We have a conjecture that “the precision of computed solutions for systems of linear equations is more closely related with componentwise condition number c(A) than normwise condition number κ(A). We conducted simulation experiments to verify this conjecture. A statistical tool, Hotelling-Williams T-Test is employed to check if difference between correlations is significant. Simulation results suggest that our conjecture is true for most of the well-known methods and matrix sizes. Keywords: condition numbers, simulation, correlation coefficients, Hotelling-Williams T-Test

Made available in DSpace on 2014-06-11T19:24:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-04-10Bitstream added on 2014-06-13T19:30:48Z : No. of bitstreams: 1 andriucci_lr_me_prud.pdf: 464115 bytes, checksum: fa5d18caccdbf16a9a556c18e0c46891 (MD5) / Esta dissertação analisa o grau da influência termo-pluviométrica em alguns indicadores do comércio de Maringá (PR). Para isso foram estudados os elementos climáticos, temperatura e precipitação, bem como os indicadores econômicos: ICMS, SCPC, Vídeo-Cheque, Consumo e Consumidores de Energia Elétrica. Realizaram-se análises gráficas, e aplicações estatísticas de correlação e regressão, bem como, o exame de um estudo de caso. Considera-se que os grupos investigados apresentaram variações nas formas de correlações. A variável temperatura influência tanto no período frio como no período quente. A precipitação apresenta praticamente um tipo de comportamento: o aumento das chuvas faz diminuir a movimentação do comércio. Os resultados das análises do estudo de caso, que investiga a correlação das vendas diárias de um supermercado, mostraram que: o aumento da temperatura correlaciona-se com o aumento nas vendas, bem como, queda na temperatura – queda nas vendas; e o aumento da precipitação correlaciona-se com a diminuição das vendas; e a queda na precipitação – aumento das vendas. Os resultados apresentados neste trabalho possuem o caráter de testes preliminares por ser uma primeira tentativa de aproximação real entre as variáveis do clima (temperatura e precipitação) com alguns indicadores do comportamento do comércio da cidade de Maringá. / This dissertation analyzes the degree of thermo-pluviometric influence on certain of Maringá’s (PR) commercial indicators. To this end the climatic elements of temperature and precipitation as well as the following economic indicators were studied: ICMS, SCPC, Video-Check, Consumption and Consumers of Electric Energy. Graphical analyses along with statistical applications of correlation and regression were performed, as well as the examination of a case study. It is believed that the groups investigated exhibited variations in the forms of correlation. The temperature variable influences as much during the cold period as during the hot period. Precipitation exhibits practically one type of behavior: increased rainfall results in diminished commercial activity. The results of the case study analysis, which investigates the correlation of daily sales of a supermarket, demonstrated the following: increased temperature is correlated with increased sales, as well as decreased temperature with a decrease in sales; while increased precipitation correlates with decreased sales; and decreased precipitation with an increase in sales. The results herein presented are in the manner of a preliminary trial, representing a first attempt at measuring the actual relationship between the climatic variables (temperature and precipitation) with certain behavioral indicators of commerce in the city of Maringá.

abstract: Estimating cointegrating relationships requires specific techniques. Canonical correlations are used to determine the rank and space of the cointegrating matrix. The vectors used to transform the data into canonical variables have an eigenvector representation, and the associated canonical correlations have an eigenvalue representation. The number of cointegrating relations is chosen based upon a theoretical difference in the convergence rates of the eignevalues. The number of cointegrating relations is consistently estimated using a threshold function which places a lower bound on the eigenvalues associated with cointegrating relations and an upper bound on the eigenvalues on the eigenvalues not associated with cointegrating relations. The proposed estimator performs better with a large number of cross-sectional observations and moderate time series length. / Dissertation/Thesis / Ph.D. Economics 2012

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Magister Scientiae - MSc / The 24-item scale has been used extensively to assess the attitudes towards AIDS precautions. This study investigated the usefulness and validity of the instrument in a South African setting, fourteen years after the development of the instrument. If a new structure could be found statistically, the HIV/AIDS prevention strategies could be more effective in aiding campaigns to change attitudes and sexual behaviour. / South Africa

Cette thèse traite de la description de la corrélation électronique et de la spectroscopie dans le cadre de la Théorie de la Fonctionnelle de la Matrice Densité Réduite (RDMFT). Dans la RDMFT, les propriétés de l'état fondamental d'un système physique sont des fonctionnelles de la matrice densité à un corps. Plusieurs approximations à la corrélation électronique ont été proposées dans la littérature. Beaucoup d'entre elles peuvent être reliés au travail de Müller, qui en a proposé une similaire à l'approximation Hartree-Fock mais qui peut produire des nombres d'occupation fractionnaires. Cela n'est pas toujours suffisant, notamment dans les matériaux fortement corrélés. Par ailleurs, l'expression des observables du système en terme de la matrice densité n'est pas toujours connue. Tel est le cas, par exemple, pour la fonction spectrale, qui est liée aux spectres de photoémission. Dans ce cas, il y a des annulations d'erreur entre l'approximation à la corrélation électronique et l'approximation à l'observable, ce qui affaiblit la théorie. Dans cette thèse, nous recherchons des approximations plus précises en exploitant le lien entre les matrices densité et les fonctions de Green. Dans la première partie de la thèse, nous nous concentrons sur la fonction spectrale. En utilisant le modèle de Hubbard, qui peut être résolu exactement, nous analysons les approximations existantes à cette observable et nous soulignons leurs points faibles. Ensuite, à partir de sa définition en terme de la fonction de Green à un corps nous dérivons une expression pour la fonction spectrale qui dépend des nombres d'occupation naturels et d'une énergie efficace qui prend en compte toutes les excitations du système. Cette énergie efficace dépend de la matrice densité à un corps ainsi que des ordres supérieurs. Des approximations simples à cette énergie efficace donnent des spectres précis dans des systèmes modèles dans des régimes à la fois de faible et de forte corrélation. Pour illustrer notre méthode sur les matériaux réels, nous calculons le spectre de photoemission du NiO massif: notre méthode donne une image qualitativement correcte dans la phase antiferromagnétique et dans la phase paramagnétique, contrairement aux méthodes de champ moyen utilisés actuellement, qui donnent un métal dans le dernier cas. La deuxième partie de la thèse est plus explorative et traite des phénomènes dépendant du temps dans la RDMFT. En général, l'évolution temporelle des matrices densité est donnée par la hiérarchie des équations de Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY), dans lequel l'équation du mouvement de la matrice densité a n corps est donnée en termes de la matrice densité à n+1 corps. La première équation de la hiérarchie relie la matrice densité à un corps à la matrice densité à deux corps. La tâche difficile est de trouver des approximations à la matrice densité à deux corps. Les approximations existantes sont des extensions adiabatiques des approximations de l'état fondamental. Nous explorons cette question en examinant de nouvelles approximations qui nous tirons de la théorie à plusieurs corps (MBPT) basée sur les fonctions de Green ainsi que de la solution exacte du modèle de Anderson à deux niveaux dans son état fondamental. Nos premiers résultats sur le modèle de Anderson soumis à divers champs externes montrent quelques caractéristiques intéressantes, qui suggèrent d'explorer davantage ces approximations aussi sur des systèmes modèles plus grands. / This thesis addresses the description of electron correlation and spectroscopy within the context of Reduced Density-Matrix Functional Theory (RDMFT). Within RDMFT the ground-state properties of a physical system are functionals of the ground-state reduced density matrix. Various approximations to electron correlation have been proposed in literature. Many of them, however, can be traced back to the work of Müller, who has proposed an approximation to the correlation which is similar to the Hartree-Fock approximation but which can produce fractional occupation numbers. This is not always sufficient. Moreover, the expression of the observables of the system in terms of the reduced density matrix is not always known. This is the case, for example, for the spectral function, which is closely related to photoemission spectra. In this case there are error cancellations between the approximation to correlation and the approximation to the observable, which weakens the theory. In this thesis we look for more accurate approximations by exploiting the link between density matrices and Green's functions. In the first part of the thesis we focus on the spectral function. Using the exactly solvable Hubbard model as illustration, we analyze the existent approximations to this observable and we point out their weak points. Then, starting from its definition in terms of the one-body Green's function, we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the one-body as well as higher-order reduced density matrices. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong-correlation regimes. To illustrate our method on real materials we calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and in the paramagnetic phases, contrary to currently used mean-field methods, which give a metal in the latter case. The second part of the thesis is more explorative and deals with time-dependent phenomena within RDMFT. In general the time evolution of the reduced density matrices is given by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations, in which the equation of motion of the n-body reduced density matrix is given in terms of the (n + 1)-body reduced density matrix. The first equation of the hierarchy relates the one-body to the two-body reduced density matrix. The difficult task is to find approximations to the two-body reduced density matrix. Commonly used approximations are adiabatic extension of ground-state approximations. We explore this issue by looking at new approximations derived from Many-Body Perturbation Theory (MBPT) based on Green's functions as well as from the exact solution of the two-level Anderson impurity model in its ground state. Our first results on the two-level Anderson model subjected to various external fields show some interesting and, at the same time, puzzling features, which suggest to explore further these approximations.

Two-phase Ti6246 alloy is a light weight material exhibiting very high strength at higher temperatures compared to the commonly used Ti64 alloy. This particular alloy is used at the later stages of compressor discs within the aero engines. However, compressor discs undergo a number of cyclic stresses, which could eventually lead to fatigue failure. In order to optimize the microstructure for design and lifing models, an improved understanding of the localised deformation mechanisms is crucial, particularly at the surface, as cracks can be initiated leading to failure and in turn affect the life expectancy of the component. Two-phase alloys in use have very complex lamellar microstructures comprising of a mixture of coarse and fine phases and their role in deformation can be very complex and difficult to understand. The focus of this study was particularly based on the importance of the beta phase in strengthening two-phase microstructures. Therefore, this study has been simplified to compare model lamellar microstructures, which have particular sizes of beta phase in between alpha lamellae. Digital Image Correlation along with high resolution imaging was used to develop a detailed understanding of the localised deformation in these microstructures. Widening the beta phase in-between alpha lamellae caused a more homogenous deformation, while ageing the beta phase with fine secondary alpha strengthened the microstructure. However, all microstructures showed that the single continuous alpha layer at beta grain boundaries depicted the highest amount of deformation, which can be detrimental for the life of the component. The behaviour of slip at the α/β interface not only depended on the size of the phases but also depended on the neighbouring crystallographic orientations and the relationship of the two phases, specifically the alignment of the close packed slip directions. Strain maps of these microstructures were subsequently related to corresponding Schmid factor maps and crystal plasticity models to improve this understanding.

Fluidization of biomass particles is an important process in the gasification, pyrolysis and combustion in order to extract energy from biomass. Studies on the fluidization of biomass particles (corn cob and walnut shell), inert particles (sand, glass bead, and alumina), which are added to facilitate fluidization of biomass, and biomass/sand mixture were performed. Experiments were carried out in a 14.5 cm internal diameter cold flow fluidization bed to determine minimum fluidization velocities with air as fluidizing medium. On the of basis of experimental data from both present work and those found in the literature, new correlations were developed to predict minimum fluidization velocity for inert particles as well as biomass particles. It was found that the proposed correlations satisfactorily predict minimum fluidization velocities and was in well agreement with experimental data. Furthermore, effect of weight percentage of biomass in the biomass/sand mixtures was studied. The weight fraction of biomass particles in the mixture was chosen in the range of 0 ~ 100 wt. %. The results show that minimum fluidization velocity of the mixtures increases with an increase in biomass content. Using the present experimental data, a new correlation was developed in terms of mass ratio for predicting values of minimum fluidization velocity of these mixtures. However, the validity of the proposed correlation should be further studied by conducting more experiments using the biomass/sand mixtures of different particle size, shape, and density.

The topic of this thesis is registration of image sequences captured by experimental ophthalmoscope. It contains anatomical description of the visual system as well as the description of functions of selected ophthalmoscopic devices. The next covered topic is theoretical summary of registration process, which is followed by an overview of the used methods, which forms the basis of the design and implementation of the registration algorithm in the Python programming language. After implementation, the accuracy and computational complexity of a registration was evaluated. Tests of optimalization of the proposed approach were performed with regards to the obtained results, through which sufficiently accurate registration has been achieved, evaluated on the basis of Euclidean distances, standard deviation and visual observation. In case of high-quality recorded sequences, values of Euclidean distances ranged from 0.60 to 4.07 pixels on the contrary, values higher than 20 pixels occurred in the case of poor-quality recordings. Standard deviation values in recordings with high enough resolution have not reached worse results than 4.12.

Baseband digital communication in electro-magnetic measurement while drilling (EM-MWD) systems is often corrupted by non-white surface noise. The inability to reliably decode the transmitted signals in a noisy environment limits the depth at which EM-MWD systems can operate. Correlation receivers, which are optimal in the presence of additive white Gaussian noise, can be sub-optimal in the presence of various types of field noise at different drilling sites. This thesis investigates the application of artificial neural networks (ANN) as communication receivers in EM-MWD baseband digital communication systems. The performances of various ANN architectures and training algorithms are studied and compared with conventional correlation receivers via computer simulations. Standard symbol error rate (SER) test results show that the NN receiver is able to adapt to site-specific noise and thus outperforms the traditional correlation receiver.