一类正六面体的Hausdorff测度的计算  

Calculation of Hausdorff Measures About a Class of Regular Hexahedrons

作　　者：聂饶荣[1] 尹建东[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2013年第3期291-296,共6页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(11261039);江西省自然科学基金资助项目(20132BAB201009)

摘　　要：考虑单位立方体内生成的一类自相似集的Hausdorff测度的计算问题,在相似比满足一定条件下,证明了自然覆盖为实现上凸密度1的最好形状,即自然覆盖为最好覆盖。作为推论,得到该类自相似集的Hausdorff测度的精确值为(3)^(1/2)s,其中s为Hausdorff维数。The problem of calculation of Hausdorff measures of a class of self-similar sets in a regular hexahe- dron was studied in this paper When the similitude ratios satisfied certain conditions,it was proved that the natural cover was the best shape for upper convex density It means that the natural cover was a best one As a result, the ex- act value of Hausdorff measure of this class of self-similar sets is （√3）s,where s is Hausdorff dimension.

关 键 词：HAUSDORFF测度 上凸密度 自相似集 

分 类 号：O174.12[理学—数学]