求幂级数收敛半径的方法

指出了文 [1 ]中一个考研题的错误解法 ,并给出求幂级数收敛半径的几种方法     

一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为

对一个带有有害时滞与垂直传染的SEIR传染病模型,在脉冲免疫接种条件下,分析了其动力学行为．运用离散动力系统的频闪映射,获得了一个‘无病’周期解,证明了当模型的一些参数在适当的条件下,该‘无病’周期解是全局吸引的．运用脉冲时滞泛函微分方程理论,获得了含有时滞的持久性的充分条件,并且证明了时滞、脉冲免疫与垂直传染对模型的动力学行为能够产生显著的影响．结论表明该时滞是“有害”时滞．     

Global dynamics behaviors for new delay SEIR epidemic disease model with vertical transmission and pulse vaccination

A robust SEIR epidemic disease model with a profitless delay and verti- cal transmission is formulated,and the dynamics behaviors of the model under pulse vaccination are analyzed.By use of the discrete dynamical system determined by the stroboscopic map,an‘infection-free’periodic solution is obtained,further,it is shown that the‘infection-free’periodic solution is globally attractive when some parameters of the model are under appropriate conditions.Using the theory on delay functional and impulsive differential equatibn,the sufficient condition with time delay for the perma- nence of the system is obtained,and it is proved that time delays,pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is‘profitless’.