Applied and Computational Mathematics

Archive

Volume 9, Issue 6, December 2020

  • A Construction of Imprimitive Groups of Rank 4 or 5

    Chang Wang, Renbing Xiao

    Issue: Volume 9, Issue 6, December 2020
    Pages: 175-178
    Received: 15 September 2020
    Accepted: 23 October 2020
    Published: 4 November 2020
    DOI: 10.11648/j.acm.20200906.11
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    Abstract: Let G be a transitive permutation group acting on a finite set Ω. For a point α of Ω, the set of the images of G acting on α is called the orbit of α under G and is denoted by αG, and the set of elements in G which fix α is called the stabilizer of α in G and is denoted by Gα. We can get some new orbits by using the natural action of the stabilizer... Show More
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  • Two-scale Finite Element Discretizations for Semilinear Parabolic Equations

    Fang Liu

    Issue: Volume 9, Issue 6, December 2020
    Pages: 179-186
    Received: 5 February 2020
    Accepted: 25 September 2020
    Published: 16 November 2020
    DOI: 10.11648/j.acm.20200906.12
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    Abstract: In this paper, to reduce the computational cost of solving semilinear parabolic equations on a tensor product domain Ω⊂ℝd with d = 2 or 3, some two-scale finite element discretizations are proposed and analyzed. The time derivative in semilinear parabolic equations is approximated by the backward Euler finite difference scheme. The two-scale finite... Show More
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  • Strong Convergence of the Hybrid Halpern Type Proximal Point Algorithm

    Liu Liu, Qing-bang Zhang

    Issue: Volume 9, Issue 6, December 2020
    Pages: 187-194
    Received: 15 May 2020
    Accepted: 12 June 2020
    Published: 16 November 2020
    DOI: 10.11648/j.acm.20200906.13
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    Abstract: Based on the proximal point algorithm, which is a widely used tool for solving a variety of convex optimization problems, there are many algorithms for finding zeros of maximally monotone operators. The algorithm works by applying successively so-called "resolvent" mappings with errors associated to the original object, and is weakly convergent in ... Show More
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  • Uniform Convergence of the Series Expansion of the Multifractional Brownian Motion

    BA Demba Bocar

    Issue: Volume 9, Issue 6, December 2020
    Pages: 195-200
    Received: 17 June 2020
    Accepted: 16 October 2020
    Published: 4 December 2020
    DOI: 10.11648/j.acm.20200906.14
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    Abstract: In this paper we define the multifractional Brownian motion and we give some properties. we study the uniform Convergence of the Serie expansion. After having determined the covariance function, we give in proposition 2 another proof of almost sure uniform convergence on compact K of the series. We will finish by showing that the m.B.f is locally a... Show More
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