on graded local cohomology modules defined by a pair of ideals

let r = ? n2n0 rn be a standard graded ring, m be a nitely-generated graded r-module, and j be a homogeneous ideal of r. in this work, we study the graded structure of the i-th local cohomology module of m, de ned by a pair of ideals (r+; j), i.e. hir +;j (m). more precisely, we discuss the niteness property and vanishing of the graded components hir +;j (m)n. also, we study the artinian property and tameness of certain submodules and quotient modules of hir +;j (m).