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CARLO BENASSI

Ricercatore Universitario
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica

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Pubblicazioni

2023 - Aree e volumi: si può sempre misurare? [Articolo su rivista]
Benassi, Carlo; Eleuteri, Michela; Lussardi, Luca
abstract

2023 - La retta di regressione incontra l'Intelligenza Artificiale [Relazione in Atti di Convegno]
Ferri, Caterina; Benassi, Carlo; Eleuteri, Michela; Monari, Pietro
abstract

2022 - A scuola di Intelligenza Artificiale [Relazione in Atti di Convegno]
Benassi, Carlo; Eleuteri, Michela; Ferri, Caterina; Monari, Pietro
abstract

2021 - Il concetto di tangenza: un percorso verticale a partire dalla scuola primaria [Relazione in Atti di Convegno]
Benassi, Carlo 6/8/1962; Eleuteri, Michela; Ferri, Caterina
abstract

2021 - The fundamental theorem of integral calculus: a Volterra’s generalization applied to flat functions [Articolo su rivista]
Benassi, Carlo 6/8/1962; Eleuteri, Michela
abstract

2020 - Lipschitz continuity results for a class of obstacle problems [Articolo su rivista]
Benassi, C.; Caselli, M.
abstract

We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of p-type, p b 2. The main novelty is the use of a linearization technique going back to [28] in order to interpret our constrained minimizer as a solution to a nonlinear elliptic equation, with a bounded right hand side. This lead us to start a Moser iteration scheme which provides the Ll bound for the gradient. The application of a recent higher di¤erentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowdledge, this is the first result for nonautomonous functionals with standard growth conditions in the direction of the Lipschitz regularity.

2010 - COVARIOGRAM OF NON-CONVEX SETS [Articolo su rivista]
Benassi, Carlo 6/8/1962; G., Bianchi; G., D’Ercole
abstract

The covariogram of a compact subset A of R(n) is the function that to each x associates the volume of the intersection of A and (A+x). Recently it has been proved that the covariogram determines any planar convex body, in the class of all convex bodies. We extend the class of sets in which a planar convex body is determined by its covariogram. Moreover, we prove that there is no pair of non-congruent planar polyominoes consisting of less than nine points that have equal discrete covariograms.

2008 - The sum of squared distances under a diameter constraint, in arbitrary dimension [Articolo su rivista]
Benassi, Carlo 6/8/1962; Malagoli, Federica
abstract

It has been conjectured by H. S. Witsenhausen that the maximum M(d,n) of $\sum_{x,y \in X} \|x−y\|_2$ over all sets X consistingof n points in the d-dimensional Euclidean space with unit diameter is attained if and only if the points of X are distributed as evenly as possible among the vertices of a regular d-dimensional simplex of edge-length 1. In this paper the authors give a proof of this conjecture.

2007 - An algorithm for reconstructing a convex polygon from its covariogram [Articolo su rivista]
Benassi, Carlo 6/8/1962; D'Ercole, Giuliana
abstract

The covariogram $g_{K}(x)$ of a convex body $K$ gives the volume of the intersections of $K$ with its translates $K+x$. Matheron conjectured in 1986 that the covariogram determines, up to translations and reflections, a convex body. Recently, Averkov and Bianchi proved Matheron's conjecture for arbitrary planar convex bodies. In this work, the authors give a new algorithm for reconstructing a convex polygon given its covariogram. This algorithm simplifies another one given in [M. Schmitt, in Mathematical morphology in image processing, 151--169, Dekker, New York, 1993].

2002 - Hybrid stabilization of planar linear systems with one-dimensional outputs [Articolo su rivista]
Benassi, Carlo 6/8/1962; Gavioli, Andrea
abstract

We consider a linear control system x'=Ax+Bu with output y=Cx, where x is two-dimensional, u,y are one-dimensional, and give necessary and sufficient conditions in order that it can be stabilized by a hybrid, linear feedback, where the action of the "switch" just depends on the sign of y. We also show, on these conditions, that the use of two control functions is enough for getting the goal.

2000 - Approximation from the Exterior of Caratheodory Multifunctions [Articolo su rivista]
Benassi, Carlo 6/8/1962; Gavioli, Andrea
abstract

We approximate a globally measurable multifunction F(t,x) which takes compact values in a euclidean space by means of a decreasing sequence of globally measurable multifunctions F_n(t,x) which are locally lipschitzian with respect to x, in the following cases: F(t,\cdot) is upper semicontinuous and takes connected values, or F(t,\cdot) is continuous.

1995 - A Metric Characterization of Convex Bodies [Articolo su rivista]
Benassi, Carlo 6/8/1962; M., Boni; Gavioli, Andrea
abstract

We show that a subset C of the euclidean space which agrees with the closure of its interior is convex if and only if for everyconvex body D which meets its interior it is possibleto control, in a suitable way, the distance of a point from the intersection between C and D by means of its respectivedistances from C and D.

1994 - Approximation from the Exterior of Multifunctions with Connected Values [Articolo su rivista]
Benassi, Carlo 6/8/1962; Gavioli, Andrea
abstract

We approximate an upper semicontinuous multifunction F from a metric space T into the compact, connected subsets of a euclidean space by means of a decreasing sequence ofmultifunctions which are locally lipschitzean with respect to theHausdorff distance.

1994 - Approximation from the Exterior of a Multifunction with connected Values Defined on an Interval [Articolo su rivista]
Benassi, Carlo 6/8/1962; Gavioli, Andrea
abstract

We approximate an upper semicontinuous multifunction F(t) from the interval [0,1] into the compact, connected subsets of a euclidean space by means of a decreasing sequence of multifunctions which are lipschitzian with respect to the Hausdorff distance.

1987 - Some Results about Relaxation of Integral Functionals [Articolo su rivista]
Benassi, Carlo 6/8/1962; Gavioli, Andrea
abstract

We give a representation formula for the integrand of the relaxed functional of the integral of the Calculus of Variations, in the case in which it is defined on vector functions of a real variable.