因子分解

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

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。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

The first kind of the digital signature schemes is based on the discrete logarithm problem and second kind of the digital signature scheme is based on discrete logarithm and factorization problem, the third kind of the digital signature schemes is based on quadratic residue problem.

本文第一章对数字签名方案进行分类，根据数字签名方案所基于的数学问题，将签名方案分为：基于离散对数问题的数字签名方案，基于素因子分解问题的数字签名方案和基于二次剩余问题的签名方案。

Decomposition and Reconstitution Methodology of Conceptual Genes was put forward to resolve this problem.

提出概念因子分解重构法用于该瓶颈问题的解决。

The primary theory of numbers aspect related integer property basic content.

摘要本论文主要讨论了整数的离散性、代数性质、有序性、整除性、最大公因数与最小公倍数、素因子分解、同余等初等数论方面的有关整数性质的基本内容。

We deeply research the radio communication networks, give two fast algorithm for computing the ST reliability of RCN, which are very simple and effective to the networks that its topological structure isn't complex, The thesis having been published to the reliability for RCN only have factor algorithm, so we can say the algorithms are the achievements of innovation, we solve the rapid computing the ST reliability for RCN problem.

对于无线通信网络可靠性计算的研究目前只有因子分解算法，因此可以说这两个算法的给出是开拓性的，解决了无线通信网络可靠性的快速计算问题。

The security of these new cryptosystems depends on some NP-complete problems in the theory of Diophantine equations and on the difficulty of large number decomposition.

这些体制的安全性依赖于求解丢番图方程中的一些NP完全问题和大数的素因子分解的困难性。

Harn and Kiesler proposed a public-key cryptosystem, digital signature and authentic encryption scheme based on Rabin's cryptosystem, in this chapter, we will analyze the security of H-K digital signature scheme and H-K authentic encryption scheme, and point out that these cryptosystem are insecure.

Shao设计了两种数字签名方案，并称这两种数字签名的安全性建立同时在离散对数和素因子分解问题之上。

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。

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。