A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Review. Precision viticulture. Research topics, challenges and opportunities in site-specific vineyard management

Precision Viticulture (PV) is a concept that is beginning to have an impact on the wine-growing sector. Its practical implementation is dependant on various technological developments: crop sensors and yield monitors, local and remote sensors, Global Positioning Systems (GPS), VRA (Variable-Rate Application) equipment and machinery, Geographic Information Systems (GIS) and systems for data analysis and interpretation. This paper reviews a number of research lines related to PV. These areas of research have focused on four very specific fields: 1) quantification and evaluation of within-field variability, 2) delineation of zones of differential treatment at parcel level, based on the analysis and interpretation of this variability, 3) development of Variable-Rate Technologies (VRT) and, finally, 4) evaluation of the opportunities for site-specific vineyard management. Research in these fields should allow winegrowers and enologists to know and understand why yield variability exists within the same parcel, what the causes of this variability are, how the yield and its quality are interrelated and, if spatial variability exists, whether site-specific vineyard management is justifiable on a technical and economic basis.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

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.

Geological and Geomorphological Cartography at Scale 1: 10.000: a Tool of Management for Towns

Geological and geomorphological mapping at scale 1:10.000 besides from being an important source of scientific information it is also a necessary tool for municipal organs in order to make proper decisions when dealing with geo-environmental problems concerning integral territorial development. In this work, detailed information is given on the contents of such maps, their social and economical application, and a balance of the investment and gains that derives from them

Accuracy in the experimental calorimetric study of the crystallization kinetics and predicitve transformation diagrams: Application to a Ga-Te amorphous alloy

The uncertainties inherent to experimental differential scanning calorimetric data are evaluated. A new procedure is developed to perform the kinetic analysis of continuous heating calorimetric data when the heat capacity of the sample changes during the crystallization. The accuracy of isothermal calorimetric data is analyzed in terms of the peak-to-peak noise of the calorimetric signal and base line drift typical of differential scanning calorimetry equipment. Their influence in the evaluation of the kinetic parameters is discussed. An empirical construction of the time-temperature and temperature heating rate transformation diagrams, grounded on the kinetic parameters, is presented. The method is applied to the kinetic study of the primary crystallization of Te in an amorphous alloy of nominal composition Ga20Te80, obtained by rapid solidification.

Tap&Go: Gamificant l'esport en dispositius Android amb NFC

El contingut d'aquest projecte, consisteix en desenvolupar una solució per a dispositius mòbils Android amb NFC, amb la finalitat de motivar i incrementar el nombre de ciutadans que practiquen esport a la ciutat de Barcelona. El projecte inclou disseny de la interfície mòbil, la creació d'una base de dades, un servei d'API Rest per accedir a les dades des dels dispositius, l'ús del servei de mapes de Google i diferents llibreries i eines per a dissenyar l'arquitectura del sistema. Es tindran en compte les restriccions en disseny i funcionalitat per part del client (ajuntament).

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

Tarracomap: Development of an archaeological application on Google Maps navigation System

This paper describes the result of a research about diverse areas of the information technology world applied to cartography. Its final result is a complete and custom geographic information web system, designed and implemented to manage archaeological information of the city of Tarragona. The goal of the platform is to show on a web-focused application geographical and alphanumerical data and to provide concrete queries to explorate this. Various tools, between others, have been used: the PostgreSQL database management system in conjunction with its geographical extension PostGIS, the geographic server GeoServer, the GeoWebCache tile caching, the maps viewer and maps and satellite imagery from Google Maps, locations imagery from Google Street View, and other open source libraries. The technology has been chosen from an investigation of the requirements of the project, and has taken great part of its development. Except from the Google Maps tools which are not open source but are free, all design has been implemented with open source and free tools.

"Pro crosis argenti". La plata al comtat de les Muntanyes de Prades: explotació, gestió i rendiment de les mines de Falset durant la baixa edat mitjana

L’objectiu de la recerca que s’ha dut a terme durant el període 2004-2007 ha estat analitzar les característiques territorials, senyorials i jurisdiccionals del domini format pel comtat de les Muntanyes de Prades i la baronia d’Entença i, a partir d’aquí, aprofundir en un aspecte concret d’aquesta senyoria: l’explotació minera de l’argent durant els segles XIV i XV. En aquest sentit, la recerca s’ha fonamentat en l’estudi de la documentació relacionada amb aquesta qüestió que hi ha dipositada a l’Arxiu Ducal de Medinaceli; la qual, però, s’ha pogut buidar i analitzar a través de la consulta de les còpies microfilmades que se’n conserven al Monestir de Poblet. Com a resultats principals s’ha aconseguit delimitar territorialment el comtat de les Muntanyes de Prades i baronia d’Entença i determinar-ne la titularitat jurisdiccional a mitjan segle XIV. A més, s’han establert els paràmetres que marquen i expliquen l’evolució de la normativa que regulava l’explotació minera de l’argent. I, finalment, s’ha pogut determinar que, segurament, la major part de l’argent produït a mitjan segle XIV es va obtenir a partir de minerals d’argent i argent natiu.

Mapa web interactiu de Barcelona

L’objectiu principal d’aquest projecte és crear un sistema que permeti generar i gestionar un mapa de navegació interactiu per a la web i per qualsevol àmbit. Per aconseguir-ho, el projecte està dividit en dos parts: el mapa de navegació i el gestor de continguts. La primera part és una interfície gràfica on hi hauran diferents menús amb les seves categories, cadascuna amb els seus filtres, i per últim, un menú per seleccionar diferents nivells de zoom. El gestor de continguts, la segona part del projecte, és l’eina que permet gestionar via web tots els aspectes relacionats amb la configuració del mapa i la gestió de continguts (menús, punts del mapa, punts d’interès i rutes).

Canvi tecnològic i desenvolupament econòmic durant la segona revolució industrial: la transferència tecnològica del sector tèxtil entre Anglaterra i Catalunya

Projecte de recerca elaborat a partir d’una estada a la University of Sussex, Gran Bretanya, entre març i juliol del 2008. L’estada ha estat centrada en obtenir fonts documentals primàries, per avançar en el projecte d’investigació sobre la transferència de tecnologia entre Catalunya i Anglaterra durant la Segona Revolució Industrial. Això ha estat possible gràcies a la consulta de les patents britàniques (Business & Intellectual Property Centre at the British Library). Així mateix, l’obtenció dels recursos documentals especialitzats de diverses biblioteques de referència situades al campus de la University of Sussex (Keith Pavitt Libray (SPRU), Library of Sussex, British Library of Development Studies) i a Ruddignton Framework Knitters’ Library a Nottingham han estat fonamentals, tal i com es pot veure en la relació detallada que es presenta.

The Hercynian ore deposits from the Catalonian Coastal Ranges

Many mineralizations, showings and geochemical anomalies have been found in the Hercynian of the Catalonian Coastal Ranges during the last ten years. Many of them are enclosed in the Paleozoic sediments and volcanics and display pre-metamorphic syngenetic characteristics. The lower carboniferous manganese and base meta1 deposits appear to be formed from hydrothermal fluids springing up in the sea floor through active fractures controlling the filling of the basins in a extensional geotectonic setting. Although less evidence and more controversy is available, similar ore forming processes could have taken place in older Paleozoic times. The deformation and metamorphism have not played an important remobilization role, and most epigenetic deposits of Hercynian age are related to the hydrothermal cells induced by the post-metamorphic granitic intrusives.

A virtual mathematics learning environment for engineering students

Teachers of the course Introduction to Mathematics for Engineers at the UOC, an online distance-learning university, have designed,developed and tested an online studymaterial. It includes basic pre-university mathematics, indications for correct follow-up of this content and recommendations for finding appropriate support and complementarymaterials. Many different resources are used,depending on the characteristics of thecontents: Flash sequences, interactive applets, WIRIS calculators and PDF files.During the last semester, the new study material has been tested with 119 students. The academic results and student satisfaction have allowed us to outline and prioritise future lines of action.

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.