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  • 1
    Electronic Resource
    Electronic Resource
    On invariant closed curves for one-step methods (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 103-122 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01399697
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  • 2
    Electronic Resource
    Electronic Resource
    A Direct Approach to Homoclinic Orbits in the Fast Dynamics of Singularly Perturbed Systems (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 671-709 
    Details
    ISSN: 1572-9222
    Keywords: Homoclinic orbits ; singular perturbations ; bifurcation ; FitzHugh–Nagumo system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Homoclinic orbits in the fast dynamics of singular perturbation problems are usually analyzed by a combination of Fenichel's invariant manifold theory with general transversality arguments (see Ref. 29 and the Exchange Lemma in Ref. 16). In this paper an alternative direct approach is developed which uses a two-time scaling and a contraction argument in exponentially weighted spaces. Homoclinic orbits with one last transition are treated and it is shown how ε-expansions can be extracted rigorously from this approach. The result is applied to a singularity perturbed Bogdanov point in the FitzHugh–Nagumo system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022663512855
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  • 3
    Electronic Resource
    Electronic Resource
    Experimentelle Prüfung von Näherungsansätzen für Chiralitätsfunktionen am Beispiel der optischen Aktivität von Methan-Derivaten im Transparenzgebiet (1973)
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 85 (1973), S. 21-27 
    Details
    ISSN: 0044-8249
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die optisch Aktivität eignet sich für detaillierte Aussagen über Konfiguration und Konformation bei Methan-Derivaten,wenn man die Chiralitätsfunktion nach der Theorie der Chiralitätsfunktionen und quantenmechanischen Theorie der optischen Aktivität der Methan-Derivate in ihre Komponenten zerlegt und diese mit dem experimentellen Ergebnis vergleicht. Im vorliegenden Beitrag wird ein erster Schritt in diese Richtung unternommen und gezeigt, daß das zweite Näherungsverfahren für die Bestimmung des konformationsunabhängigen Beitrage zur optischen Aktivität quantitativ gute Resultate liefert. Die Beschreibung des gesamten optischen Drehwinkels durch diese Komponente wird erwartungsgemäß für solche Derivate schlecht, wo spezifische Konformationen durch Wechselwirkung zwischen den Liganden, wie z. B. Wasserstoffbrückenbindungen. bevorzugt auftreten. Ein quantitatives Verständnis für solche Zusatzeffekte erscheint unter Verwendung von Analysen der hier beschriebenen Art aussichtsreich.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/ange.19730850105
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  • 4
    Electronic Resource
    Electronic Resource
    Synthese von α-Vinyl-P,P′-ethylenbis(diorganophosphanen) (1982)
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 94 (1982), S. 932-933 
    Details
    ISSN: 0044-8249
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/ange.19820941224
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  • 5
    Electronic Resource
    Electronic Resource
    Synthesis of α-Vinyl-P,P′-ethylenebis(diorganophosphanes) (1982)
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 21 (1982), S. 919-920 
    Details
    ISSN: 0570-0833
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/anie.198209192
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  • 6
    Electronic Resource
    Electronic Resource
    Herstellung von 2-Vinylphosphiranen (1982)
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 21 (1982), S. 739-743 
    Details
    ISSN: 0570-0833
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/anie.198207390
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  • 7
    Electronic Resource
    Electronic Resource
    Synthesis of 2-Vinylphosphiranes (1982)
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 21 (1982), S. 292-293 
    Details
    ISSN: 0570-0833
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: No Abstract.The complete manuscript of this communication appears in: Angew. Chem. Suppl. 1982, 739. DOI:10.1002/anie.198207390
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/anie.198202922
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  • 8
    Electronic Resource
    Electronic Resource
    Semiempirical Use of Chirality FunctionsE. Ruch and A. Schönhofer, Theor. Chim. Acta 10, 91(1968).E. Ruch and A. Schönhofer, Theor. Chim. Acta 19, 225 (1970). for the Description of the Optical Activity of Methane Derivatives in the Transparent Region (1973)
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 12 (1973), S. 30-36 
    Details
    ISSN: 0570-0833
    Keywords: Chirality functions ; Optical activity ; Methane derivatives ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The optical activity can provide detailed information about the configuration and conformation of methane derivatives if the chirality function is resolved, according to the theory of chirality functions[3] and the quantum mechanical theory of the optical activity of methane derivatives[4], into its components which are compared with experimental data. A first step in this direction is undertaken in the present article and it will be shown that the second approximation method for determining the conformationally independent contribution to the optical activity yields quantitatively good results. Description of the overall optical rotation by this component is expectedly poor where interactions between ligands, e. g. hydrogen bonding, tend to favor specific conformations. A quantitative understanding of such additional effects appears promising in conjunction with analyses of the kind described.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/anie.197300301
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  • 9
    Electronic Resource
    Electronic Resource
    Herstellung von 2-Vinylphosphiranen (1982)
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 94 (1982), S. 298-298 
    Details
    ISSN: 0044-8249
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: No Abstract.Das vollständige Manuskript dieser Zuschrift erscheint in: Angew. Chem. Suppl. 1982, 739-743
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/ange.19820940416
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