因子分解定理

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。

In this paper, we study the foundation of the constructing in CDT, and get the theorem of CDT factorization.

文章对范畴数据类型构造的基本原理作了深入探讨，并采用了一种新的方法实现了CDT同态的因子分解定理，得到了CDT构造中某些重要的性质和CDT因子分解定理。

It includes the basic structural theory of groups; groups'actions on sets and the applications of these actions; the basic structures of rings; the properties of uniquely factorized domains; the Chinese Remainder; the extensions of fields; finite fields with applications; the Galois theory with applications.

主要内容包括群的基本结构理论、群在集合上的作用及其应用、环的基本结构和因子分解理论、中国剩余定理、域的扩张理论、有限域及其应用、Galois 理论及其应用。

Meanwhile, we also provide methods for computing the weighted polar decomposition, and study error bounds for the approximate generalized positive semidefinite polar factor and perturbation bounds for weighted polar decomposition in various norms.

针对这个新的矩阵分解，我们证明了其唯一性定理，给出了其唯一性条件，讨论了其极因子的最佳逼近性质；同时，我们还探讨了矩阵加权极分解的计算问题，研究了由迭代算法引起的极因子的误差界，极因子在各种范数下的各种形式的扰动界等。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。