Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Generalized Drazin spectrum of operator matrices

Let A ∈ B（X） and B ∈ B（Y）, Me be an operator on Banach space X ＋ Y given by Mc =（A C 0 B）A generalized Drazin spectrum defined by σgD（T） = {λ∈C ： T-λI is not generalized Drazin invertible} is considered in this paper. It is shown that

Block basis property of a class of 2×2 operator matrices and its application to elasticity

A necessary and sufficient condition is obtained for the generalized eigenfunction systems of 2 ×2 operator matrices to be a block Schauder basis of some Hilbert space, which offers a mathematical foundation of solving symplectic elasticity problems by using the method of separation of variables. Moreover, the theoretical result is applied to two plane elasticity problems via the separable Hamiltonian systems.

SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS OF THE FIRST KIND AND THEIR APPLICATIONS

In this paper, we discuss some singulal integral operators, singular quadrature operators and discrethation matrices associated with singular integral equations of the first kind, and obtain some useful Properties for them. Using these operators we give a unified framework for various collocation methods of numerical solutions of singular integral equations of the fine kind, which appears very simple.

Hardy Spaces H_L^p(R^n) Associated with Higher-Order Schrdinger Type Operators

Let L = L0 ＋ V be the higher order Schrodiger type operator where L0 is a homogeneous elliptic operator of order 2m in divergence form with bounded coeffi- cients and V is a real measurable function as multiplication operator （e.g., including （-△）m＋v （m∈N） as special examples）. In this paper, assume that V satisfies a strongly subcritical form condition associated with L0, the authors attempt to establish a the- HL （R） （0 〈 p ≤ 1） associated with the higher order Schrodinger ory of Hardy space P n type operator L. Specifically, we first define the molecular Hardy space Hp （JRn） by the so-called （p, q,ε, M） molecule associated to L and then establish its characterizations by the area integral defined by the heat semigroup e-tL.

Bernoulli Numbers ＆ Vandermonde Matrices

Matrix structuring is a very beautiful way to place Bernoulli numbers, by which a new view to the numbers is opened. Natural Numbers are mathematics seeds and Natural Number System （NNS） breeds the whole world mathematically.

SINGULAR INTEGRAL OPERATORS ANDSINGULAR QUADRATURE OPERATORSASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS

In this paper, the author discusses some singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, and obtain some useful properties for them. These results improve both the classical theory of singular integral equation and the classical theory of singular quadrature.

Quantum Mechanical Image of Matrices' LDU Decomposition

For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.

New Approach for the Inversion of Structured Matrices via Newton’s Iteration

Newton’s iteration is a fundamental tool for numerical solutions of systems of equations. The well-known iteration ?rapidly refines a crude initial approximation X0?to the inverse of a general nonsingular matrix. In this paper, we will extend and apply this method to n× n?structured matrices M?, in which matrix multiplication has a lower computational cost. These matrices can be represented by their short generators which allow faster computations based on the displacement operators tool. However, the length of the generators is tend to grow and the iterations do not preserve matrix structure. So, the main goal is to control the growth of the length of the short displacement generators so that we can operate with matrices of low rank and carry out the computations much faster. In order to achieve our goal, we will compress the computed approximations to the inverse to yield a superfast algorithm. We will describe two different compression techniques based on the SVD and substitution and we will analyze these approaches. Our main algorithm can be applied to more general classes of structured matrices.

2×2分块对角算子矩阵拟谱的精细刻画

设A,B为可分Hilbert空间X中的稠定闭线性算子,M_(0)=(A00B)表示2×2分块算子矩阵.文中精细刻画算子矩阵M0在对角扰动情形下的拟点谱、拟剩余谱与拟连续谱,所得结论与点谱、剩余谱和连续谱的结果进行了比较,并用例子进行了辅证.最后,采用空间分解技巧,用主对角元的信息刻画M0在上三角扰动情形下的拟点谱分布.

基于矩阵半张量积解四元数广义Sylvester矩阵方程组

该文利用矩阵半张量积求解四元数广义Sylvester矩阵方程组.首先将实矩阵半张量积运算推广到四元数矩阵,进而利用四元数矩阵半张量积提出四元数矩阵在向量算子下的一些新结论,利用这些结论将四元数矩阵方程组转化为四元数线性方程组,最后转化为实线性方程组,从而得到四元数广义Sylvester矩阵方程组有解的充要条件及通解表达式,并给出其极小范数解.最后通过数值算例说明该方法的有效性.

缺项算子矩阵的右(左)可逆补

设H和K为无限维的Hilbert空间,对于给定的算子A∈B(H),B∈B(K,H),C∈B(K),D∈B(K),在一定条件下,利用空间分解的方法给出了缺项算子矩阵[AB?C]为右(左)可逆且具有如[???D]形式的右(左)逆补的充分必要条件。

分块对角算子矩阵在上三角扰动下的精细拟谱和固有拟谱

本文研究了对角分块算子矩阵在上三角有界扰动情形下的精细拟谱和固有拟谱的问题.利用空间分解技巧和算子的扰动原理等方法,将谱的结论推广到拟谱上,获得了对角分块算子矩阵在上三角有界扰动情形下的ε-单射性以及它的拟剩余谱与拟连续谱.最后,刻画了对角分块算子矩阵在上三角有界扰动情形下的固有拟点谱、固有拟剩余谱和固有拟连续谱.

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

非线性分块算子矩阵的Dörfner谱性质

研究了对角非线性分块算子矩阵、上三角非线性分块算子矩阵以及斜对角非线性分块算子矩阵的Dörfner谱,得到了整个算子矩阵的Dörfner谱与其内部元的Dörfner谱之间的关系。此外,利用Frobenius-Schur分解方法,得到了2×2非线性分块算子矩阵的Dörfner谱与其Schur补的Dörfner谱之间的关系。

城市轨道交通司机作业风险因素研究

为厘清城轨司机值乘作业过程中各种风险因素的致害原理及影响关系,应用工作结构—风险结构分解(WBS-RBS)法对城轨司机作业进行分解,采用决策实验室分析法—解释结构模型(DEMATEL-ISM)、交叉影响矩阵相乘分类模型(MICMAC)方法对风险因素进行分析。结果表明:身体条件不符合值乘要求(PR1)、错时错位出勤(PR2)、未进行岗前安全教育(PR3)、未穿着作业服装(OR2)4项原因因素易对其他因素产生影响,忽视车载车站行车信息(OR1)、开关门作业失误(OR7)等9项结果因素易受其他因素影响;身体条件不符合值乘要求(PR1)在风险因素分层中是最深层次原因;通过依赖性—驱动力图可以看出风险因素主要集中于依赖族和自治族区域。通过以上分析可以有针对性地对风险因素制定管控措施。

Browder Spectra and Essential Spectra of Operator Matrices

Let Mc = （ A0CB ） be a 2 × 2 upper triangular operator matrix acting on the Banach space X × Y. We prove that σr（A） ∪ σr（ B）= σr （Mc） ∪ W ,where W is the union of certain of the holes in σr（Mc） which happen to be subsets of σr（A） ∩ σr（B）, and σr（A）, σr（B）, σr（Mc） can be equal to the Browder or essential spectra of A, B, Mc, respectively. We also show that the above result isn＇t true for the Kato spectrum, left （right） essential spectrum and left （right） spectrum.

Perturbation of Spectra for a Class of 2×2 Operator Matrices

In this paper, we study the perturbation of spectra for 2 ×2 operator matrices such as Mx ={A0 XB） AC and Mz = （Az CB） on the Hilbert space H K and the sets……

Possible Spectrums of 3×3 Upper Triangular Operator Matrices

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M（D,V,F） a 3×3 upper triangular operator matrix acting on Hi ＋H2＋ H3 of theform M（D,E,F）=（A D F 0 B F 0 0 C）.For given A ∈ B（H1）, B ∈ B（H2） and C ∈ B（H3）, the sets ∪D,E,F^σp（M（D,E,F））,∪D,E,F ^σr（M（D,E,F））,∪D,E,F ^σc（M（D,E,F）） and ∪D,E,F σ（M（D,E,F）） are characterized, where D ∈ B（H2,H1）, E ∈B（H3, H1）, F ∈ B（H3,H2） and σ（·）, σp（·）, σr（·）, σc（·） denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.

On Essential Spectra of 2 × 2 Operator Matrices

Let MX=（A C X B ）be a 2×2 operator matrix acting on the Hilbert space H＋K. For given A∈B（H）,B∈B（K）and C∈B（K,H）the set UX∈B（H,K）^σe（MX）is determined, whereσe（T）denotes the essential spectrum.