R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

Adsorption of cyclic hydrocarbons on Pt and the interaction of the adsorbed species with hydrogen

The adsorption of six-membered hydrocarbon cycles and cyclopentane and the interaction of hydrogen with the adsorbed layer on polycrystalline Pt-foil have been studied. The work function change (Δφ) was followed by a Kelvin probe and the C/Pt peak ratio was determined by Auger electron spectroscopy. Combining these two techniques made it possible to distinguish between chemisorption via σ-bonds and π-complex formation. Benzene and toluene adsorbed first as π-complex while cyclohexane showed initially a partial aromatization and a π-complex-like bonding to the surface. Excess hydrocarbon or addition of hydrogen transformed the π-complex into σ-bonded species. Cyclopentane adsorbed via σ-bonds and showed no significant hydrogen effect.     

Structural characterization of nanopatterned surfaces

In this work, chemically and topographically nanopatterned surfaces were produced by a top-down processing approach for biosensing devices. The nanopatterning was the result of the combination of plasma polymerisation (pp) of biofunctional materials and colloidal lithography techniques. The morphological and chemical properties induced by the plasma deposition-etching treatment were characterised by optical method combining ellipsometry and Fourier Transform Infrared spectroscopy studies. This method supported by atomic force microscopy measurements, allowed the full optical characterization of each step of the top-down process. The optical characterization of the end-up nanopatterned samples demonstrated that the chosen process is able to produce well-defined nanostructured surfaces with controlled chemical and morphological properties.     

Ab initio potential energy surface and pressure broadening coefficients for the He-CH3F complex

Symmetry-adapted perturbation theory has been applied to compute the He-CH₃F potential with the CH₃F molecule assumed rigid. The potential has a global minimum of −48.9 cm⁻¹ at the center of mass separation of 7.2 bohr with the helium atom lying along the C-F bond on the hydrogen’s side. The computed points were fitted to an analytic energy surface with a correct asymptotic behaviour. This potential has been used to compute the pressure broadening (PB) coefficients for the (j, k) = (0, 0) → (1, 0) and (1, 0) → (2, 0) rotational transitions of CH₃F perturbed by helium for a wide range of temperatures. Close-coupling results are compared with the experimental data of Willey et al. [J. Chem. Phys. 97 (1992) 4723], Beaky et al. [J. Mol. Struct. 352/353 (1995) 245] and infinite order sudden results are compared with those of Grigoriev et al. [J. Mol. Struct. 186 (1997) 48] for the ν₆ band of CH₃F perturbed by helium at room temperature. To our knowledge, present work is the first attempt of making fully ab initio calculations of collisional cross-sections and pressure broadening coefficients for this simple symmetric top system at low and room temperature.     

An Enhancement of the Drezner—Wesolowsky Algorithm for Single-Facility Location with Maximin of Rectilinear Distance

In this note, we examine the algorithm of Drezner and Wesolowsky for locating a facility with maximin rectilinear distance to a given set of demand points. The concept of the closest-point constraint is introduced as a technique for increasing the efficiency of the algorithm. This potential increase in efficiency is demonstrated by an example.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.