Modification of the Quasilinearization Method for the Inverse Problem by Lenka Celechovská-Kozáková

“…We propose a new modification of Bellman's quasilinearization method such that at any iteration step, it works with an approximate solution of the original nonlinear system and with new approximation of parameters α(k+1) which are close enough to the previous ones. …”
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A Newton-type method and its application by V. Antony Vijesh, P. V. Subrahmanyam

“…We further obtain an existence theorem for a class of nonlinear functional integral equations involving the Urysohn operator.…”
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Global Existence for the 3D Tropical Climate Model with Small Initial Data in H˙1/2ℝ3∗ by Hui Zhang, Juan Xu

“…The well-posedness problem is an important but challenging research topic in nonlinear partial differential equations. In this paper, we establish a global-in-time existence result of strong solutions for small initial data in terms of the H˙1/2ℝ3 norm on three-dimensional tropical climate model with viscosities by derive a blow-up criterion combine with energy estimates. …”
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Operating with External Arguments of Douady and Hubbard by G. Pastor, M. Romera, G. Alvarez, J. Nunez, D. Arroyo, F. Montoya

“…The external arguments of the external rays theory of Douady and Hubbard is a valuable tool in order to analyze the Mandelbrot set, a typical case of discrete dynamical system used to study nonlinear phenomena. We suggest here a general method for the calculation of the external arguments of external rays landing at the hyperbolic components root points of the Mandelbrot set. …”
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Research progress of chaotic secure optical communication by Lilin YI, Junxiang KE

“…For the key technologies and latest research progress on chaotic secure optical communication,chaos generation methods based on different nonlinear components were introduced firstly.Then the research progress of chaotic optical communication was discussed,including how to improve the security level,and how to increase the transmission capacity and distance of chaotic optical communication.At last,the limitations and potentials of chaotic optical communication were discussed,the key technologies and research progress of chaotic secure optical communication were summarized.…”
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Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System by Xia Liu, Jinling Wang

“…A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. …”
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Renormalization group analysis for thermal turbulence by D. N. Riahi

“…Turbulent fluxes for the flow are accounted for by repeatedly recasting the governing equations with the smallest scales represented by effective larger scales. Expressions for nonlinear contributions to eddy viscosity and eddy diffusivity are determined, and leading order contributions due to buoyancy on various results and equations are estimated. …”
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A Modified Hybrid Conjugate Gradient Method for Unconstrained Optimization by Minglei Fang, Min Wang, Min Sun, Rong Chen

“…The nonlinear conjugate gradient algorithms are a very effective way in solving large-scale unconstrained optimization problems. …”
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An Iteration to a Common Point of Solution of Variational Inequality and Fixed Point-Problems in Banach Spaces by H. Zegeye, N. Shahzad

“…Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.…”
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Investigation of Cracking in Reinforced Concrete Structures by Means of Standardized Deformation Models by Mikhail V. Morgunov, Anzhelika A. Lyudkevich

“…For theoretical verification of the values of the moment of cracking, calculation methods based on the use of a nonlinear deformation model are used.A theoretical study of cracking moment using a non-linear deformation model shows that the application of a two-line diagram of concrete deformation allows to obtain the most accurate values of cracking moment.…”
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Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form by Abdelrady Okasha Elnady, M. Fayek Abd Rabbo, Hani M. Negm

“…A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. …”
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator by Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah

“…In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. …”
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On Positive Radial Solutions for a Class of Elliptic Equations by Ying Wu, Guodong Han

“…A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear term fs,u need not to be separated. Several new theorems on the existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. …”
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Global Stability of a Rational Difference Equation by Guo-Mei Tang, Lin-Xia Hu, Gang Ma

“…We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. …”
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Pricing Option with Stochastic Interest Rates and Transaction Costs in Fractional Brownian Markets by Lina Song, Kele Li

“…By the means of the hedging and replicating techniques, the new equations satisfied by zero-coupon bond and the nonlinear equation obeyed by European option are established in succession. …”
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Analytical Solution for the Gross-Pitaevskii Equation in Phase Space and Wigner Function by A. X. Martins, R. A. S. Paiva, G. Petronilo, R. R. Luz, R. G. G. Amorim, S. C. Ulhoa, T. M. R. Filho

“…In this work, we study symplectic unitary representations for the Galilei group. As a consequence a nonlinear Schrödinger equation is derived in phase space. …”
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A network status evaluation method based on random projection by Jinming ZHAO

“…In recent years，machine learning has been widely used in network management.However，the complexity of the communication network is increasing，nonlinear and uncertain factors in the network make the machine learning more difficult.In order to improve the effect of machine learning，a scheme of artificial nervous network based on random projection was proposed.The characteristic of such scheme was the introduction of randomness in machine learning and network topology，which took the learning process more adaptability，and achieve faster and more accurate convergence.…”
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The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation by Nan Li, Shaoyong Lai, Shuang Li, Meng Wu

“…A nonlinear generalization of the Camassa-Holm equation is investigated. …”
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A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation by Liquan Mei, Yali Gao, Zhangxin Chen

“…In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. …”
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The Estimate for Approximation Error of Neural Network with Two Weights by Fanzi Zeng, Yuting Tang

“…We prove that it can limitlessly approach any continuous function from limited close subset of Rm to Rn and any continuous function, which has limit at infinite place, from limitless close subset of Rm to Rn. This extends the nonlinear approximation ability of traditional BP neural network and RBF neural network.…”
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