An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.     

多时滞随机神经网络的稳定性

通过构建李雅普偌夫函数的方法和利用半鞅收敛定理对一类随机时滞神经网络的全局指数稳定进行了分析,提出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,推广了[1]中的主要结论.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

ALICE实验中光子谱仪的触发选判机制的模拟研究

对ALICE实验光子谱仪的触发选判机制进行了模拟研究, 内容包括: 1) 对光子谱仪的能量重建性能进行了研究, 通过计算机模拟检验光子谱仪探测器对大横动量范围的入射粒子的能量重建性能; 2) 对光子谱仪探测器的事件触发效率进行了研究, 通过计算机模拟分析触发阈值的选取并计算触发效率; 3) 对光子谱仪探测器的事件触发频率进行了研究, 通过计算机模拟对p-p和Pb-Pb两种碰撞模式下的触发频率分别进行了估算和讨论.     

Lower bound for the convergence rate of nonstationary Jacobi-like iteration

Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix A is an H-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with 〈A〉 as the coefficient matrix, where 〈A〉 is a comparison matrix of A.     

A quasilinearization method for a class of integro-differential equations with mixed nonlinearities

We develop an extended form of the quasilinearization method for an initial value problem involving a nonlinear integro-differential equation with mixed nonlinearities, occurring in distributed-infective and distributed-contact models. In fact, a monotone sequence of iterates converging uniformly and quadratically to a solution of the problem is obtained. Some interesting observations are presented.     

关于微分熵的一类强偏差定理

利用关于乘积分布密度的相对熵和相对熵率的概念,建立了相依连续型随机变量序列关于参考微分熵的一类强偏差定理,证明中给出了将Laplace变换应用于微分熵强偏差定理的研究的一种途径．     

BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u＂ = ｜u｜^p

In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.     

BOUNDEDNESS AND CONVERGENCE FOR THE NON-LINARD TYPE DIFFERENTIAL EQUATION

In this article, the author studies the boundedness and convergence for the non-Lienard type differential equation (x|·)=a(y)-f(x) (y|·)=b(y)β(x)-g(x) e(t) where a(y),b(y),f(x),g(x),β(x) are real continuous functions in y∈R or x∈R,β(x)≥0 for all x and e(t) is a real continuous function on R = {t: t≥0} such that the equation has a unique solution for the initial value problem. The necessary and sufficient conditions are obtained and some of the results in the literatures are improved and extended.