This dissertation contains a study about plane curves and surfaces. The two most common way to define this elements are reviewed: the parametric and the implicit definition, with emphasis on the latter. An analysis of some methods to represent plane curves and surfaces is made. One notices that this job is relatively simple when the parametric definition is used, however with the implicit definition this requires a larger number of operations. This works also presents some methods to find approximations of curves and surfaces implicitly defined that preserves the topology and that generate objects smooth enough. This is achieved basically by a subdivision of the plane (respectivelly the space), which is used to find a piecewise linear approximation of the curve (respectivelly the surface), then this approximation is subdivided to make the result smooth. In the case of surfaces the output is a triangular mesh. Some treatments are also made to improve the quality of the mesh.; Fundação de Amparo a Pesquisa do Estado de Alagoas; Esta dissertação contém um estudo a respeito de curvas planas e superfícies. São vistas as duas formas mais usuais de se definirem estes elementos: a definição paramétrica e a implícita, com ênfase nesta última. São analisadas algumas formas de representação de curvas planas e superfícies...

Abstract:It boards a study about the methodology applied in the classroom, with emphasis at the Physic teaching, but could be taken to the other matters of high school, mainly to that alumns with school delay and that needs a pedagogics resources to get the aproach of them to the subject showed trying to improve their learnship. The study was developed through the bibliographic research methodology, associated to the induce resource that allows to evaluate the methods of teaching praticed actually at High Schools, as the private as the public, to give to the teachers the resources that should change the dificulties of learning with prejudice the classmates performances. The results reacheds demonstrated that is perfectly possible to augment the physic teaching body, taking in consideration the expansion of the profit at the teaching­learnig procces, besides having allowed to shows that this methodology porpouse could be takes to others subjects of the High School to became this phase of school more suitable to the necessities of society. It concludes that the brazilian Education could receive a lot of augments, from the professional criativity on always that inside the classroom, really close of the problems showed by the classmates about learning collecting; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Aborda um estudo sobre a metodologia aplicada em sala de aula...

This work has the main purpose of conducting a survey of educational products present in dissertations and doctoral theses focused on the use of history in mathematics teaching and Didactics of mathematics with a French foundation produced in graduate programs in the strict sense of the Brazil between 1990 and 2010, the areas of Education, Mathematics Education, school of Natural Sciences and Mathematics and related areas, according to the research proposal of Mendes (2010). Our interest was to select the products that present concrete proposals for educational activities that can be used in the classroom of Basic Education and Training of Teachers of Mathematics. The research was implemented through a bibliographic study documents the Bank of dissertations and theses from CAPES, libraries and archives of some Postgraduate programs in the country who focus their studies on the subject object of this research, besides the Brazilian Digital Library Theses and Dissertations (BDBTD). From this survey we selected works that present educational products materialized in blocks of activities based on the use of teaching history of mathematics to the classroom as well as the sequence of activities based on the Teaching of Mathematics. In possession of material...

In last decades, the importance of including the contents of the Nature of Science (NOS) in Science Education has been emphasized. Several studies have focused on investigating the conceptions of NOS, supported by students and teachers, as well as design, implement and evaluate proposals that aim to provide a reflection on this theme in the educational context. Considering the complexity of such content, studies indicate the need for explicit and contextualized approaches and the History of Science (HS) is one of the possible paths to this inclusion. We started from the premise that, through a historical study, that aims to discuss the meaning and the basis of our "beliefs", we can know the process of building on what we "believe" and better understand its meaning. This thesis is part of this perspective, proposing to explore the History of the Vacuum, a themed high didactic potential still little used, in order to collaborate with the teaching content of NOS. We present actions on different fronts that originated three products in the context of this research. On the first front, we insert the research and production of instructional materials (three historical texts) to subsidize people interested in the implementation of HPS for educational context through this material. The relevance of this front is justified by the existence of gaps with regard to the production of such material for the context of teacher training. However...

In this work, we study and compare two percolation algorithms, one of then elaborated by Elias, and the other one by Newman and Ziff, using theorical tools of algorithms complexity and another algorithm that makes an experimental comparation. This work is divided in three chapters. The first one approaches some necessary definitions and theorems to a more formal mathematical study of percolation. The second presents technics that were used for the estimative calculation of the algorithms complexity, are they: worse case, better case e average case. We use the technique of the worse case to estimate the complexity of both algorithms and thus we can compare them. The last chapter shows several characteristics of each one of the algorithms and through the theoretical estimate of the complexity and the comparison between the execution time of the most important part of each one, we can compare these important algorithms that simulate the percolation.; Nesta dissertação estudamos e comparamos dois algoritmos de percolação, um elaborado por Elias e o outro por Newman e Ziff, utilizando ferramentas teóricas da complexidade de algoritmos e um algoritmo que efetuou uma comparação experimental. Dividimos este trabalho em três capítulos. O primeiro aborda algumas definições e teoremas necessários a um estudo matemático mais formal da percolação. O segundo apresenta técnicas utilizadas para o cálculo estimativo de complexidade de algoritmos...

The present essay shows strategies of improvement in a well succeded evolutionary metaheuristic to solve the Asymmetric Traveling Salesman Problem. Such steps consist in a Memetic Algorithm projected mainly to this problem. Basically this improvement applied optimizing techniques known as Path-Relinking and Vocabulary Building. Furthermore, this last one has being used in two different ways, in order to evaluate the effects of the improvement on the evolutionary metaheuristic. These methods were implemented in C++ code and the experiments were done under instances at TSPLIB library, being possible to observe that the procedures purposed reached success on the tests done; O presente trabalho propõe estratégias de melhoria em uma bem sucedida metaheur ística evolucionaria para a resolução do Problema do Caixeiro Viajante Assimétrico. Tal procedimento consiste em um algoritmo memético projetado especificamente para esse problema. Essas melhorias têm por base a aplicação de técnicas de otimização conhecidas como Path-Relinking e Vocabulary Building, sendo essa última técnica utilizada de dois modos distintos, com o intuito de avaliar os efeitos de melhoria sobre a metaheurística evolucionária empregada. Os métodos propostos foram implementados na linguagem de programação C++ e os experimentos computacionais foram realizados sobre instâncias disponibilizadas na biblioteca TSPLIB...

In this work we study a new risk model for a firm which is sensitive to its credit quality, proposed by Yang(2003): Are obtained recursive equations for finite time ruin probability and distribution of ruin time and Volterra type integral equation systems for ultimate ruin probability, severity of ruin and distribution of surplus before and after ruin; Neste trabalho estudamos um novo modelo de risco para uma empresa que é sensível a classicação de risco de crédito, proposto por Yang(2003): Obtemos equações recursivas para a probabilidade de ruína em tempo nito, distribuição do tempo de ruína, sistemas de equações integrais do tipo Volterra para severidade e distribuição conjunta do capital antes e depois da ruína

In this work, we present a risk theory application in the following scenario: In each period of time we have a change in the capital of the ensurance company and the outcome of a two-state Markov chain stabilishs if the company pays a benece it heat to one of its policyholders or it receives a Hightimes c > 0 paid by someone buying a new policy. At the end we will determine once again by the recursive equation for expectation the time ruin for this company; Neste trabalho, apresentamos uma aplicação da teoria do risco com o seguinte cenário: as mudanças no capital de uma seguradora acontecem em cada instante de tempo e o pagamento de uma indenização ou recebimento de um prêmio é decidido pelo resultado de uma cadeia de Markov de dois estados. Nesta situação calculamos a probabilidade de ruína e o tempo esperado de ruína quando o valor da indenização é um mútiplo do valor do prêmio

In this work we present a mathematical and computational modeling of electrokinetic phenomena in electrically charged porous medium. We consider the porous medium composed of three different scales (nanoscopic, microscopic and macroscopic). On the microscopic scale the domain is composed by a porous matrix and a solid phase. The pores are filled with an aqueous phase consisting of ionic solutes fully diluted, and the solid matrix consists of electrically charged particles. Initially we present the mathematical model that governs the electrical double layer in order to quantify the electric potential, electric charge density, ion adsorption and chemical adsorption in nanoscopic scale. Then, we derive the microscopic model, where the adsorption of ions due to the electric double layer and the reactions of protonation/ deprotanaç~ao and zeta potential obtained in modeling nanoscopic arise in microscopic scale through interface conditions in the problem of Stokes and Nerst-Planck equations respectively governing the movement of the aqueous solution and transport of ions. We developed the process of upscaling the problem nano/microscopic using the homogenization technique of periodic structures by deducing the macroscopic model with their respectives cell problems for effective parameters of the macroscopic equations. Considering a clayey porous medium consisting of kaolinite clay plates distributed parallel...

We present a dependent risk model to describe the surplus of an insurance portfolio, based on the article "A ruin model with dependence between claim sizes and claim intervals"(Albrecher and Boxma [1]). An exact expression for the Laplace transform of the survival function of the surplus is derived. The results obtained are illustrated by several numerical examples and the case when we ignore the dependence structure present in the model is investigated. For the phase type claim sizes, we study by the survival probability, considering this is a class of distributions computationally tractable and more general; Neste trabalho apresentamos um modelo de risco dependente para descrever o excedente de uma carteira de seguros, com base no artigo "A ruin model with dependence between claim sizes and claim intervals"(Albrecher e Boxma [1]). Obtemos uma expressão exata para a probabilidade de sobrevivência atrav es da Transformada de Laplace da função de sobrevivência do superavit. Ilustramos os resultados obtidos através de exemplos numéricos e investigamos o que acontece ao se ignorar a estrutura de dependência presente no modelo. Estudamos também a probabilidade de sobrevivência para indenizações que possuem distribuição do Tipo Fase...

The aim of this work is to provide a text to support interested in the main systems of amortization of the current market: Constant Amortization System (SAC) and French System, also known as Table Price. We will use spreadsheets to facilitate calculations involving handling exponential and decimal. Based on [12], we show that the parcels of the SAC become smaller than the French system after a certain period. Further then that, we did a comparison to show that the total amount paid by SAC is less than the French System; O objetivo deste trabalho e oferecer um texto de apoio aos interessados nos principais sistemas de amortizacção do mercado atual: Sistema de Amortização Constante (SAC) e Sistema Francês, também conhecido por Tabela Price. Utilizamos planilhas eletrônicas para facilitar os cálculos que envolvem manipulação de exponenciais e decimais. Baseados em [12], mostramos que as prestações do SAC tornam-se menores que as do Sistema Francês a partir de certo período de financiamento. Além disso, fazemos uma comparação para mostrar que o montante total pago pelo SAC e menor que o do Sistema Francês

In this work are presented, as a review and in a historical context, the most used methods to solve quadratic equations. It is also shown the simplest type of change of variables, namely: x = Ay + B where A;B 2 R, and some changes of variables that were used to solve quadratic equations throughout history. Finally, a change of variable, which has been used by the author in the classroom as an alternative method, is presented and the result of this methodoly is illustrated by the responses of a test that was done by the students in classroom; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Neste trabalho são apresentados, como revisão e num contexto hist órico, os métodos mais utilizados de resolver equações de 2º grau. E apresentado tamb ém o tipo maissimples de mudan ça de vari áveis, a saber: x = Ay + B onde A;B 2 R, e mostrado como algumas mudan ças de vari áveis foram utilizadas na resolu ção de equa çõess do segundo grau ao longo da hist ória. Finalmente, uma mudan ça de vari ável, que tem sido utilizada pelo autor em sala de aula como um m etódo alternativo, e apresentada e o resultado da aplica ção de tal m étodo e ilustrado atráv es das respostas de um teste

A necessidade de uma precisão e de uma aproximação dos resultados numéricos zeram com que diversas teorias surgissem: dentre elas, destacamos a Matemática Intervalar. A Matemática Intervalar surgiu na década de 60 com os trabalhos de pesquisa de Moore (MOORE, 1959) , em que ele propôs trabalhar com uma Matemática baseada na noção de intervalo real e não mais com um número como aproximação. Com isso, surgiu a necessidade de revisitar e reformular os conceitos e resultados da Matemática Clássica utilizando como base a noção de intervalo de Moore. Uma das áreas da Matem ática Clássica que tem tido muitas aplicações em engenharias e ciências é a Análises Numérica, onde um dos seus pilares é o Cálculo Integral e em particular as integrais de linha. Assim, é muito desejável se ter um cálculo integral dentro da própria Matemática Intervalar. No presente trabalho apresenta-se uma noção de Integral de Linha Intervalar baseada na extensão de integração proposta por Bedregal em (BEDREGAL; BEDREGAL, 2010). Para a fundamentação apresenta-se incialmente uma introdução sobre a pespectiva em que o trabalho foi realizado, considerando alguns aspectos histórico-evolutivos da Matemática Clássica. Os conceitos de Integrais de Linha Clássica...

This research has been to understand what actions can be mobilized by the teacher and the students of the ninth year of primary education by working with problem solving spatial geometry in a dynamic and interactive. We use the Cabri 3D software and digital whiteboard as a tool in solving the problems presented, and we decided to work the theme prisms because we know the problems in their teaching. The research had as its main theoretical source heuristics by Polya (2006) applied to problem solving, and Vygotsky and his colleagues seek references to discuss the mediation processes that occur during problem solving. Assuming that the subjects in social interactions build their knowledge, we seek to understand the concept of interactivity and interaction both in computerized environment and the social environment. Data collection occurred in a class of ninth year of elementary school to a state school in the State of Minas Gerais in the city of Patos de Minas, located in Upper Paranaíba. As a sample, we work with two segments, the first group of six students who were obtained through a random sample, comprising three males and three females and the second consisting of the teacher. Considering the characteristics of research, we chose a qualitative approach. As techniques and tools for data collection was used filming...

The investigation presented here is based on the scoop of the Teaching and Learning of Science and Mathematics, from the Post-Graduation program in Education in Science and Mathematics, from the Federal University of Goiás and its main goal is to study a group of second-year students from the Administration Course, evening-course, from a private college, located in Goiânia, state of Goiás, Brazil. This study relates to the Learning of Mathematics applied to administration, to Internet usage and to a free virtual learning ambience which is used as a support to face-to-face teaching - the TelEduc. Besides, the contribution given by the students presently called Monitors of applied Mathematics, Applied Mathematics: virtual resources, offered on the TelEduc ambience were also studied. Throughout the pages on this dissertation, there is a feedback , a kind of descriptive memorial of the academic life of the researcher, exploring his initial contacts with the Mathematics Learning Process and also his contacts with Educational Technology. Lately, the choice of this work methodology is justified, inspired by the principle of the utility for the research reflection, in Edgard Morin. In order to offer theoretical support, the methodology of ethnographic type research was adopted...

In this work, we study the descent of methods for problem of optimization multiobjective which we introduce an order of relation induced by an closed convex cone.We study as it wiel calculate an descent of direction and we prove that every accumalation point of the sequence generated by the descent of methods with search of Armijo is weakly efficient.; Neste trabalho, estudamos o método de descida para problemas de otimização multiobjetivo, para o qual introduzimos uma relação de ordem induzida por um cone fechado e convexo. Estudamos como calcular uma direção de descida e provamos que todo ponto de acumulação da sequência gerada pelo método de descida com busca de Armijo é fracamente eficiente.

In this dissertation we consider a primal convex optimization problem and we study variants of subgradient method applied to the dual problem obtained via a Lagrangian function. We analyze the conditional subgradient method developed by Larsson et al, which is a variant of the usual subgradient method. In this variant, the subgradients are conditioned to a constraint set, more specifically, the behavior of the objective function outside of the constraint set is not taken into account. One motivation for studying such methods is primarily its simplicity, in particular, these methods are widely used in large-scale problems. The subgradient method, when applied to a dual problem, is relatively effective to obtain a good approximation of a dual solution and the optimal value, but it is not efficient to obtain primal solutions. We study a strategy to obtain good approximations of primal solutions via conditional subgradient method, under suitable additional computational costs. This strategy consists of constructing an ergodic sequence of solutions of the Lagrangian subproblems.We show that the limit points of this ergodic sequence are primal solutions. We consider different step sizes rule, in particular, following the ideas of Nedic and Ozdaglar...

The search for solutions of nonlinear equations in the Euclidean spaces is object of interest in some areas of science and engineerings. Due the speed of convergence and computational efficiency, the inexact Newton method and its variations have been suficiently used to obtain solutions of these equations. In this dissertation we present a local analysis of convergence of the inexact Newton method and some of its variations, more specifically the inexact Newton-like method and the inexact modified Newton method. This analysis has the disadvantage to demand the previous knowledge of a zero of the operator in consideration and the hypotheses on the behavior of the operator at this zero, but on the other hand it supplies to information on the convergence rate and convergence radius.; A busca por soluçõeses de equaçõess não-lineares nos espaços Euclidianos é objeto de interesse em várias áreas da ciência e das engenharias. Devido a sua velocidade de convergência e e¯eficiência computacional, o método de Newton inexato e suas variações têm sido bastante utilizados para o propósito de obter solu»c~oes dessas equações. Nesta dissertação apresentamos uma anáalise de convergência local do método de Newton inexato e algumas de suas variações...

The Convergence theory of gradient method and gradient projection method, for minimization of continuously differentiable generalized convex functions, that is, pseudoconvex functions and quasiconvex functions is studied in this work. We shall see that under certain conditions the gradient method, as well as gradient projection method, generate a convergent sequence and the limit point is a minimizing, whenever the function has minimizing and is pseudoconvex functions. If the objective function is quasiconvex then the generated sequence converges to a stationary point whenever that point exists.; Neste trabalho trataremos da convergência do método do gradiente para minimizar funções continuamente diferenciáveis e convexas-generalizadas, isto é, pseudo-convexas ou quase-convexas. Veremos que sob certas condições o método do gradiente, assim como o método do gradiente projetado, gera uma sequência que converge para minimizador quando existe um e a função objetivo é pseudo-convexa. Quando a função objetivo é quase-convexa a sequência gerada converge para um ponto estacionário do problema quando existe um tal ponto.

This work have as the main objective present one a different way to teach the subject matrix multiplication, a way in a ludic form, applied, that can transform the teaching more pleasureable and motivate for the high scholl students, because for many this issue has no practical applications, which for many reasons is the lack of interest in learning such content. The tool used to attract as students so as teachers was the utilization of Kit LEGO® Mindstorms NXT 2.0 for the construction of the robotic arm, or robotic manipulator, that which for this propose, has three rotational joints. The LEGO kit was choosen due its easy interaction with children and adolescents, and to encourage the construction of knowledge stimulating the solution of problems that may arise during the process of building robotic arm.The application of content takes place in obtaining the four parameters Denavit-Hartenberg and those obtained after the placement of reference systems, where three of these parameters are constants obtained by measurement at robotic arm and the fourth parameter is variable dependent on the intended movement or the final position which is to be determined.; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES; O presente trabalho tem como principal objetivo apresentar mais uma opção de ensinar o assunto multiplicação de matrizes...