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     

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.     

Salting-in of alcohols in aqueous solutions by tetraalkylammonium bromides at the freezing temperature

The freezing-point depression of the ternary systems tetraalkylammonium bromides-t-butanol-water for the first five homologs of R₄NBr was measured. In the case of Bu₄NBr, the effect of size of the alcohol (methahol ton-butanol) was also investigated. From the corresponding freezing-point data for the binary systems the apparent salting constants were calculated. The true salting constantsk _s were obtained by extrapolation to infinite dilution. These are all very close to zero at the freezing temperature. From the corresponding thermochemical data the temperature dependence ofk _s was calculated, and above 5°C all the R₄NBr salts int-butanol; the salting-in increases with temperature and with the size of the hydrophobic cations. The scaled-particle theory is at present the only one which can account semiquantitatively for the temperature dependence of the salting-in effect. On leave of absence from Chemistry Department, The University, Sheffield S3 7HF, England To whom correspondence should be addressed.     

Studies on the 4-benzoylpyridine-3-carboxamide entity as a fragment model of the Isoniazid-NAD adduct

An ortho-metallation-electrophilic substitution sequence was employed as a key step to build the 4-benzoylpyridine framework. It was found that 4-benzoylpyridine-3-carboxamide and an N-pyridyl alkylated derivative both exist in a unique cyclized hemiamidal structure, not in the usually expected keto-amide open form. These structures represent fragment models of the Isoniazid-NAD adducts involved in the mechanism of action of the antituberculous drug Isoniazid.     

Fungicidal properties of meso-arylglycosylporphyrins: influence of sugar substituents on photoinduced damage in the yeast Saccharomyces cerevisiae

A series of neutral meso-arylglycosylporphyrins has been tested in order to evaluate their potency as antifungal agents against the yeast Saccharomyces cerevisiae. Photodynamic activity of these molecules results in intracellular damage as evidenced by the loss of clonogenicity and DNA fragmentation. The ability of these photosensitizers to permeate yeast cells is determined by microspectrofluorimetry and is correlated with their antifungal potency. Amphiphilic porphyrin derivatives are shown to exhibit the more pronounced photoactivity.     

A convenient synthesis of new aminomethylenedioxypyrroloindoles via an iminium salt

Cyclization of 2-(1-pyrrolyl)piperonylcarboxamide derivatives gave iminium perchlorates which afforded 9-(N-substituted-imino) and 9-(N-substituted amino)-6,7-methylenedioxypyrrolo[1,2-a]indoles.