定理的

Based on the view that the theorem of closed mested interval is an axiom,this paper deduces the essential limit of monotonic bounded sequence of number and the Dedekind theorem,and proves the general theorem of bull closed nested interval of real number .

以通常所说的闭区间套定理作为公理推出单调有界数列存在极限和Dedekind定理，并且证明了通常所说的实数满闭区间套定理

At first, we establish some new KKM type theorems involving admissible set-valued mappings and the set-valued mapping with compactly local intersection property in FC-spaces. As applications, some new coincidence theorems and fixed point theorems are proved in FC-spaces.

首先，在FC-空间中得到了涉及容许类集值映射和具有紧局部交性质的更为一般的KKM 型定理，作为应用，在FC-空间中证明了一些新的重合点定理和不动点定理。

Meantime, the Namioka-Bauer's and Wong's positive extension theorem are generalized to ordered locally convex spaces (see Theorem 5.1) and hence some new necessary and sufficient conditions of positive extension in ordered locally convex spaces are obtained

同时Namioka-Bauer 定理和 Wong定理也被推广到半序局部凸空间中(定理5.1)，从而得到了一些新的关于半序局部凸空间中正延拓的充分必要条件

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

Furthermore, the Taylor's expansion of $\varphi(t_1,t_2)$ is given and the relation between chance distribution and characteristic function such as inversion formula is obtained.

此外，我们还给出了特征函数$\varphi(t_1，t_2)$的泰勒展式，得到了机会分布与特征函数的关系式反演公式，唯一性定理，正极限定理，逆极限定理等。

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。

According to theorem of motion of centre of mass and theorem of moment of momentum about centre of mass , we derive the theorem of moment of momentum about instantaneous center of rotation.

从质心运动定理和相对质心的动量矩定理出发，导出了相对瞬心的动量矩定理。

By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskiis fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于锥上的非线性Leray-Schauder择一型定理和郭-Krasnoselskiis不动点定理，我们建立了非线性奇异耦合分数次微分方程组正解的存在性定理。

By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskii's fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于锥上的非线性Leray-Schauder择一型定理和郭-Krasnoselskii's不动点定理，我们建立了非线性奇异耦合分数次微分方程组正解的存在性定理。

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。