定理

On the basis of these theories,Rolle mean value theorem,Lagrange mean value theorem and Cauchy mean value theorem are proved by constructing nested interval.

在此基础上通过构造区间套依次证明了罗尔中值定理、拉格朗日中值定理和柯西中值定理

The sine, law of cosines's several sine law and the law of cosines are three angular corner relations and three jiao functions plants using abstract the is most common, the most important two theorems.

正弦定理和余弦定理是三角形边角关系及三角函数种最常见、最重要的两个定理。

With four continuity of non-additive set function and the relation of four convergences of the measurable function sequence,four forms Lebesgue theorem about measurable closed-valued functions on monotone measure space are discussed,respectively.

在经典测度论中，Lebesgue定理刻画了实值可测函数序列几乎处处收敛和依测度收敛之间的关系。1984~1986年，王震源[9]先后提出了较弱的"自连续"、"零可加"、"伪自连续"、"伪零可加"等重要概念，讨论了模糊测度空间上单值可测函数序列各种收敛之间的关系，推广了经典测度论中著名的Lebesgue定理以及其他定理。

In Chapter Two, Liapunov functional method and Liapunov function method with Razumikhin techniques are employed to obtain some delay independent stability results for the Cohen-Grossberg neural networks with multiply delays.

在第三章中，我们首先对一般的无时滞Cohen-Grossber神经网络模型建立了几个稳定性定理，即文中定理3.3.1-3.3.4。从其中推论可看出负的自联接起着很大的稳定化网络的作用。然后我们考虑了一般的Hopfiel神经网络模型，运用单调动力系统理论，在对激发函数做出很弱的假定下获得了与时滞相关的稳定性结果，并对时滞的大小给出很多的估计，文中定理3.4.3。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

A three solutions theorem of nonlinear operator equation in Hilbert space was given by Sun Jing-xian in 1983,in this paper,the theorem was expanded to general Banach space by using gradient method ,and some conditions was weakened,such as the local Lipschitz condition s transformation to the bounded character of F and so on.

依据H ilbert空间中非线性算子方程的一个三解定理，本文运用最速下降法将这个定理推广到了一般的Banach空间，并且减弱了原定理的某些条件，如将局部Lipschitz条件减弱为F的有界性等

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

The theoretic results on conventional theorems are far from the experiment results. Through discussing on ABA mapping, we obtain the general collage theorem and local collage theorem for ABA mapping.

本文从分析ABA映射的Collage定理入手，导出了ABA映射的广义Collage定理和ABA映射的局部Collage定理，并提出了符合实际情况的概率模型。

As applications,a Ky Fan matching theorem for transfer open covers,a Fan- Browder coincidence theorem and maximal element theorem are established.

作为应用，获得了非紧超凸度量空间中的转移开覆盖的Ky Fan匹配定理，Fan-Browder重合定理和极大元定理。

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。