Skip to main content
Log in

Replies to the comments on “Faber series method for plane problems of an arbitrarily shaped inclusion [1]”

  • Letter to the Editor
  • Published:
Acta Mechanica Aims and scope Submit manuscript

The Original Article was published on 27 April 2012

Abstract

This work presents a brief introduction to the Faber polynomials and Faber series in order to reply to the comments made by Prof. Y. Z. Chen on “Faber series method for plane problems of an arbitrarily shaped inclusion (Luo and Gao in Acta Mech 208:133–145, 2009),” and finally, it is shown that his comments and conclusion are hasty and incorrect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Luo J.C., Gao C.F.: Faber series method for plane problems of an arbitrarily shaped inclusion. Acta Mech. 208, 133–145 (2009)

    Article  MATH  Google Scholar 

  2. Curtiss J.H.: Faber polynomials and the Faber series. Am. Math. Mon. 78, 577–596 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wu X.M.: Studies on the error transformation of Faber series. Chin. Sci. Bull. 26(9), 520–523 (1981) (in Chinese)

    Google Scholar 

  4. Xie M.Q.: A note on Faber polynomials. Mathematica Applicata 2, 91–96 (1991) (in Chinese)

    Google Scholar 

  5. Shen X.C.: Approximation Theory of Complex Variables, pp. 135–249. Scientific Press, Beijing (1992) (in Chinese)

    Google Scholar 

  6. Mu L.H.: Overconvergence of the Faber series and the interpolating polynomial. Northeast. Math. J. 8(1), 103–109 (1992)

    MathSciNet  MATH  Google Scholar 

  7. Coleman J.P., Myers N.J.: The Faber polynomials for annular aectors. Math. Comput. 64, 181–203 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Liesen J.: Faber polynomials corresponding to rational exterior mapping functions. Constr. Approx. 17, 267–274 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Vlachou V.: Functions with universal Faber expansions. J. Lond. Math. Soc. Second Ser. 80, 531–543 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shen Y.L.: Faber polynomials with applications to univalent functions with quasiconformal extensions. Sci. China Ser. A Math. 52, 2121–2131 (2009)

    Article  MATH  Google Scholar 

  11. Tsirivas N.: Universal Faber and Taylor series on an unbounded domain of infinite connectivity. Complex Var. Elliptic Equ. 56, 533–542 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhu, M. Z.: Numerical Conformal Mapping and its Applications in the Electromagnetic Theory. Degree thesis, pp. 82–84. XiDian University, Xian (2008) (in Chinese)

  13. Lekhnitskii S.G.: Anisotropic Plates. Gordon and Breach, London (1968) (in Chinese)

    Google Scholar 

  14. Kosmodamianskii A.S., Kaloerov S.A.: Thermal Stress in Connected Multiply Plates, pp. 45–46. Vishcha Shkola, Kiev (1983) (in Russian)

    Google Scholar 

  15. Fan W.X., Wu J.G.: Stress concentration of a laminate weakened by multiple holes. Compos. Struct. 10, 303–319 (1998)

    Article  Google Scholar 

  16. Gao, C.F.: Strength analysis of anisotropic composite plates with N pin-loaded holes. Degree Thesis, Nanjing University of Aeronautics & Astronautics, Nanjing (1988) (in Chinese)

  17. Mazurak L.P., Berezhnyts’kyi L.T., Kachur P.S.: A method for the determination of the elastic equilibrium of isotropic bodies with curvilinear inclusions. Part 1: mathematical foundations. Mater. Sci. 34, 760–772 (1998)

    Google Scholar 

  18. Mazurak L.P., Berezhnyts’kyi L.T., Kachur P.S.: A method for the determination of the elastic equilibrium of isotropic bodies with curvilinear inclusions. Part 2. Plane problem. Mater. Sci. 35, 10–22 (1999)

    Article  Google Scholar 

  19. Suetin P.K., Pankratiev E.V.: Series of Faber Polynomials. CRC Press, Boca Raton, FL (1998)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cun-Fa Gao.

Additional information

This reply refers to the comment available at doi:10.1007/s00707-012-0663-7.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luo, JC., Gao, CF. Replies to the comments on “Faber series method for plane problems of an arbitrarily shaped inclusion [1]”. Acta Mech 223, 1561–1563 (2012). https://doi.org/10.1007/s00707-012-0676-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0676-2

Keywords

Navigation