引理

After giving the definition of copy method, we present two impor-tant lemmata and discuss the NP-completeness of the above two minsum and minmax problems.

文中在给出了复制法的定义后，又给出两个重要的引理，接下来主要讨论了上述两极小化求和及极小化极大分批排序问题的NP-完备性。

The problem of uniqueness of meromorphic functions is discussed.

给出了亚纯函数四值定理中一个引理的简化证明。

In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中，我们将Hensel的引理推广到非交换的情况，以此为起点，定义了Brauer特征标和广义分解数，构造了一类极大的半单的代数，类似于Puig的方法，给出了任意域上Brauer的第二主要定理；作为该定理的应用，我们给出了具有幂零系数扩张的块的特征标公式，幂零块的特征标公式只是它的一个简单的推论。

Secondly, by using the Sobolev inequality on the C-C spaces we prove a Fefferman-Phong type lemma. Based on which we provide nonexistence theorems to three kinds of nonlinear subelliptic parabolic equations through a relatively unified method.

其次，利用Carnot-Caratheodory空间上的Sobolev不等式证明了一个Fefferman-Phong型引理，并用比较统一的方法证明了三类非线性次椭圆抛物方程解的不存在性判定定理。

In chapter one, the basic concepts and lemmas.

第一章，基本概念和引理。

In the second chapter, we introduce some important lemmas which are the foundation of the dissertation.

第二章：介绍一些重要引理，为以后的工作做好准备。

In section 2, we give some notations and some lemmas.

在本文第二部分，我们给出一些符号及引理。

This paper firstly introduce the based knowledge of Time Scale,stability and several lemmas.

本文首先介绍时标的基础知识、稳定性的概念和几个引理。

In section one, we list some conceptions and lemmas for later use.

在第一部分中，我们介绍了本文中所要用到的基本概念与引理。

The thesis is composed of four chapters. In chapter 1,we primarily give some preliminary conceptions and lemmas.

第一章主要介绍本文中要用到的一些基本概念和基本引理。

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