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Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity

  • S. Tokarzewski
  • J. J. Telega
Article

Abstract.

By employing special continued fractions to two Stieltjes series with nonzero radii of convergence the inequalities for two- and three-point Padé approximants have been derived. These inequalities constitute an extension of the relevant relations valid for one-point Padé approximants [1,Cor.17.1] and two-point Padé ones [23, Th.1]. The Padé approximants inequalities achieved have been applied to the theory of inhomogeneous media for establishing of the new bounds on the effective transport coefficient of two-phase composite materials. As an example the low order estimations of the effective conductivity of a square array of cylinders have been computed and compared with the corresponding ones evaluated in [24].

Key words. Padé approximants, Stieltjes function, composites, bounds, effective conductivities. 

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Copyright information

© Birkhäuser Verlag, Basel, 1998

Authors and Affiliations

  • S. Tokarzewski
    • 1
  • J. J. Telega
    • 1
  1. 1.Polish Academy of Sciences, Institute of Fundamental, Technological Research, Świętokrzyska 21, 00-049 Warsaw, Poland, (Fax: +48 2699815)Poland

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