Hilbert空间中Bessel列的算子扰动

目的 研究Hilbert空间中Bessel列的算子扰动.方法 运用算子理论.结果 对于Hilbert 空间H中的一个序列f={fi}∞i=1 及算子列{T(i)j}∞i,j=1(∩)B(H,K),给出使得{∑∞j=1T(i)jfj}∞ i=1成为K中的Bessel序列的一些充分条件;证明了如果{Ti}∞i=1(∩)B(H,K) 使得Ti=T(i>N0)且 f={fi}∞i=1是 H中的Bessel列, 则{Tifi}∞i=1 是 K中的Bessel列.结论 在一定的条件下,Hilbert空间中的Bessel列经过算子扰动,还可以是Bessel列.     

Hilbert空间中Bessel列的广义扰动

运用算子理论方法,研究了Hilbert空间中Bessel列的广义扰动,对Hilbert空间H中的任一Bessel列f={fi}i∞=1,给出了序列g={gi}∞i=1={α1(1)f1,α1(2)f1,α2(2)f2,α1(3)f1,α2(3)f2,α3(3)f3,…},g={gi}∞i=1={α1(1)f1,α1(2)f2,α2(2)f2,α1(3)f3,α2(3)f3,α3(3)f3,…},g={gi}∞i=1={∑∞j=1αj(i)fj}∞i=1,成为Bessel列的充分条件。     

Hilbert空间上框架的扰动

研究了Hilbert空间上框架的扰动问题.应用算子论的方法,给出了当f={fi}i∈Z是框架时,序列{λifi}i∈Z,{Tfi}i∈Z及{Tifi}i∈Z成为框架的条件;证明了当f为框架,g为Bessel列且T 满足一定条件时,g也是一个框架.f-g     

Hilbert空间中几种基的关系

目的 研究Hilbert空间H上的Hilbert基、Bessel基、Riesz基三者间的关系,及其与Bessel列、小波Ricsz基的关系.方法 算子论方法 .结果 证明了对于Hilberr空间日的任一Schuder基{xn},序列{xn xn≠}是H的一个Besselian基且{xn xn≠}≥{xn},{xn xn≠}≥{xn≠}.结论 对于H的任一Schuder基{xn},定义U(xn xn≠):xn≠则{xn}是H的一个Besselian基当且仅当‖U‖<1.而且给出了彤eSZ基的5个等价刻画.     

Fredholm框架及其扰动

引入了Hilbert空间H的Fredholm框架概念,它是一种介于普通框架与Riesz基之间的一类特殊框架.应用算子论方法,给出了Fredholm框架的重要性质及其等价刻画,证明了H上全体Fredholm框架构成了由H中全体Bessel列组成的Banach空间中的开集.研究了Fredholm框架在小扰动下和算子扰动下的稳定性,证明了框架与Riesz基的膨胀不变性.     

逆极限空间的逐点伪轨跟踪性

证明对于由{Xi,φi,fi}∞i=1生成的逆极限系统{X∞,f∞},如果每个fi具有逐点伪轨跟踪性,则诱导映射f∞也具有逐点伪轨跟踪性.举例证明,它的逆命题不成立.     

Hilbert直和空间中的Riesz基与标准正交基

框架和基的研究是小波分析理论研究的重要内容之一。在预框架算子满足一定条件下，借助算子理论方法证明了两个Riesz基的直和是它们直和空间上的Riesz基，以及这两个Riesz基的直和构成了它们直和空间上的标准正交基的充分必要条件。并在一般框架扰动条件下，研究了一个Riesz基和一个Bessel序列的扰动性质。     

Cantor群上的Riesz乘积型测度的收敛性和连续性

研究Riesz型乘积Pn=∏nj=1(1+awj+bwj+1),其中a,b是满足条件a+b1的实数,{wj}是等概率地取值于{-1,1}的独立随机变量.记dw为Cantor群Ω={-1,1}∞上的标准哈尔测度,{概率测度列Pndw/∫ΩPndw}在Ω上会弱收敛于唯一的一个连续测度,并且这个测度关于dw是奇异的.     

实Banach空间中Lipschitzφ-半压缩算子的不动点的带误差项的迭代逼近

设 K是实 Banach空间 X中非空凸子集 ,T:K→K为 Lipschitzφ-半压缩算子 ,设 { an} ,{ bn} ,{ cn} ,{ a′n} ,{ b′n} ,{ c′n}为 [0 ,1 )中实数列且满足一定条件 ,{ μn}∞n=0 和 { νn}∞n=0 是 K中两任意有界序列 ,则带误差项的Ishikawa型迭代序列 { xn} ∞n=0 强收敛于 T的唯一不动点 ;一个相关结果处理含 φ-拟强增生算子的方程解的带误差项的 Ishikawa型迭代逼近 .     

框架和Riesz基的稳定性

从两方面讨论了Hilbert空间中框架和Riesz基的稳定性：在满足一定条件Bessel序列的扰动下，框架和Riesz基在Hilbert空间中的稳定性；把框架和Riesz基与小波结合起来，在母小波、采样序列的扰动下，小波框架和小波Riesz基在L^2（R）空间中的稳定性．对有关文献的相关结论进行了推广，目的在于可以根据框架的稳定性，设计或者选择一个更优的框架来精确地逼近信号．     

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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