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  • Open Access


    Machine Learning for Hybrid Line Stability Ranking Index in Polynomial Load Modeling under Contingency Conditions

    P. Venkatesh1,*, N. Visali2

    Intelligent Automation & Soft Computing, Vol.37, No.1, pp. 1001-1012, 2023, DOI:10.32604/iasc.2023.036268

    Abstract In the conventional technique, in the evaluation of the severity index, clustering and loading suffer from more iteration leading to more computational delay. Hence this research article identifies, a novel progression for fast predicting the severity of the line and clustering by incorporating machine learning aspects. The polynomial load modelling or ZIP (constant impedances (Z), Constant Current (I) and Constant active power (P)) is developed in the IEEE-14 and Indian 118 bus systems considered for analysis of power system security. The process of finding the severity of the line using a Hybrid Line Stability Ranking Index (HLSRI) is used for… More >

  • Open Access


    Asymmetric Consortium Blockchain and Homomorphically Polynomial-Based PIR for Secured Smart Parking Systems

    T. Haritha, A. Anitha*

    CMC-Computers, Materials & Continua, Vol.75, No.2, pp. 3923-3939, 2023, DOI:10.32604/cmc.2023.036278

    Abstract In crowded cities, searching for the availability of parking lots is a herculean task as it results in the wastage of drivers’ time, increases air pollution, and traffic congestion. Smart parking systems facilitate the drivers to determine the information about the parking lot in real time and book them depending on the requirement. But the existing smart parking systems necessitate the drivers to reveal their sensitive information that includes their mobile number, personal identity, and desired destination. This disclosure of sensitive information makes the existing centralized smart parking systems more vulnerable to service providers’ security breaches, single points of failure,… More >

  • Open Access


    Structural Interval Reliability Algorithm Based on Bernstein Polynomials and Evidence Theory

    Xu Zhang1, Jianchao Ni2, Juxi Hu3,*, Weisi Chen4

    Computer Systems Science and Engineering, Vol.46, No.2, pp. 1947-1960, 2023, DOI:10.32604/csse.2023.035118

    Abstract Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors. Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid. The uncertain parameters mainly exist in the form of intervals. This method requires a lot of calculation and is often difficult to achieve efficiently. In order to solve this problem, this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty. Based on the non-probabilistic… More >

  • Open Access


    The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

    Attaullah1,*, Kamil Zeb1, Abdullah Mohamed2

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1661-1685, 2023, DOI:10.32604/cmes.2023.023059

    Abstract Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions. Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications. Mathematical modelling has been widely used in order to better understand the transmission, treatment, and prevention of infectious diseases. Herein, we study the dynamics of a human immunodeficiency virus (HIV) infection model with four variables: S (t), I (t), C (t), and A (t) the susceptible individuals; HIV infected individuals (with no clinical symptoms of AIDS); HIV infected individuals (under ART with… More >

  • Open Access


    Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

    Kamal Shah1,2, Hafsa Naz2, Thabet Abdeljawad1,3,*, Bahaaeldin Abdalla1

    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 921-941, 2023, DOI:10.32604/cmes.2023.025769

    Abstract This research aims to understand the fractional order dynamics of the deadly Nipah virus (NiV) disease. We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system. We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem. By utilizing the Newtonian polynomials interpolation technique, we recall a powerful algorithm to interpret the numerical findings for the aforesaid model. Here, we remark that the said viral infection is caused by an RNA type virus… More > Graphic Abstract

    Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

  • Open Access


    Algebraic Properties for Molecular Structure of Magnesium Iodide

    Ali N. A. Koam1, Ali Ahmad2,*, Muhammad Azeem3, Muhammad Kamran Siddiqui4

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1131-1146, 2023, DOI:10.32604/cmes.2022.020884

    Abstract As an inorganic chemical, magnesium iodide has a significant crystalline structure. It is a complex and multi-functional substance that has the potential to be used in a wide range of medical advancements. Molecular graph theory, on the other hand, provides a sufficient and cost-effective method of investigating chemical structures and networks. M-polynomial is a relatively new method for studying chemical networks and structures in molecular graph theory. It displays numerical descriptors in algebraic form and highlights molecular features in the form of a polynomial function. We present a polynomials display of magnesium iodide structure and calculate several M-polynomials in this… More >

  • Open Access


    A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

    N. Alam1, W. A. Khan2,*, S. Obeidat1, G. Muhiuddin3, N. S. Diab1, H. N. Zaidi1, A. Altaleb1, L. Bachioua1

    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 187-209, 2023, DOI:10.32604/cmes.2022.021418

    Abstract In this article, we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials. Some fundamental properties of these functions are given. By using these generating functions and some identities, relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials, Stirling numbers are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are… More >

  • Open Access


    Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials

    Kamal Shah1,2, Hafsa Naz2, Thabet Abdeljawad1,3,*, Aziz Khan1, Manar A. Alqudah4

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 941-955, 2023, DOI:10.32604/cmes.2022.021483

    Abstract In this manuscript, an algorithm for the computation of numerical solutions to some variable order fractional differential equations (FDEs) subject to the boundary and initial conditions is developed. We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices. Further, operational matrices are constructed using variable order differentiation and integration. We are finding the operational matrices of variable order differentiation and integration by omitting the discretization of data. With the help of aforesaid matrices, considered FDEs are converted to algebraic equations of Sylvester type. Finally, the algebraic equations we get are solved with the help of… More >

  • Open Access


    LaNets: Hybrid Lagrange Neural Networks for Solving Partial Differential Equations

    Ying Li1, Longxiang Xu1, Fangjun Mei1, Shihui Ying2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 657-672, 2023, DOI:10.32604/cmes.2022.021277

    Abstract We propose new hybrid Lagrange neural networks called LaNets to predict the numerical solutions of partial differential equations. That is, we embed Lagrange interpolation and small sample learning into deep neural network frameworks. Concretely, we first perform Lagrange interpolation in front of the deep feedforward neural network. The Lagrange basis function has a neat structure and a strong expression ability, which is suitable to be a preprocessing tool for pre-fitting and feature extraction. Second, we introduce small sample learning into training, which is beneficial to guide the model to be corrected quickly. Taking advantages of the theoretical support of traditional… More >

  • Open Access


    Some Properties of Degenerate r-Dowling Polynomials and Numbers of the Second Kind

    Hye Kyung Kim1,*, Dae Sik Lee2

    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 825-842, 2022, DOI:10.32604/cmes.2022.022103

    Abstract The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics. In recent years, some mathematicians have studied degenerate version of them and obtained many interesting results. With this in mind, in this paper, we introduce the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind. We derive many interesting properties and identities for them including generating functions, Dobinski-like formula, integral representations, recurrence relations, differential equation and various explicit expressions. In addition, we explore some expressions for them that can be derived from repeated applications… More >

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