Canonical subgroups over Hilbert modular varieties

We obtain new results on the geometry of Hilbert modular varieties in positive characteristic and morphisms between them. Using these results and methods of rigid geometry, we develop a theory of canonical subgroups for abelian varieties with real multiplication. To cite this article: E.Z. Goren, P.L Kassaei, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

2-Methyl-(1Z,3E)-butadiene-1,3,4-tricarboxylic acid, "isoprenetricarboxylic acid"

[reaction: see text] The synthesis of the title compound 7 from ethyl glyoxylate and dimethyl and diethyl beta-methylglutaconate is described along with its physical properties that suggest its inability to assume a cis-dienoid structure due to steric hindrance between the methyl and carboxyl groups.     

Experimental and theoretical study of stabilization of delocalized forms of semibullvalenes and barbaralanes by dipolar and polarizable solvents. Observation of a delocalized structure that is lower in free energy than the localized form

[reaction: see text] UV/vis spectra of thermochromic semibullvalenes 1 and barbaralanes 2, which undergo rapid degenerate Cope rearrangements, display temperature-dependent shoulders (1b, 1d, 1e) or absorption maxima (1c, 2c, 2f) at the low-energy side of their strong UV bands. These long-wavelength absorptions are ascribed to Franck-Condon transitions from delocalized structures 1(deloc) and 2(deloc). Gibbs free energy differences, DeltaG*, between delocalized and localized forms were calculated from the temperature dependence of the long-wavelength absorptions. Dipolar and polarizable solvents strongly affect and even may reverse the relative stabilities of the localized and delocalized forms of 1c, 2c, and 2f. For example, DeltaG*(2c) = 8 kJ mol(-)(1) in cyclohexane, 2 kJ mol(-)(1) in dimethylformamide, and -3 kJ mol(-)(1) in N,N'-dimethylpropylene urea (DMPU), so that (2c(deloc))(DMPU) becomes the global minimum. In contrast to the case for 2c, the intensities of the long-wavelength shoulders of the yellow semibullvalenes 1b, 1d, and 1e are only moderately influenced by solvents, and the rates of Cope rearrangements of the nonthermochromic, colorless barbaralanes 2a and 2b, determined by NMR methods, are almost solvent-invariant. In search of the solute properties that are decisive in determining the influence of solvent upon DeltaG*, electrical dipole and quadrupole moments and molecular polarizabilities have been calculated using the B3LYP/6-31G* method and solvation energies have been computed with the conductorlike polarized continuum model (CPCM). The results of these calculations indicate that the solvent effects are due to the greater polarity and polarizability of the delocalized structures relative to the localized structures.     

Photoionization of highly charged ions using an ECR ion source and undulator radiation

Photoionization of Xe4+ to Xe7+ ions was studied by combining an electron cyclotron resonance ion source with synchrotron radiation. Multiconfiguration Dirac-Fock calculations were performed to interpret the data. Many autoionization lines were measured and identified, resulting from excitation of a 4d electron into nf and np orbitals followed by Auger decay of the excited states. Continuum photoionization is negligible for the higher members of the isonuclear series.     

Acyclic and cyclic thioenamino peptides: solution- and solid-phase synthesis

Seven- and 10-membered cyclic thioenamino peptides, that is, 1,4-thiazepinone (11) and cyclic thioenamino peptide 9 (which represents a potential γ-turn mimetic), were synthesized, and the structure of 11 was secured by X-ray diffraction analysis of its TFA salt. The aforementioned compounds were prepared in solution and by solid-phase synthesis. Additionally, we have prepared thioenamino diketopiperazine synthon 16.     

NQR Spin Diffusion in an Inhomogeneous Internal Field

The theory of NQR spin diffusion is extended to the case of spin lattice relaxation and spin diffusion in an inhomogeneous field. Two coupled equations describing the mutual relaxation and the spin diffusion of the nuclear magnetization and dipolar energy were obtained by using the method of nonequilibrium state operator. The equations were solved for short and long times approximation corresponding to the direct and diffusion relaxation regimes.