Note on the Cantor–Bendixson Rank of Limit Groups

We show that the Cantor–Bendixson rank of a limit group is finite as well as that of a limit group of a linear group.     

The Closeness of the τ-Standard Part of a Set

In this paper,the closeness of the τ-standard part of a set is discussed.Some related propositions of the τ-neighborhood system of a set are given.And then some related conclusions of the τ-monad of a set and the τ-standard part of a set are presented.And based on it,the necessary and sufficient conditions of the enlarged model and the saturated model are showed.Finally,some sufficient conditions that the τ-standard part of a set is closed are proved in the enlarged model and the saturated model.     

Topologies on the n-Element Set Consistent with Topologies Close to Discrete on an (n−1)-Element Set

Ukrainian Mathematical Journal - Topologies on a finite set are described by a nondecreasing sequence of nonnegative integers (vector of topologies). We study T0-topologies on the n-element set...     

On the Boundary of the Set of Morse-Smale Vector Fields on Two-dimensional Manifolds

NotatianM a compact,boundaryless,orientable or non—orientable two-dimensional manifold of class C~∞H~r(M) the Banach space of C~r(r≥1)vector fields on M∑~r(M) the set of structurally stable vector fields in H~r(M)MS~r(M) the set of Morse—Smale vector fields in H~r(M)     

The Largest Cardinals of Isomorphic Class of Topology-set-lattices on an Infinite Set

Let X be an infinite set,K={τ:τ is a topology on X},defineτ≌σ iff (f)(f is a lattice-isomorphism from τ to σ),for a given τ∈K we define τ={σ:σ∈K ＆σ≌τ}K(K)is an imcomparable class iff (τ∈K)(σ∈K)(τ≠→τ and σ are incomparable),M={K:K is an incomparable class}. Theorem 1 sup{|τ|:τ∈K}=max{|τ|:τ∈k}=|K|=2~2~[X]=exp(exp(|X|)). Theorem 2 sup{sup{|τ|:τ∈K}:KK ＆ K is an incomparable class}=sup     

The Cardinal of the Set of Non-quasi-regular Elements in a Ring

ＴｈｅＣａｒｄｉｎａｌｏｆｔｈｅＳｅｔｏｆＮｏｎ┐ｑｕａｓｉ┐ｒｅｇｕｌａｒＥｌｅｍｅｎｔｓｉｎａＲｉｎｇＤｕＸｉａｎｋｕｎ（杜现昆）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ，１３００２３）...     

The Range Set of Meromorphic Derivatives

ＴｈｅＲａｎｇｅＳｅｔｏｆＭｅｒｏｍｏｒｐｈｉｃＤｅｒｉｖａｔｉｖｅｓＩｎｄｒａｊｉｔＬａｈｉｒｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪａｄａｖｐｕｒＵｎｉｖｅｒｓｉｔｙ，Ｃａｌｃｕｔａ－７０００３２，Ｉｎｄｉａ）ＡｂｓｔｒａｃｔＩｎｔ...     

Note on the Blow-up Set for A Semilinear Parabolic Differential System

ＮｏｔｅｏｎｔｈｅＢｌｏｗ－ｕｐＳｅｔｆｏｒＡＳｅｍｉｌｉｎｅａｒＰａｒａｂｏｌｉｃＤｉｆｆｅｒｅｎｔｉａｌＳｙｓｔｅｍ￥ＣｈｅｎＦｕｊｕｎ（陈富均）（ＳｈａｎｇＱｉｕＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ４７６０００）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｎｏｔｅｄ...     

Combinatorial variations on Cantor?s diagonal

We discuss counting problems linked to finite versions of Cantor?s diagonal of infinite tableaux. We extend previous results of Brlek et al. (2004) [2] by refining an equivalence relation that reduces significantly the exhaustive generation. New enumerative results follow and allow to look at the sub-class of the so-called bi-Cantorian tableaux. We conclude with a correspondence between Cantorian-type tableaux and coloring of hypergraphs having a square number of vertices.     

依零测度的Fuzzy集运算

给出了Fuzzy集合依零测度的包含,依零测度的相等。依零测度的并．交,补运算等。并补充地研究了这些基本运算,获得了若干好的性质。Fuzzy集依零测度的基本运算比标准fuzzy集合论的相应运算更有人情味,更为接近人的智能机理。有望在智能信息处理和软计算领域取得好的应用。     

A Riesz Product Type Measure on the Cantor Group

A Riesz type product as Pn=nЛj=1（1＋awj＋bwj＋1）is studied, where a, b are two real numbers with ｜a｜ ＋ ｜b｜ 〈 1, and {wj} are indepen- dent random variables taking values in （-1, 1} with equal probability. Let dw be the normalized Haar measure on the Cantor group Ω = （-1, 1}^N. The sequence of P,~dw 1 probability measures {Pndw/E（Pn） } is showed to converge weakly to a unique continuous measure on/2, and the obtained measure is singular with respect to dw.     

局部紧空间上模糊值模糊测度的正则性

研究局部紧Hausdorff空间上模糊值模糊测度。首先,给出模糊值模糊测度的自连续和一致自连续的定义,然后引进模糊值模糊测度正则性的概念,在自连续或一致自连续的条件下,证明了局部紧空间上模糊值模糊测度的一些定理。     

基于方向信息测度的最小模糊度准则边缘检测

将像素点的方向信息测度作为判别边缘点的特性指标,借用Huang等构造的自适应确定分割阈值的思想,本文提出了一种基于方向信息测度的最小模糊度准则边缘检测方法。文中提出的方法,一方面由于采用了方向信息测度,可以很好地将边缘点和非边缘点区分开来;另一方面通过最小化模糊度,自适应地将给定图像的所有像素点按照方向信息测度分成两类,从而达到提取边缘的目的。实验结果证明,我们提出的方法能够很好地判别边缘点,有效地提取图像的边缘。     

基于鞅空间M(ln~+M)~p,L(ln~+L)~p与K(ln~+K)~p的关系研究

旨在利用概率方法探讨鞅空间K2与M1之间的鞅空间包含变化关系.首先提出了新的鞅空间M(ln+M)p,L(ln+L)p以及K(ln+K)p(其中p 1)的定义,并证明了其空间包含关系.     

基于集对分析的城市居民幸福指数测评—以济南、青岛、泰安、滨州为例

为探讨城市居民幸福感及其影响因素,采用主、客观评价相结合的方法构建了城市居民幸福指数的评价模型.首先通过对经济发展、居民生活、人口与就业结构和生活环境水平四个方面构建了居民客观幸福指数评价指标体系.对身心健康、生活便利、环境舒畅状况和自我价值实现四个方面构建了居民主观幸福指数评价指标体系.然后运用变异系数、主观G1权重赋值、集对分析评价法建立了一种基于多元联系数的综合评价模型.最后以济南、青岛、泰安、滨州为例,阐述了城市居民幸福指数集对分析模型的评价过程,评价结果合理可靠.     

The L* Partial Order on the Set of Group Matrices

In this paper,we use the L(o)wner partial order and the star partial order to introduce a new partial order (denoted by "L*") on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L* partial order is a special kind of the core par-tial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.     

Dynamics of the Action of a CAT(0) Group on the Boundary

The main theorem here gives a geometric condition on the fixed point sets of two hyperbolic isometries of a CAT(0) group which guarantees that the subgroup generated by the two elements contains a free subgroup. A result in section 3 shows that an element extends to the identity on the boundary if and only if the element is virtually central in the CAT(0) group. Finally, the two dimensional case is considered in the last section of the paper and there it is shown that powers of two hyperbolic isometries commute if and only if a geometric condition on the fixed point sets is satisfied.     

Two parameter smooth martingales on the Wiener space

We prove that two parameter smooth continuous martingales have ∞-modification and establish a Doob's inequality in terms of (p, r)-capacity for two parameter smooth martingales.     

基于模糊数分析的时机捕捉型的证券投资模型

以时机捕捉型的投资者的投资理念和操作经验为背景,本文模拟他们的证券分析和决策过程。我们视证券价格的波动为动态的模糊系统,利用模糊数的概念来定义股价波动的预测集。通过模糊数分析,我们详尽地讨论了证券价格的变化规律和显著投资时机等概念。我们获得了模糊集理论下的证券价格的期望值、投资收益率期望值、预期风险系数、风险率和损益比等数据。利用这些结果,我们得到了三个时机捕捉型的证券投资模型,为证券投资者的决策问题提供了一种新的方法。这些模型的建立依赖于投资者的知识和经验,它们的求解过程简单易行。