The National Natural Science Foundation of China (10471048), RFDP (20040422004) of Higher Education, Promotional Foundation (2005BS01016) for Middle-aged or Young Scientists of Shandong Province, and
Let F be a Hilbert filtration with respect to a Cohen-Macaulay R-module M. When G(F,M) and FK(F,M) have almost maximal depths, we show that the length λ(KInM/K