General decay and blow up of solution for a nonlinear wave equation with a fractional boundary damping

The paper deals with the study of global existence of solutions and the general decay in a bounded domain for nonlinear wave equation with fractional derivative boundary condition by using the Lyaponov functional. Furthermore, the blow up of solutions with nonpositive initial energy combined with a positive initial energy is established.     

PEG–PLGA copolymers bearing carboxylated side chains: Novel hydrogels with enhanced crosslinking via ionic interactions

Novel water‐soluble amphiphilic block copolymers with pendant carboxylic acid groups are synthesized and used for the preparation of ionically crosslinked hydrogels. d ,l ‐Lactide (DLLA) and l ?3‐(2‐benzyloxycarbonyl)ethyl‐1,4‐dioxane‐2,5‐dione (BED) are copolymerized at different ratios via organo‐catalyzed ring‐opening polymerization using a hydroxyl‐terminated poly(ethylene glycol) (PEG–OH) macroinitiator. Dynamic light‐scattering experiments show that, at low concentrations, aqueous solutions of these PEG‐P(BED‐DLLA) copolymers form micelles and aggregates. At higher concentrations, thermo‐sensitive gels are obtained, exhibiting a reversible gel‐to‐sol transition upon a temperature increase. Ionic interactions between the COOH groups and metal ions (Cu²⁺ or Ca²⁺) are shown to significantly shift the gel–sol transition to higher temperatures. Thus, the introduction of COOH groups significantly enhances the water solubility of the amphiphilic PEG–polyester copolymer and allows additional crosslinking interactions to form functionalized hydrogels with improved physical properties, making this new class of hydrogels interesting for various applications. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1222–1227     

Gold(I)/Gold(III) Catalysis that Merges Oxidative Addition and π‐Alkene Activation

Heteroarylation of alkenes with aryl iodides was efficiently achieved with a (MeDalphos)AuCl complex through Au^I/Au^III catalysis. The possibility to combine oxidative addition of aryl iodides and π‐activation of alkenes at gold is demonstrated for the first time. The reaction is robust and general (>30 examples including internal alkenes, 5‐, 6‐, and 7‐membered rings). It is regioselective and leads exclusively to trans addition products. The (P,N) gold complex is most efficient with electron‐rich aryl substrates, which are troublesome with alternative photoredox/oxidative approaches. In addition, it provides a very unusual switch in regioselectivity from 5‐exo to 6‐endo cyclization between the Z and E isomers of internal alkenols.     

(P,C) Cyclometalated Gold(III) Complexes: Highly Active Catalysts for the Hydroarylation of Alkynes

The first catalytic application of well‐defined (P,C) cyclometalated gold(III) complexes is reported. The bench‐stable bis(trifluoroacetyl) complexes 2 a , b perform very well in the intermolecular hydroarylation of alkynes. The reaction is broad in scope, it proceeds within few hours at 25 °C at catalytic loadings of 0.1–5 mol %. The electron‐rich arene adds across the C≡C bond with complete regio‐ and stereo‐selectivity. The significance of well‐defined gold(III) complexes and ligand design are highlighted in a powerful but challenging catalytic transformation.     

Applying nonlinear dynamic theory to one-dimensional pulsating detonations

The dynamical behaviour of one-dimensional pulsating detonations was investigated in detail, with the aid of nonlinear theory tools such as phase plots and correlation dimension. The period-doubling cascade, as routes to deterministic chaos, is depicted through the transformations of the shapes of the attractors. Using a correlation dimension method, the dimension of the attractors is determined and we show that the chaos within a one-dimensional pulsating detonation is deterministic.     

Estimation fonctionnelle de la densité de l'opérateur de transition d'un processus de Markov à temps discretFunctional estimate of Markov transition operator density: Discrete time case

In this study, we build a kernel estimate of the transition operator density for some discrete time continuous states Markov processes which satisfy some general conditions. Assumptions are not restrictive and results can be used on transition Markov operator, viewed as an endomorphism on L^p, p∈[1,∞[, as well as on its adjoint. The main result deals with convergence rate of built kernel estimate. To cite this article: A. Laksaci, A. Yousfate, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1035–1038.     

Experimental and Theoretical Evidence for an Agostic Interaction in a Gold(III) Complex

The first agostic interaction in a gold complex is described. The presence of a bonding C?H???Au interaction in a cationic “tricoordinate” gold(III) complex was suggested by DFT calculations and was subsequently confirmed by NMR spectroscopy at low temperature. The agostic interaction was analyzed computationally using NBO and QTAIM analyses (NBO=natural bond orbital; QTAIM=quantum theory of atoms in molecules).     

Cationic Gold(III) Alkyl Complexes: Generation,Trapping, and Insertion of Norbornene

Migratory insertion of alkenes into gold–carbon bonds, a fundamental yet unprecedented organometallic transformation, has been investigated from a discrete (P,C) cyclometalated gold(III) dimethyl complex. Methide abstraction by B(C₆F₅)₃ is shown to generate a highly reactive cationic Au^III complex that evolves spontaneously by C₆F₅ transfer from boron. In the presence of norbornene, migratory insertion into the Au? C bond proceeds readily. The resulting norbornyl complex is efficiently trapped with pyridines or chloride to give stable four‐coordinate adducts.