广义对角占优矩阵的两定理

本文根据矩阵A的一系列三元线性不等式组的非空解集的存在性,给出了判定矩阵A为广义对角占优的两个充分条件。     

Hamilton算子矩阵的半群生成定理

研究了Hamilton算子矩阵的半群生成问题,得到其生成C_0半群的若干充分必要条件,并给出其成为半群无穷小生成元时的谱分布.作为应用,基于Hamilton系统的半群方法,给出一类四阶微分方程混合问题的古典解.     

置换理想上的正则矩阵

证明置换理想上的正则矩阵可以通过满矩阵对角化．     

Subordination of Regular Kernels and Abelian Theorems for Quotients

We prove general boundary limit theorems of abelian type for quotients of functions defined in the half space . The functions considered are defined as convolutions of a kernel with Borel measures defined on the boundary . Our theorems are of the form

A Series of Regular Hadamard Matrices

Let p and 2p−1 be prime powers and p ≡ 3 (mod 4). Then there exists a symmetric design with parameters (4p², 2p² − p, p² − p). Thus there exists a regular Hadamard matrix of order 4p².     

Sign Regular Matrices of Order Two

A matrix is called sign regular of order k if every minor of order i has the same sign for each i = 1,2,<, k . If an m × n matrix is sign regular of order k for k = min { m,n } then it is called sign regular. This paper studies some properties of sign regular matrices of order two. Remarkable properties are proved when the row sums of these matrices form a monotone vector.     

Limit Theorems for Spectra of Positive Random Matrices under Dependence

We study classical ensembles of sample covariance matrices introduced by Wishart. We discuss Stein's method for the asymptotic approximation of expectations of functions of the normalized eigenvalue counting measure for high-dimensional matrices. The method is based on a differential equation for the density of the Marchenko-Pastur law. Bibliography: 19 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 92–123.     

Some Extension Theorems for Regular Functions of Several Quaternionic Variables

In this paper we study the extension theorems for solutions of inhomogeneous Cauchy-Fueter system. In particular cases, we obtain the extension theorems for regular functions of several quaternionic variables. At the end of the paper we give some applications of these theorems.     

The Semigroup Generated by Regular Boolean Matrices

The semigroup B^r_n generated by the regular n × n Boolean matrices is studied. The elements of B^r_n are characterized, Greens relations in B^r_n are determined, and the height of the poset of D-classes in B^r_n is investigated.This research was supported by a Mary Washington College Faculty Development Grant.     

Theorems of the Alternative for Cones and Lyapunov Regularity of Matrices

Standard facts about separating linear functionals will be used to determine how two cones C and D and their duals C* and D* may overlap. When T: V W is linear and K V and D W are cones, these results will be applied to C = T(K) and D, giving a unified treatment of several theorems of the alternate which explain when C contains an interior point of D. The case when V = W is the space H of n × n Hermitian matrices, D is the n × n positive semidefinite matrices, and T(X) = AX + X* A yields new and known results about the existence of block diagonal X's satisfying the Lyapunov condition: T(X) is an interior point of D. For the same V, W and D, T(X) = X – B* XB will be studied for certain cones K of entry-wise nonnegative X's.     

Multidimensional Limit Theorems Allowing Large Deviations for Densities of Regular Variation

The sums of i.i.d. random vectors are considered. It is assumed that the underlying distribution is absolutely continuous and its density possesses the property which can be referred to as regular variation. The asymptotic expressions for the probability of large deviations are established in the case of a normal limiting law. Furthermore, the role of the maximal summand is emphasized.     

Volume Comparison Theorems for Lorentzian Manifolds

Using Riccati equation techniques and the Raychaudhuri equation from General Relativity, volume comparison results are obtained for compact geodesic wedges in the chronological future of some point in a globally hyperbolic space-time and corresponding wedges in a Lorentzian space-form.     

关于超过程的几个比较定理

本文讨论了超Dawson-Watanabe过程的Laplace变换之间的相互比较,得到了依赖于其底过程和分枝特征的若干比较定理.应用比较定理可以将超布朗运动在特殊分枝下的某些性质推广到一般的超过程.同时将这些结果应用于非线性发展方程,得到了一类非线性发展方程的解之间的比较.     

Comparison Theorems for Functional Differential Equations

Our aim in this paper is to obtain the comparison principles which extend those of Grace and LALLI. The equations. L_nu(t)±f(t, u[g(t)]= 0 are compared with the equations. M_nu(t)±z(t)h([τ(t)])= 0.     

正则竞赛矩阵的数目和竞赛矩阵的整数特征值

本文给出了ｎ阶正则竞赛矩阵的数目的一个下界，该下界优于文献中的结果；讨论了正竞赛矩阵的性质；得到了整数１为竞赛矩阵的特征值的等价条件及这类矩阵的谱根与得分向量之间的关系．     

关于四元数自共轭矩阵乘积迹和特征值的几个定理

给出四元数自共轭矩阵乘积迹的几个定理及特征值之界的几个新估计，在四元数体上改进和推广了文［１－１２］的相应结果     

Graham-Witten's Conformal Invariant for Closed Four Dimensional Submanifolds

It was proved by Graham and Witten in 1999 that conformal invariants of submanifolds can be obtained via volume renormalization of minimal surfaces in conformally compact Einstein manifolds. The conformal invariant of a submanifold $\Sigma$ is contained in the volume expansion of the minimal surface which is asymptotic to $\Sigma$ when the minimal surface approaches the conformaly infinity. In the paper we give the explicit expression of Graham-Witten's conformal invariant for closed four dimensional submanifolds and find critical points of the conformal invariant in the case of Euclidean ambient spaces.