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。     

Cantor集合上的连续自映射

本文证明了Ｃａｎｔｏｒ集Ｃ上所有拓扑共轭于（单边的）有限型子移位的连续自映射的集合在H中稠密，此外Ｃ上每个拓扑传递（混合）映射均可被拓扑共轭于有限型子移位的拓仆传递（混合）映射一致逼近．     

对称Cantor集自乘积集的Hausdorff中心测度

设Cλ是由迭代函数系统(IFS){f1,f2}生成的对称Cantor集,其中f1(x)=λx, f2(x)=1-λ+λx,0<λ<1/2,x∈[0,1]．在压缩比λ满足一定条件时,本文得到了Cλ与其自身的笛卡尔乘积Cλ×Cλ的Hausdorff中心测度的计算公式．     

三分Cantor集自乘积的Hausdorff测度的估计

本文证明了三分Cantor集C自乘积集C×C的Hausdorff测度,满足1≤H~((log_3)~4)(C×C)≤1.502879.     

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.     

On the (p,q)$(p,q)$-type strong law of large numbers for sequences of independent random variables

Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 368 (2016), no. 1, 539–561) introduced a refinement of the Marcinkiewicz–Zygmund strong law of large numbers (SLLN), the so-called $(p,q)$-type SLLN, where and $q>0$. They obtained sets of necessary and sufficient conditions for this new type SLLN for two cases: , $q>p$, and . Results for the case where and remain open problems. This paper gives a complete solution to these problems. We consider random variables taking values in a real separable Banach space $\mathbf{B}$, but the results are new even when $\mathbf{B}$ is the real line. Furthermore, the conditions for a sequence of random variables $\left\{X_n,n\ge 1\right\}$ satisfying the $(p,q)$-type SLLN are shown to provide an exact characterization of stable type p Banach spaces.