求解P0函数互补问题的一种微分方程方法

本针对P0函数互补问题，给出了一种微方程方法，并且证明了P0函数互补问题的解是微分方程系统的渐进稳定平衡点。在适当的假设条件下，证明了所给出的算法具有二次收敛速度。几个数值例子表明了该算法的有效性。     

变换中含有孤立稳定点的第二积分换元定理

在不定积分第二积分换元定理的条件中,要求变换x=φ(t)不含有稳定点,即:φ′(t)≠0.当变换x=φ(t)中含有孤立稳定点时,给出了变换中含有孤立稳定点的第二积分换元定理.拓宽了第二积分换元定理的应用范围.     

Brick Walls for Nonstationary Black Holes

The validity condition of the brick-wall model is analysed in nonstationary space-time.It is shown that the model holds only in thin regions,only by using tortoise coordinates near the event horizon of a slowly varying(quasistationary)black hole.The reason for the use of tortoise cooridnates is that the stationary state solutions of quantum field equations in other coordinates do not exist for any region in nonstationary space-time.Meanwhile,the quantum corrections to the entropy of the Vaidya-Bonner black hole due to the spin fields are calculated in terms of the brick-wall model.     

全局半稳定的三次系统

当每个解都正向趋于零时,本文证明,虽然二次系统的奇点必为渐近稳定,但是在同样的条件下,某些三次系统的奇点能够是不稳定的.     

STABLE SOLUTION OF TIME DOMAIN INTEGRAL EQUATION METHODS USING QUADRATIC B-SPLINE TEMPORAL BASIS FUNCTIONS

This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.     

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.     

向量变分不等式的严格可行性问题

本篇文章首先定义了向量变分不等式的严格可行点概念,其次在假设了映射是强(D)-伪单调的情况下,证明了向量变分不等式解集非空有界与其严格可行点存在的等价性问题,推广了在数量变分不等式上得到的相应结果．     

Synchronization of Chaotic Storage-Ring Free-Electron Laser by Bi-Directional Coupling Scheme with the Coupling Strength Varied Periodically

We analyse the chaotic dynamics of storage-ring free-electron lasers and report a bi-directional coupled scheme with the coupling strength varied periodically to synchronize two chaotic storage-ring free-electron lasers. The period is the same as the period of system＇s external modulation. ,The possibility of synchronization is proven according to the Lyapunov stability theory. The results of numerical simulation are obtained. Both the numerical simulation and theoretic analysis show that two storage-ring free-electron lasers can be controlled in the synchronization in a short time with this method.     

具功能反应的三种群捕食者——食饵系统数学模型稳定性的研究

[1]中提出了具有功能反应的三种群捕食者——食饵系统的两种模型(Ⅰ)、(Ⅱ),并给出了局部渐近稳定的条件。本文研究了另外两种模型(Ⅲ)和(Ⅳ)的局部渐近稳定的条件。     

拉长截面等离子体垂直位移不稳定性及其动力稳定

本文研究了拉长截面Tokamak上等离子体的垂直位移不稳定性。计算表明,其快速振荡部分由周围导体中感生的涡流稳定;其慢速漂移部分则需由主动稳定系统予以控制。本文提出一种动力稳定的方法。它在物理上是可行的,并具有技术上简单、较低的功率要求及有利的频率效应等优点。这些说明,这种动力控制方法是一种有吸引力的控制垂直位移不稳定性的手段。