Beauty and charm physics at LEP

Recent results in charm and beauty physics at LEP are reported. They allow refined tests of strong and electroweak interactions. The importance of measuring as accurately as possible the apex of the unitarity is emphasized

Charm spectroscopy in DELPHI

The production of charmed particles has been studied using 3.5 milllion hadronic Z decays collected by the DELPHI collaboration at LEP between 1992 and 1995. Large samples of D meson decays have been exclusively reconstructed, allowing to look for D$^*pi$ and D$^*pipi$ final states. The production fractions of the narrow D$_1^0(2420)$ and D$_2^{*0}(2460)$ orbital states are measured in c and b quark jets separately. Evidence for a radial state D$^{*'}(2637)$ is presented in the D$^{*+}pi^+pi^-$ decay mode. %DB Interesting perspectives to look for the wide orbital states in semileptonic B %DB decays are discussed

Ordered and disordered dynamics in monolayers of rolling particles

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles with an offset center of mass and a non-isotropic inertia tensor. The rolling constraint is considered as a simplified model of a very strong, but rapidly decaying bond with the surface, preventing application of the standard tools of statistical mechanics. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We also investigate the dynamics of disordered gas states and show that there is a surprising and robust linear connection between distributions of angular and linear velocity for both lattice and gas states, allowing to define the concept of temperature

On one example and one counterexample in counting rational points on graph hypersurfaces

In this paper we present a concrete counterexample to the conjecture of Kontsevich about the polynomial countability of graph hypersurfaces. In contrast to this, we show that the "wheel with spokes" graphs $WS_n$ are polynomially countable