This paper addresses the maintenance of discovered frequent patterns when a batch of transactions are removed from the original dataset. We conduct an in-depth investigation on how the frequent pattern space evolves under transaction removal updates using the concept of equivalence classes. Inspired by the evolution analysis, an effective and exact algorithm TRUM is proposed to maintain frequen...

in this paper, a numerical scheme for solving singular initial/boundary value problems presented.by applying the reproducing kernel hilbert space method (rkhsm) for solving these problems,this method obtained to approximated solution. numerical examples are given to demonstrate theaccuracy of the present method. the result obtained by the method and the exact solution are foundto be in good agr...