On interpolatory divergence-free wavelets

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct compactly supported divergence-free interpolatory wavelets.

     

Exponential averaging for traveling wave solutions in rapidly varying periodic media

Reaction diffusion systems on cylindrical domains with terms that vary rapidly and periodically in the unbounded direction can be analyzed by averaging techniques. Here, using iterated normal form transformations and Gevrey regularity of bounded solutions, we prove a result on exponential averaging for such systems, i.e., we show that traveling wave solutions can be described by a spatially homogenous equation and exponentially small remainders. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gaseous alkyne ions

Using the relative abundance of metastable ions, collisional activation spectra, field ionization kinetic measurements, isotopic labelling, appearance energy and kinetic energy release data, it is shown that linear alkyne radical cations with more than six carbon atoms do not isomerize to equilibrating structures prior to decomposition. At the shortest ion lifetimes the molecular ions of linear alkynes decompose mainly by simple β-bond fission which allows an unequivocal localization of the triple bond. At medium ion lifetimes fragmentation occurs predominantly via a McLafferty rearrangement, while at long ion lifetimes competing alkyl losses prevail. These alkyl losses occur via cyclic intermediates leading to thermochemically stable cycloalkenyl ions. All these reactions occur with a high specificity with respect to the carbon and hydrogen atoms involved and are preceded by little or no hydrogen exchange reactions.     

Atomic structure of Beta-tantalum nanocrystallites.

The structural properties of beta-phase tantalum nanocrystallites prepared by room temperature magnetron sputter deposition on amorphous carbon substrates are investigated at atomic resolution. For these purposes spherical aberration-corrected high-resolution transmission electron microscopy is applied in tandem with the numerical retrieval of the exit-plane wavefunction as obtained from a through-focus series of experimental micrographs. We demonstrate that recent improvements in the resolving power of electron microscopes enable the imaging of the atomic structure of beta-tantalum with column spacings of solely 0.127 nm with directly interpretable contrast features. For the first time ever, we substantiate the existence of grain boundaries of 30 degrees tilt type in beta-Ta whose formation may be well explained by atomic agglomeration processes taking place during sputter deposition.     

Dehydration of Alkanones by Bare FeO+ Involves the ω/(ω − 1) Positions: Exclusion of Iron Carbenes as Intermediates. Preliminary Communication

Fourier-transform ion-cyclotron-resonance (FTICR) mass spectrometry has been used to uncover the mechanisms by which FeO⁺ dehydrates heptan-4-one ( 5a ) and nonan-5-one ( 6a ) in the gas phase. The study of isotopomeric ketones provides evidence that H₂O loss is not due to a 1,1-elimination, thus ruling out the intermediacy of high-valent iron-carbene species. Rather, H₂O is generated in a formal 1,2-elimination involving the ω/ω ? 1 positions of the alkyl chain (‘remote C? H bond activation’). In the consecutive alkene/H₂O elimination, the olefins (ethylene from 5a and propene from 6a ) originate from the terminal part of one alkyl chain, and the H-atom is transferred to the FeO⁺ moiety in the course of this process, builds up together with an H-atom from the ω/ω-1 position of the other alkyl chain the H₂O molecule. In either case, the O-atom of H₂O is provided by the FeO⁺ species.     

Theoretical treatment of the spectrophotometric titration of bivalent cations with complexon-iii and metal-specific indicators

It was derived theoretically that a sharp end-point of this spectrophotometrical titration is defined, in order of importance, by: 1. *K_C ? *K_I (numerically speaking, log$\text{*K}{}_{\mathrm{C}}\text{*K}{}_{\mathrm{I}}$ should be at least 4); 2. *K_I being large (numerically e.g. 10⁴-10⁵); this is already reached by choosing a high pH; 3. it being low; 4. m_t being as high as possible.     

Synthese und Charakterisierung funktionalisierter β‐Hydroxydithiozimtsäuren und deren Ester. Komplexchemisches Verhalten gegenüber Nickel(II), Palladium(II) und Platin(II)

Synthesis and Analytical Characterization of Functionalized β‐Hydroxydithiocinnamic Acids and their Esters. Complex Chemistry towards Nickel(II), Palladium(II), and Platin(II) Starting from silyl‐protected 4‐hydroxy acetophenone ( 1 ) the 1,1‐ethenedihiolato complexes 3 – 5 were synthesised using carbon disulfide and potassium‐tert‐butylate as a base. After being deprotected, the resulting 4‐hydroxy‐substituted complexes 6 – 8 were esterified with DL‐α‐lipoic acid to obtain the compounds 9 – 11 . The resulting complexes were characterized using NMR spectroscopy, mass spectrometry and IR spectroscopy. 3‐substituted β‐hydroxydithiocinnamic acid methyl ester ( 12 ) was obtained via an analogous path of reaction using silyl‐protected 3‐hydroxy acetophenone ( 2 ), carbon disulfide and methyl iodide. After removing of the silyl group the resulting hydroxy group was esterified with DL‐α‐lipoic acid. Using the dithioacid ester 14 as a ligand the Ni^II ( 15 ), Pd^II ( 16 ) and Pt^II ( 17 ) [O,S] complexes were obtained.     

An experimental study of chromatographic dynamics in open and packed non-cylindrical conduits

A systematic investigation of the influence of the perimeter shape of open and particle packed fused silica capillaries on chromatographic properties such as resistance to flow and dispersion of solutes propelled through these channels has been conducted. Verifications of these uncommon experiments with existing theoretical treatments are presented and the insights transferred to a novel polymer chip design with integrated facilities for complex separations. A comparison of the chromatographic performance of a real life proteomics sample on this chip with a capillary column of "similar" dimensions is presented.     

Determination of organophosphorus, triazine and 2,6-dinitroaniline pesticides in aqueous samples via solid-phase microextraction (SPME) and gas chromatography with nitrogen-phosphorus detection

Solid-phase microextraction (SPME) represents a very simple and rapid method for the extraction of organophosphorus, triazine and 2,6-dinitroaniline pesticides from aqueous samples without making use of any solvents. The same fiber can be used repeatedly. Moreover, a sample volume as small as 3 mL can be employed with no loss in sensitivity. 34 compounds have been extracted from aqueous samples by SPME using a 85 m polyacrylate fiber. For organophosphorus pesticides, a 100 m polydimethylsiloxane fiber has been used additionally for comparison. The fibers were directly introduced into the heated split/splitless injector of the gas chromatograph and determined using a nitrogen-phosphorus detector. The method was evaluated with respect to the limit of detection (LOD), linearity and precision. The limit of detection (LOD) depends on the compound and varies from 0.005–0.09 g/L. The method is linear over at least three orders of magnitude with coefficients of correlation usually >0.999. For triazines and 2,6-dinitroanilines the coefficient of variation (precision) is <8% while for organophosphorus compounds it may reach values up to 18% (however, if the latter compounds are extracted using the polydimethylsiloxane phase considerably higher precision is achieved). The partitioning of the analyte between the aqueous phase and the polymeric phase depends on the hydrophobicity of the compound as expressed by the octanol/water partitioning coefficient (P_ow). For triazines it was shown that there is a linear dependence of the logarithm of the analyte response on the log(P_ow) i.e. the higher the hydrophobicity, the higher the affinity of the analytes to the polymeric phase of the fiber and the higher the response. Salt addition has a strong effect on the extraction efficiency. This effect increases with decreasing hydrophobicity (increasing polarity) of the compound. The triazines ametryn, atrazine, propazine, simazine and simetryn have been identified in a ground water well sample by SPMEGC/NPD.