Search

The aim of this paper is to exploit the algorithms of paper Experimental Math. 8 (1999) in order to produce a new algebraic method for computing efficiently absolute Lagrange resolvent, a fundamental tool in constructive algebraic Galois theory. This article is composed of two parts.The main idea of the first part is to break up the calculation of absolute resolvent into smaller computations. Since a multi-resolvent is a factor of a resolvent, the whole resolvent may be computed by means of several multi-resolvents.The idea of the second part is that an irreducible polynomial over Z might be reducible over Z /pZ for certain integer p. So the first part can be applied and then, the Chinese remainder theorem allows to lift up the resolvent over Z. [Copyright &y& Elsevier]

Abstract: In this paper we analyze O''Hara''s partition bijection. We present three type of results. First, we show that O''Hara''s bijection can be viewed geometrically as a certain scissor congruence type result. Second, we obtain a number of new complexity bounds, proving that O''Hara''s bijection is efficient in several special cases and mildly exponential in general. Finally, we prove that for identities with finite support, the map of the O''Hara''s bijection can be computed in polynomial time, i.e. much more efficiently than by O''Hara''s construction. [Copyright &y& Elsevier]

Abstract: For a canonical threefold X, we know for a sufficiently large n. When , there are few known results about the integer n. This paper introduces an algorithm for computing plurigenera. Furthermore, when is small, especially 1 and 2, plurigenera are computed. This produces for and for when . Also, for and for with 8 possible exceptional cases when . [Copyright &y& Elsevier]

This paper discusses the application of Bayes's theorem to those cases where the true state of the world is not known with certainty. An algorithm is proposed that relaxes the requirement of Bayes's theorem that the true data state be known with certainty by postulating a true but unobservable elementary event, ω, which gives rise to posterior probabilities which reflect the uncertainty of the data. A derivation is presented for the calculation of Bayesian posterior probabilities which uses as its input these probabilities, rather than the true event, o, which is assumed to be unavailable. Suggestions are made as to the application of this modification of Bayes's theorem to cascaded inference processes. [ABSTRACT FROM AUTHOR]