非线性微分方程解的唯一性

运用Nevanlinna值分布理论,研究亚纯函数的唯一性问题。若f(z)为f 'f=F(z)的有限级亚纯解,其中F(z)为非零整函数且λ(F(z))< 1,当f(z)与有限级亚纯函数g(z)CM分担0、1、∞,则f=g。如果f(z)为f '+A(z)f ⁿ=F(z)的一个有限级亚纯解,其中A(z)为不等于0的多项式,F(z)为非零整函数且λ(F(z))< 1, A(z)≠F(z),若有限级亚纯函数g(z)与f(z)CM分担0、1、∞,则f=g。     

涉及微分多项式和多项式的亚纯函数正规族

k,l∈N,且k≥2,设F为D内亚纯函数族,对f∈F,在D内的零点之级≥k 1,极点之级≥2.h(z)为D内的全纯函数,在D内的零点之级≥2,且h(z)0.设a1(z),a2(z),...,ak-1(z)和b1(z),b2(z),...,bl(z)为D内的全纯函数.置H(f)(z)=f(k)(z) ak-1(z)f(k-1)(z) ... a1(z)f ′(z) b1(z)f(z) ... bl(z)f l(z).若对f∈F,有H(f)(z)≠h(z)(z∈D)成立,则F在D内正规.     

亚纯函数的正规族和微分多项式的例外函数

主要证明了定理:设F是单位圆盘△上的亚纯函数族,F中的任一函数f的极点是重级的,零点重级至少为m 1,m是正整数,h(z)≠0,a0,a1,…,am-1都是D上的全纯函数.如果对任一f∈F,L(f)(z)=f(m)(z) am-1(z)f(m-1)(z) … a1(z)f′(z) a0(z)f(z)≠h(z),z∈D,则F在D上正规.     

q移位差分方程的亚纯解及任意亚纯函数分担3个值的唯一性

用Nevanlinna理论,研究差分方程a_1(z)f(qz+p)+a_0(z)f(z)=F(z)一个有穷级超越亚纯解f(z)及任一亚纯函数g(z)分担0,1,∞IM时的唯一性问题(其中p,q为常数,满足n∈N~+,q~n≠±1,q≠0,a_1(z),a_0(z),F(z)为非零亚纯函数且级均小于1),得到了f(z)=g(z).     

一类二阶线性微分方程解的增长级

考虑一般形式的二阶线性微分方程:A2(z)f″+A1(z)f′+A0(z)f=0解的增长级,其中A2(z),A1(z)和A0(z)均为多项式,其次数分别为,m2,m1和m0.从而得到解的增长级的估计.     

关于亚纯函数正规定则

本文得到了下述关于亚纯函数的几个正规定则. 定理1:设{f(z)}为域D内亚纯函数族,其中每个f(z)的极点之级≥3.ρ(z)为D内全纯函数不恒等于零,若在D内,f(z)≠0,f(z)≠ρ(z).则在D内{f(z)}为正规. 定理2:设{f(z)}为域D内的亚纯函数族,其中每个f(z)的极点的级≥3.ρ(z)为D内仅有简单零点的全纯函数.若在D内f≠0,f~(k)(z)≠ρ(z),k≥0,则{f(z)}在D内为正规.     

亚纯函数的正规族

设F是区域D内的亚纯函数族,a,b为互相判别的非零复数,c是任意复数,k≥2,对于任意的f(z)∈F,f(z)-c的零点重级至少为k,若f(k)(z)=a(=>)f(z)=a,f(k)(z)=b(=>)f(z)=b和f(z)=c(=>)f(k)(z)=c,则F在区域D内正规.     

关于下级为有穷正数的整函数的亏整函数总数

杨乐、张广厚证明了:对於有穷正级整函数f(z),若P为f(z)的亏值总数,q是f(z)的Borel方向总数,则P≤q/2。定义1 设f(z)为亚纯函数,a(z)为∞或亚纯函数,满足     

亚纯函数的充满圆和公共Borel方向

设argz=θ0为λ级亚纯函数f(z)的λ级Borel方向(O<λ< ∞)．若argz=θo不是f′(z)的λ级Borel方向．则存在f(z)的一列λ级充满圆{DK}，K=1，…，使得，m(DK),f=0)=r(Dk，f=1)     

一类差分多项式的Picard型定理

本文利用值分布论作为工具得到以下结论:令f(z)为一个有限级超越整函数,c_1,c_2为两非零复常数并使得f(z+c_1)≠f(z+c_2),q(z)为非零多项式,则f(z)Δf_(c_1)(z)-q(z)和f(z)Δf_(c_2)(z)-q(z)两者中至少有一个具有无限多个零点.     

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