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  • Open Access


    The Kemeny’s Constant and Spanning Trees of Hexagonal Ring Network

    Shahid Zaman1, Ali N. A. Koam2, Ali Al Khabyah2, Ali Ahmad3,*

    CMC-Computers, Materials & Continua, Vol.73, No.3, pp. 6347-6365, 2022, DOI:10.32604/cmc.2022.031958

    Abstract Spanning tree () has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers. In the field of medicines, it is helpful to recognize the epidemiology of hepatitis C virus (HCV) infection. On the other hand, Kemeny’s constant () is a beneficial quantifier characterizing the universal average activities of a Markov chain. This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state . Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues.… More >

  • Open Access


    The Optimal Radius of the Support of Radial Weights Used in Moving Least Squares Approximation

    Y.F. Nie1,2, S.N. Atluri2, C.W. Zuo1

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 137-148, 2006, DOI:10.3970/cmes.2006.012.137

    Abstract Owing to the meshless and local characteristics, moving least squares (MLS) methods have been used extensively to approximate the unknown function of partial differential equation initial boundary value problem. In this paper, based on matrix analysis, a sufficient and necessary condition for the existence of inverse of coefficient matrix used in MLS methods is developed firstly. Then in the light of approximate theory, a practical mathematics model is posed to obtain the optimal radius of support of radial weights used in MLS methods. As an example, while uniform distributed particles and the 4th order spline weight function are adopted in… More >

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