Bulletin of the Korean Mathematical Society (대한수학회보)

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ON ZEROS OF THE BOUBAKER POLYNOMIALS

  • Received : 2013.01.05
  • Published : 2014.03.31
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Abstract

The Boubaker polynomials arose from the discretization of the equations of heat transfer in pyrolysis starting from an assumed solution of the form $$\frac{1}{N}e^{\frac{A}{H/z+1}}\sum_{k=0}^{\infty}{\xi}_kJ_k(t),$$ where $J_k$ is the k-th order Bessel function of the first kind. In this paper, we investigate the distribution of zeros of the Boubaker polynomials.

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References

  1. O. B. Awojoyogbe and K. Boubaker, A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials, Current Appl. Phys. 9 (2009), no. 1, 278-283. https://doi.org/10.1016/j.cap.2008.01.019
  2. K. Boubaker, A. Chaouachi, M. Amlouk, and H. Bouzouita, Enhancement of pyrolysis spray dispersal performance using thermal time-response to precursor uniform deposition, Eur. Phys. J. Appl. Phys. 37 (2007), 105-109. https://doi.org/10.1051/epjap:2007005
  3. J. Ghanouchi, H. Labiadh, and K. Boubaker, An attempt to solve the heat transfer equation in a model of pyrolysis spray using 4q-order m-Boubaker polynomials, Int. J. Heat Tech. 26 (2008), 49-52.
  4. T. Ghrib, K. Boubaker, and M. Bouhafs, Investigation of thermal diffusivity-microhardness correlation extended to surface-nitrured steel using Boubaker polynomials expansion, Mod. Phys. Lett. B 22 (2008), no. 29, 2893-2907. https://doi.org/10.1142/S021798490801731X
  5. H. Labiadh and K. M. Boubaker, A Sturm-Liouville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials, Differ. Uravn. Protsessy Upr. 2007 (2007), no. 2, 117-133.
  6. H. Labiadh, M. Dada, O. B. Awojoyogbe, K. B. Ben Mahmoud, and A. Bannour, Establishment of an ordinary generating function and a Christoffel-Darboux type first order differential equation for the heat equation related Boubaker-Turki polynomials, Differ. Uravn. Protsessy Upr. 2008 (2008), no. 1, 51-66.
  7. S. Lazzez and K. B. Ben Mahmoud, New ternary compounds stoichiometry-linked thermal behavior optimization using Boubaker polynomials, J. Alloys Compounds 476 (2009), 769-773. https://doi.org/10.1016/j.jallcom.2008.09.148
  8. T. Sheil-Small, Complex Polynomials, Cambridge Studies in Advanced Mathematics 73, Cambridge University Press, Cambridge, 2002.
  9. S. Slama, J. Bessrour, K. Boubaker, and M. Bouhafs, A dynamical model for investiga- tion of A3 point maximal spatial evolution during resistance spot welding using Boubaker polynomials, Eur. Phys. J. Appl. Phys. 44 (2008), 317-322. https://doi.org/10.1051/epjap:2008177
  10. S. Slama, M. Bouhafs, and K. B. Ben Mahmoud, A Boubaker polynomials solution to heat equation for monitoring A3 point evolution during resistance spot welding, Int. J. Heat Tech. 26 (2008), 141-146.
  11. G. Szego, Orthogonal Polynomials, (fourth ed.). Providence (RI): Amer. Math. Soc. 1975.
  12. T. Zhao, B. K. Ben Mahmoud, M. A. Toumi, O. P. Faromika, M. Dada, O. B. Awojoyogbe, J. Magnuson, and F. Lin, Some new properties of the applied-physics related Boubaker polynomials, Differ. Uravn. Protsessy Upr. (2009), no 1, 7-19.