  We use a result of Hellus about generalized local duality to describe some
generalized Matlis duals for certain quasi-\F-modules. Furthermore, we apply
this description to obtain examples for non-artinian local cohomology modules
by the theory of \F-modules. In particular, we get a new view on Hartshorne's
counterexample for a conjecture by Grothendieck about the finiteness of
$Hom_R(R/I,H^i_I(R))$ for a noetherian local Ring $R$ and an ideal $I \subseteq
R$.
