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  • AMS(MOS) 65L05, 58F08, 58F22  (1)
  • Organic Chemistry  (1)
  • Polymer and Materials Science  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 51 (1987), S. 103-122 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05, 58F08, 58F22 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number for which we derive an asymptotic expression. Our results complement those of [2, 3] where one-step methods were shown to create invariant curves if the dynamical system has a periodic orbit which is stable in either time direction or if the system undergoes a Hopf bifurcation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Liebigs Annalen 1975 (1975), S. 401-405 
    ISSN: 0075-4617
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Ozonolysis of Dihydrolinalool(+)-(R)-3,7-Dimethyl-6-octen-3-ol (dihydrolinalool, 2) is prepared from (+)-(S)-3,7-dimethyl-1.6-octadien-3-ol (linalool, 1) by partial hydrogenation. The compound is ozonized in ethyl acetate and hydrogenated, and the resulting hemi-acetal 3b reduced to (+)-(R)-3-methyl-3-hexanol (4) by the Wolff-Kishner method. The analogous procedure in methanol or ethanol yields (i-)-(2R,5S)-2-ethyl-5-methoxy-2-methyloxolane (5a) and its (-)-(2R,5R)-isomer 5b, or the corresponding 5-ethoxy compounds. The mechanism and synthetic utility of this reaction are discussed.
    Notes: Aus ( +)-(S)-3,7-Dimethyl-1,6-octadien-3-ol (Linalool, 1) erhält man durch partielle Hydrierung (+)-(R)-3,7-Dimethyl-6-octen-3-ol (Dihydrolinalool, 2). Dieses liefert nach Ozonolyse in Essigester und anschließender Hydrierung ein Halbacetal 3b, das nach Wolff-Kishner-Reduktion zu (+)-(R)-3-Methyl-3-hexanol (4) f¨hrt. Bei Verwendung von Methanol oder Äthanol sind die Reaktionsprodukte (+)-(2R,5S)-2-Äthyl-5-methoxy-2-methyloxolan (5a) sowie das (-)-(2R,SR)-Isomer 5b bzw. die anlogen 5-Äthoxyverbindungen. Bildungsweise und Anwendbarkeit dieser Reaktion werden erörtert.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    Surface and Interface Analysis 22 (1994), S. 346-349 
    ISSN: 0142-2421
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The application of ellipsometry to study the SiOx/Si system subjected to hydrostatic pressures up to 1.8 GPa at temperatures up to 1280 °C is described. The theoretical model of defects as the spherical disturbances of material has been assumed. The ellipsometric parameters have been analysed as a function of defects size and density and compared with data obtained by etching and x-ray methods. The applicability of ellipsometry for near-surface defect structure analysis has been discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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