Reproduction de : Thèse de docteur-ingénieur : mathématiques : Grenoble 1 : 1956. / Titre provenant de l'écran-titre. Bibliogr. p. 91.

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This thesis introduces the p-adic metric on the rational numbers. We then present the basic properties of this metric. Using this metric, we explore conic sections, viewed as equidistant sets. Lastly, we move on the sequences and series, and from there, we define p-adic expansions and the analytic completion of Q with respect to the p-adic metric, which leads to exploring some arithmetic properties of Qp.

The research presented in this thesis focuses on the use of feedback control for lowering acoustic levels within launch vehicle payload fairings. Due to the predominance of conical geometries within payload fairings, our work focused on the analytical modeling of conical shrouds using modal and impedance based models. Incorporating an actuating boundary condition within a sealed enclosure, resonant frequencies and mode shapes were developed as functions of geometric and mechanical parameters of the enclosure and the actuator. Using a set of modal approximations, a set of matrix equations have been developed describing the homogeneous form of the wave equation. Extending to impedance techniques, the resonant frequencies of the structure were again calculated, providing analytical validation of each model. Expanding this impedance model to first order form, the acoustic model has been coupled with actuator dynamics yielding a complete model of the system relating pressure to control voltage. Using this coupled state-space model, control design using Linear Quadratic Regulator and Positive Position Feedback techniques has also been presented. Using the properties of LQR analysis, an analytical study into the degree of coupling between actuator and cavity as a function of actuator resonance has been conducted. Constructing an experimetnal test-bed for model validation and control implementation, a small sealed enclosure was built and outfitted with sensors. Placing a control speaker at the small end of the cone the large opening was sealed with a rigid termination. An internal acoustic source was used to excite the system and pressure measurements were captured using an array of microphones located throughout the conic section. Using the parameters of this experimental test-bed, comparisons were made between LQR and PPF control designs. Using an impulse disturbance to excite the system, LQR simulations predicted reductions of 53.2% below those of the PPF design, while the control voltages corresponding to these reductions were 43.8% higher for LQR control. Actual application of these control designs showed that the ability to manually set PPF gains made this design technique much more convenient for actual implementation. Yielding overall attenuation of 38% with control voltages below 200 mV, single-channel low authority control was seen to be an effective solution for low frequency noise reduction. Control was then expanded to a larger geometry representative of Minotaur fairings. Designing strictly from experimental results, overall reductions of 38.5% were observed. Requiring slightly larger control voltages than those of the conical cavity, peak voltages were still found to be less than 306 mV. Extrapolating to higher excitation levels of 140 dB, overall power requirements for 38.5% pressure reductions were estimated to be less than 16 W. / Master of Science

Neste trabalho abordaremos alguns assuntos relacionados Ãs SeÃÃes CÃnicas: elipse, parÃbola e hipÃrbole. O trabalho està dividido em cinco capÃtulos: IntroduÃÃo; Origem das CÃnicas; EquaÃÃes das CÃnicas; Propriedades de ReflexÃo das CÃnicas; Construindo CÃnicas. No segundo capÃtulo, falaremos sobre o problema da duplicaÃÃo do cubo que, segundo a HistÃria da MatemÃtica, deu origem as cÃnicas e citaremos alguns matemÃticos cujos trabalhos contribuÃram para o desenvolvimento do estudo dessas curvas. No terceiro capÃtulo, estudaremos as equaÃÃes cartesianas das cÃnicas, bem como as suas representaÃÃes grÃficas e os principais elementos da cada cÃnica. No quarto capÃtulo, apresentaremos as propriedades de reflexÃo das cÃnicas e algumas aplicaÃÃes muito interessantes dessas propriedades. No Ãltimo capÃtulo, demonstraremos alguns mÃtodos para construir cÃnicas e em seguida faremos essas construÃÃes na prÃtica atravÃs de materiais concretos e por meio de um programa de Geometria DinÃmica, chamado Geogebra. / In this paper we discuss some issues related to Conic Sections: ellipse, parabola and hyperbole. The work is divided into five chapters: Introduction; Origin of Conic Sections; Equations of Conic Sections; Reflection Properties of Conic Sections; Building Conic Sections. In the second chapter, weâll talk about doubling the cube problem that, according to the History of Mathematics, originated the conic sections and talk about some mathematicians whose work contributed to the study of these curves. In the third chapter, we will study the Cartesian equations of conic sections, as well as their graphical representations and the main elements of each curve. In the fourth chapter, we presented the reflection properties of conic sections and some very interesting applications of these properties. In the last chapter, we will show some methods to construct conic sections and then we will make these constructs in practice through concrete materials and through a dynamic geometry program, called Geogebra.

Made available in DSpace on 2016-04-27T16:57:12Z (GMT). No. of bitstreams: 1 Marcelo Balduino Silva.pdf: 31298472 bytes, checksum: 7bddc51f9065f44543df030615d071b0 (MD5) Previous issue date: 2011-11-21 / Secretaria da Educação do Estado de São Paulo / The present dissertation proposes, based on the Mathematics curriculum of São Paulo State Educational Secretary (SEE-SP), complementary activities to the material supplied by the SEE-SP, seeking to approach less discussed aspects of the curriculum on the conic sections.The activities were elaborated according to the instruction to the material designated to the teachers for the use of digital technologies and software of dynamic geometry. Such activities were presented to the state public network teachers, in a formation course offeredby the conic section classes. During the course for the teachers formation audio records were taken of the spontaneous manifestations of the educators.Such manifestations were analyzed in order to answer the following questions: what activities could be recommended for the teacher work based on the São Paulo State curriculum? Which aspects should be taken in consideration by the public network teachers of São Paulo Statefacing the challenge of creating complementary activities to the pedagogical proposal in the teacher sguide book? The records of the teachers manifestations show the importance of continuing formations, the interest for certain approaches and possible obstacles for the implementation of such activities in the classroom / A presente dissertação propõe, baseada no currículo de Matemática do Estado de São Paulo, atividades complementares ao material fornecido pela Secretaria de Educação do Estado de São Paulo SEE-SP procurando abordar aspectos menos discutidos pelo currículo sobre as secções cônicas. As atividades foram elaboradas seguindo a orientação do material destinado aos professores para o uso de tecnologia digital e softwares de matemática dinâmica. Tais atividades foram apresentadas a professores da rede pública estadual, em curso de formação fornecido pela Pontifícia Universidade Católica de São Paulo no primeiro semestre de 2011, no qual o pesquisador foi responsável pelas aulas sobre secções cônicas. Durante o curso de formação dos professores, foram registradas em gravações de áudio, as manifestações espontâneas dos educadores. Tais manifestações foram analisadas a fim de responder as seguintes questões: Que atividades poderiam ser recomendadas para o trabalho do professor com base no currículo atual do Estado de São Paulo? Quais aspectos seriam levados em conta pelos professores da rede pública do Estado de São Paulo diante do desafio de criar atividades complementares à proposta pedagógica do caderno do professor? Os registros das manifestações dos professores mostram a importância da formação continuada, o interesse por determinadas abordagens e possíveis obstáculos na implantação em sala de aula destas atividades

Aim: The primary aim of this study was to find if there is any correlation between the corneal radius of curvature and its eccentricity. Method: 45 subjects participated in this study, 24 emmetropes, 18 myopes and three hyperopes. All subjects were free of ocular abnormalities and had no media opacities. All the subjects had normal ocular health and good visual acuity of 1.0 or better for both distance and near. The values for eccentricity and corneal radius of curvature were obtained by using a Topcon CA-100F Corneal Analyzer. Results: For the 4.5 mm zone the only significant correlation between corneal radius of curvature and eccentricity was obtained for the mean of the meridian (p = 0.007). On the other hand, we found no significant correlation for the average of two meridians or for meridian 1 and meridian 2 separately in the 8.0 mm zone. Conclusions: We found no correlation between the corneal radius of curvature and the eccentricity for both zones. In addition, no correlation could be found between the spherical equivalent of the refractive errors and the corneal eccentricity. The reason for not finding any significant correlation between the two entities could be due to factors such as smaller sample size and poor distribution of refractive errors in the sample. Moreover, there may be other factors that could influence the overall corneal shape like eye shape, axial length and corneal diameter, which was not evaluated in this study.

nÃo hà / Neste trabalho, falaremos sobre cÃnicas e equaÃÃo geral do segundo grau, histÃrico e parte teÃrica, aplicando estes conhecimentos na elaboraÃÃo de planilhas eletrÃnicas para identificar qual a cÃnica (elipse, hipÃrbole ou parÃbola, bem como seus casos degenerados) e determinar seus principais elementos a partir de suas equaÃÃes, na forma canÃnica ou geral do segundo grau. Para melhor compreensÃo e fixaÃÃo do que vai ser exposto, faremos uso de atividades interativas com a utilizaÃÃo de computador. / In this paper, we will discuss general conic and quadratic equation, historical and theoretical part, applying this knowledge in designing spreadsheets to identify which conic (ellipse, parabola or hyperbola, as well as their degenerate cases) and determine its main elements from their equations in canonical or general high school.For better understanding and assessment of what will be, we will make use of interactive activities with the use of computer.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-04-27T13:09:17Z No. of bitstreams: 2 Dissertação - Ruimar Calaça de Menezes - 2014.pdf: 3563938 bytes, checksum: 780f3827908c962633ef10e7001a936e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-04-27T13:14:20Z (GMT) No. of bitstreams: 2 Dissertação - Ruimar Calaça de Menezes - 2014.pdf: 3563938 bytes, checksum: 780f3827908c962633ef10e7001a936e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-04-27T13:14:20Z (GMT). No. of bitstreams: 2 Dissertação - Ruimar Calaça de Menezes - 2014.pdf: 3563938 bytes, checksum: 780f3827908c962633ef10e7001a936e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-03-06 / The objective of this study is to present the Quadratic Function in a new graphic perspective. The Quadratic Function content is taught in the ninth year of elementary school and rst year of high school, the following concepts are learned: equations and inequalities involving polynomials of second degree, graphing, concavity, zeros of the quadratic function, the parable vertex, minimum or maximum and applications in other elds of knowledge. Two mathematical softwares, Winplot and Geogebra, were used in order to facilitate the understanding of graphic representations of functions. The parable was discussed from a historical point of view that also included the concept of speci c terms and de nitions involving functions. The concept of tangent lines to growth and decrease of functions was related. The parable was also exhibited in the context of Analytic Geometry and Calculus, emphasizing the in uence of each coe cient in relation to the graph. The parable was studied as one of the conic sections so studied by Apollonius. Some applications of the parable in daily life, physics and modeling problems were cited. / Este trabalho tem como objetivo apresentar a Fun c~ao quadr atica em uma nova perspectiva gr a ca. O conte udo Fun c~ao Quadr atica e ensinado no nono ano do Ensino Fundamental e primeira s erie do Ensino M edio, sendo trabalhados os seguintes conceitos: equa c~oes e inequa c~oes envolvendo polin^omios de 2o grau, representa c~ao gr a ca, concavidade, zeros da fun c~ao quadr atica, v ertice da par abola, valor m nimo ou m aximo e aplica c~oes em outras areas do conhecimento. Para desenvolver este trabalho, foram utilizados os softwares matem aticos Winplot e Geogebra, com o intuito de facilitar a compreens~ao das representa c~oes gr a cas das fun c~oes. A par abola foi comentada a partir de um contexto hist orico e abrangeu tamb em o conceito de termos espec cos e de ni c~oes envolvendo fun c~oes. Foi relacionado o conceito de retas tangentes ao crescimento e decrescimento das fun c~oes. Tamb em foi exibido a par abola no contexto da Geometria Anal tica e do c alculo diferencial, salientando a in u^encia de cada coe ciente em rela c~ao ao gr a co. A par abola foi estudada como uma das sec c~oes c^onicas t~ao pesquisadas por Apol^onio. Foi citada algumas aplica c~oes da par abola no cotidiano, na f sica e em problemas de modelagem.

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)