Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Acessibilidade e longitudinalidade no pré-natal : análise de um grupo de puérperas atendidas no Hospital Universitário Cassiano Antônio de Moraes

A atenção primária visa garantir cobertura e acesso a cuidados de saúde abrangentes e aceitáveis pela população enfatizando a prevenção e a educação (STARFIELD, 2004). No Brasil a Estratégia Saúde da Família (ESF) é o modelo implantado pelo Ministério da Saúde (MS) com a finalidade de reestruturação da atenção primária e já abrange cerca de 50% da população. Segundo Starfield (2004) a atenção primária pode ser avaliada através de seus atributos essenciais: atenção de primeiro contato (utilização e acessibilidade), longitudinalidade, integralidade e coordenação de cuidados. No contexto da atenção à saúde brasileira, a mortalidade infantil é fato preocupante, principalmente a mortalidade que ocorre nos primeiros dias de vida. Este componente da mortalidade é intimamente relacionado à qualidade da atenção recebida no período gestacional. A atenção pré-natal deve incluir ações organizadas, amplas, integradas e com cobertura abrangente de promoção e prevenção da saúde, além de diagnóstico e tratamento adequado dos problemas que possam vir a ocorrer nesse período. O objetivo do presente estudo foi analisar o pré-natal de um grupo de puérperas quanto aos atributos da atenção primária acessibilidade e longitudinalidade. Para alcançar este objetivo foram realizadas 80 entrevistas com mulheres que realizaram pré-natal na atenção primária e 19 mulheres que realizaram pré-natal no Hospital Universitário Cassiano Antônio de Moraes (HUCAM). Utilizou-se parcialmente o questionário de avaliação da atenção primária PCATool. As puérperas também foram questionadas quanto à percepção da adequação do pré-natal realizado. A acessibilidade foi baixa para a maioria das entrevistadas. Nas puérperas que realizaram o pré-natal na Atenção primária a acessibilidade foi estatisticamente maior naquelas que realizaram pré-natal na ESF e naquelas que utilizaram as unidades de saúde do município de Vitória (ES). A longitudinalidade se relacionou ao tipo de unidade de saúde do pré-natal, ao número de consultas realizadas e ao índice de Ápgar no primeiro minuto. A percepção de um pré-natal adequado se relacionou com a utilização da ESF como serviço de pré-natal e à realização de seis ou mais consultas. Apesar de as puérperas do grupo que realizou o pré-natal no HUCAM perceberem o atendimento pré-natal como adequado, algumas questões revelaram fragilidades na assistência, principalmente quanto ao acesso ao serviço. A impossibilidade de receber atendimento pela equipe fora dos horários de funcionamento do ambulatório, a falta de um número de telefone no qual possam sanar dúvidas ou falar com o médico responsável pelo pré-natal, a percepção de dificuldade na marcação de consultas e a espera prolongada no dia do atendimento são pontos que devem ser melhorados nessa assistência.

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

Annotation taken, in the perspective of criminal and constitutional law, as well as in criminology, to the decision of the portuguese constitutional court, of January 13, 2011 – with respect to the problems of “consent” and “medical act”

1 – Summary of the decision taken by the Portuguese Constitutional Court, of January 13, 2011; 2 – Complete text of the decision of the Portuguese Constitutional Court, of January 13, 2011, Judge Maria João ANTUNES (Reporter), Judge Carlos Pamplona de OLIVEIRA, Judge José Borges SOEIRO, Judge Gil GALVÃO, Judge Rui Manuel Moura RAMOS (President) –in terms of the tribunalconstitucional.pt, August 1, 2011; 3 – Brief annotation to the problem of the “medical act”; 3.1 – Plus some conclusions on the brief annotation to the problem of the “medical act”; 3.2 – Brief annotation to the problem of “consent”– continuation of the previous comments; 4 – Conclusions. It must never be forgotten that “consent” does not stand as the only cause of exclusion of unlawfulness.