关于齐次Moran集的packing维数结果  

Packing Dimensional Results for Homogeneous Moran Sets

作　　者：胡晓梅[1,2] Hu Xiaomei(School of Mathematics and Statistics,Central China Normal University,Wuhan 430079;School of Mathematics and Statistics,Hubei University of Science and Technology,Hubei Xianning 437100)

机构地区：[1]华中师范大学数学与统计学学院,武汉430079 [2]湖北科技学院,湖北咸宁437100

出　　处：《数学物理学报(A辑)》2016年第5期873-878,共6页Acta Mathematica Scientia

基　　金：国家自然科学基金(11271148)资助

摘　　要：该文构造了一类特殊的齐次Moran集,称为{m_(k)}-拟齐次Cantor集,并讨论了它们的packing维数.通过调整序列{m_(k)}_(k≥1)的值,构造性证明了齐次Moran集packing维数的介值定理.此外,还得到了齐次Moran集的packing维数取得最小值的一个充分条件.In this paper,we construct a class of special homogeneous Moran set,called{m_(k)}-quasi homogeneous Cantor set and discuss their packing dimensions.By adjusting the value of{m_(k)}k≥1,we constructively prove the intermediate value theorem about packing dimensions of the homogeneous Moran sets.Moreover,we obtain a sufficient condition that the packing dimension of homogeneous Moran sets may get the minimum value.

关 键 词：齐次MORAN集 {m_(k)}-Moran集 {m_(k)}-拟齐次Cantor集 PACKING维数 

分 类 号：O174.12[理学—数学]