119 citations · 319 across the 41 of their papers we have counts for
56 papers
Generalized functions in a Non-Archimedean field
Vieri Benci
Ultrafunctions are generalized functions defined on a non-Archimedean field extending R. They provide a framework for treating problems that fall outside the classical theory of di…
Numbers and numerosities
Vieri Benci
We develop new aspects of the the of numerosity theory; more exactly, we emphasize its relation with the ordinal numbers, cardinal numbers, hyperreal numbers and surreal numbers. I…
The Euclidean Universe
Vieri Benci
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nons…
Euclidean numbers and numerosities
V. Benci, L. Luperi Baglini
Several different versions of the theory of numerosities have been introduced in the literature. Here, we unify these approaches in a consistent frame through the notion of set of…
An improved setting for generalized functions: fine ultrafunctions
Vieri Benci
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the…
A classical model for the Maxwell equations coupled with matter
Vieri Benci
We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein-Gordon equation. A simple linear interaction and a nonlinear perurbation…