非自治线性时滞微分方程的扰动全局吸引性及一致稳定性

本文研究非自治线性时滞微分方程的扰动全局吸引性及一致稳定性，主要讨论了线性部分为周期系数与非周期系数的两种情形，获得了关于零解全局吸引及一致稳定的充分条件．推广了文献中线性部分为自治情形的结果。     

Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces

Set-valued weaker contractions in uniform, locally convex and metric spaces are defined and dynamic systems of such weaker contractions are studied. Conditions guaranteeing the convergence of generalized sequences of random iterations and iterations and the existence and uniqueness of endpoints of set-valued weaker contractions are established. Our definitions and results are new for set-valued maps in uniform, locally convex and metric spaces and even for single-valued maps.     

Krein空间上算子的可定化性

从Hilbert空间(H,(·,·))上的一个有界自伴算子G可以导出不定内积[·,·]:=(G·,·),本文给出了由G所导出的Krein空间上的G-自伴、G-酉以及G-正常算子的可定化、强可定化和一致可定化性质以及这三种不同的可定化性之间的关系.     

On a new geometric constant related to the von Neumann-Jordan constant

The von Neumann-Jordan constant CNJ(X) is computed for X being ?₂−?₁ and ?_∞−?₁ space by introducing a new geometric constant γX(t). These partly give an answer to an open question posed by Kato et al. Some basic properties of this new coefficient are investigated. Moreover, we obtain a new class of Banach spaces with uniform normal structure.     

Uniform Asymptotic Expansions for Meixner Polynomials

Meixner polynomials m _n (x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. In this paper, we derive two infinite asymptotic expansions for m _n (nα;β,c) as . One holds uniformly for , and the other holds uniformly for , where a and b are two small positive quantities. Both expansions involve the parabolic cylinder function and its derivative. Our results include all five asymptotic formulas recently given by W. M. Y. Goh as special cases. April 16, 1996. Date revised: October 30, 1996.     

Neighborhood assignments and cardinal functions: a unified approach to metrization and uniformity

We use neighborhood assignments and cardinal functions to give a unified approach to metrizability and uniformity. This leads to a number of characterizations of m(X), the metrizability degree of X, u(X), the uniform weight of X, and w(X), the weight of X. For X normal (and regular), m(X) = u(X); it is unknown whether this result extends to completely regular spaces.     

R（0，θ）分布族参数的矩估计与最大似然估计

本文讨论了均匀分布族｛Ｒ（０，θ），θ＞０｝中参数θ的矩估计及最大似然估计的效率及相合性，结果表明θ修正后的最大似然估计要优于θ的矩估计。     

On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions

We establish the existence and stability results for periodic nonautonomous uniform forward attractors of periodic general dynamical systems (set-valued dynamical systems). We also investigate the dynamical behavior of nonautonomous periodic differential inclusion x^′(t)∈f(t,x(t)) on R^m with only upper semi-continuous right-hand side by applying the abstract results. Firstly, we show that if the system has a compact uniformly attracting set, then it has a periodic nonautonomous uniform forward attractor A. Secondly, we prove that A is robust with respect to both internal and external perturbations. Finally, we apply the robustness result to discuss the effects of small time delays to asymptotic stability of the system.     

Preparation of uniform rhodamine B-doped SiO2/TiO2 composite microspheres

Uniform rhodamine B (RB)-doped SiO₂/TiO₂ composite microspheres with catalytic and fluorescent properties were prepared by an easy and economical method in this paper. The composite microspheres were built up with well-dispersed silica particles as the cores, RB as both the doped agent and stabilizer, and the TiO₂ shells were obtained through the hydrolysis of TiCl₄ in water bath. The morphology and structure of the particles were characterized by scanning electron microscopy (SEM) and X-ray powder diffraction (XRD). The characterization results indicate that composite particles are all in spherical shape and have a narrow size distribution. The composite particles calcined above 500 °C reveal clear crystalline reflection peaks of the rutile TiO₂ which exhibits well catalytic property. The photocatalytic experiment was carried out in order to examine the catalytic property of composite microspheres. The fluorescent property of particles was also investigated. Dye-leakage test indicates that RB molecules entrapped in the composite particles by this method are stable inside the particles.     

On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.