一类Riemann-Loiuville型分数阶差分方程解对初值的连续依赖性

针对一类Riemann-Loiuville型分数阶差分方程,利用分数阶差分性质,构造了一个Volterra和分方程,再利用离散分数阶Gronwall不等式和离散Mittag-Leffler函数的性质,在合适的条件下获得了这个方程解对初值的连续依赖性,并用新方法证明了解的唯一性。     

(m,q)阶序列分数差分方程的解

通过构造一个特殊函数λα(n),揭示该函数的重要性质;利用特殊函数λα(n),得到线性常系数齐次(m,q)阶序列分数差分方程的特征方程.然后利用有理(m,q)阶算子分解法,结合Z变换方法求出齐次(m,q)阶序列分数差分方程的显示解;以及结合利用分数Green函数求出解非齐次(m,q)阶序列分数差分方程,得到了一般线性常系数非齐次(m,q)阶序列分数差分方程解的通解结构和基本定理.     

基于ψ-(h,r)-凹算子的非线性分数阶p,q)-差分方程的唯一迭代解

为了丰富分数阶(p,q)-差分方程边值问题的基本理论，研究了一类非线性分数阶(p,q)-差分方程非局部问题的可解性。首先，计算线性分数阶(p,q)-差分方程边值问题的Green函数并研究其性质；其次，运用基于定义在有序集上增的ψ-(h,r)-凹算子的不动点定理，证明分数阶(p,q)-差分方程解的存在唯一性定理；再次，通过选取初值，构造单调迭代序列，获得边值问题的唯一迭代解；最后，给出实例，验证本文研究结果的正确性。结果表明，在赋予非线性项f一定的条件下，非线性分数阶(p,q)-差分方程具有唯一非平凡解。研究结果拓展了分数阶量子差分方程的可解性理论，可为分数阶(p,q)-差分方程的进一步应用提供有力的理论基础。     

一阶非线性时滞差分方程的振动准则

在线性差分方程和的基础上,利用分析法和不等式法证明了一阶非线性时滞差分方程的所有解振动的充分条件,进而利用反证法,假设方程有一非振动解,结合均值不等式法,得出与条件矛盾的结果。于是得到了一阶非线性时滞差分方程在不同条件下所有解的振动准则,推广和改进了线性差分方程已有的相关结果。     

一类有序分数阶差分方程解的存在性

研究一类带有分数阶边值条件的分数阶差分方程解的存在性与唯一性.首先给出这个问题的解的表达式,然后分析格林函数的一些性质,最后运用锥拉伸与锥压缩不动点定理、压缩映像原理、Krasnosel’skii定理证明了该问题解的存在性和唯一性.     

一类二阶非线性差分方程的振动性

差分方程反映的是关于离散变量的变化规律.通过分析方程解的特别性质,可以把握离散变量的变化过程的规律.方程的振动性是研究方程定性理论的重要组成部分,从理论上探讨解的形态变化一直是近年来研究的热点.文章对已有文献中的线性差分方程进行了改进,研究了更普遍的方程,一类二阶非线性多时滞差分方程打振动性,利用分析的方法及积分中值定理,得到了该类方程振动的几个充分条件,并且应用差分方程的振动理论,研究了这类方程在特殊情形下解的一价差分的振动性,得到了一阶差分振动的充分条件,从而丰富了这类方程的研究成果.     

一类带有分数阶非局部边值条件的分数阶差分方程解的存在性

研究了一类带有非局部分数阶边值条件的分数阶差分方程解的存在性与唯一性.首先给出了这个问题解的表达式,然后分析了格林函数的一些性质,并运用压缩映像原理,Brouwer定理以及Krasnoselskii定理证明了该问题解的存在唯一性.所得结论推广了现有文献中的一些结果,并给出了具体例子用以说明文中的主要结论.     

一类具参数的分数阶差分方程边值问题解的存在唯一性

研究了阶数介于3到4之间的一类分数阶差分方程的边值问题。通过构造相应的Green函数,证明Green函数的正性性质,利用Banach压缩映像原理和Brouwer不动点定理,在合适的条件下,获得了边值问题解的存在唯一性。特别地,当阶数v=4时,原问题变为整数阶差分方程边值问题,研究结果表明,分数阶差分方程边值问题与整数阶差分方程边值问题具有本质区别。     

一类半线性分数阶反应扩散方程解的整体存在性

研究了齐次Dirichlet边界下一类半线性分数阶反应扩散方程解的整体存在性和渐近行为.通过Caffarelli-Silvestre延拓方法将非局部的分数阶Laplacian算子转化为局部可变分的算子,再用Galёrkin方法在适当的假设条件下得到方程整体解的存在性,最后利用一些基本不等式得到方程解的渐近行为.     

一类Caputo分数阶差分方程边值问题解的存在性

研究了一类Caputo分数阶差分方程边值问题解的存在性.利用Caputo分数阶差分方程及边值条件的特性给出了它的Green’s函数,借助于Banach压缩映像原理、Krasnosel’skiis不动点定理和Leray-Schauder非线性抉择定理得到边值问题解的存在性,作为应用,给出一个例子验证所得的主要结果.     

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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