（LF）—空间的正则性与完备性

设（Ｅ，ｔ）＝ｉｎｄ（Ｅｎ，ｔｎ）为（ＬＦ）－空间，我们证明了下述结果：（ｉ）（Ｅ，ｔ）为正则当且仅当存在（Ｅｎ，ｔｎ）中Ｏ的圆凸领域Ｕｎ，使Ｕ１∪→Ｕ２∪→…且（ＳＰ［Ｕ↑－ｎ＾Ｅ］，ηｎ）为速完备，这里ηｎ是以｛εＵ↑－ｎ＾Ｅ∩Ｕ：ε〉０，Ｕ∈Ｕ｝为Ｏ－邻域基的局部凸拓扑，而Ｕ为（Ｅ，ｔ）中Ｏ－领域基；（ｉｉ）若对于任意ｎ∈Ｎ，存在（Ｅｎ，ｔｎ）中Ｏ的圆凸领域Ｕｎ及ｍ＝ｍ（ｎ）≥ｎ，使Ｕ↑－ｎ     

关于序列式回缩性的标记

设α（Ｅ,Ｅ）为介于弱拓扑σ（Ｅ,Ｅ）和Ｍａｃｋｅｙ拓扑τ（Ｅ,Ｅ）之间的Ｈｅｌｌｉｎｇｅｒ－Ｔｏｅｐｌｉｔｚ拓扑,称诱导极限（Ｅ,ｔ）＝ｉｎｄ（Ｅｎ,ｔｎ）的α－序列式回缩的,若（Ｅ,α（Ｅ,Ｅ）中每个收敛于０的序列必含于某Ｅｎ且为（Ｅ,α（Ｅｎ,Ｅｎ）中收敛于０的序列,我们证明了：α－序列式回缩性蕴涵正则性,特别地,我们证明了下述结论：若诱导极限（Ｅ,ｔ）＝ｉｎｄ（Ｅｎ,Ｔｎ）中每个收敛于０的     

集值非扩张映象的迭代收敛性及不动点

设Ｄ是赋范空间Ｘ的有界凸子集，Ｔ：Ｄ→ＣＢ（Ｄ）是δ集值非扩张映象，给定Ｄ中序列｛ｘｎ｝和两个实数列｛ｔｎ｝和｛ｓｎ｝，满足（ｉ）０≤ｔｎ≤ｔ〈１和Σ（＾∞，ｎ＝１）ｔｎ＝∞，（ｉｉ）０≤ｓｎ≤１，Σ（∞，ｎ＝１）Ｓｎ〈∞和ｌｉｎｎ→∞ｔ＾－１ｎＳｎ＝０，（ｉｉｉ）ｘｎ＋１∈ｔｎＴｙｎ＋（１＋ｔｎ）ｘｎ，ｙｎ∈display status     

关于Mackey序列式回缩性

设(E,t)是局部凸空间诱导序列(E_n,t_n)_n∈N的诱导极限.则(E,t)=ind(E_n,t_n)为正则当且仅当对于(E,t)中每个Mackey收敛于o的序列(x_k)存在自然数n=n(x_k),使(x_k)含于且有界于(E_n,t_n).由此可获得关于正则性的一系列等价刻划.     

乘积空间的完备性与列紧子集的特征

设（Ｅｎ，ｄｎ）是距离空间（ｎ＝１，２，…），定义乘积空间为（П＾∞ｎ＝１Ｅｎ，Ｄ），ｄ（｛ｘｎ｝，｛ｙｎ－）＝Σ＾∞ｎ＝１Ｅｎ，ｄ）是完备距离空间当且仅当每个因子空间９Ｅｎ，ｄｎ）完备，子集Ａ∪→П＾∞Ｅｎ，列紧当且仅当Ａ在每个因子空间Ｅｎ中的投影πｎ（Ａ）列紧。     

非扩张映射序列迭代过程的收敛性

设Ｄ为赋范空间Ｘ的子集，Ｔｎ：Ｄ→Ｘ，对所有ｘ，ｙ∈Ｄ和所有的ｉ，ｊ≥１，有‖Ｔｘ－Ｔｊｙ‖≤‖ｘ－ｙ‖成立，给定Ｄ中的一个序列（ｘｎ）与两个实数序列（ｔｎ）和（ｓｎ）满足（ｉ）０≤ｔｎ≤ｔ〈１且∞∑ｎ＝１ｔｎ＝∞，（ｉｉ）０≤ｓｎ≤１且∞∑ｎ＝１Ｓｎ〈∞，（ｉｉｉ）Ｘｎ＋１＝ｔｎＴｎ（ｓｎＴｎｘｎ＋（１－ｓｎ）ｘｎ）＋（１－ｔｎ）ｘｎ，ｎ＝１，２，３，．．．证明了如果（ｘｎ）有界，则ｌｉｎｎ→∞     

随机系数代数方程平均实根个数的估计

考虑随机系数代数方程Ｆｎ（ｗ,ｔ）＝０（ｗ）＋１（ｗ）ｔ＋…＋ｎ－１（ｗ）ｔｎ－１＝０,其中ｉ（ｗ）（ｉ＝０,１,…,ｎ－１）为独立且服从标准正态分布的随机变量。令ＥＮＦ（ｗ）表示Ｆｎ（ｗ,ｔ）的平均实根个数。本文证明了ＥＮＦ（ｗ）＜２πｌｎｎ－２ｎπ＋１．２３７２７７１。     

乘积空间的完备性与列紧子集的特征

设（Ｅｎ，ｄｎ）是距离空间（ｎ＝１，２，…），定义其乘积空间为（Π∞ｎ＝１Ｅｎ，ｄ），ｄ（｛ｘｎ｝，｛ｙｎ｝）＝∑∞ｎ＝１１２ｎｄｎ（ｘｎ，ｙｎ）１＋ｄｎ（ｘｎ，ｙｎ）．本文证明了（Π∞ｎ＝１Ｅｎ，ｄ）是完备距离空间当且仅当每个因子空间（Ｅｎ，ｄｎ）完备，子集ＡΠ∞ｎ＝１Ｅｎ列紧当且仅当Ａ在每个因子空间Ｅｎ中的投影πｎ（Ａ）列紧．作为应用还给出了：可数紧的距离空间Ｘ（即存在紧子集ＤｎＸ，使Ｘ＝∪∞ｎ＝１Ｄｎ且≠ＤｎＤ０ｎ＋１，ｎ＝１，２，…）上的连续函数空间Ｃ（Ｘ），局部ｐ次可积函数空间Ｌｐｌｏｃ（Ｒ）以及序列空间Ｓ的完备性及其中子集列紧性的刻画     

某些偏微分算子的非解析亚椭圆性

讨论由向量场的平方和构成的某些二阶偏微分算子的非解析亚椭圆性．所用方法是构造这些算子的奇异解后，将这些偏微分算子的解析亚椭圆性的讨论转化成某些特殊的常微分方程的研究．该构造过程是非常清晰和直接的．而且它涉及到那些带有依赖大参数位势的广义调和振子的第一特征值和第一特征函数的研究，最终获得了如下两个结果：１）令非负整数ｌ，ｋ满足ｌ＞ｋ且ｌ＝２ｋ＋１，则算子Ｐ＝（ｘ）２＋（ｘｋｙ）２＋（ｘｌｔ）２在原点ｏ∈Ｒ３不是解析亚椭圆的．２）对非负整数ｋｉ≥１，ｉ＝１，２，３，…，ｎ，算子Ｑ＝（ｘ）２＋（ｙ）２＋ｘ２ｋ１（ｔ１）２＋…＋ｘ２ｋｎ（ｔｎ）２其中（ｘ，ｙ，ｔ１，…，ｔｎ）∈Ｒｎ＋２，则Ｑ在原点ｏ∈Ｒｎ＋２不是解析亚椭圆的．     

集值非扩张映象的迭代收敛性

设Ｄ是赋范空间Ｘ的一有界凸子集，Ｔ：Ｄ→ＣＢ（Ｄ）是一集值非扩张映象，给定Ｄ中的序列（ｘｎ）和两个实数列（ｔｎ）和（ｓｎ）满足（１）０≤ｔｎ≤ｔ〈１和∑＝∞，（２）０≤ｓｎ≤１，∑ｓｎ〈∞和ｌｉｍｔｎ＾－１ｓｎ＝０，（３）ｘｎ＋１∈ｔｎＴｙｎ＋（１－ｔｎ）ｘｎ，ｙｎ∈ｓｎＴｘｎ＋（１－ｓｎ）ｘｎ，ｎ＝１，２，３…。则ｌｉｍｄ（ｔｘｎ，ｘｎ）＝２。     

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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