The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

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.

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

Study of thermochemical treatments of cork in the 150-400ºC range using colour analysis and Ftir spectroscopy

A study of chemical transformations of cork during heat treatments was made using colour variation and FTIR analysis. The cork enriched fractions from Quercus cerris bark were subjected to isothermal heating in the temperature range 150–400 ◦C and treatment time from 5 to 90 min. Mass loss ranged from 3% (90 min at 150 ◦C) to 71% (60 min at 350 ◦C). FTIR showed that hemicelluloses were thermally degraded first while suberin remained as the most heat resistant component. The change of CIE-Lab parameters was rapid for low intensity treatments where no significant mass loss occurred (at 150 ◦C L* decreased from the initial 51.5 to 37.3 after 20 min). The decrease in all colour parameters continued with temperature until they remained substantially constant with over 40% mass loss. Modelling of the thermally induced mass loss could be made using colour analysis. This is applicable to monitoring the production of heat expanded insulation agglomerates.

Synthesis of organometallic Ruthenium(II) complexes with strong activity against several human canceer cell lines

A new family of "RuCp" (Cp=eta(5)-C5H5) derivatives with bidentate N,O and N,N'-heteroaromatic ligands revealed outstanding cytotoxic properties against several human cell lines namely, A2780, A2780CisR, HT29, MCF7, MDAMB231, and PD. IC50 values were much lower than those found for cisplatin. Crystal structure of compound 4 was determined by X-ray diffraction studies. Density functional theory (DFT) calculations performed for compound 1 showed electronic flow from the ruthenium center to the coordinated bidentate ligand, in agreement with the electrochemical studies and the existence of a metal-to-ligand charge-transfer (MLCT) band evidenced by spectroscopic data.

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Introduction to fractional linear systems. Part 1 : continuous-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Desenvolvimento de métodos rápidos para deteção de drogas no meio aquático

A vasta aplicação de antibióticos em sistemas de aquacultura tem conduzido ao aparecimento de espécies microbianas resistentes, devendo ser evitada ou, se possível, minimizada. A minimização implica um controlo muito rigoroso das doses aplicadas, algo que só pode ser realizado se todo o processo analítico for simples, barato e puder ser implementado no local. O presente trabalho descreve para este efeito um sistema sensor constituído por papel quimicamente modificado, cujo procedimento analítico foi semelhante à monitorização de pH através das conhecidas tiras indicadoras de pH universal. O papel foi modificado com base em reacções de monocamadas e assumiu uma coloração típica após contacto com o antibiótico. A intensidade da coloração estava também relacionada com a concentração desse antibiótico. Como prova deste conceito, o sensor proposto foi desenhado tendo em vista a monitorização de oxitetraciclina, um dos antibióticos utilizados neste contexto com elevada frequência. A modificação do papel foi baseada na alteração química das unidades de glucose na matriz sólida por reacção covalente com reagentes apropriados. Foram utilizadas duas estratégias diferentes para este efeito: uma foi baseada em reacções de tipo sol-gel e a outra em reacção de adição nucleófila. Posteriormente, o papel foi modificado com espécies metálicas capazes de mudar de cor na presença da oxitetraciclina. Estas modificações químicas foram avaliadas e optimizadas relativamente a vários parâmetros, no sentido de promover uma variação de cor intensa face à concentração de antibiótico. Procedeu-se ainda ao controlo desta modificação por técnicas de espectroscopia de infravermelho. A variação de cor foi avaliada por comparação visual, mas registada por imagem digital. Os materiais sensores preparados foram ainda caracterizados do ponto de vista do seu desempenho analítico. Incluíram-se aqui a identificação de uma relação linear entre coordenadas de cor e concentração, a atribuição de uma gama de concentrações capaz de fornecer uma resposta previsível e resposta cruzada face a outros antibióticos. Procedeu-se ainda à aplicação dos sensores numa amostra de água ambiental dopada com antibiótico. De uma forma geral, foi possível estabelecer um processo simples de modificação de papel capaz de aferir a presença e a quantidade de tetraciclinas, mais concretamente a oxitetraciclina. O processo aqui estabelecido é promissor, antevendo a concretização de uma metodologia simples, barata e local para a monitorização de anitbióticos em águas.