基本引理

And some results on the isometries and equivalences of quantum codes are presented, one of which generalizes one of results of Bogart et al..

研究了量子纠错码的等价性和保距同构，推广了Bogart等人的一些概念，并给出若干基本引理和定理，这些结论对进一步研究量子码的等价性和保距同构是非常有用的。

In the first section, we introduce some backgrounds and recall the definitions of weak action. crossed product and twisted H-module. At the same time, we give Lemmas 1.3. 1.5 and 1.6 being used in the following sections.

文中在给出了弱作用、crossed积、twisted H-模等基本概念的同时，又给出了在后续中需要使用的一些引理，即引理1.3、引理1.5、引理1.6。

And some results on the isometries and equivalences of quantum codes are presented, one of which generalizes one of results of Bogart et al. By these results, we construct an isometry of quantum codes which is not an equivalent mapping but preserves the symplectic inner product, i.e.

研究了量子纠错码的等价性和保距同构，推广了Bogart等人的一些概念，并给出若干基本引理和定理，这些结论对进一步研究量子码的等价性和保距同构是非常有用的。

When it was checked this year and confirmed to be correct, mathematicians around the globe breathed a sigh of relief. Mathematicians' work in this area in the last three decades was predicated on the principle that the fundamental lemma was indeed accurate and would one day be proved.

这让全世界的数学家终于松了一口气，因为在过去30年中，数学家在这一领域的工作都是在"基本引理"是正确的并且终将有一天得到证实的基础上进行的。

But he was convinced that one stepping stone that needed confirmation — dubbed the "fundamental lemma"— would be reasonably straightforward.

他认为，证明所谓的"基本引理"将是完成这项任务的一个合理跳板。

But he was convinced that one stepping stone that needed confirmation — dubbed the "fundamental lemma"— would be reasonably straightforward. He, his collaborators and his students were able to prove special cases of this fundamental theorem.

朗兰兹知道证明支撑自己构想的假设需要几代人的努力，但证明所有这些首先需要一个垫脚石，它被称作"基本引理"。

Over the past few years, Ngo Bao Chau, a Vietnamese mathematician working at Université Paris-Sud and the Institute for Advanced Study in Princeton, formulated an ingenious proof of the fundamental lemma.

过去5年来，就职于巴黎第十一大学和普林斯顿高等研究院的越南数学家吴宝珠试图用公式表述一项有关基本引理的精巧证法。2009年进行的验证证明了这一证法的正确性，全世界的数学家终于可以松一口气。

Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability.

然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用。

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。

In Chapter Two, some notations, definitions and lemmas are listed.

在第二章中，我们主要给出了本文将要用到的一些基本定义和基本引理。

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