A geometrical construction for the polynomial invariants of some reflection groups

In these notes we investigate the rings of real polynomials in four variables, which are invariant under the action of the reflectiongroups [3,4,3] and [3,3,5]. It is well known that they are rationally generated in degree 2,6,8,12 and 2,12,20,30. We give a different proof of this fact by giving explicit equations for the generating polynomials.Comment: 10 page

Semileptonic B Decays in Babar

BaBar measurements involving semileptonic decays of B mesons are reviewed. Attention is focused on the extraction of |Vub| and |Vcb| elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Recent results of inclusive and exclusive approaches are presented.Comment: 6 pages, 4 figures, Contributed to 11th Lomonosov Conference on Elementary Particle Physic

Wada Dessins associated with Finite Projective Spaces and Frobenius Compatibility

\textit{Dessins d'enfants} (hypermaps) are useful to describe algebraic properties of the Riemann surfaces they are embedded in. In general, it is not easy to describe algebraic properties of the surface of the embedding starting from the combinatorial properties of an embedded dessin. However, this task becomes easier if the dessin has a large automorphism group. In this paper we consider a special type of dessins, so-called \textit{Wada dessins}. Their underlying graph illustrates the incidence structure of finite projective spaces \PR{m}{n}. Usually, the automorphism group of these dessins is a cyclic \textit{Singer group} $\Sigma_\ell$ permuting transitively the vertices. However, in some cases, a second group of automorphisms $\Phi_f$ exists. It is a cyclic group generated by the \textit{Frobenius automorphism}. We show under what conditions $\Phi_f$ is a group of automorphisms acting freely on the edges of the considered dessins.Comment: 23 page

LHCb Level-0 Trigger Detectors

The calorimeter and muon systems are essential components to provide a trigger for the LHCb experiment. The calorimeter system comprises a scintillating pad detector and pre-shower, followed by electromagnetic and hadronic calorimeters. The calorimeter system allows photons, electrons and hadrons to be identified, and their energy to be measured. The muon system consists of five measuring stations equipped with Multi-Wire Proportional Chambers (MWPCs) and triple-Gas Electron Multiplier (GEM) detectors, separated by iron filters. It allows the muons identification and transverse momentum measurement. The status of the two systems and their expected performance is presented.Comment: 4 pages, 2 figures, proceedings of "X Pisa Meeting on Advanced Detectors", May 21-27, 2006 La Biodola, Isola d'Elba (Italy

A cortical based model of perceptual completion in the roto-translation space

We present a mathematical model of perceptual completion and formation of subjective surfaces, which is at the same time inspired by the architecture of the visual cortex, and is the lifting in the 3-dimensional rototranslation group of the phenomenological variational models based on elastica functional. The initial image is lifted by the simple cells to a surface in the rototraslation group and the completion process is modelled via a diffusion driven motion by curvature. The convergence of the motion to a minimal surface is proved. Results are presented both for modal and amodal completion in classic Kanizsa images