  The numerical solution of the recently formulated number-projected
Hartree-Fock-Bogoliubov equations is studied in an exactly soluble
cranked-deformed shell model Hamiltonian. It is found that the solution of
these number-projected equations involve similar numerical effort as that of
bare HFB. We consider that this is a significant progress in the mean-field
studies of the quantum many-body systems. The results of the projected
calculations are shown to be in almost complete agreement with the exact
solutions of the model Hamiltonian. The phase transition obtained in the HFB
theory as a function of the rotational frequency is shown to be smeared out
with the projection.
