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

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

Regulation and Productivity in the Quebec Manufacturing Sector

We investigate the impact of occupational safety and health (OSH) and environmental regulation on the rate of growth of total factor productivity (TFP) in the Quebec manufacturing sector during the 1985-88 period. Our results show that environmental regulation and OSH protective reassignments (a prevention policy with respect to OSH) have led to a reduction in productivity growth, while the presence of mandatory prevention programs and of fines for infractions to OSH rules have led to an increase in productivity growth. Interestingly, this is, to our knowledge, the first result showing that OSH regulation may have had a positive effect on productivity growth. Nous évaluons l'impact qu'ont eu les réglementations en matière de santé et sécurité du travail et d'environnement sur la croissance de la productivité totale des facteurs (PTF) du secteur manufacturier québécois au cours des années 1985-88. Nos résultats montrent que la réglementation environnementale et les réaffectations préventives (une mesure de prévention des accidents de travail) ont réduit la croissance de la productivité, alors que les mesures de prévention obligatoires et l'importance des amendes imposées pour infraction aux normes du travail ont augmenté la productivité. Notre étude est la première, à notre connaissance, qui indique un effet potentiellement positif de la réglementation sur la croissance de la productivité.Environmental regulationl Safety and health regulation; Productivity, Réglementation environnementale ; Réglementation de la santé et de la sécurité du travail ; Productivité