Sui metodi d’integrazione per Ľequazioni differenziali con due variabili indipendenti

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Mass spectrometry in the characterization of ambers. II. Free succinic acid in fossil resins of different origin

Baltic amber contains high levels of succinic acid, most of which is part of the polymer framework, and only recently has the presence of microcrystals of free succinic acid been documented by scanning electron microscopy and X‐ray diffraction analysis. The determination of succinic acid can be used for an easy identification of Baltic amber among other fossil resins and to distinguish it from imitations, widely diffused on the market, produced with natural or modified recent or sub‐fossil resins, such as copals. We report here a simple method, based on negative ion electrospray ionization mass spectrometry, for evaluating the free succinic acid content in water/methanol extracts of ambers from different origin, using a sample of about 20 mg. The limit of quantification is better than 1 ppm and, when applied to a set of amber samples of different origin, it was able to distinguish those of Baltic origin (showing free succinic acid levels in the range 50–400 ppm) from the others (for which succinic acid was undetectable, i.e. at levels lower than 1 ppm). Copyright © 2009 John Wiley & Sons, Ltd.     

Simultaneous measurements of heat of hydration and chemical shrinkage on hardening cement pastes

Isothermal calorimetry and chemical shrinkage measurements are two independent techniques used to study the development of hydration in cementitious systems. In this study, calorimetry and chemical shrinkage measurements were combined and simultaneously performed on hydrating cement paste samples. Portland cement pastes with different water to cement ratios and a cement paste containing calcium sulfoaluminate clinker and anhydrite were studied. The combined calorimetry/chemical shrinkage test showed good reproducibility and revealed the different hydration behavior of sealed samples and open samples, i.e., samples exposed to external water during hydration. Large differences between sealed and open samples were observed in a Portland cement paste with low water to cement ratio and in the calcium sulfoaluminate paste; these effects are attributed to self-desiccation of the sealed pastes. Once the setup is fully automatized, it is expected that combined calorimetry/chemical shrinkage measurements can be routinely used for investigating cement hydration.     

KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation

We prove the existence of small amplitude quasi-periodic solutions for quasi-linear and fully nonlinear forced perturbations of the linear Airy equation. For Hamiltonian or reversible nonlinearities we also prove their linear stability. The key analysis concerns the reducibility of the linearized operator at an approximate solution, which provides a sharp asymptotic expansion of its eigenvalues. For quasi-linear perturbations this cannot be directly obtained by a KAM iteration. Hence we first perform a regularization procedure, which conjugates the linearized operator to an operator with constant coefficients plus a bounded remainder. These transformations are obtained by changes of variables induced by diffeomorphisms of the torus and pseudo-differential operators. At this point we implement a Nash–Moser iteration (with second order Melnikov non-resonance conditions) which completes the reduction to constant coefficients.