零代数

In this thesis, absolute stability of Lurie control systems is studied.

中文摘要：这篇硕士论文研究了型控制系统绝对稳定问题，重点讨论判定其零解绝对稳定的几种常用的方法，得到了绝对稳定的一些充分必要条件或充分条件及代数判据。

In the first part,two methods calculating the coefficients of nilpotentclass normal forms are proposed.one is the iteration search method based onrepresentation theory of Li-algebra,and another is a new matrixrepresentation method based on the adjoint operator concepts,both are ableto be used to analyse the normal form problems with high orders and largedimensions efficiently.

在第一部分工作中，对于幂零类规范形的系数计算，分别提出了基于李代数表示论的迭代搜索的理论和方法以及基于共轭算子概念的新的矩阵表示的理论和方法，从而有效地解决了维数和阶数较高时的计算问题。

Besides, through the method of concatenation, the upper bound of algebraic immunity and the form of the annihilators of any generalized boolean function were also determined.

此外，还通过级联函数的方法确定了任意广义布尔函数的代数免疫的上界和零化子的形式。

From this,two algorithms to find low degree annihilators of a Boolean function are present:complete searching and stochastic searching.The complete one can not only get all the low degree annihilators of a Boolean function,but also get the algebraic immunity of the function.

利用完全搜索法可以得到布尔函数的所有低次零化子，同时还可以确定该布尔函数的代数免疫度；利用随机搜索法能快速得到布尔函数的任意一个低次零化子。

After descibing the concepts, definitionsand operation approaches of quantum group and SLq(2) Lie algebra, the physicalmeaning of quantum group particles is explained in the present thesis. The gaugeinvariance in SLq(2) gauge field and its thermodynamics model is considered basedon the idea of q-deformation. The zero energy gap equation and q-deformed energygap equation are derived under the assumption of q-quantization and semi-classical q-quantization, then the zero-temperature energy gap A(0,q) and crititical temperature〓 can be calculated from the q-energy gap equation.

在介绍了量子群和SLq(2)李代数的基本概念，定义和运算方法后，文中进一步阐述了量子群粒子的物理意义；在q变形思想基础上，本文研究了SLq(2)规范场及其热力学模型中的规范不变性质，并在q量子化和半经典q量子化的假设下导出了零能隙方程和q变形能隙方程；然后从q能隙方程计算了与零温度能隙△(0，q)和临界温度〓。

Nilpotency of a table algebra depends on that of their table subsets and quotient subsets, which is not fully corresponding to extension problems of nilpotent groups.

同时会发现该条件在表代数幂零性的判别方面并不完全对应于幂零群的中心扩张。

If A is D-simple, i. e., A doesn't have any nontrival D-stable ideal, we have the generalized Weyl type simple algebra A .

Der为A上所有F-结合导子组成的李代数。D为Der的任一非零交换李子代数。

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。

In Chapter 2, starting from a generalization of Hensel's Lemma to non-commutative case, we introduce the Brauer characters and the generalized decomposition numbers, and construct a kind of maximal semisimple algebras; then, similarly to Puig's methods, we prove Brauer's Second Main Theorem over arbitrary fields; applying it to blocks with nilpotent coefficient extensions, a formula on characters of such blocks is given; the formula of characters of nilpotent blocks is just an easy consequence of the fomula.

在第二章中，我们将Hensel的引理推广到非交换的情况，以此为起点，定义了Brauer特征标和广义分解数，构造了一类极大的半单的代数，类似于Puig的方法，给出了任意域上Brauer的第二主要定理；作为该定理的应用，我们给出了具有幂零系数扩张的块的特征标公式，幂零块的特征标公式只是它的一个简单的推论。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。