THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS

Suppose {Xn} is a random walk in time-random environment with state space Zd,|Xn| approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index a. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.     

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

两种新型芴类衍生物的三光子吸收特性研究

研究了两种新型芴类衍生物9，9_二（2_乙基已基）_2，7_二咔唑_9H_芴（简记为DCZF）和9 ，9_二（2_乙基已基）_2，7_二（2_（4_甲氧基）苯_2，1_乙烯基）芴（简记为BMOSF）在N ，N_二甲基甲酰胺（DMF）中的线性吸收和单光子荧光行为，并用脉冲宽度为38ps，重复 频率为10 Hz的1064 nm Nd：YAG脉冲激光研究了两种化合物的三光子吸收性质.结果表明： 两种新材料的最大线性吸收峰分别位于330和380nm，吸收区域覆盖了270—420 nm波段. 两种化合物的荧光带位于蓝_紫区，中心波长为369和442 nm，都具有较小的斯托克斯位移. 化合物DCZF和BMOSF的三光子吸收系数分别为γ_DCZF=678×10^{- 20} cm3/W²和γ_BMOSF=592×10^-20 cm³/W². 同时， 两种新材料还表现出明显的三光子吸收光限幅效应，当入射光强分别为8和6GW/cm²时，非线性透过率分别达到30%和45%. 关键词： 芴类衍生物 三光子吸收 光限幅 非线性透过率     

随机环境中马氏链的状态的性质

定义了随机环境中马氏链的强π-不可约性；给出了一个非正则本质状态不存在的充分条件；得出了在各种不可约性的条件下，状态的各种性质；研究了随机环境中马氏链的各种特性函数的性质．     

随机环境中双移民生灭过程的极限性质

引入了随机环境中双移民生灭过程的概念，定义了过程的模态指示函数，在此基础上研究了其转移矩阵的平稳分布，给出了平稳分布众数的位置与模态指示函数之间的关系．研究了平稳分布的众数与边界关系．     

随机环境中多物种分枝随机游动

引进了随机环境中多物种分枝随机游动的一般模型.在分枝过程非灭绝的情况下,讨论了系统的状态分类,得到了系统暂留及强常返的充要条件是存在k个定义在整数集上的函数分别满足某种性质.最后给出了系统强暂留的充分条件.     

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article,the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions.Several examples are given at the end.     

THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a “class property” ,i.e. two states x and y belong to same class implies the period of x is equal to the period of y.     

马氏场的遍历性及耦合

给定一族具有相同的条件分布的马氏场,本文找出了它们一致弱遍历的充要条件.在此基础上,我们还证明了一类特殊的强马氏场能够一致成功耦合的充要条件是它们一致弱遍历.