An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation by Chaeyoung Lee, Jintae Park, Soobin Kwak, Sangkwon Kim, Yongho Choi, Seokjun Ham, Junseok Kim

“…The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. …”
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Exact Travelling Wave Solutions for Isothermal Magnetostatic Atmospheres by Fan Subequation Method by Hossein Jafari, Maryam Ghorbani, Chaudry Masood Khalique

“…These equations transform to a single nonlinear elliptic equation for the magnetic vector potential . …”
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STRAIN ANALYSES OF REPAIRED PIPELINES BY ENWINDING COMPOSITE MATERIALS by YANG JiCheng, WANG YanYu

“…The results show that the circumferential strain of the defect center presents a nonlinear three stage trend with the change of internal pressure after repaired. …”
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Application of ABC-VMD and Envelope Spectrum Analysis in Gear Fault Diagnosis by Wangping Zhou, Rong Wang, Shenrong Xu

“…Aiming at the nonlinear and unsteady characteristics of gearbox fault， a parameter-optimized Variational mode decomposition （VMD） is proposed to extract the characteristic frequency. …”
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Cryptanalysis of novel extended multivariate public key cryptosystem by Xu-yun NIE, Bo LIU, Gang LU, Ting ZHONG

“…The novel extended multivariate public key cryptosystem is a new security enhancement method on multivariate public key cryptosystems,which is proposed by Qiao,et al.A nonlinear invertible transformation was used,named“tame transformation”,on the original multivariate public key cryptosystem to hide its weakness such as linearization equation.However,it is found that if there are many linearization equations satisfied by the original MPKC,there would be many quadratization equations (QE) satisfied by the improved scheme.Given a public key,after finding all QE,a valid cipheretext can be substituted into the QE to derive a set of quadratic equations on the plaintext variable.This exactly reduce the degree of the system wanted to solve.Then the corresponding plaintext can be recovered for a given valid ciphertext combining with Groebner basis method.…”
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Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains by Yudier Peña Pérez, Ricardo Abreu Blaya, Paul Bosch, Juan Bory Reyes

“…Our technique of proofs is based on the intimate relations between solutions of time-harmonic Maxwell system and those of the Dirac equation through some nonlinear equations, when both cases are reformulated in quaternionic forms.…”
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Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation by Huanhe Dong, Yanfeng Zhang, Yongfeng Zhang, Baoshu Yin

“…We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1)-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. …”
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Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces by Jiang Zhu, Lei Wei, Yeol Je Cho, Cheng Cheng Zhu

“…Also, several other important principles in nonlinear analysis are extended to cone quasi-uniform spaces. …”
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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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Study of a Biparametric Family of Iterative Methods by B. Campos, A. Cordero, Á. A. Magreñán, J. R. Torregrosa, P. Vindel

“…The dynamics of a biparametric family for solving nonlinear equations is studied on quadratic polynomials. …”
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Experimental Investigation of Water-Sand Mixed Fluid Initiation and Migration in Filling Fracture Network during Water Inrush by Bin Yang, Tianhong Yang

“…For water inrush induced by fracture network flow, the critical velocity of the incipient motion of sand particles was obtained, and the functional relation between critical velocity and particle size was established through a series of tests on the nonlinear flow characteristics of a filling fracture network. …”
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Gravitational Collapse and Singularity Removal in Rastall Theory by Ehsan Dorrani

“…In the present work, we study spherically symmetric gravitational collapse of a homogeneous fluid in the framework of Rastall gravity. Considering a nonlinear equation of state (EoS) for the fluid profiles, we search for a class of nonsingular collapse solutions and the possibility of singularity removal. …”
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A singularly perturbed HIV model with treatment and antigenic variation by Nara Bobko, Jorge P. Zubelli

“…Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.…”
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Multilevel Seismic Damage Behavior Correlation Analysis for RC Framed Structures by Jianguang Yue

“…Five structural levels, that is, material level, section level, member level, storey level, and structure level, were proposed to analyze the multilevel nonlinear mechanism of the reinforced concrete (RC) framed structures. …”
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Multiscale Systemic Risk and Its Spillover Effects in the Cryptocurrency Market by Xu Zhang, Zhijing Ding

“…We adopt wavelet packet decomposition, nonlinear Granger causality test, risk spillover network, and STVAR model; retain the mature research of multiscale systemic risk based on time and frequency; and thus extend systemic risk to different regimes. …”
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Effect of time delay on a detritus-based ecosystem by Nurul Huda Gazi, Malay Bandyopadhyay

“…This paper deals with the dynamical analysis of a nonlinear model of a detritus-based ecosystem involving detritivores and predator of detritivores. …”
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Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map by Jian-feng Zhao, Shu-ying Wang, Li-tao Zhang, Xiao-yan Wang

“…It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. …”
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Higher-order fuzzy fractional differential equations: on the existence, uniqueness and Hyers–Ulam–Rassias stability of solutions by Brahim Ghrissi, Abdelkader Amara, Youcef Henka

“…In this work, we investigate the existence, uniqueness, and different stability types, focusing on Ulam-Hyers stability, of a solution to a nonlinear fuzzy fractional differential equation with Caputo generalized Hukuhara differentiability of order ℘ ∈ (n − 1, n). …”
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Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions by Hui Li, Libo Wang, Minghe Pei

“…We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). …”
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Systems resource allocation algorithm for RIS-assisted D2D secure communication based on parallel CNN by Zhengyu ZHU, Gengwang HOU, Chongwen HUANG, Gangcan SUN, Wanming HAO, Jing LIANG

“…To meet the requirements of intelligent signal processing and physical layer security, aiming at the shortage of spectrum resources, a resource allocation algorithm for reconfigurable intelligent surface (RIS)-assisted the device to device (D2D) communication was proposed.D2D users communicated by multiplexing the spectrum resources of cellular users.Considering the constraints of D2D transmission rate, base station transmission power and RIS transmission phase shift, the problem of maximizing user security rate was formulated.To solve the nonlinear programming problem, a parallel convolutional neural network (CNN) algorithm was proposed to obtain the optimal resource allocation scheme.Simulation results show that the parallel CNN algorithm can effectively improve the secrecy rate and it is significantly better than other benchmark algorithms.…”
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