Determination of Discharge Coefficient for both Semicircular and Triangular Labyrinth Weirs by Tara H. Aurahman, Jehan M. Fattah Sheikh Suleimany, Taban K. Hamad

“…Dimensional analyses are conducted using the Buckingham π theorem to find the dependent and non-dependent variables. A nonlinear empirical equation was developed using (Statistical Package for the Social Sciences 22) software. …”
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Study on the Photosynthetic Physiological Responses of Greenhouse Young Chinese Cabbage (<i>Brassica rapa</i> L. <i>Chinensis Group</i>) Affected by Particulate Matter Based on Hyp... by Lijuan Kong, Siyao Gao, Jianlei Qiao, Lina Zhou, Shuang Liu, Yue Yu, Haiye Yu

“…Physiological Reflectance Index (PRI), Modified Chlorophyll Absorption Ratio Index (MCARI), spectral red-edge position (λr), and spectral sensitive bands were used as spectral feature variables. Through cubic polynomial and 24 combinations of spectral preprocessing and modeling methods, an inversion model of spectral features and net photosynthetic rate was established. …”
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Novel Hybrid Function Operational Matrices of Fractional Integration: An Application for Solving Multi-Order Fractional Differential Equations by Seshu Kumar Damarla, Madhusree Kundu

“…The developed algorithm was then applied to a range of benchmark problems, including both linear and nonlinear multi-order FDEs with constant and variable coefficients. Numerical comparisons with well-established methods in the literature revealed that the proposed approach not only achieved higher accuracy but also significantly reduced computational effort, demonstrating its potential as a reliable and efficient numerical tool for fractional-order modeling.…”
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MATLAB-empowered brightness defect prediction system in pulp processing bleaching stage: An empirical modelling approach by Michael, M. Thoriq Al Fath, Vikram Alexander, Gina Cynthia Raphita Hasibuan, Muhammad Syukri, Muhammad Hendra S. Ginting, Rivaldi Sidabutar, Nisaul Fadilah Dalimunthe

“…Empirical models for predicting pulp consistency at the extraction-oxidative-peroxide (EOP) and D1 stages were created using second-order polynomial equations, incorporating production rate and inlet pressure as variables. …”
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Vibration Analysis of Rotating Tapered Timoshenko Beams by a New Finite Element Model by Bulent Yardimoglu

“…This procedure reduces the number of nodal variables. The new model can also be used for uniform beams. …”
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Optimal control for high-precision repeat ground-track orbits via convex optimization by Yanchao HE, Lei ZHANG, Yijun YANG, Qian CHEN

“…The method is based on the high-order expansion availability of Poincaré mapping expressed by polynomials with different orders for the forward propagation of a point on an equatorial plane for one or more repeat cycles by the repetitive evaluation of Taylor polynomials. …”
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Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures by Nishchal K. Verma

“…The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.…”
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Reliability and reliability-based sensitivity analyses of steel moment-resisting frame structure subjected to extreme actions by Abbasali Sadeghi, Hamid Kazemi, Mayasam Samadi

“…To reduce computational costs, meta-model techniques such as Kriging, Polynomial Response Surface Methodology (PRSM) and Artificial Neural Network (ANN) are applied and their efficiency is assessed. …”
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Vibration Response and Evaluation Method of High-Speed Tracked Vehicles Driving Off-Road by Xin-yong Qiao, Ying Jin, Cheng Gu

“…Three fitting methods, namely polynomial response surface, Kriging method, and radial basis function neural network, were used to establish approximate models between the design variables and the objective function, respectively. …”
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Water footprint management in textile industry through Acid Blue 113 remediation using halloysite nanoclay as a sustainable adsorbent by Mohammed A. H. Dhaif Allah, Syed Noeman Taqui, Usman Taqui Syed, Syida Aameera Yakuth, Razia Sulthana, Rayees Afzal Mir, Akheel Ahmed Syed, Shareefraza J. Ukkund, Majed Alsubih, Saiful Islam, Wahaj Ahmad Khan

“…The optimal values of the variables were determined using interaction factors derived from multiple regression studies based on FFED to maximize the second-order polynomial equation. …”
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Reliability and Reliability-based Sensitivity Analyses of Steel Moment-Resisting Frame Structure subjected to Extreme Actions by Abbasali Sadeghi, Hamid Kazemi, Maysam Samadi

“…To reduce computational costs, meta-model techniques such as Kriging, Polynomial Response Surface Methodology (PRSM) and Artificial Neural Network (ANN) are applied and their efficiency is assessed. …”
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Optimization of Batch Extraction of Aromatics from Reformed Heavy Naphtha by Response Surface Methodology by Marwa Asad Salih, Raghad F. Almilly

“…Following a (BBD), fifteen experimental runs systematically optimized the extraction efficiency and determined the interactive effects of these variables on extraction efficiency. …”
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Stability Evaluation of Slope Based on Global Sensitivity Analysis by Zhaoxia Xu, Xiuzhen Wang, Lu Guo, Teng Yu

“…The proposed methods allow all variables to change simultaneously within their variation range and have high computational efficiency. …”
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Linear Gauss Pseudospectral Method Using Neighboring Extremal for Nonlinear Optimal Control Problems by Tianyou Zhang, Wanchun Chen, Liang Yang

“…Results show that it not only performs well in computational efficiency and accuracy but also has great adaptability and optimality. …”
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Styles energy consumption analysis of lane-changing maneuvers in autonomous vehicles: The role of driving styles by Yu Guo, Guigen Nie, Xiaowei Zou, Dongliang Zhu, Wenliang Gao, Mi Liao

“…This study addresses this gap by incorporating driving style variables and employing a quintic polynomial lane-change trajectory model, optimized through Sequential Quadratic Programming (SQP) and the Lagrange multiplier method, to assess energy consumption during lane changes. …”
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Data Assimilation Informed Model Structure Improvement (DAISI) for Robust Prediction Under Climate Change: Application to 201 Catchments in Southeastern Australia by Julien Lerat, Francis Chiew, David Robertson, Vazken Andréassian, Hongxing Zheng

“…These configurations correspond to specific polynomials of the state variables that could be used to improve equations in a revised model. …”
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ANALYSIS AND PARAMETRIC OPTIMIZATION OF ENERGY-AND-TECHNOLOGY UNITS ON THE BASIS OF THE POWER EQUIPMENT OF COMPRESSOR PLANTS OF MAIN GAS PIPELINES by V. A. Sednin, A. A. Abrazovskii

“…The application of the outlined methodological approach makes it possible to obtain a simple polynomial dependence, which significantly simplify the procedures of analysis, parametric optimization and evaluation of efficiency in the feasibility studies of the options of construction of the energy facilities.…”
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Uniaxial compressive strength of cemented coal gangue backfill based on response surface methodology by Ziqi Zhu, Ke Deng, Zhenghao Jin, Tianwen Shi, Ying Han

“…First, single-factor tests identified optimal ranges for critical variables: mass concentration (80%–81%), fly ash content (3–4 kg), and fine gangue ratio (35%–45%). …”
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Sustitución parcial de alimento balanceado comercial por saccharina rústica en pollo de engorde by Dixon Fabián Flórez-Delgado, Jesús Esteban Fonseca-García, Dubel Reinaldo Cely-Leal

“…Treatment effects were observed on the variables Con, PCF, WG, FG, FY, CY, CY, CY, PY, and EPF. …”
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Sustained release biodegradable solid lipid microparticles: Formulation, evaluation and statistical optimization by response surface methodology by Hanif Muhammad, Khan Hafeez Ullah, Afzal Samina, Mahmood Asif, Maheen Safirah, Afzal Khurram, Iqbal Nabila, Andleeb Mehwish, Abbas Nazar

“…For preparing nebivolol loaded solid lipid microparticles (SLMs) by the solvent evaporation microencapsulation process from carnauba wax and glyceryl monostearate, central composite design was used to study the impact of independent variables on yield (Y1), entrapment efficiency (Y2) and drug release (Y3). …”
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