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O número de contato do Rn (em inglês, kissing number) é o maior número de esferas de raio unitário e interiores dois-a-dois disjuntos que podem tocar simultaneamente uma esfera de raio unitário central. Nesta dissertação estudamos métodos que limitam o tamanho de tais configurações através de técnicas de otimização, como dualidade e programação semidefinida. O principal resultado obtido foi o cálculo de melhores limitantes para o número de contato nas dimensões 9 a 23; o que foi possível graças à exploração de simetrias dos polinômios presentes no limitante proposto por Bachoc e Vallentin (2008), levando à consideração de programas semidefinidos menores. Por fim, o limitante estudado é estendido para uma classe mais geral de problemas. / The kissing number of Rn is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. In this thesis we study methods to bound from above the size of such configurations using optimization techniques, like duality and semidefinite programming. The main result achieved is the computation of better bounds for the kissing number in dimensions 9 to 23; a result possible due to the exploitation of symmetries in the polynomials present in the bound proposed by Bachoc and Vallentin (2008), leading to the consideration of smaller semidefinite programs. Finally, the studied bound is extended to a bigger class of problems.

O objetivo principal deste trabalho é apresentar um estudo sobre o Teorema de Borsuk-Ulam para forma espacial esférica homotópica. Em nosso trabalho consideramos X uma n-forma espacial esférica homotópica a qual admite uma ação livre de Zp, com p> 2 primo e f : X → Rk uma função contínua e, mostramos que sob determinada relação entre os números n e k, o conjunto A(f) dos pontos de coincidência de f é não vazio / The main objective of this work is to present a study about the Borsuk- Ulam Theorem for homotopic spherical space. In our work we consider X be a n-dimensional homotopic spherical space form which admits a free action of Zp, with p> 2 prime and f : X → Rk be a continuous map and we show that, under certain relations between the numbers n and k, the set A(f) is not empty

The research described in this dissertation mainly covers the development of novel technologies for co-crystallisation along with the discovering of plumbagin co-crystal and thermodynamic interrelationship between the co-crystal polymorphs. Co-crystallisation is a fast growing field in the area of crystal design and has shown potential advantages in the field of pharmaceutical. Currently, many research groups are working on the development of new technologies for the synthesis of pure and stoichiometrically controlled co-crystals. In present study, three novel technologies have been developed for co-crystallisation, which include microwave assisted co-crystallisation, spherical crystallisation and microwave assisted sub-critical water processing. The microwave assisted co-crystallisation is a slurry based technology where, effects of drug solubility and dielectric properties of the solvent were investigated using caffeine / maleic acid as a model co-crystal pair. The mechanism of co-crystallisation under microwave irradiation has been proposed. The co-crystals of plumbagin with improved solubility were obtained with the coformers such as hydroquinone, resorcinol and urea using microwave assisted co-crystallisation technique. The spherical crystallisation technology was developed for co-crystallisation of carbamazepine / saccharin co-crystal pair and demonstrated its application for polymorphic control and as a potential technique for the purification of desired crystal form through surface energetic based separation. The thermodynamic interrelationship between Form I and Form II of carbamazepine / saccharin co-crystal was studied using different thermodynamic tests. The results obtained suggest that the carbamazepine / saccharin co-crystal polymorphs are monotropic. Microwave assisted sub-critical water processing has been explored as a green technology for the synthesis of co-crystals. Carbamazepine / saccharin co-crystal pair has been used as a model pair and effects of processing variables on the resulting crystal form and degradation of an API have been studied.

O modelo esférico desempenha um papel importante na mecânica estatística, pois ele permite a realização de cálculos exatos para estudar o comportamento crítico. Diferentes soluções do modelo esférico têm sido usadas para estudar o comportamento crítico de uma grande variedade de sistemas (com diversos tipos de desordem, com interações competitivas, de curto e de longo alcance, ferro e antiferromagnéticas, além de muitas outras situações). As soluções desses modelos apresentam uma série de anomalias a baixas temperaturas, inclusive resultados que contradizem a terceira lei da termodinâmica. Na década de 70, foi sugerido que esse comportamento anômalo a temperaturas muito baixas seria corrigido pela introdução de flutuações quânticas, que não eram levadas em conta nas soluções clássicas. De fato, a partir da quantização do modelo esférico e possível corrigir esse comportamento. Utilizamos então dois métodos distintos de quantização - quantização canônica e representação em termos de integrais funcionais - para construir versões quânticas do modelo esférico clássico, que podem ser investigadas analiticamente. Mostramos que essas formulações quânticas conduzem aos mesmos resultados. Em particular, analisamos as propriedades termodinâmicas de um modelo esférico médio\" quântico nas seguintes situações: (i) com inteirações de longo alcance, do tipo campo médio, que deve constituir um dos sistemas mais simples exibindo uma transição de fase quântica; (ii) com interações competitivas, entre primeiros e segundos vizinhos, numa situação em que ocorre um ponto multicrítico de Lifshitz; (iii) na presença de interações de longo alcance, tipo campo médio, e de um campo aleatório com média nula; (iv) na presença de desordem de sítios, como nos modelos de van Hemmen para um vidro de spin ou de Hopfield para uma rede neural com poucos padrões. Em todos esses casos há correção do comportamento anômalo a baixas temperaturas. Obtemos diagramas de fases e estudamos em cada caso a natureza das fases ordenadas. / The spherical model plays an important role in statistical mechanics, since it is amenable to exact calculations to investigate the critical behavior. Solutions of the spherical model have been used to investigate the critical behavior of a large variety os systems (with different types of disorder, with competing interactions, of short and long range, of ferro and antiferromagnetic nature, and many other situations). Solutions of these model systems display a number of anomalies at low temperatures, which include some violations of the third law of thermodynamics. In the seventies, it has been suggested that this anomalous behavior at very low temperatures would be corrected by the introduction of quantum uctuations, which were not taken into account by the classical solutions. In fact, the quantization of the spherical model leads to the correction of these effects. We then use two different methods of quantization, canonical quantization and representation in terms of functional integrals, which are still amenable to exact analytical calculations. We show that these quantum formulations lead to the same results. In particular, we analyze the thermodynamic properties of a quantum \\mean spherical model\" in the following situations: (i) with long-range, mean-field, interactions, which is perhaps the simplest model system that exhibits a quantum phase transition; (ii) with competing interactions between first and second neighbors, in which case there should be a Lifshitz multicritical point; (iii) in the presence of long-range interactions and of a random field of zero mean value; (iv) in the presence of disorder, such as the van Hemmen model for a spin glass or the Hopfield model for a neural network with just a few patterns. In all of these cases the anomalous behavior is corrected at low temperatures. We obtain a number of phase diagrams, and discuss the nature of the ordered phases.

Neste trabalho investigamos as propriedades estáticas de um modelo de vidro de spin esférico antiferromagnético com interação de multi-spins por meio do método das réplicas. O objetivo consiste em modelar materiais antiferromagnéticos diluídos como FexMg1-xCl2 e compostos antiferromagnéticos mistos como FexMn1-xTiO3 que apresentam evidências de comportamento característico da fase vidro de spin para um intervalo de valores de concentração x. Analisamos a solução réplica simétrica e a solução de Parisi com uma etapa de quebra de simetria entre réplicas, a qual espera-se que seja a solução mais geral para este modelo. Quatro fases são obtidas no diagrama de fases: paramagnética, vidro de spin, antiferromagnética e antiferromagnética com quebra de simetria ou fase mista. As linhas de transição podem ser contínuas ou descontínuas. / In this work we investigate the static properties of a multi-spin antiferromagnetic spherical spin-glass model using the replica method. The aim is to try to model diluted antiferromagnetic materials (e.g. FexMg1-xCl2) and mixed antiferromagnetic compounds (e.g. FexMn1-xTiO3) that present evidences of a spin-glass behavior for certain range of x values. The replica-symmetric and the one-step replica-symmetry-breaking solution given by Parisi are analised, the last one being expected to be the most general solution for this model. Four phases are found in the phase diagram: paramagnetic, spin glass, antiferromagnetic and mixed or glassy antiferromagnetic phase. The transition lines may be either continuous or discontinuous.

We present a system that estimates the motion of a robot relying solely on images from onboard omnidirectional camera (visual odometry). Compared to other visual odometry hardware, ours is unusual in utilizing high resolution, low frame-rate (1 to 3 Hz) omnidirectional camera mounted on a robot that is propelled using continuous tracks. We focus on high precision estimates in scenes, where objects are far away from the camera. This is achieved by utilizing omnidirectional camera that is able to stabilize the motion estimates between camera frames that are known to be ill-conditioned for narrow field of view cameras and the fact that low frame-rate of the imaging system allows us to focus computational resources on utilizing high resolution images. We employ feature based-approach for estimation camera motion. Given our hardware, possibly high ammounts of camera rotation between frames can occur. Thus we use techniques of feature matching rather than feature tracking.

Made available in DSpace on 2015-04-22T22:16:05Z (GMT). No. of bitstreams: 1 Celia Maria Nogueira Batista.pdf: 1926587 bytes, checksum: f61cde4e613a60695c9ce389a0eba8b1 (MD5) Previous issue date: 2007-12-26 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / This thesis presents a new demonstration of the result FOR Plato not the fourth century BC in Ancient Greece, to que There hum Finite number of classes Poliedro Regular congruent, using a basic theory of spherical geometry, of the agreement with the work " The solid platonicos " make Dr. John Lucas Marques Barbosa University of Ceará, presented in Manaus. / Esta dissertação apresenta uma nova demostração do resultado obtido por Platão no século IV a.C, na Grécia antiga, de que existe um número finito de classes de Poliedro regulares congruentes, usando a teoria básica da Geometria Esférica, de acordo com o trabalho "Os sólidos Platônicos", do Dr. joão Lucas Marques Barbosa da Universidade do Céara, apresentado em Manaus.

The recent popularity of Bayesian inference is due to the practical advantages of the Bayesian approach. The Bayesian analysis makes it possible to reflect ones prior beliefs into the analysis. In this thesis, we explore some asymptotic results in Bayesian nonparametric inference for restricted and unrestricted space of distributions. This thesis is divided into two parts. In the first part, we employ the Dirichlet process in a hypothesis testing framework to propose a Bayesian nonparametric chi-squared goodness-of-fit test. Our suggested method corresponds to Lo's Bayesian bootstrap procedure for chi-squared goodness-of-fit test. Indeed, our bootstrap rectifies some shortcomings of regular bootstrap which only counts number of observations falling in each bin in contingency tables. We consider the Dirichlet process as the prior for the distribution of data and carry out the test based on the Kullback-Leibler distance between the Dirichlet process posterior and the hypothesized distribution. We prove that this distance asymptotically converges to the same chi-squared distribution as the classical frequentist's chi-squared test. Moreover, the results are generalized to the chi-squared test of independence for contingency tables. In the second part, our main focus is on Bayesian nonparametric inference for a restricted group of distributions called spherically symmetric distributions. We describe a Bayesian nonparametric approach to perform an inference for a bivariate spherically symmetric distribution. We place a Dirichlet invariant process prior on the set of all bivariate spherically symmetric distributions and derive the Dirichlet invariant process posterior. Indeed, our approach is an extension of the Dirichlet invariant process for the symmetric distributions on the real line to bivariate spherically symmetric distribution where the underlying distribution is invariant under a finite group of rotations. Further, we obtain the Dirichlet invariant process posterior for the infinite transformation group and we prove that it approaches a certain Dirichlet process. Finally, we develop our approach to obtain the Bayesian nonparametric posterior distribution for functionals of the distribution's support when the support satisfies certain symmetry conditions. When symmetry holds with respect to the parallel lines of axes (for example, in two dimensional space x = a and y = b) we employ our approach to approximate the distribution of certain functionals such as area and perimeter for the support of the distribution. This suggests a Bayesian nonparametric bootstrapping scheme. The estimates can be derived based on posterior averaging. Then, our simulation results demonstrate that our suggested bootstrapping technique improves the accuracy of the estimates.

Origami is a potentially elegant and powerful source of inspiration for many engineering designs. The viable shapes (fold states) of a single device allow it to perform multiple, seemingly contradictory, functions. The fold state is a large factor in the device's performance, but there are challenges in selecting and maintaining those fold states. In this thesis we analyze existing concepts for overcoming these challenges. Those concepts are compared with those that occur in origami-based devices. From this analysis fundamental gaps were identified, specifically, shortcoming in the terminology used to refer to (1) non-flat origami states and (2) sets of facets and creases. Likewise we found a need for a comprehensive categorization method of fold states. Fold states are divided into seven types based on the set of fold angles they contain: U, P, F, UP, UF, PF, and UPF. The origami-based devices are analyzed based on their functional fold states, showing an emphasis on P and PF fold states. The fold states and their functions are tabulated. We demonstrate the table as a tool in an origami-based design method. Selecting fold states for an application is just the first step for effective use of origami. Once selected, the origami fold state must be maintained during use to perform its functions. This thesis also outlines the Origami Stability Integration Method (OSIM) for integrating a wealth of stability techniques. These techniques are categorized and analyzed to assist designers in selecting a technique for a device's application. Both methods, the fold-state selection method and the OSIM, are demonstrated in designing an origami-based ballistic barrier. The barrier is designed to stow in a compact fold state and deploy to a partially folded state to provide protection during armed conflicts. Quick deployment and a stable structure make the barrier a valuable example of origami-based design, demonstrating these two methods in addressing some of origami's design challenges.