SE（3）群上Newmark格式几何积分及其应用

常微分方程时间积分的Lie群方法是近年来学术研究的热点问题,但这些方法一般都针对任意的抽象Lie群,几何上不直观．机器人操作臂刚体运动可以用特殊欧氏群SE（3）来描述．SE（3）群是一个典型Lie群．因此,机器人动力学仿真问题就是Lie群SE（3）上的数值积分问题．文中将R^3上经典数值积分Newmark法推广到特殊欧氏群SE（3）上,运用Lie群理论得到New-mark积分在SE（3）上的数学表达．利用刚体运动的几何特点,给出了SE（3）群上Newmark格式积分的直观的几何解释．为了说明该方法的应用,推导出一般开链多体系统Newmark格式几何积分的具体积分步骤．文中提出的方法避免了Euler角参数化带来的内在的奇异性,而且由于利用了SE（3）底层的流形结构,该方法避免了四元素法采用四个参数带来的额外的计算量．数值计算结果表明该方法是有效的．     

常规三阶常微分方程在对称群作用下的可积性

针对常规三阶微分方程的可积性,采用一种不同于降阶、消元的新方法,利用对称群理论,采用将三阶常微分方程作用在Lie群上的方法,通过一个变换将方程组的任意解映成该方程组的另一个解,求出Lie群生成元,得到首次积分,进而分析微分方程的可积性.研究结果表明:常规三阶微分方程在对称群作用下不可积,同时也将研究对象从二阶微分方程拓展到三阶微分方程.     

一类改进Boussinesq方程的Lie对称群及群不变解

利用经典Lie群方法研究一类改进Boussinesq方程的Lie对称群的存在性及相应的群不变解,证明了改进Boussinesq方程存在3-参数的Lie对称群,并得到了该方程的一些行波解和非行波解.     

准坐标下完整力学系统Lie对称性的共形不变性与守恒量

研究准坐标下完整力学系统Lie对称性的共形不变性与守恒量.引入无限小单参数变换群及其生成元向量,定义准坐标下完整力学系统动力学方程的Lie对称性的共形不变性,借助Euler算子导出Lie对称性共形不变性的条件,给出其确定方程,讨论共形不变性与Noether对称性、Lie对称性以及Mei对称性之间的关系,利用规范函数满足的结构方程得到系统相应的守恒量,举例说明结果的应用.     

非自治广义Birkhoff系统的Poisson理论

研究了非自治广义Birkhoff方程的代数结构,证明非自治广义Birkhoff方程具有相容代数结构和Lie容许代数结构;建立了非自治广义Birkhoff系统的Poisson理论,包括建立系统的Poisson条件,证明了在一定条件下可由已知第一积分得到新的第一积分;讨论了与非自治广义Birkhoff系统的Poisson方法相关的动力学逆问题.结果具有普遍性,非自治Birkhoff系统的情况是该结果的特殊情况.文末举例说明了结果的应用.     

具有双不变拟Riemann度量的Lie群

本文讨论了其有双不变拟Riemann度量的Lie群及其等距变换群的一些性质,证明了:1)具有双不变拟Riemann度量的Lie群的等距变换群一定非单;2)具有双不变拟Riemann度量的Lie群半单的充要条件是其等距变换群半单且非单.     

常微分方程组接受单参数李群的判定条件

通过引入常微分方程组变量的无穷小变换,给出自治与非自治常微分方程组接受单参数李群的判定条件,从而推广了管克英等关于自治常微分方程组接受单参数李群的充要条件.     

基于Lie群的机器学习理论框架

借用具有良好数学结构的Lie群来研究机器学习,提出了基于Lie群的机器学习(ML)基本概念、对偶空间学习概念等,形成了基于Lie群的学习理论框架.该理论框架可以用代数和几何的方法来描述机器学习系统,弥补了原有机器学习理论的不足.     

用双参数李变换群积分一类非完整系统的运动方程

研究了一类简单的非完整非自治系统，利用双参数李变换群，引进微分不变量、正则坐标的方法，对这类简单的非完整非自治系统的运动方程给以完全积分，为非完整系统的积分理论提供了一种新的方法。     

Lie群上的最速下降算法

通过对Lie群及其Lie代数的基本性质及特殊结构的分析,提出了求解一般Lie群上优化问题的最速下降算法,并对算法的收敛性作了一定的分析.得到了该算法全局收敛的两个充分条件,并在一般框架下证明了该算法至少线性收敛.通过上Riemann质心的计算问题,证明该算法可行有效.     

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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