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.

Analisi dei discorsi di ringraziamento di attori e attrici alle cerimonie dei premi oscar

Il presente elaborato ha come obiettivo l’analisi dei discorsi di ringraziamento pronunciati nelle cerimonie dei premi Oscar dal 1990 al 2015 da attori e attrici, protagonisti e non protagonisti, premiati con la statuetta dorata per le loro performance recitative. L’elaborato si articola in tre capitoli: nel primo, si delinea la storia dei premi Oscar, considerati la cerimonia di premiazione cinematografica per antonomasia, con particolare attenzione ai metodi di selezione di premiati e vincitori da parte dell’Academy of Motion Pictures Arts and Sciences. Ci si concentra anche sul significato, letterale e simbolico, dei discorsi di ringraziamento, e sulla rilevanza che essi hanno all’interno della cerimonia. Nel secondo capitolo, si analizzano i discorsi di ringraziamento dei vincitori da un punto di vista linguistico, con particolare attenzione a prosodia, prossemica, retorica e deissi. Nel terzo e ultimo capitolo, infine, l’analisi assume toni più prettamente culturali, focalizzando l’attenzione sugli aspetti pragmatici e contenutistici dei discorsi, nonché nel tentativo di confrontare gli atteggiamenti delle due categorie nazionali più premiate agli Oscar: gli americani e i britannici.

Sul sentiero meno battuto: Proposta di traduzione di sei albi illustrati che si allontanano dagli stereotipi sui temi di genere, multiculturalismo e disabilita

This thesis focuses on the translation of six picture books that challenge and subvert – each one in its peculiar way – typical stereotypes found in Children’s Literature. I think that stereotyping is an all-important theme in picture books because these books are the ones that will introduce children to literature and young readers have the right to find in it every kind of model. Showing children a variety of characters that reflects the multiple forms of reality will allow them to choose which kind of person to be. In my opinion, this freedom is much needed especially here, in Italy, in this moment of history. This work also studies the stereotypes that have appeared – and are still present, to some extent – in Children’s Literature, the ways in which they are dangerous for young readers, and how they have changed over time. I centered my research on three major themes that have been subject to stereotyping: race, disability and gender. I searched for the right books to translate paying attention not only to the themes they focused on but also to how they dealt with such themes, the tone of each picture book and, obviously, its quality. The selection resulting from my research reflects a diverse world and a celebration of difference. Before actually translating them, I engaged in a deep analysis of their structures, themes and meanings, so that I would be able to enter the ‘world’ of the book and to understand its ‘secrets’ better. This analysis proved to be fundamental during the translation phase and allowed me to make conscious translation choices that I have explored in the part dedicated to the commentary of the translation.