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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 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 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].Item 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/5960048699820842In 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.Item 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/2675728978857991This 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.Item Difeomorfismos conformes que preservam o tensor de Ricci em variedades semi-riemannianas(Universidade Federal de Goiás, 2011-01-28) CARVALHO, Fernando Soares de; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991; SILVA, Rosângela Maria da; http://lattes.cnpq.br/0085316338495571NOTE: Because some programs do not copy symbols, formulas, etc... to view the summary and the contents of the file, click on PDF - dissertation on the bottom of the screen.Item Condição de Nilpotência para Grupos Localmente Finitos de expoente p e Álgebras de Lie (p-1)- Engel de Característica p (ou 0)(Universidade Federal de Goiás, 2011-04-25) CARVALHO, Lucimeire Alves de; SILVA, Jhone Caldeira; http://lattes.cnpq.br/6848751340618892; LIMA, Aline de Souza; http://lattes.cnpq.br/1518865173435209Let P be a locally finite group of prime exponent p, admitting a finite soluble automorphism group G of order n coprime to p. In this work we study the influence of the centralizers of the automorphisms in G on the structure of P. In this sense we show that if CP(G), the subgroup of fixed points is soluble of derived length d, then P is nilpotent of class bounded in terms of p, n and d. It will be also shown that if a (p-1)-Engel Lie algebra L of characteristic p (or 0) admits a finite soluble automorphism group G of order n coprime to the characteristic of L, such that CL(G), the subalgebra of fixed points, is soluble of derived length d, then the Lie algebra L is nilpotent of class bounded in terms of p, n and d.Item Sobre Regularização e Perturbação Singular(Universidade Federal de Goiás, 2011-02-24) CASTRO, Ubirajara José Gama de; MEDRADO, João Carlos da Rocha; http://lattes.cnpq.br/5021927574622286The main goal of this work is to study the behavior of Discontinuous Vector Fields in a neighborhood of a tipical singularity (tangency) using for this the regularization process developed by Teixeira and Sotomayor [9] and, using also, some technics of the Geometric Singular Perturbation Theory [2].Item Superfícies Completas com Curvatura Gaussiana Constante em H2×R e S2×R(Universidade Federal de Goiás, 2010-03-19) CINTRA, Adriana Araujo; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991In this work we classify the complete surfaces with constant Gaussian curvature into the H2×R and S2×R.We show that exists a unique complete surface, up to isometries, with positive constant Gaussian curvature into the H2×R, and greater than one, into the S2×R and that there is no complete surfaces with constant Gaussian curvature K(I) < −1 into the H2×R and S2×R. We prove that even if −1 ≤ K(I) < 0 there are infinite complete surfaces into the H2 ×R with Gaussian curvature K(I) and with additional assumption we prove there is if −1 ≤ K(I) < 0 and 0 < K(I) < 1 there is no exists complete surfaces into S2×R with Gaussian curvature K(I). These results were obtained by Aledo, Espinar and Gálvez and can be found in [1].Item Método do gradiente para funções convexas generalizadas(Universidade Federal de Goiás, 2009-12-16) COUTO, Kelvin Rodrigues; FERREIRA, Orizon Pereira; lattes.cnpq.br/0201145506453251The 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.Item Problemas Elípticos Assintoticamente Lineares(Universidade Federal de Goiás, 2012-02-02) DAMKE, Caíke da Rocha; SILVA, Edcarlos Domingos da; http://lattes.cnpq.br/7817014732764711In this dissertation we analyze questions of existence and multiplicity of solutions for Dirichlet problem in the asymptotically linear case. To obtain our main results we use variational methods, such as Montain Pass Theorem and Linking Theorem.Moreover, we use the Liapunov-Schmidt reduction.Item Sobre uma caracterização de pequena calota esférica(Universidade Federal de Goiás, 2011-02-18) DIAS, Diogo Gonçalves; FERREIRA, Walterson Pereira; http://lattes.cnpq.br/9150818921025647It is known that small spherical caps are the only compact surfaces with constant mean curvature H 6= 0 graphics whose boundary is a round circle. This characterization is a partial answer to one of the conjectures of the spherical cap and its classic demonstration involves the Maximum Principle for surfaces with constant mean curvature. What we re doing this work is to give a new proof for this characterization of small spherical cap without the use of the Principle of Maximum. In addition, we make statements alternatives other results related to Conjecture, whenever possible.Item Inflexões de Linhas Assintóticas e de Linhas de Curvatura em Superfícies(Universidade Federal de Goiás, 2010-10-19) FREITAS, Bruno Rodrigues de; GARCIA, Ronaldo Alves; http://lattes.cnpq.br/5680428710939826Quadratic points (or special hyperbolic points) are points where a surface can be approximated by a quadric to the terms of order three. We will deal with a conjecture that asserts that every closed hyperbolic surface in RP3 has not less than eight distinct quadratic points. We prove a result which states that; if a generic surface in RP3 contains a hyperbolic disk bounded by a Jordan parabolic curve, then there is an odd number of quadratic points inside this disc. We study curves formed by the inflection points of asymptotic foliations and principals in the hyperbolic domain.We studied the behavior of the inflection curve of the asymptotically foliation near a special parabolic point (the point where the asymptotic direction is tangent to the parabolic curve), and the behavior of the inflection curve of the principal foliation near a umbilic point.Item 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/0201145506453251The 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.Item Superfícies de Weingarten Lineares Hiperbólicas em R3(Universidade Federal de Goiás, 2009-08-25) GUEDES, Luciene Viana; FERREIRA, Walterson Pereira; http://lattes.cnpq.br/9150818921025647The 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.Item Superfícies mínimas com curvatura constante nas formas espaciais 4-dimensionais(Universidade Federal de Goiás, 2011-05-13) HIEDA, Lidiane Mayumi; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991This work was based on papers On Compact Minimal Surfaces with non-negative Gaussian Curvature in a Space of Constant Curvature: I and Minimal Surfaces with Constant Curvature in 4-dimensional Space Forms, by Katsuei Kenmotsu, consisting in the classification of minimal surfaces with constant Gaussian curvature K in a 4-dimensional space form without any global assumption. We will show that an isometric minimal immersion x: M2(K) → M4(c), where c is sectional curvature, is either totally geodesic, or locally Clifford Torus, or locally a Veronese surface. As a corollary, we have that there is not isometric minimal immersions with constant negative Gaussian curvature into unit sphere S4(1) even locally.Item Método de Descida para problemas de otimização multiobjetivo(Universidade Federal de Goiás, 2010-04-30) JESUS, Lays Grazielle Cardoso Silva de; PEREZ, Luis Román Lucambio; http://lattes.cnpq.br/6532280983965503In this work, we study the descent of methods for problem of optimization multiobjective which we introduce an order of relation induced by an closed convex cone.We study as it wiel calculate an descent of direction and we prove that every accumalation point of the sequence generated by the descent of methods with search of Armijo is weakly efficient.Item Sólitons de Ricci Shrinking em variedades Riemannianas completas(Universidade Federal de Goiás, 2011-09-02) LEANDRO NETO, Benedito; PINA, Romildo da Silva; http://lattes.cnpq.br/2675728978857991In this work, we started with an historical study of Ricci Solitons showing that they, often, arise as a auto-similar solution for the Ricci flow. It was demonstrated, then, some basic concepts of Riemannian Geometry and a formal definition of a Ricci Solitons. To conclude the work, it was presented a study analysis of the [6] article, establishing , among other results, two theorems: the first one, an estimation for the potential function of a Gradient Shrinking Ricci Solitons, complete non-compact, and, the second one, an estimation for the volume of a Gradient Shrinking Ricci Solitons, complete non-compact.
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