Numerical Modeling of the Internal Dispersive Shock Wave in the Ocean by Tatiana Talipova, Efim Pelinovsky, Oxana Kurkina, Andrey Kurkin

“…The theoretical model is based on extended version of the Korteweg-de Vries equation which takes into account the effects of cubic nonlinearity and Earth rotation. This model is now very popular in the physical oceanography. …”
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Hybrid quantum-classical control problems by Emanuel-Cristian Boghiu, Jesús Clemente-Gallardo, Jorge A. Jover-Galtier, David Martínez-Crespo

“…We also considered the notion of hybrid quantum-classical controllability by means of the usual definitions of geometric control theory, and we discussed how the different concepts associated to quantum controllability are lost in the hybrid context because of the nonlinearity of the dynamics. We also considered several examples of physically relevant problems, such as the spin-boson model or the notion of hybrid spline.…”
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A finite-dimensional reduction method for slightly supercritical elliptic problems by Riccardo Molle, Donato Passaseo

“…A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.…”
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Lyapunov Exponent-Based Study of Chaotic Mechanical Behavior of Concrete under Compression by Yuhu Quan, Xu Yang

“…Chaos theory is advantageous in achieving a deeper understanding of the nonlinearity and randomness of concrete behavior. In this study, the experimental data of concrete under compression were examined and discussed using Lyapunov exponent. …”
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Finite-Time Synchronizing Control for Chaotic Neural Networks by Chao Zhang, Qiang Guo, Jing Wang

“…A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. …”
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Robust Adaptive Fractional Fast Terminal Sliding Mode Controller for Microgyroscope by Juntao Fei, Zhe Wang, Xiao Liang

“…Adaptive algorithm is applied to estimate the damping and stiffness coefficients, angular velocity, and the upper bound of the lumped nonlinearities. Numerical simulations are presented to exhibit the validity of the proposed method, and the comparison with the other two methods illustrates its superiority.…”
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To the Problem of Electromechanical Interaction in Elevators with Controlled Electric Drive and Fuzzy Speed Controller by A. S. Koval, A. V. Shvayakou

“…A mathematical description of electromechanical elevator system with due account of nonlinearity of the worm gear is given in the paper. …”
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Fuzzy Wavelet Neural Network with the Improved Levenberg–Marquardt Algorithm for the AC Servo System by Run-Min Hou, Di-Fen Shi, Qiang Gao, Yuan-Long Hou

“…In this study, a fuzzy wavelet neural network with the improved Levenberg–Marquardt algorithm (FWNN-LM) is proposed to conquer nonlinearity and uncertain disturbance problems in the AC servo system. …”
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Time series data aggregation algorithm with synchronous prediction for WBAN by Ru-yan WANG, Mei-ling ZHAI, Da-peng WU

“…Due to the nonlinearity and nonstationarity of the physiological data sensed by WBAN,data aggregation cannot be effectively achieved according to the time-domain trend of data.Therefore,a novel time series data aggregation algorithm with synchronous prediction was proposed.By preprocessing the original sensing data with the multi-resolution analysis,the inherent characteristics of the physiological data can be obtained to establish a light-weight synchronous prediction model at both the sensor and sink.Numerical results show that the proposed aggregation algorithm can achieve a favorable prediction precision and a low energy consumption rate by eliminating the in-network data redundancy.…”
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Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method by Abdon Atangana, Adem Kılıçman

“…The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. …”
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Low Threshold, Wide Dynamic Range, Tunable, All-Optical Self-Modulator Based on Fano Resonance and Out-of-Plane Coupling in a Slab Photonic Crystal with a Graphene Layer by Reza Asadi, Zhengbiao Ouyang

“…We demonstrate an all-optical modulator based on self-modulation in a one-dimensional slab photonic crystal (PhC) by using optical Kerr nonlinearity of graphene and Fano resonance effect. It has been shown that the effect of Fano resonance in a one-dimensional slab PhC for intensity enhancement can provide low threshold (~1 MW/cm2), high frequency (>1 THz), and wide dynamic range (>3 THz) tunability for the all-optical self-modulator. …”
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Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces by Qinghua Zhang, Yueping Zhu, Feng Wang

“…Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account.…”
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Analytical Model for Deflections of Bonded Posttensioned Concrete Slabs by Min Sook Kim, Joowon Kang, Young Hak Lee

“…A finite element model was established based on layered and degenerated shell elements. Nonlinearities of the materials are considered using the stress-strain relationships for concrete, reinforcing steel, and prestressing tendons. …”
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Triglyceride Glucose Index Was a Predictor of 6-Month Readmission Caused by Pulmonary Infection of Heart Failure Patients by Licheng Shi, Jianan Liu, Xuanfeng Zhu, Tiantian Li, Jingli Wen, Xinyu Wang, Xu Qi

“…Only the 6-month readmission was significantly different among TyG quartiles, and it was the highest (41.9%) in the lowest quartile (ranging 6.17∼7.36). the TyG index was nonlinearly associated with 6-month readmission (p for nonlinearity = 0.009), with the lower level of TyG index increasing the risk of 6-month readmission. …”
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Membrane Transport of Nonelectrolyte Solutions in Concentration Polarization Conditions: Hr Form of the Kedem–Katchalsky–Peusner Equations by Kornelia M. Batko, Andrzej Ślęzak

“…The coefficients ψ12, ψ13, ψ22 = ψ23, ψ32 = ψ33, and ψdet depend nonlinearly on solution concentration and for C¯1 ≈ 9.24 mol m−3 are equal to zero. …”
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U-shaped association between TC/HDL-C ratio and osteoporosis risk in older adults by Chuanwei Zhao, Xiaochun Zhang, Xu Zhang, Bo Zhao, Yane Yang, Mu Lin, Wenli Qiao, Zeyao Hu, Haijie Yang

“…In sex-specific analyses, a U-shaped relationship was found in women, with a threshold at 4.35 (p for nonlinearity = 0.0016), but no significant association was found in men. …”
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Robust Adaptive Reactive Power Control for Doubly Fed Induction Generator by Huabin Wen, Yu Zeng, Lei Wang, Feng Yang, Y. D. Song

“…To accommodate the modelling nonlinearities and inherent uncertainties, a novel robust adaptive control algorithm for MSI is proposed by utilizing Lyapunov theory that ensures asymptotic stability of the system under unpredictable external disturbances and significant parametric uncertainties. …”
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Real-Time Quantification of Gas Leaks Using a Snapshot Infrared Spectral Imager by Nathan Hagen

“…After describing the special calibration needs of the hardware, we show how to regularize the gas detection/identification for optimal performance, provide example SNR spectral images, and discuss the effects of humidity and absorption nonlinearity on detection and quantification.…”
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Positive Solutions of Fractional Differential Equation with -Laplacian Operator by Teng Ren, Xiaochun Chen

“…In this paper, we study an ecological model arising from ecological economics by mathematical method, that is, study the existence of positive solutions for the fractional differential equation with -Laplacian operator , , , , , and , where are the standard Riemann-Liouville derivatives, -Laplacian operator is defined as , and the nonlinearity may be singular at both and By finding more suitable upper and lower solutions, we omit some key conditions of some existing works, and the existence of positive solution is established.…”
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Finite-Time Antisaturation Tracking Control for Hypersonic Vehicle with Uncertain Dynamics by Yuwei Cui, Yushan He, Aijun Li, Jun Li, Shuo Song

“…Furthermore, an auxiliary system is established to cope with the nonlinearity caused by actuator saturation. It is concluded by a Lyapunov-based analysis that the finite-time stability is guaranteed under the developed architecture. …”
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