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Some existence and uniqueness theorems for above problem are established by using certain fixed point theorem based on the degree theory.

用基于度理论的不动点定理，建立了一系列存在唯一性定理。

Construction and properties of the integral; convergence theorems; Radon-Nykodym theorem; Fubini's theorem; mean convergence.

积分。 积分的构造和性质；各类收敛定理；拉东(Radon-Nykodym)定理；富比尼定理；平均收敛

The Paper mainly studies forecast of a kind of time sequence which is made by using fuzzy approximation and Functional differential Equation, gives several theorems which explicate fuzzy and optimal approximation and relation between them by using the forecasting method.

主要对以模糊逼近和泛函微分方程进行时间序列预测问题作进一步的理论研究，给出了几个有关使用该预测方法时，模糊逼近与最佳逼近及其关系的定理，证明了逼近方面及预测方面的一些有意义的结果。

Fundamental theorem are theory base. These theorems are equivalent each other.

因此，基本定理是分析中的理论基础，而这些定理又是相互等价的。

In § 1, we give main definitions and basic results that are needed in the paper. In § 2, we determine the structures of somegroups by using s-normality of Sylow subgroups and the maximal subgroups of Sylow subgroups. There are the main theorems that 1 Let G be a finite group and P be a Sylow p-subgroup of G where p is a prime divisor of |G|.

我们在§1中将给出本文所需的主要概念和基本结果，在§2中讨论Sylow子群、Sylow子群的极大子群的s-正规性对群的结构的影响，主要结果是1设G为有限群，p为|G|的素因子，P为G的Sylow p-子群。

But in this paper, it is proven that the upper bound has nothing to do with the viscosity of the fluid by using decomposing theorems of spaces, Gauss's formula and Sobolev Space methods.

文中利用空间分解定理、高斯公式及Sobolev空间方法证明了不可压缩粘性流体定常旋转流在Sobolev空间［H1］3中存在一个与流体粘度无关的上界。

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。

Using generalized transfer function as a tool, a set of theorems for deciding movement stability have been constructed.

本文给出了控制系统的广义传递函数和它的连续性的定义。

In chapter 2, we first give a generalized type of the Prigons fixed point theorem and a straightforward proof of it. At the same time, we give a positive answer to an open question about convergency of iterative sequence for generalized contraction which is bring forwarded by Frigon in [3]. Secondly, by using the introduced function φ, we establish some fixed point theorems for the set-valued φ-contraction mappings in gauge spaces. These results unify and generalize the corresponding results of Cain and Nashed [1], Figon [3], Espinola and Kirk[4], Tarafder [5] et al.

第二章，首先给出Frigon不动点定理[3]的推广及其简洁证明，同时对Frigon在文[3]中提出的关于广义压缩迭代序列收敛性的公开问题给出肯定的回答；然后，通过引入φ函数，在度规空间上建立集值φ-压缩映射的不动点定理，统一并推广了Cain和Nashed[1]，Figon[3]，Espinola和Kirk[4]，Tarafder[5]等的相应结果。

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

我认为，数学的存在是不以我们的意志为转移的，我们的作用是发现它或观测它，那些我们证明的和我们称之为'创造'的定理，仅仅是对我们的观测数据的注解。

Vishnu entered a dark fourth dimensional dream that did not support his field or continued life.

毗瑟挐进入了一个第四密度的黑暗梦想，那里并不支持他的能量场或继续生命。

Leaders and decision-making persons use it to collect the data, including the information of unit work, handing in fee, oweing fee, prepaying fee,changing and afterpaying and account transfering of joining-insurance employee, and account paying of all kinds of insurances from hospitalization insurance institutions.The collected data is picked up, organized, switched and showed to user.

该子系统主要面向各级领导、决策分析人员；从各个医疗保险经办机构和定点医疗机构采集数据，包括在各个医疗保险经办机构处理的单位办公信息，单位缴费、欠费、预缴费信息，参保职工变更信息，参保职工增减变动信息，参保职工补缴信息，参保职工帐户划拨信息：包括各定点医疗机构处理的各险种帐户支出信息，各险种的统筹金支付信息等；将采集的数据提取，组织和转换，然后展示给用户。