On periodic solutions of nonlinear integral equations modelling infectious disease on measure chain

The modelling of the spread of infectious disease is carried out for time t on a measure chain T. Our approach unifies the continuous case and the discrete case . The model is described by the integral equation

where x(t) represents the proportion of the population infected at time t, f(t,x(t)) denotes the proportion of the population newly infected per unit time, and τ is the length of time an individual remains infectious. Using the measure chain calculus, we shall develop criteria for the existence of a nontrivial and nonnegative periodic solution for the modelling equation. The criteria can be implemented numerically, for this we shall give an algorithm as well as illustrative examples.     

Generalized projection and approximation of fixed points of nonself maps

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.     

PARALLEL DYNAMIC ITERATION METHODS FOR SOLVING NONLINEAR TIME—PERIODIC DIFFERENTIAL—ALGEBRAIC EQUATIONS

In this paper we presented a convergence condition of paralle dynamic iteration meth-ods for a nonlinear system of differential-algebraic equations with a periodic constraint.The convergence criterion is decided by the spectral expressjon of a linear operator derived form system partitions.Numerical experiments given here confirm the theoretical work of the paper.     

跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.     

双函数法及一类非线性发展方程的精确行波解

给出一种求解非线性发展方程精确行波解的新方法：双函数法。使用此方法，获得了一类非线性发展方程的许多精确行波解，其中包括孤波解和周期解，推广了文献用其它方法取得的结果，同时还获得了许多新的弧波解和周期解，借助于Mathemat-ica，此方法能部分地在计算机上实现。     

一类种群动力学模型的概周期解

文应用Liapunov泛函研究一类种群动力学模型概周期解的存在唯一性，推广了已有的相应结果.     

Almost automorphic solutions for abstract functional differential equations

For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations.     

Noncreasy and uniformly noncreasy Orlicz function spaces

We show that in Orlicz function spaces with Orlicz/Luxemburg norm the criteria for being noncreasy and uniformly noncreasy are interesting combinations of conditions.     

弱Silnikov现象中的全局分支问题

本文考虑在一条同宿于具一对纯虚特征值的鞍－焦点的轨道邻域内的分支问题，证明了在同宿分支值的邻域内，存在着可数无穷多个鞍结点分支值，倍周期分支值和２－脉冲同宿分支值，并且两相邻鞍结点分支值的比趋于常数１。     

周期性管柱信道的声波通信技术研究综述

井下声波通信技术利用周期性管柱信道实时传输声波数据,相比于其他通信方式,具有适应性好、复杂度低、传输效率高等优点,在随钻地质导向、油水井监测等方面有广阔的应用前景,是发展智能油田的关键技术之一。该文主要综述20世纪90年代以来关于周期性管柱信道物理模型、信道容量、声信号调制与接收方法等关键问题的研究历程和主要结论,并对通信系统的设计要点与国内外相关产品的现场应用进行梳理,为后续的技术改进提供依据。