非线性Volterra积分方程组及积分微分方程组的扰动定理

关于非线性 Volterra 积分方程和积分微分方程组的解在干扰作用下的渐近性质,近来已有了一些结果,如[1]、[2]。本文利用所建立的二个非线性的积分不等式来讨论这类问题,得到了与[1]、[2]不同的一些结果。§1.记号及引理在本文中,f(u)∈C[S、N]表示 f 是在集 S 上有定义且值域属于集 N 的连续实函数;f(u)∈C[S]表示 f 是在集 S 上有定义的连续实函数,f(a)∈X[I,R ]表示 f∈C[I,     

S——“Bolzano—Weierstrass”性质

文[1]、[2]、[3]、[4]分别讨论了S—紧性和可数S—紧性,本文则讨论一种弱于S—紧性和可数S—紧性但对于半T_1空间类来说却等价于可数S—紧性的性质.这种性质称为S—“Bolzano—Weierstrass”性质或S—列紧性质,且要求这种空间的任何无限子集都具有空间内的半聚点.     

S3与Wn的笛卡尔积交叉数

本文先构造S3×Wn的一种好画法,由这种好画法计算出Cr(S3×Wn)≦2[(n-1)2/4] [n/2] 5,然后利用数学归纳法证明Cr(S3×Wn)≧2[(n-1)2/4] [n/2] 5,从而确定了S3与Wn的笛卡尔积交叉数即Cr(S3×Wn)=2[(n-1)2/4] [n/2] 5.     

关于具有约束的有理逼近的一个注记

以往研究有理逼近问题都是考虑如下的有理分式 Q(x)=S(x)(q_0x~n q_1x~(n-1) … q_n)/(p_0x~m p_1x~(m-1) …p_m其中p_0,p_1,…p_m;;q_0,q_1,…,q_n为实参数,且都假定S(x)在所考虑区间[a,b]上恒不为零。1979年王仁宏在[1]中所究具有约束的有理逼近问题时也假定S(x)在[a,b]上恒不为零。本文把S(x)在[a,b]上恒不为零的条件放宽为S(x)在[a,b]上至多有有限个零点的条件下,仍可得到相应的误差下界估计、最佳逼近存在定理以及чебыщев型的最佳逼近定理。     

关于Lewis的模态系统S5的几个注记

本文分三个部分:其一,将应用作者在文献[4]和[5]中得到的关于S5(即S_e)和S5(即S_e)的单纯完全性定理来证明Barcan公式和Prior的导出规则RLM可以分别在S5和S5中推出.这一事实已由Prior在文献[9]中指出,但本文给出的语义证明比[9]中的语法证明要简捷一些;其二,考虑了由S5添加命题量词而得的系统S5的判定问题;Kaplan在文摘[6]中已证明S5(在[6]中记为S5Q)为可判定的.在本文中我们采用Rasiowa和Sikorski在[10]中对一大类带命题量词演算S引进的代数语义方法并具体用到Ackermann在[1]中给出的关于二阶一目谓词演算P_m~2判定问题的一些事实得到更多的结果;其三,我们再次应用S5的单纯完全性定理重新证明S5具有6个模态辞.此事系由O.Becker首先于1930年在文[3]中证明的,本文中的语义证明比Becker[3]中的语法证明似要精致一些.     

一组组合恒等式的推广

本文应用文[7]的的方法得到了个S[p/q;r]型的新组合恒等式，从而推了[1][2]的结果。     

因子链上的最大公因数幂矩阵与最小公倍数幂矩阵

设S={x1,…，xn}是由n个不同正整数组成的集合，ε∈Z^ ．本文研究了对ε∈Z^ 定义在任意因子链S上的幂矩阵(S)n^ε和[S]n^ε的奇异性及它们的行列式det(S)n^ε：与det[S]n^ε间的整除性．     

次连续广义（S）＋ 型映射及其扰动的拓扑度

本文引入了比(S)_+型映射更为一般的概念——广义(S)_+型映射。运用[1]中的方法,构造了次连续广义(S)_+型映射的拓扑度,本文还研究了准广义(S)_+型映射的特征,给出了一个映射为准广义(S)_+型映射的若干充要条件。最后,利用本文所建立的次连续(S)_+型映射度构造了准广义(S)_+型映射的广义度,改进已知结果[1—4]。     

广义自旋变相过程存在定理的一个注记

序言本文利用[1]的方法与[4]的结果,给出相空间为Y_u(S是可数集,Y_u是有限集,u∈S)的广义自旋变相过程的一个存在定理,即定理1.1,利用定理1.1证明了[1]中出现的自旋变相过程的偶合过程的存在,并由此说明证明自旋变相过程偶合过程存在的一个通行方法。最后利用定理1.1讨论广义自旋变相过程的多元偶合问题,推广了唐守正、刘秀芳在[2]中得到的大部分结果。     

对合半群和对合环的拟Moore—Penrose逆的特性

在[1]文中已把对合半群(环)的Moore—Penrose逆的特性作了讨论,本文的目的是在[1]、[2]、[3]文基础上,进一步地把拟对合半群(环)的Moore—Penrose逆的特性作些讨论,并指出了[1]文中某些结果是其特例。定义1.设对合半群(环)S中元b适合方程组axa=a(1),xax=x(2),(az)~*=ax     

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

正~~