有限秩的可解群的剩余有限性质

本文讨论了有限秩的可解群的剩余有限性质,推广了Smelkin等人关于多重循环群的几个同类结果．     

Finite Rank Operators in Closed Maximal Triangular Algebras

Ｆｉｎｉｔｅｒａｎｋｏｐｅｒａｔｏｒｓａｎｄｒａｎｋｏｎｅｏｐｅｒａｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｔｏｔｈｅｔｈｅｏｒｙｏｆｎｅｓｔａｌｇｅｂｒａｓ .Ｉｎａｎｅｓｔａｌｇｅｂｒａ ,ｅａｃｈｆｉｎｉｔｅｒａｎｋｏｐｅｒａｔｏｒｃａｎｂｅｗｒｉｔｔｅｎａｓａｆｉｎｉｔｅｓｕｍｏｆｒａｎｋｏｎｅｏｐｅｒａｔｏｒｓｗｈｉｃｈｂｅｌｏｎｇｔｏｉｔｓｅｌｆ (Ｔｈｉｓｒｅｓｕｌｔｉｓｉｎ [1 ],ｂｕｔｂｅｌｏｎｇｓｔｏＪ .Ｒ .Ｒｉｎｇｒｏｓｅ) .Ｉｎａｎａｔｕｒａｌｗａｙ ,ｗｅｍａｙａｓｋ :　Ｑｕｅｓｔｉｏｎ…     

一类变换半群的秩

设自然数n≥4,X_n={1,2,…,n},证明了X_n上的保序压缩全变换半群W_n的秩为n-1.     

The Full Transformation Semigroups of Finite Rank are Amalgamation Bases for Finite Semigroups

In this article, we prove that the full transformation semigroup on a finite set is an amalgamation base for finite semigroups.     

有限秩的可解群的正则自同构

设G是有限秩的剩余有限可解群或是有限秩的剩余有限可解群的有限扩张,α是G的一个索数p阶正则自同构且φ:G→G(g→[g,α])是满射,则G是幂零类不超过h(p)的幂零群,其中h(p)是只与p有关的函数.     

关于幂有限秩算子

An operator F ∈ B(X) is called power finite rank if F~n is of finite rank for some n ∈ N.In this note, we provide several interesting characterizations of power finite rank operators. In particular, we show that the class of power finite rank operators is the intersection of the class of Riesz operators and the class of operators with eventual topological uniform descent.     

有限秩Toeplitz算子的(半)换位子

获得了Bergman空间上形如(T_f,T_g]-T_(h~n)和[T_f,T_g]-T_(h~n)的算子为有限秩时的充要条件,其中f,g,h均为有界调和函数,n为非负自然数.     

调和Bergman空间上的Toeplitz的零积及有限秩性质

本文研究了调和Bergman空间上的Toeplitz的Brown-Halmos型零乘积问题以及有限秩的相关性质,并得到了以解析和余解析符号的Toeplitz算子乘积的有限和的零积有限秩的等价条件.     

关于有限秩的幂零群的自同构

设G是有限秩的幂零群,1=ζ_0Gζ_1G …ζ_cG=G是G的上中心列,End(ζ_iG/ζ_(i-1)G)是Abel群ζ_iG/ζ_(i-1)G的自同态环(1≤i≤c),End(ζ_iG/ζ_(i-1)G)可以自然地作成一个Lie环.α_1,α_2,…,α_n是G的n个自同构,把它们在ζ_iG/ζ_(i-1)G上的诱导自同构分别记为α_(1i),α_(2i),…,α_(ni)(1≤i≤c).如果由α_(1i),α_(2i),…,α_(ni)生成的Lie环End(ζ_iG/ζ_(i-1)G)的Lie子环都是完全可解的,那么α_1,α_2,…,α_n生成的AutG的子群具有良好的幂零性质.考虑G的下中心列,可以得到对偶的结果.     

C0半群高阶微分算子的谱

本文研究了Ｃ０半群Ｔ（ｔ）的高阶微分算子Ｔ（ｎ）（ｔ）的谱给出了Ｔ＾（ｎ）（ｔ）的谱集的一种构造方法,讨论了Ｔ（ｎ）（ｔ）的谱点与Ｔ（ｔ）的无穷小生成元Ａ的谱点之间的关系。     

The Rank of a Direct Power of a Small-Cancellation Group

We construct an example of a finitely generated group G such that rank((G )ⁿ)=2 for all n1. For each n, we construct a finitely presented group G _n such that rank((G _n )ⁿ)=2. We conjecture that if G is a word-hyperbolic group then rank(G ⁿ ) as $ n. For each m we give an example of a residually finite group K _m such that K _m has exactly two relators, but K _m has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D.     

Stable Rank One and Real Rank Zero for Crossed Products by Finite Group Actions with the Tracial Rokhlin Property

The authors prove that the crossed product of an infinite dimensional simple separable unital C＊-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C＊-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero.     

Primary Ideals and Valuation Ideals in Semigroups

Let S be a cancellation torsion-free additive semigroup with identity 0 and let S {0}. We consider the relation between the valuation ideals and primary ideals of S. We give a characterization that each primary ideal is a valuation ideal in S and also give a characterization that each valuation ideal is a primary ideal in S.AMS Subject Classification (1991): 20M14     

Finite Rank Commutators and Semicommutators of Quasihomogeneous Toeplitz Operators

We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols. We show that in this context, the situation is different from the case of harmonic Toeplitz operators. Submitted: July 23, 2007. Accepted: December 4, 2007.     

Computing Finite Semigroups,II: The First Nonconstant Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this second part assume a left zero element, describe the first nonconstant row of the multiplication table in detail, and provide a numerical profile with which it can be compared to other rows.     

套代数理想中的有限秩算子

本文研究了套代数理想中有限秩算子的性质，然后用这些性质去刻划理想．     

Arithmetical Semigroups Related to Trees and Polyhedra,II — Maps on Surfaces

This paper extends recent investigations by Arnold Knopfmacher and John Knopfmacher [10] of asymptotic enumeration questions concerning finite graphs, trees and polyhedra. The present emphasis is on the counting of non‐isomorphic maps of not necessarily connected finite graphs on arbitrary surfaces. A significant aid towards this goal is provided by an extended abstract prime number theorem, based partly on more delicate tools of analysis due to W. K. Hayman [8].     

Large Deviations for Small Buffers: An Insensitivity Result

This article focuses on a queue fed by a large number of semi-Markov modulated fluid sources, e.g., on/off sources with on and off-times that have general distributions. The asymptotic regime is considered in which the number of sources grows large, and the buffer and link rate are scaled accordingly. We aim at characterizing the exponential decay rate of the buffer overflow probability for the regime of small buffers. An insensitivity result is proven: the decay rate depends on the distributions of the on and off-times only through their means. The efficiency gain to be achieved by using small buffers is significant, as the decay rate grows fast: proportionally to the square root of the buffer size.     

Finite rank operators in closed maximal triangular algebras II

In this paper, we discuss finite rank operators in a closed maximal triangular algebra . Based on the following result that each finite rank operator of can be written as a finite sum of rank one operators each belonging to , we proved that , where , if ; and , if . We also proved that the Erdos Density Theorem holds in if and only if is strongly reducible.

     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.