Intersections of homogeneous Cantor sets with their translations

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. Research supported by the National Science Foundation of China (10671180) and Jiangsu University 05JDG041