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Curves</title> <meta name="description" content="Search results for: Time-like Curves"> <meta name="keywords" content="Time-like Curves"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/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="Time-like Curves"> <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> 370</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Time-like Curves</h1> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">370</span> An Optimal Control Problem for Rigid Body Motions on Lie Group SO(2, 1)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nemat%20Abazari">Nemat Abazari</a>, <a href="https://publications.waset.org/search?q=Ilgin%20Sager"> Ilgin Sager</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.</p> <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=Hamiltonian%20vector%20field" title=" Hamiltonian vector field"> Hamiltonian vector field</a>, <a href="https://publications.waset.org/search?q=Darboux%20vector" title=" Darboux vector"> Darboux vector</a>, <a href="https://publications.waset.org/search?q=maximum%20principle" title=" maximum principle"> maximum principle</a>, <a href="https://publications.waset.org/search?q=lie%20group" title=" lie group"> lie group</a>, <a href="https://publications.waset.org/search?q=Rigid%20body%20motion" title=" Rigid body motion"> Rigid body motion</a>, <a href="https://publications.waset.org/search?q=Lorentz%20metric." title=" Lorentz metric."> Lorentz metric.</a> </p> <a href="https://publications.waset.org/5392/an-optimal-control-problem-for-rigid-body-motions-on-lie-group-so2-1" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5392/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5392/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5392/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5392/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5392/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5392/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5392/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5392/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5392/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5392/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5392.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">1334</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">369</span> Planning Rigid Body Motions and Optimal Control Problem on Lie Group SO(2, 1)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nemat%20Abazari">Nemat Abazari</a>, <a href="https://publications.waset.org/search?q=Ilgin%20Sager"> Ilgin Sager</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.</p> <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=Hamiltonian%20vector%20field" title=" Hamiltonian vector field"> Hamiltonian vector field</a>, <a href="https://publications.waset.org/search?q=Darboux%20vector" title=" Darboux vector"> Darboux vector</a>, <a href="https://publications.waset.org/search?q=maximum%20principle" title=" maximum principle"> maximum principle</a>, <a href="https://publications.waset.org/search?q=lie%20group" title=" lie group"> lie group</a>, <a href="https://publications.waset.org/search?q=rigid%20body%20motion" title=" rigid body motion"> rigid body motion</a>, <a href="https://publications.waset.org/search?q=Lorentz%20metric." title=" Lorentz metric."> Lorentz metric.</a> </p> <a href="https://publications.waset.org/12800/planning-rigid-body-motions-and-optimal-control-problem-on-lie-group-so2-1" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12800/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12800/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12800/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12800/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12800/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12800/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12800/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12800/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12800/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12800/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12800.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">1570</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">368</span> Some Characterizations of Isotropic Curves In the Euclidean Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=S%C3%BCha%20Y%C4%B1lmaz">Süha Yılmaz</a>, <a href="https://publications.waset.org/search?q=Melih%20Turgut"> Melih Turgut</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Classical%20Differential%20Geometry" title="Classical Differential Geometry">Classical Differential Geometry</a>, <a href="https://publications.waset.org/search?q=Euclidean%20space" title=" Euclidean space"> Euclidean space</a>, <a href="https://publications.waset.org/search?q=Minimal%20Curves" title=" Minimal Curves"> Minimal Curves</a>, <a href="https://publications.waset.org/search?q=Isotropic%20Curves" title=" Isotropic Curves"> Isotropic Curves</a>, <a href="https://publications.waset.org/search?q=Pseudo%20Helix." title=" Pseudo Helix."> Pseudo Helix.</a> </p> <a href="https://publications.waset.org/1544/some-characterizations-of-isotropic-curves-in-the-euclidean-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1544/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1544/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1544/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1544/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1544/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1544/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1544/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1544/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1544/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1544/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1544.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">1982</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">367</span> A New Implementation of Miura-Arita Algorithm for Miura Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20Basiri">A. Basiri</a>, <a href="https://publications.waset.org/search?q=S.%20Rahmany"> S. Rahmany</a>, <a href="https://publications.waset.org/search?q=D.%20Khatibi"> D. Khatibi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The aim of this paper is to review some of standard fact on Miura curves. We give some easy theorem in number theory to define Miura curves, then we present a new implementation of Arita algorithm for Miura curves.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Miura%20curve" title="Miura curve">Miura curve</a>, <a href="https://publications.waset.org/search?q=discrete%20logarithm%20problem" title=" discrete logarithm problem"> discrete logarithm problem</a>, <a href="https://publications.waset.org/search?q=algebraic%20curve%20cryptography" title=" algebraic curve cryptography"> algebraic curve cryptography</a>, <a href="https://publications.waset.org/search?q=Jacobian%20group." title=" Jacobian group."> Jacobian group.</a> </p> <a href="https://publications.waset.org/16031/a-new-implementation-of-miura-arita-algorithm-for-miura-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16031/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16031/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16031/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16031/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16031/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16031/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16031/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16031/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16031/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16031/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16031.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">1463</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">366</span> Box Counting Dimension of the Union L of Trinomial Curves When α ≥ 1</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Kaoutar%20Lamrini%20Uahabi">Kaoutar Lamrini Uahabi</a>, <a href="https://publications.waset.org/search?q=Mohamed%20Atounti"> Mohamed Atounti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Feasible%20angles" title="Feasible angles">Feasible angles</a>, <a href="https://publications.waset.org/search?q=fractal%20dimension" title=" fractal dimension"> fractal dimension</a>, <a href="https://publications.waset.org/search?q=Minkowski%0D%0Asausage" title=" Minkowski sausage"> Minkowski sausage</a>, <a href="https://publications.waset.org/search?q=trinomial%20curves" title=" trinomial curves"> trinomial curves</a>, <a href="https://publications.waset.org/search?q=trinomial%20equation." title=" trinomial equation."> trinomial equation.</a> </p> <a href="https://publications.waset.org/10010081/box-counting-dimension-of-the-union-l-of-trinomial-curves-when-a-1" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010081/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010081/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010081/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010081/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010081/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010081/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010081/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010081/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010081/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010081/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010081.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">631</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">365</span> Finding More Non-Supersingular Elliptic Curves for Pairing-Based Cryptosystems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Pu%20Duan">Pu Duan</a>, <a href="https://publications.waset.org/search?q=Shi%20Cui"> Shi Cui</a>, <a href="https://publications.waset.org/search?q=Choong%20Wah%20Chan"> Choong Wah Chan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Finding suitable non-supersingular elliptic curves for pairing-based cryptosystems becomes an important issue for the modern public-key cryptography after the proposition of id-based encryption scheme and short signature scheme. In previous work different algorithms have been proposed for finding such elliptic curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3, 4, 5}. In this paper a new method is presented to find more non-supersingular elliptic curves for pairing-based cryptosystems with general embedding degree k and large values of cofactor h. In addition, some effective parameters of these non-supersingular elliptic curves are provided in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Family%20of%20group%20order" title="Family of group order">Family of group order</a>, <a href="https://publications.waset.org/search?q=kth%20root%20of%20unity" title=" kth root of unity"> kth root of unity</a>, <a href="https://publications.waset.org/search?q=non-supersingular%20elliptic%20curves%20polynomial%20field." title=" non-supersingular elliptic curves polynomial field."> non-supersingular elliptic curves polynomial field.</a> </p> <a href="https://publications.waset.org/15628/finding-more-non-supersingular-elliptic-curves-for-pairing-based-cryptosystems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15628/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15628/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15628/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15628/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15628/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15628/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15628/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15628/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15628/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15628/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15628.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">1734</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">364</span> New DES based on Elliptic Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ghada%20Abdelmouez%20M.">Ghada Abdelmouez M.</a>, <a href="https://publications.waset.org/search?q=Fathy%20S.%20Helail"> Fathy S. Helail</a>, <a href="https://publications.waset.org/search?q=Abdellatif%20A.%20Elkouny"> Abdellatif A. Elkouny</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is known that symmetric encryption algorithms are fast and easy to implement in hardware. Also elliptic curves have proved to be a good choice for building encryption system. Although most of the symmetric systems have been broken, we can create a hybrid system that has the same properties of the symmetric encryption systems and in the same time, it has the strength of elliptic curves in encryption. As DES algorithm is considered the core of all successive symmetric encryption systems, we modified DES using elliptic curves and built a new DES algorithm that is hard to be broken and will be the core for all other symmetric systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=DES" title="DES">DES</a>, <a href="https://publications.waset.org/search?q=Elliptic%20Curves" title=" Elliptic Curves"> Elliptic Curves</a>, <a href="https://publications.waset.org/search?q=hybrid%20system" title=" hybrid system"> hybrid system</a>, <a href="https://publications.waset.org/search?q=symmetricencryption." title=" symmetricencryption."> symmetricencryption.</a> </p> <a href="https://publications.waset.org/6572/new-des-based-on-elliptic-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6572/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6572/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6572/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6572/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6572/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6572/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6572/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6572/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6572/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6572/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6572.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">1737</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">363</span> On the Differential Geometry of the Curves in Minkowski Space-Time II</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=S%C3%BCha%20Y%C4%B1lmaz">Süha Yılmaz</a>, <a href="https://publications.waset.org/search?q=Emin%20%C3%96zy%C4%B1lmaz"> Emin Özyılmaz</a>, <a href="https://publications.waset.org/search?q=Melih%20Turgut"> Melih Turgut</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Frenet%20Apparatus" title="Frenet Apparatus">Frenet Apparatus</a>, <a href="https://publications.waset.org/search?q=Time-like%20Curves" title=" Time-like Curves"> Time-like Curves</a>, <a href="https://publications.waset.org/search?q=MinkowskiSpace-time." title=" MinkowskiSpace-time."> MinkowskiSpace-time.</a> </p> <a href="https://publications.waset.org/2333/on-the-differential-geometry-of-the-curves-in-minkowski-space-time-ii" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2333/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2333/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2333/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2333/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2333/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2333/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2333/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2333/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2333/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2333/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2333.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">1662</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">362</span> Regionalization of IDF Curves with L-Moments for Storm Events</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Noratiqah%20Mohd%20Ariff">Noratiqah Mohd Ariff</a>, <a href="https://publications.waset.org/search?q=Abdul%20Aziz%20Jemain"> Abdul Aziz Jemain</a>, <a href="https://publications.waset.org/search?q=Mohd%20Aftar%20Abu%20Bakar"> Mohd Aftar Abu Bakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The construction of Intensity-Duration-Frequency (IDF) curves is one of the most common and useful tools in order to design hydraulic structures and to provide a mathematical relationship between rainfall characteristics. IDF curves, especially those in Peninsular Malaysia, are often built using moving windows of rainfalls. However, these windows do not represent the actual rainfall events since the duration of rainfalls is usually prefixed. Hence, instead of using moving windows, this study aims to find regionalized distributions for IDF curves of extreme rainfalls based on storm events. Homogeneity test is performed on annual maximum of storm intensities to identify homogeneous regions of storms in Peninsular Malaysia. The L-moment method is then used to regionalized Generalized Extreme Value (GEV) distribution of these annual maximums and subsequently. IDF curves are constructed using the regional distributions. The differences between the IDF curves obtained and IDF curves found using at-site GEV distributions are observed through the computation of the coefficient of variation of root mean square error, mean percentage difference and the coefficient of determination. The small differences implied that the construction of IDF curves could be simplified by finding a general probability distribution of each region. This will also help in constructing IDF curves for sites with no rainfall station.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=IDF%20curves" title="IDF curves">IDF curves</a>, <a href="https://publications.waset.org/search?q=L-moments" title=" L-moments"> L-moments</a>, <a href="https://publications.waset.org/search?q=regionalization" title=" regionalization"> regionalization</a>, <a href="https://publications.waset.org/search?q=storm%20events." title=" storm events. "> storm events. </a> </p> <a href="https://publications.waset.org/10004224/regionalization-of-idf-curves-with-l-moments-for-storm-events" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10004224/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10004224/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10004224/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10004224/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10004224/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10004224/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10004224/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10004224/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10004224/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10004224/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10004224.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">1714</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">361</span> On Frenet-Serret Invariants of Non-Null Curves in Lorentzian Space L5</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Melih%20Turgut">Melih Turgut</a>, <a href="https://publications.waset.org/search?q=Jos%C3%A9%20Luis%20L%C3%B3pez-Bonilla"> José Luis López-Bonilla</a>, <a href="https://publications.waset.org/search?q=S%C3%BCha%20Y%C4%B1lmaz"> Süha Yılmaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The aim of this paper is to determine Frenet-Serret invariants of non-null curves in Lorentzian 5-space. First, we define a vector product of four vectors, by this way, we present a method to calculate Frenet-Serret invariants of the non-null curves. Additionally, an algebraic example of presented method is illustrated.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lorentzian%205-space" title="Lorentzian 5-space">Lorentzian 5-space</a>, <a href="https://publications.waset.org/search?q=Frenet-Serret%20Invariants" title=" Frenet-Serret Invariants"> Frenet-Serret Invariants</a>, <a href="https://publications.waset.org/search?q=Nonnull%0D%0ACurves" title=" Nonnull Curves"> Nonnull Curves</a> </p> <a href="https://publications.waset.org/8233/on-frenet-serret-invariants-of-non-null-curves-in-lorentzian-space-l5" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8233/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8233/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8233/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8233/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8233/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8233/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8233/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8233/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8233/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8233/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8233.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">1532</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">360</span> Centrifuge Modeling of Monopiles Subjected to Lateral Monotonic Loading</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=H.%20R.%20Khodaei">H. R. Khodaei</a>, <a href="https://publications.waset.org/search?q=M.%20Moradi"> M. Moradi</a>, <a href="https://publications.waset.org/search?q=A.%20H.%20Tajik"> A. H. Tajik</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The type of foundation commonly used today for berthing dolphins is a set of tubular steel piles with large diameters, which are known as monopiles. The design of these monopiles is based on the theories related with laterally loaded piles. One of the most common methods to analyze and design the piles subjected to lateral loads is the p-y curves. In the present study, centrifuge tests are conducted in order to obtain the p-y curves. Series of tests were designed in order to investigate the scaling laws in the centrifuge for monotonic loading. Also, two important parameters, the embedded depth L of the pile in the soil and free length e of the pile, as well as their ratios were studied via five experimental tests. Finally, the p-y curves of API are presented to be compared with the curves obtained from the tests so that the differences could be demonstrated. The results show that the p-y curves proposed by API highly overestimate the lateral load bearing capacity. It suggests that these curves need correction and modification for each site as the soil conditions change.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Centrifuge%20modeling" title="Centrifuge modeling">Centrifuge modeling</a>, <a href="https://publications.waset.org/search?q=monopile" title=" monopile"> monopile</a>, <a href="https://publications.waset.org/search?q=lateral%20loading" title=" lateral loading"> lateral loading</a>, <a href="https://publications.waset.org/search?q=p-y%20curves." title=" p-y curves. "> p-y curves. </a> </p> <a href="https://publications.waset.org/10008582/centrifuge-modeling-of-monopiles-subjected-to-lateral-monotonic-loading" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10008582/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10008582/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10008582/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10008582/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10008582/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10008582/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10008582/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10008582/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10008582/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10008582/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10008582.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">850</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">359</span> The Number of Rational Points on Elliptic Curves y2 = x3 + b2 Over Finite Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Bet%C3%BCl%20Gezer">Betül Gezer</a>, <a href="https://publications.waset.org/search?q=Hacer%20%C3%96zden"> Hacer Özden</a>, <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan"> Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Osman%20Bizim"> Osman Bizim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p &equiv; 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curves%20over%20finite%20fields" title="Elliptic curves over finite fields">Elliptic curves over finite fields</a>, <a href="https://publications.waset.org/search?q=rational%20points%20on%20elliptic%20curves." title=" rational points on elliptic curves."> rational points on elliptic curves.</a> </p> <a href="https://publications.waset.org/3721/the-number-of-rational-points-on-elliptic-curves-y2-x3-b2-over-finite-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3721/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3721/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3721/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3721/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3721/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3721/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3721/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3721/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3721/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3721/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3721.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">1942</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">358</span> The Number of Rational Points on Elliptic Curves and Circles over Finite Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Bet%C3%BCl%20Gezer">Betül Gezer</a>, <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan"> Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Osman%20Bizim"> Osman Bizim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curves%20over%20finite%20fields" title="Elliptic curves over finite fields">Elliptic curves over finite fields</a>, <a href="https://publications.waset.org/search?q=rational%20points%20on%0Aelliptic%20curves%20and%20circles." title=" rational points on elliptic curves and circles."> rational points on elliptic curves and circles.</a> </p> <a href="https://publications.waset.org/12784/the-number-of-rational-points-on-elliptic-curves-and-circles-over-finite-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12784/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12784/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12784/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12784/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12784/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12784/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12784/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12784/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12784/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12784/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12784.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">2041</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">357</span> Contributions to Differential Geometry of Pseudo Null Curves in Semi-Euclidean Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Melih%20Turgut">Melih Turgut</a>, <a href="https://publications.waset.org/search?q=S%C3%BCha%20Y%C4%B1lmaz"> Süha Yılmaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Semi-Euclidean%20Space" title="Semi-Euclidean Space">Semi-Euclidean Space</a>, <a href="https://publications.waset.org/search?q=Pseudo%20Null%20Curves" title=" Pseudo Null Curves"> Pseudo Null Curves</a>, <a href="https://publications.waset.org/search?q=Position%20Vectors." title=" Position Vectors."> Position Vectors.</a> </p> <a href="https://publications.waset.org/696/contributions-to-differential-geometry-of-pseudo-null-curves-in-semi-euclidean-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/696/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/696/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/696/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/696/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/696/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/696/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/696/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/696/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/696/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/696/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/696.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">1345</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">356</span> Classification of the Bachet Elliptic Curves y2 = x3 + a3 in Fp, where p ≡ 1 (mod 6) is Prime</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nazli%20Yildiz%20%C4%B0kikardes">Nazli Yildiz İkikardes</a>, <a href="https://publications.waset.org/search?q=Gokhan%20Soydan"> Gokhan Soydan</a>, <a href="https://publications.waset.org/search?q=Musa%20Demirci"> Musa Demirci</a>, <a href="https://publications.waset.org/search?q=Ismail%20Naci%20Cangul"> Ismail Naci Cangul</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we first give in what fields Fp, the cubic root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote the sets of quadratic and non-zero cubic residues modulo p. Then we use these to obtain some results on the classification of the Bachet elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curves%20over%20finite%20fields" title="Elliptic curves over finite fields">Elliptic curves over finite fields</a>, <a href="https://publications.waset.org/search?q=quadratic%20residue" title=" quadratic residue"> quadratic residue</a>, <a href="https://publications.waset.org/search?q=cubic%20residue." title=" cubic residue."> cubic residue.</a> </p> <a href="https://publications.waset.org/11483/classification-of-the-bachet-elliptic-curves-y2-x3-a3-in-fp-where-p-1-mod-6-is-prime" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11483/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11483/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11483/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11483/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11483/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11483/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11483/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11483/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11483/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11483/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11483.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">1856</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">355</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">354</span> The Elliptic Curves y2 = x3 - t2x over Fp</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curves%20over%20finite%20fields" title="Elliptic curves over finite fields">Elliptic curves over finite fields</a>, <a href="https://publications.waset.org/search?q=rational%20points%20onelliptic%20curves" title=" rational points onelliptic curves"> rational points onelliptic curves</a>, <a href="https://publications.waset.org/search?q=rank" title=" rank"> rank</a>, <a href="https://publications.waset.org/search?q=trace%20of%20Frobenius." title=" trace of Frobenius."> trace of Frobenius.</a> </p> <a href="https://publications.waset.org/5174/the-elliptic-curves-y2-x3-t2x-over-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5174/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5174/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5174/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5174/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5174/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5174/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5174/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5174/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5174/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5174/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5174.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">2031</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">353</span> Single Feed Circularly Polarized Poly Fractal Antenna for Wireless Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=V.%20V.%20Reddy">V. V. Reddy</a>, <a href="https://publications.waset.org/search?q=N.%20V.%20S.%20N.%20Sarma"> N. V. S. N. Sarma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A circularly polarized fractal boundary microstrip antenna is presented. The sides of a square patch along x- axis, yaxis are replaced with Minkowski and Koch curves correspondingly. By using the fractal curves as edges, asymmetry in the structure is created to excite two orthogonal modes for circular polarization (CP) operation. The indentation factors of the fractal curves are optimized for pure CP. The simulated results of the novel polyfractal antenna are demonstrated.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Circular%20polarization" title="Circular polarization">Circular polarization</a>, <a href="https://publications.waset.org/search?q=Fractal" title=" Fractal"> Fractal</a>, <a href="https://publications.waset.org/search?q=Koch" title=" Koch"> Koch</a>, <a href="https://publications.waset.org/search?q=Minkowski." title=" Minkowski."> Minkowski.</a> </p> <a href="https://publications.waset.org/9999663/single-feed-circularly-polarized-poly-fractal-antenna-for-wireless-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9999663/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9999663/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9999663/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9999663/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9999663/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9999663/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9999663/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9999663/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9999663/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9999663/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9999663.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">2506</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">352</span> An Approach to Polynomial Curve Comparison in Geometric Object Database</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Chanon%20Aphirukmatakun">Chanon Aphirukmatakun</a>, <a href="https://publications.waset.org/search?q=Natasha%20Dejdumrong"> Natasha Dejdumrong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In image processing and visualization, comparing two bitmapped images needs to be compared from their pixels by matching pixel-by-pixel. Consequently, it takes a lot of computational time while the comparison of two vector-based images is significantly faster. Sometimes these raster graphics images can be approximately converted into the vector-based images by various techniques. After conversion, the problem of comparing two raster graphics images can be reduced to the problem of comparing vector graphics images. Hence, the problem of comparing pixel-by-pixel can be reduced to the problem of polynomial comparisons. In computer aided geometric design (CAGD), the vector graphics images are the composition of curves and surfaces. Curves are defined by a sequence of control points and their polynomials. In this paper, the control points will be considerably used to compare curves. The same curves after relocated or rotated are treated to be equivalent while two curves after different scaled are considered to be similar curves. This paper proposed an algorithm for comparing the polynomial curves by using the control points for equivalence and similarity. In addition, the geometric object-oriented database used to keep the curve information has also been defined in XML format for further used in curve comparisons. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Bezier%20curve" title="Bezier curve">Bezier curve</a>, <a href="https://publications.waset.org/search?q=Said-Ball%20curve" title=" Said-Ball curve"> Said-Ball curve</a>, <a href="https://publications.waset.org/search?q=Wang-Ball%20curve" title=" Wang-Ball curve"> Wang-Ball curve</a>, <a href="https://publications.waset.org/search?q=DP%20curve" title=" DP curve"> DP curve</a>, <a href="https://publications.waset.org/search?q=CAGD" title=" CAGD"> CAGD</a>, <a href="https://publications.waset.org/search?q=comparison" title=" comparison"> comparison</a>, <a href="https://publications.waset.org/search?q=geometric%20object%20database." title=" geometric object database."> geometric object database.</a> </p> <a href="https://publications.waset.org/4806/an-approach-to-polynomial-curve-comparison-in-geometric-object-database" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/4806/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/4806/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/4806/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/4806/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/4806/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/4806/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/4806/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/4806/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/4806/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/4806/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/4806.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">2218</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">351</span> Rational Points on Elliptic Curves 2 3 3y = x + a inF , where p 5(mod 6) is Prime</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gokhan%20Soydan">Gokhan Soydan</a>, <a href="https://publications.waset.org/search?q=Musa%20Demirci"> Musa Demirci</a>, <a href="https://publications.waset.org/search?q=Nazli%20Yildiz%20Ikikardes"> Nazli Yildiz Ikikardes</a>, <a href="https://publications.waset.org/search?q=Ismail%20Naci%20Cangul"> Ismail Naci Cangul</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this work, we consider the rational points on elliptic curves over finite fields Fp where p &equiv; 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 &equiv; x3 + a3(mod p), where p &equiv; 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p &equiv; 1 (mod 6) is considered in [5]. The main difference between two cases is that when p &equiv; 5 (mod 6), all elements of Fp are cubic residues.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curves%20over%20finite%20fields" title="Elliptic curves over finite fields">Elliptic curves over finite fields</a>, <a href="https://publications.waset.org/search?q=rational%20points." title=" rational points."> rational points.</a> </p> <a href="https://publications.waset.org/14639/rational-points-on-elliptic-curves-2-3-3y-x-a-inf-where-p-5mod-6-is-prime" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14639/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14639/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14639/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14639/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14639/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14639/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14639/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14639/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14639/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14639/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14639.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">2250</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">350</span> Improved of Elliptic Curves Cryptography over a Ring</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=A.%20Chillali">A. Chillali</a>, <a href="https://publications.waset.org/search?q=A.%20Tadmori"> A. Tadmori</a>, <a href="https://publications.waset.org/search?q=M.%20Ziane"> M. Ziane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20Curves" title="Elliptic Curves">Elliptic Curves</a>, <a href="https://publications.waset.org/search?q=Finite%20Ring" title=" Finite Ring"> Finite Ring</a>, <a href="https://publications.waset.org/search?q=Cryptography." title=" Cryptography."> Cryptography.</a> </p> <a href="https://publications.waset.org/10001116/improved-of-elliptic-curves-cryptography-over-a-ring" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10001116/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10001116/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10001116/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10001116/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10001116/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10001116/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10001116/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10001116/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10001116/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10001116/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10001116.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">2106</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">349</span> Arabic Character Recognition Using Regression Curves with the Expectation Maximization Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Abdullah%20A.%20AlShaher">Abdullah A. AlShaher</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2<sup>nd</sup> order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shape%20recognition" title="Shape recognition">Shape recognition</a>, <a href="https://publications.waset.org/search?q=Arabic%20handwritten%20characters" title=" Arabic handwritten characters"> Arabic handwritten characters</a>, <a href="https://publications.waset.org/search?q=regression%20curves" title=" regression curves"> regression curves</a>, <a href="https://publications.waset.org/search?q=expectation%20maximization%20algorithm." title=" expectation maximization algorithm. "> expectation maximization algorithm. </a> </p> <a href="https://publications.waset.org/10009888/arabic-character-recognition-using-regression-curves-with-the-expectation-maximization-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10009888/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10009888/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10009888/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10009888/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10009888/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10009888/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10009888/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10009888/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10009888/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10009888/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10009888.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">713</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">348</span> Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Binary%20quadratic%20form" title="Binary quadratic form">Binary quadratic form</a>, <a href="https://publications.waset.org/search?q=elliptic%20curves" title=" elliptic curves"> elliptic curves</a>, <a href="https://publications.waset.org/search?q=cubic%20congruence." title=" cubic congruence."> cubic congruence.</a> </p> <a href="https://publications.waset.org/9336/positive-definite-quadratic-forms-elliptic-curves-and-cubic-congruences" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9336/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9336/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9336/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9336/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9336/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9336/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9336/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9336/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9336/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9336/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9336.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">1527</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">347</span> Entropy based Expeditive Methodology for Rating Curves Assessment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=D.%20Mirauda">D. Mirauda</a>, <a href="https://publications.waset.org/search?q=M.%20Greco"> M. Greco</a>, <a href="https://publications.waset.org/search?q=P.%20Moscarelli"> P. Moscarelli</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The river flow forecasting represents a crucial point to employ for improving a management policy addressed to the right use of water resources as well as for conjugating prevention and defense actions against environmental degradation. The difficulties occurring during the field activities encourage the development and implementation of operative computation and measuring methods addressed to time reduction for data acquisition and processing maintaining a good level of accuracy. Therefore, the aim of the present work is to test a new entropy based expeditive methodology for the evaluation of the rating curves on three gauged sections with different geometric and morphological characteristics. The methodology requires the choice of only three verticals along the measure section and the sampling of only the maximum velocity. The results underline how in most conditions the rating curves drawn can replace those built with classic methodologies, simplifying thus the procedures of data monitoring and calculation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=gauged%20station" title="gauged station">gauged station</a>, <a href="https://publications.waset.org/search?q=entropic%20approach" title=" entropic approach"> entropic approach</a>, <a href="https://publications.waset.org/search?q=expeditive%0D%0Amethodology" title=" expeditive methodology"> expeditive methodology</a>, <a href="https://publications.waset.org/search?q=rating%20curves." title=" rating curves."> rating curves.</a> </p> <a href="https://publications.waset.org/12315/entropy-based-expeditive-methodology-for-rating-curves-assessment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12315/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12315/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12315/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12315/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12315/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12315/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12315/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12315/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12315/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12315/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12315.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">1411</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">346</span> Elliptic Divisibility Sequences over Finite Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Bet%C3%BCl%20Gezer">Betül Gezer</a>, <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan"> Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Osman%20Bizim"> Osman Bizim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we study elliptic divisibility sequences over finite fields. Morgan Ward in [14], [15] gave arithmetic theory of elliptic divisibility sequences and formulas for elliptic divisibility sequences with rank two over finite field Fp. We study elliptic divisibility sequences with rank three, four and five over a finite field Fp, where p > 3 is a prime and give general terms of these sequences and then we determine elliptic and singular curves associated with these sequences. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20divisibility%20sequences" title="Elliptic divisibility sequences">Elliptic divisibility sequences</a>, <a href="https://publications.waset.org/search?q=singular%20elliptic%20divisibilitysequences" title=" singular elliptic divisibilitysequences"> singular elliptic divisibilitysequences</a>, <a href="https://publications.waset.org/search?q=elliptic%20curves" title=" elliptic curves"> elliptic curves</a>, <a href="https://publications.waset.org/search?q=singular%20curves." title=" singular curves."> singular curves.</a> </p> <a href="https://publications.waset.org/13933/elliptic-divisibility-sequences-over-finite-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13933/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13933/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13933/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13933/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13933/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13933/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13933/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13933/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13933/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13933/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13933.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">1705</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">345</span> The Use of S Curves in Technology Forecasting and its Application On 3D TV Technology</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gizem%20Intepe">Gizem Intepe</a>, <a href="https://publications.waset.org/search?q=Tufan%20Koc"> Tufan Koc</a> </p> <p class="card-text"><strong>Abstract:</strong></p> S-Curves are commonly used in technology forecasting. They show the paths of product performance in relation to time or investment in R&D. It is a useful tool to describe the inflection points and the limit of improvement of a technology. Companies use this information to base their innovation strategies. However inadequate use and some limitations of this technique lead to problems in decision making. In this paper first technology forecasting and its importance for company level strategies will be discussed. Secondly the S-Curve and its place among other forecasting techniques will be introduced. Thirdly its use in technology forecasting will be discussed based on its advantages, disadvantages and limitations. Finally an application of S-curve on 3D TV technology using patent data will also be presented and the results will be discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Patent%20analysis" title="Patent analysis">Patent analysis</a>, <a href="https://publications.waset.org/search?q=Technological%20forecasting.%20S%20curves" title=" Technological forecasting. S curves"> Technological forecasting. S curves</a>, <a href="https://publications.waset.org/search?q=3D%20TV" title=" 3D TV"> 3D TV</a> </p> <a href="https://publications.waset.org/13173/the-use-of-s-curves-in-technology-forecasting-and-its-application-on-3d-tv-technology" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13173/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13173/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13173/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13173/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13173/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13173/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13173/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13173/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13173/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13173/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13173.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">7784</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">344</span> Flow Duration Curves and Recession Curves Connection through a Mathematical Link</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Elena%20Carcano">Elena Carcano</a>, <a href="https://publications.waset.org/search?q=Mirzi%20Betasolo"> Mirzi Betasolo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This study helps Public Water Bureaus in giving reliable answers to water concession requests. Rapidly increasing water requests can be supported provided that further uses of a river course are not totally compromised, and environmental features are protected as well. Strictly speaking, a water concession can be considered a continuous drawing from the source and causes a mean annual streamflow reduction. Therefore, deciding if a water concession is appropriate or inappropriate seems to be easily solved by comparing the generic demand to the mean annual streamflow value at disposal. Still, the immediate shortcoming for such a comparison is that streamflow data are information available only for few catchments and, most often, limited to specific sites. Subsequently, comparing the generic water demand to mean daily discharge is indeed far from being completely satisfactory since the mean daily streamflow is greater than the water withdrawal for a long period of a year. Consequently, such a comparison appears to be of little significance in order to preserve the quality and the quantity of the river. In order to overcome such a limit, this study aims to complete the information provided by flow duration curves introducing a link between Flow Duration Curves (FDCs) and recession curves and aims to show the chronological sequence of flows with a particular focus on low flow data. The analysis is carried out on 25 catchments located in North-Eastern Italy for which daily data are provided. The results identify groups of catchments as hydrologically homogeneous, having the lower part of the FDCs (corresponding streamflow interval is streamflow Q between 300 and 335, namely: Q(300), Q(335)) smoothly reproduced by a common recession curve. In conclusion, the results are useful to provide more reliable answers to water request, especially for those catchments which show similar hydrological response and can be used for a focused regionalization approach on low flow data. A mathematical link between streamflow duration curves and recession curves is herein provided, thus furnishing streamflow duration curves information upon a temporal sequence of data. In such a way, by introducing assumptions on recession curves, the chronological sequence upon low flow data can also be attributed to FDCs, which are known to lack this information by nature.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Chronological%20sequence%20of%20discharges" title="Chronological sequence of discharges">Chronological sequence of discharges</a>, <a href="https://publications.waset.org/search?q=recession%20curves" title=" recession curves"> recession curves</a>, <a href="https://publications.waset.org/search?q=streamflow%20duration%20curves" title=" streamflow duration curves"> streamflow duration curves</a>, <a href="https://publications.waset.org/search?q=water%20concession." title=" water concession."> water concession.</a> </p> <a href="https://publications.waset.org/10011635/flow-duration-curves-and-recession-curves-connection-through-a-mathematical-link" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011635/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011635/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011635/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011635/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011635/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011635/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011635/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011635/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011635/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011635/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011635.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">595</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">343</span> The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Diophantine%20equation" title="Diophantine equation">Diophantine equation</a>, <a href="https://publications.waset.org/search?q=Pell%20equation" title=" Pell equation"> Pell equation</a>, <a href="https://publications.waset.org/search?q=quadratic%20form." title=" quadratic form."> quadratic form.</a> </p> <a href="https://publications.waset.org/6133/the-diophantine-equation-y2-2yx-3-0-and-corresponding-curves-over-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6133/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6133/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6133/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6133/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6133/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6133/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6133/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6133/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6133/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6133/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6133.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">1266</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">342</span> The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Musa%20Demirci">Musa Demirci</a>, <a href="https://publications.waset.org/search?q=Nazl%C4%B1%20Y%C4%B1ld%C4%B1z%20%C4%B0kikarde%C5%9F"> Nazlı Yıldız İkikardeş</a>, <a href="https://publications.waset.org/search?q=G%C3%B6khan%20Soydan"> Gökhan Soydan</a>, <a href="https://publications.waset.org/search?q=%C4%B0smail%20Naci%20Cang%C3%BCl"> İsmail Naci Cangül</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we consider the rational points on elliptic curves over finite fields Fp. We give results concerning the number of points Np,a on the elliptic curve y2 ≡ x3 +a3(mod p) according to whether a and x are quadratic residues or non-residues. We use two lemmas to prove the main results first of which gives the list of primes for which -1 is a quadratic residue, and the second is a result from [1]. We get the results in the case where p is a prime congruent to 5 modulo 6, while when p is a prime congruent to 1 modulo 6, there seems to be no regularity for Np,a. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curves%20over%20finite%20fields" title="Elliptic curves over finite fields">Elliptic curves over finite fields</a>, <a href="https://publications.waset.org/search?q=rational%20points" title=" rational points"> rational points</a>, <a href="https://publications.waset.org/search?q=quadratic%20residue." title=" quadratic residue."> quadratic residue.</a> </p> <a href="https://publications.waset.org/6891/the-number-of-rational-points-on-elliptic-curves-y2-x3-a3-on-finite-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6891/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6891/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6891/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6891/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6891/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6891/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6891/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6891/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6891/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6891/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6891.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">2402</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">341</span> An Implicit Representation of Spherical Product for Increasing the Shape Variety of Super-quadrics in Implicit Surface Modeling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Pi-Chung%20Hsu">Pi-Chung Hsu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Super-quadrics can represent a set of implicit surfaces, which can be used furthermore as primitive surfaces to construct a complex object via Boolean set operations in implicit surface modeling. In fact, super-quadrics were developed to create a parametric surface by performing spherical product on two parametric curves and some of the resulting parametric surfaces were also represented as implicit surfaces. However, because not every parametric curve can be redefined implicitly, this causes only implicit super-elliptic and super-hyperbolic curves are applied to perform spherical product and so only implicit super-ellipsoids and hyperboloids are developed in super-quadrics. To create implicit surfaces with more diverse shapes than super-quadrics, this paper proposes an implicit representation of spherical product, which performs spherical product on two implicit curves like super-quadrics do. By means of the implicit representation, many new implicit curves such as polygonal, star-shaped and rose-shaped curves can be used to develop new implicit surfaces with a greater variety of shapes than super-quadrics, such as polyhedrons, hyper-ellipsoids, superhyperboloids and hyper-toroids containing star-shaped and roseshaped major and minor circles. Besides, the newly developed implicit surfaces can also be used to define new primitive implicit surfaces for constructing a more complex implicit surface in implicit surface modeling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Implicit%20surfaces" title="Implicit surfaces">Implicit surfaces</a>, <a href="https://publications.waset.org/search?q=Soft%20objects" title=" Soft objects"> Soft objects</a>, <a href="https://publications.waset.org/search?q=Super-quadrics." title=" Super-quadrics."> Super-quadrics.</a> </p> <a href="https://publications.waset.org/9231/an-implicit-representation-of-spherical-product-for-increasing-the-shape-variety-of-super-quadrics-in-implicit-surface-modeling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9231/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9231/bibtex" target="_blank" rel="nofollow" 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