Pure and Applied Mathematics Journal

Archive

Volume 2, Issue 3, June 2013

  • On the Dynamic Response of an Ocean to Wind Stress in an Equatorial Region-II: Further Exact Solutions of the Rossby Equation

    M. Z. Rahman, A.B.M. Shamim. Ul Hasan

    Issue: Volume 2, Issue 3, June 2013
    Pages: 110-118
    Received: 24 April 2013
    Published: 30 May 2013
    DOI: 10.11648/j.pamj.20130203.11
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    Abstract: In a beforehand paper they found some exact and explicit solutions for the standard Rossby form of the equation for the stream function for some specified and realistic wind stress. This equation, which is a third order linear partial differential equation for the stream function, relates the rate of change of vertical vortices to the curl of the a... Show More
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  • Strong Reflection Principles and Large Cardinal Axioms

    J. Foukzon, E. R Men’kova

    Issue: Volume 2, Issue 3, June 2013
    Pages: 119-127
    Received: 18 May 2013
    Published: 10 June 2013
    DOI: 10.11648/j.pamj.20130203.12
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    Abstract: In this article an possible generalization of the Löb’s theorem is considered. We proved so-called uniform strong reflection principle corresponding to formal theories which has ω-models.Main result is: let κ be an inaccessible cardinal and H_κ is a set of all sets having hereditary size less than κ,then:"¬Con" ("ZFC+" ("V=" "H" _"κ" ) )
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  • Refutation Of Hard-Determinable Formulas In The System “Resolution Over Linear Equations” And Its Generalization

    Anahit Chubaryan, Armine Chubaryan, Arman Tshitoyan

    Issue: Volume 2, Issue 3, June 2013
    Pages: 128-133
    Received: 11 May 2013
    Published: 20 June 2013
    DOI: 10.11648/j.pamj.20130203.13
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    Abstract: We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret. R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in R (lin). We... Show More
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  • An Explicit Solution of Burgers’ Equation with Special Kinematic Viscosity Using Decomposition Technique

    Bolujo Joseph Adegboyegun

    Issue: Volume 2, Issue 3, June 2013
    Pages: 134-139
    Received: 23 June 2013
    Published: 10 July 2013
    DOI: 10.11648/j.pamj.20130203.14
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    Abstract: In this article, Adomian’s Decomposition Method (ADM) is employed to approximate the solution of Burgers’ equationwhich is one-dimensional non-linear differential equations in fluid dynamics. The exact solution for Burger’s equation with low kinematic viscosity does not exist in the literatures.Thus, we obtained an explicit solution for this spec... Show More
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