关于一类二维奇异积分方程的唯一解

设Ｄ是一个边界Г∈Ｃ＾１ａ（０〈ａ≤１）的有界单连域,复函数ｑ（ｚ）∈Ｃ＾１ａ（Ｄ）,│ｑ（ｚ）│≤１,等积只能在Г上成立,且在Г上等式ｑ（ｚ（ｔ）ｚ’（ｔ）＋１│ｚ∈Г＝０最多在有限个点上成立,本文给出以满足上述条件的复伸张ｑ１（ｚ）及（ｑ２（ｚ）∈Ｃ＾１ａ（Ｄ）为系数的二维奇异积分方程ｗ（ｚ）＋ｑ１（ｚ）／ｎ√√ｗ（ｔ）／（ｘ－ｚ）＾２ｄσ＋ｑ２（ｚ）／ｎ√√ｗ（ｔ）ｄσｚ／ｔ－ｚ＝ｆ（ｚ）的     

拟圆盘下有理逼近的正定理

在拟圆盘上，该文给出用有理函数逼近解析函数的两个正定理，即设Ｅ为闭的ｋ－拟圆盘，０≤ｋ≤１，ｆ（ｚ）在Ｅ的内部解析且在Ｅ上连续，则Ｅｎ，ｒ０（ｆ）＝Ｏ（ｎ＾－ａ），其中，Ｅｎ，ｒ（ｆ）＝ｉｎｆ（∥Ｒ－ｆ∥Ｅ：Ｒ∈Ｒｎ，ｒ０），＝１－ｋ。若进一步ｆ（ｚ）∈Ｌｉｐβ，０〈β≤１，则Ｅｎ（ｆ）＝Ｏ（ｎ＾－α），α＝β（１－ｋ），其中Ｅｎ（ｆ）＝ｉｎｆ（∥Ｐ（ｚ）／П（ｚ－ｚｊ）－ｆ∥Ｅ：ｐ（ｚ）∈Ｐｎ（     

一类迭代函数方程的解析解

设ｒ是个给定的正数,用Ｄ＝ Ｄｒ表示复平面Ｃ内以原点为心ｒ为半径的闭圆盘．令Ａ（Ｄ,Ｄ）＝ ｛ｆ：ｆ 为从Ｄ到Ｄ的连续映射,并且ｆ｜Ｄ０ 解析｝．设Ｇ：Ｄｎ＋ １ →Ｃ连续（ｎ≥２）,并且Ｇ｜（Ｄｎ＋ １）０ 解析,ｇ１,…,ｇｎ ∈Ａ（Ｄ,Ｄ）,本文讨论了迭代函数方程Ｇ（ｚ,ｆ（ｇ１ （ｚ））,…,ｆｎ（ｇｎ（ｚ））） ＝ ０,给出该方程在Ａ（Ｄ,Ｄ） 中有解和有唯一解的条件．     

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     

ze^z＋λ的动力系统

研究整函数族ｆλ（ｚ）＝ｚｅ＾ｚ＋λ（λ∈Ｃ）的动力系统。方法用Ｂａｋｅｒ研究ｅ＾λｚ所采用的方法。结果与结论设Ｄｐ＝｛λ∈｜ ｆλ（ｚ）有一个ｐ阶的吸性周期点｝,Ｄｐ表示Ｄｐ的一个连通分支。     

一类非自治微分迭代方程解的存在性及延拓

研究非自治微分迭代方程ｘ（ｔ）＝ｘ＾２（ｔ）－ｔ＾２）ｆ（ｘ＾〈ｎ〉（ｔ））（其中ｆ∈Ｃ（Ｒ,Ｒ）,单调递增,ｚｆ（ｚ）〉０,ｚ≠０）满足初条件ｘ（ζ）＝η（ζ≥η〉）的解性态。存在性及延拓问题。     

Milloux不等式的推广

设ψ（ｚ）＝ｌ∑ｉ＝０ａｉ（ｚ）ｆ＾ａｉ０．．．．（ｆ＾ｋｉ）＾ｋ，ｉ的ｆ的微分多项式，ψ（ｚ）≠Ｃψ（ｚ）Ｃ为任意常数。     

Banach空间中常微分方程Cauchy问题的近似解与解的关系

讨论Ｂａｎａｃｈ空间中常微分方程Ｃａｕｃｈｙ问题的近似解与解的关系，得到一个Ｃａｕｃｈｙ问题的近似解与解的关系的定理：定理设ｆ＿ｎ∈Ｃ［Ｒ＿０，Ｅ］（ｎ≥１），ｆ∈Ｃ［Ｒ＿０，Ｅ］，序列｛ｆ＿ｎ｝在Ｒ＿０上一致收敛于ｆ；又设０＜α≤ａ，ｘ＿ｎ∈Ｃ￣１［［ｔ＿０，ｔ＿０＋α］，Ｂ（ｘ＿０，ｂ）］，且满足Ｃａｕｃｈｙ问题ｘ＇＿ｎ（ｔ）＝ｆ＿ｎ（ｔ，ｘ＿ｎ（ｔ））ｘ＿ｎ（ｔ＿０）＝ｚ＿ｎ其中ｔ∈［ｔ＿０，ｔ＿０，ｔ＿０＋α］，ｎ＝１，２，…，ｚ＿ｎ∈Ｅ，ｚ＿ｎ→ｘ＿０（ｎ→∞），如果ｘ＿ｎ（ｔ）在［ｔ＿０，ｔ＿０＋α］上一致收敛于ｘ（ｔ），则ｘ∈Ｃ￣１［［ｔ＿０，ｔ＿０＋α］，Ｂ（ｘ＿０，ｂ）］，且对ｔ∈［ｔ＿０，ｔ＿０＋α］，有ｘ＇（ｔ）＝ｆ（ｔ，ｘ＿ｎ（ｔ））ｘ（ｔ＿０）＝ｘ＿０     

单位圆上H^∞,D^p空间和D^p上点乘子的关系

研究了单位圆Ｄ上Ｄ＾ｐ空间的点乘子Ｍ（Ｄ＾ｐ）,并讨论了Ｈ＾∞、Ｄ＾ｐ和Ｍ（Ｄ＾ｐ）的关系。得到：（１）当０〈ｐ≤２时,ｆ∈Ｍ（Ｄ＾ｐ）当且仅当ｆ∈Ｈ＾∞且｜ｆ′（ｚ）｜＾ｐｄＡ（ｚ）是Ｄ＾ｐ－Ｃａｒｌｅｓｏｎ测度;（２）当ｐ〉２时,Ｍ（Ｄ＾ｐ）＝Ｄ＾ｐ包含Ｈ＾∞;（３）当０〈ｐ〈１时,Ｍ（Ｄ＾ｐ）包含Ｈ＾∞包含Ｄ＾ｐ。     

拟圆盘上有理逼近的正定理

在拟圆盘上，该文给出了用有理函数逼近解析函数的两个正定理，即设Ε为闭的ｋ－拟圆盘，０≤ｋ≤１，ｆ（ｚ）在Ε的内部解析且在Ε上连续，则Εｎ，ｒ０（ｆ）＝Ｏ（ｎ－α），其中，Εｎ，ｒ０（ｆ）＝ｉｎｆ｛Ｒ－ｆΕＲ∈Ｒｇｎ，ｒ０｝，α＝１－ｋ。若进一步ｆ（ｚ）∈Ｌｉｐβ，０＜β≤１，则ΕＮ０ｎ（ｆ）＝Ｏ（ｎ－α），α＝β（１－ｋ）。其中ΕＮ０ｎ（ｆ）＝ｉｎｆ｛ｐ（ｚ）／∏Ｎ０ｊ＝１（ｚ－ｚｊ）－ｆΕｐ（ｚ）∈Ｐｎ（ｚ）｝，而ｚ１，…，ｚＮ０在Ε的外部且对于ｚ∈Ε有１≤｜∏Ｎｏｊ＝１（ｚ－ｚｊ）｜≤Ｍ。     

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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