1,570 research outputs found

    On the Margulis constant for Kleinian groups, I curvature

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    The Margulis constant for Kleinian groups is the smallest constant cc such that for each discrete group GG and each point xx in the upper half space H3{\bold H}^3, the group generated by the elements in GG which move xx less than distance c is elementary. We take a first step towards determining this constant by proving that if ⟹f,g⟩\langle f,g \rangle is nonelementary and discrete with ff parabolic or elliptic of order n≄3n \geq 3, then every point xx in H3{\bold H}^3 is moved at least distance cc by ff or gg where c=.1829
c=.1829\ldots. This bound is sharp

    Apparatus for purging systems handling toxic, corrosive, noxious and other fluids Patent

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    Fluid transferring system design for purging toxic, corrosive, or noxious fluids and fumes from materials handling equipment for cleansing and accident preventio

    The Fatou Theorem for Functions Harmonic in a Half‐Space

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135177/1/plms0149.pd

    Hausdorff Dimension and Quasiconformal Mappings

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135677/1/jlms0504.pd

    Angles and Quasiconformal Mappings†

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135391/1/plms0001.pd

    Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement

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    The transformations of functions acting on sublevel sets that satisfy a P\'olya-Szeg\H{o} inequality are characterized as those being induced by transformations of sets that do not increase the associated capacity.Comment: 9 page

    Advantageous use of metallic cobalt in the target for Pulsed Laser Deposition of cobalt-doped ZnO films

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    We investigate the magnetic properties of ZnCoO thin films grown by pulsed laser deposition (PLD) from targets made containing metallic Co or CoO precursors instead of the usual Co3O4. We find that the films grown from metallic Co precursors in an oxygen rich environment contain negligible amounts of Co metal, and have a large magnetization at room temperature. Structural analysis by X-ray diffraction and magneto-optical measurements indicate that the enhanced magnetism is due, in part, from Zn vacancies that partially compensate the naturally occurring n-type defects. We conclude that strongly magnetic films of Zn0.95Co0.05O that do not contain metallic cobalt can be grown by PLD from Co-metal-precursor targets if the films are grown in an oxygen atmosphere

    Anomalous transverse acoustic phonon broadening in the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O_3

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    The intrinsic linewidth ΓTA\Gamma_{TA} of the transverse acoustic (TA) phonon observed in the relaxor ferroelectric compound Pb(Mg1/3_{1/3}Nb2/3)0.8_{2/3})_{0.8}Ti0.2_{0.2}O3_3 (PMN-20%PT) begins to broaden with decreasing temperature around 650 K, nearly 300 K above the ferroelectric transition temperature TcT_c (∌360\sim 360 K). We speculate that this anomalous behavior is directly related to the condensation of polarized, nanometer-sized, regions at the Burns temperature TdT_d. We also observe the ``waterfall'' anomaly previously seen in pure PMN, in which the transverse optic (TO) branch appears to drop precipitously into the TA branch at a finite momentum transfer qwf∌0.15q_{wf} \sim 0.15 \AA−1^{-1}. The waterfall feature is seen even at temperatures above TdT_d. This latter result suggests that the PNR exist as dynamic entities above TdT_d.Comment: 6 pages, 4 figure

    Fractional Sobolev-Poincaré inequalities in irregular domains

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    This paper is devoted to the study of fractional (q, p)-Sobolev-PoincarĂ© in- equalities in irregular domains. In particular, the author establishes (essentially) sharp fractional (q, p)-Sobolev-PoincarĂ© inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for the usual derivatives. Furthermore, the author verifies that those domains which support the fractional (q, p)-Sobolev-PoincarĂ© inequalities together with a separation property are s-diam John domains for certain s, depending only on the associated data. An inaccurate statement in [Buckley, S. and Koskela, P., Sobolev-PoincarĂ© implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out