Arbitrary-norm hyperplane separation by variable neighbourhood search

^** Email: alejandro.karam{at}hec.ca^*** Email: gilles.caporossi{at}gerad.ca^**** Email: pierre.hansen{at}gerad.ca We consider the problem of separating two sets of points ina Euclidean space with a hyperplane that minimizes the sum ofp-norm distances to the plane of points lying on the ‘wrong’side of the plane. A variable neighbourhood search heuristicis used to determine the plane coefficients. For a set of exampleswith L₁-norm, L₂-norm and L-norm, for which the exact solutioncan be computed, we show that our algorithm finds it in mostcases and gets good approximations in the others. The use ofour heuristic solutions for problems in these norms can dramaticallyaccelerate exact algorithms. Our method can be applied on verylarge instances that are intractable by exact algorithms. Sincethe proposed approach works for truly arbitrary norms (otherthan the traditional 1, 2 and ), we can explore for the firsttime the effects of the choice of p on the generalization propertiesof p-norm hyperplane separation.     

Variable neighbourhood search for colour image quantization

^** Email: nenad.mladenovic{at}brunel.ac.uk Colour image quantization is a data compression technique thatreduces the total set of colours in a digital image to a representativesubset. This problem is first expressed as a large M-medianone. The advantages of this model over the usual minimum sum-of-squaresmodel are discussed first and then, the heuristic based on variableneighbourhood search metaheuristic is applied to solve it. Computationalexperience proves that this approach compares favourably withtwo other recent state-of-the-art heuristics, based on geneticand particle swarm searches.     

On the cross-over from half-metal to normal ferromagnet in NiMnSb

Magnetism and transport properties of the semi-Heusler compound NiMnSb are re-examined in great details. A wide set of experiments (elastic and inelastic neutron scattering, static magnetic measurements, magnetoresistance, Hall effect, thermopower, FMR) have been performed on polycrystals, single crystals or single-crystalline thin films, and the results are analysed. Special emphasis is given to the magnetic excitations and to the relaxation mechanisms in this metallic ferromagnet. At low temperatures, all experimental results hint at the existence of a fully spin-polarized conduction band (half metallic state). At higher temperature (T > 80 K), but well below the Curie temperature (730 K), a cross-over to a usual metallic ferromagnetic state is evidenced and discussed. Received 10 January 2000     

Homopolymerization of ω‐Styryl‐Polystyrene Macromonomers in the Presence of CpTiF3/MAO

Summary: ω‐Styryl‐polystyrene macromonomers were synthesized by anionic induced deactivation reactions. Their homopolymerization in the presence of a fluorinated half‐sandwich metallocene catalyst (CpTiF₃/MAO) was investigated. In spite of the intrinsic lower reactivity of these macromonomers with respect to the micromolecular monomer, coordination homopolymerization was possible. The influence of several experimental parameters on the polymerization yield and degree could be demonstrated. In most cases, under identical experimental conditions, higher polymerization yields and degrees were observed with respect to the CpTiCl₃/MAO catalyst.

The synthesis of p‐polystyryl‐substituted styrene derivatives by the homopolymerization of ω‐styryl‐polystyrene macromonomers in the presence of CpTiF₃.     

Stereoselective synthesis of 13Z retinoic acids via β-methylenealdehydes as synthons

A stereoselective synthesis of 13Z retinoic acids via β-methylenealdehydes is described. In methylene-de-oxo-bisubstitution reactions (Knoevenagel, Stobbe, etc.), these new synthons produce stereoselectively E olefins. Hence, a synthesis of 13Z retinoic acids is described, via a stereospecific monodecarboxylation of carboxy-14-retinoic acids.     

Measurement of reduced sulphur compounds contained in aqueous matrices by direct injection into a gas chromatograph with a flame photometric detector

An analytical method was developed to measure the concentration of hydrogen sulphide, methyl mercaptan, dimethyl sulphide and dimethyl disulphide contained in aqueous matrices (distilled water, tap water, kraft mill condensates and membrane bioreactor mixed liquor) by direct injection of aqueous samples into a gas chromatograph with a flame photometric detector. The analytical method requires a small sample volume (2 ml), sample preparation and analysis can be completed within 20 min and no complex sampling apparatus is needed. Consistent results and good recoveries were observed in all matrices investigated over the range of concentrations examined. The relationship between the normalized peak area obtained from GC–flame photometric detection and the concentration of the reduced sulphur compounds (RSCs) examined did not follow the theoretical power law exponent of two. The power law exponent appeared to decrease with the organic fraction associated with each RSC. The observed power law exponents for hydrogen sulphide, methyl mercaptan, dimethyl sulphide and dimethyl disulphide were 1.92, 1.90, 1.66 and 1.72, respectively.     

F/Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

¹⁹F/²⁹Si Hartmann–Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated ²⁹Si–¹⁹F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si–F internuclear distance, r=2.62±0.05 Å, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69±0.04 Å recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of 14 kHz is shown to be necessary for an effective suppression of ¹⁹F–¹⁹F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.