关于连续正整数平方和中的素数方幂

对给定的正整数k,证明了:当9|k或q|k(q=±5(mod 12)是一个素数)时,任何k个连续正整数的平方和不是素数的n次幂(n∈N);当q|k(q=±1(mod 12)是一个素数)时,可定出模q的两个剩余类,而不属于其中任何一个剩余类的每一个非负整数x所确定的k个连续正整数的平方和(x 1)2 (x 2)2 … (x k)2不是素数的n次幂(n∈N).     

寻找关于几个素数基的两类强伪素数

给出了用四次剩余特征为主要工具找K8-强伪素数和K7/2-强伪素数(具有形式n=pq,其中p,q是奇素数且q-1=k(p-1),k=8,7/2的强伪素数)的方法,表列出所有小于1024的关于前6个素数基的K8-强伪素数和关于前4个素数基的K7/2-强伪素数,总共有111个K8-强伪素数和173个K7/2-强伪素数.进一步验证了张振祥的一个论断,即PR(n)值越接近1/4时,n成为关于较多个基的强伪素数的可能性就越大.     

关于方程k(n)=n-1

关于方程(1)k(n)=n-1,其中(?)(n)为Euler函数,k为正整数,D.H.Lehmer曾经证明当k=2时,它的解至少是7个不同奇素数的乘积,当k=3时,至少是33个不同奇素数的乘积。从而证明了方程(1)的解在k>1时,至少是7个不同奇素数的乘积。在本文中,我们将证明方程(1)的解当k=2时,至少是12个不同奇素数的乘积,当k=3时,     

伯特兰猜测的推广与证明

(n,2n)中至少有一个素数,称为伯特兰猜测(华罗庚,1979),其正确性首先为俄国数学家切必雪夫所证明。但一百多年来,此猜测未能再进一步。本文将这一猜测推广为:a>1,n充分大时,(n,an)中至少有一个素数。并由此推出:对任何正整数k,n充分大时,(n,2n)中至少含有k个素数。     

第六个费马素数存在性的一个等价命题

在数论中,是否存在第六个费马素数一直是个未解决的问题.通过运用欧拉函数建立了第六个费马素数存在性的一个等价命题.也就是,第六个费马素数存在,当且仅当存在一个正整数使得方程ψ(x)=2k有34个解,其中ψ(x)为欧拉函数.     

关于Diuphantion方程x2+(x+1)2+…+(x+K-1)2=pn

指出了文献[4]中证明过程的错误,得到了比文[4]中更一般的结论,当K=4k,9k,qk(q≡±5(mod 12)为素数)时,Diuphantion方程(1)无正整数解,即K个连续正整数的平方和不是素数或素数方幂。     

推广的四素数方次和问题

用圆法研究了一个整数表为三个素数的平方与一个素数的k次方之和问题,推广了刘建亚关于四素数平方和问题的结论.该文得到例外集E(N)N12-25×4k-1 ε.     

关于1, 1/2, …, 1/n的一类初等对称函数的2-adic赋值

设n和k为正整数且n≥k.本文考虑关于1,1/2,…,1/n的第k次初等对称函数■的2-adic赋值．设p为素数．2015年,Lengyel证明v_p(H(n,k))>-klog_pn+O_k(1),其中v_p(H(n,k))表示H(n,k)的p-adic赋值,O_k(1)表示一个依赖于k的常数．2017年,Leonetti和Sanna猜想：对所有足够大的正整数n,总存在一个正的常数c=c(p,k),使得v_p(H(n,k))<-clogn,并对不超过x的正整数n证明了当n的p-adic表示是以k-1的p-adic表示为起始值时,除了至多3x^0.835个例外之外此猜想是正确的．本文给出了H(n,2)的2-adic赋值的确切值或下界,部分验证了上述猜想．     

关于同余式sum from i=1 to k(x_i~2≡0(mod p))(1≤x_1

杨波 《四川大学学报(自然科学版)》1992,(1)

关于丢番图方程x~4±(pq 4)~(1/2)x~2y~2 y~4=z~2

Aubry在1911年曾断言:当|k|=(pq 4)~(1/2),p,q均为素数(即|k±2|均为素数)时。若0k≡3(mod8),则方程x~4=kx~2y~2 y~4=z~2无xy≠0之整数解。本文对这一断言给出了一个完整的。自给的证明,同时还进一步证明了对于k值之模8分类而言,Aubry的断言是不可改进的。     

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.     

Design and analysis of generic LBS application developing platform

Location based services is promising due to its novel working style and contents.A software platform is proposed to provide application programs of typical location based services and support new applications developing efficiently. The analysis shows that this scheme is easy implemented, low cost and adapt to all kinds of mobile nework system.     

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