17-09U

It is shown, that in the Bose-Fermi-Hubbard model (used for description of the atomic boson-fermion mixture in the optical lattice) the fermion-hole symmetry exists; a correspondence between cases of the on-site repulsion and  attraction is established. Based on the phase diagrams, built with the help of corresponding transformation of model parameters in the frames of the grand canonical ensemble, the conditions of the superfluid phase existence at the boson-fermion attraction are analyzed.