Rolle中值定理的推广

对Rolle中值定理的条件作了改进，把函数可导推广为左或右可导，把有限区间推广为无限区间，把函数在区间端点处的函数值相等推广为可以不等．主要建立了如下的推广定理：设函数f（x）在有限或无限区间（a，b）上连续，f（x）在（a，b）内右（或左）可导，并存在{an}，{bn}包括（a，b）使 liman n→∞=a limbn n→∞=b limf（an）n→∞=linf（bn）n→∞=A A为实数或±∞，则存在ξ,η∈（a,b），使得f′＋（ξ）≥0,f′＋（η）≤0（或f′-（ξ）≥0,f′-（η）≤0。更进一步，设f′＋（x）（或f′-（x））在（a,b）内左（或右）连续，则存在ξ∈（a,b）使得f′＋（ξ）=0（或f′-（ξ）=0）.     

乘积系统（X1×X2×…×Xn，f1×f2×…×fn）的拓扑遍历性

记^-f=f1×f2×…×fn,^-Nn={1,2,…,n},^-X=X1×X2×…×Xn,本文给出了^-f是拓扑遍历的两个充要条件。若fi有POTP,Xi是连通的,i∈^-Nn,则^-f是拓扑遍历的27个等价条件被给出。讨论了^-f是拓扑遍历的一些充分条件和必要条件。设fi∈C^0（Xi,Xi）,Xi为紧度量空间,i∈^-Nn,证明了：①若^-f是拓扑遍历的,则^-f1,×…×^-fn：M（X1）×…×M（Xn）→M（X1）×…×M（Xn）是拓扑遍历的。②设（X∞^（j）,f∞^（j））为由{Xi^（j）,gi^（j）,fi^（j）}i=1^∞,生成的逆极限系统,j∈^Nn,则f∞^（1）×…×f∞^（n）为拓扑遍历的当且仅当^n∏j=1 fi^（j）（i=1,2,…）均为拓扑遍历的。③若存在j∈^Nn,使得对t∈^Nn且t≠j,fi均为拓扑混合的,则^-f是拓扑遍历的当且仅当fj是拓扑遍历的。     

正规族与正规函数的一个注记

设F为单位圆盘△上的一族全纯函数,a和b为2个有限的复数且有b≠a,如果对任意的z∈△且对每个f∈F,若f=α→f′=α,且f=b≥→f′=b,则存在一正整数M且对任意的f∈F,有（1-｜z｜^2）f^#（z）=（1-｜z｜^2）｜f′（z）｜/1＋｜f（z）｜^2≤M.     

关于Diophantine方程x2+4n=y3

证明了不定方程x2＋4n=y3（n∈N,x≡0（mod2）,x,y∈Z）,其中当n≥3时整数解仅有（x,y,n）=（0,4k,3k）,（±2×8k,2×4k,3k＋1）,（±11×8k,5×4k,3k＋1）,k∈N＋.     

矩阵张量积数值半径的一个不等式和一个等式（英文）

借助矩阵张量积和矩阵数值半径的性质,证明了不等式r（A1×…×Ak）≥∏ i=1 r（Ai）和等式r（A×B）=r（B×A）,其中A1,…,Ak,A,B∈L（U）.同时,举例说明了不等式r（k×A）≤rk（A）不成立.而当A1,…,Ak为正规阵时,有r（A1×…×Ak）=∏ i=1^ k r（As）.     

N指标算子稳定Lévy过程的像集Hausdorff维数结果

设X={X（t）,t∈R^＋N}为以d×d可逆矩阵B为指数的N指标R^d值算子稳定Lévy过程,讨论了X在R＋^N的子区域上的像集Hausdorff维数问题,证明了dim X（[1,2]^N）=min{d,akN＋∑j=1^k dj（1-ab/aj）,k=1,…,p},a.s., 其中a1〉a2〉…〉ap为B的p个不同的特征值实部的倒数,d1,d…,dp分别为它们所对应子空间的维数．该结论表明X在R＋^N的子区域上像集Hausdorff维数完全由B的特征值的实部来确定．     

关于ax+by型整数的结构

最大公约数是数论中一个重要概念．在柯召所著的数论讲义中给出了对于不同时为零的整数a，b存在整数x，y，有（a，b）=ax=by的表达式．在此基础上，得到如下结论：（1）对给定的整数a，b，有（a，b）=min{ax＋by｜ax＋by〉0，x∈Z，y∈Z}；（2）{ax＋by｜，x∈Z，y∈Z}={k（a，b）｜k∈Z}．     

正规族与分担值

本文研究正规族与分担值之间的关系,得到如下结果：设F是区域D内的亚纯函数族,a,b∈C,a,b≠1,若Af∈F,f和f′在D内分担1,f=a→ f′=b,则F在D内正规;设F是区域D内的全纯函数族,k∈N^＋,b∈R^＋,b∈R^＋,若Af∈F,f-1的零点重级均≥k,f=1→ f^（k）=1→f^（k＋1）=1≤f^（k＋1）≤b,则F在D内正规.     

亚纯函数的正规族

设为F区域D上亚纯函数簇,k∈Z^＋（k≥2）,m∈Z^＋,a≠0,b为两有穷复数,c（z）≠0为D上解析函数,Vf∈F,f（z）的零点之级≥m,并且f（z）在区域D上的极点总个数（计算重数）至多为m,f（z）=a→f＇（z）=b,f（z）=0→0→f＇（z）=c（z）,f＇（z）=c（z）→｜f^（k）（z）｜≤h,那么F在区域D内正规．     

爸爸同样爱你

今天,我和同学们一起学习了《乘法分配律》。乘法分配律用字母表示为（a＋b）×c=a×c＋b×c。这一定律学生运用起来总是不能得心应手。为了学生巧妙记忆和灵活掌握,我教给学生一种巧妙的记法：“a”代表妈妈,“b”代表爸爸,“×”代表爱,“b”代表我,合起来理解为：爸爸和妈妈爱我。也就是妈妈爱我加上爸爸也爱我。学生非常感兴趣。     

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.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

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