American Journal of Applied Mathematics

Volume 6, Issue 1, February 2018

  • On the Solution Procedure of Partial Differential Equation (PDE) with the Method of Lines (MOL) Using Crank-Nicholson Method (CNM)

    Mohammad Roknujjaman, Mohammad Asaduzzaman

    Issue: Volume 6, Issue 1, February 2018
    Pages: 1-7
    Received: Dec. 28, 2017
    Accepted: Jan. 16, 2018
    Published: Feb. 12, 2018
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    Abstract: In this paper we used the method of lines (MOL) as a solution procedure for solving partial differential equation (PDE). The range of applications of the MOL has increased dramatically in the last few years; nevertheless, there is no introductory to initiate a beginner to the method. This Paper illustrates the application of the MOL using Crank-Nic... Show More
  • Mathematical Model of Corrective Maintenance Based on Operability Checks for Safety Critical Systems

    Ahmed Raza

    Issue: Volume 6, Issue 1, February 2018
    Pages: 8-14
    Received: Jan. 20, 2018
    Accepted: Feb. 01, 2018
    Published: Mar. 05, 2018
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    Abstract: Maintenance based on equipment operability checks is widely used for technical systems of various physical nature. For commercial and military aircraft such checks are carried-out after a certain amount of time according to specific maintenance programs. Therefore, great attention in the research literature is paid to the mathematical modeling of m... Show More
  • Some Paradoxes of Mathematical Theory of Continues Mechanics

    Evelina Prozorova

    Issue: Volume 6, Issue 1, February 2018
    Pages: 15-19
    Received: Jan. 11, 2018
    Accepted: Jan. 29, 2018
    Published: Mar. 07, 2018
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    Abstract: The classic theory of continuum mechanics does not preserve the continuity of the environment due to the use of the conditions of equilibrium of forces and the symmetry of the stress tensor. We used many unreasonable mathematical approximations when by the Boltzmann equation is solved to describe the equations of continuum mechanics. The paper pres... Show More
  • Hamiltonicity of Mycielski Graphs

    Shuting Cheng, Dan Wang, Xiaoping Liu

    Issue: Volume 6, Issue 1, February 2018
    Pages: 20-22
    Received: Jan. 28, 2018
    Accepted: Feb. 16, 2018
    Published: Mar. 16, 2018
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    Abstract: Fisher, McKenna, and Boyer showed that if a graph G is hamiltonian, then its Mycielski graph μ(G) is hamitonian. In this note, it was shown that for a bipartite graph G, if its mycielski graph μ(G) is hamiltonian, then G has a Hamilton path.
  • On the Planarity of G++−

    Lili Yuan, Xiaoping Liu

    Issue: Volume 6, Issue 1, February 2018
    Pages: 23-27
    Received: Feb. 10, 2018
    Accepted: Mar. 01, 2018
    Published: Mar. 22, 2018
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    Abstract: Let G be a simple graph. The transformation graph G++− of G is the graph with vertex set V (G) ∪ E (G) in which the vertex x and y are joined by an edge if and only if the following condition holds:(i) x, y ∈ V (G) and x and y are adjacent in G, (ii) x, yE (G), and x and y are adjacent in G, (iii) one of x and y is in V (G) and the other is in E... Show More