十二次对称准周期结构的自相似变换及准晶胞构造

研究十二次对称准晶体模型的几何结构性质.修正了Socolar在正方形-菱形-六边形拼图模型中自相似变换的错误.在Stampfli-Ghler正方形-菱形-三角形拼图模型的基础上,成功地构造出了准晶胞,使得十二次对称准周期结构可以用覆盖理论描述. 关键词： 准晶体 拼图模型 自相似变换 覆盖理论     

A lower bound for the symbolic multifractal spectrum of a self-similar multifractal with arbitrary overlaps

By now the multifractal structure of self-similar measures satisfying the so-called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spectrum of an arbitrary self-similar measure. We emphasize that we are considering arbitrary self-similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. Our results also have applications to self-similar sets which do not satisfy the Open Set Condition (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Self-similar solutions to Lin-Reissner-Tsien equation

The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no exact solution. Travelling wave solutions are also obtained.     

An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.     

掺镱光纤放大器中脉冲自相似演化特性分析

为了研究自相似演化对于高功率超短脉冲系统产生的影响,采用非线性薛定谔方程,对掺镱光纤放大器中自相似解进行了理论分析,得到初始脉冲、脉冲宽度、增益系数、增益色散等参量变化时对其自相似演化产生不同的影响.结果表明,初始脉宽不同时,只有其初始色散长度和光纤长度相接近时,才可以实现脉冲自相似的演化;初始输入脉冲不同时均能演化成抛物线形,但是演化的进程不同;大的增益系数可以获得高功率、宽频谱的自相似脉冲;增益色散对自相似放大起滤波作用.研究结果对设计自相似脉冲放大器具有一定的借鉴价值.     

一类自相似tile成为框架集的充分必要条件

本文研究了数字集具有严格乘积形式的自相似tile成为框架集的问题.利用Zak变换,证明了自相似tile是框架集的充要条件是其数字集D={0,1,2…,N-1}.     

加倍变换下某些不可很好逼近集合的自相似结构

本文研究了在加倍变换下的不可很好逼近集合.利用迭代函数系和自相似集的方法,获得了该集合的结构以及维数函数dimΛc连续性的一个简单的证明.     

Grey Self-similar Solitary Waves in Inhomogeneous Nonlinear Media

This paper analyzes spatial grey self-similar solitary waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities. New exact self-similar solutions are found using a novel transformation and their main features are investigated by using direct computer simulations.     

Simple waves for two-dimensional compressible pseudo-steady Euler system

A simple wave is defined as a flow in a region whose image is a curve in the phase space. It is well known that ＂the theory of simple waves is fundamental in building up the solutions of flow problems out of elementary flow patterns＂ see Courant and Friedrichs＇s chassical book ＂Supersonic Flow and Shock Waves＂. This paper mainly concerned with the geometric construction of simple waves for the 2D pseudo-steady compressible Euler system. Based on the geometric interpretation, the expansion or compression simple wave flow construction around a pseudo-stream line with a bend part are constructed. It is a building block that appears in the global solution to four contact discontinuities Riemann problems.     

The Weierstrass–Mandelbrot Process Revisited

We derive a functional central limit theorem for quasi-Gaussian processes. In particular, we prove that the limit of the Mandelbrot–Weierstrass process is a complex fractional Brownian motion.