On the Korteweg-de Vries equation: an associated equation by Eugene P. Schlereth, Ervin Y. Rodin

“…The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation ut−6uux+uxxx=0and another nonlinear partial differential equation of the form zt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. …”
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Disturbance Observer-Based Adaptive Neural Network Control of Marine Vessel Systems with Time-Varying Output Constraints by Wei Zhao, Li Tang, Yan-Jun Liu

“…This article investigates an adaptive neural network (NN) control algorithm for marine surface vessels with time-varying output constraints and unknown external disturbances. The nonlinear state-dependent transformation (NSDT) is introduced to eliminate the feasibility conditions of virtual controller. …”
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Parallel time-delay estimation algorithm for GMSK mixing signals by RUI Guo-sheng1, XU Bin2, ZHANG Song2

“…Parallel time-delay estimation algorithm was proposed for GMSK mixing signals based on linear approxima-tion approach.Parallel estimation equations were built in flat-fading channel according to autocorrelation of over-sampling based mixing signals and then Cramer-Rao bound for parallel time-delay estimation was deduced.Poly-nomial fitting method was uesed to simplifying nonlinear complexity of GMSK shaping filter and estimation equations were resolved numerically by gradient descent algorithm with fast convergence.Simulation results show that its estimat-ing performance is good and the variance of estimation error is close to Cramer-Rao bound.As a non-preamble aided al-gorithm with lower complexity it is significant for the next blind processing.…”
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Terahertz Generation in an Electrically Biased Optical Fiber: A Theoretical Investigation by Montasir Qasymeh

“…The optical fiber is mediated by an electrostatic field, which induces an effective second-order nonlinear susceptibility via the Kerr effect. The THz generation is based on difference frequency generation (DFG). …”
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Generation transcritical flow influenced by dissipation over a hole by Mohammed Daher Albalwi

“…Transcritical flow of a stratified fluid over an obstacle for negative forcing amplitude (hole) that generation upstream and downstream, connected by an unsteady solution is examined. In the weakly nonlinear, weakly dispersive regime, the problem is formulated in the forced Korteweg-de Vries–Burgers framework. …”
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Mathematical Modeling for Optimal Management of Human Resources in Banking Sector of Bangladesh by Uzzwal Kumar Mallick, Md. Haider Ali Biswas

“…A system of ordinary nonlinear differential equations has three state variables including vacancies. …”
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Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators by Zhangsong Yao, Yan-Kuen Wu, Ching-Feng Wen

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Author Correction: Magnetic and pH sensitive nanocomposite microspheres for controlled temozolomide delivery in glioblastoma cells by Meysam Ahmadi, Muhammad Hossein Ashoub, Kamran Heydaryan, Sanaz Abolghasemi, Elmuez A. Dawi, Ghazal khajouei, Mahnaz Amiri

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Grey evaluation model and algorithm of network attack effectiveness by WANG Hui-mei, JIANG Liang, XIAN Ming, WANG Guo-yu

“…Network attack effect evaluation is a complex problem especially in the operation of network attack and de-fence, in which the information is incomplete and vague.The grey system theory is a powerful tool to solve the problem which has a little and uncertain information.A grey evaluation system and model, based on the evaluation index system, was proposed and grey evaluation algorithm was introduced.Using rough set theory, the nonlinear combination weight of evaluation indices was established.A simulation example was also given, which showed that the approach was brief and effective.This approach can be used to evaluate the effectiveness of single attack, as well as to compare like kind attack, so that the attack can be sorted based on the effect evaluation.…”
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Evaluation and Analysis of Multimedia Collaborative Building Design Relying on Particle Swarm Optimization Algorithm by Tao Yang

“…According to the complexity of architectural design evaluation and the nonlinear relationship between related influencing factors, we have studied the principles and methods of applying system analysis, designed comprehensive evaluation models, and comprehensively evaluated architectural design schemes.…”
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Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems by Xiaoping Wang

“…We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition 0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, where μ,ν>1 and 1/μ+1/ν=1 and α(n),β(n), and γ(n) are real-valued functions defined on ℤ.…”
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Distributed relay assignment and power allocation for full-duplex two-way relaying in wireless sensor networks by Song Li, Shuo Li, Yanjing Sun

“…We investigated the weighted sum rate maximization problem under relay assignment constraints and total power constraints on each cooperative link, which turns out to be a mixed integer nonlinear programming problem. To tackle the challenging problem, we propose a distributed relay assignment and power allocation scheme by separating the original problem into two subproblems: relay assignment and power allocation. …”
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Some Improvements of Jensen’s Inequality via 4-Convexity and Applications by Hidayat Ullah, Muhammad Adil Khan, Tareq Saeed, Zaid Mohammed Mohammed Mahdi Sayed

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CRE Solvability, Exact Soliton-Cnoidal Wave Interaction Solutions, and Nonlocal Symmetry for the Modified Boussinesq Equation by Wenguang Cheng, Biao Li

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Modeling and Simulation of Real Estate Valuation Based on Genetic Neural Network Model by Shuli Shen

“…China’s real estate market is developing rapidly, but the house price is abnormal. The nonlinear relationship between housing characteristics and real estate value is difficult to calculate, resulting in the difficulty of house price prediction. …”
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Inverse Optimal Attitude Stabilization of Flexible Spacecraft with Actuator Saturation by Chutiphon Pukdeboon

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EEG electrode setup optimization using feature extraction techniques for neonatal sleep state classification by Hafza Ayesha Siddiqa, Muhammad Farrukh Qureshi, Arsalan Khurshid, Yan Xu, Laishuan Wang, Saadullah Farooq Abbasi, Chen Chen, Wei Chen

“…With the incorporation of time and frequency-domain linear and nonlinear features into sleep staging, newborn sleep dynamics and irregularities can be better understood.…”
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A MODIFIED SHAKEDOWN ANALYSIS FOR KINEMATIC HARDENING PIPING UNDER THERMAL-MECHANICAL LOAD by HUANG Song, CHEN ZhiPing, LI You

“…The idea is to transfer the nonlinear programming resulting from the shakedown analysis with kinematic hardening and temperature-dependent nature into an elastic perfectly plastic one which can be solved with less effort. …”
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Oscillation of Two-Dimensional Neutral Delay Dynamic Systems by Xinli Zhang, Shanliang Zhu

“…We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). …”
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The impact of immune cell interactions on virus quasi-species formation by Ali Moussaoui, Vitaly Volpert

“…Numerical simulations were employed to elucidate the nonlinear dynamics and pattern formation inherent in the nonlocal model.…”
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