A finite-dimensional reduction method for slightly supercritical elliptic problems by Riccardo Molle, Donato Passaseo

“…A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.…”
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Simulation Analysis of the Dynamic Performance of Multi Tooth Meshing of Filtering Reducer based on ANSYS- LS / DYNA by Lei Xiaochun, Yang Rongsong, Zhu Bingfeng, Liu Qiang, Chen Zhiliang

“…The filtering reducer structure principle and multi tooth elastic meshing effect are introduced,with the help of explicit dynamics software ANSYS / LS- DYNA,the three- dimensional nonlinear finite element contact analysis model is established,the dynamic meshing simulation of gear transmission mechanism under a certain speed and different load torque is carried out,the tooth surface contact stress,tooth root bending stress distribution and the rules of contact force changes under the condition of multi tooth contact with time are obtained,a theoretical basis for further filter reducer gear strength analysis and fatigue life calculation is provided by this method.…”
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Robust H∞ Control Implementation in IFOC for High-Performance Electric Vehicle Induction Motors by Boudallaa Abdelhak, Chennani Mohammed, Belkhadir Ahmed, Rhofir Karim, Belkhayat Driss

“…This approach aims to optimize the motor's dynamic performance, allowing for more precise control of torque and speed. Due to the nonlinear, multivariable, and highly coupled dynamics, induction motors require particularly complex control algorithms. …”
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Optical Measurement of Cable and String Vibration by Y. Achkire, A. Preumont

“…On the one hand, the sensor is used to monitor the cable vibrations of a small scale mock-up of a cable structure in order to validate the nonlinear cable dynamics model. On the other hand, the optical sensor is used to evaluate the performance of an active tendon control algorithm with guaranteed stability properties. …”
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Electrical Switching in Thin Film Structures Based on Transition Metal Oxides by A. Pergament, G. Stefanovich, V. Malinenko, A. Velichko

“…Electrical switching, manifesting itself in the nonlinear current-voltage characteristics with S- and N-type NDR (negative differential resistance), is inherent in a variety of materials, in particular, transition metal oxides. …”
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Finite-Time Synchronizing Control for Chaotic Neural Networks by Chao Zhang, Qiang Guo, Jing Wang

“…A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. …”
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Modeling transcriptional co-regulation of mammalian circadian clock by Yanqin Wang, Xin Ni, Jie Yan, Ling Yang

“…In this paper, a scalar nonlinear differential equation with two delays, modeling the transcriptional co-regulation in mammalian circadian clock, is proposed and analyzed. …”
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FUZZY LOGIC CONTROLLER IMPLEMENTATION FOR PHOTOVOLTAIC STATION by Imad Zein, Yu. N. Petrenko

“…Solar panels have a nonlinear voltage-current characteristic, with a distinct maximum power point (MPP), which depends on the environmental factors, such as temperature and irradiation. …”
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$R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission by Toshikazu Kuniya, Mimmo Iannelli

“…We show that the spectral radius of the Fréchet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less than unity, then the disease-free steady state of the model is globally asymptotically stable, while if the value is greater than unity, then the model has a unique globally asymptotically stable endemic (nontrivial) periodic solution. …”
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Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method by Berna Bülbül, Mehmet Sezer

“…Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. …”
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On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination by Stanislas Ouaro, Ali Traoré

“…We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. …”
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On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems by El-Sayed M. E. Mostafa, Abdallah W. Aboutahoun, Fatma F. S. Omar

“…The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. …”
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New Qualitative Results for Solutions of Functional Differential Equations of Second Order by Cemil Tunç, Sultan Erdur

“…In this paper, we are concerned with the existence of periodic solutions, stability of zero solution, asymptotic stability of zero solution, square integrability of the first derivative of solutions, and boundedness of solutions of nonlinear functional differential equations of second order by the second method of Lyapunov. …”
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Solutions of the Force-Free Duffing-van der Pol Oscillator Equation by Najeeb Alam Khan, Muhammad Jamil, Syed Anwar Ali, Nadeem Alam Khan

“…A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. …”
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Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations by Yunfei Li, Shoufu Li

“…The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. …”
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Robust Adaptive Fractional Fast Terminal Sliding Mode Controller for Microgyroscope by Juntao Fei, Zhe Wang, Xiao Liang

“…Adaptive algorithm is applied to estimate the damping and stiffness coefficients, angular velocity, and the upper bound of the lumped nonlinearities. Numerical simulations are presented to exhibit the validity of the proposed method, and the comparison with the other two methods illustrates its superiority.…”
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Analysis of Dynamics Characteristic of Ring Chain Under Transmission Fault Loading by Song Ruihan, Xue He, Cui Yinghao, Wang Ting, Li Kai

“…Aiming at the transient impact of the abrupt load on the ring chain under the fault of the scraper conveyor chain jammed,taking the Φ18 mm×64 mm C class mining ring chain as the research object,by using the ANSYS/LS-DYNA finite element software,the nonlinear chain contact dynamics analysis under the condition of the chain jammed is performed,the change law of the acceleration,velocity,energy and contact force of the ring chain and the main position of the ring chain damage are obtained. …”
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Mixed Initial-Boundary Value Problem for the Capillary Wave Equation by B. Juarez Campos, Elena Kaikina, Hector F. Ruiz Paredes

“…We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. …”
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Transponder Designs for Harmonic Radar Applications by Kimmo Rasilainen, Ville V. Viikari

“…In harmonic radar, the tag is called a harmonic transponder and the necessary frequency multiplication is implemented using a nonlinear element, such as a Schottky diode. Different applications and operating frequencies of harmonic transponders are presented, along with various tag design aspects. …”
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Fault Feature Extraction of the Gearbox based on Manifold Learning Algorithm by Ma Weijin, Zhang Lin, Zhang Jiping, Huang Bincheng, Luo Chaoyang

“…The manifold learning algorithm is a method of nonlinear data dimensionality reduction and can get available low dimensional geometry,it is also better reflects the nature of things. …”
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