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.

O trabalho e a competência industriosa no beneficiamento de granitos : uma cartografia ergológica

O intuito inicial desta pesquisa foi acompanhar processos de trabalho à luz do referencial teórico da Ergologia e, portanto, concebendo o trabalho como relação dialética entre técnica e ação humana. O objetivo era cartografar o trabalho no processo de beneficiamento de granitos em uma organização de grande porte localizada no Espírito Santo e, após algum tempo em campo, o problema delineou- se do seguinte modo: como se constitui a competência industriosa no beneficiamento de granitos em uma organização de grande porte? A pesquisa justifica-se uma vez que, a despeito da relevância econômica, o cenário capixaba de rochas ornamentais apresenta problemas precários no que diz respeito à gestão. Para os Estudos Organizacionais, a relevância é reforçada pelo fato de aproximar desta área a abordagem ergológica e demarcar no debate sobre competência a noção de competência industriosa, ainda não explorada nesse campo de estudo. Para realização da pesquisa, foi praticada uma cartografia ergológica, a partir da articulação das pistas cartográficas com o referencial teórico-conceitual da Ergologia, sendo utilizadas como técnicas: observação participante durante 6 meses, com uma média de 3 visitas a campo por semana; 8 entrevistas semiestruturadas e em profundidade de cerca de 50 minutos cada com trabalhadores operacionais; uma entrevista com gerente de produção e outra com representante da área de Gestão de Pessoas; conversas com os demais trabalhadores, a fim de enriquecer o diário de campo; novas conversas e observações ao final da análise, para confrontação-validação com os trabalhadores. A sistematização dos procedimentos de análise pode ser assim descrita: a) leituras flutuantes com objetivo de fazer emergirem aspectos centrais relacionados às duas dimensões do trabalho, técnica e ação humana; b) leituras em profundidade com objetivo de fazer emergirem singularidades e especificidades relativas à dialética entre ambas; c) leituras em profundidade com objetivo de fazer emergirem aspectos relativos aos ingredientes da competência industriosa. A despeito da não delimitação de categorias analíticas e subcategorias, a partir da análise emergiram cinco eixos analíticos: 1) os procedimentos a serem empregados no processo de beneficiamento de granitos, englobando: as etapas do beneficiamento; as funções a serem desempenhadas e as tarefas a serem desenvolvidas; as normas regulamentadoras; os conhecimentos técnicos necessários para programação e operação de máquinas; a ordem de produção prescrita pelo setor comercial; 2) o trabalho real, diferenciado do trabalho como emprego de procedimentos pelo foco dado à ação humana no enfrentamento de situações reais, repletas de eventos e variabilidades, em todo o processo, englobando: preparo de carga; laminação; serrada; levigamento; resinagem; polimento-classificação; retoque; fechamento de pacote; ovada de contêiner; 3) diferentes modos de usos de si que, em tendência, são responsáveis pela constituição do agir em competência em cada etapa do processo, na dialética entre técnica e ação humana; 4) o modo como cada ingrediente da competência industriosa atua e se constitui, bem como sua concentração, em tendência, em cada etapa do processo, a partir dos tipos de usos de si que, também em tendência, são mais responsáveis pelo agir em competência, apresentando assim o perfil da competência industriosa no beneficiamento de granitos na empresa em análise; 5) dois possíveis fatores potencializadores dos ingredientes da competência industriosa, a saber, a transdução e os não-humanos. A partir de todo o exposto, as últimas considerações problematizam aspectos relativos ao debate sobre competências e práticas de gestão de pessoas a partir da competência compreendida da seguinte forma: mestria no ato de tirar partido do meio e de si para gerir situações de trabalho, em que a ação consiste na mobilização de recursos dificilmente perceptíveis e descritíveis, inerentes ao trabalhador, porém constituídos e manifestos por usos de si por si e pelos outros no e para o ato real de trabalho, marcadamente num nível infinitesimal, diante de situações que demandam aplicação de protocolos concomitante à gestão de variabilidades e eventos em parte inantecipáveis e inelimináveis.

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.

Competency Management Articulation for Human Resources

In recent years the approach to competences has gained great popularity due to process and organizational reengineering need. Taking opportunity on some recent work in this area dealing challenges that human resources face to develop planning training, I intend to identify several guidelines to develop a future architecture in a practical implementation. At this article is presented the concept development of competency management.

Mortality problems in Brazil and in Germany: past-present-future. Learning from each other?

This article was written by a Swiss-German historical demographer after having visited different Brazilian Universities in 1984 as a guest-professor. It aims at promoting a real dialog between developed and developing countries, commencing the discussion with the question: Can we learn from each other? An affirmative answer is given, but not in the superficial manner in which the discussion partners simply want to give each other some "good advice" or in which the one declares his country's own development to be the solely valid standard. Three points are emphasized: 1. Using infant mortality in S. Paulo from 1908 to 1983 as an example, it is shown that Brazil has at its disposal excellent, highly varied research literature that is unjustifiably unknown to us (in Europe) for the most part. Brazil by no means needs our tutoring lessons as regards the causal relationships; rather, we could learn two things from Brazil about this. For one, it becomes clear that our almost exclusively medical-biological view is inappropriate for passing a judgment on the present-day problems in Brazil and that any conclusions so derived are thus only transferable to a limited extent. For another, we need to reinterpret the history of infant mortality in our own countries up to the past few decades in a much more encompassing "Brazilian" sense. 2. A fruitful dialog can only take place if both partners frankly present their problems. For this reason, the article refers with much emprasis to our present problems in dealing with death and dying - problems arising near the end of the demographic and epidemiologic transitions: the superanuation of the population, chronic-incurable illnesses as the main causes of death, the manifold dependencies of more and more elderly and really old people at the end of a long life. Brazil seems to be catching up to us in this and will be confronted with these problems sooner or later. A far-sighted discussion already at this time seems thus to be useful. 3. The article, however, does not want to conclude with the rather depressing state of affairs of problems alternatingly superseding each other. Despite the caution which definitely has a place when prognoses are being made on the basis of extrapolations from historical findings, the foreseeable development especially of the epidemiologic transition in the direction of a rectangular survival curve does nevertheless provide good reason for being rather optimistic towards the future: first in regards to the development in our own countries, but then - assuming that the present similar tendencies of development are stuck to - also in regard to Brazil.

Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.

Positive solutions of fourth order problems with clamped beam boundary conditions

n this paper we make an exhaustive study of the fourth order linear operator u((4)) + M u coupled with the clamped beam conditions u(0) = u(1) = u'(0) = u'(1) = 0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green's function is nonnegative in [0, 1] x [0, 1]. When M < 0 we obtain the best estimate by means of the spectral theory and for M > 0 we attain the optimal value by studying the oscillation properties of the solutions of the homogeneous equation u((4)) + M u = 0. By using the method of lower and upper solutions we deduce the existence of solutions for nonlinear problems coupled with this boundary conditions. (C) 2011 Elsevier Ltd. All rights reserved.