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.

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.

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.

Are severe occlusal problems more frequent in permanent than deciduous dentition?

OBJECTIVE: To determine the prevalence and severity of occlusal problems in populations at the ages of deciduous and permanent dentition and to carry out a meta-analysis to estimate the weighted odds ratio for occlusal problems comparing both groups. METHODS: Data of a probabilistic sample (n=985) of schoolchildren aged 5 and 12 from an epidemiological study in the municipality of São Paulo, Brazil, were analyzed using univariate logistic regression (MLR). Results of cross-sectional study data published in the last 70 years were examined in the meta-analysis. RESULTS: The prevalence of occlusal problems increased from 49.0% (95% CI =47.4%-50.6%) in the deciduous dentition to 71.3% (95% CI =70.3%-72.3%) in the permanent dentition (p<0.001). Dentition was the only variable significantly associated to the severity of malocclusion (OR=1.87; 95% CI =1.43-2.45; p<0.001). The variables sex, type of school and ethnic group were not significant. The meta-analysis showed that a weighted OR of 1.95 (1.91; 1.98) when compared the second dentition period with deciduous and mixed dentition. CONCLUSIONS: In planning oral health services, some activities are indicated to reduce the proportion of moderate/severe malocclusion to levels that are socially more acceptable and economically sustainable.