local cohomology modules and cousin complexes

Let r be a commutative noetherian ring with non-zero identity, a an ideal of r, x an arbitrary r–module, f a filtration of spec(r) which admits x, and s, s′, t, t′ non- negative integers such that s + t = s′ + t′. in this paper, we study the membership of r–modules hs (ht−1(c(f , x))) and hs′ −1(ht′ (c(f , x))) in serre subcategories of the category of r–modules and find some sufficient conditions which ensure the existence of an isomorphism between them, where cr(f , x) is the cousin complex for x with respect to f. as applications, we give some new facts and represent some older facts about the local cohomology modules and the cousin complexes.