Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.

Geração de padrões de corte n-grupos para a indústria moveleira

Neste artigo são apresentadas propostas de soluções para o problema de geração de padrões de corte n-grupos para o corte da matéria-prima na indústria moveleira. Este problema NP-difícil aparece em diversos outros processos industriais que incluem o corte de painéis retangulares grandes de tamanho padrão em retângulos menores. O planejamento dos cortes é um aspecto importante do planejamento da produção nestas indústrias, pois efeitos negativos tais como o perda de matériaprima e tempo de preparo da máquina de corte podem ser minimizados, diminuindo assim os custos de produção. É estudada a eficiência de modelos lineares inteiros para resolver o problema do corte guilhotinado bidimensional propostos em [33,34], bem como o seu uso na geração de colunas para o problema de corte de estoque. São usados dados reais de uma fábrica de móveis de pequeno porte característica do pólo moveleiro de Votuporanga/SP. Os resultados obtidos indicam que as estratégias propostas geram perdas dentro dos requisitos exigidos pela fábrica. © SPM.

Educaçãdo matemática na realidade do ciberespaço - Que aspectos ontológicos e científicos se apresentam?

The question that leads this article is What is this virtual space in the on-line mathematics education process? We focus on the question of the real and virtual as issues taken as components of cyberspace. We investigate these notions in the history of philosophy, looking to Granger to find their meaning, to enable us to understand them and fit them into the sphere of Mathematics Education. This theoretical-philosophical article, then, claims that the virtuality of cyberspace is supported by the computer screen, built by the unification of the sciences (mathematics), technology and its applications. Software and the actions taken by Internet users update the capability of these programs in a variety of characteristics and possibilities such as space-time flow interconnections as well as during the mathematics education process.

Finiteness of hermitian levels of some algebras

We characterize the hermitian levels of quaternion and octonion algebras and of an 8-dimensional algebra D over the ground field F, constructed using a weak version of the Cayley-Dickson double process. It is shown that all values of the hermitian levels of quaternion algebras with the hat-involution also occur as hermitian levels of D. We give some limits to the levels of the algebra D over some ground field. © Soc. Paran. de Mat.

Stable singularities of co-rank one quasi homogeneous map germs from (ℂn+1, 0) to (ℂn, 0), n = 2, 3

In this article, we investigate the geometry of quasi homogeneous corank one finitely determined map germs from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. We give a complete description, in terms of the weights and degrees, of the invariants that are associated to all stable singularities which appear in the discriminant of such map germs. The first class of invariants which we study are the isolated singularities, called 0-stable singularities because they are the 0-dimensional singularities. First, we give a formula to compute the number of An points which appear in any stable deformation of a quasi homogeneous co-rank one map germ from (ℂn+1, 0) to (ℂn, 0) with n = 2, 3. To get such a formula, we apply the Hilbert's syzygy theorem to determine the graded free resolution given by the syzygy modules of the associated iterated Jacobian ideal. Then we show how to obtain the other 0-stable singularities, these isolated singularities are formed by multiple points and here we use the relation among them and the Fitting ideals of the discriminant. For n = 2, there exists only the germ of double points set and for n = 3 there are the triple points, named points A1,1,1 and the normal crossing between a germ of a cuspidal edge and a germ of a plane, named A2,1. For n = 3, there appear also the one-dimensional singularities, which are of two types: germs of cuspidal edges or germs of double points curves. For these singularities, we show how to compute the polar multiplicities and also the local Euler obstruction at the origin in terms of the weights and degrees. © 2013 Pushpa Publishing House.

Invariantes homológicos relativos e dualidade de Poincaré

Pós-graduação em Matemática - IBILCE

Modelos matemáticos para o problema integrado de dimensionamento de lotes e corte de estoque undimensional

Pós-graduação em Matemática - IBILCE

Estratégias para a redução de ciclos da serra no problema de corte de estoque na indústria moveleira

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Otimização vetorial e técnicas de mistura de herbicidas aplicadas ao controle de plantas daninhas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise não suave e aplicações em otimização

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Limitantes inferiores par ao problema de dimensionamento de lotes em máquinas paralelas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)