两类带渐近扰动的随机过程的若干性质

本文考虑两类带渐近扰动的随机模型.一类是带渐近扰动的非紧邻随机游动,考虑其常返暂留性,并给出该模型正常返性的判别.另一类是带渐近扰动的随机环境中分枝过程,通过分析其相关随机游动的极限行为,给出分枝过程灭绝和不灭绝的判别条件.     

关于一般马尔可夫过程轨道常返性及暂留性

本文讨论了一般马尔可夫过程轨道常返性及暂留性，得到了一般马尔可夫过程轨道点常返及区域常返的一些判别准则。     

直线上随机环境中可逗留的随机游动的若干性质

主要研究直线上随机环境中可逗留的随机游动的常返性与极限性质,在独立随机环境下,通过强大数定律给出了常返与暂留的一个充分条件;在一般随机环境下,通过数列的有界性给出了常返与零常返的充分条件并讨论了在独立随机环境下非常返性中的大数定律,从而推广了Solomon的研究框架.     

随机环境中马氏链状态的各种常返性与暂留性

考虑到随机环境中马氏链的状态在受到环境因素各种条件的影响下,引入了随机环境中马氏链状态的各种常返性与暂留性概念,讨论了这些常返性与暂留性的相互关系,从而说明随机环境中马氏链状态的常返性与暂留性和经典马氏链状态的常返性与暂留性有着显著的区别.     

双无限环境中马氏链的常返和暂留性

证明了常返和暂留是一对互斥概念,如果→X是π-不可约的且π是平稳的,则各种常返、暂留概念是等价的,讨论了暂留与非本质的等价性问题.     

随机环境中有界跳幅随机游动常返性暂留性的另一证明

假定环境是平稳遍历的,对具有有限跳幅的随机环境中的随机游动,该文给出了其常返性暂留性的另一证明.Bremont(2002)的文章中,通过计算逃逸概率的方法给出了证明,而该文的证明采用了鞅收敛定理的方法.     

RWdn的常返性

设X={X(z),z∈Tn}是文献[1]中定义的n参数d维随机游动(RWdn),本文主要研究RWdn的常返性,得到了关于RWdn的常返性的一些判别准则,并举例说明了几种RWdn的常返性.     

RWn^d的常返性

设X＝{X(z),z∈T^n}是文献[1]中定义的n参数d维随机游动（RWn^d)，本文主要研究RWn^d的常返性，得到了关于RWn^d的常返性的一些判别准则，并举例说明了几种RWn^d的常返性。     

带移民和拯救的二次加权分枝过程的有关性质

本文考虑一类带移民和拯救的二次加权分枝过程(QWMBPIR)的正则性、存在唯一性以及常返性和遍历性.我们首先对QWMBIR的q-矩阵发生函数的性质进行讨论,建立QWMBPIR正则性及唯一性的判别准则.进一步,对QWMBPIR的常返性及遍历性进行分析,得到过程遍历性的充分条件.     

直线上时间随机环境下随机游动的渐近性质

在状态空间是可数情形下,本文给出了时间随机环境下随机游动的一个一般模型.随后,在环境是独立同分布情形下得到了直线上时间随机环境下紧邻随机游动的一个常返与暂留准则和强大数定律;最后讨论了其中心极限定理,它类似与简单随机游动的相应结果.     

Matrix interpretation of multiple orthogonality

In this work we give an interpretation of a (s (d + 1 ) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials. We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present a matrix interpretation of the type II multi-orthogonality conditions. We state a Favard type theorem and the expression for the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite-Padé approximation in matrix form is given.     

Formal orthogonal polynomials and Hankel/Toeplitz duality

For classical polynomials orthogonal with respect to a positive measure supported on the real line, the moment matrix is Hankel and positive definite. The polynomials satisfy a three term recurrence relation. When the measure is supported on the complex unit circle, the moment matrix is positive definite and Toeplitz. Then they satisfy a coupled Szeg recurrence relation but also a three term recurrence relation. In this paper we study the generalization for formal polynomials orthogonal with respect to an arbitrary moment matrix and consider arbitrary Hankel and Toeplitz matrices as special cases. The relation with Padé approximation and with Krylov subspace iterative methods is also outlined.This research was supported by the National Fund for Scientific Research (NFWO), project Lanczos, grant #2.0042.93.     

A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra with applications to the Metro-bus public transport system in Mexico city

In this paper, an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to the Metro-bus public transport system in Mexico city. A timed event Petri net model is constructed from the data table that characterizes the transport system. A max-plus recurrence equation, with a reducible and regular matrix, is associated with the transport system timed event Petri net. Next, given the reducible and regular matrix, the problem consists of giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The generalized eigenmode obtained sets a timetable for the transport system.     

The Quantum Cellular Automaton as a Markov Process

The dynamical behavior of the Quantum Cellular Automaton (QCA) is described here as a Markov Process. Ergodicity and recurrence, emergent properties of the discrete dynamical QCA system, are defined in the context of the characteristic polynomial of the Markov transition matrix. Except for a few anomalous cases, the transition matrix can be used to predict recurrence times. Finally, a correspondence between recurrence and elementary particle mass is proposed as an example of an emergent property of the QCA system. © 1999 Elsevier Science Ltd. All rights reserved.     

一类E-Vandermonde矩阵的求逆及逆的迭代公式

本文给出一类E-Vandermonde矩阵和广义E-Vandermonde矩阵可逆的条件及逆的矩阵表达式，并给出了求逆的迭代公式．     

Spectral methods for orthogonal rational functions

We present an operator theoretic approach to orthogonal rational functions based on the identification of a suitable matrix representation of the multiplication operator associated with the corresponding orthogonality measure. Two alternatives are discussed, leading to representations which are linear fractional transformations with matrix coefficients acting on infinite Hessenberg or five-diagonal unitary matrices. This approach permits us to recover the orthogonality measure throughout the spectral analysis of an infinite matrix depending uniquely on the poles and the parameters of the recurrence relation for the orthogonal rational functions. Besides, the zeros of the orthogonal and para-orthogonal rational functions are identified as the eigenvalues of matrix linear fractional transformations of finite Hessenberg or five-diagonal matrices. As an application we use operator perturbation theory results to obtain new relations between the support of the orthogonality measure and the location of the poles and parameters of the recurrence relation for the orthogonal rational functions.     

一类广义范德蒙矩阵的求逆公式及递推公式

利用线性方程组给出了一类广义范德蒙矩阵可逆的条件及逆矩阵的矩阵表示式 ,并给出了求逆的递推公式 .     

Pascal矩阵与Vandermonde矩阵的关系

EI-Mikkawy M证明了对称Pascal矩阵Q_n和Vlandermonde矩阵V_n之间满足矩阵方程Q_n=T_nV_n,这里T_n是一个随机矩阵。本文证明了随机矩阵T_n能够分解成第一类Stirling矩阵和对角矩阵的乘积,得到了矩阵T_n的元素之间的递推关系,从而回答了EI-Mikkawy M的一个公开问题。同时得到了一些与Stirling数相关的组合恒等式。     

Deformed Heisenberg algebra with reflection and <Emphasis Type="Italic">d</Emphasis>-orthogonal polynomials

This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of d-orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when d = 1. The underlying algebraic framework allowed a systematic derivation of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy.     

Inverse comrade matrices

A comrade matrix is a square matrix whose nonzero entries are contained within the tridiagonal part and the last row. We study the inverses of such matrices, including recognition in terms of vanishing minors; inheritance by principal submainees: recurrence relations for the rows, and reconstruction of the comrade matrix.