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normality</title> <meta name="description" content="Search results for: asymptotic normality"> <meta name="keywords" content="asymptotic normality"> <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 class="d-block d-lg-none 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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="asymptotic normality"> <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> 226</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: asymptotic normality</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">226</span> The Effect of Non-Normality on CB-SEM and PLS-SEM Path Estimates</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Z.%20Jannoo">Z. Jannoo</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20W.%20Yap"> B. W. Yap</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Auchoybur"> N. Auchoybur</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Lazim"> M. A. Lazim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The two common approaches to Structural Equation Modeling (SEM) are the Covariance-Based SEM (CB-SEM) and Partial Least Squares SEM (PLS-SEM). There is much debate on the performance of CB-SEM and PLS-SEM for small sample size and when distributions are non-normal. This study evaluates the performance of CB-SEM and PLS-SEM under normality and non-normality conditions via a simulation. Monte Carlo Simulation in R programming language was employed to generate data based on the theoretical model with one endogenous and four exogenous variables. Each latent variable has three indicators. For normal distributions, CB-SEM estimates were found to be inaccurate for small sample size while PLS-SEM could produce the path estimates. Meanwhile, for a larger sample size, CB-SEM estimates have lower variability compared to PLS-SEM. Under non-normality, CB-SEM path estimates were inaccurate for small sample size. However, CB-SEM estimates are more accurate than those of PLS-SEM for sample size of 50 and above. The PLS-SEM estimates are not accurate unless sample size is very large. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CB-SEM" title="CB-SEM">CB-SEM</a>, <a href="https://publications.waset.org/abstracts/search?q=Monte%20Carlo%20simulation" title=" Monte Carlo simulation"> Monte Carlo simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=normality%20conditions" title=" normality conditions"> normality conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=non-normality" title=" non-normality"> non-normality</a>, <a href="https://publications.waset.org/abstracts/search?q=PLS-SEM" title=" PLS-SEM"> PLS-SEM</a> </p> <a href="https://publications.waset.org/abstracts/2399/the-effect-of-non-normality-on-cb-sem-and-pls-sem-path-estimates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2399.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">410</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">225</span> Progressive Type-I Interval Censoring with Binomial Removal-Estimation and Its Properties</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sonal%20Budhiraja">Sonal Budhiraja</a>, <a href="https://publications.waset.org/abstracts/search?q=Biswabrata%20Pradhan"> Biswabrata Pradhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work considers statistical inference based on progressive Type-I interval censored data with random removal. The scheme of progressive Type-I interval censoring with random removal can be described as follows. Suppose n identical items are placed on a test at time T0 = 0 under k pre-fixed inspection times at pre-specified times T1 < T2 < . . . < Tk, where Tk is the scheduled termination time of the experiment. At inspection time Ti, Ri of the remaining surviving units Si, are randomly removed from the experiment. The removal follows a binomial distribution with parameters Si and pi for i = 1, . . . , k, with pk = 1. In this censoring scheme, the number of failures in different inspection intervals and the number of randomly removed items at pre-specified inspection times are observed. Asymptotic properties of the maximum likelihood estimators (MLEs) are established under some regularity conditions. A β-content γ-level tolerance interval (TI) is determined for two parameters Weibull lifetime model using the asymptotic properties of MLEs. The minimum sample size required to achieve the desired β-content γ-level TI is determined. The performance of the MLEs and TI is studied via simulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20normality" title="asymptotic normality">asymptotic normality</a>, <a href="https://publications.waset.org/abstracts/search?q=consistency" title=" consistency"> consistency</a>, <a href="https://publications.waset.org/abstracts/search?q=regularity%20conditions" title=" regularity conditions"> regularity conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation%20study" title=" simulation study"> simulation study</a>, <a href="https://publications.waset.org/abstracts/search?q=tolerance%20interval" title=" tolerance interval"> tolerance interval</a> </p> <a href="https://publications.waset.org/abstracts/47981/progressive-type-i-interval-censoring-with-binomial-removal-estimation-and-its-properties" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47981.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">249</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">224</span> Polar Bergman Polynomials on Domain with Corners</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Laskri%20Yamina">Laskri Yamina</a>, <a href="https://publications.waset.org/abstracts/search?q=Rehouma%20Abdel%20Hamid"> Rehouma Abdel Hamid </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we present a new class named polar of monic orthogonal polynomials with respect to the area measure supported on G, where G is a bounded simply-connected domain in the complex planeℂ. We analyze some open questions and discuss some ideas properties related to solving asymptotic behavior of polar Bergman polynomials over domains with corners and asymptotic behavior of modified Bergman polynomials by affine transforms in variable and polar modified Bergman polynomials by affine transforms in variable. We show that uniform asymptotic of Bergman polynomials over domains with corners and by Pritsker's theorem imply uniform asymptotic for all their derivatives. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bergman%20orthogonal%20polynomials" title="Bergman orthogonal polynomials">Bergman orthogonal polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=polar%20rthogonal%20polynomials" title=" polar rthogonal polynomials"> polar rthogonal polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20behavior" title=" asymptotic behavior"> asymptotic behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=Faber%20polynomials" title=" Faber polynomials"> Faber polynomials</a> </p> <a href="https://publications.waset.org/abstracts/15621/polar-bergman-polynomials-on-domain-with-corners" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15621.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">445</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">223</span> Asymptotic Expansion of the Korteweg-de Vries-Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jian-Jun%20Shu">Jian-Jun Shu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20expansion" title="asymptotic expansion">asymptotic expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Korteweg-de%20Vries-Burgers%20%28KdVB%29%20equation" title=" Korteweg-de Vries-Burgers (KdVB) equation"> Korteweg-de Vries-Burgers (KdVB) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton" title=" soliton"> soliton</a> </p> <a href="https://publications.waset.org/abstracts/78883/asymptotic-expansion-of-the-korteweg-de-vries-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78883.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">249</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">222</span> Boundedness and Asymptotic Behavior of Solutions for Gierer-Meinhardt Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Henine">S. Henine</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Youkana"> A. Youkana</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work is devoted to study the global existence and asymptotic behavior of solutions for Gierer-Meinhardt systems arising in biological phenomena. We prove that the solutions are global and uniformly bounded by a positive constant independent of the time. Our technique is based on Lyapunov functional argument. Under suitable conditions, we established a result on the asymptotic behavior of solutions. These results are valid for any positive continuous initial data, and improve some recently results established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20behavior" title="asymptotic behavior">asymptotic behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=Gierer-Meinhardt%20systems" title=" Gierer-Meinhardt systems"> Gierer-Meinhardt systems</a>, <a href="https://publications.waset.org/abstracts/search?q=global%20existence" title=" global existence"> global existence</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20functional" title=" Lyapunov functional"> Lyapunov functional</a> </p> <a href="https://publications.waset.org/abstracts/39077/boundedness-and-asymptotic-behavior-of-solutions-for-gierer-meinhardt-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39077.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">388</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">221</span> Refined Procedures for Second Order Asymptotic Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gubhinder%20Kundhi">Gubhinder Kundhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20Rilstone"> Paul Rilstone</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=edgeworth%20expansions" title="edgeworth expansions">edgeworth expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20order%20asymptotics" title=" higher order asymptotics"> higher order asymptotics</a>, <a href="https://publications.waset.org/abstracts/search?q=saddlepoint%20expansions" title=" saddlepoint expansions"> saddlepoint expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20instruments" title=" weak instruments"> weak instruments</a> </p> <a href="https://publications.waset.org/abstracts/68155/refined-procedures-for-second-order-asymptotic-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/68155.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">277</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">220</span> A Heteroskedasticity Robust Test for Contemporaneous Correlation in Dynamic Panel Data Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Andreea%20Halunga">Andreea Halunga</a>, <a href="https://publications.waset.org/abstracts/search?q=Chris%20D.%20Orme"> Chris D. Orme</a>, <a href="https://publications.waset.org/abstracts/search?q=Takashi%20Yamagata"> Takashi Yamagata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes a heteroskedasticity-robust Breusch-Pagan test of the null hypothesis of zero cross-section (or contemporaneous) correlation in linear panel-data models, without necessarily assuming independence of the cross-sections. The procedure allows for either fixed, strictly exogenous and/or lagged dependent regressor variables, as well as quite general forms of both non-normality and heteroskedasticity in the error distribution. The asymptotic validity of the test procedure is predicated on the number of time series observations, T, being large relative to the number of cross-section units, N, in that: (i) either N is fixed as T→∞; or, (ii) N²/T→0, as both T and N diverge, jointly, to infinity. Given this, it is not expected that asymptotic theory would provide an adequate guide to finite sample performance when T/N is "small". Because of this, we also propose and establish asymptotic validity of, a number of wild bootstrap schemes designed to provide improved inference when T/N is small. Across a variety of experimental designs, a Monte Carlo study suggests that the predictions from asymptotic theory do, in fact, provide a good guide to the finite sample behaviour of the test when T is large relative to N. However, when T and N are of similar orders of magnitude, discrepancies between the nominal and empirical significance levels occur as predicted by the first-order asymptotic analysis. On the other hand, for all the experimental designs, the proposed wild bootstrap approximations do improve agreement between nominal and empirical significance levels, when T/N is small, with a recursive-design wild bootstrap scheme performing best, in general, and providing quite close agreement between the nominal and empirical significance levels of the test even when T and N are of similar size. Moreover, in comparison with the wild bootstrap "version" of the original Breusch-Pagan test our experiments indicate that the corresponding version of the heteroskedasticity-robust Breusch-Pagan test appears reliable. As an illustration, the proposed tests are applied to a dynamic growth model for a panel of 20 OECD countries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cross-section%20correlation" title="cross-section correlation">cross-section correlation</a>, <a href="https://publications.waset.org/abstracts/search?q=time-series%20heteroskedasticity" title=" time-series heteroskedasticity"> time-series heteroskedasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20panel%20data" title=" dynamic panel data"> dynamic panel data</a>, <a href="https://publications.waset.org/abstracts/search?q=heteroskedasticity%20robust%20Breusch-Pagan%20test" title=" heteroskedasticity robust Breusch-Pagan test "> heteroskedasticity robust Breusch-Pagan test </a> </p> <a href="https://publications.waset.org/abstracts/20403/a-heteroskedasticity-robust-test-for-contemporaneous-correlation-in-dynamic-panel-data-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20403.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">219</span> A Variant of Newton's Method with Free Second-Order Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Young%20Hee%20Geum">Young Hee Geum</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present the iterative method and determine the control parameters to converge cubically for solving nonlinear equations. In addition, we derive the asymptotic error constant. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20error%20constant" title="asymptotic error constant">asymptotic error constant</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20method" title=" iterative method"> iterative method</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20root" title=" multiple root"> multiple root</a>, <a href="https://publications.waset.org/abstracts/search?q=root-finding" title=" root-finding"> root-finding</a>, <a href="https://publications.waset.org/abstracts/search?q=order%20of%20convergent" title=" order of convergent"> order of convergent</a> </p> <a href="https://publications.waset.org/abstracts/10054/a-variant-of-newtons-method-with-free-second-order-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10054.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">293</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">218</span> Efficient Estimation for the Cox Proportional Hazards Cure Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khandoker%20Akib%20Mohammad">Khandoker Akib Mohammad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cox%20PH%20model" title="Cox PH model">Cox PH model</a>, <a href="https://publications.waset.org/abstracts/search?q=cure%20model" title=" cure model"> cure model</a>, <a href="https://publications.waset.org/abstracts/search?q=efficient%20score%20function" title=" efficient score function"> efficient score function</a>, <a href="https://publications.waset.org/abstracts/search?q=EM%20algorithm" title=" EM algorithm"> EM algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=implicit%20function" title=" implicit function"> implicit function</a>, <a href="https://publications.waset.org/abstracts/search?q=profile%20likelihood" title=" profile likelihood"> profile likelihood</a> </p> <a href="https://publications.waset.org/abstracts/124490/efficient-estimation-for-the-cox-proportional-hazards-cure-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124490.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">143</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">217</span> Analysis of an Error Estimate for the Asymptotic Solution of the Heat Conduction Problem in a Dilated Pipe</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20Maru%C5%A1i%C4%87-Paloka">E. Marušić-Paloka</a>, <a href="https://publications.waset.org/abstracts/search?q=I.%20Pa%C5%BEanin"> I. Pažanin</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Pr%C5%A1a"> M. Prša</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Subject of this study is the stationary heat conduction problem through a pipe filled with incompressible viscous fluid. In previous work, we observed the existence and uniqueness theorems for the corresponding boundary-value problem and within we have taken into account the effects of the pipe's dilatation due to the temperature of the fluid inside of the pipe. The main difficulty comes from the fact that flow domain changes depending on the solution of the observed heat equation leading to a non-standard coupled governing problem. The goal of this work is to find solution estimate since the exact solution of the studied problem is not possible to determine. We use an asymptotic expansion in order of a small parameter which is presented as a heat expansion coefficient of the pipe's material. Furthermore, an error estimate is provided for the mentioned asymptotic approximation of the solution for inner area of the pipe. Close to the boundary, problem becomes more complex so different approaches are observed, mainly Theory of Perturbations and Separations of Variables. In view of that, error estimate for the whole approximation will be provided with additional software simulations of gotten situation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20analysis" title="asymptotic analysis">asymptotic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=dilated%20pipe" title=" dilated pipe"> dilated pipe</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimate" title=" error estimate"> error estimate</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20conduction" title=" heat conduction"> heat conduction</a> </p> <a href="https://publications.waset.org/abstracts/77208/analysis-of-an-error-estimate-for-the-asymptotic-solution-of-the-heat-conduction-problem-in-a-dilated-pipe" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77208.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">236</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">216</span> Asymptotic Expansion of Double Oscillatory Integrals: Contribution of Non Stationary Critical Points of the Second Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdallah%20Benaissa">Abdallah Benaissa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider the problem of asymptotics of double oscillatory integrals in the case of critical points of the second kind, the order of contact between the boundary and a level curve of the phase being even, the situation when the order of contact is odd will be studied in other occasions. Complete asymptotic expansions will be derived and the coefficient of the leading term will be computed in terms of the original data of the problem. A multitude of people have studied this problem using a variety of methods, but only in a special case when the order of contact is minimal: the more cited papers are a paper of Jones and Kline and an other one of Chako. These integrals are encountered in many areas of science, especially in problems of diffraction of optics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20expansion" title="asymptotic expansion">asymptotic expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=double%20oscillatory%20integral" title=" double oscillatory integral"> double oscillatory integral</a>, <a href="https://publications.waset.org/abstracts/search?q=critical%20point%20of%20the%20second%20kind" title=" critical point of the second kind"> critical point of the second kind</a>, <a href="https://publications.waset.org/abstracts/search?q=optics%20diffraction" title=" optics diffraction"> optics diffraction</a> </p> <a href="https://publications.waset.org/abstracts/41450/asymptotic-expansion-of-double-oscillatory-integrals-contribution-of-non-stationary-critical-points-of-the-second-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/41450.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">350</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">215</span> Asymptotic Spectral Theory for Nonlinear Random Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Karima%20Kimouche">Karima Kimouche</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider the asymptotic problems in spectral analysis of stationary causal random fields. We impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear random fields. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=spatial%20nonlinear%20processes" title="spatial nonlinear processes">spatial nonlinear processes</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20estimators" title=" spectral estimators"> spectral estimators</a>, <a href="https://publications.waset.org/abstracts/search?q=GMC%20condition" title=" GMC condition"> GMC condition</a>, <a href="https://publications.waset.org/abstracts/search?q=bootstrap%20method" title=" bootstrap method"> bootstrap method</a> </p> <a href="https://publications.waset.org/abstracts/12479/asymptotic-spectral-theory-for-nonlinear-random-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12479.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">451</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">214</span> On Constructing a Cubically Convergent Numerical Method for Multiple Roots</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Young%20Hee%20Geum">Young Hee Geum</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose the numerical method defined by xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20error%20constant" title="asymptotic error constant">asymptotic error constant</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20method" title=" iterative method"> iterative method</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20root" title=" multiple root"> multiple root</a>, <a href="https://publications.waset.org/abstracts/search?q=root-finding" title=" root-finding"> root-finding</a> </p> <a href="https://publications.waset.org/abstracts/4187/on-constructing-a-cubically-convergent-numerical-method-for-multiple-roots" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4187.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">220</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">213</span> Portfolio Optimization under a Hybrid Stochastic Volatility and Constant Elasticity of Variance Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jai%20Heui%20Kim">Jai Heui Kim</a>, <a href="https://publications.waset.org/abstracts/search?q=Sotheara%20Veng"> Sotheara Veng</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies the portfolio optimization problem for a pension fund under a hybrid model of stochastic volatility and constant elasticity of variance (CEV) using asymptotic analysis method. When the volatility component is fast mean-reverting, it is able to derive asymptotic approximations for the value function and the optimal strategy for general utility functions. Explicit solutions are given for the exponential and hyperbolic absolute risk aversion (HARA) utility functions. The study also shows that using the leading order optimal strategy results in the value function, not only up to the leading order, but also up to first order correction term. A practical strategy that does not depend on the unobservable volatility level is suggested. The result is an extension of the Merton's solution when stochastic volatility and elasticity of variance are considered simultaneously. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20analysis" title="asymptotic analysis">asymptotic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=constant%20elasticity%20of%20variance" title=" constant elasticity of variance"> constant elasticity of variance</a>, <a href="https://publications.waset.org/abstracts/search?q=portfolio%20optimization" title=" portfolio optimization"> portfolio optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20optimal%20control" title=" stochastic optimal control"> stochastic optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20volatility" title=" stochastic volatility"> stochastic volatility</a> </p> <a href="https://publications.waset.org/abstracts/50103/portfolio-optimization-under-a-hybrid-stochastic-volatility-and-constant-elasticity-of-variance-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50103.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">299</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">212</span> The Sequential Estimation of the Seismoacoustic Source Energy in C-OTDR Monitoring Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Andrey%20V.%20Timofeev">Andrey V. Timofeev</a>, <a href="https://publications.waset.org/abstracts/search?q=Dmitry%20V.%20Egorov"> Dmitry V. Egorov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in the form of the prior prescribed size of confidence regions, and prescribed confidence coefficient value. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonparametric%20estimation" title="nonparametric estimation">nonparametric estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=sequential%20confidence%20estimation" title=" sequential confidence estimation"> sequential confidence estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=multichannel%20monitoring%20systems" title=" multichannel monitoring systems"> multichannel monitoring systems</a>, <a href="https://publications.waset.org/abstracts/search?q=C-OTDR-system" title=" C-OTDR-system"> C-OTDR-system</a>, <a href="https://publications.waset.org/abstracts/search?q=non-lineary%20regression" title=" non-lineary regression"> non-lineary regression</a> </p> <a href="https://publications.waset.org/abstracts/35690/the-sequential-estimation-of-the-seismoacoustic-source-energy-in-c-otdr-monitoring-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35690.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">356</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">211</span> Analysis of the Secondary Stationary Flow Around an Oscillating Circular Cylinder</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Artem%20Nuriev">Artem Nuriev</a>, <a href="https://publications.waset.org/abstracts/search?q=Olga%20Zaitseva"> Olga Zaitseva</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is devoted to the study of a viscous incompressible flow around a circular cylinder performing harmonic oscillations, especially the steady streaming phenomenon. The research methodology is based on the asymptotic explanation method combined with the computational bifurcation analysis. Present studies allow to identify several regimes of the secondary streaming with different flow structures. The results of the research are in good agreement with experimental and numerical simulation data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=oscillating%20cylinder" title="oscillating cylinder">oscillating cylinder</a>, <a href="https://publications.waset.org/abstracts/search?q=secondary%20streaming" title=" secondary streaming"> secondary streaming</a>, <a href="https://publications.waset.org/abstracts/search?q=flow%20regimes" title=" flow regimes"> flow regimes</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20and%20bifurcation%20analysis" title=" asymptotic and bifurcation analysis"> asymptotic and bifurcation analysis</a> </p> <a href="https://publications.waset.org/abstracts/15706/analysis-of-the-secondary-stationary-flow-around-an-oscillating-circular-cylinder" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15706.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">435</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">210</span> High Accuracy Analytic Approximations for Modified Bessel Functions I₀(x)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin">Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass"> Fernando Maass</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20approximations" title="analytic approximations">analytic approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical-physics%20applications" title=" mathematical-physics applications"> mathematical-physics applications</a>, <a href="https://publications.waset.org/abstracts/search?q=quasi-rational%20functions" title=" quasi-rational functions"> quasi-rational functions</a>, <a href="https://publications.waset.org/abstracts/search?q=special%20functions" title=" special functions"> special functions</a> </p> <a href="https://publications.waset.org/abstracts/77484/high-accuracy-analytic-approximations-for-modified-bessel-functions-i0x" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77484.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">251</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">209</span> Resolution and Experimental Validation of the Asymptotic Model of a Viscous Laminar Supersonic Flow around a Thin Airfoil</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eddegdag%20Nasser">Eddegdag Nasser</a>, <a href="https://publications.waset.org/abstracts/search?q=Naamane%20Azzeddine"> Naamane Azzeddine</a>, <a href="https://publications.waset.org/abstracts/search?q=Radouani%20Mohammed"> Radouani Mohammed</a>, <a href="https://publications.waset.org/abstracts/search?q=Ensam%20Meknes"> Ensam Meknes</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we are interested in the asymptotic modeling of the two-dimensional stationary supersonic flow of a viscous compressible fluid around wing airfoil. The aim of this article is to solve the partial differential equations of the flow far from the leading edge and near the wall using the triple-deck technique is what brought again in precision according to the principle of least degeneration. In order to validate our theoretical model, these obtained results will be compared with the experimental results. The comparison of the results of our model with experimentation has shown that they are quantitatively acceptable compared to the obtained experimental results. The experimental study was conducted using the AF300 supersonic wind tunnel and a NACA Reduced airfoil model with two pressure Taps on extrados. In this experiment, we have considered the incident upstream supersonic Mach number over a dissymmetric NACA airfoil wing. The validation and the accuracy of the results support our model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=supersonic" title="supersonic">supersonic</a>, <a href="https://publications.waset.org/abstracts/search?q=viscous" title=" viscous"> viscous</a>, <a href="https://publications.waset.org/abstracts/search?q=triple%20deck%20technique" title=" triple deck technique"> triple deck technique</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20methods" title=" asymptotic methods"> asymptotic methods</a>, <a href="https://publications.waset.org/abstracts/search?q=AF300%20supersonic%20wind%20tunnel" title=" AF300 supersonic wind tunnel"> AF300 supersonic wind tunnel</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20airfoil%20model" title=" reduced airfoil model"> reduced airfoil model</a> </p> <a href="https://publications.waset.org/abstracts/141179/resolution-and-experimental-validation-of-the-asymptotic-model-of-a-viscous-laminar-supersonic-flow-around-a-thin-airfoil" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/141179.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">240</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">208</span> Validation of Asymptotic Techniques to Predict Bistatic Radar Cross Section</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Pienaar">M. Pienaar</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20W.%20Odendaal"> J. W. Odendaal</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20C.%20Smit"> J. C. Smit</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Joubert"> J. Joubert</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Simulations are commonly used to predict the bistatic radar cross section (RCS) of military targets since characterization measurements can be expensive and time consuming. It is thus important to accurately predict the bistatic RCS of targets. Computational electromagnetic (CEM) methods can be used for bistatic RCS prediction. CEM methods are divided into full-wave and asymptotic methods. Full-wave methods are numerical approximations to the exact solution of Maxwell’s equations. These methods are very accurate but are computationally very intensive and time consuming. Asymptotic techniques make simplifying assumptions in solving Maxwell's equations and are thus less accurate but require less computational resources and time. Asymptotic techniques can thus be very valuable for the prediction of bistatic RCS of electrically large targets, due to the decreased computational requirements. This study extends previous work by validating the accuracy of asymptotic techniques to predict bistatic RCS through comparison with full-wave simulations as well as measurements. Validation is done with canonical structures as well as complex realistic aircraft models instead of only looking at a complex slicy structure. The slicy structure is a combination of canonical structures, including cylinders, corner reflectors and cubes. Validation is done over large bistatic angles and at different polarizations. Bistatic RCS measurements were conducted in a compact range, at the University of Pretoria, South Africa. The measurements were performed at different polarizations from 2 GHz to 6 GHz. Fixed bistatic angles of β = 30.8°, 45° and 90° were used. The measurements were calibrated with an active calibration target. The EM simulation tool FEKO was used to generate simulated results. The full-wave multi-level fast multipole method (MLFMM) simulated results together with the measured data were used as reference for validation. The accuracy of physical optics (PO) and geometrical optics (GO) was investigated. Differences relating to amplitude, lobing structure and null positions were observed between the asymptotic, full-wave and measured data. PO and GO were more accurate at angles close to the specular scattering directions and the accuracy seemed to decrease as the bistatic angle increased. At large bistatic angles PO did not perform well due to the shadow regions not being treated appropriately. PO also did not perform well for canonical structures where multi-bounce was the main scattering mechanism. PO and GO do not account for diffraction but these inaccuracies tended to decrease as the electrical size of objects increased. It was evident that both asymptotic techniques do not properly account for bistatic structural shadowing. Specular scattering was calculated accurately even if targets did not meet the electrically large criteria. It was evident that the bistatic RCS prediction performance of PO and GO depends on incident angle, frequency, target shape and observation angle. The improved computational efficiency of the asymptotic solvers yields a major advantage over full-wave solvers and measurements; however, there is still much room for improvement of the accuracy of these asymptotic techniques. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20techniques" title="asymptotic techniques">asymptotic techniques</a>, <a href="https://publications.waset.org/abstracts/search?q=bistatic%20RCS" title=" bistatic RCS"> bistatic RCS</a>, <a href="https://publications.waset.org/abstracts/search?q=geometrical%20optics" title=" geometrical optics"> geometrical optics</a>, <a href="https://publications.waset.org/abstracts/search?q=physical%20optics" title=" physical optics"> physical optics</a> </p> <a href="https://publications.waset.org/abstracts/58156/validation-of-asymptotic-techniques-to-predict-bistatic-radar-cross-section" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58156.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">258</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">207</span> Confidence Intervals for Quantiles in the Two-Parameter Exponential Distributions with Type II Censored Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayman%20Baklizi">Ayman Baklizi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Based on type II censored data, we consider interval estimation of the quantiles of the two-parameter exponential distribution and the difference between the quantiles of two independent two-parameter exponential distributions. We derive asymptotic intervals, Bayesian, as well as intervals based on the generalized pivot variable. We also include some bootstrap intervals in our comparisons. The performance of these intervals is investigated in terms of their coverage probabilities and expected lengths. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20intervals" title="asymptotic intervals">asymptotic intervals</a>, <a href="https://publications.waset.org/abstracts/search?q=Bayes%20intervals" title=" Bayes intervals"> Bayes intervals</a>, <a href="https://publications.waset.org/abstracts/search?q=bootstrap" title=" bootstrap"> bootstrap</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20pivot%20variables" title=" generalized pivot variables"> generalized pivot variables</a>, <a href="https://publications.waset.org/abstracts/search?q=two-parameter%20exponential%20distribution" title=" two-parameter exponential distribution"> two-parameter exponential distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=quantiles" title=" quantiles"> quantiles</a> </p> <a href="https://publications.waset.org/abstracts/28592/confidence-intervals-for-quantiles-in-the-two-parameter-exponential-distributions-with-type-ii-censored-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28592.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">414</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">206</span> Large Time Asymptotic Behavior to Solutions of a Forced Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Satyanarayana%20Engu">Satyanarayana Engu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Mohd"> Ahmed Mohd</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Murugan"> V. Murugan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Burgers%20equation" title="Burgers equation">Burgers equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Cole-Hopf%20transformation" title=" Cole-Hopf transformation"> Cole-Hopf transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Hermite%20polynomials" title=" Hermite polynomials"> Hermite polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20time%20asymptotics" title=" large time asymptotics"> large time asymptotics</a> </p> <a href="https://publications.waset.org/abstracts/65872/large-time-asymptotic-behavior-to-solutions-of-a-forced-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65872.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">334</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">205</span> The Asymptotic Hole Shape in Long Pulse Laser Drilling: The Influence of Multiple Reflections</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Torsten%20Hermanns">Torsten Hermanns</a>, <a href="https://publications.waset.org/abstracts/search?q=You%20Wang"> You Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Stefan%20Janssen"> Stefan Janssen</a>, <a href="https://publications.waset.org/abstracts/search?q=Markus%20Niessen"> Markus Niessen</a>, <a href="https://publications.waset.org/abstracts/search?q=Christoph%20Schoeler"> Christoph Schoeler</a>, <a href="https://publications.waset.org/abstracts/search?q=Ulrich%20Thombansen"> Ulrich Thombansen</a>, <a href="https://publications.waset.org/abstracts/search?q=Wolfgang%20Schulz"> Wolfgang Schulz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In long pulse laser drilling of metals, it can be demonstrated that the ablation shape approaches a so-called asymptotic shape such that it changes only slightly or not at all with further irradiation. These findings are already known from ultra short pulse (USP) ablation of dielectric and semiconducting materials. The explanation for the occurrence of an asymptotic shape in long pulse drilling of metals is identified, a model for the description of the asymptotic hole shape numerically implemented, tested and clearly confirmed by comparison with experimental data. The model assumes a robust process in that way that the characteristics of the melt flow inside the arising melt film does not change qualitatively by changing the laser or processing parameters. Only robust processes are technically controllable and thus of industrial interest. The condition for a robust process is identified by a threshold for the mass flow density of the assist gas at the hole entrance which has to be exceeded. Within a robust process regime the melt flow characteristics can be captured by only one model parameter, namely the intensity threshold. In analogy to USP ablation (where it is already known for a long time that the resulting hole shape results from a threshold for the absorbed laser fluency) it is demonstrated that in the case of robust long pulse ablation the asymptotic shape forms in that way that along the whole contour the absorbed heat flux density is equal to the intensity threshold. The intensity threshold depends on the special material and radiation properties and has to be calibrated be one reference experiment. The model is implemented in a numerical simulation which is called AsymptoticDrill and requires such a few amount of resources that it can run on common desktop PCs, laptops or even smart devices. Resulting hole shapes can be calculated within seconds what depicts a clear advantage over other simulations presented in literature in the context of industrial every day usage. Against this background the software additionally is equipped with a user-friendly GUI which allows an intuitive usage. Individual parameters can be adjusted using sliders while the simulation result appears immediately in an adjacent window. A platform independent development allow a flexible usage: the operator can use the tool to adjust the process in a very convenient manner on a tablet during the developer can execute the tool in his office in order to design new processes. Furthermore, at the best knowledge of the authors AsymptoticDrill is the first simulation which allows the import of measured real beam distributions and thus calculates the asymptotic hole shape on the basis of the real state of the specific manufacturing system. In this paper the emphasis is placed on the investigation of the effect of multiple reflections on the asymptotic hole shape which gain in importance when drilling holes with large aspect ratios. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20hole%20shape" title="asymptotic hole shape">asymptotic hole shape</a>, <a href="https://publications.waset.org/abstracts/search?q=intensity%20threshold" title=" intensity threshold"> intensity threshold</a>, <a href="https://publications.waset.org/abstracts/search?q=long%20pulse%20laser%20drilling" title=" long pulse laser drilling"> long pulse laser drilling</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20process" title=" robust process"> robust process</a> </p> <a href="https://publications.waset.org/abstracts/77744/the-asymptotic-hole-shape-in-long-pulse-laser-drilling-the-influence-of-multiple-reflections" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77744.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">213</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">204</span> Contrasted Mean and Median Models in Egyptian Stock Markets</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mai%20A.%20Ibrahim">Mai A. Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20El-Beltagy"> Mohammed El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=Motaz%20Khorshid"> Motaz Khorshid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Emerging Markets return distributions have shown significance departure from normality were they are characterized by fatter tails relative to the normal distribution and exhibit levels of skewness and kurtosis that constitute a significant departure from normality. Therefore, the classical Markowitz Mean-Variance is not applicable for emerging markets since it assumes normally-distributed returns (with zero skewness and kurtosis) and a quadratic utility function. Moreover, the Markowitz mean-variance analysis can be used in cases of moderate non-normality and it still provides a good approximation of the expected utility, but it may be ineffective under large departure from normality. Higher moments models and median models have been suggested in the literature for asset allocation in this case. Higher moments models have been introduced to account for the insufficiency of the description of a portfolio by only its first two moments while the median model has been introduced as a robust statistic which is less affected by outliers than the mean. Tail risk measures such as Value-at Risk (VaR) and Conditional Value-at-Risk (CVaR) have been introduced instead of Variance to capture the effect of risk. In this research, higher moment models including the Mean-Variance-Skewness (MVS) and Mean-Variance-Skewness-Kurtosis (MVSK) are formulated as single-objective non-linear programming problems (NLP) and median models including the Median-Value at Risk (MedVaR) and Median-Mean Absolute Deviation (MedMAD) are formulated as a single-objective mixed-integer linear programming (MILP) problems. The higher moment models and median models are compared to some benchmark portfolios and tested on real financial data in the Egyptian main Index EGX30. The results show that all the median models outperform the higher moment models were they provide higher final wealth for the investor over the entire period of study. In addition, the results have confirmed the inapplicability of the classical Markowitz Mean-Variance to the Egyptian stock market as it resulted in very low realized profits. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Egyptian%20stock%20exchange" title="Egyptian stock exchange">Egyptian stock exchange</a>, <a href="https://publications.waset.org/abstracts/search?q=emerging%20markets" title=" emerging markets"> emerging markets</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20moment%20models" title=" higher moment models"> higher moment models</a>, <a href="https://publications.waset.org/abstracts/search?q=median%20models" title=" median models"> median models</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed-integer%20linear%20programming" title=" mixed-integer linear programming"> mixed-integer linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20programming" title=" non-linear programming"> non-linear programming</a> </p> <a href="https://publications.waset.org/abstracts/42897/contrasted-mean-and-median-models-in-egyptian-stock-markets" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42897.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">314</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">203</span> Confidence Envelopes for Parametric Model Selection Inference and Post-Model Selection Inference</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=I.%20M.%20L.%20Nadeesha%20Jayaweera">I. M. L. Nadeesha Jayaweera</a>, <a href="https://publications.waset.org/abstracts/search?q=Adao%20Alex%20Trindade"> Adao Alex Trindade</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In choosing a candidate model in likelihood-based modeling via an information criterion, the practitioner is often faced with the difficult task of deciding just how far up the ranked list to look. Motivated by this pragmatic necessity, we construct an uncertainty band for a generalized (model selection) information criterion (GIC), defined as a criterion for which the limit in probability is identical to that of the normalized log-likelihood. This includes common special cases such as AIC & BIC. The method starts from the asymptotic normality of the GIC for the joint distribution of the candidate models in an independent and identically distributed (IID) data framework and proceeds by deriving the (asymptotically) exact distribution of the minimum. The calculation of an upper quantile for its distribution then involves the computation of multivariate Gaussian integrals, which is amenable to efficient implementation via the R package "mvtnorm". The performance of the methodology is tested on simulated data by checking the coverage probability of nominal upper quantiles and compared to the bootstrap. Both methods give coverages close to nominal for large samples, but the bootstrap is two orders of magnitude slower. The methodology is subsequently extended to two other commonly used model structures: regression and time series. In the regression case, we derive the corresponding asymptotically exact distribution of the minimum GIC invoking Lindeberg-Feller type conditions for triangular arrays and are thus able to similarly calculate upper quantiles for its distribution via multivariate Gaussian integration. The bootstrap once again provides a default competing procedure, and we find that similar comparison performance metrics hold as for the IID case. The time series case is complicated by far more intricate asymptotic regime for the joint distribution of the model GIC statistics. Under a Gaussian likelihood, the default in most packages, one needs to derive the limiting distribution of a normalized quadratic form for a realization from a stationary series. Under conditions on the process satisfied by ARMA models, a multivariate normal limit is once again achieved. The bootstrap can, however, be employed for its computation, whence we are once again in the multivariate Gaussian integration paradigm for upper quantile evaluation. Comparisons of this bootstrap-aided semi-exact method with the full-blown bootstrap once again reveal a similar performance but faster computation speeds. One of the most difficult problems in contemporary statistical methodological research is to be able to account for the extra variability introduced by model selection uncertainty, the so-called post-model selection inference (PMSI). We explore ways in which the GIC uncertainty band can be inverted to make inferences on the parameters. This is being attempted in the IID case by pivoting the CDF of the asymptotically exact distribution of the minimum GIC. For inference one parameter at a time and a small number of candidate models, this works well, whence the attained PMSI confidence intervals are wider than the MLE-based Wald, as expected. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=model%20selection%20inference" title="model selection inference">model selection inference</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20information%20criteria" title=" generalized information criteria"> generalized information criteria</a>, <a href="https://publications.waset.org/abstracts/search?q=post%20model%20selection" title=" post model selection"> post model selection</a>, <a href="https://publications.waset.org/abstracts/search?q=Asymptotic%20Theory" title=" Asymptotic Theory"> Asymptotic Theory</a> </p> <a href="https://publications.waset.org/abstracts/157622/confidence-envelopes-for-parametric-model-selection-inference-and-post-model-selection-inference" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/157622.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">89</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">202</span> Efficient Principal Components Estimation of Large Factor Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rachida%20Ouysse">Rachida Ouysse</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes a constrained principal components (CnPC) estimator for efficient estimation of large-dimensional factor models when errors are cross sectionally correlated and the number of cross-sections (N) may be larger than the number of observations (T). Although principal components (PC) method is consistent for any path of the panel dimensions, it is inefficient as the errors are treated to be homoskedastic and uncorrelated. The new CnPC exploits the assumption of bounded cross-sectional dependence, which defines Chamberlain and Rothschild’s (1983) approximate factor structure, as an explicit constraint and solves a constrained PC problem. The CnPC method is computationally equivalent to the PC method applied to a regularized form of the data covariance matrix. Unlike maximum likelihood type methods, the CnPC method does not require inverting a large covariance matrix and thus is valid for panels with N ≥ T. The paper derives a convergence rate and an asymptotic normality result for the CnPC estimators of the common factors. We provide feasible estimators and show in a simulation study that they are more accurate than the PC estimator, especially for panels with N larger than T, and the generalized PC type estimators, especially for panels with N almost as large as T. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=high%20dimensionality" title="high dimensionality">high dimensionality</a>, <a href="https://publications.waset.org/abstracts/search?q=unknown%20factors" title=" unknown factors"> unknown factors</a>, <a href="https://publications.waset.org/abstracts/search?q=principal%20components" title=" principal components"> principal components</a>, <a href="https://publications.waset.org/abstracts/search?q=cross-sectional%20correlation" title=" cross-sectional correlation"> cross-sectional correlation</a>, <a href="https://publications.waset.org/abstracts/search?q=shrinkage%20regression" title=" shrinkage regression"> shrinkage regression</a>, <a href="https://publications.waset.org/abstracts/search?q=regularization" title=" regularization"> regularization</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-out-of-sample%20forecasting" title=" pseudo-out-of-sample forecasting"> pseudo-out-of-sample forecasting</a> </p> <a href="https://publications.waset.org/abstracts/142686/efficient-principal-components-estimation-of-large-factor-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142686.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">150</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">201</span> Analytical Solutions for Corotational Maxwell Model Fluid Arising in Wire Coating inside a Canonical Die </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Sohail%20Khan">Muhammad Sohail Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Rehan%20Ali%20Shah"> Rehan Ali Shah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l<sub>10</sub>, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=corotational%20Maxwell%20model" title="corotational Maxwell model">corotational Maxwell model</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20homotopy%20asymptotic%20method" title=" optimal homotopy asymptotic method"> optimal homotopy asymptotic method</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20homotopy%20perturbation%20method" title=" optimal homotopy perturbation method"> optimal homotopy perturbation method</a>, <a href="https://publications.waset.org/abstracts/search?q=wire%20coating%20die" title=" wire coating die"> wire coating die</a> </p> <a href="https://publications.waset.org/abstracts/54265/analytical-solutions-for-corotational-maxwell-model-fluid-arising-in-wire-coating-inside-a-canonical-die" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54265.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">336</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">200</span> Lyapunov and Input-to-State Stability of Stochastic Differential Equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20Kadiev"> Ramazan Kadiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20stability" title="asymptotic stability">asymptotic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title=" delay equations"> delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20perturbations" title=" stochastic perturbations"> stochastic perturbations</a> </p> <a href="https://publications.waset.org/abstracts/127764/lyapunov-and-input-to-state-stability-of-stochastic-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127764.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">176</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">199</span> High Accuracy Analytic Approximation for Special Functions Applied to Bessel Functions J₀(x) and Its Zeros</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass">Fernando Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin"> Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20approximations" title="analytic approximations">analytic approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20approximations" title=" asymptotic approximations"> asymptotic approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=Bessel%20functions" title=" Bessel functions"> Bessel functions</a>, <a href="https://publications.waset.org/abstracts/search?q=quasirational%20approximations" title=" quasirational approximations"> quasirational approximations</a> </p> <a href="https://publications.waset.org/abstracts/92867/high-accuracy-analytic-approximation-for-special-functions-applied-to-bessel-functions-j0x-and-its-zeros" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/92867.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">251</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">198</span> Micromechanics Modeling of 3D Network Smart Orthotropic Structures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20M.%20Hassan">E. M. Hassan</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20L.%20Kalamkarov"> A. L. Kalamkarov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two micromechanical models for 3D smart composite with embedded periodic or nearly periodic network of generally orthotropic reinforcements and actuators are developed and applied to cubic structures with unidirectional orientation of constituents. Analytical formulas for the effective piezothermoelastic coefficients are derived using the Asymptotic Homogenization Method (AHM). Finite Element Analysis (FEA) is subsequently developed and used to examine the aforementioned periodic 3D network reinforced smart structures. The deformation responses from the FE simulations are used to extract effective coefficients. The results from both techniques are compared. This work considers piezoelectric materials that respond linearly to changes in electric field, electric displacement, mechanical stress and strain and thermal effects. This combination of electric fields and thermo-mechanical response in smart composite structures is characterized by piezoelectric and thermal expansion coefficients. The problem is represented by unit-cell and the models are developed using the AHM and the FEA to determine the effective piezoelectric and thermal expansion coefficients. Each unit cell contains a number of orthotropic inclusions in the form of structural reinforcements and actuators. Using matrix representation of the coupled response of the unit cell, the effective piezoelectric and thermal expansion coefficients are calculated and compared with results of the asymptotic homogenization method. A very good agreement is shown between these two approaches. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20homogenization%20method" title="asymptotic homogenization method">asymptotic homogenization method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20analysis" title=" finite element analysis"> finite element analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=effective%20piezothermoelastic%20coefficients" title=" effective piezothermoelastic coefficients"> effective piezothermoelastic coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=3D%20smart%20network%20composite%20structures" title=" 3D smart network composite structures"> 3D smart network composite structures</a> </p> <a href="https://publications.waset.org/abstracts/18190/micromechanics-modeling-of-3d-network-smart-orthotropic-structures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18190.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">400</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">197</span> Further Analysis of Global Robust Stability of Neural Networks with Multiple Time Delays</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sabri%20Arik">Sabri Arik</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=neural%20networks" title="neural networks">neural networks</a>, <a href="https://publications.waset.org/abstracts/search?q=delayed%20systems" title=" delayed systems"> delayed systems</a>, <a href="https://publications.waset.org/abstracts/search?q=lyapunov%20functionals" title=" lyapunov functionals"> lyapunov functionals</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20analysis" title=" stability analysis"> stability analysis</a> </p> <a href="https://publications.waset.org/abstracts/24118/further-analysis-of-global-robust-stability-of-neural-networks-with-multiple-time-delays" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24118.pdf" target="_blank" class="btn btn-primary 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