A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Stability of periodic travelling shallow-water waves determined by Newton`s equation

We study the existence and stability of periodic travelling-wave solutions for generalized Benjamin-Bona-Mahony and Camassa-Holm equations. To prove orbital stability, we use the abstract results of Grillakis-Shatah-Strauss and the Floquet theory for periodic eigenvalue problems.

Reflection of matter waves in potential structures

In this paper the behavior of matter waves in suddenly terminated potential structures is investigated numerically. It is shown that there is no difference between a fully quantum mechanical treatment and a semiclassical one with regards to energy redistribution. For the quantum case it is demonstrated that there can be substantial reflection at the termination. The neglect of backscattering by the semiclassical method brings about major differences in the case of low kinetic energies. A simple phenomenological model is shown to partially explain the observed backscattering using dynamics of reduced dimensionality.

Narration, Visualization and Mind : Movies in everyday life as a resource for utopian self-reflection

The paper is analyzing how people in late modern society characterized by de-traditionalization, use moving images as a cultural resource for the construction of meaningful subjective world views. As a theoretical concept with several dimensions, “sacralization of the self” (Woodhead & Heelas 2000: 344), is related to media theory. With a critical focus on ‘the self’, as a core aspect in contemporary media society Eric W. Rothenbuhler labels the individual self as one of “the sacred objects of modern culture” (Rothenbuhler 2006: 31).I want to emphasize the need for case studies in order to undertake a critical investigation about ‘the self’ and how consumption of fiction film is interconnected to spectator´s creation of self images, but also to understand how film engagement elicits self-reflection (Giddens 1991, Axelson 2008, Vaage 2009a). The paper make use of empirical data to illustrate and theoretically develop perspectives on how the audience uses fiction film in every-day life for the construction of the self, as well for the construction of more profound and long-lasting ideas of being part of a moral community (Brereton 2005, Jerslev 2006, Klinger 2008, Mikkola et al. 2007, Vaage 2009b). Some empirical findings support a conclusion that moving images creates a transitional space for the human mind, with the capacity of transporting the spectator from real life to fiction and back to real life again, helping the individual with an ongoing process of transforming the self, dealing with who you actually are, and who you want to become (Axelson 2008, Vaage 2009b).

The "reflection protocol" - a way to develop learning and independent thinking?

It is now-a-days more and more common in the academic world to use new forms of “learning-tools”. One of those is the “reflection protocol”, which usually consist of a few pages of freely written text, related to something the students have read. There seems to be a lot of different opinions about the value to use this method. Some teachers and students are enthusiastic and others are rather critical. To write a “reflection protocol” is not in the first place to do a summery, a review, not even to analyze a text. Instead it is about to write down thoughts and questions that comes up as a result of the reading. It is also about doing associations, reflections and to interpret a text and relate this to a theme of some kind. The purpose to use “reflection protocols” is, as we see it, mainly for the student to practice independent thinking from a scientific point of view, but it also gives a possibility to a better understanding of another person’s thinking. This seems to open up for a fruitful dialogue and a way to learn. We will in this paper discuss if that could be the case.