Piecewise Linear Bases and Besov Spaces on Fractal Sets

For a class of closed sets F R ⁿ admitting a regular sequence of triangulations or generalized triangulations, the analogues on F of the Faber—Schauder and Franklin bases are discussed. The characterizations of the Besov spaces on F in the terms of coefficients of functions with respect to these bases are proved. As a consequence, analogous characterizations of the Besov spaces on some fractal domains (including the Sierpinski gasket and the von Koch curve) by coefficients of functions with respect to the wavelet bases constructed in [26] are obtained.     

On the reaction118Sn(γ,p)117in at intermediate energies

A refined analytical calculation of the (γ, p) cross section on¹¹⁸Sn in the energy region 150–750 MeV has been performed, taking into account the contributions of single pion photoproduction. The result is in good agreement with experimental data.     

Merons at finite temperature

We prove the existence of solutions to the SU(2) Yang—Mills equations on IR⁴, periodic in time, with meron singularities along the time-axis.Supported in part by the Icelandic Science Foundation.     

A random walk representation of the Dirac propagator

We define a discrete random walk with a matrix-valued transition function and show that the scaling limit of the two-point function of the walk is given by the Dirac propagator. We study the scaling limit of similar walks with curvature-dependent transition functions, which are analogous to the Ornstein-Uhlenbeck process, and show that the Dirac propagator can be recovered by a limiting procedure.     

A multivariate approach to saccharide quantitative structure-activity relationships exemplified by two series of 9-hydroxyellipticine glycosides

Multivariate saccharide quantitative structure-activity relationships (QSARs) have been developed for two series of 9-hydroxyellipticine glycosides. In order to describe the structural variation of the glycoside moieties, thirteen chromatographic variables were used. Eleven D-glycosides and seven L-glycosides were used in separate QSARs to model 9-hydroxyellipticine glycoside antitumour activity against L 1210 leukemia. The multivariate partial least squares (PLS) method was used to establish the QSARs.     

Short and stereoselective synthesis of polysubstituted cyclohexanones

Two equivalents of dimethyl 1,3-acetonedicarboxylate reacted with α,β-unsaturated aldehydes to form novel polysubstituted cyclohexanones 2 in an efficient one-step procedure. The reactions proceeded at room temperature in the presence of catalytic amount of sodium methoxide, affording the products in high yields in a remarkably stereoselective manner. The products are of possible biological interest.     

Zeolite coated ATR crystals for new applications in FTIR-ATR spectroscopy

Thin silicalite-1 films were grown on ATR crystals and used for detection of low amounts of organic molecules in a gas flow by FTIR spectroscopy.     

Fast 29Si magic-angle-spinning NMR acquisitions by RAPT-CP 27Al --> 29Si polarization transfer

Using enhancement of the 27Al central-transition magnetization by applying RAPT prior to 27Al --> 29Si cross-polarization, we demonstrate fast acquisition of 29Si one-dimensional MAS and two-dimensional 27Al-29Si HETCOR spectra on a new sialon phase Ba2Al3Si9N13O5.     

Multivariate data analysis of dynamic amperometric biosensor responses from binary analyte mixtures-application of sensitivity correction algorithms

In this paper, it is demonstrated that a single-receptor biosensor can be used to quantitatively determine each analyte in binary mixtures using multivariate data analysis tools based on the dynamic responses received from flow injection peaks. Mixtures with different concentrations of two phenolic compounds, catechol and 4-chlorophenol, were measured with a graphite electrode modified with tyrosinase enzyme at an applied potential of −50 mV versus Ag/AgCl. A correction algorithm based on measurements of references in-between samples was applied to compensate for biosensor ageing as well as differences caused by deviations between biosensor preparations. After correction, the relative prediction errors with partial least squares regression (PLS-R) for catechol and 4-chlorophenol were 7.4 and 5.5%, respectively, using an analysis sequence measured on one biosensor. Additional validation mixtures of the two phenols were measured with a new biosensor, prepared with the same procedure but with a different batch of tyrosinase enzyme. Using the mixture responses for the first sensor as a calibration set in PLS-R, the relative prediction errors of the validation mixtures, after applying correction procedures, were 7.0% for catechol and 16.0% for 4-chlorophenol. These preliminary results indicate that by applying correction algorithms it could be possible to use less stable biosensors in continuous on-line measurements together with multivariate data analysis without time-consuming calibration procedures.