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.     

Influence of load position on the stability of shallow arches

The influence of load position of lhe snap-through instability of shallow, circular, elastic arches is investigated. Results are obtained for pinned, clamped, and clamped-pinned end conditions. The worst load position is seen to depend on the arch rise.

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Zusammenfassung Der Eifluss der Kraftlage auf die Durchschgsinstabilität von flachen, elastischen Kreisbögen wird untersucht. Es sind Ergebnisse erhalten worden für Bögen mit gelenkigen eingespannten, und gelenkig-eingespannten Lagern. Die ungünstigste Kraftlage hängt von der Bogenhöhe ab.

     

Mesomorphic bipyridine building blocks bearing an sp3 carbon and a hydroxy function

The synthesis of novel symmetrical liquid crystalline compounds based on 5-methyl-5-[2-(4-alkyloxyphenyl)-2-hydroxyethyl]-2,2-bipyridines is reported, together with some physical properties. Although the chelating head-groups are connected via a chiral sp³ carbon atom, all the materials are mesomorphic. Intermolecular hydrogen bonding between pyridino and hydroxy fragments in the mesophases is made apparent by FTIR spectroscopy.     

Postbuckling Analysis of Nonconservative Elastic Systems

Abstract

Previous work on the postbuckling and imperfection-sensitivity of elastic structures has concentrated on conservative systems. The results of Koiterand others have led to a general theory of nonlinear stability behavior for these systems. The theory must be modified when nonconservative forces are present, and this is the aim of the present paper.

Discrete, nonconservative, elastic systems which exhibit static (divergence) instability are considered. The nonlinear behavior in the neighborhood of a critical point is analyzed by means of a perturbation procedure. When the critical point is simple, the results are similar to those for conservative systems. When a coincident critical point exists, however, different types of behavior occur. In many cases there is no bifurcation at all, with only the fundamental (trivial) equilibrium path passing through the critical point. Imperfection-sensitivity is more severe than for the typical bifurcation points and can even occur when the perfect system has no bifurcation. The results are illustrated with the use of a nonlinear double pendulum model subjected to a partial follower load.     

Pertubations compactes des contractions multivoques

LetE be a Banach space, θ a multivalued contraction with closed values onE andf a continuous function fromE to itself with conditionally compact range. We prove that multifunction ψ=f+θ has fixed points if θ is convex-valued or if the range off is contained in a Lipschitz simple path. We also prove by counterexamples that the previous result is not true if the range off is only assumed to be homeomorphic to a segment or diffeomorphic to a circle.     

From the Boltzmann equation to the Stokes‐Fourier system in a bounded domain

We prove that the renormalized solutions of the Boltzmann equation considered in a bounded domain with different types of (kinetic) boundary conditions converge to the Stokes‐Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a bounded domain. © 2003 Wiley Periodicals, Inc.     

Douglas algebras which are invariant under the Bourgain map

Part of this work was done while the second author was visiting the University of Georgia, Athens/Georgia, USA.     

Acoustic diffraction by a half-plane in a viscous fluid medium

We consider the diffraction of a time-harmonic acoustic plane wave by a rigid half-plane in a viscous fluid medium. The linearized equations of viscous fluid flow and the no-slip condition on the half-plane are used to derive a pair of disjoint Wiener-Hopf equations for the fluid stresses and velocities. The Wiener-Hopf equations are solved in conjunction with a requirement that the stresses are integrable near the edge of the half-plane. Specific wave components of the scattered velocity field are given analytically. A Padé approximation to the Wiener-Hopf kernel function is used to derive numerical results that show the effect of viscosity on the velocity field in the immediate vicinity of the edge of the half-plane.     

The ground state for sticky disks

It is proven that the ground state of the two-dimensional sticky potential is the triangular lattice.Research supported in part by NSF grant MCS 78-01520-A01.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.