3,613 research outputs found

    Stable minimal hypersurfaces in RN+1+\mathbb{R}^{N+1+\ell} with singular set an arbitrary closed KK in {0}×R\{0\}\times\mathbb{R}^{\ell}

    Full text link
    With respect to a CC^{\infty} metric which is close to the standard Euclidean metric on RN+1+\mathbb{R}^{N+1+\ell}, where N7N\ge 7 and 1\ell\ge 1 are given, we construct a class of embedded (N+)(N+\ell)-dimensional hypersurfaces (without boundary) which are minimal and strictly stable, and which have singular set equal to an arbitrary preassigned closed subset K{0}×RK\subset\{0\}\times\mathbb{R}^{\ell}.Comment: Expository improvements. To appear in Annals of Mat

    The political economy of violence: the case of Venezuela

    Get PDF
    This thesis will attempt to answer the question of how can the rise in social violence be explained in the oil-rich nation of Venezuela since the 1980s? The once relatively peaceful nation of Venezuela has seen a dramatic rise in social violence over the last three decades that has placed her amongst some of the world\u27s most dangerous countries. A review of the relevant literature will reveal that the study of a social phenomenon such as violence, and in a nation such as Venezuela, is a complicated task because there are a number of different but in many cases interlinked variables that contribute to the formation of this social phenomenon. Therefore the conceptual framework will consist of a multi-variable analysis so that this study may go about to formulate an appropriate explanation based on the complex causes and effects that surround this issue. However, special attention will be given to the nation\u27s developmental history has given way to a severe socio-political crisis. But although special attention will be given to this important variable, no hierarchy of variables will be established as the convoluted nature of social events makes it very difficult to formulate one. Other factors that will also be analyzed as they contribute to the rise of social violence are: the nation\u27s vast hydrocarbon wealth (which is always an outstanding variable because of its economic importance), economic reform and liberalization, and the urbanization process. Although there have been several studies on oil-rich nations (including Venezuela), their economic dynamics, the Latin American urbanization process, and the Venezuelan political crisis, there is an absence of studies that include these intervening factors in a comprehensive manner. This thesis hopes to fill this gap

    The Symmetric Minimal Surface Equation

    Full text link
    For positive functions uC2(Ω)u\in C^{2}(\Omega) , where Ω\Omega is an open subset of Rn\mathbb{R}^{n}, the Symmetric Minimal Surface Equation (SME), is i=1nDi(Diu1+Du2)=m1u1+Du2\sum_{i=1}^{n}D_{i}\bigl(\frac{D_{i}u}{\sqrt{1+|Du|^{2}}}\bigr)=\frac{m-1}{u\sqrt{1+|Du|^{2}}}. Geometrically, the SME expresses the fact that the ``symmetric graph'' SG(u)SG(u), defined by SG(u)={(x,ξ)Ω×Rm:ξ=u(x)}SG(u)=\bigl\{(x,\xi)\in \Omega\times\mathbb{R}^{m}:|\xi|=u(x)\bigr\}, is a minimal (i.e.\ zero mean curvature) hypersurface in Ω×Rm\Omega\times\mathbb{R}^{m}. A function uC1(Ω)u\in C^{1}(\Omega) is said to be a singular solution if u1{0}u^{-1}\{0\}\neq \emptyset, and if u=limjuju=\lim_{j\to\infty}u_{j}, uniformly on each compact subset of Ω\Omega, where each uju_{j} is a positive C2(Ω)C^{2}(\Omega) solution of the SME. The present paper develops are theory of singular solutions of the SME, including existence, H\"older and Lipschitz estimates for bounded solutions, and a compactness and regularity theory. We also prove that the singular set u1{0}u^{-1}{\{0\}} is codimension at most 2

    Impurity Effects in Highly Frustrated Diamond Lattice Antiferromagnets

    Get PDF
    We consider the effects of local impurities in highly frustrated diamond lattice antiferromagnets, which exhibit large but non-extensive ground state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an ordered magnetic ground state, and provide a mechanism of degeneracy breaking. The states which are selected can be determined by a "swiss cheese model" analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of the resulting ordered phase to a competing frozen (spin glass) one. The results may explain the contrasting finding of frozen and ordered ground states in CoAl2O4 and MnSc2S4, respectively.Comment: 13 pages, 7 figure

    Spatio-temporal metrics that distinguish plays in field hockey : a pilot study

    Get PDF
    In team invasion sports, tactical behaviour can be examined using spatio-temporal data, i.e. the position of the players at a given time. A review of the spatio-temporal metrics used in team invasion sports performance analysis indicated that thousands of variations of metrics being used. Information about the distribution of metrics' individual effects can inform us of the best variable-selection method. The aim of this pilot study was to estimate the distribution of strong marginal effects of spatio-temporal metrics of field hockey plays. With institutional ethical approval, the Womens’ and Mens’ gold medal games from the EuroHockey 2015 field hockey tournament were recorded. Best, acceptable and worst-case outcomes for plays were described by 1,837 spatio-temporal metrics. Each metric's marginal effects were estimated using Cramér's V, Mutual Information and the I-score. Values for Cramér's V of 0.2 and 0.4 to mark the boundaries of small, moderate and large effects. Less than 1% of metrics show large effects with > 87% of all metrics showing small effects as per the Cramér's V thresholds. These large effect metrics where all within the 98th percentile of Mutual Information values and within the 96th percentile of the I-score values, which supports the Cramér's V distribution of marginal effects. Therefore, according to the recommendations of Tibshirani (1996), univariate variable-selection methods will be the most appropriate for selecting important metrics

    The Costs and Benefits of Educating Children in Care.

    Get PDF

    Longitudinal Spin Asymmetry and Cross Section of Inclusive pi0 Production in Polarized p+p Collisions at RHIC

    Get PDF
    We present the first measurement of the cross section and the double longitudinal spin asymmetry of inclusive pi0 production in polarized p+p collisions at Sqrt(s) = 200 GeV at mid-rapidity with the STAR detector, using the barrel electromagnetic calorimeter. The measured cross section is compared to NLO pQCD calculations and can provide constraints on the pion fragmentation functions. Fragmentation is studied directly by measuring the momentum fraction of pi0 in jets, a quantity that is affected by the fragmentation process and jet reconstruction effects. The double longitudinal spin asymmetry is compared to NLO pQCD calculations based on different assumptions for the gluon polarization in the nucleon to provide constraints on delta g/g. At the present level of statistics the measured asymmetry disfavors a large positive gluon polarization, but can not yet distinguish between other scenarios.Comment: 4 pages, 2 figures, submitted to the proceedings of the 17th International Spin Physics Symposium (SPIN2006), Kyoto, Japan, October 2 to 7, 200
    corecore