TEDE Communidade:http://repositorio.bc.ufg.br/tede/handle/tde/2882020-01-25T08:08:17Z2020-01-25T08:08:17ZOn the crossing limit cycles for piecewise linear differential systems on the planeRuiz, Jeidy Johana Jimenezhttp://repositorio.bc.ufg.br/tede/handle/tede/102602019-12-30T15:33:18Z2019-12-05T00:00:00ZTítulo: On the crossing limit cycles for piecewise linear differential systems on the plane
Autor: Ruiz, Jeidy Johana Jimenez
Primeiro orientador: Medrado, João Carlos da Rocha
Abstract: In this work we analyze the version of Hilbert’s 16th problem for piecewise linear
differential systems in the plane for a particular case, more precisely in Chapter 2
we study on the maximum numbers of crossing limit cycles that can have the planar
piecewise linear differential systems separated by a straight line S and formed by two
linear differential systems X−;X+ which singularities are symmetrical with respect to the
straight line of discontinuity S and they are on the straight line y = sx, s e R. In [24, 27]
it was proved that piecewise linear differential centers separated by a straight line have no
crossing limit cycles nevertheless in [20, 28] were studied planar discontinuous piecewise
linear differential centers where the curve of discontinuity is not a straight line, and it
was shown that the number of crossing limit cycles in these systems is non-zero. For this
reason it is interesting to study the role which plays the shape of the discontinuity curve in
the number of crossing limit cycles that planar discontinuous piecewise linear differential
centers can have. In Chapter 3 we study on the upper bounds for the maximum number
of crossing limit cycles with either two or four points on the discontinuity curve S, when
S is any conic. And finally in Chapter 4 we study on the numbers of crossing limit cycles
with four points on the discontinuity curve S, when S is a reducible cubic curve formed
either by a circle and a straight line, or by a parabola and a straight line.
Instituição: Universidade Federal de Goiás
Tipo do documento: Tese2019-12-05T00:00:00ZCondições de finitude para o produto tensorial não abeliano de gruposAlves, Thulio de Oliveirahttp://repositorio.bc.ufg.br/tede/handle/tede/100282019-09-19T13:49:29Z2019-08-08T00:00:00ZTítulo: Condições de finitude para o produto tensorial não abeliano de grupos
Autor: Alves, Thulio de Oliveira
Primeiro orientador: Oliveira, Ricardo Nunes de
Abstract: In this work we are interested in describing the conditions on which the non-abelian tensor product of groups is finite, thus we show that if G and H are groups that act compatibly on each other, then the tensor product of G and H is finite, if and only if the set of all tensor is finite. As an immediate consequence of this result, if G and H are finite, then the tensor product of G and H is finite. Furthermore we describe finite conditions for specific subgroups of the tensor product when G and H are FC-groups and also when H=G and G is a BFC-group.
Instituição: Universidade Federal de Goiás
Tipo do documento: Dissertação2019-08-08T00:00:00ZSoluções clássicas para um problema de combustão em meios porosos com n camadasBatista, Marcos Robertohttp://repositorio.bc.ufg.br/tede/handle/tede/100012019-09-10T12:26:33Z2019-08-16T00:00:00ZTítulo: Soluções clássicas para um problema de combustão em meios porosos com n camadas
Autor: Batista, Marcos Roberto
Primeiro orientador: Mota, Jesus Carlos da
Abstract: In this work, we study the classical solutions for a parabolic system of reaction-diffusion-convection equations, coupled to a system of ordinary differential equations, with boundary and initial conditions in a bounded domain. The coupled system models the propagation of a combustion front through a porous medium with n layers, where the dependent variables are the temperatures and the fuel concentrations in each layer.
Problems for parabolic equations systems coupled with Ordinary Differential Equations (ODEs) system, where the coupling occurs in both the reaction functions and the associated differential operator coefficients, are little known in the literature. In classical theory in general, the coupling appears only in the reaction functions.
Initially, using the Monotone Iterative Method, we prove the existence and uniqueness of a global solution in time for the particular case where the fuel concentrations in each layer are known functions. Next, we show the existence of the local solution in time for the complete problem when the concentrations are unknown functions. The proof is obtained by defining an operator in the Continuous Hölder function set and showing that it has a fixed point that is a local solution to the problem. This solution can be extended to a global solution in time for the problem, provided that the spatial derivatives of the temperature in each layer are bounded functions.
Instituição: Universidade Federal de Goiás
Tipo do documento: Tese2019-08-16T00:00:00ZQuadratic programming on the positive orthant with a quasiconvex objective functionZuñiga, Ruby Yohana Cuerohttp://repositorio.bc.ufg.br/tede/handle/tede/99342019-08-16T11:50:41Z2019-07-31T00:00:00ZTítulo: Quadratic programming on the positive orthant with a quasiconvex objective function
Autor: Zuñiga, Ruby Yohana Cuero
Primeiro orientador: Ferreira, Orizon Pereira
Abstract: In this work, we will study a class of real symmetric matrices that we will call subdefinite, these matrices include the positive semidefinites. For our purpose we will focus on the merely positive subdefinite matrices, that is, those matrices that are positive subdefinite but are not positive semidefinite. We will discuss the quadratic functions on Rn + and show that these functions are quasiconvex not convex, when their matrix representation is given by a merely positive subdefinite matrix. In addition, we will present a result of great importance in quadratic programming given that it allows to reduce the quasiconvexity of these nonconvex quadratic functions to the pseudoconvexity in the semipositive orthant. Finally, we will study the conditional gradient method to solve the quadratic programming problem, where the objective function is of this type.
Instituição: Universidade Federal de Goiás
Tipo do documento: Dissertação2019-07-31T00:00:00Z