Multidisciplinary Collaborative Reliability Analysis of the Gear Reducer based on Inverse Reliability Strategy by Wang Liangliang, Peng Jinshuan, Shao Yiming

“…The genetic algorithms- based collaborative optimization（ GA- CO） is one of the improved forms of CO that overcomes the difficulty of convergence given the existing of highly nonlinear consistency constraints. The IRS- GA- CO,which not only lifted the coupling between all disciplines to improve the search most probable point,the burden of system- level optimizer also can be significantly reduced. …”
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Weak solutions for a class of quasilinear elliptic equation containing the $p(\cdot )$-Laplacian and the mean curvature operator in a variable exponent Sobolev space by Junichi Aramaki

“…In this paper, we consider the equation for a class of nonlinear operators containing $p(\cdot ) $-Laplacian and mean curvature operator with mixed boundary conditions in a bounded domain $\Omega $ of $\mathbb{R}^N$, under the hypothesis $p(x)>1$ in $\overline{\Omega}$. …”
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On New χ-Fixed Point Results for λ−Υ,χ-Contractions in Complete Metric Spaces with Applications by Babak Mohammadi, Wutiphol Sintunavarat, Vahid Parvaneh

“…Finally, the existence of solutions of nonlinear integral equations is investigated via the theoretical results in this work.…”
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Finite-Time Stability of Large-Scale Systems with Interval Time-Varying Delay in Interconnection by T. La-inchua, P. Niamsup, Xinzhi Liu

“…We investigate finite-time stability of a class of nonlinear large-scale systems with interval time-varying delays in interconnection. …”
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The Exact Solutions of a Diffusive SIR Model via Symmetry Groups by R. Naz, A. G. Johnpillai, F. M. Mahomed

“…The focus of this paper is to investigate the exact solutions of a diffusive susceptible-infectious-recovered (SIR) epidemic model, characterized by a nonlinear incidence. A four-dimensional Lie point symmetry algebra is obtained for this model. …”
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Coupled bidirectional flow for adaptive image interpolation by FU Shu-jun 1, RUAN Qiu-qi 2, MU Cheng-po 3, WANG Wen-qia 1

“…An adaptive coupled bidirectional flow process was presenfed,where an inverse diffusion was performed to enhance edges along the normal directions to the isophote lines（edges）,while a normal diffusion was done to remove ar-tifacts（“jaggies”） along the tangent directions.The two converse diffusion forces were splitted into a coupled form to stop the cancellation between each other.In order to preserve image features,the nonlinear diffusion coefficients were locally adjusted according to the directional derivatives of the image.And then the above process was applied to image interpolation.Experimental results demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations and relative equations.…”
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Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates by Saeed Dinarvand, Abed Moradi

“…The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. …”
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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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Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films by Anza Hafsa, Omar, Mandallena, Jean-Philippe

“…In particular, our results are consistent with one of the basic facts of nonlinear elasticity, namely the necessity of an infinite amount of energy to compress a finite volume of matter into zero volume. …”
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Optimal Control for a Parallel Hybrid Hydraulic Excavator Using Particle Swarm Optimization by Dong-yun Wang, Chen Guan

“…Then, the optimal control problem is addressed, and PSO algorithm is introduced to deal with this nonlinear optimal problem which contains lots of inequality/equality constraints. …”
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Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series by Xiang-Chao Shi, Lan-Lan Huang, Zhen-Guo Deng, Dan Liu

“…In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.…”
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Further Results about Traveling Wave Exact Solutions of the (2+1)-Dimensional Modified KdV Equation by Yang Yang, Jian-ming Qi, Xue-hua Tang, Yong-yi Gu

“…We have faith in that this method exhibited in this paper can be used to solve some nonlinear evolution equations in mathematical physics. …”
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Spectral Element Method for Fractional Klein–Gordon Equations Using Interpolating Scaling Functions by Haifa Bin Jebreen

“…To find the solution, the generalized minimal residual method (GMRES method) and Newton’s method are used in linear and nonlinear forms of this system, respectively. The method’s convergence is proven, and some illustrative examples confirm it. …”
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On a New Reliable Algorithm by A. K. Alomari, M. S. M. Noorani, R. Nazar

“…Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.…”
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Distributed Continuous-Time Containment Control of Heterogeneous Multiagent Systems with Nonconvex Control Input Constraints by Xue Li, Lulu Wang, Yinsen Zhang

“…This paper focuses on studying containment control problem with switching communication graphs of continuous-time heterogeneous multiagent systems where the control inputs are constrained in a nonconvex set. A nonlinear projection algorithm is proposed to address the problem. …”
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A Review on the Control of Second Order Underactuated Mechanical Systems by Soukaina Krafes, Zakaria Chalh, Abdelmjid Saka

“…This paper describes some important classes of two degrees of freedom of underactuated mechanical system and also surveys review of the recent state-of-the-art concerning the mathematical modeling of these systems, their classification, and all the control strategies (linear, nonlinear, and intelligent) that have been made so far (i.e., from the year 2000 to date) to control these systems. …”
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Novel Analysis of Fractional-Order Fifth-Order Korteweg–de Vries Equations by Ahmed B. Khoshaim, Muhammad Naeem, Ali Akgul, Nejib Ghanmi, Shamsullah Zaland

“…In this paper, the ρ-homotopy perturbation transformation method was applied to analysis of fifth-order nonlinear fractional Korteweg–de Vries (KdV) equations. …”
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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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A singularly perturbed SIS model with age structure by Jacek Banasiak, Eddy Kimba Phongi, MirosŁaw Lachowicz

“…Using the Tikhonov theorem we prove that for certain classes of initial conditions the nonlinear structured SIS model can be approximated with very good accuracy by lower dimensional linear models.…”
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In Search of Chaos and Complexity of a Cognitive Language-Learning System by Gaofei Luo, Sayan Mukherjee

“…The whole analysis can be effective to understand the dynamical features and nonlinear structure of the cognitive language-learning model.…”
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