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).     

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.     

Photosensitization of TiO2 colloids by Erythrosin B in acetonitrile

Photosensitization by Erythrosin B of a TiO₂ colloidal dispersion in acetonitrile has been studied by fast kinetic spectroscopy. The dye molecules adsorbed on the TiO₂ surface had a significantly shorter lifetime (2̃ 250 ps) compared to those in homogeneous solution (≈ 1.6 ns) in acetonitrile. The photosensitization of TiO₂ occurred more efficiently from the singlet than from the triplet state of the dye.     

Proton to carbon-13 INEPT in solid-state NMR spectroscopy

A refocused INEPT through-bond coherence transfer technique is demonstrated for NMR of rigid organic solids and is shown to provide a valuable building block for the development of NMR correlation experiments in biological solids. The use of efficient proton homonuclear dipolar decoupling in combination with a direct spectral optimization procedure provides minimization of the transverse dephasing of coherences and leads to very efficient through-bond (1)H-(13)C INEPT transfer for crystalline organic compounds. Application of this technique to 2D heteronuclear correlation spectroscopy leads to up to a factor of 3 increase in sensitivity for a carbon-13 enriched sample in comparison to standard through-bond experiments and provides excellent selectivity for one-bond transfer. The method is demonstrated on a microcrystalline sample of the protein Crh (2 x 10.4 kDa).     

Alkylation of heme by the antimalarial drug artemisinin

The peroxide function of artemisinin has been activated by iron(II)-heme generated in situ from iron(III)-protoporphyrin-IX and glutathione, a biologically relevant reductant. In mild conditions, this reaction produced a high yield (85%) of heme derivatives alkylated at alpha-, beta-, and delta-meso positions by a C4-centered radical derived from artemisinin.