Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

On Strong Reality of Finite Simple Groups

In this paper we shall consider the following problem. Which finite simple groups have the property: any element is inverted by an involution?     

关于增生算子方程Ishikawa迭代法收敛率估计的注记

对严格拟压缩映射和非线性强增生算子方程的Ishikawa迭代程序的收敛性及误差估计给出一个统一的定理。我们的结果统一和改进了近期相应的结果。     

INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

The aim of this paper is to study the conditions by which a P-prime submodule can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.     

线性均衡约束最优化的一个广义投影强次可行方向法

本文讨论带线性均衡约束最优化问题,首先利用摄动技术和一个互补函数将问题等价转化为一般约束最优化问题,然后结合广义投影技术和强次可行方向法思想,建立了问题的一个新算法.算法在迭代过程中保证搜索方向不为零,从而使得每次迭代只需计算一次广义投影.在适当的条件下,证明了算法的全局收敛性,并对算法进行了初步的数值试验.     

A note on strong β-I-sets and strongly β-I-continuous functions

Summary In [6], we introduced and investigated the notions of strong β-I-open sets and strong β-I-continuous functions in ideal topological spaces. In this paper, we investigate further their important properties.     

赋序列范数的矢值序列空间ss(E)的强暴露性和暴露性

刻划了赋序列范数的矢值B anach序列空间ss(E)的强暴露性和暴露性,给出了它们的判据.     

算子权移位的换位代数的交换性

令T是以{Wk}∞k=1B(Cn)为权序列的内射算子权移位.设T是强不可约的,而且sup1k<∞‖W-1k‖< ∞.用A′(T)表示T的换位代数,radA′(T)表示A′(T)的Jacobson根.本文刻划了radA′(T)并且证明了商代数A′(T)/radA′(T)是交换的.     

Nontrivial Solutions for Resonant Hemivariational Inequalities

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown. This paper has been partially supported by the State Committee for Scientific Research of Poland (KBN) under research grants no. 2 P03A 003 25 and no. 4 T07A 027 26.     

关于完备随机内积模中的Lax-Milgram定理的注记

设(S,X)为数域K上以σ-有限测度空间(Ω,A,μ)为基的完备的RIP-模,而且α:S×S→L(μ,K)满足如下条件:(A)存在ξ∈L (μ),使得a(p,q)ξ·X~p·X~q,p,q∈S;(B)a是coercive(即,存在η∈L (μ),使得a(p,p)η·X~p2,p∈S且μ({ωη(ω)=0})=0);(C)对每个q∈S,a(·,q):S→L(μ,K)是模同态,且对每个p∈S,a(p,ξq1 ηq2)=ξ-a(p,q1) η-a(p,q2),q1,q2∈S及ξ,η∈L(μ,K).则存在唯一的连续模同态A:S→S使A-1存在且μ-a.s.有界,还满足:(1)a(p,q)=XA(p),q,p,q∈S;(2)X~A-1(p)1ηX~p,p∈S.