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exponential model</title> <meta name="description" content="Search results for: nonlinear exponential model"> <meta name="keywords" content="nonlinear exponential model"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="nonlinear exponential model"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 17715</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: nonlinear exponential model</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17715</span> Speeding up Nonlinear Time History Analysis of Base-Isolated Structures Using a Nonlinear Exponential Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nicol%C3%B2%20Vaiana">Nicolò Vaiana</a>, <a href="https://publications.waset.org/abstracts/search?q=Giorgio%20Serino"> Giorgio Serino</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The nonlinear time history analysis of seismically base-isolated structures can require a significant computational effort when the behavior of each seismic isolator is predicted by adopting the widely used differential equation Bouc-Wen model. In this paper, a nonlinear exponential model, able to simulate the response of seismic isolation bearings within a relatively large displacements range, is described and adopted in order to reduce the numerical computations and speed up the nonlinear dynamic analysis. Compared to the Bouc-Wen model, the proposed one does not require the numerical solution of a nonlinear differential equation for each time step of the analysis. The seismic response of a 3d base-isolated structure with a lead rubber bearing system subjected to harmonic earthquake excitation is simulated by modeling each isolator using the proposed analytical model. The comparison of the numerical results and computational time with those obtained by modeling the lead rubber bearings using the Bouc-Wen model demonstrates the good accuracy of the proposed model and its capability to reduce significantly the computational effort of the analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=base%20isolation" title="base isolation">base isolation</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20efficiency" title=" computational efficiency"> computational efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20exponential%20model" title=" nonlinear exponential model"> nonlinear exponential model</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20time%20history%20analysis" title=" nonlinear time history analysis"> nonlinear time history analysis</a> </p> <a href="https://publications.waset.org/abstracts/59057/speeding-up-nonlinear-time-history-analysis-of-base-isolated-structures-using-a-nonlinear-exponential-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59057.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">384</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17714</span> An Advanced Exponential Model for Seismic Isolators Having Hardening or Softening Behavior at Large Displacements</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nicol%C3%B2%20Vaiana">Nicolò Vaiana</a>, <a href="https://publications.waset.org/abstracts/search?q=Giorgio%20Serino"> Giorgio Serino</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=base%20isolation" title="base isolation">base isolation</a>, <a href="https://publications.waset.org/abstracts/search?q=hardening%20behavior" title=" hardening behavior"> hardening behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20exponential%20model" title=" nonlinear exponential model"> nonlinear exponential model</a>, <a href="https://publications.waset.org/abstracts/search?q=seismic%20isolators" title=" seismic isolators"> seismic isolators</a>, <a href="https://publications.waset.org/abstracts/search?q=softening%20behavior" title=" softening behavior"> softening behavior</a> </p> <a href="https://publications.waset.org/abstracts/59055/an-advanced-exponential-model-for-seismic-isolators-having-hardening-or-softening-behavior-at-large-displacements" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59055.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">329</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17713</span> A New Nonlinear State-Space Model and Its Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdullah%20Eqal%20Al%20Mazrooei">Abdullah Eqal Al Mazrooei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems" title="nonlinear systems">nonlinear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=state-space%20model" title=" state-space model"> state-space model</a>, <a href="https://publications.waset.org/abstracts/search?q=Kronecker%20product" title=" Kronecker product"> Kronecker product</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20estimator" title=" nonlinear estimator"> nonlinear estimator</a> </p> <a href="https://publications.waset.org/abstracts/34407/a-new-nonlinear-state-space-model-and-its-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34407.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">691</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17712</span> Nonlinear Dynamic Analysis of Base-Isolated Structures Using a Partitioned Solution Approach and an Exponential Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nicol%C3%B2%20Vaiana">Nicolò Vaiana</a>, <a href="https://publications.waset.org/abstracts/search?q=Filip%20C.%20Filippou"> Filip C. Filippou</a>, <a href="https://publications.waset.org/abstracts/search?q=Giorgio%20Serino"> Giorgio Serino</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=base-isolated%20structures" title="base-isolated structures">base-isolated structures</a>, <a href="https://publications.waset.org/abstracts/search?q=earthquake%20engineering" title=" earthquake engineering"> earthquake engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20time%20integration" title=" mixed time integration"> mixed time integration</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20exponential%20model" title=" nonlinear exponential model"> nonlinear exponential model</a> </p> <a href="https://publications.waset.org/abstracts/58215/nonlinear-dynamic-analysis-of-base-isolated-structures-using-a-partitioned-solution-approach-and-an-exponential-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58215.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">280</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17711</span> Dynamics of a Reaction-Diffusion Problems Modeling Two Predators Competing for a Prey</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Owolabi%20Kolade%20Matthew">Owolabi Kolade Matthew</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotically%20stable" title="asymptotically stable">asymptotically stable</a>, <a href="https://publications.waset.org/abstracts/search?q=coexistence" title=" coexistence"> coexistence</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20time%20differencing%20method" title=" exponential time differencing method"> exponential time differencing method</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20and%20local%20stability" title=" global and local stability"> global and local stability</a>, <a href="https://publications.waset.org/abstracts/search?q=predator-prey%20model" title=" predator-prey model"> predator-prey model</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear" title=" nonlinear"> nonlinear</a>, <a href="https://publications.waset.org/abstracts/search?q=reaction-diffusion%20system" title=" reaction-diffusion system"> reaction-diffusion system</a> </p> <a href="https://publications.waset.org/abstracts/36617/dynamics-of-a-reaction-diffusion-problems-modeling-two-predators-competing-for-a-prey" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36617.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">412</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17710</span> A Study of Population Growth Models and Future Population of India</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sheena%20K.%20J.">Sheena K. J.</a>, <a href="https://publications.waset.org/abstracts/search?q=Jyoti%20Badge"> Jyoti Badge</a>, <a href="https://publications.waset.org/abstracts/search?q=Sayed%20Mohammed%20Zeeshan"> Sayed Mohammed Zeeshan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Comparative Study of Exponential and Logistic Population Growth Models in India India is the second most populous city in the world, just behind China, and is going to be in the first place by next year. The Indian population has remarkably at higher rate than the other countries from the past 20 years. There were many scientists and demographers who has formulated various models of population growth in order to study and predict the future population. Some of the models are Fibonacci population growth model, Exponential growth model, Logistic growth model, Lotka-Volterra model, etc. These models have been effective in the past to an extent in predicting the population. However, it is essential to have a detailed comparative study between the population models to come out with a more accurate one. Having said that, this research study helps to analyze and compare the two population models under consideration - exponential and logistic growth models, thereby identifying the most effective one. Using the census data of 2011, the approximate population for 2016 to 2031 are calculated for 20 Indian states using both the models, compared and recorded the data with the actual population. On comparing the results of both models, it is found that logistic population model is more accurate than the exponential model, and using this model, we can predict the future population in a more effective way. This will give an insight to the researchers about the effective models of population and how effective these population models are in predicting the future population. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=population%20growth" title="population growth">population growth</a>, <a href="https://publications.waset.org/abstracts/search?q=population%20models" title=" population models"> population models</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20model" title=" exponential model"> exponential model</a>, <a href="https://publications.waset.org/abstracts/search?q=logistic%20model" title=" logistic model"> logistic model</a>, <a href="https://publications.waset.org/abstracts/search?q=fibonacci%20model" title=" fibonacci model"> fibonacci model</a>, <a href="https://publications.waset.org/abstracts/search?q=lotka-volterra%20model" title=" lotka-volterra model"> lotka-volterra model</a>, <a href="https://publications.waset.org/abstracts/search?q=future%20population%20prediction" title=" future population prediction"> future population prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=demographers" title=" demographers"> demographers</a> </p> <a href="https://publications.waset.org/abstracts/158205/a-study-of-population-growth-models-and-future-population-of-india" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/158205.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">124</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17709</span> X-Ray Dynamical Diffraction 'Third Order Nonlinear Renninger Effect'</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Minas%20Balyan">Minas Balyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bragg%20diffraction" title="Bragg diffraction">Bragg diffraction</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Takagi%E2%80%99s%20equations" title=" nonlinear Takagi’s equations"> nonlinear Takagi’s equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Renninger%20effect" title=" nonlinear Renninger effect"> nonlinear Renninger effect</a>, <a href="https://publications.waset.org/abstracts/search?q=third%20order%20nonlinearity" title=" third order nonlinearity"> third order nonlinearity</a> </p> <a href="https://publications.waset.org/abstracts/55035/x-ray-dynamical-diffraction-third-order-nonlinear-renninger-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55035.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">385</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17708</span> Forecasting Unemployment Rate in Selected European Countries Using Smoothing Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ksenija%20Dumi%C4%8Di%C4%87">Ksenija Dumičić</a>, <a href="https://publications.waset.org/abstracts/search?q=Anita%20%C4%8Ceh%20%C4%8Casni"> Anita Čeh Časni</a>, <a href="https://publications.waset.org/abstracts/search?q=Berislav%20%C5%BDmuk"> Berislav Žmuk</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this paper is to select the most accurate forecasting method for predicting the future values of the unemployment rate in selected European countries. In order to do so, several forecasting techniques adequate for forecasting time series with trend component, were selected, namely: double exponential smoothing (also known as Holt`s method) and Holt-Winters` method which accounts for trend and seasonality. The results of the empirical analysis showed that the optimal model for forecasting unemployment rate in Greece was Holt-Winters` additive method. In the case of Spain, according to MAPE, the optimal model was double exponential smoothing model. Furthermore, for Croatia and Italy the best forecasting model for unemployment rate was Holt-Winters` multiplicative model, whereas in the case of Portugal the best model to forecast unemployment rate was Double exponential smoothing model. Our findings are in line with European Commission unemployment rate estimates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=European%20Union%20countries" title="European Union countries">European Union countries</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20smoothing%20methods" title=" exponential smoothing methods"> exponential smoothing methods</a>, <a href="https://publications.waset.org/abstracts/search?q=forecast%20accuracy%20unemployment%20rate" title=" forecast accuracy unemployment rate"> forecast accuracy unemployment rate</a> </p> <a href="https://publications.waset.org/abstracts/18328/forecasting-unemployment-rate-in-selected-european-countries-using-smoothing-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18328.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">369</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17707</span> Nonlinear Vibration Analysis of a Functionally Graded Micro-Beam under a Step DC Voltage</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Raheli">Ali Raheli</a>, <a href="https://publications.waset.org/abstracts/search?q=Rahim%20Habibifar"> Rahim Habibifar</a>, <a href="https://publications.waset.org/abstracts/search?q=Behzad%20Mohammadi-Alasti"> Behzad Mohammadi-Alasti</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdi%20Abbasgholipour"> Mahdi Abbasgholipour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=FGM" title="FGM">FGM</a>, <a href="https://publications.waset.org/abstracts/search?q=MEMS" title=" MEMS"> MEMS</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20vibration" title=" nonlinear vibration"> nonlinear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=electrical" title=" electrical"> electrical</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20pull-in%20voltage" title=" dynamic pull-in voltage"> dynamic pull-in voltage</a> </p> <a href="https://publications.waset.org/abstracts/30377/nonlinear-vibration-analysis-of-a-functionally-graded-micro-beam-under-a-step-dc-voltage" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30377.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">456</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17706</span> A Filtering Algorithm for a Nonlinear State-Space Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdullah%20Eqal%20Al%20Mazrooei">Abdullah Eqal Al Mazrooei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kalman%20filter" title="Kalman filter">Kalman filter</a>, <a href="https://publications.waset.org/abstracts/search?q=filtering%20algorithm" title=" filtering algorithm"> filtering algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems" title=" nonlinear systems"> nonlinear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=state-space%20model" title=" state-space model"> state-space model</a> </p> <a href="https://publications.waset.org/abstracts/74331/a-filtering-algorithm-for-a-nonlinear-state-space-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74331.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">376</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17705</span> Collision Avoidance Based on Model Predictive Control for Nonlinear Octocopter Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Do%C4%9Fan%20Y%C4%B1ld%C4%B1z">Doğan Yıldız</a>, <a href="https://publications.waset.org/abstracts/search?q=Aydan%20M%C3%BC%C5%9Ferref%20Erkmen"> Aydan Müşerref Erkmen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The controller of the octocopter is mostly based on the PID controller. For complex maneuvers, PID controllers have limited performance capability like in collision avoidance. When an octocopter needs avoidance from an obstacle, it must instantly show an agile maneuver. Also, this kind of maneuver is affected severely by the nonlinear characteristic of octocopter. When these kinds of limitations are considered, the situation is highly challenging for the PID controller. In the proposed study, these challenges are tried to minimize by using the model predictive controller (MPC) for collision avoidance with a nonlinear octocopter model. The aim is to show that MPC-based collision avoidance has the capability to deal with fast varying conditions in case of obstacle detection and diminish the nonlinear effects of octocopter with varying disturbances. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=model%20predictive%20control" title="model predictive control">model predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20octocopter%20model" title=" nonlinear octocopter model"> nonlinear octocopter model</a>, <a href="https://publications.waset.org/abstracts/search?q=collision%20avoidance" title=" collision avoidance"> collision avoidance</a>, <a href="https://publications.waset.org/abstracts/search?q=obstacle%20detection" title=" obstacle detection"> obstacle detection</a> </p> <a href="https://publications.waset.org/abstracts/150063/collision-avoidance-based-on-model-predictive-control-for-nonlinear-octocopter-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150063.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">191</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17704</span> Modeling Exponential Growth Activity Using Technology: A Research with Bachelor of Business Administration Students</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=V.%20Vargas-Alejo">V. Vargas-Alejo</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20E.%20Montero-Moguel"> L. E. Montero-Moguel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=covariation%20reasoning" title="covariation reasoning">covariation reasoning</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20function" title=" exponential function"> exponential function</a>, <a href="https://publications.waset.org/abstracts/search?q=modeling" title=" modeling"> modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=representations" title=" representations"> representations</a> </p> <a href="https://publications.waset.org/abstracts/126053/modeling-exponential-growth-activity-using-technology-a-research-with-bachelor-of-business-administration-students" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/126053.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">120</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17703</span> Nonlinear Modeling of the PEMFC Based on NNARX Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shan-Jen%20Cheng">Shan-Jen Cheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Te-Jen%20Chang"> Te-Jen Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuang-Hsiung%20Tan">Kuang-Hsiung Tan</a>, <a href="https://publications.waset.org/abstracts/search?q=Shou-Ling%20Kuo">Shou-Ling Kuo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=PEMFC" title="PEMFC">PEMFC</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20modeling" title=" nonlinear modeling"> nonlinear modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=NNARX" title=" NNARX "> NNARX </a> </p> <a href="https://publications.waset.org/abstracts/25225/nonlinear-modeling-of-the-pemfc-based-on-nnarx-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25225.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">381</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17702</span> Sufficient Conditions for Exponential Stability of Stochastic Differential Equations with Non Trivial Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fakhreddin%20Abedi">Fakhreddin Abedi</a>, <a href="https://publications.waset.org/abstracts/search?q=Wah%20June%20Leong"> Wah June Leong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exponential%20stability%20in%20probability" title="exponential stability in probability">exponential stability in probability</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations"> stochastic differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20technique" title=" Lyapunov technique"> Lyapunov technique</a>, <a href="https://publications.waset.org/abstracts/search?q=Ito%27s%20formula" title=" Ito's formula"> Ito's formula</a> </p> <a href="https://publications.waset.org/abstracts/184321/sufficient-conditions-for-exponential-stability-of-stochastic-differential-equations-with-non-trivial-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184321.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">52</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17701</span> Effect of Parameters for Exponential Loads on Voltage Transmission Line with Compensation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benalia%20Nadia">Benalia Nadia</a>, <a href="https://publications.waset.org/abstracts/search?q=Bensiali%20Nadia"> Bensiali Nadia</a>, <a href="https://publications.waset.org/abstracts/search?q=Zerzouri%20Noura"> Zerzouri Noura</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an analysis of the effects of parameters np and nq for exponential load on the transmission line voltage profile, transferred power and transmission losses for different shunt compensation size. For different values for np and nq in which active and reactive power vary with it is terminal voltages as in exponential form, variations of the load voltage for different sizes of shunt capacitors are simulated with a simple two-bus power system using Matlab SimPowerSystems Toolbox. It is observed that the compensation level is significantly affected by the voltage sensitivities of loads. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=static%20load%20model" title="static load model">static load model</a>, <a href="https://publications.waset.org/abstracts/search?q=shunt%20compensation" title=" shunt compensation"> shunt compensation</a>, <a href="https://publications.waset.org/abstracts/search?q=transmission%20system" title=" transmission system"> transmission system</a>, <a href="https://publications.waset.org/abstracts/search?q=exponentiel%20load%20model" title=" exponentiel load model"> exponentiel load model</a> </p> <a href="https://publications.waset.org/abstracts/41469/effect-of-parameters-for-exponential-loads-on-voltage-transmission-line-with-compensation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41469.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">368</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17700</span> New Estimation in Autoregressive Models with Exponential White Noise by Using Reversible Jump MCMC Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Suparman%20Suparman">Suparman Suparman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=autoregressive%20%28AR%29%20model" title="autoregressive (AR) model">autoregressive (AR) model</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20white%20Noise" title=" exponential white Noise"> exponential white Noise</a>, <a href="https://publications.waset.org/abstracts/search?q=bayesian" title=" bayesian"> bayesian</a>, <a href="https://publications.waset.org/abstracts/search?q=reversible%20jump%20Markov%20Chain%20Monte%20Carlo%20%28MCMC%29" title=" reversible jump Markov Chain Monte Carlo (MCMC)"> reversible jump Markov Chain Monte Carlo (MCMC)</a> </p> <a href="https://publications.waset.org/abstracts/71720/new-estimation-in-autoregressive-models-with-exponential-white-noise-by-using-reversible-jump-mcmc-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71720.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">355</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17699</span> An Approach on Robust Multi Inversion of a Nonlinear Model for an Omni-Directional Mobile</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fernando%20P.%20Silva">Fernando P. Silva</a>, <a href="https://publications.waset.org/abstracts/search?q=Valter%20J.%20S.%20Leite"> Valter J. S. Leite</a>, <a href="https://publications.waset.org/abstracts/search?q=Erivelton%20G.%20Nepomuceno"> Erivelton G. Nepomuceno</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a nonlinear controller design for an omnidirectional mobile is presented. The robot controller consists of an inner-loop controller and an outer-loop controller, the ﬁrst is designed using state feedback (robust allocation) and the second controller is designed based on Robust Multi Inversion (RMI) approach. The objective of RMI controller is rendering the robust inversion of the dynamic, when the model is affected by uncertainties. A model nonlinear MIMO of an omni-directional robot (small-league of Robocup) is used to simulate the RMI approach. The parameters of linear and nonlinear model are varied to cause modelling uncertainties among the model and the real model (real system) generating an error in inner-loop controller signal that must be compensated by RMI controller. The simulation test results show that the RMI is capable of compensating the uncertainties and keep the system stable and controlled under uncertainties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20multi%20inversion" title="robust multi inversion">robust multi inversion</a>, <a href="https://publications.waset.org/abstracts/search?q=omni-directional%20robot" title=" omni-directional robot"> omni-directional robot</a>, <a href="https://publications.waset.org/abstracts/search?q=robocup" title=" robocup"> robocup</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20control" title=" nonlinear control"> nonlinear control</a> </p> <a href="https://publications.waset.org/abstracts/7104/an-approach-on-robust-multi-inversion-of-a-nonlinear-model-for-an-omni-directional-mobile" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7104.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">589</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17698</span> Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Triki">H. Triki</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Hamaizi"> Y. Hamaizi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20El-Akrmi"> A. El-Akrmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schr%C3%B6dinger%20equation" title="nonlinear Schrödinger equation">nonlinear Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=high-order%20effects" title=" high-order effects"> high-order effects</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20solution" title=" soliton solution"> soliton solution</a> </p> <a href="https://publications.waset.org/abstracts/11564/soliton-solutions-of-the-higher-order-nonlinear-schrodinger-equation-with-dispersion-effects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11564.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">636</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17697</span> Boundary Feedback Stabilization of an Overhead Crane Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdelhadi%20Elharfi">Abdelhadi Elharfi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A problem of boundary feedback (exponential) stabilization of an overhead crane model represented by a PDE is considered. For any $r>0$, the exponential stability at the desired decay rate $r$ is solved in semi group setting by a collocated-type stabiliser of a target system combined with a term involving the solution of an appropriate PDE. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=feedback%20stabilization" title="feedback stabilization">feedback stabilization</a>, <a href="https://publications.waset.org/abstracts/search?q=semi%20group%20and%20generator" title=" semi group and generator"> semi group and generator</a>, <a href="https://publications.waset.org/abstracts/search?q=overhead%20crane%20system" title=" overhead crane system"> overhead crane system</a> </p> <a href="https://publications.waset.org/abstracts/27507/boundary-feedback-stabilization-of-an-overhead-crane-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27507.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">406</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17696</span> Residual Life Estimation Based on Multi-Phase Nonlinear Wiener Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hao%20Chen">Hao Chen</a>, <a href="https://publications.waset.org/abstracts/search?q=Bo%20Guo"> Bo Guo</a>, <a href="https://publications.waset.org/abstracts/search?q=Ping%20Jiang"> Ping Jiang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi-phase%20nonlinear%20wiener%20process" title="multi-phase nonlinear wiener process">multi-phase nonlinear wiener process</a>, <a href="https://publications.waset.org/abstracts/search?q=residual%20life%20estimation" title=" residual life estimation"> residual life estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood%20estimation" title=" maximum likelihood estimation"> maximum likelihood estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20voltage%20plus%20capacitor" title=" high voltage plus capacitor"> high voltage plus capacitor</a> </p> <a href="https://publications.waset.org/abstracts/45882/residual-life-estimation-based-on-multi-phase-nonlinear-wiener-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45882.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">453</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17695</span> Time Delayed Susceptible-Vaccinated-Infected-Recovered-Susceptible Epidemic Model along with Nonlinear Incidence and Nonlinear Treatment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kanica%20Goel">Kanica Goel</a>, <a href="https://publications.waset.org/abstracts/search?q=Nilam"> Nilam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20incidence%20rate" title="nonlinear incidence rate">nonlinear incidence rate</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20treatment%20rate" title=" nonlinear treatment rate"> nonlinear treatment rate</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20delayed%20SVIRS%20epidemic%20model" title=" time delayed SVIRS epidemic model"> time delayed SVIRS epidemic model</a> </p> <a href="https://publications.waset.org/abstracts/91055/time-delayed-susceptible-vaccinated-infected-recovered-susceptible-epidemic-model-along-with-nonlinear-incidence-and-nonlinear-treatment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91055.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">149</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17694</span> On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Giniatoulline">A. Giniatoulline</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20method" title="Galerkin method">Galerkin method</a>, <a href="https://publications.waset.org/abstracts/search?q=Navier-Stokes%20equations" title=" Navier-Stokes equations"> Navier-Stokes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20partial%20differential%20equations" title=" nonlinear partial differential equations"> nonlinear partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Sobolev%20spaces" title=" Sobolev spaces"> Sobolev spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=stratified%20fluid" title=" stratified fluid"> stratified fluid</a> </p> <a href="https://publications.waset.org/abstracts/52024/on-the-strong-solutions-of-the-nonlinear-viscous-rotating-stratified-fluid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52024.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">309</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17693</span> Forecasting Cancers Cases in Algeria Using Double Exponential Smoothing Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Messis%20A.">Messis A.</a>, <a href="https://publications.waset.org/abstracts/search?q=Adjebli%20A."> Adjebli A.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ayeche%20R."> Ayeche R.</a>, <a href="https://publications.waset.org/abstracts/search?q=Talbi%20M."> Talbi M.</a>, <a href="https://publications.waset.org/abstracts/search?q=Tighilet%20K."> Tighilet K.</a>, <a href="https://publications.waset.org/abstracts/search?q=Louardiane%20M."> Louardiane M.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cancers are the second cause of death worldwide. Prevalence and incidence of cancers is getting increased by aging and population growth. This study aims to predict and modeling the evolution of breast, Colorectal, Lung, Bladder and Prostate cancers over the period of 2014-2019. In this study, data were analyzed using time series analysis with double exponential smoothing method to forecast the future pattern. To describe and fit the appropriate models, Minitab statistical software version 17 was used. Between 2014 and 2019, the overall trend in the raw number of new cancer cases registered has been increasing over time; the change in observations over time has been increasing. Our forecast model is validated since we have good prediction for the period 2020 and data not available for 2021 and 2022. Time series analysis showed that the double exponential smoothing is an efficient tool to model the future data on the raw number of new cancer cases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cancer" title="cancer">cancer</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20series" title=" time series"> time series</a>, <a href="https://publications.waset.org/abstracts/search?q=prediction" title=" prediction"> prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=double%20exponential%20smoothing" title=" double exponential smoothing"> double exponential smoothing</a> </p> <a href="https://publications.waset.org/abstracts/164142/forecasting-cancers-cases-in-algeria-using-double-exponential-smoothing-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/164142.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">88</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17692</span> Nonlinear Mathematical Model of the Rotor Motion in a Thin Hydrodynamic Gap</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jaroslav%20Krutil">Jaroslav Krutil</a>, <a href="https://publications.waset.org/abstracts/search?q=Simona%20Fialov%C3%A1"> Simona Fialová</a>, <a href="https://publications.waset.org/abstracts/search?q="></a>, <a href="https://publications.waset.org/abstracts/search?q=Franti%C5%A1ek%20Pochyl%C3%BD">František Pochylý</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A nonlinear mathematical model of mutual fluid-structure interaction is presented in the work. The model is applicable to the general shape of sealing gaps. An in compressible fluid and turbulent flow is assumed. The shaft carries a rotational and procession motion, the gap is axially flowed through. The achieved results of the additional mass, damping and stiffness matrices may be used in the solution of the rotor dynamics. The usage of this mathematical model is expected particularly in hydraulic machines. The method of control volumes in the ANSYS Fluent was used for the simulation. The obtained results of the pressure and velocity fields are used in the mathematical model of additional effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20mathematical%20model" title="nonlinear mathematical model">nonlinear mathematical model</a>, <a href="https://publications.waset.org/abstracts/search?q=CFD%20modeling" title=" CFD modeling"> CFD modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamic%20sealing%20gap" title=" hydrodynamic sealing gap"> hydrodynamic sealing gap</a>, <a href="https://publications.waset.org/abstracts/search?q=matrices%20of%20mass" title=" matrices of mass"> matrices of mass</a>, <a href="https://publications.waset.org/abstracts/search?q=stiffness" title=" stiffness"> stiffness</a>, <a href="https://publications.waset.org/abstracts/search?q=damping" title=" damping"> damping</a> </p> <a href="https://publications.waset.org/abstracts/23190/nonlinear-mathematical-model-of-the-rotor-motion-in-a-thin-hydrodynamic-gap" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23190.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">535</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17691</span> Nonlinear Observer Canonical Form for Genetic Regulation Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bououden%20Soraya">Bououden Soraya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20observer%20canonical%20form" title="nonlinear observer canonical form">nonlinear observer canonical form</a>, <a href="https://publications.waset.org/abstracts/search?q=observer" title=" observer"> observer</a>, <a href="https://publications.waset.org/abstracts/search?q=design" title=" design"> design</a>, <a href="https://publications.waset.org/abstracts/search?q=gene%20regulation" title=" gene regulation"> gene regulation</a>, <a href="https://publications.waset.org/abstracts/search?q=gene%20expression" title=" gene expression"> gene expression</a> </p> <a href="https://publications.waset.org/abstracts/37920/nonlinear-observer-canonical-form-for-genetic-regulation-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37920.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">432</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17690</span> Stabilization Control of the Nonlinear AIDS Model Based on the Theory of Polynomial Fuzzy Control Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shahrokh%20Barati">Shahrokh Barati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=polynomial%20fuzzy" title="polynomial fuzzy">polynomial fuzzy</a>, <a href="https://publications.waset.org/abstracts/search?q=AIDS" title=" AIDS"> AIDS</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20AIDS%20model" title=" nonlinear AIDS model"> nonlinear AIDS model</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20control%20systems" title=" fuzzy control systems"> fuzzy control systems</a> </p> <a href="https://publications.waset.org/abstracts/36231/stabilization-control-of-the-nonlinear-aids-model-based-on-the-theory-of-polynomial-fuzzy-control-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36231.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">468</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17689</span> Lie Symmetry of a Nonlinear System Characterizing Endemic Malaria</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Maba%20Boniface%20Matadi">Maba Boniface Matadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper analyses the model of Malaria endemic from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the nonlinear model. Furthermore, corresponding determining equations were constructed, and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Malaria model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=group%20theory" title="group theory">group theory</a>, <a href="https://publications.waset.org/abstracts/search?q=lie%20symmetry" title=" lie symmetry"> lie symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20solutions" title=" invariant solutions"> invariant solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=malaria" title=" malaria"> malaria</a> </p> <a href="https://publications.waset.org/abstracts/148583/lie-symmetry-of-a-nonlinear-system-characterizing-endemic-malaria" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148583.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">109</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17688</span> A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tudor%20Barbu">Tudor Barbu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=anisotropic%20diffusion" title="anisotropic diffusion">anisotropic diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20differences" title=" finite differences"> finite differences</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20denoising%20and%20restoration" title=" image denoising and restoration"> image denoising and restoration</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20PDE%20model" title=" nonlinear PDE model"> nonlinear PDE model</a>, <a href="https://publications.waset.org/abstracts/search?q=anisotropic%20diffusion" title=" anisotropic diffusion"> anisotropic diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20approximation%20schemes" title=" numerical approximation schemes"> numerical approximation schemes</a> </p> <a href="https://publications.waset.org/abstracts/48289/a-nonlinear-parabolic-partial-differential-equation-model-for-image-enhancement" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48289.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">313</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17687</span> Identification of Switched Reluctance Motor Parameters Using Exponential Swept-Sine Signal</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdelmalek%20Ouannou">Abdelmalek Ouannou</a>, <a href="https://publications.waset.org/abstracts/search?q=Adil%20Brouri"> Adil Brouri</a>, <a href="https://publications.waset.org/abstracts/search?q=Laila%20Kadi"> Laila Kadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Tarik"> Tarik</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Switched reluctance motor (SRM) has a major interest in a large domain as in electric vehicle driving because of its wide range of speed operation, high performances, low cost, and robustness to run under degraded conditions. The purpose of the paper is to develop a new analytical approach for modeling SRM parameters. Then, an identification scheme is proposed to obtain the SRM parameters. Since the SRM is featured by a highly nonlinear behavior, modeling these devices is difficult. Then, it is convenient to develop an accurate model describing the SRM. Furthermore, it is always operated in the magnetically saturated mode to maximize the energy transfer. Accordingly, it is shown that the SRM can be accurately described by a generalized polynomial Hammerstein model, i.e., the parallel connection of several Hammerstein models having polynomial nonlinearity. Presently an analytical identification method is developed using a chirp excitation signal. Afterward, the parameters of the obtained model have been determined using Finite Element Method analysis. Finally, in order to show the effectiveness of the proposed method, a comparison between the true and estimate models has been performed. The obtained results show that the output responses are very close. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=switched%20reluctance%20motor" title="switched reluctance motor">switched reluctance motor</a>, <a href="https://publications.waset.org/abstracts/search?q=swept-sine%20signal" title=" swept-sine signal"> swept-sine signal</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20Hammerstein%20model" title=" generalized Hammerstein model"> generalized Hammerstein model</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20system" title=" nonlinear system"> nonlinear system</a> </p> <a href="https://publications.waset.org/abstracts/136961/identification-of-switched-reluctance-motor-parameters-using-exponential-swept-sine-signal" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/136961.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">237</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">17686</span> Numerical Solution of Porous Media Equation Using Jacobi Operational Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20porous%20media%20equation" title="nonlinear porous media equation">nonlinear porous media equation</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Jacobi%20polynomials" title=" shifted Jacobi polynomials"> shifted Jacobi polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrix" title=" operational matrix"> operational matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20collocation%20method" title=" spectral collocation method"> spectral collocation method</a> </p> <a href="https://publications.waset.org/abstracts/80603/numerical-solution-of-porous-media-equation-using-jacobi-operational-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80603.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=nonlinear%20exponential%20model&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=nonlinear%20exponential%20model&page=3">3</a></li> <li class="page-item"><a class="page-link" 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