Applied and Computational Mathematics

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Volume 10, Issue 3, June 2021

  • Two Hypothesis on a Combinatorial Problem for Possible States on the Arrival Line for n Competitor Runners

    Nicolae Popoviciu

    Issue: Volume 10, Issue 3, June 2021
    Pages: 46-55
    Received: 9 April 2021
    Accepted: 25 May 2021
    Published: 22 June 2021
    DOI: 10.11648/j.acm.20211003.11
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    Abstract: In a very small t-time interval, several runners could occupy the same place on the arrival line (hypothesis 1). Each runner has his own name and a competition number (on the shirt). The number of runners is a natural number n. For each given n, the hypothesis creates a combinatorial problem having a lot of posible states. All notations are choose ... Show More
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  • On Shape Optimization Theory with Fractional Laplacian

    Malick Fall, Ibrahima Faye, Alassane Sy, Diaraf Seck

    Issue: Volume 10, Issue 3, June 2021
    Pages: 56-68
    Received: 17 April 2021
    Accepted: 13 May 2021
    Published: 26 June 2021
    DOI: 10.11648/j.acm.20211003.12
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    Abstract: The fractional Laplacian is a nonlocal operator that appears in biology, in physic, in fluids dynamic, in financial mathematics and probability. This paper deals with shape optimization problem associated to the fractional laplacian ∆s, 0 < s < 1. We focus on functional of the form J(Ω) = j(Ω,uΩ) where uΩ is solution to the fractional laplacian. A brief review of results related to fractiona... Show More
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  • A Review of Change Point Estimation Methods for Process Monitoring

    Ademola John Ogunniran, Kayode Samuel Adekeye, Johnson Ademola Adewara, Muminu Adamu

    Issue: Volume 10, Issue 3, June 2021
    Pages: 69-75
    Received: 15 March 2021
    Accepted: 7 April 2021
    Published: 29 June 2021
    DOI: 10.11648/j.acm.20211003.13
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    Abstract: When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for ... Show More
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  • Interpolation Method for Solving Weakly Singular Integral Equations of the Second Kind

    Emil Sobhy Shoukralla

    Issue: Volume 10, Issue 3, June 2021
    Pages: 76-85
    Received: 15 June 2021
    Accepted: 24 June 2021
    Published: 30 June 2021
    DOI: 10.11648/j.acm.20211003.14
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    Abstract: We establish a new straightforward interpolation method for solving linear Volterra integral ‎‎equations with weakly singular kernels. The proposed method is fundamentally different from all other published methods for solving this type of equations. We have modified some vector-matrix barycentric Lagrange interpolation formulas to be convenient fo... Show More
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