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    Scale-invariance laws in the recurrence interval of extreme floods: an application to the upper Po river valley (northern Italy)

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    The floods that have occurred in the upper valley of the Po river (northern Italy) were classified according to an index of strength on the basis of documentary sources available at the meteorological observatory of Moncalieri since 1780. The catalogue was ascertained to be complete only for events classified at least as moderate. Application of Cantor dust statistics and rank-ordering statistics to time-occurrences of floods provided significant evidence of scale-invariance laws that might be very helpful in assessing and reducing future hazards. The increase in the fractal dimension for floods occurring after 1890 is here related to the significant increase in the number of very heavy rainfall episodes measured all over Italy

    Towards nonuniform distributions of unisolvent weights for high-order Whitney edge elements

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    We propose to extend results on the interpolation theory for scalar functions to the case of differential k-forms. More precisely, we consider the interpolation of fields in Pr-Λk(T), the finite element spaces of trimmed polynomial k-forms of arbitrary degree r≥ 1 , from their weights, namely their integrals on k-chains. These integrals have a clear physical interpretation, such as circulations along curves, fluxes across surfaces, densities in volumes, depending on the value of k. In this work, for k= 1 , we rely on the flexibility of the weights with respect to their geometrical support, to study different sets of 1-chains in T for a high order interpolation of differential 1-forms, constructed starting from “good” sets of nodes for a high order multi-variate polynomial representation of scalar fields, namely 0-forms. We analyse the growth of the generalized Lebesgue constant with the degree r and preliminary numerical results for edge elements support the nonuniform choice, in agreement with the well-known nodal case

    Computing weights for high order Whitney edge elements

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    The interpolation of differential forms is a challenging problem that is getting increasing attention. The issue of finding unisolvent degrees of freedom to describe a differential form in terms of high-order Whitney forms is an active area of research nowadays. In this paper we deal with a family of such degrees of freedom, called weights, that fits with the physical and geometrical nature of the field to interpolate. These weights play the role of interpolation coefficients when reconstructing scalar/vector fields in terms of a set of selected multivariate polynomial forms. Weights are a generalization of the evaluations of a scalar function at a set of nodes in view of its reconstruction on multivariate polynomial bases. As in the nodal case, different sets of such weights are compared in terms of a Lebesgue constant. In this contribution, we briefly recall their definition and provide examples of algorithms in low dimension to compute their associated Lebesgue constant value. Insights to greater dimensions are offered as well

    Gli afflussi idrometeorologici

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    Vengono presentare le caratteristiche degli afflussi idrometeorologici sul territorio nazionale italiano, classificandole anche secondo un nuovo criterio
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