Pure and Applied Mathematics Journal

Archive

Volume 1, Issue 1, December 2012

  • Construction of Polynomial Solutions to the Dirichlet Boundary Value Problem for the 3-Harmonic Equation in the Unit Ball

    Valery V. Karachik, Sanjar Abdoulaev

    Issue: Volume 1, Issue 1, December 2012
    Pages: 1-9
    Published: 30 December 2012
    DOI: 10.11648/j.pamj.20120101.11
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    Abstract: Polynomial solution to the Dirichlet boundary value problem for the nonhomogeneous 3-harmonic equation in the unit ball with polynomial right-hand side and polynomial boundary data is constructed. Representation of the Green’s function of the Dirichlet boundary value problem in the unit ball in the case of polynomial data is found.
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  • Galois Groups of Polynomials and the Construction of Finite Fields

    S. M. Tudunkaya, A. I. Kiri

    Issue: Volume 1, Issue 1, December 2012
    Pages: 10-16
    Published: 30 December 2012
    DOI: 10.11648/j.pamj.20120101.12
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    Abstract: In this note an attempt was made in constructing finite fields with the aid of Galois groups of polynomials of small degree. The properties of these polynomials, their base fields and their splitting fields werediscussed. From these properties corollaries were developed upon which the constructions were done. The aim was to provide concrete and phy... Show More
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