固定合作规模网络的平均路径长度

本文提出了一种特殊的合作网络,称之为固定合作规模网络．我们重点研究了这类网络的平均路径长度,通过建立微分方程,得到平均路径长度的增加速度近似与网络规模的对数成正比．     

A Note on Attenuant Cycles of Population Models with Periodic Carrying Capacity

In this short note, we consider attenuant cycles of population models. This study concerns the second conjecture of Cushing and Henson [A periodically forced Beverton-Holt equation, J. Diff. Eq. Appl., 8 (2002), pp. 1119–1120], which was recently resolved affirmatively by Elaydi and Sacker [Global stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures, Proc. 8th Inter. Conf. Diff. Eq., Brno, (in press)]. They showed that the periodic fluctuations in the carrying capacity always reduce the average of population densities in the Beverton-Holt equation. We extend this result and give a class of population models in which the periodic fluctuations in the carrying capacity always reduce the average of population densities.     

On the Finiteness of the Number of Eigenvalues of Jacobi Operators below the Essential Spectrum

We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As an application we show that Kneser's criterion for Jacobi operators follows as a special case.     

A sampling theorem related to the Wilson transform

In this paper, we establish a sampling theorem related to the nonterminating version of the Wilson polynomials and we give a generalization of the de Branges–Wilson integral.     

极分解与广义*-Aluthge变换

首先给出了Hilbert空间上有界线性算子极分解的的若干性质.其次指出广义的*-Aluthge变换与*-Aluthge变换具有许多相似性质;例如,T_(α,β)^((*))=U|T_(α,β)((*))=U|T_(α,β)^((*))|当且仅当T是双正规的,即[|T|,|T*|]=0,其中对任意两个算子A和B,[A,B]=AB-BA.     

Krein空间上J-正常算子的可定化性

对于Krein空间上J-正常算子 的各种可定化性进行了研究. 利用可定化J-正常算子的谱函数, 给出了临界线的概念, 得到了可定化的J-正常算子成为强可定化算子和一致可定化算子的充要条件.     

不确定三重交替更新过程

在更新过程中,交替更新过程是常见的重要的过程之一.本文首先介绍不确定三重交替更新过程,其中间隔时间都是不确定变量.然后证明了关于平均工作率的极限值的不确定三重交替更新过程定理.最后给出了一个实际应用例子.     

Critical Homogenization of SDEs Driven by a Levy Process in Random Medium

We are concerned with homogenization of stochastic differential equations (SDE) with stationary coefficients driven by Poisson random measures and Brownian motions in the critical case, that is, when the limiting equation admits both a Brownian part as well as a pure jump part. We state an annealed convergence theorem. This problem is deeply connected with homogenization of integral partial differential equations.