Design of digital differentiators

A digital differentiator simply involves the derivation of an input signal. This work includes the presentation of first-degree and second-degree differentiators, which are designed as both infinite-impulse-response (IIR) filters and finite-impulse-response (FIR) filters. The proposed differentiators have low-pass magnitude response characteristics, thereby rejecting noise frequencies higher than the cut-off frequency. Both steady-state frequency-domain characteristics and Time-domain analyses are given for the proposed differentiators. It is shown that the proposed differentiators perform well when compared to previously proposed filters. When considering the time-domain characteristics of the differentiators, the processing of quantized signals proved especially enlightening, in terms of the filtering effects of the proposed differentiators. The coefficients of the proposed differentiators are obtained using an optimization algorithm, while the optimization objectives include magnitude and phase response. The low-pass characteristic of the proposed differentiators is achieved by minimizing the filter variance. The low-pass differentiators designed show the steep roll-off, as well as having highly accurate magnitude response in the pass-band. While having a history of over three hundred years, the design of fractional differentiator has become a ‘hot topic’ in recent decades. One challenging problem in this area is that there are many different definitions to describe the fractional model, such as the Riemann-Liouville and Caputo definitions. Through use of a feedback structure, based on the Riemann-Liouville definition. It is shown that the performance of the fractional differentiator can be improved in both the frequency-domain and time-domain. Two applications based on the proposed differentiators are described in the thesis. Specifically, the first of these involves the application of second degree differentiators in the estimation of the frequency components of a power system. The second example concerns for an image processing, edge detection application.

Lovelock terms and BRST cohomology

Lovelock terms are polynomial scalar densities in the Riemann curvature tensor that have the remarkable property that their Euler-Lagrange derivatives contain derivatives of the metric of an order not higher than 2 (while generic polynomial scalar densities lead to Euler-Lagrange derivatives with derivatives of the metric of order 4). A characteristic feature of Lovelock terms is that their first nonvanishing term in the expansion g λμ = η λμ + h λμ of the metric around flat space is a total derivative. In this paper, we investigate generalized Lovelock terms defined as polynomial scalar densities in the Riemann curvature tensor and its covariant derivatives (of arbitrarily high but finite order) such that their first nonvanishing term in the expansion of the metric around flat space is a total derivative. This is done by reformulating the problem as a BRST cohomological one and by using cohomological tools. We determine all the generalized Lovelock terms. We find, in fact, that the class of nontrivial generalized Lovelock terms contains only the usual ones. Allowing covariant derivatives of the Riemann tensor does not lead to a new structure. Our work provides a novel algebraic understanding of the Lovelock terms in the context of BRST cohomology. © 2005 IOP Publishing Ltd.

Neurology and psychiatry: waking up to opportunities of sleep. State of the art and clinical/research priorities for the next decade.

In recent years, evidence has emerged for a bidirectional relationship between sleep and neurological and psychiatric disorders. First, sleep-wake disorders (SWDs) are very common and may be the first/main manifestation of underlying neurological and psychiatric disorders. Secondly, SWDs may represent an independent risk factor for neuropsychiatric morbidities. Thirdly, sleep-wake function (SWF) may influence the course and outcome of neurological and psychiatric disorders. This review summarizes the most important research and clinical findings in the fields of neuropsychiatric sleep and circadian research and medicine, and discusses the promise they bear for the next decade. The findings herein summarize discussions conducted in a workshop with 26 European experts in these fields, and formulate specific future priorities for clinical practice and translational research. More generally, the conclusion emerging from this workshop is the recognition of a tremendous opportunity offered by our knowledge of SWF and SWDs that has unfortunately not yet entered as an important key factor in clinical practice, particularly in Europe. Strengthening pre-graduate and postgraduate teaching, creating academic multidisciplinary sleep-wake centres and simplifying diagnostic approaches of SWDs coupled with targeted treatment strategies yield enormous clinical benefits for these diseases.

Etnomatemática e discurso performático: a construção de identidades na escola

Este trabalho objetiva apresentar as reflexões decorrentes de uma pesquisa, realizada com mais de sessenta alunos em uma escola privada da cidade de São Paulo, que procurou avaliar como concebem diferentes povos africanos e indígenas, com a hipótese de que a escola, bem como a Educação que propõe, contribua para construção de representações incompletas dessas identidades. Além disso, o discurso descritivo apresentado pelos alunos foi entendido a partir do conceito de performatividade de Butler (1993), segundo o qual alguns discursos supostamente descritivos seriam capazes de, além de descrever um indivíduo ou um grupo, criar sobre tal indivíduo ou grupo uma representação de identidade vinculada à descrição feita. Associa-se tal construção às perspectivas de Vergani (2007) sobre exclusão, observando o modo como a Educação articula discursos e ideias provenientes do senso comum no cotidiano escolar para refletir sobre suas possíveis consequências, sob a perspectiva da Etnomatemática de D’Ambrosio (1999; 2011).

Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Modelling road traffic accidents using macroscopic second-order models of traffic flow

In this paper, we introduce a macroscopic model for road traffic accidents along highway sections. We discuss the motivation and the derivation of such a model, and we present its mathematical properties. The results are presented by means of examples where a section of a crowded one-way highway contains in the middle a cluster of drivers whose dynamics are prone to road traffic accidents. We discuss the coupling conditions and present some existence results of weak solutions to the associated Riemann Problems. Furthermore, we illustrate some features of the proposed model through some numerical simulations. © The authors 2012.

"A aprendizagem de indivíduos não-alfabetizados pertencentes a comunidades com elevados índices de analfabetismo"

Assumindo como objectivo central, identificar e caracterizar eventuais estilos de aprendizagem, existentes em comunidades com elevadas taxas de analfabetismo, a presente investigação centrou-se no estudo dos processos de aprendizagem de indivíduos analfabetos de seis localidades do concelho de Alandroal e compreendeu a realização de um estudo de caso, assente numa metodologia bidimensional. A análise descritiva e inferencial corroborou a hipótese de que foi o facto de os indivíduos se localizarem em comunidades, com determinadas características geográficas, culturais, económicas e sociais, que conduziu ao desenvolvimento de determinados saberes/maneiras de fazer, que se traduziram em eventuais estilos locais de aprendizagem. Sustenta-se que, pela sua localização geográfica e pelas dinâmicas comunitárias existentes, os contornos/singularidades do processo de aprendizagem dos inquiridos das localidades de Ferreira de Capelins e, essencialmente, de Juromenha, apresentaram-se com especial relevância.