Almost periodic solutions of discrete Volterra equations

For discrete Volterra equations with or without delay, we obtain several results concerning almost periodic solutions and asymptotically almost periodic solutions under certain conditions. We also investigate the relations among solutions of equations discussed and give an example to illustrate our results.     

A noniterative algebraic solution for Riccati equations satisfying two-point boundary-value problems

A noniterative algebraic method is presented for solving differential Riccati equations which satisfy two-point boundary-value problems. This class of numerical problems arises in quadratic optimization problems where the cost functionals are composed of both continuous and discrete state penalties, leading to piecewise periodic feedback gains. The necessary condition defining the solution for the two-point boundary value problem is cast in the form of a discrete-time algebraic Riccati equation, by using a formal representation for the solution of the differential Riccati equation. A numerical example is presented which demonstrates the validity of the approach.The authors would like to thank Dr. Fernando Incertis, IBM Madrid Scientific Center, who reviewed this paper and pointed out that the two-point boundary-value necessary condition could be manipulated into the form of a discrete-time Riccati equation. His novel approach proved to be superior to the authors' previously proposed iterative continuation method.     

受迫Li\''{e}nard方程周期解的存在唯一性

本文利用整体反函数理论证明了受迫Li\'{e}nard方程$x'+f(x)x'+g(t,x)=e(t)$周期解的存在唯一性，推广和改进了现有的结果.     

Banach空间中二阶微分方程的周期边值问题

本文在Banach空间中研究了二阶非线性微分方程的周期边值问题:-u″=f(t,u),u(0)= u(2π),u′(0)=u′,(2π)在上下解反向给定时,利用半序理论和新的比较原理,证明了该周期边值问题最小解和最大解的存在性,解的唯—性,并给出了唯一解的近似迭代序列的误差估计式．     

Reflection, transmission and circular dichroism in axially excited slab of a copper thin film helicoidal bianisotropic medium

The reflectance, transmittance and circular dichrosim in a chiral sculptured copper thin film slab of 1000-1600 nm thickness in near infra-red and visible regions based on the relative permittivity of copper in the bulk state and volumetric fraction of copper inclusion of 0.2 are obtained. At higher volumetric fraction of metallic inclusions the reflection (due to low circular Bragg phenomenon) and transmission coefficients (due to increased absorption) are too small, while for thicker slabs numerical instabilities (overflow/underflow) occur in the computation. Therefore it is recommended that the chiral sculptured thin film slab to be considered as a half space.     

一类具有偏差变元的泛函微分方程周期解的存在性

利用重合度理论研究了一类具有偏差变元的泛函微分方程周期解的存在性问题,得到了该方程具有周期解的一些充分条件.结论丰富了现有文献的结果.     

具有变时滞高阶细胞神经网络的振荡性分析

利用不动点理论和微分不等式分析等技巧,研究了变时滞高阶神经网络概周期解存在性与全局指数收敛性,并且给出了一些新的判别准则.     

Global periodic attractor of a class of third-order phase-locked loop

The uniform boundedness and existence of a global periodic attractor for a third-order phase-locked loop with general phase detector characteristics and frequency modulation input is proved under some parametric conditions. Project supported by the National Natural Science Foundation of China.     

EXISTENCE OF THE UNIFORMLY ULTIMATE BOUNDED SOLUTIONS AND PERIODIC SOLUTIONS

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