Mestrado em Matemática (IME)
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Item Tempo de sobrevivência em um modelo estocástico para evolução de espécies(Universidade Federal de Goiás, 2014-02-27) Aguiar Júnior, Dióscoros Brito; Vargas Júnior, Valdivino; http://lattes.cnpq.br/1795859800919467; Vargas Júnior, Valdivino; Gava, Renato Jacob; Silva, Tatiane Ferreira do Nascimento Melo daIn this work ,we will consider two stochastic models for evolution os species. First, births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type is killed is the one with smallest fitness. We show that there is a sharp phasetransitionwhentheprobabilityislargerthanthedeathprobability.Thesetofspecies with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the crital disappear after a finite (random) time. The second model, we consider a stochastic model for species evolution. A new species is born at rateλ and a species dies at rate µ. A random number, sampled from a given distribution F, is associated with each new species and assumed as its fitness, at the time of birth. Likewise the first model, every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time if a species with a given fitness f. We show that the survival time distribution depends crucially on whetherffc where fc is a critical fitness that is computed explicit.Item 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/5680428710939826In 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.Item 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/8910130626123426This 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.Item 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/9174074436425246In this work....Item Hipersuperfícies conformemente planas em R4(Universidade Federal de Goiás, 2009-03-13) Moreira, Lucas; Pina, Romildo da Silva; http://lattes.cnpq.br/2675728978857991language="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.