李雅普诺夫第二方法在二阶线性偏微分方程中的应用

本文将常微分方程稳定性理论中的Lyapunov第二方法应用到偏微分方程中去,着重讨论了二阶线性偏微分方程混合问题解的唯一性与稳定性;得到了三个唯一性与稳定性的定理;并通过实例说明定理的应用, 由于Lyapunov泛函比传统方法中的“能量函数”广泛得多,因而用选取适当的泛函V证明混合问题解的唯一性与稳定性要比文[1][2]中的证明简单而且广泛.     

一类具有扩散的传染病模型的渐进稳定性

讨论了具有空间扩散的传染病系统在齐次Neumann边界条件下解的整体性态.通过线性化方法给出了局部渐近稳定条件,通过构造 Lyapunov函数给出了全局稳定性的证明.     

一类三阶非线性系统的全局渐近稳定性

李雅普诺夫第二方法是研究非线性系统稳定性的基本方法之一,而Lyapunov函数的构造是解决问题的关键.本文运用"类比法"对非线性系统x g(x)x f(x,x)x h(x)=0,构造了较好的Lyapunov函数,得到其平凡解全局渐近稳定的条件,并且证明中脱离了对Lyapunov函数无穷大性质的约束,推广了旧有的结果.     

一类具有潜伏期的水源性疾病模型的稳定性

研究一类具有潜伏期的水源性疾病模型的稳定性,利用再生矩阵方法计算出基本再生数R0,并进一步通过构造Lyapunov函数证明无病平衡点和地方病平衡点的全局稳定性.     

调度策略中的稳定性证明

在实际应用中，讨论调度策略的稳定性至关重要。以往研究在给出时清空最大缓冲器调度策略稳定性的证明时，证明复杂、繁琐。笔利用动态系统的Lyapunov理论，给出了调度系统中的Lyapunov函数，证明清空最大缓冲器调度策略稳定性。     

带跳时滞随机微分方程E-M方法指数稳定性

研究带跳时滞随机微分方程Euler-Maruyama方法的指数稳定性.在全局Lipschitz条件及解析解和数值解在均方有界的条件下,证明SDDEJs的指数稳定性的充要条件是Euler-Maruyama方法下构造的数值解是指数稳定性的.避免寻找Lyapunov函数的困难,将指数稳定性的等价关系推广到带跳情形.     

Matlab在判断平面自治系统零解稳定性中的应用

旨在研究一类难以找到合适的Lyapunov函数的自治系统的零解稳定性问题.从零解稳定性的几何特征出发,基于零解稳定性理论,通过Matlab编程,结合平面自治系统的具体实例,在相平面上绘制出相应系统在原点附近的线素场,观察其走向,以此来分析零解的稳定性.然后,再利用Lyapunov第二方法,从理论上对得到的结论加以证明....     

T-S模糊广义系统稳定性分析及控制器设计

针对T-S模糊离散广义系统稳定性判别条件严格,不具备更好适用性等问题,提出一种优化判据的新方法.该方法利用模糊Lyapunov函数分析了T-S模糊离散广义系统的稳定性问题,经过推导得出了更具一般性的稳定充分条件,并对得到的结论予以严格的数学证明;基于并行分布补偿(PDC)设计了模糊控制器,在原有T-S模糊模型的基础上,引入了Lyapunov函数,然后根据稳定性判别表达式不同的处理方式,提出了更宽松的T-S模糊离散广义系统稳定性判别条件,并对推论进行了证明.对T-S模糊离散广义系统的稳定性问题的优化,使得模糊离散广义系统具有更好的通用性,更贴近实际及更稳定的控制作用.     

受媒体报道影响的离散传染病模型的分析

研究了一类受媒体报道影响的离散传染病模型.通过归纳法证明了解的正性,得到了解的有界性.利用线性化方法分析了无病平衡点和地方病平衡点的局部稳定性,并通过构造Lyapunov函数证明无病平衡点的全局稳定性及特殊情况下地方病平衡点的全局稳定性.通过数值模拟验证了当基本再生数R₀<1时无病平衡点全局渐近稳定,当R₀>1时地方病平衡点全局渐近稳定.     

飞机全电刹车系统滑移率约束反演滑模控制

针对滑移率控制中要求保持刹车工作点的稳定性问题,提出基于障碍Lyapunov函数的反演滑模控制方法并应用于飞机全电刹车系统.考虑机电作动器的非线性特性,建立系统的状态空间模型并简化为严格反馈形式,将刹车系统的控制稳定性问题等效描述为含输出约束的系统镇定问题.根据反演控制思想,采用障碍Lyapunov函数方法获得刹车压力控制律,实现对滑移率的边界约束,并设计无抖振非奇异快速终端滑模控制器应用于机电作动机构,实现对参考刹车压力的快速跟踪.通过Lyapunov方法证明闭环系统稳定性,HIL实验结果表明控制策略的有效性.     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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