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 $m$ of a Dirac manifold $M$, there is a well-defined transverse Poisson structure to the pre-symplectic leaf $P$ through $m$. 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 “quasi”-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 $k \geq 1$ 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 cúpula 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, taxonomía, morfología, glande, cúpula, Israel, Turquía