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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho e apresentada uma abordagem dos temas estudados na Geometria Analtica do Ensino Básico. Destinado a professores e alunos de iniciação científica do Ensino Médio tem por finalidade transpor a nossa limitada visualisação das formas e relações geométricas vistas na Geometria Analtica básica, estudando-as a luz de uma visão n-dimensional. Usa-se como suporte teórico a Álgebra Vetorial, que nos possibilitara o entendimento de como funciona no espaco euclidiano Rn os elementos da Geometria Analtica. Inicialmente são apresentados alguns elementos da Álgebra Vetorial que nortear~ao o estudo no referido espaço, encontrados na literatura. Apresenta-se as condições para a colinearidade e coplanaridade de pontos. Bem como o cálculo da distância entre pontos, entre ponto e reta, entre retas e entre ponto e hiperplano, as posições relativas entre retas, entre reta e o hiperplano e entre hiperplano e hiperesfera. / In this work a wider approach of the topics studied in the Analytical Geometry of Basic Education will be presented. For teachers and high school students, aims to overcome our limited visualization of geometric shapes and geometric relationships seen in the Analytic Geometry Basic, studying the light of an n-dimensional view. Is used as the theoretical support the Vector Algebra, which will enable us to understand how it works in the Euclidean space Rn elements of analytic geometry. Initially some elements of Vector Algebra that will guide the study in Euclidean space. It presents the conditions for collinearity and coplanarity of points. As well as calculating the distance between points, between point and the straight, between straights, between point and hyperplane and the relative positions between straights, between straight and hyperplane and between hyperplane and hypersphere.

Over the last several years a branch of Artificial Intelligence called Qualitative Reasoning has received much attention. A qualitative reasoner use qualitative values such as increasing, boiling and turbulent to analyze the behavior of physical systems. Existing qualitative frameworks have focused on physical systems whose qualitative values can be identified given the value of a single parameter. This precludes the application of qualitative models to physical systems whose properties require the values of several parameters. An example of such a system is the kinematics of a robotic manipulator. With this motivation, this thesis answers the following: What is a Qualitative model? Although current approaches appear diverse, they share a common mathematical foundation. This foundation is used to reformulate the qualitative model as a set of equivalence relations. The other question answered is: What extensions are needed to handle multivariate properties such as those encountered in the manipulator paradigm? The equivalence classes associated with qualitative models are geometrically shown to be connected hyperspaces. We show that existing frameworks are limited in the types of hyperspaces they can represent. The major ideas in this thesis are illustrated using manipulator kinematics. / Science, Faculty of / Computer Science, Department of / Graduate

The discovery of new geometries in the 19th century and the departure from an absolute to a relative understanding of space-time, together with the invention of higher dimensions have caused a shift towards the idealization of space. This new type of ideal space was called hyperspace. The counter-intuitive quality of hyperspace has opened up new formal possibilities and representation techniques in art and architecture. In a similar manner, with the introduction of computers, the virtual and immaterial quality of cyberspace has offered new design techniques and forms to architecture. Algorithmic design tools and the use of surface as the primary architectural element in cyberspace have caused a shift in the conception of space together with the way it is perceived. Taking its departure point from physical space, this thesis investigates the upper and lower dimensions of space in order to understand and analyze the current conception of architectural space in the virtual realm. Three types of spatial qualities are investigated in detail: the ideal characteristic of hyperspace, the visual medium of cyberspace and the algorithmic formation of hypospace.

The goal of this research was to determine if the results of a simple comparison algorithm (SCA) could be improved by adding a hyperspace analogue to language model of memory (HAL) layer to form NCA. The HAL layer provides contextual data that otherwise would be unavailable for consideration. It was found that NCA did improve the results when compared to SCA alone. However, NCA added complexity problems that limit its practicality. The complexity of this algorithm is On3 where n is equal to the number of unique symbols in the data. While there is a relativity reasonable soft upper bound for the number of unique symbols used in a language, the complexity still limits the uses of the NCA combined algorithm. The conclusion from this research is that NCA can improve results. This research also suggested that the quality of results might increase as more data is processed by NCA.

This thesis is meant to give an explication on Fredric Jameson¡¦s Utopian thinking through transcoding, establishing homologies between Lacan¡¦s Imaginary/Symbolic/Real registers, Althusser¡¦s ideology/History binary and Jameson¡¦s ideology/cognitive mapping/History orders. I think Jameson¡¦s Utopian thinking is a mechanism of praxis to induce change for a classless and human-friendly society through theoretical education on desire and formation of consciousness of the capitalistic alienation and exploitation. It is a process of signifying, with no signified. It aims at the construction of a map of the social totality, not at that of an imaginary blueprint. It stresses consciousness-raising, not goal achievement. Traditionally, Utopia features an imaginary blueprint. Nevertheless, for Jameson, the Utopian blueprint is problematic in that it is ideologically enclosed so that it is far from qualified to serve as the goal of praxis. At best, a Utopian blueprint can only be viewed as a ¡§figure¡¨ waiting for the interpretation of theory, or to put it psychoanalytically, it is a symptom of the (political) unconscious awaiting the diagnosis of a psychoanalyst. But Jameson does endorse Utopists¡¦ ¡§Utopian praxis¡¨ to map and criticize their respective social context. The critic applies the practice to the postmodern, in which time is spatialized and the individual is fragmented and deprived of the ability to think historically and to imagine an alternative future. Jameson proposes the approach of ¡§cognitive mapping¡¨ to help people to obtain a map of the postmodern hyperspace, to locate their positions in it, and to finally reconstruct in them class consciousness, which Jameson believes is the basis of praxis for a Utopia. This task has to be done through the construction of the collective subject, because of the death of the subject and the growing abstraction of postmodern hyperspace. And certainly in this undertaking, Marxist critics like Jameson play an important role. They, like a psychoanalyst, are entitled to diagnose and interpret what the current world is suffering from and to offer prescriptions. In conclusion, Fredric Jameson¡¦s Utopian thinking is a persistent process of praxis at present to form collective consciousness and subjectivity in the hope of an unspecified Utopia in the future, which is supposed to be a communist one.

Wireless communications systems underwent an evolution as the voice oriented applications evolved to data and multimedia based services. Furthermore, current wireless technologies, regulations and the un- derstanding of the technology are insufficient for the requirements of future wireless systems. Along with the rapid rise at the number of users, increasing demand for more communications capacity to deploy multimedia applications entail effective utilization of communications resources. Therefore, there is a need for effective spectrum allocation, adaptive and complex modulation, error recovery, channel estimation, diversity and code design techniques to allow high data rates while maintaining desired quality of service, and reconfigurable and flexible air interface technologies for better interference and fading management. However, traditional communications system design is based on allocating fixed amounts of resources to the user and does not consider adaptive spectrum utilization. Technologies which will lead to adaptive, intelligent, and aware wireless communications systems are expected to come up with consistent methodologies to provide solutions for the capacity, interference, and reliability problems of the wireless networks. Spectrum sensing feature of cognitive radio systems are a step forward to better recognize the problems and to achieve efficient spectrum allocation. On the other hand, even though spectrum sensing can constitute a solid base to achieve the reconfigurability and awareness goals of next generation networks, a new perspective is required to benefit from the whole dimensions of the available electro hyperspace. Therefore, spectrum sensing should evolve to a more general and comprehensive awareness providing a mechanism, not only as a part of CR systems which provide channel occupancy information but also as a communication environment awareness component of dynamic spectrum access paradigm which can adapt sensing parameters autonomously to ensure robust identification and parameter estimation for the signals over the monitored spectrum. Such an approach will lead to recognition of communications opportunities in different dimensions of spectrum hyperspace, and provide necessary information about the air interfaces, access techniques and waveforms that are deployed over the monitored spectrum to accomplish adaptive resource management and spectrum access. We define multidimensional signal analysis as a methodology, which not only provides the information that the spectrum hyperspace dimension in interest is occupied or not, but also reveals the underlaying information regarding to the parameters, such as employed channel access methods, duplexing techniques and other parameters related to the air interfaces of the signals accessing to the monitored channels and more. To achieve multidimensional signal analysis, a comprehensive sensing, classification, and a detection approach is required at the initial stage. In this thesis, we propose the multidimensional signal analysis procedures under signal identification algorithms in time, frequency. Moreover, an angle of arrival estimation system for wireless signals, and a spectrum usage modeling and prediction method are proposed as multidimensional signal analysis functionalities.

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Cette thèse se consacre premièrement à certains aspects de la définition de charges conservées en relativité générale pour les espaces asymptotiquement plats à l’infini spatial. À l’aide de la dualité gravitationnelle, présente au niveau linéarisé, on étudie également l’existence de charges topologiques, magnétiques, ainsi que leurs contributions aux superalgèbres dans les théories de supergravité N = 1 et N = 2 à quatre dimensions. La thèse est divisée en trois parties.<p>Dans la première partie, les espaces asymptotiquement plats à l’infini spatial sont décrits à l’aide d’une généralisation de la métrique de type Beig-Schmidt. La construction de charges à partir de l’étude des équations du mouvement et de la classification de tenseurs symétriques et de divergences nulles nous permet de démontrer l’unicité des charges de Poincaré pour l’ansatz non-généralisé en présence de conditions de parité. L’équivalence des charges de Ashtekar- Hansen et Mann-Marolf est ainsi revisitée. Dans le cas d’un ansatz généralisé, une régulation de la forme symplectique divergente, à l’aide de contre-termes rajoutés à l’action de Mann-Marolf, nous donne la possibilité de considérer un espace des phases sans conditions de parité, tout en gardant un principe variationnel bien défini. Le groupe asymptotique comprend alors, en plus des charges de Poincaré où les charges de Lorentz ne sont plus asymptotiquement linéaires, des charges non-triviales associées aux supertranslations et aux transformations logarithmiques.<p>Dans la deuxième partie, on étudie la dualité gravitationnelle et la définition de charges magnétiques en gravitation linéarisée. On revisite la dualité et on montre qu’une dualisation sur les indices de Lorentz facilite la compréhension de celle-ci. Les dix charges de Poincaré ainsi que leurs duales magnétiques sont alors exprimées en termes d’intégrales de surface. Nous illustrons ensuite nos résultats à travers l’étude des sources de certaines solutions électriques et de leur duales magnétiques. Les solutions électriques envisagées sont :les trous noirs de type Schwarzschild et de type Kerr ainsi que les ondes de chocs de type pp.<p>Dans la dernière partie, on établit la supersymétrie des espaces de type Taub-NUT lorentzien chargés électriquement et magnétiquement dans la supergravité N = 2. Motivé par l’existence d’une égalité BPS, on entreprend alors une recherche sur l’inclusion de la charge NUT dans l’algèbre de supersymétrie. Grâce à une complexification de la forme de Witten-Nester, cette contribution de la charge NUT à la superalgèbre est comprise comme une déformation topologique, symétrique, au crochet antisymétrique des super-charges. Ce résultat est alors appliqué à la superalgèbre N = 1 à travers l’étude des ondes de chocs de type pp.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished