The Use of Certain Equations of Mathematical Physics in Optimization of a Function on a Set. II

The use of Helmholtz (diffraction and diffusion) and heat conductivity equations for global optimization is described in Part I. Here numerical realization of these ideas is studied and the superlinear rate of convergence is demonstrated. Numerical methods are based on the idea that the solutions of diffraction (diffusion) equations (x,) and heat conductivity equation U(x,t) are convex and concave functions, respectively, in the neighborhood of the point of global minimum in some modified aim function for which the point of global minimum does not change. An idea for the construction of iterative algorithms is developed, in which a programmer, using computation results, actively participates in computations, instructing the computer as to which domains and distribution densities of random vectors are to be used.     

Multicriteria Decision Making Based on a Set of Optimization Methods

The authors provide an approach to multicriteria decision making in the analysis of complex systems. It is based on the results obtained from a number of methods (ranking as well as forming of the kernel), which increases the substantiation of the results due to increasing the completeness of alternatives comparison.     

遗传算法在求解函数优化问题中的应用

函数优化是遗传算法的经典应用领域,也是对遗传算法进行性能评价的常用算例。由此,该文首先对遗传算法作了简介,并讨论了利用遗传算法求解函数优化问题的方法,最后给出了求解Rosenbrock香蕉函数优化实例。     

Certain Problems of Asymptotic Analysis and Extensions. I

Asymptotic attainability interpreted as the approximate realization of desirable states under weak slackening of constraints is studied. Constructs ensuring the realization of asymptotically attainable states in terms of standard constraints on the choice of generalized elements and interpreted as finitely additive measures on a suitable measurable space are designed. Special attention is paid to “Boolean-valued” realizations of generalized problems (extensions) in the class of (0, 1)-measures or ultrafilters of measurable spaces and are interpreted as direct extension constructs (in the sense of transitions from exact solutions to approximate solutions).     

在图像分割中对水平集函数应用的研究

图像分割是从图像处理到图像分析的关键技术,几何活动轮廓模型是为解决图像处理和计算机视觉领域广泛存在的图像分割问题而提出来的。水平集函数是在研究几何活动轮廓模型时将界面或者演化曲线看成高一维空间中某一函数山原型。文章在分析传统水平集函数和距离保持水平集函数优缺点的基础上,引入图像相依的权系数v（I）代替常值权系数,提出了一种自适应距离保持水平集函数。然后通过对水平集函数求其偏微分方程,经过数值实现并求出其解,从而得出图形界面的基本形状和特征。     

Solution of a Matrix Problem on a Mathematical Safe for Locks of the Same Kind. I

A mathematical safe problem is first formulated in a general form. The case of a set of locks that are of the same kind and are arranged in the form of a rectangular matrix is considered. Locks are considered to be of the same kind if their states are specified by numbers from the class of residues to a definite modulus. In the case of a prime modulus, a complete solution is provided. All the results obtained are illustrated by examples.__________Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 155–167, March–April 2005.     

高阶Carotid-Kundalini函数Julia分形集的特性

Julia分形图是研究复动力系统的一种有力工具。文章研究了由高阶Carotid-Kundalini函数f(z)=cos(Nzkarccos(z))+c生成的Julia分形图的性质:当c为实数和N为实数或纯虚数时,分形图具有对称性;当N为实数,c=0时,图形具有2k+1个主瓣,和2k个从主瓣上发出的触角,且触角无界。     

计算机编程中数学算法优化策略研究

数学理论的重点表示式样是数学算法,计算统一化对数学的算法提出了不一样的要求,研究和分析计算中出现的各种问题,最终结果的获取往往采用归纳并总结的方式。在计算机信息技术的广泛普及下,计算机技术影响人们的方方面面,面对这种情况,若要大幅度提高计算机编程软件系统的频率,就必须从根本上解决计算机编程软件的中心问题。笔者从计算机的编程系统角度出发,探索数学算法优化策略,希望为以后相关人员探索数学算法提供借鉴。     

Excel函数在数据有效性设置中的应用

从实例出发,探讨了LEN、COUNTIF、MAX／MIN、AND／OR、COUNTA、OFFSET、INDIRECT等函数在教据有效性设置中的应用。     

遗传算法及其工具箱在函数优化问题中的应用

函数优化是遗传算法的经典应用领域,也是对遗传算法进行性能评价的常用算例。由此,该文首先对遗传算法的基本原理和定义,以及其工具箱作了简介,最后结合实例,简述了遗传算法及其工具箱在函数优化问题中的应用。     

基于MATLAB的自相关函数基音检测的优化

基音是语音信号的一个重要参数,它是指发浊音时声带振动所引起的周期性。基音的提取是语音处理中的重要任务。目前对基音的检测方法有很多,典型的就有自相关法,AMDF(短时平均幅度差)法,倒谱法等等。这里介绍一种自相关和倒谱相结合的算法,较传统的自相关法有一定的改进和优化。     

Attacking a Conjecture in Mathematical Physics by Combining Methods of Computational Analysis and Scientific Computing

We consider a conjecture on the sum of eigenvalues of two integral operators arising in potential and scattering theory for the case that the underlying surface is a triaxial ellipsoid. This concerns computation of Lamé functions which are anyway of great interest in electromagnetics and mechanics. We provide a new effective scheme for the numerical treatment of these special functions. It involves computing the Lamé functions with high accuracy combined with safe error estimates.     

基于FF功能块的过程控制系统优化

本文对FF现场总线标准的功能块及其结构进行了介绍,并从提高控制的分散性和安全性着手,分析了基于功能块的过程控制系统的优化方法.     

基于新集对理论下的粗糙集模型

为了用集对分析方法进一步刻画不完备信息系统，文中把新集对分析理论与粗糙集理论结合在一起，提出了一种新的集对粗糙集模型，从而拓宽了集对分析方法的应用；定义了一种不完备信息系统的上、下近似算子，得到了一些相关的性质。最后通过一个简单的例子说明了上述方法的可行性。     

一种相容粗糙集神经网络在某歼击机障诊断中的应用

本文介绍了粗糙集理论的基本概念,并把粗糙集理论中隶属度函数的概念运用到神经网络的设计中,建立了一种基于相容粗糙集的神经网络故障诊断系统.以某型歼击机故障诊断为例,实验仿真结果表明该方法提高了故障诊断准确率和效率.