Asymptotic analysis of nonselfadjoint operators generated by coupled Euler‐Bernoulli and Timoshenko beam model

In the current paper, we present a series of results on the asymptotic and spectral analysis of coupled Euler‐Bernoulli and Timoshenko beam model. The model is well‐known in the different branches of the engineering sciences, such as in mechanical and civil engineering (in modelling of responses of the suspended bridges to a strong wind), in aeronautical engineering (in predicting and suppressing flutter in aircraft wings, tails, and control surfaces), in engineering and practical aspects of the computer science (in suppressing bending‐torsional flutter of a new generation of hard disk drives, which is expected to pack high track densities (20,000+TPI) and rotate at very high speeds (25,000+RPM)), in medical science (in bio mechanical modelling of bloodcarrying vessels in the body, which are elastic and collapsible). The aforementioned mathematical model is governed by a system of two coupled differential equations and a two parameter family of boundary conditions representing the action of the self‐straining actuators. This linear hyperbolic system is equivalent to a single operator evolution equation in the energy space. That equation defines a semigroup of bounded operators and a dynamics generator of the semigroup is our main object of interest. We formulate and proof the following results: (a) the dynamics generator is a nonselfadjoint operator with compact resolvent from the class ??p with p > 1; (b) precise spectral asymptotics for the two‐branch discrete spectrum; (c) a nonselfadjoint operator, which is the inverse of the dynamics generator, is a finite‐rank perturbation of a selfadjoint operator. The latter fact is crucial for the proof that the root vectors of the dynamics generator form a complete and minimal set. In our forthcoming paper, we will use the spectral results to prove that the dynamics generator is Riesz spectral, which will allow us to solve several boundary and distributed controllability problems via the spectral decomposition method. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Skew-symmetric methods for nonsymmetric linear systems with multiple right-hand sides

By transforming nonsymmetric linear systems to the extended skew-symmetric ones, we present the skew-symmetric methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on the block and global Arnoldi algorithm which is formed by implementing orthogonal projections of the initial matrix residual onto a matrix Krylov subspace. The algorithms avoid the tediously long Arnoldi process and highly reduce expensive storage. Numerical experiments show that these algorithms are effective and give better practical performances than global GMRES for solving nonsymmetric linear systems with multiple right-hand sides.     

平均值不等式的矩阵形式

得到了几何—算术平均不等式和几何—调和平均不等式的一些矩阵形式.     

k-控制阵

给出k-控制阵的定义,讨论k-控制阵与k-圈控制阵的关系,指出k-控制阵的周期是k的一个因子,指数不大于(n-1)k m.     

一种调整模糊判断矩阵一致性的方法

依据人类判断思维的特性定义了一个模糊判断矩阵顺序一致性的标准,根据模糊一致矩阵的性质研究判断矩阵的导出矩阵,以导出矩阵为依据将初始判断矩阵进行调整,使其最终达到顺序一致性。最后给出一个算例。     

An iterative method for Bayesian Gauss–Markov image restoration

The purpose of this paper is to introduce a new method for the restoration of images that have been degraded by a blur and an additive white Gaussian noise. The model adopted here is assumed to be Bayesian Gauss–Markov linear model. By exploiting the structure of the blurring matrix and by using Kronecker product approximations, the image restoration problem is formulated as matrix equations which will be solved iteratively by projection methods onto Krylov subspaces. We give some theoretical and experimental results with applications to image restoration.     

A numerical technique for structural damage detection

A computationally attractive method is proposed in this study to provide an insight to the location and extent of structural damage. The proposed method makes use of the matrix disassembly technique and approaches the damage location and extent problem in a decoupled fashion. First, a scheme is developed to determine the damage location by calculating a damage localization vector, which is derived from the modal residual force criteria. With location determined, the corresponding damage extent can be easily obtained only by the processes of division. The algorithm is applied to a numerical example and its efficiency is demonstrated through damage simulations.     

共同均值矩阵的线性估计的泛容许性

本文给出了多元线性模型中共同均值矩阵可估函数的线性估计的泛容许性定义,并得到了共同均值矩阵可估函数的线性估计分别在齐次和非齐次线性估计类中的泛容许性特征。     

The Potential Theory of Several Intervals and Its Applications

Motivated both by digital filter design and polynomial-based matrix iteration methods, we study Green's function for the complement of a union of disjoint closed intervals. The key tool is the Schwarz—Christoffel map. Asymptotic analysis produces simple and useful leading terms for Green's function and the associated equilibrium distribution. Our results are applied to optimal lowpass filters and matrix iterations. Accepted 12 February 2001. Online publication 18 May 2001.