Cohomologie des groupes et corps d'invariants multiplieatifs

Sans résumé     

Heterodinuclear Ln[bond]Na complexes with an asymmetrical macrocyclic compartmental Schiff base

Heterodinuclear lanthanide(III)-sodium(I) complexes [LnNa(L)(Cl)(2)(CH(3)OH)] (Ln=La[bond]Nd, Sm[bond]Lu), where H(2)L is a [1+1] asymmetric compartmental macrocyclic ligand containing a N(3)O(2) Schiff base and a O(3)O(2) crown-ether-like coordination site, have been prepared and characterized by IR, (1)H, (13)C, and (23)Na NMR spectroscopy, mass spectrometry, and electron microscopy. In the solid state, the lanthanide(III) ions coordinate the Schiff-base N(3)O(2) site, and the sodium ion occupies the O(3)O(2) crownlike cavity, as shown by the X-ray crystal structures of the Nd, Eu, Gd, and Yb derivatives. In these complexes, the lanthanide(III) ion is coordinated by two chlorine atoms in the trans position and by three nitrogen and two negatively charged phenol oxygen atoms of the Schiff base, and the ion is heptacoordinated with a pentagonal bipyramidal geometry. The sodium ion is coordinated by three etheric oxygen atoms and the two phenolic oxygens that act as a bridge. A methanol molecule is also coordinated in the apical position of the resulting pentagonal pyramidal polyhedron. A detailed (1)H and (13)C NMR study was carried out in CD(3)OD for both diamagnetic and paramagnetic heterodinuclear complexes [LnNa(L)(Cl)(2)(CH(3)OH)]. The complexes are also isostructural in solution, and their structures parallel those found in the solid state. Moreover, some significative distances determined in the solid state and in solution are comparable. Finally, the potential use of these complexes as molecular probes for the selective recognition of specific metal ions has been tested. In particular, their ability to act as shift reagents and the selectivity of the O(3)O(2) site towards Li(+), Ca(2+), and K(+) were investigated by (23)Na NMR spectroscopy.     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

Cocycles d'Euler et de Maslov

Conclusion Nous espérons avoir convaincu le lecteur qu'il peut être utile de considérer la classe de Maslov comme une classe bornée. Dans [Gh], nous avons montré que la classe d'Euler bornée pour un groupe d'homéomorphismes directs du cercle rend compte de la dynamique topologique de ce groupe. Existe-t-il un résultat analogue pour Sp(2n,)? En d'autres termes, soit un groupe discret et ₁, ₂ deux représentations de dans Sp(2n,). On suppose que les cocycles ₁ ^* et ₂ ^* définissent la même classe bornée. Que peut-on en conclure sur ₁ et ₂?Par ailleurs, l'article [At l] traite aussi d'invariants sur SL(2,) différents de ceux que nous avons considérés, comme par exemple les fonctionsL de Shimizu. Est-il possible de les faire rentrer naturellement dans notre cadre?

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Design and Synthesis of a γ1β8‐Cyclodextrin Oligomer: A New Platform with Potential Application as a Dendrimeric Multicarrier

We report the synthesis and characterization of a water‐soluble, star‐shaped macromolecular platform consisting of eight β‐cyclodextrin (β‐CD) units anchored to the narrower rim of a γ‐CD core through bis(triazolyl)alkyl spacers. The efficient synthetic protocol is based on the microwave (MW)‐promoted Cu‐catalyzed 1,3‐dipolar cycloaddition of CD monoazides to CD monoacetylenes. The ligand‐hosting capability of the construct has been assessed by relaxometric titration and nuclear magnetic relaxation dispersion (NMRD) profiling, which showed it to be good, and this was supported by molecular dynamics simulations. To demonstrate the feasibility of obtaining supramolecular structures with high hosting ability, we designed a dimeric platform, formed by joining two nonamers through the γ‐CD cores through a bis(lithocholic acid) linker. With a view to the potential biological applications, cytotoxicity and extent of binding to human serum albumin were assessed. The properties of this dendrimeric multicarrier make it suitable for pharmaceutical and diagnostic purposes, ranging from targeted drug delivery to molecular imaging.     

Ternary complexes between cationic GdIII chelates and anionic metabolites in aqueous solution: an NMR relaxometric study

The (1)H and (17)O NMR relaxometric properties of two cationic complexes formed by Gd(III) with a macrocyclic heptadentate triamide ligand, L(1), and its Nmethylated analogue, L(2), have been investigated in aqueous media as a function of pH, temperature and magnetic field strength. The complexes possess two water molecules in their inner coordination sphere for which the rate of exchange has been found to be sensibly faster for the Nmethylated derivative and explained in terms of electronic effects (decrease of the charge density at the metal center) and perturbation of the network of hydrogen-bonded water molecules in the outer hydration sphere. The proton relaxivity shows a marked dependence from pH and decreases of about six units in the pH range 6.5 to 9.0. This has been accounted for by the displacement of the two water molecules by dissolved carbonate which acts as a chelating anion. The formation of ternary complexes with lactate, malonate, citrate, acetate, fluoride and hydrogenphosphate has been monitored by (1)H NMR relaxometric titrations at 20 MHz and pH 6.3 and the value of the affinity constant, K, and of the relaxivity of the adducts could be obtained. Lactate, malonate and citrate interact strongly with the complexes (log K > or =3.7) and coordinate in a bidendate mode by displacing both water molecules. Larger affinity constants have been measured for GdL(2). Acetate, fluoride and hydrogenphosphate form monoaqua ternary complexes which were investigated in detail with regard to their relaxometric properties. The NMR dispersion (NMRD) profiles indicate a large contribution to the relaxivity of the adducts from water molecules belonging to the second hydration shell of the complexes and hydrogen-bonded to the anion. A VT (17)O NMR study has shown a marked increase of the rate of water exchange upon binding which is explained by coordination of the anion in an equatorial site, thus leaving the water molecule in an apical position, more accessible for interactions with the solvent molecules of the second hydration shell which facilitate the exchange process.     

Unstable manifold,Conley index and fixed points of flows

We study dynamical and topological properties of the unstable manifold of isolated invariant compacta of flows. We show that some parts of the unstable manifold admit sections carrying a considerable amount of information. These sections enable the construction of parallelizable structures which facilitate the study of the flow. From this fact, many nice consequences are derived, specially in the case of plane continua. For instance, we give an easy method of calculation of the Conley index provided we have some knowledge of the unstable manifold and, as a consequence, a relation between the Brouwer degree and the unstable manifold is established for smooth vector fields. We study the dynamics of non-saddle sets, properties of existence or non-existence of fixed points of flows and conditions under which attractors are fixed points, Morse decompositions, preservation of topological properties by continuation and classify the bifurcations taking place at a critical point.