4,949 research outputs found
Ultra high energy neutrinos: the key to ultra high energy cosmic rays
We discuss the relation between the acceleration spectra of extragalactic
cosmic ray protons and the luminosity and cosmological evolution of their
sources and the production of ultra high energy cosmogenic neutrinos in their
propagation from the sources to us.Comment: 12 pages, 5 figures, Talk presented at the Vulcano06 workshop. Second
version with some typos remove
The beginning of cosmic ray astronomy
We discuss the anisotropic arrival directions of the ultra high energy cosmic
rays detected by Auger which I consider one of the biggest discoverie in
astrophysics during the last year.Comment: 5 pages, 2 figures, Concluding remarks at the Vulcano2008 worksho
The additive group of the rationals does not have an automatic presentation
We prove that the additive group of the rationals does not have an automatic
presentation. The proof also applies to certain other abelian groups, for
example, torsion-free groups that are -divisible for infinitely many primes
, or . The proof is combinatorial and uses most notably Freiman's
theorem on sets with small doubling.Comment: 11 page
The Eynard--Orantin recursion for the total ancestor potential
It was proved recently that the correlation functions of a semi-simple
cohomological field theory satisfy the so called Eynard--Orantin topological
recursion. We prove that in the settings of singularity theory, the relations
can be expressed in terms of periods integrals and the so called phase forms.
In particular, we prove that the Eynard-Orantin recursion is equivalent to
copies of Virasoro constraints for the ancestor potential, which follow easily
from the definition of the potential.Comment: 18 pages. arXiv admin note: text overlap with arXiv:1203.341
Ultra high energy cosmic rays and neutrinos after Auger
We discuss the main results that were recently published by the Auger
Collaboration and their impact on our knowledge of the ultra high energy cosmic
rays and neutrinos.Comment: 12 pages, 4 figures, Talk at the Vulcano 2008 meeting "Frontier
objects in astrophysics and particle physics", Vulcano, Ital
The IceTop experiment in 2010
We present the current status of the IceTop air shower array on top of the
IceCube neutrino detector that IceTop can use as a huge detector of TeV muons.
We laos give a brief discussion of different types of air shower events that
contain information on the spectrum and composition of the cosmic rays in a
wide energy range.Comment: 6 pages, 2 figures, presented at the Vulcano 2010 workshop, Vulcano,
Ital
Atmospheric neutrino challenges
We briefly review the improvements in the predictions of atmospheric neutrino
fluxes since the NOW2000 workshop. In spite of the great progress in
calculational technique the predictions are still not exact because of the
uncertainties in the two major sets of input - cosmic ray flux and hadronic
interactions on light nuclei.Comment: 6 pages, 7 postscript figures, prepared for the NOW 2004 Proceeding
Possible tau appearance experiment with atmospheric neutrinos
We suggest an experimental measurement that could detect the appearance of
the tau neutrinos in muon to tau neutrino oscillations of atmospheric neutrinos
by measuring the energy spectra of neutrino induced showers. Tau neutrinos
deposit a large fraction of their energy in showers generated in
CC interactions and the subsequent tau--lepton decay.
The appearance of tau neutrinos will enhance the spectrum of neutrino induced
showers in energy ranges corresponding to the neutrino oscillation parameters.
A shower rate lower than the `no oscillation' prediction is an indication for
oscillations into sterile neutrinos.Comment: RevTeX, four pages with 4 postscript figure
Computing parabolically induced embeddings of semisimple complex Lie algebras in Weyl algebras
An arbitrary proper parabolic subalgebra of a simple complex
Lie algebra induces an embedding , and more generally an embedding , where is the Weyl
algebra in variables, is the dimension of the nilradical of , and is an arbitrary -module. We give an elementary
proof of this known fact, report on a computer program computing the
embeddings, and tabulate exceptional Lie algebra embeddings , , , , arising in this fashion
Pre-Plactic Algebra and Snakes
We study a factor Hopf algebra of the Malvenuto-Reutenauer
convolution algebra of functions on symmetric groups
that we coined
pre-plactic algebra. The pre-plactic algebra admits the Poirier-Reutenauer
algebra based on Standard Young Tableaux as a factor and it is closely related
to the quantum pseudo-plactic algebra introduced by Krob and Thibon in the
non-commutative character theory of quantum group comodules. The connection
between the quantum pseudo-plactic algebra and the pre-plactic algebra is
similar to the connection between the Lascoux-Sch\"utzenberger plactic algebra
and the Poirier-Reutenauer algebra. We show that the dimensions of the
pre-plactic algebra are given by the numbers of alternating permutations
(coined snakes after V.I. Arnold). Pre-plactic algebra is instrumental in
calculating the Hilbert-Poincar\'e series of the quantum pseudo-plactic
algebra.Comment: 12 pages. Comments are welcome
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