NMR studies of the chalcogen analogues of benzofuran. IV—Proton,carbon-13 and selenium-77 magnetic resonance in nitrobenzo[b]selenophenes

The ¹H, ¹³C and ⁷⁷Se chemical shifts have been measured for mononitrobenzo[ b ]selenophenes. For the homocyclic nuclei, the observed ¹H- and ¹³C-values calculated from the empirical increments of nitrobenzene. Anomalous effects are observed in the 2- and 3-substituted derivatives and the nature of the Se? NO₂ interactions in the former is discussed. ⁷⁷Se chemical shifts of the 4-, 5- and 7-nitro derivatives are approximately correlated with the CNDO calculated electron densities; they also compare well with those of selenoanisoles and other phenyl alkyl selenides. The chemical shifts are also compared with the corresponding values in other heterocycles containing a selenophene moiety.     

1H and 13C NMR studies of two monosubstituted [2.2]paracyclophanes

250 MHz ¹H NMR of two monosubstituted [2.2]paracyclophanes shows that whether the substituent is an electron releasing group, OMe, or a withdrawing group, CO₂Me, the transannular effect is deshielding. 62.86 MHz ¹³C NMR shows that among the six transannular effects, only one has a sign which changes with the nature of the substituent (–4.6 ppm for OMe but +3.3 ppm for CO₂Me).     

Sur la structure des alkylcycloarsoxanes (RAsO)α

Organometallic compounds of general formula (RAsO)_α are associated as trimers (R = C₂H₅, C₃H₇, C₄H₉) or even as a tetramer (R = CH₃). Their physicochemical properties show them to be cyclic, the oxygen atoms being located in the bridging position. A “limited” electron delocalization may occur in these rings.     

Sur un théorème de prolongement fonctionnel de Keldych concernant le problème de Dirichlet

Sans résumé Ces recherches ont fait l'objet d'exposés, d'abord au Séminaire de théorie du potential (Paris, javier 1960).     

Evolution of Orbits and Quantum Correlation Functions by Quadratic Hamiltonians

Quantum systems with quadratic Hamiltonians are considered. Some results about the time evolution of homogeneous polynomials and of quantum correlation functions are given. The image of arbitrary orbit of Weyl–Heisenberg group under this time evolution is shown to be again an orbit of this group. For quantum free particle it is shown that its time evolution intersects arbitrary such orbit at most once. A result about existence of more orbits having the same dispersion of some quantum position is presented.PACS: 02.20.Qs, 02.30.Sa     

Statistics of Fourier modes of velocity and vorticity in turbulent flows: intermittency and long-range correlations

We perform a statistical analysis of experimental fully developed turbulence longitudinal velocity data in the Fourier space. We address the controversial issue of statistical intermittency of spatial Fourier modes by acting on the finite spectral resolution. We derive a link between velocity structure functions and the flatness of Fourier modes thanks to cascade models. Similar statistical behaviors are recovered in the analysis of spatial Fourier modes of vorticity obtained in an acoustic scattering experiment. We conclude that vorticity is long-range correlated and found more intermittent than longitudinal velocity.