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Item Tempo de sobrevivência em um modelo estocástico para evolução de espécies(Universidade Federal de Goiás, 2014-02-27) Aguiar Júnior, Dióscoros Brito; Vargas Júnior, Valdivino; http://lattes.cnpq.br/1795859800919467; Vargas Júnior, Valdivino; Gava, Renato Jacob; Silva, Tatiane Ferreira do Nascimento Melo daIn this work ,we will consider two stochastic models for evolution os species. First, births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type is killed is the one with smallest fitness. We show that there is a sharp phasetransitionwhentheprobabilityislargerthanthedeathprobability.Thesetofspecies with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the crital disappear after a finite (random) time. The second model, we consider a stochastic model for species evolution. A new species is born at rateλ and a species dies at rate µ. A random number, sampled from a given distribution F, is associated with each new species and assumed as its fitness, at the time of birth. Likewise the first model, every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time if a species with a given fitness f. We show that the survival time distribution depends crucially on whetherffc where fc is a critical fitness that is computed explicit.Item Análise combinatória: uma questão de lógica e linguagens(Universidade Federal de Goiás, 2013-03-01) Alvim, Karina Guerra Cardoso; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Vieira, Elisabeth Cristina FariaThe objective of this work is to address the Combinatorial Analysis as a theme that can be treated in the classroom, without the utilization of mathematical formulas in problem solving. For this it will presented a method of reasoning that, basing on logic and languages, underscores the importance of: To read, interpret and analyze texts that are presented in the mother tongue; Formulate conjectures, make choices and seek strategies of count; and Make the correct translation between languages maternal and mathematics. Expected to show from this approach that the Combinatorial Analysis, besides its importance in various elds of knowledge, may also be seen by students and teachers as a challenging and stimulating content.Item O uso da calculadora simples em sala de aula(Universidade Federal de Goiás, 2013-04-11) Arruda, Dilermano Honório de; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Seimetz, Rui; Smith, Ole PeterO objetivo deste estudo é apresentar uma ferramenta que todos possuem, que é fácil de carregar e que portanto tem alcance popular. Nas primeiras seções apresenta-se algumas operações matemáticas elementares executadas com uma calculadora simples. Começa-se por estudar a operação de divisão de inteiros e como encontrar o resto na calculadora, como operar com frações em uma calculadora e responder na forma de fração, como encontrar a fração geratriz de uma dízima periódica ou ainda como extrair a raíz "n-ésima"de um número real. Para cada operação destas há a preocupação de se expôr também suas devidas aplicações e, quando necessário, de se realizar estudos matemáticos mais profundos como, por exemplo, no caso das congruências módulo m nas dízimas ou derivadas para raízes n-ésima. Em iterações com a adição, por exemplo, trabalha-se o uso adequado de algumas teclas para um procedimento rápido no estudo das progressões aritméticas, juro simples e funções polinomiais do 1o grau. Já na seção de iterações com o produto, propõe-se um estudo das progressões geométricas, funções exponenciais e juro composto. Iterando com as fórmulas de Maclaurin, veremos como é possível utilizar a calculadora simples para encontrar valores das funções trigonométricas circulares e hiperbólicas, bem como os valores dos logaritmos decimais e neperianos. Esse trabalho mostra ao leitor que pelo conhecimento matemático pode se otimizar a calculadora simples, responder questões que antes os cálculos ficariam apenas indicados, ganhar tempo nos cálculos e utilizar o tempo restante para melhor elaborar a estratégia de resolução, e demais vantagens que o leitor descobrirá.Item O número de ouro e construções geométricas(Universidade Federal de Goiás, 2013-03-22) Azevedo, Natália de Carvalho de; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Cruz, José Yunier Bello; Seimetz, Rui; Martins, Ivonildes RibeiroThe golden number and its geometry remote from Ancient Greece. The golden number is a real number that can be represented geometrically by dividing a segment in extreme and mean ratio. It is related to the act of determining a point C on a segment AB in order to obtain equal ratios between AB : AC and AC : CB. Its value is obtained by numerical solution of the quadratic equation obtained from this equality. From ruler and compass constructions of the golden mean other geometric constructions are made: triangles, rectangles, pentagons and spirals. The golden number has been present in arts, architecture and nature for years, and it presented in this work as a tool for study, focusing on presentation to high school students.Item Ciclos limite para a equação de Abel generalizada(Universidade Federal de Goiás, 2009-10-30) Belisário, Hugo Leonardo da Silva; Garcia, Ronaldo Alves; http://lattes.cnpq.br/5680428710939826In this work we conducted a study on the equations of the type dx dt = nå i=0 ai(t)xi; (A) where ai 2 C1, i = 0; ;n and 0 t 1. An equation of the form (A) is called a generalized Abel equation. Our study refers to the problem proposed by C. Pugh: There is a natural number N depending only on n, such that the equation (A) has at most N limit cycles? Initially we study the problem of C. Pugh for n = 1 and n = 2, for which the equation (A) has at most one and two limit cycles, respectively. For n = 3, A. Lins Neto shows that if a3(t) does not change sign on [0;1], then the equation (A) has at most three limit cycles. Also A. Lins Neto shows that, given a natural number l, it is possible to construct an equation of the form (A) with n = 3 that has at least l limit cycles. Still for n = 3, A. Gasull and J. Llibre study the problem of C. Pugh considering that a2(t) does not change sign on [0;1], and M. J. Alvarez, A. Gasull and H. Giacomini also study the problem of C. Pugh considering that there are real numbers a and b such that aa3(t)+ba2(t) does not change sign on [0;1] and a1(t) = a0(t) = 0. Besides this, we study some more general results studied by A. Gasull and A. Guillamon.Item Hipersuperfícies de rotação com curvatura escalar constante em Rn e Hn(Universidade Federal de Goiás, 2014-02-25) Carvalho, Marcos Túlio Alves de; Pina, Romildo da Silva; http://lattes.cnpq.br/2675728978857991; Pina, Romildo da Silva; Araújo, Kellcio Oliviera; Pieterzack, Maurício DonizettiInthiswork,basedonthearticlesMariaLuízaLeiteandOscasPalmas,wepresentedthe classificationofthecompleterotationhypersurfaceswithconstantscalarcurvature,inRn eHn withn>3.Item Existência de uma solução não trivial para uma classe de problemas elípticos super quadrático(Universidade Federal de Goiás, 2013-12-13) Cavalcante, Thiago Rodrigues; Silva, Edcarlos Domingos da; http://lattes.cnpq.br/7817014732764711; Silva, Edcarlos Domingos da; Cardoso, José Anderson Valença; Carvalho, Marcos Leandro MendesIn this dissertation we analyze questions of existence of a weak solution for a class of superlineares elliptic Dirichlet problems. Here we do not consider the Ambrosseti Rabinovitz condition , which restricts some nonlinearities. We obtain main results of this dissertation via Variational Methods, such as Mountain Pass Theorem and Linking Theorem. Furthermore, weusePalais-Smalecondition(P.S.) or Cerami condition(Ce)Item Máximos e Mínimos: uma abordagem para o ensino médio(Universidade Federal de Goiás, 2013-04-12) Costa, Marcos Antônio da; Silva, Maxwell Lizete da; lattes.cnpq.br/9078818338290451We deal with extremum values problems. Our focus is the high school students. We present simple ideas and techniques on solving classical optimization problems. Among other problems we cite the classical isoperimetric ploblem and the Heron0s problem. We are based on the book Stories About Maxima and Minima by Tikhomirov which lead with these classical problems using only elementary mathematical subjects.Item Tópicos de álgebra linear e aplicações em problemas de economia e de engenharia(Universidade Federal de Goiás, 2013-04-12) Cruvinel, Frederico Borges; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Souza, Flávio Raimundo de; Melo, Maurílio MárcioThis work shows the importance of the Linear Algebra and in particular of the theory of Matrices and Linear Systems to solve practical problems in various areas. We show examples of Applications of Linear Systems in closed and open models of Leontief in Economics, in closed circuits (Law Kirccho ) and in projects of construction of steel structures.Item Condições de solubilidade p-ádica de pares de formas diagonais e alguns casos especiais(Universidade Federal de Goiás, 2009) Ferreira, Alaídes Inácio Stival; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426This text is above solvability in systems of two forms additive over p-adics fields: with of degree k and variables n > 4k at lesat p > 3k4 ; with of degree an k odd integer at least n > 6k+1 variables; and with of degree 5 and p > 101 for n ≥ 31 variables, and for all p with n ≥ 36 variables, with the possible exceptions of p = 5 and p = 11.Item Probabilidade - Uma proposta de ensino - O uso do teorema da multiplicação de probabilidades como um facilitador e integrador de diversas abordagens deste assunto(Universidade Federal de Goiás, 2013-03-01) Fonseca, Vanessa Jacob da; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Seimetz, Rui; Vieira, Elisabeth Cristina FariaThis work aims to establish links between the di erent possible ways to resolve some issues involving the calculation of the probability of an event occurring through the use of the Multiplication of Probability Theorem (Theorem 2) and, from it, to show that we can solve problems involving simultaneous withdrawals, originally settled by Combinatorial Analysis, replacing them by successive withdrawals without replacement, considering the range of possible clusters (Theorem 4). Highlighting some precursors and their contributions to the development of Probability Theory, such as Cardano, Pascal, Laplace and Kolmogorov, among others. Exemplify, through problem solving, application of Theorem 4 to show the simpli cation of the calculation of probabilities applied, and propose activities that encourage discussion in the classroom, in order to clarify with the teacher's intervention, concepts such as Independent Events and using the Binomial Distribution.Item A importância das matrizes e transformações lineares na computação gráfica(Universidade Federal de Goiás, 2013-03-22) Gonçalves, Haniel Soares; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Souza, Flávio Raimundo de; Martins, Ivonildes RibeiroLinear algebra and in particular the theory of matrices and the theory of linear transformations are areas of mathematics that can be applied not only within the mathematics, but also in many other areas of human knowledge, such as physics, chemistry, biology, all engineering, computing, economics, etc... We present examples through the importance of the matrices and linear transformations in the theory of graphic computation.Item Fi: o número de ouro(Universidade Federal de Goiás, 2014-03-01) Kfouri, Viviane de Oliveira; Tonon, Durval José; http://lattes.cnpq.br/3688981956532711; Tonon, Durval José; Couto, Maria Socorro Duarte da Silva; Baumann, Luis Rodrigo FernandesIt is shown, in this work, a study about the golden number, represented by the greek character (pronounced as \Fi"), in tribute to the greek sculptor F dias, who used to use this number in his works. It is done an algebraic approach, which is shown how to reach the number , using reasons, proportions and equations of second grade. It is also used geometric constructions for its achievement. The used metodology is made of theory and practice, proposing activities where the concret assists the instruction of abstract geometry, in the construction, for example, of the golden rectangle and the logarithmic spiral. It is also shown the intrinsic relationship of the golden number and the Fibonacci sequence and, as well, it is shown that is an irrational and algebric number. The main goal is to promote the thinking of the importance of this number through a project to be developed at the same time as the classes, for students of secondary schools.Item Os três momentos pedagógicos no ensino de ciências na educação de jovens e adultos da rede pública de Goiânia, Goiás: o caso da dengue(Universidade Federal de Goiás, 2013-11-09) Lyra, Daniella Galiza Gama; Barrio, Juan Bernardino Marques; http://lattes.cnpq.br/6859482550702496; Oliveira, Leandro Gonçalves; Muenchen, Cristiane; Ferrari, Paulo Celso; Barrio, Juan Bernardino MarquesThe Youth and Adult Education (YAE) has a long history in Brazil , the achievements and setbacks, but with a great social importance has contributed significantly to the reduction of illiteracy in the country. Aiming the process of learning in Youth and Adult Education, this work analyze/use a teaching strategy, the Three Pedagogical Moments articulated with the Paulo Freire’s proposal for a liberating and emancipatory education that facilitates learning of scientific contents. The subjects on this study are students of 5th and 6th levels from two public schools in Goiânia, who attend Youth and Adult Education. The survey data were obtained by recording lectures and answering to a questionnaire, which emerged from the analysis categories: naive curiosity and epistemological (CIE); [re]construction concept: from naive to scientific (CIC); the role of questioning: awareness and dialogical (PCD). Content analysis of these categories can be considered that the Three Pedagogical Moments proved an interesting and productive strategy in working with these students. Besides encouraging their participation in class, giving freedom for students to express themselves, it allowed the promotion of meaningful learning of scientific themes, in this case, DengueItem Raiz quadrada de matrizes de ordem nxn(Universidade Federal de Goiás, 2014-03-07) Mendonça Junior, Ronaldo Caetano de; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Costa, Eudes Antonio da; Dias, Ivonildes Ribeiro MartinsThetopicsarepresentedintheinterestofmakingitlessabstractcertainunfamiliar content to middle school students . To do this , create a chronology of operations and conditions that precede and enable the calculation of the nth Root of a Square Matrix . Initially a brief summary is made of arrays in Chapter 3 , diagonalization of matrices , creates this environment of initial conditions to calculate the roots of matrices , in Chapter 4 , is de…ned and calculated the square root of a matrix of order 3 , in order that by example number 13 , bring greater materiality to the reader , as in Chapter5startedtheworkofgeneralization,wherewede…neandcalculatethesquare of a matrix of order n root . Finally Chapter 6, covers all concepts constructed in the previous sections for defnition and presentation of the methodology for calculating the nth root of a square matrix .Item O estudo de determinantes sob a ótica do grupo de permutações(Universidade Federal de Goiás, 2013-02-28) Moraes, Walter José Rodrigues de; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Martins, Ivonildes RibeiroThe study of determinants development through the permutations made on their lines or columns dates back to 1812, a memory presented by Cauchy to the French Academy of Sciences. The present work is, in some way, a historical rescue. Firstly, a permutation is de ned: from a superior point of view there is a bijective application and, as such, the set of permutations has a group structure; from the elementary point of view, there is an ordainment of a group's elements. The fundamental fact is, secondly, that the de nition of determinant adjusts perfectly to both conceptions, based on the parity of the permutations. Based on the de nitions, the determinants properties are presented and, therefore, it is possible to proceed with the appropriate justi cations about their validity. A rule that associates each square matrix to a real number will de ne a real function of the variable matrix, the determinant function. This is the actual way in which determinants are presented in higher levels: the determinant is the unique alternated multilinear function of the lines (columns) of a square matrix, as indicated in [10]. By this presentation there is in mind the fact that it can be served as an inspiration to posterior studies.Item Método do Ponto proximal usando distâncias generalizadas separáveis - reescala e seleção do comprimento do passo(Universidade Federal de Goiás, 2008-05-29) Moreira Neto, Alvaro; Silva, Geci José Pereira da; http://lattes.cnpq.br/9174074436425246In this work....Item Hipersuperfícies conformemente planas em R4(Universidade Federal de Goiás, 2009-03-13) Moreira, Lucas; Pina, Romildo da Silva; http://lattes.cnpq.br/2675728978857991language="eng">The present work has been based by the [16] and [17] articles, from Oscar J. Garay. In that articles he studied the conformally flat hypersurfaces in the R4 space, wich have the mean curvature vector H like an eigenvector of their Laplacian Operator, i.e., DH = lH, l 2R .We showed that these hypersurfaces are isoparametrics and, consequently, they are either a minimal hypersurface, or an around 3-sphere S3(r) , or a cylinder over a 2-sphere S2(r) R, or a cylinder over a circle S(r) R2.Item GEOGEBRA - uma proposta para auxiliar o ensino da geometria plana(Universidade Federal de Goiás, 2013-10-01) Oliveira, Edimaldo Fialho Nunes de; Santos, Fabiano Fortunato Teixeira dos; http://lattes.cnpq.br/6866594296187427; Santos, Fabiano Fortunato Teixeira dos; Souza, Flávio Raimundo de; Souza, Anyelle Nogueira deThis work aimed to propose the use of the software GeoGebra - Operating System Linux - as a tool for di erentiated content of Plane Geometry for High School. The relevance of this research lies in the fact of being a GeoGebra software free access which makes it possible to carry out the activities proposed in this work in any school that has a laboratory computer basics. It is also believed that a tool can be GeoGebra useful for promoting a dynamic di erentiated classes of plane geometry, usually worked Just chalk on blackboard. This study proposes the use of software in 5 topics: Resolution equation of the second degree by the geometric method, Cycle Trigonometric; Baricentro; Arc capable and Ret golden angle. The research proved satisfactory, reaching the objectives set and con? Rmando the hypotheses. The realization of this work is also intended to call the re? Exon educators living with the paradigm of new technologies within schools. It is expected that reading text presented to stimulate the use of information technology resources for the greater good that is the constant pursuit of a quality education for our students.Item Poliedros e o Teorema de Euler(Universidade Federal de Goiás, 2014-03-21) Parreira, José Roberto Penachia; Tonon, Durval José; http://lattes.cnpq.br/3688981956532711; Tonon, Durval José; Souza, Flávio Raimundo de; Lemes, Max ValérioThis work aims is to demonstrate the Euler's Theorem for polyhedra, given by the equation V A + F = 2, where V; A and F are the numbers of vertices, edges and faces, respectively, the polyhedron. A historical survey of the main characters who contributed to the theme was elaborated. De nitions and properties of polygons and polyhedra were given. The statements were constructed in three distinct ways. The rst by Cauchy, commented by Professor Elon Lages Lima. This statement is valid for any polyhedron homeomorphic to a sphere and has the path planning of the polyhedron withdrawing one of its faces. The second statement was prepared by the professor Zoroastro Azambuja Filho, valid for any convex polyhedron, and its path projection of the polyhedron on a plane and comparison of the internal angles of polygons with projection angles of the polygon faces. The third statements was presented by Legendre, also valid for any convex polyhedron, and its path in the projection of a spherical polyhedron surface. We use the Girard's Formula, the sum of the interior angles of a spherical triangle, to complete the demonstration. This work also suggests methods of applying the proof of Euler's Theorem in the classroom for high school students, and resolution of vestibular exercises involving the subject.