Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA)not equal 0, epsilon(AB)=epsilon(BB)=0), hyperbranched polymers (epsilon(AB)not equal 0, epsilon(AA)=epsilon(BB)=0), and dimers (epsilon(BB)not equal 0, epsilon(AA)=epsilon(AB)=0). These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when epsilon(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.

Evaluation of IMRT and VMAT techniques with and without flattening filter using pareto optimal fronts

Mestrado em Radiações Aplicadas às Tecnologias da Saúde.

How foam-like is the shear-induced lamellar phase of an ionic liquid crystal?

Philosophical Magazine Letters Volume 88, Issue 9-10, 2008 Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes

Linear and sliding-mode control design for matrix converter-based unified power flow controllers

This paper presents the design and compares the performance of linear, decoupled and direct power controllers (DPC) for three-phase matrix converters operating as unified power flow controllers (UPFC). A simplified steady-state model of the matrix converter-based UPFC fitted with a modified Venturini high-frequency pulse width modulator is first used to design the linear controllers for the transmission line active (P) and reactive (Q) powers. In order to minimize the resulting cross coupling between P and Q power controllers, decoupled linear controllers (DLC) are synthesized using inverse dynamics linearization. DPC are then developed using sliding-mode control techniques, in order to guarantee both robustness and decoupled control. The designed P and Q power controllers are compared using simulations and experimental results. Linear controllers show acceptable steady-state behaviour but still exhibit coupling between P and Q powers in transient operation. DLC are free from cross coupling but are parameter sensitive. Results obtained by DPC show decoupled power control with zero error tracking and faster responses with no overshoot and no steady-state error. All the designed controllers were implemented using the same digital signal processing hardware.

Tetranuclear COPPER(II) complexes with macrocyclic and open-chain disiloxane ligands as catalyst precursors for hydrocarboxylation and oxidation of alkanes and 1-phenylethanol

Two new tetranuclear complexes [Cu-4(mu-O)(L-1)-Cl-4] and [Cu-4(mu(4)-O)(L-2)(2)Cl-4] (2), where H2L1 is a macrocyclic ligand resulting from [2+2] condensation of 2,6-diformy1-4-methylphanol (DFF) and 1,3-bis(aminopropy1)tetramethyldisiloxane, and HL2 is a 1:2 condensation product: of DFF with trimethylsilyl p-aminobenzoate, have been prepared. The structures of the products were established by Xray diffraction. The complexes have been characterised by FTIR, UV/Vis spectroscopy, ES1 mass-spectrometry and magnetic susceptibility measurements. The latter revealed that the letrftriuclear complexes can be descr bed as two ferromagnetically coupled dinuclear units, in which the two copper(II) ions interact antiferromacinetically. The ccimpi.iunds act as homogeneous catalyst precursors for a number of single-pot reactions, including (I) hydrocarbaxylation, with CO, H2O and K2S2O8, of a variety of linear and cyclic (n = 5-8) alkanes into the corresponding Cn+1 carboxylic acids, (ii) peroxidative oxidation of cyclohexane, and (iii) solvent-free microwave-assisted oxidation of 1-phenyletha.nol.

Trits(Pyrazol-1-YL)methane metal complexes for catalytic mild oxidative functionalizations of alkanes, alkanes and ketones

This work concerns recent advances (since 2005) in the oxidative functionalization of alkanes, alkenes and ketones, under mild conditions, catalyzed by homoscorpionate tris(pyrazol-1-yl)methane metal complexes. The main types of such homogeneous or supported catalysts are classified, and the critical analysis of the most efficient catalytic systems in the different reactions is presented. These reactions include the mild oxidation of alkanes (typically cyclohexane as a model substrate) with hydrogen peroxide (into alkyl hydroperoxides, alcohols, and ketones), the hydrocarboxylation of gaseous alkanes (with carbon monoxide and potassium peroxodisulfate) into the corresponding Cn+1 carboxylic acids, as well as the epoxidation of alkenes and the Baeyer-Villiger oxidation of linear and cyclic ketones with hydrogen peroxide into the corresponding esters and lactones. Effects of various reaction parameters are highlighted and the preferable requirements for a prospective homogeneous or supported C-scorpionate-M-based catalyst in oxidative transformations of those substrates are identified. (C) 2014 Elsevier B.V. All rights reserved.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

Scorpionate complexes as catalysts for alkane functionalization

A survey of the scorpionate tris(pyrazolyl)methane complexes synthesized by our group is presented, as well as their structural features and catalytic applications toward the funtionalization of linear and cyclic light alkanes.

Comporta de vigas: dimensionamento e análise estrutural

As comportas de vigas de fundo, objecto de estudo no presente trabalho, são essenciais devido à sua capacidade de controlo do fluxo de água em casos de emergência. Assim este trabalho visou o dimensionamento e análise estrutural de uma comporta dessa natureza. Para o seu dimensionamento foi essencial a norma DIN19704-1:1998, que define todos os padrões que devem ser levados em conta numa construção hidráulica em aço. Deste modo, após uma breve descrição do enquadramento e do estado da arte relativamente a este assunto, foram apresentados ao longo do trabalho, os cálculos dos principais componentes mecânicos que fazem parte dum projecto de uma comporta de vigas. Para comprovar a validade do dimensionamento da comporta realizado através da norma, recorreu-se a um software de análise e simulação por elementos finitos, COSMOSWorks, no sentido de assim prever o comportamento mecânico em análise estática linear, que as solicitações mecânicas em presença têm sobre a comporta. Os resultados da comparação entre o dimensionamento teórico e a análise de tensões através do COSMOSWorks nos elementos mais críticos da estrutura, permitem concluir globalmente que a comporta está bem dimensionada tendo em conta os esforços que tem de suportar.

Simulação numérica do comportamento dinâmico de uma laje

Nesta dissertação pretende-se simular o comportamento dinâmico de uma laje de betão armado aplicando o Método de Elementos Finitos através da sua implementação no programa FreeFEM++. Este programa permite-nos a análise do modelo matemático tridimensional da Teoria da Elasticidade Linear, englobando a Equação de Equilíbrio, Equação de Compatibilidade e Relações Constitutivas. Tratando-se de um problema dinâmico é necessário recorrer a métodos numéricos de Integração Directa de modo a obter a resposta em termos de deslocamento ao longo do tempo. Para este trabalho escolhemos o Método de Newmark e o Método de Euler para a discretização temporal, um pela sua popularidade e o outro pela sua simplicidade de implementação. Os resultados obtidos pelo FreeFEM++ são validados através da comparação com resultados adquiridos a partir do SAP2000 e de Soluções Teóricas, quando possível.

Avaliação do risco associado a movimentos verticais de navios em manobra no porto da Praia da Vitória

O risco associado a um navio em manobra pode ser avaliado pela probabilidade do movimento vertical de um ponto do navio ultrapassar um determinado limiar pré-definido. Essa excedência pode originar danos tanto no próprio navio como nas estruturas portuárias envolventes. Este trabalho surge no seguimento de um estudo efectuado no Laboratório Nacional de Engenharia Civil (LNEC), no qual foi desenvolvido um conjunto de ferramentas de avaliação da função resposta do navio quando sujeito à agitação marítima e, partindo dessas ferramentas, foi obtido um procedimento para determinação do espectro dos movimentos verticais de um ponto de um navio parado sujeito àquele estado de agitação (Rodrigues, 2010). No presente estudo, estendeu-se esse procedimento de modo a avaliar a influência da velocidade de avanço do navio no espectro dos movimentos verticais do mesmo. O percurso de entrada do “N/M Fernão Gomes” no porto da Praia da Vitória foi o caso de estudo considerado. A agitação marítima incidente no navio cobriu o período de Janeiro de 2009 a Dezembro de 2010 e foi obtida com base no modelo previsão de escala regional (WAVEWATCH III) e posteriormente transferida para o interior do porto com o recurso a modelos numéricos de propagação de ondas (SWAN e DREAMS). Foi também assumido que a altura do movimento vertical do navio segue uma distribuição de Rayleigh, a qual possibilita a determinação da altura significativa desse movimento vertical, bem como a implementação de um procedimento para determinar a probabilidade de a altura do movimento vertical do navio não exceder um limiar pré-definido e consequentemente mostrar, através da análise dos resultados, a influência da velocidade de avanço do navio. Da análise dos resultados concluiu-se que a velocidade tem uma influência significativa nos resultados. No final avaliou-se a contribuição dos resultados anteriormente determinados, para a análise do risco associado aos movimentos verticais do navio quando em manobra no porto em estudo.