Enrique Alfonso Sánchez Pérez

Asymmetric distances to improve n-dimensional Pareto fronts graphical analysis

Visualization tools and techniques to analyze n-dimensional Pareto fronts are valuable for designers and decision makers in order to analyze straightness and drawbacks among design alternatives. Their usefulness is twofold: on the one hand, they provide a practical framework to the decision maker in order to select the preferable solution to be implemented; on the other hand, they may improve the decision makers design insight,i.e. increasing the designers knowledge on the multi-objective problem at hand. In this work, an order based asymmetric topology for finite dimensional spaces is introduced. This asymmetric topology, associated to what we called asymmetric distance, provides a theoretical and interpretable framework to analyze design alternatives for n-dimensional Pareto fronts. The use of this asymmetric distance will allow a new way to gather dominance and relative distance together. This property can be exploited inside interactive visualization tools. Additionally, a composed norm based on asymmetric distance has been developed. The composed norm allows a fast visualization of designer preferences hypercubes when Level Diagram visualization is used for multidimensional Pareto front analysis. All these proposals are evaluated and validated through different engineering benchmarks; the presented results show the usefulness of this asymmetric topology to improve visualization interpretability.

A phenomenological model for sonic crystals based on artificial neural networks

A phenomenological model that simulates the acoustic attenuation behavior of sonic crystals is developed in this paper. The input of the model is a set of parameters that characterizes each experimental setup, and the output is a simulation of the associated attenuation spectrum. The model consists of a combination of a multiresolution analysis based on wavelet functions and a set of artificial neural networks. An optimized coupling of these tools allows us to drastically reduce the experimental data needed, and to obtain a fast computational model that can be used for technological purposes.

THE DAUGAVET EQUATION FOR BOUNDED VECTOR-VALUED FUNCTIONS

Requirements under which the Daugavet equation and the alternative Daugavet equation hold for pairs of nonlinear maps between Banach spaces are analysed. A geometric description is given in terms of nonlinear slices. Some local versions of these properties are also introduced and studied, as well as tests for checking if the required conditions are satisfied in relevant cases.

Pietsch--Maurey--Rosenthal factorization of summing multilinear operators

The main purpose of this paper is the study of a new class of summing multilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A mixed Pietsch-Maurey-Rosenthal type factorization theorem for these operators is proved under weaker convexity requirements than the ones that are needed in the Maurey-Rosenthal factorization through products of L-spaces. A by-product of our factorization is an extension of multilinear operators defined by a q-concavity type property to a product of special Banach function lattices which inherit some lattice-geometric properties of the domain spaces, as order continuity and p-convexity. Factorization through Fremlin’s tensor products is also analyzed. Applications are presented to study a special class of linear operators between Banach function lattices that can be characterized by a strong version of q-concavity. This class contains q-dominated operators, and so the obtained results provide a new factorization theorem for operators from this class.

Approximation of integration maps of vector measures and limit representations of Banach function spaces

We study when the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon-Nikodým derivatives. We will show that this can sometimes be done, but there are also principal cases in which this cannot be done. The positive cases are obtained using the circle of ideas of the approximation property for Banach spaces. The negative ones are given by means of an adequate use of the Daugavet property. As an application, we analyse when the norm in a space of integrable functions

Maharam-type kernel representation for operators with a trigonometric domination

L^1(m)

THE SUPPORT LOCALIZATION PROPERTY OF THE STRONGLY EMBEDDED SUBSPACES OF BANACH FUNCTION SPACES

can be computed as a limit of the norms of the spaces of integrable functions with respect to the Radon-Nikodým derivatives of

Product spaces generated by bilinear maps and duality

m

A Non-linear Approach to Signal Processing by Means of Vector Measure Orthogonal Functions

.

Optimal domain and integral extension of operators : acting in function spaces

Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in