Isoperimetric inequalities in Riemann surfaces of infinite type

75 pages, 1 figure.-- MSC2000 code: 30F45.MR#: MR1715412 (2000j:30075)Zbl#: Zbl 0935.30028Research partially supported by a grant from Dirección General de Enseñanza Superior (Ministerio de Educación y Ciencia), Spain.Publicad

Approximation theory for weighted Sobolev spaces on curves

17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.Research of V. Álvarez, D. Pestana and J.M. Rodríguez partially supported by a grant from DGI, BFM2000-0206-C04-01, Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I

36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first (J.M.R.), third (E.R.) and fourth (D.P.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Weighted Sobolev spaces on curves

45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.Research of second (D.P.), third (J.M.R.) and fourth (E.R.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II

32 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482MR#: MR1928169 (2003h:42034)Zbl#: Zbl 1095.42014^aWe present a definition of general Sobolev spaces with respect to arbitrary measures, $W^{k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C^\infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.Research partially supported by a grant from DGES (MEC), Spain.Publicad

Routing design for less-than-truckload motor carriers using ant colony techniques

One of the most important challenges for Less-Than-Truck-Load carriers consists of determining how to consolidate flows of small shipments to minimize costs while maintaining a certain level of service. For any origin-destination pair, there are several strategies to consolidate flows, but the most usual ones are: peddling/collecting routes and shipping through one or more break-bulk terminals. Therefore, the target is determining a route for each origin-destination pair that minimizes the total transportation and handling cost guaranteeing a certain level of service. Exact resolution is not viable for real size problems due to the excessive computational time required. This research studies different aspects of the problem and provides a metaheuristic algorithm (based on Ant Colonies Optimization techniques) capable of solving real problems in a reasonable computational time. The viability of the approach has been proved by means of the application of the algorithm to a real Spanish case, obtaining encouraging results

The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler