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math.FA2013
Basic properties of ultrafunctions
Vieri Benci, Lorenzo Luperi Baglini
Ultrafunctions are a particular class of functions defined on a non-Archimedean field. They provide generalized solutions to functional equations which do not have any solutions am…
math.LO2013
Partition Regularity of Nonlinear Polynomials: a Nonstandard Approach
Lorenzo Luperi Baglini
In 2011, Neil Hindman proved that for every natural number the polynomial \begin{equation*} \sum_{i=1}^{n} x_{i}-\prod\limits_{j=1}^{m} y_{j} \end{equation*} has monochromati…