泛灰线性方程组的泛灰矩阵求解方法

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .根据泛灰数的性质 ,定义了泛灰矩阵 ,提出了泛灰线性方程组的泛灰矩阵解法 ,并给出了算例 .     

有界上三角算子矩阵的亏谱

讨论了希尔伯特空间上有界上三角算子矩阵的亏谱扰动性质,当对角元算子给定时,得到上三角算子矩阵的亏谱恰等于对角元算子的亏谱之并集的充要条件,特别地,给出有界上三角Hamilton型算子矩阵相应问题成立的条件,并辅以实例佐证.     

灰对角矩阵的一些性质

本文根据灰对角矩阵的定义，得到一些性质．     

有界灰矩阵的非奇异性与秩

本文重新论述有界灰方阵的非奇异性判别问题,提出“条件非奇异”与“最大非奇异子元值域”的新概念,指出现有结果的局限性,给出了一些实用判据,并对灰逆阵的存在性条件与定义域作了研究.此外,本文又提出有界灰矩阵的“灰秩”的新概念与算法,建立了有界灰矩阵恒满秩、恒不满秩、条件满秩的判据。     

格上的T-幂等矩阵

利用完备的分配格L上三角模定义L上的矩阵运算，给出这些运算的一些基本性质，并且讨论L上的T-幂等矩阵。     

矩阵初等变换的推广及其应用

矩阵的初等变换及矩阵的分块是矩阵理论中的两个重要方法，本将初等变换推广到分块矩阵上去，在引进了准初等变换概念后，证明了它的某些性质，本的目的在于简化某些矩阵运算，并希望本建立的概念与结论得到更加广泛的应用。     

泛灰线性方程组的白化求解方法与应用

在概述泛灰数的概念与泛灰行列式运算的基础上 ,介绍了泛灰线性方法程组的泛灰解法 .由于泛灰行列式运算复杂 ,根据泛灰的性质 ,提出了泛灰线性方程组的白化解法 .理论证明这种求解方法的正确性 .并给出了算例 .     

一类无穷矩阵变换的刻划

对于一类经典的矢值序列空间,引入了一类重要子集,它包括了该序列空间的全部全有界集和许多非全有界集.利用Antosik-Mikusinski基本矩阵定理和该子集族,获得了一个无穷矩阵收敛定理,进而给出了一类经典无穷矩阵变换的刻划.     

矩阵初等变换的推广及其应用

矩阵的初等变换及矩阵的分块是矩阵理论中的两个重要方法。本文将初等变换推广到分块矩阵上去，在引进了准初等变换概念后，证明了它的某些性质。本文的目的在于简化某些矩阵运算，并希望本文建立的概念与结论得到更加广泛的应用。     

一类矢值序列空间上的矩阵变换定理

对于一类经典的矢值序列空间,文中引入一类重要子集,它包括了该序列空间的全部有界集和许多非有界集.利用Antosik-Mikusinski基本矩阵定理和该子集族,获得了一个无穷矩阵收敛定理,并且给出了一类经典无穷矩阵变换的更强刻画.此结果改进了算子级数序列赋值收敛定理.     

河流分类的灰色理论模型

根据灰色关联度的定义，运用加权广义距离构造目标函数，建立了一种灰色综合评判理论模型．应用该模型对辽宁省15条河流进行了综合评价，结果表明该模型分辨率高、可靠性强，并且具有数学推导严谨、科学合理等特点．     

Grey dynamic input-output analysis

A system whose information is partially known and partially unknown is named as a grey system and it is general situation in reality. On the basis of grey number/matrix and their covered operation, some definitions of grey functions are enumerated. Combining grey system theory with traditional dynamic input-output analysis, we propose the grey dynamic input-output analysis. It has two types, i.e., the continuous and the disperse. The most important results are the computational formulas of the matrix-covered set of inverse grey investment coefficient matrix. By using them, we can forecast and control the economic system under the uncertain situation. For the calculation of the matrix-covered set of inverse grey matrices, we obtain the desired formulas, which can be applied to general grey matrices. The formulas can greatly promote the development of grey theory and enrich the applied fields of uncertain mathematics. The modified case illustrates our method.     

On solving optimization problems with proportion-constraints

The purpose of this paper is to establish sufficient conditions for the existence of solutions to mathematical programs where the variables of the solution satisfy given proportions. These conditions rely on convergence properties of powers of nonnegative matrices when these powers form a bounded sequence. We assume that if an arbitrary vectorx is premultiplied by elements of this sequence, the limit of the sequence (which might be a Cesaro (C, 1) limit) gives an improvement of the objective.This research was supported by NSF Grants ENG 76-15599 and ENG76-12266 and ONR Contract N00014-75-C-0493.     

基于灰色线性回归组合模型的长沙、武汉房地产投资预测研究

本文通过对长沙、武汉2001-2007年房地产投资额的历史数据进行分析,分别建立了两市的灰色线性回归组合模型.模型较好地拟合了长沙、武汉的房地产投资情况,运用该模型得到了两市2008、2009年的预测值,并对其房地产投资发展趋势的异同进行比较分析,对房地产市场的发展具有一定的指导意义.     

一类灰色动态投入产出优化模型的设计及其在农业经济发展规划中的应用

本文应用灰色系统理论和方法，把动态Ｌｅｏｎｔｉｅｆ投入产出模型和线性规划结合起来，建立一种灰色动态投入产出优化模型，在山东省农业经济发展规划定量研究中，应用该模型取得比较满意的结果．     

关于粗糙集和灰色系统之间某些关系的探讨

首先介绍粗糙集与灰色系统两种理论,并对二者进行比较。接着介绍普通粗糙集、P-粗糙集以及灰色集的定义,并就灰色集、模糊集和经典集合三者进行对比分析。我们提出了点灰度和集灰度两种灰度概念用于描述灰色系统的信息不确定性。通过P粗糙集导出相应的灰色集,并研究相关的灰度、粗糙度与边界域的性质和关系。分析表明使用导出的灰色集对系统的信息不确定性的估计与相应的粗糙集是一致的,因此两种理论在描述和处理不确定性信息系统方面的一定的相关性,将两种理论相结合来处理某些不确定性信息系统可能更为有效。     

On some characterisations of totally unimodular matrices

A characterisation of totally unimodular matrices is derived from a result of Hoffman and Kruskal. It is similar in spirit to a result of Baum and Trotter. Its relation with some other known characterisations is discussed and in the particular case where the matrices have (0, 1) entries, we derive some properties of the associated unimodular hypergraphs. Similar results for balanced and perfect matrices are also reviewed.     

Spectrum of certain tridiagonal matrices when their dimension goes to infinity

This paper deals with the spectra of matrices similar to infinite tridiagonal Toeplitz matrices with perturbations and with positive off-diagonal elements. We will discuss the asymptotic behavior of the spectrum of such matrices and we use them to determine the values of a matrix function, for an entire function. In particular we determine the matrix powers and matrix exponentials.     

A note onQ-matrices

This paper concerns three classes of matrices that are relevant to the linear complementarity problem. We prove that within the class ofP ₀-matrices, theQ-matrices are precisely the regular matrices.Research supported by Department of Energy, Contract EY-76-S-03-0326 PA # 18.     

Additive Decomposition of Real Matrices

The orthogonal orbit ${\cal O}(A)$ of an n × n real matrix A is the set of real matrices of the form $P^t \ AP$ where $P^t P = I_n$ . We show that $A/ \| A\|$ is an affine sum of four orthogonal matrices, and note that $A^t$ can always be written as an affine combination of no more than 2 n m 1 matrices in ${\cal O}(A)$ . This improves some recent results of Zhan, and answers some of his questions. Other related results are also discussed.