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  • General Chemistry  (3)
  • Asymptotic expansions  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On the asymptotic behavior of the bestL ∞-approximation by polynomials (1987)
    Springer
    Constructive approximation 3 (1987), S. 377-388 
    Details
    ISSN: 1432-0940
    Keywords: Algebraic polynomials ; Entire functions ; Asymptotic expansions ; Chebyshev approximation ; 41A10 ; 41A25 ; 41A50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetE n (f) denote the sup-norm-distance (with respect to the interval [−1, 1]) betweenf and the set of real polynomials of degree not exceedingn. For functions likee x , cosx, etc., the order ofE n (f) asn→∞ is well known. A typical result is $$2^{n - 1} n!E_{n - 1} (e^x ) = 1 + 1/4n + O(n^{ - 2} ).$$ It is shown in this paper that 2 n−1 n!E n−1(e x ) possesses a complete asymptotic expansion. This result is contained in the more general result that for a wide class of entire functions (containing, for example, exp(cx), coscx, and the Bessel functionsJ k (x)) the quantity $$2^{n - 1} n!E_{n - 1} \left( f \right)/f^{(n)} \left( 0 \right)$$ possesses a complete asymptotic expansion (providedn is always even (resp. always odd) iff is even (resp. odd)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890576
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  • 2
    Electronic Resource
    Electronic Resource
    Makromolekulare organische Komplexbildner zur Anreicherung von Uran und Kupfer aus Meerwasser (1960)
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 72 (1960), S. 921-921 
    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.19600722321
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  • 3
    Electronic Resource
    Electronic Resource
    Die Wirkung verschiedener Bodenstruktur-Verbesserungsmittel (1955)
    Weinheim : Wiley-Blackwell
    Zeitschrift für die chemische Industrie 67 (1955), S. 699-704 
    Details
    ISSN: 0044-8249
    Keywords: Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Jeglicher Pflanzenwuchs ist weitgehend von der Bodenstruktur abhängig. Kalk kann nur indirekt eine Krümelbildung des Bodens verursachen. In letzter Zeit sind außer Eisen(III)-Verbindungen, welche unter Umständen erst nach längerer Zeit wirksam werden, vor allem verschiedene synthetische organische Bodenstruktur-Verbesserungsmittel bekannt geworden, die zahlreichen Anforderungen gerecht werden. Eigenschaften und Wirkungsweise derartiger Mittel werden zusammengestellt und durch und durch eigene Befunde ergänzt.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/ange.19550672204
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  • 4
    Electronic Resource
    Electronic Resource
    Structure and Specificity of Organic Chelating AgentsBased on lectures given at colleges and institutes in Germany and in the U.S.A. (1964)
    Weinheim : Wiley-Blackwell
    Angewandte Chemie International Edition in English 3 (1964), S. 325-332 
    Details
    ISSN: 0570-0833
    Keywords: Chelates ; Ligands ; Macromolecules ; N ligands ; Chalcogen ligands ; Metal enrichment ; Chemistry ; General Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Macromolecular chelating agents possessing high selectivity for rare metal ions have been synthetized. One of these, with the complexing group of glyoxal bis-2-mercaptoanil, is suitable for selective enrichment of gold from sea-water, while another is suitable for copper and uranium. - The enrichment of metallic ions in nature is discussed, taking hemocyanin as an example. - Both stereochemistry and isomerism, as well as cyclic conjugation during chelate formation, may influence the selectivity of complexing agents. The quasi-aromatic properties of chelates are discussed.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/anie.196403251
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