OSCILLATION OF SYSTEMS OF IMPULSIVE DELAY PARABOLIC EQUATIONS ABOUT BOUNDARY VALUE PROBLEMS

In this paper,oscillation of solutions to a class of impulsive delay para- bolic partial differential equations system with higher order Laplace operator is studied.Under two different boundary value conditions,we establish some sufficient criteria with respect to the oscillations of such systems,employing first-order impulsive delay differential inequalities.The results fully reflect the influence action of impulsive and delay in oscillation.     

相控阵雷达的关键技术与物理学的波动知识

应用波的相干原理分析了相控阵雷达的工作原理.以波的形成、波的发射和回波的接收等三个环节为主线,简要地介绍了由固态技术、光电子技术、计算机技术和信号处理技术所形成的相控阵雷达关键技术的背景、现状,并展望了相控阵雷达关键技术的未来.     

On the two-armed bandit problem with non-observed Poissonian switching of arms

We consider the symmetrical case of the Poissonian variant of the two-armed bandit problem. We suppose that at jump-times of a non-observed Poisson process sequential switching of the bandit arms occurs. The optimality of the myopic policy is proved for all sufficiently large switching rates. In this case, explicit formulas which are good approximation for the value function are found as well.     

一类时滞脉冲微分方程的概周期解的存在性

运用锥上的不动点定理，研究一类脉冲时滞微分方程的概周期解，得到了保证系统存在概周期解的一组充分条件。     

ASYMPTOTIC PROPERTY FOR A LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH DELAYS AND DISPERSION

An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution.     

一类中立型时滞抛物偏微分方程的强迫振动性

研究了一类中立型时滞抛物偏微分方程:t(u(x,t)-pu(x,t-τ))-∑rk=1ak(t)Δu(x,t-ρk(t))+∑mj=1qj(t)u(x,t-σj(t))=e(x,t),的强迫振动性(其中(x,t)∈Ω×[0,∞)≡G,Ω是n维欧几里得空间Rn中带有逐段光滑边界Ω的有界区域,Δ是Rn中带有三类不同边值条件的拉普拉斯算子,强迫项e(x,t)是定义在G上的一个振荡函数),给出了一些新的振动性判据,这些结果推广了已知的一些结论.     

中立型对数种群模型的正周期解存在性

本文利用k-集压缩算子的拓朴度抽象连续定理和某些分析技巧,研究了一类中立型对数种群模型dN/dt=N(t)[r(t)-a(t)lnN(t-σ)-b(t)d/dtlnN(t-r)]的正周期解存在性问题。得到了正周期解存在性的新结果。     

一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支

研究一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

ASYMPTOTIC BEHAVIOR OF DELAY DISCRETE-TIME NEURAL NETWORKS WITH CRITICAL THRESHOLD

This paper is concerned with a delay discrete-time system arising as a discrete-time network of two neurons with McCulloch-Pitts nonlinearity. We obtain the asymptotic behaviors of the solutions of the system for some cases. The results obtained improve and extend the corresponding results established recently by Zhou, Yu and Huang [1].     

On numerical approximation using differential equations with piecewise-constant arguments

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for stability and oscillation of a class of linear delay equations with continuous and piecewise constant arguments. This research was partially supported by Hungarian NFSR Grant No. T046929.