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The Limit of the Numerical Method of Inverting the Laplace Transformation and the Uniqueness of Relaxation Distribution Function Obtained by the Method

  • Mitsuhiro Matsumoto
  • Hiroshi Watanabe

Abstract

It is shown that the high frequency components of the relaxation distribution function (RDF) lose their significance in the process of numerical inversion of the Laplace transformation. Five different methods of approximating the RDF are compared. The methods of approximating the RDF by a polynomial, that is by a continuous function, reproduce all features of the original function, whereas the method of approximating the RDF by line spectra shows a great deal of arbitrariness in the result. This can be understood in terms of the loss of high frequency components in the process of transformation. The effect of approximating the RDF by a set of rectangles or trapezia on the inverting procedure is also discussed.

Keywords

Decay Curve Solid Curf Master Curve Laplace Transformation High Frequency Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Matsumoto M, Watanabe H and Yoshioka K, Kolloid-Z, Z Polym., 250 (1972) 298.CrossRefGoogle Scholar
  2. 2.
    Tsuji K, Watanabe H and Yoshioka K, Adv. Md. Relaxation Prcoesses, 8 (1976) 49.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • Mitsuhiro Matsumoto
    • 1
  • Hiroshi Watanabe
    • 2
  1. 1.Department of Chemistry, College of General EducationTokushima UniversityTokushimaJapan
  2. 2.Department of Chemistry, College of General EducationUniversity of TokyoMeguro, TokyoJapan

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