On a class of fields admitting only cyclic extensions of prime power degree

We will give three characterizations of such fields and an application to quadratic forms in characteristic 2. This work has been supported by D.I.U.C. (Dirección de Investigaciones de la Pontificia Universidad Católica de Chile).     

The Serial Property and Restricted Balanced Contributions in discrete cost sharing problems

We show that the Serial Poperty and Restricted Balanced Contributions characterize the subsidy-free serial cost sharing method (Moulin (1995)) in discrete cost allocation problems. This research has been partially supported by the Universidad del País Vasco (project UPV 00031.321-15352/2003), MCyT under projects BEC2003-08182 and SEJ2004-07554, and by the Generalitat Valenciana under project GRUPOS04/13.     

On approximate solutions to some nonlinear diffusion problems

In the paper an approximate solution to a nonlinear diffusion problem in semiconductor production is considered. Some integral operator methods are used to estimate an error between this approximate solution and the exact one.This paper has been written when the author was a Visiting Professor in the Universidad de Extremadura.     

Compactness properties for trace-class operators and applications to quantum mechanics

Interpolation inequalities of Gagliardo-Nirenberg type and compactness results for self-adjoint trace-class operators with finite kinetic energy are established. Applying these results to the minimization of various free energy functionals, we determine for instance stationary states of the Hartree problem with temperature corresponding to various statistics. Authors’ addresses: Jean Dolbeault, Ceremade (UMR CNRS no. 7534) – Université Paris-Dauphine, Place de Lattre de Tassigny, 75775 Paris, Cedex 16, France; Patricio Felmer, Departamento de Ingeniería Matemática, and Centro de Modelamiento Matemático, UMI 2807 CNRS-Uchile, Universidad de Chile, Blanco Encalada 2120 (5to piso), Santiago, Chile; Juan Mayorga-Zambrano, Departamento de Ingeniería Matemática – Universidad de Chile, Blanco Encalada 2120 (4to piso), Santiago, Chile     

Power series solutions to some nonlinear diffusion problems

In this paper power series solution to some nonlinear diffusion problems in semiconductor production are considered. The convergence proof for power series solutions is presented.This paper has been written when the first author was a Visiting Professor in the Universidad de Extremadura.     

Strongly taut finitely generated monoids

A strongly taut monoid is a monoid in which all the powers of any element of the monoid have the same elasticity, that is, the ratio between the maximum and the minimum length of the factorizations of an element remains unchanged under powers. We give a procedure to determine if a finitely generated commutative monoid is strongly taut. The authors are supported by the project MTM2004-01446 and FEDER funds. The authors would like to thank the referee and P. Baginski for their heplful comments and suggestions. Author’s addresses: P. A. García-Sánchez, Departamento de álgebra, Universidad de Granada, E-18071 Granada, Espa?a; D. Llena, Departamento de Geometría, Topología y Química Orgánica, Universidad de Almería, 04120 Almería, Espa?a; J. C. Rosales, Departamento de álgebra, Universidad de Granada, E-18071 Granada, Espa?a     

Rational forms of nilpotent Lie algebras and Anosov diffeomorphisms

We compute the set of all rational forms up to isomorphism for some real nilpotent Lie algebras of dimension 8. This is part of the classification of nilmanifolds admitting an Anosov diffeomorphism in dimension at most 8. Author’s address: FaMAF and CIEM, Universidad Nacional de Córdoba, Córdoba, Argentina     

Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion

This paper concerns with the existence, uniqueness and asymptotic behaviour of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is presented. Partially supported by CMM, Universidad de Chile, and CI²MA, Universidad de Concepción.     

Metrizability of spaces of holomorphic functions with the Nachbin topology

In this paper we prove, among other things, that the space of all holomorphic functions on an open subset U of a complex metrizable space E, endowed with the Nachbin ported topology, is metrizable only if E has finite dimension. This answers a question by Mujica in [J. Mujica, Gérmenes holomorfos y funciones holomorfas en espacios de Fréchet, Publicaciones del Departamento de Teoría de Funciones, Universidad de Santiago, Spain, 1978].     

Solutions for a class of neutral differential equations with nonatomicD-operator

This paper is concerned with the existence and uniqueness of solutions to first-order linear differential equations of neutral type with a nonatomicD-operator. We use an algebraic approach, in the context of the theory of convolution operators. Necessary and sufficient conditions are given for the initial value problem to have unique solutions for a class of equations.This work was done while the author was at the Department of Mathematics, Virginia Polytechnic Institute and State University.Instituto de Desarrollo Tecnológico para la Industria Quimica (INTEC), dependent on Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and the Universidad Nacional del Litoral (UNL).     

Linear waves at the free surface of a saturated porous media

The principal aim of this paper is to study the propagation of linear waves at the free surface of a saturated porous media. This problem is formulated as an eigenvalue problem with complex eigenvalues, and the solution is given in term of an orthogonal eigenfunction expansion, whose completeness has been taken for granted in the literature regarding the problem as a classical Sturm-Liouville problem, which is not the case due to the complex nature of the eigenvalues. The main purpose of the present work is to prove the completeness of the eigenfunctions for all possible physical values of the parameters involved, even for some values of the parameters, where previous numerical works have found abnormal behavior of the eigenvalues. In those cases if we mistakenly consider the problem as a Sturm-Liouville one, as has been done before, the eigenfunction expansion will not hold, but indeed we will prove that it does.On leave from Institute de Mecánica de los Fluidos, Universidad Central de Venezuela, Caracas, Venezuela.     

Characterizing the inf-sup condition on product spaces

In this paper we establish characterization results for the continuous and discrete inf-sup conditions on product spaces. The inf-sup condition for each component of the bilinear form involved and suitable decompositions of the pivot space in terms of the associated null spaces are the key ingredients of our theorems. We illustrate the theory through its application to bilinear forms arising from the variational formulations of several boundary value problems. Dedicated to Professor Ivo Babuska on the occasion of his 82nd birthday. This research was partially supported by Centro de Modelamiento Matemático (CMM) of the Universidad de Chile, by Centro de Investigación en Ingenierí a Matemática (CI²MA) of the Universidad de Concepción, by FEDER/MCYT Project MTM2007-63204, and by Gobierno de Aragón (Grupo Consolidado PDIE).     

Prevalence of hyperbolicity for complex singular cycles

In this article we consider two kinds of complex singular cycles arising for vector fields defined on three-dimensional manifolds. We prove that, under some generic conditions, any one parameter family of vector fields passing through these cycles has the following property: Hyperbolicity is a prevalent phenomena.Dedicated to the memory of Professor R. Mañé.Partially Supported by Fondecyt 1941080 and Dirección de Investigación Universidad de Santiago de Chile     

A real delivery problem dealt with Monte Carlo Techniques

In this paper we use Monte Carlo Techniques to deal with a real world delivery problem of a food company in Valencia (Spain). The problem is modeled as a set of 11 instances of the well known Vehicle Routing Problem, VRP, with additional time constraints. Given that VRP is a NP-hard problem, a heuristic algorithm, based on Monte Carlo techniques, is implemented. The solution proposed by this heuristic algorithm reaches distance and money savings of about 20% and 5% respectively. This work has been partially supported by thePlan de Incentivo a la Investigación/98 of the Universidad Politécnica de Valencia, under the project “Técnicas Monte Carlo aplicadas a Problemas de Rutas de Vehículos”.     

On measures of weak noncompactness

Summary In this paper an axiomatic approach to the notion of a measure of weak noncompactness is presented. Several properties of the defined measures are given. Moreover, we provide a few concrete realizations of the accepeted axiomatic system in some Banach spaces.This paper was done while the first author visited the Universidad de los Andes (Venezuela).     

Sensitivity analysis in A class of dynamic optimization models

A general model of dynamic optimization, deterministic, in discrete time, and with infinite time horizon is considered. We assume that there are parameters in the formulation of the model. Conditions for stability of the optimal solution are studied. Analysis of steady state comparative statics and comparative dynamics are presented. In addition we apply these results to a quadratic case and to an economic example: a one sector growth model. This research was financed by the Universidad Complutense de Madrid, project PR295/95-6073     

New spaces of functions and hyperfunctions for Hankel transforms and convolutions

In this paper we study the Hankel transformation and convolution on certain spaces of entire functions and its dual that is a space of hyperfunctions and contains the (even)-Schwartz space S _e ′. We prove that the Hankel transform is an automorphism of . Also the Hankel convolutors of are investigated. Authors’ addresses: Jorge J. Betancor, Claudio Jerez and Lourdes Rodríguez-Mesa, Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271 La Laguna (Sta. Cruz de Tenerife), Espa?a; Sandra M. Molina, Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350 (7600), Mar del Plata, Argentina     

Asymptotic behavior of the eigenvalues of the one-dimensional weighted<Emphasis Type="Italic">p</Emphasis>-Laplace operator

In this paper we study the spectral counting function for the weightedp-laplacian in one dimension. First, we prove that all the eigenvalues can be obtained by a minimax characterization and then we show the existence of a Weyl-type leading term. Finally we find estimates for the remainder term. The first author is supported by Universidad de Buenos Aires grant TX48, by ANPCyT PICT No. 03-05009. The second author is supported by CONICET and Universidad de San Andres.     

A counterexample on non-archimedean regularity

A non-regular inductive sequence of non-archimedean reflexive Fréchet spaces is constructed. On the other hand, it is proved that every inductive sequence of reflexive Banach spaces over a spherically complete field is regular. Also, some applications are given. Research partially supported by Ministerio de Educación y Ciencia, MTM2006-14786. Authors’ addresses: N. De Grande-De Kimpe, Groene Laan 36 (302) B 2830, Willebroek, Belgium; C. Perez-Garcia, Department of Mathematics, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros s/n, 39071 Santander, Spain