An adaptive p-refinement procedure for the implementation of the displacement model of the hybrid-{T}refftz finite element formulation is presented. The procedure is designed to select and implement automatically the degrees of freedom in the domain (displacements) and on the boundary (surface forces) of the element to attain a prescribed level of accuracy. This accuracy is measured on the strain energy of the system for a prescribed finite element mesh. Local measures of error can be easily accounted for. The performance of the adaptive procedure suggested is illustrated using two-dimensional potential problems.

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Co-combustion tests of dry sewage sludges with coal were performed in a pilot bubbling FBC aiming at the characterization of ashes and determining the behaviour of heavy metals in the process. The tests showed compliance with the regulatory levels as far as heavy metal emissions were concerned. The bottom ashes, which accounted for about 70% of the total ash production, were obtained in a granular form, with diameters ranging from 0.5 to 4 mm. The heavy metals were distributed in ashes obtained from different locations of the installation and their concentrations were found to vary depending on the location of capture. The increase in heavy metals content in bottom ashes was not found to lead to higher leachability and ecotoxicity compared to sewage sludges, suggesting that there could be opportunities for their further use. Mercury suffered vaporisation inside the reactor, thus leaving bottom ashes free of contamination by it. However, there was observed a strong retention of mercury in cyclone ashes due to the presence of unburned carbon which probably acted as an adsorbent. The effluent mercury was also found to be mostly associated with the particulate fraction, being less than 20% emitted in gaseous forms. The results suggested that the combustion of the sewage sludge could successfully be carried out and the amount of unburned carbon leaving the combustor but captured in cyclone was large enough to ensure substantial retention of mercury at low temperatures, hence could contribute to an improvement of the mercury release which still remains an issue of great concern to resolve during combustion of waste materials.

The paper is devoted to the compactness of the commutators \(aS_\Gamma - S_\Gamma aI\) and \(W_\alpha S_\Gamma - S_\Gamma W_\alpha\), where \(S_\Gamma\) is the Cauchy singular integral operator, \(a\) is a bounded measurable function, \(W_\alpha\) is the shift operator given by \(W_\alpha f = f\circ\alpha\), and \(\alpha\) is a bi-Lipschitz homeomorphism (shift). The cases of the unit circle and the unit interval are considered. We prove that these commutators are compact on rearrangement-invariant spaces with nontrivial Boyd indices if and only if the function a or, respectively, the derivative of the shift a has vanishing mean oscillation.

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A synthesis on the state of art on dinosaur knowledge in Portugal is presented. The following genera have been recognized: Ceratosaurus, Torvosaurus, Lourinhanosaurus, Allosaurus, cf. Compsognathus, Stokesosaurus, cf. Richardoestesia, cf. Archaeopteryx, Euronychodon, cf. Paronychodon, Dinheirosaurus, Lourinhasaurus, Lusotitan, cf. Pleurocoelus, Lusitanosaurus, Dacentrurus, Dracopelta, Phyllodon, Hypsilophodon, Alocodon, Trimucrodon, Draconyx, Iguanodon, and Taveirosaurus. Most are from Late Jurassic localities at the Lourinhã area and Guimarota. A new genus, Lusotitan, is here raised to include the Late Jurassic ‘Brachiosaurus’ atalaiensis. Lower Cretaceous until Cenomanian material is scarce, except for dinosaur footprints. An interesting Late-Cretaceous, mostly small dinosaur association has been collected between Aveiro and Taveiro.

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We prove necessary conditions for the Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions associated with local properties of the space, of the curve, and of the weight. As an example, we consider weighted Nakano spaces \(L^{p(\cdot)}_w\) (weighted Lebesgue spaces with variable exponent). Moreover, our necessary conditions become also sufficient for weighted Nakano spaces over nice curves whenever \(w\) is a Khvedelidze weight, and the variable exponent \(p(t)\) satisfies the estimate \(|p(\tau)-p(t)|\le A/(-\log|\tau-t|)\).

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The hybrid-{T}refftz displacement element is applied to the elastodynamic analysis of bounded and unbounded media in the frequency domain. The displacements are approximated in the domain of the element using local solutions of the wave equation, the Neumann conditions are enforced directly and the surface forces are approximated on the Dirichlet and inter-element boundaries of the finite element mesh. Two alternative elements are developed to model unbounded media, namely a finite element with absorbing boundaries and an unbounded element that satisfies explicitly the Sommerfeld condition. The finite element equations are derived from the fundamental relations of elastodynamics written in the frequency domain. The numerical implementation of these equations is discussed and numerical tests are presented to assess the performance of the formulation.