二阶线性微分方程振荡结果的注记

证明存在非常数多项式P1(z) =ζ1zn+… ,P2 (z) =ζ2 zn+…和级小于n的整函数Q ,0 <ζ2 / ζ1<1使方程 f″+(eP1(z) +eP2 (z) +Q) f =0有非平凡解 f满足λ(f)≤n .回答了K .Ishizaki提出的问题     

分圆域Q(ζ15)的幂元整基

称一个伽罗华数域L有一个幂元整基,如果它的代数整数环具有形式Z[α],其中α∈L.并且此时称α为幂元整基的生成元.两个幂元整基的生成元α和α′称为等价的,如果α′=m±σ(α),其中m∈Z并且σ∈Gal(L/Q).讨论了分圆域Q(ζ15)的幂元整基的生成元,其中ζ15是15次本原单位根.众所周知ζ15,(1-ζ15)-1和(1 ζ15)-1都是分圆域Q(ζ15)的幂元整基的生成元.证明了当α α-Z时α是分圆域Q(ζ)的幂元整基的生成元当且仅当α与ζ等价.     

一类整函数系数微分方程解的增长性

研究了k(≥2）阶线性微分方程f^(k) (Q1(z)e^p1(z) Q2(z)e^p2(x)f=P3(z)的解的增长级,其中P1(z)= ζ1z^n …,P2(z)=ζ2z^n …为非常数多项式,P3（z)为非零多项式,Q1（z),Q2(z)均为级小于n的整函数不同时恒为零。     

余弦函数和指数函数在复合意义下的分解

本文讨论了函数cos s,cos(s~(1/2))和e~(?)在复合意义下的分解,主要证明了:cos z的所有形如cos z=fog(z)的分解(f为亚纯函数,g为整函数)是以下三种:(i)f(ζ)=cos(ζ~(1/2)),g(z)=z~2;(ii)f(ζ)=T_n(ζ),g(z)=cos(z/n),其中T_n(ζ)是n(≥2)次Tchebycheff多项式(iii)f(ζ)=(1/2)(ζ~n ζ~(-n)),g(z)=e~(tz/n),n为非零整数。     

一类带双复变量广义无穷积分的求解

本文应用复变函数的方法解决了在概率论与数理统计中常出现的积分integral from n=1 to ∞(t~(z-1)e~(-ζ1)dt)(其中z、ζ皆为复数)的计算公式为在Rez>0,Reζ>0的条件下integral from n=1 to ∞(t~(z-1)e~(-ζ1)dt)=Γ(z)/ζ~z     

关于Hurwitz Zeta函数的积分均值

设ζ(s,α)为HurwitzZeta函数.当Re(s)>1时,定义ζ(s,α)=∑∞n=01(n+α)s(实数α>0),ζ′(s,α)、ζ″(s,α)分别表示关于复变量s的一阶导数、二阶导数.利用解析方法及三角和估计给出了ζ(s,α)对参数α的积分均值的一些有趣的渐近公式.     

有限相依随机过程的Cramér定理

设ζ_1ζ_n(n≥1)是i.i.d.实值随机变量,a_1,…,a_m是一组实数。定义X_a=sum from i=1 to (?) (a_iζ_i+a,(?)=1/n sum from i=1 to n (X_a)。)本文证明:若Eexp(tζ)<∞(A|t|<η),则服从大偏差原理。     

关于Hurwitz zeta函数的均值公式

设ζ(s,α)为Hurwitzzeta函数。当Re(s)>1时,定义ζ(s,α)=∑∞n=01(n+α)s(实数α>0),ζ′(s,α)表示关于复变量s的一阶导数,利用解析方法及三角和估计给出了ζ(s,α)对参数α的二次积分均值的一些有趣的渐近公式.     

n值逻辑系统L*n中广义重言式的计量化研究

基于均匀概率空间的无穷乘积,通过考虑使某一公式的赋值不小于(或大于)ζ(ζ∈[0,1])的那些赋值映射之集在总赋值集合中所占的份额,在n值R0-命题逻辑系统L*n中引入公式的ζ-真度及ζ+-真度概念,从而将重言式的概念进行双重程度化;提出了σ-(ζ-重言式)和σ-(ζ+-重言式)理论;研究了ζ-真度(ζ+-真度)与广义重言式及程度化的广义重言式之间的关系,给出了广义真度推理规则.     

Plana求和公式与Riemann Zeta函数ζ(2k+1)的数值计算

Riomann—Zota 函数ζ(s)=sum from n=1 to ∞ 1/n~s、首先,1736年证明了ζ(2)π~2/6之后,ζ(2k)(k=1,2,…)相继求得,但ζ(3)ζ(5),…,ζ(2k+1)…迄今尚未求得,1978年6月在法国马数学会议上,Apery 宣布证明了ζ(3)是无理数。本文给出用 Plana 求和公式对函数ζ(3)的数值计算并与级数求和对比进行数值分析,同时也给出了ζ(5),ζ(7)、ζ(9)的部分数值计算结果。     

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.     

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.     

An Analysis of Catherine＇s Character——Wuthering Heights

Wuthering Heights, Emily Bronte＇s only novel, was published in December of 1847 under the pseudonym Ellis Bell. The book did not gain immediate success, but it is now thought one of the finest novels in the English language. Catherine is the key character of this masterpiece, because everybody and everything center on her though she had a short life. We can understand this masterpiece better if we know Catherine well.     

Lower Paleozoic oil relationships within Williston Basin, Canada

The Williston Basin is a significant petroleum province, containing oil production zones that include the Middle Cambrian to Lower Ordovician, Upper Ordovician, Middle Devonian, Upper Devonian and Mississippian and within the Jurassic and Cretaceous. The oils of the Williston Basin exhibit a wide range of geochemical characteristics defined as "oil families", although the geochemical signature of the Cambrian Deadwood Formation and Lower Ordovician Winnipeg reservoired oils does not match any "oil family". Despite their close stratigraphic proximity, it is evident that the oils of the Lower Palaeozoic within the Williston Basin are distinct. This suggests the presence of a new "oil family" within the Williston Basin. Diagnostic geochemical signatures occur in the gasoline range chromatograms, within saturate fraction gas chromatograms and biomarker fingerprints. However, some of the established criteria and cross-plots that are currently used to segregate oils into distinct genetic families within the basin do not always meet with success, particularly when applied to the Lower Palaeozoic oils of the Deadwood and Winnipeg Formation.     

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     

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