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1)  Table of I h group elements product
Ih群元素乘法表
2)  Matrix representation of I h group
Ih群矩阵表示
3)  finite field multiplication
域元素乘法
1.
Improved algorithm of finite field multiplication in optimal normal basis;
一种基于优化正规基的域元素乘法改进算法
2.
This paper gives the general formula of finite field multiplication in optimal normal basis.
给出基域GF(2m)上优化正规基域元素乘法的一般计算公式,针对Rosing算法中预计算较多的问题,结合Ning-Yin算法思想,提出一种改进算法和3种预计算方法。
4)  group multiplication
群乘表
1.
By using stereographic projection of each point group,all symmetry operation and generating operation of the point groups are listed,and group multiplication table of maximal proper point group 822 is filled in.
运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表。
2.
All symmetry operation and generating operation of the point groups were listed,and their group multiplication table of maximal proper point group 10 22 was filled in.
绘出了各点群的极赤投影图;列出了各点群的所有群元和生成元;填写出了最大的固有点群10 22的群乘表。
3.
By using stereographic projection of each point group,all symmetry operation and generating operation of the point groups were listed,and group multiplication table of maximal proper point group 822 was filled in.
从理论上对准晶体中十二方晶系各点群进行了研究,绘出了十二方晶系7个点群的极赤投影图;列出了各点群的所有对称操作及生成操作;填写出了其中最大固有点群12 22的群乘表;在自定义的十二方坐标系中,导出了十二方晶系各点群所有对称操作的矩阵,这48个3×3矩阵的矩阵元有7种可能取值:0,±1,±2,±3,而3恰恰是反映十二方晶系准晶体所具有的准周期平移序的无理数。
5)  multiplicative semigroup
乘法半群
1.
By a system of linear equations on multiplicative semigroup,we present a general mathematical method to solve the inverse lattice problems in physics.
用乘法半群上的线性方程组来求解晶体原子间对势反演的逆问题。
2.
In this paper, it is proved that if n≥2 and R is an effective semiring or a semiring in which all idempotents are central elements, then Φ:Tn(R)→Tn(R) is a multiplicative semigroup automorphism if and only if there exist a invertible G∈Tn(R) and a semiring automorphism τ of R such that Φ(A)=G-1τ(A)G for all A=(aij)n×n inTn(R).
证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G。
6)  Abelian(multiplicative)group
Abel(乘法)群
补充资料:乘法半群


乘法半群
multiplicative semi - group

  乘法半群【md均声Cative胭川~g川叩;My脸,11~皿即no理厂pynoal 结合环(assoc通石Ven吧)的乘法半群,即该环的所有元素矣宇乘法形成的半群(~一gro叩).非结合环关于乘法仅形成广群(grouPoid),称为环的乘法广群(multiPlicati说grouPoid). O.A.地aH图a撰郭元春译牛凤文校
  
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