Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

On international cost-sharing of pharmaceutical R&D

Ramsey pricing has been proposed in the pharmaceutical industry as a principle to price discriminate among markets while allowing to recover the (fixed) R&D cost. However, such analyses neglect the presence of insurance or the fund raising costs for most of drug reimbursement. By incorporating these new elements, we aim at providing some building blocks towards an economic theory incorporating Ramsey pricing and insurance coverage. We show how coinsurance affects the optimal prices to pay for the R&D investment. We also show that under certain conditions, there is no strategic incentive by governments to set coinsurance rates in order to shift the financial burden of R&D. This will have important implications to the application of Ramsey pricing principles to pharmaceutical products across countries.

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Digital-domain self-calibration technique for video-rate pipeline A/D converters using Gaussian white noise

Electronics Letters Vol.38, nº 19

Problèmes posés par la population sporo-pollinique d'un niveau à plantes de la série de Buarcos (Portugal)

L'analyse pollinique des sédiments argileux, riches en macrorestes de végétaux, du "Belasien» (Crétacé inférieur) de Buarcos a permis reconnaître la présence d'une riche microflore. On a, nottament, reconnu la présence de: Concavisporites punctatus, Auritulinosporites complexis, Chomotriletes sp., Trilobosporites cf. bernissartensis, Apiculatisporites vulgaris, Cicatricosisporites sp. 1, Cicatricosisporites sp. 2. Cicatricosisporites sp. 3, Cicatricosisporites sp. 4, Cicatricosisporites sp. 5, Cicatricosisporites sp. 6. Costatoperforosporites fistulosus, Ceratosporites sp. l, C. cf. equalis, Ischyosporites teixeirae n. sp., Liburnisporites sp. AequitriraditeS cf. spinulosus, Cedripites lusitanicus, Clavatipollenites cf. hughesi. Après discution de la stratigraphie des diffèrentes espèces on sugère une âge barremo-aptien pour cette association malgré la présence de l'ensemble Apiculalisporites vulgaris-Classopollls major plutôt d'âge Aptien.

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Using fractional derivatives for the joint ontrol of hexapod robots

This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

O Cristianismo no Japão e o Episcopado de D. Luís Cerqueira

Dissertação de doutoramento em História dos Descobrimentos e da Expansão Portuguesa

Veículo ZEV (sem emissões)

A crescente dependência energética do Petr óleo e o impacto ambiental daí resultante, tanto como as excessivas autonomias e desempenho dos veículos perante as nossas necessidades, leva a que Portugal, a Europa, o Mundo, necessitem de apostar em inovar e alterar costumes, de forma a que o nosso planeta se mantenha sustentável e de maneira a aumentar a qualidade de vida de todos nós. As emissões proveniente dos veículos representam uma excessiva parcela na poluição atmosférica causada pela queima dos derivados do petróleo. Uma das soluções mais viáveis para a redução de emissões, passaria pela implementação de leis que fomentassem a compra dos veículos ZEV. Este trabalho pretende provar a inviabilidade do uso contínuo de combustíveis fósseis, destaca as principais características dos veículos eléctricos e os benefícios destes quando comparados com os veículos convencionais, descreve as características dos veículos eléctricos comercializados em Portugal e apresenta a sugestão, com base no estudo elaborado, de um veículo ZEV que se adapte às necessidades do cidadão europeu.

Difficultés d'adaptation de questionaire sur les transmissions entre famille et écoles en contextes linguistiques et culturels différents

Les résultats des études PISA – aussi bien en ce qui concerne celle de 2000 comme celle de 2003 - n’ont guêre été satisfaisants pour de nombreux pays de l’OCDE (ce n’est pas le cas pour la Belgique!). Par exemple Portugal, s’il présente des résultats comparables à la moyenne des pays européens ou même supérieurs pour la région de Lisbonne et la vallée du Tage, présente des résultats inférieurs pour l’ensemble du territoire. La Suisse est, curieusement, un autre pays qui se situe en deçà des expectatives. Selon le rapport 2003 (Ramalho, 2004 :50), les études comparatives en littéracie (lecture) et en numéracie n’ont pas démontré de différence significative par rapport aux résultats de 2000. Nous avons pris connaissance d’une étude suisse qui avait pris pour point de départ des résultats également défavorables, pour ce pays, au même rapport PISA : cette recherche analyse l’insertion socio-économique des familles comme également l’influence des transmissions familiales sur les parcours scolaires des élèves.

Indicadores das condições nutricionais na região Polonoroeste: V. Desnutrição protéico-energética e parasitoses intestinais em um grupo de crianças de 3 a 72 meses de idade da cidade de Mirassol D'Oeste, Mato Grosso, Brasil

Este trabalho tem por objetivo caracterizar a desnutrição protéico-energética associada a parasitose intestinal em grupo de 149 crianças de ambos os sexos, na faixa etária de 3 a 72 meses, da cidade de Mirassol D'Oeste, na região do Projeto Polonoroeste em Mato Grosso. De cada criança foram coletados os seguintes dados: sexo, peso, idade e amostra de fezes para exame parasitológico. Os dados peso/idade obtidos foram analisados pelos critérios de GOMEZ. Utilizou-se como padrão de referência o National Center for Health Statistic (NCHS). Para diagnóstico dos parasitas intestinais executou-se o método de Hoffman, Pons e Janer. O grupo estudado constitui-se em sua maioria de crianças desnutridas, sendo a forma leve de desnutrição mais comum que as formas moderada e grave. As enteroparasitoses foram encontradas em 69% das amostras examinadas. A "Giardia lamblia" foi o protozoário mais comum e o "Ancilostomídeo" o helminto mais encontrado. O teste X² não mostrou relação de dependência entre o estado nutricional e a freqüência de enteroparasitoses.

Télédetection en milieu périurbain. Détection et localisation du changement de l'occupation du sol par intégration des donnés-satellite SPOT HRV dans un système d'information géographique

Thèse pour obtenir le grade de DOCTEUR DE L' UNIVERSITÉ PARIS XII, Discipline: Urbanisme Aménagement