Salvatore Flavio Vassallo

INEQUALITIES FOR DUAL ISOPERIMETRIC DEFICITS

We study dual isoperimetric deficits of star bodies. We introduce the dual Steiner ball of a star body, and use it to establish an inequality for the L p distance, p = 2 and p = ∞, between the radial functions of two convex bodies. By applying this inequality, we find dual Bonnesen-type inequalities for convex bodies. Finally, we use a general form of Grusss inequality to derive dual Favard-type inequalities for star and convex bodies. The results contribute to the dual Brunn–Minkowski theory initiated by E. Lutwak, and continue the attempt to understand the relation between this and the classical Brunn–Minkowski theory.

A covering problem for plane lattices

AbstractLet ℒ be a plane lattice and {v1, v2} a Minkowski reduced base of ℒ. In this note we prove that if a convex body K has minimal width w(K) ≥ |v2| sin ϕ+|v1|(

Some problems of non uniform geometric probability relative to plane lattices

\sqrt 3 /2

The Brunn–Minkowski Inequality, Minkowski's First Inequality, and Their Duals☆☆☆

), where ϕ is the acute angle between v1 and v2, then K is a covering set for ℒ.

Test online di matematica: il Progetto M.In.E.R.Va

The M.In.E.R.Va. project, which was presented at EDULEARN 2014 and 2016, was developed to help students of secondary schools to recover their deficiencies in Mathematics. As the experimentation has produced good results, we extended the project to Calculus and Financial Mathematics courses in Catholic University in Milan. We will use Rasch Analysis and other statistical techniques (e.g. Classical Test Theory and Item Response Theory) to prove the “goodness” of the multiple-choice questions that we used in the online exercises and to perform a differential analysis, dividing students in subgroups, in order to individuate the “disturbing” variables. We found that a few questions were problematic. In this case, the common approach is to change the question. We preferred instead to change the didactic approach to the subject of the question and to change the question only if the performance remains low. Since this trial showed quite good results, we can conclude that the platform can be successfully used to point out early problematic subjects and to intervene immediately.

Minimal properties for convex annuli of plane convex curves

RésuméDans ce travail on déterminera la probabilité pour qu’un cercle aléatoire coupe un réseau de points ou de droites ou de rectangles dans le plan euclidien si les coordonnées du centre du cercle suivent la loi de probabilité de densité la fonction

THE M.IN.E.R.VA. PROJECT

f(x, y) = \frac{1}{4}e^{ - |x - x_0 | - |y - y_0 |}