... dimension. In Section 3, we prove the maximal sequences, it is used to find the lower local dimension. The proof of the MainTheorem will be given in the last section.2. The formula for calculating ... µ}be the attainable values of α(s), i.e., the range of function α definning in the supp µ. In this paper, we consider the interest second case with a =9(a ≡ 0 (mod 3)).Our result is the following.Main ... Wang, Tiling the line with translates of one tile, InventionsMath. 124(1996), 341 - 365.10. S. M. Ngai and Y. Wang, Hausdorff dimention of the self - similar sets with over-laps,J. London Math....