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1. Introduction. Compound decision theory and empirical Bayes methodology , acclaimed as " two breakthroughs " by Neyman (1962), are the most important contributions of Herbert Robbins to statistics. The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related(More)
Let X;Xn, n ≥ 1, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers n−k/p ∑ 1≤i1<i2<···<ik≤n Xi1Xi2 : : :Xik → 0 a.s. for k = 2 without regularity conditions on X, for k ≥ 3 in three cases: (i) symmetric X, (ii) P”X ≥ 0• = 1 and (iii) regularly varying P”ŽXŽ(More)
Suspension cultures of Taxus yunnanensis cells were inoculated with cells of different culture ages (12–24 days) at various densities [50–250 g fresh weight (fw)/l], and treated (on day 7) with a mixture of elicitors, including Ag+, chitosan and methyl jasmonate. The biomass productivity (during the production stage) increased dramatically with inoculum(More)
Points P1, . . . , Pn in the unit square define a convex n-chain if they are below y = x and, together with P0 = (0, 0) and Pn+1 = (1, 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established by(More)
The surface dynamics and thermodynamics of metal nanowires are investigated in a continuum model. Competition between surface tension and electron-shell effects leads to a rich stability diagram, with fingers of stability extending to extremely high temperatures for certain magic conductance values. The linearized dynamics of the nanowire’s surface are(More)
The release of conduction-band electrons from a metal surface by a subfemtosecond extreme ultraviolet (XUV) pulse and their propagation through the solid provoke a dielectric response in the solid that acts back on the photoelectron wave packet. We calculated the (wake) potential associated with this photoelectron self-interaction in terms of bulk and(More)
This study aimed to investigate the absorption mechanism of three curcumin constituents in rat small intestines. Self-emulsification was used to solubilize the three curcumin constituents, and the rat in situ intestinal perfusion method was used to study factors on drug absorption, including drug mass concentration, absorption site, and the different types(More)
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