Modified Hybrid Discriminant Analysis Methods and Their Applications in Machine Learning by Liwen Huang

“…This paper presents a new hybrid discriminant analysis method, and this method combines the ideas of linearity and nonlinearity to establish a two-layer discriminant model. …”
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On the solvability of a higher-order semilinear ODE by Cristian-Paul Danet

“…The last result is stated when the nonlinearity has asymptotic behaviour at both infinity and zero.…”
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Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems by Bo Zheng

“…A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. …”
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Brezis Nirenberg type results for local non-local problems under mixed boundary conditions by Lovelesh Sharma

“…., the combination of classical Laplace operator and fractional Laplace operator) and critical nonlinearity. Also, we focus on identifying the optimal constant in the mixed Sobolev inequality, which we show is never achieved. …”
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An Existence Result of Positive Solutions for Fully Second-Order Boundary Value Problems by Yongxiang Li, Yaya Shang

“…An existence result of positive solutions is obtained for the fully second-order boundary value problem  -u′′(t)=f(t,u(t),u′(t)),  t∈[0,1],  u(0)=u(1)=0, where f:[0,1]×R+×R→R is continuous. The nonlinearity f(t,x,y) may be sign-changing and superlinear growth on x and y. …”
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A Novel Construction of Substitution Box Based on Polynomial Mapped and Finite Field With Image Encryption Application by Abid Mahboob, Muhammad Asif, Imran Siddique, Aysha Saleem, Muhammad Nadeem, Dariusz Grzelczyk, Jan Awrejcewicz

“…In the modern block cipher, the substitution box (S-box) is a nonlinear constituent that plays a substantial role to create the confusion in ciphertext. …”
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RETRACTED ARTICLE: Associations of composite dietary antioxidant index with cardiovascular disease mortality among patients with type 2 diabetes by Chan Yang, Qiangfei Yang, Xi Peng, Xinqiong Li, Guocheng Rao

“…Restricted cubic spline analyses were utilized to explore the nonlinear association of CDAI with CVD mortality, and nonlinearity was tested by the likelihood ratio test. …”
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U-shaped association between TC/HDL-C ratio and osteoporosis risk in older adults by Chuanwei Zhao, Xiaochun Zhang, Xu Zhang, Bo Zhao, Yane Yang, Mu Lin, Wenli Qiao, Zeyao Hu, Haijie Yang

“…In sex-specific analyses, a U-shaped relationship was found in women, with a threshold at 4.35 (p for nonlinearity = 0.0016), but no significant association was found in men. …”
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DISCRETENESS ERRORS OF FREQUENCY LEVEL GAUGES AND METHODS OF THEIR MINIMIZATION by V. B. Goncharov, V. D. Ivchenko

“…The report examines the main causes of errors in the measurement of the level of rocket fuel components by variable frequency sensors - the speed of the wave propagation, the period of modulation, the nonlinearity of the amplitude-frequency characteristics of the generator and circuits, frequency deviation and difference frequency. …”
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Fuzzy Adaptive Variable Structure Control of Second-Order Robotic Manipulators with Dead Zones by Songyu Wang, Xianmin Hou

“…Our controller is effective for the system with or without sector nonlinearity. Finally, a simulation example is presented to illustrate the correctness of the theoretical derivation.…”
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Global Analysis for Rough Solutions to the Davey-Stewartson System by Han Yang, Xiaoming Fan, Shihui Zhu

“…The new ingredient in this paper is an interaction Morawetz estimate, which generates a new space-time Lt,x4 estimate for nonlinear equation with the relatively general defocusing power nonlinearity.…”
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Uniform Attractors for Nonclassical Diffusion Equations with Memory by Yongqin Xie, Yanan Li, Ye Zeng

“…After that, the existence and the structure of a compact uniform attractor for the nonautonomous nonclassical diffusion equation with fading memory are proved under the following conditions: the nonlinearity f satisfies the polynomial growth of arbitrary order and the time-dependent forcing term g is only translation-bounded in Lloc2(R;L2(Ω)).…”
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Multiplicity results for asymmetric boundary value problems with indefinite weights by Francesca Dalbono

“…We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form u″+f(t,u)=0, u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. …”
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Lyapunov Exponent-Based Study of Chaotic Mechanical Behavior of Concrete under Compression by Yuhu Quan, Xu Yang

“…Chaos theory is advantageous in achieving a deeper understanding of the nonlinearity and randomness of concrete behavior. In this study, the experimental data of concrete under compression were examined and discussed using Lyapunov exponent. …”
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Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions by Motlatsi Molati, Chaudry Masood Khalique

“…We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.…”
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APPLICATIONS OF QUASI-STATIC METHOD IN STATIC FAILURE SIMULATION FOR LARGE AIRCRAFT WINGBOX by YU Ming, LING XiaoTao, WANG QianPing

“…The strength problems of large-aircraft wingbox is complex.Studying the bearing characteristics of wingbox,plays an important role in wing structure refined design,weight optimization and development cost saving.Based on the explicit time integration,this paper simulated the static loading process of typical wingbox section until failure in quasi-static limits,while taking the material nonlinearity and damage characteristics into consideration.Both the strain distribution and the strength prediction agree well with the experimental results.The study provides a reference for evaluating the ultimate strength of aircraft assembly.…”
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Positive Solutions of Fractional Differential Equation with -Laplacian Operator by Teng Ren, Xiaochun Chen

“…In this paper, we study an ecological model arising from ecological economics by mathematical method, that is, study the existence of positive solutions for the fractional differential equation with -Laplacian operator , , , , , and , where are the standard Riemann-Liouville derivatives, -Laplacian operator is defined as , and the nonlinearity may be singular at both and By finding more suitable upper and lower solutions, we omit some key conditions of some existing works, and the existence of positive solution is established.…”
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Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type by W. Weera, P. Niamsup

“…This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable. …”
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Convex Sweeping Processes with Noncompact Perturbations and with Delay in Banach Spaces by A. G. Ibrahim, F. Aladsani

“…The second is to give a technique to overcome the arising problem from the nonlinearity of the normalized mappings, when we deal with sweeping processes with noncompact valued perturbations and associated with a multivalued function depending on time and state.…”
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Construction and Research of Lightweight Cryptography SOPT-S Boxes Based on Inverse Mapping in Galois Field by Zhaolong Fan, Qijian Xu, Yongju Xu, Fei Wang

“…It is shown that the SOPT-S boxes perform better in cryptographic properties such as differential uniformity, algebraic degree and avalanche effect than PRESENT, of which the algebraic degree achieves to n-1, avalanche effect to 1/2 and both of them achieve to the best, besides, it has an equivalent nonlinearity compared with PRESENT. In addition, the hardware overhead is also the same as the latter, so that it can provide a reference for the designing of nonlinear layer of lightweight cryptography algorithm.…”
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