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.

Vorsorglicher Rechtsschutz. Vorsorgliche Massnahmen im internationalen Kontext, offene Fragen im neuen Arrestrecht und Sicherungsmassnahmen der ZPO, mit Beiträgen von Dr. Isabelle Chabloz, Dr. Richard Gassmann, PD Dr. Pascal Grolimund, Dr. Jürg Roth, Prof. Dr. Daniel Staehelin

Am 9. September 2011 führte das Institut für Verfahrensrecht und Internationales Privatrecht (CIVPRO) der Universität Bern in bewährter Zusammenarbeit mit der schweizerischen SchKG-Vereinigung die zweite Schweizer Tagung für Internationales Zivilverfahrensrecht durch. Im Mittelpunkt der Tagung standen vorsorgliche Massnahmen im internationalen Kontext vor dem Hintergrund der neuesten Entwicklungen, namentlich (aber nicht nur) des neuen Lugano-Übereinkommens. Der Tagungsband enthält die auf den Vorträgen basierenden, überarbeiteten und erweiterten Beiträge namhafter Autorinnen und Autoren zum vorsorglichen Rechtsschutz im neuen IZPR (Pascal Grolimund). Besondere Aufmerksamkeit gilt dem neuen Arrestrecht sowohl im als auch ausserhalb des Anwendungsbereichs des Lugano-Übereinkommens (Richard Gassmann und Jürg Roth). Ebenso enthält der Band Beiträge zu den Sicherungsmassnahmen in der Realvollstreckung (Daniel Staehelin) sowie zur Anerkennung ausländischer vorsorglicher Massnahmen (Isabelle Chabloz).

The Ideology, Politics and Autonomous Art of Richard Weiner: (An Event in Discourse)"

The first aim of the project was to compile documentation on the life and work of Richard Weiner, a Czech journalist, writer and poet who spent the best part of his life as Paris correspondent for Lidove noviny. Langerova looked at the contexts and the growing independence of certain parts of his work, the distribution of thematic compositional elements into different parts of discourse and their position in the autonomous space of a work of art. Looking at the features of minority literature and the contemporary contexts of Weiner's life and work Langerova focuses on the situation of the Jewish community (Wiener came from an assimilated Jewish family). For this minorities, the function of language as a medium of communication which is able to create an autonomous world became increasingly important. Literature, which is based on this function of language, is a political matter par excellence before it begins forming as an autonomous, independent and divergent place. This means that everything private and intimate is closely connected to political and social responsibility, while supposedly objective genres contain subjective features. Another important characteristic is "nomadism", which asks the question of "Where do I belong". This was very important in Czechoslovakia after World War I , as in the issue of Zionism. Although Weiner rejected Zionism, he asks this question in his writing and it is reflected at a symbolic level in his work, which shows a fundamental thematic and compositional plan of a journey, cross-roads and wandering. These theses were reflected in Weiner's life, which was a series of continuous transfers and unplanned moves, often when he thought he had found his place. As well as tracing the course of his life, and his relations with and views of other writers, Langerova looks at his writings in various areas. Her major focus is the divergence of trivial and great events into different types of discourse in Richard Weiner's work, their transfer (small into great, trivial into mythical) and their historical context.

Restoring the Richard's Cabin - Nevada City Living History Museum

Highlands College Historic Preservation student, Paul Hart, enjoyed an internship in which he researched and accurately reconstructed parts of the Richard's Cabin at the Nevada City Living History Museum.