Orthogonal polynomials on the unit circle and their derivatives

We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle.     

Incremental unknowns preconditioning for solving the Helmholtz equation

An efficient preconditioner is developed for solving the Helmholtz problem in both high and low frequency (wavenumber) regimes. The preconditioner is based on hierarchical unknowns on nested grids, known as incremental unknowns (IU). The motivation for the IU preconditioner is provided by an eigenvalue analysis of a simplified Helmholtz problem. The performance of our preconditioner is tested on the iterative solution of two‐dimensional electromagnetic scattering problems. When compared with other well‐known methods, our technique is shown to often provide a better numerical efficacy and, most importantly, to be more robust. Moreover, for the best performance, the number of IU levels used in the preconditioner should be designed for the coarsest grid to have roughly two points per linear wavelength. This result is consistent with the conventional sampling criteria for wave phenomena in contrast with existing IU applications for solving the Laplace/Poisson problem, where the coarsest grid comprises just one interior point. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Inverse gas chromatography of lignocellulosic fibers coated with a thermosetting polymer: Use of peak maximum and conder and young methods

The Conder and Young (CY) and the peak maximum (PM) methods were used to estimate the retention time of n-alkane probes on chemithermomechanical pulp (CTMP) wood fibers treated with a low molecular weight grade phenol-formaldehyde resin (PFR). Thermodynamic functions (ΔH_a^o, ΔG_a^o, and ΔS_a^o) and the London dispersive component of the surface energy were derived from these retention times. Treated wood fibers show a high energy surface due to the presence of the thermoset resin on their surface. Values of ΔH_a^o obtained from the CY method were higher than those obtained with the PM method at relatively high temperatures and with relatively low molecular weight alkanes. The results from the two methods were identical at low temperature (293 K) and with the relatively high molecular weight alkane n-undecane.     

Une note sur les lemmes div–curl

Let $\text{Ω}$ be a strongly Lipschitz domain of $\text{R}{}^{\mathrm{n}}$ (n?2). We give endpoint versions of div–curl lemmata on $\text{Ω}$, for a given function f on $\text{Ω}$ whose gradient belongs to a Hardy space on $\text{Ω}$. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

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.     

One-pot synthesis of an ionic half-sandwich complex of neodymium. Application to isoprene polymerisation catalysis

The reaction of one equivalent of Nd(BH₄)₃(THF)₃ with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene.     

A new synthesis of ampicillin and related investigations

Quaternization of (S)-α-bromophenylacetic acid amide (8) with hexamethylentetramine (hexamine) preceded with ca. 80% inversion of configuration. Accordingly, starting from the trimethylsilylester of N-(S)-(α-bromo-α-phenylacetyl)-6-aminopenicillanic acid (4) quaternization with hexamine and subsequent hydrolysis afforded N-(R)-α-phenylglycyl-6-aminopenicillanic acid (1, ampicillin). Some other model reactions have been investigated.     

Preparation and Crystal Structure Determination of the New Intermetallic Compound RbGa3

The compound has tetragonal symmetry, space group I4 m2 with: a=b=6.315(2) and c = 15.000(2) Å and contains 6 formula units. Diffraction data with 0 < 2θ < 50° (MoKα radiation) were collected on a Nonius CAD-4 automatic diffractometer within the octant hkl. The structure was solved by Patterson synthesis and refined by full-matrix least squares to a final R(F) of 4.9% for 159 independent reflections with I > 3σ(I). The structure consists of a stacking of gallium triangular-faced dodecahedra linked to each others through direct and bifurcated Ga? Ga bonds in a non-compact netting leaving room for a sublattice of rubidium atoms with shortened Rb? Rb distances.