Abstract
1. On certain subrings of prime rings with derivationsLet R be a noncommutative prime ring with nonzero derivation d. U is a noncentral Lie ideal of R and U^{d} is not contained in Z. If d is outer, then the subring of R generated by {[d(x),x] ;x belong to U} contains a nonzero ideal of R except charR=2 and R satisfies S_{4}.2. Jordan generalized derivations on semiprime ringsLet R be a 2-torson free semiprime ring, then every Jordan generalized derivation on R is a generalized derivation.