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.

La fiscalità delle perdite dei gruppi transfrontalieri: tra regimi nazionali e libertà di stabilimento

Caratteristica comune ai regimi di consolidamento previsti dai diversi ordinamenti, è quella di consentire la compensazione tra utili e perdite di società residenti, e, di negare, o rendere particolarmente difficoltosa, la stessa compensazione, quando le perdite sono maturate da società non residenti. La non considerazione delle perdite comporta una tassazione al lordo del gruppo multinazionale, per mezzo della quale, non si colpisce il reddito effettivo dei soggetti che vi appartengono. L’effetto immediato è quello di disincentivare i gruppi a travalicare i confini nazionali. Ciò impedisce il funzionamento del Mercato unico, a scapito della libertà di stabilimento prevista dagli artt. 49-54 del TFUE. Le previsioni ivi contenute sono infatti dirette, oltre ad assicurare a società straniere il beneficio della disciplina dello Stato membro ospitante, a proibire altresì allo Stato di origine di ostacolare lo stabilimento in un altro Stato membro dei propri cittadini o delle società costituite conformemente alla propria legislazione. Gli Stati membri giustificano la discriminazione tra società residenti e non residenti alla luce della riserva di competenza tributaria ad essi riconosciuta dall’ordinamento europeo in materia delle imposte dirette, dunque, in base all’equilibrata ripartizione del potere impositivo. In assenza di qualsiasi riferimento normativo, va ascritto alla Corte di Giustizia il ruolo di interprete del diritto europeo. La Suprema Corte, con una serie di importanti pronunce, ha infatti sindacato la compatibilità con il diritto comunitario dei vari regimi interni che negano la compensazione transfrontaliera delle perdite. Nel verificare la compatibilità con il diritto comunitario di tali discipline, la Corte ha tentato di raggiungere un (difficile) equilibrio tra due interessi completamenti contrapposti: quello comunitario, riconducibile al rispetto della libertà di stabilimento, quello degli Stati membri, che rivendicano il diritto di esercitare il proprio potere impositivo.

Technological processes study for high value health ingredients and foods production

This PhD thesis describes set up of technological models for obtaining high health value foods and ingredients that preserve the final product characteristics as well as enrich with nutritional components. In particular, the main object of my research has been Virgin Olive Oil (VOO) and its important antioxidant compounds which differentiate it from all other vegetables oils. It is well known how the qualitative and quantitative presence of phenolic molecules extracted from olives during oil production is fundamental for its oxidative and nutritional quality. For this purpose, agronomic and technological conditions of its production have been investigated. It has also been examined how this fraction can be better preserved during storage. Moreover, its relation with VOO sensorial characteristics and its interaction with a protein in emulsion foods have also been studied. Finally, an experimental work was carried out to determine the antioxidative and heat resistance properties of a new antioxidant (EVS-OL) when used for high temperature frying such as is typically employed for the preparation of french fries. Results of the scientific research have been submitted for a publication and some data has already been published in national and international scientific journals.

Dynamics and control issues of multi-rotor platforms

This thesis deals with the analytic study of dynamics of Multi--Rotor Unmanned Aerial Vehicles. It is conceived to give a set of mathematical instruments apt to the theoretical study and design of these flying machines. The entire work is organized in analogy with classical academic texts about airplane flight dynamics. First, the non--linear equations of motion are defined and all the external actions are modeled, with particular attention to rotors aerodynamics. All the equations are provided in a form, and with personal expedients, to be directly exploitable in a simulation environment. This has requited an answer to questions like the trim of such mathematical systems. All the treatment is developed aiming at the description of different multi--rotor configurations. Then, the linearized equations of motion are derived. The computation of the stability and control derivatives of the linear model is carried out. The study of static and dynamic stability characteristics is, thus, addressed, showing the influence of the various geometric and aerodynamic parameters of the machine and in particular of the rotors. All the theoretic results are finally utilized in two interesting cases. One concerns the design of control systems for attitude stabilization. The linear model permits the tuning of linear controllers gains and the non--linear model allows the numerical testing. The other case is the study of the performances of an innovative configuration of quad--rotor aircraft. With the non--linear model the feasibility of maneuvers impossible for a traditional quad--rotor is assessed. The linear model is applied to the controllability analysis of such an aircraft in case of actuator block.

Nonlinear Approaches to Attitude Control Using Magnetic and Mechanical Actuation

This thesis argues the attitude control problem of nanosatellites, which has been a challenging issue over the years for the scientific community and still constitutes an active area of research. The interest is increasing as more than 70% of future satellite launches are nanosatellites. Therefore, new challenges appear with the miniaturisation of the subsystems and improvements must be reached. In this framework, the aim of this thesis is to develop novel control approaches for three-axis stabilisation of nanosatellites equipped with magnetorquers and reaction wheels, to improve the performance of the existent control strategies and demonstrate the stability of the system. In particular, this thesis is focused on the development of non-linear control techniques to stabilise full-actuated nanosatellites, and in the case of underactuation, in which the number of control variables is less than the degrees of freedom of the system. The main contributions are, for the first control strategy proposed, to demonstrate global asymptotic stability derived from control laws that stabilise the system in a target frame, a fixed direction of the orbit frame. Simulation results show good performance, also in presence of disturbances, and a theoretical selection of the magnetic control gain is given. The second control approach presents instead, a novel stable control methodology for three-axis stabilisation in underactuated conditions. The control scheme consists of the dynamical implementation of an attitude manoeuvre planning by means of a switching control logic. A detailed numerical analysis of the control law gains and the effect on the convergence time, total integrated and maximum torque is presented demonstrating the good performance and robustness also in the presence of disturbances.

Catalytic upgrading of carboxylic acids and esters to bio fuels and bio chemicals

The research activity was focused on the transformation of methyl propionate (MP) into methyl methacrylate (MMA), avoiding the use of formaldehyde (FAL) thanks to a one-pot strategy involving in situ methanol (MeOH) dehydrogenation over the same catalytic bed were the hydroxy-methylation/dehydration of MP with FAL occurs. The relevance of such research line is related to the availability of cheap renewable bio-glycerol from biodiesel production, from which MP can be obtained via a series of simple catalytic reactions. Moreover, the conventional MMA synthesis (Lucite process) suffers from safety issues related to the direct use of carcinogenic FAL and depends on non-renewable MP. During preliminary studies, ketonization of carboxylic acids and esters has been recognized as a detrimental reaction which hinders the selective synthesis of MMA at low temperature, together with H-transfer hydrogenation with FAL or MeOH as the H-donor at higher temperatures. Therefore, ketonization of propionic acid (PA) and MP was investigated over several catalysts (metal oxides and metal phosphates), to obtain a better understanding of the structure-activity relationship governing the reaction and to design a catalyst for MMA synthesis capable to promote the desired reaction while minimizing ketonization and H-transfer. However, ketonization possesses scientific and industrial value itself and represents a strategy for the upgrade of bio oils from fast pyrolysis of lignocellulosic materials, a robust and versatile technology capable to transform the most abundant biomass into liquid biofuels. The catalysts screening showed that ZrO2 and La2O3 are the best catalysts, while MgO possesses low ketonization activity, but still, H-transfer parasitic hydrogenation of MMA reduces its yield over all catalysts. Such study resulted in the design of Mg/Ga mixed oxides that showed enhanced dehydrogenating activity towards MeOH at low temperatures. It was found that the introduction of Ga not only minimize ketonization, but also modulates catalyst basicity reducing H-transfer hydrogenations.

Non-Equilibrium Atmospheric Plasma As A Novel Route To Nanomaterial Synthesis And Processing For Biomedical Applications

Since last century, the rising interest of value-added and advanced functional materials has spurred a ceaseless development in terms of industrial processes and applications. Among the emerging technologies, thanks to their unique features and versatility in terms of supported processes, non-equilibrium plasma discharges appear as a key solvent-free, high-throughput and cost-efficient technique. Nevertheless, applied research studies are needed with the aim of addressing plasma potentialities optimizing devices and processes for future industrial applications. In this framework, the aim of this dissertation is to report on the activities carried out and the results achieved concerning the development and optimization of plasma techniques for nanomaterial synthesis and processing to be applied in the biomedical field. In the first section, the design and investigation of a plasma assisted process for the production of silver (Ag) nanostructured multilayer coatings exhibiting anti-biofilm and anti-clot properties is described. With the aim on enabling in-situ and on-demand deposition of Ag nanoparticles (NPs), the optimization of a continuous in-flight aerosol process for particle synthesis is reported. The stability and promising biological performances of deposited coatings spurred further investigation through in-vitro and in-vivo tests which results are reported and discussed. With the aim of addressing the unanswered questions and tuning NPs functionalities, the second section concerns the study of silver containing droplet conversion in a flow-through plasma reactor. The presented results, obtained combining different analysis techniques, support a formation mechanism based on droplet to particle conversion driven by plasma induced precursor reduction. Finally, the third section deals with the development of a simulative and experimental approach used to investigate the in-situ droplet evaporation inside the plasma discharge addressing the main contributions to liquid evaporation in the perspective of process industrial scale up.

Preparation and characterization of multifunctional bio-based polymers exhibiting enhanced properties

Driven by environmental reasons and the expected depletion of crude oil, bio-based polymers are currently undergoing a renaissance in the attempt to replace fossil-based ones. The present work aims at contributing in the development of the steps that start from biomass and move to new polymeric multifunctional materials. The study focuses on two bio-based building blocks (itaconic and vanillic acids) characterized by exploitable functionalities, i.e. a lateral double bond and a substituted aromatic ring respectively, able to confer interesting properties to the final polymers. The lateral double bond of dimethyl itaconate was functionalized via thia-Michael addition reaction obtaining a thermo-stable building block that can undergo polycondensation under classical conditions of reaction. The addition of a long lateral chain allows the polymer to express antimicrobial activity against Staphylococcus aureus making it attractive for packaging and targeting antimicrobial applications. Moreover, the architecture of the homopolymer was modified by means of copolymerization with dimethyl 2,5-furandicarboxylate thus improving the rigidity and obtaining a thermo-processable material. Potential applications as thermoset or thermoplastic material have been discussed. As concerns vanillic acid, the presence of aromatic rings on the polymer backbone imparts high thermal stability, but brittle behaviour in the homopolymer. Therefore, the architecture of the polyester was successfully tuned by means of copolymerization with a flexible bio-based comonomer, i.e. ω-pentadecalactone, providing processable random copolymers. An in depth investigation of water transport mechanism has been undertaken on the synthesized polyesters. Since the copolymers present a succession of aromatic and aliphatic units, as a consequence of the chemical structure water vapor permeability interposes between polyethylene and poly(ethylene terephthalate) proving that the copolyesters are suitable for packaging applications. Moving towards a sustainable model of development, novel sustainable synthetic pathways for the eco-design of new bio-based polymeric structures with high value functionalities and different potential applications have been successfully developed.