Association of the body roundness index with chronic diarrhea and chronic constipation: findings based on the National Health and Nutrition Examination Survey 2005–2010 data by Yinda Wang, Fei Chen, Binzhong Zhang, Zhengwei Song

“…RCS analysis further uncovered statistically significant nonlinear positive associations of BRI and with diarrhea (P = 0.005) and constipation (P = 0.037). …”
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Association of anxiety status and anxiety duration with constipation in adult Americans: a cross-sectional study using data from the NHANES 2007–2010 by Xinran Li, Conghui Bian, Hui Dai, Xingrui Chen, Haihua Qian, Dan Zhang

“…Smoothed curve fitting was applied to investigate both linear and nonlinear associations between anxiety duration and constipation risk. …”
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Associations of comprehensive dietary antioxidant index with postmenopausal femur bone mineral density and osteoporosis: data from the national health and nutrition examination sur... by Jianbo Sun, Jie Wang, Wu Hu, He Huang, Hongmou Zhao

“…Moreover, there were nonlinear relationships between CDAI and risk of osteoporosis. …”
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Effect of Laser Distance Measurement for Fatigue Crack Detection on Aluminium Plate Using Laser Doppler Vibro-Meter by Tino Hermanto, Arya Rudi Nasution, Habib Satria, Hermansyah Hermasnyah, Yopan Rahmad Aldori, Ruztamreen Bin Jenal, Abd Rahman Bin Dullah, Adly Zulqarnain bin Mohamad

“… Fatigue cracks can occur because the material is unable to withstand the load applied repeatedly. A nonlinear vibroacoustic method was introduced to overcome this problem. …”
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Formation of the Educational Trajectory: Educational Motives and Choices in the Narratives of Students from Moscow Leading Universities by A. V. Noskova, D. V. Goloukhova, E. I. Kuzmina

“…Informants described their subjective educational experience as a sequence of choices they made in the space of higher education.Analysis  of  students’  narratives  made  it  possible  to  qualitatively  differentiate  between  linear  and  nonlinear  trajectories,  as  well  as  their  subtypes,  differing  in  their  internal  motivation and educational settings. …”
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The Associations of Platelet Activation and Coagulation Parameters with Obstructive Sleep Apnoea: A Large-Scale Observational Study by Jundong Yang, Wenjun Xue, Zhicheng Wei, Caiqiong Hou, Huaming Zhu, Huajun Xu, Xiaolin Wu, Yunhai Feng, Xinyi Li

“…Conclusion. Our study revealed nonlinear relationships between PDW and APTT, and AHI and ODI, in OSA, with AHI and ODI increasing the risk of an abnormal PDW and thus also the cardiovascular risk. …”
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Green approach to synthesis polymer composites based on chitosan with desired linear and non-linear optical characteristics by Dyari M. Mamand, Sarkawt A. Hussen, Shujahadeen B. Aziz

“…The oscillator’s strength ( $$\:{S}_{0}$$ ) and wavelength ( $$\:{\lambda\:}_{0}$$ ) were determined via the Sellmeier model using the linear refractive index. The first-order nonlinear ( $$\:{\chi\:}^{\left(1\right)}$$ ), second-order non-linear ( $$\:{\chi\:}^{\left(2\right)}$$ ) and third-order nonlinear optical susceptibility ( $$\:{\chi\:}^{\left(3\right)}$$ ) were determined for all the films.…”
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The numerical models of the estimation of the electrooptical parameters of GaAs by Albertas Pincevičius, Rimantas-Jonas Rakauskas, Svajonė Vošterienė

“…The system of the six nonlinear ordinary differen­tial equations is solved. …”
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On Transformation Involving Basic Analogue of Multivariable H-Function by Dinesh Kumar, Frédéric Ayant, Jessada Tariboon

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Compensating Trajectory of a Kind of Long-pitch Constrained Conveyor Chain by Li Shujing, Hong Lin, Liang Yanshu

“…The conveyor chain model which include constrained and free pin is established.Through analyzing each position of pin in static and the movement velocity and displacement of pin in one period are calculated according to its coordinate.The mathematical model of each pin in the state of motion is established and the motion trajectory of free pin should include two parts because of the polygonal action of the chain is proposed.Aiming at the problem of the nonlinear equations in the mathematical model of chain is hard to calculate,a kind of solution method based on fundamental theorem of calculus is presented.Finally,motion trajectory of top and bottom edge free pin is obtained by using the MATLAB point depiction method.A computation method is provided for the analysis of trajectory constrained conveyor chain and the design of constrained trajectory.…”
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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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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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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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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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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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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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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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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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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
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