Numerical stability of biorthogonal wavelet transforms

For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL . These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.     

Metal island coated polymer sensor for direct determination of the volume effect of chaotropic agents

A new optical sensor is presented, based on the analyte reaction resulting in swelling and shrinking of a thin polymer layer. Changing the concentration of ions in a new bisazide photo-cross-linked poly(vinylpyrrolidone) polymer results in a concentration-dependent volume change of the hydrated gel. The volume response of the sensor induced by different ions is fully reversible over more than 250 cycles. The response of the device depends on the type, the charge and the concentration of the ions. The sensor material is part of an optical thin film system which transforms the variations in volume of the polymer into spectral information. The steady state of the sensor response is obtained within 60 s. The response time is mainly limited by the pump rate, the back pressure and the total volume of the system but not by the swelling of the sensor polymer. A comparative study of ion effects has demonstrated a fundamental correlation of the polymer swelling properties with the Hofmeister series of chaotropic agents. Thus it is concluded that the photopolymer, which is solubilized in aqueous solutions by the interaction of its amide structure with the solvent, behaves like the backbone amide structure of proteins.     

Consequences of the ‘Pedersen papers’ on crown type chemistry at Würzburg and Bonn Universities: From heteroaromatic crowns and podands to large molecular and crystalline cavities including multisite receptors,cascade molecules,chromoionophores, siderophores,surfactant-type,and extreme ligands

We thank the editors of this issue for the opportunity to present the historic development of crown chemistry at the Universities of Wurzburg and Bonn in memory of C. J. Pedersen, the originator of the crown ethers. His legacy of science has tremendously stimulated research at both universities.This paper is dedicated to the memory of the late Dr C. J. Pedersen.     

Thioacetylacetone: structural and vibrational assignments.

Thioacetylacetone and its variously deuterated isotopomers have been investigated using electronic and vibrational spectroscopy combined with quantum chemical calculations. Thioacetylacetone is known for its photochromic properties, but the structures of the initial and final forms have been the subject of a long debate. Analysis of the IR spectra recorded in low-temperature argon and xenon matrices, room-temperature solutions, and in the gas phase has allowed us to establish the nature of the photochromic species and of its precursor. Similar to the case of another beta-thioxoketone, monothiodibenzoylmethane, the photo-product has been assigned to the nonchelated SH exo-rotamer of the (Z)-enethiol tautomeric form, whereas the dominant ground-state species corresponds to the chelated (Z)-enol tautomeric form. Detailed vibrational assignments have been proposed for both forms based on quantum chemical calculations and polarization experiments. In the case of the chelated (Z)-enol species prevailing in the ground state, a second-order perturbative anharmonic analysis at the B3LYP/cc-pVTZ level indicated strong anharmonic effects associated with the intramolecular hydrogen bond, leading to a shift of more than 600 cm-1 of the wavenumber of the OH-stretching vibration. A small fraction of the SH endo-rotameric chelated (Z)-enethiol form was also detected under unperturbed conditions. The (Z)-enethiol form can be converted into the (Z)-enol form by irradiation at 290 nm.     

Separation and determination of aluminium by single-column ion-chromatography

A quick, reliable method for the determination of Al(III) in the presence of other metal ions is presented. A Chromatographic system consisting of a low-capacity cation-exchange column, an eluent of diprotonated p-phenylenediamine, and a conductivity detector was used to measure the retention times for various cations. During the course of this work, it was found that Al(III) was eluted later than most bivalent metal ions but earlier than other tervalent metal ions. Therefore the concentration of eluent was adjusted so that an early sharp peak was obtained for Al(III) and the bivalent metal ions were eluted as a group. Through analysis of an NBS standard, as well as of solutions containing Al(III) and other metal ions, the method was shown to be precise, accurate and rapid for determination of Al(III) without interference from common bivalent metal ions.