Mestrado em Matemática

URI Permanente para esta coleção

http://repositorio.ufes.br/handle/10/17496

Nível: Mestrado Acadêmico
Ano de início: 2006
Conceito atual na CAPES: 3
Ato normativo: Homologado pelo CNE ( Port. MEC 609, de 14/03/2019, DOU 18/03/2019)
Periodicidade de seleção: Anual
Área(s) de concentração: Matemática
Url do curso: https://matematica.ufes.br/pt-br/pos-graduacao/PPGMAT/detalhes-do-curso?id=1401

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Agora exibindo 1 - 20 de 48

Cotas superiores para o número de pontos racionais e aplicações às torres de corpos de funções
(Universidade Federal do Espírito Santo, 2010-08-19) Silva, Thiago Filipe da; Oliveira, José Gilvan de; Noseda, Francesco; Conte, Luciane Quoos
Soluções positivas de um sistema elíptico semilinear nos casos crítico e supercrítico
(Universidade Federal do Espírito Santo, 2011-06-30) Reis, Fernando Pereira Paulucio; Xavier, Magda Soares; Furtado, Marcelo Fernandes; Silva, João Pablo Pinheiro da
In this work we study the existence of multiple positive solutions for a system of elliptic equations involving critical Sobolev exponent in a bounded domain in RN. These results were demonstrated by Pigong Han. The sub-supersolution method allows to obtain a minimal solution when a parameter " > 0 is small enough. In the critical case, by using the variational method, we may prove the existence of a second positive solution. In the supercritical case, by using the Pohozaev identity, we obtain that the existence of solutions is related to the existence of nonnegative solutions for two linear elliptic problems
Existência de solução de energia mínima para uma equação de Schrödinger não linear
(Universidade Federal do Espírito Santo, 2012-03-06) Rocha, Karlo Fernandes; Xavier, Magda Soares; Silva, João Pablo Pinheiro da; Furtado, Marcelo Fernandes
In this work we study the existence of solution of a quasilinear Schr¨odinger equation in R N , demonstrated by Ruiz and Siciliano. By working in an appropriated functions space, by using a variational identity demonstrated by Pucci and Serrin, a set M containing all nontrivial solutions of the equation is obtained. By using a concentrationcompactness result due to Lions, it is possible to prove that the infimum of the functional associated with the equation, restricted to the set M, is achieved at some u which is a positive ground state solution
Multiplicidade e concentração de soluções positivas para uma equação elíptica quasilinear
(Universidade Federal do Espírito Santo, 2012-03-07) Oliveira Junior, José Carlos de; Xavier, Magda Soares; Silva, João Pablo Pinheiro da; Furtado, Marcelo Fernandes
In this work, we study results on existence and concentration of positive solutions for a Schrödinger equation in R N involving the p-laplacian operator with 2 = p < N, a subcritical nonlinearity, a positive parameter ? and a potencial a(x) satisfying some hypotheses. Such problem was rst studied by Bartsch and Wang [5] in the case of laplacian operator (p = 2). We present versions of the results of [5] in the case of the p-laplacian, which were demonstrated by Furtado [17, 18].
Classificação de estruturas de Nambu lineares e p-formas singulares
(Universidade Federal do Espírito Santo, 2012-08-13) Almeida, Carla Rodrigues; Alves, Magno Branco; Câmara, Leonardo Meireles; Bursztyn, Henrique; Corrêa Júnior, Maurício Barros
The aim of this work is to study the foliations that arise from Nambu structures and present the relationship between differential forms and some of this structures. More specifically, to make a study of the Poisson geometry and of singular foliations, emphasiz-ing the case of the simplectic foliation that arises from the Poisson structure and then, to present the Nambu geometry, studying the case of the foliations that arise from the this structures of order grater than or equal to three. In this particular case, we shall show how this Nambu structures are related with differential formas and, by this relationship, classify linear Nambu structure through a result of classification of integrable differential p-forms
Processos de Markov via o adjunto formal dos operadores de Feller
(Universidade Federal do Espírito Santo, 2012-08-16) Speroto, Adalto; Valentim, Fábio Júlio da Silva; Silva, Jean Carlos da; Romero, Freddy Rolando Hernandez
The main aim of this work is the study of spectral properties of a class of the second order operators, the formal adjoint of the generalized Feller diferential operators. In particular, to deduce that these operators are generators of a strongly continuous contraction semi-group and therefore, to obtain a corresponding class of Markov processes. As a secondary objective, we will establish some results for stochastic processes. We will establish the connection of Markov processes, operators and infinitesimal generators of semi-groups.
Parametrizações de superfícies triangulares
(Universidade Federal do Espírito Santo, 2012-09-06) Telau, Antônio Carlos; Carmo, Fabiano Petronetto do; Aguiar, Edilson de; Paiva Neto, Afonso
Two types of triangular surface parameterizations are proposed in this work: spherical and planar parameterization. We highlight among the applications of this technique, texture mapping and manipulation/deformation of surfaces. In the planar case, a surface with boundary is parameterized in a planar convex polygon, as from the planar immersion of its graph. The theory presented characterizes the set of parameterizations of a given surface, when convex polygon is fixed, from matrices which satisfy a set of conditions. In the case spherical, advanced results of graph theory are used to determine parameterizations of closed surfaces. In this case, we characterize the set of spherical parameterizations of a given surface as the set of all spherical immersions of your graph where each vertex is a spherical projection of some convex combination of its neighbors. In both cases, algorithms based on the methodology propose have been implemented and we presente some results obtained by the proposed algorithms. The results are analyzed and limitations of the algorithms are discussed
Teoria de calibre e geometria via conexões de Cartan-Ehresmann
(Universidade Federal do Espírito Santo, 2012-12-07) Santos, Diego Henrique Carvalho dos; Alves, Magno Branco; Câmara, Leonardo Meireles; Macarini, Leonardo Magalhães; Bochi, Jairo da Silva
The aim of this work is to present how works the correspondence between the gauge theory and connections in ber bundles. More precisely establishing a dictionary between gauge theory of the quantum mechanics of a charged particle under the in‡uence of an electromagnetic eld and the studies of connections in circle bundles and line bundles. Then, we analyzed two objects of studies in physics using the knowledge acquired in the study of the geometry of ber bundles. The Chern classes and the holonomy of a connection will provide a geometrical visualization of, respectively, magnetic monopoles and the Aharonov-Bohm e¤ect
Métodos de projeção multidimensional
(Universidade Federal do Espírito Santo, 2013-05-10) Dal Col Júnior, Alcebíades; Carmo, Fabiano Petronetto do; Gonçalves Junior, Etereldes; Nonato, Luís Gustavo
The problem we are interested in solving comes from a area of knowledge called data visualization. In our studies, groups of objects are analyzed to produce the input data of our problem, each object is represented by attributes, have so a list of attributes for each object. The idea is to represent, through these lists of attributes, objects through points in R 2 so that we can conduct a group of objects. As we said each object is represented by a list of attributes, this may be interpreted as a point of a multidimensional space. For example, if they are considered m valued attributes for all objects can interpret them as points in a space of dimension m, or m-dimensional. But we want to produce a visualization of the data on the computer screen through points in R 2 , it was then performs a process known as multidimensional projection, that is obtaining points in a low dimensional space representing points in a high dimensional space preserving neighborhood relations as much as possible. Various methods of multidimensional projection are found in the literature. In this work, study and implement methods NNP, Force, LSP, PLP and LAMP. These methods deal with the problem in different ways: geometrically; linear systems, in particular, laplacian systems; and mappings related orthogonal. The lists of attributes associated with the groups of objects are called dataset. Two sets of data in this paper present trends grouping known a priori, therefore were used to give credibility to our implementations of the methods. Two other data set are studied and these were not provided with such feature, the methods of multidimensional projection are then used to define trends grouping for these two data sets.
Sistemas semidinâmicos impulsivos
(Universidade Federal do Espírito Santo, 2013-07-23) Nolasco, Victor Hugo; Demuner, Daniela Paula; Bonotto, Everaldo de Mello; Castro, Fábio Corrêa de
This work is an introduction the theory of impulsive semidynamical systems. Impulsive systems are a natural generalization of the classical theory of continuous semidynamical systems. First chapter presents the theory of continuous semidynamical systems. The second chapter is devoted to impulsive semidynamical systems theory. In this chapter, we study some properties of the impulsive systems. Interested in studying the asymptotic behavior of a impulsive semidynamical systems, in the third and fourth chapters of this work concepts like invariance, dissipativity and global attractor are presented. The study of these concepts for impulsive systems provides us with assurances that a particular process approaches of a standard in the future. Moreover, the center of Levinson is defined for compact dissipative impulsive semidynamical systems and some of it’s topological properties, for example, compactness and connectedness are studied.
Superfície mínima discreta
(Universidade Federal do Espírito Santo, 2014-02-27) Moreira, Nadia Cardoso; Carmo, Fabiano Petronetto do; Crissaff, Lhaylla dos Santos; Gonçalves Júnior, Etereldes; Araujo, Alancardek Pereira
The Minimal Surfaces problem emerged from the study of the Calculus of Variations with the meaning of being a regular surface of smallest area among those that set a specific boundary. This problem was proposed by Lagrange in 1760 and is called the Plateau Problem due to experimental studies of the physicist Joseph Antoine Ferdinand Plateau. This work proposes a numerical solution to a discrete version of the Plateau Problem from the proposed method by Pinkall and Polthier. Of the discrete viewpoint case, surfaces are simplicial complexes with certain restrictions and we use the concepts of Dirichlet Energy over applications that have triangulated surfaces as domain in order to developed a mathematically consistent algorithm to obtain a minimum surface given a boundary.
Alguns teoremas limites para sequências de variáveis aleatórias
(Universidade Federal do Espírito Santo, 2014-10-16) Waiandt, Euclésio Rangel; Valentim, Fábio Júlio da Silva; Demuner, Daniela Paula; Gonçalves, Ana Patricia Carvalho
The Central Limit Theorem and the Law of Large Numbers are among the most important results of probability theory. The first one seeks conditions under which v????-E???? ?? ???????? converges in distribution to the normal distribution with parameters 0 and 1, when ?? tends to infinity, where ???? is the sum of ?? independent random variables. At the same time, the second gives conditions such that ????-E???? ?? converges to zero, or equivalently, that ???? ?? converges to the expectation of the random variables, if they are identically distributed. In both cases, the sequences discussed are of the type ????+???? ???? , where ???? > 0 and ???? are real constants. Characterizing the possible limits of such sequences is one of the goals of this dissertation, as they not only converge to a degenerated random variable or a random variable with normal distribution, as the Law of Large Numbers and the Central Limit Theorem, respectively. Thus, we are naturally led to the study of infinitely divisible and stable distributions and their limits theorems. This becomes the main objective of this dissertation. In order to prove the theorems, the method of Lyapunov is applied as the main strategy, which analyzes the convergence of the sequence of characteristic functions related to the random variables. So we carry out a detailed approach of such functions in this research.
Soluções de vórtice das equações de Ginzburg-Landau
(Universidade Federal do Espírito Santo, 2014-12-01) Galkina, Olesya; Alves, Magno Branco; Macarini, Leonardo Magalhães; Câmara, Leonardo Meireles
In this work we study a theorem of C.H. Taubes concerning vortex solution to the Ginzburg-Landau equations, which describe superconductivity. To prove the theorem we need to show the existence of a solution to a non-linear elliptic partial di erential equation of second order. To obtain the existence of solution we study a non-linear functional de ned on an appropriate Sobolev space. We also include two auxiliary chapters concerning complex line bundles and analytical preliminaries.
Teorema de decomposição de Lévy-Itô
(Universidade Federal do Espírito Santo, 2014-12-15) Pereira Junior, Silvano Antonio Alves; Valentim, Fábio Júlio da Silva; Araujo, Alancardek Pereira; Franco, Tertuliano Franco Santos
In this work we present an introduction to the study of Levy processes following those presented in the book (TANKOV, 2003). For this we will briefly review some results of the theory of Probability needed to the study. Then we study the Poisson processes, random measures and Poisson random measures. Next we introduce the Lévy processes and infinitely divisible distributions, we present the measure of Lévy and then the main result of this work, the Decomposition Theorem of Lévy-Itô .
Pontos de Galois de curvas planas projetivas em característica positiva
(Universidade Federal do Espírito Santo, 2015-01-01) Lima, Gyslane Aparecida Romano dos Santos de; Bayer, Valmecir Antonio dos Santos; Guimarães, Andréa Gomes; Oliveira, José Gilvan de
In this dissertation we study Galois points in an algebraic non singular plane curve C P2 of degree d 4 in positive characteristic p > 2. The results of H. Yoshihara on the number of inner (respectively outer) Galois points are generalized in this case, under the assumption that d 6 1 modulo p (respectively d 6 0 modulo p). We determine all the number of inner and outer Galois points, in the case that p = d and for quartic curves in three characteristic.
Álgebra diferencial e equações diferenciais polinomiais
(Universidade Federal do Espírito Santo, 2015-01-01) Silva, Flávio da; Bayer, Valmecir Antônio dos Santos; Merlo, Leandro Colau; Alves, Magno Branco
In this dissertation we study systems of parametric differential polynomial equations. The main result is the determination of an explicit expression for an implicit such equation.
Formas modulares e o problema dos números congruentes
(Universidade Federal do Espírito Santo, 2015-10-29) Reis, Alexandre Silva dos; Oliveira, José Gilvan de; Conte, Luciane Quoos; Bayer, Valmecir Antonio dos Santos
Complex lattices, complex tori and elliptic curves are objects that although having different structures and nature, are equivalent. It is possible by means of a complex lattice to obtain a complex torus and hence, to obtain an elliptic curve; and that “path”’ can also be done in reverse. This connection will be the main object of study in this work, which will also address a careful manner some issues related to it, such as the special linear group, modular forms and modular curves. Finally, as an application of the concepts and tools studied, the congruent numbers problem is considered. This problem besides being closely related to elliptic curves, has a relationship with the famous Birch and Swinnerton-Dyer conjecture, one of the Millennium Problems.
O Apéry-algoritmo para uma singularidade plana com dois ramos
(Universidade Federal do Espírito Santo, 2015-12-18) Vieira, Stéfani Concolato; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Hernandes, Marcelo Escudeiro
Apery showed, if (??) is a irreductible algebroid plane curve and (?? (1)) is its blowup, then the semigroups ??(??) e ??(?? (1)) associated the curves (??) and (?? (1)) respectively, they can be related. The Apery set is a special generating set of a semigroup with conductor. There is a formula to get the Apery set for ??(?? (1)) from that of ??(??) and vice versa. This does not happen in general for non plane algebroid curves. Through that result of Apery, is possible to show how one can get the semigroup from the multiplicity sequence and vice versa. The main result here is a specie of generalization of results to the case of a plane algebroid curve with two branches, this is, the results of Barucci, Fröberg e D’Anna. We will show how the semigroups ??(??) and ??(?? (1)) are strictly related in the case that (??) has two branches through of Apery set, which it is not finite, but it is a finite union of its components. Furthermore, we will characterize a multiplicity tree of a plane algebroid curve with two branches of purely numerical form
Cadeias de Markov: tempo de mistura, cuttoff e redes
(Universidade Federal do Espírito Santo, 2016-02-19) Carneiro, Filipe Ribeiro; Valentim, Fábio Júlio da Silva; Romero, Freddy Rolando Hernandez; Costalonga, João Paulo
This work deals with Markov chains in discrete time and finite state space. We treat the convergence of these objects, and define the total variation distance and studied some of their properties , as well as ways of estimating the mixing time, for example, using the eigenvalues of the transition matrix. Present is the one by one relationship between reversible Markov chains and graphs, and how the network theory can help in Markov Chains context. We also define and show some results concerning the so called Cutoff phenomenon, concluding by exhibiting a counter-example due to Aldous.
NURBS e o método isogeométrico
(Universidade Federal do Espírito Santo, 2016-02-26) Rocha, Franciane Fracalossi; Carmo, Fabiano Petronetto do; Gonçalves Junior, Etereldes; Sousa, Fabrício Simeoni de
The isogeometric method proposes the use of NURBS (Non Uniform Rational Basis Spline) basis of functions for the partial differential equations solutions space, it is inspired by the finite element method. NURBS curves and surfaces are tools used in geometric computational modeling to represent objects. This dissertation deals with the NURBS basis and the NURBS curves and surfaces construction, considering mathematical concepts and emphasizing the main properties. It also presents the NURBS basis application on isogeometric method, detailing the formulation in one and two dimensions. With this, we will approach the Laplace and heat partial differential equations solution through the isogeometric method.

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