Heisenberg群上分数阶Ginzburg-Landau方程解的有界性

本文证明Heisenberg群上分数阶的Keller-Osserman定理和Kato不等式,给出Heisenberg群上分数阶Ginzburg-Landau方程解的有界性.这个结果把欧氏空间上分数阶Ginzburg-Landau方程的结果推广到了Heisenberg群上.     

Ginzburg-Landau方程动力性态的Fourier谱逼近

0　引言和符号立方Schrodinger方程或更一般的形式Ginzburg-Landau方程出现在许多物理和化学问题中.例如在非线性光学的细束流中有方程2ikux+2⊥u+n2n0k2|u|2u=0对于二维流,有方程n2n0k2|u|2u=-2kiut-uxx-uyy还有等离子体的Langmuir波;一维单色波的自调制;二维定态平面波的自聚集;在非相对论下超导电子对在电磁场中运动等均可用非线性Schrodinger方程和Ginzburg-Landau方程来描述[1-4].另外,反应扩散方程描述的化学反应方程的研究中也出现Ginzburg-Landau方程,如相对于稳态浓度c*的扰动浓度c-c*就满足Ginzburg-Landau方程[5,6].由…     

应用多项式完全判别系统方法求解时空分数阶复Ginzburg-Landau方程

研究了时空分数阶复Ginzburg-Landau方程.首先通过分数阶复变换将时空分数阶复Ginzburg-Landau方程转化为一个常微分方程.然后将常微分方程化为初等积分形式.最后用多项式完全判别系统法求得一系列精确解,其中包含有孤立波解、有理函数解、三角函数周期解、Jacobi椭圆函数双周期解.     

一维广义Ginzburg-Landau方程的有限维惯性形式

得到了一维广义Ginzburg-Landau方程的有限维惯性形式的存在性.     

3维Ginzburg-Landau方程涡旋集的结构

在假定外加磁场|hex|=o(|lnε|)以及涡旋能量以|lnε|阶爆破的前提下,借助几何测度论工具,分析了三维Ginzburg-Landau超导方程涡旋集的结构.粗略地说,它是由线段构成的一维可求长集合.     

2+1维Ginzburg-Landau方程的精确波解

分析研究了一个具有三次增益效应和五次耗散项的2+1维Ginzburg-Landau方程.利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解.     

拟线性复Ginzburg-Landau方程的能控性

本文研究一类拟线性复Ginzburg-Landau方程的能控性问题.首先,建立一个关于(具有C~1-主部系数的)线性复Ginzburg-Landau方程的整体Carleman估计.然后,基于一个(具有L~2-观测的)能观性不等式,并通过提高线性化问题控制函数的正则性,结合不动点技术,证明所考虑的拟线性方程的局部零能控性和局部近似能控性.     

Ginzburg-Landau方程的非齐次初边值问题

研究具非线性边界条件的一类广义Ginzburg-Landau方程解的整体存在性．推导了Ginzburg-Landau方程的非齐次初边值问题光滑解的几个积分恒等式,由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计;通过逼近技巧、先验估计和取极限方法证明了Ginzburg-Landau方程的非齐次初边值问题整体弱解的存在性．     

R3中各向异性Landau-Lifshitz方程的部分正则解

证明了当三维空间中各向异性Landau-Lifshitz方程的弱解满足稳定性条件时,其解具有部分正则性,并且对易面类型的方程,利用Ginzburg-Landau逼近构造了一个整体的部分正则解.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

负相依随机变量之和的概率大偏差不等式

本文建立了负相依随机变量序列的概率大偏差不等式，并推广了以往文献的结果．     

Using Repertory Grids for Problem Construction

In the last couple of years, O.R. workers have expressed interest in the use of repertory grids as a part of their armoury for tackling messy problems in organizations. This paper is designed to describe some of our experiences of using grids to aid the process of problem construction. It will also express some of our views of the theoretical and technical aspects of their use for working on problems.The principles behind the use of grids invite the design of other methods for managing qualitative problem data. The paper will briefly introduce some we have found helpful.     

Using multi-objective evolutionary algorithms for single-objective optimization

In recent decades, several multi-objective evolutionary algorithms have been successfully applied to a wide variety of multi-objective optimization problems. Along the way, several new concepts, paradigms and methods have emerged. Additionally, some authors have claimed that the application of multi-objective approaches might be useful even in single-objective optimization. Thus, several guidelines for solving single-objective optimization problems using multi-objective methods have been proposed. This paper offers a survey of the main methods that allow the use of multi-objective schemes for single-objective optimization. In addition, several open topics and some possible paths of future work in this area are identified.     

Bounds for the quasi-stationary distribution of some specialized Markov chains

The quasi-stationary distributions of Markov chains have been investigated by many papers and are known to have considerable practical importance in, e.g., biological, chemical and applied probability models. However, computation of the quasi-stationary distributions is often nontrivial, which has limited its use in practice despite the usefulness of its own, except for some simple cases. This paper develops some bounds, which are relatively easy to calculate, for the quasi-stationary distribution of some specialized Markov chains.     

A distribution-free test for symmetry in hierarchical data

Distribution-free tests for permutational symmetry of correlated variables have been offered recently in the literature. However, situations arise when all the planned measurements are available only on some subjects, while others drop out at various stages of the experiment. The present paper offers a distribution-free statistic for testing permutational symmetry of correlated variables in such hierarchical data, and develops a large-sample chi-square approximation. Explicit expressions for the test statistic have been provided for some special cases.     

非奇H-矩阵的实用判别准则

非奇H-矩阵在科学和工程实际中有着广泛地应用,但在实际中判定一个矩阵是否为非奇H-矩阵是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了一些比较实用的新条件,改进和推广了现有的一些结论,并给出相应的一些数值算例来说明结果的有效性.     

时滞矩阵微分方程的等度稳定性

在矩阵值范数定义的广义赋范空间上利用矩阵Liapunov泛函研究了时滞矩阵微分方程的等度稳定性,得出了若干新结果.     

二阶泛函微分方程的振动性质

在本文中，我们研究了一类较广泛的二阶非线性泛函微分方程的振动性质。文中指出，在一定条件下，方程的非振动解仅有两类，而且给出了每一类非振动解存在的必要条件，同时也建立了方程振动的若干充分判据。     

Combinatorial devices for sequential analysis

Summary For Brownian motion, escape probabilities over curved boundaries have been studied in some detail. Since sequential analysis is not concerned with really large samples, the approximation by the Brownian motion is questionable; neither the central limit theorem nor the renewal theorem regulating the overshoot may be appropriate tools. The present paper shows that combinatorial results developed in fluctuation theory have some bearing on the calculation of escape probabilities. The main result is a kind of tangential approximation for random walks crossing a curved boundary.     

关于一个级数的计算公式

It is one of the most interesting problems in number theory to compute some especial series by using Zeta and Gamma functions,and results have been obtained for some especial series.In this paper,we give an important formula which is proved also by using Zeta and Gamma functions.