关于空间H_0~1(Ω)和W_0~(1,p)(Ω)的对偶空间表示的注记

通过研究H_0~1(Ω)的对偶空间H~(-1)(Ω),发现H~(-1)(Ω)的Riesz表示唯一,但在(L2(Ω))N+1中的表示不唯一.同样地,对于W_0~(1,p)(Ω)的对偶空间W-1,p'(Ω),在W_0~(1,p)(Ω)有唯一表示,但在(Lp'(Ω))N+1中的表示不唯一.     

非局部扩散的非自治抛物方程动力学行为

考虑带非局部扩散的非自治抛物方程解的长时间行为,当时间符号项于L_(loc)~2(R;H~(-1)(Ω))和L_(loc)~2(R;L~2(Ω))中平移有界时,证明该系统所对应的过程在L~2(Ω)与H_0~1(Ω)中存在一致吸引子。     

一类微分算子生成的半群与发展方程初值问题的解

本文首先给出并讨论了一类广义微分算子A_(2k)=(-1)~(k-1)D~(2k);(A_(2k-1)=(-1)~(k-1)D~(2k-1))在定义域H~(2k)(H~(2k 1)))上生成的强连续半群.讨论了算子及其生成半群的自伴性,谱性,并将其应用于发展方程Cauchy问题,给出了一类线性偏微分方程的解.     

Sobolev方程混合有限元方法的最大模误差估计

基于R -T空间Vh×Wh H(div;Ω)×L2 (Ω) ,本文讨论了Sobolev方程 -div{α ut+b1 u}=f的初边值问题混合有限元方法的最大模误差估计 .得到了数值解在L∞( 0 ,T ;L∞(Ω) )模下的拟最优阶误差估计 (有限元空间指数k =0 )和最优阶误差估计 (有限元空间指数k≥ 1)以及在L∞( 0 ,T ;L∞(Ω) 2 )模下的拟最优阶误差估计 .     

带衰退记忆项的弱阻尼波方程的全局吸引子（英文）

讨论了带有线性记忆项和混合微分项的弱阻尼波方程解的长时间行为.证明了方程在非线性项满足临界增长条件下,在空间H_0~1(Ω)×L~2(Ω)×L_μ~2(R+,R_0~1(Ω))中存在全局吸引子,其中半群的紧性通过压缩函数方法得到.     

多维拟左连续局部鞅的可选表示性

本文定义了k维可选过程对k维拟左连续局部鞅的随机积分,然后建立了k维拟左连续局部鞅的可选表示性基本定理,这推广了一维情形下严加安、Yoeurp[1]中的相应结果.设(Ω,F,P)为完备概率空间,(F_t)_(t≥0)为F的子σ域族,满足通常条件.本文采用如下记号:M_0~b—零初值有界鞅空间,L_0—零初值局部鞅空间,H~1—H~1鞅空间,H_0~1—零初值H~1鞅空间.本文中随机过程符号右上角的数字都是附标,若要表示幂次,则加括号后再写上幂次.若M~1,M~2,…,M~k为拟左连续局部鞅,则称M=(M~1,M~2,…,M~k)为k维拟左连续局部     

Laplace算子的特征函数系在三个空间中的完备性证明方法

考虑Laplace算子在Dirichlet边界条件下的特征值和特征函数的性质问题,利用变分方法给出了Laplace算子的特征值和特征函数的存在性。运用特征值序列趋向于无穷大,首先证明了特征函数系在空间H_0~1(Ω)中是一组正交完备系,然后利用空间H_0~1(Ω)在空间L~2(Ω)中的稠密性,证明了特征函数系在空间L~2(Ω)中是一组标准正交完备系,最后利用二阶椭圆型偏微分方程解的L~2先验估计结果,给出了特征函数系在空间H~2(Ω)∩H_0~1(Ω)中是一组完备系。对经典知识给予了深刻发掘,并给予严密完善的证明。     

关于Dirichlet L—函数

设 S(t,x)=π~(-1)argL(1/2+it,x)A.Fujii 在[1]中研究了integral from T+H to T(S(t+h,x)-S(t,x))~2dt并给出了一个渐公式。本文研究更一般情况。得到如下结果:定理1 设 T~(1/2+a)≤H≤T,(A>0),00),00为任取的实数。当 T≥T_0(a,δ)时,我们有     

多维线性Sobolev型发展方程的外初边值问题

本文研究R~n中任一个有界集的外域上SObolev方程的初边值问题 是R~n中任一有界集的外域且其边界■Ω光滑. 假设有:m≥2[n/2]+3,ρ(x),ψ(x)∈H~(2(m-1))(Ω);a_(ij)(i,j=1,2,…n)及f∈■w~(k·∞)(0,T;H~(m-k-1)(Ω)),则(G)存在唯一的经典解.     

广义神经传播型非线性拟双曲方程解的熄灭性

本文对广义神经传播型非线性拟双曲方程具第一类边界条件的初边值问题,得到了其解的递增解的熄灭性,并进一步讨论了他的C~(?)(O,T,H~2(Ω))∩C~2(O,T,L~2(Ω))解的熄灭现象。     

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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