Descripción: In this note we give some remarks and improvements on our recent paper [5] about an optimization problem for the p-Laplace operator that were motivated by some discussion that we had with Prof. Cianchi. © 2009 Elsevier Ltd. All rights reserved.

Descripción: Chromatic scheduling polytopes arise as solution sets of the bandwidth allocation problem in certain radio access networks supplying wireless access to voice/data communication networks to customers with individual communication demands. This bandwidth allocation problem is a special chromatic scheduling problem; both problems are N P-complete and, furthermore, there exist no polynomial-time algorithms with a fixed quality guarantee for them. As algorithms based on cutting planes are shown to be successful for many other combinatorial optimization problems, the goal is to apply such methods to the bandwidth allocation problem. For that, knowledge on the associated polytopes is required. The present paper contributes to this issue, introducing new classes of valid inequalities based on variations and extensions of the covering-clique inequalities presented in [J. Marenco, Chromatic scheduling polytopes coming from the bandwidth allocation problem in point-to-multipoint radio access systems, Ph.D. Thesis, Universidad de Buenos Aires, Argentina, 2005; J. Marenco, A. Wagler, Chromatic scheduling polytopes coming from the bandwidth allocation problem in point-to-multipoint radio access systems, Annals of Operations Research 150-1 (2007) 159-175]. We discuss conditions ensuring that these inequalities define facets of chromatic scheduling polytopes, and we show that the associated separation problems are N P-complete. © 2008 Elsevier B.V. All rights reserved.

Descripción: In this paper we study the optimization problem for the first eigenvalue of the p-Laplacian plus a potential V with respect to V, when the potential is restricted to a bounded, closed and convex Bet of Lq(Ω).

Descripción: We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) d x in the class of functions W1, G (Ω), with a constraint on the volume of {u > 0}. The conditions on the function G allow for a different behavior at 0 and at ∞. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂ {u > 0} ∩ Ω is smooth. © 2007 Elsevier Inc. All rights reserved.

Descripción: A Three-Dimensional Finite Volume Arbitrary Lagrangian-Eulerian simulation code was developed to study different plasma physics problems in 3D+t. The code is based on a complex multi-component species program with transport and radiation terms written and applied to plasma and fusion physics problems. The integration domain is represented with a structured irregular mesh, with fixed connectivity made of hexahedral cells. Coordinates and velocities are assigned to cell vertices. After each calculation cycle, mesh vertices are moved arbitrary over the fluid. The adaptive method consists of shifting mesh vertices over the fluid in order to keep a reasonable mesh structure and increase the spatial resolution where the physical solution demands. The code was a valuable tool for parametric study of different physical problems, mainly optimization of Plasma Focus Machine, detonation and propagation of thermonuclear reactions, and Kelvin-Helmholtz instabilities in the boundary layer of the terrestrial magnetopause. © 2009 IOP Publishing Ltd.

Descripción: We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂ { u > 0 } ∩ Ω, is smooth. © 2006 Elsevier Inc. All rights reserved.

Descripción: We study the dependence on the subset A ⊂ Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p = 2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction. © 2005 Elsevier SAS. All rights reserved.

Descripción: In this work we study a particular way of dealing with interference in combinatorial optimization models representing wireless communication networks. In a typical wireless network, co-channel interference occurs whenever two overlapping antennas use the same frequency channel, and a less critical interference is generated whenever two overlapping antennas use adjacent channels. This motivates the formulation of the minimum-adjacency vertex coloring problem which, given an interference graph G representing the potential interference between the antennas and a set of prespecified colors/channels, asks for a vertex coloring of G minimizing the number of edges receiving adjacent colors. We propose an integer programming model for this problem and present three families of facet-inducing valid inequalities. Based on these results, we implement a branch-and-cut algorithm for this problem, and we provide promising computational results. © 2011 Elsevier B.V. All rights reserved.