The Chang-Łoś-Suszko theorem in a topological setting

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.     

N指标d维广义Wiener过程象集的m项代数和的几个性质

设珮犠（狋）：犚犖＋ →犚犱是犖指标犱维广义Ｗｉｅｎｅｒ过程，对任意紧集犈１，…，犈犿犚犖＞ ，该文研究了犿项代数和珮犠（犈１）…珮犠（犈犿）的Ｈａｕｓｄｏｒｆｆ维数，Ｐａｃｋｉｎｇ维数和正的Ｌｅｂｅｓｇｕｅ测度及内点的存在性． 其结果包含并推广了布朗单的结果．     

Free probability and the von Neumann algebrasof free groups

This short note summarizes the circumstances of the birth of free probability theory andsome of the recent achievements.     

广义Sierpinski集

本文考察了包括平面上的各种广义 Cantor集 ,Sierpinski集和包括某些连续不可微曲线在内的广义 Sierpinski集 .由相似变换 ,导出了它们的级数表达式 ,并利用它和字符串空间的对应关系 ,计算出它们的Hausdorff维数     

Gorenstein代数上的Hopf代数作用

令H是有限维Hopf代数，A是左H-模代数。本文证明了A是Gorenstein代数的充分必要条件。A^H也是Gorenstein代数的条件。它是Enochs EE,GarciaJJ和del RioA关于群作用相应的理论的推广，同时给出A/A^H是Frobenius扩张的条件。     

Universal spaces for asymptotic dimension

We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of asymptotic dimension with asymptotic inductive dimension.     

The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

基于ZBLANⅩⅣPr,Yb频率上转换发光的三维立体显示

本文对利用ZBLANⅩⅣPr,Yb频率上转换发光的三维立体显示做了研究,探讨了其中的一些物理问题.在实验中,我们利用Yb³⁺离子敏化的方法提高Pr³⁺的上转换发光效率;通过降低能引起单频上转换发光的激光强度来提高寻址点和非寻址点在显示过程中的对比度.     

Hausdorff dimension of a random invariant set

The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension.