10,238 research outputs found

    Location of Poles for the Hastings-McLeod Solution to the Second Painlev\'{e} Equation

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    We show that the well-known Hastings-McLeod solution to the second Painlev\'{e} equation is pole-free in the region argx[π3,π3][2π3,4π3]\arg x \in [-\frac{\pi}{3},\frac{\pi}{3}]\cup [\frac{2\pi}{3},\frac{ 4 \pi}{3}], which proves an important special case of a general conjecture concerning pole distributions of Painlev\'{e} transcedents proposed by Novokshenov. Our strategy is to construct explicit quasi-solutions approximating the Hastings-McLeod solution in different regions of the complex plane, and estimate the errors rigorously. The main idea is very similar to the one used to prove Dubrovin's conjecture for the first Painlev\'{e} equation, but there are various technical improvements.Comment: 31 pages, 2 figures. Minor revision, to appear in Constructive Approximatio

    Social Capital in Rural China: Its Impact on Economic Development, Grassroots Governance, and Democratic Participation

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    Does social capital generate positive influences on economic development and democratic governance? This question has important theoretical and policy implications for the contemporary world, especially for the developing countries. The primary goals of this study are to investigate the stock of two types of social capital—bridging social capital and bonding social capital—in rural China, and furthermore to examine the impacts of these two types of social capital upon economic development, grassroots governance, and democratic participation in rural China. In this study bridging social capital has been measured by the participation in inclusive social networks and general trust among villagers, and bonding social capital has been measured by the participation in exclusive social networks (the clan organizations) and parochial trust among villagers. In terms of the stock of social capital, this study has found that: (1) the traditional, bonding social capital still has a very solid foundation in rural China; (2) the modern, bridging social capital is in formation in rural China, even though the stock of this type of social capital is very moderate. Case studies as well as a series of statistical analyses are applied to assess the impacts of different types of social capital. Based on a nation-wide survey of 410 villages in rural China, this study has indicated that both subjective norms and objective networks of the bridging social capital—the general trust and participation in inclusive social networks—have a significant and positive impact on economic development, grassroots governance, and democratic participation in rural China. However, both subjective norms and objective networks of the bonding social capital—the parochial trust and participation in exclusive networks (the clan organizations)—generate negative impacts on such domains

    Difluoro­[2-(quinolin-2-yl)phenolato]borane

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    The title compound, C15H10BF2NO, was synthesized by the reaction of 2-(quinolin-2-yl)phenol and boron trifluoride etherate. The quinoline ring system and the benzene ring are twisted, making a dihedral angle of 8.3 (2)°. In the crystal, π–π inter­actions between the aromatic rings [centroid–centroid distance = 3.638 (9) Å] link the mol­ecules into chains propagating in [100]
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