Fractional calculus analysis of the cosmic microwave background

Cosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.

An evaluation of the direct agglutination test to diagnose "Mal de Caderas" disease

Se evaluó la utilidad de la prueba de aglutinación directa (AD) para diagnosticar el Mal de Caderas. Se emplearon cuarenta y cuatro sueros provenientes de dos lotes de equinos naturalmente infectados con el Trypanosoma evansi (Lote 1 y Lote 2). La AD fue positiva (Aglutinación > 1:512) en 13 de 16 equinos (81.2%), de los que se aislaron los parásitos. En doce de estos animales (92%) se detectaron IgM anti T. evansi mediante la AD realizada con 2-mercaptoetanol (AD + 2-ME). La AD fue positiva en 17 de los 28 equinos que resultaron negativos al diagnóstico parasitológico. Un tercer lote de cinco equinos infectados con T. evansi que presentaba elevados títulos de AD, fue tratado con Suramina Sódica (Nagano1-Bayer). La AD + 2-ME evidenció en cuatro animales que, gran parte de estos anticuerpos se ubicaban en la fracción IgM. Posterior al tratamiento farmacológico y, en concordancia de la negativización de la parasitemia, la detección de la IgM anti T. evansi no fue posible, mientras que los anticuerpos IgG continuaron detectándose a los doce meses post-tratamiento en valores de 1:512, en tres animales. Cincuenta sueros de equinos de una zona libre del parásito, que se emplearon como controles, fueron negativos a la AD. Se recomienda la utilización de la AD y AD + 2-ME para el uso de rutina en el diagnóstico del Mal de Caderas de los equinos, en combinación con otros métodos parasitológicos sensibles.

A calculus for modeling and analyzing conversations in service-oriented computing

Dissertação apresentada para a obtenção do Grau de Doutor em Informática pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Synthesis of biodiesel from wastes of food industry via direct transesterification with methanol/carbon dioxide mixtures

Dissertation presented at Faculdade de Ciências e Tecnologia from Universidade Nova de Lisboa to obtain the degree of Master in Chemical and Biochemical Engineering

Does corruption inhibit foreign direct investment?

Globalization creates new opportunities for firms to invest abroad and many economies are making active efforts to attract Foreign Direct Investment (FDI) in order to promote economic growth. Decisions to invest abroad depend on a complex set of factors, but the least corrupt countries may attract more foreign direct investment because they provide a more favorable climate for investors. In this paper we investigate the impact of corruption on FDI inflows in 73 countries, over the period 1998-2008. Our results suggest that countries where corruption is lower, the FDI inflows are greater, and so controlling corruption may be an important strategy for increase FDI inflows.

Condition-Based Diagnosis of Mechatronic Systems Using a Fractional Calculus Approach

While fractional calculus (FC) is as old as integer calculus, its application has been mainly restricted to mathematics. However, many real systems are better described using FC equations than with integer models. FC is a suitable tool for describing systems characterised by their fractal nature, long-term memory and chaotic behaviour. It is a promising methodology for failure analysis and modelling, since the behaviour of a failing system depends on factors that increase the model’s complexity. This paper explores the proficiency of FC in modelling complex behaviour by tuning only a few parameters. This work proposes a novel two-step strategy for diagnosis, first modelling common failure conditions and, second, by comparing these models with real machine signals and using the difference to feed a computational classifier. Our proposal is validated using an electrical motor coupled with a mechanical gear reducer.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Fractional Calculus: Quo Vadimus? (Where Are We Going?)

Discussions under this title were held during a special session in frames of the International Conference “Fractional Differentiation and Applications” (ICFDA ’14) held in Catania (Italy), 23-25 June 2014, see details at http://www.icfda14.dieei.unict.it/. Along with the presentations made during this session, we include here some contributions by the participants sent afterwards and also by few colleagues planning but failed to attend. The intention of this special session was to continue the useful traditions from the first conferences on the Fractional Calculus (FC) topics, to pose open problems, challenging hypotheses and questions “where to go”, to discuss them and try to find ways to resolve.

Fractional Calculus: Application in modeling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

Short-Circuit Impedance of Power Transformers: the Fractional Order Calculus Approach

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

On the Estimation of the Short-Circuit Impedance of Power Transformers Using Fractional Order Calculus

This paper reports investigation on the estimation of the short circuit impedance of power transformers, using fractional order calculus to analytically study the influence of the diffusion phenomena in the windings. The aim is to better characterize the medium frequency range behavior of leakage inductances of power transformer models, which include terms to represent the magnetic field diffusion process in the windings. Comparisons between calculated and measured values are shown and discussed.