Towards NIR emission: 2-(1H-tetrazol-1-yl)pyridine as versatile ligand for the synthesis of two new families of cationic and neutral Ir(III) complexes.

In the last decades, cyclometalated Ir(III) complexes have drawn a large interest for their unique properties: they are excellent triplet state emitters, thus the emission is phosphorescent in nature; typically high quantum yields and good stability make them good candidates for luminescent materials. Moreover, through an opportune choice of the ligands, it is possible to tune the emission along the whole visible spectra. Thanks to these interesting features, Ir(III) complexes have found different applications in several areas of applied science, from OLEDs to bioimaging. In particular, regarding the second application, a remarkable red-shift in the emission is required, in order to minimize the problem of the tissue penetration and the possible damages for the organisms. With the aim of synthesizing a new family of NIR emitting Ir(III) complexes, we envisaged the possibility to use for the first time 2-(1H-tetrazol-1-yl)pyridine as bidentate ligand able to provide the required red-shift of the emission of the final complexes. Exploiting the versatility of the ligand, I prepared two different families of heteroleptic Ir(III) complexes. In detail, in the first case the 2-(1H-tetrazol-1-yl)pyridine was used as bis-chelating N^N ligand, leading to cationic complexes, while in the second case it was used as cyclometalating C^N ligand, giving neutral complexes. The structures of the prepared molecules have been characterised by NMR spectroscopy and mass spectrometry. Moreover, the neutral complexes’ emissive properties have been measured: emission spectra have been recorded in solution at both room temperature and 77K, as well as in PMMA matrix. DFT calculation has then been performed and the obtained results have been compared to experimental ones.

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.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.