Sui diffeomorfismi di varietà isotopi all'identità

Riassunto Si considera il gruppoI(M) dei diffeomorfismi di una varietà differenziabileM che sono diffeotopi all'identità per una diffeotopia a supporto compatto. Viene dato (in maniera costruttiva) un insieme di generatori perI(M), costituito dai diffeomorfismi a supporto in uno degli aperti di un fissato ricoprimento. Conseguentemente si introduce una metrica suI(M) la quale induce una topologia che, pur essendo strettamente più fine dell'usuale topologiaC ^∞, rende ancoraI(M) gruppo topologico connesso.

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Summary LetM be a differentiable manifold. We prove that, iff is a diffeomorphism ofM ontoM which is isotopic to the identity by an isotopy having compact support thenf is a product of diffeomorphisms having a support of given size. As a consequence a distance δ on Diff₀ (M) is given such that it induces a topology stronger than the usualC ^∞-topology, even if it does not disconnect Diff₀ (M).

     

Holography in partially coherent light

A Michelson interferometer has been used to obtain good holographic carrierfringes of the order of 200 to 300 fringes/ mm over an area of 1 cm × 1.5 cm with a Hg-are source and extended aperture with and without filter. The fringes have been used to record holograms. The image reconstruction has been done with light from the Hg-arc without the use of any filter. Experimental results for a continuous-tone object have been presented. The advantages and disadvantages and some of the potential applications of this technique have been mentioned.     

Reciprocal and variational theorems for nonlocal theory of viscoelastic materials

Summary We study some variational and reciprocal problems for viscoelastic materials with nonlocal constitutive equations and in particular with dissipative boundary conditions.

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Riassunto Si determinano alcuni teoremi variazionali e di reciprocitá per materiali viscoelastici con una dipendenza anche spaziale e con condizioni al contorno dissippative.

     

Determination of the Relative Configurations in the Side Chains of the Antibiotics Hedamycin and Pluramycin A; Synthesis and NMR. Data of Suitable Model Compounds

Several diepoxyhexanoates and epoxyhexenoates were prepared by epoxidation of methyl 2-methyl-2,4-hexadienoate or by Darzens condensation. Their ¹ H- and ¹³C-NMR. spectra were measured and assigned. Comparison of these data with the spectra of the antibiotics hedamycin ( 1 ) and pluramycin A ( 2 ) allowed the determi-nation of the relative configurations in the side chains of these antibiotics. They were found to be (14R*,16S*,17R*,18S*) for hedamycin ( 1 ) and (14R*,16S*,17Z) for pluramycin A ( 2 ).     

13C direct detected experiments: optimization for paramagnetic signals

To optimize 13C direct detected experiments for the observation of signals close to a paramagnetic center, we have assessed the sensitivity of different sequences based on CO-Cali coherence transfer. Features of CACO experiments were tested for Calbindin D9k, in which one of the two native Ca2+ ions is replaced by the paramagnetic Ce3+ ion. We have studied the comparison of single vs multiple quantum coherence transfer evolution as well as the influence of in-phase vs anti-phase detection of 13CO signals and finally the comparison of a coherence transfer step based on a CyO in plane with respect to a Cy ali in plane. The acquisition of the anti-phase component of the signal, accomplished by the removal of the last refocusing steps, allowed the identification of some signals unobserved with other pathways. The structural dependency of paramagnetism-induced nuclear relaxation is such that the identification of the most suitable coherence transfer pathway is not known "a priori" but it is driven by the relative proximity of Cali and CO to the paramagnetic center.     

The Suzuki homocoupling reaction under high-intensity ultrasound

The Pd-catalysed Suzuki homocoupling of boronic acids was successfully carried out in water under high-intensity ultrasound (HIU). Heterogeneous catalysis with Pd/C, facilitating work up and purification, could be used without adding phosphine ligands. Reaction rates and yields were strongly influenced by the oxidant employed; excellent results were obtained using either molecular oxygen or 3-bromo-4-hydroxycoumarin. 3-Arylation of the latter with the Suzuki procedure had failed, exclusively affording the homocoupling products, symmetric biaryls. Besides offering a number of operational advantages, the use of HIU broadens the field of application for the Suzuki reaction.     

Mixing of non-Newtonian fluids in steadily forced systems

We investigate mixing in a viscoelastic and shear-thinning fluid-a very common combination in polymers and suspensions. We find that competition between elastic and viscous forces generates self-similar mixing, lobe transport, and other characteristics of chaos. The mechanism by which chaos is produced is evaluated both in experiments and in a simple model. We find that chaotic flow is generated by spontaneous oscillations, the magnitude and frequency of which govern the extent of chaos and mixing.     

The Helmholtz equation with impedance in a half-space

In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ${\mathbb{R}}_{+}^3$ with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data. To cite this article: M. Durán et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).