A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Extracción de parámetros de un resonador FBAR por optimización

L’objectiu d’aquest projecte que consisteix a elaborar un algoritme d’optimització que permeti, mitjançant un ajust de dades per mínims quadrats, la extracció dels paràmetres del circuit equivalent que composen el model teòric d’un ressonador FBAR, a partir de les mesures dels paràmetres S. Per a dur a terme aquest treball, es desenvolupa en primer lloc tota la teoria necessària de ressonadors FBAR. Començant pel funcionament i l’estructura, i mostrant especial interès en el modelat d’aquests ressonadors mitjançant els models de Mason, Butterworth Van-Dyke i BVD Modificat. En segon terme, s’estudia la teoria sobre optimització i programació No-Lineal. Un cop s’ha exposat la teoria, es procedeix a la descripció de l’algoritme implementat. Aquest algoritme utilitza una estratègia de múltiples passos que agilitzen l'extracció dels paràmetres del ressonador.

A public-key cryptosystem based on second order linear sequences

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

A theoretical and practical study on linear reforms of dual taxes

We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.

Codis Z2Z4-additius en Magma

En aquest projecte es presenta el desenvolupament d'un paquet d'aplicacions en l'entorn de programació matemàtica Magma, per al tractament dels codis anomenats Z2Z4-additius. Els codis Z2Z4-additius permeten representar alguns codis binaris, com a codis lineals en l'espai dels codis Z2Z4-additius. Aquest fet permetrà l'estudi de tota una sèrie de codis binaris no lineals que fins ara eren intractables.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

Quasiconformal maps, analytic capacity, and non linear potentials

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Health care utilization among immigrants and native-born populations in 11 European countries. Results from the Survey of Health, Ageing and Retirement in Europe

Objective: This study examines health care utilization of immigrants relative to the native-born populations aged 50 years and older in eleven European countries. Methods. We analyzed data from the Survey of Health Aging and Retirement in Europe (SHARE) from 2004 for a sample of 27,444 individuals in 11 European countries. Negative Binomial regression was conducted to examine the difference in number of doctor visits, visits to General Practitioners (GPs), and hospital stays between immigrants and the native-born individuals. Results: We find evidence those immigrants above age 50 use health services on average more than the native-born populations with the same characteristics. Our models show immigrants have between 6% and 27% more expected visits to the doctor, GP or hospital stays when compared to native-born populations in a number of European countries. Discussion: Elderly immigrant populations might be using health services more intensively due to cultural reasons.

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

La programació al servei de la matemàtica

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. La programació al servei de la matemàtica és un programa informàtic fet amb Excel i Visual Basic. Resol equacions de primer grau, equacions de segon grau, sistemes d'equacions lineals de dues equacions i dues incògnites, sistemes d'equacions lineals compatibles determinats de tres equacions i tres incògnites i troba zeros de funcions amb el teorema de Bolzano. En cadascun dels casos, representa les solucions gràficament. Per a això, en el treball s'ha hagut de treballar, en matemàtiques, amb equacions, nombres complexos, la regla de Cramer per a la resolució de sistemes, i buscar la manera de programar un mètode iteratiu pel teorema de Bolzano. En la part gràfica, s'ha resolt com fer taules de valors amb dues i tres variables i treballar amb rectes i plans. Per la part informàtica, s'ha emprat un llenguatge nou per l'alumne i, sobretot, ha calgut saber decidir on posar una determinada instrucció, ja que el fet de variar-ne la posició una sola lí­nea ho pot canviar tot. A més d'això, s'han resolt altres problemes de programació i també s'ha realitzat el disseny de pantalles.