讨论了阶化向量空间和李超代数的基本性质。
The general properties of graded vector space and Lie superalgebras are discussed.
讨论了李超代数上的左超对称结构与其上的1维上同调群的关系。
It discusses the relationship between left-supersymmetric structures on Lie superalgebra and its 1 th cohomology group.
最后一部分中，我们讨论左对称代数和李代数上的左对称结构在着色李超代数中进一步的推广。
In the last part, we further generalize left symmetric algebra and left symmetric structure on Lie algebras into Lie color algebras.
定理3 可解李三超系的任意包络李超代数是可解的，而且若李三超系有可解的包络李超代数，则它也是可解的。
Theorem 3 Any enveloping Lie superalgebra of a solvable Lie triple supersystem is solvable, and if a Lie triple supersystem has some solvable enveloping Lie superalgebra, it is solvable.
首先根据有限交换群上对称双特征标的概念，给出着色李超代数的定义，并介绍关于着色李超代数的一些基本概念与基础知识。
First, we give the definition of Lie color superalgebras using the symmetric bicharacter on a finite commutative group, and also we introduce some fundamental notions about Lie color superalgebras.
因为一个Z2-阶化群可以对应一个李超代数，所以对Z2-阶化群的性质进行了讨论。并对一些特殊类型的群确定了它们的Z2-阶化结构。
Since a Lie superalgebra can be associa ted with a Z2-graded group, properties of Z2-groups are discussed and Z2-graded structures of some special class es of groups are determined.
本文提出了数据超立方体模型，并在代数表达方面进行了改进，使得其可以支持OLAP操作。
In this paper, we address this issue by proposing a model of a data-cube and an algebra to support OLAP operations on this cube.
结论是交换超算符方法的理论基础是李代数。
The conclusion is that the theoretical foundation of commutative hyper-operator method is Lie algebra.
逐次超松弛迭代(SOR)法是求解代数方程组应用较为广泛和有效的方法之一。
The successive overrelaxation (SOR) method is one of the more efficient and widely used iterative methods for solving linear systems.
给出了超有限因子到其中的套代数的对角上的忠实正常的条件期望的一个刻画，证明了超有限因子中的套代数的中心恰好是纯量构成的。
The description is given for the faithful normal conditional expectation from a hyperfinite factor onto the diagonal of nest algebra of the hyperfinite factor.
还证明了很多有限次代数数域不与上述的超积初等等价。
Also, it is proved that many algebraic number fields of finite degree are not elementarily equivalent to the above-mentioned ultraproducts.
采用弯曲射线追踪算法计算走时，分别用最小二乘QR分解算法与代数重建技术就恰定方程组、超定方程组与欠定方程组进行了成像计算。
LSQR and ART algorithms are applied separately to calculate tomography for the determined system of equation, overdetermined system of equation and underdetermined system of equation.
采用弯曲射线追踪算法计算走时，分别用最小二乘QR分解算法与代数重建技术就恰定方程组、超定方程组与欠定方程组进行了成像计算。
LSQR and ART algorithms are applied separately to calculate tomography for the determined system of equation, overdetermined system of equation and underdetermined system of equation.
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