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.