Matemática

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Programa de Pós-Graduação em Matemática

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URL do programa: http://www.matematica.ufes.br/pos-graduacao/PPGMAT

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Agora exibindo 1 - 20 de 56

Propriedades características das hiperesferas euclidianas
(Universidade Federal do Espírito Santo, 2008-06-06) Lozório, Weslley Marinho; Malacarne, Jose Miguel; Guimarães Filho, Florêncio Ferreira; Lima, Levi Lopes de
The study of hypersurfaces of Euclidean spaces which have a constant elementary symmetric function is a classical topic in Differential Geometry. In this topic the more simple geometric problem is to characterize the compact hypersurfaces and the prototypical result was obtained by H. Liebmann in 1899: the round spheres are the only compact surfaces in the three dimensional Euclidean space that have constant Gaussian curvature. In 1956 A.D. Alexandrov obtained a remarkable characterization of the Euclidean round hyperspheres: they are the only compact hypersurfaces of m-dimensional Euclidean space (m ¸ 3) that have constant mean curvature. The ideas used by Alexandrov became well-know as Alexandrovs reflection method and were used in several other problems. In 1977, R.C. Reilly presented a new proof of Alexandrovs theorem, the Reillys method, which also become fundamental tool in this topic. In fact, A. Ros in 1987, using the Reillys method, obtained a new extension of the Alexandrovs theorem characterizing the round hyperspheres as the only compact hypersurfaces of the m-dimensional Euclidean space that have a constant elementary symmetric function of the principal curvatures. This result implies, in particular, the Liebmanns theorem. In 1988, N. Korevaar presented a new proof of the Ross theorem, using the Alexandrov reflection method. The main goal of this Master thesis is to present proofs by Alexandrov, Reilly, Ros, and Korevaar of some theorems that characterizes the Euclidean round hyperspheres
Curvas nodais maximais via curvas de Fermat
(Universidade Federal do Espírito Santo, 2009-01-01) Profilo, Stanley; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Fantin, Silas
We study the rational projective nodal plane curves in the projective plane P2(C) by using the Fermat curve Fn : Xn+Y n+Zn = 0. We deal with the theory of dual curves in the projective plane and a special type of group action of Zn x Zn on the Fermat curve and its dual to construct, for any positive integer n maior ou igual a 3, a rational nodal plane curve of degree equal to n -1. A rational nodal plane curve is a projective rational plane curve (that is, a genus zero curve) that presents as singularities only nodal points, that is, singularities of multiplicity two with distinct tangents. The basic reference is the paper "On Fermat Curves and Maximal Nodal Curves"by Matsuo OKA published in Michigan Math. Journal, v.53. in 2005.
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
Existência de solução para uma equação de Schrodinger quasilinear
(Universidade Federal do Espírito Santo, 2010-11-26) Ribeiro, Maico Felipe Silva; Xavier, Magda Soares; Silva, Elves Alves de Barros e; Furtado, Marcelo Fernandes
In this paper we study the existence of solution of a quasilinear stationary Schrodinger equation in the autonomous and nonautonomous cases. These results were demonstrated by Colin and Jeanjean. Applying a change of variables, the quasilinear equation is reduced to a semilinear one, whose associated functional is well defined in the usual Sobolev space H1(RN).The existence of solution for the autonomous case is obtained as a consequence of a result due to Berestycki and Lions. In the nonautonomous case, we show that the associated functional satisfies the mountain pass geometric hypotheses. Using a version of Mountain Pass Theorem without the compactness condition, we obtain a Cerami sequence in the minimax level weakly convergent to a solution v0. In the proof that v0 is nontrivial, the main tool is a concentration-compactness result due to Lions
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
Pontos singulares e pontos de Galois de quárticas planas singulares
(Universidade Federal do Espírito Santo, 2011-08-04) Buosi, Carolina Cruz Mendes; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Abdon, Miriam
In this work we study singular plane projective curves of degree four and its Galois points. For this, we fix k, an algebraically closed field of characteristic zero, as the ground field of our discussion. To understand the structure of the function fields of these curves, we use projections: we choose a point P ? P 2 and we project a curve C ? P 2 to a line from P, that is the center of projection. This projection induces an extension field k(C) | k(P 1 ), where k(C) is the rational function field of C. We want to know if there exist intermediate fields in this extension. We analyse two situations: P belongs to the curve C and P doesn’t belong to C
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.
Semigrupos e o teorema de Gorenstein para singularidades de curvas algébricas planas
(Universidade Federal do Espírito Santo, 2013-11-08) Lannes, Andréa Maria Silva; Bayer, Valmecir Antonio dos Santos; Oliveira, José Gilvan de; Salomão, Rodrigo
The main goal of this dissertation is to present the Gorenstein Theorem for plane curve singularities. We consider two cases: firstly the local case when the singularity has only one branch and after the semilocal case when the singularity has several branches. In the local case the local equation is given by an irreducible series of k[[X, Y ]] and in the semilocal case it is given by a finite product of irreducible series wich are not pairwise associated. A local equation given by such a power series f is called an algebroid plane curve. The following are objects associated to an algebroid plane curve: The local ring O = O(f), its integral closure O˜ of O in its full ring of fractions and the conductor ideal of O˜ in O. We may say that these data encode all the algebraic / geometric informations of the algebroid plane curve (f). Gorenstein Theorem, that was proved in [Go] by D. Gorenstein states that, in both cases (local or semi-local), the codimension (as k-vector spaces) of the conductor ideal in the ring O is equal to the codimension of the ring O in the ring O˜. This provides us with a certain symmetry which is reflected in the semigroup associated to the algebroid plane curve (f). Thus, we also study the symmetry of semigroups of the natural numbers and relate them to the symmetry of the ring O in the local case.
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.
Uma breve análise do movimento browniano
(Universidade Federal do Espírito Santo, 2014-12-12) Duque, Oscar Mario Londoño; Valentim, Fábio Júlio da Silva; Cansino, Hugo Alexander de La Cruz; Cortez, Milton Edwin Cobo
This text has as main objective to study an introductory way Brownian motion. We intend to present some properties of their trajectories, in particular, addressing questions of continuity, differentiability and recurrence. Furthermore, Brownian motion identified as an example of different classes of stochastic processes, for example, as a Markov process, Gaussian, Lévy and martingale. Finalized with construction of some processes from Brownian motion.
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 .

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