A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation by E. Momoniat

“…The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. …”
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Effect of Size Distribution on the Dust Acoustic Solitary Waves in Dusty Plasma with Two Kinds of Nonthermal Ions by Samira Sharif Moghadam, Davoud Dorranian

“…Effect of dust size, mass, and charge distributions on the nonlinear dust acoustic solitary waves (DASWs) in a dusty plasma including negatively charged dust particles, electrons, and nonthermal ions has been studied analytically. …”
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Adaptive Control for Multi-Agent Systems Governed by Fractional-Order Space-Varying Partial Integro-Differential Equations by Zhen Liu, Yingying Wen, Bin Zhao, Chengdong Yang

“…This paper investigates a class of multi-agent systems (MASs) governed by nonlinear fractional-order space-varying partial integro-differential equations (SVPIDEs), which incorporate both nonlinear state terms and integro terms. …”
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Heat Transfer Analysis on the Hiemenz Flow of a Non-Newtonian Fluid: A Homotopy Method Solution by Yasir Khan, Zdeněk Šmarda

“…The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. …”
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Concrete constructions of 2-resilient rotation symmetric Boolean functions with 7 variables by Jiao DU, Lin LI, Ziwei ZHAO, Yueyue LI, Tianyin WANG

“…Based on the properties of the 2-tuples distribution matrix of the rotation symmetric orbits, all 7-variable 2-resilient rotation symmetric Boolean functions were constructed concretely.The results show that there are only 280 nonlinear 2-resilient rotation symmetric Boolean functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msubsup> <mi mathvariant="double-struck">F</mi> <mn>2</mn> <mn>7</mn> </msubsup> </math></inline-formula>.Furthermore, there are at least 280 nonlinear 2-resilient rotation symmetric Boolean functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msubsup> <mi mathvariant="double-struck">F</mi> <mn>2</mn> <mrow> <mn>7</mn><mi>k</mi></mrow> </msubsup> </math></inline-formula> for any odd number k.…”
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Modeling and dynamic analysis of split torsion transmission system considering backlash and center distance errors by Jingwei Ding, Guanghu Jin

“…The findings indicate that the impact of center distance error on the system’s dynamics is linear, whereas the effect of backlash is nonlinear. Moreover, the center distance error in the parallel-level stage and the backlash in the split-torsion stage are critical factors influencing the system’s dynamic characteristics. …”
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RESEARCH ABOUT FAULT DIAGNOSIS OF BEARING BASED ON INSTRINSIC TIME SCALE DECOMPOSITION AND CONVOLUTIONAL NEURAL NETWORK by XIAO JunQing, YUE MinNan, LI Chun, JIN JiangTao, XU ZiFei, MIAO WeiPao

“…The working environment of rolling bearing is complex, the nonlinear vibration signal and the interference of environmental noise lead to the difficulty of fault diagnosis. …”
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Research on House Price Prediction based on Machine Learning by Yang Xiangjun

“…In recent years, machine learning techniques have shown remarkable potential in house price prediction, as these models can mine the complex nonlinear correlations in large amounts of historical data to produce more detailed and accurate predictions. …”
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PARAMETER ESTIMATION AND CONFIDENCE LIMIT CALCUALTION METHOD OF THREE-PARAMETER WEIBULL DISTRIBUTION by ZHANG JianFeng, XU Fang, ZHANG Yan, HUANG XiaoBo, JIA ZhuoHan

“…A correlation-regression method was proposed to solve the problem of low accuracy of parameter estimation and confidence limit calculation of the three-parameter Weibull distribution.The method was combined by the correlation coefficient method （Fu method） and the nonlinear regression method which makes full use of the convenience of Fu method and the excellent estimation effect of the nonlinear regression method in estimating the three-parameter Weibull distribution.In order to verify the effectiveness of the proposed method，the correlation-regression method，Fu method and Method combining maximum likelihood estimation and empirical formulae (referred to as the “MMPDS method”） were applied to the parameter estimation and confidence limit calculation of the data distribution of a certain alloy strength value with different sample sizes，and calculation consequence of different methods was compared and analyzed.Results show that the correlation-regression method has highest parameter estimation and confidence limit calculation accuracy among the above methods.When the sample size is less than 100，its advantage is more significant，and it can accurately calculate the parameters and confidence limits of the Weibull distribution.…”
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The crack path in fuselage panel under mixed mode biaxial loading by Alexander Zakharov, Valery Shlyannikov, Andrey Tumanov

“…This paper provides the background for practical applications of nonlinear fracture resistance parameters for structural integrity assessment of aviation structures with initial cracks. …”
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Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions by Mohsin Kamran, Muhammad Abbas, Abdul Majeed, Homan Emadifar, Tahir Nazir

“…The unidirectional propagation of long waves in certain nonlinear dispersive system is explained by the Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. …”
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Feature Extraction and Wear Damage Degree Identification of Planetary Gear based on PSO-FC Optimization KPCA by Yan He, Zongyan Wang

“…When the planetary gear transmission system fails， its signal transmission is coupled with each other， and the nonlinear characteristic is presented， which makes the fault type and damage degree of the planetary gear to be difficultly recognized. …”
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Combination linear lines of position and neural network for mobile station location estimation by Chien-Sheng Chen

“…It is much easier to solve two linear line equations rather than nonlinear circular ones. Artificial neural networks are widely used techniques in various areas due to overcoming the problem of exclusive and nonlinear relationships. …”
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Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy by Yong-Hui Xia, Xiaoqing Yuan, Kit Ian Kou, Patricia J. Y. Wong

“…The essential condition of these previous results is based on the assumption that the nonlinear term satisfies |f(t,x)|≤μe−ε|t|. However, this condition is very restricted. …”
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A Collocation Method for Solving Fractional Riccati Differential Equation by Yalçın Öztürk, Ayşe Anapalı, Mustafa Gülsu, Mehmet Sezer

“…Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. …”
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A New Finite-Time Bounded Control of Stochastic Itô Systems with (x,u,v)-Dependent Noise: Different Quadratic Function Approach by Zhiguo Yan, Zhongwei Lin

“…Moreover, the finite-time bounded controller design problem is studied and two sufficient conditions for the existence of state and output feedback controllers are presented in terms of nonlinear matrix inequalities. An algorithm is given for solving the obtained nonlinear matrix inequalities. …”
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Microwave Tomography for Brain Imaging: Feasibility Assessment for Stroke Detection by Serguei Y. Semenov, Douglas R. Corfield

“…The study was conducted using MWT computer simulations and 2D head model with stroke. A nonlinear Newton reconstruction approach was used. …”
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Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data by Jinru Wang, Zijuan Geng, Fengfeng Jin

“…Motivated by Dohono's work, we propose new linear and nonlinear wavelet estimators f^lin(m),f^non(m) for density derivatives f(m) when the random samples have size-bias. …”
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Partitioned Quasi-Newton Approximation for Direct Collocation Methods and Its Application to the Fuel-Optimal Control of a Diesel Engine by Jonas Asprion, Oscar Chinellato, Lino Guzzella

“…First results indicate a significantly faster convergence of the nonlinear program solver when the method proposed is used instead of the standard quasi-Newton approximation.…”
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Power spectral analysis of voltage-gated channels in neurons by Christophe Magnani, Lee E. Moore

“…It explores the use of linear and nonlinear (quadratic sinusoidal analysis) approaches to characterize neuronal function. …”
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