查询词典 unique factorization domain

This paper discusses the relation beween order classification and isomorphic classification , gives some important characteristic properties of a cyclic group with order n and a important property of a p-group with finite order, introduces two factorization method of direct product for commutative p-group with finite order, presents some new problems.

讨论了阶分类与同构分类的关系，给出了n阶循环群的几个重要的特征性质和有限p-群的一个重要性质，介绍了有限交换p-群直积分解的两种方法，提出了一些新的问题。

By using the group-chain, the wavefunctions of the 4f〓 configuration for RE ions are also expressed as linear combinations of group-chain basis functions in Butler's irreducible representation notation. The matrix elements of the CF Hamiltonian then are calculated by means of the Wigner-Eckart theorem and factorization lemma of the jm factors. Before the CF level fitting, a point-charge calculation of the conventional CF parameters B〓 has been performed by means of the lattice-sum technique from the known crystal structure data. The corresponding parameters in the group-chain are calculated by the conversion relationship between two schemes that proved identical in essence, which are usually used as initial values in the fit to the experimental levels. The ratios of the same k-value CF parameters are suggested as the constraint conditions in the fit, in order to utilize fully the symmetry distortion degree of the studied system.

利用群链理论，属稀土离子4f〓组态的波函数表示为以不可约表示标记的群链基波函数的线性组合；借助Wigner-Eckart定理和2jm和3jm因子的分解定律计算了晶场哈密顿的矩阵元；根据点电荷模型和已知晶体结构数据，利用点阵求和技术计算得到传统晶场参数B〓初值，相应的非传统形式的群链参数初值则由两种方案下的转换关系求得；这些初值通常作为非线性拟合晶场能级计算的初值，系统的对称性畸变信息则反映在以同阶晶场参数的比值作为能级拟合的约束条件。

To get high numerical stability and computational efficiency, U-D factorization-based DFP and BFGS algorithms are developed.

该算法解决了H阵的正定性问题，保证了算法的数值稳定性，并大大提高了计算效率。

Two forms of implicit TVD schemes are proposed in this paper for the simulation of nonequilibrium flows past hypersonic re entry vehicle, which are derived from the diagonal form of an approximate factorization algorithm and lower upper scheme applied to the implicit part of Harten Yee's TVD scheme respectively.

针对高超音速化学非平衡流提出了两种隐式格式。一种是近似因子分解算法对角化形式在隐式TVD格式上的推广，另一种可视为隐式TVD格式的LU分解形式。

A parallel algorithm for certain real symmetric block-tridiagonal linear systems on distributed-memory multicomputers is proposed. This algorithm is based on the block factorization of the coefficient matrix. This algorithm is used to solving the block-tridiagonal linear systems resulted from the finite difference approximation to Poisson's equation with Dirichlet boundary conditions. Then we get a parallel algorithm which speedup tends to linear speedup.

7研究了一类实对称块三对角线性方程组的分布式并行求解，提出了一种基于块矩阵分解的高效分布式并行算法，将其应用于求解带Dirichlet边界条件的Poisson方程导出的块三对角线性方程组，得到加速比趋于线性加速比的分布式并行算法，理论上说，这也是并行算法的理想情况。

Finally, summed up the basic concepts of polynomials, divisibility theory, factorization theory, theory of polynomial roots.

最后总结出了多项式的基本概念，整除性理论，因式分解理论，多项式根的理论。

The connection between two different approaches to singular H∞ control problems based on geometric control theory and-lossless factorization theory respectively is established. This paper illustrates the eigenspace structure of singular H∞ control systems.

文中建立了基于几何控制理论和基于J-无损分解理论的两种不同的奇异H∞控制分析方法之间的联系，并揭示了具有无穷远零点的奇异 H∞控制系统的特征空间结构。

This course, which discusses elementary of computational number theory, includes the following subjects:(1) Fundamental properties of Integers;(2) Congruences;(3) Congruent equations;(4) Legendre and Jacobi symbols;(5) Primitive roots;(6) Primality testing and factorization;(7) Index computation and discrete logarithm computation;(8) Other computational problems.

本课程将讨论计算数论的基本知识，主要包括以下内容：(1)整数基本性质；(2)同余；(3)同余式；(4) Legendre和Jacobi符号；(5)原根；(6)素性测试和大数分解；(7)指数计算和离散对数计算；(8)其他计算问题。

This paper gives a reconstruction method based on rational B-spline and factorization method.

本文提出了一种有理B-样条方法与因式分解法相结合的重建方法。

This paper presents a new scheme based on Nonnegative Matrix Factorization and simplex-based method to solve this problem.

本文提出一种新的基于非负矩阵因式分解(Nonnegative Matrix Factorization，NMF)算法和单形方法相结合的混合像元分解方法去解决上述问题。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。