Solving the Gleason problem on linearly convex domains

Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions . Received: 2 July 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

Quotient normed cones

Given a normed cone (X, p) and a subconeY, we construct and study the quotient normed cone (X/Y,p) generated byY. In particular we characterize the bicompleteness of (X/Y, ‖·‖ ^p ,p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)^*, || · ‖·‖^p,p) can be identified as a distinguished subcone of the dual cone (X ^*, || · ||_{p, u}). Furthermore, some parts of the theory are presented in the general setting of the spaceCL(X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.     

Boundary-variation solution of eigenvalue problems for elliptic operators

We present an algorithm which, based on certain properties of analytic dependence, constructs boundary perturbation expansions of arbitrary order for eigenfunctions of elliptic PDEs. The resulting Taylor series can be evaluated far outside their radii of convergence—by means of appropriate methods of analytic continuation in the domain of complex perturbation parameters. A difficulty associated with calculation of the Taylor coefficients becomes apparent as one considers the issues raised by multiplicity: domain perturbations may remove existing multiple eigenvalues and criteria must therefore be provided to obtain Taylor series expansions for all branches stemming from a given multiple point. The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work. While our proofs, constructions and numerical examples are given for eigenvalue problems for the Laplacian operator in the plane, other elliptic operators can be treated similarly.     

A new diversity induction mechanism for a multi-objective ant colony algorithm to solve a real-world time and space assembly line balancing problem

Time and space assembly line balancing considers realistic multi-objective versions of the classical assembly line balancing industrial problems. It involves the joint optimisation of conflicting criteria such as the cycle time, the number of stations, and/or the area of these stations. The different problems included in this area also inherit the precedence constraints and the cycle time limitations from assembly line balancing problems. The presence of these hard constraints and their multi-criteria nature make these problems very hard to solve. Multi-objective constructive metaheuristics (in particular, multi-objective ant colony optimisation) have demonstrated to be suitable approaches to solve time and space assembly line balancing problems. The aim of this contribution is to present a new mechanism to induce diversity in an existing multi-objective ant colony optimisation algorithm for the 1/3 variant of the time and space assembly line balancing problem. This variant is quite realistic in the automative industry as it involves the joint minimisation of the number and the area of the stations given a fixed cycle time limit. The performance of our proposal is validated considering ten real-like problem instances. Moreover, the diversity induction mechanism is also tested on a real-world instance from the Nissan plant in Barcelona (Spain).     

On the Bergman Theory for Solenoidal and Irrotational Vector Fields. II. Conformal Covariance and Invariance of the Main Objects

This is a continuation of our work (González-Cervantes et al. in On the Bergman theory for solenoidal and irrotational vector fields. I. General theory. Operator theory: advances and applications. Birkhauser, accepted) where for solenoidal and irrotational vector fields theory as well as for the Moisil–Théodoresco quaternionic analysis we introduced the notions of the Bergman space and the Bergman reproducing kernel and studied their main properties. In particular, we described the behavior of the Bergman theory for a given domain whenever the domain is transformed by a conformal map. The formulas obtained hint that the corresponding objects (spaces, operators, etc.) can be characterized as conformally covariant or invariant, and in the present paper we construct a series of categories and functors which allow us to give such characterizations in precise terms.     

Relaxed loading conditions for higher order homogenisation approaches

The present paper deals with the formulation of minimal loading conditions for the application of numerical homogenisation techniques, namely the FE² methodology. Based on the set of volume averaging rules connecting the heterogeneous micro and the homogeneous macro scale, the minimal constraints on the deformation of a micro volume are derived for a classical Cauchy continuum as well as for a micromorphic continuum theory. For both cases, numerical studies are included highlighting the main aspects of the proposed procedure within the context of small deformations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An accelerated minimal gradient method with momentum for strictly convex quadratic optimization

BIT Numerical Mathematics - In this article we address the problem of minimizing a strictly convex quadratic function using a novel iterative method. The new algorithm is based on the well-known...     

Application of average dynamic programming to inventory systems

We show the existence ofaverage cost (AC-) optimal policy for an inventory system withuncountable state space; in fact, the AC-optimal cost and an AC-optimal stationary policy areexplicitly computed. In order to do this, we use a variant of thevanishing discount factor approach, which have been intensively studied in recent years but the available results not cover the inventory problem we are interested in.The work of the first author (OVA) was partially supported by Fondo del Sistema de Investigación del Mar de Cortéz under grant SIMAC/94/CT-005. The work of the second author (RMdO) was partially supported by Consejo Nacional de Ciencia y Tecnologia (CONACyT) under grant 0635P-E9506.