Residual Finiteness of Finitely Generated Quasi-commutative Semigroups

A semigroup S is called residually finite if for any pair of distinct elements a,b∈S, there exists a congruence P on S such that S/p is finite and (a,b) P. In1958, Malcev proved the following theorem: Any finitely generated abelian semigroupis residually finite . In this paper,we prove that a finitely generated quasi-commu-tative semigroup is residually finite. It generalizes the above theorem.     

关于正交表L_12(3×2~4)和L_(20)(5×2~8)

§1.介绍正交表L_(12)(3×2~4)和L_(20)(5×2~8) 我们在推广应用正交试验法过程中,遇到有些工农业试验,其中有一个定性因素是多水平的,而其他因素可取二水平的.如小麦品种和密度、肥料、播种期等栽培条件的试验     

The Classification of Exponential Paths in Sp(2)

众所周知，四阶以上辛群中指数型道路的Ｍａｓｌｏｖ指标可以取任意整数．本文给出了二阶辛群中指数型道路的分类及其Ｍａｓｌｏｖ指标的取值范围，指出了与高阶情形的不同之处．     

The normalizer of γ1(N) in psl2(R)

We find the full normalizer of γ₁(N) in psl₂(R).     

Cyclical Deformations of Quadrangles in S_κ~2 and Defining Properties of Alexandrov Spaces

This paper is mainly devoted to proving the four equivalent defining properties of a CBA(κ)space.The proof is based on an interesting tool we established which describes the cyclical five-step deformation procedure for quadrangles in the model 2-plane S_κ~2, including the limit shape of each step.As a byproduct we give a complete list of cyclical deformation procedures for all kinds of quadrangles on S_1~2.At last we make a contrast of geometric properties of CBA with CBB spaces, including a comparison between their defining properties and a discussion about Alexandrov's Lemma.     

When Is a Subspace of B(H) Ideal?

Let be a real or complex Hilbert space and let () denote the algebra of all bounded linear operators on . We show that if N is a subspace of (H) and for positive operators P₁, P₂ and every A N, P₁P₂A^* + AP₁P₂ N then N is an ideal. Furthermore if is an infinite dimensional real space then N = (H).AMS Subject Classification (1991): Primary 47B47, 47D25     

弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．     

Analytic Properties for Holomorphic Matrix-valued Maps in C~(2×2)

In this paper, we investigate some analytic properties for a class of holomorphic matrixvalued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on C~(2×2) and Julia set of one dimensional complex dynamic system.     

WAVELET ANALYSIS IN SOBOLEV SPACE H_(2π)~(-1) OF PERIODIC DISTRIBUTIONS

In Sobolev space H2π-1 of periodic distributions, a multiresolution analysis is established, and then it is shown that a corresponding orthonormal basis generated by a single mother function except the first element.     

分布式L_(1/2)正则化

研究数据集被分割并存储于不同处理器时的特征提取和变量选择问题,其中处理器通过某种网络结构相互连接.提出分布式L_(1/2)正则化方法,基于ADMM算法给出分布式L_(1/2)正则化算法,证明了算法的收敛性.算法通过相邻处理器之间完成信息交互,其变量选择结果与数据集不分割时利用L_(1/2)正则化相同.实验表明,所提出的新算法有效、实用,适合于分布式存储数据处理.     

某些广义插值在L_p ~(2π)和L_p(R)空间的逼近(英文)

给出了两种插值算子，并研究了它们在和L~(2π)_p和Lp（R）L空间上的逼近阶．用实数α阶的积分模给出逼近度．     

ON THE CONSTRUCTIONS OFPRE-WAVELETS IN L_2(R~s)

1.IntroductionForagivensetacgLZ:=LZ(R')wedenotebyS(di)theLZ-closureofallfinitecombinationsofmulti-integeraEZ'translationsofallofE4.Asequenceofclosedsubspaces{Vk}k.zgLZformsamultiresolutionanalysisofLZifitsatisfiesthefollowingconditions:(iii)f6Vk~scf.=f(2.)EVk l,kEZ,fEVO~f('~or)EVO,or6Z";(tv)ThereisafunctionyiEVO,calledscalefunction,suchthat(W'--or))....isaRieszbasisforfo,i.e.,VO=S(W)andMIJIdll5lid*all5MZlldllwith0相似文献   

(a~(1/2))~2与(a~2)~(1/2)的异同

<正>学习二次根式时,经常要遇到与二次根式有关的两个重要式子:(a^(1/2))(1/2))²与(a2与(a²)2)^(1/2).这两个式子在形式上很相近,既有不同点又有相同点,因此一不小心就很容易把它们混淆了.一、不同点1.运算顺序不同(a(1/2).这两个式子在形式上很相近,既有不同点又有相同点,因此一不小心就很容易把它们混淆了.一、不同点1.运算顺序不同(a^(1/2))(1/2))²是对实数a先开方再平方,表示a的算术平方根的平方;(a2是对实数a先开方再平方,表示a的算术平方根的平方;(a²)2)^(1/2)是对实数a先平方再开方,表示a的平方的算术平方根.     

(a~(1/2))~2和(a~2)~(1/2)告状记

(a~(1/2))~2和(a~2)~(1/2)兄妹俩,一来到花果山就受到众猴儿的青睐,争相和他俩交朋友,哪知有的小猴对他俩不礼貌,有时还受到了委屈,于是他俩就到猴王那里去告状,兄妹俩来到猴王面前,深深行了个鞠躬礼说:“报告猴王,小猴儿常把我俩张冠李戴,用我俩来解题时,     

(a~(1/2))~2与(a~2)~(1/2)的辨析

(a~(1/2))2与(a~2)~(1/2)在二次根式中扮演着十分重要的角色,由于这两个二次根式的外表较相似,有些同学在运算中往往对它们产生了混淆,发生这样或那样的错误．下面谈谈这两个概念的区别与联系．