Thin sets of integers in harmonic analysis and <Emphasis Type=Italic>p</Emphasis>-stable random fourier series

We investigate the behaviour of some thin sets of integers defined through random trigonometric polynomials when one replaces Gaussian or Rademacher variables with p-stable ones, 1 < p < 2. We show that in one case, this behaviour is essentially the same as in the Gaussian case, whereas in another case, it is entirely different.     

Single step hybrid coating process to enhance the electrosteric stabilization of inorganic particles

We report on a single-step coating process and the resulting colloidal stability of silica-coated spindle-type hematite nanoparticles (NPs) decorated with a layer of poly(acrylic acid) (PAA) polyelectrolyte chains that are partially incorporated into the silica shell. The stability of PAA coated NPs as a function of pH and salt concentration in water was compared to bare hematite particles and simple silica-coated hematite NPs, studying their electrophoretic mobility and the hydrodynamic radius by dynamic light scattering. Particles coated with this method were found to be more stable upon the addition of salt at pH 7, and their aggregation at the pH of the isoelectric point is reversible. The hybrid coating appears to increase the colloidal stability in aqueous media due to the combination of the decrease of the isoelectric point and the electrosteric stabilization. This coating method is not limited to hematite particles but can easily be adapted to any silica-coatable particle.     

Totally geodesic discs in strongly convex domains

We prove that every isometry from the unit disk Δ in ${\mathbb{C}}$ , endowed with the Poincaré distance, to a strongly convex bounded domain Ω of class ${\mathcal{C}^3}$ in ${\mathbb{C}^n}$ , endowed with the Kobayashi distance, is the composition of a complex geodesic of Ω with either a conformal or an anti-conformal automorphism of Δ. As a corollary we obtain that every isometry for the Kobayashi distance, from a strongly convex bounded domain of class ${\mathcal{C}^3}$ in ${\mathbb{C}^n}$ to a strongly convex bounded domain of class ${\mathcal{C}^3}$ in ${\mathbb{C}^m}$ , is either holomorphic or anti-holomorphic.     

Metal Linkage Effects on Ultrafast Energy Transfer

We report the preparation of several new porphyrin homodimers bridged by a platinum(II) ion in which very intense electronic communication through the coordination link occurs. Moreover, the synthesis of a new porphyrin dyad and its photophysical properties are reported. This dyad exhibits the fastest singlet energy transfer ever reported for synthetic systems between a zinc(II) porphyrin and a porphyrin free base. This extremely fast transfer (～100 femtoseconds) is in the same range as the fastest one measured in natural systems. This feature is due to the platinum(II) linker, which allows for strong MO couplings between the two porphyrin units as experimentally supported by electrochemistry and corroborated by DFT computations.