Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Common Tangents to Spheres in ℝ3

We prove that four spheres in ℝ³ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.     

A Spherical Decomposition for Riemannian Open 3-Manifolds

We show that open 3-manifolds that have a locally finite decomposition along 2-spheres are characterized by the existence of a Riemannian metric with respect to which the second homotopy group of the manifold is generated by small elements. Received: November 2005 Revision: February 2006 Accepted: May 2006     

Light Scattering by Cylindrical Fibers with High Aspect Ratio Using the Null‐Field Method with Discrete Sources

The problem of computing light scattering by cylindrical fibers with high aspect ratio in the framework of the Null‐Field method with discrete sources is treated. Numerical experiments for investigating the scattering properties of two fiber geometries are performed using distributed spherical vector wave functions as discrete sources.     

Measurement of acoustic particle velocities in enclosed sound field: Assessment of two Laser Doppler Velocimetry measuring systems

The performances of two Laser Doppler Velocimetry (LDV) systems adapted for measuring the acoustic particle velocities are assessed in enclosed sound field. This assessment is performed by comparing the acoustic velocities measured by means of LDV to reference acoustic velocities estimated from sound pressure measurements. The two LDV systems are based on a single optical bench which delivers an optical signal called Doppler signal. The Doppler signal, which is frequency modulated, is analyzed by means of two signal processing systems, the BSA (Burst Spectrum Analyser from Dantec) on the one hand, and a system specifically developed for the estimation of the acoustic velocity on the other hand. Once the experimental setup has been optimized for minimizing the errors made on the reference velocities, the assessment is performed and shows that both systems can measure the acoustic velocity in enclosed field in two the frequency ranges [0-4 kHz] and [0-2 kHz] respectively for acoustic velocity amplitudes of 10 mm/s and 1 mm/s.