Programa de Pós-graduação em Matemática

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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 Souza
If 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.
Álgebras associadas a grafos orientados em níveis e a propriedade da Koszulidade
(Universidade Federal de Goiás, 2014-11-20) Vasconcelos, José Eder Salvador de; Lima, Aline de Souza; Silva, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; Rodrigues, Paulo Henrique de Azevedo; Lima, Aline de Souza; Guerreiro, Marinês; Lemos, Manoel José Machado Soares; Castonguay, Diane
In this work we study classes of algebras associated with layered directed graphs. Let 􀀀 be a layered directed graph. We determine the algebra Ap􀀀q; generated by the edges of the graph, satisfying a set of quadratic relations R; and the dual algebra Ap􀀀q!, associated with grpAp􀀀qq. For each P Autp􀀀q we determine: the algebra Ap􀀀 q; where 􀀀 is the subgraph of 􀀀 whose vertices are xed by ; the graded trace generating functions Tr pAp􀀀q; tq and Tr pAp􀀀q!; tq: We also determine the multiplicities of the irreducible representations of AutpAp􀀀qq acting on Ap􀀀q and Ap􀀀q!: We show that for a layered directed graph 􀀀, satisfying some hypotheses, AutpAp􀀀qq K Autp􀀀q. Finally, we verify the property Tr pAp􀀀q; tq Tr pAp􀀀q!; tq 1 for all P Autp􀀀q, called koszulity property. We consider two classes of algebras, the algebra associated to the Hasse graph of the partially ordered set of faces of a star polygon, Ap􀀀 q; and the algebra associated with the Hasse graph of the lattice of subespaces of a nite dimensional vector space over Fq; ApLpn; qqq:
Um algoritmo para estimar a dimensão do segundo grupo de homologia de um grupo finitamente apresentado
(Universidade Federal de Goiás, 2012-04-12) VIEIRA, Flavio Pinto; SERCONEK, Shirlei; http://lattes.cnpq.br/2718527331501182; ADORNO, Ticianne Proença Bueno; http://lattes.cnpq.br/7769491630579878
The main goal of this work is to establish a primary bound for the dimension of the second homology group of a group G, with coefficients in a field k of characteristic p, H2(G;k), using the operating system GAP. It will be presented with several examples, where in some cases, will be calculated the exact dimensions and in other cases only an upper bound.
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 Pereira
In 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.
Algoritmo proximal inexato tipo descida para otimização suave
(Universidade Federal de Goiás, 2013-05-20) Godoi, Gean Henrique; Silva, Geci José Pereira da; http://lattes.cnpq.br/9174074436425246; Silva, Geci José Pereira da; Santos, Paulo Sérgio Marques dos; Ferreira, Orizon Pereira
The proximal method is a standard regularization approach in optimization. In this work we focus on a stopping rule of this algorithm, when smoothness is present, so that Newton-like method can be used to solve the subproblems. The basis for our stopping test is a "sufficient" decrease in the objective function where we establish the convergence of the algorithm obtained.
Alguns problemas de soma-zero com peso
(Universidade Federal de Goiás, 2015-03-02) Pereira, Nara Reges Faria de Paiva; Rodrigues, Paulo Henrique de Azevedo; http://lattes.cnpq.br/8910130626123426; Rodrigues, Paulo Henrique de Azevedo; Chagas, Sheila Campos; Chaves, Ana Paula de Araújo
In this work we study some results about Davenport’s constant for finite abelian groups. We also study some weighted zero-sum problems for especific cyclic groups and for this we prove some relations between the invariants sA, gA e hA for such groups.
Altura e equidistribuição de pontos algébricos
(Universidade Federal de Goiás, 2017-06-20) Santos, Jefferson Marques; Chaves, Ana Paula de Araújo; http://lattes.cnpq.br/2332073500640724; Chaves , Ana Paula de Araújo; Lopes , José Othon Dantas; Rodrigues , Paulo Henrique de Azevedo; Oliveira, Ricardo Nunes de
The concept of roots of a polynomial is quite simple but has several applications. This concept extends more generally to the case of "small" algebraic points sequences in a curve. This dissertation aims to estimate the size of algebraic numbers by means of Weil height. In addition to showing that they are distributed evenly around the unit circle, through Bilu Equidistribution Theorem.
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 de
In 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.
Aplicações da álgebra linear nas cadeias de Markov
(Universidade Federal de Goiás, 2013-04-11) Silva, Carlos Eduardo Vitória da; Mota, Jesus Carlos da; http://lattes.cnpq.br/8457974658695539; Mota, Jesus Carlos da; Seimetz, Rui; Smith, Ole Peter
The theory of linear algebra and matrices and systems particularly are linear math topics that can be applied not only within mathematics itself, but also in various other areas of human knowledge, such as physics, chemistry, biology, all engineering, psychology, economy, transportation, administration, statistics and probability, etc... The Markov chains are used to solve certain problems in the theory of probability. Applications of Markov chains in these problems, depend directly on the theory of matrices and linear systems. In this work we use the techniques of Markov Chains to solve three problems of probability, in three distinct areas. One in genetics, other in psychology and the other in the area of mass transit in a transit system. All work is developed with the intention that a high school student can read and understand the solutions of three problems presented.
Aplicações para o princípio de indução matemática
(Universidade Federal de Goiás, 2014-09-26) Silva Júnior, Normando; Silva, Maxwell Lizete da; http://lattes.cnpq.br/9078818338290451; Silva, Maxwell Lizete da; http://lattes.cnpq.br/9078818338290451; Krindges, André; Lima, Lidiane dos Santos Monteiro
This paper sought to systematically present knowledge on the number theory in a clear and acessible way to a broader community than the mathematical academics, the principle of mathematical induction PMI, was the background and the main tool to all demonstrations so to permeate almost all the results and, in each section, at least one numerical example was given, thus making it easier to readers beginning their studies in math and always seeking to at least encourage the investigative feeling on all readers. The continuous fractions, subject commonly overlooked, yet with vast applications in Physics and Calculus, proved to be familiar with the Fibonacci numbers. Sequentially, two classic game problems were presented, The Hanoi Tower and the problem of the false coin, which could, from simple examples be generalized demonstrating solutions for the problems at any given natural number. Finally, the linear recurrences of second order and the higher order arithmetic progression were shown to have deep connections with the Fibonacci sequence, so then, these numbers became the main motivators for all the paper, that prizes for demonstrable results through PMI or related to this sequence of numbers, and always sought to strengthen the admiration of the dialogues with branches apparently so fixed that are the familiar through the appearance of the Fibonacci numbers in these topics.
Uma apresentação policíclica para o multiplicador de Schur e o quadrado tensorial não abeliano de um grupo policíclico
(Universidade Federal de Goiás, 2015-03-19) Silva, Jefferson dos Santos e; Dias, Ivonildes Ribeiro Martins; Silva, Jhone Caldeira; Silva, Jhone Caldeira; Dias, Ivonildes Ribeiro Martins; Oliveira, Ricardo Nunes de; Rocco, Noraí Romeu
In this work, based on [9], describes an effective method for computing a consistent polycyclic presentation for the nonanbeian tensor square G G of a group G given by a consistent polycyclic presentation.
Bifurcações de campos vetoriais em duas zonas com simetria
(Universidade Federal de Goiás, 2017-11-28) Castro, Ubirajara José Gama de; Medrado, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286; Tonon, Durval José; Pessoa, Cláudio Gomes; Martins, Ricardo Miranda; Oliveira, Regilene Delazari dos Santos
In this work we study reversible vector fields in two zones and equivariant vector fields in two zones. Our main result is the classification of the symmetric singularities of codimensions 0,1 and 2 of such vector fields. More precisely, in the reversible case in R3, where the dimension of the fixed points variety of the involution associated to the vector field is 2, we present all bifurcation diagram of the codimensions 1 and 2 singularities, describing the changes in the behavior of the symmetric singularities and tangents of the vector field with the transition manifold, S, according to the variation of the bifucartion parameter. We also show the existence of invariant cylinders and, in this case, doing small perturbations we determine invariant manifolds that persisted and we determine the number of limit cycles that were born. When the vector field defined on two zones is equivariant, the dynamic is enriched with the emergence of the sliding vector field and we also do a local study and the classification of singularities (and pseudo-singularities) of codimensions 0,1 and 2. We show the existence of homoclinic sliding orbit and that it is a codimension one phenomenon. Moreover, provided the symmetry we get a double Shilnikov sliding orbit.
Bifurcações em sistemas dinâmicos suaves por partes
(Universidade Federal de Goiás, 2015-03-06) Tsujii, Marcos; Tonon , Durval José; http://lattes.cnpq.br/3688981956532711; Tonon, Durval José; http://lattes.cnpq.br/3688981956532711; Mizukoshi, Marina Tuyako; Carvalho, Tiago de
In this work, we will study the dynamics in smooth vector elds, in vector elds near the boundary and in piecewise-smooth vector elds and each of their most popular types of bifurcations up to now.
Campos descontínuos com chaveamento no Rn
(Universidade Federal de Goiás, 2016-05-13) Silva , Tharsis Souza; Jaquemard , Alain Guy; Garcia , Ronaldo Alves; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4787335Z3; Garcia , Ronaldo Alves; Buzzi , Claudio Aguinaldo; Teixeira , Marco Antonio; Jaquemard , Alain Guy; Medrado , João Carlos da Rocha
In this work we _rstly study a relay system X on the Rn that, under certain conditions, it has a one parameter family of 1-periodic orbits that arises in the origin and increase inde_nitely. We study yet another relay system class X_, that it is formed from the initial relay system by aditions of nilpotent parameters that, under certain conditions, it has the same result of the previous, and yet family of periodic orbits that arises in the origin and ends in a loop, or family that bifurcate of a loop and arise inde_nitelly. Furthermore the periodic solutions are explicitely given by Euler polynomials. Finally we study a third order di_erential equation with relay looking for periodic orbits of di_erent degrre of di_erentiability and this is done by the associated vector _eld with jump.
Campos vetoriais suaves por partes: modelos predador-presa
(Universidade Federal de Goiás, 2015-03-06) Silva, Lucyjane de Almeida; Medrado, João Carlos da Rocha; Medrado, João Carlos da Rocha; Lima, Maurício Firmino Silva; Tonon, Durval José
In this work we study the global qualitative behavior of three predator-prey models. We analyze the existence of limit cycle and canard cycle and we investigate the kinds of bifurcation that can occur. In the first model, Gause predator-prey with a refuge, we analyze the effects of a prey refuge on the ecosystem qualitative behavior. Employing the carrying capacity of the prey population in the Gause Model with a refuge we obtain the second model, for which we analyze the effects of the carrying capacity and we compare the results. In the third model we consider the continuous threshold harvesting strategies ocurring when the predator density is above a certain threshold. We note that the model has a complex dynamics with multiple internal equilibria and different types of bifurcation.
Uma caracterização da planaridade de uma família de funções binomiais sobre corpos finitos via curvas algébricas
(Universidade Federal de Goiás, 2022-08-26) Chu, Daniel; Tenório, Wanderson; http://lattes.cnpq.br/6406888404650319; Tenório, Wanderson; Tizziotti, Guilherme Chaud; Cunha, Gregory Duran
In this work, we study a family of binomial functions given by $$ f_{a,b}(x)=ax^{2^{2^m}+1}+bx^{2^m+1}, \quad \mbox{with } \ a,b\in\mathbb{F}_{q^3}^\times, $$ over a finite field of characteristic 2. The aim consists to show that is possible to relate the planarity of the family above to a cubic plane projective curve $\mathcal{C}_{a,b}$. From this method, it is possible establish a characterization of the pairs $(a,b)\in(\mathbb{F}_{q^3}^\times)^2$ such that the function $f_{a,b}(x)$ is planar.
Centros Persistentes
(Universidade Federal de Goiás, 2010-03-05) ROCHA, Valdomiro; MEDRADO, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286
The problem of destingnishing whether a monodromic critical point with imaginary eigenvalues of a family of a planar analitical vector field is a center or a focus was already solved by Lyapunov. This is the famous center-focus problem which was solved by calculating the so-called Lyapunov constants and see whether or not they are zero. We present a few ways to calculate them acording the approaches that they use: camputation of a Lyapunov function; use of normal forms; computation of the power of expansion of a solution in polar coordinates; use of the algebraic structure of Lyapunov constants; method of Lyapunov-Schmit and Melnikov functions. Despite all of the above the centerfocus problem for a simple family as the cube is resisting all attempts at solution. For this reason the centers, we propose to grade the in three levels in order to make the problem more feasible.
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 de
In 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.
Ciclos limite e singularidades típicas de sistemas de equações diferenciais suaves por partes
(Universidade Federal de Goiás, 2017-03-07) Cespedes, Oscar Alexander Ramírez; Medrado, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286; Tonon, Durval José; Buzzi, Claudio Aguinaldo; Silva, Paulo Ricardo da; Martins, Ricardo Miranda
In this work, we analize the version of Hilbert’s 16th problem for a piecewise linear differential system, PWLS, in R2. More precisely,we determinete the maximum number of certain types of limit cycles when the system is define in two zones separated by a straight line. Some results on the maximum number of cycles of a PWLS defined in two sectors were established. In addition, we classify typical singularities of a piecewise smooth systemin R3, taking into account the behavior of the associated sliding field.
Ciclos limite e superfícies invariantes em sistemas diferenciais
(Universidade Federal de Goiás, 2016-05-13) Freitas, Bruno Rodrigues de; Medrado, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286; Medrado, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286; Buzzi, Claudio Aguinaldo; Carvalho, Tiago de; garcia, Ronaldo Alves; Teixeira, Marco Antonio
We consider a class of piecewise linear di erential systems in R3 separated by a plane and we study its global and local dynamics. More precisely, we give conditions to the existence of invariant surfaces and limit cycles, presenting the maximum number of limit cycles and characterizing these invariant surfaces. Also, we obtain results about the T-singularity obtained by a perturbation of piecewise linear di erential systems. In our approach, we use many techniques, as an extension of the theorem’s Rolle for vector fields, Theory of Sturm’s sequence, extendedcomplete Tchebyche systems and extensions of Averaging theory.

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