The reverse mortgage market has been expanding rapidly in developed economies in recent years. Reverse mortgages provide an alternative source of funding for retirement income and health care costs. Increase in life expectancies and decrease in the real income at retirement continue to worry those who are retired or close to retirement. Therefore, financial products that help to alleviate the "risk of living longer" continue to be attractive among the retirees. Reverse mortgage contracts involve a range of risks from the insurer's perspective.

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.

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.