基本引理

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we inducted the absolute value norm in the two-dimensional vector interspace, and also proved the two-dimensional vector interspace is a Banach Interspace. Thirdly, we define two-dimensional vector-valued functions on a interval by the definition of -fine partitions in part 1. Then, some sufficient and necessary conditions of integrabel are given, and discuss the property of the integral on two-dimensional vector-valued functions.

主要包括以下内容：在第一部分，我们介绍了本文所用到的几个基本概念和引理；第二部分，我们在二维向量空间中引入了绝对值范数，并且证明了二维向量空间是一个Banach空间；在第三部分中，通过第一部分关于-精细分划的定义，我们给出了在某区间上二维向量值函数积分的定义以及可积的充分必要条件，并讨论了二维向量值函数积分的一些性质。

In Chapter 2, we will give an introduction into the theory of Diophantine approximation for formal Laurent series over a finite base field.

在这一节，我们发展一些重要的基本性质，例如：广义Borel-Cantelli引理及数论中类似的结果等。

For the aforesaid reasons, in the second chapter ,this article estimates some parameters in the two-parameters Weibull distribution by the hybrid ALT method,and gives the inverse moment estimator for the shape parameter,at the same time the confidence interval of the accelerated coefficient is given .

基本研究问题：设应力水平V下产品的寿命服从两参数威布尔分布，则在混合应力加速寿命试验下产品寿命T的分布函数为：记T/t_0=X则X的分布函数为其中令λ=θ~m由上式得λ的极大似然估计又由(2.2.1)式知，是来自均值为λ的指数分布的次序统计量记则有又由引理2.2.1，若又、r，长，乞=1，2，…，n，则有(1)2 。。

Under the cases of the linear interconnected systems with all its subsystems are one dimension, a theorem to judge the properties of single loop interactions has been given; the study also indicated that the properties of interactions cann't independent of the properties of subsystems in the multi-loop interaction conditions, and a all field root locus method has been proposed to decide the properties of interactions; a interaction stabilizable theorem has been given, and the efficacy of interactions with respect to the interconnected systems has been configured, Some primary results are reported which are induced by using a method of computer aided test to study block interactions, the stationary feedback efficacy of closed loop interactions have been discussed and a stability guess has been proposed.

本文提出互连系统的合作稳定性概念及其原理，给出了互连系统的本原稳定度、稳定中心、回路关连的级数以及关连的性质等基本定义；并在此基础上对线性互连系统进行关连分析，给出了一系列涉及到关连与互连系统稳定性关系的命题、引理、定理及其证明；其中，在子系统都是一维的线性定常互连系统情况，得出了单回路关连性质判断的定理；并指出在多回路关连条件下，关连的性质不能独立于子系统的性质，以及用全域根轨迹法判断关连性质的方法；给出了关连可稳定理，并对关连对互连系统的影响作用进行了分析。本文还用机辅试验的方法研究块阵关连并给出一些初步结果，本中还探讨了回路关连的静态反馈作用并提出一个判稳猜想。

Based on Wilson\'s lemma on evenly distributed differences, elementary number theory and fundamental theory of finite field, the finite field construction for strict optimal OOCs is proposed and the basic idea of this construction is investigated. The main steps and flow chart of assistance design by computer are obtained.

3基于Wilson均匀分布差引理、初等数论及有限域的基本理论，提出一种严格最佳光正交码的有限域构造法，对该构造法的基本设计思想进行深入的理论分析，得到该构造法计算机辅助设计的主要步骤及流程。

Under some moderate conditions, the prior estimate of the solutions of the system is obtained. Making use of constructing Picard iterative sequence, Doob martingale inequality, Gronwall inequality, Borel-Cantelli lemma and some fundamental inequalities, together with the uniform Lipschitz conditions, the existence and uniqueness of the solution for stochastic functional differential equations with infinite delay is derived on the interval t0,∞.

在适当的条件下，得到了随机泛函微分方程的解的先验估计；再结合一致Lipschitz条件，通过构造Picard迭代序列，利用Doob较不等式、Gronwall不等式、Borel-Cantelli引理及一些基本不等式，得到该方程的解在区间[t0，∞]上是存在且唯一的。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced.And some basic properties, such as separation lemma, were presented.

其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理。

This article discuss some basic conception , character ,lemma and axiom about keeping shape changed method .

本文主要论述了保形变换的一些基本的概念，性质，和重要的引理，定理。

It is organized as follows:In Chapter 1, we introduce proximal point algorithms" framework and current research situation, optimization problems and variational inequalities" background and current research situation, and some basic concepts and lemmas, which are used in this dissertation.

本文具体安排如下：第一章简要介绍了邻近点算法的基本框架和研究现状，最优化问题和变分不等式问题的背景和研究现状，以及本文需要用到的一些基本概念和引理。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新