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Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics.

角动量：算符，对易代数，本征值和本征态，球谐函数。

Following the constraint of AMFI on the SGS stress model, a non-linear SGS stress model is developed, based on the tensor algebra and Taylor expansion theory, in terms of resolvable strain rate tensor and rotation tensor.

根据旋转湍流SGS模型的建模规则，利用张量代数和Taylor近似理论发展了一种由大涡应变率和旋转张量构成的非线性SGS应力模型，并满足AMFI条件。

We also can give the structure theorem for finite dimensional basic Hopf algebra of tame type in the radical graded case.

对于Tame型的Basic Hopf代数，我们可以给出的是根分次情形的结构定理。

The fact that a fuzzy ideal of a BCI algebra is closed if and only if it is a fuzzy subalgebra is proved.

证明了BCI代数的一个Fuzzy理想是闭的，当且仅当它是一个Fuzzy子代数。

There is a close relationship between a left L-comdule algebra A and its coinvariants subalgebra C.

注意到左L-余模代数A和它的余不变子代数C存在很密切的关联，我们称此关系是Morita关系。

So in a noncommutative mathrm C^*-algebra, there must exist a hereditarymathrm C^*-subalgebra which is not a closed ideal.

因此在非交换的 mathrm C^*-代数中必有一个非闭理想的遗传子代数。

Then we study the adjoint action of the quantum algebra u_qf(K, H and discuss the structure of its locally finite subalgebra.

讨论了量子代数U_qf(K，H上的伴随作用并给出了其局部有限子代数的结构定理。

Over a field of arbitrary characteristic, we construct a class of associative superalgebras of Weyl type and a class of Lie superalgebras of Weyl type from ∧(2, 2) and the polynomial algebra of the special deravation subalgebra of it. In addition, we prove that the sufficient and necessary conditions of the simplicity of the associative and the Lie superalgebras.

在任意特征域上，从∧(2，2)和它的特殊导子的子空间的多项式代数出发，构造了一类Weyl型结合超代数和一类Weyl型李超代数，进而给出并证明了它们为单的充要条件。

In chapter 1, we introduce the development of module theory and it s applications in the development of algebra,and present conditions of development of prime submodule s,prime radicals,isolated submodules.

本文讨论了环与模范畴中一个重要的子模类—孤立子模的一些性质以及它与强不可约子模等之间的一些联系，并引入了强孤立子模和局部孤立子模的概念，探讨了它们的一系列性质，在第一章中，介绍了模论的发展，模论在代数的发展中所起的重要作用以及素子模，素根和孤立子模的发展现状；在第二章中，给出了与本课题有关的重要概念及其结论。

And there is a natural graded G-algebra isomophism〓.3where Nis the subvariety of all the ad-nilpotent elements in the Lie algebraof G.

并且存在分次G-代数同构〓6这里N是G的Lie代数中的伴随幂零元全体。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。