Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. Part II: Clenshaw-Lord type approximants

Laurent-Padé (Chebyshev) rational approximantsP _m (w, w ⁻¹)/Q _n (w, w ⁻¹) of Clenshaw-Lord type [2,1] are defined, such that the Laurent series ofP _m /Q _n matches that of a given functionf(w, w ⁻¹) up to terms of orderw ^±(m+n) , based only on knowledge of the Laurent series coefficients off up to terms inw ^±(m+n) . This contrasts with the Maehly-type approximants [4,5] defined and computed in part I of this paper [6], where the Laurent series ofP _m matches that ofQ _n f up to terms of orderw ^±(m+n ), but based on knowledge of the series coefficients off up to terms inw ^±(m+2n). The Clenshaw-Lord method is here extended to be applicable to Chebyshev polynomials of the 1st, 2nd, 3rd and 4th kinds and corresponding rational approximants and Laurent series, and efficient systems of linear equations for the determination of the Padé-Chebyshev coefficients are obtained in each case. Using the Laurent approach of Gragg and Johnson [4], approximations are obtainable for allm≥0,n≥0. Numerical results are obtained for all four kinds of Chebyshev polynomials and Padé-Chebyshev approximants. Remarkably similar results of formidable accuracy are obtained by both Maehly-type and Clenshaw-Lord type methods, thus validating the use of either.     

Zur Theorie der Randwertaufgaben

Ohne ZusammenfassungDie vorliegende Arbeit bildet einen Auszug meiner in Göttingen (1903) erschienenen Dissertation. Einige Änderungen sind aber eingetreten, insbesondere wird dem Beweise der Existenz der ausgezeichneten Lösungen (§ 2) eine einfachere Gestalt gegeben.     

Excitation and relative differential oscillator strengths for trifluoromethyl sulphur pentafluoride, SF5CF3, in the UV–VUV region by electron energy loss spectroscopy

Electron energy loss spectroscopy (EELS) has been used to study the photo-absorption spectrum of trifluoromethyl sulphur pentafluoride (SF₅CF₃) for the first time. Comparison is made with the EELS spectrum of sulphur hexafluoride (SF₆). The photolysis of the compound is discussed with relevance to estimated lifetimes in the atmosphere. It is estimated that the lifetime of SF₅CF₃ is of the order of 1000 years.     

Mikroskopische chemische Reaktionen der S?uren von Chlor, Brom und Jod

Ohne Zusammenfassung     

Scattering of He atoms from rough surfaces

Three diverse rough surfaces have been studied using inelastic He scattering. The first is an ion bombarded Ag(110) surface where a broadened specular peak remains visible but scattering remains entirely elastic as viewed by the incoherent component. The second is a cleaved Te(10 ) surface composed of helical chains where the roughness originates from thermal oscillations and scattering is almost entirely inelastic. Thirdly, a glass (7740) disc is shown to be physically rough but the surface is sufficiently rigid to yield largely elastic incoherent scattering.     

Perfluorocarbon imaging in vivo: a 19F MRI study in tumor-bearing mice

Multiresonance perfluorocarbon emulsions (Oxypherol and Fluosol-DA) were imaged in tumor-bearing mice using 19F spin-echo magnetic resonance imaging in vivo. Multiple thin-slice fluorine images free of chemical shift artifacts were obtained in 13 minutes and these were correlated with proton images obtained during the same experiment to delineate the anatomic distribution of perfluorocarbons. Sequential images were used to determine the time course of the distribution and the retention of the compounds in tumors and organs. 19F MR spectroscopy was used ex vivo to determine with high sensitivity the relative concentration of perfluorocarbons in different tissues and organs and to confirm the results obtained from imaging experiments. The fluorine images visually demonstrated the preferential localization of the perfluorocarbons in the liver and spleen; shortly after injection, the images also revealed the highly vascularized tumor-chest wall interface. Imaging and spectroscopy together showed that the perfluorocarbons were removed from the blood pool within hours and remained sequestered in tissues at later times; the highest concentrations were found in the spleen and liver, where the agents were retained without spectral changes for the duration of these studies. The perfluorocarbons accumulated within tumors at dose-dependent concentrations, one to two orders of magnitude smaller than those observed in the spleen and liver.     

Spatial release from masking in normally hearing and hearing-impaired listeners as a function of the temporal overlap of competing talkers

Listeners with sensorineural hearing loss are poorer than listeners with normal hearing at understanding one talker in the presence of another. This deficit is more pronounced when competing talkers are spatially separated, implying a reduced "spatial benefit" in hearing-impaired listeners. This study tested the hypothesis that this deficit is due to increased masking specifically during the simultaneous portions of competing speech signals. Monosyllabic words were compressed to a uniform duration and concatenated to create target and masker sentences with three levels of temporal overlap: 0% (non-overlapping in time), 50% (partially overlapping), or 100% (completely overlapping). Listeners with hearing loss performed particularly poorly in the 100% overlap condition, consistent with the idea that simultaneous speech sounds are most problematic for these listeners. However, spatial release from masking was reduced in all overlap conditions, suggesting that increased masking during periods of temporal overlap is only one factor limiting spatial unmasking in hearing-impaired listeners.     

Histidine and deuterium-labelled histidine by asymmetric catalytic reduction and assignment of the absolute stereochemistry by neutron diffraction

We describe an efficient and convenient route for the preparation of enantiomerically pure d-labelled histidine by asymmetric hydrogenation with a Rh–diphosphine complex in the presence of strong non-coordinating acids. A single-crystal neutron diffraction study of the selectively dideuterated N-benzoyl-histidine methyl ester, tetrafluoroborate salt determined the absolute stereochemistry. This allowed us to clarify the role of H⁺ in the whole reduction process.     

Radical identification by liquid chromatography/thermospray mass spectrometry

Radical adducts of 5,5-dimethyl-1-pyrroline N-oxide (DMPO) with hydroxyl, methanol-derived, and ethanol-derived radicals were detected by a combination of liquid chromatography with either electron paramagnetic resonance or thermospray mass spectrometry (LC/EPR or LC/TSP-MS) in the Fenton system (with methanol or ethanol). One radical adduct was observed in the reaction of DMPO with the hydroxyl radical or the methanol-derived radical, while two adducts were detected in the reaction of DMPO with ethanol-derived radicals. The LC/TSP-MS spectra showed quasi-molecular ions [M + H]+ at m/z 146 and m/z 160 for the methanol-derived and ethanol-derived radical adducts, respectively, and an apparent molecular ion M+ at m/z 130 for the hydroxyl radical adduct. Use of methyl-D3 alcohol (CD3OH) and ethyl-D5 alcohol (CD3CD2OH) indicated that carbon-centered radicals are formed. Experiments with partially deuterated ethanol (CD3CH2OH and CH3CD2OH) indicated that the two adducts observed in the reaction of DMPO with ethanol-derived radicals correspond to the two diastereomeric adducts of DMPO with the alpha-hydroxyethyl free radical.