La formula di Eulero per i poliedri fra storia e didattica

Questa tesi riguarda la formula di Eulero per i poliedri: F - S + V = 2 dove F indica il numero di facce, S il numero di spigoli e V quello dei vertici di un poliedro. Nel primo capitolo tratteremo i risultati ottenuti da Cartesio: egli fu il primo a considerare non solo le caratteristiche geometriche ma anche metriche di un solido. Partendo dall'analogia con le figure piane, riuscì a ricavare importanti relazioni nei solidi convessi, riguardanti il numero e la misura degli angoli piani, degli angoli solidi e delle facce. Non arrivò mai alla formulazione conosciuta oggi ma ne intuì le caratteristiche topologiche, che però non dimostrò mai. Nel secondo capitolo invece ci occuperemo di ciò che scoprì Eulero. Il manoscritto contenente i risultati di Cartesio era scomparso e quindi questi non erano più conosciuti dai matematici; Eulero, in accordo con quanto avviene per i poligoni, desiderava ottenere un metodo di classificazione per i poliedri e si mise a studiare le loro proprietà. Oltre alla sua formula, in un primo articolo ricavò importanti relazioni, e in un secondo lavoro ne propose una dimostrazione. Riportiamo in breve anche un confronto tra il lavoro di Cartesio e quello di Eulero. Il terzo capitolo invece riguarda il metodo e il rigore nella formulazione di teoremi e dimostrazioni: I. Lakatos ne fa un esame critico nel libro "Dimostrazioni e Confutazioni - la logica della scoperta matematica", simulando una lezione dove a tema compaiono la Formula di Eulero e le sue dimostrazioni. Noi cercheremo di analizzare questo suo lavoro. Su questi tre autori e i loro lavori riportiamo alcune considerazioni biografiche e storiche che possono offrire interessanti spunti didattici: infatti nel quarto e ultimo capitolo ci occuperemo di alcune considerazioni didattiche a proposito della Formula. La struttura sarà quella di un'ipotetica lezione a studenti di Scuola Media Inferiore e utilizzeremo i risultati ottenuti nei precedenti capitoli e una personale esperienza di tirocinio.

Progettazione del sistema di controllo di una vettura di formula sae

Il seguente lavoro di tesi è finalizzato alla realizzazione dell’elettronica di controllo per una vettura prototipo, Nel Capitolo 1 della tesi viene descritto più nel dettaglio il progetto Formula SAE, introducendo gli aspetti peculiari della competizione; successivamente segue una breve descrizione del team UniBo Motorsport. Il Capitolo 2 descrive l’elettronica implementata nella stagione 2013 evidenziandone i punti di forza e le debolezze al fine di poter trarre delle conclusioni per comprendere la direzione intrapresa con questo lavoro di tesi. Nel Capitolo 3 viene presentata la soluzione proposta,motivandone le scelte e la necessità di suddividere il lavoro in più unità distinte, mantenendo le peculiarità tecniche del già eccellente lavoro effettuato nel corso degli anni da chi mi ha preceduto ed aggiungendo quelle funzionalità che permettono di mantenere la soluzione in una posizione dominante nel panorama della Formula Student. La progettazione dell’hardware che compone la soluzione proposta è descritta nel Capitolo 4, introducendo dapprima la metodologia adottata per la progettazione partendo dalle specifiche fino ad arrivare al prodotto finito ed in seguito ne viene descritta l’applicazione ad ogni unità oggetto del lavoro. Sono state progettate da zero tre unità: una centralina di controllo motore (ECU), una di controllo veicolo (VCU) ed un controller lambda per la gestione di sonde UEGO. Un aiuto fondamentale nella progettazione di queste tre unità è stato dato da Alma Automotive, azienda che fin dal principio ha supportato, anche economicamente, le varie evoluzioni dell’hardware e del software della vettura. Infine viene descritto nel capitolo 5 il software che verrà eseguito sulle unità di controllo, ponendo particolare risalto al lavoro di adattamento che si è reso necessario per riutilizzare il software in uso negli anni precedenti.

Taylor formula for Kolmogorov equations

After briefly discuss the natural homogeneous Lie group structure induced by Kolmogorov equations in chapter one, we define an intrinsic version of Taylor polynomials and Holder spaces in chapter two. We also compare our definition with others yet known in literature. In chapter three we prove an analogue of Taylor formula, that is an estimate of the remainder in terms of the homogeneous metric.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Interpretazione per i media: il caso particolare delle interviste sul podio della Formula 1

This dissertation analyses the live simultaneous interpretation from English into Italian of six 2013 Formula 1 World Championship podium interviews and focuses on four main aspects: how the interpreter handled the décalage at the end of the interview and during the turn-taking; if he used any marker to indicate that he was starting to translate a new turn of the source text; what he did when overlapped speech in the source texts occurred; what happened when the Italian commentators talked during the interpreter’s translation. In the first chapter a description mainly of what a Formula 1 podium interview is and what an interpreter translates during the Formula 1 weekends is present. In the second chapter a literature review on media interpreting, with particular attention put on Straniero Sergio’s paper on translating Formula 1 press-conferences (2003), and turn-taking is provided. In the third chapter the methodology used to obtain and process the video and audio files of source and target texts and to transcribe them is described. We concentrated primarily on Thibault’s multimodal text transcription techniques (2000) and on how they were used and adapted to fit the purposes of this dissertation. In the fourth chapter the results obtained through the analysis of the source and target texts are shown and described, focusing only on the objectives of the dissertation, without aiming to provide a qualitative evaluation of the interpretations. In the fifth and last chapter the conclusions and some final remarks are made, based on the results obtained during the analysis and the hope for a more in depth knowledge of Italian Formula 1 interpreter’s working conditions.

Formula Zero: Traduzione trilingue inglese-italiano-spagnolo di un policy statement sulla sicurezza stradale della Federazione Internazionale dell'Automobile (FIA)

The aim of this dissertation is to provide a trilingual translation from English into Italian and from Italian into Spanish of a policy statement from the Fédération Internationale de l’Automobile (FIA) regarding road safety. The document, named “Formula Zero: a strategy for reducing fatalities and injuries on track and road”, was published in June 2000 and involves an approach about road safety inspired by another approach introduced in Sweden called ‘Vision Zero’. This work consists of six sections. The first chapter introduces the main purposes and activities of the Federation, as well as the institutions related to it and Vision Zero. The second chapter presents the main lexical, morphosyntactic and stylistic features of the institutional texts and special languages. In particular, the text contains technical nomenclature of transports and elements of sport language, especially regarding motor sport and Formula One. In the third chapter, the methodology is explained, with all the resources used during the preliminary phase and the translation, including corpora, glossaries, expert consultancy and specialised sites. The fourth chapter focuses on the morphosyntactic and terminology features contained in the text, while the fifth chapter presents the source text and the target texts. The final chapter deals with all the translation strategies that are applied, alongside with all the challenging elements detected. Therefore, the dissertation concludes with some theoretical and practical considerations about the role of inverse translation and English as Lingua Franca (ELF), by comparing the text translated into Spanish to the original in English, using Italian as a lingua franca.

Formula integrale di Poisson

Il tema centrale di questa tesi è lo studio del problema di Dirichlet per il Laplaciano in R^2 usando le serie di Fourier. Il problema di Dirichlet per il Laplaciano consiste nel determinare una funzione f armonica e regolare in un dominio limitato D quando sono noti i valori che f assume sul suo bordo. Ammette una sola soluzione, ma non esistono criteri generali per ricavarla. In questa tesi si mostra come la formula integrale di Poisson, sotto determinate condizioni, risolva il problema di Dirichlet in R^2 e in R^n.

Computation of discrete cosine transform using Clenshaw's recurence formula

Clenshaw’s recurrenee formula is used to derive recursive algorithms for the discrete cosine transform @CT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented here requires one fewer delay element per coefficient and one fewer multiply operation per coeflident compared with two recently proposed methods. Clenshaw’s recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The M v e al gorithms apply to arbitrary lengtb algorithms and are appropriate for VLSI implementation.

Mortality and morbidity in the city of Bern, Switzerland, 1805-1815 with special emphasis on infant, child and maternal deaths

This article contributes to the research on demographics and public health of urban populations of preindustrial Europe. The key source is a burial register that contains information on the deceased, such as age and sex, residence and cause of death. This register is one of the earliest compilations of data sets of individuals with this high degree of completeness and consistency. Critical assessment of the register's origin, formation and upkeep promises high validity and reliability. Between 1805 and 1815, 4,390 deceased inhabitants were registered. Information concerning these individuals provides the basis for this study. Life tables of Bern's population were created using different models. The causes of death were classified and their frequency calculated. Furthermore, the susceptibility of age groups to certain causes of death was established. Special attention was given to causes of death and mortality of newborns, infants and birth-giving women. In comparison to other cities and regions in Central Europe, Bern's mortality structure shows low rates for infants (q0=0.144) and children (q1-4=0.068). This could have simply indicated better living conditions. Life expectancy at birth was 43 years. Mortality was high in winter and spring, and decreased in summer to a low level with a short rise in August. The study of the causes of death was inhibited by difficulties in translating early 19th century nomenclature into the modern medical system. Nonetheless, death from metabolic disorders, illnesses of the respiratory system, and debilitation were the most prominent causes in Bern. Apparently, the worst killer of infants up to 12 months was the "gichteren", an obsolete German term for lethal spasmodic convulsions. The exact modern identification of this disease remains unclear. Possibilities such as infant tetanus or infant epilepsy are discussed. The maternal death rate of 0.72% is comparable with values calculated from contemporaneous sources. Relevance of childbed fever in the early 1800s was low. Bern's data indicate that the extent of deaths related to childbirth in this period is overrated. This research has an explicit interdisciplinary value for various fields including both the humanities and natural sciences, since information reported here represents the complete age and sex structure of a deceased population. Physical anthropologists can use these data as a true reference group for their palaeodemographic studies of preindustrial Central Europe of the late 18th and early 19th century. It is a call to both historians and anthropologists to use our resources to a better effect through combination of methods and exchange of knowledge.