Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flamesJustification mathématique d'une équation intégro-différentielle non linéaire pour un modèle de flamme sphérique

This Note is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [7]. The paper [7] derives, by means of a three-scale matched asymptotic expansion, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis number – i.e., the ratio between thermal and molecular diffusion – to be strictly less than unity. In this Note, we give the main ideas of a rigorous proof of the validity of this model, under the additional restriction that the Lewis number is close to 1. To cite this article: C. Lederman et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 569–574.     

Schematization of networks

We study the problem of computing schematized versions of network maps, like railroad or highway maps. Every path of the schematized map has two or three links with restricted orientations, and the schematized map must be topologically equivalent to the input map. Our approach can handle several types of schematizations, and certain additional constraints can be added, such as a minimum vertical distance between two paths. Our algorithm runs in O(nlogn) time, and experimental results showing the quality of the output are given.     

Pyrazolo[3,4-d][1,2,3]triazolo[1,5-a]pyrimidine: a new ring system through Dimroth rearrangement

Derivatives of the new ring system pyrazolo[3,4-d][1,2,3]triazolo[1,5-a]pyrimidine were synthesized from the corresponding angular isomers, through a Dimroth rearrangement, in quantitative yields. Preliminary computational studies demonstrated that this class of compounds could be a good candidate as DNA intercalating agents.     

Convex Transitive Norms on Spaces of Continuous Functions

A norm on a Banach space X is called maximal when no equivalentnorm has a larger group of isometries. If, besides this, thereis no equivalent norm with the same isometries (apart from itsscalar multiples), the norm is said to be uniquely maximal,which is equivalent to the convex-transitivity of X: the convexhull of the orbits under the action of the isometry group onthe unit sphere is dense in the unit ball of X. The main resultof the paper is that the complex C₀() is convex-transitive inits natural supremum norm if is a connected manifold (withoutboundary). As a complement, it is shown that if is a connectedmanifold of dimension at least two, then the diameter norm isconvex transitive on the corresponding space of real functions.2000 Mathematics Subject Classification 46B15, 47B99     

Experimental violation of Bell's inequality beyond Tsirelson's bound

The correlations between two qubits belonging to a three-qubit system can violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Tsirelson's bound [A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate such a violation by 7 standard deviations by using a three-photon polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II spontaneous parametric down-conversion. In addition, using part of our results, we obtain a violation of the Mermin inequality by 39 standard deviations.     

Enhancing the violation of the einstein-podolsky-rosen local realism by quantum hyperentanglement

Mermin's observation [Phys. Rev. Lett. 65, 1838 (1990)] that the magnitude of the violation of local realism, defined as the ratio between the quantum prediction and the classical bound, can grow exponentially with the size of the system is demonstrated using two-photon hyperentangled states entangled in polarization and path degrees of freedom, and local measurements of polarization and path simultaneously.     

Bipartite bell inequalities for hyperentangled states

We show that bipartite Bell inequalities based on the Einstein-Podolsky-Rosen criterion for elements of reality and derived from the properties of some hyperentangled states allow feasible experimental verification of the fact that quantum nonlocality grows exponentially with the size of the subsystems, and Bell loophole-free tests with currently available photodetection efficiencies.     

Preparation and characterization of ZrO2:Sm amorphous thin films by solid state photochemical deposition method

Thin films of ZrO₂ loaded with 10, 30 and 50 mol% Sm were prepared by a photochemical method using thin films of metal acetylacetonate complexes as precursors. The photolysis of these films induces the fragmentation of the acetylacetonate ligand and the partial reduction of metal ion together with volatile organic compounds. When the metallic complex is exposed to air, the product of the reaction is metal oxide. The photoreactivity of these films was monitored by FT-IR spectroscopy, followed by a post-annealing treatment process. The obtained films were characterized by X-ray photoelectron spectroscopy and atomic force microscopy.Photoluminescense studies of the films employed 400 nm radiation for excitation of the Sm ions present. The emission spectra showed signals arising from the ⁴G_5/2→⁶H_J (J=3/2, 7/2, 9/2) transitions, where the ⁴G_5/2→⁶H_3/2 transition has the highest intensity. The concentration dependence of the PL intensity was also studied. A maximum PL intensity was observed with 10 mol% Sm content but then diminished with higher Sm concentrations.