Two-dimensional local null controllability of a rigid structure in a Navier–Stokes fluid

We consider the two-dimensional motion of a rigid structure immersed in an incompressible fluid governed by Navier–Stokes equations. The control force acts on a fixed subset of the fluid domain. We prove that our system is null controllable; that is, for small initial data, the system can be driven at rest and the structure can be driven to the origin at a given $T>0$. The result holds for a structure symmetric with respect to the center of mass and for initial conditions satisfying strong compatibility conditions. To cite this article: M. Boulakia, A. Osses, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

A simple and versatile method to synthesize N-acyl-benzotriazoles

An efficient method for the synthesis of N-acyl-benzotriazoles from a wide variety of protected amino acids, as well as from compounds frequently used in drug discovery such as biotin and N-Fmoc polyethylene glycol, has been developed. The reaction of carboxylic acid derivatives with benzotriazole in the presence of T3P® yielded the corresponding N-acyl-benzotriazoles, which were obtained in high purity following a simple work-up procedure, in most cases via precipitation of the desired product in water.     

Separations of antifungal compounds in capillary electrophoresis with two anionic cyclodextrins

CD‐CZE methods were developed for complete stereoisomeric separations of a series of six γ‐lactam analogues, of which some were neutral, or cationic depending on the background electrolyte nature. The tested cyclodextrin was the versatile sulfobutylether‐ β‐CD, used either in a phosphate buffer using capillaries dynamically coated with polyethylene oxide or in a borate buffer using uncoated capillaries. Long‐end and short‐end modes and concentration variations of chiral selectors allowed finding conditions of complete separation of four out of the six derivatives (i.e., 1 , 2 , 3, and 4 ) in short run times, confirming their broad range of applications. To separate the two last compounds, the highly sulfated‐ γ‐CD was examined as chiral selector in acidic phosphate conditions. The enantiomers of the γ‐lactam analogues 5 and 6 were baseline resolved with 5.5 and 4%, respectively as concentration in the buffer.     

Ultrafast all-optical integrator based on a fiber Bragg grating: proposal and design

We demonstrate a simple technique for the implementation of an all-optical integrator based on a uniform-period fiber Bragg grating (FBG) in reflection that is designed to present a decreasing exponential impulse response. The proposed FBG integrator is readily feasible and can perform close to ideal integration of few-picosecond and subpicosecond pulses.     

Radical Cyclisation of α‐Halo Aluminium Acetals: A Mechanistic Study

α‐Bromo aluminium acetals are suitable substrates for Ueno–Stork‐like radical cyclisations affording γ‐lactols and acid‐sensitive methylene‐γ‐lactols in high yields. The mechanistic study herein sets the scope and limitation of this reaction. The influence of the halide (or chalcogenide) atom X (X=Cl, Br, I, SPh, SePh) in the precursors α‐haloesters, as well as influence of the solvent and temperature was studied. The structure of the aluminium acetal intermediates resulting from the reduction of the corresponding α‐haloesters has been investigated by low‐temperature ¹³C‐INEPT diffusion‐ordered NMR spectroscopy (DOSY) experiments and quantum calculations, providing new insights into the structures of these thermally labile intermediates. Oxygen‐bridged dimeric structures with a planar Al₂O₂ ring are proposed for the least hindered aluminium acetals, while monomeric structures seem to prevail for the most hindered species. A comparison against the radical cyclisation of aluminium acetals derived from allyl and propargyl alcohols with the parent Ueno–Stork has been made at the BHandHLYP/6‐311++G(d,p) level of theory, highlighting mechanistic similarities and differences.