The constructions of general connections on the fibred product of q copies of the first jet prolongation

We describe all natural operators $A$ transforming general connections $\mathrm{\Gamma }$ on fibred manifolds $Y\to M$ and torsion-free classical linear connections $\mathrm{\Lambda }$ on $M$ into general connections $A(\mathrm{\Gamma },\mathrm{\Lambda })$ on the fibred product $J^{<q>}Y\to M$ of $q$ copies of the first jet prolongation $J^{1}Y\to M$.