查询词典 factorization theorem

By using the theory of factor theorem and determinant in higher Alge-bra, the factorization method of Circulant Symmetric function is given.

本文利用高等代数的因式定理理论和行列式理论，给出了轮换对称函数的因式分解方法。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

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。

On the other hand, all the results obtained in here are helpfulto further precisely test perturbative QCD and NRQCD factorization theorem.

同时本文的计算结果也有助于进一步精确检验微扰QCD及NRQCD因子化定理。

In this thesis, we use the Min-Max criterion and Parks-McClellan algorithm to design this optimal approximation error of spectrum. Moreover, we give constraint of this optimal spectrum to get the positive spectrum. Then the positive spectrum can be factored by Spectrum Factorization Theorem and can be realized by FIR system.

我们利用最小化最大误差指标，及Parks-McClellan演算法，设计出具有最佳误差的频谱，并对此频谱做限制式上的处理，来得到正数列频谱，并将所得到之正数列频谱利用分解理论做分解，并以FIR系统实现之。

There are so many similarities between the new class of RH〓 and the class A〓, it is to be expected, therefore, that the Jones'factorization theorem for A〓 weights might be extended to include some information about the reverse H〓1der classes via those results concerning RH〓-weights, and we do it.

具体地说，就是借助于极小算子定义了RH〓算子，类似于A〓权的分解，我们对RH〓权的结构做了细致的刻划；第四、我们定义了一类新的算子—几何极小算子并致力于把A〓权的结果推广到鞅论上。

Based on the factorization theorem for lepton induced hard diffractive scattering and color octet heavy quarkonium production mechanism,ηc diffractive production in the direct photon process is studied.

华北电力大学数理学院，河北保定071003利用轻子硬衍射过程的因子化方法和重夸克偶素的色八重态产生机制，研究了ηc的光生衍射过程。

First, based on the factorization theorem for lepton-induced hard diffractive scat-tering and the factorization framework of the nonrelativistic Quantum Chromodynamics for quarkonia production, We present a study of J/〓+jet diffractive productionin the direct photon processes at DESY HERA.

首先，基于轻子引起的inclusive硬衍射散射的因子化定理和重夸克偶素产生的非相对论QCD因子化框架，我们研究了DESY HERA对撞机上J／〓+jet的衍射直接光产生。

Four seminars of special topics at an accessible level were organized at 4:00 - 5:00pm each afternoon. Prof. Shufang Su of the University of Arizona gave the first seminar on the ''Dark matter search and the LHC". Prof. Tao Han of the University of Wisconsin-Madison spoke on the ''Methodology of collider phenomenology" on the second day. Prof. Hsiang-Nan Li of the Academia Sinica, Taipei, gave a talk on the ''Perturbative QCD and the factorization Theorem". Prof. Lian-Tao Wang finished up in the last day to speak on the ''Monte Carlo techniques in high energy physics".

每个下午16：00-17：00是专题讲座时间，分别由美国亚利桑那大学的苏淑芳教授做了有关"寻找暗物质与LHC"的讲座，美国威斯康星-麦迪逊大学的韩涛教授做了有关"对撞机现象学研究的方法"的讲座，台湾中央研究员的李湘楠教授做了"微扰QCD和因子化定理"的讲座，王连涛教授最后做了"高能物理中的蒙特卡洛方法"的讲座。

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。