椭圆型Cardinal样条

获得Ｒ＾ｄ上齐次椭圆型Ｃａｒｄｉｎａｌ样条插值的存在唯一性,并获得Ｓｏｂｏｌｅｖ类上的函数在Ｌｐ（Ｒ＾ｄ）（１≤ｐ≤∞）尺度下的插值误差估计,以及Ｓｏｂｏｌｅｖ类在Ｌ２（Ｒ＾ｄ）尺度下的一些极值问题的解;拓广了Ｌａｐｌａｃｅ型的结果。     

基于一个函数类的Cardinal样条插值

考察了基于一个函数类的Ｃａｒｄｉｎａｌ样条插值。被插函数属于Ｓｏｂｏｌｅｖ函数类。并得到了Ｌｐ（Ｒ＾ｄ）尺度下的误差估计。     

缓增样条的平均维数及逼近阶

确定了ｒ阶缓增样条类的平均维数的精确估计，并证明了缓增样条函数类是Ｓｏｂｏｒｅｖ类Ｗ２＾ｒ（Ｒ）在Ｌ２（Ｒ）尺度下的一个最优子空间。     

椭圆型Cardinal样条的逼近

考察了椭圆型算子所确定的Ｓｏｂｏｌｅｖ函数类的平均宽度，以及椭圆型Ｃａｒｄｉｎａｌ样条所构成的多尺度分析，拓广了Ｌａｐｌａｃｅ型结果。     

用神经网络逼近函数及其导数

对于给定的函数ｆ∈Ｗ′Ｍ［－π,π］ｄ,Ｍｂａｓｋｅｒ和Ｍｉｃｈｅｌｉ已构造出具体的神经网络逼近Ｓｏｂｏｌｅｖ类函数及其导数并给出逼近阶的估计。但对于给定的函数φ∈Ｗ′Ｍ（Ｒ′）并没有考虑。文章通过一个定理和Ｍｂａｓｋｅｒ的一个结果,对给定的函数φ∈Ｗ′Ｍ（Ｒ′）构造出具体的神经网络逼近Ｓｏｂｏｌｅｖ类函数及其导数并给出逼近阶的估计。     

各向同性Sobolev类S W_p~r(R~d)的平均宽度

通过在上方估计中用指数型整函数作逼近工具，在下方估计中使用离散化的技巧，得到了各向同性Ｓｏｂｏｌｅｖ类ＳＷｒｐＲｄ在Ｌｐ（Ｒｄ）（１≤ｐ＜）中的平均σ－Ｋ宽度和平均σ－Ｌ宽度的弱渐近估计。     

各向异性Besov光滑函数类的一个极子空间

考虑了各向异性 Besov类的样条函数逼近 ,证明了多项式样条函数空间为各向异性 Besov类 Srpθ( Rd)关于无穷维 Kolmogorov宽度的弱渐近极子空间     

Ωp^rΩp^r在L^q内的n宽度

研究了由线性微分算子Ｐｒ（Ｄ）＝Ｄ＾σП（Ｄ＾２－ｔｊ＾２Ｉ）在３处不同的边界的边界条件下确定的Ｓｏｂｏｌｅｖ类Ωｐ＾ｒ，Ωｐ＾４，Ωｐ＾２ｌ＋１在Ｌ＾ｑ尺度下的宽度计算问题，得到了在１〈ｑ〈ｐ〈∞条件下Ｋｏｌｍｏｇｏｒｏｖ，Ｇｅｌｆａｎｄ和线性宽度的精确值，并构造出相应的极子空间及最优线性算子：在１〈ｐ≤ｑ〈≤∞条件下得到了Ｂｅｍｓｔｅｉｎ宽度的精确值，并构造出相应的极子空间。     

具有一定混合光滑性的多元函数的整函数逼近

讨论了定义域是Ｒ＾ｄ的，具有一定混合光滑性的Ｌｑ（Ｒ＾ｄ）类的函数利用Ｌｑ（Ｒ＾ｄ）的一些线性子空间的逼近，后者是由一些其谱含于某种双曲十字集内的整函数所构成者，得到了最佳逼近值的渐近估计。     

用球面多项式最佳逼近阶刻画Besov空间

设Ｅｎ（ｆ）ｐ表示ｆ∷Ｌ＾ｐ的ｎ次最佳逼近,Ｅｎ（ｆ）ｐ＝ｄｉｓｔ（ｆ;ｎ,Ｌ＾ｐ）－ｉｎｆ＾ｈｎ∈ｎ｜｜ｆ－ｈｎ｜｜ｐ,Ｄ＾ｐ．ｒ表示序列型子空间,则在球面函数的Ｈｏｌｄｅｒ范数下,Ｄ＾ｐ．ｒ为Ｂａｎａｃｈ空间,且有结论：若ｆ∈Ｌ＾ｐ（１≤ｐ〈∞）以及ｒ,ｎ∈Ｎ,则有Ｅｎ（ｆ）≤ｃｏｎｓｔＫ．（ｆ,ｎ＾－ｒ,Ｌ＾ｐ,Ｄ＾ｐ．ｒ）。又用球面函数的Ｈｏｌｄｅｒ范数,定义了一类Ｂｅｓｏｖ空间,用球面最     

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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