On the mean value of Smarandache prime part Pp(n)and Pp(n)

For any positive integer n, the Smarandache Superior Prime Part Pp(n) is the smallest prime number greater than or equal to n. For any positive integer n >= 2, the Smarandache Inferior Prime Part Pp(n) is the largest prime number less than or equal to n. The main purpose of this paper is using the elementary and analytic methods to study the asymptotic properties of (S-n(n) - I-n(n)), K-n(n)/L-n(n), (K-n(n) - L-n(n))), and give several interesting asymptotic formula for them, where S-n(n) = 1/n Sigma(n)(i=1) Pp(n), In(n) = 1/n Sigma(n)(i=1) Pp(n) and Kn(n) = ( Sigma(n)(i=1) Pp(n))(1/n) , Ln(n) = (Sigma(n)(i=1) Pp(n))(1/n.)