Reactions CO/H2 en phase liquide. Synthese de precurseurs de l'ethanol par homologation du methanol.: I. Influences de la temperature et de la pression

The CO/H₂ homologation of methanol to acetaldehyde and subsequently to its dimethyl acetal in the presence of cobalt acetate promoted by iodine was examined under various conditions. Temperature and pressure were found as critical parameters. High pressures (140 MPa) and low temperatures (160–170°C) give optimal yields and selectivity to acetaldehyde. According to pressure, temperature, contact time, gas ratio and ligand/catalyst ratio, the reaction is oriented towards acetaldehyde, its dimethyl acetal or methyl acetate.     

Etude quantitative de la distinction entre une liaison de covalence et une liaison de coordination: les molecules de borazane et d'aminoborane

Résumé On propose un exemple quantitatif de la distinction entre une liaison de covalence et une liaison de coordination; cette différenciation, fondée sur les propriétés de la molécule une fois formée, semble très nette pour les énergies de liaison, les populations de recouvrement et les charges des groupes; en particulier, un critère récent, proposé par deux des auteurs, est remarquablement vérifié. Enfin, on essaie de préciser la signification des symboles chimiques traditionnels.

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Quantitative studies of the difference between a covalence and a coordination bond: The molecules of amine-borane and aminoborane

An illustration of the distinction between these two types of chemical bonds is proposed, which is based on the properties of the molecule once built. Bond energies, overlap populations and group charges vary considerably from one compound to the other; more, a recent criterion given by two of the authors seems to be particularly suitable for describing the character of the bond. Lastly, one tries to give an explicit signification to the usual chemical symbols.

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Zusammenfassung Es wird ein quantitatives Beispiel der Unterscheidung zwischen einer kovalenten und einer koordinativen Bindung angegeben, die auf den Eigenschaften des vorliegenden Moleküls beruht. Sie erscheint sehr günstig für die Bindungsenergien, die Überlagerungspopulationen und die Gruppenladungen. Insbesondere wird ein Kriterium, das kürzlich von zwei der Autoren angegeben wurde, gut verifiziert. Schließlich wird versucht, die üblichen chemischen Symbole zu präzisieren.

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Les auteurs tiennent à remercier très vivement M. M. Berthier et Millié d'avoir mis à leur disposition le programme de localisation indispensable à ce travail, ainsi que Mademoiselle Le Guen et le C.I.R.C.E. pour la réalisation des calculs sur l'ordinateur IBM 360-75.     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism

The aim of this work is to propose an accurate and efficient numerical approximation for high frequency diffraction of electromagnetic waves. In the context of the boundary integral equations presented in F. Collino and B. Després, to be published in J. Comput. Appl. Math., the strategy we propose combines the microlocal discretization (T. Abboud et al., in: Third International Conference on Mathematical Aspects of Wave Propagation Phenomena, SIAM, 1995, pp. 178–187) and the multilevel fast multipole method (J.M. Song, W.C. Chew, Microw. Opt. Tech. Lett. 10 (1) (1995) 14–19). This leads to a numerical method with a reduced complexity, of order O(N^4/3ln(N)+N_iterN^2/3), instead of the complexity O(N_iterN²) for a classical numerical iterative solution of integral equations. Computations on an academic geometry show that the new method improves the efficiency, for a solution with a good level of accuracy. To cite this article: A. Bachelot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

Persistency in quadratic 0–1 optimization

This paper is concerned with persistency properties which allow the evaluation of some variables at all maximizing points of a quadratic pseudo-Boolean function. Hammer, Hansen and Simeone (1984) have proposed to determine these variables using a procedure described by Balinski for computing a strongly complementary pair of optimal primal and dual solutions for arbitrary linear programs. We propose a linear time algorithm for determining these variables from a best roof off, i.e. from a lowest upper linear bound off.     

A Law of Large Numbers for the Zeroes of Heine–Stieltjes Polynomials

We determine the limiting density of the zeroes of Heine–Stieltjes polynomials (or of any set of points satisfying the conclusion of Heine–Stieltjes Theorem) in the thermodynamic limit and use this to prove a strong law of large numbers for the zeroes.     

The Lyapunov Exponent of Products of Random 2×2 Matrices Close to the Identity

We study products of arbitrary random real 2×2 matrices that are close to the identity matrix. Using the Iwasawa decomposition of SL(2,?), we identify a continuum regime where the mean values and the covariances of the three Iwasawa parameters are simultaneously small. In this regime, the Lyapunov exponent of the product is shown to assume a scaling form. In the general case, the corresponding scaling function is expressed in terms of Gauss’ hypergeometric function. A number of particular cases are also considered, where the scaling function of the Lyapunov exponent involves other special functions (Airy, Bessel, Whittaker, elliptic). The general solution thus obtained allows us, among other things, to recover in a unified framework many results known previously from exactly solvable models of one-dimensional disordered systems.     

Air-dispersion measurement by second-harmonic heterodyne interferometry

Interferometers with long optical paths in air usually require knowledge and control of air dispersion. In addition, the measurements at several wavelengths and the dispersion properties of air allow errors caused by air turbulence to be compensated for. An innovative technique for air-dispersion measurement is described for long-baseline ground-based stellar interferometers. The technique combines second-harmonic interferometry and heterodyne detection to permit high-resolution measurement even for low optical powers. Experimental results show measurements of air dispersion in good agreement with the values predicted from the Edlén equation.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.