22,319 research outputs found

    Normal approximation for nonlinear statistics using a concentration inequality approach

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    Let TT be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for TT are obtained. The bounds are the best possible for many known statistics. Applications to U-statistics, multisample U-statistics, L-statistics, random sums and functions of nonlinear statistics are discussed.Comment: Published at http://dx.doi.org/10.3150/07-BEJ5164 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Electron-doped phosphorene: A potential monolayer superconductor

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    We predict by first-principles calculations that the electron-doped phosphorene is a potential BCS-like superconductor. The stretching modes at the Brillouin-zone center are remarkably softened by the electron-doping, which results in the strong electron-phonon coupling. The superconductivity can be introduced by a doped electron density (n2Dn_{2D}) above 1.3×10141.3 \times10^{14} cm2^{-2}, and may exist over the liquid helium temperature when n2D>2.6×1014n_{2D}>2.6 \times10^{14} cm2^{-2}. The maximum critical temperature is predicted to be higher than 10 K. The superconductivity of phosphorene will significantly broaden the applications of this novel material

    A Reverse-Shock Model for the Early Afterglow of GRB 050525A

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    The prompt localization of gamma-ray burst (GRB) 050525A by {\em Swift} allowed the rapid follow-up of the afterglow. The observations revealed that the optical afterglow had a major rebrightening starting at 0.01\sim 0.01 days and ending at 0.03\sim 0.03 days, which was followed by an initial power-law decay. Here we show that this early emission feature can be interpreted as the reverse shock emission superposed by the forward shock emission in an interstellar medium environment. By fitting the observed data, we further constrain some parameters of the standard fireball-shock model: the initial Lorentz factor of the ejecta γ0>120\gamma_0>120, the magnetic energy fraction ϵB>4×106\epsilon_B>4\times10^{-6}, and the medium density n<2cm3n<2 {\rm cm^{-3}}. These limits are consistent with those from the other very-early optical afterglows observed so far. In principle, a wind environment for GRB 050525A is disfavored.Comment: 11 pages, 1 figure, accepted for publication in Ap