New results on the linearization of Nambu structures

In a paper with Jean-Paul Dufour in 1999 \cite{DufourZung-Nambu1999}, we gave a classification of linear Nambu structures, and obtained linearization results for Nambu structures with a nondegenerate linear part. There was a case left open in \cite{DufourZung-Nambu1999}, namely the case of smooth linearization of Nambu structures with a Type 1 hyperbolic linear part which satisfies a natural signature condition. In this paper, we will show that such hyperbolic Nambu structures are also smoothly linearizable. We will also give a strong version of the analytic linearization theorem in the analytic case, improving a result obtained in \cite{DufourZung-Nambu1999}.Comment: 1st version, 12 page

On restricted Analytic Gradients on Analytic Isolated Surface Singularities

Let (X,O) be a real analytic isolated surface singularity at the origin o of a real analytic manifold M equipped with a real analytic metric g. Given a real analytic function f:(M,O) --> (R,0) singular at O, we prove that the gradient trajectories for the metric g|(X,O) of the restriction f|X escaping from or ending up at the origin O do not oscillate. Such a trajectory is thus a sub-pfaffian set. Moreover, in each connected component of X\O where the restricted gradient does not vanish, there is always a trajectory accumulating at O and admitting a formal asymptotic expansion at

Description of an operational tool for determining global solar radiation at ground using geostationary satellite images

International audienceAn operational tool for the fine-scale mapping of the incident solar radiation at ground is presented. This tool called "Heliosat station" makes use of image acquired in the visible spectral range by meteorological geostationary satellite to produce accurate maps of global radiation. Satellite data are directly received at ground by a cheap HF receiver and processed by a personal computer IBM-PC compatible using the already known Heliosat method. This method has been successfully tested during 30 consecutive months beginning January 1983. The first prototype of the Heliosat station was realized in 1985. Now a Heliosat station is routinely operated by Agence Française pour la Maîtrise de l'Energie since January 1987 for mapping solar radiation over Europe

The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems

In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincar\'e--Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincar\'e--Liapunov method.Comment: 24 pages, no figure

Two new plumage mutations in the Japanese quail: "curly" feather and "rusty" plumage

BACKGROUND: The genetics of plumage of Japanese quail is of interest both from a biological standpoint, for comparative studies between avian species, and from a zootechnical standpoint, for identifying commercial selection lines or crosses. There are only few plumage mutations reported in quail, and the present work describes a new color variant "rusty" and a new feather structure "curly", and their heredity from an F1 and F2 segregation experiment. RESULTS: Curly feathers result from abnormal early growth caused by transient joining of follicle walls of adjacent feathers around 10 days of age, but the expression of the trait is variable. Rusty plumage color results from the replacement of the wild-type plumage pattern on the tip of the feather by a reddish coloration, but the pigmentation of the bottom part of the feather is not affected. Two lines breeding true for the curly or the rusty phenotype were developed. Both characters are determined by autosomal recessive mutations which are independent. The curly mutation has also a positive effect on body weight at 5 weeks of age. CONCLUSION: The curly line is a new model which may be used for further work on the growth of the feather, and the rusty mutation is a new addition to the panel of plumage mutations available for comparative studies in poultry, and more generally among avian species