Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.

Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.

Obras para voz e piano de Frederico de Freitas: a vocalidade entre fado e canção

Durante a sua vida Frederico de Freitas abordou praticamente todos os géneros musicais, demonstrando uma imensa e notória versatilidade tanto na música erudita como na não erudita. O repertório para canto e piano representa uma parte substancial da sua obra vocal e, apesar de menos divulgado, não pode deixar de se considerar de grande importância. É precisamente neste género que mais se evidencia a versatilidade do seu estilo composicional. Este repertório abrange, assim, os géneros erudito e ligeiro, ou popular, pelo que as suas canções refletem a facilidade com que se movia de um meio para outro. Enquanto investigador, os estudos que realizou sobre música medieval portuguesa, o número elevadíssimo de recolhas de melodias tradicionais portuguesas que fez ao longo da vida e as investigações que realizou sobre o fado deram origem, paralelamente à composição de canções eruditas, a harmonizações de melodias medievais, a arranjos de temas na música tradicional e à composição de fados. Do ponto de vista interpretativo, a diversidade de estilos presentes nas canções de Frederico de Freitas exige do cantor lírico uma versatilidade e capacidade de se adaptar, ainda que mantendo a matiz da sua formação erudita, ao estilo próprio de cada canção. Com vista a uma interpretação estilística e vocalmente adequada, e por representarem um universo tão diferenciado, esta tese de doutoramento centra a sua atenção na problemática da vocalidade das suas canções.

Psycho-physio dynamics in violin-piano duo: a pianist's perspective

The case study looked at psychological and physiological responses to stress in musicians, comparing a newly formed and a consolidated violin-piano duo. The common element between these duos was the pianist. Using the psychological tests (STAI Y1 and Y2, K-MPAI, MMPI-2, ICAC), the immunoassay saliva test to measure cortisol (stress hormone) and non- invasive device VitalJacket® developed at the University of Aveiro, Portugal, participants were monitored under various performance conditions. Others quantitative and qualitative dataset were collected including a pianist’s personal diary (analyzed by psychiatrist), semi-structured interviews with members of long-terms chamber music duo and perceptual evaluations (listening test) of the performances by expert listeners. The variables included two performance venues (European university and secondary school), as well as well-known repertoire, recently known repertoire and newly known repertoire. The latter was given approximately one week before each recital. The psychological and physiological dataset were collected for a total of eight recitals – two series of four recitals each. The unexpected results show that state anxiety levels and stress of the pianist, who does not present an anxious profile, either in social or in musical terms, are always higher when playing with a well-known partner. Possible explanations may be due to the highest expectations for quality of performance and implications of mirror neurons (since the reactions are very different according to the partner). In other words, the “known” (i.e., the consolidated duo) can become “trapped” within a predetermined space, especially at the psychological level, while the “unknown” (the occasional duo) seems to be less involved and therefore more reassuring and exciting in positive terms. In addition, the preference of the expert audience is for the consolidated duo.

Seasonal and storm induced morphological variations at praia de Faro, península do Ancão, southern Portugal

Dissertação de Mestrado, Estudos Marinhos e Costeiros, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 2009

Seasonal variations in gross biochemical composition, percent edibility, and condition index of the clam Ruditapes Decussatus cultivated in the Ria Formosa (South Portugal)

The grooved carpet shell clam, Ruditapes decussatus (L. 1758), is one of the most popular and profitable molluscs exploited in rearing plots in the Mediterranean. However, annual catch has been declining steadily since the early nineties. In order to understand the seasonality of its nutritional value, thus providing an improved basis for economical valuation of the resource, gross biochemical composition, percentage edibility and condition index were investigated during a year with monthly periodicity in a commercially exploited population of the clam Ruditapes decussatus in the Ria Formosa, a temperate mesotidal coastal lagoon located in the south of Portugal. Our results show that total and non-protein nitrogen co-varied during the year, resulting in a protein content that peaked in the warmest months. Although complementary in summer, carbohydrate and lipid contents showed irregular annual trends. The observed seasonality was comparable to that shown by studies elsewhere at similar latitudes, and are underpinned by the reproductive cycle of the species. Our results show the clams to be at their prime nutritional value at the beginning of summer, when protein content peaks.

Effect of nitrogen and potassium fertilisation on vegetative growth and flowering of mature carob trees (Ceratonia siliqua): variations in leaf area index and water use indices

This work aimed to assess how potassium (K) and nitrogen (N) fertilisation may affect the use of precipitation in terms of vegetative and flowering response of 15-year-old carob trees during a 3-year experiment. A field trial was conducted in 1997, 1998 and 1999 in Algarve (Southern Portugal) in a calcareous soil. Four fertilisation treatments were tested: no fertiliser (control); 0.8 kg N/tree (N treatment); 1 kg K 2 O/tree (K treatment) and 0.8 kg N/tree plus 1 kg K 2 O/tree (NK treatment). No irrigation was applied during the experimental period. Branch length increments were measured every month throughout the growing season and inflorescence number was registered once per year. There was a strong seasonal effect on vegetative growth, since low levels of precipitation (115 mm) during October 1998–March 1999 suppressed the increment in branch length. N supplied to the trees (N and NK treatments) tended to increase water use indices in terms of vegetative growth. No response to K alone was observed in trees fertilised only with K. The number of inflorescences increased throughout the experimental period, particularly for N and NK treatments, and a reduction of the precipitation amount during April, May and June, may also enhance flowering. This knowledge could be important when making decisions concerning fertilisation under dry conditions. The results reported here indicate that tree growth (expressed as the branch growth) and flower production under dry-farming conditions, may be achieved by applying 0.8 kg of N (as ammonium nitrate) per tree during the growing season. However, N uptake and use depends on soil water availability.

On the assessment of time-shift variations from backscattered ultrasound for large temperature changes in biological phantoms

This work reports the assessment of time-shifts (TS) from backscattered ultrasound (BSU) signals when large temperature variations (up to 15 degrees C) were induced in a gel-based phantom. The results showed that during cooling temperature is linear with TS at a rate of approximately 74 ns/degrees C. However during a complete heating/cooling cycle, the relation is highly non-linear. This can be explained by the fact that during cooling the temperature distribution is more uniform. Another problem to report is that TS is very sensitive to external movements.

Temporal and Georaphical Variations in Grass Pollen Seasons in Areas of Western Europe: an Analysis of Season dates at Sites of the European Pollen Information System.

Geographical and temporal variations in the start dates of grass pollen seasons are described for selected sites of the European Pollen Information Service. Daily average grass pollen counts are derived from Network sites in Finland, the Netherlands, Denmark, United Kingdom, Austria, Italy and Spain, giving a broad longitudinal transect over Western Europe. The study is part of a larger project that also examines annual and regional variations in the severity, timing of the peak and duration of the grass pollen seasons. For several sites, data are available for over twenty years enabling long term trends to be discerned. The analyses show notable contrasts in the progression of the seasons annually with differing lag times occurring between southern and northern sites in various years depending on the weather conditions. The patterns identified provide some insight into geographical differences and temporal trends in the incidence of pollinosis. The paper discusses the main difficulties involved in this type of analysis and notes possibilities for using data from the European Pollen Information service to construct pan European predictive models for pollen seasons.

Variations in the Work and Lives of Teachers: Relative and Relational Effectiveness

The VITAE project is a four‐year (2001–2005) research study, commissioned by the Department for Education and Skills, conducted with 300 teachers in 100 schools in seven local education authorities in England. The project aimed to identify factors that may affect their work and lives over time and how these factors may, in turn, impact on their teaching and subsequent pupil progress and outcomes. It combined quantitative and qualitative methods of data collection and analysis in order to define and examine notions of teachers' relational and relative effectiveness. The first part of the paper addresses the nature of effectiveness and three key themes relating to the changing contexts of teachers' work, lives and effectiveness: the challenge of reform to notions of professionalism; professional identities; changes in teachers' work and lives. The research design and early findings and their effects upon the development of the research form the second part. The final part of the paper discusses three sets of understandings which are fundamental to any consideration of teachers' work, lives and effectiveness: relative and relational effectiveness; teacher identities; teachers' life and work contexts. The research suggests that policy‐makers, school leaders and teachers themselves need to attend to these if teacher recruitment, retention and standards are to improve.

Teachers’ Constructs Of Effective Classroom Practice: Variations Across Career Phases.

This paper outlines a theoretical framework which offers an explanation of the complexity of how teachers define their effectiveness in relation to their classroom practice. The research from which this framework emerged was a two-year, mixed method study of 81 primary and secondary school teachers. The use of repertory grid interviews combined with a number of other methods is unique in a study of teachers’ practice and, from the elicited constructs, seven key themes emerged. These themes, analysed in relation to three broad career phases, indicate a number of issues important for teachers as they transfer from early-to-late career.

Relatório de estágio: mestrado em ensino da música

Resumo I - O projecto “Piano e outros Instrumentos/orquestra” consiste na implementação do formato Piano e Orquestra em complemento às aulas individuais e aos ensaios de conjunto. O trabalho foi dirigido a um grupo de três alunos com idades de 9, 12 e 16 anos, do curso de Iniciação, Básico e Secundário da EMNSC (Escola de Música de Nossa Senhora do Cabo). Foram criados momentos distintos em cada fase. Estimulou-se o desenvolvimento de competências musicais e de estratégias metacognitivas visando a evolução dos alunos e a eficácia na realização do estudo individual. O Projecto foi criado com o objectivo de desenvolver as competências musicais, a motivação para realização do estudo individual e de grupo, o espírito e a audição crítica, o controlo dos factores psicológicos, a ansiedade, o aumento da autoconfiança, a aprendizagem, a melhoria da atitude positiva no momento da execução pública e o incremento do interesse pelas actividades relacionadas com a prática musical. A realização deste projecto visou analisar o grau de motivação, o desenvolvimento e a aquisição de competências musicais dos alunos de piano que frequentaram semanalmente aulas individuais, aulas extra de preparação, ensaios com Orquestra “Da Capo”, ensaios com a Orquestra Maior, duos com violoncelo e com canto. Um dos objectivos era comparar o grau de motivação e desenvolvimento dos alunos quando estudam obras nas aulas individuais que constituem o programa curricular e, por outro lado, quando o fazem em peças seleccionadas especificamente para este Projecto. Esta experiência visou proporcionar um conhecimento nos diversos domínios da música, uma visão diferente da funcionalidade do piano em conjunto com os outros instrumentos, a descoberta das sonoridades do piano contrastante e ao mesmo tempo, integrante com outros instrumentos, as formas de funcionamento dos instrumentos de corda, de sopro, dos assuntos relacionados com a afinação e pretendendo-se assim apurar o sentido de fazer parte integrante de um todo.

Leitura à primeira vista ao piano: relatório de estágio

A frequência de um Estágio de Ensino Especializado proporciona uma oportunidade de proximidade entre futuro docente e aluno. A observação de metodologias e o envolvimento com a música e contexto musical das escolas e alunos é algo fundamental para a formação correcta de docentes. Devido ao carácter prático do ensino de um instrumento, esta interacção demonstra-se fundamental para a experiência pedagógica. Neste estágio pretendeu-se aumentar o grau de qualidade de ensino e o número de ferramentas pedagógicas, comparando-as com ferramentas aprendidas e articuladas por experiência pré-adquirida como docente. A pedagogia de ensino de piano tem vindo a sofrer várias modificações e adaptações, como reflexo do meio e dos recursos disponíveis. A existência de conservatórios onde os alunos podem frequentar um grande número de disciplinas trouxe vantagens significativas para a sua cultura musical. Embora o estudo do instrumento continue a ser a prática principal, a diminuição nos horários de estudo obriga a uma selecção criteriosa dos conteúdos programáticos deste instrumento, de modo a não por em causa o desenvolvimento técnico dos alunos. Uma área raramente encontrada nestes conteúdos é a leitura à primeira vista. A investigação aqui apresentada pretendeu compreender como se realiza a leitura à primeira vista de uma partitura ao piano e como se pode desenvolver esta competência. Recorrendo a fontes bibliográficas consultadas e à análise de métodos de ensino representativos, foram alvo de investigação a forma como um leitor lê à primeira vista uma partitura, qual a importância do tacto e da visão, e até que ponto esta competência pode ser estudada e desenvolvida. Quais são os factores-chave da leitura à primeira vista? Até que ponto a prática ao instrumento pode influenciar esta capacidade? Embora a leitura à primeira vista tenha sido retirada como disciplina e forma de avaliação em vários estabelecimentos de ensino, a realização de alguns inquéritos pretendeu avaliar a importância dada a esta disciplina, entre professores e alunos.

Assigning real-time tasks on heterogeneous multiprocessors with two unrelated types of processors

A preliminary version of this paper appeared in Proceedings of the 31st IEEE Real-Time Systems Symposium, 2010, pp. 239–248.

Synthesis and structural characterization of new Piano-stool Ruthenium(II) complexes bearing 1-Butylimidazole heteroaromatic ligand

New cationic ruthenium(II) complexes with the formula [Ru(eta(5)-C5H5)(LL)(1-BuIm)] [Z], with (LL) = 2PPh(3) or DPPE, and Z = CF3SO3-, PF6-, BPh4-, have been synthesized and fully characterized. Spectroscopic and electrochemical studies revealed that the electronic properties of the coordinated 1-butylimidazole were clearly influenced by the nature of the phosphane coligands (LL) and also by the different counter ions. The solid state structures of the six complexes determined by X-ray crystallographic studies, confirmed the expected distorted three-legged piano stool structure. However the geometry of the 1-butylimidazole ligand was found considerably different in all six compounds, being governed by the stereochemistry of the mono and bidentate coligands (PPh3 or DPPE).