查询词典 Lie algebra

Lie group method ; Lie theory ; Matrix exponentiaE Symmetric space ; Lie triple system

非线性度李群方法；李理论；矩阵指数；对称空间；李三系

Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method.

文中首先给出相空间中地震波的李群表述和算法，也即地震波的辛群表述和辛算法，辛群是李群的子群，辛算法是特殊的李群算法。

In the fifth chapter,we study dipolarizations in some quadratic Lie algebras.Inthe first section,we obtain some results on the classification of dipolarizations in gen-eral quadratic Lie algebras,and prove that there exist dipolarizations in the solvablequadratic Lie algebras whose Cartan subalgebras consist of semisimple elements.

第五章讨论了某些二次李代数的双极化，在第一节中，我们给出了二次李代数的双极化的一些分类结果；特别证明Cartan子代数是由半单元组成的二次李代数上存在双极化，第二节确定了四维扩张Heisenberg代数的所有双极化，在第三节中，我们构造了2n+2维扩张Heisenberg代数的六类双极化，我们发现两个不同于半单李代数情形的有趣事实：（1）在扩张Heisenberg代数上同时存在对称和非对称双极化；（2）对应于扩张Heisenberg代数的双极化的特征元有的是半单的有的是幂零的。

Whispering Steppe Love is dear, love is rare Love is never where your eyes would stare Unexpectedly, even blindingly Love will show its face to you, no lie Fears 3subside, clearly why Time has come for me to stand aside 4Unencumberedly, though 5reluctantly Upon the 6whispering 7steppes I lie with pride It was the 8cradle of my hopes now lies my resting grave The warmth of life has left me half-embraced For those who 9rendered fears and pain I will surely pay with a smile you can't escape Free at last, from the past Time has come for me to greet the vast Unencumberedly, though reluctantly Upon the whispering steppes I lie

细语吟咽的草原爱之珍，爱之罕爱令双目不可逼视就那么出人意料，甚至茫然无绪地爱呈现出至真性情，没有谎言湮灭了惧栗，也明白了时空于我就这样静止的缘由无所畏惧，却又犹豫迟疑地我走上这为之骄傲的细语吟咽的草原这里，过去是我希望的摇篮，如今是我安息之地对那些在幸福生活中抛弃过我的令我忧虑痛苦的人而今我要报以一个你们怎也躲不掉的笑容自由了，终于脱离过去的阴影自由了广阔天地在我面前展现无所畏惧，却又犹豫迟疑地我走上这为之骄傲的细语吟咽的草原注释： 1 The room is turning slowly away from the moon。

The life lies in its intensity but not to lie in its length, the life significance lies in climbs unceasingly and closely examines but does not lie in sits idle and enjoys the fruits, the life value will lie in surmounted unceasingly but models shape tomorrow a newly ego.

生命在于它的强度而不在于它的长度，生命的意义在于不断地攀登和追问而不在于坐享其成，生命的价值在于不断地超越而塑形明日的新我。

From the view of the number of composition series and table subset of order or elementary abelian table algebra is depicted by making use of fundamental theorem on homomorphism of table algebra.

分别从合成列及表基的p阶、阶表子集的数目角度刻画了初等abelian表代数。

Arad and Blau proved that an abelian table algebra can be viewed as a group algebra of some abelian group G. Chapter 3 of this paper gives the structural theorem of abelian table algebras by defining a group structure in table basis. Furthermore, the structure of elementary abelian table algebras is discussed using the number of composition series of table algebras.

Arad和Blau证明了abel表代数等价于某个有限生成abel群G的群代数，受此启发本文第3节通过定义表基的一个群结构给出了abel表代数的结构定理，并从合成列数目的角度对初等abel表代数进行了细致刻画。

Also prove that every bounded linear approximately local Hilbert space representation of a abelian von Neumann algebra is a representation,every bounded linear approximately 2- local Hilbert space representation of a von Neumann algebra is a representation.

同时证明了交换von Neumann代数的有界近似局部表示是表示，每个von Neumann代数的有界近似2—局部表示是表示。

Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis .

向量空间的一个中心主题在现代数学，因此，线性代数被广泛使用在抽象代数和功能分析。

In addition to calculus with linear algebra, I had two semesters of mathematical analysis, partial differential equations, abstract algebra was also a senior this semester in the measurement theory.

除了微积分跟线性代数，我还上了两个学期的数学分析，偏微分方程，抽象代数还有在大四这个学期上的测量理论。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。