On the probability that n and [n c] are coprime

We prove that for any positive real number which is not an integer, the density of the integers which are coprime to , a result conjectured by Moser, Lambek and Erd Hs. This revised version was published online in June 2006 with corrections to the Cover Date.     

The pyridyl-tag strategy applied to the hydrocarbon/perfluorocarbon phase-switching of a porphyrin and a fullerene

A new hydrocarbon/perfluorocarbon phase-switching strategy based on coordination of pyridyl-tagged molecules to a highly fluorinated dicopper-carboxylate complex possessing two accessible axial coordination sites is described. When a chloroform solution of the tetrapyridyl-substituted porphyrin 3 (0.1 mM, 2 mL) is layered on a perfluorodecalin solution of 2 (3.25 mM, 1.5 mL), complete extraction of the porphyrin into the fluorous phase is observed after 30 min of stirring. Quantitative release of both the porphyrin and 2 is achieved simply by adding excess THF to the biphasic system, the THF acting as a pyridine competing ligand. The recovered perfluorocarbon solution containing 2 can be reused for another complexation with the same efficiency. The scope of this approach is emphasized by the phase-switching of a dipyridyl-substituted fullerene, another example of a molecule for which solubilization in perfluorocarbons is very challenging.     

Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides

At microwave frequencies, hollow metallic waveguides behave in certain aspects as a "one-dimensional plasma." This feature will be advantageously used for simulating the propagation of electromagnetic (EM) waves in left-handed metamaterials provided the hollow waveguide is periodically loaded with split ring resonators. It will be shown that EM transmission in this structure is feasible within a certain frequency band even if the transverse dimensions of the waveguide are much smaller than the associated free-space wavelength. This effect can be qualitatively and quantitatively explained by the left-handed metamaterial theory, thus providing a new experimental validation for such a theory.     

Carbon nanotubes as schottky barrier transistors

We show that carbon nanotube transistors operate as unconventional "Schottky barrier transistors," in which transistor action occurs primarily by varying the contact resistance rather than the channel conductance. Transistor characteristics are calculated for both idealized and realistic geometries, and scaling behavior is demonstrated. Our results explain a variety of experimental observations, including the quite different effects of doping and adsorbed gases. The electrode geometry is shown to be crucial for good device performance.     

Milliwatt-peak-power pulse characterization at 1.55 microm by wavelength-conversion frequency-resolved optical gating

A novel wavelength-conversion configuration based on four-wave mixing in an optical fiber has been used to generate a frequency-resolved optical gating (FROG) trace identical to that obtained from second-harmonic generation (SHG). The use of an optical fiber waveguide permits enhanced measurement sensitivity compared with that of conventional SHG-FROG and has been used for complete characterization of 1-mW peak-power picosecond pulses at 1.55 microm from an unamplified semiconductor laser diode gain switched at 10 GHz.     

Clustering for routing in densely populated areas

This paper introduces a new approach for generating school bus routes in a dense urban area. First, a districting algorithm is used to determine clusters including appropriate numbers of students. Then, for each cluster, a route and the stops along this route are determined. Numerical results are reported and compared with those obtained previously. Although the algorithm has been developped and tested in a specific context, it could easily be extended to more general vehicle routing problems.