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.

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.

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.

Fractional order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.

Análise técnica aplicada aos mercados cambiais estudo comparativo das cotações EUR/USD, GBP/USD E JPY/USD

Mestrado em Contabilidade e Análise Financeira

Neural correlations during brain activation in arithmetical tasks – an approach using electroencephalographic data

Dissertação apresentada na Faculdade de Ciências e Tecnologiea da Universidade Nova de Lisboa, para obtenção do Grau de Mestre em Engenharia Biomédica

Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

Miocene marine-continental correlations in the Lisbon area and some discussion related to personnal experience

Sandpit exploitation near Lisbon allowed collecting of many Miocene, non marine fossils. These sands are part of the mostly marine Miocene series in the Lower Tagus basin. The particularly favourable situation led several researchers to deal with marine-continental correlations. Difficulties often concern methodologic aspects. Some poorly based interpretations exerced a lasting influence. A critical approach is presented. Analysis requires data. Methods based upon models often lead to the temptation of fitting data in order to confirm a priori conclusions, or of mixing up data as if of equal statistic value while they have not at all the same weight. Erroneous interpretations' uncritical repetition for many years "upgraded" them into absolute truth. Another point is endemism vs. europeism. Miocene mammals from Lisbon compared well with corresponding French, contemporaneous taxa, while this was apparently not true for Spanish ones. Too much accent had been put on the endemic character of Spanish, or even regional, mammalian faunas. Nationalist bias and sensationalism also weigh, albeit negatively. Meanwhile nearly all the more evident examples as the rhinoceros Hispanotherium are discredited as Iberian endemisms. Taxa may appear as endemic just because they have not yet been found elsewhere. At least for the medium to large-sized mammals, with their huge geographic distribution, faunal differences depend much more on ecology, climate and environmental conditions. Emphasis on differences may also result from researchers that are often in a precarious situation and need very much to achieve short-term, preferably sensational results. Overvalued differences may mask real similarities. Unethic and not scientific behaviour are further enhanced by "nomina nuda" tricks that may simply be a way to circunvent or cheat the Priority Rule. On the other hand, access to communication networks may present as sensational novelties items that are not new at all, misleading the audience. A new class of "science people" arose, created by the media and not by the value of their real achievements. Discussion is presented on sedimentation processes and discontinuities that are often regarded as absolute precision dating tools, as well as on some geochemical and paleomagnetic interpretations. A very good chronologie frame has been obtained for the basin under study on the basis of an impressive set of data, providing a rather detailed and accurate frame for Miocene marine-continental correlations.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Reply to: Comments on “Particle Swarm Optimization with Fractional-Order Velocity”

We agree with Ling-Yun et al. [5] and Zhang and Duan comments [2] about the typing error in equation (9) of the manuscript [8]. The correct formula was initially proposed in [6, 7]. The formula adopted in our algorithms discussed in our papers [1, 3, 4, 8] is, in fact, the following: ...

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Prognostic modelling of breast cancer patients: a benchmark of predictive models with external validation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Electrotécnica e de Computadores – Sistemas Digitais e Percepcionais pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Fractional order modelling of dynamic backlash

This paper studies the dynamical properties of systems with backlash and impact phenomena. This type of non-linearity can be tackled in the perspective of the fractional calculus theory. Fractional and integer order models are compared and their influence upon the emerging dynamics is analysed. It is demonstrated that fractional models can memorize dynamical effects due to multiple micro-collisions.

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Using interval graphs in an order processing optimization problem

In this paper we address an order processing optimization problem known as minimization of open stacks (MOSP). We present an integer pro gramming model, based on the existence of a perfect elimination scheme in interval graphs, which finds an optimal sequence for the costumers orders.