  We present physical arguments as well as numerical evidence to show that the
Cooper pair (gap) function vanishes on the Fermi surface in strongly correlated
electron systems such as \tJ and \lU Hubbard models in one and two dimensions.
Using exact diagonalization, we study a correlation function which is a measure
of the gap function even in a finite system, and present numerical results for
this correlation function on small clusters of 8 (Hubbard) and 16 ($t-J$)
sites.
