Bollettino dell Unione Matematica Italiana

Ganie, Javid Ahmad; Bhat, Altaf Ahmad; Wani, Shahid Ahmed

2023 Bollettino dell Unione Matematica Italiana

doi: 10.1007/s40574-023-00386-4

The definitions and applications of the Natural transform of two variables in q-calculus are proposed in this paper. First, we define Natural transform convergence as absolute convergence. Furthermore, we provide several properties and examples to demonstrate the efficacy and performance of the proposed results. We then use these findings to solve some generalised partial differential equations.

Fantini, Veronica

2023 Bollettino dell Unione Matematica Italiana

doi: 10.1007/s40574-023-00385-5

Since the pioneering work of Kontsevich and Soibelman (in: The unity of mathematics, Springer, Berlin, 2006), scattering diagrams have started playing an important role in mirror symmetry, in particular in the study of the reconstruction problem. This paper aims at introducing the main ideas on the subject describing the role of scattering diagrams in relation to the SYZ conjecture and the HMS conjecture.

Macca, E.; Russo, G.

2023 Bollettino dell Unione Matematica Italiana

doi: 10.1007/s40574-023-00387-3

In this work we compute the numerical solution of the Exner model of sedimentation when a train of waves is imposed at the inflow boundary (E. Macca in Shock-Capturing methods: Well-Balanced Approximate Taylor and Semi-Implicit schemes. PhD thesis, Universit‘a degli Studi di Palermo, Palermo, (2022) and Major Revision, (2023)). The numerical solver is a second order finite-volume scheme, with semi-implicit time discretization based on Implicit-Explicit (IMEX) schemes, which guarantees better stability properties than explicit ones, still at a lower cost than fully implicit schemes. We show the effect of spurious reflected waves generated at the outflow edge of the computational domain, propose two remedies, and show how such spurious effects can be reduced by suitable non-reflecting boundary conditions.