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Points</title> <meta name="description" content="Search results for: Off-Step Points"> <meta name="keywords" content="Off-Step Points"> <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 navbar-toggler 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class="badge badge-info">796</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">795</span> The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields 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 let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Elliptic%20curve" title="Elliptic curve">Elliptic curve</a>, <a href="https://publications.waset.org/search?q=conic" title=" conic"> conic</a>, <a href="https://publications.waset.org/search?q=rational%20points." title=" rational points."> rational points.</a> </p> <a href="https://publications.waset.org/726/the-number-of-rational-points-on-conics-cpk-x2-ky2-1-over-finite-fields-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/726/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/726/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/726/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/726/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/726/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/726/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/726/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/726/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/726/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/726/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/726.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">1728</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">794</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">793</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">792</span> Salient Points Reduction for Content-Based Image Retrieval</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yao-Hong%20Tsai">Yao-Hong Tsai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Salient points are frequently used to represent local properties of the image in content-based image retrieval. In this paper, we present a reduction algorithm that extracts the local most salient points such that they not only give a satisfying representation of an image, but also make the image retrieval process efficiently. This algorithm recursively reduces the continuous point set by their corresponding saliency values under a top-down approach. The resulting salient points are evaluated with an image retrieval system using Hausdoff distance. In this experiment, it shows that our method is robust and the extracted salient points provide better retrieval performance comparing with other point detectors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Barnard%20detector" title="Barnard detector">Barnard detector</a>, <a href="https://publications.waset.org/search?q=Content-based%20image%20retrieval" title=" Content-based image retrieval"> Content-based image retrieval</a>, <a href="https://publications.waset.org/search?q=Points%20reduction" title=" Points reduction"> Points reduction</a>, <a href="https://publications.waset.org/search?q=Salient%20point." title=" Salient point."> Salient point.</a> </p> <a href="https://publications.waset.org/5861/salient-points-reduction-for-content-based-image-retrieval" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/5861/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/5861/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/5861/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/5861/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/5861/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/5861/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/5861/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/5861/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/5861/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/5861/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/5861.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">1469</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">791</span> Automated Feature Points Management for Video Mosaic Construction</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Jing%20Li">Jing Li</a>, <a href="https://publications.waset.org/search?q=Quan%20Pan"> Quan Pan</a>, <a href="https://publications.waset.org/search?q=Stan.%20Z.%20Li"> Stan. Z. Li</a>, <a href="https://publications.waset.org/search?q=Tao%20Yang"> Tao Yang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A novel algorithm for construct a seamless video mosaic of the entire panorama continuously by automatically analyzing and managing feature points, including management of quantity and quality, from the sequence is presented. Since a video contains significant redundancy, so that not all consecutive video images are required to create a mosaic. Only some key images need to be selected. Meanwhile, feature-based methods for mosaicing rely on correction of feature points? correspondence deeply, and if the key images have large frame interval, the mosaic will often be interrupted by the scarcity of corresponding feature points. A unique character of the method is its ability to handle all the problems above in video mosaicing. Experiments have been performed under various conditions, the results show that our method could achieve fast and accurate video mosaic construction. Keywords?video mosaic, feature points management, homography estimation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Video%20mosaic" title="Video mosaic">Video mosaic</a>, <a href="https://publications.waset.org/search?q=feature%20points%20management" title=" feature points management"> feature points management</a>, <a href="https://publications.waset.org/search?q=homography%20estimation." title=" homography estimation. "> homography estimation. </a> </p> <a href="https://publications.waset.org/6227/automated-feature-points-management-for-video-mosaic-construction" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6227/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6227/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6227/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6227/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6227/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6227/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6227/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6227/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6227/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6227/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6227.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">1823</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">790</span> The Determination of Rating Points of Objects with Qualitative Characteristics and their Usagein Decision Making Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=O.%20Poleshchuk">O. Poleshchuk</a>, <a href="https://publications.waset.org/search?q=E.%20Komarov"> E. Komarov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper presents the method developed to assess rating points of objects with qualitative indexes. The novelty of the method lies in the fact that the authors use linguistic scales that allow to formalize the values of the indexes with the help of fuzzy sets. As a result it is possible to operate correctly with dissimilar indexes on the unified basis and to get stable final results. The obtained rating points are used in decision making based on fuzzy expert opinions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=complete%20orthogonal%20semantic%20space" title="complete orthogonal semantic space">complete orthogonal semantic space</a>, <a href="https://publications.waset.org/search?q=qualitativecharacteristic" title=" qualitativecharacteristic"> qualitativecharacteristic</a>, <a href="https://publications.waset.org/search?q=rating%20points." title=" rating points."> rating points.</a> </p> <a href="https://publications.waset.org/13326/the-determination-of-rating-points-of-objects-with-qualitative-characteristics-and-their-usagein-decision-making-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13326/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13326/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13326/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13326/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13326/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13326/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13326/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13326/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13326/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13326/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13326.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">1209</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">789</span> The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields 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> Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Singular%20curve" title="Singular curve">Singular curve</a>, <a href="https://publications.waset.org/search?q=elliptic%20curve" title=" elliptic curve"> elliptic curve</a>, <a href="https://publications.waset.org/search?q=rational%20points." title=" rational points."> rational points.</a> </p> <a href="https://publications.waset.org/11/the-number-of-rational-points-on-singular-curvesy-2-xx-a2-over-finite-fields-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11.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">1445</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">788</span> Circular Approximation by Trigonometric Bézier Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Maria%20Hussin">Maria Hussin</a>, <a href="https://publications.waset.org/search?q=Malik%20Zawwar%20Hussain"> Malik Zawwar Hussain</a>, <a href="https://publications.waset.org/search?q=Mubashrah%20Saddiqa"> Mubashrah Saddiqa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Control%20points" title="Control points">Control points</a>, <a href="https://publications.waset.org/search?q=rational%20trigonometric%20B%C3%A9zier%20curves" title=" rational trigonometric Bézier curves"> rational trigonometric Bézier curves</a>, <a href="https://publications.waset.org/search?q=radius%20error" title=" radius error"> radius error</a>, <a href="https://publications.waset.org/search?q=shape%20measure" title=" shape measure"> shape measure</a>, <a href="https://publications.waset.org/search?q=weight%20functions." title=" weight functions."> weight functions.</a> </p> <a href="https://publications.waset.org/10000225/circular-approximation-by-trigonometric-bezier-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000225/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000225/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000225/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000225/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000225/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000225/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000225/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000225/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000225/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000225/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000225.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">4689</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">787</span> A Survey on Facial Feature Points Detection Techniques and Approaches</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rachid%20Ahdid">Rachid Ahdid</a>, <a href="https://publications.waset.org/search?q=Khaddouj%20Taifi"> Khaddouj Taifi</a>, <a href="https://publications.waset.org/search?q=Said%20Safi"> Said Safi</a>, <a href="https://publications.waset.org/search?q=Bouzid%20Manaut"> Bouzid Manaut</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Automatic detection of facial feature points plays an important role in applications such as facial feature tracking, human-machine interaction and face recognition. The majority of facial feature points detection methods using two-dimensional or three-dimensional data are covered in existing survey papers. In this article chosen approaches to the facial features detection have been gathered and described. This overview focuses on the class of researches exploiting facial feature points detection to represent facial surface for two-dimensional or three-dimensional face. In the conclusion, we discusses advantages and disadvantages of the presented algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Facial%20feature%20points" title="Facial feature points">Facial feature points</a>, <a href="https://publications.waset.org/search?q=face%20recognition" title=" face recognition"> face recognition</a>, <a href="https://publications.waset.org/search?q=facial%20feature%0D%0Atracking" title=" facial feature tracking"> facial feature tracking</a>, <a href="https://publications.waset.org/search?q=two-dimensional%20data" title=" two-dimensional data"> two-dimensional data</a>, <a href="https://publications.waset.org/search?q=three-dimensional%20data." title=" three-dimensional data."> three-dimensional data.</a> </p> <a href="https://publications.waset.org/10005826/a-survey-on-facial-feature-points-detection-techniques-and-approaches" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10005826/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10005826/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10005826/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10005826/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10005826/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10005826/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10005826/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10005826/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10005826/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10005826/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10005826.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">1681</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">786</span> Practical Issues for Real-Time Video Tracking</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Vitaliy%20Tayanov">Vitaliy Tayanov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we present the algorithm which allows us to have an object tracking close to real time in Full HD videos. The frame rate (FR) of a video stream is considered to be between 5 and 30 frames per second. The real time track building will be achieved if the algorithm can follow 5 or more frames per second. The principle idea is to use fast algorithms when doing preprocessing to obtain the key points and track them after. The procedure of matching points during assignment is hardly dependent on the number of points. Because of this we have to limit pointed number of points using the most informative of them. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=video%20tracking" title="video tracking">video tracking</a>, <a href="https://publications.waset.org/search?q=real-time" title=" real-time"> real-time</a>, <a href="https://publications.waset.org/search?q=Hungarian%20algorithm" title=" Hungarian algorithm"> Hungarian algorithm</a>, <a href="https://publications.waset.org/search?q=Full%0AHD%20video." title=" Full HD video."> Full HD video.</a> </p> <a href="https://publications.waset.org/11442/practical-issues-for-real-time-video-tracking" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11442/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11442/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11442/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11442/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11442/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11442/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11442/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11442/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11442/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11442/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11442.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">1537</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">785</span> Multiple-Points Fault Signature's Dynamics Modeling for Bearing Defect Frequencies</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Muhammad%20F.%20Yaqub">Muhammad F. Yaqub</a>, <a href="https://publications.waset.org/search?q=Iqbal%20Gondal"> Iqbal Gondal</a>, <a href="https://publications.waset.org/search?q=Joarder%20Kamruzzaman"> Joarder Kamruzzaman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Occurrence of a multiple-points fault in machine operations could result in exhibiting complex fault signatures, which could result in lowering fault diagnosis accuracy. In this study, a multiple-points defect model (MPDM) is proposed which can simulate fault signature-s dynamics for n-points bearing faults. Furthermore, this study identifies that in case of multiple-points fault in the rotary machine, the location of the dominant component of defect frequency shifts depending upon the relative location of the fault points which could mislead the fault diagnostic model to inaccurate detections. Analytical and experimental results are presented to characterize and validate the variation in the dominant component of defect frequency. Based on envelop detection analysis, a modification is recommended in the existing fault diagnostic models to consider the multiples of defect frequency rather than only considering the frequency spectrum at the defect frequency in order to incorporate the impact of multiple points fault.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Envelop%20detection" title="Envelop detection">Envelop detection</a>, <a href="https://publications.waset.org/search?q=machine%20defect%20frequency" title=" machine defect frequency"> machine defect frequency</a>, <a href="https://publications.waset.org/search?q=multiple%20faults" title=" multiple faults"> multiple faults</a>, <a href="https://publications.waset.org/search?q=machine%20health%20monitoring." title=" machine health monitoring."> machine health monitoring.</a> </p> <a href="https://publications.waset.org/15172/multiple-points-fault-signatures-dynamics-modeling-for-bearing-defect-frequencies" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15172/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15172/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15172/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15172/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15172/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15172/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15172/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15172/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15172/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15172/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15172.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">2275</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">784</span> Method for Determining the Probing Points for Efficient Measurement of Freeform Surface</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Yi%20Xu">Yi Xu</a>, <a href="https://publications.waset.org/search?q=Zexiang%20Li"> Zexiang Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=eigenvalue-optimal%20optimization" title="eigenvalue-optimal optimization">eigenvalue-optimal optimization</a>, <a href="https://publications.waset.org/search?q=freeform%20surface%20inspection" title=" freeform surface inspection"> freeform surface inspection</a>, <a href="https://publications.waset.org/search?q=sampling%20size%20and%20location" title="sampling size and location">sampling size and location</a>, <a href="https://publications.waset.org/search?q=sampled%20points." title=" sampled points."> sampled points.</a> </p> <a href="https://publications.waset.org/6255/method-for-determining-the-probing-points-for-efficient-measurement-of-freeform-surface" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6255/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6255/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6255/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6255/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6255/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6255/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6255/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6255/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6255/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6255/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6255.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">1239</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">783</span> Ranking DMUs by Ideal PPS in Data Envelopment Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=V.Rezaie">V.Rezaie</a>, <a href="https://publications.waset.org/search?q=M.Khanmohammady"> M.Khanmohammady</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An original DEA model is to evaluate each DMU optimistically, but the interval DEA Model proposed in this paper has been formulated to obtain an efficiency interval consisting of Evaluations from both the optimistic and the pessimistic view points. DMUs are improved so that their lower bounds become so large as to attain the maximum Value one. The points obtained by this method are called ideal points. Ideal PPS is calculated by ideal of efficiency DMUs. The purpose of this paper is to rank DMUs by this ideal PPS. Finally we extend the efficiency interval of a DMU under variable RTS technology. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Data%20envelopment%20analysis%20%28DEA%29" title="Data envelopment analysis (DEA)">Data envelopment analysis (DEA)</a>, <a href="https://publications.waset.org/search?q=Decision%20makingunit%20%28DMU%29" title=" Decision makingunit (DMU)"> Decision makingunit (DMU)</a>, <a href="https://publications.waset.org/search?q=Interval%20DEA" title=" Interval DEA"> Interval DEA</a>, <a href="https://publications.waset.org/search?q=Ideal%20points" title=" Ideal points"> Ideal points</a>, <a href="https://publications.waset.org/search?q=Ideal%20PPS" title=" Ideal PPS"> Ideal PPS</a>, <a href="https://publications.waset.org/search?q=Return%20to%20scale%28RTS%29." title=" Return to scale(RTS)."> Return to scale(RTS).</a> </p> <a href="https://publications.waset.org/12/ranking-dmus-by-ideal-pps-in-data-envelopment-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/12/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/12/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/12/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/12/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/12/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/12/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/12/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/12/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/12/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/12/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/12.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">1926</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">782</span> Health-Related QOL of Motorists with Spinal Cord Injury in Japan</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hiroaki%20Hirose">Hiroaki Hirose</a>, <a href="https://publications.waset.org/search?q=Hiroshi%20Ikeda"> Hiroshi Ikeda</a>, <a href="https://publications.waset.org/search?q=Isao%20Takeda"> Isao Takeda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Japanese version of the SF-36 has been employed to assess individuals’ health-related QOL (HRQOL). This study aimed to clarify the HRQOL of motorists with a spinal cord injury, in order to compare these individuals' SF-36 scores and national standard values. A total of 100 motorists with a spinal cord injury participated in this study. Participants’ HRQOL was evaluated using the Japanese version of the SF-36 (second edition). The score for each subscale was standardized based on data on the Japanese population. The average scores for NPF, NRP, NBP, NGH, NVT, NSF, NRE, and NMH were 10.9, 41.8, 45.9, 47.1, 46.1, 46.7, 46.0, and 47.4 points, respectively. Subjects showed significantly lower scores for NPF and NRP compared with national standard values, which were both ≤ 45.0 points, but relatively normal scores for the other items: NBP, NGH, NVT, NSF, NRE and NMH (> 45.0 points). The average scores for PCS, MCS and RCS were 21.9, 56.0, and 50.0 points, respectively. Subjects showed a significantly lower PCS score (≤ 20.0 points); however, the MCS score was higher (> 55.0 points) along with a relatively normal RCS score in these individuals (= 50.0 points). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Health-related%20QOL%20%28HRQOL%29" title="Health-related QOL (HRQOL)">Health-related QOL (HRQOL)</a>, <a href="https://publications.waset.org/search?q=SF-36" title=" SF-36"> SF-36</a>, <a href="https://publications.waset.org/search?q=motorist" title=" motorist"> motorist</a>, <a href="https://publications.waset.org/search?q=spinal%20cord%20injury" title=" spinal cord injury"> spinal cord injury</a>, <a href="https://publications.waset.org/search?q=Japan." title=" Japan."> Japan.</a> </p> <a href="https://publications.waset.org/10002464/health-related-qol-of-motorists-with-spinal-cord-injury-in-japan" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10002464/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10002464/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10002464/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10002464/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10002464/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10002464/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10002464/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10002464/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10002464/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10002464/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10002464.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">2261</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">781</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">780</span> LEED Empirical Evidence in Northern and Southern Europe</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Svetlana%20Pushkar">Svetlana Pushkar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The Leadership in Energy and Environmental Design (LEED) green building rating system is recognized in Europe. LEED uses regional priority (RP) points that are adapted to different environmental conditions. However, the appropriateness of the RP points is still a controversial question. To clarify this issue, two different parts of Europe: northern Europe (Finland and Sweden) and southern Europe (Turkey and Spain) were considered. Similarities and differences in the performances of LEED 2009-new construction (LEED-NC 2009) in these four countries were analyzed. It was found that LEED-NC 2009 performances in northern and southern parts of Europe in terms of Sustainable Sites (SS), Water Efficiency (WE), Materials and Resources (MR), and Indoor Environmental Quality (EQ) were similar, whereas in Energy and Atmosphere (EA), their performances were different. WE and SS revealed high performances (70-100%); EA and EQ demonstrated intermediate performance (40-60%); and MR displayed low performance (20-40%). It should be recommended introducing the following new RP points: for Turkey - water-related points and for all four observed countries - green power-related points for improving the LEED adaptation in Europe.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Green%20building" title="Green building">Green building</a>, <a href="https://publications.waset.org/search?q=Europe" title=" Europe"> Europe</a>, <a href="https://publications.waset.org/search?q=LEED" title=" LEED"> LEED</a>, <a href="https://publications.waset.org/search?q=regional%20priority%20points." title=" regional priority points. "> regional priority points. </a> </p> <a href="https://publications.waset.org/10010051/leed-empirical-evidence-in-northern-and-southern-europe" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010051/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010051/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010051/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010051/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010051/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010051/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010051/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010051/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010051/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010051/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010051.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">829</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">779</span> Relationship of Arm Acupressure Points and Thai Traditional Massage</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Boonyarat%20Chaleephay">Boonyarat Chaleephay</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The purpose of this research paper was to describe the relationship of acupressure points on the anterior surface of the upper limb in accordance with Applied Thai Traditional Massage (ATTM) and the deep structures located at those acupressure points. There were 2 population groups; normal subjects and cadaver specimens. Eighteen males with age ranging from 20-40 years old and seventeen females with ages ranging from 30-97 years old were studies. This study was able to obtain a fundamental knowledge concerning acupressure point and the deep structures that related to those acupressure points. It might be used as the basic knowledge for clinically applying and planning treatment as well as teaching in ATTM.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Acupressure%20point%20%28AP%29" title="Acupressure point (AP)">Acupressure point (AP)</a>, <a href="https://publications.waset.org/search?q=Applie%20Thai%20Traditional%20Medicine%20%28ATTM%29" title=" Applie Thai Traditional Medicine (ATTM)"> Applie Thai Traditional Medicine (ATTM)</a>, <a href="https://publications.waset.org/search?q=Paresthesia" title=" Paresthesia"> Paresthesia</a>, <a href="https://publications.waset.org/search?q=Numbness." title=" Numbness."> Numbness.</a> </p> <a href="https://publications.waset.org/9997135/relationship-of-arm-acupressure-points-and-thai-traditional-massage" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9997135/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9997135/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9997135/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9997135/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9997135/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9997135/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9997135/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9997135/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9997135/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9997135/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9997135.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">2172</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">778</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">777</span> A Case Study to Assess the Validity of Function Points</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Neelam%20Bawane%20nee%27%20Singhal">Neelam Bawane nee' Singhal</a>, <a href="https://publications.waset.org/search?q=C.%20V.%20Srikrishna"> C. V. Srikrishna</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Function%20Points" title="Function Points">Function Points</a>, <a href="https://publications.waset.org/search?q=Data%20Flow%20Diagram" title=" Data Flow Diagram"> Data Flow Diagram</a>, <a href="https://publications.waset.org/search?q=Lines%20ofCodes." title=" Lines ofCodes."> Lines ofCodes.</a> </p> <a href="https://publications.waset.org/1072/a-case-study-to-assess-the-validity-of-function-points" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1072/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1072/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1072/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1072/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1072/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1072/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1072/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1072/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1072/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1072/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1072.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">3672</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">776</span> Investigation of the Possibility to Prepare Supervised Classification Map of Gully Erosion by RS and GIS</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ali%20Mohammadi%20Torkashvand">Ali Mohammadi Torkashvand</a>, <a href="https://publications.waset.org/search?q=Hamid%20Reza%20Alipour"> Hamid Reza Alipour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study investigates the possibility providing gully erosion map by the supervised classification of satellite images (ETM+) in two mountainous and plain land types. These land types were the part of Varamin plain, Tehran province, and Roodbar subbasin, Guilan province, as plain and mountain land types, respectively. The position of 652 and 124 ground control points were recorded by GPS respectively in mountain and plain land types. Soil gully erosion, land uses or plant covers were investigated in these points. Regarding ground control points and auxiliary points, training points of gully erosion and other surface features were introduced to software (Ilwis 3.3 Academic). The supervised classified map of gully erosion was prepared by maximum likelihood method and then, overall accuracy of this map was computed. Results showed that the possibility supervised classification of gully erosion isn-t possible, although it need more studies for results generalization to other mountainous regions. Also, with increasing land uses and other surface features in plain physiography, it decreases the classification of accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Supervised%20classification" title="Supervised classification">Supervised classification</a>, <a href="https://publications.waset.org/search?q=Gully%20erosion" title=" Gully erosion"> Gully erosion</a>, <a href="https://publications.waset.org/search?q=Map." title=" Map."> Map.</a> </p> <a href="https://publications.waset.org/3500/investigation-of-the-possibility-to-prepare-supervised-classification-map-of-gully-erosion-by-rs-and-gis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3500/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3500/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3500/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3500/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3500/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3500/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3500/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3500/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3500/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3500/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3500.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">1827</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">775</span> Facial Expressions Animation and Lip Tracking Using Facial Characteristic Points and Deformable Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hadi%20Seyedarabi">Hadi Seyedarabi</a>, <a href="https://publications.waset.org/search?q=Ali%20Aghagolzadeh"> Ali Aghagolzadeh</a>, <a href="https://publications.waset.org/search?q=Sohrab%20Khanmohammadi"> Sohrab Khanmohammadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Face and facial expressions play essential roles in interpersonal communication. Most of the current works on the facial expression recognition attempt to recognize a small set of the prototypic expressions such as happy, surprise, anger, sad, disgust and fear. However the most of the human emotions are communicated by changes in one or two of discrete features. In this paper, we develop a facial expressions synthesis system, based on the facial characteristic points (FCP's) tracking in the frontal image sequences. Selected FCP's are automatically tracked using a crosscorrelation based optical flow. The proposed synthesis system uses a simple deformable facial features model with a few set of control points that can be tracked in original facial image sequences. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Deformable%20face%20model" title="Deformable face model">Deformable face model</a>, <a href="https://publications.waset.org/search?q=facial%20animation" title=" facial animation"> facial animation</a>, <a href="https://publications.waset.org/search?q=facialcharacteristic%20points" title=" facialcharacteristic points"> facialcharacteristic points</a>, <a href="https://publications.waset.org/search?q=optical%20flow." title=" optical flow."> optical flow.</a> </p> <a href="https://publications.waset.org/14909/facial-expressions-animation-and-lip-tracking-using-facial-characteristic-points-and-deformable-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14909/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14909/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14909/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14909/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14909/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14909/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14909/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14909/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14909/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14909/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14909.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">1633</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">774</span> Robust Face Recognition using AAM and Gabor Features</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sanghoon%20Kim">Sanghoon Kim</a>, <a href="https://publications.waset.org/search?q=Sun-Tae%20Chung"> Sun-Tae Chung</a>, <a href="https://publications.waset.org/search?q=Souhwan%20Jung"> Souhwan Jung</a>, <a href="https://publications.waset.org/search?q=Seoungseon%20Jeon"> Seoungseon Jeon</a>, <a href="https://publications.waset.org/search?q=Jaemin%20Kim"> Jaemin Kim</a>, <a href="https://publications.waset.org/search?q=Seongwon%20Cho"> Seongwon Cho</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a face recognition algorithm using AAM and Gabor features. Gabor feature vectors which are well known to be robust with respect to small variations of shape, scaling, rotation, distortion, illumination and poses in images are popularly employed for feature vectors for many object detection and recognition algorithms. EBGM, which is prominent among face recognition algorithms employing Gabor feature vectors, requires localization of facial feature points where Gabor feature vectors are extracted. However, localization method employed in EBGM is based on Gabor jet similarity and is sensitive to initial values. Wrong localization of facial feature points affects face recognition rate. AAM is known to be successfully applied to localization of facial feature points. In this paper, we devise a facial feature point localization method which first roughly estimate facial feature points using AAM and refine facial feature points using Gabor jet similarity-based facial feature localization method with initial points set by the rough facial feature points obtained from AAM, and propose a face recognition algorithm using the devised localization method for facial feature localization and Gabor feature vectors. It is observed through experiments that such a cascaded localization method based on both AAM and Gabor jet similarity is more robust than the localization method based on only Gabor jet similarity. Also, it is shown that the proposed face recognition algorithm using this devised localization method and Gabor feature vectors performs better than the conventional face recognition algorithm using Gabor jet similarity-based localization method and Gabor feature vectors like EBGM. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Face%20Recognition" title="Face Recognition">Face Recognition</a>, <a href="https://publications.waset.org/search?q=AAM" title=" AAM"> AAM</a>, <a href="https://publications.waset.org/search?q=Gabor%20features" title=" Gabor features"> Gabor features</a>, <a href="https://publications.waset.org/search?q=EBGM." title=" EBGM."> EBGM.</a> </p> <a href="https://publications.waset.org/3583/robust-face-recognition-using-aam-and-gabor-features" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/3583/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/3583/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/3583/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/3583/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/3583/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/3583/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/3583/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/3583/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/3583/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/3583/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/3583.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">2206</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">773</span> Error Propagation of the Hidden-Point Bar Method: Effect of Bar Geometry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Said%20M.%20Easa">Said M. Easa</a>, <a href="https://publications.waset.org/search?q=Ahmed%20Shaker"> Ahmed Shaker</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The hidden-point bar method is useful in many surveying applications. The method involves determining the coordinates of a hidden point as a function of horizontal and vertical angles measured to three fixed points on the bar. Using these measurements, the procedure involves calculating the slant angles, the distances from the station to the fixed points, the coordinates of the fixed points, and then the coordinates of the hidden point. The propagation of the measurement errors in this complex process has not been fully investigated in the literature. This paper evaluates the effect of the bar geometry on the position accuracy of the hidden point which depends on the measurement errors of the horizontal and vertical angles. The results are used to establish some guidelines regarding the inclination angle of the bar and the location of the observed points that provide the best accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Hidden%20point" title="Hidden point">Hidden point</a>, <a href="https://publications.waset.org/search?q=accuracy" title=" accuracy"> accuracy</a>, <a href="https://publications.waset.org/search?q=error%20propagation" title=" error propagation"> error propagation</a>, <a href="https://publications.waset.org/search?q=surveying" title="surveying">surveying</a>, <a href="https://publications.waset.org/search?q=evaluation" title=" evaluation"> evaluation</a>, <a href="https://publications.waset.org/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/search?q=geometry." title=" geometry."> geometry.</a> </p> <a href="https://publications.waset.org/14226/error-propagation-of-the-hidden-point-bar-method-effect-of-bar-geometry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14226/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14226/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14226/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14226/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14226/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14226/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14226/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14226/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14226/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14226/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14226.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">1722</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">772</span> Intuitionistic Fuzzy Points in Semigroups</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Sujit%20Kumar%20Sardar%20Manasi%20Mandal%20Samit%20Kumar%20Majumder">Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Semigroup" title="Semigroup">Semigroup</a>, <a href="https://publications.waset.org/search?q=Regular%28intra-regular%29%20semigroup" title=" Regular(intra-regular) semigroup"> Regular(intra-regular) semigroup</a>, <a href="https://publications.waset.org/search?q=Intuitionistic%20fuzzy%20point" title=" Intuitionistic fuzzy point"> Intuitionistic fuzzy point</a>, <a href="https://publications.waset.org/search?q=Intuitionistic%20fuzzy%20subsemigroup" title=" Intuitionistic fuzzy subsemigroup"> Intuitionistic fuzzy subsemigroup</a>, <a href="https://publications.waset.org/search?q=Intuitionistic%20fuzzy%20ideal" title=" Intuitionistic fuzzy ideal"> Intuitionistic fuzzy ideal</a>, <a href="https://publications.waset.org/search?q=Intuitionistic%20fuzzy%20interior%20ideal" title=" Intuitionistic fuzzy interior ideal"> Intuitionistic fuzzy interior ideal</a>, <a href="https://publications.waset.org/search?q=Intuitionistic%20fuzzy%20semiprime%20ideal" title=" Intuitionistic fuzzy semiprime ideal"> Intuitionistic fuzzy semiprime ideal</a>, <a href="https://publications.waset.org/search?q=Intuitionistic%20fuzzy%20prime%20ideal." title=" Intuitionistic fuzzy prime ideal."> Intuitionistic fuzzy prime ideal.</a> </p> <a href="https://publications.waset.org/8848/intuitionistic-fuzzy-points-in-semigroups" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8848/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8848/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8848/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8848/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8848/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8848/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8848/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8848/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8848/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8848/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8848.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">1849</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">771</span> Study of Single Network Adjustment Using QOCA Software in Korea</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Seongchan%20Kang">Seongchan Kang</a>, <a href="https://publications.waset.org/search?q=Hongsik%20Yun"> Hongsik Yun</a>, <a href="https://publications.waset.org/search?q=Hyukgil%20Kim"> Hyukgil Kim</a>, <a href="https://publications.waset.org/search?q=Minwoo%20Park"> Minwoo Park</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For this study, this researcher conducted a precision network adjustment with QOCA, the precision network adjustment software developed by Jet Propulsion Laboratory, to perform an integrated network adjustment on the Unified Control Points managed by the National Geographic Information Institute. Towards this end, 275 Unified Control Points observed in 2008 were selected before a network adjustment is performed on those 275 Unified Control Points. The RMSE on the discrepancies of coordinates as compared to the results of GLOBK was ±6.07mm along the N axis, ±2.68mm along the E axis and ±6.49mm along the U axis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Network%20adjustment" title="Network adjustment">Network adjustment</a>, <a href="https://publications.waset.org/search?q=QOCA" title=" QOCA"> QOCA</a>, <a href="https://publications.waset.org/search?q=unified%20control%20point." title=" unified control point."> unified control point.</a> </p> <a href="https://publications.waset.org/303/study-of-single-network-adjustment-using-qoca-software-in-korea" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/303/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/303/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/303/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/303/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/303/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/303/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/303/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/303/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/303/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/303/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/303.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">1849</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">770</span> Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Benshi%20Zhu">Benshi Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Discrete%20eigenvalue%20problems" title="Discrete eigenvalue problems">Discrete eigenvalue problems</a>, <a href="https://publications.waset.org/search?q=positive%20solutions" title=" positive solutions"> positive solutions</a>, <a href="https://publications.waset.org/search?q=semipositone" title="semipositone">semipositone</a>, <a href="https://publications.waset.org/search?q=three%20critical%20points%20theorem" title=" three critical points theorem"> three critical points theorem</a> </p> <a href="https://publications.waset.org/13982/positive-solutions-for-semipositone-discrete-eigenvalue-problems-via-three-critical-points-theorem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/13982/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/13982/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/13982/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/13982/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/13982/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/13982/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/13982/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/13982/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/13982/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/13982/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/13982.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">1253</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">769</span> X-Corner Detection for Camera Calibration Using Saddle Points</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Abdulrahman%20S.%20Alturki">Abdulrahman S. Alturki</a>, <a href="https://publications.waset.org/search?q=John%20S.%20Loomis"> John S. Loomis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper discusses a corner detection algorithm for camera calibration. Calibration is a necessary step in many computer vision and image processing applications. Robust corner detection for an image of a checkerboard is required to determine intrinsic and extrinsic parameters. In this paper, an algorithm for fully automatic and robust X-corner detection is presented. Checkerboard corner points are automatically found in each image without user interaction or any prior information regarding the number of rows or columns. The approach represents each X-corner with a quadratic fitting function. Using the fact that the X-corners are saddle points, the coefficients in the fitting function are used to identify each corner location. The automation of this process greatly simplifies calibration. Our method is robust against noise and different camera orientations. Experimental analysis shows the accuracy of our method using actual images acquired at different camera locations and orientations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Camera%20Calibration" title="Camera Calibration">Camera Calibration</a>, <a href="https://publications.waset.org/search?q=Corner%20Detector" title=" Corner Detector"> Corner Detector</a>, <a href="https://publications.waset.org/search?q=Saddle%0D%0APoints" title=" Saddle Points"> Saddle Points</a>, <a href="https://publications.waset.org/search?q=X-Corners." title=" X-Corners."> X-Corners.</a> </p> <a href="https://publications.waset.org/10003988/x-corner-detection-for-camera-calibration-using-saddle-points" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10003988/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10003988/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10003988/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10003988/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10003988/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10003988/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10003988/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10003988/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10003988/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10003988/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10003988.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">3153</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">768</span> Optimized Facial Features-based Age Classification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Md.%20Zahangir%20Alom">Md. Zahangir Alom</a>, <a href="https://publications.waset.org/search?q=Mei-Lan%20Piao"> Mei-Lan Piao</a>, <a href="https://publications.waset.org/search?q=Md.%20Shariful%20Islam"> Md. Shariful Islam</a>, <a href="https://publications.waset.org/search?q=Nam%20Kim"> Nam Kim</a>, <a href="https://publications.waset.org/search?q=Jae-Hyeung%20Park"> Jae-Hyeung Park</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The evaluation and measurement of human body dimensions are achieved by physical anthropometry. This research was conducted in view of the importance of anthropometric indices of the face in forensic medicine, surgery, and medical imaging. The main goal of this research is to optimization of facial feature point by establishing a mathematical relationship among facial features and used optimize feature points for age classification. Since selected facial feature points are located to the area of mouth, nose, eyes and eyebrow on facial images, all desire facial feature points are extracted accurately. According this proposes method; sixteen Euclidean distances are calculated from the eighteen selected facial feature points vertically as well as horizontally. The mathematical relationships among horizontal and vertical distances are established. Moreover, it is also discovered that distances of the facial feature follows a constant ratio due to age progression. The distances between the specified features points increase with respect the age progression of a human from his or her childhood but the ratio of the distances does not change (d = 1 .618 ) . Finally, according to the proposed mathematical relationship four independent feature distances related to eight feature points are selected from sixteen distances and eighteen feature point-s respectively. These four feature distances are used for classification of age using Support Vector Machine (SVM)-Sequential Minimal Optimization (SMO) algorithm and shown around 96 % accuracy. Experiment result shows the proposed system is effective and accurate for age classification. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=3D%20Face%20Model" title="3D Face Model">3D Face Model</a>, <a href="https://publications.waset.org/search?q=Face%20Anthropometrics" title=" Face Anthropometrics"> Face Anthropometrics</a>, <a href="https://publications.waset.org/search?q=Facial%20Features%0AExtraction" title=" Facial Features Extraction"> Facial Features Extraction</a>, <a href="https://publications.waset.org/search?q=Feature%20distances" title=" Feature distances"> Feature distances</a>, <a href="https://publications.waset.org/search?q=SVM-SMO" title=" SVM-SMO"> SVM-SMO</a> </p> <a href="https://publications.waset.org/6689/optimized-facial-features-based-age-classification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6689/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6689/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6689/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6689/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6689/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6689/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6689/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6689/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6689/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6689/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6689.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">2047</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">767</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" 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