Applied and Computational Mathematics

Volume 5, Issue 3, June 2016

  • Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

    Liangqiang Zhou, Shanshan Liu, Fangqi Chen

    Issue: Volume 5, Issue 3, June 2016
    Pages: 97-102
    Received: 7 June 2016
    Published: 8 June 2016
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    Abstract: Bifurcation behaviors are very important for the design of sensors. Using the sub-harmonic Melnikov method, the sub-harmonic bifurcation of single-walled carbon nanotube based mass sensor is investigated in this paper. The parametric conditions for sub-harmonic bifurcation of this system are obtained. It is presented that when the ratio of the exci... Show More
  • On the Line Successive Overrelaxation Method

    I. K. Youssef, Salwa M. Ali, M. Y. Hamada

    Issue: Volume 5, Issue 3, June 2016
    Pages: 103-106
    Received: 17 May 2016
    Accepted: 30 May 2016
    Published: 13 June 2016
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    Abstract: A line version of the KSOR method is introduced, LKSOR method. Comparison of the performance of some different iterative techniques with their line format (Jacobi – Gauss Seidel and SOR) are considered. Implementation of LKSOR method for several different formulas in different mesh geometries is discussed. The proposed method considers the advantag... Show More
  • Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems

    Dianzi Liu

    Issue: Volume 5, Issue 3, June 2016
    Pages: 107-113
    Received: 14 June 2016
    Published: 15 June 2016
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    Abstract: Problems with mixed integer-continuous design variables are a class of complicated optimization problems that commonly exist in practical engineering design work. In this paper, a hybrid algorithm combining metamodel-based Multipoint Approximation Method (MAM) and Hooke-Jeeves direct search technique is presented to efficiently seek the optimum sol... Show More
  • A Continuous-Time Multi-Agent Systems Based Algorithm for Constrained Distributed Optimization

    Ping Liu, Huaqing Li, Liping Feng

    Issue: Volume 5, Issue 3, June 2016
    Pages: 114-120
    Received: 25 May 2016
    Accepted: 7 June 2016
    Published: 18 June 2016
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    Abstract: This paper considers a second-order multi-agent system for solving the non-smooth convex optimization problem, where the global objective function is a sum of local convex objective functions within different bound constraints over undirected graphs. A novel distributed continuous-time optimization algorithm is designed, where each agent only has a... Show More
  • Application of the Adomian Decomposition Method to Oscillating Viscous Flows

    Chi-Min Liu

    Issue: Volume 5, Issue 3, June 2016
    Pages: 121-132
    Received: 3 June 2016
    Accepted: 13 June 2016
    Published: 29 June 2016
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    Abstract: In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition ser... Show More
  • Several Kinds of Chromatic Numbers of Multi-fan Graphs

    Shunqin Liu

    Issue: Volume 5, Issue 3, June 2016
    Pages: 133-137
    Received: 10 July 2016
    Published: 11 July 2016
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    Abstract: Coloring problem is a classical difficult problem of graph theory. It is a fundamental problem in scientific computation and engineering design. In recent years, a variety of graph coloring problems frequently appeared and solved many problems in production. It is a difficult problem to discuss the chromatic number of a given graph class. In the pa... Show More
  • The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

    Shaohui Wang, Mohammad Reza Farahani, M. R. Rajesh Kanna, Muhammad Kamran Jamil, R. Pradeep Kumar

    Issue: Volume 5, Issue 3, June 2016
    Pages: 138-141
    Received: 21 April 2016
    Accepted: 3 May 2016
    Published: 13 July 2016
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    Abstract: Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between vertices u,v V(G) is called the distance, d(u,v), between the vertices u,v. Mathematical chemistry is the area of research engaged in new application of mathematics in... Show More
  • Solving a Class of Nonlinear Delay Integro–differential Equations by Using Differential Transformation Method

    Mohammad Bagher Moghimi, Abdollah Borhanifar

    Issue: Volume 5, Issue 3, June 2016
    Pages: 142-149
    Received: 30 April 2016
    Accepted: 14 June 2016
    Published: 13 July 2016
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    Abstract: In this paper, differential transformation method is used to find exact solutions of nonlinear delay integro– differential equations. Many theorems are presented that required for applying differential transformation method for nonlinear delay integro–differential equation. The validity and efficiency of the proposed method are demonstrated through... Show More
  • Distributed Subgradient Algorithm for Multi-agent Convex Optimization with Local Constraint Sets

    Qingguo Lü, Huaqing Li, Li Xiao

    Issue: Volume 5, Issue 3, June 2016
    Pages: 150-159
    Received: 12 June 2016
    Accepted: 20 June 2016
    Published: 13 July 2016
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    Abstract: This paper considers a distributed constrained optimization problem, where the objective function is the sum of local objective functions of distributed nodes in a network. The estimate of each agent is restricted to different convex sets. To solve this optimization problem which is not necessarily smooth, we study a novel distributed projected sub... Show More
  • The Numerical Solution of the TVD Runge-Kutta and WENO Scheme to the FPK Equations to Nonlinear System of One-Dimension

    Wang Wenjie, Feng Jianhu, Xu Wei

    Issue: Volume 5, Issue 3, June 2016
    Pages: 160-164
    Received: 19 June 2016
    Accepted: 27 June 2016
    Published: 23 July 2016
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    Abstract: Firstly, it was studied to the Fokker-Planck-Kolmogorov (FPK) equations for nonlinear stochastic dynamic system. Secondly, it was discussed to the third-order TVD Runge-Kutta difference scheme totime for differitial equations and the fifth-order WENO scheme for differitial operators. And combined he third-order TVD Runge-Kutta difference scheme wit... Show More
  • The Application of Matrix in Control Theory

    Yuanyuan Zhang

    Issue: Volume 5, Issue 3, June 2016
    Pages: 165-168
    Received: 23 July 2016
    Published: 25 July 2016
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    Abstract: This paper presents a new way to justify the controllability of linear ordinary systems. This way is based on the maximum geometric multiplicity of eigenvalues for the coefficient matrix of the linear ordinary equation. This method is equivalent to other discrimination laws for controllability.