<p>This thesis deals with the Open Mapping Theorem for analytic functions on domains in the complex plane: A non-constant analytic function on an open subset of the complex plane is an open map.</p><p>As applications of this fundamental theorem we study Schwarz’s Lemma and its consequences concerning the groups of conformal automorphisms of the unit disk and of the upper halfplane.</p><p>In the last part of the thesis we indicate the first steps in hyperbolic geometry.</p> / <p>Denna uppsats behandlar satsen om öppna avbildningar för analytiska funktioner på domäner i det komplexa talplanet: En icke-konstant analytisk funktion på en öppen delmängd av det komplexa talplanet är en öppen avbildning.</p><p>Som tillämpningar på denna fundamentala sats studeras Schwarz’s lemma och dess konsekvenser för grupperna av konforma automorfismer på enhetsdisken och på det övre halvplanet.</p><p>I uppsatsens sista del antyds de första stegen inom hyperbolisk geometri.</p>

This thesis deals with the Open Mapping Theorem for analytic functions on domains in the complex plane: A non-constant analytic function on an open subset of the complex plane is an open map. As applications of this fundamental theorem we study Schwarz’s Lemma and its consequences concerning the groups of conformal automorphisms of the unit disk and of the upper halfplane. In the last part of the thesis we indicate the first steps in hyperbolic geometry. / Denna uppsats behandlar satsen om öppna avbildningar för analytiska funktioner på domäner i det komplexa talplanet: En icke-konstant analytisk funktion på en öppen delmängd av det komplexa talplanet är en öppen avbildning. Som tillämpningar på denna fundamentala sats studeras Schwarz’s lemma och dess konsekvenser för grupperna av konforma automorfismer på enhetsdisken och på det övre halvplanet. I uppsatsens sista del antyds de första stegen inom hyperbolisk geometri.

A identificação de observações influentes e/ou aberrantes de um conjunto de dados é conhecida como uma parte das análises de diagnóstico. Esta técnica de diagnóstico têm como uma das finalidades verificar a robustez de um modelo estatístico, pois a não identificação dos dados influentes pode afetar a análise ou obter resultados incorretos. As metodologias comumente utilizadas para o diagnóstico de observações influentes em modelos de regressão são métodos de influência global (Belsey et al., 1980). Cook (1986) introduziu um método geral para avaliar a influência local de pequenas perturbações no modelo estatístico ou nos dados, usando diferentes tipos de perturbações. Como complemento às técnicas de detecção de observações discrepantes, é proposto o método procura \\forward\", por Atkinson e Riani (2000), que é uma metodologia para detectar observações atípicas mascaradas. Neste trabalho, propomos o uso da influência local com procura \"forward\" na obtenção de observações mascaradas influentes considerando modelos de regressão linear. / The identification of influential and/or atypical observations in a data set is known as a part of the diagnostic analysis. One of the purposes of the diagnostic analysis is to verify the robustness of a statistical model, as the non-identification of influential observations can affect the analysis or may cause the obtainment of incorrect results. The most commonly used methodology for the diagnostic of influential observations in regression models are the global influence (Belsey et al., 1980). Cook (1986) introduced a general method to evaluate the local influence of small perturbations in the statistical model or in the data set using different perturbation schemes. As a complement to the techniques of detection atypical observations, it is proposed the forward search procedure by Atkinson e Riani (2000), which is a methodology to detect the masked atypical observations in a data set. In this work we propose the use of the local influence approach together with the forward search to obtain the masked influential observations in linear regression models.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-06-09T17:37:21Z No. of bitstreams: 1 fabriciomatosferreira.pdf: 457154 bytes, checksum: 39a00f23ce89d7948ef54eee13b6380a (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-06-29T12:08:53Z (GMT) No. of bitstreams: 1 fabriciomatosferreira.pdf: 457154 bytes, checksum: 39a00f23ce89d7948ef54eee13b6380a (MD5) / Made available in DSpace on 2017-06-29T12:08:53Z (GMT). No. of bitstreams: 1 fabriciomatosferreira.pdf: 457154 bytes, checksum: 39a00f23ce89d7948ef54eee13b6380a (MD5) Previous issue date: 2015-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Teorias com derivadas de alta ordem e sua invariância sob transformações conformes são ferramentas poderosas em Teoria Quântica de Campos em espaços curvos. O principal propósito de nosso estudo é trabalhar no sentido de obter uma generalização do operador quadridimensional conforme de Paneitz para um operador análogo em seis dimensões (∆6). A consecução de um operador conformalmente invariante contendo seis derivadas justifica a escolha de se trabalhar nesta dimensão como um recurso mais simples para sua obtenção. Tal operador seria de fundamental importância na integração da anomalia conforme em teorias com derivadas de sexta ordem. A forte relação entre operadores conformes e a densidade de Euler foi investigada em D = 2 e D = 4. O termo da densidade de Euler - o qual é conhecido em 4D como termo topológico de Gauss-Bonnet - foi estendido a seis dimensões. Em dimensões pares, tal termo é representado por potências de D/2 de contrações dos tensores de Riemann e Ricci, cada um dos quais contendo D derivadas. A transformação dos escalares de terceira ordem na curvatura os quais aparecem no estudo da anomalia conforme e da densidade de Euler em seis dimensões foi obtida como um primeiro passo rumo ao nosso objetivo de obter ∆6. / Higher-derivative theories and their invariance under conformal transformati ons are powerful tools in Quantum Field Theory in curved spaces. The main purpose of our study is to work towards achievement of a generalization of the four dimensional Paneitz conformal operator to analogous six dimension one (∆6). Achieving a six deri vative conformally invariant operator justifies the choice of working in such dimension as a simpler resource for obtaining it. This operator would be of fundamental account in the integration of the conformal anomaly in sixth order derivatives theories. The strong relation between conformal operators and Euler density has been investigated in D = 2 e D = 4. Euler density term - which 4D version is known as topological Gauss-Bonnet term - was extended to the six dimension. In even dimensions, it is represented by D/2 powers of contracted Riemann and Ricci tensors, each of them carrying D derivatives. The transformation of the third order curvature scalars that arise in the study of the conformal anomaly and Euler density in six dimension was obtained as a first step to our goal of achieving ∆6.

Verallgemeinerungen bekannter Existenz- und Eindeutigkeitsaussagen für gebietsfüllende Kreispackungen. Für jedes beschränkte, einfach zusammenhängende Gebiet und für jeden zulässigen Komplex existiert eine gebietsfüllende, verallgemeinerte Kreispackung, die einer beliebigen der folgenden Normalisierungen genügt. alpha-beta-gamma: drei Randkreise sind je einem Randpunkt (Primende) zugeordnet alpha-gamma: ein Kreis mit fixem Mittelpunkt und ein Randkreis mit zugeordnetem Primende alpha-beta: zwei Kreise mit fixen Mittelpunkten Bedingungen werden angegeben, unter welchen die aufgeführten Normalisierungen eindeutige Lösungen implizieren, welche zudem stetig von den Normalisierungsparametern abhängen. Ist der Alpha-Kreis ein innerer Kreis, dann wird gezeigt, dass die alpha-beta Normalisierung im Allg. keine Eindeutigkeit liefert. Bedingungen werden aufgeführt, die nicht-entartete Lösungen (klassische Kreispackungen) garantieren. Alle Beweise sind möglichst elementar und unabhängig von existierenden Kreispackungs-Ergebnissen. / Existing existence and uniqueness results in the field of domain filling circle packings are generalized. For every bounded, simply connected domain, for every admissible complex, and under any of the following normalizations it is shown that there is a domain filling generalized circle packing. alpha-beta-gamma: three boundary disks are each associated with a boundary point (prime end) alpha-gamma: one disk with fixed center and one boundary disk with associated prime end alpha-beta: two disks with fixed centers Conditions are given under which the stated normalizations yield unique solutions, which then depend continuous on some normalization parameters. For the special case of an interior alpha disk it is shown that the alpha-beta normalization does not yield uniqueness in general. Several conditions are stated that guarantee non-degenerate solutions (classical circle packings). All proofs are kept as elementary as possible and independent of existing circle packing results.

[pt] Esta tese apresenta um estudo sobre métodos semianalíticos para modelagem de guias de ondas com contornos complexos. Os campos eletromagnéticos dentro de meios não homogêneos e anisotrópicos são resolvidos por meio de harmônicos cilíndricos como base para outras abordagens numéricas, como o método de perturbação regular (RPM), o método de perturbação de material em cavidade (CMPM) e o método de casamento de pontos (PMM). As novas soluções semianalíticas que exploramos aqui podem ser empregadas para a análise de comunicação sem fio ao longo de túneis, bem como para a modelagem de sensores realistas de perfilagem durante a perfuração em problemas geofísicos de baixa frequência. Estudamos o potencial do RPM ao combiná-lo com os princípios da transformação óptica (TO) para analisar um guia de onda coaxial excêntrico preenchido com materiais anisotrópicos. Além disso, estendemos o CMPM clássico proposto por Harrington para lidar com meios anisotrópicos para resolver os números de onda de corte dos campos modais no mesmo guia de onda de maneira aproximada, mas numericamente eficiente. Outra solução de perturbação é proposta combinando as correções de baixa ordem do RPM no CMPM para fornecer correções de alta ordem para os números de onda de corte dos modos suportados pelo guia. Uma formulação matemática de um método semianalítico baseado em PMM para resolver guias de onda preenchidos com meios anisotrópicos e com camadas arbitrárias também é apresentada. Uma versão melhorada deste método é introduzida para modelar estruturas guiadas cilíndricas de múltiplas camadas não circulares. Essas soluções baseadas em casamento de pontos representam boas alternativas para abordagens de força bruta, como métodos de elementos finitos e de diferenças finitas. / [en] This thesis presents a study on semi-analytic methods for modeling waveguides with complex-shaped boundaries. The electromagnetic fields inside inhomogeneous and anisotropic media are solved via cylindrical harmonics as a basis for other numerical approaches, including the regular perturbation method (RPM), the cavity-material perturbation method (CMPM), and the point-matching method (PMM). The novel semi-analytic solutions we have explored here can be employed for the analysis of wireless communication along tunnels and boreholes as well as for the modeling of realistic logging-whiledrilling (LWD) sensors and their environments at low-frequency geophysical problems. We studied the potential of the RPM when combining it with the transformation optics (TO) principles to analyze an eccentric coaxial waveguide filled with anisotropic materials. Furthermore, we have extended the classical CMPM proposed by Harrington to handling anisotropic media for solving the cutoff wavenumbers of the modal fields in the same eccentric coaxial waveguide in an approximated but numerically efficient manner. Another perturbation solution is proposed here and combines the low-order corrections from RPM into the CMPM for providing high-order corrections to the cutoff wavenumbers of the modes supported in this guide. A mathematical formulation of a semi-analytic point-matching method for solving more complex anisotropic-filled waveguides with an arbitrary number of layers is also presented. An improved version of this method is introduced for modeling noncircular multi-layered cylindrical guided structures. Such point-matching-based solutions represent good alternatives to brute-force approaches such as finiteelement and finite-difference methods and motivate further investigations. We present a series of validation results showing the accuracy, efficiency, and potential limitations of the explored methods.

The complex and coupled physical processes taking place in the atmosphere, ocean and land surface are described in Global Circulation Models (GCMs). These models have become the main tools to simulate climate variability and project future climate change. GCMs have the potential to give physically reliable estimates of climate change at global, continental or regional scales, but their projections are currently of too course horizontal resolution to capture the smaller scale features of climate and climate change. This situation stems from the fact that GCM simulations, which are effectively three-dimensional simulations of the coupled atmosphere-ocean-land system, are computationally extremely expensive. Therefore, downscaling techniques are utilised to do perform simulations over preselected areas that are of sufficiently detailed to represent the climate features at the meso-scale. Dynamic regional climate models (RCMs), based on the same laws of physics as GCMs but applied at high resolution over areas of interest, have become the main tools to project regional climate change. The research presented here utilises the Conformal-Cubic Atmospheric Model (CCAM), a variable-resolution global atmospheric model that can be applied in stretched-grid mode to function as a regional climate model. As is the case with RCMs, CCAM has the potential to improve climate simulations along rough topography and coastal areas when applied at high spatial resolution, whilst side-stepping the lateral boundary condition problems experienced by typical limited-area RCMs. CCAM has been developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia. The objective in the study is to test capability of a regional climate model, CCAM, to realistically simulate cumulus convection at different spatial scales over regions with steep topography, such as the eastern escarpment of South Africa. Since both GCMs and RCMs are known to have large biases and shortcomings in simulating rainfall over the steep eastern escarpment of southern Africa and in particular Lesotho, the paper “Model simulations of rainfall over southern Africa and its eastern escarpment” (Chapter 3) has a focus on verifying model performance over this region. In the paper the CCAM simulations include six 200 km resolution Atmospheric Model Intercomparison Project (AMIP) simulations that are forced with sea surface temperatures and one 50 km resolution National Centre for Environmental Prediction (NCEP) reanalysis simulation that is forced with sea surface temperatures and synoptic scale atmospheric forcings. These simulations are verified against rain gauge data sets and satellite rainfall estimates. The results reveal that at these resolutions the model is capable of simulating the key synoptic-scale features of southern African rainfall patterns. However, rainfall totals are often drastically overestimated. A key aspect of model performance is the representation of the diurnal cycle in convection. For the case of South Africa, the realistic representation of the complex patterns of rainfall over regions of steep topography is also of particular importance. At a larger spatial scale, the model also needs to be capable of representing the west-east rainfall gradient found over South Africa. The ability of CCAM to simulate the diurnal cycle in rainfall as well as the complex spatial patterns of rainfall over eastern South Africa is analysed in “High Resolution Rainfall Modelling over the Eastern Escarpment of South Africa” (Chapter 4). The simulations described in the paper have been performed at 8km resolutions in the horizontal and span a thirty-year long period. These are the highest resolution climate simulations obtained to date for the southern African region, and were obtained through the downscaling reanalysis data of the European Centre for Medium-range Weather Forecasting (ECMWF). The simulations provide a test of the robustness of the CCAM convective rainfall parameterisations when applied at high spatial resolution, in particular in representing the complex rainfall patterns of the eastern escarpment of South Africa. / M (Geography and Environmental Management), North-West University, Potchefstroom Campus, 2015

The complex and coupled physical processes taking place in the atmosphere, ocean and land surface are described in Global Circulation Models (GCMs). These models have become the main tools to simulate climate variability and project future climate change. GCMs have the potential to give physically reliable estimates of climate change at global, continental or regional scales, but their projections are currently of too course horizontal resolution to capture the smaller scale features of climate and climate change. This situation stems from the fact that GCM simulations, which are effectively three-dimensional simulations of the coupled atmosphere-ocean-land system, are computationally extremely expensive. Therefore, downscaling techniques are utilised to do perform simulations over preselected areas that are of sufficiently detailed to represent the climate features at the meso-scale. Dynamic regional climate models (RCMs), based on the same laws of physics as GCMs but applied at high resolution over areas of interest, have become the main tools to project regional climate change. The research presented here utilises the Conformal-Cubic Atmospheric Model (CCAM), a variable-resolution global atmospheric model that can be applied in stretched-grid mode to function as a regional climate model. As is the case with RCMs, CCAM has the potential to improve climate simulations along rough topography and coastal areas when applied at high spatial resolution, whilst side-stepping the lateral boundary condition problems experienced by typical limited-area RCMs. CCAM has been developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia. The objective in the study is to test capability of a regional climate model, CCAM, to realistically simulate cumulus convection at different spatial scales over regions with steep topography, such as the eastern escarpment of South Africa. Since both GCMs and RCMs are known to have large biases and shortcomings in simulating rainfall over the steep eastern escarpment of southern Africa and in particular Lesotho, the paper “Model simulations of rainfall over southern Africa and its eastern escarpment” (Chapter 3) has a focus on verifying model performance over this region. In the paper the CCAM simulations include six 200 km resolution Atmospheric Model Intercomparison Project (AMIP) simulations that are forced with sea surface temperatures and one 50 km resolution National Centre for Environmental Prediction (NCEP) reanalysis simulation that is forced with sea surface temperatures and synoptic scale atmospheric forcings. These simulations are verified against rain gauge data sets and satellite rainfall estimates. The results reveal that at these resolutions the model is capable of simulating the key synoptic-scale features of southern African rainfall patterns. However, rainfall totals are often drastically overestimated. A key aspect of model performance is the representation of the diurnal cycle in convection. For the case of South Africa, the realistic representation of the complex patterns of rainfall over regions of steep topography is also of particular importance. At a larger spatial scale, the model also needs to be capable of representing the west-east rainfall gradient found over South Africa. The ability of CCAM to simulate the diurnal cycle in rainfall as well as the complex spatial patterns of rainfall over eastern South Africa is analysed in “High Resolution Rainfall Modelling over the Eastern Escarpment of South Africa” (Chapter 4). The simulations described in the paper have been performed at 8km resolutions in the horizontal and span a thirty-year long period. These are the highest resolution climate simulations obtained to date for the southern African region, and were obtained through the downscaling reanalysis data of the European Centre for Medium-range Weather Forecasting (ECMWF). The simulations provide a test of the robustness of the CCAM convective rainfall parameterisations when applied at high spatial resolution, in particular in representing the complex rainfall patterns of the eastern escarpment of South Africa. / M (Geography and Environmental Management), North-West University, Potchefstroom Campus, 2015

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / Planar microstrip antennas are desirable in many telemetry applications because they are small in size, light in weight, and conformal to most surfaces. The design and optimization of circularly-polarized omnidirectional microstrip arrays using a new software simulation tool are discussed in this paper. Critical design issues such as the optimization of each array element for circular polarization and the minimization of mutual couplings as well as feed network mismatch are examined. The software tool, which consists of a novel graphical user interface and a full-wave numerical simulator for a flat mounting surface, provides a testbed environment for the user to explore new designs as well as optimizing existing designs. Using this tool, the design of several wraparound arrays with different mounting cylinder radii are presented. Comparisons between measured and simulated data for two S-band 8-element wraparound arrays are also presented.

Most modern engines utilise pistons with an offset gudgeon pin. In internal combustion engines, the offset is to the major thrust side of the piston. The piston thrust side is the part of the piston perpendicular to the gudgeon pin that carries the majority of side loading during the power stroke. Primary reason for having the gudgeon pin positioned eccentrically is to prevent the piston from slamming into the cylinder bore after the connecting rod journal passes the top dead centre. This phenomenon is referred to as piston slap, and is more pronounced in compression ignition and high performance engines due to higher combustion pressure than that of commercial spark ignition engines. The coming together of the piston and the bore results in scuffing, at best, or, catastrophic failure at worst. Clearance space between bore and piston is filled by a lubricant film. The main role of the lubricant is to separate the piston and bore by reacting to the applied load. Investigating the above problem requires a holistic approach, whereby a dynamic three degree-of-freedom piston model is coupled with a lubrication model to represent the actual system. The dynamic model determines the motion of the piston in combined axial, lateral and rotation about the gudgeon pin. The reactive forces due to lubricant films on the major and minor thrust sides of the piston play significant roles in piston dynamics and are evaluated by either quasi-static or transient solution of the lubricant contact conjunctions. The novel quasi-static analysis is carried out in the sense of its detailed approach, including many key practical features. not incorporated in other analyses, hitherto reported in literature. These features include first and foremost the development of a specific contact mechanics model for evaluation of conforming contacts for piston skirt against liner or bore. The quasi-static analysis includes many practical feature not encountered in other literature on the subject, such as detailed surface irregularities and modification features, and with thermal distortion. The analysis has been extended to thermohydrodynamics, as well as micro-hydrodynamics, all with high computational mesh densities, and robust methods of solution in space and time domains, including effective influence Newton-Raphson method and linear acceleration integration scheme. The transient tribo-elasto-multi-body dynamics problem includes physics of motion study from film thickness prediction and secondary motion evaluation of the order of micrometers and minutes of arc to large rigid body dynamics, including simultaneous solution of the contact problem at both major and minor thrust sides. Such a comprehensive solution has not hitherto been reported in literature. The thesis discusses many aspects of piston dynamics problem, through the broad spectrum of vehicle manufacture, with many pertinent practical engineering issues. In particular, it provides solutions for high performance Formula 1 racing engines. This is the first ever comprehensive analysis of piston tribodynamics for this range of engines at very high combustion pressures. This study has shown the paramount influence of profile of piston in promoting lubrication between the contiguous bodies, as evident from the pattern of lubricant flow through the contact. Deformation of the bodies increases the volume of lubricant in the contact. During the reversal in direction of piston motion, when the entraining velocity momentarily cases and reversal takes place, the load is held by an elastic squeeze.