Estimation de la fonction de régression pour variable explicative et réponse fonctionnelles dépendantes

We consider a kernel estimate of the regression when the response variable is in a Banach space and the explanatory variable takes its values in a semi-metric space. Our main result states the almost complete convergence (with rate) of the constructed estimate when the sample considered is a β-mixing sequence.     

The steady motions of a satellite with a two-degree-of-freedom powered gyroscope in a central gravitational field and their stability

The positions of relative equilibrium of a satellite carrying a two-degree-of-freedom powered gyroscope, in the axes of the framework of which only dissipative forces can act, are investigated within the limits of a restricted circular problem. For the case when the “satellite - gyroscope” system possesses the property of a gyrostat and the axis of the gyroscope frame is directed parallel to one of the principal central axes of inertia of the satellite, all the equilibrium positions are found as a function of the magnitude of the angular momentum of the rotor. It is established that the minimum number of equilibrium positions is equal to 32 and, in certain ranges of values of the system parameters, it can reach 80. All the positions satisfying the sufficient conditions for stability are also determined. The number of them is either equal to 4 or 8 depending on the values of the system parameters.     

Problème de Dirichlet pour une équation de Monge-Ampère réelle elliptique dégénérée en dimension

RÉSUMÉ. On considère dans un ouvert borné de , à bord régulier, le problème de Dirichlet

où , est positive et s'annule sur un ensemble fini de points de . On démontre alors sous certaines hypothèses sur et si est assez petit, que le problème (1) possède une solution convexe unique .

ABSTRACT. We consider in a bounded open set of , with regular boundary, the Dirichlet problem

where , is positive and vanishes on , a finite set of points in . We prove, under some hypothesis on and if is sufficiently small, that the problem (1) has a unique convex solution .

     

Analysis of the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame

A method that enables a conclusion to be drawn regarding the nature of the Lyapunov stability of the equilibria positions of autonomous systems with partial dissipation from the nature of the secular stability and truncated equations of the linear approximation is developed based on the Barbashin–Krasovskii theorem. The method is used to investigate the stability of the equilibria of a satellite carrying a two-degree-of-freedom powered gyroscope with dissipation in the axis of the frame in a circular orbit. For the case when the axis of the gyroscope frame is oriented parallel to one of the principal axes of inertia of the satellite, the nature of the Lyapunov stability of all the equilibria, with the exception of a few branching points, is determined. It is established that gyroscopic stabilization, which is possible when there is no dissipation in the axis of the frame for certain equilibria that are unstable in the secular sense, breaks down when dissipation occurs.     

The equilibria and stability of a dynamically symmetrical satellite with a two-degree-of-freedom powered gyroscope

For a dynamically symmetrical satellite carrying a two-degree-of-freedom powered gyroscope, all the relative equilibria in a circular orbit are found as a function of the angular momentum of the rotor and the angle between the precession axis of the gyroscope and the plane of dynamical symmetry. The case with no spring on the axis of the gyroscope frame and the case with a spring whose stiffness satisfies definite conditions are considered. The secular stability of the equilibria is investigated. For a system with dissipation in the axis of the gyroscope frame, the Barbashin–Krasovskii theorem is used to perform a detailed analysis, which enables the character of the Lyapunov stability of all the equilibria to be determined, with the exception of a few points. The results of a numerical solution of the problem of the optimal values of the system parameters, for which asymptotically stable equilibria are obtained with maximum speed, are presented.     

Structure, thermal, and infrared analyses of [NH3(CH2)3NH3]2[Ni(HP2O7)2(H2O)2] ? 4H2O

[NH₃(CH₂)₃NH₃]₂[Ni(HP₂O₇)₂(H₂O)₂] 4H₂O (NiDAP) is a new diphosphate of transition metallic and organic cations obtained from a mixture of H₄P₂O₇, 2NiCO₃ Ni(OH)₂ 4H₂O and NH₂(CH₂)₃NH₂ in a 1:1/6:1 molar ratio. This mixed organo-mineral compound crystallizes in the triclinic system, P¯, with the unit cell dimensions: a = 7.3678(3)~Å, b = 7.8018(5)Å, c = 11.1958(7)Å, = 76.914(4), = 81.052(4), = 85.46(1), V = 618.57(6)ų and Z = 1. The crystal structure of NiDAP consists of a complex anion, [Ni(HP₂O₇)₂(H₂O)₂]^4– and a diammoniumpropane cation. The complex anion is built up from two neutral water molecules (OW1) and two diphosphosphoric anions coordinated to Ni(II) in a bidentate chelating manner. (OW1) molecules link anionic complexes, [Ni(HP₂O₇)₂(H₂O)₂]^4– to create a thick bidimensional layers parallel to the (a, b) plane. These layers are interconnected in three dimensions through hydrogen bonds established between organic cations, the remaining water molecules OW2, OW3, and some external oxygen atoms of the anionic complex arrays. NiDAP was also characterized by IR spectroscopy, TG-DTA, and DSC analyses.     

Mega three-photon absorption cross-section enhancement in pseudoisocyanine J-aggregates

Herein we report an extraordinary three-photon absorption cross-section (sigma'3) enhancement in J-aggregates supramolecular systems. The much higher value of sigma'3 in PIC J-aggregate (2.5 x 10(-71) cm6 s2 ph(-2)) compared to typical values obtained in organic molecules (10(-80) cm6 s2 ph(-2)) is attributed to the strong molecular transition dipole moment coupling in the supramolecular assembly. Three-photon absorption of PIC J-aggregates and monomer aqueous solutions were measured using the well known open aperture Z-scan technique pumping with a 25 ps pulse laser-OPG system at 1720 nm. This novel result opens new expectations for applications of supramolecular systems in bioimaging and medicine.     

On the higher-order strong isochronism of Cauchy-Riemann systems with homogeneous polynomial perturbations of a linear center

We indicate the maximum order of the general and partial (with an initial polar angle) strong higher-order isochronism of Cauchy-Riemann systems with homogeneous polynomial perturbations of a linear center.