On idempotent generated semigroups

We provide short and direct proofs for some classical theorems proved by Howie, Levi and McFadden concerning idempotent generated semigroups of transformations on a finite set.Comment: three page

Dynamically generated baryon resonances

Identifying a zero-range exchange of vector mesons as the driving force for the s-wave scattering of pseudo-scalar mesons off the baryon ground states, a rich spectrum of molecules is formed. We argue that chiral symmetry and large-$N_c$ considerations determine that part of the interaction which generates the spectrum. We suggest the existence of strongly bound crypto-exotic baryons, which contain a charm-anti-charm pair. Such states are narrow since they can decay only via OZI-violating processes. A narrow nucleon resonance is found at mass 3.52 GeV. It is a coupled-channel bound state of the $(\eta_c N), (\bar D \Sigma_c)$ system, which decays dominantly into the $(\eta' N)$ channel. Furthermore two isospin singlet hyperon states at mass 3.23 GeV and 3.58 GeV are observed as a consequence of coupled-channel interactions of the $(\bar D_s \Lambda_c), (\bar D \Xi_c)$ and $(\eta_c \Lambda),(\bar D \Xi_c')$ states. Most striking is the small width of about 1 MeV of the lower state. The upper state may be significantly broader due to a strong coupling to the $(\eta' \Lambda)$ state. The spectrum of crypto-exotic charm-zero states is completed with an isospin triplet state at 3.93 GeV and an isospin doublet state at 3.80 GeV. The dominant decay modes involve again the $\eta'$ meson.Comment: Talk presented at N*2005, 10 pages, 1 figur