关于函数极值的几个定理

在函数极值的一般理论的基础上，得出了形如ｆ′（ｘ）＝ｇ（ｘ）φ（ｘ）的一类可导函数ｆ（ｘ）有极值的充分条件：设函数ｆ（ｘ）在ｘ０点的某邻域二阶可导，且ｆ′（ｘ）＝ｇ（ｘ）φ（ｘ），ｆ′（ｘ０）＝０．（１）若φ（ｘ０）＞０，则当ｇ′（ｘ０）＞０时，ｆ（ｘ０）为ｆ（ｘ）的极小值；当ｇ′（ｘ０）＜０时，ｆ（ｘ０）为ｆ（ｘ）的极大值．（２）若φ（ｘ０）＜０，则当ｇ′（ｘ０）＞０时，ｆ（ｘ０）为ｆ（ｘ）的极大值；当ｇ′（ｘ０）＜０时，ｆ（ｘ０）为ｆ（ｘ）的极小值．     

一类极限圆型二阶非线性微分方程的充要条件

借助于极限圆型的二阶线性微分方程（ｒ（ｔ）ｘ′（ｔ））′＋ａ（ｔ）ｘ（ｔ）＝０,讨论了二阶非线性微分方程（ｒ（ｔ）ｘ′（ｔ））′＋Ｐ（ｔ）ｘ′（ｔ）＋ａ（ｔ）ｘ（ｔ）＋ｂ（ｔ）ｆ（ｔ,ｘ）＝０,建立了其属于ＬＣ（解平方可积）或ＬＣ∩ＬＳ（ＬＳ表示解有界）的充分条件     

线性微分方程幂级数解的收敛半径

给出微分方程Ｙ″＋Ｐ（ｘ）ｙ′＋Ｑ（ｘ）ｙ＝０的幂级数解ｙ＝∑ｎ＝０＾∞ａｎ（ｘ－ｘ０）＾ｎ其系数满足二项递推公式ａｎ＋ｐ＝ｆ（ｎ）ａｎ的收敛半径的求法。     

守恒双曲型方程式初边值问题的隐式解及一维情形下激波稀疏波的确定

１　一维守恒双曲型标量方程的初边值问题解法讨论一维标量守恒双曲型方程　ｕｔ＋ｆ（ｕ）ｘ＝０（１）的纯初值问题　ｕ（ｘ,０）＝φ１（ｘ）（－∞＜ｘ＜∞）（２）及初边值问题　ｕ（ｘ,０）＝φ１（ｘ）,（０≤ｘ＜∞）　ｕ（０,ｔ）＝φ２（ｔ）（０≤ｔ＜∞）（３）并得到如下结果：１）问题（１）,（２）当１＋ｆ″φ１′ｔ≠０时的隐式解为　ｕ（ｘ,ｔ）＝φ１（ｘ－ｆ′（ｕ（ｘ,ｔ））ｔ）（４）２）问题（１）,（３）当１＋φ′１ｆ″ｔ≠０,１－φ２′ｘｆ″／（ｆ′）２≠０时的解为　ｕ（ｘ,ｔ）＝φ１（ｘ－ｆ′…     

一致收敛性与有效解的极限性质

本文考虑带参数的多目标规划ＶＰ（ｕ,ｖ,ｗ）,Ｄ（ｖ）－Ｍｉｎ｛ｘ∈Ｘ０（ｗ）｝,其中目标函数ｆ（ｘ,ｕ）关于变元ｕ在ｕ处一致收敛于ｆ（ｘ）＝ｆ（ｘ,ｕ）     

关于刘玉琏第3版《数学分析讲义》所述一个“定理”的注记

构造一个函数，说明“Ｖｘ∈Ｉ，ｆ（ｘ）≥０，（ｆ（ｘ）≤０），而使ｆ（ｘ）＝０的点仅是一些孤立点”不能作为“函数ｆ（ｘ）在区间Ｉ严格增加（严格减少）”这一结论成立的必要条件。     

高阶摄动波动方程的Lp-Lp′估计

考虑下面高阶摄动方程解ｕ（ｘ,ｔ）的ＬｐＬｐ′估计：ｔｕ＋（－Δ）ｍｕ＋Ｖ（ｘ）ｕ＝０,ｕ（ｘ,０）＝０,ｕｔ（ｘ,０）＝ｆ（ｘ）,｛ｘ∈Ｒｎ,ｎ＞３ｍ．假设势函数Ｖ（ｘ）和初值ｆ（ｘ）具紧支集,Ｖ（ｘ）是小势,则上面问题的解满足‖ｕ（·,ｔ）‖ｐ′≤ｃｔ－ｄ‖ｆ‖ｐ,ｔ＞０,这里ｍ≥１,ｄ＝ｎｍ（１ｐ－１ｐ′）＝１,１ｐ＋１ｐ′＝１,ｍ２ｎ≤１ｐ－１２＜ｍｎ．     

关于一个组合型Bernstein多项式的逼近阶

以Ｊａｃｏｂｉ多项式的零点作为插值的节点,构造了一个组合型的Ｂｅｒｎｓｔｅｉｎ多项式算子Ｃｎ（ｆ,ｘ）．若ｆ（ｘ）∈Ｃｊ［－１,１］,０≤ｊ≤５,则Ｃｎ（ｆ,ｘ）对ｆ（ｘ）的逼近程度均达到最佳。即｜Ｃｎ（ｆ,ｘ）－ｆ（ｘ）｜＝Ｏ１ｎｊ＋１＋１ｎｊωｆ（ｊ）,１ｎ,（０≤ｊ≤５）．     

有返回轨道的区间连续自映射

设ｆ∈Ｃ０（Ｉ），若存在ｘ∈Ｉ及正整数ｎ，正奇数ｄ及非负偶数ｐ使得ｆｎ（Ｘ）≤Ｘ＜ｆ（ｘ）且ｆｄ（ｘ）≤ｆｐ（ｘ），或者ｆｎ（ｘ）≥ｘ＞ｆ（ｘ）且ｆｄ（ｘ）≥ｆｐ（ｘ），则ｆ２含有湍流，即，存在着Ｉ中的点ｒ＜ｓ＜ｔ使得ｆ２（［ｒ，ｓ］）（［ｓ，ｔ］［ｒ，ｔ］）。这一结论改进了ＴＹＬｉ，ＭＭｉｓｉｕｒｅｗｉｃｚ等人在“Ｎｏｄｉｖｉｓｉｏｎｉｍｐｌｉｅｓｃｈａｏｓ”中的命题３．６．此外，本文还简化了该文中的命题２．３及３．４的证明。     

一类双曲型方程解的爆破（Blow—up）现象

ＬａｉＳｈａｏｙｏｎｇ＆ＭｕＣｈｕｎｌａｉ（ＡｐｐｌＭａｔｈ－ＪＣＶ,１９９７,１２Ｂ：３２１）研究了在ｆ（ｘ）,ｇ（ｘ）,Ｇ（ｕ）满足一定条件下,如下方程ｕｔ－Δｕ＝εＧ（ｕ）,ｔ≥０,ｘ∈Ｒ３,ε＞０充分小,ｕ（ｔ,ｘ）＝ｆ（ｘ）,ｕｔ（ｔ,ｘ）＝ｇ（ｘ）,ｘ∈Ｒ３｛解的渐近理论及应用．且在假设ｆ（ｘ）≡０,ｇ（ｘ）及Ｇ（ｕ）满足一定条件下得到了以上双曲型问题整体解的非存在性．因此,本文的工作可以看成是ＬａｉＳｈａｏｙｏｎｇ＆ＭｕＣｈｕｎｌａｉ工作的继续．     

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