And I say to myself: “What a fractional world!”

This paper discusses several complex systems in the perspective of fractional dynamics. For prototype systems are considered the cases of deoxyribonucleic acid decoding, financial evolution, earthquakes events, global warming trend, and musical rhythms. The application of the Fourier transform and of the power law trendlines leads to an assertive representation of the dynamics and to a simple comparison of their characteristics. Moreover, the gallery of different systems, both natural and man made, demonstrates the richness of phenomena that can be described and studied with the tools of fractional calculus.

Root locus of fractional linear systems

In this paper an algorithm for the calculation of the root locus of fractional linear systems is presented. The proposed algorithm takes advantage of present day computational resources and processes directly the characteristic equation, avoiding the limitations revealed by standard methods. The results demonstrate the good performance for different types of expressions.

Microstructure, mechanical properties and chemical degradation of brazed AISI 316 stainless steel/alumina systems

The main aims of the present study are simultaneously to relate the brazing parameters with: (i) the correspondent interfacial microstructure, (ii) the resultant mechanical properties and (iii) the electrochemical degradation behaviour of AISI 316 stainless steel/alumina brazed joints. Filler metals on such as Ag–26.5Cu–3Ti and Ag–34.5Cu–1.5Ti were used to produce the joints. Three different brazing temperatures (850, 900 and 950 °C), keeping a constant holding time of 20 min, were tested. The objective was to understand the influence of the brazing temperature on the final microstructure and properties of the joints. The mechanical properties of the metal/ceramic (M/C) joints were assessed from bond strength tests carried out using a shear solicitation loading scheme. The fracture surfaces were studied both morphologically and structurally using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and X-ray diffraction analysis (XRD). The degradation behaviour of the M/C joints was assessed by means of electrochemical techniques. It was found that using a Ag–26.5Cu–3Ti brazing alloy and a brazing temperature of 850 °C, produces the best results in terms of bond strength, 234 ± 18 MPa. The mechanical properties obtained could be explained on the basis of the different compounds identified on the fracture surfaces by XRD. On the other hand, the use of the Ag–34.5Cu–1.5Ti brazing alloy and a brazing temperature of 850 °C produces the best results in terms of corrosion rates (lower corrosion current density), 0.76 ± 0.21 μA cm−2. Nevertheless, the joints produced at 850 °C using a Ag–26.5Cu–3Ti brazing alloy present the best compromise between mechanical properties and degradation behaviour, 234 ± 18 MPa and 1.26 ± 0.58 μA cm−2, respectively. The role of Ti diffusion is fundamental in terms of the final value achieved for the M/C bond strength. On the contrary, the Ag and Cu distribution along the brazed interface seem to play the most relevant role in the metal/ceramic joints electrochemical performance.

Multidimensional scaling analysis of electricity market prices

This paper studies the impact of energy and stock markets upon electricity markets using Multidimensional Scaling (MDS). Historical values from major energy, stock and electricity markets are adopted. To analyze the data several graphs produced by MDS are presented and discussed. This method is useful to have a deeper insight into the behavior and the correlation of the markets. The results may also guide the construction models, helping electricity markets agents hedging against Market Clearing Price (MCP) volatility and, simultaneously, to achieve better financial results.

Replication in distributed systems using IEC 61499 standard

The international Electrotechnical Commission (IEC) 61499 architecture incorporated several function block with which distributed control application may be developed, and how these are interpreted and executed. However, due the distributed nature of the control applications, many issues also need to be taken into account. Most of these are due to the new error model and failure modes of the distributed hardware on which the distributed application is executed and also due the incomplete standards definition of the execution models. IEC 61499 frameworks does not clarify how to handle with replication of software and hardware components. In this paper we propose a replication model for IEC 61499 applications and which mechanisms and protocols may be used for their support.

Fractional control of dynamic systems

The concepts involved with fractional calculus (FC) theory are applied in almost all areas of science and engineering. Its ability to yield superior modeling and control in many dynamical systems is well recognized. In this article, we will introduce the fundamental aspects associated with the application of FC to the control of dynamic systems.

Control and dynamics of fractional order systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fixed point transformations in the adaptive control of fractional-order MIMO systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

Combining global tabu search with local search for solving systems of equalities and inequalities

This papers aims at providing a combined strategy for solving systems of equalities and inequalities. The combined strategy uses two types of steps: a global search step and a local search step. The global step relies on a tabu search heuristic and the local step uses a deterministic search known as Hooke and Jeeves. The choice of step, at each iteration, is based on the level of reduction of the l2-norm of the error function observed in the equivalent system of equations, compared with the previous iteration.

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.

Credit risk measures: a case of renewable energy companies

The Basel III will have a significant impact on the European banking sector. In September 2010, supervisors of various countries adopted the new rules proposed by the prudential Committee on Banking Supervision to be applied to the business of credit institutions (hereinafter called ICs) in a phased manner from 2013, assuming to its full implementation by 2019. The purpose of this new regulation is to limit the excessive risk that these institutions took on the period preceding the global financial crisis of 2008. This new regulation is known in slang by Basel III. Depending on the requirement of Basel II for banks and their supervisors to assess the soundness and adequacy of internal risk measurement and credit management systems, the development of methodologies for the validation of internal and external evaluation systems is clearly an important issue . More specifically, there is a need to develop tools to validate the systems used to generate the parameters (such as PD, LGD, EAD and ratings of perceived risk) that serve as starting points for the IRB approach for credit risk. In this context, the work is composed of a number of approaches and tools used to evaluate the robustness of these elements IRB systems.

Reshaping higher education systems in the MENA region: the contribution of remote and virtual labs

Learning is not only happening in school or university; it is also an important aspect of the daily life that allows students to remain in their biological and physical environment helping to reshape it, by applying what they have learnt. Today, the higher education sector is a part of important strategies used by countries in order to foster their development. Despite its geographical location, i.e. its closeness to Europe and Asia, the MENA (Middle East and North Africa) region still needs an integrated strategy for the advancement, reform, and update of its higher educational landscape. Although some solutions have been experimented in the region in the field of higher education, they have not been able to raise the quality of education to the level comparable that observed in developed countries. In other words, many MENA higher education systems are facing problems, for which solution ought to be sought. We analyse the situation of higher education systems in the MENA countries and the factors that affect the delay in achieving the level of education existing in other world regions, e.g. Europe, especially in the higher education sector. During the discussion, the impact of new technology-enhanced tools, such as remote laboratories, in the process of development and consolidation of MENA universities, is particularly stressed.

Using SysML in systems design

System of systems involves several secondary systems working together with its creation gathering the knowledge of several distinct disciplines and teams, each one with their own background and methods, leading to a difficult communication between them. SysML, a language originated from UML, enables that communication, without background interference, with the use of a rich notation for systems design. This paper analyzes its use through the experience gained in the design of a chemical system with SysML.

On the fractional order control of heat systems

The differentiation of non-integer order has its origin in the seventeenth century, but only in the last two decades appeared the first applications in the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated namely the fractional PID and the Smith predictor. Extensive simulations are presented assessing the performance of the proposed fractional-order algorithms.