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    Some notes on degree spectra of the structures

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    In the paper the problem of existence of an algebraic structure with the degree spectra {x: x ≮ b} is studied for arbitrary degree b. © Springer-Verlag Berlin Heidelberg 2007

    Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe

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    The Standard Model of particle physics assumes that the so-called fundamental constants are universal and unchanging. Absorption lines arising in molecular clouds along quasar sightlines offer a precise test for variations in the proton-to-electron mass ratio, mu, over cosmological time and distance scales. The inversion transitions of ammonia are particularly sensitive to mu compared to molecular rotational transitions. Comparing the available ammonia spectra observed towards the quasar B0218+357 with new, high-quality rotational spectra, we present the first detailed measurement of mu with this technique, limiting relative deviations from the laboratory value to |dmu/mu| < 1.8x10^{-6} (95% confidence level) at approximately half the Universe's current age - the strongest astrophysical constraint to date. Higher-quality ammonia observations will reduce both the statistical and systematic uncertainties in these measurements.Comment: Science, 20th June 2008. 22 pages, 5 figures (12 EPS files), 2 tables, including Supporting Online Material; v2: Corrected reference for laboratory mu-variation bound

    On differential graded categories

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    Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen and Toen-Vaquie.Comment: 30 pages, correction at the end of 3.9, corrections and added references in 5.

    A lower bound for coherences on the Brown-Peterson spectrum

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    We provide a lower bound for the coherence of the homotopy commutativity of the Brown-Peterson spectrum, BP, at a given prime p and prove that it is at least (2p^2 + 2p - 2)-homotopy commutative. We give a proof based on Dyer-Lashof operations that BP cannot be a Thom spectrum associated to n-fold loop maps to BSF for n=4 at 2 and n=2p+4 at odd primes. Other examples where we obtain estimates for coherence are the Johnson-Wilson spectra, localized away from the maximal ideal and unlocalized. We close with a negative result on Morava-K-theory.Comment: This is the version published by Algebraic & Geometric Topology on 26 February 200
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