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 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

Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions

Positivity and variational methods in second and fourth order boundary value problems

Tese de doutoramento, Matemática (Análise Matemática), Universidade de Lisboa, Faculdade de Ciências, 2010We study the existence of solutions for a nonlocal singular second order ordinary differential equation. We obtain results through Krasnoselskii’s fixed point Theorem and using some properties of the eigenvalues of the underlying singular linear problem and, on a different approach, through the monotone method associated with well-ordered lower and upper solutions. We deal with second and fourth order problems in infinite intervals, where we prove the existence of an homoclinic or an heteroclinic solution. For the second order we consider both superlinear and bounded nonlinearities, and prove existence results through variational methods. A non-variational approach was made for a second order problem with a dissipative term and a p-laplacian problem was also adressed. Simpler fourth order bvp’s were also tackled from a variational point of view. We also analyse fourth order boundary value problems related to beam deflection theory, generalizing some well known results for the second order. We analysed two types of problems: the case where the correspondent fourth order operator can be decomposed in two positive second order operators and the case where that cannot be done. The results are obtained through topological arguments in association with lower and upper solutions.Centro de Matemática e Aplicações Fundamentais (CMAF); PhD fellowship by Fundação para a Ciência e a Tecnologia (FCT)- ; FCT project POCI/MAT/57258/2004; ISE

O impacto das variáveis cognitivas no rendimento escolar

Nesta comunicação propomo-nos: (i) discutir o conceito de inteligência no âmbito da psicometria; (ii) analisar em que medida os desempenhos cognitivo e escolar se relacionam; (iii) analisar a importância das variáveis cognitivas na predição do rendimento escolar; e (iv) discutir que aptidões cognitivas específicas (conteúdos) assumem maior relevo no rendimento escolar. Este estudo considerou uma amostra representativa de estudantes portugueses entre o 5º e o 12º ano de escolaridade (n= 4899). Os estudantes realizaram os subtestes que integram a Bateria de Provas de Raciocínio (BPR) na versão apropriada ao seu nível escolar. Juntos dos serviços escolares, obtivemos as classificações escolares destes alunos nas disciplinas de Português e Matemática. Os coeficientes de correlação entre o desempenho cognitivo e o rendimento escolar sugerem uma maior associação entre as habilidades cognitivas e o rendimento escolar nas disciplinas cujo conteúdo curricular mais se aproxima dos conteúdos dos itens das provas. Para além disso, observa-se uma progressiva diminuição nos coeficientes de correlação à medida que se avança na escolaridade, sugerindo uma menor importância das variáveis cognitivas para o rendimento escolar nos níveis de escolaridade mais elevados. Por último, os resultados sugerem que mais do que os processos cognitivos parece ser importante o conteúdo das tarefas, à medida que se avança na escolaridade. Neste sentido, se explica as correlações mais elevadas envolvendo as provas de raciocínio verbal e de raciocínio numérico ao longo dos vários anos de escolaridade.Fundação para a Ciência e a Tecnologia (FCT

Automatic Completion of Data Gaps Applied to a System of Water Pumps

We consider a time series with real data from a water lift station, equipped with three water pumps which are activated and deactivated depending on certain starting and halting thresholds. Given the water level and the number of active pumps, both read every 5 min, we aim to infer when each pump was activated or deactivated. To do so, we build an algorithm that sets a hierarchy of criteria based on the past and future of a given interval to identify which thresholds have been crossed during that interval. We then fill the gaps between the 5 min time steps, modeling the water level continuously with a piecewise linear function. This filling takes into account not only every water level reading and every previously identified change of status, but also the fact that activation and deactivation of a pump has no immediate effect on water level. This allows for the fulfillment of the ultimate objective of the problem in its real context, which is to provide the water management company an estimate of how long each pump has been working. Additionally, our estimates correct the errors contained in the time series regarding the number of active pumps

Functions with average and bounded motions of a forced discontinuous oscillator

In this paper we prove the existence of bounded solutions in the real line for the equation u+ sign( u) = p( t), where p is a function with average. Some useful density results for the space of functions with zero average are also obtained.info:eu-repo/semantics/publishedVersio

The modelling of urban running races

Abstract In this paper, we model mass running urban races, taking into consideration several conditioning factors. The main goal is to find ideal configurations of the start of the race, splitting it into several waves, reducing the density of athletes and the overall time lost, when comparing the normal race results with a race without density constraints. This model takes into account distinct realistic runners’ profiles, changes in slope and width on the race course and its influence on the running pace. Moreover, density levels, dynamics of the start of the race and time between the departure of waves are also considered

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIURWe study positive solutions y(u) for the first order differential equation y' = q(cy(1/p) - f(u)) where c > 0 is a parameter, p > 1 and q > 1 are conjugate numbers and f is a continuous function in [0, 1] such that f(0) = 0 = f(1). We shall be particularly concerned with positive solutions y(u) such that y(0) = 0 = y(1). Our motivation lies in the fact that this problem provides a model for the existence of travelling wave solutions for analogues of the FKPP equation in one space dimension, where diffusion is represented by the p-Laplacian operator. We obtain a theory of admissible velocities and some other features that generalize classical and recent results, established for p = 2