代数

In section 2.2,we prove that if the set of arrows in a quiver is not empty,then NQ is not semisimple.We construct the nonsovable subalgebra of NQ when there is no less than one circle whose length is bigger than one ,and there is no loop in quiver Q,thus leads to a conclusion that NQ is nonsovable .

我们还对只有一个单循环和一个单循环及若干单箭头的箭图，给出了其项链李代数的某些中心元素的具体形式，在2.2节中，我们对非平凡图，即当箭图中有箭头时，利用H中的元素证明了N_Q不是半单纯李代数。

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。

We introduce the notion of characteristic pairs and give the definition of dual characteristic pairs of Dirac structures on Lie bialgebroids. Using the dual characteristic pairs, we give the if and only if conditions for which a maximally isotropic subbundle of the double of a Lie bialgebroid is a Dirac structure.

本文在李双代数胚上，引入了Dirac结构的特征对并给出对偶特征对的概念，利用对偶特征对，给出李双代数胚double的极大迷向子丛是Dirac结构的充要条件；其次，分别利用特征对与对偶特征对，将可约Dirac结构分为第一类可约与第二类可约，在此基础上，建立Poisson流形的两类对应约化定理。

Based on the theory of corelations on coalgebras, a method for constructing the cogenerated subcoalgebra is proposed.

基于共代数上的共关系理论，提出了共生成子共代数的一种构造方法。

Furthermore, using the correspondence between the cocongruence corelations and the subcoalgebras on Set, a way to construct the co-generated subcoalgebra is given in this paper.

进一步利用共同余共关系与子共代数之间的对应，给出了集合范畴上共生成子共代数的一种构造方式。

And there is a natural graded B-algebra isomophism〓.where n is the subvariety of all the ad-nilpotent elements in the Lie algebra of B.

并且存在分次B-代数同构〓5这里n是B的Lie代数中伴随幂零元全体。

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 algebra of quaternions, the first noncommutative algebra was thus sudd ly born.

四元数的代数，第一非交换的代数，就这样在一夜之间诞生了。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

Third,the paper sets up a mathematical model for indirect tax shifting through algebraic method, it concludes a general rule on indirect tax shifting from VAT payers to others, the buyers only takes the full tax burden when there isn't any demand elasticity or full supply elasticity, and the sellers only takes the full tax burden when there is full supply elasticity or no demand elasticity, sellers and buyers share the tax burden respectively, the tax share amount has a straight line dependence to the commodity demand or supply elasticity, the proportion of indirect tax burden of sellers equal to the proportion between demand elasticity and the sum of demand and supply elasticity.

第三，本文用代数推理的办法推导出测算间接税税负转嫁的代数模型，从而得出增值税纳税人间接税税负转嫁的一般规律：销售者和购买者各自负担部分税负，其负担的份额取决于商品供求弹性的对比关系，销售者负担的间接税税负比例等于需求弹性系数占供求弹性系数之和的比例。

And discuss some key point of integrated management system design, include hazard identification and risk assessment and risk control in the occupational health and safety management, the measure of satisfaction target of customer, the flawlessness of law system, the integration of the integrated management system and enterprise standardization system, unify lead institution and work orgnization, integreted internal audit and integrated management review.

同时，论述了一体化管理体系构建中的几个主要问题，包括职业健康安全管理中的危险源辨识、风险评价和风险控制、顾客满意度的科学监测、法律、法规体系的完善、一体化管理体系与企业标准化体系的有机结合、统一的领导机构和工作机构、一体化的内部审核和管理评审。

Deepwater Taranaki is investigated for its petroleum potential, using all available seismic data tied to shallow-water wells.

运用与浅水井相关的现有全部震波探测数据考察了深海区塔拉纳基盆地的油藏前景。