查询词典 unique factorization domain

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The basic factorization algorithm over algebraic extension fields is Trager's algorithm.

代数扩域上的基本算法是Trager算法。

Zhi applied the lifting technique to the factorization over successive algebraic extension fields.

支丽红则将提升技巧用于多个扩域上的因式分解算法。

Wu, Hu, and Wang independently put forward factorization algorithms over successive algebraic extension fields based on methods of equation solving.

为了解决这一问题，吴文俊，胡森、王东明分别提出了基于方程求解的多个扩域上的因式分解算法。

Based on this, to the recent years the related questions which appear frequently in the middle school mathematics competition, nimble utilization the aliquot concept, the relative prime nature, the combinatorial nature, the factorization, as well as the conclusion of the continual integer product nimbly can by aliquot knowledge and the methods, and so on, carried on the proof and the explanation.

在此基础上，对近年来在中学数学竞赛中频繁出现的相关问题，灵活运用整除概念、互素性质、组合性质、因式分解以及个连续整数的乘积能被整除的结论等知识和方法，来进行证明与解答。

In chapter 2, based on Amari\'s alpha divergence, a non-negative matrix factorization algorithm is introduced.

在第二章，基于Amari alpha散度，我们引入了一类基于非负矩阵分解的盲信号分离算法。

Firstly, based on natural gradient and nonlinear principal component analysis, a matrix equation is obtained by block recursive updating,and then the matrix equation is solved using QR factorization and back substitution to obtain the optimal separating matrix.

此外，结合自然梯度和非线性主分量分析提出了一种块递归的盲源分离方法，构造出按块递归更新的矩阵方程，然后用QR分解和回代法求解该矩阵方程得到最优分离矩阵。

Firstly, based on natural gradient and nonlinear principle component analysis, a matrix equation is obtained by block recursive updating, and then the matrix equation is solved by using QR factorization and back substitution to obtain the optimal separating matrix.

首先基于自然梯度和非线性主分量分析，构造出按块递归更新的矩阵方程，然后用QR分解和回代法逐块求解该矩阵方程得到最优分离矩阵。

The last part of the chapter is devoted to the elementary factorization theory of commutative monoids with cancellation property and of commutative domains

后一部分主要介绍了关于交换幺半群的关于消去律的初等的因式分解理论以及交换整环的理论

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。