Sur les valeurs propres d'un oscillateur harmonique perturbé

Sans résumé Dedicated to Professor Shmuel Agmon     

Finding nonnormal bent functions

The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions.     

Disorder arising from the location of enantiomers in a twist-boat structure: 2,6-trans-2,4,6-tris(trichloromethyl)-1-oxa-3,5-dithian

Crystals of the title compound are orthorhombic, Pca2₁;a=27.586(4),b=10.509(3),c=11.080(2) Å,V=3212(1) ų,Z=8. The structure was solved by direct methods, from data collected at room temperature on an Enraf-Nonius CAD4 diffractometer, and refined by full-matrix least squares to a finalR value of 0.055 using 2043 reflections. One of the two independent molecules in the asymmetric unit is disordered. The disorder is manifested mainly between the oxygen atom and one sulfur atom and is caused by opposite enantiomers occupying corresponding positions in different unit cells. The endocyclic torsion angles in both independent molecules are very similar but the disposition of the heteroatoms on the twist-boat framework is different in the two molecules. Site occupancy of the two models on this framework in the disordered molecule is in the ratio 2179 with the smaller proportion being very similar to the ordered molecule and the remainder similar to that found in the normal molecule oftrans-4-chloro-2,4,6-tris(trichloromethyl)-1-oxa-3,5-dithian (Irving and Irving, 1988).     

Determination of the correlation effects in molecules using the complete error potential

Summary The complete error potential is used for the study of the correlation of molecules. The correlation can be seen as a relaxation of the electrons and a relaxation of the nuclei. From the Fermi sea, the electronic relaxation gives rise to a partial excitation of each orbital which collectively generates a linear, a surface or a volume pressure; the resulting forces acting on the nuclei are defined in a general theory of the intramolecular forces. H₃, H ₃ ⁺ , the diatoms and the hydrid of the first nine elements are taken as examples.     

Sensitivity of metal nanoparticle surface plasmon resonance to the dielectric environment

Electrodynamic simulations of gold nanoparticle spectra were used to investigate the sensitivity of localized surface plasmon band position to the refractive index, n, of the medium for nanoparticles of various shapes and nanoshells of various structures. Among single-component nanoparticles less than 130 nm in size, sensitivities of dipole resonance positions to bulk refractive index are found to depend only upon the wavelength of the resonance and the dielectric properties of the metal and the medium. Among particle plasmons that peak in the frequency range where the real part of the metal dielectric function varies linearly with wavelength and the imaginary part is small and slowly varying, the sensitivity of the peak wavelength, lambda, to refractive index, n, is found to be a linearly increasing function of lambda, regardless of the structural features of the particle that determine lambda. Quasistatic theory is used to derive an analytical expression for the refractive index sensitivity of small particle plasmon peaks. Through this analysis, the dependence of sensitivity on band position is found to be determined by the wavelength dependence of the real part, epsilon', of the particle dielectric function, and the sensitivity results are found to extend to all particles with resonance conditions of the form, epsilon' = -2chin(2), where chi is a function of geometric parameters and other constants. The sensitivity results observed using accurate computational methods for dipolar plasmon bands of gold nanodisks, nanorods, and hollow nanoshells extend, therefore, to particles of other shapes (such as hexagonal and chopped tetrahedral), composed of other metals, and to higher-order modes. The bulk refractive index sensitivity yielded by the theory serves as an upper bound to sensitivities of nanoparticles on dielectric substrates and sensitivities of nanoparticles to local refractive index changes, such as those associated with biomolecule sensing.     

Polymerisation en phase homogene du methyl-2 thiiranne amorcee par les thiolates de cadmium et de zinc. Influence des interactions monomere-metal sur la stereoregularite des polymeres

The stereoregularity of polymethylthiiranes initiated by zinc and cadmium thiolates depends upon the nature of the metal, temperature, solvent and the monomer/initiator concentrations ratio. Complexation of the metal with monomer has been studied by (¹³C) and (¹H) NMR on a model molecule, dimethylcadmium. Cryoscopic measurements made on a soluble cadmium thiolate have shown the presence of aggregates. The relationship between these observations and polymer stereoregularity is discussed.