由Cantor展式定义的Besicovitch-Eggleston子集

本文研究了由Cantor展式所确定的一类Besicovitch-Eggleston子集.应用Billingsley定理,得到了这类集合的维数.并且表明无穷符号空间和有限符号空间上的Besicovitch-Eggleston子集的性质是有区别的.     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

弱STP-紧L-子集

在L-拓扑空间中引进了弱STP-紧性,它是一种介于良S-紧和弱PS-紧的紧性.文中给出弱STP-紧子集的定义,讨论了它的一些刻画,并的出一些好的性质.     

关于贴近度的定义

本文在［１］的基础上，指出了［１］中的Ｆｕｚｚｙ子集贴近度定义的不完善之处，并给出了另一较完善的Ｆｕｚｚｙ子集贴近度的定义和性质．     

自由半群的估计熵和△-弱混合集

本文对自由半群作用的动力系统引入了估计熵和△-弱混合集的概念,得到一些性质.通过引入△-熊混沌集,给出了△-弱混合集的一个等价刻画.     

超空间与原空间动力系统之间的关系

设(X,d,f)为拓扑动力系统,其中X为局部紧可分的可度量化空间,d为紧型度量,f为完备映射,用2X表示由X的所有非空闭子集构成的集族,(2X,ρ,2f)为由(X,d,f)所诱导的赋予hit-or-miss拓扑的超空间动力系统.本文引入了余紧点传递和弱拓扑传递的定义.特别的,在X满足一定的条件时,给出了点传递,弱拓扑传递和余紧点传递之间的关系,并研究了(X,d,f)的余紧传递点,回复点和几乎周期点分别与(2X,ρ,2f)的传递点,回复点和几乎周期点之间的蕴含关系.这些结论丰富了赋予hit-or-miss拓扑的超空间的研究内容.     

作用模糊子集推理方法的研究与应用

针对实用模糊控制过程,提出作用模糊子集和作用模糊控制规则的概念;根据模糊逻辑推理中真值的产生、传递和接收机理,提出作用模糊子集推理方法;比较分析了作用模糊子集推理方法与CRI法的推理结果;利用该推理方法实现了试验室温度模糊控制试验。     

凸模糊子集的再定义

给出基于t-范上的凸模糊子集的定义,讨论这种凸模糊子集的同态像性质,重点研究了Tm-凸模糊子集的生成线,证明每一个TA－凸模糊子集为凸子集生成的Tm-凸模糊子集。     

Phase-Type分布的一个新稠密子集及其性质

针对目前常用的Phase-Type分布稠密子集存在的问题,对Hyper-Erlang分布进行扩展,给出了Phase-Type分布一个新的稠密子集E-HErD,证明了该新稠密子集的稠密性,并给出了其若干相关性质.     

完备度量空间中的混沌判定

本文研究完备度量空间上的离散动力系统的混沌标准,证明了如果完备度量空间X上的连续映射f具有正则非退化返回排斥子或连接不动点的正则非退化异宿环,则存在f的不变闭子集A,使得f限制在此不变闭子集上的子系统与两个符号的符号动力系统拓扑共轭,从而获得具有这类结构的连续映射f具有Devaney混沌、分布混沌、正拓扑熵及ω-混沌,...     

Transitive points via Furstenberg family

Let (X,T) be a topological dynamical system and F be a Furstenberg family (a collection of subsets of Z₊ with hereditary upward property). A point x∈X is called an F-transitive one if {n∈Z₊:Tnx∈U}∈F for every non-empty open subset U of X; the system (X,T) is called F-point transitive if there exists some F-transitive point. In this paper, we aim to classify transitive systems by F-point transitivity. Among other things, it is shown that (X,T) is a weakly mixing E-system (resp. weakly mixing M-system, HY-system) if and only if it is {D-sets}-point transitive (resp. {central sets}-point transitive, {weakly thick sets}-point transitive).It is shown that every weakly mixing system is Fip-point transitive, while we construct an Fip-point transitive system which is not weakly mixing. As applications, we show that every transitive system with dense small periodic sets is disjoint from every totally minimal system and a system is Δ^?(Fwt)-transitive if and only if it is weakly disjoint from every P-system.     

Quasi-convex subsets in Alexandrov spaces with lower curvature bound

We introduce quasi-convex subsets in Alexandrov spaces with lower curvature bound, which include not only all closed convex subsets without boundary but also all extremal subsets. Moreover, we explore several essential properties of such kind of subsets including a generalized Liberman theorem. It turns out that the quasi-convex subset is a nice and fundamental concept to illustrate the similarities and differences between Riemannian manifolds and Alexandrov spaces with lower curvature bound.     

Devaney混沌的随机性质

讨论了Devaney混沌的随机性质,证明了如果度量空间上的连续变换f是弱混合的,那么f是拓扑传递的,并且若f的周期点稠密,则f还是初值敏感的.     

CHAOS AND TOPOLOGICAL MIXING OF TREE MAPS

In the present paper we show that a tree map is totally transitive iff it is topologically mixing. Using this result, we prove that the tree maps having a chaotic (or scrambled) subset with full Lebesgue measure is dense in the space consisting of all topologically mixing (transitive, respectively) maps.     

Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

Almost Chebyshev set with respect to bounded subsets

The uniqueness and existence of restricted Chebyshev center with respect to arbitrary subset are investigated. The concept of almost Chebyshev sets with respect to bounded subsets is introduced. It is proved that each closed subset in a reflexive locally uniformly convex (uniformly convex, respectively) Banach space is an almost Chebyshev subset with respect to compact convex subsets (bounded convex subsets and bounded subsets, respectively). Project supported by the National Natural Science Foundation of China, Natural Science Foundation of Zhejiang Province, and the State Major Key Project for Basic Researchers of China.     

Classification problems for shifts on modules over a principal ideal domain

In this paper we study symbolic dynamics over alphabets which are modules over a principal ideal domain, considering topological shifts which are also submodules. Our main result is the classification, up to algebraic and topological conjugacy, of the torsion-free, transitive, finite memory shifts.

     

On relatively weakly almost Lindelöf subsets

Summary A subset Y of a space X is weakly almost Lindel?f in X if for every open cover U of X, there exists a countable subfamily V of U such that Y ⊆ comp (∩V ). We investigate the relationship between relatively weakly almost Lindel?f subsets and relatively almost Lindel?f subsets, and also study various properties of relatively weakly almost Lindel?f subsets.     

Intuitionistic notions of boundedness in ℕ

We consider notions of boundedness of subsets of the natural numbers ? that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ? to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most of the results do not require countable choice. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)