  Fiber cones of 0-dimensional ideals with almost minimal multiplicity in
Cohen-Macaulay local rings are studied. Ratliff-Rush closure of filtration of
ideals with respect to another ideal is introduced. This is used to find a
bound on the reduction number with respect to an ideal. Rossi's bound on
reduction number in terms of Hilbert coefficients is obtained as a consequence.
Sufficient conditions are provided for the fiber cone of 0-dimensional ideals
to have almost maximal depth. Hilbert series of such fiber cones are also
computed.
