查询词典 unique factorization theorem

A new way for LU-SGS approximate factorization deducing is proposed.

在LU近似因式分解的过程中，本文采用了一种新的推导方式。

In the framework of QCD factorization, it is shown that the hard part of the matrix elements can be disentangled from the soft part and are thus calculable.

所以剩下的艰巨的挑战就是如何可靠的估计强子矩阵元。

When giving a new sample, DNMF makes use of the code matrix and base matrix factorized from the original dataset to initialize the factorization of new samples set.

当增加样本时，DNMF使用原样本集分解产生的编码矩阵和基矩阵对新样本集的分解进行初始化，使迭代从接近于阈值的位置开始，有效的减少了迭代次数，缩短了收敛时间。

Inverse of the sparse matrix is then factorized recursively with Cholesky factorization. Thereafter, a preconditioner in a form of successive multiplication is constructed.

然后采用Cholesky分解方法将该稀疏阵的逆阵进行递归分解，得到一个矩阵连乘形式的预条件阵。

The universal transverse polarization phenomcna for inclusively produced hyperons haveeluded the successful quantum chromodynamicsdescription in the past decades.Inthis thesis,we report their QCD-motivated factorization approach.

高能强子碰撞过程中单举产生超子的横极化现象一直缺乏成功的量子色动力学描述针对这一问题本文中给出了一个量子色动力。。。

The factorization of a complex skew-symmetric normal matrix ,which is similar to a complex symmetric normal matrix ,was demonstrated using a logically similar method.

提出一个复矩阵是对称酉矩阵的充要条件，并用逻辑上类似的方法证明一个类似于复对称正规矩阵的复斜对称正规矩阵的分解，最后对复斜对称矩阵得到了类似于复对称矩阵Takagi分解的结论。

It is then proved that every equation in the hierarchy possesses the Hamiltonian structure if L has a skew-symmetric factorization and the first equation in the hierarchy satisfies some simple condition (K〓=θf〓 and f〓 is a gradient function).

然后在L具有反对称分解L=θJ，及等谱发展方程族中第一个方程满足简单条件（K〓=θf〓，f〓一个梯度函数）的假设下，获得了整个方程族的Hamilton结构。

Some necessary and sufficient conditions are introduced for the existence of the weighted Moore-Penrose inverse of the morphisms with universal factorization,and also given are some pertinent formulae.

文献[3]引进了广义Moore-Penrose逆，并讨论了交换环上具有秩分解的矩阵广义Moore-Penrose逆存在的充要条件。

This kind of parallel processing hugely improves the computational speed, and can change some NP problems that cannot be accomplished by classical computers, i.e., the complexity of the problems exponentially increases with the increase of bits, to P problems, i.e., the complexity of the problems polynomially increases with the increase of bits. In 1994 Peter Shor at Bell Laboratory proved that quantum computers could efficiently solve the problem of Large Number Factorization, which was the security footstone of nowaday classical cryptosystems, while none of any classical computers could implement this.

这种并行处理极大地提高了计算速度，可以把一些经典计算中无法计算的NP问题即问题的复杂度随着比特位数的增长而指数上升，变成P问题即问题的复杂度随着比特位数的增长以多项式上升。1994年，Bell实验室的Peter Shor证明量子计算机可以有效解决经典计算机所不能解决的大数因子分解问题，而这恰恰是目前经典密码的安全性基础。

With the help of comparison theorem, sufficient conditions which guarantee permanence of the system are obtained. For the almost periodic case, by constructing a suitable Liapunov function, we obtained that the system has a unique globally asymptotically stable positive almost periodic solution. Finally, we study a multispecies predator-prey system with stage structure and Holling II type functional response.

第二部分考虑具有阶段结构的非自治扩散捕食系统，利用比较定理得到该系统持久生存的充分条件，其后在概周期情形下通过构造合适的Liapunov函数得到了保证该系统存在唯一一个全局渐近稳定的概周期解的条件。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。