广义的Fan-Ha截口定理

为了进一步研究极小极大不等式,首先引进了H-空间,将极小极大定理中的闭性条件与凸性条件进一步削弱,利用反证法与有限交性质将Fan-Ha截口定理以及极小极大定理推广为非线性H-空间上更一般的形式设(X,{ΓA}),(Y,{ΓD})为2个HausdorffH-空间,BCX×Y,且满足如下条件a.对每个x∈X,{y∈Y,(x,y)B}为H-凸集或空集.b.对每个y∈Y,{x∈X,(x,y)∈C}为X中的紧闭集.c.对每个x∈X,存在AxX×Y,Ax=Px×Qx.其中Px为X中的紧闭集,Qx为Y中的紧集.d.又假设存在X的非空紧集K,对每个X的有限子集N,存在X的紧子集LN,LNN,使得①对每个y∈Y,LN∩{x∈X,(x,y)∈Az,对所有z∈LN}是零调的;②对每个x∈LN＼K,{y∈Y,(x,y)∈Az,对所有z∈LN}{y∈Y,(x,y)∈B};e.对每个x∈K,{y∈Y,(x,y)∈Az,对所有z∈X}=.则存在x0∈X,使得{x0}×YC.利用广义的Fan-Ha截口定理,容易将参考文献[1]中的所有结论推广到H-空间上.     

S-凸性与局部S-凸空间

本文以L~s[0,1](0相似文献   

凸度量空间中的不动点和最佳逼近

讨论了凸度量空间上不动点的存在和最佳逼近问题.主要得到以下结论:设(X,d)是一个凸度量空间,F是X的非空闭子集,T:F→X是一个连续映射且T(F)包含于X的一个紧子集D中,则T有不动点当且仅当对每一个ε>0,T具有ε-不动点;设(X,d)是一个完备的一致凸度量空间,M是X的一个闭凸集,如果对每一个x∈X,PM(x)是单点集,那么最近点投影P:X→M是连续的;设(X,d)是严格凸度量空间,MX是非空闭集,且是T-正则的,如果T是紧自映射且u∈X使d(T(x),u)≤d(x,u),x∈M,那么M中每一个u的最佳逼近点都是T的不动点.     

一个距离空间

本文在一个给定的距离空间的基础上,构造一个新的距离空间,进一步讨论两个空间之间的关系及新距离空间的一些性质。 设E是一个以d为距离函数的距离空间,而且d是有界的,即存在一个正数M使对任意的x,y∈E有d(x,y)≤M。令F(E)表示E的一切非空闭子集所组成的集合,现在我们就在F(E)上定义一个距离函数h。若X、Y∈F(E)令     

局部凸拓扑矢量空间内的广义拟变分不等式

设X是局部凸空间E的仿紧凸子集 ,F :X→ 2 X 是集值映象 ,φ :X×X→R是实泛函 .研究下列抽象广义拟变分不等式 (AGQVI) :求 ^x∈X使得 ^x∈F(^x)和 φ(^x ,y)≤ 0 , y∈F(^x) ,其中 φ(x ,y)关于x是 0 转移紧下半连续的和关于y是 0 对角拟凹的 .作为应用 ,作者得到了最近文献中关于广义拟变分不等式的很多已知结果的推广 .     

系统中的均衡态问题--Kakutani 不动点定理的应用

本文讨论 Kakutani定理在对策理论中的应用 .Kakutani定理　设 X是 Rn中的一个有界闭凸集 .对于每一点 x∈X,若 F( x)是 X的一个非空凸子集 ,当 {( x,y) | y∈F( x) }是闭的 ,则在 X中一定有点 x*,使得x*∈F( x*) .此定理中所指的 x*,在对策理论中 ,对于所有的参与者 ,给出了最     

局部凸空间中的半连续映射

文中得到如下结果: 定理1 设1)X是Z的不空凸子集,K∈2~Z;2)g:X×X→Z使得X_(λg)是u·s·c;3)对于任一x∈X,集Ex是不空凸的,如果X是紧的,则有x∈X使g(x,x)∈K。 定理2 设i)定理1的条件中的设1)、2)被满足,但以g1代g;ii)有紧集M X,使得对于任一x∈X,{y∈M/g1(x,y)∈K}是不空凸的。如果X是拟完备的,则有x∈X使g(x, x)∈K。 定理3 设i)定理1条件中的设1)、2)、3)被满足;ii)X是拟完备闭的。如果有紧集M∈2~Z及α∈X°,使得对于任一x∈X,恒有满足(9)的y∈M。则有x∈X使得g(x,x)∈K。     

一个不动点原理的拓广定理

由完备距离空间X→X的压缩映象F的一意不动点问题,S.Banach的著名定理考虑的条件是: ρ(Fx,Fy)≤αρ(x,y) (0<α<1,x,y∈X) 近十几年来,对于这种不动点问题又有一些研究。有的数学家从改变常数α为函数α(t)出发,得出了花样繁多的结果。 1968年,F.E.BROWDEr考虑的是:完备距离空间X的闭子集D,设D的直径为d,算子F:D→D满足条件     

关于联合可逼近子空间和的一个注记

设G是Banach空间X的闭子集.G称为在X中是联合可逼近的(simultaneously proximinal),如果对每个有界集A■X,都存在g∈G,使得d(A,G)≡inf_(u∈G)sup_(a∈A)‖a-u‖=sup_(a∈A)‖a-g‖.证明了Banach空间中的弱紧凸集与联合可逼近凸集的和是联合可逼近的.作为推论,证明了对于Banach空间X的自反子空间F和联合可逼近子空间G,如果F+G是闭的,则F+G是联合可逼近的.     

另一类广义双拟变分不等式

设2~X是X的非空子集全体所成之集合,E,F是Φ上的拓扑矢量空间(Φ是实数域R或复数域C),(·,·):F×E→Φ为双线性泛函,X是E的非空子集,S:X→2~E和M,T:X→2~F是集值映象和f:X×X→R.则广义双拟变分不等式问题(GBQVIP)是y∈X,使得y∈S(y)和inf Re(f—w,y—x)+f(y,x)≤0,x∈S(y)和f∈M(y).最近Shih-Tan在X为紧凸集和f≡0的情形下研究了上述GBQVIP解的存在性.本文讨论另一类双拟变分不等式问题,即找y∈X,使得y∈S(y)和(f—w,y—x)+f(y,x)≤0,x∈X和f∈M(y).得出了几个变分不等式和GBQVIP解的存在性定理.这些定理改进和推广了Ding-Tan的结果     

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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