The natural functions on the cotangent bundle of higher order vector tangent bundles over fibered manifolds

For natural numbers r, s, g, rn, n with s >= r <= q we determine all natural functions g : T*(J((r,s,q))(Y,R-1,R-1)0)* -> R for any fibered manifold Y with IR-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n, with s >= r we determine all natural functions g : T*(J((r,s))(Y,R)(0))* -> R for any Y as above. (C) Central European Science Journals. All rights reserved.