Tight compactly supported wavelet frames of arbitrarily high smoothness

Based on Ron and Shen's new method for constructing tight wave-let frames, we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness.

     

Determination of HCHs,PCBs, and DDTs in brain tissues of marine mammals off different age

The concentrations of a number of polychlorinated biphenyls and chlorinated pesticides in brain tissues of marine mammals of different age and regional origin were determined by using high-resolution capillary gas chromatography and electron capture detection. Brain tissues of two neonatal and three stillborn northern fur seals (Callorhinus ursinus) collected in the Bering Sea, Pacific Ocean, were examined. In addition, cerebrum, cerebellum, and hypothalamus of one adult female common dolphin (Delphinus delphis) stranded on the coast of Massachusetts, Atlantic Ocean, were examined. It showed clearly that α-HCH was dominant in all brain tissues (90–203 ng/g extractable lipids) compared with other tissues like liver or blubber (45–61 ng/g extractable lipids). This excess of α-HCH in brain tissue was due to only one enantiomer, (+)-α-HCH, whereas in other tissues both enantiomers contributed to the α-HCH concentration. Comparing the overall general xenobiotic burden, the HCH isomers (99–216 ng/g extractable lipids) resemble the PCB (17–105 ng/g extractable lipids) and DDT (111–171 ng/g extractable lipids) levels in brain tissues. The latter two groups exceed the HCHs in liver tissue and in blubber. On a single compound basis, the highest levels are found in brain for α-HCH (fur seal pups: 90–203 ng/g extractable lipids, adult dolphin: 221–305 ng/g extractable lipids), 2,2′,4,4′,5,5′-hexachlorobiphenyl (PCB153) (fur seal pups: 4–25 ng/g extractable lipids, adult dolphin: 260–377 ng/g extractable lipids) and 4,4′-DDE (fur seal pups: 104–164 ng/g extractable lipids, adult dolphin: 364–625 ng/g extractable lipids). The levels of α-HCH and 4,4′-DDE are comparable. No significant difference concerning the xenobiotic burden between neonatal and stillborn northern fur seals could be seen in contrast to the higher concentrations of the adult common dolphin. The patterns of some xenobiotics in the samples were compared with each other by using statistical methods like the similarity index and the principal component analysis (PCA).     

Irregular sampling of wavelet and short-time Fourier transforms

We obtain irregular sampling theorems for the wavelet transform and the short-time Fourier transform. These sampling theorems yield irregular weighted frames for wavelets and Gabor functions with explicit estimates for the frame bounds.     

The atomistic origin of the inverse piezoelectric effect in α-quartz

Ab initio calculations have been carried out using the FP-APW+lo method in order to understand the atomic origin of the inverse piezoelectric effect in α-quartz. The external electric field was modelled by a saw-like potential V_ext in order to achieve translational symmetry within a supercell (SC) containing 72 atoms. The original trigonal quartz structure was repeated along the [110] direction, which corresponds to the direction of the external field. An electric field with 550 kV/mm was applied and the atomic positions of the SC were relaxed until the forces acting on the atoms vanished. In parts of the SC, V_ext changes almost linearly and thus the relaxed atomic positions can be used to determine the structural response due to the external electric field. The calculations provide the piezoelectric modulus of the correct order of magnitude. In contrast to previous models and in agreement with recent experimental results, the atomic origin of the piezoelectric effect can be described by a rotation of slightly deformed SiO₄ tetrahedra against each other. The change of the Si-O bond lengths and the tetrahedral O-Si-O angles is one order of magnitude smaller than that of the Si-O-Si angles between neighbouring tetrahedra. The calculated changes of X-ray structure factors are in agreement with experiment when the theoretical data are extrapolated down to the much smaller field strength that is applied in the experiment (E<10 kV/mm).     

N,N'-dimethyl-2,3-dialkylpyrazinium salts as redox-switchable surfactants? Redox, spectral, EPR and surfactant properties

N,N'-dimethyl-2,3-dialkylpyrazinium salts show reversible transitions between all redox stages and a monolayer formation at the air-water interface that suggests their use as redox-switchable surfactants.     

The anisotropy of conductivity of n-type germanium in strong d.c. fields

The electric conductivity ofn-type germanium at large d.c. field intensities has been measured in three directions of symmetry of the cubic lattice. From these data the repopulation of valleys of the conduction band has been determined. Measurements were done with three materials of different purity. The variation of repopulation between these materials can be explained qualitatively by the influence of Coulomb scattering at ionized impurities. The data are compared with those ofNathan and theoretical data ofFranz andReik et al. The relations of these data to those of the current component perpendicular to the field direction (Sasaki et al.) are also given.     

Direct determination of the rate constant of the reaction NO + HO2 → NO2 + OH with the LMR

The rate of the reaction was determined in an isothermal discharge flow reactor with a combined ESR–LMR detection under pseudo-first-order conditions in HO₂. The rate constant was identical in experiments with two different HO₂ sources: F + H₂O₂ and H + O₂ + M. The absolute rate constant at T = 293 K was measured as In the range 2 ≤ p mbar ≤ 17 no pressure dependence for k₁ was found.