Tiling Hamming Space with Few Spheres

We show that if the collection of all binary vectors of lengthnis partitioned intokspheres, then eitherk2 orkn+2. Moreover, such partitions withk=n+2 are essentially unique.     

Suzuki cross-coupling reactions using reverse-phase glass beads in aqueous media

Reverse-phase glass beads have been employed in Suzuki reactions to provide, in aqueous media, a route to diverse polar substrates in good yield and with low levels of palladium leaching.     

The mathematics of scattering by unbounded,rough, inhomogeneous layers

In this paper we study, via variational methods, a boundary value problem for the Helmholtz equation modelling scattering of time harmonic waves by a layer of spatially varying refractive index above an unbounded rough surface on which the field vanishes. In particular, in the 2D case with TE polarization, the boundary value problem models the scattering of time harmonic electromagnetic waves by an inhomogeneous conducting or dielectric layer above a perfectly conducting unbounded rough surface, with the magnetic permeability a fixed positive constant in the medium. Via analysis of an equivalent variational formulation, we show that this problem is well-posed in two important cases: when the frequency is small enough; and when the medium in the layer has some energy absorption. In this latter case we also establish exponential decay of the solution with depth in the layer. An attractive feature is that all constants in our estimates are bounded by explicit functions of the index of refraction and the geometry of the scatterer.     

Fast separations with open tubular ion exchange capillary columns

Fused silica columns of 4.6 μm i.d. were coated with 3-sulfopropylsilane as a cation exchanger and 3-(2-aminoethyl-amino)-propylsilane as an anion exchanger. Fast separations of cations (< 25 seconds) and of anions (< 35 seconds) were obtained, using a potentiometric microelectrode as a detector. In proceeding towards smaller i.d.s, a mixture of alkali metal cations could be separated successfully in an uncoated fused silica capillary of 2.3 μm i.d. as a result of retention by the surface silanol groups at pH 9.4.     

Photoplastic studies of strain distributions in the cold drawing of polycarbonate cylindrical bars: the rate effect

Strain distributions in the cold drawing of polycarbonate cylindrical bars were obtained at three nominal strain rates using the method of photoplasticity. Optical-mechanical constitutive equations were interpreted based on a physical model. The strain distribution in the necked portion of the rod is shown to be nonuniform, regardless of the strain rate. Comparison between the integrated diameters and the measured diameters gives an average error between 4 and 12 percent. An interesting trend in the fringe patterns with and without a central loop has been observed and attributed to the higher strain-rate effect for patterns without a central loop.     

Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

Persistent properties and an application to algebras of logic

Received May 20, 1997; accepted in final form July 21, 1997.