弹性结构振动系统的分层近似建模

已知弹性结构线性振动系统的具有不同置信度的分层次固有频率和振型,以及用合理的离散化方法得到了系统的刚度矩阵K和质量矩阵M,并假设了M、K中之一较可靠,本文给出在这些条件下,考虑到不同层次的置信度的近似建模方法,对建模方法以及所得结果的唯一性也给出了严格的数学证明;最后的数字例子不仅证实了这一方法的可行性,并且表明这一方法优于所列文献[4]给出的方法。     

基于投影近似子空间跟踪技术的自聚焦算法

基于特征向量法的自聚焦算法具有比相位梯度自聚焦(Phase Gradient Autofocus,简称PGA)算法更好的算法性能,但该算法必须对协方差矩阵进行特征分解,所以运算量大.利用投影近似子空间跟踪(Projection Approxima-tion Subspace Tracking,简称PAST)技术的自聚焦算法可以解决上述问题.通过实际数据处理结果对比,证明基于PAST技术的自聚焦算法是一种可满足实时处理要求的有效自聚焦方法.     

改进的基于二维主分量分析的掌纹识别

主分量分析(PCA)是一种在众多生物特征识别中获得成功应用的特征提取技术,是一种基于二阶统计的在最小均方误差意义上的最优维数据压缩技术,它所提取的各特征分量之间是互不相关的。传统的PCA变换是对图像向量的分析,但向量维数一般都很高。二维主分量分析方法是最近兴起的针对图像矩阵的主分量分析方法,与一维主分量分析相比能更精确的计算原始数据的协方差矩阵。将其应用于掌纹识别,并在主分量的选取上加以改进,选取了更适合于分类的主分量。实验结果表明,该方法不仅有更高的识别率,而且维数更低。     

一维Anderson无序模型电子局域态

本文应用一种新方法,得到了包括次近邻相互作用,且无序点阵从五百到一万的一维安德逊无序模型电子本征态。结果表明此模型的本征态随着无序点阵的增加均从扩展态变为局域态,且变化的快慢受系统无序度的影响。     

ON THE APPLICATION OF GENERALIZED INVERSE FOR COMPUTING EIGEN-SENSITIVITY

In this paper the mathematical definition of the minimum energygeneralized inverse is given and its application for computing eigen-sensitivity isdemonstrated.By comparing it with the others,this paper clarifies the merits of thepresent algorithm.Furthermore,an erroneous relation which is still widely used isrectified.     

Sharp upper and lower bounds for the Laplacian spectral radius and the spectral radius of graphs

In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively.     

On the Representation of Symmetric Isotropic 4-Tensors

This note provides short proof of the representation of a symmetric isotropic 4-tensor in an n-dimensional real Euclidean space. This revised version was published online in August 2006 with corrections to the Cover Date.     

矩阵的特征值和特征向量同时求解的一种方法

本文给出了通过λ－矩阵的初等变换，同时求得特征值和特征向量的一种方法。     

On Some Applications of the Ordinary and Extended Duhamel Products

Let C _A ⁽ⁿ⁾ (D) denote the algebra of all n-times continuously differentiable functions on holomorphic on the unit disk D = {z C : |z| < 1}. We prove that C _A ⁽ⁿ⁾ (D) is a Banach algebra with multiplication the Duhamel product and describe its maximal ideal space. Using the Duhamel product we prove that the extended spectrum of the integration operator , on C _A ⁽ⁿ⁾ (D) is C\{0}. We also use the Duhamel product in calculating the spectral multiplicity of a direct sum of the form A. We also consider the extension of the Duhamel product and describe all invariant subspaces of some weighted shift operators.Original Russian Text Copyright © 2005 Karaev M. T.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 553–566, May–June, 2005.     

Galerkin eigenvector approximations

How close are Galerkin eigenvectors to the best approximation available out of the trial subspace? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace--and this occurs more rapidly than the underlying rate of convergence of the approximate eigenvectors. Both orthogonal-Galerkin and Petrov-Galerkin methods are considered here with a special emphasis on nonselfadjoint problems, thus extending earlier studies by Chatelin, Babuska and Osborn, and Knyazev. Consequences for the numerical treatment of elliptic PDEs discretized either with finite element methods or with spectral methods are discussed. New lower bounds to the of a pair of operators are developed as well.