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.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.

Persistence characteristics in financial prices: evidence from the portuguese stock market returns

The objective of this article is to provide additional knowledge to the discussion of long-term memory, leaning over the behavior of the main Portuguese stock index. The first four moments are calculated using time windows of increasing size and sliding time windows of fixed size equal to 50 days and suggest that daily returns are non-ergodic and non-stationary. Seeming that the series is best described by a fractional Brownian motion approach, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA). The findings indicate evidence of long term memory in the form of persistence. This evidence of fractal structure suggests that the market is subject to greater predictability and contradicts the efficient market hypothesis in its weak form. This raises issues regarding theoretical modeling of asset pricing. In addition, we carried out a more localized (in time) study to identify the evolution of the degree of long-term dependency over time using windows 200-days and 400-days. The results show a switching feature in the index, from persistent to anti-persistent, quite evident from 2010.

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.

In vitro susceptibility of Paracoccidioides brasiliensis yeast form to antifungal agents

A study was conducted to determine the susceptibility of P. brasiliensis yeast form to amphotericin B (A), ketoconazole (K), 5-fluorocytosine (5-FC) and rifampin (R). The three isolates tested produced minimal inhibitory concentrations (MICs) (mcg/ml) in the following range: A: 0.09-0.18; K: 0.001-0.007; 5-FC: 62.5-250 and R: 40-80. The minimal fungicidal concentrations (MFC) were several times higher than the corresponding MICs. Precise MFC for 5-FC were not obtained (> 500 mcg/ml). Combination of K plus A proved synergic, with the fractional inhibitory concentration (FIC) indices revealing synergy when the drugs were combined at the 1 to 1 and 1 to 5 MIC ratios. R (40 mcg/ml) appeared to antagonize K. These results indicate promise for the combined use of K plus A as a therapeutical regimen.

Which differintegration?

IEE Proceedings Vision, Image & Signal Processing, vol. 152, nº 6

Modelização de equivalente eléctrico para rede de nervuras de folhas vegetais

A tese tem como objectivo principal a criação de um modelo equivalente eléctrico da rede de nervuras de algumas folhas vegetais e analisar o seu comportamento a estímulos eléctricos, analisando-se também a respectiva resposta em frequência. A motivação desta tese passa pela observação dos sistemas existentes na natureza. Neste caso, as folhas vegetais e analisar se são sistemas de ordem fraccionária ou não. Para a sua elaboração, fez-se uma breve abordagem à estrutura das plantas, sob o ponto de vista da botânica e elaborou-se um método de fotografia das amostras, mapeamento da rede de nervuras e medição dos segmentos que compõem essa mesma rede. A tese termina com um capítulo de resultados experimentais.

A new approach to the initial value problem

5th Portuguese Conference on Automatic Control, September, 5-7, 2002, Aveiro, Portugal

Long-term dependence in financial prices: evidence from the Belgian stock market returns

This article aims to contribute to the discussion of long-term dependence, focusing on the behavior of the main Belgian stock index. Non-parametric analyzes of the general characteristics of temporal frequency show that daily returns are non-ergodic and non-stationary. Therefore, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA), under the fractional Brownian motion approach, and we found slight evidence of long-term dependence. These results refute the random walk hypothesis with i.i.d. increments, which is the basis of the EMH in its weak form, and call into question some theoretical modeling of asset pricing. Other more localized complementary study, to identify the evolution of the degree of dependence over time windows, showed that the index has become less persistent from 2010. This may mean a maturing market by the extension of the effects of current financial crisis.

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Os modelos na compreensão dos números racionais fracionários

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Significados de fração – um estudo numa turma de 3.º ano

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e do 2.º Ciclo do Ensino Básico

Describing function of two masses with backlash

This paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional dynamics is compared with that of standard models.

Discretization of complex-order algorithms for control applications

In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.

Complex-order dynamics in hexapod locomotion

This paper studies the dynamics of foot–ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot–ground transfer function, which presents complex-order dynamics.