Etude théorique d'une chaine polyénique infinie par la méthode LCAO-SCF-CO

Résumé La méthode LCAO-SGF-CO permet de montrer que dans une chaine polyénique infinie, les liaisons sont alternativement courtes et longues.

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The LCAO-SCF-CO method is used to show that an infinite polyenic chain exhibits marked bond alternation.

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Zusammenfassung Das LCAO-SCF-CO-Rechenverfahren bietet die Möglichkeit, in einer unendlichen Polyenkette festzustellen, da\ die Bindungen abwechselnd kurz und lang sind.

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Titulaire d'une bourse de spécialisation de l'IRSIA.

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Nous tenons à exprimer nos vifs remerciements à la Société AGFA.-GEVAERT et à l'Institut pour l'encouragement de la Recherche Scientifique dans l'Industrie et l'Agriculture (I.R.S.I.A.) pour l'aide matérielle accordée au laboratoire de Chimie Quantique et pour la bourse de spécialisation octroyée à l'un de nous (J.M.A.).     

Diffraction of light by two superposed parallel ultrasonic waves,having arbitrary frequencies. General symmetry properties; method of solution by series expansion

In this study about the diffraction of light by superposed parallel ultrasonics, with frequency ration ₁:n ₂, we deduce a general symmetry property for the intensities of the diffraction pattern: if the intensities of the ordersn and ?n are equal the phase-difference must be of the form:

$$\delta = \frac{{n_1 - n_2 }}{{n_1 }} \begin{array}{*{20}c} \pi \\ 2 \\ \end{array} + p \frac{\pi }{{n_1 }}$$     

The construction of self-adjoint operators of Hill with periodic eigenfunctions

We find necessary and sufficient conditions to guarantee the existence resp. coexistence of linear independent periodic zero-elements of period mω, m ? ?, of Hill's differential operator D² + Q, with ω being the minimal period of the function Q. These conditions enable us to construct an unbounded self-adjoint operator which only has periodic eigenfunctions with prescribed period.     

Double Bragg and Bragg/normal diffraction of two laser beams by ultrasound

An accurate theory is developed describing the diffraction of two light beams incident at various Bragg angles on an ultrasonic beam, taking into account the phase-difference between the two light waves. The general results are outside the range of the Raman-Nath approximation and a comparison is made with an alternative configuration in which one of the light waves is normally incident.     

Diffraction of light bv two parallel superposed supersonic waves,one being the second harmonic,the other the third harmonic of the same fundamental. Description of two methods leading to approximate solutions in finite form

The diffraction of light by superposed parallel ultrasonic waves, with frequency ratio 2:3, is solved by the NOA-method (N?th order approximation method). Explicit calculations of the intensities are given forN = 2. The same problem is also treated with the SA-method (method of successive approximations). The latter results are improved by iteration. In both methods the general symmetry property of the diffraction pattern is verified, namely, that symmetry with respect to the zero order occurs when the phase-difference of the supersonic waves δ = (2k + 1) π/4.     

Optimal Trajectory Tracking of Underwater Vehicle-Manipulator Systems Through the Clifford Algebras and of the Davies Method

The manipulation in singular regions generates an instantaneous reduction in the mechanism mobility which can result in some disturbances in the trajectory tracking. In proximity of the singularities, small velocities in the end-effectors generates high speeds in the joints due to the gradual reduction of the mobility. The phenomenon of kinematic singularity generates a instantaneous instability in torque profile of the redundant robotic systems by the transformation of secondary joints to primary joints. The disturbances of the underwater environment intensifies the effects of the kinematic singularities because the hydrodynamic strongly oppose to torque variations. This work presents a methodology for using dual quaternions in the posture feedback of a Underwater Vehicle-Manipulator System (UVMS) using the Davies method which avoids kinematic singularities and ensures the optimal torque profiles.     

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MACROCYCLES [Agrave] ATOMES DE PHOSPHORE ET DE BORE HYPERVALENTS DÉTERMINATION DE LEUR TAILLE PAR SPECTROMÉTRIEDE MASSE

Abstract

Macrorings bearing hexacoordinated phosphorus atoms or (and) tetracoordinated boron atoms, have been prepared from condensation of phenyldichlorophosphane in presence of diethylamine, or (and) boric or phenylboronic acids with some polyphenols. Their structures-have been established by NMR, microanalysis and mass spectrometry. These compounds are constituted according to (1 + 1), (2 + 2) and (3 + 3) stoichiometry.