Tetrafenilciclopentadienon-derivati ed analoghi: sintesi, "self-assembly" e caratterizzazione reologica

Gels are materials that are easier to recognize than to define. For all practical purpose, a material is termed a gel if the whole volume of liquid is completely immobilized as usually tested by the ‘tube inversion’ method. Recently, supramolecular gels obtained from low molecular weight gelators (LMWGs) have attracted considerable attention in materials science since they represent a new class of smart materials sensitive to external stimuli, such as temperature, ultrasounds, light, chemical species and so on. Accordingly, during the past years a large variety of potentialities and applications of these soft materials in optoelectronics, as electronic devices, light harvesting systems and sensors, in bio-materials and in drug delivery have been reported. Spontaneous self-assembly of low molecular weight molecules is a powerful tool that allows complex supramolecular nanoscale structures to be built. The weak and non-covalent interactions such as hydrogen bonding, π–π stacking, coordination, electrostatic and van der Waals interactions are usually considered as the most important features for promoting sol-gel equilibria. However, the occurrence of gelation processes is ruled by further “external” factors, among which the temperature and the nature of the solvents that are employed are of crucial importance. For example, some gelators prefer aromatic or halogenated solvents and in some cases both the gelation temperature and the type of the solvent affect the morphologies of the final aggregation. Functionalized cyclopentadienones are fascinating systems largely employed as building blocks for the synthesis of polyphenylene derivatives. In addition, it is worth noting that structures containing π-extended conjugated chromophores with enhanced absorption properties are of current interest in the field of materials science since they can be used as “organic metals”, as semiconductors, and as emissive or absorbing layers for OLEDs or photovoltaics. The possibility to decorate the framework of such structures prompted us to study the synthesis of new hydroxy propargyl arylcyclopentadienone derivatives. Considering the ability of such systems to give π–π stacking interactions, the introduction on a polyaromatic structure of polar substituents able to generate hydrogen bonding could open the possibility to form gels, although any gelation properties has been never observed for these extensively studied systems. we have synthesized a new class of 3,4-bis (4-(3-hydroxy- propynyl) phenyl) -2, 5-diphenylcyclopentadienone derivatives, one of which (1a) proved to be, for the first time, a powerful organogelator. The experimental results indicated that the hydroxydimethylalkynyl substituents are fundamental to guarantee the gelation properties of the tetraarylcyclopentadienone unit. Combining the results of FT-IR, 1H NMR, UV-vis and fluorescence emission spectra, we believe that H-bonding and π–π interactions are the driving forces played for the gel formation. The importance of soft materials lies on their ability to respond to external stimuli, that can be also of chemical nature. In particular, high attention has been recently devoted to anion responsive properties of gels. Therefore the behaviour of organogels of 1a in toluene, ACN and MeNO2 towards the addition of 1 equivalent of various tetrabutylammonium salts were investigated. The rheological properties of gels in toluene, ACN and MeNO2 with and without the addition of Bu4N+X- salts were measured. In addition a qualitative analysis on cation recognition was performed. Finally the nature of the cyclic core of the gelator was changed in order to verify how the carbonyl group was essential to gel solvents. Until now, 4,5-diarylimidazoles have been synthesized.

The Feynman-Kac formula and applications to PDEs

The thesis presents a probabilistic approach to the theory of semigroups of operators, with particular attention to the Markov and Feller semigroups. The first goal of this work is the proof of the fundamental Feynman-Kac formula, which gives the solution of certain parabolic Cauchy problems, in terms of the expected value of the initial condition computed at the associated stochastic diffusion processes. The second target is the characterization of the principal eigenvalue of the generator of a semigroup with Markov transition probability function and of second order elliptic operators with real coefficients not necessarily self-adjoint. The thesis is divided into three chapters. In the first chapter we study the Brownian motion and some of its main properties, the stochastic processes, the stochastic integral and the Itô formula in order to finally arrive, in the last section, at the proof of the Feynman-Kac formula. The second chapter is devoted to the probabilistic approach to the semigroups theory and it is here that we introduce Markov and Feller semigroups. Special emphasis is given to the Feller semigroup associated with the Brownian motion. The third and last chapter is divided into two sections. In the first one we present the abstract characterization of the principal eigenvalue of the infinitesimal generator of a semigroup of operators acting on continuous functions over a compact metric space. In the second section this approach is used to study the principal eigenvalue of elliptic partial differential operators with real coefficients. At the end, in the appendix, we gather some of the technical results used in the thesis in more details. Appendix A is devoted to the Sion minimax theorem, while in appendix B we prove the Chernoff product formula for not necessarily self-adjoint operators.

Fractal sets and their applications in medicine

La geometria euclidea risulta spesso inadeguata a descrivere le forme della natura. I Frattali, oggetti interrotti e irregolari, come indica il nome stesso, sono più adatti a rappresentare la forma frastagliata delle linee costiere o altri elementi naturali. Lo strumento necessario per studiare rigorosamente i frattali sono i teoremi riguardanti la misura di Hausdorff, con i quali possono definirsi gli s-sets, dove s è la dimensione di Hausdorff. Se s non è intero, l'insieme in gioco può riconoscersi come frattale e non presenta tangenti e densità in quasi nessun punto. I frattali più classici, come gli insiemi di Cantor, Koch e Sierpinski, presentano anche la proprietà di auto-similarità e la dimensione di similitudine viene a coincidere con quella di Hausdorff. Una tecnica basata sulla dimensione frattale, detta box-counting, interviene in applicazioni bio-mediche e risulta utile per studiare le placche senili di varie specie di mammiferi tra cui l'uomo o anche per distinguere un melanoma maligno da una diversa lesione della cute.

Machine Learning Unsupervised Methods in the Design of an On-board Health Monitoring System for Satellite Applications

The dissertation starts by providing a description of the phenomena related to the increasing importance recently acquired by satellite applications. The spread of such technology comes with implications, such as an increase in maintenance cost, from which derives the interest in developing advanced techniques that favor an augmented autonomy of spacecrafts in health monitoring. Machine learning techniques are widely employed to lay a foundation for effective systems specialized in fault detection by examining telemetry data. Telemetry consists of a considerable amount of information; therefore, the adopted algorithms must be able to handle multivariate data while facing the limitations imposed by on-board hardware features. In the framework of outlier detection, the dissertation addresses the topic of unsupervised machine learning methods. In the unsupervised scenario, lack of prior knowledge of the data behavior is assumed. In the specific, two models are brought to attention, namely Local Outlier Factor and One-Class Support Vector Machines. Their performances are compared in terms of both the achieved prediction accuracy and the equivalent computational cost. Both models are trained and tested upon the same sets of time series data in a variety of settings, finalized at gaining insights on the effect of the increase in dimensionality. The obtained results allow to claim that both models, combined with a proper tuning of their characteristic parameters, successfully comply with the role of outlier detectors in multivariate time series data. Nevertheless, under this specific context, Local Outlier Factor results to be outperforming One-Class SVM, in that it proves to be more stable over a wider range of input parameter values. This property is especially valuable in unsupervised learning since it suggests that the model is keen to adapting to unforeseen patterns.