无限维测度空间上的微分演算(Ⅰ)

As a generalization of Guassian measures, CM-measures on R~∞ are presented here. We study the cores of Laplace-Beltrami operators with respeot to them and the commutative relations between differential operators on R~∞ and the symmetric diffusion semi-groups generated by the Lallace-Beltrami operators. Using these results, the Littlwood-Paley inequlities will be established in the following paper on more general measure spaces than Wiener space.     

On multifractal of Cantor dust

We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust, The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure, Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self- similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.     

Co-RS-compact Topologies

A topoogy R(r)is constructed from a given topology r on a set X.R(r)iscoarser than r,and the following are some results based on this topology:1.Continuity and RS-continuity are equivalent if the codomain is retopologized by R(τ).2.Each topological spase has a coarser extremely disconnected topology3.The class of semi-open sets with respect to R(r)is a topology4.T_2 and semi-T_2 properties are equivalent on a space whose topology is R(r).5.Minboal R_0-spaces are RS-compact.6.MaxAnalα-compact spaces are RS-compact.     

Large Deviations for Empirical Measures of Not Necessarily Irreducible Countable Markov Chains with Arbitrary Initial Measures

All known results on large deviations of occupation measures of Markov processes are based on the assumption of （essential） irreducibility. In this paper we establish the weak＊ large deviation principle of occupation measures for any countable Markov chain with arbitrary initial measures. The new rate function that we obtain is not convex and depends on the initial measure, contrary to the （essentially） irreducible case.     

Propagation of Density-Oscillations in Solutions to the Compressible Navier-Stokes-Poisson System

Concerning a bounded sequence of finite energy weak solutions to the compressible Navier-Stokes-Poisson system （denoted by CNSP）, which converges up to extraction of a subsequence, the limit system may not be the same system. By introducing Young measures as in [6, 15], the authors deduce the system （HCNSP） which the limit functions must satisfy. Then they solve this system in a subclass where Young measures are convex combinations of Dirac measures, to give the information on the propagation of density-oscillations. The results for strong solutions to （CNSP） （see Corollary 6.1） are also obtained.     

ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF ESSENTIAL SPECTRA OF MULTIDIMENSIONAL TRANSPORT EQUATION

In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.     

Co-RS-紧拓扑

A topoogy R(τ) is constructed from a given topology τ on a set X. R(τ) is coarser than τ, and the following are some results based on this topology:1. Continuity and RS-continuity are equivalent if the codomain is retopologized by R(τ).2. Each topological space has a coarser extremely disconnected topology.3. The class of semi-open sets with respect to R(τ) is a topology.4. T₂ and semi-T₂ properties are equivalent on a space whose topology is R(τ).5. Minimal R₀-spaces are RS-compact.6. Maximal a-compact spaces are RS-compact.     

EXISTENCE OF WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

0 IntroductionRecently, the study of ordinary differential equations in a Banach spacehas been developed extensively by using the strong topology, see [2],13],[4]. Atpresent, however, there is no reference or paper which systematically studiesweak solutions of the Cauchy problem of ordinary differential equation in theweak topology. In references [l],15],[7] and [8], several results of weak solutionsare proved. In this paper, we shall give the other results of weak solutions,some of which are…     

EXISTENCE THEOREMS FOR RANDOM MEASURES

Two existence theorems of random measures on a separable complete metric space areproved.It seems that the theory of random measures in locally compact spaces and that inseparable complete metric spaces are essentially different by noting that the critera fortightness of the locally finite measures is much more tedious than that of the Radommeasures.     

Hausdorff measures of the image, graph and level set of bifractional Brownian motion

Let BH,K = {BH,K(t), t ∈ R+} be a bifractional Brownian motion in Rd. This process is a selfsimilar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of BH,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.     

On the absence of invariant measures with locally maximal entropy for a class of shifts of finite type

We prove that for a class of shifts of finite type, , any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.

     

集值映射空间在紧开拓扑下的$\aleph_0$性质

本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若$X,Y$为$\aleph_0$空间,则$X$到$Y$上的点紧致的连续集值映射族依紧开拓扑是$\aleph_{0}$空间,从而将Michael$^{[1]}$的结论推广到更大的映射空间类上.     

No submaximal topology on a countable set is -complementary

Two -topologies and given on the same set , are called transversal if their union generates the discrete topology on . The topologies and are -complementary if they are transversal and their intersection is the cofinite topology on . We establish that for any connected Tychonoff topology there exists a connected Tychonoff transversal one. Another result is that no -complementary topology exists for the maximal topology constructed by van Douwen on the rational numbers. This gives a negative answer to Problem 162 from Open Problems in Topology (1990).

     

First countable, countably compact spaces and the continuum hypothesis

We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah's iteration theorems appearing in Chapters V and VIII of Proper and improper forcing (1998), as well as Eisworth and Roitman's (1999) iteration theorem. We close the paper with a ZFC example (constructed using Shelah's club-guessing sequences) that shows similar results do not hold for closed pre-images of .

     

抽象凸空间上的弱KKM映射, 相交定理和极大极小不等式

In this paper,we introduce the concept of weakly KKM map on an abstract convex space without any topology and linear structure,and obtain Fan＇s matching theorem and intersection theorem under very weak assumptions on abstract convex spaces.Finally,we give several minimax inequality theorems as applications.These results generalize and improve many known results in recent literature.     

强拟\alpha-预不变凸函数

研究了一类重要的广凸函数------强拟$\alpha$-预不变凸函数,讨论了它与拟\,$\alpha$-预不变凸函数、严格拟\,$\alpha$-预不变凸函数及半严格拟\,$\alpha$-预不变凸函数之间的关系,并在中间点的强拟\,$\alpha$-预不变凸性下得到了它的三个重要的性质定理,同时给出了强拟\,$\alpha$-预不变凸函 数在数学规划中的两个重要应用,这些结果在一定程度上完善了对强拟\,$\alpha$-预不变凸函数的研究.     

具$w_0$-距离度量空间中$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的最佳逼近点定理

本文提出了一类称为$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的新的非自映射,并引进了关于$\eta$的$\alpha$-逼近可容许映射和关于$\eta$的$(\alpha,d)$正则映射的概念.基于这些新概念,在$w_0$-距离度量空间中研究了此类新压缩最佳逼近点的存在唯一性,并给出了一个新的定理,推广和补充了文[Ayari, M. I. et al. Fixed Point Theory Appl., 2017, 2017: 16]和[Ayari, M. I. et al. Fixed Point Theory Appl., 2019, 2019: 7]中的结果.给出了一个例子来说明主要结果的有效性.进一步地,作为推论得到关于两个映射的最佳逼近点和公共不动点定理.作为其中一个推论的应用,讨论了一类Volterra型积分方程组的求解问题.     

一般化凸空间上的几乎不动点, 不动点和拟变分不等式

The definitions of S-KKM property and Γ-invariable property for multi-valued map- ping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational inequality theorem for acyclic map on Hausdorff Φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.     

关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记

D.M. Speegle 在文献[1] 中给出了具有常数 $\alpha$的性质${\cal A}$ 的定义,并且证明了任意无限维的可分一致光滑Banach空间都具有这样的性质,而且常数 $\alpha\in [0,1)$.本文给出了一个使得无限维可分Banach空间具有这种性质的充分条件,以及几个关于文献[1] 的注解.     

半覆盖远离性质与有限群的结构

In this paper,the so-called π-cover-avoiding properties of subgroups are defined and investigated.In terms of this property,we characterize the π-solvability of finite groups.Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.