Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.

Mathematical models based on non-linear integral and integro-differential equations are gaining increasing attention in mathematical epidemiology due to their ability to incorporate the past infection dynamic into its current development. This property is particularly suitable to represent the evolution of diseases where the dependence of infectivity on the time since becoming infected plays a crucial role.

In March 2019, the PRISMA (PRecursore IperSpettrale della Missione Applicativa) hyper-spectral satellite was launched by the Italian Space Agency (ASI), and it is currently operational on a global basis. The mission includes the hyperspectral imager PRISMA working in the 400-2500 nm spectral range with 237 bands and a panchromatic (PAN) camera (400-750 nm). This paper presents an evaluation of the PRISMA top-of-atmosphere (TOA) L1 products using different in situ measurements acquired over a fragmented rural area in Southern Italy (Pignola) between October 2019 and July 2021.