Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments by Cristóbal González, Antonio Jiménez-Melado

“…In the case of q(t,s)=(t-s)+, its solutions with asymptotic behavior given by ω(t) yield solutions of the second order nonlinear abstract differential equation y''(t)-ω''(t)+F(t,y(γ1(t)),…,y(γN(t)))=0, with the same asymptotic behavior at ∞ as ω(t).…”
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Seismic Performance of Steel Frames with Semirigid Connections by Iman Faridmehr, Mahmood Md. Tahir, Tom Lahmer, Mohd Hanim Osman

“…The nonlinear stiffness matrix method was incorporated to investigate the structural performance of steel portal frames with semirigid connections. …”
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Analyzing dead core formation in catalyst pellets of various geometries under non-isothermal conditions by M. Menaka, R. Manimaran, S. Saravanakumar, L. Rajendran, A. Eswari

“…The model investigates the nonlinear reaction-diffusion equations governing reactions within catalyst pellets, focusing on the spatial distribution and transformation of substances. …”
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Resonant Tunneling Nanostructures: Eliminating Current Saturation on Negative Differential Conductivity Region in Compact Dissipative Simulations by Natalia Vetrova, Evgeny Kuimov, Sergey Meshkov, Vladimir Sinyakin, Mstislav Makeev, Vasiliy Shashurin

“…This makes the developed compact model effective for simulating the operation of a wide range of devices with a resonant tunneling diode as a nonlinear element, regardless of the position of the operating point.…”
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Detection of the onset of numerical chaotic instabilities by lyapunov exponents by Alicia Serfaty De Markus

“…It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. …”
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Base Isolation of Buildings with Curved Surface Sliders: Basic Design Criteria and Critical Issues by Fernando Saitta, Paolo Clemente, Giacomo Buffarini, Giovanni Bongiovanni, Antonello Salvatori, Cristian Grossi

“…For all these reasons, the use of nonlinear analysis, revised and detailed in this paper, is advisable for the isolation system made of curved surface sliders.…”
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Research on the time-varying charging and dynamic data routing strategy for rechargeable wireless sensor networks by Jiang-hong HAN, Xu DING, Lei SHI, Dong HAN, Zhen-chun WEI

“…The energy problem of wireless sensor networks could be solved by recharging sensor nodes periodically through the wireless energy transfer technique,which ld made sensor nodes remain optional persistently.However,appropriate charging and routing strategies were also in great needs.According to the optimization object of maximizing the vacation time ratio of a wireless charging equipment,the continuous time-varying model,the discrete (N+1)-phased nonlinear model and the solvable discrete (N+1)-phased linear model for the charging and routing strategy were proposed successively.The feasibility of these models was proved as well.In conclusion,after solving the last proposed model,the optimized charging and routing strategies were obtained for networks in different scales.…”
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An Efficient Series Solution for Fractional Differential Equations by Mohammed Al-Refai, Mohamed Ali Hajji, Muhammad I. Syam

“…We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. …”
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Multipoint BVP for the Langevin Equation under φ-Hilfer Fractional Operator by Mohammed A. Almalahi, Satish K. Panchal, Fahd Jarad

“…In this research paper, we consider a class of boundary value problems for a nonlinear Langevin equation involving two generalized Hilfer fractional derivatives supplemented with nonlocal integral and infinite-point boundary conditions. …”
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A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order by F. Soleymani, S. Karimi Vanani, M. Jamali Paghaleh

“…To test the derived methods from the class, we apply them to a lot of nonlinear scalar equations. Numerical examples suggest that the novel class of derivative-free methods is better than the existing methods of the same type in the literature.…”
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Crashworthiness Design for Bionic Bumper Structures Inspired by Cattail and Bamboo by Tao Xu, Nian Liu, Zhenglei Yu, Tianshuang Xu, Meng Zou

“…In this study, we evaluated the bionic bumper structure models by using nonlinear finite element (FE) simulations for their crashworthiness under full-size impact loading. …”
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Possibilities for Advanced Encoding Techniques at Signal Transmission in the Optical Transmission Medium by Filip Čertík, Rastislav Róka

“…An attention is focused on the high data rate signal transmission in the optical fiber influenced by linear and nonlinear environmental effects presented by the prepared simulation model. …”
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An Agent-Based Model of Opinion Polarization Driven by Emotions by Frank Schweitzer, Tamas Krivachy, David Garcia

“…This information feeds back on the dynamics of emotional states and individual opinions in a nonlinear manner. We derive the critical conditions for emotional interactions to obtain either consensus or polarization of opinions. …”
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Multifractal Detrended Cross-Correlation Analysis of the Return-Volume Relationship of Bitcoin Market by Wei Zhang, Pengfei Wang, Xiao Li, Dehua Shen

“…The empirical results based on multifractal detrended cross-correlation analysis (MF-DCCA) reveal that (1) the nonlinear dependencies and power-law cross-correlations in return-volume relationship are found; (2) all cross-correlations are multifractal, and there are antipersistent behaviors of cross-correlation for q=2; (3) the price of small fluctuations is more persistent than that of the volume, while the volume of larger fluctuations is more antipersistent; and (4) the rolling window method shows that the cross-correlations of return-volume are antipersistent in the entire sample period.…”
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Sledgehamr: Simulating Scalar Fields with Adaptive Mesh Refinement by Malte Buschmann

“…Understanding the nonlinear dynamics of coupled scalar fields often necessitates simulations on a 3D mesh. …”
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On the stabilization of internally coupled map lattice systems by Weihong Huang

“…The adaptive adjustment mechanism is applied to the stabilization of an internally coupled map lattice system defined by xi,t+1=G((1−αi−βi)xi,t+αixi+1,t+βixi−1,t), where f:ℝ→ℝ is a nonlinear map, and α and β are nonnegative coupling constants that satisfy the constraint αi+βi<1, for all x∈ℝ, i=1,2,…,n. …”
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Influence of Center Component Floating on the Load-sharing Characteristic of Planetary Transmission System by Yangyang Du, Xiaosun Wang, Xue Yang, Bo Jiao, Shijing Wu

“…In order to investigate the load-sharing performance of the 2K-H planetary gear transmission system， a translation-torsion coupling dynamics model is established with considering the nonlinear factors of time-varying meshing stiffness and the overall meshing error and so on， the dimensionless differential equations with 18 degrees of freedom of the system are deduced in this model. …”
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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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Similarity Solutions for Flow and Heat Transfer of Non-Newtonian Fluid over a Stretching Surface by Atta Sojoudi, Ali Mazloomi, Suvash C. Saha, Y. T. Gu

“…Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. …”
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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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