A nonlinear inequality and application to global asymptotic stability of perturbed systems

The goal of this work is to present a new nonlinear inequality which is used in a study of the Lyapunov uniform stability and uniform asymptotic stability of solutions to time‐varying perturbed differential equations. New sufficient conditions for global uniform asymptotic stability and/or practical stability in terms of Lyapunov‐like functions for nonlinear time‐varying systems is obtained. Our conditions are expressed as relation between the Lyapunov function and the existence of specific function which appear in our analysis through the solution of a scalar differential equation. Moreover, an example in dimensional two is given to illustrate the applicability of the main result. Copyright © 2014 John Wiley & Sons, Ltd.     

The contribution of K.-H. Elster to generalized conjugation theory and nonconvex duality

This article surveys the main contributions of K.-H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization.     

二次概周期系数微分方程的概周期解

利用指数二分性,Schauder不动点定理和Grownwall不等式证明了一类概周期系数微分方程的概周期解、有界解的存在唯一性及概周期解的全局吸引性.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

一个R2上含双曲函数核的Hilbert型不等式

通过引入参数,构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开,建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用,通过赋予参数不同的值,建立了一些有意义的特殊结果。     

NA序列部分和的矩完全收敛性

讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果.     

运用Poincaré-Miranda定理数值验证变分不等式解的存在性

本文运用Poincaré-Miranda定理数值验证变分不等式问题解的存在性.证明这一新方法相对于已有的方法更具有普遍性,并通过数值例子说明本方法的高效性.     

Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach

Recent simulation results imply the lowering of the ground-state correlation energy per counterion at a charged planar wall, compared with that of the 2D and 3D one-component plasma systems. Our aim is to correctly evaluate the ground-state energy of strongly-coupled counterion systems by considering a quasi-2D bound state where bound counterions are confined to a layer of molecular thickness. We use a variational approach based on the Gibbs-Bogoliubov inequality for the lower-bound free energy so that the liquid-state theory can be incorporated into the formulations. The soft mean spherical approximation demonstrates that the lowered ground-state energy can be reproduced by the obtained analytical form of a quasi-2D bound state.     

Exploiting the Massey Gap

In this paper, we find new refinements to the Massey inequality, which relates the Shannon and guessing entropies, introducing a new concept: the Massey gap. By shrinking the Massey gap, we improve all previous work without introducing any new parameters, providing closed-form strict refinements, as well as a numerical procedure improving them even further.