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 temporal pattern of customer satisfaction: a construal-level approach

Customer satisfaction has been traditionally studied and measured regardless of the time elapsed since the purchase. Some studies have recently reopened the debate about the temporal pattern of satisfaction. This research aims to explain why “how you evaluate a service depends on when you evaluate it” on the basis of the theoretical framework proposed by Construal-Level Theory (CLT). Although an empirical investigation is still lacking, the literature does not deny that CLT can be applied also with regard to past events. Moreover, some studies support the idea that satisfaction is a good predictor of future intentions, while others do not. On the basis of CLT, we argue that these inconsistent results are due to the different construal levels of the information pertaining to retrospective and prospective evaluations. Building on the Two-Factor Theory, we explain the persistence of certain attributes’ representations over time according to their relationship with overall performance. We present and discuss three experiments and one field study that were conducted a) to test the extensibility of CLT to past events, b) to disentangle memory and construal effects, c) to study the effect of different temporal perspective on overall satisfaction judgements, and d) to investigate the temporal shift of the determinants of customer satisfaction as a function of temporal distance.

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.

Verso il consumo sostenibile: i prodotti biologici nelle abitudini alimentari degli italiani

Scegliere di consumare in modo sostenibile significa passare ad un nuovo modello di consumo. Tale modello richiede una maggiore consapevolezza e responsabilità da parte dei consumatori, unite all'adozione di nuovi stili di vita e di scelte d’acquisto, che permettano il raggiungimento di elevati livelli di benessere nel rispetto dell'ambiente. Un notevole sforzo è stato compiuto recentemente dai policy maker per incoraggiare il consumo sostenibile quali implementazioni dello sviluppo sostenibile. Ancora lunga, tuttavia, è la strada da percorrere per raggiungere pienamente questo obiettivo. Tra i prodotti sostenibili, il biologico si è rivelato di gran lunga il più rappresentativo: le statistiche di questo mercato mostrano, infatti, tendenze positive, sebbene il consumo risulti ancora eterogeneo e contenuto rispetto al consumo di alimenti convenzionali. Ciò mostra che il comportamento dei consumatori non è ancora abbastanza reattivo alle suddette politiche. Il presente studio si propone di contribuire alla ricerca sul consumo sostenibile approfondendo i fattori che incoraggiano o impediscono il consumo di prodotti alimentari biologici in Italia. Adottando un nuovo approccio si cerca di capire come i diversi segmenti di diete alimentari affrontino gli alimenti biologici in termini di consumi e di atteggiamenti. Un'analisi multivariata a più fasi è stata condotta su un campione di 3.004 consumatori. Un’analisi delle componenti principali non lineare è stata applicata alle variabili ordinali che misurano il consumo di ventuno categorie di alimenti. Successivamente è stata applicata la cluster analysis che ha dato luogo a quattro segmenti di abitudini alimentari. I prodotti biologici sono diventati parte delle abitudini alimentari in Italia in quasi un terzo della popolazione. Il consumo sembra essersi affermato soprattutto nel segmento con abitudini alimentari sane. Una scarsa attenzione ad una dieta sana, gli stili di vita, il reddito, l'accessibilità, la mancanza di consapevolezza condizionano le abitudini alimentari a scapito di un consumo più sostenibile.