Additive adaptive thinking in 1st and 2nd grades pupils

This paper is part of the Project “Adaptive thinking and flexible computation: Critical issues”. It discusses what is meant by adaptive thinking and presents the results of individual interviews with four pupils. The main goal of the study is to understand pupils’ reasoning when solving numerical tasks involving additive situations, and identify features associated with adaptive thinking. The results show that, in the case of first grade pupils, the semantic aspects of the problem are involved in its resolution and the pupils’ performance appears to be related to the development of number sense. The 2nd grade pupils seem to see the quantitative difference as an invariant numerical relationship.

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.

Simulation of the velocity field in compound channel flow using different closure models

1st European IAHR Congress,6-4 May, Edinburg, Scotland

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

What kind of employees become awarded as employees of the year in Finland?

Enterprise and Work Innovation Studies,6,IET, pp.53-73

Networking as a route for corporate foresight in SMEs

Paper presented at the 1st Winter School of PhD Programme on Technology Assessment on the December 6th and 7th, 2010, at the Universidade Nova de Lisboa campus of Caparica (Portugal). A final version was developed for the unit “Project III” of the same PhD programme on Technology Assessment at the Universidade Nova de Lisboa in 2010-11 under the supervision of Prof. António Brandão Moniz

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Relatório de estágio de qualificação profissional (fase intercalar do estágio)

No âmbito do Mestrado em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico e da Prática Pedagógica Supervisionada, realizada em contexto de Creche, foi desenvolvido o presente relatório de estágio de qualificação profissional na Educação Pré-Escolar. A prática educativa sustentou-se num quadro teórico-concetual de referência, com vista à construção de saberes para a Educação de Infância, pelo compromisso e responsabilização progressiva da ação docente, tendo sido encarado como um momento de singular importância. Desta forma, este documento procura ilustrar o processo de desenvolvimento de competências profissionais pela estudante para este nível de educação. Nesta linha de pensamento, importa referenciar a metodologia de investigação-ação, que fundamentou a prática pedagógica da estudante ao longo das várias etapas do processo educativo: Observação, Planificação, Ação, Avaliação, Comunicação e Articulação. Assim, apoiada em estratégias e atitudes investigativas e reflexivas, esta metodologia potenciou a transformação, melhoria e adequação das suas práticas. O contexto de formação assumiu-se, portanto, como um lugar privilegiado de articulação entre teoria e prática, onde o processo de ensino e aprendizagem ficou pautado por intencionalidades educativas com vista ao desenvolvimento integral de cada criança, bem como pela construção de saberes e competências profissionais pela estagiária, elencadas nos Decretos-Lei n.º 240 e 241 de 2001. Tomando em consideração o processo desenvolvido, importa realçar a importância de uma formação profissional ao longo da vida, de modo a potenciar o desenvolvimento de uma atitude perante a Educação cada vez mais crítica, problematizadora, indagadora, reflexiva e investigativa, em prol do desenvolvimento holístico de cada criança.

Planning, operations and data handling of planetary science missions

Dissertação para obtenção do Grau de Mestre em Engenharia Física