Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I

We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.Comment: Presented on International conference "Order, Algebra and Logics", Vanderbilt University, 12-16 June, 2007 25 pages, 2 figure

TeV gamma-UHECR anisotropy by decaying nuclei in flight: first neutrino traces?

Ultra High Cosmic Rays) made by He-like lightest nuclei might solve the AUGER extragalactic clustering along Cen A. Moreover He like UHECR nuclei cannot arrive from Virgo because the light nuclei fragility and opacity above a few Mpc, explaining the Virgo UHECR absence. UHECR signals are spreading along Cen-A as observed because horizontal galactic arms magnetic fields, bending them on vertical angles. Cen A events by He-like nuclei are deflected as much as the observed clustered ones; proton will be more collimated while heavy (iron) nuclei are too much dispersed. Such a light nuclei UHECR component coexist with the other Auger heavy nuclei and with the Hires nucleon composition. Remaining UHECR spread group may hint for correlations with other gamma (MeV-Al^{26} radioactive) maps, mainly due to galactic SNR sources as Vela pulsar, the brightest, nearest GeV source. Other nearest galactic gamma sources show links with UHECR via TeV correlated maps. We suggest that UHECR are also heavy radioactive galactic nuclei as Ni^{56}, Ni^{57} and Co^{60} widely bent by galactic fields. UHECR radioactivity (in $\beta$ and $\gamma$ channels) and decay in flight at hundreds keV is boosted (by huge Lorentz factor (nearly a billion) leading to PeVs electrons and consequent synchrotron TeVs gamma offering UHECR-TeV correlated sky anisotropy. Moreover also rarest and non-atmospheric electron and tau neutrinos secondaries at PeVs, as the first two rarest shower just discovered in ICECUBE, maybe the first signature of such expected radioactive secondary tail.Comment: 7 pages,3 figures. arXiv admin note: substantial text overlap with arXiv:1201.015

Resolution of puzzles from the LSND, KARMEN, and MiniBooNE experiments

This work has attempted to reconcile puzzling neutrino oscillation results from the LSND, KARMEN and MiniBooNE experiments. We show that the LSND evidence for $\bar{\nu}_\mu \to \bar{\nu}_e$ oscillations, its long-standing disagreement with the results from KARMEN, and the anomalous event excess observed by MiniBooNE in $\nu_\mu$ and $\bar{\nu}_\mu$ data could all be explained by the existence of a heavy sterile neutrino ($\nu_h$). All these results are found to be consistent with each other assuming that the $\nu_h$ is created in $\nu_\mu$ neutral-current interactions and decays radiatively into a photon and a light neutrino. Assuming the $\nu_h$ is produced through mixing with $\nu_\mu$, the combined analysis of the LSND and MiniBooNe excess events suggests that the $\nu_h$ mass is in the range from 40 to 80 MeV, the mixing strength is $|U_{\mu h}|^2 \simeq 10^{-3}-10^{-2}$, and the lifetime is $\tau_{\nu_h} \lesssim 10^{-9}$ s. Surprisingly, this LSND-MiniBooNE parameters window is found to be unconstrained by the results from the most sensitive experiments searching for heavy neutrino. We set new limits on $|U_{\mu h}|^2$ for the LSND-MiniBooNE favorable mass region from the precision measurements of the Michel spectrum by the TWIST experiment. The results obtained provide a strong motivation for a sensitive search for the $\nu_h$ in a near future $K$ decay or neutrino experiments, which fit well in the existing/planned experimental programs at CERN or FNAL. The question of whether the heavy neutrino is Dirac or Majorana particle is briefly discussed.Comment: 24 pages, 28 figures, version to appear in PR