K(■)上可解多项式代数中左Grbner基的计算

给定域K的单代数扩域K(■)上可解多项式代数A=K(■)[a1,…,an],设A的子代数A0=K[a1,…,an]是K上可解多项式代数.通过考察A与多项式代数A0[x]之间的结构关系,给出将A中左Grbner基的计算转换为A0[x]中左Grbner基计算的有效方法.     

有限域上的特征多项式与最小多项式

<正> 设F 是有限域,K 是F 的有限扩域。[K∶F]=m。K 中任一元α的最小多项式是指一个首项系数为1,最低次多项式f(x),使f(α)=0。所谓α的特征多项式g(x)是把α看成F 上的线性空间k 中的左乘线性性变换的特征多项式。本文给出α~t 的特征多项式与最小多项式的求法。     

关于Bernstein—Durrmeyer多项式的Lp逼近阶

本文利用K——泛函和光滑模给出Bernstein-Durrmeyer多项式Dn(f,x)在Lp[0,1]空间中的逼近阶。     

再论多项式的Hensel提升

R是有限链环,M是其极大理想,K=R/M;则建立了K[x]中一类多项式在R[x]中的Hensel提升;证明了多项式的Hensel提升不依赖于n的选择,证明了K[x]中任一首一多项式f(x)在R[x]中具有Hensel提升的充要条件是f(0)≠0且f(x)在其分裂域中无重根。     

(R,k)-多项式与平坦性

设K是一个域，一个超曲面f(x1,x2,…,xn)＝0的坐标环是K[x1,…xn]/f,令R＝K[x1,…,xn-1],则K[x1,…,xn]＝R[xn].坐标环为R[xn]/f．根据Hilberx合冲定理,R[xn]的整体同调维数是n．本文中假设R是一个有单位元的交换环，f是R上的一个多项式，A＝R[x]/(f)．我们定义了一个(R，k)-多项式，它是首一多项式的推广，即当k＝0时，它是环R上的一个首一多项式．本文的主要结果是当f是(R,k)-多项式时，A是忠实平坦的R-模，并且当A的同调维数为有限时，其整体同调维数满足GD(A)≤GD(R)≤GD(A)+pdR(A)≤GD(A)+1，这里我们认为R的同调维数是有限的．     

零维理想的仿射代数簇

设K为一个域,I是多项式环K[x1,x2,…,xn]上的零维理想．研究了,的仿射代数簇V（I）中包含的点至多的个数及其等价命题,V（I）中包含的点的个数与商环K[x1,x2,…,xn]／I（V）及K[x1,x2,…,xn]／√I作为K上的向量空间时的维数之间的关系．     

加倍纽结的Conway多项式

J.H.Conway在他的经典文章〔1〕中给出了一个纽结不变量——位势函数(PotentialFunction),即今天被人们称为Conway多项式的整系数Lattrent多项式▽_k(x)。本文将给出关于加倍纽结的一些有意义的结论,其中所有的K都表示一个拧转q圈的加倍纽结。定理1 K的Conway多项式▽_k(x)=1-qx~2。定理2 Arf(K)= 定理3 当q为奇数时,K跨越等价(Pass Equivalent)于三叶形纽结;当q为偶数时,K跨越等价于平凡纽结。     

一类置换多项式的另一种证明

Luyan Wang给出了当3|(-1)和5|(q-1)时,f(x)=xμ(xμ+1)∈Fq[x}是置换多项式的等价条件,并给出相应的证明,本文给出f(x)=xμ(xμ+1)是置换多项式的另一种等价条件。     

保凸性逼近的一类误差估计

以Π_n记阶数不超过n的代数多项式的全体,在代数多项式的逼近问题中,保凸性的代数多项式的逼近问题,即对于凸函数f(x)∈C[-1,1]用凸的p_n(x)∈Π_n逼近的问题,很引入注意。R.K.Beatson和A.S.Shvedov[1],[4]曾证明,对于凸函数f(x)∈C[-1,1],存在着凸的p_n(x)∈Π_n,使得     

环链的Homfly多项式的微分性质

本文通过Homfly多项式的性质研究了环链的Alexander多项式的微分性质,给出一阶Alexander多项式的刻画,研究了纽结的Homfly多项式的整除性质,证明了纽结的Homfly多项式的K阶偏导数在x=1,y=-1,z=0时能被k!整除.     

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     

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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