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  • Physical Chemistry  (2)
  • singular perturbations  (2)
  • 1980-1984  (4)
  • 1955-1959
  • 1930-1934
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 19 (1984), S. 63-77 
    ISSN: 1432-1416
    Keywords: Slow coevolution ; singular perturbations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An S→I→S epidemic transmitted by two similar strains of parasite acting on a host population of three genotypes which differ in their reaction to the disease is modelled and analyzed. Singular perturbation techniques are used to reduce the original system of nine differential equations to a coupled system of two equations describing the slowtime coevolution of gene frequency and parasite strain frequency.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 19 (1984), S. 79-94 
    ISSN: 1432-1416
    Keywords: Epidemics ; slow-genetic evolution ; singular perturbations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mathematical models of a vector-borne infectious disease acting on a host population consisting of three genotypes which differ in susceptibility to, recovery from, and death due to the disease are presented and analyzed. Singular perturbation techniques are used to obtain a single differential equation describing the slow time evolution of gene frequencies.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 15 (1983), S. 461-468 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The thermal unimolecular decomposition of diethyl carbonate-1,1,1,2,2-d5 has been examined in the high-pressure-limiting region. The observed chemistry is consistent with a simple, competitive two-channel model: The intramolecular isotope effect kH/kD has been determined, and the relative Arrhenius parameters for the two channels are given by \documentclass{article}\pagestyle{empty}\begin{document}$$ k_{\rm H} /k_D = (0.80 \pm 0.18)\,\exp [(1140 \pm 260){\rm cal/mol/RT}] $$\end{document} over the temperature range of 540-620 K. These Arrhenius parameters predict an isotope effect kH/kD = 5.4 at 300 K.
    Additional Material: 2 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Chemical Kinetics 13 (1981), S. 1277-1288 
    ISSN: 0538-8066
    Keywords: Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: According to our experiments the bromide ion concentration exhibits in the bromate-ascorbic acid-malonic acid-perchloric acid system three extrema as a function of time. To describe this peculiar phenomenon, the kinetics of four component reactions have been studied separately. The following rate equations were obtained:Bromate-ascorbic acid reaction: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - d[{\rm BrO}_3^ -]/dt = k_1 [{\rm BrO}_3][{\rm H}_2 {\rm A],}} & {k_1 = 8.3 \times 10^{ - 3} M^{ - 1} \cdot {\rm s}^{ - {\rm 1}} } \\ \end{array} $$\end{document}Bromate-bromide ion reaction: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - d[{\rm BrO}_3^ -]/dt = k_2 [{\rm BrO}_3][{\rm Br}^ -][{\rm H}^ +]^2,} & {k_2 = 3.6M^{ - 3} \cdot {\rm s}^{ - 1} } \\ \end{array} $$\end{document}Bromide-ascorbic acid reaction: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - d[{\rm Br}_{\rm 2}]/dt = k_3 [{\rm Br}_2][{\rm H}_2 {\rm A],}} & {k_3 \ge 1.7 \times 10^{ - 3} \cdot {\rm s}^{ - 1} } \\ \end{array} $$\end{document}Bromine-malonic acid reaction: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} { - d[{\rm Br}_{\rm 2}]/dt = k_4 k_4 [{\rm Br}_2][{\rm H}_2 {\rm M}]/(k_4 + k_5 [{\rm Br}_2]),} & {k_4 = 6 \times 10^{ - 3} {\rm s}^{ - 1} } \\ \end{array}, \quad {\rm }k_{ - 4} \ge 1.7 \times 10^{ - 3} \cdot {\rm s}^{ - 1} \quad {\rm }k_5 \ge 1 \times 10^7 M^{ - 1} \cdot {\rm s}^{ - 1} $$\end{document} k4 = 6 × 10-3 s-1, k-4 ≥ 1.7 × 103 s-1, k5 ≥ 1 × 107M-1 · s-1Taking into account the stoichiometry of the component reactions and using these rate equations, the concentration versus time curves of the composite system were calculated. Although the agreement is not as good as in the case of the component reactions, it is remarkable that this kinetic structure exhibits the three extrema found.
    Additional Material: 5 Ill.
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