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He is known for his contribution to real analysis, partly collected in his book "Fondamenti per la teorica delle funzioni di variabili reali".Dini attended the Scuola Normale Superiore in order to become a teacher. In 1865, a scholarship enabled him to visit Paris, where he studied under Charles Hermite as well as Joseph Bertrand, and published several papers.In 1866, he was appointed to the University of Pisa, where he taught algebra and geodesy.In 1871, he succeeded Betti as professor for analysis and geometry.In this paper, we develop some considerations concerning the structure of coalescence, breakage and volume ‘scattering’ kernels appearing in the evolution equation related to a new model for the dynamics of liquid–liquid dispersions and show some numerical simulations.