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Journal articles on the topic 'Nonlinear analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 May 2024

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1

Coarita, Ever, and Leonardo Flores. "Nonlinear Analysis of Structures Cable - Truss." International Journal of Engineering and Technology 7, no. 3 (June 2015): 160–69. http://dx.doi.org/10.7763/ijet.2015.v7.786.

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2

Yin, Tao, and Yiming Wang. "Nonlinear analysis and prediction of soybean futures." Agricultural Economics (Zemědělská ekonomika) 67, No. 5 (May 20, 2021): 200–207. http://dx.doi.org/10.17221/480/2020-agricecon.

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We use chaotic artificial neural network (CANN) technology to predict the price of the most widely traded agricultural futures – soybean futures. The nonlinear existence test results show that the time series of soybean futures have multifractal dynamics, long-range dependence, self similarity, and chaos characteristics. This also provides a basis for the construction of a CANN model. Compared with the artificial neural network (ANN) structure as our benchmark system, the predictability of CANN is much higher. The ANN is based on Gaussian kernel function and is only suitable for local approximation of nonstationary signals, so it cannot approach the global nonlinear chaotical hidden pattern. Improving the prediction accuracy of soybean futures prices is of great significance for investors, soybean producers, and decision makers.

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3

Allen, Bradford D., and James Carifio. "Nonlinear Analysis." Evaluation Review 19, no. 1 (February 1995): 64–83. http://dx.doi.org/10.1177/0193841x9501900103.

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4

Guillaume, Philippe. "Nonlinear Eigenproblems." SIAM Journal on Matrix Analysis and Applications 20, no. 3 (January 1999): 575–95. http://dx.doi.org/10.1137/s0895479897324172.

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5

Benilan, P., and P. Wittbold. "Nonlinear Absorptions." Journal of Functional Analysis 114, no. 1 (May 1993): 59–96. http://dx.doi.org/10.1006/jfan.1993.1063.

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6

Owino, Joseph Owuor. "GROUP ANALYSIS OF A NONLINEAR HEAT-LIKE EQUATION." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 13, 2023): 3113–31. http://dx.doi.org/10.47191/ijmcr/v11i1.03.

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We study a nonlinear heat like equation from a lie symmetry stand point. Heat equation have been employed to study ow of current, information and propagation of heat. The Lie group approach is used on the system to obtain symmetry reductions and the reduced systems studied for exact solutions. Solitary waves have been constructed by use of a linear span of time and space translation symmetries. We also compute conservation laws using multiplier approach and by a conservation theorem due to Ibragimov.

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7

Fujino, Naoki, and Mitsuru Yamazaki. "Hyperbolic conservation laws with nonlinear diffusion and nonlinear dispersion." Journal of Differential Equations 228, no. 1 (September 2006): 171–90. http://dx.doi.org/10.1016/j.jde.2006.03.025.

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8

R, Rakesh. "Nonlinear Analysis for Parameter Estimation by Multi Objective Single Variable Inverse Analysis." Journal of Advanced Research in Dynamical and Control Systems 12, SP7 (July 25, 2020): 529–38. http://dx.doi.org/10.5373/jardcs/v12sp7/20202136.

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9

Lin, Yanping, and Hong-Ming Yin. "Nonlinear parabolic equations with nonlinear functionals." Journal of Mathematical Analysis and Applications 168, no. 1 (July 1992): 28–41. http://dx.doi.org/10.1016/0022-247x(92)90187-i.

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10

Song, Jiecheng, and Merry Ma. "Climate Change: Linear and Nonlinear Causality Analysis." Stats 6, no. 2 (May 15, 2023): 626–42. http://dx.doi.org/10.3390/stats6020040.

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The goal of this study is to detect linear and nonlinear causal pathways toward climate change as measured by changes in global mean surface temperature and global mean sea level over time using a data-based approach in contrast to the traditional physics-based models. Monthly data on potential climate change causal factors, including greenhouse gas concentrations, sunspot numbers, humidity, ice sheets mass, and sea ice coverage, from January 2003 to December 2021, have been utilized in the analysis. We first applied the vector autoregressive model (VAR) and Granger causality test to gauge the linear Granger causal relationships among climate factors. We then adopted the vector error correction model (VECM) as well as the autoregressive distributed lag model (ARDL) to quantify the linear long-run equilibrium and the linear short-term dynamics. Cointegration analysis has also been adopted to examine the dual directional Granger causalities. Furthermore, in this work, we have presented a novel pipeline based on the artificial neural network (ANN) and the VAR and ARDL models to detect nonlinear causal relationships embedded in the data. The results in this study indicate that the global sea level rise is affected by changes in ice sheet mass (both linearly and nonlinearly), global mean temperature (nonlinearly), and the extent of sea ice coverage (nonlinearly and weakly); whereas the global mean temperature is affected by the global surface mean specific humidity (both linearly and nonlinearly), greenhouse gas concentration as measured by the global warming potential (both linearly and nonlinearly) and the sunspot number (only nonlinearly and weakly). Furthermore, the nonlinear neural network models tend to fit the data closer than the linear models as expected due to the increased parameter dimension of the neural network models. Given that the information criteria are not generally applicable to the comparison of neural network models and statistical time series models, our next step is to examine the robustness and compare the forecast accuracy of these two models using the soon-available 2022 monthly data.

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11

Hoang, N. S., and Alexander G. Ramm. "A nonlinear inequality." Journal of Mathematical Inequalities, no. 4 (2008): 459–64. http://dx.doi.org/10.7153/jmi-02-40.

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12

Mei, Ming. "Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping." Journal of Differential Equations 247, no. 4 (August 2009): 1275–96. http://dx.doi.org/10.1016/j.jde.2009.04.004.

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13

Lagnese, J. E., and G. Leugering. "Uniform stabilization of a nonlinear beam by nonlinear boundary feedback." Journal of Differential Equations 91, no. 2 (June 1991): 355–88. http://dx.doi.org/10.1016/0022-0396(91)90145-y.

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14

Nakao, Mitsuhiro. "Global attractors for nonlinear wave equations with nonlinear dissipative terms." Journal of Differential Equations 227, no. 1 (August 2006): 204–29. http://dx.doi.org/10.1016/j.jde.2005.09.013.

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15

Goodall, Colin, and Albert Gifi. "Nonlinear Multivariate Analysis." Technometrics 34, no. 3 (August 1992): 357. http://dx.doi.org/10.2307/1270046.

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16

Takane, Yoshio, and Albert Gifi. "Nonlinear Multivariate Analysis." Journal of the American Statistical Association 87, no. 418 (June 1992): 587. http://dx.doi.org/10.2307/2290303.

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17

Kocherlakota, S., and A. Gifi. "Nonlinear Multivariate Analysis." Biometrics 49, no. 3 (September 1993): 956. http://dx.doi.org/10.2307/2532221.

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18

Hill, M. O., and A. Gifi. "Nonlinear Multivariate Analysis." Journal of Ecology 78, no. 4 (December 1990): 1148. http://dx.doi.org/10.2307/2260960.

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19

Toland, J. F. "APPLIED NONLINEAR ANALYSIS." Bulletin of the London Mathematical Society 17, no. 5 (September 1985): 487–89. http://dx.doi.org/10.1112/blms/17.5.487.

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20

Toland, J. F. "NONLINEAR FUNCTIONAL ANALYSIS." Bulletin of the London Mathematical Society 18, no. 5 (September 1986): 522–23. http://dx.doi.org/10.1112/blms/18.5.522.

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21

Semmes, Stephen. "Nonlinear Fourier analysis." Bulletin of the American Mathematical Society 20, no. 1 (January 1, 1989): 1–19. http://dx.doi.org/10.1090/s0273-0979-1989-15681-4.

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22

De Leeuw, J. "Nonlinear Multivariate Analysis." American Journal of Evaluation 11, no. 2 (June 1, 1990): 155–57. http://dx.doi.org/10.1177/109821409001100214.

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23

Handl, Andreas. "Nonlinear multivariate analysis." Computational Statistics & Data Analysis 14, no. 4 (November 1992): 548. http://dx.doi.org/10.1016/0167-9473(92)90072-n.

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24

De Leeuw, J. "Nonlinear multivariate analysis." Evaluation News 11, no. 2 (June 1990): 155–57. http://dx.doi.org/10.1016/0191-8036(90)90050-2.

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25

Van der Schaft, Arjan. "Nonlinear systems analysis." Automatica 30, no. 10 (October 1994): 1631–32. http://dx.doi.org/10.1016/0005-1098(94)90103-1.

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26

Jolliffe, Ian, and A. Gifi. "Nonlinear Multivariate Analysis." Applied Statistics 41, no. 2 (1992): 429. http://dx.doi.org/10.2307/2347573.

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27

De Leeuw, Jan. "Nonlinear multivariate analysis." Evaluation Practice 11, no. 2 (June 1990): 155–57. http://dx.doi.org/10.1016/0886-1633(90)90050-n.

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28

Vatanshenas, Ali. "Nonlinear Analysis of Reinforced Concrete Shear Walls Using Nonlinear Layered Shell Approach." Nordic Concrete Research 65, no. 2 (December 1, 2021): 63–79. http://dx.doi.org/10.2478/ncr-2021-0014.

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Abstract This study discusses nonlinear modelling of a reinforced concrete wall utilizing the nonlinear layered shell approach. Rebar, unconfined and confined concrete behaviours are defined nonlinearly using proposed analytical models in the literature. Then, finite element model is validated using experimental results. It is shown that the nonlinear layered shell approach is capable of estimating wall response (i.e., stiffness, ultimate strength, and cracking pattern) with adequate accuracy and low computational effort. Modal analysis is conducted to evaluate the inherent characteristics of the wall to choose a logical loading pattern for the nonlinear static analysis. Moreover, pushover analysis’ outputs are interpreted comprehensibly from cracking of the concrete until reaching the rupture step by step.

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29

Lan, Shengrui, and Jusheng Yang. "Nonlinear finite element analysis of arch dam — II. Nonlinear analysis." Advances in Engineering Software 28, no. 7 (October 1997): 409–15. http://dx.doi.org/10.1016/s0965-9978(97)00012-4.

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30

Drábek, Pavel. "Two notions which affected nonlinear analysis (Bernard Bolzano lecture)." Mathematica Bohemica 139, no. 4 (2014): 699–711. http://dx.doi.org/10.21136/mb.2014.144146.

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31

Gouskov, A. M., M. A. Guskov, D. D. Tung, and G. Y. Panovko. "Nonlinear Regenerative Dynamics Analysis of the Multicutter Turning Process." Nelineinaya Dinamika 15, no. 2 (2019): 145–58. http://dx.doi.org/10.20537/nd190204.

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32

Vakhnenko, O. O., and V. O. Vakhnenko. "Linear Analysis of Extended Integrable Nonlinear Ladder Network System." Ukrainian Journal of Physics 59, no. 6 (June 2014): 640–49. http://dx.doi.org/10.15407/ujpe59.06.0640.

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33

Mavinga, N., and M. N. Nkashama. "Steklov–Neumann eigenproblems and nonlinear elliptic equations with nonlinear boundary conditions." Journal of Differential Equations 248, no. 5 (March 2010): 1212–29. http://dx.doi.org/10.1016/j.jde.2009.10.005.

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34

Goriely, Alain, and Michael Tabor. "Nonlinear dynamics of filaments II. Nonlinear analysis." Physica D: Nonlinear Phenomena 105, no. 1-3 (June 1997): 45–61. http://dx.doi.org/10.1016/s0167-2789(97)83389-1.

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35

Chen, Su-Huan, Tao Xu, and Zhong-Sheng Liu. "Nonlinear frequency spectrum in nonlinear structural analysis." Computers & Structures 45, no. 3 (October 1992): 553–56. http://dx.doi.org/10.1016/0045-7949(92)90439-7.

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36

Güttel, Stefan, and Françoise Tisseur. "The nonlinear eigenvalue problem." Acta Numerica 26 (May 1, 2017): 1–94. http://dx.doi.org/10.1017/s0962492917000034.

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Nonlinear eigenvalue problems arise in a variety of science and engineering applications, and in the past ten years there have been numerous breakthroughs in the development of numerical methods. This article surveys nonlinear eigenvalue problems associated with matrix-valued functions which depend nonlinearly on a single scalar parameter, with a particular emphasis on their mathematical properties and available numerical solution techniques. Solvers based on Newton’s method, contour integration and sampling via rational interpolation are reviewed. Problems of selecting the appropriate parameters for each of the solver classes are discussed and illustrated with numerical examples. This survey also contains numerous MATLAB code snippets that can be used for interactive exploration of the discussed methods.

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37

Gerasimchuk, V. S., I. V. Gerasimchuk, and N. I. Dranik. "Solutions of Nonlinear Schrodinger Equation with Two Potential Wells in Linear / Nonlinear Media." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 2 (June 25, 2016): 168–76. http://dx.doi.org/10.15407/mag12.02.168.

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38

Alam, Rafikul, and Sk Safique Ahmad. "Sensitivity Analysis of Nonlinear Eigenproblems." SIAM Journal on Matrix Analysis and Applications 40, no. 2 (January 2019): 672–95. http://dx.doi.org/10.1137/17m1153236.

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39

Osborne, Alfred R. "Nonlinear Fourier Analysis: Rogue Waves in Numerical Modeling and Data Analysis." Journal of Marine Science and Engineering 8, no. 12 (December 9, 2020): 1005. http://dx.doi.org/10.3390/jmse8121005.

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Nonlinear Fourier Analysis (NLFA) as developed herein begins with the nonlinear Schrödinger equation in two-space and one-time dimensions (the 2+1 NLS equation). The integrability of the simpler nonlinear Schrödinger equation in one-space and one-time dimensions (1+1 NLS) is an important tool in this analysis. We demonstrate that small-time asymptotic spectral solutions of the 2+1 NLS equation can be constructed as the nonlinear superposition of many 1+1 NLS equations, each corresponding to a particular radial direction in the directional spectrum of the waves. The radial 1+1 NLS equations interact nonlinearly with one another. We determine practical asymptotic spectral solutions of the 2+1 NLS equation that are formed from the ratio of two phase-lagged Riemann theta functions: Surprisingly this construction can be written in terms of generalizations of periodic Fourier series called (1) quasiperiodic Fourier (QPF) series and (2) almost periodic Fourier (APF) series (with appropriate limits in space and time). To simplify the discourse with regard to QPF and APF Fourier series, we call them NLF series herein. The NLF series are the solutions or approximate solutions of the nonlinear dynamics of water waves. These series are indistinguishable in many ways from the linear superposition of sine waves introduced theoretically by Paley and Weiner, and exploited experimentally and theoretically by Barber and Longuet-Higgins assuming random phases. Generally speaking NLF series do not have random phases, but instead employ phase locking. We construct the asymptotic NLF series spectral solutions of 2+1 NLS as a linear superposition of sine waves, with particular amplitudes, frequencies and phases. Because of the phase locking the NLF basis functions consist not only of sine waves, but also of Stokes waves, breather trains, and superbreathers, all of which undergo complex pair-wise nonlinear interactions. Breather trains are known to be associated with rogue waves in solutions of nonlinear wave equations. It is remarkable that complex nonlinear dynamics can be represented as a generalized, linear superposition of sine waves. NLF series that solve nonlinear wave equations offer a significant advantage over traditional periodic Fourier series. We show how NLFA can be applied to numerically model nonlinear wave motions and to analyze experimentally measured wave data. Applications to the analysis of SINTEF wave tank data, measurements from Currituck Sound, North Carolina and to shipboard radar data taken by the U. S. Navy are discussed. The ubiquitous presence of coherent breather packets in many data sets, as analyzed by NLFA methods, has recently led to the discovery of breather turbulence in the ocean: In this case, nonlinear Fourier components occur as strongly interacting, phase locked, densely packed breather modes, in contrast to the previously held incorrect belief that ocean waves are weakly interacting sine waves.

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40

Liu, Xiaofang, and Guodong Sun. "Nonlinear character analysis for bistability in virus–immune dynamics." Future Virology 14, no. 10 (October 2019): 655–62. http://dx.doi.org/10.2217/fvl-2019-0059.

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Structured abstract Aim: The nonlinear characters of two linearly stable equilibrium states (virus and immune) for a theoretical virus-immune model are analyzed. Methods: Conditional nonlinear optimal perturbation (CNOP), Lyapunov method and linear singular vector method. Results & conclusion: Two linearly stable equilibrium states (immune-free and immune) with linear methods are nonlinearly unstable using the CNOP method. When the CNOP-type of initial perturbation is used in the model, the immune-free (immune) equilibrium state will be made into the immune (immune-free) equilibrium state. Through computing the variations of nonlinear terms of the model, the nonlinear effect of immune proliferation plays an important role in abrupt changes of the immune-free equilibrium state compared with the linear term. For the immune equilibrium state, the nonlinear effect of viral replication is also an important factor.

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41

Wu, Xiao Hong, Wen Jie Xu, Bin Wu, and Sheng Wei Qiu. "Apple Grading Using Principal Component Analysis and Kernel Fisher Discriminant Analysis Combined with NIR Spectroscopy." Advanced Materials Research 710 (June 2013): 529–33. http://dx.doi.org/10.4028/www.scientific.net/amr.710.529.

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Principal component analysis (PCA) and kernel Fisher discriminant analysis (KFDA) were applied to grade Fuji apples combined with near infrared reflectance (NIR) spectroscopy. Firstly, PCA was used to reduce the dimensionality of NIR spectra acquired by the Antaris II FT-NIR spectrophotometer on apples. Secondly, nonlinear discriminant information was extracted by kernel Fisher discriminant analysis (KFDA). Finally, the k-nearest neighbors algorithm with leave one out strategy was utilized to classify apple samples into two grades. LDA can only solve linearly separable problems, and it is not suitable in solving some nonlinear problems. But unlike LDA, KFDA can solve nonlinearly separable problems, and it projects data onto a high-dimensional feature space by the nonlinear mapping. Experimental results showed that KFDA achieved higher classification rate compared with LDA.

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42

Hayashi, Nakao, Elena I. Kaikina, and Pavel I. Naumkin. "Subcritical nonlinear heat equation." Journal of Differential Equations 238, no. 2 (July 2007): 366–80. http://dx.doi.org/10.1016/j.jde.2007.04.007.

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43

Ding, Juntang. "Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions." Journal of Function Spaces 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/8107657.

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This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions:g(u)t=∇·au∇u+fu in Ω×0,T, ∂u/∂n=bx,u,t on ∂Ω×(0,T), u(x,0)=u0(x)>0, in Ω¯,whereΩ⊂RN (N≥2)is a bounded domain with smooth boundary∂Ω. We obtain the conditions under which the solutions either exist globally or blow up in a finite time by constructing auxiliary functions and using maximum principles. Moreover, the upper estimates of the “blow-up time,” the “blow-up rate,” and the global solutions are also given.

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44

De Brito, Eliana Henriques. "Nonlinear equations." Applicable Analysis 24, no. 1-2 (January 1987): 13–26. http://dx.doi.org/10.1080/00036818708839653.

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45

DATE, G., M. KRISHNA, and M. V. N. MURTHY. "ASYMPTOTIC ANALYSIS AND SPECTRUM OF THREE ANYONS." International Journal of Modern Physics A 09, no. 15 (June 20, 1994): 2545–61. http://dx.doi.org/10.1142/s0217751x94001011.

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The spectrum of anyons confined in a harmonic oscillator potential shows both linear and nonlinear dependence on the statistical parameter. While the existence of exact linear solutions has been shown analytically, the nonlinear dependence has been arrived at by numerical and/or perturbative methods. We develop a method which shows the possibility of a nonlinearly interpolating spectrum. To be specific we analyze the eigenvalue equation in various asymptotic regions for the three-anyon problem.

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46

Wang, Shu, Jucheng Deng, and Jine Shi. "Doubly Nonlinear Parabolic Equation with Nonlinear Boundary Conditions." Journal of Mathematical Analysis and Applications 255, no. 1 (March 2001): 109–21. http://dx.doi.org/10.1006/jmaa.2000.7179.

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47

Marion, Martine, and Roger Temam. "Nonlinear Galerkin Methods." SIAM Journal on Numerical Analysis 26, no. 5 (October 1989): 1139–57. http://dx.doi.org/10.1137/0726063.

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48

Sampaio, Júlio Cesar Santos, and Igor Leite Freire. "Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/804703.

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The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out.

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49

Nakao, Mitsuhiro. "Global and periodic solutions for nonlinear wave equations with some localized nonlinear dissipation." Journal of Differential Equations 190, no. 1 (May 2003): 81–107. http://dx.doi.org/10.1016/s0022-0396(02)00092-x.

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50

Zhang, Linghai. "Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations." Journal of Differential Equations 263, no. 7 (October 2017): 3627–86. http://dx.doi.org/10.1016/j.jde.2017.02.020.

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