Approximation par des Nombres Algébriques de Degré Borné et Dimension de Hausdorff

We compute the generalized Hausdorff measure of sets of real numbers close to infinitely many algebraic numbers of fixed degree. Thus, we provide an extension to results of Jarn?́k and of Baker and Schmidt.     

Water injection effects on hot supersonic jet noiseEffets de la température sur le rayonnement acoustique des jets supersoniques en présence d'injection d'eau

The effects of temperature both on supersonic jet noise with water injection (used for noise reduction) and on the efficiency of the method are investigated. The location of injection varies from 1.5D to 15D while the other parameters remain fixed to their optimum values. One notices better overall noise level reductions by injecting close to the nozzle exit. Moreover spectral analysis emphasizes that attenuation in high and low frequencies depends on the location of injection. Finally, the jet temperature does not greatly affect the efficiency of this method as the measured attenuation is similar to that encountered with supersonic jets with ambiant temperature. To cite this article: Y. Marchesse et al., C. R. Mecanique 330 (2002) 1–8     

Tailored Cyclic and Linear Polycarbosilazanes by Barium‐Catalyzed N−H/H−Si Dehydrocoupling Reactions

Ba[CH(SiMe₃)₂]₂(THF)₃ catalyzes the fast and controlled dehydrogenative polymerization of Ph₂SiH₂ and p‐xylylenediamine to afford polycarbosilazanes. The structure (cyclic versus linear; end‐groups) and molecular weight of the macromolecules can be tuned by adjusting the Ph₂SiH₂/diamine feed ratio. A detailed analysis of the resulting materials (mol. wt up to ca. 10 000 g mol^?1) is provided.     

Osmotic pressure and structures of monodisperse ordered foam

We present an experimental and numerical study of the osmotic pressure in monodisperse ordered foams as a function of the liquid fraction. The data are compared to previous results obtained for disordered monodisperse and polydisperse concentrated emulsions. Moreover, we report a quantitative investigation of the transition from a bubble close packing to a bcc structure as a function of the liquid volume fraction. These findings are discussed in the context of theoretical models that have been proposed in the literature.     

Sums of the error term function in the mean square for ζ(s)

Sums of the form are investigated, where is the error term in the mean square formula for . The emphasis is on the case k = 1, which is more difficult than the corresponding sum for the divisor problem. The analysis requires bounds for the irrationality measure of e^2πm and for the partial quotients in its continued fraction expansion. Authors’ addresses: Y. Bugeaud, Université Louis Pasteur, Mathématiques, 7 rue René Descartes, F-67084 Strasbourg cedex, France; A. Ivić, Katedra Matematike RGF-a, Universitet u Beogradu, Đušina 7, 11000 Beograd, Serbia     

Total synthesis of norbadione A

A short, convergent synthesis of the mushroom pigment norbadione A is described. The construction of an appropriately substituted naphtholactone intermediate involved a regioselective Diels-Alder reaction between a bis(triisopropylsilyloxy)diene and 2,6-dichlorobenzo-1,4-quinone. A double Suzuki-Miyaura cross-coupling between a diboronate and two identical enol triflates was another key feature of the synthesis.     

Synthesis and structures of new binuclear zinc alkyl,aryl and aryloxo complexes

The synthesis of a series of binuclear zinc complexes with Cl, N and O bridges is reported. The reaction of EtZnCl with B(C₆F₅)₃ in the presence of hexamethylbenzene affords the arene complex [Zn(μ-Cl)(C₆F₅)(η-C₆Me₆)]₂ in which the C₆Me₆ ligand may be regarded as η³-bonded. The comproportionation of Zn[N(SiMe₃)₂]₂ with ZnBu^t₂ or Zn(C₆F₅)₂ · toluene gave [Bu^tZn{μ-N(SiMe₃)₂}]₂ and [C₆F₅Zn{μ-N(SiMe₃)₂}]₂, respectively, with three-coordinate zinc. The reaction of ZnEt₂ with C₆F₅OH in the presence of pyridine gave [EtZn(μ-OC₆F₅)(py)]₂, while ZnMe₂ and C₆F₅OH followed by recrystallisation from THF gave [Zn(OC₆F₅)(μ-OC₆F₅)(THF)₂]₂ with five-coordinate zinc in a trigonal-bipyramidal geometry. The structures of these compounds have been determined.     

Analysis of constrained Willmore surfaces

This paper investigates the regularity of constrained Willmore immersions into ?^m≥3 locally around both “regular” points and around branch points, where the immersive nature of the map degenerates. We develop local asymptotic expansions for the immersion and its first and second derivatives, given in terms of residues computed as circulation integrals. We deduce explicit “point removability” conditions ensuring that the immersion is smooth. Our results apply in particular to Willmore immersions and to parallel mean curvature immersions in any codimension.     

Biomimetic total synthesis and antimicrobial evaluation of anachelin H

The first biomimetic total synthesis of the iron chelator anachelin H isolated from the cyanobacterium Anabaena cylindrica is reported. A first generation approach delivered one enantiomeric series of the polyketide fragment. Comparison of the 1H NMR data suggested the relative configuration of this anachelin fragment. The relative and absolute configuration of anachelin H was then established by total synthesis. A second generation approach involved the enzymatic conversion of N,N-dimethyltyramine to the anachelin chromophore. It was demonstrated that the enzyme tyrosinase is activated by the product during this reaction, the anachelin chromophore can serve as a tyrosinase activator. Anachelin H was evaluated against a panel of eleven bacterial and fungal pathogens, and moderate antibiotic activity (32 microg/mL) against Moraxella catarrhalis was found.