Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition

We show the incompleteness of a usually used version of the generalized Ambrosetti?CRabinowitz condition in superlinear problems, also used in the paper cited in the title, and we propose a complete one.     

Riemann–Hilbert formulation for the KdV equation on a finite interval

The initial-boundary value problem for the KdV equation on a finite interval is analyzed in terms of a singular Riemann–Hilbert problem for a matrix-valued function in the complex k-plane which depends explicitly on the space–time variables. For an appropriate set of initial and boundary data, we derive the k-dependent “spectral functions” which guarantee the uniqueness of Riemann–Hilbert problem's solution. The latter determines a solution of the initial-boundary value problem for KdV equation, for which an integral representation is given. To cite this article: I. Hitzazis, D. Tsoubelis, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Triazene formation via reaction of imidazol-2-ylidenes with azides

Treatment of N-heterocyclic carbenes (as their free carbenes or generated in situ) with alkyl, aryl, acyl or tosyl azides afforded the respective substituted triazenes in excellent yields.     

Mechanisms of single-electron capture by the dichlorocarbene dication

The single-electron capture (SEC) by dichlorocarbene dications with eight different atomic and molecular target gases, CCl ₂ ²⁺ + G → CCl ₂ ⁺ + G⁺, has been studied by product ion spectroscopy and ion kinetic energy spectroscopy. The experimental data have been interpreted in the framework of a theoretical model mat describes the charge exchange process. Exothermic charge exchange is handled within the Landau-Zener model, whereas endothermic charge exchange is described by the Demkov model. The calculated data reproduce qualitatively the essential features of the experimental results: (1) the appearance of a reaction window centered at an exothermicity in the 4–4.5-eV range, (2) the lower SEC cross sections for endothermic charge exchange, (3) the wider internal energy distributions obtained for CCl ₂ ⁺ in the endothermic regime than in the exothermic one, which results in larger dissociation yields, (4) the excitation of molecular targets that accompany their ionization in the SEC process, and (5) the kinetic energy released on the CCl⁺ + Cl fragments in dissociative SEC.     

Barrier Crossing in Dihydrofolate Reductasedoes not involve a rate-promoting vibration

We have studied atomic motions during the chemical reaction catalyzed by the enzyme dihydrofolate reductase of Escherichia coli (EcDHFR), an important enzyme for nucleic acid synthesis. In our earlier work on the enzymes human lactate dehydrogenase and purine nucleoside phosphorylase, we had identified fast sub-ps motions that are part of the reaction coordinate. We employed Transition Path Sampling (TPS) and our recently developed reaction coordinate identification methodology to investigate if such fast motions couple to the reaction in DHFR on the barrier-crossing timescale. While we identified some protein motions near the barrier crossing event, these motions do not constitute a compressive promoting vibration, and do not appear as a clearly identifiable protein component in reaction.     

A practical way of grafting maleic anhydride onto polypropylene providing high anhydride contents without sacrificing excessive molar mass

This study reports a reactive extrusion process leading to very high levels of anhydride grafting (2.5–3 wt %) along polypropylene backbone without recovering grafted PP waxes at the die exit. Such high graftings are attainable without excessive degradation of the PP chain by using a brominated reagent. Simultaneously, this brominated reagent allows the tuning of the grafted PP crystallinity via epimerization of the PP backbone. Indeed, the synthesis of a mainly isotactic/atactic stereoblock polymer containing high levels of grafted succinic anhydride moieties is demonstrated by NMR and melting enthalpies recorded by DSC are definitely observed depressed and broadened. Grafting levels of around 3 wt % have been achieved and ascertained by both chemical titration and NMR spectroscopy. In addition, FTIR spectroscopy reveals an unusual observation: for the first time, only one single pair of symmetric and asymmetric carbonyl stretching bands are observed on those grafted PP, while, in other processes of anhydride grafting, those symmetric and asymmetric bands were both split in at least two bands. This suggests, for the here reported process, the absence of interacting grafted anhydride rings, i.e., absence of closely grafted anhydride moieties and absence of poly(maleic anhydride). All those observations support that this “bromine route” brings a really new grafting process for PP. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2936–2947, 2008     

Polynomial auction algorithms for shortest paths

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/many destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithms withO (n min{m, n logn}) andO(n ²) running time. Our computational experiments show that these algorithms outperform their closest competitors on randomly generated dense all destinations problems, and on a broad variety of few destination problems.Research supported by NSF under Grant No. DDM-8903385, by the ARO under Grant DAAL03-86-K-0171, by a CNR-GNIM grant, and by a Fullbright grant