Kinematics and Transmission Performance Analyses of a 2T2R Type 4-DOF Spatial Parallel Manipulator by Haiyan An, Bin Li, Shoujun Wang, Weimin Ge

“…For the inverse position analysis, the explicit expression can be obtained from the independent motion parameters of the given mechanism, and the forward position problem is solved by calculating a set of nonlinear equation systems. Then we obtained the workspace of the mechanism based on the analytic formulae of the inverse displacement. …”
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A New Theoretical Method for Solving Forward Kinematics of the Parallel Mechanisms Based on Transfer Matrix by Jin Wang, Zijian Jing, Junli Guo, Tao Qin, Han Li, Xin Li, Zhenchuang Li, Fanhui Meng, Bo Qi

“…While the existing inverse kinematics solution theory is comprehensive, developing a forward solution model is challenging due to the nonlinear nature of the attitude equation. To address this issue, a new method based on the transfer matrix approach is proposed in this research to calculate the forward kinematics of parallel mechanisms. …”
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A local meshless radial basis functions based method for solving fractional integral equations by Mehdi Radmanesh, Mohammad Ebadi

“…To demonstrate the effectiveness of the LRBFCM, the paper provides test problems encompassing linear, nonlinear, Volterra, and Fredholm types of Fractional Integral Equations (FIEs). …”
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Fuel Costs Minimization on a Steel Billet Reheating Furnace Using Genetic Algorithms by Harley S. O. Santos, Paulo E. M. Almeida, Rodrigo T. N. Cardoso

“…In this study, the operation of a reheating furnace is modeled as a nonlinear optimization problem with the goal of minimizing fuel cost while satisfying a desired discharge temperature. …”
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An Analytical Optimisation Framework for Airport Terminal Capacity Expansion by Sultan Alodhaibi, Robert L. Burdett, Prasad K. D. V. Yarlagadda

“…As this model is stochastic and nonlinear, a Simulated Annealing (SA) metaheuristic was implemented and tested. …”
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Efficient optimisation of physical reservoir computers using only a delayed input by Enrico Picco, Lina Jaurigue, Kathy Lüdge, Serge Massar

“…The experimental system is an optoelectronic setup based on a fiber delay loop and a single nonlinear node. It is tested on several benchmark tasks and reservoir operating conditions. …”
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Efficient Convex Optimization of Reentry Trajectory via the Chebyshev Pseudospectral Method by Chun-Mei Yu, Dang-Jun Zhao, Ye Yang

“…The Chebyshev-Gauss Legend (CGL) node points are used to transcribe the original dynamic constraint into algebraic equality constraint; therefore, a nonlinear programming (NLP) problem is concave and time-consuming to be solved. …”
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Stability, Multistability, and Complexity Analysis in a Dynamic Duopoly Game with Exponential Demand Function by Hui Li, Wei Zhou, Tong Chu

“…In this paper, a discrete-time dynamic duopoly model, with nonlinear demand and cost functions, is established. …”
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Exp-Function Method for a Generalized MKdV Equation by Yuzhen Chai, Tingting Jia, Huiqin Hao, Jianwen Zhang

“…The method constructing soliton solutions in this paper may be useful for the investigations on the other nonlinear mathematical physics model and the conclusions of this paper can give theory support for the study of dynamic features of models in the shallow water.…”
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A Phenomenological Thermal-Mechanical Viscoelastic Constitutive Modeling for Polypropylene Wood Composites by Xiongqi Peng, Hongling Yin, Jun Chen, Xue Liu

“…Based on the Maxwell viscoelastic model, a nonlinear thermal-mechanical viscoelastic constitutive model is developed for the PP wood composite by decoupling the effect of temperature with that of the strain rate. …”
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Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay by M. Rajchakit, P. Niamsup, T. Rojsiraphisal, G. Rajchakit

“…A cost function is considered as a nonlinear performance measure for the closed-loop system. …”
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Physics-Informed Neural Network-Based Input Shaping for Vibration Suppression of Flexible Single-Link Robots by Tingfeng Li, Tengfei Xiao

“…The vibration suppression of flexible robotic arms is challenging due to their nonlinear spatiotemporal dynamics. This paper presents a novel physics-informed neural network (PINN)-based input-shaping method for the vibration suppression problem. …”
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Simulation of commutation process DC traction motor of quarry dump truck by V. V. Kharlamov, Yu. V. Moskalev, S. N. Naiden

“…The article considers a nonlinear multiple regression model based on which a model of the commutation process of the DC traction motor of a quarry dump truck. …”
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Accurate Parameter Estimation for Unbalanced Three-Phase System by Yuan Chen, Hing Cheung So

“…After converting the three-phase waveforms into a pair of orthogonal signals via the αβ-transformation, the nonlinear least squares (NLS) estimator is developed for accurately finding the frequency, phase, and voltage parameters. …”
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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation by Naveed Iqbal, Azmat Ullah Khan Niazi, Ramsha Shafqat, Shamsullah Zaland

“…In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form  0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy metric space and I=0,T is a real line interval. …”
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Using Chebyshev’s polynomials for solving Fredholm integral equations of the second kind by José Antonio Ezquerro, Miguel Ángel Hernández-Verón

“…So, we present a strategy that consists of approximating the kernel of the nonlinear integral equation by a Chebyshev interpolation polynomial, which is separable. …”
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Optical Solutions of the Date–Jimbo–Kashiwara–Miwa Equation via the Extended Direct Algebraic Method by Ghazala Akram, Naila Sajid, Muhammad Abbas, Y. S. Hamed, Khadijah M. Abualnaja

“…In this study, the solutions of 2+1-dimensional nonlinear Date–Jimbo–Kashiwara–Miwa (DJKM) equation are characterized, which can be used in mathematical physics to model water waves with low surface tension and long wavelengths. …”
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Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
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A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term by Shengmao Fu, Ji Liu

“…It is proved that, given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln(1/δ). …”
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Autonomous Close Formation Flight Control with Fixed Wing and Quadrotor Test Beds by Caleb Rice, Yu Gu, Haiyang Chao, Trenton Larrabee, Srikanth Gururajan, Marcello Napolitano, Tanmay Mandal, Matthew Rhudy

“…This paper discusses the implementation and flight testing of nonlinear dynamic inversion (NLDI) controllers for close formation flight (CFF) using two distinct UAV platforms: a set of fixed wing aircraft named “Phastball” and a set of quadrotors named “NEO.” …”
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