Let R be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules (M, N) over R we study applications of rigidity of Tor(M, N), based on ideas by Huneke, Wiegand and Jorgensen. We then focus on the hypersurfaces with isolated singularity and even dimension, and show that modules over such rings behave very much like those over regular local rings. Connecti...

This contribution considers the problem of transforming a regular matrix pair (A;B) to generalized Schur form. The focus is on blocked algorithms for the reduction process that typically includes two major steps. The rst is a two-stage reduction of a regular matrix pair (A;B) to condensed form (H;T ) using orthogonal transformations Q and Z such that H = QAZ is upper Hessenberg and T = QBZ is u...

An algorithm for reduction of a regular matrix pair (A; B) to block Hessenberg-triangular form is presented. This condensed form Q T (A; B)Z = (H; T), where H and T are block upper Hessenberg and upper triangular, respectively, and Q and Z orthogonal, may serve as a rst step in the solution of the generalized eigenvalue problem Ax = Bx. It is shown how an elementwise algorithm can be reorganize...

Frequent pattern mining is the fundamental and most dominant research area in data mining. Maximal frequent patterns are one of the compact representations of frequent itemsets. There is more number of algorithms to find maximal frequent patterns that are suitable for mining transactional databases. Users not only interested in occurrence frequency but may be interested on frequent patterns tha...

1 Kasner, "Conformal Classification of Analytic Arcs or Elements, Poincare's Local Problem of Conformal Geometry," Trans. Am. Math. Soc., 16, 333-349 (1915). The theory of a pair of regular arcs, including the horn angle, is given in "Conformal Geometry," Proceedings Cambridge International Congress Mathematicians, 1912, and a paper appearing in Scripta Mathematica, 1945. 2 Kasner and De Cicco,...

Since the scheduling of sports leagues involves many kinds of constraints and the minimization of costs or travel distances, sports scheduling has become a very active field, providing both interesting and challenging problems to the combinatorial optimization community. In this work we describe the automatic scheduling of the regular phase of the Argentine first division volleyball league and ...

Graph navigational languages define binary relations in terms of pair of nodes in a graph subject to the existence of a path satisfying a certain regular expression. The goal of this paper is to give a novel characterization of navigational languages in terms of the structure of the graph embracing the results of a query. We define novel graph-based query evaluation semantics and efficient algo...

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by the Poisson random impulses, but their difference has not been fully quantified. Here, we analyze a pair of uncoupled oscillat...

We define the operation of Petrie duality for maps, describing its general properties both geometrically and algebraically. We give a number of examples and applications, including the construction of a pair of regular maps, one orientable of genus 17, the other non-orientable of genus 52, which embed the 40-vertex cage of valency 6 and girth 5 discovered independently by Robertson and Anstee. ...

We present a machine learning system, called BONSAI, for knowledge acquisition from positive and negative examples of strings, and report some experiments on protein data using the PIR and GenBank databases. This learning system is constructed with an algorithmic learning theory for decision trees over regular patterns, which is newly developed for this work. As a hypothesis, the system tries t...