Regularity of Wiener-Hopf plus Hankel operators

In this thesis we consider Wiener-Hopf-Hankel operators with Fourier symbols in the class of almost periodic, semi-almost periodic and piecewise almost periodic functions. In the first place, we consider Wiener-Hopf-Hankel operators acting between L2 Lebesgue spaces with possibly different Fourier matrix symbols in the Wiener-Hopf and in the Hankel operators. In the second place, we consider these operators with equal Fourier symbols and acting between weighted Lebesgue spaces Lp(R;w), where 1 < p < 1 and w belongs to a subclass of Muckenhoupt weights. In addition, singular integral operators with Carleman shift and almost periodic coefficients are also object of study. The main purpose of this thesis is to obtain regularity properties characterizations of those classes of operators. By regularity properties we mean those that depend on the kernel and cokernel of the operator. The main techniques used are the equivalence relations between operators and the factorization theory. An invertibility characterization for the Wiener-Hopf-Hankel operators with symbols belonging to the Wiener subclass of almost periodic functions APW is obtained, assuming that a particular matrix function admits a numerical range bounded away from zero and based on the values of a certain mean motion. For Wiener-Hopf-Hankel operators acting between L2-spaces and with possibly different AP symbols, criteria for the semi-Fredholm property and for one-sided and both-sided invertibility are obtained and the inverses for all possible cases are exhibited. For such results, a new type of AP factorization is introduced. Singular integral operators with Carleman shift and scalar almost periodic coefficients are also studied. Considering an auxiliar and simpler operator, and using appropriate factorizations, the dimensions of the kernels and cokernels of those operators are obtained. For Wiener-Hopf-Hankel operators with (possibly different) SAP and PAP matrix symbols and acting between L2-spaces, criteria for the Fredholm property are presented as well as the sum of the Fredholm indices of the Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. By studying dependencies between different matrix Fourier symbols of Wiener-Hopf plus Hankel operators acting between L2-spaces, results about the kernel and cokernel of those operators are derived. For Wiener-Hopf-Hankel operators acting between weighted Lebesgue spaces, Lp(R;w), a study is made considering equal scalar Fourier symbols in the Wiener-Hopf and in the Hankel operators and belonging to the classes of APp;w, SAPp;w and PAPp;w. It is obtained an invertibility characterization for Wiener-Hopf plus Hankel operators with APp;w symbols. In the cases for which the Fourier symbols of the operators belong to SAPp;w and PAPp;w, it is obtained semi-Fredholm criteria for Wiener-Hopf-Hankel operators as well as formulas for the Fredholm indices of those operators.

Educar (para) o pensar : desenvolvimento de competências reflexíveis em professores e alunos do 1º CEB : contributos da "Filosofia para Crianças"

O presente estudo inscreve-se na área científica da Formação de Professores, incidindo, particularmente, na compreensão do processo de desenvolvimento das competências reflexivas percebidas como factor de promoção do seu próprio desenvolvimento profissional e pessoal, do desenvolvimento da capacidade de pensar dos seus alunos, da revalorização dos processos curriculares de ensino-aprendizagem e de inovação dos contextos educacionais. Num contexto de complexidade, incerteza e mudança, importa repensar estratégias de formação de professores e de alunos para que possam constituir-se como fatores potenciadores do desenvolvimento da competência reflexiva. Estratégias que convocam, quer o professor, quer o aluno, para um tipo de questionamento de maior exigência reflexiva e consideradas potenciadoras do pensamento crítico, criativo e de cuidado com o outro, numa perspetiva educativa centrada no cuidar, que valoriza a dimensão humana, a atuação responsável, ética e solidária, em todos os planos da vida. Neste estudo propomo-nos retomar algumas das estratégias de formação já configuradas no movimento Filosofia para Crianças e que se constituíram como um programa de formação em contexto, no qual se procurou aprofundar e compreender as múltiplas dimensões e modos como interatuam os diferentes participantes da relação educativa em práticas curriculares reconfiguradas à luz dos pressupostos que sustentam este estudo. Do ponto de vista metodológico, a investigação inscreve-se num paradigma de natureza qualitativa e interpretativa, de matriz hermenêutica e ecológica, configurando uma abordagem de tipo complexo, e com características de estudo de caso, que considera indispensável a participação ativa do sujeito na construção do conhecimento próprio, bem como o carácter de imprevisibilidade e de recursividade das condições e subsistemas em que tal ocorre. No sentido de construir uma visão integrada do objeto em estudo, foram desenvolvidos procedimentos específicos (mixed-methods), nomeadamente análise documental, entrevista semiestruturada, observação participante e inquirição por questionário. O estudo, que decorreu na região centro do país, envolveu 5 professoras do 1.º Ciclo do Ensino Básico, 100 alunos do mesmo nível de ensino e os seus pais/encarregados de educação, inquiridos através de questionário e desenvolveu-se em duas fases. A primeira destinou-se à formação teórico-prática das professoras e, na segunda, foram desenvolvidas sessões práticas de Filosofia para Crianças com os alunos. Os portfolios reflexivos construídos pelos participantes e pela investigadora principal constituíram outra fonte da informação recolhida no estudo empírico. Os resultados do estudo situam-se a quatro níveis: no que respeita aos saberes básicos, ao perfil de competência dos professores, à sua formação e às estratégias e recursos considerados como potenciadores de um pensar de mais elevada qualidade. Quanto ao primeiro nível, o presente estudo releva o carácter estruturante e epistémico de aprender a pensar (bem), salientando que este se processa numa maior amplitude e profundidade dos conteúdos da própria reflexão, às quais subjaz uma visão ampla de cidadania planetária e socialmente comprometida, evidenciando uma ampliação do quadro referencial dos saberes básicos e considerados imprescindíveis para a educação dos cidadãos. A um segundo nível, salienta-se a exigência de um perfil de competência profissional que permita aos professores desenvolver nos seus alunos um pensar de qualidade e, simultaneamente, melhorar a sua própria competência reflexiva. Neste sentido, o estudo aponta para a continuidade das respostas que têm vindo a ser equacionadas por vários autores nacionais e internacionais que, ao abordarem a problemática da formação, do conhecimento profissional e do desenvolvimento identitário dos professores, têm acentuado a importância dos modelos crítico-reflexivos da formação e de uma supervisão ecológica, integradora, não standard e humanizada, no desenvolvimento das sociedades contemporâneas. Conforme os dados sugerem, admite-se que a formação integral dos cidadãos passa pela inclusão e interligação de diferentes áreas do conhecimento que, concertada e complementarmente, possam contribuir para o desenvolvimento da sensibilidade, do pensamento crítico e criativo, de uma cultura da responsabilidade e de uma atitude ética mais ativa e interventiva. Neste sentido, reafirma-se a importância de um trajeto formativo que promova a efetiva articulação entre teoria e a prática, o diálogo crítico-reflexivo entre saberes científicos e experiência, que focalize o profissional na sua praxis e saliente a sua conexão com o saber situado em contexto vivencial e didático- -pedagógico. Realça-se a pertinência de dinâmicas formativas que, a exemplo de “comunidades de investigação/aprendizagem”, na sua aceção de redes de formação que, na prossecução de projetos e propósitos comuns, incentivam a construção de itinerários próprios e de aprendizagens individuais, mobilizando processos investigativos pessoais e grupais. Evidencia-se a valorização de práticas promotoras da reflexão, do questionamento, da flexibilidade cognitiva como eixos estruturadores do pensamento e da ação profissional e como suporte do desenvolvimento profissional e pessoal, corroborando a importância dos processos transformadores decorrentes da experiência, da ação e da reflexão sobre ela. Finalmente, no que respeita às estratégias e recursos, os dados permitem corroborar a riqueza e o potencial do uso de portfolios reflexivos no desenvolvimento de competências linguísticas, comunicacionais, reflexivas e meta-reflexivas e o entendimento de que o processo de construção da identidade profissional ocorre e desenha-se numa dinâmica reflexiva- -prospetiva (re)confirmadora ou (re)configuradora de ideias, convicções, saberes e práticas, ou seja, identitária. De igual modo, a investigação releva a importância da construção de portfolios, por parte dos alunos, para o desenvolvimento da qualidade do seu pensamento, sublinhando-se o seu carácter inovador nesta área. Evidencia-se, ainda, a diversidade de estratégias que respeitem os interesses, necessidades e expectativas dos alunos e o seu contexto de vida, tal como o recurso a materiais diversificados que, atentos ao conteúdo da mensagem, possibilitem a autonomia do pensamento, o exercício efetivo da reflexão crítica e do questionamento, na sua articulação com as grandes questões que sempre despertaram a curiosidade humana e cuja atualidade permanece. Materiais e recursos que estabeleçam o diálogo entre razão e imaginação, entre saber e sensibilidade, que estimulem o envolvimento dos alunos na resolução de problemas e na procura conjunta de soluções e na construção de projetos individuais na malha dos projetos comuns. Reafirma-se, pois, a importância da humanização do saber, a educação pensada como vivência solidária de direitos e deveres. Uma perspetiva educacional humanista que assenta nas trajetórias de vida, na recuperação de experiências pessoais e singulares, que procura compreender a identidade como um processo em (re)elaboração permanente. O presente estudo integra-se na rede de cooperação científica Novos saberes básicos dos alunos no século XXI, novos desafios à formação de professores sendo que, e na linha das investigações produzidas neste âmbito, destaca que o alargamento das funções do professor do 1.º Ciclo do Ensino Básico, que colocando a tónica da ação pedagógica no como se aprende e para quê e na possibilidade de aprender e incorporar o imprevisível, incide no desenvolvimento de um conjunto de capacidades que vão para além das tradicionalmente associadas ao ensinar a ler, escrever e contar. Releva-se, pois, a pertinência da criação de ambientes educativos nos quais professores e alunos entreteçam, conjunta e coerentemente, conhecer, compreender, fazer, sentir, dizer, ver, ouvir e (con)viver em prol de uma reflexão que nos encaminhe no sentido de ser(mos) consciência.

On the Faria's inequality for the Laplacian and signless Laplacian spectra: a unified approach

Let p(G)p(G) and q(G)q(G) be the number of pendant vertices and quasi-pendant vertices of a simple undirected graph G, respectively. Let m_L±(G)(1) be the multiplicity of 1 as eigenvalue of a matrix which can be either the Laplacian or the signless Laplacian of a graph G. A result due to I. Faria states that mL±(G)(1) is bounded below by p(G)−q(G). Let r(G) be the number of internal vertices of G. If r(G)=q(G), following a unified approach we prove that mL±(G)(1)=p(G)−q(G). If r(G)>q(G) then we determine the equality mL±(G)(1)=p(G)−q(G)+mN±(1), where mN±(1) denotes the multiplicity of 1 as eigenvalue of a matrix N±. This matrix is obtained from either the Laplacian or signless Laplacian matrix of the subgraph induced by the internal vertices which are non-quasi-pendant vertices. Furthermore, conditions for 1 to be an eigenvalue of a principal submatrix are deduced and applied to some families of graphs.

An Empirical Evaluation of the Reversal Theory State Measure: Tracking Changes in the Experience of Video Commercials of Three Leading Running Brands

Abstract of paper delivered at the 17th International Reversal Theory Conference, Day 3, session 4, 01.07.15

An Empirical Evaluation of the Reversal Theory State Measure Using Three Running Brand Video Commercials

This paper reports on the first known empirical use of the Reversal Theory State Measure (RTSM) since its publication by Desselles et al. (2014). The RTSM was employed to track responses to three purposely-selected video commercials in a between-subjects design. Results of the study provide empirical support for the central conceptual premise of reversal theory, the experience of metamotivational reversals and the ability of the RTSM to capture them. The RTSM was also found to be psychometrically sound after adjustments were made to two of its three component subscales. Detailed account and rationale is provided for the analytical process of assessing the psychometric robustness of the RTSM, with a number of techniques and interpretations relating to component structure and reliability discussed. Agreeability and critique of the two available versions of the RTSM – the bundled and the branched – is also examined. Researchers are encouraged to assist development of the RTSM through further use, taking into account the analysis and recommendations presented.

Supporting conceptualisation processes in collaborative networks: a case study on an R&D project

The development of new products or processes involves the creation, re-creation and integration of conceptual models from the related scientific and technical domains. Particularly, in the context of collaborative networks of organisations (CNO) (e.g. a multi-partner, international project) such developments can be seriously hindered by conceptual misunderstandings and misalignments, resulting from participants with different backgrounds or organisational cultures, for example. The research described in this article addresses this problem by proposing a method and the tools to support the collaborative development of shared conceptualisations in the context of a collaborative network of organisations. The theoretical model is based on a socio-semantic perspective, while the method is inspired by the conceptual integration theory from the cognitive semantics field. The modelling environment is built upon a semantic wiki platform. The majority of the article is devoted to developing an informal ontology in the context of a European R&D project, studied using action research. The case study results validated the logical structure of the method and showed the utility of the method.

On international cost-sharing of pharmaceutical R&D

Ramsey pricing has been proposed in the pharmaceutical industry as a principle to price discriminate among markets while allowing to recover the (fixed) R&D cost. However, such analyses neglect the presence of insurance or the fund raising costs for most of drug reimbursement. By incorporating these new elements, we aim at providing some building blocks towards an economic theory incorporating Ramsey pricing and insurance coverage. We show how coinsurance affects the optimal prices to pay for the R&D investment. We also show that under certain conditions, there is no strategic incentive by governments to set coinsurance rates in order to shift the financial burden of R&D. This will have important implications to the application of Ramsey pricing principles to pharmaceutical products across countries.

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.

The vibrational spectra and the normal coordinate analysis of thiocarbonye halides /|nby C. R. Subramaniam. -- 260 St. Catharines, Ont. : [s. n.],

The infrared and the Raman spectra of eSelF has been obtained for the first time and has been analysed to give the in-plane normal vibrational frequencies of the molecule, in the ground state. A normal co-ordinate analysis has been carried out for the molecules CSF2, CSClF and eSel 2 using a Urey-Bradley type of potential function and the elements of the [L] matrix elements, the distribution of the potential energy in Urey-Bradley space, and the displacement vector diagrams for the normal modes of vibration for these molecules, have been obtained. The bond for~e constants obtained through the normal co-ordinate analysis, have given some interesting results. The stretching force constant, Kes ' varies markedly with halogen substitution and the force constants KeF and Keel also vary with substitution.

Sources of perceived support from friends in exercise : an application of self-determination theory /

Background: This study examined three social factors (i.e., autonomy support, structure, and involvement) and their relationship with the motivational processes proposed by Vallerand ( 1 997). This study explored sources of support for exercise participation. -~ ' Methods: Participants (N = 425) completed self-reported instruments which assessed variables outlined within Vallerand's ( 1 997) HMIEM. Results: Structural equation modeling analyses predicting the cognitive/affective and exercise behaviour accounted for 23 percent of variance in positive affect, 10 percent of variance in negative affect, 38 percent of variance in physical self-concept, and 4 percent of variance in exercise behaviour. Exploratory analyses revealed that friends, romantic partners, and educators to be consistent sources for providing autonomy support, structure, and involvement, f !,< r - r* Summary: This study is among the first to examine perceived sources oi autonomy support, structure, and involvement from friends in the exercise context and suggest such perceptions may contribute to motivating exercise behaviour in post-secondary students.

Health-Enhancing Physical Activity and Well-Being: Is it How Often, How Long, or How Much Effort that Matters? A Test of Basic Psychological Needs Theory

The primary objectives of the present study were 1) to examine the relationship between health-enhancing physical activity (HEPA) and well-being across the previous day and 2) to examine the role of basic psychological need satisfaction as a potential mediator of the HEPA – well-being relationship. Participants (N = 203) were a convenience sample of undergraduate students with data collected cross sectionally. HEPA was generally associated with well-being (r‟s ranged from .18 to .62). Multiple mediation analyses supported psychological need satisfaction as mechanisms underpinning the HEPA – well- being relationship. Subsequent analyses demonstrated that effort put forth in HEPA activities, as opposed to frequency or duration, uniquely predicted well-being. The role of effort was further highlighted in the multiple mediation analyses. As such future research may wish to investigate the utility of a HEPA program that facilitates effortful engagement and fulfillment of basic psychological needs.

Generator Matrix Based Search for Extremal Self-Dual Binary Error-Correcting Codes

Self-dual doubly even linear binary error-correcting codes, often referred to as Type II codes, are codes closely related to many combinatorial structures such as 5-designs. Extremal codes are codes that have the largest possible minimum distance for a given length and dimension. The existence of an extremal (72,36,16) Type II code is still open. Previous results show that the automorphism group of a putative code C with the aforementioned properties has order 5 or dividing 24. In this work, we present a method and the results of an exhaustive search showing that such a code C cannot admit an automorphism group Z6. In addition, we present so far unpublished construction of the extended Golay code by P. Becker. We generalize the notion and provide example of another Type II code that can be obtained in this fashion. Consequently, we relate Becker's construction to the construction of binary Type II codes from codes over GF(2^r) via the Gray map.

Vertical R&D Sprillovers, Cooperation, Market Structure, and Innovation.

This paper studies vertical R&D spillovers between upstream and downstream firms. The model incorporates two vertically related industries, with horizontal spillovers within each industry and vertical spillovers between the two industries. Four types of R&D cooperation are studied : no cooperation, horizontal cooperation, vertical cooperation, and simultaneous horizontal and vertical cooperation. Vertical spillovers always increase R&D and welfare, while horizontal spillovers may increase or decrease them. The comparison of cooperative settings in terms of R&D shows that no setting uniformly dominates the others. Which type of cooperation yields more R&D depends on horizontal and vertical spillovers, and market structure. The ranking of cooperative structures hinges on the signs and magnitudes of three competitive externalities (vertical, horizontal, and diagonal) which capture the effect of the R&D of a firm on the profits of other firms. One of the basic results of the strategic investment literature is that cooperation between competitors increases (decreases) R&D when horizontal spillovers are high (low); the model shows that this result does not necessarily hold when vertical spillovers and vertical cooperation are taken into account. The paper proposes a theory of innovation and market structure, showing that the relation between innovation and competition depends on horizontal spillovers, vertical spillovers, and cooperative settings. The private incentives for R&D cooperation are addressed. It is found that buyers and sellers have divergent interests regarding the choice of cooperative settings and that spillovers increase the likelihood of the emergence of cooperation in a decentralized equilibrium.

Organizational Design of R&D Activities

This paper addresses the question of whether R&D should be carried out by an independent research unit or be produced in-house by the firm marketing the innovation. We define two organizational structures. In an integrated structure, the firm that markets the innovation also carries out and finances research leading to the innovation. In an independent structure, the firm that markets the innovation buys it from an independent research unit which is financed externally. We compare the two structures under the assumption that the research unit has some private information about the real cost of developing the new product. When development costs are negatively correlated with revenues from the innovation, the integrated structure dominates. The independent structure dominates in the opposite case.