Commuting and stable feedback design for switched linear systems

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.     

Quantization of Underdamped, Critically Damped, and Overdamped Electric Circuits with a Power Source

We have investigated the quantum mechanical effect of the underdamped, critically damped, and overdamped electric circuits with a power source. The charge of the underdamped circuit oscillates while those of the critically damped and overdamped ones don't. The wave function of the system of overdamped circuit represented parabolic cylinder function while underdamped circuit was represented by well-known Hermite polynomial. The eigenvalues of underdamped circuit is discrete while those of the critically damped and overdamped ones are given as continuously.     

有界变量线性规划的基线算法

本文对有界变量线性规划的算法进行了研究，得到了一种解此问题的新算法。文中根据基线算法的算法原理，通过对BL表的旋转，在各变量满足界约束的条件下，使目标函数值不断增大，直至得到有界硬上界，从而得到问题的最优解。文中给出了有界变量线性规划基线算法的计算步骤，并给出了一个例子。与单纯形法相比，采用基线算法解有界变量线性规划操作更简单。迭代次数少，解题速度更快。     

非参数回归函数估计的渐近正态性

本文研究了独立或相依样本时非参数回归函数的Ｎａｄａｒａｙａ-Ｗａｔｓｏｎ估计，在简洁合理的条件下，证明了估计量的渐近正态性．获得的结论可在时间序列分析中得到应用．     

Banach空间上有界可逆线性变换逆变换的结构

Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.     

用于波分复用系统的多峰干涉滤光片

介绍了用于波分复用系统的多峰干涉滤光片的设计原理,提出了滤光片透射峰位置的确定方法,讨论了影响滤光片半宽度和截止度的因素,给出了滤光片的膜厚容差分析结果,表明透射率监控标准偏差在<0.5%范围内,可以得到波形良好的多峰滤光片,最后给出了实验结果.     

用于机械振动实时监测的光纤光栅有源传感装置

把一对中心反射波长分别为1562.11nm和1562.71nm的光纤光栅粘贴在均质、等厚、等腰三角形悬臂梁上下表面作为环形腔光纤激光器端镜，当机械振动激励自由端时，通过观测激光输出脉冲，地施加于自由端的机械振动的频率进行了实时监测；观察两光栅波长漂移量差值的变化，可在0～6.1mm的范围内判断所测振动的振幅。低于100Hz时，实验结果与实际值基本吻合。     

凹整数规划的分枝定界解法

凹整数规划是一类重要的非线性整数规划问题，也是在经济和管理中有着广泛应用的最优化问题．本文主要研究用分枝定界方法求解凹整数规划问题，这一方法的基本思想是对目标函数进行线性下逼近，然后用乘子搜索法求解连续松弛问题．数值结果表明，用这种分枝定界方法求解凹整数规划是有效的．     

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. In this paper we consider the influence of the refined interfaces on the steady state errors for second‐order three‐point difference approximations of flow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to refinement‐induced errors, it is sufficient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, different to local truncation error, and reflects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth refinement grids and on uniform grids. The conclusion seems to support the numerical findings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181: 280–316) that refinement does not necessarily reduce the numerical error. Copyright © 2005 John Wiley & Sons, Ltd.     

Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations

The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L ₂-estimates) and the least absolute deviation estimates (L ₁-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.