查询词典 finitely generated algebra

Building on Turing's contribution, Shannon had demonstrated how Boolean algebra and logic could be used in the analysis and synthesis of switching and computer circuits.

在图灵理论的基础之上，香农演示了布尔代数与逻辑如何用于开关与计算机电路的分析与综合。

On the AFS theory, we define a homomorphism mapping between the EI algebra and the ring of Boolean matrix.

在EI代数的子代数的基础上，对概念的EI代数表示和布尔矩阵表示进行了讨论。

It is proved that a semiring is complemented if and only if it is a direct product of some Boolean algebra and Boolean ring by studying the relations of congruences on the complemented semiring, so the complemented semiring is the commutative semiring.

s-内射模。通过研究可补半环S的性质及S上的同余关系，证明出可补半环与布尔环和布尔代数的直积是等价的，因而可补半环是交换半环。

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

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。

In section 1.1. we define the mapping a on circle in double quiver Q of a quiver Q, and give a strict defition of bracket operation in Lie algebra,then prove it is a Lie bracket.

循环上的映射σ，用它给出了项链李代数括号运算的一个严格定义，并用此定义证明了这是一个李运算。

Let R be an arbitrary commutative ring with identity, gl the general linear lie algebra over R consisting of all n × n matricesover R and with the bracket operation = xy -yx, t the lie subalgebraof gl consisting of all n×n upper triangular (resp., strictly upper triangular ) matrices over R and d the lie subalgebra of gl consisting of all n×n diagonal matrices over R.

在第三章中，对R是交换环的情形，讨论了典型李代数的导子代数的结构问题：设R是一个含幺交换环，gl是R上一般线性李代数。t是gl的所有n阶上三角矩阵(相应地，严格上三角矩阵)构成的子代数，d是gl的所有n阶对角阵构成的李代数。

This simple result is at the root of the arithmetic and algebra of Brownian motion and particle diffusion.

这个简单的结果是粒子扩散和布朗运动的算术和代数基础。

The number of being serviced Buffer selected as discrete index, the work number of Buffer as continuous state, an algebra-differential equation of the switched arrival system was naturally developed.

采用被服务Buffer编号为离散标识，Buffer中待处理任务数为连续状态，建立了系统的代数微分方程模型。

I received another paper and a table of signs by return mail, and I set to work to learn the notation. But on the night before the algebra examination, while I was struggling over some very complicated examples, I could not tell the combinations of bracket, brace and radical.

在考代数的头天夜里我忙于运算复杂的习题，对于那些括号、大括号和方根的联合使用老是分辨不清。

World War II: Battle of Saipan - Americans take Saipan.

1944年的今天，美国在塞班战役中拿下塞班岛。

When the scorner, the rejecter of truth, has become presumptuous; when the routine of work in the various money-making lines is carried on without regard to principle; when the student is eagerly seeking knowledge of everything but his Bible, Christ comes as a thief.{DA 635.3

当讥诮和拒绝真理的人，到了任意妄为时，当追求财利者罔顾按道义经营谋利时，当学人正在兢兢业业地研究各种知识，而单把圣经丢在一边时，基督要像贼一样来临。