Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Learning from experience: Analysis of the civil litigation regarding building structures on the court of bologna in the years 2011/2012

The present work is aimed to the study and the analysis of the defects detected in the civil structure and that are object of civil litigation in order to create an instruments capable of helping the different actor involved in the building process. It is divided in three main sections. The first part is focused on the collection of the data related to the civil proceeding of the 2012 and the development of in depth analysis of the main aspects regarding the defects on existing buildings. The research center “Osservatorio Claudio Ceccoli” developed a system for the collection of the information coming from the civil proceedings of the Court of Bologna. Statistical analysis are been performed and the results are been shown and discussed in the first chapters.The second part analyzes the main issues emerged during the study of the real cases, related to the activities of the technical consultant. The idea is to create documents, called “focus”, addressed to clarify and codify specific problems in order to develop guidelines that help the technician editing of the technical advice.The third part is centered on the estimation of the methods used for the collection of data. The first results show that these are not efficient. The critical analysis of the database, the result and the experience and throughout, allowed the implementation of the collection system for the data.