Collineation group as a subgroup of the symmetric group

Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the projective group and an arbitrary self-bijection of $\Psi$ transforming a triple of collinear points to a non-collinear triple. It is well-known from \cite{KantorMcDonough} that if $\Psi$ is finite then $H$ contains the alternating subgroup $\mathfrak{A}_{\Psi}$ of $\mathfrak{S}_{\Psi}$. We show in Theorem \ref{density} below that $H=\mathfrak{S}_{\Psi}$, if $\Psi$ is infinite.Comment: 9 page

On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes

The sensitivity of a search for sources of TeV neutrinos can be improved by grouping potential sources together into generic classes in a procedure that is known as source stacking. In this paper, we define catalogs of Active Galactic Nuclei (AGN) and use them to perform a source stacking analysis. The grouping of AGN into classes is done in two steps: first, AGN classes are defined, then, sources to be stacked are selected assuming that a potential neutrino flux is linearly correlated with the photon luminosity in a certain energy band (radio, IR, optical, keV, GeV, TeV). Lacking any secure detailed knowledge on neutrino production in AGN, this correlation is motivated by hadronic AGN models, as briefly reviewed in this paper. The source stacking search for neutrinos from generic AGN classes is illustrated using the data collected by the AMANDA-II high energy neutrino detector during the year 2000. No significant excess for any of the suggested groups was found.Comment: 43 pages, 12 figures, accepted by Astroparticle Physic

Search for stable quarks produced by the Tevatron

An experiment has been run at the Tevatron to search for stable fractionally charged particles (i.e., quarks) produced by the 800 GeV/c proton beam. The experiment was performed in two phases. In the first run, 1.0 x 10/sup 15/ protons passed through a series of four mercury targets which were distributed among several lead degraders. The lead degraders were arranged so that fractionally charged particles over a wide range of production angles, masses, and energies would stop in the mercury targets. A small amount of this mercury has been analyzed for fractional charge in an automated Millikan apparatus. A second run, which had an integrated proton intensity of 4.1 x 10/sup 13/, used liquid nitrogen tanks to stop any fractionally charged particles produced when the proton beam interacted in an upstream lead target. In the four tanks, electrically charged gold-plated glass fibers attracted and then trapped any fractional charges which were stopped in the liquid nitrogen. After the exposure, the wires were moved through small beads of mercury in which the gold was dissolved. One of these small beads of mercury also has been analyzed in the same Millikan apparatus. The results from the first run show that the upper limit for quark production is less than 1 x 10/sup -6/ quarks per proton interaction at 90% confidence limit, the results from the second run show that the upper limit is 9.3 x 10/sup -10/. The analysis of the mercury is continuing