计算Kdv方程守恒密度的待定系数法

秩为ｒ的不可约单项式的集合Ｓｒ可以直接转化为Ｓ（ｒ＋１），多项式守恒密度Ｔ（ｒ＋１）＝Ｔ＿（ｒ＋１）￣０＋Ｕ＿（ｒ＋１），Ｔ＿（ｒ＋１）￣０的每一项都含因子ｕ＿０，可从Ｔ＿ｒ得到Ｕ＿（ｒ＋１）（ＣＳ＿（ｒ＋１））的每一项不含因子ｕ＿０，Ｕ＿（ｒ＋１）与Ｔ＿（ｒ＋１）￣０的项之间存在着特殊的相关性，由此可分批求出Ｕ＿（ｒ＋１）中的特定系数且不涉及Ｘ＿（ｒ＋１）。     

关于C．C．Yang的涉及亚纯函数增长性的几个问题

得到如下一些结果：（１）设ｆ是任一亚纯函数，若ｌｉｎｒ→∞Ｔ（ｒ，ｆ（ｚ＋１））／Ｔ（ｒ，ｆ（ｚ））＝∞，则级ρｆ＝∞。（２）设ｆ，ｇ１，ｇ２，皆为非常整函数，且Ｔ（ｒ，ｆ）＝Ｏ（（ｌｏｇｒ）＾），ｇ２的级为有穷，Σａ≠∞δ（α，ｇ２）＝１，Ｔ（ｒ，ｇ１）＝ｏ（Ｔ（ｒ，ｇ２））（ｒ→∞）。则Ｔ（ｒ，ｆ（ｇ１））＝ｏ（Ｔ（ｒ，ｆ（ｇ２））（ｒ→∞），其中Ｔ（ｒ，ｆ）＝Ｏ（（ｌｏｇｒ）＾α表示，当ｒ→     

关于差分方程un＋r=Σ（n＋r,i=1）aiun＋r—i—bn的显示解

给出了差分方程｛ｕｎ＋ｒ＝Σ（ｎ＋ｒ，ｉ＝ｉａｉｕｎ＋ｒ－ｉ＋ｂｎ ｕｉ＝ｃｉ ｉ＝０，１，…，ｒ－１的一个显示解，ｕｎ＝ｄｎ＋Σ（ｎ，ｉ＝ｄｎｉｋ＋ｋ＋２…＋ｉｋｉ（Σ（ｉ，ｊ＝１ｋｊ）！Π（ｉ，ｊ＝１）ａｉｋｊ／Π（ｉ，ｊ＝１）ｋｊ！．     

一类新算子的同时逼近

引入一种新的正线性算子并研究它对于无界函数的同时逼近.设ｆ∈Ｃβ[０，∞），ｒ∈N，ｆ（ｘ）在[０，∞）存在ｒ阶导数，则ｌｉｍｎ∞Ｍ（ｒ）ｎ，α（ｆ（ｔ），ｘ）＝ｆ（ｒ）（ｘ）；若ｆ（ｒ）（ｘ）∈Ｃ（ａ－η，ｂ＋η）（η＞０），则Ｍ（ｒ）ｎ，α（ｆ，ｘ）ｆ（ｒ）（ｘ）在ｘ∈[ａ，ｂ]一致成立.设ｆ∈Ｃβ[０，∞），ｆ（ｘ）在[０，∞）上存在ｒ＋２阶导数，则ｌｉｍｎ∞ｎ[Ｍ（ｒ）ｎ，α（ｆ，ｘ）－ｆ（ｒ）（ｘ）]＝α[ｒ（ｒ＋１）ｆ（ｒ）（ｘ）＋（２（ｒ＋１）ｘ＋ｒ）ｆ（ｒ＋１）（ｘ）＋ｘ（１＋ｘ）ｆ（ｒ＋２）（ｘ）]；若ｆ（ｒ＋２）（ｘ）∈Ｃａ－η，ｂ＋η）（η＞０），则上式在[ａ，ｂ]一致成立.     

线性变换与其导数增长性比较的一个注记

研究了超越亚纯函数的分式线性变换的特征函数与其导数的特征函数增长性的比较，并由Ｎｅｖａｎｌｉｎｎａ理论推导出一个定理，其主要结果为：Ｔ（ｒ，Ｆ）＜４０λλ－１ｌｏｇｅλλ－１Ｔ（λｒ，ｆ′）＋ｌｏｇ＋（λｒ）＋ｌｏｇ＋｜ｆ（０）｜＋５＋ｌｏｇ＋ａｄ＋ｌｏｇ＋ｂｄ＋ｌｏｇ２（ｃ＝０）Ｔ（ｒ，Ｆ）＜４０λλ－１ｌｏｇｅλλ－１Ｔ（λｒ，Ｆ′）＋ｌｏｇ＋（λｒ）＋ｌｏｇ＋｜Ｆ（０）｜＋５＋ｌｏｇ＋ａｄ－ｂｃｃ２＋ｌｏｇ＋ｄｃ＋ｌｏｇ２＋ｈ（ｒ）（ｃ≠０）     

五次(0,3)类缺插值样条的局部渐近性质

本文讨论［１］中所定义的五次（０，3）类缺插值样条Ｓｎ（ｘ），当ｆ∈ｃθ［０，１］时，的局部渐近性质。得到： 定理 设ｆ（ｘ）∈Cθ［０，１］，Sｎ（ｘ）是ｆ（ｘ）的五次（0，3）类（ｉ）型缺插值样条，＝Ⅰ，Ⅱ，Ⅲ，Ⅳ，那么对于任意固定的ｘ∈（０，１），当 n→时有 Ｓｎ（ｘ）＝ｆ（ｘ）－［Ｂθ（ｕ）－１／４２］·ｆ（６）（ｘ）·ｈ６／６！＋ｏ（ｈ６）和 Ｓｎ（ｒ）（ｘ）＝＝ｆ（ｒ）（ｘ）－Ｂ６－ｒ（ｕ）ｆ（６）（ｘ）·ｈ６－ｒ／（６－ｒ）！＋ｏ（ｈ６－ｒ），ｒ＝１，２，３，４，5。其中Ｂ１（ｕ）是首项系数为１的ｊ次Ｂｅｒｎｏｕｌｌｉ多项式；u＝（ｘ－γｈ）ｉ　γ＝［ｎｘ］。     

关于Schur代数的一点注记

证明了当ｒ≤ｎ和ｒ＞ｎ＞（ｒ－ｎ＋１）１时，群代数ＫＧ（ｒ）同构于Ｅｎｄｓｋ（ｎ，ｋ）     

关于（K，d）－算术图的两个猜想

文献［１］中猜想：（１）若Ｃ４ｔ＋１是（Ｋ，ｄ）－算术图，则有非负整数ｒ，使得Ｋ＝２ｄｔ＋２ｒ；（２）如果Ｃ４ｔ＋３是（Ｋ，ｄ）－算术图，则有非负整数ｒ，使得Ｋ＝（２ｔ＋１）ｄ＋２ｒ。本文证明了这两个猜想均是正确的     

方程x（t）＝—f（x（t），x（t—r＿1），（t—r＿2））非常数周期解的存在性

研究了方程ｘ（ｔ）＝─ｆ（ｘ（ｔ），ｘ（ｔ─ｒ＿１），（ｔ─ｒ＿２））（Ａ）非常数周期解的存在性。证明了在某些条件下，方程（Ａ）有以４ｒ＿１／（１＋４ｎ）（ｎ为非负整数）为周期的非常数振动的周期解。     

复合整函数的增长性

得到如下结果：设ｆ 和ｇ 是超越整函数,且 Ｔ（ ｒ ,ｆ） ＝ Ｏ（ｅ（ｌｏｇ ｒ） α, Ｔ（ ｒ ,ｇ１ ） ＝ Ｏ（（ｌｏｇｒ） β）（ 即存在正常数 Ｋ１ 和 Ｋ２ ,使有 Ｋ２ ≤ Ｔ（ ｒ ,ｇ１）（ｌｏｇｒ） β ≤ Ｋ１） ,如果 Ｔ（ ｒ ,ｇ１） ～ Ｔ（ ｒ ,ｇ２）（ ｒ →∞） ,则 Ｔ（ｒ ,ｆ（ ｇ１）） ～ Ｔ（ ｒ ,ｆ（ ｇ２）（ ｒ →∞,ｒ  Ｅ） ．其中０ ＜ α＜ １ ,β＞ １ 及αβ＜ １ , Ｅ 是有限线性测度的正实数集合。这个结果解决了 Ｃ． Ｃ． Ｙａｎｇ 提出的关于复合函数的特征函数的一个问题。     

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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