Programa de Pós-graduação em Matemática

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VARIEDADES QUASE EINSTEIN
(Universidade Federal de Goiás, 2006-03-31) CARDOSO, Márcia do Socorro Borges de Araújo; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991
This dissertation is based about two works on quase Einstein manifolds. The first, published in 2000, by M. C. Chaki and R. K. Maity, on quase Einstein manifolds which are not conformally flat, and they determine sufficient condition so that the same ones are conformally flat. Already the second work, published by U. C. De and Gopal Chandre Ghosh, in 2004, establish a relation between the manifolds of amost constant curvature and the quasi Einstein manifolds, find necessary and sufficient conditions for a quasi Einstein manifolds to be of almost constant curvature, in follow prove an existence theorem on quase Einstein manifolds with other such manifolds like weak symmetries and semi-symmetries Ricci.
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/8457974658695539
Transitional 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.
Convergência local do método de Newton inexato e suas variações do ponto de vista do princípio majorante de kantorovich
(Universidade Federal de Goiás, 2007-12-14) GONAÇALVES, Max Leandro Nobre; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251
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.
Uma melhora das cotas de Feng-Rao e de Miura para a distância mínima de códigos definidos sobre uma variedade afim
(Universidade Federal de Goiás, 2007-12-18) MESQUITA, Aline Mota de; RODRIGUES, Paulo Henrique de Azevedo; lattes.cnpq.br/8910130626123426
In this work we present some linear codes and we discuss about parameters of cyclic codes families that lead to the characterization of the Goppa codes, which we describe minimum distance bounds when it is given for an affine variety. When this code is defined like this, we say that it is an improved geometric Goppa code. The first bounds mentioned in this work was given by Feng and Rao in [6] (Feng-Rao bound), later improved by Miura in [18],[19] (weakly Feng-Rao bound), that in its turn has been improved by G. Salazar, D. Dunn and S. B. Graham in [22] (advisory bound and strong advisory estimate). This work was based in this last article. We finishing the dissertation showing families of codes for which we verified the veracity of the improvement of bounds.
Códigos geometricamente uniformes em espaços hiperbólicos
(Universidade Federal de Goiás, 2008-02-15) MACHADO, Ana Paula Faria; SOUZA, Mário José de; http://lattes.cnpq.br/4862963990848505
In this dissertation we define geometrically uniform codes in Euclidean spaces, presenting some symmetrical properties of these codes. Build geometrically uniforme partitions and starting these we define generalized coset codes. We generalize the concept of geometrically uniform codes to hyperbolic spaces. We show a characterization of generalized coset codes through the concept of G-linear codes.
Superfícies Mínimas em H3 e H2 x R
(Universidade Federal de Goiás, 2008-02-20) RUYS, Wesley da Silva; CORRO, Armando Mauro Vasquez; http://lattes.cnpq.br/4498595305431615
In this work we study some results from the article of Mercuri, F., Piu, P., Montaldo, S; Weierstrass Representation Formula for Minimal Surfaces in H3 and H2 x R. Therefore, we do a study of the minimal surfaces simply connected in three-dimensional Riemaniann manifold. Furthermore, searching for to determine the necessary conditions to find minimal surfaces in these spaces. Moreover, to give examples of the surfaces in the three-dimensional Heisenberg group and in the product of the hyperbolic with the real line.
Transformações de Ribaucour para hipersuperfícies em formas espaciais
(Universidade Federal de Goiás, 2008-02-29) SOUTO, Leonardo Antônio; LEMES, Max Valério; http://lattes.cnpq.br/6512955169729670
The theory of Ribaucour transformations for hypersurfaces in space forms is presented. A method to obtaining linear Weingarten surfaces in a three-dimensional space form is showed. By applying the theory to the cylinder, we obtain a two-parameter family of linear Weingarten surfaces. A new one-parameter family of complete constant mean curvature surfaces in the unit sphere, locally associated to the flat torus, is obtained. We construct new families of constant mean curvature 1 (cmc-1) surfaces which are locally associated to Enneper cousin.
Curvatura de Lie das hipersuperfícies de Dupin
(Universidade Federal de Goiás, 2008-03-28) VITOR, Erivelton Paulo; RODRIGUES, Luciana Maria Dias de ávila; http://lattes.cnpq.br/6564647402919278
In this work we study some results from the article of Tomas E. Cecil, On the Lie curvature of Dupin hypersurfaces [4]. We study the basic concepts of Lie sphere geometry, which given the framework for the study of Dupin hypersurfaces in the Lie sphere geometry. We construct example of a non-compact proper Dupin hypersurface immersed in Sn on which the Lie curvature Ψ = 1/2 which is not Lie equivalent to an open subset of an isoparametric hypersurface in Sn. We also produce example on which Lie curvature Ψ has a constant value c, 0 < c < 1.
Hipersuperfacies Conformemente Planas no Espaço Euclidiano R4
(Universidade Federal de Goiás, 2008-03-28) SOUSA, Marcio Lemes de; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991
In this work we develop the article "Conformally Flat Hypersurfaces in Euclidean 4-space II", of Suyama, where is presented the study on conformally °at hypersurfaces in the Euclidean 4-spaces R4. From a surface with constant Gaussian curvature positive or negative in either Euclidean 3-space R3 or the standard 3-sphere S3, we constructed a family of conformally °at hypersurfaces in R4, with three distinct principal curvatures
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/9174074436425246
In this work....
Classificação das superfícies de revolução tipo Delaunay completas
(Universidade Federal de Goiás, 2008-05-30) SOUZA, Luiz Gustavo Alves de; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991
In this dissertation we have studied the articles The Surfaces of Delaunay, by James Eells, and Classi¯cation des Surfaces de Type Delaunay, by Ricardo Sa Earp and Eric Toubiana. Based on the ¯rst work we have classi¯ed the surfaces of revolution of constant mean curvature known as surfaces of Delaunay. By using the second one we have looked at special surfaces of Weingarten, whose mean and gaussian curvatures satis¯es the relation H = f(H2 ¡ K); where f is an elliptic function of class C1. We have classi¯ed the complete surfaces of revolution, that satis¯es the Weingarten relation. They are known as surfaces of Delaunay Type
Derivaçao de uma Equação Diferencial Parcial Não-Linear na Propagação de Frentes de Reação em Química
(Universidade Federal de Goiás, 2008-08-29) CARDOSO FILHO, João Lopes; ALARCON, Eduardo Arbieto; http://lattes.cnpq.br/5960048699820842
In this dissertação we deducted a nonlinear evolution equations which model vertical propagation of chemical reaction fronts. We establish which the initial value problem ∂tu - ∂²x u - ½(∂xu)² - µ(1-∂²x) - ½u = 0, x Є [-π, π], t > 0 u(.,0) = ø, 2 π - periódica it is a the Cauchy problem locally well-posed.
Movimentos sob atração focal em campos vetoriais planares
(Universidade Federal de Goiás, 2008-08-29) MARTINS, Tiberio Bittencourt de Oliveira; GARCIA, Ronaldo Alves; http://lattes.cnpq.br/5680428710939826
In this work, we develop the article On the motion under focal attraction in a rotating medium , of J. Sotomayor, which deals with a bidimensional differential system that model the following Biological problem: in a shallow recipient with circular section, with liquid in, spinning with angular speed ω, there are platyhelminthes, flatworms organisms, they are attracted by a fix lighting point near of the border of the recipient and they swim with a speed v in the direction of the this point. The problem is to show that there exists an equilibrium point where platyhelminthes go to cluster by the time passing. It s analyzed the dynamic of the model: existence of critical points and stability of the system and bifurcations. We analyzed three modifications of this system too. In the last part, it s discussed a criterium for non existence of periodic orbits of a planar vector fields in a simply connected region.
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/8910130626123426
This 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.
Hipersuperfícies conformemente planas em R4
(Universidade Federal de Goiás, 2009-03-13) Moreira, Lucas; Pina, Romildo da Silva; http://lattes.cnpq.br/2675728978857991
language="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.
Superfícies de Weingarten Lineares Hiperbólicas em R3
(Universidade Federal de Goiás, 2009-08-25) GUEDES, Luciene Viana; FERREIRA, Walterson Pereira; http://lattes.cnpq.br/9150818921025647
The present work has been based by the [1] from Juan A. Aledo S´anches and Jos´e M. Espinar and [2] from Rafael L´opez articles. In those articles they studied hiperbolic linear Weingarten surfaces in R3 space, this is, surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH+bK =c, where a, b, c 2 R. A such surface is said to be hiperbolic when the discriminant D := a2+4bc < 0.We obtain a representation for rotational hyperbolic linear Weingarten surfaces in terms of its Gauss map and we also present, in the case a 6= 0, a classification of linearWeingarten surfaces of hyperbolic rotation. As a consequence we obtain, in the case a 6=0, a family of complete hyperbolic linear Weingarten surfaces in R3. This contrasts with Hilbert s theorem that there do not exist complete surfaces with constant negative Gaussian curvature immersed in R3.
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/5680428710939826
In 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.
Método do gradiente para funções convexas generalizadas
(Universidade Federal de Goiás, 2009-12-16) COUTO, Kelvin Rodrigues; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251
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.
Métricas de Randers Localmente Dualmente Flat
(Universidade Federal de Goiás, 2010-02-26) Fernandes, Karoline Victor; SOUZA, Marcelo Almeida de; http://lattes.cnpq.br/1343419041226215
We will study the Finsler metric, on a manifold M, defined as the sum of a Riemannian metric and a 1-form, they are known as Randers metric. We will classify those that are locally dually flat, that is, for all point exists a coordinate system in which the equation of the geodesic has a special form, the coefficients of spray is given in terms of the metric one and a local scalar function, we will also characterize the Randers metric that is locally dually flat with almost isotropic flag curvature
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.

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