Multi index model - uma abordagem para aplicação ao mercado accionista em Portugal

O mercado accionista, de uma forma global, tem-se revelado nos últimos tempos uma das principais fontes de incentivo ao mercado de valores mobiliários. O seu impacto junto do público em geral é enorme e a sua importância para as empresas é vital. Interessa, então, perceber como é que a teoria financeira tem obordado a avaliação e a compreensão do processo de formação de uma cotação. Desde os anos 50 até aos dias de hoje, interessa perceber como é que os diferentes autores têm tratado esta abordagem e quais os resultados deste confronto. Interessa sobretudo perceber o abordogem de Stephen Ross e a teoria do arbitragem. Na sequência desta obordagem e com o aparecimento do Multi Index Model, passou a ser possível extimar com maior precisão a evolução da cotação, na medida em que esta estaria dependente de um vasto conjunto de variavéis, que abragem uma vasta área de influência. O contributo de Ross é por isso decisivo. No final interessa reter a melhor técnica e teoria, que defende os interesses do investidor. Face o isto resta, então, saber qual a melhor técnica estatística para proceder a estes estudos empíricos.

On development of fractional calculus during the last fifty years

Fractional calculus generalizes integer order derivatives and integrals. During the last half century a considerable progress took place in this scientific area. This paper addresses the evolution and establishes an assertive measure of the research development.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order α to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulator's end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of α in order to get repetitive trajectories in the joint space.

Recent history of fractional calculus

This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date.

Some pioneers of the applications of fractional calculus

In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Lévy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair.

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.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Proposta de modelo para obtenção do Work Index das rochas

Este trabalho pretende estabelecer uma relação entre o Work Index e algumas propriedades das rochas. Através da pesquisa bibliográfica foram identificadas varias propriedades com possível influência no valor do Work Index, das quais foram seleccionadas a massa volúmica aparente, a resistência à carga pontual, a composição química, a composição mineralógica e a abrasividade. Adicionalmente a porosidade aberta e resistência à compressão também foram analisadas. Assim foram analisadas 10 amostras de rocha, quatro de granitos, uma de quartzodiorito, uma de ardósia, uma de serpentinito, uma de calcário, uma de mármore e uma de sienito nefelínico, sobre as quais já eram conhecidos os valores de cinco das propriedades referidas previamente, tendo sido determinados os valores das ainda desconhecidas, resistência à carga pontual e a abrasividade que está representada através do resultado do ensaio capon. Devido à dificuldade de execução do ensaio de determinação do Work Index de Bond foram recolhidos dados bibliográficos de valores do Work Index para as amostras de rocha seleccionadas e adoptado o valor médio para cada uma. Os dados obtidos foram tratados estatisticamente através do método de análise de componentes principais assim como através de regressões lineares simples e múltiplas. A análise de componentes principais permitiu identificar várias propriedades da rocha com possível influência sobre o Work Index de entre as analisadas. Foi possível estabelecer uma relação entre o Work Index e quatro das propriedades seleccionadas, designadamente a porosidade aberta, a resistência à compressão, a resistência à carga pontual e a abrasividade.