845 research outputs found

    Teoremes de representació per a àlgebres de Boole finites i retícles distributius finits

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    Un dels problemes centrals de les matemàtiques és el de la classificació. Per a cada tipus d objecte, tenim la corresponent noció d isomorfisme i ens interessa saber sota quines circumstàncies dos objectes d aquest tipus són isomorfs. A vegades, podem trobar a cada classe d isomorfia un invariant canònic, que pertany a una família ben coneguda, i que ens serveix per establir quan dos objectes són isomorfs: ho són si, i només si, els invariants canònics de les seves classes són el mateix. A partir d'aquí, en algunes ocasions també podem trobar un representant canònic isomorf a aquests objectes amb el qual estem familiaritzats. Els teoremes de representació són els que ens permetran reduir-nos al cas conegut en cas de que els invariants canònics esmentats anteriorment siguin el mateix que el del representant canònic. En aquest treball, ens centrem al cas particular del teorema de representació de Stone i el teorema de representació de Birkhoff, els quals estudien els representants canònics de les àlgebres de Boole i els reticles distributius respectivament

    Periodic time dependent Hamiltonian systems and applications

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    [eng] A dynamical system is one that evolves with time. This definition is so diffuse that seems to be completely useless, however, gives a good insight of the vast range of applicability of this field of Mathematics has. It is hard to track back in the history of science to find the origins of this discipline. The works by Fibonacci, in the twelfth century, concerning the population growth rate of rabbits can be already considered to belong to the above mentioned field. Newton's legacy changed the prism through the humankind watched the universe and established the starting shot of several areas of knowledge including the study of difierential equations. Newton's second law relates the acceleration, the second derivative of the position of a body with the net force acting upon it. The formulation of the law of universal gravitation settled the many body problem, the fundamental question around the field of celestial mechanics has grown. Newton itself solved the two body problem, providing an analytical proof of Kepler's laws. In the subsequent years a number of authors, among of them Euler and Lagrange, exhausted Newton's powerful ideas but none of them was able to find a closed solution of the many body problem. By the end of the nineteenth century, Poincaré changed again the point of view: The French mathematician realized that the many body problem could not be solved in the sense his predecessors expected, however, many other fundamental questions could be addressed by studying the solutions of not quantitatively but by means of their geometrical and topological properties. The ideas that bloomed in Poincaré's mind are nowadays a source of inspiration for modern scientist facing problems located along all the spectrum of human knowledge. Poincaré understood that invariant structures organize the long term behaviour of the solutions of the system. Invariant objects are, therefore, the skeleton of the dynamics. These invariant structures and their linear normal behaviour are to be analyzed carefully and this shall lead to a good insight on global aspects of the phase space. For nonintegrable systems the task of studying invariant objects and their stability is, in general, a problem which is hard to be handled rigorously. Usually, the hypotheses needed to prove specific statements on the solutions of the systems reduce the applicability of the results. This is especially relevant in physical problems: Indeed, we cannot, for instance, choose the mass of Sun to be suficiently small. The advent of the computers changed the way to undertake studies of dynamical systems. The task of writing programs for solving, numerically, problems related to specific examples is, at the present time, as important as theoretical studies. This has two main consequences: On the first hand, more involved models can be chosen to study real problems and this allow us to understand better the relation between abstract concepts and physical phenomena. Secondly, even when facing fundamental questions on dynamics, the numerical studies give us data from which build our theoretical developments. Nowadays, a large number of commercial (or public) software packages helps scientist to study simple problems avoiding the tedious work to master numerical algorithms and programming languages. These programs are coded to work in the largest possible number of different situations, therefore, they do not have the eficiency that programs written specifically for a certain purpose have. Some of the computations presented in this dissertation cannot be performed by using commercial software or, at least, not in a reasonable amount of time. For this reason, a large part of the work presented here has to do with coding and debugging programs to perform numerical computations. These programs are written to be highly eficient and adapted to each problem. At the same time, the design is done so that specific blocks of the code can be used for other computations, that is, there exist a commitment between eficiency and reusability which is hard to achieve without having full control on the code. Under these guiding principles we undertake the study of applied dynamical systems according to the following stages: From a particular problem we get a simple model, then perform a number of numerical experiments that permits us to understand the invariant objects of the system, with that information, we can isolate the relevant phenomena and identify the key elements playing a role on it. Next, we try to find an even simpler model in which we can develop theoretical arguments and produce theorems that, with more effort, can be generalized or related to other problems which, in principle, seem to be difierent to the original one. Paraphrasing Carles Simó, from a physical problem we can take the lift to the abstract world, use theoretical arguments, come out with conclusions and, finally, lift down to the real world and apply these conclusions to specific problems (maybe not only the original one). This methodology has been developed in the last decades over the world when it turned out to outstand among the most powerful approaches to cope with problems in applied mathematics. The group of Dynamical Systems from Barcelona has been one of the bulwarks of this development from the late seventies to the present days. Following the guidelines presented in the previous section, we concern with several problems, mostly from the field of celestial mechanics but we also deal with a phenomenon coming from high energy physics. All these situations can be modeled by means of periodically time dependent Hamiltonian systems. To cope with those investigations, we develop software which can be used to perform computations in any periodically perturbed Hamiltonian system. We split the contents of this dissertation in two parts. The first one is devoted to general tolos to handle periodically time dependent Hamiltonians, even though we fill this first part with a number of illustrating examples, the goal is to keep the exposition in the abstract setting. Most of the contents of Part I deal with the development of software used to be applied in the second part. Some of the software has not been applied to the specific contents of Part II, this is left for future work. We also devote a whole chapter to some theoretical issues that, while are motivated by physical problems, they fall out of the category of periodic time dependent Hamiltonians. This splitting of contents has the intention of reecting, somehow, the basic methodological principles presented in the previous paragraph, keeping separated the abstract and the physical world but keeping in mind the lift

    Ecological restoration of cold-water corals on the Mediterranean continental shelf

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    [eng] Cold-water coral (CWC) habitats dwell on continental shelves, slopes, canyons, seamounts, and ridge systems around the world’s oceans, from 50 m to depths up to 4000 m. CWC species provide heterogeneous habitats supporting a myriad of associated fauna and form highly diverse CWC reefs and CWC gardens. Main threats, currently impacting CWC ecosystems come from anthropogenic stressors, such as fishing activities, oil and gas exploitation and the incipient mining activity. Likewise, climate change, causing changes in the water column, is also affecting these ecosystems. Life-history traits of CWC species (long lifespans, slow growth and limited recruitment) make them very vulnerable to current and potential threats. Given their limited recovery capacity, interest to preserve and restore CWC ecosystem is steadily growing. The creation of Marine Protected Areas and active ecological restoration actions are nowadays the best management tools to conserve native ecosystems and represents an opportunity to revert the anthropogenic damage that has already taken place. Through passive (natural regeneration after the cessation of stressors) and active (human interacts with biotic and/or abiotic ecosystem features) approaches, restoration activities seek to accelerate the recovery of ecosystem structure and functioning relative to a reference model. Contrarily to terrestrial and shallow-water marine ecosystems, ecological restoration in intermediate (50 – 200 m) and deep marine (> 200 m) environments has received lesser attention. To date, only few restoration actions at local scales have been carried out at those depths, mainly due to technical and economic limitations which questions its wide application. Scaling-up restoration actions and make them affordable are the main present challenges for CWC restoration. In this sense, in order to move forward towards the conservation of intermediate and deep-sea ecosystems, the general aim of the present thesis is to assess the impact of fishing activity on CWC gardens as well as to explore the feasibility of novel active ecological restoration techniques. All the work performed during this thesis has been carried out at the Cap de Creus marine area (North-Western Mediterranean Sea), specifically at the continental shelf (60 – 130 m), where gorgonians, sponges, and sea pen species form CWC gardens supporting a variety of mobile associated fauna. The target species is the yellow gorgonian Eunicella cavolini (Koch, 1887) which dominate in the area forming density patches. In the first chapter, the impact of artisanal fishing was quantified to evaluate the threat of this activity on CWC gardens and to provide essential information to mitigate such impact. The rest of chapters (2, 3 and 4) evaluated, for the first time, the viability to actively restore degraded E. cavolini populations. Specifically, in the second chapter, gorgonians obtained from bycatch (accidentally caught of non-target species) of local artisanal fishers, were transplanted to artificial structures deployed on the continental shelf (805 m). This pilot study demonstrated, for the first time, the high survival of E. cavolini transplants. Following, and going one step forward, in the third chapter, field experiments and modeling approaches were combined to develop and technically validate an innovative large-scale and cost- effective restoration method for CWC gardens. Successful results evidenced the feasibility of recovering bycatch E. cavolini and returning them to their natural habitat with this novel method so-called “badminton method”. Finally, in the fourth and last chapter, a large- scale restoration action of E. cavolini populations was carried out in collaboration with local artisanal fishers during two consecutive fishing seasons by applying the technique previously developed. A large number of gorgonians (460 colonies) were successfully reintroduced and survived at the end of the action (2 years) at 80-100 m depth. The results suggested an initial establishment of a new gorgonian population, which will potentially evolve toward a comparable natural population in terms of size and spatial structure, if natural recruitment also occurs. Moreover, an economic evaluation was performed, also confirming the cost efficiency of this method aimed at enhancing the recovery of impacted CWC gardens. The lack of knowledge of some key ecological processes of CWC ecosystems as well as the technical limitations hinder a complete evaluation of restoration efforts performed. However, this thesis represents a promising improvement for the conservation and recovery of CWCs that could be extended to other areas and regions.[cat] Els coralls d’aigua freda habiten en les plataformes continentals, talussos, canyons, muntanyes submarines i dorsals oceàniques d’arreu del món, des de 50 a 4000 metres de profunditat. Les espècies de coralls d’aigua freda creen hàbitats heterogenis que donen suport a una infinitat de fauna associada i formen esculls i boscos de coralls altament diversos. Les principals amenaces que actualment impacten aquests ecosistemes de coralls d’aigua freda son d’origen antròpic, com ara l’activitat pesquera, l’explotació de petroli i gas i l’incipient explotació minera. Així mateix, el canvi climàtic, el qual provoca canvis en la columna d’aigua, també està afectant aquests ecosistemes. Les característiques vitals dels coralls d’aigua freda (longevitat, creixement lent i reclutament limitat) els fan molt vulnerables a les amaces tan actuals com futures. Atesa la seva limitada capacitat de recuperació, l’interès per preservar i restaurar els ecosistemes de coralls d’aigua freda està en constant creixement. La creació d’àrees marines protegides i les accions restauració ecològica activa són avui en dia les millors eines de gestió per conservar ecosistemes autòctons i representen una oportunitat per revertir els danys antròpics que ja han tingut lloc. A través d’enfocaments passius (regeneració natural després del cessament del impacte) i actius (l’ésser humà interacciona amb les característiques biòtiques i/o abiòtiques de l’ecosistema), les activitats de restauració busquen accelerar la recuperació de l’estructura i funcionament dels ecosistemes en funció a un model de referència. Contràriament als ecosistemes terrestres i d’aigües someres, la restauració ecològica enfocada a ambients marins intermedis (50–200 m) i profunds (> 200 m) ha rebut menor atenció. Fins ara, a aquestes profunditats només s’han dut a terme algunes poques accions de restauració a escala local, principalment a causa de limitacions tècniques i econòmiques que qüestionen la seva àmplia aplicació. Els principals reptes actuals per la restauració de coralls d’aigua freda són incrementar l’escala espacial de les accions de restauració i fer-les econòmicament més assequibles. En aquest sentit, per avançar en la conservació dels ecosistemes de fons intermedis i profunds, l’objectiu general de la present tesi és avaluar l’impacte de l’activitat pesquera sobre els boscos de coralls d’aigua freda i explorar la viabilitat de innovadores tècniques de restauració activa. Tot el treball realitzat en aquesta tesi s’ha dut a terme a la zona marina del Cap de Creus (Nord-Oest del mar Mediterrani), contretament a la plataforma continental (60 – 130 m) on espècies de gorgònies, esponges i plomalls formen boscos de coralls d’aigua freda donant suport a una gran varietat de fauna mòbil associada. L’espècie objectiu és la gorgònia groga Eunicella cavolini (Koch, 1887) la qual domina a la zona formant denses agregacions. En el primer capítol, es va quantificar el impacte de la pesca artesanal per avaluar l’amenaça d’aquesta activitat sobre els boscos de coralls d’aigua freda i proporcionar informació essencial per mitigar aquest impacte. La resta de capítols (2, 3 i 4) van avaluar, per primera vegada, viabilitat de restaurar activament les poblacions degradades de E.cavolini. Especificament, en el segon capítol és van trasplantar les gorgònies capturades accidentalment pels pescadors artesanals de la zona, a estructures artificials fondejades a la plataforma continental (85 m). Aquest estudi pilot va demostrar per primera vegada l’alta supervivència dels transplantaments d’E.cavolini. Seguidament, i anant un pas més enllà, al tercer capítol es van combinar experiments de camp i modelització per desenvolupar i validar tècnicament una nova tècnica de restauració per als boscos de coralls d’aigua freda, a gran escala i econòmicament assequible. Els exitosos resultats van evidenciar la viabilitat de recuperar les colònies de E.cavolini capturades accidentalment i retornar-les al seu hàbitat natural amb aquesta innovadora tècnica , anomenada “el mètode bàdminton”. Finalment, al quart i últim capítol, es va dur a terme una acció de restauració de les poblacions de E.cavolini a gran escala, amb la col·laboració de pescadors artesanals de la zona i al llarg de dues temporades de pesca consecutives aplicant la tècnica desenvolupada anteriorment. Un gran nombre de gorgònies (460 colònies) van ser re-introduïdes amb èxit i van sobreviure al final de l’acció (2 anys) a 80-100 m de profunditat. Els resultats van suggerir l'establiment inicial d'una nova població gorgònies, que potencialment evolucionarà cap a una població natural comparable en termes d’estructura de talles i estructura espacial, sempre i quan es produeix també un reclutament natural. D'altra banda, es va fer una avaluació econòmica, que va confirmar la rendibilitat d'aquest mètode dirigit a millorar la recuperació dels boscos de coralls d’aigua freda impactats. El desconeixement d'alguns processos ecològics claus en els ecosistemes de coralls d’aigua freda, així com les limitacions tècniques, dificulten una avaluació completa dels esforços de restauració realitzats. Tanmateix, aquesta tesi suposa una millora prometedora per a la conservació i recuperació dels coralls d’aigua feda, que es podria estendre a altres zones i regions

    Ferran Via i Freixas. Un pianista internacionál

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    Ministrers i joglars a la Catalunya nova (segles XIV-XVII)

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    Un dels períodes més interessants per a conèixer la música en la societat catalana és el que comprèn els segles xiv i xvii. El nostre article se centra en aquest període per parlar de la presència social de la música, dels músics i de les institucions musicals que en aquesta època van actuar en l'àmbit de la Catalunya Nova centrant-nos, sobretot, en les àrees d'influència de Vilafranca del Penedès i de Tortosa, amb aportacions de Lleida i de les Illes Balears per obtenir-ne una visió de conjunt.One of the most interesting periods to get to know the role played by music in Catalan culture is the 16th and 17th century. Our article focuses on this period to talk about the social presence of music, musicians and musical institutions that, in this period, acted within a specific area called “Catalunya Nova” (to the south of Barcelona). We particularly focus our research on the spheres of influence of Vilafranca del Penedès and Tortosa, with some contributions from Lleida and the Balearic Islands in order to achieve an overall view

    Rellegint Llorens i Barba: de la consciència i l’art

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    La figura de Francesc Xavier Llorens i Barba (1820-1872) ha estat cabdal per a la històriade la filosofia a la Universitat de Barcelona i en la cultura catalana contemporània. Enaquest article analitzem quatre nous manuscrits que són de les lliçons de filosofia i d’històriade la filosofia que va impartir entre les dècades del 1860 i del 1870. Aquests manuscrits,conservats al Centre de Documentació VINSEUM, donen noves perspectives a laseva obra i permeten rellegir-lo amb interès des del present.The philospher Francesc Xavier Llorens i Barba (1820-1872) was one of the most importantthinkers in the history of philosophy both at the University of Barcelona and in contemporaryCatalan culture. In this article, we analyse four new manuscripts that are lessons(on philosophy, logic, and history of philosophy) that he dictated in the years between1860 and 1870. These manuscripts have been preserved by the VINSEUM DocumentationCentre (CDV - Vilafranca del Penedès), and provide new perspectives on his work and theopportunity to reread him with renewed interest

    Review

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    Obra ressenyada: Josep Mª TERRICABRAS (ed.), La Filosofia d'Eduard Nicol. Girona: Documenta Universitaria, 201

    Música simfònica i òpera a Vilafranca. Segle XVIII

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    En aquest article tractem la música des de diferents àmbits. Tot i mostrar la riquesa de la música simfònica i operística que es va produir i que s'interpretà al Penedès (i, per extensió, a Catalunya), també copsem la presència de la música en altres àmbits de la vida. Aquest fet permet un acostament singular al segle xviii i, més concretament, a la cultura musical d'aquest moment. I suposa revaluar la música en la Catalunya del segle xviii .In this paper we deal with music from different fields. Apart from evidencing the wealth of symphonic and operatic music that was produced and interpreted in El Penedès region and in Catalonia at large, it also highlights the presence of music in other aspects of life. This allows a singular approach to the 18th century and, more precisely, to the musical culture of that time, as well as a reassessment of the music and the musicians of 18th-century Catalonia and their position in the European context

    Lluís Farré i Magre (1907-1991). La filosofia com a llibertat

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    Lluís Farré i Magre (1907-199). La filosofia com a lliberta
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