An efficient collocation scheme for new type of variable-order fractional Lane–Emden equation by H. Azin, A. Habibirad, E. Hesameddini, M.H. Heydari

“…The operational matrix of the V-O fractional derivative is obtained for the Vt-L polynomials. In the established approach, these polynomials are applied to transform the main problem into an algebraic equations system. …”
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An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties by Feng Kong, Penghao Si, Shengwen Yin

“…To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. …”
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An Efficient Petrov–Galerkin Scheme for the Euler–Bernoulli Beam Equation via Second-Kind Chebyshev Polynomials by Youssri Hassan Youssri, Waleed Mohamed Abd-Elhameed, Amr Ahmed Elmasry, Ahmed Gamal Atta

“…Utilizing a suitable combination of second-kind Chebyshev polynomials as a basis in spatial variables, the proposed method elegantly and simultaneously satisfies pinned–pinned and clamped–clamped boundary conditions. …”
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Efficient Numerical Schemes for a Heterogeneous Reaction–Diffusion System with Applications by Samima Akhter, Md. Ariful Islam Arif, Rubayyi T. Alqahtani, Samir Kumar Bhowmik

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Efficient Probabilistic Evaluation and Sensitivity Analysis of Load Supply Capability for Renewable-Energy-Based Power Systems by Jie Zhang, Kaixiang Fu, Weizhi Huang, Yilin Zhang, Qing Sun, Yuan Chi, Junjie Tang

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Advanced hybrid intelligence evaluation of nanomedicine delivery to various organs using machine learning and adaptive tree structured Parzen estimator by Wael A. Mahdi, Adel Alhowyan, Ahmad J. Obaidullah

“…Abstract We have examined the efficiency of drug delivery for targeted therapy by theoretical models. …”
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An Innovative Online Adaptive High-Efficiency Controller for Micro Gas Turbine: Design and Simulation Validation by Rui Yang, Yongbao Liu, Xing He, Zhimeng Liu

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An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials by Jianping Liu, Xia Li, Limeng Wu

“…An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. …”
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An Operational Matrix Technique Based on Chebyshev Polynomials for Solving Mixed Volterra-Fredholm Delay Integro-Differential Equations of Variable-Order by Kamal R. Raslan, Khalid K. Ali, Emad M. H. Mohamed, Jihad A. Younis, Mohamed A. Abd El salam

“…In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) of variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) of the first kind with the spectral collocation method. …”
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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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Knowledge-Based Shape Optimization of Morphing Wing for More Efficient Aircraft by Alessandro De Gaspari, Sergio Ricci

“…Dedicated crossover and mutation strategies are used to allow the parametric framework to be efficiently incorporated into the genetic algorithm. …”
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Efficient Equivalence Checking Technique for Some Classes of Finite-State Machines by Vladimir A. Zakharov

“…By means of the developed approach an efficient equivalence checking algorithm for the class of simple grammars corresponding to deterministic single-state pushdown automata is constructed.…”
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Energy and Spectral Efficiency Analysis for UAV-to-UAV Communication in Dynamic Networks for Smart Cities by Mfonobong Uko, Sunday Ekpo, Ubong Ukommi, Unwana Iwok, Stephen Alabi

“…UAV-to-UAV communication networks, despite their adaptability, have significant limits stemming from onboard battery constraints, inclement weather, and variable flight trajectories. This work presents a thorough examination of energy and spectral efficiency in UAV-to-UAV communication over four frequency bands: 2.4 GHz, 5.8 GHz, 28 GHz, and 60 GHz. …”
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Smart synergistic Fenton oxidation: CCD-optimized pathway for efficient 4-nitrophenol degradation by Neha Pandey, Nayna Agarwal, Prabir Ghosh, Gurudatta Singh, Kapil Kumar

“…A novel aspect of this study is the use of a sustainable, waste-derived heterogeneous catalyst (Fe-loaded fly ash brick clay, Fe-FABC), which promotes both high degradation efficiency and environmental sustainability. Polynomial modeling and surface response plots confirmed strong predictive capabilities for degradation performance under varied conditions. …”
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Prediction of Maximum Precipitation in Turkey with Polynomial Regression by Fatih Dikbaş, Orhan Koç

“…Understanding the expected variability in precipitation events and predicting the location and yearly periods of probable extreme precipitation are important for the efficient prevention of potential natural catastrophes like floods and dam failures. …”
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Energy-efficient resource allocation scheme for device-to-device communication underlaying LTE-A uplink by Zheng-cang ZHU, Ji-hong ZHAO, Rui TANG, Hua QU, Lu-yao WANG, Zhao-xin CAO

“…To cope with the co-channel interference between cellular links and device-to-device (D2D) links concurrently transmitting with the long term evolution-advanced (LTE-A) uplink spectrum,a joint resource allocation scheme was pro-posed to maximize the global energy efficiency of D2D links.The above problem can be decomposed into the power control subproblem and the channel assignment subproblem.Specifically,the power control subproblem can be optimally solved with the help of Dinkelbach method and Lagrange duality.Based on the above results,the channel assignment subproblem turns out to be the set packing problem which was generally NP-hard problem,Therefore,a heuristic algo-rithm was further devised to achieve a tradeoff between performance and complexity.Simulations show that the proposed joint resource allocation scheme outperforms the ones where only single resource variable is optimized,and it achieves the polynomial-time complexity at only minor performance loss when compared to the global optimum.…”
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Polynomial Chaos Expansion Approach to Interest Rate Models by Luca Di Persio, Gregorio Pellegrini, Michele Bonollo

“…The Polynomial Chaos Expansion (PCE) technique allows us to recover a finite second-order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochastic quantity ξ, hence acting as a kind of random basis. …”
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Polynomial and Differential Networks for End-to-End Autonomous Driving by Youngseong Cho, Kyoungil Lim

“…This study introduces a novel model for predicting control variables in end-to-end autonomous driving by leveraging polynomial and differential networks. …”
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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

“…Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. …”
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