Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q   (p>0) by Jing Li

“…The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. …”
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Stress-Softening Formulae of Polymer Bearings by M. H. B. M. Shariff, Anoop Sivasankaran, Zanin Kavazović

“…We furthermore found that, in a nonlinear deformation, the shape factor plays an important role in stress softening. …”
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Synchronization of Chaotic Delayed Neural Networks via Impulsive Control by Yang Fang, Kang Yan, Kelin Li

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Numerical Approaches of the Generalized Time-Fractional Burgers’ Equation with Time-Variable Coefficients by Dumitru Vieru, Constantin Fetecau, Nehad Ali Shah, Jae Dong Chung

“…The generalized time-fractional, one-dimensional, nonlinear Burgers equation with time-variable coefficients is numerically investigated. …”
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Computation offloading and resource allocation strategy based on deep reinforcement learning by Feng ZENG, Zheng ZHANG, Zhigang CHEN

“…In order to expand the coverage and computing power of vehicle edge network, a computation offloading architecture was proposed for space-air-ground integrated vehicle network (SAGVN).With the consideration of the delay and energy consumption constraints of computing tasks, as well as the spectrum, computing and storage constraints in the SAGVN, the joint optimization problem of computation offloading decision and resource allocation was modeled as a mixed integer nonlinear programming problem.Based on the reinforcement learning method, the original problem was transformed into a Markov process, and a deep reinforcement learning algorithm was proposed to solve the problem.The proposed algorithm has the good convergence.The simulation results show that the proposed algorithm outperforms other algorithms in terms of task delay and success rate.…”
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The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey-Stewartson Equations and Comparison between Them and Exact Solutions by Hassan A. Zedan, W. Barakati, Nada Hamad

“…HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained.…”
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Three-Dimensional Laplace Adomian Decomposition Method and Singular Pseudoparabolic Equations by Hassan Eltayeb, Diaa Eldin Elgezouli, Adem Kilicman, Imed Bachar

“…In this work, the solution of the linear, nonlinear, and coupled system fractional singular two-dimensional pseudoparabolic equation is examined by using a three-dimensional Laplace Adomian decomposition method (3-DLADM). …”
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Observer-Based PID Security Control for Discrete-Time T-S Fuzzy Systems under Distributed Dynamic Event-Triggered Mechanism by Sisi Lin, Mengzhuo Luo, Shouming Zhong, Kaibo Shi, Xingxu Tan

“…This study addresses the observer-based proportional-integral-derivative (PID) security control problem for nonlinear discrete-time fuzzy systems subject to deception attacks. …”
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Newton Method to Recover the Phase Accumulated during MRI Data Acquisition by Oh-In Kwon, Chunjae Park

“…To maximize signal intensity, the injected current nonlinear encoding (ICNE) method extends the duration of the current injection until the end of the MR data reading. …”
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An Entropy Model of Credit Risk Contagion in the CRT Market by Tingqiang Chen, Ying Chen, Xindan Li, Jining Wang

“…Thus, an entropy spatial model is introduced, in which the spatial distance and nonlinear coupling between the banks and the investors, the transfer ability of credit risk of banks, and investor appetite for risk in the CRT network are considered. …”
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Restrictive metric regularity and generalized differential calculus in Banach spaces by Boris S. Mordukhovich, Bingwu Wang

“…We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X). …”
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Support vector machine based fast Monte Carlo reliability evaluation method for composite power system by Yuxiao LEI, Gengfeng LI, Yuxiong HUANG, Zhaohong BIE

“…A fast Monte Carlo reliability evaluation method for composite power system based on support vector machine (SVM) was proposesd.Firstly,sample data for training the SVM model was obtained by enumerating component failures and calculating the corresponding minimum load shedding.Then,the SVM algorithm was used to mine the nonlinear mapping relationship between component failures and minimum load shedding,and the minimum load shedding estimation model was trained.Finally,the model was combined with the Monte Carlo simulation.By randomly sampling component states,for each state,the estimation model obtained by the training directly gave the minimum load shedding,thereby achieving a rapid assessment of the reliability of the composite power system.The proposed method is applied to the IEEE RTS 79 system,which verifies its effectiveness.…”
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A Graph Embedding Method Based on Sparse Representation for Wireless Sensor Network Localization by Xiaoyong Yan, Aiguo Song, Hao Yan

“…Therefore, the algorithm can effectively solve the nonlinear problem while ranging, and it becomes less affected by the measuring error and beacon nodes quantity.…”
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Slip Effect on MHD Chemically Reacting Convictive Boundary Layer Flow with Heat Absorption by Mekonnen Shifferaw Ayano, Negussie Tadege Demeke

“…The system of coupled nonlinear equations is solved numerically and the effects of various parameters on the velocity, the microrotation, the temperature, and the concentration field are calculated. …”
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A Study on ψ-Caputo-Type Hybrid Multifractional Differential Equations with Hybrid Boundary Conditions by Fouad Fredj, Hadda Hammouche, Mohammed S. Abdo, Wedad Albalawi, Abdulrazak H. Almaliki

“…Besides, the Ulam–Hyers stability for the proposed problem is investigated by applying the techniques of nonlinear functional analysis. In the end, we provide an example to illustrate the applicability of our results.…”
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Common Fixed Points of (α,η) − (θ,ϝ) Rational Contractions with Applications by Mujahid Abbas, Hira Iqbal, Manuel De La Sen

“…As application, we establish the existence of solutions of nonlinear elastic beam equations and first-order periodic problem.…”
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Synchronous Modification Design for Bilateral Tooth Surface of Spiral Bevel Gear by Dual Duplex Spread Blade Method by Jianjun Yang, Xinfang Hu, Hua Zhang, Shaowu Nie

“…The mathematical model and constraint function of the target tooth surface errors based on the optimization of machining tool setting are constructed. The nonlinear constrained optimization function is used to derive the machining parameters of the gear. …”
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Measurement and simulation of strain fields around crack tips under mixed-mode fatigue loading by Y. Hos, M. Vormwald, J.L.F. Freire

“…The mechanical material behavior has been assumed as linear elastic in a first approach for calculating stress intensity factors. The nonlinear nature of the cyclic deformation has been taken into account by applying a cyclic plasticity model, and plasticity-induced crack closure is captured by a contact formulation.…”
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Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation by Jinhua Wang, Hongjun Xiang, Yuling Zhao

“…We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. …”
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Flux Transport Characteristics of Free Boundary Value Problems for a Class of Generalized Convection-Diffusion Equation by Yunbin Xu, Meihua Wei

“…A class of singular nonlinear boundary value problems are obtained and solved by using Adomian decomposition method (ADM). …”
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