2+1维欧拉方程的奇异解（英文）

借助于推广的CK方法,获得了2+1维欧拉方程的等价变换和新旧解之间的关系。基于拉普拉斯方程的解,给出了构造欧拉方程某些显式解的公式,并列出了部分奇异解.利用所求出的等价变换及其求解公式,得到了2+1维欧拉方程一些随时间演化的新奇异解.     

旋转浅水和欧拉方程的渐近极限

基于测度值解的概念，研究了旋转浅水和欧拉方程的渐近极限问题.在好初值条件下，证明了当弗劳德数趋近于零时，旋转浅水和欧拉方程的测度值解收敛于旋转湖方程的经典解.     

Ait-Sahalia利率模型数值解收敛性分析

【目的】为研究一类高度非线性的广义Ait-Sahalia利率模型,对其数值解的收敛性进行证明。【方法】首先引入迭代方法证明方程存在唯一的全局正解;然后从经典欧拉(Euler-Maruyama, EM)数值格式出发,得到了广义Ait-Sahalia利率模型的驯服(tamed)欧拉数值解;最后修正方程系数所满足的条件,证明方程的驯服欧拉数值解依概率收敛于方程的解析解。【结果】对于漂移项和扩散项都高度非线性的随机微分方程,通过改进经典欧拉方法及处理方程漂移项和扩散项的系数条件,可获得具有依概率收敛性质的数值解。【结论】本研究结果可推广至其他类型的利率模型数值解研究,对金融衍生品分析和定价具有一定的指导意义。     

欧拉方程求特解的比较系数法

根据非齐次欧拉方程的解的性质,介绍一种不通过常数变异法而直接求解非齐次欧拉方程的特解的比较系数法。     

一类包含完美数的欧拉函数方程的可解性

欧拉函数方程是一类重要的丢番图方程.本研究利用欧拉函数的性质与初等数论的方法,讨论含完美数的三元变系数欧拉函数方程 φ(abc)=2φ(a)+3φ(b)+4φ(c)-k,(k=6,28)的可解性,并证明:当k=6时,该方程共有51组正整数解;当k=28时,该方程共有25组正整数解.     

三元欧拉函数方程φ(abc)=φ(a)+3(b)+5φ(c)的正整数解

研究了欧拉函数方程φ(abc)=φ(a)+3(b)+5φ(c)的正整数解,φ(n)是欧拉函数。通过初等数论中的相关知识、方法与技巧,得到了该方程的19组正整数解。     

混合型欧拉函数方程φ(abc)=2φ(a)φ(b)+8φ(c)的正整数解

利用初等数论方法及欧拉函数有关性质,研究三元变系数混合型欧拉函数方程φ(abc)=2φ(a)φ(b)+8φ(c)正整数解的问题.结果得出了该方程共计95组正整数解.     

用函数变换法求解二阶欧拉方程

通过“函数变换”将二阶欧拉方程降阶为可积的一阶线性微分方程,从而得到其积分形式的通解,还得到了一类非齐次欧拉方程特解的简单公式。该方法比用“自变量代换”法将欧拉方程转化为常系数线性微分方程进而求其解的过程更简单、更直接。     

一个包含完全数的非线性欧拉函数方程的解

讨论了一个包含完全数的非线性欧拉函数φ(n)的方程φ(mn)=4φ(m)+7φ(n)+28的解。利用完全数的性质、整数的分解以及欧拉函数φ(n)的性质给出方程全部25组解。     

三元变系数欧拉函数方程φ(abc)=2φ(a)+3φ(b)+4φ(c)的正整数解

研究了欧拉函数方程φ(abc)=2φ(a)+3φ(b)+4φ(c)的可解性问题,其中φ(n)为欧拉函数.利用初等数论相关内容,提出求解该方程的新的数学技巧,得到该方程所有共计70组正整数解.该方程的求解方法可用来解决类似的欧拉函数方程问题.     

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.     

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     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

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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