r－不可分矩阵的本原指数（Ⅱ）

本文给出了 n阶 r-不可分矩阵的本原指数的上界 ,即任 n阶 r—不可分矩阵 A的本原指数 (A)≤n+(r- ) 2r (1≤ r相似文献   

完全正矩阵的整数分解

n阶矩阵A称为完全正的,如果A有分解:A=BB^T,其中B为元素非负矩阵,B的最小可能列数称为A的分解指数.本文考察低阶双非负矩阵在整数环上的完全正分解及其分解指数.     

非负矩阵与有向图的谱半径

本文给出非负矩阵的谱半径的上界、下界,由此给出有向图的谱半径的界.     

反对称正交对称矩阵反问题

本文讨论一类反对称正交对称矩阵反问题及其最佳逼近．研究了这类矩阵的一些性质，利用这些性质给出了反问题解存在的一些条件和解的一般表达式，不仅证明了最佳逼近解的存在唯一性，而且给出了此解的具体表达式．     

Bounds for the Least Laplacian Eigenvalue of a Signed Graph

A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated.     

Universal elementary constituents of potential transformations shifting waves (qualitative theory)

It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization of a chosen bound state in a potential well of finite width are as well applicable to the scattering functions if states of the continuous spectrum are considered as bound states normalized to unity but distributed on an infinite interval with vanishing density. The potential perturbations of the same type on the half-axis concentrate the scattering wave at the origin, thus creating a bound state embedded into the continuous spectrum (zero width resonance).     

The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

矩阵对角相似的图论判别法

本文证明了任意两个ｎ阶复矩阵Ａ和Ｂ为对角相似的充要条件是：它们有相同的伴随有向图，并且以此有向图为基础有向图，以Ａ和Ｂ的对应非零元素比值为弧权值的赋权有向图满足“无向圈平衡条件”。我们还给出了矩阵对角相似条件在非负矩阵谱理论研究中的一个应用。     

具有奇异值分解性质的代数

设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.     

审讯过程的数学模型

本文从经济学的观点出发，利用对策论方法建立了审讯过程的数学模型，并由此研究了讯问人三种主要策略对审讯成功的效度。