随机环境中的马氏链状态分类

给出了随机环境中马氏链的特征数和状态的定义,讨论了状态间的传递性,自反性,对称性,是经典马氏链相应结果的一般化.并运用位势方法研究了状态间的关系,它们在极限理论的研究中非常有用.     

随机变量序列的大数定律及常返性定理

对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律.     

Extremal maximal sectorial extensions of sectorial relations

The extremal maximal sectorial extensions of a not necessarily densely defined sectorial relation (multivalued linear operator) in a Hilbert space are characterized in terms of a construction which goes back to Sebestyén and Stochel. In particular the two extreme maximal sectorial extensions, namely the Friedrichs extension and the Kreĭn extension, are characterized. For this purpose a survey is given of the connection between closed sectorial forms and maximal sectorial relations.     

A class of deformational flow test cases for linear transport problems on the sphere

A class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position and shape. This process makes the exact solution available at the end of the simulation, and facilitates assessment of the accuracy of the underlying transport scheme. A procedure to eliminate possible cancellations of errors when the flow reverses is proposed.     

Nonlinear branching processes with immigration

The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.     

On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

基于可拓变换的二维随机变量分布律的研究

建立了随机事元之间的关系事元,研究随机事件之间的关系.利用关系元刻画了两个随机事件之间的关系.运用可拓变换初步研究了二维离散型随机变量的分布律和边缘分布律的传导分布.     

SUPERCONVERGENCE OF A DISCONTINUOUS GALERKIN METHOD FOR FIRST-ORDER LINEAR DELAY DIFFERENTIAL EQUATIONS

This paper deals with the discontinuous Galerkin (DG) methods for delay differential equations.By an orthogonal analysis in each element,the superconvergence re...     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.