30,919 research outputs found
High energy tau neutrinos: production, propagation and prospects of observations
High energy tau neutrinos with energy greater than several thousands of GeV
may be produced in some astrophysical sites. A summary of the intrinsic high
energy tau neutrino flux estimates from some representative astrophysical sites
is presented including the effects of neutrino flavor oscillations. The
presently envisaged prospects of observations of the oscillated high energy tau
neutrino flux are mentioned. In particular, a recently suggested possibility of
future observations of Earth-skimming high energy tau neutrinos is briefly
discussed.Comment: 4 pages, 2 figs, talk given at 28th International Cosmic Ray
Conference (ICRC 2003), Tsukuba, Japan, 31 July-7 Aug, 2003, appeared in its
proceedings edited by T. Kajita et al., HE, pp. 1431-143
Weak KAM theory for general Hamilton-Jacobi equations II: the fundamental solution under Lipschitz conditions
We consider the following evolutionary Hamilton-Jacobi equation with initial
condition: \begin{equation*} \begin{cases}
\partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=\phi(x), \end{cases}
\end{equation*} where . Under some assumptions on
the convexity of with respect to and the uniform Lipschitz of
with respect to , we establish a variational principle and
provide an intrinsic relation between viscosity solutions and certain minimal
characteristics. By introducing an implicitly defined {\it fundamental
solution}, we obtain a variational representation formula of the viscosity
solution of the evolutionary Hamilton-Jacobi equation. Moreover, we discuss the
large time behavior of the viscosity solution of the evolutionary
Hamilton-Jacobi equation and provide a dynamical representation formula of the
viscosity solution of the stationary Hamilton-Jacobi equation with strictly
increasing with respect to
Crystal of affine and Hecke algebras at a primitive th root of unity
Let with and . In
this paper we give a new realization of the crystal of affine
using the modular representation theory of the
affine Hecke algebras of type and their level two cyclotomic
quotients with Hecke parameter being a primitive th root of unity. We
categorify the Kashiwara operators for the crystal as the functors of taking
socle of certain two-steps restriction and of taking head of certain two-steps
induction. For any finite dimensional irreducible -module , we prove
that the irreducible submodules of which belong to
(Definition 6.1) occur with multiplicity two. The main
results generalize the earlier work of Grojnowski and Vazirani on the relations
between the crystal of affine and the affine
Hecke algebras of type at a primitive th root of unity
A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations
In this paper, we consider the following Hamilton-Jacobi equation with
initial condition: \begin{equation*} \begin{cases}
\partial_tu(x,t)+H(x,t,u(x,t),\partial_xu(x,t))=0, u(x,0)=\phi(x). \end{cases}
\end{equation*} Under some assumptions on the convexity of w.r.t.
, we develop a dynamical approach to viscosity solutions and show that there
exists an intrinsic connection between viscosity solutions and certain minimal
characteristics.Comment: This paper has been withdrawn by the author due to a crucial error in
Lemma 3.
Weak KAM theory for general Hamilton-Jacobi equations III: the variational principle under Osgood conditions
We consider the following evolutionary Hamilton-Jacobi equation with initial
condition: \begin{equation*} \begin{cases}
\partial_tu(x,t)+H(x,u(x,t),\partial_xu(x,t))=0,\\ u(x,0)=\phi(x), \end{cases}
\end{equation*} where . Under some assumptions on
the convexity of with respect to and the Osgood growth of
with respect to , we establish an implicitly variational
principle and provide an intrinsic relation between viscosity solutions and
certain minimal characteristics. Moreover, we obtain a representation formula
of the viscosity solution of the evolutionary Hamilton-Jacobi equation
A hybrid partial sum computation unit architecture for list decoders of polar codes
Although the successive cancelation (SC) algorithm works well for very long
polar codes, its error performance for shorter polar codes is much worse.
Several SC based list decoding algorithms have been proposed to improve the
error performances of both long and short polar codes. A significant step of SC
based list decoding algorithms is the updating of partial sums for all decoding
paths. In this paper, we first proposed a lazy copy partial sum computation
algorithm for SC based list decoding algorithms. Instead of copying partial
sums directly, our lazy copy algorithm copies indices of partial sums. Based on
our lazy copy algorithm, we propose a hybrid partial sum computation unit
architecture, which employs both registers and memories so that the overall
area efficiency is improved. Compared with a recent partial sum computation
unit for list decoders, when the list size , our partial sum computation
unit achieves an area saving of 23\% and 63\% for block length and
, respectively.Comment: 5 pages, presented at the 2015 IEEE International Conference on
Acoustics, Speech, and Signal Processing (ICASSP
Variational principle for contact Tonelli Hamiltonian systems
We establish an implicit variational principle for the equations of the
contact flow generated by the Hamiltonian with respect to the
contact 1-form under Tonelli and Osgood growth assumptions. It
is the first step to generalize Mather's global variational method from the
Hamiltonian dynamics to the contact Hamiltonian dynamics.Comment: arXiv admin note: text overlap with arXiv:1408.379
Comparison of high-energy galactic and atmospheric tau neutrino flux
We compare the tau neutrino flux arising from the galaxy and the earth
atmosphere for 10^3 < E/GeV < 10^11. The intrinsic and oscillated tau neutrino
fluxes from both sources are calculated. The intrinsic galactic \nu_{\tau} flux
(E > 10^3 GeV) is calculated by considering the interactions of high-energy
cosmic-rays with the matter present in our galaxy, whereas the oscillated
galactic \nu_{\tau} flux is coming from the oscillation of the galactic
\nu_{\mu} flux. For the intrinsic atmospheric \nu_{\tau} flux, we extend the
validity of a previous calculation from E < 10^6 GeV up to E < 10^11 GeV. The
oscillated atmospheric \nu_{\tau} flux is, on the other hand, rather
suppressed. We find that, for 10^3 < E/GeV < 5\cdot 10^7, the oscillated
\nu_{\tau} flux along the galactic plane dominates over the maximal intrinsic
atmospheric \nu_{\tau} flux, i.e., the flux along the horizontal direction. We
also briefly mention the presently envisaged prospects for observing these
high-energy tau neutrinos.Comment: 12 pages, 4 figures, comparison with atmospheric tau neutrino flux
adde
Large N_c Expansion in Chiral Quark Model of Mesons
We study SU(3)_L\timesSU(3)_R chiral quark model of mesons up to the next
to leading order of expansion. Composite vector and axial-vector mesons
resonances are introduced via non-linear realization of chiral SU(3) and vector
meson dominant. Effects of one-loop graphs of pseudoscalar, vector and
axial-vector mesons is calculated systematically and the significant results
are obtained. We also investigate correction of quark-gluon coupling and
relationship between chiral quark model and QCD sum rules. Up to powers four of
derivatives, chiral effective lagrangian of mesons is derived and evaluated to
the next to leading order of . Low energy limit of the model is
examined. Ten low energy coupling constants in ChPT are
obtained and agree with ChPT well.Comment: 49 pages, latex file, 6 eps figure
Solutions to the ABS lattice equations via generalized Cauchy matrix approach
The usual Cauchy matrix approach starts from a known plain wave factor vector
and known dressed Cauchy matrix . In this paper we start from a matrix
equation set with undetermined and . From the starting equation set we
can build shift relations for some defined scalar functions and then derive
lattice equations. The starting matrix equation set admits more choices for
and and in the paper we give explicit formulae for all possible and
. As applications, we get more solutions than usual multi-soliton solutions
for many lattice equations including the lattice potential KdV equation, the
lattice potential modified KdV equation, the lattice Schwarzian KdV equation,
NQC equation and some lattice equations in ABS list.Comment: 24 page
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