希尔伯特空间中关于保持距离的Aleksandrov问题

设X和Y是希尔伯特空间,T:X→Y为一映射,证明了若T保1和另外一个实数,则T是一个线性变换,从而部分解决了Aleksandrov问题.     

诱导模糊拓扑空间的映射性质

1975年,M.D.Weiss给出了分明拓扑空间(X.T)的诱导模糊拓扑空间(X.ω(T))的定义。并得到了分明拓扑空间和与之相应的诱导模糊拓扑空间之间关于连续性,紧性和连通性相互关系的几个有趣的性质。例如,映射f:(X.ω(T))→(Y,ω(T~*))是模糊连续的当且仅当f:(X,T)→(Y,T~*)是连续的。本文继续M.D.Weiss在这方面的工作,引入了模糊商映射、模糊紧映射、模糊强完备映射、模糊半闭映射、模糊保紧映射和模糊连通映射诸概念。证明了f:(X,ω(T))→(Y,ω(T~*))是模糊紧映射(相应地,模糊强完备映射,模糊半闭映射或模糊连通映射)当且当仅f(X,T)→(Y,T~*)是紧映射(相应地,强完备映射,半闭映射,连通映射)。如果(Y,T)是T_2空间,则f:(X,ω(T))→(Y,ω(T~*))是模糊保紧映射当且仅当f:(X,T)→(Y,T~*)是保紧映射。     

SOME PROPERTIES OF SUPER-DECOMPOSABLE OPERATORS

In this paper,the following main resvlts have been proved:1.Let T∈B(X) be a super-decomposable operator,then for any hyperinvariant subspace Y of T,the operator T/Y is super-decomposable.2.The operator T∈B(X) is super-decomposable if and only if T/Y is super-decomposable for any hyperinvariant subspace Y of T.3. If T∈B(X) has on open spectral resolvent,then T is superdecomposable.     

关于几类非正常算子

我们在研究亚正常算子时,注意到对Hilbert 空间中的算子T 的直角分解T=X+iY 有下面的恒等式(T-z)~*(T-z)=(X-x)~2+(Y-y)~2+i[X,Y],(1)这儿z=x+iy,[X,Y]=XY-YX,而亚正常算子的许多性质是由(1) 和条件i[X,Y]≥0. (2)导出的.同样在研究半亚正常算子时,我们对算子T 的极分解T=UP 有下面的恒等式     

三角代数上的导子

设R是有单位元的交换环,A,B是R上的单式代数,M是非零(A,B)-单式双模,且作为A,B-模都是忠实的.记T=(A M0B)={(a m0b)a∈A,b∈B,m∈}M为A,B,M构成的三角代数.利用三角代数T上导子的性质,给出T上分别满足广义恒等式D([X,Y])=k[X,Y]和D([X,Y])=k[D(X),Y]的导子结构,以及满足广义恒等式D(X。Y)=kX。Y和D(X。Y)=kD(X)。Y的导子结构,其中k为R中单位.     

半群Q(F,k)的极大正则子半带

设T(X)是X上的全变换半群且Y是X的子集,令F(X,Y)={α∈T(X)|Xα■Yα■Y}.当|Y|=n≥4,对2≤k≤n-1,研究了半群F(X,Y)的理想Q(F,k)={α∈F(X,Y)||im(α)|≤k},得到了它的极大正则子半带的完全分类.     

矩阵方程AX＋YB＝D及AX＋XA＝D的最优解

本文考虑如下问题问题Ⅰ.给定A∈Rm×n,B∈Rt×p,D∈Rm×p,设L1={[X,y]X∈Rm×p,Y∈Rm×t,‖AX+YB-D‖=min},求[X,Y]∈L1,使得‖[X,Y]‖=(‖X‖2+‖Y‖2)1/2=min问题Ⅱ.给定A∈SRm×m,B∈Rm×m,(a)设S1={XX∈SPm×m,‖AX+XA-B‖=min}求     

有关矩阵控制关系的几个结果

对于2个m×n实矩阵X和Y,如果存在一个m阶双随机矩阵S,使得X=SY,则称矩阵Y控制X,记作Y X.在rankY=m的前提下,给出了Y X的若干充要条件.     

分布自由的回归函数核估计的收敛速度

设(X1,Y1)、(X2,Y2)、…是取值于Rp×R上的随机向量(X,Y)的一列i.i.d样本,回归函数m(x)=E(Y|X=x)的核估计为mn(x)=n∑i=1 YiK(x-Xi/hn)/n∑i=1 K(x-Xi/hn)在不要求X具有密度函数f(x),对分布自由,即对所有X的分布μ和在核函数改进为包括无界支撑的,甚至不可积的情形下得出了回归函数m(x)=E(Y|X=x)的核估计及在删失情形下的收敛速度.     

矩阵方程AXAT+BYBT=C的对称最优解及最佳逼近

考虑以下问题:问题1:给定A∈Rm×n,B∈Rm×l,C∈Rm×m,L={(X,Y)|AXAT BYBT=C,X∈SRn×n,Y∈SRl×l}≠φ,找(X⌒,Y⌒)∈L,使得‖(X⌒,Y⌒)‖=(‖X‖2 ‖Y‖2)(1)/(2)=min.问题2:任意给定(X∧)∈Rn×n,(Y∧)∈Rl×l,找(X∧,Y∧)∈L,使得‖(X∧)-(X～)‖2 ‖(Y∧)-(Y～)‖2=min(X,Y)∈L(‖X-(X～)‖2 ‖Y-(Y～)‖2).讨论了矩阵方程AXAT BYBT=C有解的充要条件,得到了L的具体表达式,给出了问题1与问题2的唯一解证明与显式表示.     

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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