On a factorization of the Schrödinger and Klein–Gordon operators

A general scheme for factorizing second‐order time‐dependent operators of mathematical physics is given, which allows a reduction of corresponding second‐order equations to biquaternionic equations of first order. Examples of application of the proposed scheme are presented for both constant and variable coefficients. Copyright © 2008 John Wiley & Sons, Ltd.     

Bismuth Modified Gold Microelectrode for Pb(II) Determination in Wine Using Alkaline Medium

Electrodeposition of bismuth on gold microelectrodes for determination of Pb(II) by square wave anodic stripping voltammetry (SWASV) was accomplished by an in situ procedure in alkaline solution. A linear calibration plot for Pb(II) in the concentration range 40 to 6700 nmol L^?1 (r=0.998) was obtained, the detection limit was found to be 12.5 nmol L^?1 (S/N=3) and the relative standard deviation in solutions containing 1 μmol L^?1 Pb(II) was 4% (n=12). The analytical performance of the proposed sensor was tested by measuring the Pb(II) concentration in a wine sample. The result was in good agreement with the one obtained by GFAAS.     

Rheological properties of PDMS/clay nanocomposites and their sensitivity to microstructure

The effect of microstructure on the rheology of clay/polymer nanocomposites is investigated using dispersions of organically treated clay in nearly Newtonian poly(dimethylsiloxane). Degree of dispersion and floc size are altered by using two different dispersion procedures and by changing the shear history. The scaling for dynamic moduli of attractive colloids applies, except for a possible relaxation mechanism at very low frequencies. The time to reach the crossover at a given frequency is found to be extremely sensitive to the dispersion procedure used. Hydrodynamic and elastic components of the steady state stress, on the other hand, evolve in a very similar fashion for the different systems. Although the relaxation times of the elastic stress components change drastically with flow-induced changes in structure, the dispersion process hardly has an effect at all. Intermittent start-up flows in the forward and reverse directions show that anisotropy persists long after the flow has been arrested, even at shear rates where no large reversible flocs are present. The degree of dispersion only had a limited effect on the anisotropy. Finally, the effect of shear on structure recovery has been studied. Very low shear rates are found to increase the rate of recovery, even for small strains.     

On optimal zero-preserving corrections for inconsistent linear systems

This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional functions. A branch-and-bound algorithm for solving this nonconvex program is proposed, based on suitably overestimating the denominator function for computing lower bounds. Computational experience is presented to demonstrate the efficacy of this approach.     

Favorskii rearrangement of a highly functionalized meso-dihaloketone

This paper describes studies on the feasibility of an asymmetric Favorskii rearrangement of a meso-dihaloketone substrate. In the racemic series, metal amide bases in the presence of amines give poor to reasonable yields of ring-contracted unsaturated cyclopentyl amides, whilst amines in aqueous solvent mixtures afford cyclopentyl amides in good to excellent yields. A range of chiral non-racemic amines are screened, a tiny diastereo-bias is observed and a tentative mechanistic rationale for the diastereoselective process is proposed.     

Poly(vinylpyrrolidone)‐based films grown on copper surfaces

The influence of molecular weight and the amount of the poly(vinylpyrrolidone) (PVP) on the growth of poly(vinylpyrrolidone)–based films on copper surfaces was studied by electrochemical, infrared and electronic spectroscopy, and thermogravimetric methods. Complex polymer/metal ions were deposited onto a copper surface, as the result of the electrochemically generated reaction of copper cations with PVP and SCN^?, in sulfuric acid media. Spontaneous film growth on copper surfaces was generated and characterized as a Cu(II)/PVP/SCN^? complex. Infrared spectra and thermal gravimetric curves of the films generated at + 0.7 V were compared with the chemically synthesized complex, and show the same patterns. The oxidation process can be described as: Cu(0)→Cu(I) and Cu(I)→Cu(II), and the copper complex formed at more positive potentials was characterized as Cu(II)/PVP/SCN^?, with copper bonded to the oxygen atom of PVP and thiocyanate ligand N‐linked. This study focuses on the complex formation on a copper surface in acid media and its characterization through electrochemical and spontaneously generated reactions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2206–2214, 2009