上海师范大学数理信息学院数学学科与动力系统方向创新团队简介

动力系统是一门应用十分广泛的交叉学科．这门学科以常微分方程理论为基础，近几十年来迅速发展并受到广泛重视，在解的基本理论、稳定性理论、周期解理论、解算子理论、分岔理论等许多方面都出现了重要成果，并在科学技术的诸多领域得到广泛应用．因此，动力系统的研究既是一件非常有意义的工作，也是一个富有挑战性的前沿方向．含参数微分系统（可能是二维或高维系统，也可能是无穷维系统）一般有两类，即正常扰动与奇异摄动．对这些系统的研究一般有理论分析和数值方法两种，这两学科互相促进又互相补充．     

模糊逼近算法与人工神经网络预测功能

有些实际问题是无法用已知的很多定量预测方法预测的，这更是在预测中有极大局限性的人工神经网络难以解决的问题．本文通过对预测问题模糊逼近算法的研究，提出新的模糊逼近泛函微分方程定量预测方法，并从而化为能用人工神经网络预测的方法，扩充人工神经网络解决实际问题的功能．     

周期变系数常微分方程动力系统稳定性分析的Liapunov指数判据

对于周期变系数常微分方程(组)描述的动力系统,建立了稳定性分析的Liapunov指数的判别准则当其动力系统的全部Liapunov特征指数小于零时,动力系统就是稳定性的;否则,如果动力系统中只要有一个Liapunov特征指数大于零,则动力系统就丧失稳定性．这一判别方法对于高维变系数常微分方程动力系统,相对于稳定性分析的Floquet经典方法而言,具有计算量小和定量搜索方便等优点．     

一个非线性偏微分方程的孤立波

用动力系统分支方法研究了一个非线性偏微分方程，给出了参数空间的划分，在各种参数条件下得到了孤立波的个数，在某些参数条件下得到了孤立波解的解析表达式．     

一类时滞方程的近似解

研究了一类时滞微分方程的近似解问题．对于一类带阻尼和一般力的时滞微分方程问题求得一致有效渐近展开式,给出了共振解筒洁的近似解析表达公式．应用该公式,大量工程中的时滞动力系统共振问题可方便地得到近似解析解以及振幅、频率、周期和相位等．所得结果使文[1～3]等的研究结论成为筒单推论．     

周期变系数常微分方程动力系统稳定性分析的Liapunov指？…

对于周期变系数常微分方程（组）描述的动力系统,建立了稳定性分析的Ｌｉａｐｕｎｏｖ指数的判别准则,当其动力学系统在全部Ｌｉａｐｕｎｏｖ特征指数小于地,动力系统就是稳定性的,否则,如果动力系统中只要有一个Ｌｉａｐｕｎｏｖ特征指数大于零,则动力系统就丧失稳定性,这一判别方法对于高维变系数常微分方程动力系统,相对于稳定性分析的Ｆｌｏｑｕｅｔ经典方法而言,具有计算量小和定量搜索方便等优点。     

非线性动力系统刚性方程精细时程积分法

讨论了非线性动力系统刚性常微分方程的数值积分算法，给出了非线性动力系统刚性方程的单步精细时程积分法，揭示了精细时程分不仅具有显式积分格式，而且具有绝对稳定性和高精度的特点，避免了刚性方程的计算危险性，算例进一步表明了精细时程积分算法求解刚性方程的有效性。     

等离子体阴极鞘层电子输运过程的随机模拟

提出了描述电子运动的动力系统模型,应用模糊数学方法,建立了随机向量过程的随机度函数概念,用ＭｏｎｔｅＣａｒｌｏ方法对氦直流辉光放电平板阴极中电子输运过程进行了计算机随机模拟和数值分析,对电子运动若干因素及特征作了较为细致的刻划．结果与实验相符．     

害虫治理与半连续动力系统几何理论

从害虫治理的实际问题出发,建立了一类脉冲状态反馈控制害虫的防治模型.提出了半连续动力系统几何理论,并应用这一理论证明了该模型至少存在一个阶1周期解.结合具体实例,介绍了阶1同宿分支和脉冲环面动力系统的基本理论与分析方法.     

不确定分数阶微分方程理论与应用研究进展

具有记忆性及历史相关特性的不确定分数阶微分方程，自2015年被提出以来，被广泛应用于不确定动力系统演化过程的建模，因此，对该类方程的研究已然成为一个重要课题。该文介绍了不确定分数阶微分方程的定义与性质，总结了近年来关于不确定分数阶微分方程理论与应用方面的研究进展，并对不确定分数阶微分方程未来的研究方向进行了展望。     

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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