A proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards

We prove a recent theorem by C. Culter every polygonal outer billiard in the affine plane has a periodic trajectory.      

Molecule-to-metal bonds: electrografting polymers on conducting surfaces.

Electrografting is a powerful and versatile technique for modifying and decorating conducting surfaces with organic matter. Mainly based on the electro-induced polymerization of dissolved electro-active monomers on metallic or semiconducting surfaces, it finds applications in various fields including biocompatibility, protection against corrosion, lubrication, soldering, functionalization, adhesion, and template chemistry. Starting from experimental observations, this Review highlights the mechanism of the formation of covalent metal-carbon bonds by electro-induced processes, together with major applications such as derivatization of conducting surfaces with biomolecules that can be used in biosensing, lubrication of low-level electrical contacts, reversible trapping of ionic waste on reactive electrografted surfaces as an alternative to ion-exchange resins, and localized modification of conducting surfaces, a one-step process providing submicrometer grafted areas and which is used in microelectronics.     

Mlcrolasers based on silica microspheres

Light can be confined efficiently in the high-Q, small-volume whispering-gallery-modes observed in silica microspheres. By coupling these microspheres to eroded optical fibers and fiber tips, direct mapping of the whispering-gallery modes has been achieved and the mode numbers have been assessed. The properties of these modes have allowed us to obtain laser action with very low thresholds in Nd-doped silica microspheres. Further projects in the field of non-linear optics and cavity quantum electrodynamics are described.     

Mask‐free Localized Grafting of Organic Polymers at the Micrometer or Submicrometer Scale on Composite Conductors or Semiconductor Substrates

This work presents a new one‐step process enabling the mask‐free localized functionalization by organic polymers of the conducting or semiconducting parts of composite surfaces at the micrometer and submicrometer scale. The functionalization is carried out via cathodic electrografting of suitable precursors of composite cathodes, which gives an insulating polymer film strongly grafted to selected parts of the composite electrodes and guarantees that the resolution is that of the pre‐existing pattern, even when the whole surface is dipped into the reaction medium. The presumed mechanism is based on a regioselective extraction of electrons from the composite surface according to its apparent local work function in solution.     

Erratum: Symmetric iterative interpolation processes

Communicated by Charles A. Micchelli.     

Decomposition algorithms for the tree edit distance problem

We study the behavior of dynamic programming methods for the tree edit distance problem, such as [P. Klein, Computing the edit-distance between unrooted ordered trees, in: Proceedings of 6th European Symposium on Algorithms, 1998, p. 91–102; K. Zhang, D. Shasha, SIAM J. Comput. 18 (6) (1989) 1245–1262]. We show that those two algorithms may be described as decomposition strategies. We introduce the general framework of cover strategies, and we provide an exact characterization of the complexity of cover strategies. This analysis allows us to define a new tree edit distance algorithm, that is optimal for cover strategies.     

Sensors measuring oxygen activity in melts: Development of impedance method for“in-situ” diagnostics and control electrolyte/liquid-metal electrode interface

An impedance method for periodic“in-situ” diagnostics of the solid electrolyte/liquid-metal electrode interface during the lifespan of yttria-stabilized zirconia (YSZ)-based sensors measuring oxygen partial pressure in melts was developed. It was found that the impact of polarization effects on YSZ, stipulated by corrosive measuring environments (molten alkaline metals), is increasing with increase of the working temperature, which may lead to the appearance blocking reaction layers at the electrolyte/liquid-metal electrode interface. The proposed impedance method allows obtaining necessary information about the electrolyte/liquid-metal electrode interface and about the character and the level of polarization of the liquid-metal electrode.     

The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

Sulfonated poly(aryl ether ether ketone ketone)s containing fluorinated moieties as proton exchange membrane materials

A series of sulfonated poly(aryl ether ether ketone ketone)s statistical copolymers with high molecular weights were synthesized via an aromatic nucleophilic substitution polymerization. The sulfonation content (SC), defined as the number of sulfonic acid groups contained in an average repeat unit, could be controlled by the feed ratios of monomers. Flexible and strong membranes in sodium sulfonate form could be prepared by the solution casting method, and readily transformed to their proton forms by treating them in 2 N sulfuric acid. The polymers showed high T_gs, which increased with an increase in SC. Membranes prepared from the present sulfonated poly(ether ether ketone ketone) copolymers containing the hexafluoroisopropylidene moiety (SPEEKK‐6F) and copolymers containing the pendant 3,5‐ditrifluoromethylphenyl moiety (SPEEKK‐6FP) had lower water uptakes and lower swelling ratios in comparison with previously prepared copolymers containing 6F units. All of the polymers possessed proton conductivities higher than 1 × 10^?2 S/cm at room temperature, and proton conductivity values of several polymers were comparable to that of Nafion at high relative humidity. Their thermal stability, oxidative stability, and mechanical properties were also evaluated. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2299–2310, 2006     

Blocage par injection de modes sous- harmoniques d’un oscillateur utilisant une ligne à retard à ondes de surface

A nonlinear regeneration pulsed oscillator driven by a monochromatic source has been built. Subharmonics of the resonance carrier/modulation are measured with an accuracy of 10^-10 thanks to the use of a double beats measurement set-up. The multiscale analysis of frequency readings reveals a rich fine structure which is in agreement with the nonlinear topological approach of synchronized states.