Iron salts catalyzed synthesis of β-N-substituted aminoacrylates

The direct condensation of amines with β-ketoesters to produce functional enamine derivatives has been investigated with iron Lewis acid catalysts. FeCl₃·6H₂O shows good catalytic activity and makes possible the chemo- and stereoselective formations of (Z)-enamine derivatives from aliphatic and aromatic primary amines under mild conditions.     

Counting Function of Magnetic Resonances for Exterior Problems

We study the asymptotic distribution of the resonances near the Landau levels \({\Lambda_q =(2q+1)b}\), \({q \in \mathbb{N}}\), of the Dirichlet (resp. Neumann, resp. Robin) realization in the exterior of a compact domain of \({\mathbb{R}^3}\) of the 3D Schrödinger operator with constant magnetic field of scalar intensity \({b > 0}\). We investigate the corresponding resonance counting function and obtain the main asymptotic term. In particular, we prove the accumulation of resonances at the Landau levels and the existence of resonance-free sectors. In some cases, it provides the discreteness of the set of embedded eigenvalues near the Landau levels.     

Selective Ruthenium‐Catalyzed Hydrochlorination of Alkynes: One‐Step Synthesis of Vinylchlorides

An unprecedented ruthenium‐catalyzed direct and selective alkyne hydrochlorination is reported and leads to vinylchlorides in excellent yields with atom economy. The reaction proceeds at room temperature from terminal alkynes and provides a variety of chloroalkenes. Only the regioisomer resulting from the formal Markovnikov addition is selectively formed. Mechanistic studies show the stereoselective syn addition of HCl to alkynes at room temperature and suggest a chloro hydrido Ru^IV species as a key intermediate of the reaction.     

Ruthenium-catalyzed reductive amination of allylic alcohols

Straighforward access to various saturated amines from allylic alcohols and isostructural mixture can now be achieved in the presence of arene ruthenium catalyst featuring phosphinesulfonate ligand and a hydrogen donor.     

New ruthenium metathesis catalysts with chelating indenylidene ligands: synthesis, characterization and reactivity

Six new ruthenium complexes bearing a bidentate (κ(2)O,C)-isopropoxy-indenylidene and PPh(3) or PCy(3) ligands have been synthesized and characterized by (1)H, (13)C NMR spectroscopy and X-ray crystallography. Some of these complexes were synthesized in dimethyl carbonate, a green solvent that was recently shown to be suitable for several catalytic transformations including olefin metathesis. The thermal stability and catalytic efficiency of the PCy(3)-containing complexes have been evaluated in a series of test reactions.     

Non-linear oscillatory rheological properties of a generic continuum foam model: Comparison with experiments and shear-banding predictions

The occurrence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarios in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e. the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary whose amplitude is history dependent and thus depends on the sample preparation.     

Asymptotics of the scattering phase for the Dirac operator: High energy, semi-classical and non-relativistic limits

In this paper we prove several results for the scattering phase (spectral shift function) related with perturbations of the electromagnetic field for the Dirac operator in the Euclidean space. Many accurate results are now available for perturbations of the Schrödinger operator, in the high energy regime or in the semi-classical regime. Here we extend these results to the Dirac operator. There are several technical problems to overcome because the Dirac operator is a system, its symbol is a 4×4 matrix, and its continuous spectrum has positive and negative values. We show that we can separate positive and negative energies to prove high energy asymptotic expansion and we construct a semi-classical Foldy-Wouthuysen transformation in the semi-classical case. We also prove an asymptotic expansion for the scattering phase when the speed of light tends to infinity (non-relativistic limit).     

AN ACCURATE FINITE DIFFERENCE SCHEME FOR SOLVING CONVECTION-DOMINATED DIFFUSION EQUATIONS

Approximating convection-dominated diffusion equations requires a very accurate scheme for the convection term. The most famous is the method of backward characteristics, which is very precise when a good interpolation procedure is used. However, this method is difficult to implement in 2D or 3D. The goal of this paper is to show that it is possible to construct finite difference schemes almost as accurate as the method of characteristics. Starting from a family of second- and third- order Lax–Wendroff-type schemes, a TVD and L^∞- stable scheme that is easy to implement in higher dimensions is constructed. Numerical tests are performed on various model problems whose solution is known and on classical problems. Comparisons with some other limiter schemes and the method of characteristics are discussed. © 1997 by John Wiley & Sons, Ltd.