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.

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.

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In recent years much attention has been given to global supply chains. However, the emphasis has been on forward chains, with reverse flows been insufficiently studied. In this work, we study closed loop supply chains and analyse the impact caused by the introduction of new facility sites into an already existing supply chain. The model considers both strategic and tactical decisions allowing for the design of a global supply chain with reverse flows. The impact of the network redesign is analysed and the associated costs calculated. The obtained MILP is solved using a standard Branch and Bound solver. The results obtained prove that the proposed model handles satisfactorily the network redesign problem.

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The thermal decompositions of methyl azidoformate (N3COOMe), ethyl azidoformate (N3COOEt) and 2-azido-N,N-dimethylacetamide (N3CH2CONMe2) have been studied by matrix isolation infrared spectroscopy and real-time ultraviolet photoelectron spectroscopy. N2 appears as an initial pyrolysis product in all systems, and the principal interest lies in the fate of the accompanying organic fragment. For methyl azidoformate, four accompanying products were observed: HNCO, H2CO, CH2NH and CO2, and these are believed to arise as a result of two competing decomposition routes of a four-membered cyclic intermediate. Ethyl azidoformate pyrolysis yields four corresponding products: HNCO, MeCHO, MeCHNH and CO2, together with the five-membered-ring compound 2-oxazolidone. In contrast, the initial pyrolysis of 2-azido-N,N-dimethyl acetamide, yields the novel imine intermediate Me2NCOCHNH, which subsequently decomposes into dimethyl formamide (HCONMe2), CO, Me2NH and HCN. This intermediate was detected by matrix isolation IR spectroscopy, and its identity confirmed both by a molecular orbital calculation of its IR spectrum, and by the temperature dependence and distribution of products in the PES and IR studies. Mechanisms are proposed for the formation and decomposition of all the products observed in these three systems, based on the experimental evidence and the results of supporting molecular orbital calculations.

The thermal decompositions of methyl azidoformate (N3COOMe), ethyl azidoformate (N3COOEt) and 2-azido-N,N-dimethylacetamide (N3CH2CONMe2) have been studied by matrix isolation infrared spectroscopy and real-time ultraviolet photoelectron spectroscopy. N2 appears as an initial pyrolysis product in all systems, and the principal interest lies in the fate of the accompanying organic fragment. For methyl azidoformate, four accompanying products were observed: HNCO, H2CO, CH2NH and CO2, and these are believed to arise as a result of two competing decomposition routes of a four-membered cyclic intermediate. Ethyl azidoformate pyrolysis yields four corresponding products: HNCO, MeCHO, MeCHNH and CO2, together with the five-membered-ring compound 2-oxazolidone. In contrast, the initial pyrolysis of 2-azido-N,N-dimethyl acetamide, yields the novel imine intermediate Me2NCOCHNH, which subsequently decomposes into dimethyl formamide (HCONMe2), CO, Me2NH and HCN. This intermediate was detected by matrix isolation IR spectroscopy, and its identity confirmed both by a molecular orbital calculation of its IR spectrum, and by the temperature dependence and distribution of products in the PES and IR studies. Mechanisms are proposed for the formation and decomposition of all the products observed in these three systems, based on the experimental evidence and the results of supporting molecular orbital calculations.

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