Bernoulli Polynomials Method for Solving Integral Equations with Singular Kernel by Muna M. Mustafa, Heba A. Abd-Alrazak

“…Also, assuming that the denominator of the kernel will never be zero or have an imaginary value due to the selected nodes of the unique two kernel variables. With the 4th and 8th-degree Bernoulli polynomials as an example, the current approach provides a solution very close to the exact solution in the test examples. …”
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Indirect Method for Optimal Control Problem Using Boubaker Polynomial by Baghdad Science Journal

“…In this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. …”
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Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System by Zhenyi Ji, Wenyuan Wu, Yong Feng, Guofeng Zhang

“…Then, the positive polynomial system is converted into an equation system by adding some variables. …”
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Local Polynomial Regression Solution for Partial Differential Equations with Initial and Boundary Values by Liyun Su, Tianshun Yan, Yanyong Zhao, Fenglan Li

“…Local polynomial regression (LPR) is applied to solve the partial differential equations (PDEs). …”
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Numerical solutions for fractional optimal control problems using Mü‎‎‎‎‎‎‎ntz-Legendre polynomials by Mohammad Sahabi, Allahbakhsh Yazdani Cherati

“…Utilizing the unique properties of Müntz-Legendre polynomials when dealing with fractional operators, these polynomials are used to approximate the state and control variables in the considered problems. …”
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Tunnel composting Optimisation using polynomial models with moisture and density control for electrical conductivity stabilisation by Tiago Santos, Isabel Bentes, Carlos Afonso Teixeira

“…These conditions minimise the need for corrective aeration or irrigation, enhancing process efficiency. Future studies may incorporate variables such as the carbon-to-nitrogen (C/N) ratio, microbial activity, and germination index to expand the model’s robustness and applicability. …”
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Uncertainty evaluation of surface profile measurement error based on adaptive sparse grid polynomial chaos expansion by Ke Zhang, Xinya Zheng, Ruiyu Zhang

“…This model is optimized using Cholesky decomposition to handle variable correlations, sparse grid integration for efficient generation of multidimensional integration points, and maximum entropy method for direct reconstruction of probability distributions, thereby achieving efficient evaluation of the measurement error and uncertainty of surface profile. …”
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Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis by Khadijeh Sadri, Hossein Aminikhah

“…For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. …”
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Interval Uncertainty Analysis for Wheel–Rail Contact Load Identification Based on First-Order Polynomial Chaos Expansion by Shengwen Yin, Haotian Xiao, Lei Cao

“…In IFOPCE, the polynomial chaos expansion (PCE) is first utilized to approximate the relationship between strain responses, wheel–rail loads, and uncertain variables. …”
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STRUCTURAL GLOBAL SENSITIVITY METHOD BASED ON PARTIAL DERIVATIVE WHOLE DOMAIN INTEGRAL by TU LongWei, LIU Jie, LIU GuangZhao, ZHANG Zheng

“…In view of the problems that the traditional variance-based Sobol’method had a low solving efficiency,lacked of enough robustness,and it cannot further effectively decompose and reasonably distribute the influences of the high-order cross subterms,a practical and effective structural global sensitivity method was proposed in this paper based on partial derivative whole domain integral and optimal polynomial surrogate model. …”
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High-accuracy solution of pantograph differential equations subject to mixed boundary conditions via shifted Vieta–Lucas polynomials by R. M. Hafez, H. M. Ahmed

“…A Galerkin method (GM) is formulated for constant coefficient-type equations, and a spectral collocation method (SCM) is given for variable coefficient cases. The basis functions are developed to fulfill the given MTBCs, which reduces implementation and enhances accuracy. …”
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On a Solution of a Third Kind Mixed Integro-Differential Equation with Singular Kernel Using Orthogonal Polynomial Method by Ahmad Alalyani, M. A. Abdou, M. Basseem

“…Using the separation of variables technique, we have a system of Fredholm integral equations (FIEs) that can be transformed into an algebraic system after using orthogonal polynomials. …”
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Improved Multiverse Optimization Algorithm for Fuzzy Flexible Job-Shop Scheduling Problem by Jin-Cheng Fang, A-Feng Zeng, Shao-Feng Zheng, Wen-Di Zhao, Xu He

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Optimal Dynamics Control in Trajectory Tracking of Industrial Robots Based on Adaptive Gaussian Pseudo-Spectral Algorithm by Jing Zhang, Xiaokai Zhu, Te Chen, Guowei Dou

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A simple and efficient attack on the Merkle-Hellman knapsack cryptosystem. by Jingguo Bi, Lei Su, Haipeng Peng, Lin Wang

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Sign-Entropy Regularization for Personalized Federated Learning by Koffka Khan

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The Numerical Approximation of Caputo Fractional Derivatives of Higher Orders Using a Shifted Gegenbauer Pseudospectral Method: A Case Study of Two-Point Boundary Value Problems of... by Kareem T. Elgindy

“…The method employs a strategic variable transformation to express the Caputo FD as a scaled integral of the <i>m</i>th-derivative of the Lagrange interpolating polynomial, thereby mitigating singularities and improving numerical stability. …”
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Knowledge-Based Shape Optimization of Morphing Wing for More Efficient Aircraft by Alessandro De Gaspari, Sergio Ricci

“…It is adopted for the design of a variable camber morphing wing to investigate the effect of conformal leading and trailing edge control surfaces. …”
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Efficient Equivalence Checking Technique for Some Classes of Finite-State Machines by Vladimir A. Zakharov

“…It turns out that such a checking can be performed by the variable elimination technique which relies on some combinatorial and algebraic properties of prefix-free regular languages. …”
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Hybrid modeling approach for precise estimation of energy production and consumption based on temperature variations by Wulfran Fendzi Mbasso, Reagan Jean Jacques Molu, Ambe Harrison, Mukesh Pushkarna, Fritz Nguemo Kemdoum, Emmanuel Fendzi Donfack, Pradeep Jangir, Pierre Tiako, Milkias Berhanu Tuka

“…The hybrid model, which combines sinusoidal and polynomial functions, achieved an accuracy of 79.15% in estimating energy consumption using temperature as a predictor variable. …”
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