Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations

This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations; such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [t_n,t_n+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical quadrature. The main purpose of this paper is to present a detailed analysis of the implications of the location of quadrature nodes on the accuracy and stability of the overall method. Comparisons between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau, and uniformly spaced points are presented. Also, for a given set of quadrature nodes, quadrature rules may be formulated that include or exclude function values computed at the left-hand endpoint t_n. Quadrature rules that do not depend on the left-hand endpoint (which are referred to as right-hand quadrature rules) are shown to lead to L(α)-stable implicit methods with α≈π/2. The semi-implicit analog of this property is also discussed. Numerical results suggest that the use of uniform quadrature nodes, as opposed to nodes based on Gaussian quadratures, does not significantly affect the stability or accuracy of these methods for orders less than ten. In contrast, a study of the reduction of order for stiff equations shows that when uniform quadrature nodes are used in conjunction with a right-hand quadrature rule, the form and extent of order-reduction changes considerably. Specifically, a reduction of order to is observed for uniform nodes as opposed to for non-uniform nodes, where Δt denotes the time step and ε a stiffness parameter such that ε→0 corresponds to the problem becoming increasingly stiff. AMS subject classification (2000) 65B05     

Theoretical study of the shifts of electronic spectra from solute-solvent interaction

Previous theories of spectral solvent shifts are briefly discussed. The basic dipole approximation is analyzed both theoretically and in relation to experimental information. On account of the restricted validity of this approximation — especially for molecules consisting of several polar groups — another, electrostatic model, originating from the Born charging, is investigated. This model is applied to semi-empirical PPP-calculations of spectral solvent shifts of some quinones. Among other things, this model predicts that not only n → π⁸ transitions may be blue shifted but also certain π → π* transitions. When the electrostatic effect is small, other terms may be responsible for the solvent shift, e.g. polarizability. The cavity effect is not expected to be important in the present context.     

Vanadium

Ohne Zusammenfassung     

Cyclohexanol dehydrogenation over Cu/SiO2 and CuO/SiO2: A comparison

Various CuO/SiO₂ catalysts were prepared and characterized by XRD, surface area and metal area measurements. While dehydrogenation activity for cyclohexanol was observed at 473–573 K on reduced catalysts, it was observed only at 573 K on the unreduced catalyst.IICT Communication No: 3261     

Data on subglottal pressure and SPL at varied vocalloudness and pitch in 8- to 11-year-old children

Phonation threshold pressure has been defined as the minimum subglottalpressure to generate phonation. Previous research has indicated that children may habitually employ higher subglottal pressures than adults. In the present investigation sound pressure level (SPL) and subglottal pressures at different pitch levels were measured at and above phonation threshold in nine children. Phonation threshold values were scattered in reasonable agreement with Titzes' prediction, although a discrepancy was noted regarding the frequency dependence in some voices. At normal conversational loudness and loudest level of phonation the children's PS values were between two to four and four to eight times the predicted threshold values, respectively. At normal conversational loudness and habitual pitch subglottal pressures were lower than those previously observed for children, but similar to those found for female adults. The SPL in softest and loudest phonation were somewhat lower as compared to previous phonetogram data for children and for female adults. At normal loudness and habitual pitch the SPL values were similar to those of female adults. For a doubling of P_s mean SPL increased by 10.5 dB on the average.     

Formant transitions in fricative identification: the role of native fricative inventory

The distribution of energy across the noise spectrum provides the primary cues for the identification of a fricative. Formant transitions have been reported to play a role in identification of some fricatives, but the combined results so far are conflicting. We report five experiments testing the hypothesis that listeners differ in their use of formant transitions as a function of the presence of spectrally similar fricatives in their native language. Dutch, English, German, Polish, and Spanish native listeners performed phoneme monitoring experiments with pseudowords containing either coherent or misleading formant transitions for the fricatives /s/ and /f/. Listeners of German and Dutch, both languages without spectrally similar fricatives, were not affected by the misleading formant transitions. Listeners of the remaining languages were misled by incorrect formant transitions. In an untimed labeling experiment both Dutch and Spanish listeners provided goodness ratings that revealed sensitivity to the acoustic manipulation. We conclude that all listeners may be sensitive to mismatching information at a low auditory level, but that they do not necessarily take full advantage of all available systematic acoustic variation when identifying phonemes. Formant transitions may be most useful for listeners of languages with spectrally similar fricatives.     

Sugar-thioacetamide backbone in oligodeoxyribonucleosides for specific recognition of nucleic acids

The amide linkage being shorter than the natural phosphate linkage, an additional atom is introduced into oligodeoxyribonucleosides (ODNs) with sugar-thioacetamide backbone that show very good RNA recognition properties.     

Optical properties and upconversion in Pr3+ doped in aluminum, barium, calcium fluoride glass--I

The absorption and the fluorescence spectra of Pr3+ ion doped in aluminum, barium, calcium fluoride (ABCF) glass have been studied. Judd-Ofelt theory has been used to derive the optical parameters, viz. the oscillator strength, transition probability, branching ratio, stimulated emission cross section, etc. A broadband upconversion has been observed at different wavelengths throughout the visible region when pumped with 810 nm radiation from a Ti-sapphire laser.     

Hydroxy(tosyloxy)iodo]benzene mediated alpha-azidation of ketones

Reaction of various ketones with [hydroxy(tosyloxy)iodo]benzene (HTIB) followed by treatment of the alpha-tosyloxy ketones thus generated in situ with NaN3 offers a one-pot procedure for the synthesis of alpha-azido ketones. The HTIB used in this conversion may also be generated in situ by using iodosobenzene in combination with p-toluene-sulphonic acid.