因子分解

In this paper, firstly the elimination tree theory is introduced in brief, and the structure of Jacobian matrix is determined by use of symbolic factorization; then by use of sparse vector method each column of lower triangular matrix L and each row of upper triangular matrix U are solved.

介绍了消去树理论，并采用符号因子分解技术确定雅可比矩阵的结构，然后采用稀疏向量法求取L阵的每行和U阵的每列。

The main contributions of the paper are listed as follows:(1) Propose methods of key-locks, such as equations set, Newton's interpolation formula, and the prime factor decomposition theorem, to implement access control.

论文的主要研究成果为：(1)提出了利用方程组、牛顿插值公式和素因子分解因式等钥—锁配对法来实现一般的访问控制。

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。

Baed on this result,the nonlinear problem of decomposition of multivariate polynomial is converted into series of linear problem and dedsion of divisibility of polynomial.

计算机出现后，研究多元多项式因子分解的构造和算法实现问题成为计算机代数的重要课题。对此，国内外众多学者作了大量工作。

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。

In chapter 4, the factorization and cascade decomposition for first order singular systems have been discussed, the if and only if conditions have been obtained, the invariaty of minimality under factoiization and cascade decomposition has been proved.

第四章，讨论了一阶奇异系统的因子分解和级联分解，给出了其具有上述分解的充要条件，证明了极小性在分解下的不变性；对具有一阶奇异系统实现的有理函数矩阵，给出了判定其为正实函数的充要条件，推广了著名的正实引理。

Factors with prescribed properties such as factors including or excluding some given edge, maximum or minimum factors, factor covering and connected factors; 3. Factorizations of graphs; 4. k-extendable graph and its generalizations. Fractional graph theory is a relatively younger research branch.

例如，因子与图的最小度，韧度，联结数：邻域并等参数之间的关系；2·研究图的有限制条件的因子，例如，有约束条件的因子，图的连通因子，图的最大最小因子；3·图的因子分解；4·k-可扩图及其推广等。

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。

Nyang and Song proposed a digital signature scheme based on quadratic residue problem.

对Shimada公钥密码体制进行推广，提出一种新的密码体制，这种新的公钥密码体制的安全性建立在一般形式的素因子分解问题之上，攻击这种新的密码体制等价于对一般形式的大整数进行素因子分解，并设计一种新的数字签名方案和新的认证加密方案。

If no factor is found, the exponent is released back into the unassigned testing pool for Lucas-Lehmer testing or further factoring.

如果没有发现因子，该指数被退回到未分配的测试池中，以便进行 Lucas-Lehmer 测试，或者进行进一步的因子分解。

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。