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Multiscale methods, such as the power spectrum, are suitable diagnostic tools for studying the second order statistics of a gridded field. For instance, in the case of Numerical Weather Prediction models, a drop in the power spectrum for a given scale indicates the inability of the model to reproduce the variance of the phenomenon below the correspondent spatial scale. Hence, these statistics provide an insight into the real resolution of a gridded field and must be accurately known for interpolation and downscaling purposes. In this work, belonging to the EU INTERREG IIIB Alpine Space FORALPS project, the power spectra of the precipitation fields for two intense rain events, which occurred over the north-eastern alpine region, have been studied in detail. A drop in the power spectrum at the shortest scales (about 30 km) has been found, as well as a strong matching between the precipitation spectrum and the spectrum of the orography. Furthermore, it has also been shown how the spectra help understand the behavior of the skill scores traditionally used in Quantitative Precipitation Forecast verification, as these are sensitive to the amount of small scale detail present in the fields.

The aim of this work is to model a didactive 3D virtual museum room that could be considered a modern reinterpretation of the neogrec-neopompeian theme inside the first international exhibition in Italy, settled in the Palace of Exhibition of Rome, built for this event by Pio Piacentini and inaugurated in 1883. Through a series of programs like Blender, Sketchfab and Unity, it was possible to insert and model 12 selected neogrec-neopompeian paintings in an octagonal museum room, heart of the original exposition structure, and compare similitudes and contrasts among them at the same time just because nowdays some of the painting are part of private collections or they went lost. The realization of the 3D room is based principally on the documents Guida Critica all’Esposizione by Luigi Bellinzoni, published by Treves brothers in 1883 and obtained with the Rovereto’s municipal library concession and also the Official General Catalogue of 1883, published by Edoardo Perino in Rome. In this two volumes we can find the original plant of the exposition and the disposition of the different rooms inside the museum, starting point for the reconstruction of the 3D model.

We prove the existence of a solution for an elliptic problem in dimension n = 1, which involves a non linear term for which neither continuity nor growth condition is assumed: this term can “blow up”, taking values ±∞.