Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

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.

O feminino na obra de Uanhenga Xitu

Interessa-nos para este artigo perscrutar as representações da vida social em narrativas do escritor angolano Uanhenga Xitu, mormente no que diz respeito à personagem feminina e ao papel da mulher nas sociedades tradicionais angolanas. Nas narrativas cujas ações se passam no interior de Angola, as representações sociais da mulher revelam um modus vivendi diferenciado daquele experimentado por mulheres que migram para a capital, Luanda, espaço em que a noção de vida comunitária, tão significativa nas sociedades tradicionais, perde seu significado. Os trabalhos lá executados, por exemplo, serão em favor do colono, como os dos empregados domésticos, e não para a coletividade. Já nos espaços interiores, mais distantes da mão pesada do colonizador, as representações da vida social dos angolanos são mais expressivas e essa diferenciação revela que a migração do campo para a cidade, no caso de um país dominado pela colonização, metaforiza o abandono de um tipo de (con)vivência social em favor de outro. Como a política colonial portuguesa foi assimilacionista, essa migração será sinônimo de busca de adesão ao modus vivendi do outro, muitas vezes para sofrer menos os efeitos da dominação. Para essa discussão, não é por livre escolha que se tratará das personagens femininas na obra de Xitu, posto que as mulheres em seus textos ganham vez e voz para a expressão do proprium angolano, como se o autor as quisesse homenagear em sinal do reconhecimento de sua importância na construção e preservação da memória, que é capaz de criar laços identitários entre as milenares gerações passadas e as futuras, como esboçaremos (Esta reflexão teve origem no estudo desenvolvido no doutoramento, intitulado Entre dois contares: o espaço da tradição na escrita de Uanhenga Xitu, defendida em 1996 na FFLCH-USP, e orientada pela Dra. Maria Aparecida Santilli, falecida em março de 2008).

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Dynamics of the Dow Jones and the NASDAQ stock indexes

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indices. We analyze the Dow Jones Industrial Average ( ∧ DJI) and the NASDAQ Composite ( ∧ IXIC) indexes at a daily time horizon. The methods and algorithms that have been explored for description of physical phenomena become an effective background, and even inspiration, for very productive methods used in the analysis of economical data. We start by applying the classical concepts of signal analysis, Fourier transform, and methods of fractional calculus. In a second phase we adopt a pseudo phase plane approach.

Logística e estão da cadeia de abastecimento

Relatório apresentado ao Instituto Superior De Contabilidade e Administração Do Porto para obtenção do grau de Mestre em Logística Orientado por António Jorge S. T. Duarte