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In this paper we develop a general decomposition theory (Section 5) for submonoids and subgroups of rings under ◦, in terms of semidirect, reverse semidirect and general

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This paper develops a recursion formula for the conditional moments of the area under the absolute value of Brownian bridge given the local time at 0.. The method of power series

Acknowledgement.This work was partially done while the second author was visiting the University of Texas at Austin and Texas A&M University, and in the Linear Analysis Workshop