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Pure and Applied Mathematics Journal

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Volume 4, Issue 1, February 2015

  • Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments

    Katya Georgieva Dishlieva

    Issue: Volume 4, Issue 1, February 2015
    Pages: 1-8
    Received: 29 December 2014
    Accepted: 11 January 2015
    Published: 27 January 2015
    DOI: 10.11648/j.pamj.20150401.11
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    Abstract: Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are spe... Show More
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  • Applying Minimum Travel Cost Approach on 43–Nodes Travelling Salesman Problem

    Mohamed Eleiche

    Issue: Volume 4, Issue 1, February 2015
    Pages: 9-23
    Received: 28 December 2014
    Accepted: 11 January 2015
    Published: 30 January 2015
    DOI: 10.11648/j.pamj.20150401.12
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    Abstract: The minimum travel cost is a new approach to solve the Travelling Salesman Problem (TSP). The TSP library website (TSPLIB) provides several TSP problems with their best knownsolutions as a means to test any proposed algorithm. The present paper successfully applies the minimum travel cost algorithmto the 43 nodes P43problem which has the value of 5... Show More
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  • Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup

    Melis Minisker

    Issue: Volume 4, Issue 1, February 2015
    Pages: 24-25
    Received: 1 January 2015
    Accepted: 21 January 2015
    Published: 1 February 2015
    DOI: 10.11648/j.pamj.20150401.13
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    Abstract: In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.
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  • On the Accelerated Overrelaxation Method

    I. K. Youssef, M. M. Farid

    Issue: Volume 4, Issue 1, February 2015
    Pages: 26-31
    Received: 29 December 2014
    Accepted: 25 January 2015
    Published: 2 February 2015
    DOI: 10.11648/j.pamj.20150401.14
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    Abstract: A new variant of the accelerated over relaxation (AOR) method for solving systems of linear algebraic equations, the KAOR method is established. The treatment depends on the use of the extrapolation techniques introduced by Hadjidimos (1978) and the KSOR introduced by Youssef (2012) and its modified version published in (2013). The KAOR is an extra... Show More
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  • Controllability of Co-Operative Neumann Parabolic Systems

    Mohammed Shehata

    Issue: Volume 4, Issue 1, February 2015
    Pages: 32-38
    Received: 10 January 2015
    Accepted: 25 January 2015
    Published: 2 February 2015
    DOI: 10.11648/j.pamj.20150401.15
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    Abstract: In this communication, we introduce and study the various controllability problems for Neumann co-operative parabolic linear system involving Laplace operator with distributed or boundary controls and with observations belong to different spaces.
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