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  • General Chemistry  (7)
  • Optical activity  (2)
  • CR: 5.17  (1)
  • FitzHugh–Nagumo system  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 671-709 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 29 (1978), S. 209-226 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we give a simple stability theory for finite difference approximations to linear ordinary boundary value problems. In particular we consider stability with respect to a maximum norm including all difference quotients up to the order of the differential equation. It is shown that stability in this sense holds if and only if the principal part of the differential equation is discretized in a “stable way”. This last property is characterized by root conditions which we prove to be satisfied for some classes of finite difference schemes. Our approach simplifies and generalizes some known results of the literature where Sobolev norms or merely the maximum norm are used.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2234
    Keywords: Optical activity ; Chirality functions ; Phosphanes and phos-phinoxides
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Die molaren Drehungen von 7 Horner-Phosphanen und 16 Phosphinoxiden werden als experimentelle Basis für einen Test approximativer Chiralitätsfunktionen verwendet. Unter Zugrundelegung der Gerüstsymmetrie C3v für diese Verbindungsklasse stellen Zweiligandenfunktionen eine gute Näherung dar; eine Approximation unter Verwendung ligandenspezifischer Zahlen führt nur bei einigen Beispielen zum Erfolg.
    Notes: Abstract Seven optically active phosphanes and sixteen phosphin-oxides are used to test approximative chirality functions experimentally. Based onC 3v -symmetry of the molecular skeleton two-ligand-functions yield a good approximation for the experimental data. Ligand-specific parameters can only be gained from a few compounds.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 94 (1982), S. 932-933 
    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
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  • 5
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 94 (1982), S. 298-298 
    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
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  • 6
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 21 (1982), S. 919-920 
    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
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  • 7
    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
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  • 8
    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
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  • 9
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 21 (1982), S. 292-293 
    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
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  • 10
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 21 (1982), S. 739-743 
    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
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