给定悬挂点的三圈图的零阶广义Randic指数

对于简单的连通图G,它的零阶广义Randic指数0Rα(G)定义为Σv∈V(G)[dG(v)]α,其中α是一个给定的实数,dG(v)是G中顶点v的度.简单连通图G的零阶广义Randic指数是化学图论中一个重要的拓扑指数,其在化学领域中有着广泛的研究及应用.基于此对于任意的α(≠0,1),它给出了顶点个数为n,悬挂点为k的所有三圈图的零阶广义Randic指数0Rα的一些紧的界.     

有r(≥3)个圈仙人掌图的零阶广义Randic指数的界

设G为一简单连通图,则G的零阶广义Randic指数定义为R0α(G)=∑v∈V(G)dα(v),其中d(v)为顶点v的度数,α为非0和1的实数;图G称之为仙人掌图,如果G的每一块要么是一条边,要么是一个圈.此文主要研究有r(≥3)个圈仙人掌图的零阶广义Randic指数的界.     

(0,p(D))三角插值多项式对函数及其导数的同时逼近

证明了(0,p(D))三角插值多项式Rn(x)的s(s=0,1,…,q)阶导数一致收敛于函数f(x)的s(s=0,1,…,q)阶导数:设f(x)∈C2π,f(x)具有q阶连续导数,且f(q)(x)∈Lipα.0<α<1,若βk=Op(in)n(n)-f(s)(n)=Olnnnq+α,(k=0,1,2,…,n-1),则R(s)nq-s+α(s=0,1,…,q).     

具有极值Randic’指标的二树图研究

简单连通图的Randic’指数是化学图论中一个重要的拓扑指数,其在化学领域中有着广泛的研究及应用.我们给出了一个具有n个顶点的二树图的最大和最小的Randic’指数,即2n-4/2(n-1)+1/n-1≤R(G)≤n/2-11/4+23/3+6/3+2/2同时当二树图达到这两个界限时,它的图也被刻画了出来.     

图与其补图谱半径之和的新上界

该文给出了图与其补图谱半径之和ρ(G)+ρ(Gc)的新上界,对任一n阶图G,有:p(G)+p(GC)≤((2-1/t)n(n-1))和p(G)+p(GC)≤((2-1/T)n(n-1))其中t=min{k,(k-)},T=max{k,(k-)},k,(k-)分别为图G和其补图Gc的色数.从而改进了[6],[8],[10]的结果.     

带参数的对偶Hardy—Hilbert型不等式的改进

利用加强不等式对Hardy-Hilbert型不等式做了改进,建立了一些新的形如∞∑(n=1) ∞∑(m=1)(anbn/max{m,n})<{∞∑(n=1)[pq-θq/n(1/p)apn}1/p{{∞∑(n-=1)[pq-θp/n(1-q)]bqn}1/q(1-R)k的不等式,其中 R=[Sp(α,γ)-Sq(βγ)]2≠0.     

关于 Randic 指数及图的直径

设图G=(V , E)是简单图,其中V是顶点集,E是边集.对G中任意顶点v∈V, dv表示点v的度数.图G的Randic指数也称为图G的连通性指数,定义为R=R(G)=∑uv∈E(1)/(dndv).关于连通图的Randic指数R与直径D有如下猜想:R-D≥2-(n+1)/(2)且(R)/(D)≥(1)/(2)+(2-1)/(n-1),两个等式都成立当且仅当G≌Pn.本文将简化该猜想,并进一步证明当D≤(2(n-1)(3)/(2))/(n-3+2 2)或D≤n-3时,猜想成立     

顶点最大度被限制的图的边转发指数

对于给定的n阶连通图G,一个路由选择R是指G中的n(n-1)条路集,其中每个有序点对都有路集中的一条路连接.图G关于R的边转发指数π(G,R)是R中路经过一条边的最大条数.图G的边转发指数π(G)是G关于任何路由选择R的边转发指数π(G,R)的最小值.符号πΔ,n表示所有顶点数为n,最大度至多为△的图中最小边转发指数.当n≥4p 1,且n()[4p [1/3(2p-1)]-1,6p]时,其中p≥1,确定了πn-2p,n的值.     

一类具有有限零因子的环

N.Ganesan在[1]中证明:若R是具有n(≥2)个零因子的交换环,则R的元数|R|有上界n~2。本文证明,当|R|≠n~2,(n>2)时,|R|的上界为n(n-2),并给出|R|=n(n-2)时R的分类。在本文中,R恒表示具有n(>2)个零因子的交换环。主要结论是: 定理1.设R是具有n个零因子的交换环,N是R的幂零根,|R|≠n~2,则|R|≤n(n-2)。这里n>2,当N≠0;n>3,当N=0。     

正相协序列生成的平均移动过程的Baum-Katz大数定律的精确渐近性

设{εt;t ∈ N*}是一严平稳零均值正相协随机变量序列,0＜Eε21＜∞,及σ2=0＜Eε21 2∞∑j=2Eε1εj,0＜σ2＜ ∞,{aj;j ∈N}是一实数序列,并且∞∑j=0|aj|＜ ∞.义移动平均过程Xt=∞∑j=0ajεt-j,t≥1,令Sn=n∑t=1Xt,n≥1.假设对某个δ'＞0有E|ε1|2 δ' ＜ ∞,对某个ρ＞0有μ(n)=0(n-ρ),给出了∞∑n=1nr/p-2P{|Sn|≥εn1/p},∞∑n=11/nP{|Sn|≥εn1/p}当ε→0时的精确渐近性.     

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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