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.

Application of different instrumental techniques to the selective evaluation of bio-sensible compounds in foodstuff of animal and vegetable origin

This PhD thesis describes the application of some instrumental analytical techniques suitable to the study of fundamental food products for the human diet, such as: extra virgin olive oil and dairy products. These products, widely spread in the market and with high nutritional values, are increasingly recognized healthy properties although their lipid fraction might contain some unfavorable components to the human health. The research activity has been structured in the following investigations: “Comparison of different techniques for trans fatty acids analysis” “Fatty acids analysis of outcrop milk cream samples, with particular emphasis on the content of Conjugated Linoleic Acid (CLA) and trans Fatty Acids (TFA), by using 100m high-polarity capillary column” “Evaluation of the oxidited fatty acids (OFA) content during the Parmigiano-Reggiano cheese seasoning” “Direct analysis of 4-desmethyl sterols and two dihydroxy triterpenes in saponified vegetal oils (olive oil and others) using liquid chromatography-mass spectrometry” “Quantitation of long chain poly-unsatured fatty acids (LC-PUFA) in base infant formulas by Gas Chromatography, and evaluation of the blending phases accuracy during their preparation” “Fatty acids composition of Parmigiano Reggiano cheese samples, with emphasis on trans isomers (TFA)”

Predictive Ability of NGAL as a Marker of Renal Damage: evaluation of Multiple Clinical Settings

Introduction. Neutrophil Gelatinase-Associated Lipocalin (NGAL) belongs to the family of lipocalins and it is produced by several cell types, including renal tubular epithelium. In the kidney its production increases during acute damage and this is reflected by the increase in serum and urine levels. In animal studies and clinical trials, NGAL was found to be a sensitive and specific indicator of acute kidney injury (AKI). Purpose. The aim of this work was to investigate, in a prospective manner, whether urine NGAL can be used as a marker in preeclampsia, kidney transplantation, VLBI and diabetic nephropathy. Materials and methods. The study involved 44 consecutive patients who received renal transplantation; 18 women affected by preeclampsia (PE); a total of 55 infants weighing ≤1500 g and 80 patients with Type 1 diabetes. Results. A positive correlation was found between urinary NGAL and 24 hours proteinuria within the PE group. The detection of higher uNGAL values in case of severe PE, even in absence of statistical significance, confirms that these women suffer from an initial renal damage. In our population of VLBW infants, we found a positive correlation of uNGAL values at birth with differences in sCreat and eGFR values from birth to day 21, but no correlation was found between uNGAL values at birth and sCreat and eGFR at day 7. systolic an diastolic blood pressure decreased with increasing levels of uNGAL. The patients with uNGAL <25 ng/ml had significantly higher levels of systolic blood pressure compared with the patients with uNGAL >50 ng/ml ( p<0.005). Our results indicate the ability of NGAL to predict the delay in functional recovery of the graft. Conclusions. In acute renal pathology, urinary NGAL confirms to be a valuable predictive marker of the progress and status of acute injury.

Development of instrumental and sensory analytical methods of food obtained by traditional and emerging technologies

The consumer demand for natural, minimally processed, fresh like and functional food has lead to an increasing interest in emerging technologies. The aim of this PhD project was to study three innovative food processing technologies currently used in the food sector. Ultrasound-assisted freezing, vacuum impregnation and pulsed electric field have been investigated through laboratory scale systems and semi-industrial pilot plants. Furthermore, analytical and sensory techniques have been developed to evaluate the quality of food and vegetable matrix obtained by traditional and emerging processes. Ultrasound was found to be a valuable technique to improve the freezing process of potatoes, anticipating the beginning of the nucleation process, mainly when applied during the supercooling phase. A study of the effects of pulsed electric fields on phenol and enzymatic profile of melon juice has been realized and the statistical treatment of data was carried out through a response surface method. Next, flavour enrichment of apple sticks has been realized applying different techniques, as atmospheric, vacuum, ultrasound technologies and their combinations. The second section of the thesis deals with the development of analytical methods for the discrimination and quantification of phenol compounds in vegetable matrix, as chestnut bark extracts and olive mill waste water. The management of waste disposal in mill sector has been approached with the aim of reducing the amount of waste, and at the same time recovering valuable by-products, to be used in different industrial sectors. Finally, the sensory analysis of boiled potatoes has been carried out through the development of a quantitative descriptive procedure for the study of Italian and Mexican potato varieties. An update on flavour development in fresh and cooked potatoes has been realized and a sensory glossary, including general and specific definitions related to organic products, used in the European project Ecropolis, has been drafted.

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.

Movement Analysis by means of inertial sensors: from bench to bedside

in the everyday clinical practice. Having this in mind, the choice of a simple setup would not be enough because, even if the setup is quick and simple, the instrumental assessment would still be in addition to the daily routine. The will to overcome this limit has led to the idea of instrumenting already existing and widely used functional tests. In this way the sensor based assessment becomes an integral part of the clinical assessment. Reliable and validated signal processing methods have been successfully implemented in Personal Health Systems based on smartphone technology. At the end of this research project there is evidence that such solution can really and easily used in clinical practice in both supervised and unsupervised settings. Smartphone based solution, together or in place of dedicated wearable sensing units, can truly become a pervasive and low-cost means for providing suitable testing solutions for quantitative movement analysis with a clear clinical value, ultimately providing enhanced balance and mobility support to an aging population.

Sensory and instrumental profiling of apples: a new tool for quality assessment

Food suppliers currently measure apple quality considering basic pomological descriptors. Sensory analysis is expensive, does not permit to analyse many samples, and cannot be implemented for measuring quality properties in real time. However, sensory analysis is the best way to precisely describe food eating quality, since it is able to define, measure, and explain what is really perceivable by human senses and using a language that closely reflects the consumers’ perception. On the basis of such observations, we developed a detailed protocol for apple sensory profiling by descriptive sensory analysis and instrumental measurements. The collected sensory data were validated by applying rigorous scientific criteria for sensory analysis. The method was then applied for studying sensory properties of apples and their changes in relation to different pre- and post-harvest factors affecting fruit quality, and demonstrated to be able to discriminate fruit varieties and to highlight differences in terms of sensory properties. The instrumental measurements confirmed such results. Moreover, the correlation between sensory and instrumental data was studied, and a new effective approach was defined for the reliable prediction of sensory properties by instrumental characterisation. It is therefore possible to propose the application of this sensory-instrumental tool to all the stakeholders involved in apple production and marketing, to have a reliable description of apple fruit quality.

A multi-instrumental approach to the study of equatorial ionosphere over South America

An extensive study of the morphology and the dynamics of the equatorial ionosphere over South America is presented here. A multi parametric approach is used to describe the physical characteristics of the ionosphere in the regions where the combination of the thermospheric electric field and the horizontal geomagnetic field creates the so-called Equatorial Ionization Anomalies. Ground based measurements from GNSS receivers are used to link the Total Electron Content (TEC), its spatial gradients and the phenomenon known as scintillation that can lead to a GNSS signal degradation or even to a GNSS signal ‘loss of lock’. A new algorithm to highlight the features characterizing the TEC distribution is developed in the framework of this thesis and the results obtained are validated and used to improve the performance of a GNSS positioning technique (long baseline RTK). In addition, the correlation between scintillation and dynamics of the ionospheric irregularities is investigated. By means of a software, here implemented, the velocity of the ionospheric irregularities is evaluated using high sampling rate GNSS measurements. The results highlight the parallel behaviour of the amplitude scintillation index (S4) occurrence and the zonal velocity of the ionospheric irregularities at least during severe scintillations conditions (post-sunset hours). This suggests that scintillations are driven by TEC gradients as well as by the dynamics of the ionospheric plasma. Finally, given the importance of such studies for technological applications (e.g. GNSS high-precision applications), a validation of the NeQuick model (i.e. the model used in the new GALILEO satellites for TEC modelling) is performed. The NeQuick performance dramatically improves when data from HF radar sounding (ionograms) are ingested. A custom designed algorithm, based on the image recognition technique, is developed to properly select the ingested data, leading to further improvement of the NeQuick performance.