1) power LCM matrix
幂LCM矩阵
1.
In this paper,a necessary and sufficient conditions on the gcd closed set S with |S|=4 such that the power GCD matrix(Se)on S divides the power LCM matrix on S in the ring M4(Z) of 4×4 matrices over the integers is proved.
在本文中,我们给出了关于四元gcd封闭集S的充分必要条件,使得在环M4(Z)中,定义在S上的e次幂GCD矩阵(Se)整除e次幂LCM矩阵[Se]。
2.
Shaofang Hong conjectured in 2002 that for a given positive integer t there is a positive integer k(t) depending only on t, such that if n≤k(t), then the power LCM matrix ([x_i, x_j]~t) defined on any gcd-closed set S={x_1,…,x_n} is nonsingular; but for n≥k(t)+1, there exists a gcd-closed set S={x_1,…,x_n} such that the power LCM matrix ([x_i, x_j]~t) on S is singular.
洪绍方在2002年猜想:对于给定的一个正整数t,存在一个仅由t决定的正整数k(t),使得当n≤k(t)时,定义在任意gcd闭集S={x1,…,xn}上的幂LCM矩阵([xi,xj]t)是非奇异的;而当n≥k(t)+1,则存在一个gcd闭集S={x1,…,xn},使得定义在其上的幂LCM矩阵([xi,xj]t)奇异。
3.
In this paper, we showthat for any real number e ≥1 and n ≤7, the power LCM matrix ([x_i,x_j]~e) definedon any gcd-closed set S = {x_1,.
第i 行j 列元素由xi 和xj 的最小公倍数的e次幂[x_i,x_j]~e 构成的n ×n矩阵([x_i,x_j]~e),称为定义在S 上的e次幂LCM矩阵。
2) LCM power matrices
LCM幂矩阵
3) The inverses of GCD and LCM matrices
GCD和LCM幂矩阵的逆矩阵
4) LCM matrix
LCM矩阵
1.
It is proved in this paper that if S consists of two relatively prime divisor chains,then the GCD matrix on S divides the LCM matrix on S.
作者证明:若S由两个互素的因子链构成,那么在n阶整数矩阵环中,GCD矩阵(S)整除LCM矩阵[S]。
2.
The authors prove a clai mof Hongstatingthat 270 is the secondleast pri mitive singularnumber,and showthe LCM matrix on a gcd-closed setSsuch that each element ofSis strictlybetween 180 and 270 is nonsingular.
以S中的任意两个元xi,xj,i=1,2,…,n,j=1,2,…,n的最小公倍数为i行j列元素的矩阵称为S上的最小公倍数矩阵(LCM矩阵),记为[S]。
3.
Similarly we can definethe LCM matrix [S].
同样我们可以定义LCM矩阵[S]。
5) Least commonmultiple matrix
最小公倍(LCM)矩阵
补充资料：彻幂
1.见"彻幂"。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条