Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

A projection into the ideas and technologies of "non-place" and "space of flow" in urban context

The meaning of a place has been commonly assigned to the quality of having root (rootedness) or sense of belonging to that setting. While on the contrary, people are nowadays more concerned with the possibilities of free moving and networks of communication. So, the meaning, as well as the materiality of architecture has been dramatically altered with these forces. It is therefore of significance to explore and redefine the sense and the trend of architecture at the age of flow. In this dissertation, initially, we review the gradually changing concept of "place-non-place" and its underlying technological basis. Then we portray the transformation of meaning of architecture as influenced by media and information technology and advanced methods of mobility, in the dawn of 21st century. Against such backdrop, there is a need to sort and analyze architectural practices in response to the triplet of place-non-place and space of flow, which we plan to achieve conclusively. We also trace the concept of flow in the process of formation and transformation of old cities. As a brilliant case study, we look at Persian Bazaar from a socio-architectural point of view. In other word, based on Robert Putnam's theory of social capital, we link social context of the Bazaar with architectural configuration of cities. That is how we believe "cities as flow" are not necessarily a new paradigm.

History of Restoration in Iran: Origins and Developments from 1900 to 1978

This thesis tends to study the origins and developments of the restoration in Iran from its very first moments till the Islamic revolution of 1978. The thesis is its first study of its kind. While almost all recent occidental ideologies regarding the thematic of restoration and conservation of historic monuments are translated and published in Iran, very little efforts have been done regarding the study of the origins of the formation of restoration in the country. The diversity of Iranian contexts, multiplicity of the intervening factors and other factors characterized a different background for the raise and developments of restoration in the country; in the thesis the influencing and characterizing factors in the formation and development of restoration in Iran will be defined and studied in detail with relative examples; due to the complexity of the Iranian context and in order to consider all influencing and characterizing factors the thesis, parallel to have formation and development of restoration, as the main scope of the research, the developments influencing factors will be confronted with necessary flashbacks to the main theme, when and where necessary. A great care will be given to the period of the activity of the restoration experts of IsMEO which is thesis will be called as the period of the introduction of the modern principles of restoration into Iranian context; the fundamental ideologies, practical and theoretical principles of IsMEO will be identified and studied in details; important case of studies of the restoration of IsMEO will be analyzed in details and the innovative aspect of the presence of Italian experts of IsMEO will be revealed.

The genetic history of Italians: new-insights from uniparentally-inherited markers

Genetic differences among human groups can be ascribed both to the broad-scale extents of pre-historical and historical migrations and to the fine-scale impacts of socio-cultural and geographic heterogeneity. In this thesis, the genetic information provided by uniparental markers were exploited to address different aspects of the Italian population history, by combining macro- and micro-geographic investigations at different spatial and temporal scales. To firstly assess the overall Italian variability, Y-chromosome and mtDNA markers were deeply typed in ~900 individuals from continental Italy, Sicily and Sardinia. Sex-biased patterns and contrasting demographic histories were observed for males and females. Differential European and Mediterranean contributions were invoked to explain the paternal genetic sub-structure observed in peninsular Italy, compared to the homogeneous maternal genetic landscape. If Neolithic showed to be one principal determinant of the detected paternal structure, local insights into specific Italian regional contexts highlighted the importance of Post-Neolithic contributions. Among them, migrations from the Balkans (particularly Greece) during late Metal Ages, played a relevant role in the cultural and genetic transitions occurred in Sicily and Southern Italy. On a finer geographic and temporal perspective, the more recent layers of Italian genetic history and some aspects of the gene-culture interaction were assessed by exploring the genetic variability within two “marginal populations”: Arbereshe of Southern Italy and Partecipanza in Northern Italy. The Arbereshe are Albanian-speaking communities settled in Sicily and Calabria since the end of Middle Ages. Despite sharing common genetic and cultural backgrounds, these groups revealed diverging micro-evolutionary histories, implying different founding events and different patterns of cultural isolation and local admixture. Partecipanza is an idiosyncratic institution of Medieval origin aimed at sharing and devolving collective lands. This case-study exemplified that socio-economic stratification within the same population may induce sex-biased genetic structuring and the maintenance of otherwise hidden historical genetic traces.