微分中值定理的几个推广结论

本文将微分中值定理中的闭区间[a,b]推广到无限区间[a, ∞)或(-∞, ∞)、开区间(a,b)推广到无限区间(a, ∞)或(-∞, ∞),从而得出与之相应的几个结论.     

罗尔定理的推广形式

将罗尔定理要求f(x)在(a，b)可导推广到f(x)在(a，b)内除有限个点处存在 ∞或-∞的导数时均有有限导数存在的情况，及将f(x)在[a，b]连续推广到f(x)在(a，b)有界或无界，并对f(x)在(a，b)可导的情况给予了证明．     

微分中值定理证明研究

在学习了导数之后,要想运用导数这一概念去分析和解决更复杂的问题,只知道怎样计算导数还是不够的,还需要掌握微分中值定理,它是微分应用的桥梁,对微分中值定理有必要进行更深入的研究.微分中值定理包括三个定理:[1]罗尔(Rolle)定理:假设函数 f(x)在闭区间[a,b]上连续,在开区间(a,b)内可导,且f(b)=f(a),则在(a,b)内至少存在一点ξ,使得 f’(ξ)=0.[2]拉格朗日(Lagrange)定理:假设函数 f(x)在闭区间[a,b]上连续,在开区间(a,b)内可     

关于微分和积分中值定理“中值点”位置的估计

对微分中值定理和积分中值定理中“中值点”在区间(a,b)内的位置进行了讨论,并给出了一种实用的近似估计。     

Rolle中值定理的推广

对Rolle中值定理的条件作了改进，把函数可导推广为左或右可导，把有限区间推广为无限区间，把函数在区间端点处的函数值相等推广为可以不等．主要建立了如下的推广定理：设函数f（x）在有限或无限区间（a，b）上连续，f（x）在（a，b）内右（或左）可导，并存在{an}，{bn}包括（a，b）使 liman n→∞=a limbn n→∞=b limf（an）n→∞=linf（bn）n→∞=A A为实数或±∞，则存在ξ,η∈（a,b），使得f′＋（ξ）≥0,f′＋（η）≤0（或f′-（ξ）≥0,f′-（η）≤0。更进一步，设f′＋（x）（或f′-（x））在（a,b）内左（或右）连续，则存在ξ∈（a,b）使得f′＋（ξ）=0（或f′-（ξ）=0）.     

关于第二积分中值定理“中间点”的渐近性

本文给出并证明了第二积分中值定理的波勒形式和维尔斯特拉斯形式中,当区间[a,x]中的x→a时,“中间点”ξ→x,即 lim ξ—a/x—a=1;当[x,b]中的x→b时,“中间点”ξ→x,即lim b—ξ/b—x=1 1985年李文荣研究了当区间长度趋于零时柯西中值定理和推广的积分中值定理“中间点”的渐近性。在这之前,1982年的美国数学月刊上已有两篇文章,研究了当区间长度趋于零时,积分中值定理和泰勒定理“中间点”的渐近性。本文给出并证明了第二积分中值定理的波勒(O.Bonnet)形式和维尔斯特拉斯(Weierstrass)形式“中间点”的渐近性有关定理。     

Луэин定理的再推广

在专著中对关于可测函数连续性质的定理作了推广(以下称此推广了的定理为定理)。本文对定理中的条件又作了一些推广。首先,将定理中B是测度有限的集合改为测度无限的集合,将闭区间[a,b]改为无限区间(-∞,+∞),得到以下定理:     

关于积分中值定理的一个注记

本文给出并论证了积分中值定理中的ξ,当 b→a~+时,将趋于(a,b)的中点,即·第一,二积分中值定理中的ξ分别有积分中值定理若函数 f(x)在区间[a,b]上连续,则在[a,b]上至少存在一点ξ,使得     

关于积分第一中值定理

关于积分第一中值定理(推广了的形式)的叙述,二十多年来,我国高等学校理科采用的各种版本,基本上大同小异。例如,有如下的叙述方式:定理1 设在区间[a,b]上函数f(x)连续而g(x)可积,并且g(x)在整个区间[a,b]上不变号。则有一点ξ∈[a,b]使     

关于微分中值定理的中间点

近年来,不少文章讨论积分中值定理中的中间点的渐近性质,并得到许多有趣的结果。但对于微分中值定理中间点的渐近性质,目前讨论甚少,本文主要讨论微分中值定理的中间点,并给它中间点的渐近估计式,结果为: 定理1 设f(x)在[a,b]上连续,(a,b)内可导,如果f(x)-f(a)是关于x—a的a阶无穷小,a≠1,则拉格朗日微分中值公式f(x)—f(a)=f(ξ)(x—a)中的中间点ξ     

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     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

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