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.     

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.     

Sur l'intégration des équations aux dérivées partielles du type elliptique

Sans résumé     

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     

Oxygenolysis of flavonoid compounds: DFT description of the mechanism for quercetin.

Flavonoids are naturally occurring phenol derivatives present in substantial amounts in a large variety of plants, fruits and vegetables daily eaten by humans. Most of these compounds exhibit several interesting biological activities, such as antiradical and antioxidant actions. Indeed, by complexation with specific enzymes, flavonoids are notably liable to metabolize molecular dioxygen. On the basis of experimental results describing oxygenolysis of the flavonoid quercetin, activated by the enzyme quercetin 2,3-dioxygenase (2,3-QD),ur attention has focused on the role of metal center in the activation of the substrate quercetin. Thus, in the present study, by means of DFT calculations at the B3LYP/ 6-31(+)G* level on model molecular systems, we describe different mechanisms for dioxygen metabolization by quercetin. Stationary points are described, and energetic and structural analyses along the reaction paths are reported. Our calculations show that the copper cation must act as an oxidant towards the substrate and that the reaction proceeds through a 1,3-cycloaddition.     

A case of oligomerization on attempted chlorination of an α-hydroxy acetal with the triphenylphosphine tetrachloromethane reagent

Treatment of methyl 3,5-dideoxy-β-$\text{D}$-$\text{erythro}$-pentofuranoside $\text{8}$ with the Ph₃P-CCl₄ reagent gave none of the expected 2-chloro derivative but a mixture of l→2 linked oligosaccharides, $\text{9}$, $\text{10}$ with some higher homologues, terminated by αa 2-chloro-2,3,5-trideoxy-α-$\text{D}$-$\text{threo}$-pentofuranosyl unit at the non reducing end.