摘要
给定一族生成方式{F_(j)}^(m)_(j=1)及自然数集N的一个划分{E_(j)}^(m)_(j=1),从[0,1]^(2)出发,本研究定义一类平面数字限制集,并结合几种分形维数的定义及相关引理,得出这类平面数字限制集的几种分形维数,如Hausdorff维数、上盒维数、填充维数以及Assouad维数.
Let{F_(j)}^(m)_(j=1) be a family of generating modes and{E_(j)}^(m)_(j=1) be a division of natural number set N.In this paper,starting from[0,1]^(2),we firstly define a kind of sets defined by digit restrictions on plane,and then,combining with the definitions of several fractal dimensions and related lemmas,we get their fractal dimensions.For example,Hausdorff dimension,upper box dimension,packing dimension,and Assouad dimension.
作者
董家梅
席玉佩
DONG Jiamei;XI Yupei(Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics,Hubei University, Wuhan 430062, China)
出处
《湖北大学学报（自然科学版）》
CAS
2022年第3期320-324,共5页
Journal of Hubei University：Natural Science
作者简介
董家梅(1995-),女,硕士生,E-mail:djm7940@163.com。
