Seepage Problem, The Sierpinski Carpet Lattice Point On The Map

Percolation model was firsely proposed by Broadbent S.R.and Hammersley J.M. and has been well studied in the past three decades.This not only extend the reserch fields of probability,but also theorlize for Stat. Physics.The study of percolation in the past focused on the bond percolation and site percolation about the gragh with translation invariance,such as (?)~d,triangular lattice-(?)~3 and(?)~6.With the development of fractal,many scientists are intrested in it.They try their best to do it like Mandelbrot B.B and others and make good achievements.Then the random process on the fractal make great progress by it .We study the Bernoulli bond percolation problem on planer Sierpinski Carpet.In Kumagai.T.[8],he has proved the prime problem the existence of critical probability ,exponencial decays and continuity of θ(p) under an assumption .In Higuchi and Wu [9],they have solved all the prime problem on the Sierpinski Carpet with T = {0,1,2}~2\(1, l),they extend the Branching argument ·to the percolation in their prove, and gain the same conclusion under the different means to [8].We just want to extend the method in [9] to the other Sierpinski Carpet percolation model with special character,we can get the same conclusion in [9],then we combine it with the theorem in [8] or [9],and we can resolve the percolation prime problem.