Global existence results for impulsive functional differential equations

In this paper, we investigate the existence of solutions of impulsive delay differential equation

     

New Preparation Method of Nanocrystalline Materials by Impulse Plasma in Liquid

A new method to fabricate nanomaterials by using Impulse Plasma in Liquid is presented. Impulse plasma appears from inter-electrode space break-down in high potential difference between two electrodes submerged into a dielectric liquid, while the power supply is relatively small that is insufficient to excite an arc discharge. By changing the dielectric liquid, we can obtain metallic particles, oxides, carbides. This method does not require vacuum chamber and high energy, thus, can provide economical preparation of various types of nanomaterials. Nanocrystalline powder of titanium oxide was prepared using purified water as a dielectric liquid. Metallic nanoparticles of ytterbium, silver and copper were also prepared by the impulse plasma between a pair of the same material electrodes submerged in styrene. In addition, fullerene C₆₀ was synthesized by the impulse plasma in toluene. Nanoparticles of TiC, WC, TaC were also synthesized by the impulse plasma in styrene.     

On a stochastic demand jump inventory model

This paper considers a Quasi-Variational Inequality (QVI) arising from a stochastic demand jump inventory model in a continuous review setting with a fixed ordering cost and where demand is made up of a deterministic part (which is a function of the stock level) punctuated by random jumps. Under some restrictions on the parameters, a solution to the QVI is found which corresponds to an (s,S) policy.     

On the existence and stability of a unique almost periodic solution of Schoener’s competition model with pure-delays and impulsive effects

In this paper, we consider an almost periodic Schoener’s competition model with delays and impulsive effects. Sufficient conditions which guarantee the permanence of the model and the existence of a unique uniformly asymptotically stable positive almost periodic solution are obtained. The result of this paper is completely new. An suitable example is employed to illustrate the feasibility of the main results.     

与随机控制有关的一类变分方程(Ⅱ)

此篇借助本文（Ｉ）（见本刊Ｖｏｌ．４４,Ｎｏ．４,ｐ．７２７－７３６）的结论证明了一类变分方程解的存在性,分析了本文方法上的独特之处,指出这类变分方程在一类应用条件相当广泛的新随机控制模型的研究中起了重要作用．     

Stationary oscillation for high-order Hopfield neural networks with time delays and impulses

We investigate stationary oscillation for high-order Hopfield neural networks with time delays and impulses. In a recent paper [J. Zhang, Z. J. Gui, Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays, Journal of Computational and Applied Mathematics 224 (2008) 602-613], the authors claim that they obtain a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e. stationary oscillation) for high-order Hopfield neural networks with time delays and impulses. In this paper, we point out that the main result of the recent paper is unture, and present a new sufficient condition of stationary oscillation for the neural networks. A numerical example is given to illustrate the effectiveness of the obtained result.