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.

Modello bayesiano per la riduzione dell'incertezza nella previsione delle piene del fiume Reno

Many efforts have been devoting since last years to reduce uncertainty in hydrological modeling predictions. The principal sources of uncertainty are provided by input errors, for inaccurate rainfall prediction, and model errors, given by the approximation with which the water flow processes in the soil and river discharges are described. The aim of the present work is to develop a bayesian model in order to reduce the uncertainty in the discharge predictions for the Reno river. The ’a priori’ distribution function is given by an autoregressive model, while the likelihood function is provided by a linear equation which relates observed values of discharge in the past and hydrological TOPKAPI model predictions obtained by the rainfall predictions of the limited-area model COSMO-LAMI. The ’a posteriori’ estimations are provided throw a H∞ filter, because the statistical properties of estimation errors are not known. In this work a stationary and a dual adaptive filter are implemented and compared. Statistical analysis of estimation errors and the description of three case studies of flood events occurred during the fall seasons from 2003 to 2005 are reported. Results have also revealed that errors can be described as a markovian process only at a first approximation. For the same period, an ensemble of ’a posteriori’ estimations is obtained throw the COSMO-LEPS rainfall predictions, but the spread of this ’a posteriori’ ensemble is not enable to encompass observation variability. This fact is related to the building of the meteorological ensemble, whose spread reaches its maximum after 5 days. In the future the use of a new ensemble, COSMO–SREPS, focused on the first 3 days, could be helpful to enlarge the meteorogical and, consequently, the hydrological variability.

Studio e messa a punto del modello maximum-slope per l'analisi dei parametri perfusionali da sequenza di immagini tomografiche

Miglioramento delle prestazioni del modello mono-compartimentale del maximum slope dovuto all'introduzione di sistemi per l'eliminazione degli outliers.

Sviluppo di sistemi per l'analisi della combustione in tempo reale per motori endotermici alternativi

I moderni motori a combustione interna diventano sempre più complessi L'introduzione della normativa antinquinamento EURO VI richiederà una significativa riduzione degli inquinanti allo scarico. La maggiore criticità è rappresentata dalla riduzione degli NOx per i motori Diesel da aggiungersi a quelle già in vigore con le precedenti normative. Tipicamente la messa a punto di una nuova motorizzazione prevede una serie di test specifici al banco prova. Il numero sempre maggiore di parametri di controllo della combustione, sorti come conseguenza della maggior complessità meccanica del motore stesso, causa un aumento esponenziale delle prove da eseguire per caratterizzare l'intero sistema. L'obiettivo di questo progetto di dottorato è quello di realizzare un sistema di analisi della combustione in tempo reale in cui siano implementati diversi algoritmi non ancora presenti nelle centraline moderne. Tutto questo facendo particolare attenzione alla scelta dell'hardware su cui implementare gli algoritmi di analisi. Creando una piattaforma di Rapid Control Prototyping (RCP) che sfrutti la maggior parte dei sensori presenti in vettura di serie; che sia in grado di abbreviare i tempi e i costi della sperimentazione sui motopropulsori, riducendo la necessità di effettuare analisi a posteriori, su dati precedentemente acquisiti, a fronte di una maggior quantità di calcoli effettuati in tempo reale. La soluzione proposta garantisce l'aggiornabilità, la possibilità di mantenere al massimo livello tecnologico la piattaforma di calcolo, allontanandone l'obsolescenza e i costi di sostituzione. Questa proprietà si traduce nella necessità di mantenere la compatibilità tra hardware e software di generazioni differenti, rendendo possibile la sostituzione di quei componenti che limitano le prestazioni senza riprogettare il software.

Immunomodulatory therapy to achieve maximum efficacy: doses, monitoring, compliance, and self-infusion at home

The Oxford Programme for Immunomodulatory Immunoglobulin Therapy has been operating since 1992 at Oxford Radcliffe Hospitals in the UK. Initially, this program was set up for patients with multifocal motor neuropathy or chronic inflammatory demyelinating poly-neuropathy to receive reduced doses of intravenous immunoglobulin (IVIG) in clinic on a regular basis (usually every 3 weeks). The program then rapidly expanded to include self-infusion at home, which monitoring showed to be safe and effective. It has been since extended to the treatment of other autoimmune diseases in which IVIG has been shown to be efficacious.

Maximum flight velocity of blood drops in analysing blood traces

When analysing blood spatters, traces often occur which regarding the collision angle, cannot be allocated to any supposed centre of origin. Drops following highly curved (ballistic) trajectories usually form these types of traces. The reconstruction of such trajectories requires knowledge of the mass, the diameter (of which approximations are known) and the velocity of the blood drops. This article provides an upper range of the velocity in relation to the diameter of the blood drops based on physical laws. This is very helpful in analysing ballistic trajectories.

Early last glacial maximum in the southern Central Andes reveals northward shift of the westerlies at similar to 39 ka

The latitudinal position of the southern westerlies has been suggested to be a key parameter for the climate on Earth. According to the general notion, the southern westerlies were shifted equatorward during the global Last Glacial Maximum (LGM: ~24–18 ka), resulting in reduced deep ocean ventilation, accumulation of old dissolved carbon, and low atmospheric CO2 concentrations. In order to test this notion, we applied surface exposure dating on moraines in the southern Central Andes, where glacial mass balances are particularly sensitive to changes in precipitation, i.e. to the latitudinal position of the westerlies. Our results provide robust evidence that the maximum glaciation occurred already at ~39 ka, significantly predating the global LGM. This questions the role of the westerlies for atmospheric CO2, and it highlights our limited understanding of the forcings of atmospheric circulation.

A randomized comparison of microtip and air-charged catheter for the measurement of maximum urethral closure pressure

Measurements of maximum urethral closure pressure (MUCP) are a part of urodynamic investigations preceding an incontinence surgery and a part of urethral function tests.