Sliding of self-similar sets

This paper deals with the Lipschitz equivalence of slidings of self-similar sets by graph-directed construction and martingale theory.     

弱非线性复合体中的高阶非线性响应

利用谱表示理论和微扰展开法，从理论上给出了适合于一般微结构复合体系的有效非线性响 应的一般表示式，并结合有效媒质近似（EMA），在弱非线性条件下研究了由三阶非线性组 分（体积分数为p）和线性组分构成的非线性复合体系的有效非线性响应，讨论了复合 体系的有效介电常数ε～e=εe+χe|E0|2+ηe|E0| 4中的有效三次非线性响应χe和有效高次非线性响应ηe与体积分数p和 退极化因子L之间的关系，分析了非线性组分的介电常数为复数情形时体系的有效高阶非线 性响应，从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响.  关键词： 非线性复合介质 有效非线性响应 谱表示理论     

含杂质无格点基底表面分枝状凝聚体的计算机模拟

根据含杂质熔融玻璃表面金原子凝聚的实验规律，在原子团簇具有随机的线扩散步长和刚性 转动角度的特征条件下，建立了含杂质无格点基底表面的各向异性团簇-团簇凝聚模型，对 团簇的无规扩散、刚性转动以及凝聚全过程进行了计算机模拟，系统地研究了基底表面无规 分布的杂质区域对分枝状凝聚体诸多特性的影响，所得结果与实验事实相符合. 关键词： 薄膜生长 Monte Carlo模拟 分形     

Fractal patterns of fluid domains for displacement processes in porous media

Percolation invasion displacement of a compressible defender is examined for two cases: when only the smallest accessible site is entered at each step and when all accessible sites less than the size given by a reducing back pressure are entered at each time step. Although the fractions of invading fluid are different, their scaling properties are equivalent. The effect of limited control of a back pressure in a real displacement and the effect of viscosity in a real time displacement are examined. In these cases the scaling properties of a percolation process at breakthrough are removed. As a result, one should expect that realistic displacement models will not have the singular properties usually attributed to percolation processes.     

A necessary and sufficient condition for the existence of an exponential attractor

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.     

分形拟极限集的可积性

本文讨论了螺线型拟极限集的可积性.作为应用,研究了Feigenbaum乘积映射的分 形拟极限集.     

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.     

基于相空间、熵和复杂度变化的表面肌电信号分析

采集20名男性实验对象在静态背伸疲劳负荷试验和动态等长负荷试验中的表面肌电信号,用混沌、分形理论的方法处理肌电信号、周期信号、随机信号,研究它们的延迟时间、重构相空间、熵值和复杂度等非线性指标的变化规律和特点.结果发现,表面肌电信号的延迟时间、重构相空间、熵值和复杂度等各种非线性特性均介于周期信号和随机信号之间,表现出混沌信号的特征.     

一类非均匀分形插值函数的可微性

本文研究一类分形插值函数的可微性问题，通过构造一迭代函数系，利用迭代函数系的唯一吸引子。给出了一类分形插值函数。并获得了此类分形插值函数在[0，1]区间上几乎处处可微和在[0，1]区间上某一点不可微判定的充分条件，推广了文献[2]的结论。     

Localized Coherent Structures with Chaotic and Fractal Behaviors in a(2+1)-Dimensional Modified Dispersive Water-Wave System

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1 )-dimensionalphysical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 1)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable localized coherent soliton excitationslike dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractalbehaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.