IME - Instituto de Matemática e Estatística
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O IME - Instituto de Matemática e Estatística, da Universidade Federal de Goiás, oferece Graduação em: Matemática; e, Estatística; Além de Especialização (Lato Sensu) em: Matemática; e, Educação Matemática.
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Item Structurall stability of parabolic points and periodic asymptotic lines(1997) Garcia, Ronaldo Alves; Tello, Jorge Manuel SotomayorItem A proximal regularization of the steepest descent method in riemannian manifolds(1999) Cruz Neto, João Xavier da; Ferreira, Orizon Pereira; Lucambio Pérez, Luis RománItem On Ribaucour transformations for hypersurfaces(1999) Corro, Armando Mauro Vasquez; Ferreira, Walterson Pereira; Tenenblat, KetiItem Lines of principal curvature around umbilics and whitney umbrellas(2000) Garcia, Ronaldo Alves; Gutierrez Vidalon, Carlos Teobaldo; Tello, Jorge Manuel SotomayorIn this paper is studied the configuration of lines of curvature near a Whitney 3 umbrella which is the unique stable singularity for maps of surfaces into R . The pattern of such configuration is established and characterized in terms of the 3-jet of the map. The result is used to establish an expression for the Euler-Poincare characteristic in terms of the number of umbilics and umbrellas.Item O V postulado de Euclides(2000) Pina, Romildo da SilvaApresentamos neste trabalho algumas versões equivalentes ao quinto postulado de Euclides, que surgiram ao longo dos anos, na tentativa de provar que o mesmo poderia ser obtido a partir dos outros quatro primeiros postulados. O quinto postulado desempenhou um papel fundamental para o desenvolvimento da geometria , pois foi questionando a sua veracidade que se descobriram outros modelos de geometria , diferentes da Euclidiana, o que hoje chamamos de geometria não - Euclidiana.Item Monotone point-to-set vector field(2000) Cruz Neto, João Xavier da; Ferreira, Orizon Pereira; Lucambio Pérez, Luis RománWe introduce the concept of monotone point-to-set field in Riemannian man- ifold and give a characterization, that make clear in this definition the occult geometric meaning. We will show that the sub-differential operator of a Rieman- nian convex function is a monotone point-to-set field. The concept of directional derivative, which appears already in other publications, plays an important role in the proof of the result above. We study some of its properties, in particular, we obtain the chain rule, which is fundamental in our work. Some topological consequences of the existence of strictly monotone point-to-set fields are pre- sented.Item Structurally stable configurations of lines of mean curvature and umbilc points on surfaces immersed in R3(2001) Garcia, Ronaldo Alves; Tello, Jorge Manuel SotomayorItem Oxidation fronts in a simplified model for two-phase flow in porous media(2002) Mota, Jesus Carlos da; Souza, Aparecido J. de; Garcia, Ronaldo Alves; Teixeira, Pedro W.Item A simplified oxidation model for two-phase flow in porous media(2002) Mota, Jesus Carlos da; Souza, Aparecido Jesuino de; Marchesin, Dan; Pedro Wilson, TeixeiraItem Geometric mean curvature lines on surfaces immersed in R3(2002) Garcia, Ronaldo Alves; Tello, Jorge Manuel SotomayorHere are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature 1C is positive) of an oriented surface immersed in R3. The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given by K which is the geometric mean curvature of the principal curvatures k1, k2 of the immersion. The singularities of the foliations are the umbilic points and parabolic curves, where k1 = k2 and 1C = 0, respectively. Here are determined the structurally stable patterns of geometric mean curvature lines near the umbilic points, parabolic curves and geometric mean curvature cycles, the periodic leaves of the foliations. The generi-city of these patterns is established. This provides the three essential local ingredients to establish sufficient conditions, likely to be also necessary, for Geometric Mean Curvature Structural Stability. This study, outlined at the end of the paper, is a natural analog and complement for the Arithmetic Mean Curvature and Asymptotic Structural Stability of immersed surfaces studied previously by the authors.Item Umbilic and tangential singularities on configurations of principal curvature lines(2002) Garcia, Ronaldo Alves; Tello, Jorge Manuel SotomayorNeste trabalho são estudadas as linhas de curvaturas principais de uma superfície com bordo e da superfície regular, sem bordo, obtida pelo processo de engrossamento e regularização. É analisada a relação entre as tangências quadráticas das folheações principais com o bordo e os pontos umbílicos Darbouxianos, da superfície sem bordo, que bifurcam dos referidos pontos de tangências.Item A simplified oxidation model for two-phase flow in porous media(2002) Mota, Jesus Carlos da; Sousa, Alberto Jose de; Marchesin, Dan; Reuther, Paula Werneck TeixeiraItem Dinâmica de populações via inclusões diferenciais fuzzy(2002) Chalco Cano, Yurilev; Bassanezi, Rodney Carlos; Rojas Medar, Marko Antonio; Mizukoshi, Marina TuyakoItem Estabilidade local de sistemas dinâmicos fuzzy(2003) Mizukoshi, Marina Tuyako; Barros, Laecio Carvalho de; Bassanezi, Rodney CarlosItem Ricci tensors with rotational symmetry on lR n 1(2003) Garcia, Ronaldo Alves; Pina, Romildo da SilvaItem Projeto ótimo de manipuladores 3R considerando seu volume de trabalho(2003) Bergamaschi, Paulo Roberto; Gonzalez, Fernando R.; Nogueira, Antônio Carlos; Saramago, Sezimária de Fátima PereiraItem A metric property of umbilic points(2003) Garcia, Ronaldo Alves; Tello, Jorge Manuel SotomayorIn the space of cubic forms of surfaces, regarded as a G-space and endowed with a natural invariant metric, the ratio of umbilic points with a negative index to those with a positive index is evaluated in terms of the asymmetry of the metric, defined here. This work contains also a section with references pertinent to umbilic points and one with a discussion of a connection of the above defined ratio with that reported in 1977 by Berry and Hannay in the domain of Statistical Physics.Item An optimal design of 3R manipulators taking into account regular workspace boundary(2004) Bergamaschi, Paulo Roberto; Saramago, Sezimária de Fátima Pereira; Nogueira, Antônio CarlosItem Generalized solutions to the KdV hierarchy in 2-dimension(2004) Melo, Maurilio MárcioItem Aplicação de algoritmos genéticos para o projeto ótimo de manipuladores 3R considerado envoltórias regulares(2004) Gonzales, Fernando R.; Saramago, Sezimária de Fátima Pereira; Bergamaschi, Paulo Roberto