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The nested algebraic Bethe ansatz is presented for the anisotropicsupersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatzequations of the model are obtained on a one-dimensional closed lattice and anexpression for the energy is given.Comment: 7 pages (revtex), minor modifications. To appear in Mod. Phys. Lett.

BETHE ANSATZ SOLUTION OF THE CLOSED ANISOTROPIC SUPERSYMMETRIC U MODEL WITH QUANTUM SUPERSYMMETRY