查询词典 unique factorization theorem

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

This paper introduced a dollar polynomial divisible in nature, the nature of the greatest common divisor, factorization properties, factorization and its applications in nature.

本论文介绍一元多项式的整除性质，最大公因式的性质，因式分解性质、因式分解性质及其应用。

At last, we briefly compare the QCD factorization to the"generalized factorization"and PQCD method.

最后，我们简要比较了QCD因子化和"推广的因子化"及PQCD方法之间的差别。

A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix.

谱法LU分解的优点是在对大量具有相同非零结构的矩阵分解时，通过建立包含所有具有不同非零元素的列对应的自相关函数的分解表，使得随后的所有矩阵分解只需通过查表实现。

In Chapter 5, a new method with direct partitioned column updates of cholesky factorization for solving large scale sparse unconstrained optimization problems is proposed, which depends on a consistent partition of the columns and cholesky factorization of the Hessian matrix.

第5章基于稀疏Hesse阵的列的相容分划，并在其Cholesky分解的基础上建立了求解大型稀疏无约束优化问题的直接校正Cholesky因子算法。

Firstly, applying spectral factorization to minimize an integral square performance criterion containing tracking error and control energy, an optimal control law for the nominal model is derived on condition of control energy constraint. Then, for model uncertainty, using spectral factorization to minimize the variance of the actual system performance from the nominal performance over all frequency range, a robust controller design method is abtained, which has optimal robustness of the system nominal performance to model errors.

首先针对控制对象的标称模型应用谱分解最小化一个包含跟踪误差和控制能量在内的积分平方性能指标，导出一个控制能量约束条件下的最优控制律；然后再针对模型不确定性应用谱分解最小化实际系统性能和标称性能在整个频段上的方差，得到一个鲁棒控制器的设计方法，可使系统的标称性能对模型误差具有最优的鲁棒性。

NMF is a new method for feature extraction and data dimension reduction. It has an advantage over traditional algorithms in the simplicity of implementation and the interpretability of factorization form and factorization result.

中文摘要： NMF是一种特征提取与数据降维的新方法，相较于一些传统算法，具有实现上的简便性、分解形式和分解结果上的可解释性等优点。

The paper available mapping of integral coefficient polynomial and rational number, obtain factorization from factorization of polynomial by the way of sieve in true fraction series.

利用整系数多项式与正有理数的对应，将多项式因式分解通过对真分数序列筛选的办法求得因式，给出了整系数多项式因式分解的一种新方法。

This process, known as prime factorization, should output a list of8–6. Prime Factorization.

这个过程叫做求素因子分解，它输出的所有因子之积应该是原来的数字。

Given the language of section 102(2), the Supreme Court's rejection of substantive review under NEPA seems unjustifiable in principle

按照第102条的规定，最高法院否决《国家环境政策法》所规定的实质性复审在原则上似乎是不正当的。

ObjectiveTo explore the effect of variable hip abduction orthosis on children spastic cerebral palsy.

目的探讨髋关节矫形器在儿童痉挛型脑性瘫痪康复中的作用。