Giuseppe Corrente^1,2,*, Carlo Vincenzo Stanzione^3,4, Vittoria Stanzione⁵

Journal of Quantum Computing, Vol.5, pp. 55-70, 2023, DOI:10.32604/jqc.2023.044786

Abstract The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a Hamiltonian cycle problem, using different models of computations and especially the probabilistic and quantum ones. Starting from the classical probabilistic approach of random walks, we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine (QTM), which can be a useful conceptual project tool for quantum algorithms. Introducing several constraints to the graphs,… More >

Abdulghani Ragaa Alharbi^*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2193-2209, 2023, DOI:10.32604/cmes.2022.018445

Abstract The Riemann wave system has a fundamental role in describing waves in various nonlinear natural phenomena, for instance, tsunamis in the oceans. This paper focuses on executing the generalized exponential rational function approach and some numerical methods to obtain a distinct range of traveling wave structures and numerical results of the two-dimensional Riemann problems. The stability of obtained traveling wave solutions is analyzed by satisfying the constraint conditions of the Hamiltonian system. Numerical simulations are investigated via the finite difference method to verify the accuracy of the obtained results. To extract the approximation solutions to the underlying problem, some ODE… More >

I. Vallirathi^1,*, S. Ebenezer Juliet²

Computer Systems Science and Engineering, Vol.44, No.3, pp. 2349-2360, 2023, DOI:10.32604/csse.2023.024864

Abstract Wireless Sensor Network (WSNs) is an infrastructure-less wireless network deployed in an increasing number of wireless sensors in an ad-hoc manner. As the sensor nodes could be powered using batteries, the development of WSN energy constraints is considered to be a key issue. In wireless sensor networks (WSNs), wireless mobile chargers (MCs) conquer such issues mainly, energy shortages. The proposed work is to produce an energy-efficient recharge method for Wireless Rechargeable Sensor Network (WRSN), which results in a longer lifespan of the network by reducing charging delay and maintaining the residual energy of the sensor. In this algorithm, each node… More >

Amr M. S. Mahdy^1,*, Mohamed S. Mohamed¹, Ahoud Y. Al Amiri², Khaled A. Gepreel¹

Intelligent Automation & Soft Computing, Vol.31, No.2, pp. 899-915, 2022, DOI:10.32604/iasc.2022.017801

Abstract In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through… More >

Kecheng Li, Jianlong Qu, Jinqiang Tan, Zhanjun Wu, Xinsheng Xu^*

Structural Durability & Health Monitoring, Vol.15, No.1, pp. 53-67, 2021, DOI:10.32604/sdhm.2021.014559

Abstract In this paper, the local buckling of cylindrical long shells is discussed under axial pulse loads in a Hamiltonian system. Using this system, critical loads and modes of buckling of shells are reduced to symplectic eigenvalues and eigensolutions respectively. By the symplectic method, the solution of the local buckling of shells can be employed to the expansion series of symplectic eigensolutions in this system. As a result, relationships between critical buckling loads and other factors, such as length of pulse load, thickness of shells and circumferential orders, have been achieved. At the same time, symmetric and unsymmetric buckling modes have… More >

Adnan A. Hnaif^*, Abdelfatah A. Tamimi, Ayman M. Abdalla, Iqbal Jebril

CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 505-519, 2021, DOI:10.32604/cmc.2021.016123

Abstract Many routing protocols, such as distance vector and link-state protocols are used for finding the best paths in a network. To find the path between the source and destination nodes where every node is visited once with no repeats, Hamiltonian and Hypercube routing protocols are often used. Nonetheless, these algorithms are not designed to solve the problem of a node failure, where one or more nodes become faulty. This paper proposes an efficient modified Fault-free Hamiltonian Cycle based on the Hypercube Topology (FHCHT) to perform a connection between nodes when one or more nodes become faulty. FHCHT can be applied… More >

Ibrahim M. Hezam^1,2,*

CMC-Computers, Materials & Continua, Vol.67, No.1, pp. 1153-1167, 2021, DOI:10.32604/cmc.2021.014710

Abstract Since COVID-19 was declared as a pandemic in March 2020, the world’s major preoccupation has been to curb it while preserving the economy and reducing unemployment. This paper uses a novel Bi-Level Dynamic Optimal Control model (BLDOC) to coordinate control between COVID-19 and unemployment. The COVID-19 model is the upper level while the unemployment model is the lower level of the bi-level dynamic optimal control model. The BLDOC model’s main objectives are to minimize the number of individuals infected with COVID-19 and to minimize the unemployed individuals, and at the same time minimizing the cost of the containment strategies. We… More >

Cheinshan Liu^{1, 2}, Chunglun Kuo¹, Jiangren Chang^{3, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.1, pp. 33-48, 2020, DOI:10.32604/cmes.2020.08490

Abstract In the optimal control problem of nonlinear dynamical system, the Hamiltonian formulation is useful and powerful to solve an optimal control force. However, the resulting Euler-Lagrange equations are not easy to solve, when the performance index is complicated, because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations. To be a numerical method, it is hard to exactly preserve all the specified conditions, which might deteriorate the accuracy of numerical solution. With this in mind, we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator, which can exactly… More >

Chein-Shan Liu¹, Su-Ying Zhang², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 29-48, 2012, DOI:10.3970/cmes.2012.088.029

Abstract With a detailed investigation of n linear algebraic equations Bx=b, we find that the scaled residual dynamics for y∈Sⁿ⁻¹ is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm based on the Jordan structure. The algorithms preserving the length of y are developed as the structure preserving algorithms (SPAs), which can significantly accelerate the convergence speed and are robust enough against the noise in the numerical… More >

Chein-Shan Liu ^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 73-94, 2007, DOI:10.3970/cmes.2007.017.073

Abstract The primary objectives of the present exposition focus on five different types of representations of the plastic equations obtained from an elastic-perfectly plastic model by employing different corotational stress rates. They are (a) an affine nonlinear system with a finite-dimensional Lie algebra, (b) a canonical linear system in the Minkowski space, (c) a non-canonical linear system in the Minkowski space, (d) the Lie-Poisson bracket formulation, and (e) a two-generator and two-bracket formulation. For the affine nonlinear system we prove that the Lie algebra of the vector fields is so(5,1), which has dimensions fifteen, and by the Lie theory the superposition… More >