  Let $(R, \frak m)$ be a generalized Cohen-Macaulay local ring of dimension
$d$, and $f_1, \ldots, f_r$ a part of system of parameters of $R$. In this
paper we give explicit numbers $N$ such that the lengths of all lower local
cohomology modules and the Hilbert function of $R/(f_1, \ldots, f_r)$ are
preserved when we perturbs the sequence $f_1, \ldots, f_r$ by $\varepsilon_1,
\ldots, \varepsilon_r \in {\frak m}^N$. The second assertion extends a previous
result of Srinivas and Trivedi for generalized Cohen-Macaulay rings.
