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.

Language and Embodiment: sensory-motor and linguistic-social experience. Evidence on sentence comprehension

In this work I address the study of language comprehension in an “embodied” framework. Firstly I show behavioral evidence supporting the idea that language modulates the motor system in a specific way, both at a proximal level (sensibility to the effectors) and at the distal level (sensibility to the goal of the action in which the single motor acts are inserted). I will present two studies in which the method is basically the same: we manipulated the linguistic stimuli (the kind of sentence: hand action vs. foot action vs. mouth action) and the effector by which participants had to respond (hand vs. foot vs. mouth; dominant hand vs. non-dominant hand). Response times analyses showed a specific modulation depending on the kind of sentence: participants were facilitated in the task execution (sentence sensibility judgment) when the effector they had to use to respond was the same to which the sentences referred. Namely, during language comprehension a pre-activation of the motor system seems to take place. This activation is analogous (even if less intense) to the one detectable when we practically execute the action described by the sentence. Beyond this effector specific modulation, we also found an effect of the goal suggested by the sentence. That is, the hand effector was pre-activated not only by hand-action-related sentences, but also by sentences describing mouth actions, consistently with the fact that to execute an action on an object with the mouth we firstly have to bring it to the mouth with the hand. After reviewing the evidence on simulation specificity directly referring to the body (for instance, the kind of the effector activated by the language), I focus on the specific properties of the object to which the words refer, particularly on the weight. In this case the hypothesis to test was if both lifting movement perception and lifting movement execution are modulated by language comprehension. We used behavioral and kinematics methods, and we manipulated the linguistic stimuli (the kind of sentence: the lifting of heavy objects vs. the lifting of light objects). To study the movement perception we measured the correlations between the weight of the objects lifted by an actor (heavy objects vs. light objects) and the esteems provided by the participants. To study the movement execution we measured kinematics parameters variance (velocity, acceleration, time to the first peak of velocity) during the actual lifting of objects (heavy objects vs. light objects). Both kinds of measures revealed that language had a specific effect on the motor system, both at a perceptive and at a motoric level. Finally, I address the issue of the abstract words. Different studies in the “embodied” framework tried to explain the meaning of abstract words The limit of these works is that they account only for subsets of phenomena, so results are difficult to generalize. We tried to circumvent this problem by contrasting transitive verbs (abstract and concrete) and nouns (abstract and concrete) in different combinations. The behavioral study was conducted both with German and Italian participants, as the two languages are syntactically different. We found that response times were faster for both the compatible pairs (concrete verb + concrete noun; abstract verb + abstract noun) than for the mixed ones. Interestingly, for the mixed combinations analyses showed a modulation due to the specific language (German vs. Italian): when the concrete word precedes the abstract one responses were faster, regardless of the word grammatical class. Results are discussed in the framework of current views on abstract words. They highlight the important role of developmental and social aspects of language use, and confirm theories assigning a crucial role to both sensorimotor and linguistic experience for abstract words.

A multilevel converter structure for grid-connected PV plants

A new conversion structure for three-phase grid-connected photovoltaic (PV) generation plants is presented and discussed in this Thesis. The conversion scheme is based on two insulated PV arrays, each one feeding the dc bus of a standard 2-level three-phase voltage source inverter (VSI). Inverters are connected to the grid by a traditional three-phase transformer having open-end windings at inverters side and either star or delta connection at the grid side. The resulting conversion structure is able to perform as a multilevel VSI, equivalent to a 3-level inverter, doubling the power capability of a single VSI with given voltage and current ratings. Different modulation schemes able to generate proper multilevel voltage waveforms have been discussed and compared. They include known algorithms, some their developments, and new original approaches. The goal was to share the grid power with a given ratio between the two VSI within each cycle period of the PWM, being the PWM pattern suitable for the implementation in industrial DSPs. It has been shown that an extension of the modulation methods for standard two-level inverter can provide a elegant solution for dual two-level inverter. An original control method has been introduced to regulate the dc-link voltages of each VSI, according to the voltage reference given by a single MPPT controller. A particular MPPT algorithm has been successfully tested, based on the comparison of the operating points of the two PV arrays. The small deliberately introduced difference between two operating dc voltages leads towards the MPP in a fast and accurate manner. Either simulation or experimental tests, or even both, always accompanied theoretical developments. For the simulation, the Simulink tool of Matlab has been adopted, whereas the experiments have been carried out by a full-scale low-voltage prototype of the whole PV generation system. All the research work was done at the Lab of the Department of Electrical Engineering, University of Bologna.

The language of action. How language translates the dynamics of our actions.

The general aim of the thesis was to investigate how and to what extent the characteristics of action organization are reflected in language, and how they influence language processing and understanding. Even though a huge amount of research has been devoted to the study of the motor effects of language, this issue is very debated in literature. Namely, the majority of the studies have focused on low-level motor effects such as effector-relatedness of action, whereas only a few studies have started to systematically investigate how specific aspects of action organization are encoded and reflected in language. After a review of previous studies on the relationship between language comprehension and action (chapter 1) and a critical discussion of some of them (chapter 2), the thesis is composed by three experimental chapters, each devoted to a specific aspect of action organization. Chapter 3 presents a study designed with the aim to disentangle the effective time course of the involvement of the motor system during language processing. Three kinematics experiments were designed in order to determine whether and, at which stage of motor planning and execution effector-related action verbs influence actions executed with either the same or a different effector. Results demonstrate that the goal of an action can be linguistically re-activated, producing a modulation of the motor response. In chapter 4, a second study investigates the interplay between the role of motor perspective (agent) and the organization of action in motor chains. More specifically, this kinematics study aims at deepening how goal can be translated in language, using as stimuli simple sentences composed by a pronoun (I, You, He/She) and a verb. Results showed that the perspective activated by the pronoun You reflects the motor pattern of the “agent” combined with the chain structure of the verb. These data confirm an early involvement of the motor system in language processing, suggesting that it is specifically modulated by the activation of the agent’s perspective. In chapter 5, the issue of perspective is specifically investigated, focusing on its role in language comprehension. In particular, this study aimed at determining how a specific perspective (induced for example by a personal pronoun) modulates motor behaviour during and after language processing. A classical compatibility effect (the Action-sentence compatibility effect) has been used to this aim. In three behavioural experiments the authors investigated how the ACE is modulated by taking first or third person perspective. Results from these experiments showed that the ACE effect occurs only when a first-person perspective is activated by the sentences used as stimuli. Overall, the data from this thesis contributed to disentangle several aspects of how action organization is translated in language, and then reactivated during language processing. This constitutes a new contribution to the field, adding lacking information on how specific aspects such as goal and perspective are linguistically described. In addition, these studies offer a new point of view to understand the functional implications of the involvement of the motor system during language comprehension, specifically from the point of view of our social interactions.

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.

L'italiano di apprendenti lituani: elementi acquisizionali e implicazioni didattiche

La ricerca, che ha per oggetto lo studio dell’apprendimento guidato dell’italiano come lingua seconda da parte di apprendenti lituani, si articola in quattro capitoli. I primi due costituiscono il quadro teorico della ricerca, dedicando il primo ai fondamenti teorici e ricerche empiriche in generale e il secondo alle ricerche sull’apprendimento dell’italiano come L2. Nel terzo capitolo viene presentata la metodologia della ricerca, mentre nel quarto capitolo vengono presentati i risultati, concentrandosi in particolare sull’ortografia, sulla morfologia del nome, sulla categoria del verbo e sugli aspetti sintattici.In base ai risultati conseguiti, che in parte confermano i percorsi acquisizionali rilevati in contesto di apprendimento spontaneo, vengono all’ultimo suggerite alcune proposte applicative.

Non-Covalent Interaction: Revealed by Rotational Spectroscopy

The pulsed jet Fourier transform microwave spectroscopy have been applied to several molecular complexes involving H2O, freons, methane, carboxylic acids, and rare gas. The obtained results showcase the suitability of this technique for studying the intermolecular interactions. The rotational spectra of three water adducts of halogenated organic molecules, i.e. chlorotrifluoroethylene, isoflurane and alfa,alfa,alfa,-trifluoroanisole, have been investigated. It has been found that, the halogenation of the partner molecules definitely changes the way in which water will link to the partner molecule. Quadrupole hyperfine structures and/or the tunneling splittings have been observed in the rotational spectra of difluoromethane-dichloromethane, chlorotrifluorometane-fluoromethane, difluoromethane-formaldehyde and trifluoromethane-benzene. These features have been useful to describe their intermolecular interactions (weak hydrogen bonds or halogen bonds), and to size the potential energy surfaces of their internal motions. The rotational spectrum of pyridine-methane pointed out that methane prefers to locate above the ring and link to pyridine through a C-H•••π weak hydrogen bond, rather than the C-H•••n interaction. This behavior, typical of complexes of pyridine with rare gases, suggests classifying CH4, in relation to its ability to form molecular complexes with aromatic molecules, as a pseudo rare gas. The conformational equilibria of three bi-molecules of carboxylic acids, acrylic acid-trifluoroacetic acid, difluoroacetic acid-formic acid and acrylic acid-fluoroacetic acid have been studied. The increase of the hydrogen bond length upon H→D isotopic substitution (Ubbelohde effect) has been deduced from the elongation of the carboxylic carbons C•••C distance. The van der Waals complex tetrahydrofuran-krypton shows that the systematic doubling of the rotational lines has been attributed to the residual pseudo-rotation of tetrahydrofuran in the complex, based on the values of the Coriolis coupling constants, and on the type (mu_b) of the interstate transitions.

Catálogo y estudio de las gramáticas de italiano para hispanohablantes: siglos XVIII y XIX

El objetivo de la presente investigación, el catálogo y estudio de las gramáticas de italiano destinadas a hispanohablantes de los siglos XVIII y XIX, se encuadra en el macrosector gramaticográfico de la historiografía lingüística, en el cual el estudio de las gramáticas de las lenguas dirigidas a hablantes nativos y a hablantes extranjeros, con los consiguientes cruces y trasvases de tradiciones gramaticales, es de significativo interés como destacan: (i) las tesis doctorales defendidas en los últimos quince años; (ii) los proyectos de investigación dirigidos y coordinados por prestigiosos estudiosos del sector; (iii) los congresos organizados para destacar y compartir las principales actualizaciones en torno a los estudios gramaticográficos; y (iv) las publicaciones que surgen de los tres puntos anteriores. El estudio presenta dos partes centrales: la primera (constituida por los capítulos 2 y 3) es la de catálogo y estudio de las diecinueve gramáticas que conforman el corpus en base a ocho áreas descriptivas (1. información catalográfica, 2. autor, 3. editor, 4. hiperestructura, 5. elementos peritextuales, gramaticales y didácticos, 6. variedad de textos y su secuencia didáctica, 7. caracterización, fuentes e influencias, y 8. localización); la segunda (capítulo 4) es la de estudio gramaticográfico de conjunto de los datos más relevantes de las areas de estudio utilizadas en las dos primeras partes. De este modo, daremos un panorama de conjunto sobre (i) la cronología de las obras y sus ediciones y rempresiones; (ii) la nacionalidad, profesión, condición religiosa, etc. de autores; (iii) la geografía de ediciones y editores; (iv) la descripción hiperestructural de las obras; (v) la estructura de los elementos peritextuales; (vi) las partes gramaticales y elementos que las componen; (vii) el verbo: definiciones y paradigma verbal; (vii) los elementos didácticos; (viii) las líneas de descripción gramatical; (ix) la localización de las gramáticas en las bibliotecas españolas.

Prediction Nomogram for 68Ga-PSMA-11 PET/CT in different clinical settings of PSA failure after radical treatment for Prostate Cancer

Objective The objective of this study was to develop a clinical nomogram to predict gallium-68 prostate-specific membrane antigen positron emission tomography/computed tomography (68Ga-PSMA-11-PET/CT) positivity in different clinical settings of PSA failure. Materials and methods Seven hundred three (n = 703) prostate cancer (PCa) patients with confirmed PSA failure after radical therapy were enrolled. Patients were stratified according to different clinical settings (first-time biochemical recurrence [BCR]: group 1; BCR after salvage therapy: group 2; biochemical persistence after radical prostatectomy [BCP]: group 3; advanced stage PCa before second-line systemic therapies: group 4). First, we assessed 68Ga-PSMA-11-PET/CT positivity rate. Second, multivariable logistic regression analyses were used to determine predictors of positive scan. Third, regression-based coefficients were used to develop a nomogram predicting positive 68Ga-PSMA-11-PET/CT result and 200 bootstrap resamples were used for internal validation. Fourth, receiver operating characteristic (ROC) analysis was used to identify the most informative nomogram’s derived cut-off. Decision curve analysis (DCA) was implemented to quantify nomogram’s clinical benefit. Results 68Ga-PSMA-11-PET/CT overall positivity rate was 51.2%, while it was 40.3% in group 1, 54% in group 2, 60.5% in group 3, and 86.9% in group 4 (p < 0.001). At multivariable analyses, ISUP grade, PSA, PSA doubling time, and clinical setting were independent predictors of a positive scan (all p ≤ 0.04). A nomogram based on covariates included in the multivariate model demonstrated a bootstrap-corrected accuracy of 82%. The nomogram-derived best cut-off value was 40%. In DCA, the nomogram revealed clinical net benefit of > 10%. Conclusions This novel nomogram proved its good accuracy in predicting a positive scan, with values ≥ 40% providing the most informative cut-off in counselling patients to 68Ga-PSMA-11-PET/CT. This tool might be important as a guide to clinicians in the best use of PSMA-based PET imaging.

Способы лексикализации события движения в русском языке в сопоставлении с итальянским

В данной работе рассматривается лексикализация события движения в русском языке в сопоставлении с итальянским. Цель нашей работы двойная: с одной стороны, мы рассмотрим пространственную семантику выбранных нами глагольных префиксов и определим их семантический вклад в лексикализацию события движения. С другой стороны, мы проанализируем соответствия русских приставочных глаголов движения при переводе на итальянский язык. В частности, мы сосредоточимся на том, выражается ли вклад префикса, передается ли он полностью или частично, какие нюансы его пространственной семантики могут опускаться, а какие выражаются обязательно и какими языковыми средствами. Работа состоит из введения, трех глав и заключения. В Первой главе представляется теоретическая рамка, на которую опирается сопоставительный анализ. Рассматриваются понятия движения и перемещения согласно семантическим толкованиям, приведенным как в русскоязычной литературе, так и в работах на других языках. Кроме того, концептуализация пространства описывается в русле когнитивного подхода к изучению языка. Представлена классификация языков по лексикализации события движения, введенной Л. Талми, а также основные последующие исследования, посвященные лексикализации события движения в различных языках, проведенные в русле типологического подхода. Отдельный параграф первой главы посвящается вкладу исследований, проведенных Д. Слобиным в области лексикализации компонентов движения, в частности, способа движения в различных языках. Во Второй главе описываются система бесприставочных глаголов движения в русском языке и основные подходы к их изучению. Регулярно проводятся параллели с итальянской системой глаголов движения. Далее в этой главе представлен обзор системы приставочных глаголов движения русского языка. Отдельно мы рассматриваем главные подходы к изучению семантики глагольных префиксов, фокусируясь на их пространственных значениях. В Третьей главе представляется подбор глагольных префиксов с пространственной семантикой, выбранных для целей сопоставительного анализа. Для каждого префикса предлагается словарное толкование, описывается его пространственная семантика согласно концепциям, разработанным различными авторами, и проводится анализ контекстов употребления приставочных глаголов в русском языке и возможные стратегии их передачи на итальянский язык. Выводы изложены в заключении, прилагается также список литературы.