查询词典 algebra

The relationships among Boolean algebra, set algebra, logic, and binary arithmetic have given Boolean algebras a central role in the development of electronic digital computers.

由于布尔代数，集合代数，逻辑学和二进制算术之间的内在联系，使得布尔代数的理论在电子计算机的发展中起到举足轻重的作用。

Like ordinary algebra, Boolean algebra has its own unique identities based on the bivalent states of Boolean variables.

象普通代数，布尔代数具有基于布尔变量的二价规定的独特的特性。

For example, the set algebra for the set T defined above corresponds to a Boolean algebra of 32 elements.

例如，上文定义的集合 T 的集合代数就对应一个有 32 个元素的布尔代数。

For example,the set algebra for the set T defined above corresponds to a Boolean algebra of 32 elements.

例如，上面定义的集合T的集合代数就对应于一个有32个元素的布尔代数。

We construct the Tai Chi algebra based on Boolean algebra for philosophical reflection and formal improvements.

我们建构的太极代数基于对其作哲学上的反思和形式上的改进。

Then we study the typical property of theirs form the starting of nature and constitute of the two types of Lie algebra, and we calculated separately their dimension, center, commutator algebra, Killing type, Cartan subalgebra, structure formula, root system, and so on.

本文主要研究了两类典型的李代数即李代数so*(2n)和g*，首先介绍了一些李代数的基本知识，并且给出了这两类李代数的组成结构，然后从这两类李代数的本质构成出发，研究它们的一些典型性质，分别讨论了它们的维数，中心，换位子代数，Killing型，Cartan子代数，结构公式，根系等。

Based on the methods and techniques of covering theory, the structure of module category of tame concealed algebra, one-point extension, vector space category, finite enlargement, degeneration theory, stable equivalence and combinatorial method, we will classify all of the three-point algebras with Gabriel quiver the system quiver Q according to representation type. We get the classification theorem: Let A=kQ/I be a three-point algebra given by the system quiver Q.

本文综合利用覆盖理论，tame concealed代数模范畴的结构，单点扩张，向量空间范畴，有限enlargement，退化理论，稳定等价以及组合的方法等多种方法和技巧，将所有由系统箭图Q给出的三点代数按表示型进行分类，得到如下分类定理：Q是系统箭图，I是kQ的一个admissible理想。

We give some examples of BiFrobenius algebras based on the extensions of algebras and coalgebras . Let H be a bialgebra of finite dimension . Then T= H⊕H* has an algebra structure and a coalgebra structure also . We discuss the properties of T , and get the necessary and sufficient condition for T to be a BiFrobenius algebra .

然后根据代数余代数的平凡扩张给出一类BiFrobenius代数的例子，设H是有限维双代数， T= H⊕H*既有代数结构也有余代数结构，研究T的性质，给出了T成为BiFrobenius代数的充要条件，即定理3.9。

Associated it we define a root system. In a suitable condition we define a Lie algebra to realize this root system, namely, using an Euler cocycle given by intersection matrix, we define an infinitely dimensional vector space with the Lie operation becomes a Lie algebra.

在适当的条件之下，我们给出了该根系的一个李代数实现，即利用该相交矩阵确定的一个欧拉cocycle和根系，我们定义了一个无限维向量空间和李运算，并且证明了这个无限维向量空间在该李运算之下构成一个李代数。

"Applied algebra" introduce application of algebra in cryptography and coding theory.

应用代数主要内容是一些代数知识在密码学和编码学中的应用。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷