Zeta and L-functions of elliptic curves

In questa tesi si studiano alcune proprietà fondamentali delle funzioni Zeta e L associate ad una curva ellittica. In particolare, si dimostra la razionalità della funzione Zeta e l'ipotesi di Riemann per due famiglie specifiche di curve ellittiche. Si studia poi il problema dell'esistenza di un prolungamento analitico al piano complesso della funzione L di una curva ellittica con moltiplicazione complessa, attraverso l'analisi diretta di due casi particolari.

Laboratory verification of predicted permanent deformation in asphalt materials following climate change.

In the past a change in temperature of 5°C most often occurred over intervals of thousands of years. According to estimates by the IPCC, in the XXI century is expected an increase in average temperatures in Europe between 1.8 and 4.0°C in the best case caused by emissions of carbon dioxide and other GHG from human activities. As well as on the environment and economic context, global warming will have effects even on road safety. Several studies have already shown how increasing temperature may cause a worsening of some types of road surface damages, especially rutting, a permanent deformation of the road structures consisting in the formation of a longitudinal depression in the wheelpath, mostly due to the rheological behavior of bitumen. This deformation evolves during the hot season because of the heating capacity of the asphalt layers, in fact, the road surface temperature is up to 24°C higher than air. In this thesis, through the use of Wheeltrack test, it was studied the behavior of some types of asphalt concrete mixtures subjected to fatigue testing at different temperatures. The objectives of this study are: to determine the strain variation of different bituminous mixture subjected to fatigue testing at different temperature conditions; to investigate the effect of aggregates, bitumen and mixtures’ characteristics on rutting. Samples were made in the laboratory mostly using an already prepared mixtures, the others preparing the asphalt concrete from the grading curve and bitumen content. The same procedure was performed for each specimen: preparation, compaction using the roller compactor, cooling and heating before the test. The tests were carried out at 40 - 50 - 60°C in order to obtain the evolution of deformation with temperature variation, except some mixtures for which the tests were carried out only at 50°C. In the elaboration of the results were considered testing parameters, component properties and the characteristics of the mixture. Among the testing parameters, temperature was varied for each sample. The mixtures responded to this variation with a different behavior (linear logarithmic and exponential) not directly correlated with the asphalt characteristics; the others parameters as load, passage frequency and test condition were kept constant. According to the results obtained, the main contribution to deformation is due to the type of binder used, it was found that the modified bitumen have a better response than the same mixtures containing traditional bitumen; to the porosity which affects negatively the behavior of the samples and to the homogeneity ceteris paribus. The granulometric composition did not seem to have interfered with the results. Overall has emerged at working temperature, a decisive importance of bitumen composition, than the other characteristics of the mixture, that tends to disappear with heating in favor of increased dependence of rutting resistance from the granulometric composition of the sample considered. In particular it is essential, rather than the mechanical characteristics of the binder, its chemical properties given by the polymeric modification. To confirm some considered results, the maximum bulk density and the air voids content were determined. Tests have been conducted in the laboratories of the Civil Engineering Department at NTNU in Trondheim according to European Standards.

Assessment and Protection of maritime-vernacular architectural Heritage on the Mediterranean Coasts. Documentation and Preservation Strategies for the Dry Docks on the Island of Formentera.

The importance of vernacular architecture as an integral part of our cultural heritage is often undervalued, and the management of rural constructions of heritage value often requires the application of more flexible and adjusted preservation principles compared to monumental assets. For vernacular architecture, the preservation and consolidation concern not only their physical substance but also their intangible values and purpose in society. More than other heritage values, the vernacular raises the question of prospective functions it can fulfill in contemporary societies without undermining its legacy. This work analyzes the topic by studying the case study of the dry docks on the Balearic Island of Formentera, including abundant documentation of traditional construction techniques and materials realized through a field study, followed by the assessment of threats to and opportunities for vernacular architecture on Formentera, closing with suggestions for the maintenance and potential functions of the dry docks. For this, a comparative case study was introduced: the capanni da pesca at the Adriatic coast of Italy. The suggestions focus on the importance of maintenance for rural heritage, expressed through the creation of a guide for owners of protected dry docks highlighting good and bad practice examples and recurrent works of care. Furthermore, the thesis seeks to raise awareness for the significance of landscape and social factors in the discourse about vernacular heritage sites. Ultimately, different outlines of tourism development are proposed. The idea is to explore rural and sustainable tourism as a tool for territory development and enhancement of the cultural heritage value by helping to prevent the destination's decline through careful evaluation of its limits of acceptable change and identifying beneficial, sustainable scenarios for the future of the heritage asset and the respective community.