The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as ``model corre\-ction" is the problem we address in this paper in the context of linear constraints over the reals. The correction of the right hand side alone, which is very close to a fuzzy constraints approach, was one of the first proposals to deal with inconsistency, as it may be mapped into a linear problem. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, that provide corrections with quite rigid patterns, the optimization of the important Frobenius norm was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer.

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The Late Jurassic Lourinhã Formation contains a diverse dinosaur fauna comprising theropods, sauropods, stegosaurs, ankylosaurs and several genera of ornithopods.
The sedimentology in the area favours preservation of footprints, and footprints from most of the dinosaurs represented by skeletal remains are present in the area. During fieldwork in the summer of 2003 a new, large, tridactyl footprint was found at the beach of Vale Frades, approximately 6 km north of Lourinhã, Portugal. The footprint was found together with a stegosaur footprint on a clay bed exposed within the tidal zone. The footprints were preserved as sandstone casts standing on a pedestal of clay. This unusual type of preservation is the result of the footprints having first been emplaced in clay, and then filled with sand. During the present day erosion from the sea, the harder sandstone cast of the footprints protects the subjacent clay layers from erosion. Owing to the immediate danger of erosion of, the footprint was collected and is now on display at Museu da Lourinhã (ML 1000). The footprint is 70 cm long and 69 cm wide, the toes are short and broad, with indications of short blunt claws. The

divarication angle between the outer digits is close to 90 degrees. The dimensions and general

morphology of the footprint identifies it as deriving from an ornithopod dinosaur with an estimated hip height of 4.13 metres. Although very large ornithopods are known from the Cretaceous, the largest known Jurassic ornithopod is Camptosaurus from USA, and the largest known from Portugal is the camptosaurid Draconyx loureiroi. Neither of these reached the body size suggested by the new footprint. So far the footprint described herein is s the only evidence for a Jurassic ornithopod of that size.

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This paper is mainly focused on the characterisation of a glass material (GM) obtained from the thermal treatment of a bottom ash (BA) produced at the Municipal Solid Waste (MSW) incineration plant of Valorsul. By melting the BA at 1400ºC during 2 hours, and without using any chemical additives, a homogeneous black-coloured glass was obtained. The thermal and mechanical properties of this glass were characterised. The thermal expansion coefficient, measured by dilatometry, was 9-10 x 10-6 per ºC and the modulus of rupture, determined by four-point bending test, was 75±6 MPa, which are similar values to those exhibited by commercial soda-lime-silica glasses used in structural applications. The chemical and the ecotoxicological leaching behaviour of the GM were also analysed. The GM was submitted to a leaching procedure composed of 15 sequential extraction cycles. A liquid/solid (L/S) ratio of 2 l/kg was applied in each cycle. The leachates were filtered through a membrane of PTFE (porosity: 0.45 µm). The filtered leachates were characterised for different chemical parameters and for an ecotoxicological indicator (bacterium Vibrio fischeri). The GM was also submitted to a microwave acidic digestion for the assessment of the total metal content. The crude BA was also submitted to the same experimental procedures. The GM showed levels of chemical emission and ecotoxicity for V. fischeri much lower than those determined for the crude BA. Similar characterisation studies will be pursued with the glass-ceramics produced by adequate thermal treatment of the glass, in order to investigate the effect of the crystallization on the final properties.

Logistics performance can be affected by the presence of uncertainties in the decision making process. To reduce decision making uncertainties, a topology of sources of supply chain ({SC)} uncertainty is proposed, in order to identify different types of uncertainty. A conceptual framework is developed for the analysis of decision making uncertainty sources in {SC’s}, providing the basis for the design and selection of improved {SC} scenarios. A case study is presented to illustrate the potential of simulation techniques in modeling scenarios for the Supply Chain: a set of performance measures is proposed, and results are obtained based on a predetermined selection criterion.

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We prove Szegö's strong limit theorem for Toeplitz determinants with a symbol having a nonstandard smoothness. We assume that the symbol belongs to the Wiener algebra and, moreover, the sequences of Fourier coefficients of the symbol with negative and nonnegative indices belong to weighted Orlicz classes generated by complementary \(N\)-functions both satisfying the \(\Delta_2^0\)-condition and by weight sequences satisfying some regularity, and compatibility conditions.