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.

The abuse of intellectual property rights and regulations in China: a law and economic analysis

From the institutional point of view, the legal system of IPR (intellectual property right, hereafter, IPR) is one of incentive institutions of innovation and it plays very important role in the development of economy. According to the law, the owner of the IPR enjoy a kind of exclusive right to use his IP(intellectual property, hereafter, IP), in other words, he enjoys a kind of legal monopoly position in the market. How to well protect the IPR and at the same time to regulate the abuse of IPR is very interested topic in this knowledge-orientated market and it is the basic research question in this dissertation. In this paper, by way of comparing study and by way of law and economic analyses, and based on the Austrian Economics School’s theories, the writer claims that there is no any contradiction between the IPR and competition law. However, in this new economy (high-technology industries), there is really probability of the owner of IPR to abuse his dominant position. And with the characteristics of the new economy, such as, the high rates of innovation, “instant scalability”, network externality and lock-in effects, the IPR “will vest the dominant undertakings with the power not just to monopolize the market but to shift such power from one market to another, to create strong barriers to enter and, in so doing, granting the perpetuation of such dominance for quite a long time.”1 Therefore, in order to keep the order of market, to vitalize the competition and innovation, and to benefit the customer, in EU and US, it is common ways to apply the competition law to regulate the IPR abuse. In Austrian Economic School perspective, especially the Schumpeterian theories, the innovation/competition/monopoly and entrepreneurship are inter-correlated, therefore, we should apply the dynamic antitrust model based on the AES theories to analysis the relationship between the IPR and competition law. China is still a developing country with relative not so high ability of innovation. Therefore, at present, to protect the IPR and to make good use of the incentive mechanism of IPR legal system is the first important task for Chinese government to do. However, according to the investigation reports,2 based on their IPR advantage and capital advantage, some multinational companies really obtained the dominant or monopoly market position in some aspects of some industries, and there are some IPR abuses conducted by such multinational companies. And then, the Chinese government should be paying close attention to regulate any IPR abuse. However, how to effectively regulate the IPR abuse by way of competition law in Chinese situation, from the law and economic theories’ perspective, from the legislation perspective, and from the judicial practice perspective, there is a long way for China to go!

Structure-Property Relationships and Charge Transport Modeling of Organic Molecular Materials

From the perspective of a new-generation opto-electronic technology based on organic semiconductors, a major objective is to achieve a deep and detailed knowledge of the structure-property relationships, in order to optimize the electronic, optical, and charge transport properties by tuning the chemical-physical characteristics of the compounds. The purpose of this dissertation is to contribute to such understanding, through suitable theoretical and computational studies. Precisely, the structural, electronic, optical, and charge transport characteristics of several promising organic materials recently synthesized are investigated by means of an integrated approach encompassing quantum-chemical calculations, molecular dynamics and kinetic Monte Carlo simulations. Particular care is addressed to the rationalization of optical and charge transport properties in terms of both intra- and intermolecular features. Moreover, a considerable part of this project involves the development of a home-made set of procedures and parts of software code required to assist the modeling of charge transport properties in the framework of the non-adiabatic hopping mechanism applied to organic crystalline materials. As a first part of my investigations, I mainly discuss the optical, electronic, and structural properties of several core-extended rylene derivatives, which can be regarded to as model compounds for graphene nanoribbons. Two families have been studied, consisting in bay-linked perylene bisimide oligomers and N-annulated rylenes. Beside rylene derivatives, my studies also concerned electronic and spectroscopic properties of tetracene diimides, quinoidal oligothiophenes, and oxygen doped picene. As an example of device application, I studied the structural characteristics governing the efficiency of resistive molecular memories based on a derivative of benzoquinone. Finally, as a second part of my investigations, I concentrate on the charge transport properties of perylene bisimides derivatives. Precisely, a comprehensive study of the structural and thermal effects on the charge transport of several core-twisted chlorinated and fluoro-alkylated perylene bisimide n-type semiconductors is presented.

Harnack inequalities in sub-Riemannian settings

In the present thesis, we discuss the main notions of an axiomatic approach for an invariant Harnack inequality. This procedure, originated from techniques for fully nonlinear elliptic operators, has been developed by Di Fazio, Gutiérrez, and Lanconelli in the general settings of doubling Hölder quasi-metric spaces. The main tools of the approach are the so-called double ball property and critical density property: the validity of these properties implies an invariant Harnack inequality. We are mainly interested in the horizontally elliptic operators, i.e. some second order linear degenerate-elliptic operators which are elliptic with respect to the horizontal directions of a Carnot group. An invariant Harnack inequality of Krylov-Safonov type is still an open problem in this context. In the thesis we show how the double ball property is related to the solvability of a kind of exterior Dirichlet problem for these operators. More precisely, it is a consequence of the existence of some suitable interior barrier functions of Bouligand-type. By following these ideas, we prove the double ball property for a generic step two Carnot group. Regarding the critical density, we generalize to the setting of H-type groups some arguments by Gutiérrez and Tournier for the Heisenberg group. We recognize that the critical density holds true in these peculiar contexts by assuming a Cordes-Landis type condition for the coefficient matrix of the operator. By the axiomatic approach, we thus prove an invariant Harnack inequality in H-type groups which is uniform in the class of the coefficient matrices with prescribed bounds for the eigenvalues and satisfying such a Cordes-Landis condition.

Le opere di urbanizzazione a scomputo degli oneri

Le considerazioni sviluppate in questo scritto si pongono come obiettivo quello di fare chiarezza sul delicato tema delle opere di urbanizzazione a scomputo. La normativa concernente la realizzazione delle opere pubbliche a scomputo totale o parziale degli oneri di urbanizzazione è stata oggetto di svariate modifiche e interpretazioni giurisprudenziali, che si sono susseguite dopo l'importante pronuncia della Corte di Giustizia Europea. E' con questa sentenza che i Giudici del Kirchberg introducono un particolare obbligo procedurale a carico dei privati: nel caso in cui singole opere superino i valori di rilevanza europea, esse devono essere affidate, applicando le procedure di gara previste dalla direttiva 37/93/CEE. Va precisato che sino a quel momento l'affidamento diretto delle opere al privato costituiva nell'ottica del Legislatore lo strumento per realizzare le infrastrutture necessarie per consentire gli insediamenti edilizi che la pubblica amministrazione spesso non era in grado di effettuare. In questo panorama legislativo la sentenza della Corte di Giustizia, appare del tutto dirompente. Infatti, introducendo il principio secondo cui anche la realizzazione diretta delle opere di urbanizzazione da parte del privato deve sottostare alle regole delle procedure europee in materia di appalti, mette inevitabilmente a confronto due normative, quella degli appalti pubblici e quella dell'urbanistica, che sino a quel momento erano riuscite a viaggiare in modo parallelo, senza dar luogo a reciproche sovrapposizioni. Il Legislatore nazionale ha, con molta fatica, recepito il principio comunitario ed è stato negli anni quasi costretto, attraverso una serie di modifiche legislative, ad ampliarne la portata. La presente ricerca, dopo aver analizzato i vari correttivi apportati al Codice degli appalti pubblici vuole, quindi, verificare se l'attuale quadro normativo rappresenti un vero punto di equilibrio tra le contrapposte esigenze di pianificazione del territorio e di rispetto dei principi comunitari di concorrenza nella scelta del contraente.

Structure-property relations in polymers from renewable resources

The present research project focuses its attention on the study of structure-property relations in polymers from renewable sources (bio-based polymers) such as polymers microbially produced, i.e. polyhydrohyalkanoates (PHAs) or chemically synthesized using monomers from renewable sources, i.e. polyammide 11 (PA11). By means of a broad spectrum of experimental techniques, the influence of different modifications on bio-based polymers such as blending with other components, copolymerization with different co-monomers and introduction of branching to yield complex architectures have been investigated. The present work on PHAs focused on the study of the dependence of polymer properties on both the fermentation process conditions (e.g. bacterial strain and carbon substrate used) and the method adopted to recover PHAs from cells. Furthermore, a solvent-free method using an enzyme and chemicals in an aqueous medium, was developed in order to recover PHAs from cells. Such a method allowed to recover PHA granules in their amorphous state, i.e. in native form useful for specific applications (e.g. paper coating). In addition, a commercial PHA was used as polymeric matrix to develop biodegradable and bio-based composites for food packaging applications. Biodegradable, non-toxic, food contact plasticizers and low cost, widely available lignocellulosic fibers (wheat straw fibers) were incorporated in such a polymeric matrix, in order to decrease PHA brittleness and the polymer cost, respectively. As concerns the study of polyamide 11, both the rheological and the solid-state behavior of PA11 star samples with different arm number and length was studied. Introduction of arms in a polymer molecule allows to modulate melt viscosity behavior which is advantageous for industrial applications. Also, several important solid-state properties, in particular mechanical properties, are affected by the presence of branching. Given the importance of using ‘green’ synthetic strategies in polymer chemistry, novel poly(-amino esters), synthesized via enzymatic-catalyzed polymerization, have also been investigated in this work.

Estimation of Quasi-Rational DSGE Models

Small-scale dynamic stochastic general equilibrium have been treated as the benchmark of much of the monetary policy literature, given their ability to explain the impact of monetary policy on output, inflation and financial markets. One cause of the empirical failure of New Keynesian models is partially due to the Rational Expectations (RE) paradigm, which entails a tight structure on the dynamics of the system. Under this hypothesis, the agents are assumed to know the data genereting process. In this paper, we propose the econometric analysis of New Keynesian DSGE models under an alternative expectations generating paradigm, which can be regarded as an intermediate position between rational expectations and learning, nameley an adapted version of the "Quasi-Rational" Expectatations (QRE) hypothesis. Given the agents' statistical model, we build a pseudo-structural form from the baseline system of Euler equations, imposing that the length of the reduced form is the same as in the `best' statistical model.

Variabilita' ed evoluzione dei prioni: Mutabilita' in vitro

I prioni, privi di acidi nucleici, esistono come ceppi e possono mutare, in particolare quando attraversano una barriera di specie. Numerosi studi convergono sulla conclusione che le caratteristiche ceppo-specifiche siano inscritte nella conformazione della PrPSc, con la variabilità di ceppo associata a varianti conformazionali della PrPSc. In questo studio ci siamo avvalsi del PMCA, tecnica che riproduce in vitro molti aspetti della biologia dei prioni, per mettere a punto condizioni sperimentali di replicazione che permettessero di osservare fenomeni di mutazione e selezione, onde investigare i meccanismi molecolari e di popolazione alla base della mutabilità dei prioni. In condizioni di replicazione eterologa, che mima la trasmissione tra diverse specie, è stato inizialmente possibile identificare un mutante difettivo della scrapie, caratterizzato da una diversa conformazione della PrPSc e capace di replicare in vitro ma non più in vivo. Le condizioni in cui tale mutante è emerso hanno permesso di sviluppare ulteriori ipotesi di lavoro, basate sul concetto della quasi-specie. Impartendo diversi regimi di replicazione e seguendo l’evoluzione di due ceppi, è stato possibile evidenziare fenomeni di mutazione anche in condizioni di replicazione omologa, in assenza di forti pressioni selettive. In entrambi i ceppi sono emerse varianti conformazionali di PrPSc durante passaggi replicativi ad ampia popolazione, mentre le popolazioni sottoposte a ripetuti colli di bottiglia hanno mostrato un rapido declino del tasso di replicazione. Sono stati infine investigati l’efficacia e il potenziale mutageno di molecole anti-prioniche, ottenendo importanti risultati preliminari sull’efficacia di molecole che legano la PrPC. Questi risultati evidenziano come la mutabilità sia una caratteristica intrinseca dei prioni e supportano l’idea che i prioni siano molto variabili, similmente alle quasi-specie virali, e perciò adattabili e proni a fenomeni di mutazione e selezione. Tali conclusioni hanno impatto su problematiche sanitarie quali lo studio del potenziale zoonotico e i fenomeni di farmaco-resistenza dei prioni.

Tailoring, synthesis and structure-property relationships of 2,3-thienoimide based molecular materials

Organic molecular semiconductors are subject of intense research for their crucial role as key components of new generation low cost, flexible, and large area electronic devices such as displays, thin-film transistors, solar cells, sensors and logic circuits. In particular, small molecular thienoimide (TI) based materials are emerging as novel multifunctional materials combining a good processability together to ambipolar or n-type charge transport and electroluminescence at the solid state, thus enabling the fabrication of integrated devices like organic field effect transistors (OFETs) and light emitting transistor (OLETs). Given this peculiar combination of characteristics, they also constitute the ideal substrates for fundamental studies on the structure-property relationships in multifunctional molecular systems. In this scenario, this thesis work is focused on the synthesis of new thienoimide based materials with tunable optical, packing, morphology, charge transport and electroluminescence properties by following a fine molecular tailoring, thus optimizing their performances in device as well as investigating and enabling new applications. Investigation on their structure-property relationships has been carried out and in particular, the effect of different π-conjugated cores (heterocycles, length) and alkyl end chain (shape, length) changes have been studied, obtaining materials with enhanced electron transport capability end electroluminescence suitable for the realization of OFETs and single layer OLETs. Moreover, control on the polymorphic behaviour characterizing thienoimide materials has been reached by synthetic and post-synthetic methodologies, developing multifunctional materials from a single polymorphic compound. Finally, with the aim of synthesizing highly pure materials, simplifying the purification steps and avoiding organometallic residues, procedures based on direct arylation reactions replacing conventional cross-couplings have been investigated and applied to different classes of molecules, bearing thienoimidic core or ends, as well as thiophene and anthracene derivatives, validating this approach as a clean alternative for the synthesis of several molecular materials.