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)     

Cylindrical spike model for the formation of diamondlike thin films by ion deposition

T /n_S of n_T rearrangements and n_S atoms in the spike volume as the crucial parameter characterizing the ability of a given ion–target combination to achieve complete rearrangement of the spike volume. n_T/n_S>1 is the optimum condition for diamondlike film growth. For aC films the ion energy dependence of n_T/n_S agrees well with the measured sp³ bond fraction. For Ar⁺-ion-assisted deposition of aC we find n_T/n_S>1 above 50 eV with no pronounced ion energy dependence. Furthermore, our model predicts optimum conditions for the formation of cubic boron nitride between 50 eV and 3 keV. Accepted: 14 October 1997     

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.     

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.     

Stable gaseous aziridinium ions

Gaseous protonated aziridine ions are produced at the threshold from β-phenoxyethylamine molecular ions. The evidence for this is collisional activation spectra, using various precursors (including labelled analogues) under electron impact and field ionization conditions. Partial conversion to the acyclic \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm CH}_{\rm 3} {\rm CH = }\mathop {\rm N}\limits^ + {\rm H}_{\rm 2} $\end{document} isomer occurs at higher electron energies and is rationalized by means of a potential energy surface constructed from energetic data.     

Freie Auflösungen äußerer Potenzen

Let R be a commutative noetherian ring with identity. To a finite free resolution F of an R-module M and every integer p1 we associate finite free complexes C _* ^p F. C _* ^p F is a free resolution of PM-the p-th exterior power of M if the degree of torsionfreeness of M is large enough. Using C _* ^p F we further study the degree of torsionfreeness of PM. As an application we prove a special case of a conjecture of P. Hackman concerning a connection between rank and torsionfreeness of a module.     

Sensitized photoconduction in a polydiacetylene crystal (DCHD)

The photoconductivity of DCHD displays a maximum near 3.6 eV coinciding with the maximum of the S_o → S₁ absorption of the carbazole group. It is attributed to a sensitization involving charge transfer from the excited chromophore to the chain. The rate constant for non-radiative decay of the carbazole singlet due to energy transfer to the chain is 1.6 × 10¹³ s^?1, and for charge transfer ≈ 3 × 10¹¹ s^?1.     

Dioxygen activation by a low-valent cobalt complex employing a flexible tripodal N-heterocyclic carbene ligand

The novel versatile cobalt(I) tris-carbene complex [(TIMEN(xyl))Co]Cl (1) (where TIMEN = (tris[2-(3-arylimidazol-2-ylidene)ethyl]amine) reacts with CO, one-electron oxidizers such as CH(2)Cl(2), and O(2) to yield the cobalt complexes [(TIMEN(xyl))Co(CO)]Cl (2), [(TIMEN(xyl))Co(Cl)]Cl (3), and peroxo species [(TIMEN(xyl))Co(O(2))](BPh(4)) (5). All new complexes were fully characterized by (1)H NMR, UV/vis, and IR spectroscopy as well as superconducting quantum interference device (SQUID) magnetization measurements and single-crystal X-ray crystallography. The nucleophilic character of the eta(2)-bound dioxygen ligand in 5 was confirmed by density functional theory (DFT) studies and allows for oxygen-transfer reactions with electron-deficient organic substrates, such as benzoyl chloride.