常曲率空间中平均曲率为常数的迷向子流形

设M~α是n维黎曼流形,S~(n+p)(C)是(n+p)维截面曲率为常数C的黎曼流形,设f:M~n(?)S~(n+p)(C)是具有常中曲率H的迷向浸入,设K和R分别是M~n的截面曲率的下确界和数量曲率。本文给出K和R满足一定的关系,从而得到这种子流形是全脐子流形的几个充分条件。     

空间形式S^n＋p（C）中的全脐子流形

设M~n是空间形式S~(n p)(c)中具有平行中曲率向量的正曲率紧致子流形,其中p>1。在[1]中,我们给M~n的数量曲R率以下界,即R≥n/(3p-5)[(3p-5)n-(4p-6)](c H~2)则M~n是S~(n p)(c)的全脐子流形。本文给R以上界,则仍有M~n是S~(n p)(c)的全脐子流形。     

低维的迷向子流形

设^-M^n p(c）是单连通空间形式，M^n(n≤4)是^-M^n p中具有常平均曲率H的紧致连通迷向子流形；本文证得如下结果：若M的截面曲率KM≥n/2（n 1)(H^2 c），则M是全脐的或是^-M^n p中某个全脐超曲面中的Veronese流形。     

球面中的紧致极小子流形

<正>对于球面中的紧致极小子流形,一个基本的问题是它具有什么样的性质?S.T.Yau在[1]中从截面曲率的角度,讨论了这个问题,N.Ejiri[2]从Ricci曲率的角度研究了这种子流形,得出:“设M是一浸入在n+p维球面S~(n+p)中的n维单连通紧致定向的极小子流形,且其浸入是满的,如果n≥4,且M的Ricci曲率≥n-2,则M或是全     

伪球面及其子流形的一些性质

(n+p)一维伪球面H~(n+p)(-a~2)是指具有负常数截面曲率-a~2的完备、单连通的双曲空间。近来已有一些文章讨论伪球面上子流形的性质。本文采用在黎曼流形中引入半对称度量联络的方法来研究H~(n+p)(-a~2)及其子流形,得到共形平坦子流形为全脐点的一个条件。     

单位球面低维子流形的Pinching定理

设M是n p维单位球面S~(n p)的n维紧致子流形,n=2,3,4;M具有平行平均曲率向量,若M的第二基本形式长度的平方S≤(2/3)n处处成立,则M是全脐点的或Veronese曲面。     

球面中常平均曲率子流形

本文将陈省身和Yau的定理推广到完备子流形的情形和M~n是全脐子流形的情形,得到如下定理。定理1 设M~n(n≥2,是S~(n+p) (1) (P>((n-1)(n-2))/2)中完备的极小子流形,如果supS≤n/(2-(2/((n-1)(n-2))))则M~n是全测地的或supS=n/(2-(2/((n-1)(n-2)))) 定理2 设M~n(n≥2)是S~(n+p) (1) (P>(((n-1)(n-2))/2)中具有平行平均曲率向量的紧致子流形,如果M~n的截面曲率为正且S<((((1+H~2)n)/2-(1/(q-1)))+nH~2),则M~n是全脐子流形。(q=((n-1)(n+2))/2) 其中M~n是浸入在单位球面S~(n+p) (1)中的n维子流形,S是M~n的第二基本形式长度平方,H是M~n的平均曲率。     

欧氏空间中全拟脐子流形

令Rn+p为(n+p)维欧氏空间,而Mn为Rn+p中n维定向的等距浸入紧致无边子流形.记ξ为Mn的单位平均曲率向量场,而Hi为Mn沿 ξ方向的i-平均曲率.如果存在一个整数r(1≤r≤n-1)使得Hr和Hr+1均为非零常数,则Mn必全拟脐.     

球空间具平行单位平均曲率向量的完备子流形

设M是n维完备黎曼流形,等距浸入(n+p)维单位球空间Sn+p,具有平行的单位平均曲率向量.则或者M局部地是Sn+p的一个(n+1)维全测地子流形Sn+1中的超曲面片;或者supSa≥n.其中supS是M的第二基本形式长度的平方的上确界.进一步,若n≤7,或者M整体地是Sn+p的一个(n+1)维全测地子流形Sn+1中的超曲面;或者supS(1+12sgn(p-2))>n.所得结果推广了具有平行的平均曲率向量的紧致子流形的结果.     

具有平行平均曲率向量的伪脐子流形的Pinching定理

设M2n p q是n p q维δ-pinching黎曼流形,M1n p(c1)为M2n p q中的n p维常曲率为c1的子流形,设Mn为M1n p(c1)中具有平行平均曲率向量的紧致伪脐子流形.本文给出Mn是M1n p(c1)的全脐子流形的几个充分条件.     

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     

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