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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Modular quantum signal processing in many variables by Zane M. Rossi, Jack L. Ceroni, Isaac L. Chuang

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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

“…Abstract We propose two precise spectral techniques based on shifted Vieta–Lucas polynomials (SVLPs) for the solution of pantograph-type differential equations (PTDEs) subject to general mixed-type boundary conditions (MTBCs). …”
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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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Investigation on Free Vibration of Rotating Cylindrical Shells with Variable Thickness by Liu Xiangdong, Hou Xiaoli, Bai Bin, Zeng Maolin

“…In order to improve the performance and efficiency of the rotating cylindrical shell (RCS), one of the effective ways reduces the mass of the RCS. …”
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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 Penalized Orthogonal Kriging Method for Selecting a Global Trend by Xituo Zhang, Guoxing Gao, Jianxin Zhao, Xinmin Li

“…In this paper, we introduce a new method for combining orthogonal kriging with penalized variable selection. Furthermore, an efficient algorithm is given to select the correct mean function. …”
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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

“…The parameterization method exploits the implicit properties of the Bernstein polynomial least squares fitting to allow both local and global shape control. …”
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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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An Eighth-Order Numerical Method for Spatial Variable-Coefficient Time-Fractional Convection–Diffusion–Reaction Equations by Yuelong Feng, Xindong Zhang, Leilei Wei

“…In this paper, we propose a high-order compact difference scheme for a class of time-fractional convection–diffusion–reaction equations (CDREs) with variable coefficients. Using the Lagrange polynomial interpolation formula for the time-fractional derivative and a compact finite difference approximation for the spatial derivative, we establish an unconditionally stable compact difference method. …”
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An adaptive sliding mode fault-tolerant control of variable speed reaching law for steer-by-wire systems by Jinwen Yang, Yinquan Yu, Dequan Zeng, Yiming Hu, Junhui Liu, Kai Liu, Giuseppe Carbone, Shaohua Luo, Xiaofeng Zhu

“…By integrating an adjustment function into the constant-velocity reaching polynomial and designing an adaptive law, dynamic updating of the control law is achieved. …”
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A Convergent Legendre Spectral Collocation Method for the Variable-Order Fractional-Functional Optimal Control Problems by Zahra Pirouzeh, Mohammad Hadi Noori Skandari, Kameleh Nassiri Pirbazari

“…In addition, the matrix differentiation is calculated accurately and efficiently, overcoming the difficulties posed by variable-order fractional derivatives. …”
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High-Order Spectral Method of Density Estimation for Stochastic Differential Equation Driven by Multivariate Gaussian Random Variables by Hongling Xie

“…There are some previous works on designing efficient and high-order numerical methods of density estimation for stochastic partial differential equation (SPDE) driven by multivariate Gaussian random variables. …”
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Classification of traffic accidents’ factors using TrafficRiskClassifier by Wei Sun, Lili Nurliyana Abdullah, Fatimah binti Khalid, Puteri Suhaiza binti Sulaiman

“…Furthermore, the TrafficRiskClassifier model delineates a functional nexus between accident risk and variables such as weather, road conditions, and personal factors, employing a polynomial regression approach. …”
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Opportunities of aluminum sludge dredging with soft magnetic conditioner for dewaterability enrichment by Manasik M. Nour, Maha A. Tony, Woo Hyoung Lee, Hossam A. Nabwey

“…The optimal values for ZSF-Conditioner, hydrogen peroxide (H2O2), and pH were determined to be 43 mg L− 1, 430 mg L− 1, and 3.5, respectively, achieving a CST reduction efficacy of 74 ± 3%, which was consistent with the predicted efficiency from the polynomial model. Thus, the experimental data confirmed the effectiveness of the system for Al-Sludge conditioning, highlighting its notable implementation and safe technology.…”
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