Construction of Target Controllable Image Segmentation Model Based on Homotopy Perturbation Technology by Shu-Li Mei

“…The solution of the variational model is the nonlinear PDEs deduced by the variational approach. …”
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Coupled Fixed Point Theorems for Weak Contraction Mappings under F-Invariant Set by Wutiphol Sintunavarat, Yeol Je Cho, Poom Kumam

“…We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. …”
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Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function by Yazdan Jamshidi Khezeli, Hossein Nezamabadi-pour

“…In this work, we improve the performance of FLR classifier by defining a new nonlinear positive valuation function. As a consequence, the modified algorithm achieves better classification results. …”
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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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Analytical Analysis of Fractional-Order Physical Models via a Caputo-Fabrizio Operator by Fatemah Mofarreh, A. M. Zidan, Muhammad Naeem, Rasool Shah, Roman Ullah, Kamsing Nonlaopon

“…Furthermore, due to the straightforward implementation, the proposed method can solve other nonlinear fractional-order problems.…”
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A Fractional-Order Investigation of Vaccinated SARS-CoV-2 Epidemic Model with Caputo Fractional Derivative by Badr Saad T. Alkahtani

“…The whole quantity of each compartment is divided into small parts, and then the sum of these all parts is written as a series solution for each agent of the system, while the nonlinear part is decomposed using the Adomian polynomial. …”
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Research of Grinding Surface Roughness of Face Gear based on Analysis of Orthogonal Experiment by Liu Jinhua, Ming Xingzu, Gao Qin

“…The regression model of grinding wheel speed,feed rate and grinding depth is established by using multivariate nonlinear regression analysis method. The effect status of grinding wheel speed,feed speed and grinding depth on the face gear roughness are analyzed. …”
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Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations by A. R. Seadawy, W. Amer, A. Sayed

“…Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.…”
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Dynamics Characteristic Analysis of Spur Gear Pairs based on Tooth Surface Friction by Lu Fengxia, Wang Haofei, Zhu Rupeng, Bao Heyun, Jiang Huihui

“…A bending-torsional nonlinear dynamics model of the spur gear pair with 6-DOF is established and the dimensionless dynamics equations are derived.The tooth surface friction,time-varying stiffness,gear backlashes as well as gear mesh errors are considered in this model.Based on the location of the contact line,the mathematical expressions of the tooth surface friction and the friction torque are both derived.The effects of tooth surface friction on the dynamic behaviors of the system are studied.The results show that the tooth surface friction can increase the vibration of the system,and the effect is more obvious on the vibration in the perpendicular direction to the meshing line.The degree of the chaotic motion of the system can be reduced by the tooth surface friction,and the bifurcation of the system becomes blurred at the high meshing frequency and chaotic motion appears earlier by the tooth surface friction.…”
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Helicopter Control Energy Reduction Using Moving Horizontal Tail by Tugrul Oktay, Firat Sal

“…For this intention complex, physics-based, control-oriented nonlinear helicopter models are used. Equations of MHT are integrated into these models and they are together linearized around straight level flight condition. …”
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Exact Solutions of Travelling Wave Model via Dynamical System Method by Heng Wang, Longwei Chen, Hongjiang Liu

“…By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrödinger-Boussinesq equations are studied. …”
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Multiple Slip Effects on MHD Unsteady Flow Heat and Mass Transfer Impinging on Permeable Stretching Sheet with Radiation by Fazle Mabood, Stanford Shateyi

“…Suitable similarity variables are used to transform governing partial differential equations into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved numerically by applying an implicit finite difference method with quasi-linearization technique. …”
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Improved Multiple Lyapunov Functions of input-to-output Stability and input-to-state Stability for Switched Systems by Shizhang Chen, Chongyang Ning

“…This paper investigates the Lyapunov characterizations of input-to-output stability (IOS) and input-to-state stability (ISS) for nonlinear switched systems. The restriction on the negativity of derivatives of Lyapunov functions is relaxed; additionally, subsystems are not restricted to be ISS/IOS throughout the state space. …”
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A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems by A. H. Bhrawy, M. A. Alghamdi

“…A new spectral collocation approximation based on the Gauss-Lobatto quadrature nodes of shifted Legendre polynomials is investigated for solving the nonlinear multiterm FDEs. The main advantage of this approximation is that the solution is expanding by a truncated series of Legendre-Galerkin basis functions. …”
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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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Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems by Aziz Belmiloudi

“…Firstly, we introduce the perturbation problem of the nonlinear governing coupled system of equations (the deviation from the desired target). …”
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A Fractional Trust Region Method for Linear Equality Constrained Optimization by Honglan Zhu, Qin Ni, Liwei Zhang, Weiwei Yang

“…These results give the base of further research on nonlinear optimization.…”
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A Robust Control for an Aerial Robot Quadrotor under Wind Gusts by Li Ding, Zhenwei Wang

“…A robust flight controller based on linear active disturbance rejection control (LADRC) is proposed for stability control of an aerial robot quadrotor under wind gusts. The nonlinear dynamical model of the quadrotor, considering the wind disturbance, is firstly established through Newton-Euler method. …”
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Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions by Min Li, Jian-Ping Sun, Ya-Hong Zhao

“…In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. …”
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Multi-label feature selection algorithm based on joint mutual information of max-relevance and min-redundancy by Li ZHANG, Cong WANG

“…Feature selection has played an important role in machine learning and artificial intelligence in the past decades.Many existing feature selection algorithm have chosen some redundant and irrelevant features,which is leading to overestimation of some features.Moreover,more features will significantly slow down the speed of machine learning and lead to classification over-fitting.Therefore,a new nonlinear feature selection algorithm based on forward search was proposed.The algorithm used the theory of mutual information and mutual information to find the optimal subset associated with multi-task labels and reduced the computational complexity.Compared with the experimental results of nine datasets and four different classifiers in UCI,the proposed algorithm is superior to the feature set selected by the original feature set and other feature selection algorithms.…”
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