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  • Physical Chemistry  (4)
  • 47A56  (1)
  • 49A10  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Integral equations and operator theory 20 (1994), S. 249-305 
    ISSN: 1420-8989
    Keywords: 47A56 ; 47A57 ; 15A54
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In many problems the local zero-pole structure (i.e. locations of zeros and poles together with their orders) of a scalar rational functionw is a key piece of structure. Knowledge of the order of the pole or zero of the rational functionw at the point λ is equivalent to knowledge of the $$\mathcal{R}(\lambda )$$ -module $$w\mathcal{R}(\lambda )$$ (where $$\mathcal{R}(\lambda )$$ is the space of rational functions analytic at λ). For the more intricate case of a rationalp×m matrix functionW, we consider the structure of the module $$W\mathcal{R}^{m \times 1} (\lambda )$$ as the appropriate analogue of zero-pole structure (location of zeros and poles together with directional information), where $$\mathcal{R}^{m \times 1} (\lambda )$$ is the set of column vectors of heightm with entries equal to rational functions which are analytic at λ. Modules of the form $$W\mathcal{R}^{m \times 1} (\lambda )$$ in turn can be explicitly parametrized in terms of a collection of matrices (C λ,A λ,B λ,B λ,Γ λ) together with a certain row-reduced(p−m)×m matrix polynomialP(z) (which is independent of λ) which satisfy certain normalization and consistency conditions. We therefore define the collection (C λ,A λ,Z λ,B λ,Γ λ,P(z)) to be the local spectral data set of the rational matrix functionW at λ. We discuss the direct problem of how to compute the local spectral data explicitly from a realizationW(z)=D+C(z−A) −1 B forW and solve the inverse problem of classifying which collections λ→(C λ,A λ,Z λ,B λ,Γ λ,P(z)) satisfying the local consistency and normalization conditions arise as the local spectral data sets of some rational matrix functionW. Earlier work in the literature handles the case whereW is square with nonzero determinant.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 51 (1987), S. 181-197 
    ISSN: 0945-3245
    Keywords: AMS(MOS): Primary 65k10 ; 49A10 ; 49D99 ; Secondary 73G05 ; CR: G1.6
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A numerical method for computing minimizers in one-dimensional problems of the calculus of variations is described. Such minimizers may have unbounded derivatives, even when the integrand is smooth and regular. In such cases, because of the Lavrentiev phenomenon, standard finite element methods may fail to converge to a minimizer. The scheme proposed is shown to converge to an absolute minimizer and is tested on an example. The effect of quadrature is analyzed. The implications for higher-dimensional problems, and in particular for fracture in nonlinear elasticity, are discussed.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 29 (1997), S. 421-429 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Real-time kinetic measurements are reported for the Cl + CH3CO → CH2CO + HCl reaction. The experiments utilize infrared spectroscopy to determine the time dependence of the ketene formed via this reaction and of the CO produced from the subsequent rapid reaction between chlorine atoms and ketene. The reaction is investigated over a pressure range of 10-200 torr and a temperature range of 215-353 K. Within experimental error the rate constant under these conditions is k5a = (1.8 ± 0.5) × 10-10 cm3 s-1. We have also examined the Cl + CH2CO reaction and found it to have a rate constant of k6 = (2.5 ± 0.5) × 10-10 cm3 s-1 independent of temperature. © John Wiley & Sons, Inc. Int J Chem Kinet 29: 421-429, 1997.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 21 (1989), S. 1077-1089 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Fourier transform infrared spectroscopy was used to identify and quantify products of the self reaction of ethylperoxy radicals, C2H5O2, formed in the photolysis of Cl2/C2H6 mixtures in 700 torr total pressure of synthetic air at 295 K. From these measurements, branching ratios for the reaction channels of k1a/(k1a + k1b) = 0.68 and k1c/(k1a + k1b + k1c) ≤ 0.06 were established. Additionally, using the relative rate technique, the rate constant for the reaction of Cl atoms with C2H5OOH was determined to be (1.07 ± 0.07) × 10-10 × cm3 molecule-1 s-1. Results are discussed with respect to the previous kinetic and mechanistic studies of C2H5O2 radicals.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 22 (1990), S. 1257-1269 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The mechanisms for the Cl-initiated and OH-initiated atmospheric oxidation of t-butyl alcohol (TBA), methyl t-butyl ether (MTBE), and dimethyl ether (DME) have been determined. For TBA the only products observed are equimolar amounts of H2CO and acetone, and its atmospheric oxidation can be represented by (7), The mechanism for the atmospheric oxidation of DME is also straight forward, with the only observable product being methyl formate, The mechanism for the atmospheric oxidation of MTBE is more complex, with observable products being t-butyl formate (TBF) and H2CO. Evidence is presented also for the formation of 2-methoxy-2-methyl propanal (MMP), which is highly reactive and presumably oxidized to products. The atmospheric oxidation of MTBE can be represented by (9) and (10), In terms of atmospheric reactivity, DME, TBA, and MTBE all compare favorably with methanol. In terms of rate of reaction in the atmosphere, DME, MTBE, and TBA are 1.4, 0.40, and 0.28 times as reactive as CH3OH towards OH on a per carbon basis. With regard tochemistry, atmospheric oxidation of CH3OH yields highly reactive H2CO as the sole carbon-containing product. In contrast, only 25% of the carbon in TBA is converted to H2CO, with the balance yielding unreactive acetone. For DME, all the carbon is converted to methyl formate which is unreactive. Finally, for MTBE, 60% is converted to unreactive TBF while the remaining 40% produces highly reactive MMP.Final assessment of the impact of these materials on the atmospheric reactivity of vehicle emissions requires the determination of their emissions rates under realistic operating conditions.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 28 (1996), S. 627-635 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The kinetics and mechanism of the gas-phase reaction of Cl atoms with CH2CO have been studied with a FTIR spectrometer/smog chamber apparatus. Using relative rate methods the rate of reaction of Cl atoms with ketene was found to be independent of total pressure over the range 1-700 torr of air diluent with a rate constant of (2.7 ± 0.5) × 10-10 cm3 molecule-1 s-1 at 295 K. The reaction proceeds via an addition mechanism to give a chloroacetyl radical (CH2ClCO) which has a high degree of internal excitation and undergoes rapid unimolecular decomposition to give a CH2Cl radical and CO. Chloroacetyl radicals were also produced by the reaction of Cl atoms with CH2ClCHO; no decomposition was observed in this case. The rates of addition reactions are usually pressure dependent with the rate increasing with pressure reflecting increased collisional stabilization of the adduct. The absence of such behavior in the reaction of Cl atoms with CH2CO combined with the fact that the reaction rate is close to the gas kinetic limit is attributed to preferential decomposition of excited CH2ClCO radicals to CH2Cl radicals and CO as products as opposed to decomposition to reform the reactants. As part of this work ab initio quantum mechanical calculations (MP2/6-31G(d,p)) were used to derive ΔfH298(CH2ClCO) = -(5.4 ± 4.0) kcal mol-1. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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