标量

To raise the efficiency of scalar multiplication on elliptic curve,a scalar multiplication algorithm based on double base number system over binary field was improved.

为了提高椭圆曲线标量乘法效率，对二元域上椭圆曲线的基于双基数的标量乘法进行改进。

Using a decomposition in canonical form, a multi-sensor distributed optimal fusion reduced-order filter for each state component is proposed based on the component fusion algorithm weighted by scalars in the linear minimum variance sense for descriptor discrete stochastic linear systems with multiple sensors. It requires in parallel the calculating of a series of scalar weights.

对带多个传感器广义离散随机线性系统，利用典范型分解，基于线性最小方差各分量按标量加权融合算法，给出了多传感器分布式最优分量融合降阶滤波器，它要求并行计算一系列标量权重。

This is coincident with the third law of black hole thermodynamics.

当两个截断因子满足和标量场相同的关系时，得到的熵是标量场熵的7／2倍。

Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.

本文首先介绍了椭圆曲线密码的有关基本概念；其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算，对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析，给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法，并对IEEE P1363 标准给出的标量乘法做了改进，使得标量乘法的运算效率提高了近10%；最后介绍了利用复乘计算标量乘法的方法，对已有的方法进行总结归纳，得出完整的计算过程，并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法，得出一类普遍的结果，并给出了进一步用复乘加快标量乘法的思路。

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。

In Chapter 2, we introduce a new scalar function of the vector optimization problem by virtue of the spectral function in Euclidean Jordan algebra. Correspondingly, we define the spectral scalar optimization problem and spectral scalar solution.

第二章借助欧几里德若当代数中谱函数的概念，引入了欧几里德若当代数向量优化新的标量函数——谱标量函数，并进一步定义了相应的谱标量优化问题及其谱标量解。

3D solid visualization class and 3D surface visualization class have thefunction of visualizing the scalar and vector. Moreover, 3D surface visualization classcan produce 2D data file. Picture class provides function of marking on the picture.

其次，运用 VTK 标量和矢量可视化技术实现了三维数据场的矢量和标量可视化，包括三维体数据场标量和矢量单视区显示及三维体数据场剖面标量和矢量单视区/四视区显示；使三维面数据可视化类具备了三维面数据场标量单视区显示功能和剖切面生成二维数据文件的功能，并且在三维面数据可视化类中内嵌了数据预处理算法。

Also ,, and constitute the first radial scalar meson nonet, it is supposed that these states would likely correspond to the observed states ,, and ,respectively. The scalar state may be a good candidate for the ground scalar glueball.

结果表明，和组成基态标量介子九重态，它们分别对应于实验上观测到的共振态，，和；，，和组成第一径向激发标量介子九重态，它们分别对应于实验上观测到的，，和共振态；而是基态标量胶球很好的候选者。

In the quarkonium-quarkoniumglueball mixing scheme, we quantitatively present the quarkonia-glueball content of the isoscalar scalar states and the isoscalar pseudoscalar states, and find that it is necessary to introduce additional glueball components in the ground isoscalar pseudoscalar mesons.

在介子—介子—胶球混合的框架下，我们定量地给出了同位旋为零的标量态和同位旋为零的赝标态的夸克-胶球内容，发现基态同位旋为零的赝标介子中有必要引入附加的赝标胶球成分，标量介子和标量胶球间存在强烈的混合。

Finally,we discuss the mixing and decays of multi-resonances via studying the properties of the pseudoscalar and scalar mesons.For the pseudoscalar mesons, we find the eta(1410) is mainly a glueball state by studying the decays of the ground pseudoscalar mesons. For the scalar mesons, we suggest the ground mesons contain neglect

对于赝标介子，通过研究它们的衰变发现eta(1410)的主要成分是胶球，对于标量介子，借助描述五个标量介子混合的质量矩阵，通过拟合观察到的标量介子的质量，发现基态标量介子中的胶球成分可以忽略，而其径向激发态中含有比较多的胶球成分。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。