基于模糊邻域系的α-粗糙集及其应用

本文引入了基于模糊邻域系的α-粗糙集模型,研究了其基本性质,建立了其约简理论,并借助于α-粗糙集给出了模糊邻域系粗糙集的分解定理,从而建立了其与邻域系粗糙集的联系。     

光测设备数据交汇计算方法研究

通过对靶场试验中传统数据交汇计算方法的分析,针对光学装备数据交汇计算中存在的目标在基线附近精度畸变的问题,提出了一种新的数学模型“最短距离法”．该方法与水平投影法和垂直投影法的数据交汇计算方法相比,具有计算精度高和适用范围广等优点,拓展了采用光学装备进行测量的适用范围,大大提高了测试装备布站的灵活性．     

AN EFFECTIVE CONTINUOUS ALGORITHM FOR APPROXIMATE SOLUTIONS OF LARGE SCALE MAX-CUT PROBLEMS

An effective continuous algorithm is proposed to find approximate solutions of NP-hardmax-cut problems.The algorithm relaxes the max-cut problem into a continuous nonlinearprogramming problem by replacing n discrete constraints in the original problem with onesingle continuous constraint.A feasible direction method is designed to solve the resultingnonlinear programming problem.The method employs only the gradient evaluations ofthe objective function,and no any matrix calculations and no line searches are required.This greatly reduces the calculation cost of the method,and is suitable for the solutionof large size max-cut problems.The convergence properties of the proposed method toKKT points of the nonlinear programming are analyzed.If the solution obtained by theproposed method is a global solution of the nonlinear programming problem,the solutionwill provide an upper bound on the max-cut value.Then an approximate solution to themax-cut problem is generated from the solution of the nonlinear programming and providesa lower bound on the max-cut value.Numerical experiments and comparisons on somemax-cut test problems(small and large size)show that the proposed algorithm is efficientto get the exact solutions for all small test problems and well satisfied solutions for mostof the large size test problems with less calculation costs.     

LF相对乘积空间与近似良紧性

通过引入相对乘积空间证明了近似良紧性关于相对乘积运算而言хоновти乘积定理成立.     

关于变摆长的单摆运动与相关的铅直运动的耦合

研究了一个变摆长单摆运动的例子,在平面极坐标系下给出了描述该运动的二阶微分方程组.采用微分方程高精度数值解法得到了随时间变化的摆角、摆长、摆长变化率以及运动轨迹的数值精确解.在小摆角近似下,采用迭代方法推导出摆角、摆角变化率的一级近似解析表达式和摆长、摆长变化率的二级近似解析表达式.由解析表达式得到的数值结果与数值精确解相比较,二者在前几个摆动周期内相吻合.     

一个单摆周期近似公式

利用“局部常化”方法给出了一个精度较高的单摆周期公式.摆角在0°到90°范围内,其计算结果可以代替查椭圆积分表.     

苯酚与对氯酚竞争吸附数学模型研究

对氯苯酚;苯酚与对氯酚竞争吸附数学模型研究     

包膜型多功能缓/控释肥料的研究现状及进展

缓/控释肥料能够在保证粮食产量的前提下,提高养分利用率,减少肥料养分流失对环境造成的危害。包膜型缓/控释肥料对养分具有更好的控释效果,通过包膜材料的组成设计,最有可能实现养分的释放速率与作物的需肥规律相匹配。本文综述了包膜型缓/控释肥料的国内外研究现状,肥料养分的控释机理和释放性能评价方法,阐述了包膜型缓/控释肥料研究和应用中存在的问题及未来的发展趋势。     

基于快速傅立叶变换的二阶可靠度分析方法

建立了一种基于快速傅立叶变换的二阶可靠度分析方法。状态函数在利用两点近似技术近似为二阶多项式后,进一步变换为统计上独立的中间变量之和。对于中间变量的线性形式表示的状态函数,其概率密度的傅立叶变换是各中间变量的概率密度的傅立叶变换之积。因此,状态函数的概率密度可由其傅立叶变换函数的逆变换求得。文中的傅立叶变换和相应的逆变换均由高效的快速傅立叶变换技术完成。该方法可应用于正态和非正态分布问题。由于在构造二阶近似中采用了近似技术,因而具有很好的计算效率。数值算例验了该方法的应用、效率和精度。     

Response analysis of randomly excited nonlinear systems with symmetric weighting Preisach hysteresis

An approximate method for analyzing the response of nonlinear systems with the Preisach hysteresis of the non-local memory under a stationary Gaussian excitation is presented based on the covariance and switching probability analysis. The covariance matrix equation of the Preisach hysteretic system response is derived. The cross correlation function of the Preisach hysteretic force and response in the covariance equation is evaluated by the switching probability analysis and the Gaussian approximation to the response process. Then an explicit expression of the correlation function is given for the case of symmetric Preisach weighting functions. The numerical result obtained is in good agreement with that from the digital simulation. The project supported by the National Natural Science Foundation of China (19972059) and Zhejiang Provincial Natural Science Foundation (101046)