A vector Chebyshev algorithm

We consider polynomials orthogonal relative to a sequence of vectors and derive their recurrence relations within the framework of Clifford algebras. We state sufficient conditions for the existence of a system of such polynomials. The coefficients in the above relations may be computed using a cross-rule which is linked to a vector version of the quotient-difference algorithm, both of which are proved here using designants. An alternative route is to employ a vector variant of the Chebyshev algorithm. This algorithm is established and an implementation presented which does not require general Clifford elements. Finally, we comment on the connection with vector Padé approximants. This revised version was published online in June 2006 with corrections to the Cover Date.     

The application of the shapiro reaction to the stereoselective synthesis of E-trisubstituted olefins for cation-olefin cyclization by three component coupling

A method is described for the rapid and stereoselective assembly of E-trisubstituted olefins by a convergent process from three components     

Catalytic‐chain‐transfer polymerization of styrene revisited: The importance of monomer purification and polymerization conditions

The cobaloxime‐mediated catalytic‐chain‐transfer polymerization of styrene at 60 °C was studied with an emphasis on the effects of monomer purification and polymerization conditions. Commonly used purification methods, such as column chromatography and simple vacuum distillation, were not adequate for obtaining kinetic data to be used in mechanistic modeling. A purification regime involving inhibitor removal with basic alumina, followed by polymerization of the styrene in the presence of the cobaloxime and subsequent vacuum distillation, was found to be essential to this end. It was then possible to quantitatively investigate effects such as the initiator concentration and conversion dependencies of the apparent chain‐transfer constant that resulted from the occurrence of cobalt–carbon bond formation. A value of about 9 × 10³ was found for the true chain‐transfer constant to cobaloxime boron fluoride, that is, its value in the absence of cobalt–carbon bond formation. Furthermore, previous predictions were confirmed: the measured chain‐transfer constant decreased with increasing initiator concentration and conversion. Finally, it was confirmed that the presence of light increased the amount of free Co(II) catalyst in agreement with other studies. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 752–765, 2003     

Singularities in forward scattering through random media

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ^z, and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q_c, the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

X-ray reflectivity study on gold films during sputter deposition

We performed in-situ X-ray reflectivity measurements of gold films during sputter deposition on polished silicon substrates. The measurements were performed at several substrate temperatures and under two argon pressures. The gold surfaces were also examined by scanning tunneling microscopy after deposition to obtain their real-space topographic images. These images were used to complement the X-ray reflectivity measurements in determining the effect of argon pressure on the gold surface and its height-height difference functions. An approximation for height-height difference functions was employed to analyze the X-ray reflectivity data. The measured interface width during growth followed a simple power law, consistent with recent theoretical results of dynamic scaling behavior. The scaling exponents, however, do not agree well with predictions based on some models in 2 + 1 dimensions.     

GaAs multiple quantum well microresonator modulators grown on silicon substrates

We report new results on the modulation characteristics of GaAs/AlGaAs asymmetric Fabry-Perot modulators grown on silicon substrates. We discuss factors affecting device performance and evaluate these by growing p-i-n quantum well diodes, and multilayer reflector stacks on silicon. Using data from these test structures we have designed an asymmetric microresonator modulator and achieve, experimentally, a 40% reflection change with only 5 V and a contrast ratio of 7.4 dB, also with 5 V.Formerly at:Philips Research Laboratories, Redhill, UK     

On graphs having domination number half their order

In this paper we present a characterization of connected graphs of order 2n with domination numbern. Using this class of graphs, we determine an infinite class of graphs with the property that the domination number of the product of any two is precisely the product of the domination numbers.     

Hydroxylation and dehydroxylation at Cu(III) surfaces

X-ray photoelectron spectroscopy has shown how both chemisorbed oxygen present at a Cu(III) surface and nitric oxide introduced into the gas phase can induce hydroxylation of the surface from an adlayer of molecularly adsorbed water at 80 K. The interaction of water vapour with a clean Cu(III) surface is also reported.