Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

Extraction of antioxidants from corn by-products for applications in bio-based polymer matrices

The objective of this dissertation is the evaluation of the exploitability of corn cobs as natural additives for bio-based polymer matrices, in order to hone their properties while keeping the fundamental quality of being fully bio-derived. The first part of the project has the purpose of finding the best solvent and conditions to extract antioxidants and anti-degrading molecules from corn cobs, exploiting room and high-temperature processes, traditional and advanced extraction methods, as well as polar and nonpolar solvents. The extracts in their entirety are then analysed to evaluate their antioxidant content, in order to select the conditions able to maximise their anti-degrading properties. The second part of the project, instead, focuses on assessing chemical and physical properties of the best-behaving extract when inserted in a polymeric matrix. To achieve this, low-density polyethylene (LDPE) and poly (butylene succinate – co – adipate) (PBSA) are employed. These samples are obtained through extrusion and are subsequently characterised exploiting the DSC equipment and a sinusoidally oscillating rheometer. In addition, extruded polymeric matrices are subjected to thermal and photo ageing, in order to identify their behaviour after different forms of degradation and to assess their performances with respect to synthetically produced anti-degrading additives.

(In)Visibili. Difficoltà, scelte e implicazioni nella mediazione nazionale dei personaggi non-binary

Con il progressivo aumentare del numero di personaggi non-binary nelle serie televisive in lingua inglese, dal punto di vista della mediazione nazionale italiana si va a delineare un interessante campo di studio, determinato dallo scontro fra la predilezione, da parte di questi personaggi, di pronomi ed espressioni neutre e la struttura grammaticale italiana, basata, invece, sull’esclusiva contrapposizione fra maschile e femminile. Il presente elaborato, allora, si pone l’obiettivo di individuare, attraverso una selezione di casi di studio, le difficoltà che sorgono automaticamente nel momento della realizzazione dell’edizione italiana di queste serie, le strategie adottate ai fini di rendere neutro il linguaggio italiano e le loro implicazioni nei confronti dei personaggi non-binary. Il metodo di studio consiste nel confronto fra la versione originale e l’edizione italiana (comprensiva di doppiaggio e sottotitoli) delle battute relative ai personaggi non binari di riferimento, con conseguente analisi delle differenze e somiglianze rilevate. I tre casi presi in considerazione nel corso della trattazione (Sex Education, One Day at a Time e Grey’s Anatomy) permettono, in definitiva, di individuare come rischio primario l’invisibilità del non binarismo di genere agli occhi e alle orecchie degli spettatori italiani e, così, lo snaturamento dell’intento e del valore dell’edizione originale.