Lobatto deferred correction for stiff two-point boundary value problems

An iterated deferred correction algorithm based on Lobatto Runge-Kutta formulae is developed for the efficient numerical solution of nonlinear stiff two-point boundary value problems. An analysis of the stability properties of general deferred correction schemes which are based on implicit Runge-Kutta methods is given and results which are analogous to those obtained for initial value problems are derived. A revised definition of symmetry is presented and this ensures that each deferred correction produces an optimal increase in order. Finally, some numerical results are given to demonstrate the superior performance of Lobatto formulae compared with mono-implicit formulae on stiff two-point boundary value problems. (C) 1998 Elsevier B.V. Ltd. All rights reserved.

ON THE MINIMUM ABSOLUTE VALUE of THE DISCRIMINANT of ABELIAN FIELDS of DEGREE p(2)

Let p be a prime number. A formula for the minimum absolute value of the discriminant of all Abelian extensions of Q of degree p(2) is given in terms of p.

Tunneling time through a barrier using the local value of a time operator

A time for a quantum particle to traverse a barrier is obtained for stationary states by setting the local value of a time operator equal to a constant. This time operator, called the tempus operator because it is distinct from the time of evolution, is defined as the operator canonically conjugate to the energy operator. The local value of the tempus operator gives a complex time for a particle to traverse a barrier. The method is applied to a particle with a semiclassical wave function, which gives, in the classical limit, the correct classical traversal time. It is also applied to a quantum particle tunneling through a rectangular barrier. The resulting complex tunneling time is compared with complex tunneling times from other methods.

Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.

Population dynamics and net primary production of the aquatic macrophite Nymphaea rudgeana C. F. Mey in a lotic environment of the Itanhaém River basin (SP, Brazil)

Neste trabalho, foi estudada a dinâmica populacional e estimada a produção primária líquida da macrófita aquática Nymphaea rudgeana em um braço do rio Itanhaém (Estado de São Paulo, Brasil). Esta espécie apresenta uma ampla variação anual de biomassa, em função da estação do ano, no local estudado. A partir do mês de novembro (13,1 g PS/m²), pode ser observado um aumento gradual da biomassa, atingindo o máximo em fevereiro (163,1 g PS/m²). Posteriormente, a biomassa diminui, mantendo-se em níveis baixos até um novo período de crescimento. A diminuição de biomassa está associada ao desenvolvimento de macrófitas flutuantes (Pistia stratiotes e Salvinia molesta) e, subseqüentemente, às condições ambientais desfavoráveis (valores de salinidade elevados) ao seu desenvolvimento. A produção primária líquida de N. rudgeana foi obtida a partir dos dados de biomassa e seu valor é estimado entre 3,02 e 3,82 t/ha/ano.

Aplicação do earned value em projetos complexos - um estudo de caso na EMBRAER

O gerenciamento do Earned Value vem obtendo aceitação crescente nas empresas e entre profissionais tais como gerentes de projetos e funcionais, devido à sua efetividade no controle dos resultados do projeto. Earned Value é definido como uma ferramenta de controle que permite avaliar simultaneamente de maneira quantitativa como se encontram os custos e prazos em uma data de controle, permitindo também prever a data de término e o valor gasto (VARGAS, 2005). Este artigo avalia a aplicabilidade do earned value como ferramenta de controle de projetos aeronáuticos na EMBRAER. Contribui também para a aplicação do earned value no controle de projetos complexos. Utilizam-se como técnicas de coleta de dados: entrevistas, observações e análise documental. Conclui-se que o earned value é utilizado apenas nos projetos da área de aviação de defesa, por ser uma exigência contratual. O uso do earned value nas áreas de programas executivos e comerciais restringe-se às fases de definição conjunta, projeto detalhado e certificação, pois o escopo do projeto é bem definido, o cronograma é detalhado e os custos são previstos e obtidos com maior acuidade. Nas demais fases de desenvolvimento do produto, o uso do earned value é restrito, devido principalmente às constantes alterações de escopo do produto e do projeto.

Iterated deferred correction for linear two-point boundary value problems

An analysis of iterated deferred correction based on various classes of implicit Runge-Kutta formulae is given. Out of different possibilities considered, it is shown that those based purely on Lobatto formulae have the best stability. The enhanced stability of Lobatto schemes is very important for the efficient integration of excessively stiff boundary value problems and this is demonstrated by means of some numerical results.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

The influence of zero-value subtraction on the performance of two laser fluorescence devices for detecting occlusal caries in

Background. The aim of this study was to evaluate the influence of zero-value subtraction on the performance of two laser fluorescence (LF) devices developed to 'detect occlusal caries.Methods. The authors selected 119 permanent molars. Two examiners assessed three areas (cuspal, middle and cervical) of both mesial and distal portions of the buccal surface and one occlusal site using an LF device and an LF pen. For each tooth, the authors subtracted the value measured in the cuspal, middle and cervical areas in the buccal surface from the value measured in the respective occlusal site.Results. The authors observed differences among the readings for both devices in the cuspal, middle and cervical areas in the buccal surface as well as differences for both devices with and without the zero-value subtraction in the occlusal surface. When the authors did not perform the zero-value subtraction, they found statistically significant differences for sensitivity and accuracy far the LF device. When this was done with the LF pen, specificity increased and sensitivity decreased significantly.Conclusions. For the LF device, the zero-value subtraction decreased the sensitivity. For this reason, the authors concluded that clinicians can obtain measures with the LF device effectively without using zero-value subtraction. For the LF pen, however, the absence of the zero-value subtraction changed both the Sensitivity and specificity, and so the authors concluded that clinicians should not eliminate this step from the procedure.Clinical Implications. When using the LF device, clinicians might not need to perform the zero-value subtraction; however, for the LF pen, clinicians should do so.