The present master thesis compares die theories of colors created by Johann Wolfgang von Goethe and Rudolf Steiner, who both created their individual theory as a reaction regarding another one published approximately a century prior to them. The thesis presents their theories and compares them on the basis of a certain set of categories. Their circumstances of origin, contemporaneous usage, interdisciplinarity and creation of the chromatic circle as an explanatory tool are defined and discussed. Furthermore a description of noticeable differences and similarities is added and the author points out the possible influences of the chromatic theories towards other poetical, philosophical or paedagogical works of the respetive creator.

Orientador: Suzinei Aparecida Siqueira Marconato / Banca: Maria Aparecida Bená / Banca: Jamil Viana Pereira / Resumo: As funções estudadas no Ensino Médio se resumem às polinomiais de primeiro e segundo grau, modulares, exponenciais, logarítmicas e trigonométricas. Os problemas de encontrar zeros de função são recorrentes e auxiliam na construção de gráficos e em suas análises. Dessa forma, o presente trabalho tem o objetivo de apresentar três métodos numéricos (métodos da bissecção, de Newton-Raphson e das secantes) para encontrar os zeros de função. Em especial, o método de Newton-Raphson é um exemplo de equação discreta, cujo ponto fixo será o zero da função. A teoria das Equações Discretas será abordada no Capítulo 3. No Capítulo 4, discutiremos o método gráfico que introduz os métodos numéricos. Na sequência, nos Capítulos 5, 6 e 7, é que, de fato, abordaremos os três métodos numéricos. Por fim, apresentamos uma proposta de atividade para o Ensino Médio. Para além de encontrar os zeros de função, os métodos numéricos motivam o estudo inicial de recorrência, limites e derivadas. Além disso, as aplicações dos métodos em sala de aula podem ser realizadas com o auxílio de softwares matemáticos que trabalhem com planilhas e gráficos / Abstract: The functions studied in high school are summarized in polynomials of first and second degree, modular, exponential, logarithmic and trigonometric. The problems to find zeros of functions are recurrent and assist in constructing the graphs and their analysis. Thus, this dissertation aims to present three numerical methods (methods of bisection, Newton-Raphson and secant) to find the zeros of function. In particular, the Newton-Raphson method is an example of a discrete equation which the fixed point will be the zero of function. The theory of discrete equations will be discussed in Chapter 3. Chapter 4 outlines the graphical method which introduces the numerical methods. Following, in Chapter 5, 6 and 7, is that, in fact, we'll discuss the three numerical methods. Finally, we present a proposed activity for high school. In addition to finding the zeros of function, the numerical methods motivate the initial study of recurrence, limits and derivatives. Furthermore, the applications of methods in the classroom can be performed with the aid of mathematical software to work with spreadsheets and charts / Mestre

La thèse a pour objectif le développement de méthodes performantes pour la résolution de problèmes non linéaires ne mécanique des solides. Il est coutume d'utiliser une méthode de type Newton qui conduit à la résolution d'une séquence de systèmes linéaires. De plus, la prise en compte des relations linéaires imposées à l'aide de multiplicateurs de Lagrange confère aux matrices une structure de point-selle. Dans un cadre plus général, nous proposons, étudions et illustrons deux classes d'enrichissement de préconditionneurs (limited memory preconditioners) pour la résolution de séquences de systèmes linéaires par une méthode de Krylov. La première est un extension au cas symétrique indéfini d'une méthode existante, développée initialement dans le cadre symétrique défini positif. La seconde est plus générale dans le sens où elle s'applique aus systèmes non symétriques. Ces deux familles peuvent être interprétées comme des variantes par blocs de formules de mise à jour utilisées dans différentes méthodes d'optimisation. Ces techniques ont été développées dans le logiciel de mécanique des solides Code_Aster (dans un environnement parallèle distribué via la bibliothèque PETSc) et sont illustrées sur plusieurs études industrielles. Les gains obtenus en terme de coût de calcul sont significatifs (jusqu'à 50%), pour un surcoût mémoire négligeable. / The thesis aims at developing efficient numerical methods to solve nonlinear problems arising un solid mechanics. In this field, Newton methods are currently used, requiring the solution of a sequence of linear systems. Furthermore, the imposed linear relations are dualized with the Lagrange multipliers, leading to matrices with a saddle point structure. In a more general framework, we propose two classes of preconditioners (named limited memory preconditioners) to solve sequences of linear systems with a Krylov subspace method. The first class is based on an extension of a method initially developed for symmetric positive definite matrices to the symmetric indefinite case. Both families can be interpreted as block variants of updating formulas used in numerical optimization. They have been implemented into the Code_Aster solid mechanics software (in a parallel distributed environement using the PETSc library). These new preconditioning strategies are illustrated on several industrial applications. We obtain significant gains in computational cost (up to 50%) at a marginal overcost in memory.

Made available in DSpace on 2016-06-02T20:28:31Z (GMT). No. of bitstreams: 1 DissCS.pdf: 762215 bytes, checksum: d3e016bba7e01e919bb3bc4e78b15d5d (MD5) Previous issue date: 2006-02-24 / Financiadora de Estudos e Projetos / In this work, we study the relation between Milnor's number and the Newton's number of a formal series. The former is always greater than or equal to the latter and equality occurs whan the formal series f has non-degenerate newtonian principal part at the origin. / Neste trabalho, estudamos a relação que existe entre o número de Milnor de uma série formal com o número de Newton. O número de Milnor de uma série formal é sempre maior ou igual ao número de Newton e a igualdade entre os números é obtida sempre que a série formal f possui parte principal Newton não-degenerada na origem.

Made available in DSpace on 2015-06-17T19:34:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-09-29. Added 1 bitstream(s) on 2015-06-18T12:49:14Z : No. of bitstreams: 1 000832285.pdf: 454402 bytes, checksum: 49609651ea8a2fa968ca19324e011ebc (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / As funções estudadas no Ensino Médio se resumem às polinomiais de primeiro e segundo grau, modulares, exponenciais, logarítmicas e trigonométricas. Os problemas de encontrar zeros de função são recorrentes e auxiliam na construção de gráficos e em suas análises. Dessa forma, o presente trabalho tem o objetivo de apresentar três métodos numéricos (métodos da bissecção, de Newton-Raphson e das secantes) para encontrar os zeros de função. Em especial, o método de Newton-Raphson é um exemplo de equação discreta, cujo ponto fixo será o zero da função. A teoria das Equações Discretas será abordada no Capítulo 3. No Capítulo 4, discutiremos o método gráfico que introduz os métodos numéricos. Na sequência, nos Capítulos 5, 6 e 7, é que, de fato, abordaremos os três métodos numéricos. Por fim, apresentamos uma proposta de atividade para o Ensino Médio. Para além de encontrar os zeros de função, os métodos numéricos motivam o estudo inicial de recorrência, limites e derivadas. Além disso, as aplicações dos métodos em sala de aula podem ser realizadas com o auxílio de softwares matemáticos que trabalhem com planilhas e gráficos / The functions studied in high school are summarized in polynomials of first and second degree, modular, exponential, logarithmic and trigonometric. The problems to find zeros of functions are recurrent and assist in constructing the graphs and their analysis. Thus, this dissertation aims to present three numerical methods (methods of bisection, Newton-Raphson and secant) to find the zeros of function. In particular, the Newton-Raphson method is an example of a discrete equation which the fixed point will be the zero of function. The theory of discrete equations will be discussed in Chapter 3. Chapter 4 outlines the graphical method which introduces the numerical methods. Following, in Chapter 5, 6 and 7, is that, in fact, we'll discuss the three numerical methods. Finally, we present a proposed activity for high school. In addition to finding the zeros of function, the numerical methods motivate the initial study of recurrence, limits and derivatives. Furthermore, the applications of methods in the classroom can be performed with the aid of mathematical software to work with spreadsheets and charts

Dans ce travail de thèse, nous nous sommes consacrés au développement d’un système robotique permettant de reproduire en laboratoire l’ensemble des perturbations subies par un sujet humain dans un transport en commun afin d’analyser et de comprendre le mécanisme de son équilibre postural. La reproduction en laboratoire des perturbations nécessitent la conception d’une plateforme dynamique non contrainte dans son déplacement. L’analyse de l’équilibre humain nécessite également le développement d’un modèle du pendule inversé de l’homme afin de définir des indices quantitatifs d’équilibre et de procéder à des analyses statistiques et comparatives. Grâce aux objectifs fixés par ce travail de recherche, nous avons réalisé une plateforme mobile omnidirectionnelle compacte pouvant supporter un sujet pesant 120kg. Cette plateforme confère au sujet placé dessus une meilleure perception de confort et de sécurité. Ses performances en termes de poursuite de trajectoire et de commande des accélérations ont été effectuées et évaluées. Ces performances sont très satisfaisantes par rapport aux expérimentations menées dans le métro puisque les accélérations réalisées sont supérieures aux valeurs exigées par ce moyen de transport. Ainsi, la plateforme est capable de reproduire une perturbation compatible avec le métro. Nous avons proposé deux méthodes d’analyse basées sur des accéléromètres triaxiaux connectés et synchronisés à la plateforme pour l’évaluation des paramètres de couple et de position articulaires de la cheville, du genou et de la hanche du sujet. Les résultats obtenus sont comparables à ceux obtenus par un système plus couteux de capture de mouvement avec logiciel biomécanique. De nouveaux indices d’équilibre ont été proposés à partir des paramètres biomécaniques de 22 sujets. Ces indices peuvent être exploités par les thérapeutes pour analyser et prévoir la capacité de maintien de l’équilibre d’un passager dans le métro ou plus généralement dans les transports en commun. / In this thesis, we achieved the development of a robotic system to reproduce in laboratory all the disturbances undergone by a human subject in public transport in order to make an analysis of postural balance. Reproductive simulated disturbances in laboratory require developing a dynamic platform unconstrained in its movement. Analysis of postural balance also requires the development of an inverted pendulum model to define quantitative indices of stability and to make comparative and statistical analysis. According the objectives of this research work, we realized a compact omnidirectional mobile platform capable of supporting a weight of about 120kg. This platform gives the subject placed on it a better perception of comfort and safety. Its performances in terms of trajectory tracking and acceleration control are carried out and evaluated. These performances are very satisfactory compared to experiments in the subway since the produced accelerations are higher than the values required by this means of transport. Thus, the platform is able to reproduce the perturbation compatible with the subway. We proposed two methods of analysis based on triaxial accelerometers connected and synchronized platform for evaluating torque and joint position of the ankle, knee and hip of the subject. The results obtained are comparable to those obtained by more expensive motion capture system with biomechanical software. New postural balance indices have been proposed from the biomechanical parameters of 22 subjects. These indices can be used by therapists to analyze and predict the ability of maintaining the balance of a passenger in the subway or more generally in public transport.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação de Mestrado Profissional em Ensino de Física, Mestrado Nacional Profissional em Ensino de Física, 2017. / Submitted by Raquel Almeida (raquel.df13@gmail.com) on 2017-08-01T16:26:31Z No. of bitstreams: 1 2017_JoãoPauloFerreiradaSilva.pdf: 3800317 bytes, checksum: 93963775381231f8f74ce40d6f0eea38 (MD5) / Approved for entry into archive by Raquel Viana (raquelviana@bce.unb.br) on 2017-08-25T21:39:08Z (GMT) No. of bitstreams: 1 2017_JoãoPauloFerreiradaSilva.pdf: 3800317 bytes, checksum: 93963775381231f8f74ce40d6f0eea38 (MD5) / Made available in DSpace on 2017-08-25T21:39:08Z (GMT). No. of bitstreams: 1 2017_JoãoPauloFerreiradaSilva.pdf: 3800317 bytes, checksum: 93963775381231f8f74ce40d6f0eea38 (MD5) Previous issue date: 2017-08-25 / Este trabalho tem por finalidade apresentar uma unidade didática que possibilite ao professor ensinar alguns conceitos de Física, mais especificamente a 2ª. Lei de Newton e força de atrito, para estudantes com deficiência visual. A unidade didática é composta por um texto de apoio em braile, exercícios para a utilização de calculadoras sonoras ou soroban e um material concreto constituído de uma maquete tátil inclinável e um carrinho de madeira com vetores reguláveis para facilitar o aprendizado dos estudantes. A sequência da aula baseia-se na teoria da aprendizagem significativa de Ausubel e nos princípios da Defectologia de Vygotsky. Participaram da pesquisa quatro estudantes da sala de recursos sendo três cegos e um com baixa visão. A coleta de dados restringiu-se a observação sobre a aplicação dos textos, dos exercícios da unidade didática e do desempenho de cada estudante nos exercícios propostos, ao utilizar o recurso de cálculo escolhido, para a resolução dos mesmos. A unidade didática possibilitou dinamismo para a aula e uma maior interação do estudante com os conceitos trabalhados, além de permitir a inclusão do estudante com deficiência visual numa aula de Física. / The purpose of this paper is to present a didactic unit proposal that allows the teacher to present some concepts of Physics, more specifically the 2nd Newton's law and frictional force, for students with visual impairment. The didactic unit is composed by supporting text in Braille, exercises for the sound calculator and soroban and a concrete material consisting of a tiltable tactile model and a wooden cart with adjustable vectors to facilitate student learning. The sequence of the lesson is based on Ausubel's theory of meaningful learning and the principles of Vygotsky's Defectology. Four students participated on the research; three were blind and one with low vision. The data collection was restricted to the observation of the application of texts, exercises of the didactic unit and the performance of each student in the proposed exercises, using the chosen calculation resources. The didactic unit made possible dynamism for the class and a greater interaction of the student with the concepts and in a more concrete way, besides allowing inclusion of the visually impaired student in a Physics class.

This thesis interrogated the relationship between abolition and the evangelical revival in Britain through the life of John Newton. Newton, though not representative of every abolitionist, was a vital figure in the movement. His influence on Hannah More and William Wilberforce along with his contributions to the Parliamentary hearings made him a key aspect of its success. How he came to fulfill that role was a long and complex journey, both in terms of his religion and his understanding of slavery. He began his life under the spiritual direction of his pious, Dissenting mother, became an atheist by nineteen, and then an influential, evangelical minister in the Church of England in his later adulthood. In the midst of that journey, Newton was impressed, joined the crew of a slave ship, was himself enslaved, became a slave ship captain, and then, eventually, a fervent abolitionist. Though it was far from straightforward, Newton's evangelical Calvinistic theology seems to have driven him to ultimately condemn the slave trade. Understanding the relationship between Newton’s two conversions—to evangelical Christianity and abolitionism—gives modern readers’ insight into the intellectual roots of the abolitionist movement more broadly, the dynamics between Christianity and politics, as well as how individual moral choice can affect history.

Este projeto de pesquisa teve o objetivo de desenvolver uma nova abordagem para a resolução do Fluxo de Potência Ótimo. Para isso, foram obtidos dados teóricos, a partir de um levantamento bibliográfico, que explicitaram os conceitos de otimização aplicados ao sistema estático de energia elétrica. A pesquisa fundamentou-se metodologicamente nos métodos: Newton-Langragiano, Penalidade e Função Barreira Logarítmica de Newton Projetada. Os sistemas de equações resultantes das condições de estacionaridade da função Lagrangiana foram resolvidos pelo método de Newton. Na implementação computacional foram utilizadas técnicas de esparsidade. Foram realizadas estudos para validação e a verificação da abordagem proposta nos sistemas de 3, 14, 30 e 118 barras. / This research project had the objective of developing a new approach for the resolution of the Optimum Power Flow. For this purpose, theoretical data were obtained through a bibliographical survey, which explained the optimization concepts applied to the electrical energy static system. The research was based on the methods: Newton-Lagrangian, Penalty and Projected Newton Barrier Function. The systems of equations resulting from the Lagrangian function stationarity conditions were resolved through the Newton\'s method. In the computational implementation, sparsity techniques had been used. Studies had been carried out for the proposed approach validation and verification in the systems of 3, 14, 30 and 118 buses.

O Presente trabalho foi elaborado a partir de uma pesquisa aplicada em uma instituiÃÃo de ensino pÃblico com alunos do primeiro ano do ensino mÃdio, na qual buscou-se investigar os equÃvocos cometidos pelos discentes no que diz respeito ao estudo do uso do livro didÃtico para desenvolver o das leis de Newton. O tema à de muita relevÃncia pois, comumente à verificado que uma parcela dos estudantes nÃo compreende os conceitos relativos a este tÃpico e, como consequÃncia nÃo conseguem solucionar exercÃcios referentes ao assunto. EvidÃncias do trabalho aqui apresentado, apontam que o livro didÃtico quando faz uso de uma linguagem inapropriada na abordagem dos conceitos contribui para a disseminaÃÃo da dificuldade do aprendizado em relaÃÃo as leis de Newton, fazendo com que a resoluÃÃo de exercÃcios relacionados ao assunto torne-se uma dificuldade difÃcil de ser superado. No capÃtulo de introduÃÃo, sÃo levantadas algumas hipÃteses para a dificuldade de compreensÃo no estudo das leis de Newton bem como o contexto do estudo de fÃsica. Para a construÃÃo do referencial teÃrico discutiu-se a aprendizagem significativa, o papel do livro didÃtico no processo de ensino-aprendizagem e a formaÃÃo de professores no Brasil. O capÃtulo trÃs aborda o procedimento metodolÃgico utilizado para realizaÃÃo da pesquisa, enquanto o quarto capÃtulo apresenta a anÃlise e discussÃo dos resultados. Para construÃÃo da pesquisa foi utilizado um questionÃrio on-line (google drive), aplicada apÃs o assunto ser ministrado em aula pelo mestrando em duas turmas, uma turma controle e outra avaliada. Em uma das duas turmas do primeiro ano do ensino mÃdio, a aula foi ministrada de maneira expositiva usando como referÃncia a metodologia utilizada por um livro didÃtico de ampla adoÃÃo no paÃs, enquanto em uma segunda, a aula foi apresentada utilizando-se como referencial o material de apoio denominado produto educacional (sugerido no apÃndice b do trabalho). IndÃcios apontam no sentido de que o uso de linguagem inapropriada comumente utilizada por alguns livros didÃticos, possui reflexo relevante na dificuldade de compreensÃo das leis de Newton. A metodologia sugerida no estudo deste tÃpico no presente trabalho (denominado produto educacional) indica que o uso de linguagem mais coesa e a aplicaÃÃo de exemplos mais apropriados parece propiciar um melhor nÃvel de entendimento dos alunos. / This dissertation was prepared from an applied research in a public educational institution with the first year high school students, in which we sought to investigate the mistakes made by students with regard to the study of textbook use to develop the laws of Newton. The theme is very relevant therefore is commonly reported that a portion of students do not understand the concepts related to this topic and as a consequence can not solve exercises on the topic. Evidence of the work presented here, show that the textbook when he makes use of inappropriate language in the concepts approach contributes to the spread of the difficulty of learning in relation to Newton's laws, making the resolution of exercises related to the subject becomes-a difficult difficult to overcome. In the introductory chapter, raised some hypotheses to the difficulty of understanding the study of Newton's laws of physics and the study of the context. For the construction of the theoretical framework discussed the significant learning, the role of the textbook in the teaching-learning process and the training of teachers in Brazil. Chapter three discusses the approach used to conduct the survey, while the fourth chapter presents the analysis and discussion of results. For construction of the research was used an online questionnaire (google drive) applied after the subject to be taught by graduate student in class into two groups, one control group and one evaluated. In one of the two first-year high school classes, the class was given an expository manner with reference to the methodology used by a textbook widespread adoption in the country, while in a second, the lesson was presented using as reference the support material called educational product (suggested in Appendix b of the work). Evidence points to the effect that the use of inappropriate language commonly used by some textbooks, has significant reflection on the difficulty of understanding of the laws of Newton. The methodology suggested in the study of this topic in this study (called educational product) indicates that the use of more cohesive language and the application of more appropriate examples seems to provide a better level of understanding of the students.