算术根

我们知道,正数或负数的偶次方都是正数。例如:(+2)~2=4,(-2)~2=4。所4的平方根有两个,一个是+2,一个是-2。一般地,我们可以证明,在复数域中,an 次方根有 n 个数,而且可以指明:当 n 是奇数而 a 是实数时,a 的 n 次方根中必有一个是实数,且与 a 同号,而其余的根则是虚数;当 n 是偶数,而 a 是实数时,a 的 n 次方根中必有二个是数,它们的绝对值相等而符号相反,而其余的根则是虚数;当 n 是偶数而 a 是负实数时,an 次方根都是虚数。为了用一个记号表示一个确定的值,我们规定“a~(1/n)”只表示正数 a 的正方根,因为     

关于二阶实矩阵的一个问题

设n是正整数,A是二阶实矩阵.该文证明了:如果An=E2且│A-E2│=n,其中E2是二阶单位矩阵,则必有n=3,A=(abc-1-a),其中a、b、c是适合a2 a bc 1=0的实数.     

关于奇完全数的存在问题

如果正整数n适合δ（n）＝2n，则称n是完全数。w（n）是n的不同素因数的个数。本文证明了：如果n为奇数且w（n）2，则n不是完全数；如果正奇数n有标准分解式，其中p1、p2、…、ps是适合p1＜p2＜…＜ps的素数，a1、a2、…、as是正整数，则当a1＝1时，n不是完全数。     

关于n长路的(a,b;n)-优美标号

证明了a=4时,Gvozdjak猜想成立.即路Pn存在一个(a,b;n)-优美标号,当且仅当整数a,b,n满足:(1)b-a与n(n+1)/2有相同的奇偶性;(2)0<|b-a|≤(n+1)/2;(3)n/2≤a+b≤3n/2.在a=4时,成立.     

Diophantine方程(a~n-1)((a+1)~n-1)=x~2的可解性

设a是大于1的正整数,v2(a)表示2可以整除a的最高次幂.运用初等数论方法研究了方程(an-1)((a+1)n-1)=x2的可解性.证明了当a满足以下3个条件之一时该方程无解(x,n):(i)a是偶数,v2(a)是奇数;(ii)a是偶数,v2(a)=2;(iii)a是奇数且a≡5或9(mod 16).同时也证明了至少有5/6的正整数a可使该方程没有适合n2的解(x,n).     

一类ab+cd=ef(a,b,c,d,e,f∈{n,n+1,n+2})的不定方程

给出并证明了关于不定方程ab cd=ef(a,b,c,d,e,f∈｛n,n 1,n 2｝)的正整数解的几个定理,其中a,b,c,d,e,f中有三个是n,二个是n 2,一个是n 1.     

非固定步长的无向循环图的支撑树数

图的支撑树数是图的重要的不变量,也是网络可靠性的重要量度.循环图是一个重要的图类,可应用于局域网和分布系统的设计中.对有固定步长的循环图,其支撑树数已得到了研究.本文考虑有非固定步长的无向循环图Cpn(a1,a2-,…,ak,q1n,q2n,…,qmn),这里a1,a2,…,ak,q2,q2,…,qm,n和p都是正整数,a1≤a2≤…≤ak≤n/2,q1≤q2≤…≤qm≤p/2,且n是可变化的,因而有些步长并非固定.给出其支撑树数的一个公式,并得到其渐近性态和常数系数的线性递归关系.     

平方根和立方根序列的均值公式

利用解析的方法讨论了两个均值问题:1.(1)/((a2(n))2)和(1)/((a3(n))2)及其它们推广形式的均值问题,得到了几个结果,其中a2(n)>和a3(n)是F.Smarandache平方根和立方根序列;2.(a2(n))(1)/(3)和(a3(n))(1)/(3)的均值问题,得到了两个有规律的结果,其中a2(n)和a3(n)是F.Smarandache平方根和立方根序列.     

哥德巴赫猜想是正确的

把一偶数表为二质数之和可有一种或多种表示法.如8可表为3+5,10可表为3+7和5+5。文中把3+5和3+7,5+5叫着表达式.若一偶数 a 有 r 个表达式,就用 G(a)=r 表示之,故 G(8)=1,G(10)=2.本文用两种方法求出两种结论如下:结论1.设 a≥18是偶数,a=2n.若6|a,则 G(a)>n/(log~2n),若6(?)a,则 G(a)>n/(2log~2n).结论2.设 a≥6是偶数.若6|a,则 G(a)>a/(2log~2a),若6(?)a,则 G(a)>a/(4log~2a).对于两个结论作了此较,它们实际上是大同小异.     

关于三项式χ^n—bχ—a的二次整系数因式

设n≥5,a,b≠0,n∈N,a,b∈Z,本文利用Gel'found-Baker方法证明了,如果三项式xn-bx a有二次整系数因式,则除了n≡2(mod 6)且b=1,a=-1,与n≡2(mod 3)且b=-1,a=-1这些明显情形外,必定有n＜max(8/7|b|,512900).     

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