具有摄动的两类马氏决策规则

在状态空间和行动集均有限的条件下,[1-5]讨论了时间离散的,平稳的马氏决策规划的摄动模型,其中,[1,3,4]讨论了单摄动模型,[5]讨论了具有加权准则的摄动模型,[6,7]讨论了时间离散的,平稳的马氏报酬过程的摄动模型,但[6,7]仅考虑了摄动对最优值的影响,而没有考虑摄动对最优策略的影响,本文将讨论具有摄动的非平衡平均马氏均策规划和连续时间折扣马氏决策规划。     

具有强非线性状态方程的机械零部件可靠性灵敏度分析方法

基于可靠性灵敏度设计的随机摄动技术,结合可靠性分析的矩方法、矩阵微分理论和Kronecker代数的相关理论,讨论了实际中存在着高度非线性极限状态方程结构的可靠性灵敏度问题．在已知随机变量前4阶矩的前提下,对基于摄动法的可靠性灵敏度计算方法进行了修正,提出了具有高度非线性结构的可靠性灵敏度计算方法．并结合实例证明了采用此方法大大提高了可靠性灵敏度的计算精度,并为工程实际提供了更加可信的理论依据．     

线性弹性方程组的边界层估计

一、奇摄动问题 众所周知,弹性理论中的应力函数是满足双调和方程的。我们考虑线性弹性方程组的奇摄动问题     

摄动级数的奇性判别法

本文主要研究摄动理论中Van Dyke方法的数学方面,讨论了摄动级数的奇性判别法。文中导出了具有复共轭奇点情况下的符号判别法和Domb-Syke图示法,推广了Van Dyke关于实奇点的结论,考虑了低阶奇点对判别法则的影响;最后,作者还提出了由Euler变换获得的新摄动级数,来确定原摄动级数奇点位置的方法。     

正交条件与Melnikov函数

本文讨论正交条件与Melnikov函数之间的关系。从摄动理论的观点看来,Melnikov函数实质上来自保证摄动展开为一致有效所应满足的正交条件。     

屈曲杆大挠度弹性曲线的摄动解及其不完全分岔问题的奇异摄动解法

本文用摄动法求解了屈曲杆大挠度情况下的弹性曲线,并考虑支座处的缺陷对分岔(失稳)问题的影响,用奇异摄动的不完全分岔理论进行了计算,给出了分岔图解,并对其物理意义进行了讨论.     

一类奇摄动边值问题的激波解

考虑了一个二阶奇摄动非线性边值问题,利用匹配展开法研究了该问题的激波解,并证明了问题的激波解的一致有效性.     

一类二阶奇摄动边值问题的激波解

考虑了一个二阶奇摄动非线性边值问题,利用匹配展开法研究了该问题的激波解,讨论了该问题的激波位置与边界条件的关系.     

基于摄动法的压敏储层非线性渗流问题研究

研究地层压力变化对渗流特征的影响,对低渗透储层、碳酸盐岩储层,或其他致密性储层的油气开采和储层改造都具有重要意义.在考虑渗流压力梯度平方项存在的前提下,运用摄动法求解的相关理论,将渗透率随压力的变化融入到渗流问题的求解过程中,有效地求解了该类压敏型储层的非线性渗流问题.结果表明,在实际应用中,尤其是在储层压敏性较弱的情况下,可考虑直接用0阶摄动解即可满足较好的计算精度;储层的压敏性越强,越适宜通过用摄动解的修正,来达到精确求解的目的.     

一类四阶非线性方程奇摄动边值问题解的估计

本文考虑了一类四阶非线性方程边值问题的奇摄动，在适当的条件下，构造了其渐近展开式，证明了解的存在性及高阶一致有效渐近估计。     

扰动色谱方程黎曼解的极限-delta激波的行成和转换

本文主要讨论扰动色谱方程delta激波解的行成和转换,并讨论上述方程的黎曼问题.当扰动参数趋于零时,通过研究黎曼解的极限,我们可以观察到如下两个重要现象:激波和接触间断重合行成delta激波,一类激波(一个变量含有delta函数).     

非线性方程分枝解理论在线性闭环系统极点摄动量估计中的应用

本文利用非线性方程小分枝解的理论,研究多变量定常线性控制系统的状态矩阵与控制矩阵受到摄动时,闭环系统的极点所受到的摄动量的估计问题.     

扰动反应扩散型方程的近似对称约化

利用近似的广义条件对称方法研究扰动的反应扩散型方程的近似对称约化问题,得到所研究方程完全的分类并借助于近似广义条件对称将扰动的偏微分方程约化为扰动的常微分方程组.     

Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

Email: valery{at}techunix.technion.ac.il Received on January 31, 2006; Accepted on October 5, 2006 An infinite horizon linear-quadratic optimal control problemfor a singularly perturbed system with multiple point-wise anddistributed small delays in the state variable is considered.The set of Riccati-type equations, associated with this problemby the control optimality conditions, is studied. Since thesystem in the control problem is singularly perturbed, the equationsof this set are also perturbed by a small parameter of the singularperturbations. The zero-order asymptotic solution to this setof equations is constructed and justified. Based on this asymptoticsolution, parameter-free sufficient conditions for the existenceand uniqueness of solution to the original optimal control problemare established.     

On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell

We state the initial equations and the boundary conditions for determining the parameters that describe a quasistatic electromagnetic field perturbed by the action of external electric currents in a this nonferromagnetic shell. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Analysis of Local Dynamics of Difference and Close to Them Differential-Difference Equations

We study the local dynamics of one class of nonlinear difference equations which is important for applications. Using perturbation theory methods, we construct sets of singularly perturbed differential-difference equations that are close (in a sense) to initial difference equations. For the problem on the stability of the zero equilibrium state and for certain infinite-dimensional critical cases, we propose a method that allows us to construct analogs of normal forms. We mean special nonlinear boundary value problems without small parameters, whose nonlocal dynamics describes the structure of solutions to initial equations in a small neighborhood of the equilibrium state. We show that dynamic properties of difference and close to them differential-difference equations considerably differ.     

Approximate conservation laws of nonlinear perturbed heat and wave equations

We construct approximate conservation laws for non-variational nonlinear perturbed (1+1) heat and wave equations by utilizing the partial Lagrangian approach. These perturbed nonlinear heat and wave equations arise in a number of important applications which are reviewed. Approximate symmetries of these have been obtained in the literature. Approximate partial Noether operators associated with a partial Lagrangian of the underlying perturbed heat and wave equations are derived herein. These approximate partial Noether operators are then used via the approximate version of the partial Noether theorem in the construction of approximate conservation laws of the underlying perturbed heat and wave equations.     

The Propagation of Shock Waves in Incompressible Fluids: The Case of Freshwater

In this paper we investigate the basic features of shock waves propagation in freshwater in the framework of a hyperbolic model consisting of the one-dimensional Euler equations closed by means of polynomial equations of state extracted from experimental tabulated data available in the literature (Sun et al. in Deep-Sea Res. I 55:1304–1310, 2008). The Rankine–Hugoniot equations are numerically solved in order to determine the Hugoniot locus representing the set of perturbed states that can be connected through a k-shock to an unperturbed state. The results are found to be consistent with those previously obtained in the framework of the EQTI model by means of a modified Boussinesq equation of state.     

Sound field of a point monochromatic source in a stratified ocean perturbed by large-scale flow

Starting from the complete system of hydrodynamic equations for the field of a point sound source in a plane-stratified ocean perturbed by a flow, a representation is obtained in the form of a sum of normal waves. Comparison with similar results for the quasipotential equations makes it possible to estimate the effect of replacing the generalized equation of state by an approximate state equation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 49–60, 1986.The author is grateful to V. S. Buldyrev for a useful discussion of this study.     

Perturbation of Volterra Difference Equations

A fixed point theorem is used to investigate nonlinear Volterra difference equations that are perturbed versions of linear equations. Sufficient conditions are established to ensure that the stability properties of linear Volterra difference equations are preserved under perturbation. The existence of asymptotically periodic solutions of perturbed Volterra difference equations is also proved.