Furi-Martelli-Vignoli spectrum and Feng spectrum of nonlinear block operator matrices

We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.

BLOCK H-MATRICES AND SPECTRUM OF BLOCK MATRICES

The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got.

Criteria for Discrete Spectrum of 1D Operators

For discrete spectrum of 1D second-order differential/difference operators(with or without potential(killing),with the maximal/minimal domain),a pair of unified dual criteria are presented in terms of two explicit measures and the harmonic function of the operators.Interestingly,these criteria can be read out from the ones for the exponential convergence of four types of stability studied earlier,simply replacing the‘finite supremum’by‘vanishing at infinity’.Except a dual technique,the main tool used here is a transform in terms of the harmonic function,to which two new practical algorithms are introduced in the discrete context and two successive approximation schemes are reviewed in the continuous context.All of them are illustrated by examples.The main body of the paper is devoted to the hard part of the story,the easier part but powerful one is delayed to the end of the paper.

ON SPECTRAL PROPERTIES OF A NEW OPERATOR OVER SEQUENCE SPACES c AND c_0

In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces？∞, c and c0 according to a new matrix operator W which is obtained by matrix product.

Numerical Solution of Two-Dimensional Nonlinear Stochastic Ito-Volterra Integral Equations by Applying Block Pulse Functions

This paper investigates the numerical solution of two-dimensional nonlinear stochastic Itô-Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.

ON THE SPECTRUM OF SINGULAR HAMILTONIAN DIFFERENTIAL SYSTEMS

In this paper, we study a bounded-below singular Hamiltonian system. Sufficient and necessary conditions are obtained for the existence and the number of eigenvalues on the left-axis. The main results of this paper are the extension and improvement of Weyl spectral theorem for singular sccond order differential equations.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

无界分块算子矩阵的可分解性及其应用

无界分块算子矩阵广泛地出现于系统理论、非线性分析以及发展方程问题等领域,在理论和实际应用两方面都受到广泛关注。首先,利用算子局部谱理论得到无界分块算子矩阵可分解性的刻画,其次,给出算子矩阵可分解性保持对角稳定的条件,推广并得到分块算子矩阵在无界情形下的一些局部谱性质。最后,作为应用考察Hamilton算子的可分解性并举例予以说明。

多边矩阵的块行列式Det运算

说明了多边矩阵的块求行列式Det运算的概念,并进一步证明了多边矩阵剖面的块求行列式Det运算的基本定理,给出了一些多边矩阵的求行列式Det运算代数性质。作为该概念的应用领域,探索了多边矩阵的块求行列式Det运算和多边矩阵的块求迹Tr运算之间的关系。

块H-矩阵与块矩阵的谱

利用G_函数概念研究块H_矩阵 ,引入若干块矩阵概念· 获得了块H_矩阵的等价刻划 ,得到了一般块矩阵特征值的由G_函数描述的分布域 ,由于用G_函数刻划 。

Legendre小波求解非线性分数阶Fredholm积分微分方程

为了求解非线性分数阶Fredholm积分微分方程的数值解,通过Legendre多项式,得出了Legendre小波,并由block pulse函数给出了Legendre小波的分数阶积分算子矩阵,利用block pulse函数与Legendre小波的积分算子矩阵的性质将非线性分数阶Fredholm积分微分方程转化为非线性代数方程组,进而可以求得原积分微分方程的数值解.结果表明:随着点数的增多,数值解的精度也越来越高.文中给出的算例表明了该方法的可行性和有效性.

2×2上三角算子矩阵的Drazin谱

设■是从Hilbert空间H⊕K到H⊕K中的2×2上三角算子矩阵.该文主要研究M_C的Drazin可逆性和M_C的Drazin谱.此外,对给定算子A∈B(H)和B∈B(K),将给出在一定条件下所有上三角算子矩阵M_C的Drazin谱的交■σ_D(M_C)的具体表达式.

应用Haar小波求解非线性分数阶Fredholm积分微分方程

Fredholm积分微分方程的数值算法一直是近些年来研究的重要课题.利用Haar小波研究了非线性分数阶Fredholm积分微分方程.Haar小波具有正交性,可计算性以及小支集性.结合block pulse函数给出了Haar小波的分数阶积分算子矩阵,并利用该函数的定义与Haar小波的积分算子矩阵的性质,将非线性分数阶Fredholm积分微分方程转换为非线性代数方程,从而便于计算机求解.最后给出算例表明该方法的有效性.

两个算子乘积的一种广义逆序律

利用算子分块矩阵的技巧,研究了两个算子乘积的{1,3,4}-逆的广义逆序律,给出了闭值域有界线性算子的{1,3,4}-逆的一般矩阵表示,证明了当R(A)、R(B)和R(AB)都闭时,B{1,3,4}A{1,3,4}AB{1,3,4}当且仅当R(A*AB)=R(B)(R(B)∩N(A))且B*(R(B)∩N(A))=B+(R(B)∩N(A)).

采用Hilbert谱带通滤波和暂态波形识别的谐振接地系统故障选线新方法

利用谐振接地系统发生单相接地故障后,非故障线路的暂态零序电流波形相似,而故障线路暂态零序电流波形与非故障线路差别较大的特点,提出一种基于故障暂态零序电流波形时频局部特征识别的接地选线新方法。将故障后各线路首个工频周波内的零序电流波形经Hilbert谱带通滤波分解为多频带分量,在时域上对各频带分量做等间隔划分,得等面积的时频小块,以其面积为元素生成各线路的分块时频谱矩阵,进而综合运用相关系数法及欧氏距离法求取各线路相对于其他线路的综合相似系数,结合选线判据确定故障线路。仿真结果表明,该选线方法能适应各种故障条件及影响因素,具有裕度高,选线准确等特点。

3×3阶上三角算子矩阵的点谱和剩余谱扰动

基于值域的稠密性和闭性,有界线性算子T的点谱和剩余谱可分别细分为σ_(p,1)(T),σ_(p,2)(T)和σ_(r,1)(T),σ_(r,2)(T).设H_1,H_2,H_3为无穷维复可分Hilbert空间,给定A∈B(H_1),B∈B(H_2),C∈B(H_3),结合分析方法与算子分块技巧给出了M_(D,E,F)的上述四种谱随D,E,F扰动的完全描述.

一种新型的认知无线电频谱空穴自适应检测算法

根据认知无线电实际频谱需求,通过对弱信号检测技术的研究,该文首次在认知无线电领域提出了一种基于三重矩阵累积估计的频谱空穴检测算法,该算法将频域块自适应滤波与矩阵重构、累积估计和频域平滑相结合实现弱信号检测。最后以QPSK调制信号为例进行了算法的计算机仿真,给出了性能分析。仿真结果表明该检测算法能够快速有效地实现弱信号检测并具有较高的检测概率,完全可以应用于认知无线电的频谱空穴检测。

Legendre小波在非线性分数阶微分方程中的应用

针对一类非线性分数阶微分方程,采用Legendre小波法对非线性分数阶微分方程进行研究.结合BlockPulse函数给出Legendre小波的分数阶积分算子矩阵,利用Block Pulse函数的定义与Legendre小波积分算子矩阵的性质将非线性分数阶微分方程转换为非线性代数方程组,进而对其数值解和误差分析进行研究.结果表明:随着点数增多,数值解的精确度增加.数值算例验证了小波法的可行性和有效性.

CAS小波法求高阶弱奇异非线性积分微分方程数值解

为了求高阶变系数且带有弱奇异积分核非线性Volterra-Fredholm积分微分方程的数值解,文章结合CAS小波的性质及block pulse函数,给出任意阶弱奇异积分的近似求积公式,同时也给出CAS小波的积分算子矩阵,进而可以化简所求非线性积分微分方程,将原问题转换为求非线性方程组的解,数值算例验证了该方法的有效性。

一类循环分块矩阵的一些结果

引进了Ｒ－循环分块矩阵的概念，讨论了它的一般性质．特别，当Ｒ＝Ｉｎ时，得到了其块谱分解定理、矩阵范数意义下的圆盘定理以及非奇异的几个充分条件．