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perturbation problem</title> <meta name="description" content="Search results for: singular perturbation problem"> <meta name="keywords" content="singular perturbation problem"> <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> 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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="singular perturbation problem"> <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> 7430</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: singular perturbation problem</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">7430</span> Exponential Spline Solution for Singularly Perturbed Boundary Value Problems with an Uncertain-But-Bounded Parameter </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Waheed%20Zahra">Waheed Zahra</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20El-Beltagy"> Mohamed El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=Ashraf%20El%20Mhlawy"> Ashraf El Mhlawy</a>, <a href="https://publications.waset.org/abstracts/search?q=Reda%20Elkhadrawy"> Reda Elkhadrawy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider singular perturbation reaction-diffusion boundary value problems, which contain a small uncertain perturbation parameter. To solve these problems, we propose a numerical method which is based on an exponential spline and Shishkin mesh discretization. While interval analysis principle is used to deal with the uncertain parameter, sensitivity analysis has been conducted using different methods. Numerical results are provided to show the applicability and efficiency of our method, which is ε-uniform convergence of almost second order. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem" title="singular perturbation problem">singular perturbation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=shishkin%20mesh" title=" shishkin mesh"> shishkin mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20small%20parameters" title=" two small parameters"> two small parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20spline" title=" exponential spline"> exponential spline</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20analysis" title=" interval analysis"> interval analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20analysis" title=" sensitivity analysis"> sensitivity analysis</a> </p> <a href="https://publications.waset.org/abstracts/91560/exponential-spline-solution-for-singularly-perturbed-boundary-value-problems-with-an-uncertain-but-bounded-parameter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91560.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">274</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">7429</span> Regularization of Gene Regulatory Networks Perturbed by White Noise</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20I.%20Kadiev">Ramazan I. Kadiev</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title="ill-posed problems">ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</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=switching%20nonlinearities" title=" switching nonlinearities"> switching nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/85883/regularization-of-gene-regulatory-networks-perturbed-by-white-noise" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85883.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">194</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">7428</span> Robust Numerical Method for Singularly Perturbed Semilinear Boundary Value Problem with Nonlocal Boundary Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Habtamu%20Garoma%20Debela">Habtamu Garoma Debela</a>, <a href="https://publications.waset.org/abstracts/search?q=Gemechis%20File%20Duressa"> Gemechis File Duressa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20boundary%20condition" title="nonlocal boundary condition">nonlocal boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=nonstandard%20fitted%20operator" title=" nonstandard fitted operator"> nonstandard fitted operator</a>, <a href="https://publications.waset.org/abstracts/search?q=semilinear%20problem" title=" semilinear problem"> semilinear problem</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation" title=" singular perturbation"> singular perturbation</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20convergent" title=" uniformly convergent"> uniformly convergent</a> </p> <a href="https://publications.waset.org/abstracts/130967/robust-numerical-method-for-singularly-perturbed-semilinear-boundary-value-problem-with-nonlocal-boundary-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/130967.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">7427</span> Setting Uncertainty Conditions Using Singular Values for Repetitive Control in State Feedback</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20A.%20Alsubaie">Muhammad A. Alsubaie</a>, <a href="https://publications.waset.org/abstracts/search?q=Mubarak%20K.%20H.%20Alhajri"> Mubarak K. H. Alhajri</a>, <a href="https://publications.waset.org/abstracts/search?q=Tarek%20S.%20Altowaim"> Tarek S. Altowaim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A repetitive controller designed to accommodate periodic disturbances via state feedback is discussed. Periodic disturbances can be represented by a time delay model in a positive feedback loop acting on system output. A direct use of the small gain theorem solves the periodic disturbances problem via 1) isolating the delay model, 2) finding the overall system representation around the delay model and 3) designing a feedback controller that assures overall system stability and tracking error convergence. This paper addresses uncertainty conditions for the repetitive controller designed in state feedback in either past error feedforward or current error feedback using singular values. The uncertainty investigation is based on the overall system found and the stability condition associated with it; depending on the scheme used, to set an upper/lower limit weighting parameter. This creates a region that should not be exceeded in selecting the weighting parameter which in turns assures performance improvement against system uncertainty. Repetitive control problem can be described in lifted form. This allows the usage of singular values principle in setting the range for the weighting parameter selection. The Simulation results obtained show a tracking error convergence against dynamic system perturbation if the weighting parameter chosen is within the range obtained. Simulation results also show the advantage of weighting parameter usage compared to the case where it is omitted. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=model%20mismatch" title="model mismatch">model mismatch</a>, <a href="https://publications.waset.org/abstracts/search?q=repetitive%20control" title=" repetitive control"> repetitive control</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20values" title=" singular values"> singular values</a>, <a href="https://publications.waset.org/abstracts/search?q=state%20feedback" title=" state feedback"> state feedback</a> </p> <a href="https://publications.waset.org/abstracts/99234/setting-uncertainty-conditions-using-singular-values-for-repetitive-control-in-state-feedback" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99234.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">155</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">7426</span> Polynomial Chaos Expansion Combined with Exponential Spline for Singularly Perturbed Boundary Value Problems with Random Parameter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=W.%20K.%20Zahra">W. K. Zahra</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20El-Beltagy"> M. A. El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20R.%20Elkhadrawy"> R. R. Elkhadrawy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem" title="singular perturbation problem">singular perturbation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20chaos%20expansion" title=" polynomial chaos expansion"> polynomial chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=Shishkin%20mesh" title=" Shishkin mesh"> Shishkin mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20small%20parameters" title=" two small parameters"> two small parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20spline" title=" exponential spline"> exponential spline</a> </p> <a href="https://publications.waset.org/abstracts/100441/polynomial-chaos-expansion-combined-with-exponential-spline-for-singularly-perturbed-boundary-value-problems-with-random-parameter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/100441.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">160</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">7425</span> The Norm, Singular Value and Condition Number Analysis for the Hadamard Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Emine%20Tu%C4%9Fba%20Aky%C3%BCz">Emine Tuğba Akyüz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=condition%20number" title="condition number">condition number</a>, <a href="https://publications.waset.org/abstracts/search?q=Hadamard%20matrix" title=" Hadamard matrix"> Hadamard matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=norm" title=" norm"> norm</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20value" title=" singular value"> singular value</a> </p> <a href="https://publications.waset.org/abstracts/9350/the-norm-singular-value-and-condition-number-analysis-for-the-hadamard-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9350.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">343</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">7424</span> Existence and Uniqueness of Solutions to Singular Higher Order Two-Point BVPs on Time Scales</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhenjie%20Liu">Zhenjie Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mixed%20monotone%20operator" title="mixed monotone operator">mixed monotone operator</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problem" title=" boundary value problem"> boundary value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20scale" title=" time scale"> time scale</a>, <a href="https://publications.waset.org/abstracts/search?q=green%27s%20function" title=" green's function"> green's function</a>, <a href="https://publications.waset.org/abstracts/search?q=positive%20solution" title=" positive solution"> positive solution</a>, <a href="https://publications.waset.org/abstracts/search?q=singularity" title=" singularity"> singularity</a> </p> <a href="https://publications.waset.org/abstracts/7268/existence-and-uniqueness-of-solutions-to-singular-higher-order-two-point-bvps-on-time-scales" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7268.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">256</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">7423</span> Optimal Perturbation in an Impulsively Blocked Channel Flow</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Avinash%20Nayak">Avinash Nayak</a>, <a href="https://publications.waset.org/abstracts/search?q=Debopam%20Das"> Debopam Das</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=blocked%20channel%20flow" title="blocked channel flow">blocked channel flow</a>, <a href="https://publications.waset.org/abstracts/search?q=calculus%20of%20variation" title=" calculus of variation"> calculus of variation</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamic%20stability" title=" hydrodynamic stability"> hydrodynamic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20perturbation" title=" optimal perturbation"> optimal perturbation</a> </p> <a href="https://publications.waset.org/abstracts/23334/optimal-perturbation-in-an-impulsively-blocked-channel-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23334.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">421</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">7422</span> Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rogelio%20Luck">Rogelio Luck</a>, <a href="https://publications.waset.org/abstracts/search?q=Yucheng%20Liu"> Yucheng Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20value%20decomposition" title="singular value decomposition">singular value decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=impulse%20response%20function" title=" impulse response function"> impulse response function</a>, <a href="https://publications.waset.org/abstracts/search?q=Green%E2%80%99s%20function" title=" Green’s function "> Green’s function </a>, <a href="https://publications.waset.org/abstracts/search?q=Toeplitz%20matrix" title=" Toeplitz matrix "> Toeplitz matrix </a>, <a href="https://publications.waset.org/abstracts/search?q=Hankel%20matrix" title=" Hankel matrix"> Hankel matrix</a> </p> <a href="https://publications.waset.org/abstracts/127083/continuous-time-and-discrete-time-singular-value-decomposition-of-an-impulse-response-function" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127083.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">156</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">7421</span> Application of Regularized Low-Rank Matrix Factorization in Personalized Targeting </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kourosh%20Modarresi">Kourosh Modarresi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Netflix problem has brought the topic of “Recommendation Systems” into the mainstream of computer science, mathematics, and statistics. Though much progress has been made, the available algorithms do not obtain satisfactory results. The success of these algorithms is rarely above 5%. This work is based on the belief that the main challenge is to come up with “scalable personalization” models. This paper uses an adaptive regularization of inverse singular value decomposition (SVD) that applies adaptive penalization on the singular vectors. The results show far better matching for recommender systems when compared to the ones from the state of the art models in the industry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20optimization" title="convex optimization">convex optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=LASSO" title=" LASSO"> LASSO</a>, <a href="https://publications.waset.org/abstracts/search?q=regression" title=" regression"> regression</a>, <a href="https://publications.waset.org/abstracts/search?q=recommender%20systems" title=" recommender systems"> recommender systems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20value%20decomposition" title=" singular value decomposition"> singular value decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=low%20rank%20approximation" title=" low rank approximation"> low rank approximation</a> </p> <a href="https://publications.waset.org/abstracts/19547/application-of-regularized-low-rank-matrix-factorization-in-personalized-targeting" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19547.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">455</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">7420</span> Solving Ill-Posed Initial Value Problems for Switched Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20dynamical%20systems" title="hybrid dynamical systems">hybrid dynamical systems</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title=" ill-posed problems"> ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=switching%20nonlinearities" title=" switching nonlinearities"> switching nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/85884/solving-ill-posed-initial-value-problems-for-switched-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85884.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">184</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">7419</span> Rough Oscillatory Singular Integrals on Rⁿ</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20M.%20Al-Qassem">H. M. Al-Qassem</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Cheng"> L. Cheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Pan"> Y. Pan </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=oscillatory%20singular%20integral" title="oscillatory singular integral">oscillatory singular integral</a>, <a href="https://publications.waset.org/abstracts/search?q=rough%20kernel" title=" rough kernel"> rough kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20integral" title=" singular integral"> singular integral</a>, <a href="https://publications.waset.org/abstracts/search?q=Orlicz%20spaces" title=" Orlicz spaces"> Orlicz spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=Block%20spaces" title=" Block spaces"> Block spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=extrapolation" title=" extrapolation"> extrapolation</a>, <a href="https://publications.waset.org/abstracts/search?q=L%5E%7Bp%7D%20boundedness" title=" L^{p} boundedness"> L^{p} boundedness</a> </p> <a href="https://publications.waset.org/abstracts/2152/rough-oscillatory-singular-integrals-on-r" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2152.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">357</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">7418</span> Singular Value Decomposition Based Optimisation of Design Parameters of a Gearbox </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehmet%20Bozca">Mehmet Bozca</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (µmax and µmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Singular%20value" title="Singular value">Singular value</a>, <a href="https://publications.waset.org/abstracts/search?q=optimisation" title=" optimisation"> optimisation</a>, <a href="https://publications.waset.org/abstracts/search?q=gearbox" title=" gearbox"> gearbox</a>, <a href="https://publications.waset.org/abstracts/search?q=torsional%20vibration" title=" torsional vibration"> torsional vibration</a> </p> <a href="https://publications.waset.org/abstracts/32486/singular-value-decomposition-based-optimisation-of-design-parameters-of-a-gearbox" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32486.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">360</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">7417</span> Clutter Suppression Based on Singular Value Decomposition and Fast Wavelet Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ruomeng%20Xiao">Ruomeng Xiao</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhulin%20Zong"> Zhulin Zong</a>, <a href="https://publications.waset.org/abstracts/search?q=Longfa%20Yang"> Longfa Yang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Aiming at the problem that the target signal is difficult to detect under the strong ground clutter environment, this paper proposes a clutter suppression algorithm based on the combination of singular value decomposition and the Mallat fast wavelet algorithm. The method first carries out singular value decomposition on the radar echo data matrix, realizes the initial separation of target and clutter through the threshold processing of singular value, and then carries out wavelet decomposition on the echo data to find out the target location, and adopts the discard method to select the appropriate decomposition layer to reconstruct the target signal, which ensures the minimum loss of target information while suppressing the clutter. After the verification of the measured data, the method has a significant effect on the target extraction under low SCR, and the target reconstruction can be realized without the prior position information of the target and the method also has a certain enhancement on the output SCR compared with the traditional single wavelet processing method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=clutter%20suppression" title="clutter suppression">clutter suppression</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20value%20decomposition" title=" singular value decomposition"> singular value decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20transform" title=" wavelet transform"> wavelet transform</a>, <a href="https://publications.waset.org/abstracts/search?q=Mallat%20algorithm" title=" Mallat algorithm"> Mallat algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=low%20SCR" title=" low SCR"> low SCR</a> </p> <a href="https://publications.waset.org/abstracts/181202/clutter-suppression-based-on-singular-value-decomposition-and-fast-wavelet-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181202.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">118</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">7416</span> The Improved Laplace Homotopy Perturbation Method for Solving Non-integrable PDEs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Noufe%20H.%20Aljahdaly">Noufe H. Aljahdaly</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Laplace homotopy perturbation method (LHPM) is an approximate method that help to compute the approximate solution for partial differential equations. The method has been used for solving several problems in science. It requires the initial condition, so it solves the initial value problem. In physics, when some important terms are taken in account, we may obtain non-integrable partial differential equations that do not have analytical integrals. This type of PDEs do not have exact solution, therefore, we need to compute the solution without initial condition. In this work, we improved the LHPM to be able to solve non-integrable problem, especially the damped PDEs, which are the PDEs that include a damping term which makes the PDEs non-integrable. We improved the LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for damped PDE as the initial condition for non-damped PDE. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-integrable%20PDEs" title="non-integrable PDEs">non-integrable PDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20Kawahara%20equation%3B" title=" modified Kawahara equation;"> modified Kawahara equation;</a>, <a href="https://publications.waset.org/abstracts/search?q=laplace%20homotopy%20perturbation%20method" title=" laplace homotopy perturbation method"> laplace homotopy perturbation method</a>, <a href="https://publications.waset.org/abstracts/search?q=damping%20term" title=" damping term"> damping term</a> </p> <a href="https://publications.waset.org/abstracts/172304/the-improved-laplace-homotopy-perturbation-method-for-solving-non-integrable-pdes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/172304.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">100</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">7415</span> HPPDFIM-HD: Transaction Distortion and Connected Perturbation Approach for Hierarchical Privacy Preserving Distributed Frequent Itemset Mining over Horizontally-Partitioned Dataset</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuad%20Ali%20Mohammed%20Al-Yarimi">Fuad Ali Mohammed Al-Yarimi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many algorithms have been proposed to provide privacy preserving in data mining. These protocols are based on two main approaches named as: the perturbation approach and the Cryptographic approach. The first one is based on perturbation of the valuable information while the second one uses cryptographic techniques. The perturbation approach is much more efficient with reduced accuracy while the cryptographic approach can provide solutions with perfect accuracy. However, the cryptographic approach is a much slower method and requires considerable computation and communication overhead. In this paper, a new scalable protocol is proposed which combines the advantages of the perturbation and distortion along with cryptographic approach to perform privacy preserving in distributed frequent itemset mining on horizontally distributed data. Both the privacy and performance characteristics of the proposed protocol are studied empirically. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=anonymity%20data" title="anonymity data">anonymity data</a>, <a href="https://publications.waset.org/abstracts/search?q=data%20mining" title=" data mining"> data mining</a>, <a href="https://publications.waset.org/abstracts/search?q=distributed%20frequent%20itemset%20mining" title=" distributed frequent itemset mining"> distributed frequent itemset mining</a>, <a href="https://publications.waset.org/abstracts/search?q=gaussian%20perturbation" title=" gaussian perturbation"> gaussian perturbation</a>, <a href="https://publications.waset.org/abstracts/search?q=perturbation%20approach" title=" perturbation approach"> perturbation approach</a>, <a href="https://publications.waset.org/abstracts/search?q=privacy%20preserving%20data%20mining" title=" privacy preserving data mining"> privacy preserving data mining</a> </p> <a href="https://publications.waset.org/abstracts/20805/hppdfim-hd-transaction-distortion-and-connected-perturbation-approach-for-hierarchical-privacy-preserving-distributed-frequent-itemset-mining-over-horizontally-partitioned-dataset" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20805.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">505</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">7414</span> Sharp Estimates of Oscillatory Singular Integrals with Rough Kernels </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Al-Qassem">H. Al-Qassem</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20Cheng"> L. Cheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Pan"> Y. Pan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=oscillatory%20singular%20integral" title="oscillatory singular integral">oscillatory singular integral</a>, <a href="https://publications.waset.org/abstracts/search?q=rough%20kernel" title=" rough kernel"> rough kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20integral" title=" singular integral"> singular integral</a>, <a href="https://publications.waset.org/abstracts/search?q=orlicz%20spaces" title=" orlicz spaces"> orlicz spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20spaces" title=" block spaces"> block spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=extrapolation" title=" extrapolation"> extrapolation</a>, <a href="https://publications.waset.org/abstracts/search?q=L%5E%7Bp%7D%20boundedness" title=" L^{p} boundedness"> L^{p} boundedness</a> </p> <a href="https://publications.waset.org/abstracts/40363/sharp-estimates-of-oscillatory-singular-integrals-with-rough-kernels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40363.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">7413</span> Stochastic Control of Decentralized Singularly Perturbed Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Walid%20S.%20Alfuhaid">Walid S. Alfuhaid</a>, <a href="https://publications.waset.org/abstracts/search?q=Saud%20A.%20Alghamdi"> Saud A. Alghamdi</a>, <a href="https://publications.waset.org/abstracts/search?q=John%20M.%20Watkins"> John M. Watkins</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Edwin%20Sawan"> M. Edwin Sawan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=decentralized" title="decentralized">decentralized</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=output" title=" output"> output</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturb" title=" singular perturb"> singular perturb</a> </p> <a href="https://publications.waset.org/abstracts/45093/stochastic-control-of-decentralized-singularly-perturbed-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45093.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">370</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">7412</span> Numerical Approach for Solving the Hyper Singular Integral Equation in the Analysis of a Central Symmetrical Crack within an Infinite Strip</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ikram%20Slamani">Ikram Slamani</a>, <a href="https://publications.waset.org/abstracts/search?q=Hicheme%20Ferdjani"> Hicheme Ferdjani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study focuses on analyzing a Griffith crack situated at the center of an infinite strip. The problem is reformulated as a hyper-singular integral equation and solved numerically using second-order Chebyshev polynomials. The primary objective is to calculate the stress intensity factor in mode 1, denoted as K1. The obtained results reveal the influence of the strip width and crack length on the stress intensity factor, assuming stress-free edges. Additionally, a comparison is made with relevant literature to validate the findings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=center%20crack" title="center crack">center crack</a>, <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomial" title=" Chebyshev polynomial"> Chebyshev polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=hyper%20singular%20integral%20equation" title=" hyper singular integral equation"> hyper singular integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Griffith" title=" Griffith"> Griffith</a>, <a href="https://publications.waset.org/abstracts/search?q=infinite%20strip" title=" infinite strip"> infinite strip</a>, <a href="https://publications.waset.org/abstracts/search?q=stress%20intensity%20factor" title=" stress intensity factor"> stress intensity factor</a> </p> <a href="https://publications.waset.org/abstracts/167367/numerical-approach-for-solving-the-hyper-singular-integral-equation-in-the-analysis-of-a-central-symmetrical-crack-within-an-infinite-strip" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167367.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">144</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">7411</span> Study on Sharp V-Notch Problem under Dynamic Loading Condition Using Symplectic Analytical Singular Element</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiaofei%20Hu">Xiaofei Hu</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhiyu%20Cai"> Zhiyu Cai</a>, <a href="https://publications.waset.org/abstracts/search?q=Weian%20Yao"> Weian Yao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=V-notch" title="V-notch">V-notch</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20stress%20intensity%20factor" title=" dynamic stress intensity factor"> dynamic stress intensity factor</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=precise%20time%20domain%20expanding%20algorithm" title=" precise time domain expanding algorithm"> precise time domain expanding algorithm</a> </p> <a href="https://publications.waset.org/abstracts/83948/study-on-sharp-v-notch-problem-under-dynamic-loading-condition-using-symplectic-analytical-singular-element" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/83948.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">172</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">7410</span> Controller Design for Highly Maneuverable Aircraft Technology Using Structured Singular Value and Direct Search Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Marek%20Dlapa">Marek Dlapa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The algebraic approach is applied to the control of the HiMAT (Highly Maneuverable Aircraft Technology). The objective is to find a robust controller which guarantees robust stability and decoupled control of longitudinal model of a scaled remotely controlled vehicle version of the advanced fighter HiMAT. Control design is performed by decoupling the nominal MIMO (multi-input multi-output) system into two identical SISO (single-input single-output) plants which are approximated by a 4th order transfer function. The algebraic approach is then used for pole placement design, and the nominal closed-loop poles are tuned so that the peak of the µ-function is minimal. As an optimization tool, evolutionary algorithm Differential Migration is used in order to overcome the multimodality of the cost function yielding simple controller with decoupling for nominal plant which is compared with the D-K iteration through simulations of standard longitudinal manoeuvres documenting decoupled control obtained from algebraic approach for nominal plant as well as worst case perturbation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algebraic%20approach" title="algebraic approach">algebraic approach</a>, <a href="https://publications.waset.org/abstracts/search?q=evolutionary%20computation" title=" evolutionary computation"> evolutionary computation</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithms" title=" genetic algorithms"> genetic algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=HiMAT" title=" HiMAT"> HiMAT</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20control" title=" robust control"> robust control</a>, <a href="https://publications.waset.org/abstracts/search?q=structured%20singular%20value" title=" structured singular value"> structured singular value</a> </p> <a href="https://publications.waset.org/abstracts/99453/controller-design-for-highly-maneuverable-aircraft-technology-using-structured-singular-value-and-direct-search-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99453.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">140</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">7409</span> Quadriceps Muscle Activity in Response to Slow and Fast Perturbations following Fatiguing Exercise</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nosratollah%20Hedayatpour">Nosratollah Hedayatpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamid%20Reza%20Taheri"> Hamid Reza Taheri</a>, <a href="https://publications.waset.org/abstracts/search?q=Mehrdad%20Fathi"> Mehrdad Fathi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Introduction: Quadriceps femoris muscle is frequently involved in various movements e.g., jumping, landing) during sport and/or daily activities. During ballistic movement when individuals are faced with unexpected knee perturbation, fast twitch muscle fibers contribute to force production to stabilize knee joint. Fast twitch muscle fiber is more susceptible to fatigue and therefor may reduce the ability of the quadriceps muscle to stabilize knee joint during fast perturbation. Aim: The aim of this study was to investigate the effect of fatigue on postural response of the knee extensor muscles to fast and slow perturbations. Methods: Fatigue was induced to the quadriceps muscle using a KinCom Isokinetic Dynamometer (Chattanooga, TN). Bipolar surface electromyography (EMG) signals were simultaneously recorded from quadriceps components (vastus medialis, rectus femoris, and vastus lateralis) during pre- and post-fatigue postural perturbation performed at two different velocities of 120 ms and 250 mes. Results: One-way ANOVA showed that maximal voluntary knee extension force and time to task failure, and associated EMG activities were significantly reduced after fatiguing knee exercise (P< 0.05). Two-ways ANOVA also showed that ARV of EMG during backward direction was significantly larger than forward direction (P< 0.05), and during fast-perturbation it was significantly higher than slow-perturbation (P< 0.05). Moreover, ARV of EMG was significantly reduced during post fatigue perturbation, with the largest reduction identified for fast-perturbation compared with slow perturbation (P< 0.05). Conclusion: A larger reduction in muscle activity of the quadriceps muscle was observed during post fatigue fast-perturbation to stabilize knee joint, most likely due to preferential recruitment of fast twitch muscle fiber which are more susceptible to fatigue. This may partly explain that why knee injuries is common after fast ballistic movement. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=electromyography" title="electromyography">electromyography</a>, <a href="https://publications.waset.org/abstracts/search?q=fast-slow%20perturbations" title=" fast-slow perturbations"> fast-slow perturbations</a>, <a href="https://publications.waset.org/abstracts/search?q=fatigue" title=" fatigue"> fatigue</a>, <a href="https://publications.waset.org/abstracts/search?q=quadriceps%20femoris%20muscle" title=" quadriceps femoris muscle"> quadriceps femoris muscle</a> </p> <a href="https://publications.waset.org/abstracts/10440/quadriceps-muscle-activity-in-response-to-slow-and-fast-perturbations-following-fatiguing-exercise" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10440.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">525</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">7408</span> Encryption Image via Mutual Singular Value Decomposition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adil%20Al-Rammahi">Adil Al-Rammahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Image or document encryption is needed through e- government data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=image%20cryptography" title="image cryptography">image cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20values%20decomposition" title=" singular values decomposition"> singular values decomposition</a> </p> <a href="https://publications.waset.org/abstracts/13714/encryption-image-via-mutual-singular-value-decomposition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13714.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">436</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">7407</span> Numerical Regularization of Ill-Posed Problems via Hybrid Feedback Controls</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Stepanov">Eugene Stepanov</a>, <a href="https://publications.waset.org/abstracts/search?q=Arkadi%20Ponossov"> Arkadi Ponossov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20feedback%20control" title="hybrid feedback control">hybrid feedback control</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title=" ill-posed problems"> ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=step-like%20nonlinearities" title=" step-like nonlinearities"> step-like nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/86303/numerical-regularization-of-ill-posed-problems-via-hybrid-feedback-controls" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86303.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">245</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">7406</span> Investigating Safe Operation Condition for Iterative Learning Control under Load Disturbances Effect in Singular Values</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20A.%20Alsubaie">Muhammad A. Alsubaie</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An iterative learning control framework designed in state feedback structure suffers a lack in investigating load disturbance considerations. The presented work discusses the controller previously designed, highlights the disturbance problem, finds new conditions using singular value principle to assure safe operation conditions with error convergence and reference tracking under the influence of load disturbance. It is known that periodic disturbances can be represented by a delay model in a positive feedback loop acting on the system input. This model can be manipulated by isolating the delay model and finding a controller for the overall system around the delay model to remedy the periodic disturbances using the small signal theorem. The overall system is the base for control design and load disturbance investigation. The major finding of this work is the load disturbance condition found which clearly sets safe operation condition under the influence of load disturbances such that the error tends to nearly zero as the system keeps operating trial after trial. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=iterative%20learning%20control" title="iterative learning control">iterative learning control</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20values" title=" singular values"> singular values</a>, <a href="https://publications.waset.org/abstracts/search?q=state%20feedback" title=" state feedback"> state feedback</a>, <a href="https://publications.waset.org/abstracts/search?q=load%20disturbance" title=" load disturbance"> load disturbance</a> </p> <a href="https://publications.waset.org/abstracts/108485/investigating-safe-operation-condition-for-iterative-learning-control-under-load-disturbances-effect-in-singular-values" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/108485.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">158</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">7405</span> Heat Transfer Enhancement by Localized Time Varying Thermal Perturbations at Hot and Cold Walls in a Rectangular Differentially Heated Cavity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nicolas%20Thiers">Nicolas Thiers</a>, <a href="https://publications.waset.org/abstracts/search?q=Romain%20Gers"> Romain Gers</a>, <a href="https://publications.waset.org/abstracts/search?q=Olivier%20Skurtys"> Olivier Skurtys</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we study numerically the effect of a thermal perturbation on the heat transfer in a rectangular differentially heated cavity of aspect ratio 4, filled by air. In order to maintain the center symmetry, the thermal perturbation is imposed by a square wave at both active walls, at the same relative position of the hot or cold boundary layers. The influences of the amplitude and the vertical location of the perturbation are investigated. The air flow is calculated solving the unsteady Boussinesq-Navier-Stokes equations using the PN - PN-2 Spectral Element Method (SEM) programmed in the Nek5000 opencode, at RaH= 9x107, just before the first bifurcation which leads to periodical flow. The results show that the perturbation has a major impact for the highest amplitude, and at about three quarters of the cavity height, upstream, in both hot and cold boundary layers. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=direct%20numerical%20simulation" title="direct numerical simulation">direct numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer%20enhancement" title=" heat transfer enhancement"> heat transfer enhancement</a>, <a href="https://publications.waset.org/abstracts/search?q=localized%20thermal%20perturbations" title=" localized thermal perturbations"> localized thermal perturbations</a>, <a href="https://publications.waset.org/abstracts/search?q=natural%20convection" title=" natural convection"> natural convection</a>, <a href="https://publications.waset.org/abstracts/search?q=rectangular%20differentially-heated%20cavity" title=" rectangular differentially-heated cavity"> rectangular differentially-heated cavity</a> </p> <a href="https://publications.waset.org/abstracts/109171/heat-transfer-enhancement-by-localized-time-varying-thermal-perturbations-at-hot-and-cold-walls-in-a-rectangular-differentially-heated-cavity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/109171.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">144</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">7404</span> Adjustment of the Whole-Body Center of Mass during Trunk-Flexed Walking across Uneven Ground</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soran%20Aminiaghdam">Soran Aminiaghdam</a>, <a href="https://publications.waset.org/abstracts/search?q=Christian%20Rode"> Christian Rode</a>, <a href="https://publications.waset.org/abstracts/search?q=Reinhard%20Blickhan"> Reinhard Blickhan</a>, <a href="https://publications.waset.org/abstracts/search?q=Astrid%20Zech"> Astrid Zech</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Despite considerable studies on the impact of imposed trunk posture on human walking, less is known about such locomotion while negotiating changes in ground level. The aim of this study was to investigate the behavior of the VBCOM in response to a two-fold expected perturbation, namely alterations in body posture and in ground level. To this end, the kinematic data and ground reaction forces of twelve able participants were collected. We analyzed the vertical position of the body center of mass (VBCOM) from the ground determined by the body segmental analysis method relative to the laboratory coordinate system at touchdown and toe-off instants during walking across uneven ground — characterized by perturbation contact (a 10-cm visible drop) and pre- and post-perturbation contacts — in comparison to unperturbed level contact while maintaining three postures (regular erect, ~30° and ~50° of trunk flexion from the vertical). The VBCOM was normalized to the distance between the greater trochanter marker and the lateral malleoli marker at the instant of TD. Moreover, we calculated the backward rotation during step-down as the difference of the maximum of the trunk angle in the pre-perturbation contact and the minimal trunk angle in the perturbation contact. Two-way repeated measures ANOVAs revealed contact-specific effects of posture on the VBCOM at touchdown (F = 5.96, p = 0.00). As indicated by the analysis of simple main effects, during unperturbed level and pre-perturbation contacts, no between-posture differences for the VBCOM at touchdown were found. In the perturbation contact, trunk-flexed gaits showed a significant increase of VBCOM as compared to the pre-perturbation contact. In the post-perturbation contact, the VBCOM demonstrated a significant decrease in all gait postures relative to the preceding corresponding contacts with no between-posture differences. Main effects of posture revealed that the VBCOM at toe-off significantly decreased in trunk-flexed gaits relative to the regular erect gait. For the main effect of contact, the VBCOM at toe-off demonstrated changes across perturbation and post-perturbation contacts as compared to the unperturbed level contact. Furthermore, participants exhibited a backward trunk rotation during step-down possibly to control the angular momentum of their whole body. A more pronounced backward trunk rotation (2- to 3-fold compared with level contacts) in trunk-flexed walking contributed to the observed elevated VBCOM during the step-down which may have facilitated drop negotiation. These results may shed light on the interaction between posture and locomotion in able gait, and specifically on the behavior of the body center of mass during perturbed locomotion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=center%20of%20mass" title="center of mass">center of mass</a>, <a href="https://publications.waset.org/abstracts/search?q=perturbation" title=" perturbation"> perturbation</a>, <a href="https://publications.waset.org/abstracts/search?q=posture" title=" posture"> posture</a>, <a href="https://publications.waset.org/abstracts/search?q=uneven%20ground" title=" uneven ground"> uneven ground</a>, <a href="https://publications.waset.org/abstracts/search?q=walking" title=" walking"> walking</a> </p> <a href="https://publications.waset.org/abstracts/86029/adjustment-of-the-whole-body-center-of-mass-during-trunk-flexed-walking-across-uneven-ground" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86029.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">181</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">7403</span> The Dynamics of Unsteady Squeezing Flow between Parallel Plates (Two-Dimensional)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jiya%20Mohammed">Jiya Mohammed</a>, <a href="https://publications.waset.org/abstracts/search?q=Ibrahim%20Ismail%20Giwa"> Ibrahim Ismail Giwa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coupled%20differential%20equation" title="coupled differential equation">coupled differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Homotopy%20Perturbation%20Method" title=" Homotopy Perturbation Method"> Homotopy Perturbation Method</a>, <a href="https://publications.waset.org/abstracts/search?q=plates" title=" plates"> plates</a>, <a href="https://publications.waset.org/abstracts/search?q=squeezing%20flow" title=" squeezing flow"> squeezing flow</a> </p> <a href="https://publications.waset.org/abstracts/20444/the-dynamics-of-unsteady-squeezing-flow-between-parallel-plates-two-dimensional" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20444.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">474</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">7402</span> Principle Components Updates via Matrix Perturbations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aiman%20Elragig">Aiman Elragig</a>, <a href="https://publications.waset.org/abstracts/search?q=Hanan%20Dreiwi"> Hanan Dreiwi</a>, <a href="https://publications.waset.org/abstracts/search?q=Dung%20Ly"> Dung Ly</a>, <a href="https://publications.waset.org/abstracts/search?q=Idriss%20Elmabrook"> Idriss Elmabrook</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X <span style="color: rgb(84, 84, 84); font-family: arial, sans-serif; font-size: small; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">∈ </span> R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=online%20data%20updates" title="online data updates">online data updates</a>, <a href="https://publications.waset.org/abstracts/search?q=covariance%20matrix" title=" covariance matrix"> covariance matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=online%20principle%20component%20analysis" title=" online principle component analysis"> online principle component analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20perturbation" title=" matrix perturbation"> matrix perturbation</a> </p> <a href="https://publications.waset.org/abstracts/76536/principle-components-updates-via-matrix-perturbations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76536.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">195</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">7401</span> Bayesian Network and Feature Selection for Rank Deficient Inverse Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kyugneun%20Lee">Kyugneun Lee</a>, <a href="https://publications.waset.org/abstracts/search?q=Ikjin%20Lee"> Ikjin Lee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Parameter estimation with inverse problem often suffers from unfavorable conditions in the real world. Useless data and many input parameters make the problem complicated or insoluble. Data refinement and reformulation of the problem can solve that kind of difficulties. In this research, a method to solve the rank deficient inverse problem is suggested. A multi-physics system which has rank deficiency caused by response correlation is treated. Impeditive information is removed and the problem is reformulated to sequential estimations using Bayesian network (BN) and subset groups. At first, subset grouping of the responses is performed. Feature selection with singular value decomposition (SVD) is used for the grouping. Next, BN inference is used for sequential conditional estimation according to the group hierarchy. Directed acyclic graph (DAG) structure is organized to maximize the estimation ability. Variance ratio of response to noise is used to pairing the estimable parameters by each response. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bayesian%20network" title="Bayesian network">Bayesian network</a>, <a href="https://publications.waset.org/abstracts/search?q=feature%20selection" title=" feature selection"> feature selection</a>, <a href="https://publications.waset.org/abstracts/search?q=rank%20deficiency" title=" rank deficiency"> rank deficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=statistical%20inverse%20analysis" title=" statistical inverse analysis"> statistical inverse analysis</a> </p> <a href="https://publications.waset.org/abstracts/75870/bayesian-network-and-feature-selection-for-rank-deficient-inverse-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/75870.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> <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=singular%20perturbation%20problem&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem&page=5">5</a></li> <li class="page-item"><a class="page-link" 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