Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Polynomial and linearized normal forms for almost periodic differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Patrimoni Digital de Catalunya, a year and a half experience

E-repositories are part of the e-science, and they are based on the e-infrastructure. The Centre de Supercomputació de Catalunya (CESCA) together with the Consorci de Biblioteques Universitàries de Catalunya (CBUC) started in 1999 a cooperative repository, named TDR, to file, in digital format, the full-text of the read thesis at the universities of our country in order to spread them worldwide in open access, while at the same time, preserving the intellectual copyright of the authors. Since then, four additional cooperative repositories have been created: RECERCAT for research papers; RACO for scientific, cultural and erudite Catalan magazines; MDC for Catalan digital collections of pictures, maps, posters and old magazines; and PADICAT for archiving Catalan digital web content; The main objective of the latter is to archive Catalan web sites. That is, PADICAT collects, processes and provides permanent access to the entire cultural, scientific and general output of Catalonia in digital format. The repository manager is the Biblioteca de Catalunya, as the institution responsible for compiling, processing and distributing the bibliographic heritage of Catalonia, while CESCA is the technology partner. On September 11th, 2006 the repository went into operation for the general public, with some thirty websites archived. After one year and a half, it has 2.720 captures of more than 1.000 websites. This includes 34 million files (HTML, images...) and two terabytes of data. The objective of this paper is to present PADICAT and our experience developing and managing it.We describe the repository briefly, we explain the technology used to implement it and we comment our experiences during its first year and a half.

Plot Suite

Una Plot Suite és una aplicació web que permet localitzar plots d’una Base de Dades a partir de formularis. S’obtindran taules on apareixeran els plots amb les seves característiques i es podrà obtenir còpies dels plots sol·licitats. Gràcies al seu disseny es podran afegir nous plots a la Base de Dades i fins i tot modificar l’estructura d’una manera molt intuïtiva.

Diseño de filtros de onda acústica basados en estructuras "half lattice"

En los últimos tiempos la telefonía móvil ha experimentado una reducción de los terminales gracias a la miniaturización de los filtros a frecuencias de microondas. Los filtros pasa banda más utilizados son los basados en la tecnología SAW, sin embargo son incompatibles con tecnologías de silicio y su comportamiento se degrada a frecuencias superiores de 3 GHz, por ello los estudios actuales se centran en la tecnología BAW. Las dos arquitecturas convencionales de filtros basados en resonadores BAW unidos eléctricamente son el ladder y lattice. Sin embargo, en este proyecto se estudiará la topología half lattice, la cual presenta un mejor comportamiento y unas dimensiones más reducidas. Para ello se obtendrán las ecuaciones de diseño del filtro, y con ellas se realizará la implementación a partir de la frecuencia central y el ancho de banda relativo.

New trends in world wine consumption and its impact on the Spanish wineries during the second half of the twentieth century

The main goal of this research is explain the impact of the new trends of wine consumption, and the way these enterprises adapted to the circumstances. The hypothesis is that the Spanish companies had to start a deep and traumatic restructuring process, with the aim of surviving adequately in the changeable wine national and international markets. Heavy technological investments were made, with serious finance problems, during the eighties and nineties. We will see this from two specific cases, the Cooperatives "San Isidro" and "Rosario", located in the Region of Murcia, in the Spanish southeast.

Non-characteristic half-lives in radioactive decay

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that explore a method for fitting power-laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation.

Interferència dels trastorns de personalitat en la capacitat parental. Comparació entre població normal i diagnosticada

En aquesta investigació, hem comparat tres mostres (amb diagnòstic de transtorn de la personalitat, amb trets disfuncionals de la personalitat i sans) per tal de valorar quina disposa d’un funcionament parental més acurat. Dels resultats obtinguts, malgrat el petit tamany de la mostra, podem afirmar que els progenitors sans obtenen millors resultats que els altres dos, i que els que disposen de trets disfuncionals tenen un funcionament més adequats que els que tenen un diagnòstic.

Estudi comparatiu de detecció de Virus del Papiloma Humà entre pell psoriàsica i pell normal.

Existeix un debat continu sobre la rellevància del Virus del papiloma humà (VPH) en l’etiopatogènia de la psoriasi. S’ha reportat un elevat percentatge de detecció de VPH en pacients psoriàsics, sobretot el VPH5 i 36, suggerint que podrien correspondre a l’antigen causal de la cascada inmunològica. El propòsit de l’estudi és utilitzar un mètode ampli per a la detecció d’ADN tant de beta com gamma-papilomavirus en 30 biòpsies de pell psoriàsica i 30 biòpsies de pell sana. Avaluarem si els VPH són detectats de forma més freqüent en pell psoriàsica en comparació amb pell sana, i quins són els VPH específics més sobreexpresats.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p.There are many statistical tests being used to check whether empirical marker data obeys theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE)are numerical in nature, requiring the computation of a test statistic and a p-value.There is however, ample space for the use of graphics in HWE tests, in particular for the ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent yearsbut at the moment few applications concern the description of natural phenomena withthis type of probability models, as well as the interpretation of their parameters. Theskew–normal distributions family represents an extension of the normal family to whicha parameter (λ) has been added to regulate the skewness. The development of this theoreticalfield has followed the general tendency in Statistics towards more flexible methodsto represent features of the data, as adequately as possible, and to reduce unrealisticassumptions as the normality that underlies most methods of univariate and multivariateanalysis. In this paper an investigation on the shape of the frequency distribution of thelogratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells,has been performed. Samples have been collected around the active center of Vulcanoisland (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals ofabout six months. Data of the logratio have been tentatively modeled by evaluating theperformance of the skew–normal model for each well. Values of the λ parameter havebeen compared by considering temperature and spatial position of the sampling points.Preliminary results indicate that changes in λ values can be related to the nature ofenvironmental processes affecting the data

Probability distribution of the radionuclide half-lives

Power law distributions, a well-known model in the theory of real random variables, characterize a wide variety of natural and man made phenomena. The intensity of earthquakes, the word frequencies, the solar ares and the sizes of power outages are distributed according to a power law distribution. Recently, given the usage of power laws in the scientific community, several articles have been published criticizing the statistical methods used to estimate the power law behaviour and establishing new techniques to their estimation with proven reliability. The main object of the present study is to go in deep understanding of this kind of distribution and its analysis, and introduce the half-lives of the radioactive isotopes as a new candidate in the nature following a power law distribution, as well as a \canonical laboratory" to test statistical methods appropriate for long-tailed distributions.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.