Hadronic Events at LEP

The hadronic events collected by LEP between 1989 and 2000 have changed dramatically our understanding of QCD, which has now been established as a part of the Standard Model. Still in many sectors (nonperturbative in particular) science analysis needs to be completed, and some new studies are just starting.Comment: 4 pages; invited talk at the IFAE, Lecce (Italy), May 200

The Stern diatomic sequence via generalized Chebyshev polynomials

Let a(n) be the Stern's diatomic sequence, and let x1,...,xr be the distances between successive 1's in the binary expansion of the (odd) positive integer n. We show that a(n) is obtained by evaluating generalized Chebyshev polynomials when the variables are given the values x1+1, ..., xr+1, and we derive a formula expressing the same polynomials in terms of sets of increasing integers of alternating parity. We also show that a(n) = Det(Ir + Mr), where Ir is the rxr identity matrix, and Mr is the rxr matrix that has x1,...,xr along the main diagonal, then all 1's just above and below the main diagonal, and all the other entries are 0

Mathematical Contributions to the Dynamics of the Josephson Junctions: State of the Art and Open Problems

Mathematical models related to some Josephson junctions are pointed out and attention is drawn to the solutions of certain initial boundary problems and to some of their estimates. In addition, results of rigorous analysis of the behaviour of these solutions when the time tends to infinity and when the small parameter tends to zero are cited. These analyses lead us to mention some of the open problems.Comment: 11 page

GLAST, the Gamma-ray Large Area Space Telescope

GLAST, a detector for cosmic gamma rays in the range from 20 MeV to 300 GeV, will be launched in space in 2005. Breakthroughs are expected in particular in the study of particle acceleration mechanisms in space and of gamma ray bursts, and maybe on the search for cold dark matter; but of course the most exciting discoveries could come from the unexpected.Comment: 6 pages, 3 figures. Invited talk at the hird International Workshop "New Worlds in Astroparticle Physics", September 2000, University of the Algarve. Faro, Portugal. To be published in the Proceeding

On the transition from parabolicity to hyperbolicity for a nonlinear equation under Neumann boundary conditions

An integro differential equation which is able to describe the evolution of a large class of dissipative models, is considered. By means of an equivalence, the focus shifts to the perturbed sine- Gordon equation that in superconductivity finds interesting applications in multiple engineering areas. The Neumann boundary problem is considered, and the behaviour of a viscous term, defined by a high order derivative with small diffusion coefficient , is investigated. The Green function, expressed by means of Fourier series, is considered, and an estimate is achieved. Furthermore, some classes of solutions of the hyperbolic equation are determined, proving that there exists at least one solution with bounded derivatives. Results obtained prove that diffusion effects are bounded and tend to zero when e tends to zero.Comment: Meccanica (2018). arXiv admin note: text overlap with arXiv:1602.0907

A wave equation perturbed by viscous terms: fast and slow times diffusion effects in a Neumann problem

A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient {\epsilon}, is investigated. Results obtained prove that for slow time {\epsilon}t < 1 waves are propagated almost undisturbed, while for fast time t > 1 {\epsilon} diffusion effects prevail.Comment: Ricerche di Matematica (2018