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Item Método subgradiente incremental para otimização convexa não diferenciável(Universidade Federal de Goiás, 2014-12-18) Adona, Vando Antônio; Melo, Jefferson Divino Gonçalves de; http://lattes.cnpq.br/8296171010616435; Melo, Jefferson Divino Gonçalves de; Gonçalves, Max Leandro Nobre; Haeser, Gabriel; Ginart, Jorge BarriosWe consider an optimization problem for which the objective function is the sum of convex functions, not necessarily differentiable. We study a subgradient method that executes the iterations incrementally selecting each component function sequentially and processing the subgradient iteration individually. We analyze different alternatives for choosing the step length, highlighting the convergence properties for each case. We also analyze the incremental model in other methods, considering proximal iteration and combinations of subgradient and proximal iterations. This incremental approach has been very successful when the number of component functions is large.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 semi-local do método de Gauss-Newton sob uma condição majorante(Universidade Federal de Goiás, 2014-12-18) Aguiar, Ademir Alves; Gonçalves, Max Leandro Nobre; http://lattes.cnpq.br/7841103869154032; Gonçalves, Max Leandro Nobre; Gonçalves, Douglas Soares; Melo, Jefferson Divino Gonçalves deIn this dissertation we present a semi-local convergence analysis for the Gauss-Newton method to solve a special class of systems of non-linear equations, under the hypothesis that the derivative of the non-linear operator satisfies a majorant condition. The proofs and conditions of convergence presented in this work are simplified by using a simple majorant condition. Another tool of demonstration that simplifies our study is to identify regions where the iteration of Gauss-Newton is “well-defined”. Moreover, special cases of the general theory are presented as applications.Item Lançamento oblíquo: uma abordagem matemática(Universidade Federal de Goiás, 2016-03-31) Almeida, Francisco Fabio Monteiro de; Lima, Lidiane dos Santos Monteiro; http://lattes.cnpq.br/3020743359147341; Lima, Lidiane dos Santos Monteiro; Lima, Thaynara Arielly de; Souza, Flávio Raimundo deThe main goal of this work is to verify that we can assign the oblique launch a mathematical approach. To reach this conclusion, we address important issues of mathematics and physics, as linear functions and quadratic functions , and uniform and uniformly varied movements. These concepts were presented to facilitate understanding and implement an equation that allows to determine the moment of rise, the maximum height and horizontal reach, knowing an shot's angle, the initial velocity and gravity's acceleration.Item Ondas de Choques Transicionais Para Modelos Quadráticos de Duas Leis de Conservação(Universidade Federal de Goiás, 2007-11-29) ALMEIDA, Gisele Detomazi; MOTA, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539Transitional shock waves arises in solution of initial values problems for non linear systems of conservation laws that are not strictly hyperbolic. These waves are discontinuous solutions that posses viscous profile but do not conform to the Lax characteristic criterion, where inequalities between the shock propagation speed and the characteristic speeds must to be satisfied. These waves arise as transition between wave groups associated with distinct characteristic families. In this work we studied transitional shock waves for a system of two conservation laws with quadratic fux functions and positive defined viscosity matrix. In particular, we studied the transitional shock waves with viscous profile defined by orbits laying on straightlines. We show from examples, for systems with quadratic fux functions and viscosity matrix chosen in a convenience way, that is necessary to use transitional shock waves to solve the Riemann problem (initial data constant by parts) for these systems.Item Uma proposta de oficina sobre códigos para a contextualização do estudo de aritmética e matrizes no ensino médio(Universidade Federal de Goiás, 2015-08-07) Alves, Bruno Coelho; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Lima, Lidiane dos Santos MonteiroThis work aims to present the content of Error-Correcting Codes to teachers, in a way to use this content in their classes. A code representing a particular word or symbol by another word or symbol. This study handle with the error correcting codes, especially that said linears. Thus, the concept of code is disclosed along two examples. The Linear Algebra and Algebra requirements are exposed, handling the concept of nite elds, the de nition of linear space and linear transformation. The error correcting codes, from alphabets de ned in nite elds, allow sending messages, even in noisy channels, they can be interpreted with a lower probability of error. This process is done in linear codes through linear transformations. Hamming codes and Reed-Solomon codes are exemples of linear codes which are showed in this work. After presented the theoretical basis of content, it is proposed a workshop that has as target students from the nal years of High School. This workshop explore some common feature codes, such as the use of check digits and the interpretation of texts by digital machines by zeros and ones. It is hoped that this work can assist the release of some current research topics among teachers and encourage the use of new methodologies for teaching content that is considered di cult and useless to several students of High School.Item Condições de finitude para o produto tensorial não abeliano de grupos(Universidade Federal de Goiás, 2019-08-08) Alves, Thulio de Oliveira; Oliveira, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997; Oliveira, Ricardo Nunes de; Bastos Júnior, Raimundo de Araújo; Vieira, Ewerton RochaIn this work we are interested in describing the conditions on which the non-abelian tensor product of groups is finite, thus we show that if G and H are groups that act compatibly on each other, then the tensor product of G and H is finite, if and only if the set of all tensor is finite. As an immediate consequence of this result, if G and H are finite, then the tensor product of G and H is finite. Furthermore we describe finite conditions for specific subgroups of the tensor product when G and H are FC-groups and also when H=G and G is a BFC-group.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 Convergência do Método do Ponto Proximal para Funções que Satisfazem a Desigualdade de Łojasiewicz(Universidade Federal de Goiás, 2012-06-27) AMARAL, José Henrique Salazar do; BENTO, Glaydston de Carvalho; http://lattes.cnpq.br/1089906772427394This paper presents an analysis of convergence of the proximal point method for functions that satisfy the inequality of Lojasiewicz.Item Tomada de decisões e o aprendizado de matemática financeira: uma experiência com aplicativos para smartphone(Universidade Federal de Goiás, 2018-10-05) Amim Júnior, Jair Elias; Faria, Elisabeth Cristina de; http://lattes.cnpq.br/5007480938176936; Faria, Elisabeth Cristina de; Vargas Júnior, Valdivino; Moraes, Moema GomesThe present work was a technical report that introduced the course and the results of the investigate work accomplished in the Professional Mathematics Master’s Program in National Network (Profmat). I proposed a method of teaching Financial Mathematics focused in the use of financial applications for smartphone, having as main objective to verify the students' development in relation to the made decisions in situations that are offered to them the possibility to choose the applications to assist in the resolution of problems. As main benchmark was used the heuristics of problem solving proposed by George Polya (1995), the use of smartphones and Applications as Pedagogic tools, according to Voltolini (2016) and Soares (2016): the creating of a virtual learning environmoent, according to Shitsuka (2012), and the critic mathematics education associated with resolution of problem, according to Skovsmose (2000). From the application of the method it resulted an electronic textbook of studies as education product, whose title is "Financial Mathematical with Use of Applications for Smartphone." Aimed for teachers of the Basic Education, the electronic textbook has theoretical summaries and links for the resolutions of the exercises in videos posted on YouTube. A qualitative research was carried out in four meetings, and the instruments of data collection were questionnaires, record sheets and videos captured by the participating students themselves. This allowed to observe the capacity of the students' autonomy in the choice of the applications. The critical glance that they developed when analyzing interest rates and options of payments, serves with foundation for the construction of a financial education to be used in daily routine.Item Introdução à análise convexa: conjuntos e funções convexas(Universidade Federal de Goiás, 2013-03-18) Amorim, Ronan Gomes de; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Sandoval, Wilfredo Sosa; Cruz, José Yunier Bello; Pérez, Luis Román LucambioThis paper presents the main ideas concerning convex sets and functions. Our aim is to deal, didactically, with the main topics concerning convexity, as well as the consequent exploitation of the envolved mathematical concepts. In this sense, we have made a bibliographic revision approaching important theorems, lemmas, corollaries and propositions designed both to first readers and to those who want to work with applications arising from convexity. We hope that this study may constitute an important research source either for students, teachers or researchers who wish to learn more about convex sets.Item Sobre uma Construção Relacionada ao Quadrado Tensional não-Abeliano de um Grupo(Universidade Federal de Goiás, 2011-07-01) ANDRADE, Agenor Freitas de; RODRIGUES, Paulo Henrique de Azevedo; lattes.cnpq.br/8910130626123426; OLIVEIRA, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997Let G and Gj be isomorphic groups. We study the group V (G) which is an extension of the non-abelian tensor square of a group G, G G. Looking for V (G) as an operator in the class of groups, we observe that this operator preserves some properties of the group G such as finiteness, nilpotency and solubility. For a p-group finite G we find an upper bound for the order of G G. Finally, we verified computationally, for some groups, and that the results and also the bounds for the orders of the groups shown here are actually respected.Item A coexistência de quatro ciclos limite em campos vetoriais seccionalmente lineares em R3(Universidade Federal de Goiás, 2012-07-30) ANDRADE, Kamila da Silva; MEDRADO, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286In this work we study continuous, symmetric and piecewise linear vector fields on R3, we investigate the existence of limit cycles using the closing equations method. More specifically, we study a two parameters family of this vector fields and we show the coexistence of four limit cycles and too, its realization on Chua s circuit.Item Superfícies translacionais no espaço isotrópico(Universidade Federal de Goiás, 2019-03-01) Andrade, Thamara Policarpo Mendes de; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Pereira, Rosane Gomes; Carretero, José Luis TeruelTranslation Surfaces are obtained by translating curves contained in non-parallel planes. In this paper, the results of the Aydin, M. E; Ergut, M. Affine Translation Surfaces in the Isotropic Space [3]. Are considered the Affine Translation Surfaces type 1 in the Isotropic 3- Space I3, obtained for translating of two curves in the planes not necessarily orthogonal. The objective was to characterize the Weingarten Affine Translation Surfaces, which satisfy certain conditions with respect to Gaussian and mean curvatures. In addition, results were obtained for Translation Surfaces satisfying \Delta _{I,II }ri = \lambda_{i}ri, finding explicit solutions for the parameterization of such surfaces. Some examples are presented, as well as their respective graphs that were plotted using the Mathematical software.Item A matemática da educação financeira(Universidade Federal de Goiás, 2016-08-07) Andreatini Neto, Alessandro; Souza, Mário José de; http://lattes.cnpq.br/4862963990848505; Souza, Mário José de; Souza, Flávio Raimundo de; Lima, Thaynara Arielly deThis paper aims to promote a re ection about the didactic potential interfaces between nancial education and math content covered in high school through a course of nancial education. O rst course module presents a tool to organize spending so systematic . In the second module discusses the di erent types of loan and credit. The third module has been the most common investments and how they workItem Criptografia de curvas elípticas(Universidade Federal de Goiás, 2017-03-15) Angulo, Rigo Julian Osorio; Chaves, Ana Paula de Araújo; http://lattes.cnpq.br/2332073500640724; Chaves, Ana Paula de Araújo; http://lattes.cnpq.br/2332073500640724; Rodrigues, Paulo Henrique de Azevedo; Godinho, Hemar TeixeiraAccording to history, the main objective of cryptography was always to provide security in communications, to keep them out of the reach of unauthorized entities. However, with the advent of the era of computing and telecommunications, applications of encryption expanded to offer security, to the ability to: verify if a message was not altered by a third party, to be able to verify if a user is who claims to be, among others. In this sense, the cryptography of elliptic curves, offers certain advantages over their analog systems, referring to the size of the keys used, which results in the storage capacity of the devices with certain memory limitations. Thus, the objective of this work is to offer the necessary mathematical tools for the understanding of how elliptic curves are used in public key cryptography.Item Geogebra como recurso facilitador do processo de ensino-aprendizagem de curvas planas(Universidade Federal de Goiás, 2018-05-07) Araújo, Cláudio Lourenço; Smith, Ole Peter; http://lattes.cnpq.br/9938244088922275; Smith, Ole Peter; Pina, Romildo da Silva; Silva, Silvia Cristina Belo eThe objective of this work is to contribute to the teaching-learning process of planas curves, in high school as wellas in higher education. To achieve this goal, we present the concepts, de_nitions and studies of planas curves, addressing algebra and geometry through Geogebra Software. Using this tool, we will approach mechanically generated curves (roulettes) and discuss some concepts. The theme provides us with a re_ection on the use of Geogebra software as a facilitating tool in the teaching-learning process. The possibility of being able, on a single screen, to analyze the algebraic and geometric behavior of planas curves contributes to the construction of mathematical knowledge. To this end, we will conduct a brief discussion on the use of Geogebra Software in teaching. Then we will present the main concepts of _at curves such as parameterization, tangent vector, normal vector, Frenet system, arc length, reparametrization, curvature, evolute and involute. In the discussion of all these concepts, Geogebra is present, in order to assist in the discussion and to show the possibilities of its use. Finally, we discuss a proposed activity in the classroom.Item Ação de automorfismos livres de pontos fixos(Universidade Federal de Goiás, 2016-05-13) Araujo, Daniel dos Santos; Oliveira, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Oliveira, Ricardo Nunes de; http://lattes.cnpq.br/0563210461148997; Acciarri, Cristina; Lima, Aline de SouzaIf a Zn-graded Lie ring L admits a fixed point free automorphism of order n, then L is soluble and the derived length of L is bounded in function only on n. In this work, we study some results about the derived length of the Zn-graded Lie rings and in the particular case that n = 6, we also study properties to the nilpotency class of the lower central series of L. For this, we introduce some basic results of Lie algebras theory and Lie rings, as well preliminary concepts of modules and tensor product. Finally, we study a Lie ring associated to a group once many problems in group theory can be treated by linear methods about Lie algebras and Lie rings.Item Programação linear e suas aplicações: definição e métodos de soluções(Universidade Federal de Goiás, 2013-03-18) Araújo, Pedro Felippe da Silva; Cruz, José Yunier Bello; http://lattes.cnpq.br/8377200040018415; Cruz, José Yunier Bello; Sandoval, Wilfredo Sosa; Melo, Jefferson Divino Gonçalves deProblems involving the idea of optimization are found in various elds of study, such as, in Economy is in search of cost minimization and pro t maximization in a rm or country, from the available budget; in Nutrition is seeking to redress the essential nutrients daily with the lowest possible cost, considering the nancial capacity of the individual; in Chemistry studies the pressure and temperature minimum necessary to accomplish a speci c chemical reaction in the shortest possible time; in Engineering seeks the lowest cost for the construction of an aluminium alloy mixing various raw materials and restrictions obeying minimum and maximum of the respective elements in the alloy. All examples cited, plus a multitude of other situations, seek their Remedy by Linear Programming. They are problems of minimizing or maximizing a linear function subject to linear inequalities or Equalities, in order to nd the best solution to this problem. For this show in this paper methods of problem solving Linear Programming. There is an emphasis on geometric solutions and Simplex Method, to form algebraic solution. Wanted to show various situations which may t some of these problems, some general cases more speci c cases. Before arriving eventually in solving linear programming problems, builds up the eld work of this type of optimization, Convex Sets. There are presentations of de nitions and theorems essential to the understanding and development of these problems, besides discussions on the e ciency of the methods applied. During the work, it is shown that there are cases which do not apply the solutions presented, but mostly t e ciently, even as a good approximation.Item A curvatura Gaussiana via ângulo de contato de superfícies imersas em S3(Universidade Federal de Goiás, 2015-02-27) Argote, Fernando Arnulfo Zuñiga; Corro, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615; Corro, Armando Mauro Vasquez; Santos, João Paulo dos; Pieterzack, Maurício DonizettiIn this work we refer to the study of a geometric invariant surfaces immersed in Euclidean 3-dimensional sphere S3. Such invariant, known as angle contact, is the complementary angle between the distribution of contact d and the tangent space of the surface. Montes and Verderesi [22] characterized the minimal surfaces in S3 with constant contact angle and Almeida, Brazil and Montes [4] studied some properties of immersed constant mean curvature into a round sphere S3 with constant contact angle. The our aim of this work is to deduce a general formula involving the Gaussian curvature, the mean curvature and the contact angle of surfaces immersed in Euclidean sphere 3-dimensional, which shows that the surface is flat if the contact angle is constant. Moreover, we deduce that the Clifford tori are the unique compact surfaces with constant mean curvature having such propriety. Keywords