<p>The recent state of art in the magnetic resonance area putsforward the electron paramagnetic resonance, EPR, and nuclearmagnetic resonance, NMR, experiments on prominent positions forinvestigations of molecular and electronic structure. A mostdifficult aspect of such experiments is usually the properinterpretation of data obtained from high-resolution spectra,that, however, at the same time opens a great challenge forpure theoretical methods to interpret the spectral features.This thesis constitutes an effort in this respect, as itpresents and discusses calculations of EPR and NMR parametersof paramagnetic molecules. The calculations are based on newmethodology for determination of properties of paramagneticmolecules in the framework of the density functional theory,which has been developed in our laboratory.</p><p>Paramagnetic molecules are, in some sense, very special. Thepresence of unpaired electrons essentially modifies theirspectra. The experimental determination of the magneticresonance parameters of such molecules is, especially in theNMR case, quite complicated and requires special techniques ofspectral detection. The significant efforts put into suchexperiments are completely justi fied though by the importantroles of paramagnetic species playing in many areas, such as,for example, molecular magnets, active centers in biologicalsystems, and defects in inorganic conductive materials.</p><p>The first two papers of this thesis deal with thetheoretical determination of NMR parameters, such as thenuclear shielding tensors and the chemical shifts, inparamagnetic nitroxides that form core units in molecularmagnets. The developed methodology aimed to realize highaccuracy in the calculations in order to achieve successfulapplications for the mentioned systems. Theeffects of hydrogenbonding are also described in that context. Our theory forevaluation of nuclear shielding tensors in paramagneticmolecules is consistent up to the second order in the finestructure constant and considers orbital, fully isotropicdipolar, and isotropic contact contributions to the shieldingtensor.</p><p>The next three projects concern electron paramagneticresonance. The wellknown EPR parameters, such as the g-tensorsand the hyperfine coupling constants are explored. Calculationsof electronic g-tensors were carried out in the framework of aspin-restricted open-shell Kohn-Sham method combined with thelinear response theory recently developed in our laboratory.The spincontamination problem is then automatically avoided.The solvent effects, described by the polarizable continuummodel, are also considered. For calculations of the hyperfinecoupling constants a so-called restricted-unrestricted approachhas been developed in the context of density functional theory.Comparison of experimentally and theoretically determinedparameters shows that qualitative mutual agreement of the twosets of data can be easily achieved by employing the proposedformalisms.</p>

The integrability of an m-component system of hydrodynamic type, Ut = v(u)ux, by the generalized hodograph method requires the diagonalizability of the m x m matrix v(u). The diagonalizability is known to be equivalent to the vanishing of the corresponding Haantjes tensor. This idea is applied to hydrodynamic chains - infinite-component systems of hydrodynamic type for which the 00 x 00 matrix v(u) is 'sufficiently sparse'. For such 'sparse' systems the Haantjes tensor is well-defined, and the calculation of its components involves only a finite number of summations. The calculation of the Haantjes tensor is done by using Mathematica to perform symbolic calculations. Certain conservative and Hamiltonian hydrodynamic chains are classified by setting Haantjes tensor equal to zero and solving the resulting system of equations. It is shown that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability of such sysyems. In the cases of the Hamiltonian hydrodynamic chains we were able to first construct one extra conservation law and later a generating function for conservation laws, thus establishing the integrability.

Tensor products of Banach Spaces are studied. An introduction to tensor products is given. Some results concerning the reciprocal Dunford-Pettis Property due to Emmanuele are presented. Pelczyriski's property (V) and (V)-sets are studied. It will be shown that if X and Y are Banach spaces with property (V) and every integral operator from X into Y* is compact, then the (V)-subsets of (X⊗F)* are weak* sequentially compact. This in turn will be used to prove some stronger convergence results for (V)-subsets of C(Ω,X)*.

Neste trabalho, fazemos um estudo dos campos tensoriais antissimétricos em geral e, em particular, do campo tensorial antissimétrico de ordem dois. Utilizando o método de quantização BRST-BFV para teorias redutíveis no formalismo hamiltoniano, mostramos a equivalência quântica do campo tensorial antissimétrico de ordem dois não-massivo ao campo escalar em 4 dimensões e ao campo vetorial no gauge de Lorentz em 5 dimensões. Também é mostrada a equivalência entre as formulações de 1ª e 2ª ordem do campo tensorial antissimétrico de ordem dois. Por fim, é efetuada a quantização BRST-BFV de um modelo de partícula relativística com spin com duas supersimetrias acrescido de um termo Chern-Simons, mostrando que a amplitude de transição obtida equivale à amplitude de transição do \"rotacional\" de um campo tensorial antissimétrico de ordem qualquer. O caso massivo também é tratado brevemente. / In this work, we make a study of anti symmetric tensor fields in general, and, in particular, of the anti symmetric tensor fields of order two. Using the BRST-BFV quantization method for reducible theories in the Hamiltonian formalism, we show the quantum equivalence of the massless anti symmetric tensor field of order two to the scalar field in 4 dimensions, and to the vector field in the Lorentz gauge in 5 dimensions. It is also shown the quantum equivalence between the 1st and 2nd order formulations for the anti symmetric tensor field of order two. Finally, it is made the BRST-BFV quantization of a model of relativistic spinning particle with two super symmetries with a Chern-Simons term, showing that the transition amplitude obtained is equivalent to the transition amplitude for the field strength of an anti symmetric tensor field of any order. The massive case is also treated in breaf.

Esclerose Múltipla (MS) é uma doença neurodegenerativa que tem ganhado grande atenção nas últimas décadas, sendo o diagnóstico por imagens de ressonância magnética (MRI) um grande aliado para a avaliação da doença.Porém, um dos principais desafios é garantir uma maior sensibilidade e especificidade para detecção de diferentes lesões no sistema nervoso central (CNS) e assim classificar as diferentes variantes da MS, auxiliando na tomada de decisão para o tratamento farmacológico. Nas últimas décadas, a técnica de imagens ponderadas por difusão (DWI), em especial a técnica de imagem por tensor de difusão (DTI), têm sido evidenciada com grande potencial para o estudo da MS, apresentando uma melhora significativa para a detecção de lesões sutis, ainda em estágios iniciais da MS. Desta forma, as técnicas de processamento de imagens estão em constante aprimoramento para que sejam adaptados às novas modalidades de aquisição de imagens. Neste estudo focamos o desenvolvimento de uma técnica de processamento digital de imagens multimodais a fim de proporcionar uma solução viável para a rotina de diagnóstico por imagem em MS. Um conjunto de 25 pacientes de uma variante de MS foi selecionado aleatoriamente do banco de imagens do HCFMRP. Três modalidades de imagens foram coletadas para a avaliação da segmentação automatica (T1, T2-FLAIR e DTI), assim como a segmentação manual do especialista para cada paciente. Três métodos de segmentação multimodal automática de lesões foram analisados (Bayesiano, Frequentista e Agrupamento) afim de analisar a sensibilidade e especificidade de detecção de lesões na substância branca aparentemente normal (NAWM). Os resultados sugerem que o método de segmentação Bayesiano apresenta maior robustes e precisão na definição tanto de lesões visivelmente contrastantes em T1 e T2-FLAIR (i.e. lesões hipo e hiperintensas) assim como lesões da NAWM evidentes nos mapas quantitativos de DTI (FA e ADC). O erro associado à técninca automática de segmentação ficou em torno de 1.51 +- 0.51 % do volume total de lesões marcadas pelo especialista. Concluímos que o uso de ferramentas multimodais de segmentação de imagens MRI alcançou patamares razoáveis de detecção de lesões de MS, tornando assim uma ferramenta computacional hábil para uso no diagnóstico clínico. / Multiple sclerosis (MS) is a neurodegenerative disease that has gained great attention in the last decades, which magnetic resonance imaging (MRI) have shown as an important tool for the disease evaluation. However, one of the main challenges is guaranteeing greater lesion detection sensitivity and specificity in the whole central nervous system (CNS) and thus classify the different variants of MS, which aids in decision making for pharmacological treatment. In the last decades, the diffusion-weighted imaging (DWI) technique, especially the diffusion tensor imaging approach (DTI), has been evidenced with great potential for the study of MS, presenting a significant improvement for the detection of lesions even in early stages of MS. Hence, the techniques of image processing are constantly improving in order to be adapted on a multimodal image evaluation. In this study, the development of a multimodal digital image processing technique to provide a viable solution to the MS imaging routine was focused. A set of 25 patients from a MS variant was randomly selected from the HCFMRP imaging database. Three MR imaging modalities were collected for the evaluation of our automatic segmentation (T1, T2-FLAIR and DTI), as well as manual segmentation of the specialist for each patient. Three methods of automatic multimodal segmentation of MS lesions were analyzed (Bayesian, Frequentist and Clustering) in order to analyze the sensitivity and specificity of lesion detection in the apparently normal white matter (NAWM). The results suggest that the Bayesian segmentation method presented greater robustness and precision in the definition of visibly contrasting lesions in T1 and T2-FLAIR (i.e. hypo and hyperintense lesions) as well as NAWM lesions that are evident in quantitative DTI (FA and ADC). The error associated with the automatic segmentation technique was around 1.51 +- 0.51 % of the total lesion volume being evaluated by the a specialist. We conclude that the use of multimodal MRI images can be used in an automatic segmentation tools, reaching reasonable levels of MS lesion detection, thus making it a useful tool for clinical diagnosis.

Neste trabalho, fazemos um estudo dos campos tensoriais antissimétricos em geral e, em particular, do campo tensorial antissimétrico de ordem dois. Utilizando o método de quantização BRST-BFV para teorias redutíveis no formalismo hamiltoniano, mostramos a equivalência quântica do campo tensorial antissimétrico de ordem dois não-massivo ao campo escalar em 4 dimensões e ao campo vetorial no gauge de Lorentz em 5 dimensões. Também é mostrada a equivalência entre as formulações de 1ª e 2ª ordem do campo tensorial antissimétrico de ordem dois. Por fim, é efetuada a quantização BRST-BFV de um modelo de partícula relativística com spin com duas supersimetrias acrescido de um termo Chern-Simons, mostrando que a amplitude de transição obtida equivale à amplitude de transição do \"rotacional\" de um campo tensorial antissimétrico de ordem qualquer. O caso massivo também é tratado brevemente. / In this work, we make a study of anti symmetric tensor fields in general, and, in particular, of the anti symmetric tensor fields of order two. Using the BRST-BFV quantization method for reducible theories in the Hamiltonian formalism, we show the quantum equivalence of the massless anti symmetric tensor field of order two to the scalar field in 4 dimensions, and to the vector field in the Lorentz gauge in 5 dimensions. It is also shown the quantum equivalence between the 1st and 2nd order formulations for the anti symmetric tensor field of order two. Finally, it is made the BRST-BFV quantization of a model of relativistic spinning particle with two super symmetries with a Chern-Simons term, showing that the transition amplitude obtained is equivalent to the transition amplitude for the field strength of an anti symmetric tensor field of any order. The massive case is also treated in breaf.

The inflationary paradigm is one which was designed to answer questions that arose from classical Hot Big Bang cosmology. The period of rapid expansion in the early Universe provides a mechanism to solve the flatness, horizon and relic problems. More importantly, since the theory was first introduced it has been realised that it also provides a mechanism to generate the initial perturbations from which structure in the Universe can grow. In the zoo of potential inflationary models there is a dominant class: slow-roll inflation. The idea that the energy density of the inflationary field is dominated by its potential highly simplifies the calculations required to predict observable quantities. This simplification relies on all the information required to know the subsequent dynamics of the field to be encoded in the space Φ-Φ̇; it must be an effective phase space. I show that Φ-Φ̇ can be considered to be such a space for the most general scalar-tensor theory which gives second-order equations of motion: Horndeski theory. There are theoretical issues associated with this reduction that are illuminated through specific examples in which they occur. A theoretical issue with inflation is that there is an overabundance of models, with some capable of predicting any value of the possible observables. The second block of work in this thesis looks at a particular set of models that make the same observational prediction. These 'attractor' models utilise a non-minimal coupling between the inflationary fields and gravity and are studied in depth, both in the case of one and several fields. Firstly, I examine the Universal Attractors, a single field subset of these models. I show, in detail, the observational prediction such a model makes in the case of a strong non-minimal coupling and then examine the constraints it would be possible to put on such a coupling if a confirmed detection of primordial gravitational waves was made. Despite the discussion existing in the literature there is a small deviation of the Universal Attractor models from the predictions of the Starobinsky model. Furthermore, the coupling, ξ is found to be constrained so that |ξ| < 1 in the case where there a level of detectable primordial tensor modes. While the attractor models have an effective one-field description in reality there are several other fields that are assumed to be fixed during the inflationary phase. This claim requires careful examination as the field-space of the models generally is not flat. This curvature can cause a destabilising effect with certain parameters and so I investigate how susceptible the α-attractors and related models are to the destabilisation. A key result of this chapter is to highlight how important it is to not rely on the slow-roll approximation when assessing the effect of the instability, as the region where the effect begins to become large corresponds with the region where slow-roll begins to break down. Assuming the slow-roll approximation is valid leads to an over-estimation of the effect that the instability mechanism has. Despite this, some of the models considered are seen to experience the instability for certain ranges of model parameters. Making the assumption that any occurrence of the instability will, at the very least, move the observational prediction of the model outside the currently constrained range allows a constraint on the model parameter in question which directly translates to a theoretical lower bound on the tensor-scalar ratio, r > 0.0005.

<p>This thesis describes new methods for automatic crack detection in pavements. Cracks in pavements can be used as an early indication for the need of reparation. </p><p>Automatic crack detection is preferable compared to manual inventory; the repeatability can be better, the inventory can be done at a higher speed and can be done without interruption of the traffic. </p><p>The automatic and semi-automatic crack detection systems that exist today use Image Analysis methods. There are today powerful methods available in the area of Computer Vision. These methods work in higher dimensions with greater complexity and generate measures of local signal properties, while Image Analyses methods for crack detection use morphological operations on binary images. </p><p>Methods for digitalizing video data on VHS-cassettes and stitching images from nearby frames have been developed. </p><p>Four methods for crack detection have been evaluated, and two of them have been used to form a crack detection and classification program implemented in the calculation program Matlab. </p><p>One image set was used during the implementation and another image set was used for validation. The crack detection system did perform correct detection on 99.2 percent when analysing the images which were used during implementation. The result of the crack detection on the validation data was not very good. When the program is being used on data from other pavements than the one used during implementation, information about the surface texture is required to calibrate the crack detection.</p>

This thesis describes new methods for automatic crack detection in pavements. Cracks in pavements can be used as an early indication for the need of reparation. Automatic crack detection is preferable compared to manual inventory; the repeatability can be better, the inventory can be done at a higher speed and can be done without interruption of the traffic. The automatic and semi-automatic crack detection systems that exist today use Image Analysis methods. There are today powerful methods available in the area of Computer Vision. These methods work in higher dimensions with greater complexity and generate measures of local signal properties, while Image Analyses methods for crack detection use morphological operations on binary images. Methods for digitalizing video data on VHS-cassettes and stitching images from nearby frames have been developed. Four methods for crack detection have been evaluated, and two of them have been used to form a crack detection and classification program implemented in the calculation program Matlab. One image set was used during the implementation and another image set was used for validation. The crack detection system did perform correct detection on 99.2 percent when analysing the images which were used during implementation. The result of the crack detection on the validation data was not very good. When the program is being used on data from other pavements than the one used during implementation, information about the surface texture is required to calibrate the crack detection.

The dielectric tensor of Ga2O3 in the monoclinic (β) phasewas determined by generalized spectroscopic ellipsometry in a wide spectral range from 0.5 eV to 8.5 eV as well as by density functional theory calculations combined with many-body perturbation theory including quasiparticle and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to |εxz| ≈ 0.30 and cannot be neglected. Even in the transparent spectral range where it is quite small (|εxz| < 0.02) it causes a rotation of the dielectric axes around the symmetry axis of up to 20◦.