查询词典 lie to

Assume a Lie algebra g has a form B which has all the useful properties of Killingform:bilinearity nondegeneracy,symmetry and invariance.Note that for such a Liealgebra the adjoint representation is equivalent to the coadjoint representation.We callit a symmetric self-dual Lie algebra and the form B an invariant scalar product.

在第一部分的最后一节，我们引进了拟Heisenberg代数的概念，证明了这些李代数均为具有非极大秩的CN李代数，进一步我们还证明了这些CN李代数构成的集合与极大秩幂零李代数构成的集合之间存在着1-1对应关系。

Without using Lie derivative and Lie bracket operation of differential geometry , we only use the algebra method to give a sufficient condition of single input exact feedback linearizable bilinear systems.

摘 要 研究了单输入的双线性系统的精确线性化及其鲁棒控制器设计问题，避免了用微分几何的李导数、李括号的复杂运算，只用纯代数的方法给出了一般单输入双线性系统精确线性化的充分条件。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

The latter is essentially derived from the geometric realization of Happels triangulated equivalence between stable module category of repetitive algebra and bounded derived category of finite dimensional algebra. In terms of this realization, we deduce that the Lie algebra realized by derived category of a finite dimensional algebra is isomorphic to the Lie algebra realized by stable module category of the corresponding repetitive algebra.

后者本质上是Happel关于重复代数的稳定模范畴和导出范畴的三角等价的一个几何实现及其应用，使用这种几何实现，我们可以证明在重复代数的稳定模范畴上定义的李代数同构于相应的导出范畴上实现的李代数。

In section 2 ,if one Lie colour algebra can be decomposed to direct sum of two ideas ,the same as the center.And when the center is zero , the derivation and the inner derivation can be also decomposed .Lie colour algebra L is complete if and only if its two ideas are both complete .

第二部分首先讨论了若李color代数L可以分解为两个理想的直和，则中心也可以分解为两个理想的直和，而且当中心为零时导子和内导子也有同样的理想直和分解，并且L完备的充要条件是两个理想都完备。

The differences of the various schools of thoughts and their exponents during the period from pre-Qin times to the early years of the Han Dynast do not lie in their advocacies, for they are all autocracism affirmers; nor do they lie in their historical conditions, for they all regard that autocracism should be conducted under any historical conditions, i.

中国诸子百家之不同，不在于是否主张专制，因为他们都是肯定专制的专制主义论者；也不在于主张在何种历史条件下应该专制，因为他们都认为专制在任何历史条件下都是应该的，他们都是永恒的超历史的专制主义论者。

In another word, if we want to make an area have notable effect of agglomeration, the key does not lie in the size of advantage of agglomeration, but lie in the factors of elasticity of substitution of industry agglomeration.

或者说，要使一个地区有明显的集聚效果，关键不在于该地区集聚优势到底有多大，在于它替代其他地区的能力，进一步说，是在于集聚的替代弹性的影响因素。

It is easy to see that the bialgebra H we find,canbe regarded as the enveloping algebra of a Lie algebra,whose generators are thoseof the Lie algebra of type A and n-1 other elements which commute with genera-tors above.

可以看出，我们找到的H作为代数，恰为在An-1型李代数上增加与之可换的n-1个生成元后得到的包络代数，其自然表示的矩阵元恰好生成代数AR。

Say that Taishan is located in 12 kilometres of to the north of Henan province Xiu Wu County place , are just like a mouthful of big pot because of the lie of a mountain is lofty, cover above mountain peaks,"cover Pusan " in be called in the ancient times towering because of its lie of a mountain, forest dense, intermountain Chang is had cloud and mist to curl up ,"cloud Taishan is called" therefore.

云台山位于河南省修武县以北12公里处，，因为山势突兀，好像一口大锅，覆盖在群峰之上，在古代被称为&覆釜山&又因为它山势高耸，森林茂密，山间常有云雾缭绕，因此又被称为&云台山&。

Well, I want to get a tan and I haven't time to lie in the sun, so I lie under the sun lamp every night for five minutes.A: That's finr, as long as you don't fall asleep.

嗯，我想晒晒黑，但又没有时间躺在阳光下，只能每天晚上在紫外线灯下躺五分钟。A：那不错，只要你不睡着。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。