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polynomials</title> <meta name="description" content="Search results for: Chebyshev polynomials"> <meta name="keywords" content="Chebyshev polynomials"> <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 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action="https://publications.waset.org/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="Chebyshev polynomials"> <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> 80</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Chebyshev polynomials</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">80</span> Generalized Chebyshev Collocation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Junghan%20Kim">Junghan Kim</a>, <a href="https://publications.waset.org/search?q=Wonkyu%20Chung"> Wonkyu Chung</a>, <a href="https://publications.waset.org/search?q=Sunyoung%20Bu"> Sunyoung Bu</a>, <a href="https://publications.waset.org/search?q=Philsu%20Kim"> Philsu Kim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Generalized%20Chebyshev%20Collocation%20method" title="Generalized Chebyshev Collocation method">Generalized Chebyshev Collocation method</a>, <a href="https://publications.waset.org/search?q=Generalized%20Chebyshev%20Polynomial" title=" Generalized Chebyshev Polynomial"> Generalized Chebyshev Polynomial</a>, <a href="https://publications.waset.org/search?q=Initial%20value%20problem." title=" Initial value problem."> Initial value problem.</a> </p> <a href="https://publications.waset.org/9999909/generalized-chebyshev-collocation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999909/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999909/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999909/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999909/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999909/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999909/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999909/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999909/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999909/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999909/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999909.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">2640</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">79</span> System Overflow/Blocking Transients For Queues with Batch Arrivals Using a Family of Polynomials Resembling Chebyshev Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Vitalice%20K.%20Oduol">Vitalice K. Oduol</a>, <a href="https://publications.waset.org/search?q=C.%20Ardil"> C. Ardil</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The paper shows that in the analysis of a queuing system with fixed-size batch arrivals, there emerges a set of polynomials which are a generalization of Chebyshev polynomials of the second kind. The paper uses these polynomials in assessing the transient behaviour of the overflow (equivalently call blocking) probability in the system. A key figure to note is the proportion of the overflow (or blocking) probability resident in the transient component, which is shown in the results to be more significant at the beginning of the transient and naturally decays to zero in the limit of large t. The results also show that the significance of transients is more pronounced in cases of lighter loads, but lasts longer for heavier loads.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=batch%20arrivals" title="batch arrivals">batch arrivals</a>, <a href="https://publications.waset.org/search?q=blocking%20probability" title=" blocking probability"> blocking probability</a>, <a href="https://publications.waset.org/search?q=generalizedChebyshev%20polynomials" title=" generalizedChebyshev polynomials"> generalizedChebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=overflow%20probability" title=" overflow probability"> overflow probability</a>, <a href="https://publications.waset.org/search?q=queue%20transientanalysis" title=" queue transientanalysis"> queue transientanalysis</a> </p> <a href="https://publications.waset.org/3687/system-overflowblocking-transients-for-queues-with-batch-arrivals-using-a-family-of-polynomials-resembling-chebyshev-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3687/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3687/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3687/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3687/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3687/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3687/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3687/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3687/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3687/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3687/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3687.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">1481</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">78</span> Computable Function Representations Using Effective Chebyshev Polynomial</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mohammed%20A.%20Abutheraa">Mohammed A. Abutheraa</a>, <a href="https://publications.waset.org/search?q=David%20Lester"> David Lester</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Approximation%20Theory" title="Approximation Theory">Approximation Theory</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20Polynomial" title=" Chebyshev Polynomial"> Chebyshev Polynomial</a>, <a href="https://publications.waset.org/search?q=Computable%20Functions" title=" Computable Functions"> Computable Functions</a>, <a href="https://publications.waset.org/search?q=Computable%20Real%20Arithmetic" title=" Computable Real Arithmetic"> Computable Real Arithmetic</a>, <a href="https://publications.waset.org/search?q=Integration" title=" Integration"> Integration</a>, <a href="https://publications.waset.org/search?q=Numerical%20Analysis." title=" Numerical Analysis."> Numerical Analysis.</a> </p> <a href="https://publications.waset.org/5501/computable-function-representations-using-effective-chebyshev-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5501/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5501/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5501/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5501/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5501/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5501/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5501/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5501/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5501/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5501/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5501.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">3087</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">77</span> A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Abdulkawi">M. Abdulkawi</a>, <a href="https://publications.waset.org/search?q=Z.%20K.%20Eshkuvatov"> Z. K. Eshkuvatov</a>, <a href="https://publications.waset.org/search?q=N.%20M.%20A.%20Nik%20Long"> N. M. A. Nik Long</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Singular%20integral%20equations" title="Singular integral equations">Singular integral equations</a>, <a href="https://publications.waset.org/search?q=Cauchy%20kernel" title=" Cauchy kernel"> Cauchy kernel</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=interpolation." title=" interpolation."> interpolation.</a> </p> <a href="https://publications.waset.org/10339/a-note-on-the-numerical-solution-of-singular-integral-equations-of-cauchy-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10339/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10339/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10339/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10339/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10339/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10339/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10339/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10339/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10339/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10339/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10339.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">1655</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">76</span> Numerical Solution of Riccati Differential Equations by Using Hybrid Functions and Tau Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Changqing%20Yang">Changqing Yang</a>, <a href="https://publications.waset.org/search?q=Jianhua%20Hou"> Jianhua Hou</a>, <a href="https://publications.waset.org/search?q=Beibo%20Qin"> Beibo Qin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hybrid%20functions" title="Hybrid functions">Hybrid functions</a>, <a href="https://publications.waset.org/search?q=Riccati%20differential%20equation" title=" Riccati differential equation"> Riccati differential equation</a>, <a href="https://publications.waset.org/search?q=Blockpulse" title=" Blockpulse"> Blockpulse</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=Tau%20method" title=" Tau method"> Tau method</a>, <a href="https://publications.waset.org/search?q=operational%20matrix." title=" operational matrix."> operational matrix.</a> </p> <a href="https://publications.waset.org/7461/numerical-solution-of-riccati-differential-equations-by-using-hybrid-functions-and-tau-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7461/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7461/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7461/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7461/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7461/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7461/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7461/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7461/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7461/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7461/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7461.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">2589</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">75</span> Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=jianhua%20Hou">jianhua Hou</a>, <a href="https://publications.waset.org/search?q=Changqing%20Yang">Changqing Yang</a>, <a href="https://publications.waset.org/search?q=and%20Beibo%20Qin">and Beibo Qin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hybrid%20functions" title="Hybrid functions">Hybrid functions</a>, <a href="https://publications.waset.org/search?q=Fredholm%20integral%20equation" title=" Fredholm integral equation"> Fredholm integral equation</a>, <a href="https://publications.waset.org/search?q=Blockpulse" title=" Blockpulse"> Blockpulse</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=product%20operational%20matrix." title=" product operational matrix."> product operational matrix.</a> </p> <a href="https://publications.waset.org/16762/hybrid-function-method-for-solving-nonlinear-fredholm-integral-equations-of-the-second-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16762/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16762/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16762/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16762/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16762/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16762/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16762/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16762/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16762/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16762/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16762.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">1401</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">74</span> On Bounds For The Zeros of Univariate Polynomial</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Matthias%20Dehmer1%20J%C3%BCrgen%20Kilian">Matthias Dehmer1 Jürgen Kilian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated.Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds for the moduli of the zeros of complex polynomials. That means, we provide disks in the complex plane where all zeros of a complex polynomial are situated. Such bounds are extremely useful for obtaining a priori assertations regarding the location of zeros of polynomials. Based on the proven bounds and a test set of polynomials, we present an experimental study to examine which bound is optimal.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=complex%20polynomials" title="complex polynomials">complex polynomials</a>, <a href="https://publications.waset.org/search?q=zeros" title=" zeros"> zeros</a>, <a href="https://publications.waset.org/search?q=inequalities" title=" inequalities"> inequalities</a> </p> <a href="https://publications.waset.org/5624/on-bounds-for-the-zeros-of-univariate-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5624/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5624/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5624/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5624/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5624/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5624/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5624/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5624/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5624/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5624/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5624.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">1873</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">73</span> Edge Detection in Low Contrast Images</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Koushlendra%20Kumar%20Singh">Koushlendra Kumar Singh</a>, <a href="https://publications.waset.org/search?q=Manish%20Kumar%20Bajpai"> Manish Kumar Bajpai</a>, <a href="https://publications.waset.org/search?q=Rajesh%20K.%20Pandey"> Rajesh K. Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title="Chebyshev polynomials">Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=Fractional%20order%0D%0Adifferentiator" title=" Fractional order differentiator"> Fractional order differentiator</a>, <a href="https://publications.waset.org/search?q=Laplacian%20of%20Gaussian%20%28LoG%29%20method" title=" Laplacian of Gaussian (LoG) method"> Laplacian of Gaussian (LoG) method</a>, <a href="https://publications.waset.org/search?q=Low%20contrast%0D%0Aimage." title=" Low contrast image."> Low contrast image.</a> </p> <a href="https://publications.waset.org/10000808/edge-detection-in-low-contrast-images" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000808/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000808/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000808/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000808/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000808/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000808/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000808/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000808/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000808/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000808/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000808.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">3276</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">72</span> Bilinear and Bilateral Generating Functions for the Gauss’ Hypergeometric Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Manoj%20Singh">Manoj Singh</a>, <a href="https://publications.waset.org/search?q=Mumtaz%20Ahmad%20Khan"> Mumtaz Ahmad Khan</a>, <a href="https://publications.waset.org/search?q=Abdul%20Hakim%20Khan"> Abdul Hakim Khan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Appell%E2%80%99s%20functions" title="Appell’s functions">Appell’s functions</a>, <a href="https://publications.waset.org/search?q=Gauss%20hypergeometric%20functions" title=" Gauss hypergeometric functions"> Gauss hypergeometric functions</a>, <a href="https://publications.waset.org/search?q=Heat%20polynomials" title=" Heat polynomials"> Heat polynomials</a>, <a href="https://publications.waset.org/search?q=Kampe%E2%80%99%20de%20Fe%E2%80%99riet%20function" title=" Kampe’ de Fe’riet function"> Kampe’ de Fe’riet function</a>, <a href="https://publications.waset.org/search?q=Laguerre%20polynomials" title=" Laguerre polynomials"> Laguerre polynomials</a>, <a href="https://publications.waset.org/search?q=Lauricella%E2%80%99s%20function" title=" Lauricella’s function"> Lauricella’s function</a>, <a href="https://publications.waset.org/search?q=Saran%E2%80%99s%20functions." title=" Saran’s functions."> Saran’s functions.</a> </p> <a href="https://publications.waset.org/10000794/bilinear-and-bilateral-generating-functions-for-the-gauss-hypergeometric-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000794/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000794/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000794/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000794/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000794/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000794/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000794/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000794/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000794/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000794/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000794.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">1644</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">71</span> Rigid Registration of Reduced Dimension Images using 1D Binary Projections</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Panos%20D.%20Kotsas">Panos D. Kotsas</a>, <a href="https://publications.waset.org/search?q=Tony%20Dodd"> Tony Dodd</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this work is to present a method for rigid registration of medical images using 1D binary projections when a part of one of the two images is missing. We use 1D binary projections and we adjust the projection limits according to the reduced image in order to perform accurate registration. We use the variance of the weighted ratio as a registration function which we have shown is able to register 2D and 3D images more accurately and robustly than mutual information methods. The function is computed explicitly for n=5 Chebyshev points in a [-9,+9] interval and it is approximated using Chebyshev polynomials for all other points. The images used are MR scans of the head. We find that the method is able to register the two images with average accuracy 0.3degrees for rotations and 0.2 pixels for translations for a y dimension of 156 with initial dimension 256. For y dimension 128/256 the accuracy decreases to 0.7 degrees for rotations and 0.6 pixels for translations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=binary%20projections" title="binary projections">binary projections</a>, <a href="https://publications.waset.org/search?q=image%20registration" title=" image registration"> image registration</a>, <a href="https://publications.waset.org/search?q=reduceddimension%20images." title=" reduceddimension images."> reduceddimension images.</a> </p> <a href="https://publications.waset.org/14264/rigid-registration-of-reduced-dimension-images-using-1d-binary-projections" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14264/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14264/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14264/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14264/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14264/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14264/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14264/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14264/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14264/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14264/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14264.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">1459</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">70</span> Optimal Image Representation for Linear Canonical Transform Multiplexing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Navdeep%20Goel">Navdeep Goel</a>, <a href="https://publications.waset.org/search?q=Salvador%20Gabarda"> Salvador Gabarda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4 × 4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4 × 4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4 × 4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chirp%20signals" title="Chirp signals">Chirp signals</a>, <a href="https://publications.waset.org/search?q=Image%20multiplexing" title=" Image multiplexing"> Image multiplexing</a>, <a href="https://publications.waset.org/search?q=Image%0D%0Atransformation" title=" Image transformation"> Image transformation</a>, <a href="https://publications.waset.org/search?q=Linear%20canonical%20transform" title=" Linear canonical transform"> Linear canonical transform</a>, <a href="https://publications.waset.org/search?q=Polynomial%0D%0Aapproximation." title=" Polynomial approximation."> Polynomial approximation.</a> </p> <a href="https://publications.waset.org/10003258/optimal-image-representation-for-linear-canonical-transform-multiplexing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10003258/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10003258/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10003258/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10003258/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10003258/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10003258/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10003258/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10003258/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10003258/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10003258/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10003258.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">2130</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">69</span> Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kazuo%20Komatsu">Kazuo Komatsu</a>, <a href="https://publications.waset.org/search?q=Hitoshi%20Takata"> Hitoshi Takata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=nonlinear%20system" title="nonlinear system">nonlinear system</a>, <a href="https://publications.waset.org/search?q=nonlinear%20observer" title=" nonlinear observer"> nonlinear observer</a>, <a href="https://publications.waset.org/search?q=formal%20linearization" title=" formal linearization"> formal linearization</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20interpolation." title="Chebyshev interpolation.">Chebyshev interpolation.</a> </p> <a href="https://publications.waset.org/3847/design-of-nonlinear-observer-by-using-chebyshev-interpolation-based-on-formal-linearization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3847/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3847/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3847/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3847/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3847/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3847/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3847/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3847/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3847/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3847/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3847.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">1594</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">68</span> Near-Lossless Image Coding based on Orthogonal Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Krishnamoorthy%20R">Krishnamoorthy R</a>, <a href="https://publications.waset.org/search?q=Rajavijayalakshmi%20K"> Rajavijayalakshmi K</a>, <a href="https://publications.waset.org/search?q=Punidha%20R"> Punidha R</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a near lossless image coding scheme based on Orthogonal Polynomials Transform (OPT) has been presented. The polynomial operators and polynomials basis operators are obtained from set of orthogonal polynomials functions for the proposed transform coding. The image is partitioned into a number of distinct square blocks and the proposed transform coding is applied to each of these individually. After applying the proposed transform coding, the transformed coefficients are rearranged into a sub-band structure. The Embedded Zerotree (EZ) coding algorithm is then employed to quantize the coefficients. The proposed transform is implemented for various block sizes and the performance is compared with existing Discrete Cosine Transform (DCT) transform coding scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Near-lossless%20Coding" title="Near-lossless Coding">Near-lossless Coding</a>, <a href="https://publications.waset.org/search?q=Orthogonal%20Polynomials%0ATransform" title=" Orthogonal Polynomials Transform"> Orthogonal Polynomials Transform</a>, <a href="https://publications.waset.org/search?q=Embedded%20Zerotree%20Coding" title=" Embedded Zerotree Coding"> Embedded Zerotree Coding</a> </p> <a href="https://publications.waset.org/13669/near-lossless-image-coding-based-on-orthogonal-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13669/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13669/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13669/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13669/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13669/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13669/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13669/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13669/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13669/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13669/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13669.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">1944</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">67</span> Numerical Inverse Laplace Transform Using Chebyshev Polynomial </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Vinod%20Mishra">Vinod Mishra</a>, <a href="https://publications.waset.org/search?q=Dimple%20Rani"> Dimple Rani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chebyshev%20polynomial" title="Chebyshev polynomial">Chebyshev polynomial</a>, <a href="https://publications.waset.org/search?q=Numerical%20inverse%20Laplace%20transform" title=" Numerical inverse Laplace transform"> Numerical inverse Laplace transform</a>, <a href="https://publications.waset.org/search?q=Odd%20cosine%20series." title=" Odd cosine series. "> Odd cosine series. </a> </p> <a href="https://publications.waset.org/10004329/numerical-inverse-laplace-transform-using-chebyshev-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004329/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004329/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004329/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004329/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004329/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004329/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004329/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004329/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004329/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004329/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004329.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">1402</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">66</span> Multi-objective Optimization of Vehicle Passive Suspension with a Two-Terminal Mass Using Chebyshev Goal Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Chuan%20Li">Chuan Li</a>, <a href="https://publications.waset.org/search?q=Ming%20Liang"> Ming Liang</a>, <a href="https://publications.waset.org/search?q=Qibing%20Yu"> Qibing Yu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> To improve the dynamics response of the vehicle passive suspension, a two-terminal mass is suggested to connect in parallel with the suspension strut. Three performance criteria, tire grip, ride comfort and suspension deflection, are taken into consideration to optimize the suspension parameters. However, the three criteria are conflicting and non-commensurable. For this reason, the Chebyshev goal programming method is applied to find the best tradeoff among the three objectives. A simulation case is presented to describe the multi-objective optimization procedure. For comparison, the Chebyshev method is also employed to optimize the design of a conventional passive suspension. The effectiveness of the proposed design method has been clearly demonstrated by the result. It is also shown that the suspension with a two-terminal mass in parallel has better performance in terms of the three objectives. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Vehicle" title="Vehicle">Vehicle</a>, <a href="https://publications.waset.org/search?q=passive%20suspension" title=" passive suspension"> passive suspension</a>, <a href="https://publications.waset.org/search?q=two-terminal%20mass" title=" two-terminal mass"> two-terminal mass</a>, <a href="https://publications.waset.org/search?q=optimization" title="optimization">optimization</a>, <a href="https://publications.waset.org/search?q=Chebyshev%20goal%20programming" title=" Chebyshev goal programming"> Chebyshev goal programming</a> </p> <a href="https://publications.waset.org/8202/multi-objective-optimization-of-vehicle-passive-suspension-with-a-two-terminal-mass-using-chebyshev-goal-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8202/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8202/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8202/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8202/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8202/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8202/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8202/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8202/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8202/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8202/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8202.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">1759</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">65</span> Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Taweechai%20Nuntawisuttiwong">Taweechai Nuntawisuttiwong</a>, <a href="https://publications.waset.org/search?q=Natasha%20Dejdumrong"> Natasha Dejdumrong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Newton%20interpolation" title="Newton interpolation">Newton interpolation</a>, <a href="https://publications.waset.org/search?q=Lagrange%20interpolation" title=" Lagrange interpolation"> Lagrange interpolation</a>, <a href="https://publications.waset.org/search?q=linear%0D%0Acomplexity." title=" linear complexity."> linear complexity.</a> </p> <a href="https://publications.waset.org/10010689/fast-and-efficient-algorithms-for-evaluating-uniform-and-nonuniform-lagrange-and-newton-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010689/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010689/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010689/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010689/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010689/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010689/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010689/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010689/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010689/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010689/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010689.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">617</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">64</span> On the Construction of m-Sequences via Primitive Polynomials with a Fast Identification Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Abhijit%20Mitra">Abhijit Mitra</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper provides an in-depth tutorial of mathematical construction of maximal length sequences (m-sequences) via primitive polynomials and how to map the same when implemented in shift registers. It is equally important to check whether a polynomial is primitive or not so as to get proper m-sequences. A fast method to identify primitive polynomials over binary fields is proposed where the complexity is considerably less in comparison with the standard procedures for the same purpose. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Finite%20field" title="Finite field">Finite field</a>, <a href="https://publications.waset.org/search?q=irreducible%20polynomial" title=" irreducible polynomial"> irreducible polynomial</a>, <a href="https://publications.waset.org/search?q=primitive%20polynomial" title=" primitive polynomial"> primitive polynomial</a>, <a href="https://publications.waset.org/search?q=maximal%20length%20sequence" title=" maximal length sequence"> maximal length sequence</a>, <a href="https://publications.waset.org/search?q=additive%20shift%20register" title=" additive shift register"> additive shift register</a>, <a href="https://publications.waset.org/search?q=multiplicative%0Ashift%20register." title=" multiplicative shift register."> multiplicative shift register.</a> </p> <a href="https://publications.waset.org/2641/on-the-construction-of-m-sequences-via-primitive-polynomials-with-a-fast-identification-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2641/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2641/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2641/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2641/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2641/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2641/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2641/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2641/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2641/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2641/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2641.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">3939</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">63</span> Best Coapproximation in Fuzzy Anti-n-Normed Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=J.%20Kavikumar">J. Kavikumar</a>, <a href="https://publications.waset.org/search?q=N.%20S.%20Manian"> N. S. Manian</a>, <a href="https://publications.waset.org/search?q=M.%20B.%20K.%20Moorthy"> M. B. K. Moorthy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. </p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fuzzy-n-normed%20space" title="Fuzzy-n-normed space">Fuzzy-n-normed space</a>, <a href="https://publications.waset.org/search?q=best%20coapproximation" title=" best coapproximation"> best coapproximation</a>, <a href="https://publications.waset.org/search?q=co-proximinal" title=" co-proximinal"> co-proximinal</a>, <a href="https://publications.waset.org/search?q=co-Chebyshev" title=" co-Chebyshev"> co-Chebyshev</a>, <a href="https://publications.waset.org/search?q=F-best%20coapproximation" title=" F-best coapproximation"> F-best coapproximation</a>, <a href="https://publications.waset.org/search?q=orthogonality" title=" orthogonality"> orthogonality</a> </p> <a href="https://publications.waset.org/9997820/best-coapproximation-in-fuzzy-anti-n-normed-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997820/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997820/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997820/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997820/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997820/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997820/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997820/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997820/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997820/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997820/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997820.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">1630</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">62</span> Some Results on the Generalized Higher Rank Numerical Ranges</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Mohsen%20Zahraei">Mohsen Zahraei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for Є > 0, the notion of Birkhoff-James approximate orthogonality sets for Є−higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural generalization of the standard higher rank numerical ranges. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Rank%E2%88%92k%20numerical%20range" title="Rank−k numerical range">Rank−k numerical range</a>, <a href="https://publications.waset.org/search?q=isometry" title=" isometry"> isometry</a>, <a href="https://publications.waset.org/search?q=numerical%20range" title=" numerical range"> numerical range</a>, <a href="https://publications.waset.org/search?q=rectangular%20matrix%20polynomials." title=" rectangular matrix polynomials."> rectangular matrix polynomials.</a> </p> <a href="https://publications.waset.org/10002343/some-results-on-the-generalized-higher-rank-numerical-ranges" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002343/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002343/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002343/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002343/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002343/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002343/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002343/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002343/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002343/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002343/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002343.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">1582</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">61</span> 4D Flight Trajectory Optimization Based on Pseudospectral Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kouamana%20Bousson">Kouamana Bousson</a>, <a href="https://publications.waset.org/search?q=Paulo%20Machado"> Paulo Machado</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the indirect or direct methods. The indirect methods are based on maximum principle of Pontryagin, on the other hand, in the direct methods it is necessary to transform into a nonlinear programming problem. We propose an approach based on direct methods with a pseudospectral integration scheme built on Chebyshev polynomials. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pseudospectral%20Methods" title="Pseudospectral Methods">Pseudospectral Methods</a>, <a href="https://publications.waset.org/search?q=Trajectory%20Optimization" title=" Trajectory Optimization"> Trajectory Optimization</a>, <a href="https://publications.waset.org/search?q=4DTrajectories" title=" 4DTrajectories"> 4DTrajectories</a> </p> <a href="https://publications.waset.org/11036/4d-flight-trajectory-optimization-based-on-pseudospectral-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11036/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11036/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11036/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11036/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11036/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11036/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11036/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11036/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11036/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11036/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11036.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">2411</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">60</span> Holistic Face Recognition using Multivariate Approximation, Genetic Algorithms and AdaBoost Classifier: Preliminary Results</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=C.%20Villegas-Quezada">C. Villegas-Quezada</a>, <a href="https://publications.waset.org/search?q=J.%20Climent"> J. Climent</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Several works regarding facial recognition have dealt with methods which identify isolated characteristics of the face or with templates which encompass several regions of it. In this paper a new technique which approaches the problem holistically dispensing with the need to identify geometrical characteristics or regions of the face is introduced. The characterization of a face is achieved by randomly sampling selected attributes of the pixels of its image. From this information we construct a set of data, which correspond to the values of low frequencies, gradient, entropy and another several characteristics of pixel of the image. Generating a set of “p" variables. The multivariate data set with different polynomials minimizing the data fitness error in the minimax sense (L∞ - Norm) is approximated. With the use of a Genetic Algorithm (GA) it is able to circumvent the problem of dimensionality inherent to higher degree polynomial approximations. The GA yields the degree and values of a set of coefficients of the polynomials approximating of the image of a face. By finding a family of characteristic polynomials from several variables (pixel characteristics) for each face (say Fi ) in the data base through a resampling process the system in use, is trained. A face (say F ) is recognized by finding its characteristic polynomials and using an AdaBoost Classifier from F -s polynomials to each of the Fi -s polynomials. The winner is the polynomial family closer to F -s corresponding to target face in data base.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=AdaBoost%20Classifier" title="AdaBoost Classifier">AdaBoost Classifier</a>, <a href="https://publications.waset.org/search?q=Holistic%20Face%20Recognition" title=" Holistic Face Recognition"> Holistic Face Recognition</a>, <a href="https://publications.waset.org/search?q=Minimax%20Multivariate%20Approximation" title=" Minimax Multivariate Approximation"> Minimax Multivariate Approximation</a>, <a href="https://publications.waset.org/search?q=Genetic%20Algorithm." title=" Genetic Algorithm."> Genetic Algorithm.</a> </p> <a href="https://publications.waset.org/5603/holistic-face-recognition-using-multivariate-approximation-genetic-algorithms-and-adaboost-classifier-preliminary-results" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5603/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5603/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5603/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5603/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5603/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5603/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5603/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5603/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5603/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5603/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5603.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">1497</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">59</span> Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=M.%20Saravi">M. Saravi</a>, <a href="https://publications.waset.org/search?q=F.%20Ashrafi"> F. Ashrafi</a>, <a href="https://publications.waset.org/search?q=S.R.%20Mirrajei"> S.R. Mirrajei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chebyshev%20polynomials" title="Chebyshev polynomials">Chebyshev polynomials</a>, <a href="https://publications.waset.org/search?q=Clenshaw%20method" title=" Clenshaw method"> Clenshaw method</a>, <a href="https://publications.waset.org/search?q=ODEs" title=" ODEs"> ODEs</a>, <a href="https://publications.waset.org/search?q=Spectral%20methods" title=" Spectral methods"> Spectral methods</a> </p> <a href="https://publications.waset.org/10826/numerical-solution-of-linear-ordinary-differential-equations-in-quantum-chemistry-by-clenshaw-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10826/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10826/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10826/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10826/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10826/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10826/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10826/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10826/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10826/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10826/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10826.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">1420</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">58</span> Rational Chebyshev Tau Method for Solving Natural Convection of Darcian Fluid About a Vertical Full Cone Embedded in Porous Media Whit a Prescribed Wall Temperature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kourosh%20Parand">Kourosh Parand</a>, <a href="https://publications.waset.org/search?q=Zahra%20Delafkar"> Zahra Delafkar</a>, <a href="https://publications.waset.org/search?q=Fatemeh%20Baharifard"> Fatemeh Baharifard</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Tau%20method" title="Tau method">Tau method</a>, <a href="https://publications.waset.org/search?q=semi-infinite" title=" semi-infinite"> semi-infinite</a>, <a href="https://publications.waset.org/search?q=nonlinear%20ODE" title=" nonlinear ODE"> nonlinear ODE</a>, <a href="https://publications.waset.org/search?q=rational%20Chebyshev" title=" rational Chebyshev"> rational Chebyshev</a>, <a href="https://publications.waset.org/search?q=porous%20media." title=" porous media."> porous media.</a> </p> <a href="https://publications.waset.org/2817/rational-chebyshev-tau-method-for-solving-natural-convection-of-darcian-fluid-about-a-vertical-full-cone-embedded-in-porous-media-whit-a-prescribed-wall-temperature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2817/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2817/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2817/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2817/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2817/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2817/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2817/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2817/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2817/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2817/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2817.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">1933</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">57</span> A Numerical Solution Based On Operational Matrix of Differentiation of Shifted Second Kind Chebyshev Wavelets for a Stefan Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rajeev">Rajeev</a>, <a href="https://publications.waset.org/search?q=N.%20K.%20Raigar"> N. K. Raigar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Operational%20matrix%20of%20differentiation" title="Operational matrix of differentiation">Operational matrix of differentiation</a>, <a href="https://publications.waset.org/search?q=Similarity%0D%0Atransformation" title=" Similarity transformation"> Similarity transformation</a>, <a href="https://publications.waset.org/search?q=Shifted%20second%20kind%20Chebyshev%20wavelets" title=" Shifted second kind Chebyshev wavelets"> Shifted second kind Chebyshev wavelets</a>, <a href="https://publications.waset.org/search?q=Stefan%0D%0Aproblem." title=" Stefan problem."> Stefan problem.</a> </p> <a href="https://publications.waset.org/10001955/a-numerical-solution-based-on-operational-matrix-of-differentiation-of-shifted-second-kind-chebyshev-wavelets-for-a-stefan-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10001955/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10001955/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10001955/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10001955/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10001955/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10001955/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10001955/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10001955/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10001955/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10001955/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10001955.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">2001</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">56</span> Fuzzy Fingerprint Vault using Multiple Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Daesung%20Moon">Daesung Moon</a>, <a href="https://publications.waset.org/search?q=Woo-Yong%20Choi"> Woo-Yong Choi</a>, <a href="https://publications.waset.org/search?q=Kiyoung%20Moon"> Kiyoung Moon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fuzzy%20vault" title="Fuzzy vault">Fuzzy vault</a>, <a href="https://publications.waset.org/search?q=fingerprint%20recognition%20multiple%20polynomials." title=" fingerprint recognition multiple polynomials."> fingerprint recognition multiple polynomials.</a> </p> <a href="https://publications.waset.org/4275/fuzzy-fingerprint-vault-using-multiple-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4275/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4275/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4275/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4275/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4275/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4275/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4275/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4275/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4275/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4275/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4275.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">1547</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">55</span> Image Adaptive Watermarking with Visual Model in Orthogonal Polynomials based Transformation Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Krishnamoorthi%20R.">Krishnamoorthi R.</a>, <a href="https://publications.waset.org/search?q=Sheba%20Kezia%20Malarchelvi%20P.%20D."> Sheba Kezia Malarchelvi P. D.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an image adaptive, invisible digital watermarking algorithm with Orthogonal Polynomials based Transformation (OPT) is proposed, for copyright protection of digital images. The proposed algorithm utilizes a visual model to determine the watermarking strength necessary to invisibly embed the watermark in the mid frequency AC coefficients of the cover image, chosen with a secret key. The visual model is designed to generate a Just Noticeable Distortion mask (JND) by analyzing the low level image characteristics such as textures, edges and luminance of the cover image in the orthogonal polynomials based transformation domain. Since the secret key is required for both embedding and extraction of watermark, it is not possible for an unauthorized user to extract the embedded watermark. The proposed scheme is robust to common image processing distortions like filtering, JPEG compression and additive noise. Experimental results show that the quality of OPT domain watermarked images is better than its DCT counterpart. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Orthogonal%20Polynomials%20based%20Transformation" title="Orthogonal Polynomials based Transformation">Orthogonal Polynomials based Transformation</a>, <a href="https://publications.waset.org/search?q=Digital%20Watermarking" title="Digital Watermarking">Digital Watermarking</a>, <a href="https://publications.waset.org/search?q=Copyright%20Protection" title=" Copyright Protection"> Copyright Protection</a>, <a href="https://publications.waset.org/search?q=Visual%20model." title=" Visual model."> Visual model.</a> </p> <a href="https://publications.waset.org/6832/image-adaptive-watermarking-with-visual-model-in-orthogonal-polynomials-based-transformation-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6832/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6832/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6832/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6832/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6832/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6832/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6832/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6832/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6832/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6832/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6832.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">1696</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">54</span> Optimal Control of a Linear Distributed Parameter System via Shifted Legendre Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sanjeeb%20Kumar%20Kar">Sanjeeb Kumar Kar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Optimal%20control" title="Optimal control">Optimal control</a>, <a href="https://publications.waset.org/search?q=linear%20systems" title=" linear systems"> linear systems</a>, <a href="https://publications.waset.org/search?q=distributed%20parametersystems" title=" distributed parametersystems"> distributed parametersystems</a>, <a href="https://publications.waset.org/search?q=Legendre%20polynomials." title=" Legendre polynomials."> Legendre polynomials.</a> </p> <a href="https://publications.waset.org/5466/optimal-control-of-a-linear-distributed-parameter-system-via-shifted-legendre-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5466/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5466/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5466/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5466/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5466/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5466/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5466/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5466/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5466/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5466/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5466.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">1311</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">53</span> Codebook Generation for Vector Quantization on Orthogonal Polynomials based Transform Coding</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=R.%20Krishnamoorthi">R. Krishnamoorthi</a>, <a href="https://publications.waset.org/search?q=N.%20Kannan"> N. Kannan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a new algorithm for generating codebook is proposed for vector quantization (VQ) in image coding. The significant features of the training image vectors are extracted by using the proposed Orthogonal Polynomials based transformation. We propose to generate the codebook by partitioning these feature vectors into a binary tree. Each feature vector at a non-terminal node of the binary tree is directed to one of the two descendants by comparing a single feature associated with that node to a threshold. The binary tree codebook is used for encoding and decoding the feature vectors. In the decoding process the feature vectors are subjected to inverse transformation with the help of basis functions of the proposed Orthogonal Polynomials based transformation to get back the approximated input image training vectors. The results of the proposed coding are compared with the VQ using Discrete Cosine Transform (DCT) and Pairwise Nearest Neighbor (PNN) algorithm. The new algorithm results in a considerable reduction in computation time and provides better reconstructed picture quality.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Orthogonal%20Polynomials" title="Orthogonal Polynomials">Orthogonal Polynomials</a>, <a href="https://publications.waset.org/search?q=Image%20Coding" title=" Image Coding"> Image Coding</a>, <a href="https://publications.waset.org/search?q=Vector%20Quantization" title=" Vector Quantization"> Vector Quantization</a>, <a href="https://publications.waset.org/search?q=TSVQ" title=" TSVQ"> TSVQ</a>, <a href="https://publications.waset.org/search?q=Binary%20Tree%20Classifier" title=" Binary Tree Classifier"> Binary Tree Classifier</a> </p> <a href="https://publications.waset.org/5503/codebook-generation-for-vector-quantization-on-orthogonal-polynomials-based-transform-coding" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5503/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5503/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5503/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5503/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5503/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5503/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5503/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5503/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5503/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5503/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5503.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">2150</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">52</span> Factoring a Polynomial with Multiple-Roots</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Feng%20Cheng%20Chang">Feng Cheng Chang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A given polynomial, possibly with multiple roots, is factored into several lower-degree distinct-root polynomials with natural-order-integer powers. All the roots, including multiplicities, of the original polynomial may be obtained by solving these lowerdegree distinct-root polynomials, instead of the original high-degree multiple-root polynomial directly. The approach requires polynomial Greatest Common Divisor (GCD) computation. The very simple and effective process, “Monic polynomial subtractions" converted trickily from “Longhand polynomial divisions" of Euclidean algorithm is employed. It requires only simple elementary arithmetic operations without any advanced mathematics. Amazingly, the derived routine gives the expected results for the test polynomials of very high degree, such as p( x) =(x+1)1000. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Polynomial%20roots" title="Polynomial roots">Polynomial roots</a>, <a href="https://publications.waset.org/search?q=greatest%20common%20divisor" title=" greatest common divisor"> greatest common divisor</a>, <a href="https://publications.waset.org/search?q=Longhand%20polynomial%20division" title=" Longhand polynomial division"> Longhand polynomial division</a>, <a href="https://publications.waset.org/search?q=Euclidean%20GCD%20Algorithm." title=" Euclidean GCD Algorithm."> Euclidean GCD Algorithm.</a> </p> <a href="https://publications.waset.org/10086/factoring-a-polynomial-with-multiple-roots" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10086/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10086/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10086/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10086/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10086/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10086/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10086/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10086/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10086/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10086/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10086.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">1577</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">51</span> A Comparison of Recent Methods for Solving a Model 1D Convection Diffusion Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ashvin%20Gopaul">Ashvin Gopaul</a>, <a href="https://publications.waset.org/search?q=Jayrani%20Cheeneebash"> Jayrani Cheeneebash</a>, <a href="https://publications.waset.org/search?q=Kamleshsing%20Baurhoo"> Kamleshsing Baurhoo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chebyshev%20Pseudospectral%20collocation%20method" title="Chebyshev Pseudospectral collocation method">Chebyshev Pseudospectral collocation method</a>, <a href="https://publications.waset.org/search?q=convection-diffusion%20equation" title=" convection-diffusion equation"> convection-diffusion equation</a>, <a href="https://publications.waset.org/search?q=restrictive%20Taylor%20approximation." title=" restrictive Taylor approximation."> restrictive Taylor approximation.</a> </p> <a href="https://publications.waset.org/8074/a-comparison-of-recent-methods-for-solving-a-model-1d-convection-diffusion-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8074/apa" target="_blank" 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