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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 101 (1995), S. 363-369 
    ISSN: 1432-2064
    Keywords: 35P15 ; 58C50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this note, we adopt a probabilistic method for estimating the first Dirichlet eigenvalue. The results improve or contain some known ones, especially for large dimension. Moreover, our estimates are sharp for some typical cases.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 98 (1994), S. 299-306 
    ISSN: 1432-2064
    Keywords: 58G32 ; 58C50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary By using coupling methods, some lower bounds are obtained for the first Neumann eigenvalue on Riemannian manifolds. This method is new and the results improve some known estimates. An example shows that our estimates can be sharp.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Rapid Communications 19 (1998), S. 135-137 
    ISSN: 1022-1336
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Poly(ether ether ketone) (PEEK) containing sodium sulfonate groups can be prepared directly from sodium 2,5-dihydroxybenzenesulfonate and 4,4′-difluorobenzophenone. This method is more advantageous than sulfonation of PEEK, avoiding possible degradation and crosslinking. The polymer shows high permeability of water vapor and high selectivity of permeation of water vapor versus nitrogen and can be used as gas dehumidification membrane material.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Macromolecular Chemistry and Physics 199 (1998), S. 1421-1426 
    ISSN: 1022-1352
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A new monomer, sodium 5,5′-carbonylbis(2-fluorobenzenesulfonate) (1), was synthesized by sulfonation of 4,4′-difluorobenzophenone (2) with fuming sulfuric acid. Poly(ether ether ketone)s containing sodium sulfonate groups were synthesized directly via aromatic nucleophilic substitution from the sodium sulfonate-functionalized monomer 1 and Bisphenol A (3) in the presence of potassium carbonate in dimethyl sulfoxide. The polycondensation proceeds without any side reactions. The differential scanning calorimetry measurement indicated that the polymers are amorphous and the glass transition temperatures increase with the content of sodium sulfonate groups in the polymer chain. The degree of substitution with sodium sulfonate groups has strong influence on their thermal stability and solubility.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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