Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.

The research presented in this thesis was carried out as part of a collaboration between the groups of Dr Tanja van Mourik at the School of Chemistry, University of St Andrews and Professor Jonathan Tennyson at the Department of Physics and Astronomy at University College London. This thesis presents State-Averaged Complete Active Space Self Consistent Field (SA-CASSCF) calculations on nucleic acid bases, deoxyribose and phosphoric acid H₃PO₄). In the case of uracil, for comparison, Multireference Configuration Interaction calculations were also performed. The SA-CASSCF orbitals were subsequently used in R-matrix electron scattering calculations using the close-coupling model. Of major importance for obtaining accurate SA-CASSCF results is the choice of the active space and the number of calculated states. Properties such as the electronic energy, number of configurations, excitation energy and dipole moment were considered in the choice of active space. Electron-collision calculations were performed on two of the most stable isomers of phosphoric acid, a weakly dipolar form with all OH groups pointing up and a strongly dipolar form where one OH group points down. A broad shape resonance at about 7 eV was found for both isomers. Ten-state close-coupling calculations suggest the presence of narrow, Feshbach resonances in a similar energy region. Elastic and electronically inelastic cross sections were calculated for both isomers. The R-matrix calculations on uracil were done by the group from UCL. R-matrix calculations are currently being done on guanine. Scattering calculations on the other DNA bases will be performed in the near future.

Approved for public release, distribution is unlimited / Radar polarimetry is a recent development seeing active research only in the last few decades. The phenomenon that optimal (maximal power) reflected fields exist in both the co-polarized and cross polarized channels of the receiving radar antenna was first introduced by Kennaugh and Huynen. Current research efforts focus on target scattering matrices and relating them to physical attributes of the target. This thesis provides a comprehensive survey of the polarimetry theories that have been put forth by various researchers to characterize, manipulate and optimize target radar returns via polarization states. One such theory is the Target Decomposition (TD) theorem that seeks to decompose the target returns into individual scattering mechanisms. The topic of optimization of polarization states of the incident field for maximizing power return is also examined. Two models are implemented in Matlab to verify and demonstrate these polarimetry theories. The first model uses TD theorems to simulate foliage clutter and study its effect on the polarization of the incident electric field. A (simulated) static dihedral target is introduced and its effect on wave polarization is also simulated. The second model studies optimization of polarization states. Both models are able to produce the expected results for known canonical targets. / Civilian, Republic of Singapore

Dans cette thèse, nous considérons le problème de la localisation de source dans les grands réseaux de capteurs, quand le nombre d'antennes du réseau et le nombre d'échantillons du signal observé sont grands et du même ordre de grandeur. Nous considérons le cas où les signaux source émis sont déterministes, et nous développons un algorithme de localisation amélioré, basé sur la méthode MUSIC. Pour ce faire, nous montrons de nouveaux résultats concernant la localisation des valeurs propres des grandes matrices aléatoires gaussiennes complexes de type information plus bruit / In this thesis, we consider the problem of source localization in large sensor networks, when the number of antennas of the network and the number of samples of the observed signal are large and of the same order of magnitude. We also consider the case where the source signals are deterministic, and we develop an improved algorithm for source localization, based on the MUSIC method. For this, we fist show new results concerning the position of the eigen values of large information plus noise complex gaussian random matrices

La théorie des processus de branchement multi-type en environnement i.i.d. est considérablement moins développée que dans le cas univarié, et les questions fondamentales ne sont pas résolues en totalité à ce jour. Les réponses exigent une compréhension profonde du comportement des produits des matrices i.i.d. à coefficients positifs. Sous des hypothèses assez générales et lorsque les fonctions génératrices de probabilité des lois de reproduction sont “linéaire fractionnaires”, nous montrons que la probabilité de survie à l’instant n du processus de branchement multi-type en environnement aléatoire est proportionnelle à 1/√n lorsque n → ∞. La démonstration de ce résultat suit l’approche développée pour étudier les processus de branchement uni-variés en environnement aléatoire i. i. d. Il utilise de façon cruciale des résultats récents portant sur les fluctuations des normes de produits de matrices aléatoires i.i.d. / The theory of multi-type branching process in i.i.d. environment is considerably less developed than for the univariate case, and fundamental questions are up to date unsolved. Answers demand a solid understanding of the behavior of products of i.i.d. matrices with non-negative entries. Under mild assumptions, when the probability generating functions of the reproduction laws are fractional-linear, the survival probability of the multi-type branching process in random environment up to moment n is proportional to 1/√n as n → ∞. Techniques for univariate branching process in random environment and methods from the theory of products of i.i.d. random matrices are required.

O objetivo deste trabalho é comparar as estruturas de vizinhanças espaciais ou matrizes de pesos espaciais da classe de modelos autorregressivos e de médias móveis espaço-temporais (STARMA). O modelo STARMA é empregado para descrever dados de séries temporais espacialmente localizados, ele é caracterizado pela dependência linear defasada tanto no espaço quanto no tempo. Foram realizadas simulações utilizando vários modelos de covariância espaço-temporal para comparar diferentes estruturas de construção da matriz de pesos espaciais com a finalidade de identificar a melhor matriz. As matrizes espaciais com pesos exponenciais apresentaram os melhores desempenhos de ajuste dos modelos STAR; e mostram uma estabilidade em relação à medida de ajuste. Por fim para ilustração, será ajustado um modelo STARMA para um conjunto de dados mensais do índice FIPEZAP de preço imobiliário de venda para apartamentos de dois dormitórios de seis cidades metropolitanas de São Paulo. / The objective of this work is to compare spatial neighborhoods structures, or the same as spatial weights matrices of the class of space-time autoregressive and moving average models STARMA. The STARMA model is used to describe spatially localized time series datas, it is characterized by the linear dependence lagged both in space and time. Simulations were performed using several space-time covariance models to compare different structures of construction of the weight matrix with the purpose of identifying the best matrix. The spatial matrices with exponential weights presented the best adjustment performances of the STAR models ans showed a stability in relation to the adjustment measure. Finally, for illustration, a STARMA model will be adjusted for a set of monthly data of the FIPEZAP real estate price index for two bedroom apartments in six metropolitan cities of São Paulo.

Três ensembles, respectivamente relacionados com as distribuições Gaussiana, Lognormal e de Levy, são abordados neste trabalho primordialmente do ponto de vista da termodinâmica de seus espectros. Novas expressões para as grandezas termodinâmicas sao encontradas para os ensembles de Stieltjes e de Bertuola-Pato, e a conexão destes com os ensembles Gaussianos e estabelecida. Esta tese também se compromete com a continuação do desenvolvimento e aprimorarão do ensemble generalizado de Bertuola-Pato, estendendo alguns resultados para os ensembles simplifico e unitário generalizados, alem do ortogonal generalizado já introduzido anteriormente por A. C. Bertuola e M. P. Pato. / Three ensembles, related to the Gaussian, the Lognormal and the L´evy distributions respectively, have been studied in this work and were investigated most of all in what concerns their spectral thermodynamics. New expressions for the thermodynamics quantities were found for the Stieltjes and the Bertuola-Pato ensembles, and the connection with the gaussian ensembles is established. This work concerned with the development continuity and with the improvement of Bertuola-Pato generalized ensemble, extending some of the results to the simplectic and unitary generalized ensembles, besides the orthogonal generalized ensemble introduced before by A. C. Bertuola and M. P. Pato.

De acordo com o conceito de sistemas de liberação controlada, o presente estudo foi baseado na utilização de polímeros hidrofílicos biocompatíveis, formadores de hidrogéis, para o desenvolvimento de matrizes na forma de filmes finos. Os polímeros utilizados para a formação das matrizes foram a quitosana proveniente das cascas de camarão, o amido de milho modificado e a poli(N-vinil-2-pirrolidona) - PVP. As matrizes foram reticuladas utilizando glutaraldeído. O fármaco escolhido para testar a capacidade de liberação dos dispositivos foi o anti-inflamatório não esteroidal (AINE) diclofenaco sódico. Para obtenção das matrizes com propriedades adequadas para essa finalidade, foram testadas misturas de quitosana-amido e quitosana-PVP. Após a triagem qualitativa, os dispositivos foram avaliados quanto à citotoxidade, intumescimento máximo, fração gel, parâmetros cinéticos associados à absorção de vapor de água e à capacidade de liberação de diclofenaco sódico in vitro. As formulações de quitosana-PVP foram as que apresentaram melhores propriedades para a aplicação proposta nesse estudo, se destacando a formulação A3, com alto percentual de liberação, boas propriedades de manuseio, poucos componentes na formulação diminuindo o potencial alergênico e aprovação no teste de citotoxicidade em células de camundongo (NCTC) pelo método de incorporação do vermelho neutro. / According to the concept of drug delivery systems, this study has based on the use of biocompatible hydrophilic polymers hydrogels-forming for the development of matrices in the form of thin films. The polymers used for forming the matrices were chitosan from shrimp shells, modified maize starch and poly(N-vinyl-2-pyrrolidone) PVP. The matrices were cross-linked using glutaraldehyde. The drug chosen to test the ability of the devices release was the non-steroidal anti-inflammatory drug (NSAID) sodium diclofenac. Mixtures between chitosan-starch and chitosan-PVP tested to obtain the matrices with suitable properties for this purpose. The devices after qualitative screening had evaluated for cytotoxicity, maximum swelling, gel fraction, kinetic parameters associated with absorbing water vapor and the release of diclofenac sodium able to in vitro. The formulations based on chitosan-PVP were the presents the best properties, in evidence formulation A3, with high percentage of delivery, good handing properties, few compounds/components reducing the allergenic potential and successful in vitro cell viability red uptake cytotoxicity assay, using cell culture mouse cells (NCTC).

Neste trabalho buscamos caracterizar o espectro de uma classe de operadores bloco--Jacobi limitados definidos em $l^2(\\Lambda,\\mathbb{C}^L)$ ($\\Lambda: \\mathbb{Z}_+\\times\\{0,1,\\ldots,L-1\\}$ representa uma faixa de largura $L\\ge 2$ no semi--plano $\\mathbb{Z}_+^2$) e sujeitos a perturbações esparsas (no sentido que as distâncias entre as ``barreiras\'\' crescem geometricamente à medida que estas se afastam da origem) distribuídas aleatoriamente. Tais operadores são construídos a partir da soma de Kronecker de matrizes de Jacobi $J$, cada qual atuando em uma direção do espaço. Demonstramos, por meio da bloco--diagonalização do operador, que %o estudo de suas principais propriedades espectrais dependem da %se limita à caracterização da ``medida de mistura\'\' $\\frac{1}{L}\\sum_{j=0}^{L-1}\\mu_j$, $\\mu_j$ a medida espectral associada à matriz de Jacobi $J^j=J+2\\cos(2\\pi j/L)I $. Para tanto, buscamos primeiramente caracterizar cada uma das medidas $\\mu_j$, explorando e aperfeiçoando algumas técnicas bastante conhecidas no estudo de operadores esparsos unidimensionais. Demonstramos, por exemplo, que a seqüência de ângulos de Prüfer (variáveis que, juntamente com os raios de Prüfer, parametrizam as soluções da equação de autovalores) é uniformemente distribuída no intervalo $[0,\\pi)$, o %que %resultado que nos permite determinar o comportamento assintótico médio das soluções da equação de autovalores. Tal resultado, aliado às técnicas desenvolvidas por Marchetti \\textit{et. al.} em \\cite{MarWre} e a uma adaptação dos critérios de Last e Simon \\cite{LS} para operadores esparsos, nos permitem demonstrar a existência de uma transição aguda (pontual) entre os espectros singular--contínuo e puramente pontual. Empregamos em seguida os resultados de Jitomirskaya e Last presentes em \\cite{JitLast} e obtemos a dimensão Hausdorff exata associada à medida $\\mu_j$, dada por $\\alpha_j=1+\\frac{4(1-p^2)^2}{p^2(4- (\\lambda-2\\cos(2\\pi j/L))^2)}$ ($\\lambda\\in[-2,2]$), recuperando um resultado análogo obtido por Zlato\\v s em \\cite{Zla}. Por fim, adaptamos tais resultados à situação da medida de mistura associada à matriz bloco--Jacobi, obtendo $\\alpha=\\min_{j\\in\\mathcal{I}(\\lambda)}\\alpha_j$, $\\mathcal{I}(\\lambda):\\{m \\in\\{0,1,\\ldots,L-1\\}:\\lambda\\in[-2+2\\cos(2\\pi j/L),2+2\\cos(2\\pi j/L)]\\}$, como sua dimensão Hausdorff exata. Estudamos modelos idênticos com esparsidades sub e super-geométricas, obtendo na primeira situação um espectro puramente pontual (de dimensão Hausdorff nula) e na segunda um espectro puramente singular--contínuo (de dimensão Hausdorff 1). Finalmente, verificamos a existência de transição entre os espectros puramente pontual e singular--contínuo em um modelo com esparsidade super-geométrica cuja dimensão Hausdorff associada à medida espectral é nula. / In this work we attempt to caracterize the spectrum of a class of limited block--Jacobi operators defined in $l^2(\\Lambda,\\mathbb{C}^L)$ ($\\Lambda: \\mathbb{Z}_+\\times\\{0,1,\\ldots,L-1\\}$ represents a strip of width $L\\ge 2$ on the semi--plane $\\mathbb{Z}_+^2$) subject to a sparse perturbation (which means that the distance between the ``barries\'\' grow geometrically with their distance to the origin) randomly distributed. Such operators are defined as Kronecker sums of unidimensional Jacobi matrices $J$, each one acting in different directions of the space. We prove, by means of a block--diagonalization of the operator, that %the study of its most relevant spectral properties depend on %is related to the caracterization of the ``mixture measure\'\' $\\frac{1}{L}\\sum_{j=0}^{L-1}\\mu_j$, $\\mu_j$ the spectral measure of the Jacobi matrix $J^j=J+2\\cos(2\\pi j/L)I$. For this, we must characterize at first each one of the measures $\\mu_j$, exploiting and improving some well known techniques developed in the study of unidimensional sparse operators. We prove, for instance, that the sequence of Prüfer angles (variables which parametrize the solutions of the eigenvalue equation) are uniform distributed on the interval $[0,\\pi)$, a result which gives us condition to determine the average asymptotic behavior of the solutions of the eigenvalue equation. Such result, in association with the techniques developed by Marchetti \\textit{et. al.} in \\cite{MarWre} and with an adaptation of Last--Simon \\cite{LS} criteria for sparse operator, permit us to prove the existence of a sharp transition between singular continuous and pure point spectra. Following on, we use the results from Jitomirskaya--Last of \\cite{JitLast} and obtain the exact Hausdorff dimension of the measure $\\mu_j$, given by $\\alpha_j=1+\\frac{4(1-p^2)^2}{p^2(4-(\\lambda-2\\cos(2\\pi j/L))^2)}$ ($\\lambda\\in[- 2,2]$), recovering an analogous result due to Zlato\\v s in \\cite{Zla}. At last, we adapt these results to the mixture measure of the block--Jacobi matrix, obtaining $\\alpha=\\min_{j\\in\\mathcal{I}(\\lambda)}\\alpha_j$, $\\mathcal{I}(\\lambda):\\{m \\in\\{0,1,\\ldots,L-1\\}:\\lambda\\in[-2+2\\cos(2\\pi j/L),2+2\\cos(2\\pi j/L)]\\}$, as its exact Hausdorff dimension. We study as well identical models with sub and super geometric sparsities conditions, obtaining a pure point spectrum (with null Hausdorff dimension) in the first case, and a purely singular continuous spectrum (such that its Hausdorff dimension is 1) in the second. Finally, we prove the existence of a transition between pure point and singular continuous spectra in a model with sub--geometric sparsity whose Hausdorff dimension related to the spectral measure is null.

Este trabalho é o resultado da minha pesquisa desen-volvida sobre a gravura de reprodução da Escola de Xilografia do Horto e seus desdobramentos. Focada em um processo criativo pessoal, apresento uma série de gravuras realizadas na madeira umburana e em metal, utili-zando ferramentas como o buril e goivas. Também faz parte desta pesqui-sa um CD com imagens fotográficas de todas as matrizes pertencentes ao acervo do Museu Florestal Octávio Vecchi. / This work is the result of my research developed on the reproduction engraving of the School Horto florestal of Woodcut-ting and its deployments. Introducing a series of prints made in umbura-na wood and metal using tools like the chisel and gouge, focused on a personal creative process. This research also contains a CD recorded with images of all matrices belonging to the Forest Museum Octavio Vecchi.