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After a historical motivation of the definition of a Lie group we shall develop basic manifold theory, vector fields, tangent spaces leading to the Exponential mapping for an affine connection.

在简单介绍了李群的定义的历史来源之后，我们将讨论关於流形理论、向量场和切空间，进而引出仿射联络的指数映射的基本知识。

Firstly, we calculate the Lie point symmetry of 1+2-dimensional nonlinear evolution equation:Which arises from the motion of plane curves in affine geometry.

我们首先计算了来自射影几何的平面曲线运动的非线性发展方程：所容许的李点对称群。

The man said affirmatively,"I never tell a lie."

"那当然！"这个人肯定地说，"我从不说谎。"

21 Ahithophel answered, Lie with your father's concubines whom he left to take care of the palace.

16：21 亚希多弗对押沙龙说、你父所留下看守宫殿的妃嫔、你可以与他们亲近。

He is free and must choose either the Wise Lord and his rule or Ahriman, the Lie.

他是自由的，必须选择英明的主和他的统治这一方；以及邪神和谎言那一方。

AIt is wrong to tell a lie.

说谎是不对的。

Bree: Listen, I don't expect you to lie about the alcoholism.

听好了，我不是让你为酗酒这件事对他们撒谎。

Based on the filtered Lie algebra of the universal enveloping algebra, the algebraic structure of projected subsystems are studied. It is proved that they have simple decompositions, and the construction of the representations is given as well as the corresponding criterion for project limit controllability.

基于泛包络代数的滤李代数结构，研究了投影子系统的代数结构，证明它们具有简单的分解形式，并给出了它们的表示的构造方法和投影极限能控性的判别定理。

In the recent years, due to there being intrinsic relationships between tilting theory and quantum group, Lie algebra and other algebraic branch, tilting theory has been one of the international hot topics.

现在，由于倾斜理论与量子群，李代数等其它代数学科的本质联系，倾斜理论成为国际研究热点之一。1998年，I。

In the study of the recognition of bifurcation broblems, Gaffney establishes D -equivalence theory by introducing unipotent algebraic group and nilpotent Lie algebras.

借助于奇点理论中的一个基本概念，这一问题常常可以转化为有限维的情形来处理。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。