1,435 research outputs found

    Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results

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    We achieve a detailed understanding of the nn-sided planar Poisson-Voronoi cell in the limit of large nn. Let p_n{p}\_n be the probability for a cell to have nn sides. We construct the asymptotic expansion of logp_n\log {p}\_n up to terms that vanish as nn\to\infty. We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to leading order as nn\to\infty, and after appropriate scaling, these become independent random variables whose laws we determine; and to next order in 1/n1/n they have nontrivial long range correlations whose expressions we provide. The nn-sided cell tends towards a circle of radius (n/4\pi\lambda)^{\half}, where λ\lambda is the cell density; hence Lewis' law for the average area A_nA\_n of the nn-sided cell behaves as A_ncn/λA\_n \simeq cn/\lambda with c=1/4c=1/4. For nn\to\infty the cell perimeter, expressed as a function R(ϕ)R(\phi) of the polar angle ϕ\phi, satisfies d2R/dϕ2=F(ϕ)d^2 R/d\phi^2 = F(\phi), where FF is known Gaussian noise; we deduce from it the probability law for the perimeter's long wavelength deviations from circularity. Many other quantities related to the asymptotic cell shape become accessible to calculation.Comment: 54 pages, 3 figure

    Seleção de primers ISSR para análises genéticas em Tucumã-do-Pará (Astrocaryum vulgare Mart.).

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    Dentre as espécies oleaginosas existentes na Amazônia o tucumã (Astrocaryum vulgare Mart.) se destaca com grande potencialidade nas indústrias alimentícia, medicinal e como matéria prima ao mercado de biodiesel. Marcadores ISSR são utilizados em estudos de diversidade e variabilidade genética por não necessitarem de informação prévia da seqüência de DNA. Este trabalho teve como objetivo selecionar primers ISSR para análises genéticas em tucumã-do-pará. Foram aplicados 100 primers ISSR do Set 9 da UBC em cinco amostras de DNA de tucumã representantes de genótipos conservados no BAG da Embrapa Amazônia Oriental em Belém-PA. As PCR?s foram feitas em temperatura de anelamento padrão (Ta=47ºC). A análise foi feita visualmente considerando a amplificação ou não amplificação de produtos. Dos 100 primers 54 não amplificaram bandas. Dos 46 que revelaram produtos, 17 produziram bandas claras e inespecíficas, enquanto 29 primers revelaram bandas específicas. Com o presente estudo foi possível selecionar preliminarmente 26 primers capazes de amplificar regiões de A. vulgare, e sugere-se inicialmente, os primers ISSR UBC 890 e UBC 891 que melhor amplificaram, para estudos de divergência genética do tucumã-do-pará

    Diastereo-selectivity in diels–alder cycloadditions of erythrose benzylidene-acetal 1,3-Butadienes with maleimides

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    Maleimides were combined with D-erythrose benzylidene-acetal 1,3-butadienes 1 and 2 to study the facial selectivity of the Diels-Alder cycloadditions. The selectivity was found to be from moderate to good. The reaction diastereotopicity can be reversed with the temperature. Simultaneous coordination of diene 1, having a free hydroxyl group, and maleimide 3 to a chiral bimetallic Lewis acid catalyst (LACASA-DA reaction) occurs with complete diastereo-control to give a single adduct, using an extra chiral inductor either R- or S-BINOL.Thanks are due to FCT for project funding PTDC/QUI/67407/2006 and FCT and FEDER for funding the NMR spectrometer Bruker Avance III 400 as part of the National NMR Network. V. C. M. D. also thanks for PhD grant (SFRH/BD/61290/2009)
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