随机环境马氏链上一类集合的分形维数

假设{Xn}是随机环境的马氏链，引入Hopf Markov链，在此基础上定义了绕积Markov链，用此方法，将正则马氏链下一类集合的分形维数的结果推广到了随机环境马氏链下一类集合，并且获得了相应的结论．     

基于小波变换及布朗分形模型的纹理分割

在研究小波变换及布朗分形模型的基础上，定义了水平分维数，垂直分维数，对角分维数，并将它们作为纹理特征量来实现纹理的分割．实验结果表明，这些特征量能够很好地反映纹理特征，从而分割时不需有关图象中纹理类别的先验信息，较以往方法在准确度和计算复杂程度上都有很大提高．     

再探武汉地区雨强分维数随时间变化

对武汉大学电波综合观测站于１９９１年的降雨曲线进行测量，当采样时间为５ｍｉｎ时，用单变量雨强时间序列进一步研究了降雨这一大气过程中雨强分维数随时间的变化特性．结果表明，在灾害性降雨天气前后其雨强分维数仍然发生了显著性的改变．     

表面分形球、柱的光散射

分形和分维是近些年才兴起的一门处理复杂事物的新方法￣［１］。本文主要研究具有表面分形的球、柱的光散射特征。我们首先利用几何光学近似研究了一种表面满足自仿射原理的分形均匀球的散射，其散射特性与分维存在一定的关系。我们还利用微扰法讨论了表面具有沟槽的分形柱的光散射的分形特征。     

4＋2D维Einstein－Maxwell量子宇宙

利用推广的Ｈａｒｔｌｅ－Ｈａｗｋｉｎｇ假设，研究了４＋２Ｄ维Ｅｉｎｓｔｅｉｎ－Ｍａｘｗｅｌｌ量子宇宙，计算了微超空间波函数的近似解．发现当Ｄ≤２时存在与观测宇宙相符合的暴胀解．     

Using Fractal Function Auto correlative Method to Confirm Fractal Dimension of Function Graph

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｈｙｐｏｔｈｅｓｉｓｏｆａｓｔａｔｉｓｔｉｃａｌｙｌｏｃａｌｙｉｓｏｔｒｏｐｉｃｈｏｍｏｇｅｎｅｏｕｓｔｕｒｂｕｌｅｎｔｆｉｅｌｄｗａｓｔｈｅｂａｓｅｏｆＫｏｌｍｏｇｏｒｏｖ’ｓｍｏｄｅｌ［１］．Ｔｈｅｓｅｃｏｎｄｏ...     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

Resistivity exponent of two-dimensional lattice animals

We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) L , is found to be =1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts 0.8. Our value for differs from earlier measurements of this quantity by other methods yielding =1.17±0.05 and 1.22±0.08 by Havlin et al.On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.     

Transfer processes in fractal media

An irreversible process in fractal media involves coupling relation between the space and the time. The present note displays how the fractional derivation has to be introduced to describe this effect. As a result the law of the chemical diffusion to a fractal is given.     

分形粗糙面双站散射的快速前后向迭代法数值模拟

为模拟复杂分形表面特别是在低掠角入射条件下的双站散射,发展了一种结合前后向迭代方法(FBM)与谱加速算法(SAA)快速求解散射场的Monte Carlo数值方法,计算了在TE,TM锥形波入射在一维分形导体粗糙面的双站散射以及有规则异物存在时的双站散射,讨论了分形粗糙面双站散射的角度性分布与其分数维的关系. 关键词： GFBM/SAA 分形粗糙面 双站散射