3,641 research outputs found
On the local structure of Dirac manifolds
We give a local normal form for Dirac structures. As a consequence, we show
that the dimensions of the pre-symplectic leaves of a Dirac manifold have the
same parity. We also show that, given a point of a Dirac manifold ,
there is a well-defined transverse Poisson structure to the pre-symplectic leaf
through . Finally, we describe the neighborhood of a pre-symplectic leaf
in terms of geometric data. This description agrees with that given by Vorobjev
for the Poisson caseComment: minor correction
Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms
In this paper, we derive simple point-optimal sign-based tests in the context of linear and
nonlinear regression models with fixed regressors. These tests are exact, distribution-free, robust
against heteroskedasticity of unknown form, and they may be inverted to obtain confidence
regions for the vector of unknown parameters. Since the point-optimal sign tests depend on the
alternative hypothesis, we propose an adaptive approach based on split-sample techniques in
order to choose an alternative such that the power of point-optimal sign tests is close to the
power envelope. The simulation results show that when using approximately 10% of sample to
estimate the alternative and the rest to calculate the test statistic, the power of point-optimal sign
test is typically close to the power envelope. We present a Monte Carlo study to assess the
performance of the proposed âquasiâ-point-optimal sign test by comparing its size and power to
those of some common tests which are supposed to be robust against heteroskedasticity. The
results show that our procedures are superior
Stability of higher order singular points of Poisson manifolds and Lie algebroids
We study the stability of singular points for smooth Poisson structures as
well as general Lie algebroids. We give sufficient conditions for stability
lying on the first (not necessarily linear) approximation of the given Poisson
structure or Lie algebroid at a singular point. The main tools used here are
the classical Lichnerowicz-Poisson cohomology and the deformation cohomology
for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide
several examples of stable singular points of order for Poisson
structures and Lie algebroids. Finally, we apply our results to pre-symplectic
leaves of Dirac manifolds.Comment: corrected typo
Cupule aud acorn basic morpbological differences between Quercus ithaburensis Decne. subsp. ithaburensis and Quercus ithaburensis subsp. macrolepis (Kotschy) Hedge & Yalt
Estructura del glande y de la cĂșpula de Quercus ithaburensis Decne. subsp. ithaburensis y de Quercus ithaburensis subsp. inacrolepis (Kotschy) Hedge & Yalt.: Diferencias esenciales.Key words. Quercus ithaburensis, taxonomy, morphology, acorn, cupule, Israel, Turkey.Palabras clave. Quercus ithaburensis, taxonomĂa, morfologĂa, glande, cĂșpula, Israel, TurquĂa
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