Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Theory of enhanced magnetic anisotropy induced by Pt adatoms on two-dimensional Co clusters supported on a Pt(111) substrate

Calculations are reported of the magnetic anisotropy energy of two-dimensional (2D) Co nanostructures on a Pt(111) substrate. The perpendicular magnetic anisotropy (PMA) of the 2D Co clusters strongly depends on their size and shape, and rapidly decreases with increasing cluster size. The PMA calculated is in reasonable agreement with experimental results. The sensitivity of the results to the Co-Pt spacing at the interface is also investigated and, in particular, for a complete Co monolayer we note that the value of the spacing at the interface determines whether PMA or in-plane anisotropy occurs. We find that the PMA can be greatly enhanced by the addition of Pt adatoms to the top surface of the 2D Co clusters. A single Pt atom can induce in excess of 5 meV to the anisotropy energy of a cluster. In the absence of the Pt adatoms the PMA of the Co clusters falls below 1 meV/Co atom for clusters of about 10 atoms whereas, with Pt atoms added to the surface of the clusters, a PMA of 1 meV/Co atom can be maintained for clusters as large as about 40 atoms. The effect of placing Os atoms on the top of the Co clusters is also considered. The addition of 5d atoms and clusters on the top of ferromagnetic nanoparticles may provide an approach to tune the magnetic anisotropy and moment separately.

Sonogashira coupling on an extended gold surface in vacuo: reaction of phenylacetylene with iodobenzene on Au(111)

Temperature-programmed reaction measurements supported by scanning tunneling microscopy have shown that phenylacetylene and iodobenzene react on smooth Au(111) under vacuum conditions to yield biphenyl and diphenyldiacetylene, the result of homocoupling of the reactant molecules. They also produce diphenylacetylene, the result of Sonogashira cross-coupling, prototypical of a class of reactions that are of paramount importance in synthetic organic chemistry and whose mechanism remains controversial. Roughened Au(111) is completely inert toward all three reactions, indicating that the availability of crystallographically well-defined adsorption sites is crucially important. High-resolution X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure spectroscopy show that the reactants are initially present as intact, essentially flat-lying molecules and that the temperature threshold for Sonogashira coupling coincides with that for C−I bond scission in the iodobenzene reactant. The fractional-order kinetics and low temperature associated with desorption of the Sonogashira product suggest that the reaction occurs at the boundaries of islands of adsorbed reactants and that its appearance in the gas phase is rate-limited by the surface reaction. These findings demonstrate unambiguously and for the first time that this heterogeneous cross-coupling chemistry is an intrinsic property of extended, metallic pure gold surfaces: no other species, including solvent molecules, basic or charged (ionic) species are necessary to mediate the process.

The surface structure of BaO on Pt(111): (2x2)-reconstructed BaO(111)

The surface structure of BaO(111) has been determined using STM and computer modelling. The BaO(111) surface was prepared in thin film form on Pt(111) and presents a surface with twice the lattice parameter expected for that of the bulk termination, i.e. a (2 x 2) reconstruction. Computer modelling indicates that the bulk termination is unstable, but that the (2 x 2) reconstructed BaO(111) surface has a low surface energy and is hence a stable surface reconstruction. The (2 x 2) reconstruction consists of small, three-sided pyramids with (100) oriented sides and either oxygen or barium ions at the apices. Less regular surface reconstructions containing the same pyramids are almost equally stable, indicating that we may also expect less regular regions to appear with a fairly random distribution of these surface species. The simulations further suggest that a regular (4 x 4) reconstruction built up of bigger pyramids is even more energetically favourable, and some evidence is found for such a structure in the STM. (c) 2006 Elsevier B.V. All rights reserved.

Chemoselective catalytic hydrogenation of acrolein on Ag(111): effect of molecular orientation on reaction selectivity

The adsorption and hydrogenation of acrolein on the Ag(111) surface has been investigated by high resolution synchrotron XPS, NEXAFS, and temperature programmed reaction. The molecule adsorbs intact at all coverages and its adsorption geometry is critically important in determining chemoselectivity toward the formation of allyl alcohol, the desired but thermodynamically disfavored product. In the absence of hydrogen adatoms (H(a)), acrolein lies almost parallel to the metal surface; high coverages force the C=C bond to tilt markedly, likely rendering it less vulnerable toward reaction with hydrogen adatoms. Reaction with coadsorbed H(a) yields allyl alcohol, propionaldehyde, and propanol, consistent with the behavior of practical dispersed Ag catalysts operated at atmospheric pressure: formation of all three hydrogenation products is surface reaction rate limited. Overall chemoselectivity is strongly influenced by secondary reactions of allyl alcohol. At low H(a) coverages, the C=C bond in the newly formed allyl alcohol molecule is strongly tilted with respect to the surface, rendering it immune to attack by H(a) and leading to desorption of the unsaturated alcohol. In contrast with this, at high H(a) coverages, the C=C bond in allyl alcohol lies almost parallel to the surface, undergoes hydrogenation by H(a), and the saturated alcohol (propanol) desorbs.

Chemical composition and reactivity of water on clean and oxygen-covered Pd{111}

The chemical composition and dissociation behaviour of water adsorbed on clean and oxygen pre-covered Pd{111} was studied using high-resolution time-resolved and temperature-programmed X-ray photoelectron spectroscopy. We find that water remains intact at all temperatures up to desorption on the clean surface and at high oxygen coverage(0.69 ML) when a surface oxide is formed. The highest desorption peaks occur at 163 K from the clean surface and at 172 K from the surface oxide. At the intermediate coverage of 0.20 ML oxygen reacts with coadsorbed water at 155 K, to generate a mixed H2O/OH layer exhibiting a (root 3- x root 3)R30 degrees diffraction pattern, which is stable up to 177 K. The measured ratio between intact water and the hydroxyl species in this layer varies between 1.5 and 2 depending on temperature. (C) 2008 Elsevier B.V. All rights reserved.