morphisms is that those on the topological side are functional. Towards obtaining the topological duality, we develop a universal construction which associates to an arbitrary lattice two distributive lattice envelopes with a Galois connection between them. This is a modification of a construction of the injective hull of a semilattice by Bruns and Lakser, adjusting their concept of ‘admissibility’ to the finitary case. Finally, we show that the dual spaces of the distributive envelopes of a lattice coincide with completions of quasi-uniform spaces naturally associated with the lattice, thus giving a precise spatial meaning to the distributive envelopes.     

Cones,semicontinuous functions,and continuous lattices

The purpose of this paper is to introduce a notion which is a generalization of convex sets and to use this notion to construct continuous lattices which are shown to be related to lattices of lower-semicontinuous functions. The end results of this development is a characterization of lattices of lower-semicontinuous functions in terms of a class of continuous lattices introduced in this paper (see Theorem 8). Then material is introduced which leads to a complementary result in Theorem 11 which characterizes the continuous lattices that can be lattices of lower-semicontinuous functions.     

Primes,irreducibles and extremal lattices

This paper studies certain types of join and meet-irreducibles called coprimes and primes. These elements can be used to characterize certain types of lattices. For example, a lattice is distributive if and only if every join-irreducible is coprime. Similarly, a lattice is meet-pseudocomplemented if and only if each atom is coprime. Furthermore, these elements naturally decompose lattices into sublattices so that often properties of the original lattice can be deduced from properties of the sublattice. Not every lattice has primes and coprimes. This paper shows that lattices which are long enough must have primes and coprimes and that these elements and the resulting decompositions can be used to study such lattices.The length of every finite lattice is bounded above by the minimum of the number of meet-irreducibles (meet-rank) and the number of join-irreducibles (join-rank) that it has. This paper studies lattices for which length=join-rank or length=meet-rank. These are called p-extremal lattices and they have interesting decompositions and properties. For example, ranked, p-extremal lattices are either lower locally distributive (join-rank=length), upper locally distributive (meet-rank=length) or distributive (join-rank=meet-rank=length). In the absence of the Jordan-Dedekind chain condition, p-extremal lattices still have many interesting properties. Of special interest are the lattices that satisfy both equalities. Such lattices are called extremal; this class includes distributive lattices and the associativity lattices of Tamari. Even though they have interesting decompositions, extremal lattices cannot be characterized algebraically since any finite lattice can be embedded as a subinterval into an extremal lattice. This paper shows how prime and coprime elements, and the poset of irreducibles can be used to analyze p-extremal and other types of lattices.The results presented in this paper are used to deduce many key properties of the Tamari lattices. These lattices behave much like distributive lattices even though they violate the Jordan-Dedekind chain condition very strongly having maximal chains that vary in length from N-1 to N(N-1)/2 where N is a parameter used in the construction of these lattices.     

剩余格与正则剩余格的特征定理

本文进一步研究了具有广泛应用的一类模糊逻辑代数系统——剩余格，并引入了正则剩余格的概念，对剩余格与正则剩余格的定义进行了讨论，给出了剩余格与正则剩余格的特征定理，其中包含剩余格与正则剩余格的等式特征，从而这两个格类都构成簇．本文还讨论了剩余格与正则剩余格公理系统的独立性，以及它们与相近代数结构的关系．     

半连续格和半代数格的映射性质

研究了半连续格及半代数格的一些映射性质,讨论了强连续格的函数空间,给出了强连续格到方体的嵌入定理.     

有限Chevalley群作用下的子代数轨道生成的格

讨论了一般情形Chevalley群作用下的子代数轨道生成的格.在同类型格中,研究了不同格之间的包含关系,并对格中子代数的特性及格的几何性进行了刻画.     

Semicontinuous lattices

In this paper we introduce and study a new type of lattices, semicontinuous lattices, by using semiprime ideals. Such lattices have many properties similar to that of continuous lattices, and are closely related to the theory of continuous lattices. Received November 3, 1995; accepted in final form March 13, 1997.