We consider the homogeneous Cantor sets which are generalization of symmetric perfect sets, and give a formula of the exact Hausdorff measures for a class of such sets.
We pursue the study on homogeneous Cantor sets with their translations. We get the fractal structure of intersection I（t）, and find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero v...We pursue the study on homogeneous Cantor sets with their translations. We get the fractal structure of intersection I（t）, and find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from shifting numbers with the coding of t. Concretely, a very brief calculation formula of the measure with the coding of t is given.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10771075)
文摘We consider the homogeneous Cantor sets which are generalization of symmetric perfect sets, and give a formula of the exact Hausdorff measures for a class of such sets.
基金the National Science Foundation of China (10671180)Jiangsu University 05JDG041
文摘We pursue the study on homogeneous Cantor sets with their translations. We get the fractal structure of intersection I（t）, and find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from shifting numbers with the coding of t. Concretely, a very brief calculation formula of the measure with the coding of t is given.
