Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

Weighted irregular Gabor tight frames and dual systems using windows in the Schwartz class

We give a characterization for the weighted irregular Gabor tight frames or dual systems in L²(Rn) in terms of the distributional symplectic Fourier transform of a positive Borel measure on R2n naturally associated with the system and the short-time Fourier transform of the windows in the case where the window (or at least one of the windows in the case of dual systems) belongs to S(Rn). This result implies that, for certain classes of windows such as generalized Gaussians or “extreme-value” windows, the only weighted irregular Gabor tight frames (or even dual systems with both windows in the same class) that can be constructed with these windows are the trivial ones, corresponding to the measure μ=1 on R2n. Furthermore, we show that, if a such Gabor system admits a dual which is of Gabor type, then the Beurling density of the associated measure exists and is equal to one.     

Efficient synthesis of phosphorus-containing dendrimers capped with isosteric functions of amino-bismethylene phosphonic acids

An efficient synthetic strategy to synthesize phosphorus-containing dendrimers capped with isosteric acid functions derived from tyramine is described. The method is demonstrated on a first generation dendrimer that can be easily capped with 12 amino(bismethylene) sulfonic acids and amino(bismethylene) carboxylic acids that are strict analogs of the corresponding amino(bismethylene) phosphonic acids.     

Multiplurifunctionalized Phosphorus Dendrimers: Selective Functionalization of P(X)CL2 Terminal Groups

Abstract

Dendrimers are hyperbranched macromolecules constituted of repetitive branched units. They are synthesized step-by-step, a method which ensures a perfectly defined structure. This mini-review reports examples of rare “multiplurifunctionalized” dendrimers that have several types of functional groups precisely located on each terminal branching point. They are obtained thanks to the specificity of the reactivity of each Cl of P(X)Cl₂ (X = generally S, but also O) terminal groups on the surface of poly(phosphorhydrazone) dendrimers.     

Sur les automorphismes analytiques des variétés hyperboliques

Results of H. Cartan about holomorphic automorphisms on bounded domains are generalized to the case of hyperbolic manifolds in the sense of Kobayashi. In this setting, we give an identity theorem together with its topological version. We show also that a sequence of automorphisms which converges uniformly on some nonempty open set, has a limit on the whole space which is an automorphism. At the end of the paper, conditions are given for the sequence of iterates of a self holomorphic map in order to be an automorphism.     

N2-broadening coefficients in the ν2 and ν4 bands of PH3

N₂-broadening coefficients are measured for 61 transitions of PH₃ in the ^QR branch of the ν₂ band and the ^PP, ^RP, ^SP, and ^PQ branches of the ν₄ band, using a tunable diode-laser spectrometer. The recorded lines with J values ranging from 1 to 16 and K from 0 to 11 are located between 1008 and 1106 cm⁻¹. The collisional widths are determined by fitting each spectral line with a Voigt profile, a Rautian profile, and a speed-dependent Rautian profile. The latter models provide larger broadening coefficients than the Voigt model. These coefficients have also been calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to the electrostatic contributions. The theoretical results are in good agreement with the experimental data and reproduce the J dependence of the broadenings, but their decrease at high J values is overestimated for the ^QR (J, K) transitions.     

Conversations on mind, matter, and mathematics

Conclusion  The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities. It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book is to cast a spotlight on this confrontation.     

Approche non paramétrique du filtrage de système non linéaire à temps discret et à paramètres inconnus

Particle filters are presently among the most powerful tools for filtering discrete time non linear systems. However the presence of unknown parameters in the system equations makes their use more complex and can even impair their convergence properties. This Note shows how an on-line consistent estimation of these parameters can be obtained simultaneously to that of the state variables to be filtered. This approach relies upon a kernel-based non parametric estimation of conditional probability densities from successive Monte Carlo generations of system particles. To cite this article: V. Rossi, J.-P. Vila, C. R. Acad. Sci. Paris, Ser. I 340 (2005).