具有非线性扰动的线性多时变时滞系统的有记忆状态反馈控制

本文探讨一类非线性扰动满足范数有界的线性多时变时滞系统的有记忆状态反馈控制,通过构造恰当的Lyapunov泛涵,利用Jensen不等式来处理泛涵导数中的交叉项,应用线性矩阵不等式技术和Schur补引理,我们得到了系统镇定的时滞相关的充分条件,并给出了有记忆状态反馈控制器的设计方法.最后,数值例子验证了文中所得的结论的保守性更低及求解方法的有效性.     

非线性不等式组的信赖域算法

对于非线性不等式组的求解,采用构造辅助函数将非线性不等式组转化成为一个非线性方程组。文中采用光滑信赖域方法对非线性方程组进行逐次逼近从而求得问题的解。算法的全局收敛性和局部超线性收敛性得到了保证,数值试验表明算法对于小规模问题是切实可行的。     

带迭代积分的滞后型非线性积分不等式及其应用

Growall-Bellman型积分不等式在微分方程解的稳定性,有界性,渐近性与解的其它定性与定量性质的分析方面具有十分重要的作用.本文研究了几类带有迭代积分的滞后型非线性积分不等式.利用分析的方法和微分不等式的一般理论,给出未知函数的上界估计.最后将本文结果应用到一类非线性微分一积分方程中,得到所有解的一个上界估计,从而为微分方程解的估计、动力系统及控制工程理论的研究提供了理论依据.     

含有n个无关变元的Mate-Nevai型非线性积分不等式

讨论了Mate-Nevai型积分不等式,得到几个含有n个无关变元的Mate-Nevai型非线性积分不等式。利用所得结论讨论某些非线性偏微分方程解的有界性。     

大长度数的准确表示及其运算算法研究

在现有计算机的数表示法中,数的精度和长度都有限制,本文提出一种大长度数的表示法,并给出了使用这种表示法后的二进制数和十进制数之间的转换算法,整数、小数以及带小数的四种运算(加减乘除)的算法.     

Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers

 It is shown that a q-periodic sequence over the finite field F _q passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity is large. The consequences of this result for nonlinear and inversive pseudorandom number generators are worked out. Received: October 2, 2001 Keywords: Pseudorandom number generator, Nonlinear method, Inversive method, Linear complexity, Marsaglia's lattice test.     

一些相依序列的强大数律和收敛速度

本文研究了正相协序列、负相协序列、强正相依序列以及鞅差序列的强极限性质.利用负相协序列和弱鞅序列的极大值矩不等式以及随机变量的截尾方法,得到了上述相依序列的强大数定律、强收敛速度以及相应的随机变量序列上确界的可积性.本文不仅将独立情形下的强大数定律推广到以上相依序列,并且还给出了其收敛速度.     

解带线性或非线性约束最优化问题的混合三项记忆梯度投影算法

利用Rosen投影矩阵,结合Solodov投影技巧建立求解带线性或非线性不等式约束优化问题的混合三项记忆梯度Rosen投影算法,并证明了算法的收敛性。数值例子表明该算法是有效的。     

混合序列强大数定律的收敛速度

本文在对混合速度没有任何限制的条件下讨论了ρ－ｍｉｘｉｎｇ序列大数定律的收敛速度问题．     

区间数排序

从数学意义和实际应用的角度出发,提出了区间数序关系的公理化定义;具体给出了区间数的θ序和L-θ序两类序关系;讨论了它们秘具有的一些良好性质;并且从多个角度论述了θ=0.5时两类序关系的本质及合理性。     

Efficient Numerical Scheme for Solving Large System of Nonlinear Equations

A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this paper. Convergence analysis demonstrates that the local order of convergence of the numerical method is five. The computer algebra system CAS-Maple, Mathematica, or MATLAB was the primary tool for dealing with difficult problems since it allows for the handling and manipulation of complex mathematical equations and other mathematical objects. Several numerical examples are provided to demonstrate the properties of the proposed rapidly convergent algorithms. A dynamic evaluation of the presented methods is also presented utilizing basins of attraction to analyze their convergence behavior. Aside from visualizing iterative processes, this methodology provides useful information on iterations, such as the number of diverging-converging points and the average number of iterations as a function of initial points. Solving numerous highly nonlinear boundary value problems and large nonlinear systems of equations of higher dimensions demonstrate the performance, efficiency, precision, and applicability of a newly presented technique.     

On Numerical Simulation of Cyclic Viscoplastic and Viscoelastic Constitutive Laws with the Large Time Increment Method

Computations on structures having a strongly non-linear time-dependentbehavior, even nowadays, require considerable computational times. Thereduction of the computational costs is crucial for the use ofsimulations in industrial areas. The large time increment method, whichbreaks completely with traditional methods, is developed for thispurpose. This method is based on a two-stage iterative procedure, whichtakes into account the whole load in one increment time, irrespective ofthe loading time.The aim of this paper is to show and understand how this algorithmworks, and to assess its performance, for several classes ofconstitutive laws. This algorithm is tested on one-dimensional periodicloading problems. The theory is developed for a simple viscoelasticmodel and for one viscoplastic model using material state variables, andconstructed in the framework of thermodynamics of irreversibleprocesses.The numerical experiments allowed us to confirm the theoreticalbasis of this algorithm. The results are remarkable since the computingtime is reduced by a factor between 3 and 15 according to the loading,in comparison to other classical methods. Furthermore, the algorithmcorrects rapidly perturbations due to a bad initialisation.On the one hand we show that the Large Time Increment Method can beadapted to a wide range of models. On the other hand the efficiency hasbeen measured in several loading cases and for different constitutivelaws. This opens new research perspectives such as the adaptation ofthis algorithm to a finite elements code, in order to achievethree-dimensional computations.     

直觉模糊数的表示和结构刻划

本文给出了直觉模糊数的表示定理:包括区间表示、函数表示、嵌入定理,并将直觉模糊数空间嵌入到一类特殊的二维模糊数空间—方模糊数空间,给出了直觉模糊数的结构定理;最后,利用方模糊数与一般二维模糊数的逼近定理,给出了二维模糊数的直觉模糊数逼近。