Index theory for quasi-crystals I. Computation of the gap-label group

In this paper, we give a complete solution to the gap labelling conjecture for quasi-crystals. The method adopted relies on the index theory for laminations, and the main tools are the Connes-Skandalis longitudinal K-theory index morphism together with the measured index formula.     

Magnetic properties of fcc (Co95Fe5)1-xAlx ribbons

Rapidly quenched (Co₉₅Fe₅)_1-xAl_x ribbons are investigated by X‐ray diffraction, magnetization, and Mössbauer effect measurements. A single fcc phase is obtained for all ribbons x ? 10 at.%. The lattice constant increases linearly with x and is discussed in connection with magnetic moment. The influence of Al substitution on both magnetization and Fe‐atom hyperfine field (H) is studied. At 296 K, the magnetization decreases linearly while H drops nonlinearly as x increases. Al substitution leads to substantial differences in iron hyperfine fields in bcc and fcc systems. Fe moment is perturbed differently by Al substitution in fcc (Co₉₅Fe₅)_1-xAl_x and bcc Fe–Al systems.     

Differential characters in K-theory

We define the new notion of R/Z-differential K-characters and study some properties. In particular, we show that the spectral eta invariant is an R/Z-secondary invariant in this theory.     

On the blow-up criterion of 3D Navier-Stokes equations

In this paper we prove some properties of the maximal solution of Navier-Stokes equations. If the maximum time is finite, we establish that the growth of is at least of the order of (see Eq. (1.4)), also we give some new blow-up results. Specific properties and standard techniques are used.     

Index Theory and Non-Commutative Geometry I. Higher Families Index Theory

We prove an index theorem for foliated manifolds. We do so by constructing a push forward map in cohomology for a k-oriented map from an arbitrary manifold to the space of leaves of an oriented foliation, and by constructing a Chern–Connes character from the k-theory of the compactly supported smooth functions on the holonomy groupoid of the foliation to the Haefliger cohomology of the foliation. Combining these with the Connes–Skandalis topological index map and the classical Chern character gives a commutative diagram from which the index theorem follows immediately.     

A higher Lefschetz formula for flat bundles

In this paper, we prove a fixed point formula for flat bundles. To this end, we use cyclic cocycles which are constructed out of closed invariant currents. We show that such cyclic cocycles are equivariant with respect to isometric longitudinal actions of compact Lie groups. This enables us to prove fixed point formulae in the cyclic homology of the smooth convolution algebra of the foliation.

     

How M?ssbauer spectroscopy can improve Li-ion batteries

In the domain of Li-ion batteries, M?ssbauer spectroscopy is mainly used for the characterization of electrode materials and the analysis of electrochemical reactions. Depending on the properties under investigation, different approaches are often considered, which are based on ex situ, in situ and operando measurements. The specific electrochemical cells and sample preparations used for such measurements are described in this paper. Applications to selected examples of cathode and anode materials are presented in order to show how M?ssbauer spectroscopy, when associated with other techniques, provides essential information to understand the mechanisms and improves the performances of Li-ion batteries.     

Polyphenols contents,heavy metals analysis and in vitro antibacterial activity of extracts from Cladanthus arabicus and Bubonium imbricatum of Moroccan Origin

Abstract

Aim of this study was to evaluate polyphenols and major and trace elements of Cladanthus arabicus and Bubonium imbricatum, along with their in vitro antibacterial activity against six multidrug resistant Enterobacteriaceae (Escherichia coli S33/16, E. coli S34/16, Proteus mirabilis S32/16, Klebsiella pneumoniae S12/16, Enterobacter cloacae S5/16, and Salmonella sp S12/14). UV spectrophotometry, ultra-high-performance liquid chromatography coupled to mass spectrometry and inductively coupled plasma mass spectrometry were used to evaluate total polyphenol content, quali-quantitative profile of single polyphenols and inorganic elements of the extract. The antibacterial activity was investigated by standard methods. Twelve polyphenols were identified in both plants and these were more concentrated in B. imbricatum than C. arabicus extracts. High levels of minerals, essential trace elements and tolerable levels of heavy metals (Cd, As and Pb) were found. Furthermore, the extracts showed also a strong in vitro antibacterial activity, particularly versus E. coli S33/16 (MIC, 0.125?mg ml^?1).     

Calcul du label des gaps pour les quasi-cristauxComputation of the gap-labelling for quasi-crystals

We give in the present Note a proof of the Bellissard gap-labelling conjecture for quasi-crystals. Our main tools are the measured index theorem for laminations on the one hand, and the naturality of the longitudinal Chern character on the other hand. To cite this article: M.-T. Benameur, H. Oyono-Oyono, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 667–670.