Locality and Bell's inequality

We prove that the locality condition is irrelevant to Bell in equality. We check that the real origin of the Bell's inequality is the assumption of applicability of classical (Kolmogorovian) probability theory to quantum mechanics. We describe the chameleon effect which allows to construct an experiment realizing a local, realistic, classical, deterministic and macroscopic violation of the Bell inequalities.Comment: 23 pages, Plain TeX, A talk given at Capri conference, July 2000, Corrected and Extended versio

Separable solutions of quasilinear Lane-Emden equations

For $0 < p-1 < q$ and $\ge=\pm 1$, we prove the existence of solutions of -\Gd_pu=\ge u^q in a cone $C_S$, with vertex 0 and opening $S$, vanishing on \prt C_S, under the form u(x)=|x|^\gb\gw(\frac{x}{|x|}). The problem reduces to a quasilinear elliptic equation on $S$ and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral type identity.Comment: To appear in Journal of the European Mathematical Societ

The full coverage approach to the detection of Extensive Air Showers

A shower array exploiting the full coverage approach with a high segmentation of the readout allow to image the front of atmospheric showers with unprecedented resolution and detail. The grid distance determines the energy threshold (small energy showers are lost in the gap between detectors) and the quality of the shower sampling. Therefore, this experimental solution is needed to detect showers with a threshold in the 100 GeV range. The full coverage approach has been exploited in the ARGO-YBJ experiment. In this contribution we will summarise the advantages of this technique and discuss possible applications in new wide field of view detectors.Comment: Invited Talk to 21st International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 202