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Journal articles on the topic 'Nonlinear function'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

WU, Jian, Qingwei CAO, and Hui LI. "AN APPROACH FOR MADM PROBLEMS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS BASED ON NONLINEAR FUNCTIONS." Technological and Economic Development of Economy 22, no. 3 (2015): 336–56. http://dx.doi.org/10.3846/20294913.2014.989931.

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This paper investigates an approach for multiple attribute decision making (MADM) problems with interval-valued intuitionistic fuzzy numbers (IVIFNs). To do that, the nonlinear score, accuracy and hesitation functions of IVIFNs are developed based on the normal distribution. The novelty of these nonlinear functions is that they have an additional variance value, which can have more information to rank IVIFNs than Xu and Chen’s score function and Ye’s accuracy function. Based on these nonlinear functions, a ranking method for IVIFNs is proposed. Furthermore, a nonlinearly optimized model is pro

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2

Baliti, Jamal, Mohamed Hssikou, and Mohammed Alaoui. "Monte Carlo simulation of nonlinear gravity driven Poiseuille–Couette flow in a dilute gas." Monte Carlo Methods and Applications 24, no. 3 (2018): 153–63. http://dx.doi.org/10.1515/mcma-2018-0014.

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Abstract Through the direct simulation Monte Carlo, the Boltzmann equation is solved numerically for dilute hard spheres gas between two infinite parallel plates in relative motion and at the same time the particles feel the action of a uniform body force along the same direction as the moving plate. The study is conducted on the effect of the external force on the nonlinear properties of the Poiseuille–Couette flow. We have been interested in the bulk properties, to inhibit the influence of finite-size effects, while ignoring linear effects like Knudsen boundary layer to investigate the gener

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3

M Ehteshamul Haque, T. "Theoretical Study of the Nonlinear Response Function in Metal Optics." International Journal of Scientific Engineering and Research 4, no. 10 (2016): 123–24. https://doi.org/10.70729/ijser151042.

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4

Landolt, O. "Analog nonlinear function synthesis." IEEE Micro 16, no. 5 (1996): 50–52. http://dx.doi.org/10.1109/40.540080.

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5

Peng, Jiehua, Jiashi Tang, and Zili Chen. "Parameter Identification of Weakly Nonlinear Vibration System in Frequency Domain." Shock and Vibration 11, no. 5-6 (2004): 685–92. http://dx.doi.org/10.1155/2004/634785.

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A new method of identifying parameters of nonlinearly vibrating system in frequency domain is presented in this paper. The problems of parameter identification of the nonlinear dynamic system with nonlinear elastic force or nonlinear damping force are discussed. In the method, the mathematic model of parameter identification is frequency response function. Firstly, by means of perturbation method the frequency response function of weakly nonlinear vibration system is derived. Next, a parameter transformation is made and the frequency response function becomes a linear function of the new param

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6

Ryabov, Vladimir V. "Criteria for maximal nonlinearity of a function over a finite field." Discrete Mathematics and Applications 33, no. 2 (2023): 117–26. http://dx.doi.org/10.1515/dma-2023-0012.

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Abstract An n-place function over a field with q elements is called maximally nonlinear if it has the greatest nonlinearity among all such functions. Criteria and necessary conditions for maximal nonlinearity are obtained, which imply that, for even n, the maximally nonlinear functions are bent functions, but, for q > 2, the known families of bent functions are not maximally nonlinear. For an arbitrary finite field, a relationship between the Hamming distances from a function to all affine mappings and the Fourier spectra of the nontrivial characters of the function are found.

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Leonessa, Alexander, Wassim M. Haddad, and Vijaysekhar Chellaboina. "Nonlinear robust hierarchical control for nonlinear uncertain systems." Mathematical Problems in Engineering 5, no. 6 (2000): 499–542. http://dx.doi.org/10.1155/s1024123x99001210.

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A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuo

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8

Chang, R. J. "Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators." Journal of Applied Mechanics 58, no. 1 (1991): 266–71. http://dx.doi.org/10.1115/1.2897162.

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A new approach based on the maximum entropy method is developed for deriving the stationary probability density function of a stable nonlinear stochastic system. The technique is implemented by employing the density function with undetermined parameters from the entropy method and solving a set of algebraic moment equations from a nonlinear stochastic system for the unknown parameters. For a wide class of stochastic systems with given density functions, an explicit density function of the stochastic system perturbed by a nonlinear function of states and noises can be obtained. Three nonlinear

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9

Abulwafa, Essam M., Mohammed A. Abdou, and Aber H. Mahmoud. "The Variational-Iteration Method to Solve the Nonlinear Boltzmann Equation." Zeitschrift für Naturforschung A 63, no. 3-4 (2008): 131–39. http://dx.doi.org/10.1515/zna-2008-3-403.

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The time-dependent nonlinear Boltzmann equation, which describes the time evolution of a single-particle distribution in a dilute gas of particles interacting only through binary collisions, is considered for spatially homogeneous and inhomogeneous media without external force and energy source. The nonlinear Boltzmann equation is converted to a nonlinear partial differential equation for the generating function of the moments of the distribution function. The variational-iteration method derived by He is used to solve the nonlinear differential equation of the generating function. The moments

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10

Vitanov, Nikolay K., Zlatinka I. Dimitrova, and Kaloyan N. Vitanov. "On the Use of Composite Functions in the Simple Equations Method to Obtain Exact Solutions of Nonlinear Differential Equations." Computation 9, no. 10 (2021): 104. http://dx.doi.org/10.3390/computation9100104.

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We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities. We present an amended version of the methodology, which is based on the use of composite functions. The number of steps of the SEsM was reduced from seven to four in the amended version of the methodology. For the case of nonlinear differential equations with polynomial nonlinearities, SEsM can reduce the solved equations to a system of nonlinear algebraic equations. Each nontrivial solution of this algebraic system leads to an exact s

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11

Rao, Murali, and Zoran Vondraćek. "Nonlinear potentials in function spaces." Nagoya Mathematical Journal 165 (March 2002): 91–116. http://dx.doi.org/10.1017/s0027763000008163.

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We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capacities, equilibrium potentials and measures of finite energy.

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12

Zhou, Hong, Deqing Huang, Wu-Sheng Wang, and Jian-Xin Xu. "Some New Difference Inequalities and an Application to Discrete-Time Control Systems." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/214609.

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Two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

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13

Lawlor, Orion Sky. "GPU-Accelerated Rendering of Unbounded Nonlinear Iterated Function System Fixed Points." ISRN Computer Graphics 2012 (March 20, 2012): 1–17. http://dx.doi.org/10.5402/2012/825782.

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Nonlinear functions, including nonlinear iterated function systems, have interesting fixed points. We present a non-Lipschitz theoretical approach to nonlinear function system fixed points which generalizes to noncontractive functions, compare several methods for evaluating such fixed points on modern graphics hardware, and present a nonlinear generalization of Barnsley’s Deterministic Iteration Algorithm. Unlike the many existing randomized rendering algorithms, this deterministic method avoids noncoherent branching and memory access and takes advantage of programmable texture mapping hardwar

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14

Kavitha, C., and A. Gowrisankar. "Fractional integral approach on nonlinear fractal function and its application." Mathematical Modelling and Control 4, no. 3 (2024): 230–45. http://dx.doi.org/10.3934/mmc.2024019.

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The shape and dimension of the fractal function have been significantly influenced by the scaling factor. This paper investigated the fractional integral of the nonlinear fractal interpolation function corresponding to the iterated function systems employed by Rakotch contraction. We demonstrated how the scaling factors affect the flexibility of fractal functions and their different fractional orders of the Riemann fractional integral using certain numerical examples. The potentiality application of Rakotch contraction of fractal function theory was elucidated based on a comparative analysis o

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15

Grigoraş, Carmen, and Victor Grigoraş. "Multiple Algebraic Function Nonlinear Systems." Bulletin of the Polytechnic Institute of Iași. Electrical Engineering, Power Engineering, Electronics Section 69, no. 2 (2023): 57–69. http://dx.doi.org/10.2478/bipie-2023-0009.

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Abstract In order to obtain a more complex dynamic behaviour for a nonlinear system several methods were used, including higher order design, system parameters variation and connecting analogue and discrete subsystems. The present paper analyses an approach to generate wide bandwidth signals by connecting three elementary algebraic building blocks to obtain a more complex non-linear function to be included in the analogue dynamic system. The resulting non-linear system attractor is presented, its Poincare section is analysed and statistical numerical simulations results are shown to highlight

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16

Roberts, Kathleen, and Kristopher Lee. "Nonlinear isometries between function spaces." Annals of Functional Analysis 8, no. 4 (2017): 460–72. http://dx.doi.org/10.1215/20088752-2017-0010.

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17

Frame, Michael, and Maureen Angers. "Some nonlinear iterated function systems." Computers & Graphics 18, no. 1 (1994): 119–25. http://dx.doi.org/10.1016/0097-8493(94)90123-6.

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18

Li, Zhan, Hong Cheng, and Hongliang Guo. "General Recurrent Neural Network for Solving Generalized Linear Matrix Equation." Complexity 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/9063762.

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This brief proposes a general framework of the nonlinear recurrent neural network for solving online the generalized linear matrix equation (GLME) with global convergence property. If the linear activation function is utilized, the neural state matrix of the nonlinear recurrent neural network can globally and exponentially converge to the unique theoretical solution of GLME. Additionally, as compared with the case of using the linear activation function, two specific types of nonlinear activation functions are proposed for the general nonlinear recurrent neural network model to achieve superio

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19

Afzal, Arfan Raheen, Cheng Dong, and Xuewen Lu. "Estimation of partly linear additive hazards model with left-truncated and right-censored data." Statistical Modelling 17, no. 6 (2017): 423–48. http://dx.doi.org/10.1177/1471082x17705993.

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In this article, we consider an additive hazards semiparametric model for left-truncated and right-censored data where the risk function has a partly linear structure, we call it the partly linear additive hazards model. The nonlinear components are assumed to be B-splines functions, so the model can be viewed as a semiparametric model with an unknown baseline hazard function and a partly linear parametric risk function, which can model both linear and nonlinear covariate effects, hence is more flexible than a purely linear or nonlinear model. We construct a pseudo-score function to estimate t

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20

Hou, Zong Yi, and Wu Sheng Wang. "Difference Inequalities and Application to Discrete-Time Control Systems." Advanced Materials Research 889-890 (February 2014): 978–81. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.978.

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In this paper, two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

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21

Nassirharand, Amir, and Sze Hong Teh. "Describing function-based identification of nonlinear transfer functions for nonlinear systems from experimental/simulation data." International Journal of Modelling, Identification and Control 25, no. 2 (2016): 93. http://dx.doi.org/10.1504/ijmic.2016.075270.

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22

Khurshudyan, Asatur Zh. "New Green’s functions for some nonlinear oscillating systems and related PDEs." International Journal of Modern Physics C 29, no. 04 (2018): 1850032. http://dx.doi.org/10.1142/s0129183118500328.

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During the past three decades, the advantageous concept of the Green’s function has been extended from linear systems to nonlinear ones. At that, there exists a rigorous and an approximate extension. The rigorous extension introduces the so-called backward and forward propagators, which play the same role for nonlinear systems as the Green’s function plays for linear systems. The approximate extension involves the Green’s formula for linear systems with a Green’s function satisfying the corresponding nonlinear equation. For the numerical evaluation of nonlinear ordinary differential equations,

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23

Ryabov, Vladimir G. "Maximally nonlinear functions over finite fields." Discrete Mathematics and Applications 33, no. 1 (2023): 41–53. http://dx.doi.org/10.1515/dma-2023-0005.

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Abstract An n-place function over a field F q $ \mathbf {F}_q $ with q elements is called maximally nonlinear if it has the largest nonlinearity among all q-valued n-place functions. We show that, for even n=2, a function is maximally nonlinear if and only if its nonlinearity is q n − 1 ( q − 1 ) − q n 2 − 1 $ q^{n-1}(q - 1) - q^{\frac n2-1} $ ; for n=1, the corresponding criterion for maximal nonlinearity is q − 2. For q > 2 $ q \gt 2 $ and even n=2, we describe the set of all maximally nonlinear quadratic functions and find its cardinality. In this case, all maximally nonlinear quadratic

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24

Khurshudyan, Asatur Zh. "Nonlinear implicit Green’s functions for numerical approximation of partial differential equations: Generalized Burgers’ equation and nonlinear wave equation with damping." International Journal of Modern Physics C 29, no. 07 (2018): 1850054. http://dx.doi.org/10.1142/s0129183118500547.

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A representation formula for second-order nonhomogeneous nonlinear ordinary differential equations (ODEs) has been recently constructed by M. Frasca using its Green’s function, i.e. the solution of the corresponding nonlinear differential equation with a Dirac delta function instead of its nonhomogeneity. It has been shown that the first-order term–the convolution of the nonlinear Green’s function and the right-hand side, analogous to the Green’s representation formula for linear equations — provides a numerically efficient solution of the original equation, while the higher order terms add co

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25

Villalón and Medina-Rios. "Transfer Function with Nonlinear Characteristics Definition Based on Multidimensional Laplace Transform and its Application to Forced Response Power Systems." Energies 12, no. 21 (2019): 4061. http://dx.doi.org/10.3390/en12214061.

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In this research, the concept of nonlinear transfer function with nonlinear characteristics is introduced through the multidimensional Laplace transform and modal series (MS) method. The method of modal series is applied to the power systems dynamics analysis in order to consider nonlinear oscillations and modal interactions, which contribute to the response of the system's dynamic following disturbances. The method of MS allows the inclusion of input excitation functions obtained as Laplace domain kernels superposed to obtain a transfer function. Applying the Volterra series expansion through

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26

Sun, Chaojiao, Bo Jing, and Zongcheng Liu. "Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function." Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4085929.

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An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorou

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27

Alci, Musa, and Selami Beyhan. "Fuzzy functions with function expansion model for nonlinear system identification." Intelligent Automation & Soft Computing 23, no. 1 (2016): 87–94. http://dx.doi.org/10.1080/10798587.2015.1136107.

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28

Nurhidayat, Irfan, Zijun Hao, Chu-chin Hu, and Jein-Shan Chen. "An ordinary differential equation approach for nonlinear programming and nonlinear complementary problem." International Journal of Industrial Optimization 1, no. 1 (2020): 1. http://dx.doi.org/10.12928/ijio.v1i1.764.

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We consider an ordinary differential equation (ODE) approach for solving non- linear programming (NLP) and nonlinear complementary problem (NCP). The Karush- Kuhn Tucker (KKT) optimality conditions can be converted to NCP. Based on the Fischer-Burmeister (FB) function and the Natural-Residual (NR) function are obtained the new NCP-functions. A special technique is employed to reformulate of the NCP as the system of nonlinear algebraic equations (NAEs) later on reformulated once more by force. of an original time-like function into an ODE. Afterwards, a group preserving scheme (GPS) is a packag

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29

KILIC, RECAI, and FATMA YILDIRIM DALKIRAN. "RECONFIGURABLE IMPLEMENTATIONS OF CHUA'S CIRCUIT." International Journal of Bifurcation and Chaos 19, no. 04 (2009): 1339–50. http://dx.doi.org/10.1142/s0218127409023664.

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Chua's circuit is very suitable as a programmable chaos generator because of its robust nonlinearity. In addition to exhibiting a rich variety of bifurcation and chaos phenomenon, this circuit can be modeled and realized with a fixed main system block and many different nonlinear function blocks such as piecewise-linear function, cubic-like function, piecewise-quadratic function and other trigonometric functions. This paper presents a FPAA (Field Programmable Analog Array) based programmable implementation of Chua's circuit. Nonlinear function blocks used in Chua's circuit are modeled with an

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30

Zhou, Dapeng. "Analysis and Research on Nonlinear Complex Function Approximation Problem Based on Deep Learning." Scientific Programming 2022 (March 10, 2022): 1–10. http://dx.doi.org/10.1155/2022/6559868.

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Shallow models have limited ability to express high-dimensional nonlinear complex functions. Based on deep learning, a Gaussian radial basis function neural network (RBFNN) is proposed, which is an analysis method of nonlinear complex function approximation based on the Gaussian-RBFNN model. The proposed method can approximate single-variable and binary complex nonlinear functions, and the approximation error is less than 0.1, which can achieve the ideal approximation effect. Finally, the proposed method is applied to analyze the nonlinear complex stock prediction approximation problem, and th

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31

Messner, W., and R. Horowitz. "Identification of a Nonlinear Function in a Dynamical System." Journal of Dynamic Systems, Measurement, and Control 115, no. 4 (1993): 587–91. http://dx.doi.org/10.1115/1.2899184.

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Using an adaptive method introduced in (Messner et al., 1991), a standard identification technique for linear systems can be extended to identify nonlinear functions in dynamical systems under a mild condition. Specifically, the assumption is that the nonlinear function can be represented as a integral equation of the first kind. The method identifies the nonlinear function indirectly by estimating the influence function of the integral equation. By analogy to linear methods the kernel of the integral equation serves as the “regressor,” while the influence function is the “parameter” to be ide

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32

Nedeljkov, Marko, and Michael Oberguggenberger. "Ordinary differential equations with delta function terms." Publications de l'Institut Math?matique (Belgrade) 91, no. 105 (2012): 125–35. http://dx.doi.org/10.2298/pim1205125n.

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This article is devoted to nonlinear ordinary differential equations with additive or multiplicative terms consisting of Dirac delta functions or derivatives thereof. Regularizing the delta function terms produces a family of smooth solutions. Conditions on the nonlinear terms, relating to the order of the derivatives of the delta function part, are established so that the regularized solutions converge to a limiting distribution.

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33

Lee, Mi Jin, and Jum-Ran Kang. "General Stability for the Viscoelastic Wave Equation with Nonlinear Time-Varying Delay, Nonlinear Damping and Acoustic Boundary Conditions." Mathematics 11, no. 22 (2023): 4593. http://dx.doi.org/10.3390/math11224593.

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This paper is focused on energy decay rates for the viscoelastic wave equation that includes nonlinear time-varying delay, nonlinear damping at the boundary, and acoustic boundary conditions. We derive general decay rate results without requiring the condition a2>0 and without imposing any restrictive growth assumption on the damping term f1, using the multiplier method and some properties of the convex functions. Here we investigate the relaxation function ψ, namely ψ′(t)≤−μ(t)G(ψ(t)), where G is a convex and increasing function near the origin, and μ is a positive nonincreasing function.

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34

Krzyżak, Adam. "Nonlinear function learning using optimal radial basis function newtworks." Nonlinear Analysis: Theory, Methods & Applications 47, no. 1 (2001): 293–302. http://dx.doi.org/10.1016/s0362-546x(01)00177-8.

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35

So, GunBaek. "Design of an Intelligent NPID Controller Based on Genetic Algorithm for Disturbance Rejection in Single Integrating Process with Time Delay." Journal of Marine Science and Engineering 9, no. 1 (2020): 25. http://dx.doi.org/10.3390/jmse9010025.

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The integrating process with time delay (IPTD) is a fundamentally unstable open-loop system due to poles at the origin of the transfer function, and designing controllers with satisfactory control performance is very difficult because of the associated time delay, which is a nonlinear element. Therefore, this study focuses on the design of an intelligent proportional-integral-derivative (PID) controller to improve the regulatory response performance to disturbance in an IPTD, and addresses problems related to optimally tuning each parameter of the controller with a real coded genetic algorithm

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36

KHASMINSKII, R. "NONLINEAR FILTERING OF SMOOTH SIGNALS." Stochastics and Dynamics 05, no. 01 (2005): 27–35. http://dx.doi.org/10.1142/s0219493705001262.

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A nonlinear online Kalman type filter is proposed for the estimation of unknown function S(t) with the known smoothness β for the diffusion observed process with small, of the order ε2, diffusion coefficient. Assuming that the drift coefficient of the observed process depends on an unknown function S(t), we propose an approach to the analysis of this estimator based on the Lyapunov's functions method. The best possible rate of convergence of risks to 0, as ε → 0, is proven for β ≤ 2.

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Liu, Jianbin, Lei Yang, and Kongqing Yang. "Nonlinear transform and Jacobi elliptic function solutions of nonlinear equations." Chaos, Solitons & Fractals 20, no. 5 (2004): 1157–64. http://dx.doi.org/10.1016/j.chaos.2003.09.038.

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Özeren, M. Sinan, and Nazmi Postacioglu. "Nonlinear landslide tsunami run-up." Journal of Fluid Mechanics 691 (December 13, 2011): 440–60. http://dx.doi.org/10.1017/jfm.2011.482.

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AbstractInhomogeneous nonlinear shallow-water equations are studied using the Carrier–Greenspan approach and the resulting equations are solved analytically. The Carrier–Greenspan transformations are commonly used hodograph transformations that transform the nonlinear shallow-water equations into a set of linear equations in which partial derivatives with respect to two auxiliary variables appear. Yet, when the resulting initial-value problem is treated analytically through the use of Green’s functions, the partial derivatives of the Green’s functions have non-integrable singularities. This ha

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Niezgoda, Marek. "Nonlinear Sherman-type inequalities." Advances in Nonlinear Analysis 9, no. 1 (2018): 168–75. http://dx.doi.org/10.1515/anona-2018-0098.

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Abstract An important class of Schur-convex functions is generated by convex functions via the well-known Hardy–Littlewood–Pólya–Karamata inequality. Sherman’s inequality is a natural generalization of the HLPK inequality. It can be viewed as a comparison of two special inner product expressions induced by a convex function of one variable. In the present note, we extend the Sherman inequality from the (bilinear) inner product to a (nonlinear) map of two vectorial variables satisfying the Leon–Proschan condition. Some applications are shown for directional derivatives and gradients of Schur-co

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Chen, Xiaojiao, Zhe Gao, Ruicheng Ma, and Xiaomin Huang. "Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises." Transactions of the Institute of Measurement and Control 42, no. 9 (2020): 1618–31. http://dx.doi.org/10.1177/0142331219893788.

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Hybrid extended-unscented Kalman filters (HEUKFs) for continuous-time nonlinear fractional-order systems with process and measurement noises are investigated in this paper. The Grünwald-Letnikov difference and the fractional-order average derivative (FOAD) method are adopted to discretize the investigated nonlinear fractional-order system, and the nonlinear functions in the system description are coped with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The first-order Taylor expansion used in the EKF method is performed for the nonlinear function at the current time.

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Ozorio de Almeida, A. M., and O. Brodier. "Nonlinear semiclassical dynamics of open systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1935 (2011): 260–77. http://dx.doi.org/10.1098/rsta.2010.0261.

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A semiclassical approximation for an evolving density operator, driven by a ‘closed’ Hamiltonian and ‘open’ Markovian Lindblad operators, is reviewed. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian is a quadratic function and the Lindblad operators are linear functions of positions and momenta. The semiclassical formulae are interpreted within a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra ‘open’ term in the double Ha

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Frasca, Marco, and Asatur Zh Khurshudyan. "Green’s functions for higher order nonlinear equations." International Journal of Modern Physics C 29, no. 10 (2018): 1850104. http://dx.doi.org/10.1142/s0129183118501048.

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The well-known Green’s function method has been recently generalized to nonlinear second-order differential equations. In this paper, we study possibilities of exact Green’s function solutions of nonlinear differential equations of higher order. We show that, if the nonlinear term satisfies a generalized homogeneity property, then the nonlinear Green’s function can be represented in terms of the homogeneous solution. Specific examples and a numerical analysis support the advantage of the method. We show how, for the Bousinesq and Kortweg–de Vries equations, we are forced to introduce higher or

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Wang, Shujian, Ming Xu, Xunhe Zhang, and Yuting Wang. "Fitting Nonlinear Equations with the Levenberg–Marquardt Method on Google Earth Engine." Remote Sensing 14, no. 9 (2022): 2055. http://dx.doi.org/10.3390/rs14092055.

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Google Earth Engine (GEE) has been widely used to process geospatial data in recent years. Although the current GEE platform includes functions for fitting linear regression models, it does not have the function to fit nonlinear models, limiting the GEE platform’s capacity and application. To circumvent this limitation, this work proposes a general adaptation of the Levenberg–Marquardt (LM) method for fitting nonlinear models to a parallel processing framework and its integration into GEE. We compared two commonly used nonlinear fitting methods, the LM and nonlinear least square (NLS) methods.

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Wang, Shujian, Ming Xu, Xunhe Zhang, and Yuting Wang. "Fitting Nonlinear Equations with the Levenberg–Marquardt Method on Google Earth Engine." Remote Sensing 14, no. 9 (2022): 2055. http://dx.doi.org/10.3390/rs14092055.

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Abstract:

Google Earth Engine (GEE) has been widely used to process geospatial data in recent years. Although the current GEE platform includes functions for fitting linear regression models, it does not have the function to fit nonlinear models, limiting the GEE platform’s capacity and application. To circumvent this limitation, this work proposes a general adaptation of the Levenberg–Marquardt (LM) method for fitting nonlinear models to a parallel processing framework and its integration into GEE. We compared two commonly used nonlinear fitting methods, the LM and nonlinear least square (NLS) methods.

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Maissam Jdid and Florentin Smarandache. "Graphical Method for Solving Neutrosophical Nonlinear Programming Models." Neutrosophic Systems with Applications 9 (September 8, 2023): 41–47. http://dx.doi.org/10.61356/j.nswa.2023.67.

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An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under study is classical data. In this research, we will present a study through, which we present t

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Qin, YongZhou, and Wu-Sheng Wang. "A Generalized Nonlinear Sum-Difference Inequality of Product Form." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/247585.

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We establish a generalized nonlinear discrete inequality of product form, which includes both nonconstant terms outside the sums and composite functions of nonlinear function and unknown function without assumption of monotonicity. Upper bound estimations of unknown functions are given by technique of change of variable, amplification method, difference and summation, inverse function, and the dialectical relationship between constants and variables. Using our result we can solve both the discrete inequality in Pachpatte (1995). Our result can be used as tools in the study of difference equati

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Ram, Dayal Pankaj, Kumar Arun, and Sindhi Chandrawati. "EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION." International Journal of Engineering Technologies and Management Research 5, no. 1 (2018): 1–7. https://doi.org/10.5281/zenodo.1149113.

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<strong><em>The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters</em>.</strong>

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Huang, Shongming, Stephen J. Titus, and Douglas P. Wiens. "Comparison of nonlinear height–diameter functions for major Alberta tree species." Canadian Journal of Forest Research 22, no. 9 (1992): 1297–304. http://dx.doi.org/10.1139/x92-172.

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Twenty nonlinear height–diameter functions were fitted and evaluated for major Alberta species based on a data set consisting of 13 489 felled trees for 16 different species. All functions were fitted using weighted nonlinear least squares regression (wi = 1/DBHi) because of the problem of unequal error variance. The examination and comparison of the weighted mean squared errors, the asymptotic t-statistics for the parameters, and the plots of studentized residuals against the predicted height show that many concave and sigmoidal functions can be used to describe the height–diameter relationsh

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Kurosawa, Kaoru, Takashi Satoh, and Kentaro Yamamoto. "Highly Nonlinear t-Resilient Functions." JUCS - Journal of Universal Computer Science 3, no. (6) (1997): 721–29. https://doi.org/10.3217/jucs-003-06-0721.

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High resilient and high nonlinear Boolean functions are desirable for secure key generators in stream ciphers, for example. This paper first shows that there exists a tradeoff between resiliency and nonlinearity. Then we show a new simple design method for high resilient and high nonlinear Boolean functions. Our method gives higher non- linearity than [Zhang and Zheng 95] while their method gives larger resiliency than our method. Further, the proposed method provides a tradeoff between resiliency t and nonlinearity NF by using an intermediate parameter l. If we choose a large l, then a small

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Mu, Gui, Jun Liu, Zhengde Dai, and Xi Liu. "Combined Exp-Function Ansatz Method and Applications." Abstract and Applied Analysis 2013 (2013): 1–3. http://dx.doi.org/10.1155/2013/234319.

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Our aim is to present a combined Exp-function ansatz method. This method replaces the traditional assumptions of multisolitons by a combination of the hyperbolic functions and triangle functions in Hirota bilinear forms of nonlinear evolution equation. Using this method, we can obtain many new type analytical solutions of various nonlinear evolution equations including multisoliton solutions as well as breath-like solitons solutions. These solutions will exhibit interesting dynamic diversity.

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