General n-canonical divisors on two-dimensional smoothable semi-log-terminal singularities

In this paper we calculate genaral n-canonical divisors on smoothable semi-log-terminal singularities in dimension 2, in other words, the full sheaves associated to the double dual of the nth tensor power of the dualizing sheaves of these singularities. And as its application we give the inequality which bound the Gorenstein index by the local self intersection number of the n-canonical divisor of these singularities.