30,919 research outputs found

    High energy tau neutrinos: production, propagation and prospects of observations

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    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

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    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 Ο•(x)∈C(M,R)\phi(x)\in C(M,\mathbb{R}). Under some assumptions on the convexity of H(x,u,p)H(x,u,p) with respect to pp and the uniform Lipschitz of H(x,u,p)H(x,u,p) with respect to uu, 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 H(x,u,p)H(x,u,p) with respect to uu

    Crystal of affine sl^β„“\widehat{\mathfrak{sl}}_{\ell} and Hecke algebras at a primitive 2β„“2\ellth root of unity

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    Let β„“βˆˆN\ell\in\mathbb{N} with β„“>2\ell>2 and I:=Z/2β„“ZI:=\mathbb{Z}/2\ell\mathbb{Z}. In this paper we give a new realization of the crystal of affine sl^β„“\widehat{\mathfrak{sl}}_{\ell} using the modular representation theory of the affine Hecke algebras HnH_n of type AA and their level two cyclotomic quotients with Hecke parameter being a primitive 2β„“2\ellth 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 HnH_n-module MM, we prove that the irreducible submodules of resHnβˆ’2HnM\rm{res}_{H_{n-2}}^{H_n}M which belong to B^(∞)\widehat{B}(\infty) (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 sl^β„“\widehat{\mathfrak{sl}}_{\ell} and the affine Hecke algebras of type AA at a primitive β„“\ellth root of unity

    A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations

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    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 H(x,t,u,p)H(x,t,u,p) w.r.t. pp, 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

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    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 Ο•(x)∈C(M,R)\phi(x)\in C(M,\mathbb{R}). Under some assumptions on the convexity of H(x,u,p)H(x,u,p) with respect to pp and the Osgood growth of H(x,u,p)H(x,u,p) with respect to uu, 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

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    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 L=4L=4, our partial sum computation unit achieves an area saving of 23\% and 63\% for block length 2132^{13} and 2152^{15}, 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

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    We establish an implicit variational principle for the equations of the contact flow generated by the Hamiltonian H(x,u,p)H(x,u,p) with respect to the contact 1-form Ξ±=duβˆ’pdx\alpha=du-pdx 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

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    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

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    We study SU(3)_L\timesSU(3)_R chiral quark model of mesons up to the next to leading order of 1/Nc1/N_c 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 1/Nc1/N_c. Low energy limit of the model is examined. Ten low energy coupling constants Li(i=1,2,...,10)L_i(i=1,2,...,10) 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

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    The usual Cauchy matrix approach starts from a known plain wave factor vector rr and known dressed Cauchy matrix MM. In this paper we start from a matrix equation set with undetermined rr and MM. 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 rr and MM and in the paper we give explicit formulae for all possible rr and MM. 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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