摘要
本文利用n阶整数元方阵作为表示基,以Z^n上的有限个点矩阵作为表示系数,构造了空间R^n中的点矩阵的加法表示系统和乘法表示系统,并分别给出了这两种表示系统导出的分形矩阵在不满足开集条件下的Hausdorff维数的上下界.
In this paper,by using the matrix with integral elements as the basis of representing system,and the finite point matrices in Z^n as the coefficients of representing system,we construct the additive representing system and multiplicative representing system of point matrices in R^n.Moreover,we discuss the upper and lower bounds of the Hausdorff dimension of the fractal matrix in R^n induced from the two representing systems,which does not satisfy the open set conditions.
出处
《数学进展》
CSCD
北大核心
2015年第2期229-238,共10页
Advances in Mathematics（China）
基金
海南省自然科学基金项目(No.113003
No.111002)
