NOTE ON THE OSCILLATION OF THE SOLUTION FOR GENERALIZED LIENARD EQUATIONS

Ｃｏｎｓｉｄｅｒｉｎｇｓｙｓｔｅｍ：ｘ＝φ（ｙ）－Ｆ（ｘ），ｙ＝－ｇ（ｘ）｛（Ｅ）ｉｎｗｈｉｃｈＦ（ｘ）＝∫ｘ０ｆ（ｔ）ｄｔ，ｆ（ｘ），ｇ（ｘ），φ（ｙ）ａｒｅｃｏｎｔｉｎｕｏｕｓ，ａｎｄｓａｔｉｓｆｙｔｈｅｃｏｎｄｉｔｉｏｎｓｗｈｉｃｈｅｎｓｕｒ...     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.     

关于一类二阶微分方程的振动性的注记(英文)

考虑一类具连续分布滞量的二阶非线性泛函微分方程,获得了该方程的所有解振动的充分条件.     

一维接触过程的光滑性与稳定性

本文证明了一维接触过程在适当的小扰动下，其极点平稳分布除在临界点λ＿ｃ处外总是光滑的．特别，一维接触过程本身的极点平稳分布关于其参数除在临界点处外总是光滑的．     

基于三维矩阵重构争论有向图的域间路由振荡检测算法

边界网关协议(Border G atew ay P rotoco l,BGP)是当前In ternet域间路由协议的事实标准,基于策略的路由选择过程使它不再是严格意义上的距离矢量协议,也不再具有距离矢量协议的收敛性.V aradhan指出,自治系统各自为政的策略配置方式会导致全局策略冲突,引起永久性的路由振荡.针对该问题,G riffin利用稳定路径问题(S tab le Path P rob lem,SPP)模型形式化的抽象出BGP协议行为,并以此为基础提出了一种分布式的策略冲突检测算法,尽管该算法完全避免了传统方法的缺陷,但仍然存在泄漏策略信息和对BGP协议改动太大以及浪费网络资源的问题.本文提出了一种基于安全多方计算的检测路由策略冲突的方法,用于在怀疑BGP路由发生振荡时,动态的检测系统中是否存在策略冲突.该方法采纳了G riffin的理论基础,同时由于巧妙的运用了安全多方计算协议,可以完全解决G riffin算法的问题,具有很好的实用性.     

The Lagrangian Globalization Method for Nonsmooth Constrained Equations

The difficulty suffered in optimization-based algorithms for the solution of nonlinear equations lies in that the traditional methods for solving the optimization problem have been mainly concerned with finding a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. One method to overcome this difficulty is the Lagrangian globalization (LG for simplicity) method. This paper extends the LG method to nonsmooth equations with bound constraints. The absolute system of equations is introduced. A so-called Projected Generalized-Gradient Direction (PGGD) is constructed and proved to be a descent direction of the reformulated nonsmooth optimization problem. This projected approach keeps the feasibility of the iterates. The convergence of the new algorithm is established by specializing the PGGD. Numerical tests are given. This author's work was done when she was visiting The Hong Kong Polytechnic University. His work is also supported by the Research Grant Council of Hong Kong.     

Volterra积分方程和泛函微分方程的振动性

本文建立了Ｖｏｌｔｅｒａ积分方程和一阶泛函微分方程解的振动准则．     

Extending the scope of enantiomer separation by capillary supercritical fluid chromatography on immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex)

Immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex) with a cyclodextrin content of approximately 30 % by weight, previously employed as a versatile chiral stationary phase for the separation of enantiomers by GC, has been used for the separation of enantiomers by capillary supercritical fluid chromatography (SFC). A considerable number of racemates could be resolved, e.g. aromatic alcohols, amino alcohols (TFA derivatives), and underivatized acids. Many pharmaceutical compounds were among those analyzed, including several NSAIDs (e.g. ibuprofen and ketoprofen), a steroidal drug (nor-gestrel), a barbiturate (hexobarbital), and others. Among the racemates resolved were many which cannot be analyzed by GC owing to low volatility or decomposition at elevated temperatures. For two racemates, analysis temperature and mobile phase density were systematically varied to give constant analysis times or capacity factors k. Low temperatures (ca 60 °C) yielded the best separation in term of separation factor, α, or resolution, R_s, even though higher densities had to be used. In comparison with GC, capillary SFC was able to furnish higher separation factors and similar resolution. The applicability of capillary SFC for the analysis of mixtures of cyclodextrin derivatives, e.g. those used in the synthesis of Chirasil-Dex, was, furthermore, demonstrated.     

Enantioseparation of Novel Chiral Tetrahedral Clusters on a Chiral Stationary Phase (CSP) by High Performance Liquid Chromatography

In recent years, the synthesis of chiral tetrahedral clusters has been studied extensively and various types are accessible , which are a kind of organometallic compounds with greatly growing interest due to their potential application to asymmetric reaction catalysts. As an efficient