Classes caractéristiques d''une π-algèbre et suite spectrale en K-théorie bivariante

Résumé Pour tout groupe discret et pour toute -algèbre D, la C ^*-algèbre D(E) (dont la définition exacte est donnée dans la section 4) est la version équivariante de la C ^*-algèbre C(B, D) des fonctions continues sur B, le classifiant du groupe, à valeurs dans D et qui s'annulent à l'infini. Si D désigne une autre -algèbre, nous définissons une suite spectrale en K-théorie bivariante dont les premiers termes sont donnés par les groupes H ^p (B, KK(D, D)) et qui converge (lorsque B est de dimension finie) vers KK(B; D(E), D(E)). Cette suite spectrale généralise celle de Kasparov mais est obtenue de manière différente: en étendant la définition des quasihomomorphismes aux C(X)-algèbres (X est une espace topologique localement compact), on a recours à des méthodes homotopiques telles les décompositions de Postnikov et le calcul des groupes d'homotopie des espaces d'équivalences d'homotopie. Sous certaines hypothèses, ces mÊmes constructions nous permettent de définir, pour toute -algèbre D, une obstruction, appelée classe secondaire de la -algèbre D, qui détermine la différentielle d ₂ de la suite spectrale de Kasparov.

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For all discrete group and all -algebra D, the C ⁺-algebra D(E) (whose exact definition is given in Section 4) is the equivariant version of the C ^*-algebra C(B, D) of continuous functions from B (the classifiant of the group) to D, vanishing at infinity. If D is another -algebra, we define a spectral sequence in bivariant K-theory whose first terms are given by the groups H ^p (B, KK(D, D)) and which converges (if B of finite dimension) to KK(B; D(E), D(E)). This spectral sequence generalises the spectral sequence given by Kasparov but it is obtained in a quite different way: by extending the definition of quasihomomorphisms to the C(X)-algebras (where X is a locally compact topological space), we use homotopical methods, like Postnikov decompositions and the calculus of homotopy groups of spaces of homotopy equivalences. Furthermore, under certain hypotheses, with these constructions, we define an obstruction, called the secondary class of the -algebra D, which determines the differential d ₂ of the Kasparov spectral sequence.

     

The electron-releasing homoconjugated carbonyl group. Application to the total syntheses of 3-deoxy-, 4-deoxy-hexose, lividosamine and derivatives

The regioselective electrophilic addition of benzeneselenyl bromide to (−)-(1S,4S)-7-oxabicyclo[2.2.1]-hept-5-en-2-one were exploited to develop efficient syntheses of methyl 3-deoxy--D-arabino-hexofuranoside and 4-deoxy-D-lyxo-hexopyranose. Similarly, D-lividosamine (3-deoxy-D-glucosamine) was derived from (+)-(1R,4R)-7-oxabicyclo[2.2.1]hept-5-en-2-one.     

Vibrational Spectra of Anhydrous Lanthanum,Europium, Gadolinium,and Dysprosium Nitrates and Oxinitrates

IR. and Raman spectra of LnONO₃ (50–4,000 cm^?1, Ln?La, Gd, Eu, and Dy) are reported and discussed. The low frequency region of the spectra reflects the cubic structure of these compounds. The dimensions of the cubic unit cells determined by X-Ray powder diagrams are: 12.81 ± 0.05 Å for EuONO₃, 12.69 ± 0.05 Å for GdONO₃, and 12.67 ± 0.05 Å for DyONO₃. The vibrational frequencies of the nitrato group are consistent with a bidentate nitrate of C_2v symmetry. The synthesis of anhydrous Ln (NO₃)₃ (Ln?La, Gd, Eu, and Dy) by dehydration of the corresponding penta- or hexahydrates is described. The IR. and Raman spectra (50-4,000 cm^?1) are analysed. Splitting of the bands point to a complex structure of these compounds. All six vibrational modes of the nitrato group are observed and the data are again consistent with bidentate NO^?₃ moieties. Finally, an analytical control of the purity of Ln (NO₃)₃ is suggested.     

The compton defect in ammonia as observed using 35 keV incident electrons

Using a 35 keV electron beam incident on NH₃, precision measurements of the energy loss position of the Compton peak have been performed. The observed Compton peak is found to be at larger energy losses than predicted for an electron scattered through the same angle from a stationary unbound electron. This defect has been studied for the momentum transfer range 0.5 au < K < 11 au, and is shown to be nonzero even at large K values. A sudden increase in the magnitude of the defect is observed when the inner electrons start contributing to the maximum of the Compton profile. This could suggest the possibility that the defect is related to the binding energies of the target electrons.     

Principal active species of horseradish peroxidase, compound I: a hybrid quantum mechanical/molecular mechanical study

The active species, Compound I, of horseradish peroxidase (HRP) has been investigated by quantum mechanical/molecular mechanical (QM/MM) calculations using 10 different QM regions. In accord with experimental data, the lowest doublet and quartet states are found to be virtually degenerate, with two unpaired electrons on the FeO moiety and one localized on the porphyrin in an a(2u)-dominant orbital with a minor, but nonnegligible, a(1u) component. The proximal ligand appears to be imidazole rather than imidazolate. The hydrogen-bonding network around the FeO moiety (i.e., Arg38 and His42) has significant influence on the axial bonds and the spin density distribution in the FeO moiety. Including this network in the QM region was found to be essential for reproducing the experimental M?ssbauer parameters. The protein environment shapes most of the subtle features of Compound I of HRP.     

Quantitative information on pore size distribution from the tangents of comparison plots

The comparison plot obtained from the nitrogen adsorption data has a similar shape to that of the curve of accumulating pore volume of a solid. The intrinsic nature of this relation is discussed. It is known that the derivatives of the accumulating pore volume with respect to the pore size are the pore size distribution (PSD) of the solid. Thus, the tangent curve of the comparison plot can display, at least qualitatively, the PSD of a solid, over a wide range of pore sizes (from approximately 1 to 50 nm) because the comparison plot is applicable to both micropores and mesopores. Quantitative pore structure information can be derived from the comparison plots by establishing a relationship between the t value and the pore size from the samples with uniform pore structure and known pore sizes, such as MCM-41 and alumina pillared clay samples. A calculation procedure to derive quantitative PSD from the comparison plots is suggested, giving reasonable results. This study proposes concise and reliable methods based on the comparison plots to derive information on pore structure in porous solids.