Search results for "Function"
showing 10 items of 14432 documents
ÉQUATIONS DIFFÉRENTIELLES À COEFFICIENTS DANS DES CORPS DE SÉRIES GÉNÉRALISÉES.
2007
We express the connection between the support of some equations and those of generalized series solutions. On the one hand we prove that any real power series solution of a sub-analytic differential equation belong to a lattice (i.e. an additive sub semi-group of positive reals). On the other hand we consider the field Mr of series with well-ordered support included in the Hahn product Hr with finite rank r (i.e. the lexicographic product of r copies of the reals). We equip Mr with a "Hardy type" derivation and define some well-ordered sets T1, ..., Tr such that : for all equation F(y,...,y(n))=0 with F in Mr[[Y0,...,Yn]] and whose support Supp F is a well-ordered subset of Hr, and for all …
Contribution à l'estimation non paramétrique des quantiles géométriques et à l'analyse des données fonctionnelles
2008
In this dissertation we study the nonparametric geometric quantile estimation, conditional geometric quantiles estimation and functional data analysis. First, we are interested to the definition of geometric quantiles. Different simulations show that Transformation-Retransformation technique should be used to estimate geometric quantiles when the distribution is not spheric. A real study shows that, data are better modelized by geometric quantiles than by marginal one's, especially when variables that make up the random vector are correlated. Then we estimate geometric quantiles when data are obtained by survey sampling techniques. First, we propose an unbaised estimator, then using lineari…
Unfolding of saddle-nodes and their Dulac time
2016
Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a b…
Compressed Drinfeld associators
2004
Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.
Birman's conjecture for singular braids on closed surfaces
2003
Let M be a closed oriented surface of genus g≥1, let Bn(M) be the braid group of M on n strings, and let SBn(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map η : SBn(M)→ℤ[Bn(M)], introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective.
Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale
2002
L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur Terre ou programme d'exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l'angle de gîte cinématique et le coût est l'intégrale du flux thermique. Par ailleurs il y a des contraintes sur l'état (flux thermique, accélération normale et pression dynamique). Notre étude est essentiellement géométrique et fondée sur une évaluation de l'ensemble des états accessibles en tenant compte des contraintes sur l'état. On esquisse une analyse des extrémales du Principe du …
Sensitivity analysis for time optimal orbit transfer
2001
The minimum time transfer of a satellite around the Earth is studied. In order to deal numerically with low thrusts, a new method is introduced: Based on a so-called noncontrollability function, the technique treats the ha1 time as a parameter. The properties of the method arc studied by means of an infinite dimensional sensitivity analysis. The numerical results obtained by this approach for very low thrusts are given
3D Geosynchronous Transfer of a Satellite: Continuation on the Thrust
2003
The minimum-time transfer of a satellite from a low and eccentric initial orbit toward a high geostationary orbit is considered. This study is preliminary to the analysis of similar transfer cases with more complicated performance indexes (maximization of payload, for instance). The orbital inclination of the spacecraft is taken into account (3D model), and the thrust available is assumed to be very small (e.g. 0.3 Newton for an initial mass of 1500 kg). For this reason, many revolutions are required to achieve the transfer and the problem becomes very oscillatory. In order to solve it numerically, an optimal control model is investigated and a homotopic procedure is introduced, namely cont…
Convergence rate of a relaxed inertial proximal algorithm for convex minimization
2018
International audience; In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.
Injectivity domain of ellipsoid of revolution. The oblate case.
2010
Study of the convexity of the injectivity domains on an oblate ellipsoid.