Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (leaves 112-113).

In this diploma thesis, we create a collection of folk songs with piano accompaniments for primary school. The complexity of said accompaniments is offered in two versions: basic one for beginners and more advanced one for skilled piano players. This collection contains songs in major and minor key, duple and triple time.

Orientadores: Sergio Antonio Tozoni, Alexander Kushpel / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T21:23:04Z (GMT). No. of bitstreams: 1 Oliveira_FernandaMourade_M.pdf: 1054228 bytes, checksum: 75fe14a8c8e718328bbee826a80d14ae (MD5) Previous issue date: 2005 / Resumo: O objetivo da dissertação e desenvolver um texto em português sobre Análise Harmônica na esfera d-dimensional real e aplicar os resultados deste texto no estudo de um teorema de multiplicadores. Nos dois primeiros capítulos e realizado um estudo sobre funções harmônicas em um domínio do espaço euclidiano Rd+1, harmônicos esféricos, representações de SO(d+1), harmônicos zonais, polinômios ultraesféricos e sobre o operador de Laplace Beltrami para a esfera. Finalmente, no terceiro capítulo é estudado um teorema de multiplicadores recente, o qual fornece condições suficientes para que um operador multiplicador seja limitado de Lp(Sd) em Lq(Sd), para quaisquer p e q, 1=p, q=8. Como aplicação deste teorema são obtidas estimativas superiores para n-larguras de Kolmogorov de classes de Sobolev nos espaços Lq(Sd), 1=p, q= 8, g > 0 / Abstract: The purpose of this work is to develop a text in Portuguese about Harmonic Analysis on the d-dimensional real sphere Sd and to apply the results of the text to study a multiplier theorem. In the first two chapters it is made a study about harmonic functions in a domain of the euclidian space Rd+1, spherics harmonics, representations of SO(d+1), zonal harmonics, ultraspherics polynomials and about the Laplace Beltrami operator on the sphere. Finally, in the third chapter it is studied a recent multiplier theorem which gives sufficient conditions for a multiplier operator be bounded from Lp(Sd) to Lq(Sd), for 1=p, q=8. As application of this theorem are obtained upper bounds for n-widths of Kolmogorov type of Sobolev classes in the spaces Lq(Sd), 1=p, q= 8, g > 0 / Mestrado / Matematica / Mestre em Matemática

La thèse se compose de 3 parties. Dans la partie I, nous considérons des problèmes à lafrontière pour une EDP de Laplace dans un domaine simplement connexe de bordLispschitz continu. Depuis des données Dirichlet et Neumann suffisamment régulièresdisponibles sur une partie de la frontière, nous développons une méthode non-itérative derésolution de ce problème de Cauchy, régularisé par une contrainte en norm L2 portantsur la solution sur la partie complémentaire du bord. Notre approche par les fonctionsanalytiques de la variable complexe permet d'imposer des contraintes ponctuellessupplémentaires possédant un intêret pratique pour incorporer des mesures corrompues.La partie II concerne la structure spectrale d'un opérateur de Poisson tronqué intervenantdans diverses applications physiques. Nous établissons d'importantes propriétés dessolutions, des connexions avec d'autres problèmes, ainsi que, pour des valeursasymptotiques d'un paramètre, des formulations sous forme d'autres équations intégralesou EDO solubles. Dans la partie III, nous traitons un problème inverse particulier issud'expériences pratiques effectuées avec un microscope SQUID. Depuis des mesurespartielles de la composante verticale du champ magnétique, le but est de retrouvercertaines propriétés de l'aimantation d'un échantillon de roche. Nous présentons denouvelles méthodes utilisant les transformations de Kelvin et de Fourier pour l'estimationdu moment magnétique. / The thesis consists of three parts. In Part I, we consider partially overdeterminedboundary-value problemS for Laplace PDE in a planar simply connected domain withLipschitz boundary. Assuming Dirichlet and Neumann data available on its part to be realvaluedfunctions of certain regularity, we develop a non-iterative method for solving thisill-posed Cauchy problem choosing as a regularizing parameter L2 bound of the solutionon complementary part of the boundary. The present complex-analytic approach alsonaturally allows imposing additional pointwise constraints on the solution which, onpractical side, can help incorporating outlying boundary measurements without changingthe boundary into a less regular one. Part II is concerned with spectral structure of atruncated Poisson operator arising in various physical applications. We deduce importantproperties of solutions, discuss connections with other problems and pursue differentreductions of the formulation for large and small values of asymptotic parameter yieldingsolutions by means of solving simpler integral equations and ODEs. In Part III, we dealwith a particular inverse problem arising in real physical experiments performed withSQUID microscope. The goal is to recover certain magnetization features of a sample frompartial measurements of one component of magnetic field above it. We develop newmethods based on Kelvin and Fourier transformations resulting in estimates of netmoment components.

In this thesis, an approach for robot motion control with collision avoidance and human-following is investigated. Using velocity potential fields approach in a modified, quasi-harmonic, solution, the navigation controller is developed. A quasi-harmonic function based controller uses harmonic solutions for collision avoidance and smoothly changes toward a non-harmonic solution which tends toward a zero velocity command only when approaching the goal. After the motion controller was created, human-following strategy was designed to let a non-holonomic robot have the ability to follow a human in an unknown environment with obstacles. The approach is based on velocity potential fields that permit to generate velocity vector commands that drive the robot at a safe distance with regard to the human while avoiding obstacles. The quasi-harmonic approach is investigated analytically using symbolic math solutions of MAPLETM as well as in simulations using MATLABTM. Motion simulations of both holonomic and non-holonomic robot motion illustrate how the proposed approach operates. Experiments are also made with LEGO MINDSTROMS NXT robot to test the algorithm in environment with simple and complex obstacles.

L’analyse examina l’impact des relations tonales, des fonctions et des types formels transformés sur l’unité compositionnelle dans les œuvres orchestrales de Max Reger. Le contexte théorique est celui de nouvelles Formenlehre et Harmonielehre. La forme conçue comme une succession des fonctions fut analysée sur la base de la théorie des fonctions formelles de Caplin. Son apparatus analytique a été combiné avec le modèle sophistiqué de ponctuation et le concept de la déformation de la théorie de la sonate de Hepokoski et Darcy. En examinant les relations et la structure tonales, l’analyse adhère au concept de la monotonalité de Schoenberg. L’attention analytique fut focalisée sur les motifs harmoniques dérivés des accords, des progressions et de la ligne de basse. La Grundgestalt (une configuration fondamentale) fut perçue comme une structure motivique ou un contour intervallique quasi-arythmique. L’analyse montra comment Reger avait confirmé la clarté de l’unité tonale du mouvement ou de l’œuvre. / The analysis examined the impact of tonal relations and transformed formal types and functions on the compositional unity in Max Reger’s orchestral works. The theoretical background consisted of New Formenlehre and Harmonielehre. The form conceived as a succession of functions, was analyzed on the basis of Caplin’s formal function theory. His analytical apparatus was combined with the sophisticated punctuation model and the concept of “deformation” developed in the competing sonata theory of Hepokoski and Darcy. In consideration of tonal relationships and structure, the analysis adhered to Schoenberg’s concept of monotonality. The analytical attention was focused on harmonic motives derived from chords, progressions and the bass line. The Grundgestalt (basic configuration) was perceived as a motivic structure or quasi-arrhythmic interval contour. The analysis showed how Reger has confirmed the clarity of the tonal unity of a movement or work in whole.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1980. / Microfiche copy available in Archives and Science. / Vita. / Bibliography: leaves 196-201. / byLee-Lueng Fu. / Ph.D.

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