Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.

Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints

On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.

Os padrões e a resolução de problemas no 1º ciclo do ensino básico: potencialidades para o ensino-aprendizagem da matemática

Mestrado (PES II), Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico, 27 de Junho de 2014, Universidade dos Açores (Relatório de Estágio).

O impacto do ensino de estratégias morfológicas no desenvolvimento da escrita: um estudo de intervenção

Dissertação de mestrado em ciências da educação especialidade educação especial

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Prática de ensino supervisionada II: a sequência didática como estratégia para escrita de textos no 1º ano de escolaridade

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1º e 2º CEB

Prática de ensino supervisionado no 1.º e 2.º ciclo do ensino básico: a comunicação (em) matemática em contexto de sala de aula

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e 2.º ciclo do Ensino Básico

Guest editorial: OPTIMAX 2013

In 2012 we were awarded an Erasmus Intensive Programme grant to facilitate OPTIMAX 2013, a three week duration residential summer school held within the UK during August 2013. The summer school helped to further develop student radiographer skills in optimising x-radiation dose and image quality. With a major emphasis on visual techniques to determine image quality, lesion visibility, lesion detection performance and physical measures of image quality (eg signal to noise ratio (SNR)) we conducted controlled laboratory experiments on phantoms using Computed Radiography, CT and Full Field Digital Mammography. Mathematical modelling was used for radiation dose estimation. Sixty seven people from 5 European countries participated. This included 49 PhD, MSc and BSc students. Discipline areas included radiography, physics, biomedical science and nuclear medicine.

Enterprises' internationalisation strategy: skills in exportation and customs law

Economical development has always been connected to the commercial exchanges between people, due to the necessity to suppress their needs. With the increasing growth of international business and more competitive and demanding markets, exportation has become an important first step to internationalisation. Unlike what happened in the past, companies must be aware that the enrolment in the current global market is risky and requires elaborated technical procedures. Internationalisation should not be treated as an isolated event of business management. The first part of this paper aims to understand the export process and fit it in the current stage of international trade, keeping in mind the framework of export under the customs law. Then, we tried to understand how Portuguese companies should face this process in their internationalisation strategy, and what skills organisations must acquire to be able to export competitively in the current scenario of globalisation. The investigation was based on interviews in companies that, through a process of internationalisation by exportation, have implemented themselves strongly in extern markets. This investigation allowed us to analyse the companies’ motivations to become international, as well as the selection criteria for the export destinations. It was also possible to identify the main obstacles to the internationalisation of Portuguese companies. We concluded that companies that choose exportation as a way to become international acquire specific skills that enable them to become competitive in international trade. However, studies have failed to answer the second initial question about whether the measures implemented by Customs potentiate exports.

Práticas de ensino supervisionadas do 1º e 2º ciclo do ensino básico: a prática de resolução de problemas na aquisição do conceito de comprimento e de perímetro no 3.º ano de escolaridade

Relatório final apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1.º e 2.º Ciclos do Ensino Básico

Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.

Modellus: Learning Physics with Mathematical Modelling

Tese de doutoramento em Ciências da Educação, área de Teoria Curricular e Ensino das Ciências

Futures of work and skills: some foresight exercises in Europe and USA

The Knowledge-based society brought a new way of living and working. The increasing decline of work in primary sector and traditional industries, related with the significant increase of employment in the service sector and in the knowledge work, changed the way companies and individuals establish their relations, the way work and life is organised. These changes are usual and fast and so the feeling of insecurity and unpredictability become more and more sharp. In this context, foresight exercises are necessary tools helping in the identification of the key variables and main trends of evolution. This report will present some foresight studies about work and skills in Europe and USA, in order to contribute to think about possible evolutions and trends.