一类二维流场模型的周期解与浑沌解的共存性*

本文研究Kelvin-Stuart猫眼流在周期扰动下的动力学行为,运用Melnikov方法确定出振动型周期轨产生偶数阶次谐分枝、旋转型周期轨产生任意阶次谐分枝的条件,并进一步发现周期解与浑沌解共存的复杂现象.     

Jacobi椭圆函数有理式的Fourier级数*

本文列出了手册[1]及文献[2]中未计算过的九十余个Jacobi椭圆函数sn(u,k),cn(u,k),dn(u,k)的有理函数的Fourier展式.对于用Melnikov方法研究可积系统在周期扰动下的次谐波分枝与浑沌性质,及其他工程物理中的计算问题,这些公式可供查阅应用.     

浑沌简介

浑沌现象涉及到数学、物理学、化学、生物学等许多学科.本文简要介绍浑沌理论的研究现状、判断和研究浑沌现象的方法.     

软弹簧Duffing方程在次谐与超次谐区域中的一些现象

本文用Melnikov-Holmes方法讨论了软弹簧Duffinz方程在小扰动之下进入浑沌的情况,发现在有限浑沌区间中次谐与浑沌共存的复杂现象。     

软弹簧系统在周期小扰动下通向浑沌的道路

本文用Mel'nikov-Holmes方法讨论了软弹簧系统在周期小扰动作用下进入浑沌的途径.发现对于这类系统,由于所加扰动的方式不同,系统会以不同次谐分叉序列通向浑沌,且随着外加频率的变化这种序列会以不同的排列方式把系统导入浑沌.     

浑沌与怪引子的某些泛系研究

文[1]讨论了泛浑沌及泛怪引子与泛系算子ε₇(g)之间的联系。文[2]讨论了不动泛系定理在这些典型的非线性问题研究中的应用。本文首先给出了增关系、极大泛浑沌等几个概念,讨论了它们之间的关系;本文还讨论了g的泛浑沌与它的传递包的泛浑沌的关系以及在一定条件下两个增关系的泛浑沌相同的条件。     

二个自由度 Hamilton 系统的浑沌性质

近年来,关于浑沌现象的实验研究与数值计算的文献大量涌现,解析方法的研究也在开展,文[1—3]对这方面的工作做了很好的总结.Holmes 依照 Melnikov 方法提出的方法是目前处理浑沌现象的极少数解析方法之一.文[5]对单个自由度的 Hamilton 系统在弱周期扰动下的浑沌性质进行了讨论.在[6]中,Holmes 进一步提出处理二个自由度Hamilton 系统方法,并用此法讨论了一个人为的例子.本文处理在非线性振动领域中广     

最简单的典型浑沌运动——兼论浑沌运动的判别之一二

本文讨论了浑沌三种不同的定义;介绍了四种最简单的典型浑沌运动,即符号动力系统,Smale 马蹄,帐篷状映射和具有单峰的一维映射,其中,尤其强调了映射拓扑共轭概念的重要性.     

应用浑沌理论分析电力系统中的浑沌现象

本文应用浑沌理论并根据电力系统模型的特点,首次提出了求取电力系统浑沌模型Melnikov函数的数值近似法,解决了无法求得实际电力系统模型中同宿轨道解析式的困难,并由此分析了单机准无穷大电力系统模型中的浑沌现象,推导出了在该系统中产生浑沌现象的解析条件。     

不动泛系定理的新研究:泛浑沌和泛怪引子

关于浑沌、引子、怪引子等的研究是非线性分析中的重要课题.文[1]在泛系方法论的框架下,讨论了这些问题,提出了泛浑沌、泛引子和泛怪引子的概念,这些概念去掉了诸如连续性、紧性等条件,突出反映了一集合上的二元关系的性质.已有的研究结果指出,泛浑沌、泛引子和泛怪引子分别对应于某个特定的泛系算子作用下的不动子集.本文继续文[1、2]的工作,探讨了存在这类泛系不动子集的条件以及它们的构造和相互间的联系.     

Some aspects of polaritons and plasmons in materials

We have studied the interaction of optical phonons with photons. So, we have calculated the coupled modes of photons and transverse optical phonons and likewise, the dielectric function. We have found an alternative relation of the splitting between the frequencies of the longitudinal optical (LO) and transverse optical (TO) phonons in crystals. Likewise, we have studied the plasmon resonance frequency. We have determined the phonon–photon and the plasmon–photon coupling constant in ionic crystals and in metals, respectively, which is very close to the elastic force constant, and we have evaluated the bulk modulus. Further we have applied these results to tetrahedrally bonded III–V semiconductors.     

Multi-level scheduling decisions in a class of FMS using simulation based metamodels

This paper pertains to a detailed simulation study conducted on a typical Flexible Manufacturing System (FMS). Initially, the configurations of the FMS under study have been established. Two types of FMSs have been evolved: one is failure free and the other is failure prone. For each of these cases, simulation models have been developed using SLAMSYSTEM. Orders arriving randomly at the FMS are subjected to three levels of scheduling decisions namely, launching of parts into the system, routing of parts through machines and sequencing of parts on AGVs at a central buffer. The simulation results have been used to develop metamodels for the two types of FMSs. These metamodels have been subjected to statistical analysis to ascertain their adequacy to represent the simulation models. These metamodels have been found to be useful for simulating the FMSs under study so as to evaluate various multi-level scheduling decisions in the FMS.     

Dissipative Nonlinear Evolution Equations and Chaos

In this article we have studied the nonlinear interaction between ellipticity and dissipation in a set of model equations (1.1) and established the relation between this interaction and chaos. In addition to theoretical investigations, extensive numerical simulations with these equations have been made, and different routes to chaos have been found. The numerical studies have revealed the chaotic nature of the solutions.     

A computational study on different penalty approaches for solving constrained global optimization problems with the electromagnetism-like method

In this article, the application of the electromagnetism-like method (EM) for solving constrained optimization problems is investigated. A number of penalty functions have been tested with EM in this investigation, and their merits and demerits have been discussed. We have also provided motivations for such an investigation. Finally, we have compared EM with two recent global optimization algorithms from the literature. We have shown that EM is a suitable alternative to these methods and that it has a role to play in solving constrained global optimization problems.     

On the foundations of game theory: The case of non-Archimedean utilities

Contrary to what appears to have become an accepted part of the folklore of game theory, a finite two-person zero-sum game with non-Archimedean utilities may have no equilibrium-point solution, and either one or both players may have no “minimax” strategy. Even when both players have “minimax” strategies, such a game may lack an equilibrium point.     

一类由一维概率密度函数构造多维概率密度函数的方法

将文献[1]给出的由一维连续型随机变量的概率密度函数构造二维连续型随机变量的概率密度函数的方法,推广为由一维连续型随机变量的概率密度函数构造三维连续型随机变量的概率密度函数的情况,并作出了证明和举例说明.说明利用本文的方法构造多维概率密度函数,其方法简单易行.     

Home Care optimization: impact of pattern generation policies on scheduling and routing decisions

In Home Care optimization, operators have to be assigned to patients by taking into account compatibility skill constraints, and patient visits have to be scheduled in a given planning horizon. Moreover, operator tours have to be determined. Integer Linear Programming models have been proposed which use the concept of patterns, i.e. a priori scheduling profiles, to combine the diverse decision levels. Computational results on real instances show that pattern generation policies are crucial to address scheduling and routing in large Home Care instances.     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

Preservation of the existence of fixed and coincidence points under homotopy of mappings of ordered sets

In problems of topology and analysis, well-known theorem on the preservation by any continuous homotopy of the property of a mapping to have a fixed point and the property of a pair of mappings to have a coincidence point are extensively applied. Thus, for contraction mappings and some of their generalizations, Frigon’s results on the preservation of the property to have a fixed point by a homotopy of a special type are known. This paper presents theorems on the preservation by order homotopy of the property of a pair of mappings to have a coincidence point. As a corollary, conditions under which such a homotopy preserves the property of a mapping to have a fixed point are obtained.     

Evaluation of the multiobjective ant colony algorithm performances on biobjective quadratic assignment problems

The difficulty of resolving the multiobjective combinatorial optimization problems with traditional methods has directed researchers to investigate new approaches which perform better. In recent years some algorithms based on ant colony optimization (ACO) metaheuristic have been suggested to solve these multiobjective problems. In this study these algorithms have been reported and programmed both to solve the biobjective quadratic assignment problem (BiQAP) instances and to evaluate the performances of these algorithms. The robust parameter sets for each 12 multiobjective ant colony optimization (MOACO) algorithms have been calculated and BiQAP instances in the literature have been solved within these parameter sets. The performances of the algorithms have been evaluated by comparing the Pareto fronts obtained from these algorithms. In the evaluation step, a multi significance test is used in a non hierarchical structure, and a performance metric (P metric) essential for this test is introduced. Through this study, decision makers will be able to put in the biobjective algorithms in an order according to the priority values calculated from the algorithms’ Pareto fronts. Moreover, this is the first time that MOACO algorithms have been compared by solving BiQAPs.