利用伪辛空间上一类子空间构作d~e析取矩阵

利用伪辛空间上一类子空间m维(m,0,0,0)型子空间的性质构作了d~e析取矩阵M_q(2v+1,m,d),并利用子空间的计数定理计算了它的参数.通过研究N(m,0,0,0;2v+1)的单调性,得到了矩阵M_q(2v+1,m,d)的最优值.     

关于酉对称矩阵的QR分解及其算法

为了简化大型行(列)酉对称矩阵的QR分解,研究了行(列)酉对称矩阵的性质,获得了一些新的结果,给出了行(列)酉对称矩阵的QR分解的公式和快速算法,它们可极大地减少行(列)酉对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度.同时推广和丰富了邹红星等(2002)的研究内容,拓宽了实际应用领域的范围.     

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plusnoise type sample covariance matrices Cn =1/N (Rn + σXn) (Rn + σXn)*,under the assumption that the entries of Xn are ...     

二次矩阵方程X~2-bX-C=O的正定解

研究二次矩阵方程X2-bX-C=O(b>0,C为n×n阶正定阵)的正定解,证明了解的存在唯一性并且给出了求解方法.     

一类禽流感模型的全局稳定性

在饲养业中不可避免着人类行为的干涉,基于饲养业实际研究了一类染病者即刻被隔离的SEQS模型,其中常数输入是必须的且输入者中必含潜伏期者.利用三维空间的Bendixson-Dulac定理证明系统不存在周期解,从而唯一的正平衡点一旦存在即是全局稳定的.     

矩阵的一种特殊运算及其应用

针对元素为非负实数的矩阵,引入矩阵的一种双目运算——换乘运算,讨论了这种运算的一些主要性质.举例说明这种运算在城市公交路线查询中的应用,和其他查询算法相比,这种方法具有一次运算,永久利用结果的优点.     

Complementarity properties of the Lyapunov transformation over symmetric cones

The well-known Lyapunov's theorem in matrix theory/continuous dynamical systems asserts that a square matrix A is positive stable if and only if there exists a positive definite matrix X such that AX +XA* is positive definite. In this paper, we extend this theorem to the setting of any Euclidean Jordan algebra V . Given any element a ∈ V , we consider the corresponding Lyapunov transformation La and show that the P and S-properties are both equivalent to a being positive. Then we characterize the R0 -property for La and show that La has the R0 -property if and only if a is invertible. Finally, we provide La with some characterizations of the E0 -property and the nondegeneracy property.     

保欧氏度量偏序的变换

设L(R~n)表示n维欧氏空间R~n的所有线性变换构成的集合,‖ξ‖表示向量ξ的欧氏长度,由欧氏长度建立起向量间的序关系,令:PO(R~n)={f∈L(R~n)■|ξ,η∈R~(n×1),‖ξ‖≤‖η‖■‖f(ξ)‖≤‖f(η)‖}则PO(R~n)是欧氏空间R~n中保欧氏度量偏序变换构成的集合,讨论了PO(R~n)的结构,证明了保持这种序关系的变换由正交变换和伸缩变换组成.     

Nonparametric estimation of location parameter after a preliminary test on regression in the multivariate case

For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied efficiency results are presented.     

Structural modeling in a class of systems using fuzzy sets theory

On the basis of fuzzy sets theory, we propose a method for structuring hierarchy for the several complex problems, and call it Fuzzy Structural Modeling (FSM) method. An important requirement for structural modeling of complex systems is that the necessary data is acquired and organized into a form such that a structural model can be developed. The main purpose of this method is to describe and illustrate a formal procedure for constructing the graphic presentation of the hierarchical arrangement given the necessary information concerning the relation of each element to each other element. The procedure permits an automatic development of the graphic structure that portrays the hierarchy.