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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 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 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 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 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 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 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. KeywordsItem Um algoritmo proximal com quase-distância(Universidade Federal de Goiás, 2015-02-25) Assunção Filho, Pedro Bonfim de; Bento, Glaydston de Carvalho; http://lattes.cnpq.br/1089906772427394; Bento, Glaydston de Carvalho Bento; Cruz Neto, João Xavier da; Ferreira, Orizon PereiraIn this work, based in [1, 18], we study the convergence of method of proximal point (MPP) regularized by a quasi-distance, applied to an optimization problem. The objective function considered not is necessarily convex and satisfies the property of Kurdyka- Lojasiewicz around by their generalized critical points. More specifically, we will show that any limited sequence, generated from MPP, converge the a generalized critical point.Item Sobre uma classe de álgebras associadas a duas famílias de grafos orientados(Universidade Federal de Goiás, 2015-03-02) Barboza, Marcelo Bezerra; Lima, Aline de Souza; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Silva, Jhone Caldeira; Lima, Aline de Souza; Chagas, Sheila Campos; Oliveira, Ricardo Nunes deGiven a directed layered graph , we present the algebra A() as a quotient of the free associative or tensor algebra (with unit, over an arbitrarily fixed field of scalars), freely generated by the set of edges in . We calculate the Hilbert series associated with the grading on A() coming from degree in the tensor algebra. We also calculate the group of automorphisms of A() that preserve the (ascending) filtration associated with the grading mentioned above. Despite the fact the main results within this notes remain true for a relatively large class of directed graphs, we stay close to the ones Dn and Ln, n 3, that is, those consisting, respectively, on the Hasse diagram of the partially ordered sets of faces in a regular polygon containing n edges and the power set of {1, . . . , n}. The work teaching us all of the above is [1], by Colleen Duffy.Item Sequências monótonas aplicadas a um problema de cauchy para um sistema de reação-difusão-convecção(Universidade Federal de Goiás, 2015-08-07) Barros, Carlos Eduardo Rosado de; Mota, Jesus Carlos da; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4787068H6; Mota, Jesus Carlos da; Bastos, Waldemar Donizete; Silva, Maxwell LizeteIn this work, mainly based on the articles, [1], [2] and [7], one studies a reactiondiffusion- convection system, related the propagation of a combustion front through a porous medium, giving origin a Cauchy problem. Such a problem has been approached by the methode of the monotone iterations, which leads to an unique time-global solution.Item Gradiente ricci solitons e variedades de Einstein com métrica produto torcido(Universidade Federal de Goiás, 2016-03-31) Batista, Elismar Dias; Souza, Marcelo Almeida de; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4797616Y0; Pina, Romildo da Silva; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4782462D0; Pina, Romildo da Silva; Souza, Marcelo Almeida dea; Santos, João Paulo dosThis work is based on the articles [26] and [27], where we studied Einstein manifolds and gradient Ricci soliton with twisted product structure. As a result, we prove the following: if M is an Einstein warped product space with nonpositive scalar curvature and compact base, then M is a Riemannian product space. Besides, we show that the Riemannian product Rp×F is a gradient Ricci soliton if and only if F is Ricci soliton gradient. Then, we show that the warped product R×f B is gradient Ricci solitons with f ′′ 6= 0, therefore F is Einstein. By using these results, we build nontrivial examples of gradient Ricci soliton where the fiber is either an Einstein manifold or a nontrivial gradient Ricci soliton.Item Ciclos limite de grande amplitude em sistemas lineares definidos por partes(Universidade Federal de Goiás, 2023-01-10) Becatti, Fernanda dos Anjos Félix; Freitas, Bruno Rodrigues de; http://lattes.cnpq.br/4201351441514126; Freitas, Bruno Rodrigues de; Cristiano, Rony; Carvalho, Tiago deIn this paper we deal with a family of piecewise smooth planar linear systems with two zones, we study about the maximum number of limit cycles that can be obtained when studying the orbit at infinity. We start from a canonical form with 12 parameters and reduce the number of parameters to 5 for the analysis. We investigate questions related to stability, characterization of the orbits and other properties that can be obtained by studying the family of systems under consideration.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 Superfícies de Bianchi com ângulo de Chebyshev constante(Universidade Federal de Goiás, 2010-10-01) BEZERRA, Adriano Cavalcante; CORRO, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615The Bianchi surfaces belong to a class of surfaces with negative Gaussian curvature, discovered by generalization of Backlund transformation for surfaces with constant negative Gaussian curvature [3]. Today these areas are studied from the viewpoint of the theory of integrable systems. In this paper we study Bianchi surfaces parameterized by a Generalized Chebyshev net and show that such a surfaces with Chebyshev constant angle is a piece of a right helicoid, see [1].