Let (a0, · · · , ak−1) be a sequence of positive integers and m a positive integer. We prove that “almost every” real quadratic unit ǫ of norm (−1)k admits at leastm distinct factorizations into a product of purely periodic irrationals of the form ǫ = [a0; a1, . . . , ak−1, x, y]× [a1; a2, . . . , x, y, a0] × · · · × [y; a0, . . . , ak−1, x]. Periods exhibited in this expression are not assumed...

A Fréchet algebra endowed with a multiplicatively convex topology has two types of invariants: homotopy invariants (topological K-theory and periodic cyclic homology) and secondary invariants (multiplicative Ktheory and the non-periodic versions of cyclic homology). The first aim of this paper is to establish a Riemann-Roch-Grothendieck theorem which describes direct images for homotopy and sec...

The problem of maximal hub covering as a challenging problem in operation research. Transportation programming seeks to find an optimal location of a set of hubs to reach maximum flow in a network. Since the main structure's parameters of the problem such as origin-destination flows, costs and travel time, change periodically in the real world applications, new issues arise in handling it. In t...

0. Introduction. This paper continues the study of the noncommutative innn-itesimal cohomology we introduced in 3]. This is the cohomology of sheaves on a noncommutative version of the commutative innnitesimal site of Grothendieck ((8]). Grothendieck showed that, for a smooth scheme X of characteristic zero, the cohomology of the structure sheaf on the innnitesimal site gives de Rham cohomol-og...