关于图存在[a,b]-因子的邻域并条件的注记

设G是一个阶为n的图,a,b,k为正整数且1≤a〈b,2≤k≤[b／a],δ（G）为G的顶点的最小度．若δ（G）≥a,n≥（a＋b）（k（a＋b）-2）/b,且对V（G）的任意独立子集{x1,x2,…,xk}有｜NG（x1）∪NG（x2）∪…∪NG（xk）｜≥an／（a＋b）,则G存在[a,b]-因子．     

含对称平均的不等式及其应用

用降维法建立了含九个正实数a1,a2,…,an的第一k次对称平均∑n^k（a）=[（k^n）^-1 1≤il＜…＜ik≤nj=1 ∑ ∏^k aij]^1/k,第二k次对称平均σn^k（a）=（k^n）^-1 1≤il＜…＜ik≤n ∑ （ai1 ai2…aik）^1/k,第三k次对称平均∏n^k（a）=（1≤il＜…＜ik≤n ∏ ai1＋ai2＋…＋aik/k）^（n^k）^-1的一个不等式链∏n^k（a）≥∑n^n＋1-k（a）≥σn^n＋1-k（a）（1＜k＜n）,并将此结果用于正定矩阵及单形．     

围道积分法计算一种类型的广义积分——利用留数定理计算实变函数定积分

本文基于高等数学计算∫-∞ ^ ＋∞（xn＋a1x^n-1＋…an/xm＋b1x^m-1＋…bm）dx（m-n≥2））的困难,引用一种新的计算方法,运用留数定理加以计算.     

巧用排序原理证国内外不等式竞赛题

[排序原理]：设有两个数组，a1≥a2≥……≥an，及b1≥b2≥……≥bn．侧有：（顺序和）（乱序和）……①（逆序和）……②其中，j1，j2……jn是1．2……n，。的任一排列，当且仅当a1=a2=……=an，b1=b2=……=bn时“=”号成立，（对人，j。，j3……j一的任一排列均成立）．证明：不妨设乱序和S中人一切若人一。，则看人；），且在和S中含有项a＊b．则：。／一十。入，＜。‘。＋。／．事实上，右一左一（。－。，）（八一切．）2小…·伊由不等式（③知人一n时，调换X一。I勿，＋……。。勿。＋。山中bJ．位g（其余不动》．所得和几＞S，…     

关于2G与路的并的优美标号

设G是有q条边的优美二部图,优美标号为θ,pm是有m条边的简单路,C=k 0〈k〈q,k≠θ（v）,v∈V（G{）},a=maxC,b=minC,h=min q-a＋2,b{}＋2.图G∪G∪Pm是两个图G与一条简单通路的不交并.证明了：当m=1或m≥h时,图G∪G∪Pm是优美的.应用此结论,得到：对所有的s≥2,t≥2,当m=1或m≥3时,图Ks,t∪Ks,t∪Pm是优美的.     

微积分中的三点注记

对∞∑n=1（-1）^n=1 1/（n＋k1）＋（n＋k2）＋…＋（n＋km）n≥1 1≤k1〈k2〈…〈km m≥给出求和方法。对四类方程f（x,y,z）=0证明在奇异点处,无切平面。对n维单位球体体积Vn（n≥2） n=5 V5体积最大,lim n→＋∞Vn=0     

图CnUP4的优美性

证实了圈CnUP4，当n＝12k＋1（k≥5），n＝12k＋3(k≡0，1，5（mod6），且k≥5），n＝12k＋5（k≡1，2（mod4），且k≥5）时的优美性。     

亚纯函数的正规族

设为F区域D上亚纯函数簇,k∈Z^＋（k≥2）,m∈Z^＋,a≠0,b为两有穷复数,c（z）≠0为D上解析函数,Vf∈F,f（z）的零点之级≥m,并且f（z）在区域D上的极点总个数（计算重数）至多为m,f（z）=a→f＇（z）=b,f（z）=0→0→f＇（z）=c（z）,f＇（z）=c（z）→｜f^（k）（z）｜≤h,那么F在区域D内正规．     

Catalan数的一些结论

Catalan数是指n个1和n个0构成2n项a1,a2,…,a2n,其部分和恒满足a1＋a2＋…＋ak≥k/2,k=1,2,…,2n的排列。这类排列的个数为catalan数,记为Cn=1/（n＋1） （2n/n）（n≥0）,给出了Catalan数的有关性质及其相关的结论,以及有关的例子。     

有关Hamilton图与连通度的一个充分条件

利用插点方法和H-序列,证明了如果G是n阶简单图,k=k（G）≥k≥2．而（a1,a2,…,ak＋1）是H-序列,若对于任意的Y∈Ik＋1^（e）（G）,有∑i=1^k＋1aisi（Y）＋sk＋1（Y）〉n＋k＋k-3,则G是Hamilton-图,该定理也是对这方面已有的某些定理的有效推广。     

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

正~~