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‎polynomials</title> <meta name="description" content="Search results for: Zernike ‎polynomials"> <meta name="keywords" content="Zernike ‎polynomials"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Zernike ‎polynomials"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 80</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Zernike ‎polynomials</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">80</span> Numerical Simulation of Laser ‎Propagation through Turbulent ‎Atmosphere Using Zernike ‎Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Moradi%20%E2%80%8E">Mohammad Moradi ‎</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, propagation of a laser beam through turbulent ‎atmosphere is evaluated. At first the laser beam is simulated and then ‎turbulent atmosphere will be simulated by using Zernike polynomials. ‎Some parameter like intensity, PSF will be measured for four ‎wavelengths in different Cn2. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=laser%20beam%20propagation" title="laser beam propagation">laser beam propagation</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20screen" title=" phase screen"> phase screen</a>, <a href="https://publications.waset.org/abstracts/search?q=turbulent%20atmosphere" title=" turbulent atmosphere"> turbulent atmosphere</a>, <a href="https://publications.waset.org/abstracts/search?q=Zernike%20%E2%80%8Epolynomials" title=" Zernike ‎polynomials"> Zernike ‎polynomials</a> </p> <a href="https://publications.waset.org/abstracts/35907/numerical-simulation-of-laser-propagation-through-turbulent-atmosphere-using-zernike-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35907.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">511</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">79</span> An Audit of Climate Change and Sustainability Teaching in Medical School</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Tiachachat">M. Tiachachat</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Mihoubi"> M. Mihoubi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Bell polynomials are special polynomials in combinatorial analysis that have a wide range of applications in mathematics. They have interested many authors. The exponential partial Bell polynomials have been well reduced to some special combinatorial sequences. Numerous researchers had already been interested in the above polynomials, as evidenced by many articles in the literature. Inspired by this work, in this work, we propose a family of special polynomials named after the 2-successive partial Bell polynomials. Using the combinatorial approach, we prove the properties of these numbers, derive several identities, and discuss some special cases. This family includes well-known numbers and polynomials such as Stirling numbers, Bell numbers and polynomials, and so on. We investigate their properties by employing generating functions <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=2-associated%20r-Stirling%20numbers" title="2-associated r-Stirling numbers">2-associated r-Stirling numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20exponential%20partial%20Bell%20polynomials" title=" the exponential partial Bell polynomials"> the exponential partial Bell polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20function" title=" generating function"> generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=combinatorial%20interpretation" title=" combinatorial interpretation"> combinatorial interpretation</a> </p> <a href="https://publications.waset.org/abstracts/157494/an-audit-of-climate-change-and-sustainability-teaching-in-medical-school" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/157494.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">110</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">78</span> Polar Bergman Polynomials on Domain with Corners</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Laskri%20Yamina">Laskri Yamina</a>, <a href="https://publications.waset.org/abstracts/search?q=Rehouma%20Abdel%20Hamid"> Rehouma Abdel Hamid </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we present a new class named polar of monic orthogonal polynomials with respect to the area measure supported on G, where G is a bounded simply-connected domain in the complex planeℂ. We analyze some open questions and discuss some ideas properties related to solving asymptotic behavior of polar Bergman polynomials over domains with corners and asymptotic behavior of modified Bergman polynomials by affine transforms in variable and polar modified Bergman polynomials by affine transforms in variable. We show that uniform asymptotic of Bergman polynomials over domains with corners and by Pritsker's theorem imply uniform asymptotic for all their derivatives. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bergman%20orthogonal%20polynomials" title="Bergman orthogonal polynomials">Bergman orthogonal polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=polar%20rthogonal%20polynomials" title=" polar rthogonal polynomials"> polar rthogonal polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20behavior" title=" asymptotic behavior"> asymptotic behavior</a>, <a href="https://publications.waset.org/abstracts/search?q=Faber%20polynomials" title=" Faber polynomials"> Faber polynomials</a> </p> <a href="https://publications.waset.org/abstracts/15621/polar-bergman-polynomials-on-domain-with-corners" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15621.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">445</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">77</span> Chebyshev Polynomials Relad with Fibonacci and Lucas Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vandana%20N.%20Purav">Vandana N. Purav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=" title=""></a> </p> <a href="https://publications.waset.org/abstracts/24133/chebyshev-polynomials-relad-with-fibonacci-and-lucas-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24133.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">368</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">76</span> A Novel Breast Cancer Detection Algorithm Using Point Region Growing Segmentation and Pseudo-Zernike Moments</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aileen%20F.%20Wang">Aileen F. Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mammography has been one of the most reliable methods for early detection and diagnosis of breast cancer. However, mammography misses about 17% and up to 30% of breast cancers due to the subtle and unstable appearances of breast cancer in their early stages. Recent computer-aided diagnosis (CADx) technology using Zernike moments has improved detection accuracy. However, it has several drawbacks: it uses manual segmentation, Zernike moments are not robust, and it still has a relatively high false negative rate (FNR)–17.6%. This project will focus on the development of a novel breast cancer detection algorithm to automatically segment the breast mass and further reduce FNR. The algorithm consists of automatic segmentation of a single breast mass using Point Region Growing Segmentation, reconstruction of the segmented breast mass using Pseudo-Zernike moments, and classification of the breast mass using the root mean square (RMS). A comparative study among the various algorithms on the segmentation and reconstruction of breast masses was performed on randomly selected mammographic images. The results demonstrated that the newly developed algorithm is the best in terms of accuracy and cost effectiveness. More importantly, the new classifier RMS has the lowest FNR–6%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computer%20aided%20diagnosis" title="computer aided diagnosis">computer aided diagnosis</a>, <a href="https://publications.waset.org/abstracts/search?q=mammography" title=" mammography"> mammography</a>, <a href="https://publications.waset.org/abstracts/search?q=point%20region%20growing%20segmentation" title=" point region growing segmentation"> point region growing segmentation</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-zernike%20moments" title=" pseudo-zernike moments"> pseudo-zernike moments</a>, <a href="https://publications.waset.org/abstracts/search?q=root%20mean%20square" title=" root mean square"> root mean square</a> </p> <a href="https://publications.waset.org/abstracts/10488/a-novel-breast-cancer-detection-algorithm-using-point-region-growing-segmentation-and-pseudo-zernike-moments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10488.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">453</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">75</span> Video Text Information Detection and Localization in Lecture Videos Using Moments </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Belkacem%20Soundes">Belkacem Soundes</a>, <a href="https://publications.waset.org/abstracts/search?q=Guezouli%20Larbi"> Guezouli Larbi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a robust and accurate method for text detection and localization over lecture videos. Frame regions are classified into text or background based on visual feature analysis. However, lecture video shows significant degradation mainly related to acquisition conditions, camera motion and environmental changes resulting in low quality videos. Hence, affecting feature extraction and description efficiency. Moreover, traditional text detection methods cannot be directly applied to lecture videos. Therefore, robust feature extraction methods dedicated to this specific video genre are required for robust and accurate text detection and extraction. Method consists of a three-step process: Slide region detection and segmentation; Feature extraction and non-text filtering. For robust and effective features extraction moment functions are used. Two distinct types of moments are used: orthogonal and non-orthogonal. For orthogonal Zernike Moments, both Pseudo Zernike moments are used, whereas for non-orthogonal ones Hu moments are used. Expressivity and description efficiency are given and discussed. Proposed approach shows that in general, orthogonal moments show high accuracy in comparison to the non-orthogonal one. Pseudo Zernike moments are more effective than Zernike with better computation time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=text%20detection" title="text detection">text detection</a>, <a href="https://publications.waset.org/abstracts/search?q=text%20localization" title=" text localization"> text localization</a>, <a href="https://publications.waset.org/abstracts/search?q=lecture%20videos" title=" lecture videos"> lecture videos</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo%20zernike%20moments" title=" pseudo zernike moments"> pseudo zernike moments</a> </p> <a href="https://publications.waset.org/abstracts/109549/video-text-information-detection-and-localization-in-lecture-videos-using-moments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/109549.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">152</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">74</span> An Accurate Computation of 2D Zernike Moments via Fast Fourier Transform </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20S.%20Al-Rawi">Mohammed S. Al-Rawi</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Bastos"> J. Bastos</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Rodriguez"> J. Rodriguez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Object detection and object recognition are essential components of every computer vision system. Despite the high computational complexity and other problems related to numerical stability and accuracy, Zernike moments of 2D images (ZMs) have shown resilience when used in object recognition and have been used in various image analysis applications. In this work, we propose a novel method for computing ZMs via Fast Fourier Transform (FFT). Notably, this is the first algorithm that can generate ZMs up to extremely high orders accurately, e.g., it can be used to generate ZMs for orders up to 1000 or even higher. Furthermore, the proposed method is also simpler and faster than the other methods due to the availability of FFT software and/or hardware. The accuracies and numerical stability of ZMs computed via FFT have been confirmed using the orthogonality property. We also introduce normalizing ZMs with Neumann factor when the image is embedded in a larger grid, and color image reconstruction based on RGB normalization of the reconstructed images. Astonishingly, higher-order image reconstruction experiments show that the proposed methods are superior, both quantitatively and subjectively, compared to the q-recursive method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomial" title="Chebyshev polynomial">Chebyshev polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20transform" title=" fourier transform"> fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=fast%20algorithms" title=" fast algorithms"> fast algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20recognition" title=" image recognition"> image recognition</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo%20Zernike%20moments" title=" pseudo Zernike moments"> pseudo Zernike moments</a>, <a href="https://publications.waset.org/abstracts/search?q=Zernike%20moments" title=" Zernike moments"> Zernike moments</a> </p> <a href="https://publications.waset.org/abstracts/58226/an-accurate-computation-of-2d-zernike-moments-via-fast-fourier-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58226.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">265</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">73</span> Image Analysis for Obturator Foramen Based on Marker-controlled Watershed Segmentation and Zernike Moments</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Seda%20Sahin">Seda Sahin</a>, <a href="https://publications.waset.org/abstracts/search?q=Emin%20Akata"> Emin Akata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Obturator foramen is a specific structure in pelvic bone images and recognition of it is a new concept in medical image processing. Moreover, segmentation of bone structures such as obturator foramen plays an essential role for clinical research in orthopedics. In this paper, we present a novel method to analyze the similarity between the substructures of the imaged region and a hand drawn template, on hip radiographs to detect obturator foramen accurately with integrated usage of Marker-controlled Watershed segmentation and Zernike moment feature descriptor. Marker-controlled Watershed segmentation is applied to seperate obturator foramen from the background effectively. Zernike moment feature descriptor is used to provide matching between binary template image and the segmented binary image for obturator foramens for final extraction. The proposed method is tested on randomly selected 100 hip radiographs. The experimental results represent that our method is able to segment obturator foramens with % 96 accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=medical%20image%20analysis" title="medical image analysis">medical image analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=segmentation%20of%20bone%20structures%20on%20hip%20radiographs" title=" segmentation of bone structures on hip radiographs"> segmentation of bone structures on hip radiographs</a>, <a href="https://publications.waset.org/abstracts/search?q=marker-controlled%20watershed%20segmentation" title=" marker-controlled watershed segmentation"> marker-controlled watershed segmentation</a>, <a href="https://publications.waset.org/abstracts/search?q=zernike%20moment%20feature%20descriptor" title=" zernike moment feature descriptor"> zernike moment feature descriptor</a> </p> <a href="https://publications.waset.org/abstracts/31425/image-analysis-for-obturator-foramen-based-on-marker-controlled-watershed-segmentation-and-zernike-moments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31425.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">434</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">72</span> Hosoya Polynomials of Mycielskian Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sanju%20Vaidya">Sanju Vaidya</a>, <a href="https://publications.waset.org/abstracts/search?q=Aihua%20Li"> Aihua Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hosoya%20polynomial" title="hosoya polynomial">hosoya polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=mycielskian%20graph" title=" mycielskian graph"> mycielskian graph</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20vulnerability%20measure" title=" graph vulnerability measure"> graph vulnerability measure</a>, <a href="https://publications.waset.org/abstracts/search?q=topological%20index" title=" topological index"> topological index</a> </p> <a href="https://publications.waset.org/abstracts/172528/hosoya-polynomials-of-mycielskian-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/172528.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">70</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">71</span> Bernstein Type Polynomials for Solving Differential Equations and Their Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yilmaz%20Simsek">Yilmaz Simsek</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generating%20functions" title="generating functions">generating functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20basis%20functions" title=" Bernstein basis functions"> Bernstein basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomials" title=" Bernstein polynomials"> Bernstein polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Bezier%20curves" title=" Bezier curves"> Bezier curves</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a> </p> <a href="https://publications.waset.org/abstracts/67937/bernstein-type-polynomials-for-solving-differential-equations-and-their-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67937.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">274</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">70</span> A Fuzzy Approach to Liver Tumor Segmentation with Zernike Moments </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abder-Rahman%20Ali">Abder-Rahman Ali</a>, <a href="https://publications.waset.org/abstracts/search?q=Antoine%20Vacavant"> Antoine Vacavant</a>, <a href="https://publications.waset.org/abstracts/search?q=Manuel%20Grand-Brochier"> Manuel Grand-Brochier</a>, <a href="https://publications.waset.org/abstracts/search?q=Ad%C3%A9la%C3%AFde%20Albouy-Kissi"> Adélaïde Albouy-Kissi</a>, <a href="https://publications.waset.org/abstracts/search?q=Jean-Yves%20Boire"> Jean-Yves Boire</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a new segmentation approach for liver lesions in regions of interest within MRI (Magnetic Resonance Imaging). This approach, based on a two-cluster Fuzzy C-Means methodology, considers the parameter variable compactness to handle uncertainty. Fine boundaries are detected by a local recursive merging of ambiguous pixels with a sequential forward floating selection with Zernike moments. The method has been tested on both synthetic and real images. When applied on synthetic images, the proposed approach provides good performance, segmentations obtained are accurate, their shape is consistent with the ground truth, and the extracted information is reliable. The results obtained on MR images confirm such observations. Our approach allows, even for difficult cases of MR images, to extract a segmentation with good performance in terms of accuracy and shape, which implies that the geometry of the tumor is preserved for further clinical activities (such as automatic extraction of pharmaco-kinetics properties, lesion characterization, etc). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=defuzzification" title="defuzzification">defuzzification</a>, <a href="https://publications.waset.org/abstracts/search?q=floating%20search" title=" floating search"> floating search</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20clustering" title=" fuzzy clustering"> fuzzy clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=Zernike%20moments" title=" Zernike moments "> Zernike moments </a> </p> <a href="https://publications.waset.org/abstracts/32509/a-fuzzy-approach-to-liver-tumor-segmentation-with-zernike-moments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32509.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">452</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">69</span> Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Taweechai%20Nuntawisuttiwong">Taweechai Nuntawisuttiwong</a>, <a href="https://publications.waset.org/abstracts/search?q=Natasha%20Dejdumrong"> Natasha Dejdumrong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lagrange%20interpolation" title="Lagrange interpolation">Lagrange interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20complexity" title=" linear complexity"> linear complexity</a>, <a href="https://publications.waset.org/abstracts/search?q=monomial%20matrix" title=" monomial matrix"> monomial matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=Newton%20interpolation" title=" Newton interpolation"> Newton interpolation</a> </p> <a href="https://publications.waset.org/abstracts/110424/fast-and-efficient-algorithms-for-evaluating-uniform-and-nonuniform-lagrange-and-newton-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110424.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">234</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">68</span> Some Results on the Generalized Higher Rank Numerical Ranges</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Zahraei">Mohsen Zahraei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> ‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8E%E2%80%8ERank-k%20numerical%20range%E2%80%8E" title="‎‎Rank-k numerical range‎">‎‎Rank-k numerical range‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Eisometry%E2%80%8E" title=" ‎isometry‎"> ‎isometry‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Enumerical%20range%E2%80%8E" title=" ‎numerical range‎"> ‎numerical range‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Erectangular%20matrix%20polynomials" title=" ‎rectangular matrix polynomials"> ‎rectangular matrix polynomials</a> </p> <a href="https://publications.waset.org/abstracts/28955/some-results-on-the-generalized-higher-rank-numerical-ranges" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28955.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">459</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">67</span> Forward Stable Computation of Roots of Real Polynomials with Only Real Distinct Roots</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nevena%20Jakov%C4%8Devi%C4%87%20Stor">Nevena Jakovčević Stor</a>, <a href="https://publications.waset.org/abstracts/search?q=Ivan%20Slapni%C4%8Dar"> Ivan Slapničar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=roots%20of%20polynomials" title="roots of polynomials">roots of polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20decomposition" title=" eigenvalue decomposition"> eigenvalue decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=arrowhead%20matrix" title=" arrowhead matrix"> arrowhead matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20relative%20accuracy" title=" high relative accuracy"> high relative accuracy</a> </p> <a href="https://publications.waset.org/abstracts/40100/forward-stable-computation-of-roots-of-real-polynomials-with-only-real-distinct-roots" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40100.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">418</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">66</span> Fractional Order Differentiator Using Chebyshev Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Koushlendra%20Kumar%20Singh">Koushlendra Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Manish%20Kumar%20Bajpai"> Manish Kumar Bajpai</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Kumar%20Pandey"> Rajesh Kumar Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A discrete time fractional orderdifferentiator has been modeled for estimating the fractional order derivatives of contaminated signal. The proposed approach is based on Chebyshev’s polynomials. We use the Riemann-Liouville fractional order derivative definition for designing the fractional order SG differentiator. In first step we calculate the window weight corresponding to the required fractional order. Then signal is convoluted with this calculated window’s weight for finding the fractional order derivatives of signals. Several signals are considered for evaluating the accuracy of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20order%20derivative" title="fractional order derivative">fractional order derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=chebyshev%0D%0Apolynomials" title=" chebyshev polynomials"> chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=S-G%20differentiator" title=" S-G differentiator"> S-G differentiator</a> </p> <a href="https://publications.waset.org/abstracts/21346/fractional-order-differentiator-using-chebyshev-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21346.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">648</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">65</span> A Survey on Routh-Hurwitz Stability Criterion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mojtaba%20Hakimi-Moghaddam">Mojtaba Hakimi-Moghaddam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hurwitz%20polynomials" title="Hurwitz polynomials">Hurwitz polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Routh-Hurwitz%20stability%20criterion" title=" Routh-Hurwitz stability criterion"> Routh-Hurwitz stability criterion</a>, <a href="https://publications.waset.org/abstracts/search?q=continued%20fraction%20expansion" title=" continued fraction expansion"> continued fraction expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=pure%20imaginary%20roots" title=" pure imaginary roots"> pure imaginary roots</a> </p> <a href="https://publications.waset.org/abstracts/72768/a-survey-on-routh-hurwitz-stability-criterion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72768.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">329</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">64</span> The K-Distance Neighborhood Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soner%20Nandappa%20D.">Soner Nandappa D.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Mohammed%20Naji"> Ahmed Mohammed Naji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vertex%20degrees" title="vertex degrees">vertex degrees</a>, <a href="https://publications.waset.org/abstracts/search?q=distance%20in%20graphs" title=" distance in graphs"> distance in graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operation" title=" graph operation"> graph operation</a>, <a href="https://publications.waset.org/abstracts/search?q=Nk-polynomials" title=" Nk-polynomials"> Nk-polynomials</a> </p> <a href="https://publications.waset.org/abstracts/52946/the-k-distance-neighborhood-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52946.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">550</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">63</span> On Hankel Matrices Approach to Interpolation Problem in Infinite and Finite Fields</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ivan%20Baravy">Ivan Baravy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Berlekamp-Massey%20algorithm" title="Berlekamp-Massey algorithm">Berlekamp-Massey algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20interpolation" title=" exponential interpolation"> exponential interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20fields" title=" finite fields"> finite fields</a>, <a href="https://publications.waset.org/abstracts/search?q=Hankel%20matrices" title=" Hankel matrices"> Hankel matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=Hankel%20polynomials" title=" Hankel polynomials"> Hankel polynomials</a> </p> <a href="https://publications.waset.org/abstracts/21861/on-hankel-matrices-approach-to-interpolation-problem-in-infinite-and-finite-fields" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21861.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">521</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">62</span> Large Time Asymptotic Behavior to Solutions of a Forced Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Satyanarayana%20Engu">Satyanarayana Engu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Mohd"> Ahmed Mohd</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Murugan"> V. Murugan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Burgers%20equation" title="Burgers equation">Burgers equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Cole-Hopf%20transformation" title=" Cole-Hopf transformation"> Cole-Hopf transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Hermite%20polynomials" title=" Hermite polynomials"> Hermite polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20time%20asymptotics" title=" large time asymptotics"> large time asymptotics</a> </p> <a href="https://publications.waset.org/abstracts/65872/large-time-asymptotic-behavior-to-solutions-of-a-forced-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65872.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">334</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">61</span> Convergence Analysis of Cubic B-Spline Collocation Method for Time Dependent Parabolic Advection-Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bharti%20Gupta">Bharti Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20K.%20Kukreja"> V. K. Kukreja</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cubic%20B-spline%20basis" title="cubic B-spline basis">cubic B-spline basis</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20norms" title=" spectral norms"> spectral norms</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Chebyshev%20polynomials" title=" shifted Chebyshev polynomials"> shifted Chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20points" title=" collocation points"> collocation points</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimates" title=" error estimates"> error estimates</a> </p> <a href="https://publications.waset.org/abstracts/73363/convergence-analysis-of-cubic-b-spline-collocation-method-for-time-dependent-parabolic-advection-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73363.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">223</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">60</span> On One New Solving Approach of the Plane Mixed Problem for an Elastic Semistrip</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Natalia%20D.%20Vaysfel%E2%80%99d">Natalia D. Vaysfel’d</a>, <a href="https://publications.waset.org/abstracts/search?q=Zinaida%20Y.%20Zhuravlova"> Zinaida Y. Zhuravlova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=semi%20strip" title="semi strip">semi strip</a>, <a href="https://publications.waset.org/abstracts/search?q=Green%27s%20Matrix" title=" Green's Matrix"> Green's Matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20transformation" title=" fourier transformation"> fourier transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=orthogonal%20polynomials%20method" title=" orthogonal polynomials method"> orthogonal polynomials method</a> </p> <a href="https://publications.waset.org/abstracts/16233/on-one-new-solving-approach-of-the-plane-mixed-problem-for-an-elastic-semistrip" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16233.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">431</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">59</span> A Modified Decoupled Semi-Analytical Approach Based On SBFEM for Solving 2D Elastodynamic Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Fakharian">M. Fakharian</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20I.%20Khodakarami"> M. I. Khodakarami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a new trend for improvement in semi-analytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific sub-parametric elements. Mapping functions are uses as a class of higher-order Lagrange polynomials, special shape functions, Gauss-Lobatto -Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=2D%20elastodynamic%20problems" title="2D elastodynamic problems">2D elastodynamic problems</a>, <a href="https://publications.waset.org/abstracts/search?q=lagrange%20polynomials" title=" lagrange polynomials"> lagrange polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=G-L-Lquadrature" title=" G-L-Lquadrature"> G-L-Lquadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=decoupled%20SBFEM" title=" decoupled SBFEM"> decoupled SBFEM</a> </p> <a href="https://publications.waset.org/abstracts/20245/a-modified-decoupled-semi-analytical-approach-based-on-sbfem-for-solving-2d-elastodynamic-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20245.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">444</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">58</span> Graphical Theoretical Construction of Discrete time Share Price Paths from Matroid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Min%20Wang">Min Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Sergey%20Utev"> Sergey Utev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The lessons from the 2007-09 global financial crisis have driven scientific research, which considers the design of new methodologies and financial models in the global market. The quantum mechanics approach was introduced in the unpredictable stock market modeling. One famous quantum tool is Feynman path integral method, which was used to model insurance risk by Tamturk and Utev and adapted to formalize the path-dependent option pricing by Hao and Utev. The research is based on the path-dependent calculation method, which is motivated by the Feynman path integral method. The path calculation can be studied in two ways, one way is to label, and the other is computational. Labeling is a part of the representation of objects, and generating functions can provide many different ways of representing share price paths. In this paper, the recent works on graphical theoretical construction of individual share price path via matroid is presented. Firstly, a study is done on the knowledge of matroid, relationship between lattice path matroid and Tutte polynomials and ways to connect points in the lattice path matroid and Tutte polynomials is suggested. Secondly, It is found that a general binary tree can be validly constructed from a connected lattice path matroid rather than general lattice path matroid. Lastly, it is suggested that there is a way to represent share price paths via a general binary tree, and an algorithm is developed to construct share price paths from general binary trees. A relationship is also provided between lattice integer points and Tutte polynomials of a transversal matroid. Use this way of connection together with the algorithm, a share price path can be constructed from a given connected lattice path matroid. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=combinatorial%20construction" title="combinatorial construction">combinatorial construction</a>, <a href="https://publications.waset.org/abstracts/search?q=graphical%20representation" title=" graphical representation"> graphical representation</a>, <a href="https://publications.waset.org/abstracts/search?q=matroid" title=" matroid"> matroid</a>, <a href="https://publications.waset.org/abstracts/search?q=path%20calculation" title=" path calculation"> path calculation</a>, <a href="https://publications.waset.org/abstracts/search?q=share%20price" title=" share price"> share price</a>, <a href="https://publications.waset.org/abstracts/search?q=Tutte%20polynomial" title=" Tutte polynomial "> Tutte polynomial </a> </p> <a href="https://publications.waset.org/abstracts/118431/graphical-theoretical-construction-of-discrete-time-share-price-paths-from-matroid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/118431.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">138</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">57</span> A New Approach for Solving Fractional Coupled Pdes </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prashant%20Pandey">Prashant Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present article, an eﬀective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diﬀusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution proﬁles of the coupled system are presented graphically for diﬀerent particular cases. The salient feature of the present article is ﬁnding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher eﬃciency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs conﬁrms the super-linearly convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20coupled%20PDE" title="fractional coupled PDE">fractional coupled PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20and%20convergence%20analysis" title=" stability and convergence analysis"> stability and convergence analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Laguerre%20polynomials" title=" Laguerre polynomials"> Laguerre polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/125320/a-new-approach-for-solving-fractional-coupled-pdes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125320.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">145</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">56</span> On-Road Text Detection Platform for Driver Assistance Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Guezouli%20Larbi">Guezouli Larbi</a>, <a href="https://publications.waset.org/abstracts/search?q=Belkacem%20Soundes"> Belkacem Soundes</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The automation of the text detection process can help the human in his driving task. Its application can be very useful to help drivers to have more information about their environment by facilitating the reading of road signs such as directional signs, events, stores, etc. In this paper, a system consisting of two stages has been proposed. In the first one, we used pseudo-Zernike moments to pinpoint areas of the image that may contain text. The architecture of this part is based on three main steps, region of interest (ROI) detection, text localization, and non-text region filtering. Then, in the second step, we present a convolutional neural network architecture (On-Road Text Detection Network - ORTDN) which is considered a classification phase. The results show that the proposed framework achieved ≈ 35 fps and an mAP of ≈ 90%, thus a low computational time with competitive accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=text%20detection" title="text detection">text detection</a>, <a href="https://publications.waset.org/abstracts/search?q=CNN" title=" CNN"> CNN</a>, <a href="https://publications.waset.org/abstracts/search?q=PZM" title=" PZM"> PZM</a>, <a href="https://publications.waset.org/abstracts/search?q=deep%20learning" title=" deep learning"> deep learning</a> </p> <a href="https://publications.waset.org/abstracts/161507/on-road-text-detection-platform-for-driver-assistance-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/161507.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">83</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">55</span> Prime Graphs of Polynomials and Power Series Over Non-Commutative Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Walaa%20Obaidallah%20Alqarafi">Walaa Obaidallah Alqarafi</a>, <a href="https://publications.waset.org/abstracts/search?q=Wafaa%20Mohammed%20Fakieh"> Wafaa Mohammed Fakieh</a>, <a href="https://publications.waset.org/abstracts/search?q=Alaa%20Abdallah%20Altassan"> Alaa Abdallah Altassan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Algebraic graph theory is defined as a bridge between algebraic structures and graphs. It has several uses in many fields, including chemistry, physics, and computer science. The prime graph is a type of graph associated with a ring R, where the vertex set is the whole ring R, and two vertices x and y are adjacent if either xRy=0 or yRx=0. However, the investigation of the prime graph over rings remains relatively limited. The behavior of this graph in extended rings, like R[x] and R[[x]], where R is a non-commutative ring, deserves more attention because of the wider applicability in algebra and other mathematical fields. To study the prime graphs over polynomials and power series rings, we used a combination of ring-theoretic and graph-theoretic techniques. This paper focuses on two invariants: the diameter and the girth of these graphs. Furthermore, the work discusses how the graph structures change when passing from R to R[x] and R[[x]]. In our study, we found that the set of strong zero-divisors of ring R represents the set of vertices in prime graphs. Based on this discovery, we redefined the vertices of prime graphs using the definition of strong zero divisors. Additionally, our results show that although the prime graphs of R[x] and R[[x]] are comparable to the graph of R, they have different combinatorial characteristics since these extensions contain new strong zero-divisors. In particular, we find conditions in which the diameter and girth of the graphs, as they expand from R to R[x] and R[[x]], do not change or do change. In conclusion, this study shows how extending a non-commutative ring R to R[x] and R[[x]] affects the structure of their prime graphs, particularly in terms of diameter and girth. These findings enhance the understanding of the relationship between ring extensions and graph properties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=prime%20graph" title="prime graph">prime graph</a>, <a href="https://publications.waset.org/abstracts/search?q=diameter" title=" diameter"> diameter</a>, <a href="https://publications.waset.org/abstracts/search?q=girth" title=" girth"> girth</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20series%20ring" title=" power series ring"> power series ring</a> </p> <a href="https://publications.waset.org/abstracts/192430/prime-graphs-of-polynomials-and-power-series-over-non-commutative-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192430.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">18</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">54</span> Numerical Solution of Space Fractional Order Linear/Nonlinear Reaction-Advection Diffusion Equation Using Jacobi Polynomial</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=space%20fractional%20order%20linear%2Fnonlinear%20reaction-advection%20diffusion%20equation" title="space fractional order linear/nonlinear reaction-advection diffusion equation">space fractional order linear/nonlinear reaction-advection diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Jacobi%20polynomials" title=" shifted Jacobi polynomials"> shifted Jacobi polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrix" title=" operational matrix"> operational matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title=" Caputo derivative"> Caputo derivative</a> </p> <a href="https://publications.waset.org/abstracts/79521/numerical-solution-of-space-fractional-order-linearnonlinear-reaction-advection-diffusion-equation-using-jacobi-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79521.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">445</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">53</span> The Efficacy of an Ideal RGP Fitting on Higher Order Aberrations (HOA) in 65 Keratoconus Patients</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ghandehari-Motlagh">Ghandehari-Motlagh</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad"> Mohammad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Purpose: To evaluate of the effect of an ideal fit of RGPs on HOA and keratoconus indices. Methods: In this cohort study, 65 keratoconus eyes with more than 3 lines(Snellen)improvement between BSCVA and BCVA(RGP) were imaged with Pentacam HR and their topometric and Zernike analysis findings without RGP were recorded. After 6 months or later of RGP fitting (Rose-K,Boston XO2), imaging with pentacam was repeated and the above information were recorded. Results: 65 different grades of keratoconus eyes with mean age of 27.32 yrs/old(SD +_5.51)enrolled including M 28(43.1%) and F 37(56.9%). 44(67.7%) with family Hx of Kc and 21(31.25%)without any Kc in their families. 54 (83.1%) with and 11 (16.9%) without any ocular allergy Hx. Maximum percent of age of onset of kc was 15 ys/old(29.2%).This study showed there are meaningful correlations between with and without RGP Pentacam indices and HOA in each grade of Kc.92.3% of patients had foreign body sensation but 96.9% had 11-20 hours/day RGP wear that confirms on psychologic effect of an ideal fit on patient’s motivation. Conclusion: With the three points touch principle of RGP fitting in Kc corneas, the patients will have a decrease in HOA and so delayed need for PK or LK. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=keratoconus" title="keratoconus">keratoconus</a>, <a href="https://publications.waset.org/abstracts/search?q=rigid%20gas%20permeable%20lens" title=" rigid gas permeable lens"> rigid gas permeable lens</a>, <a href="https://publications.waset.org/abstracts/search?q=aberration" title=" aberration"> aberration</a>, <a href="https://publications.waset.org/abstracts/search?q=fitting" title=" fitting"> fitting</a> </p> <a href="https://publications.waset.org/abstracts/23868/the-efficacy-of-an-ideal-rgp-fitting-on-higher-order-aberrations-hoa-in-65-keratoconus-patients" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23868.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">415</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">52</span> Optimal Image Representation for Linear Canonical Transform Multiplexing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Navdeep%20Goel">Navdeep Goel</a>, <a href="https://publications.waset.org/abstracts/search?q=Salvador%20Gabarda"> Salvador Gabarda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4x4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4*4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4*4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chirp%20signals" title="chirp signals">chirp signals</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20multiplexing" title=" image multiplexing"> image multiplexing</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20transformation" title=" image transformation"> image transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20canonical%20transform" title=" linear canonical transform"> linear canonical transform</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20approximation" title=" polynomial approximation"> polynomial approximation</a> </p> <a href="https://publications.waset.org/abstracts/35260/optimal-image-representation-for-linear-canonical-transform-multiplexing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35260.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">412</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">51</span> Analysis of Various Copy Move Image Forgery Techniques for Better Detection Accuracy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Grishma%20D.%20Solanki">Grishma D. Solanki</a>, <a href="https://publications.waset.org/abstracts/search?q=Karshan%20Kandoriya"> Karshan Kandoriya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In modern era of information age, digitalization has revolutionized like never before. Powerful computers, advanced photo editing software packages and high resolution capturing devices have made manipulation of digital images incredibly easy. As per as image forensics concerns, one of the most actively researched area are detection of copy move forgeries. Higher computational complexity is one of the major component of existing techniques to detect such tampering. Moreover, copy move forgery is usually performed in three steps. First, copying of a region in an image then pasting the same one in the same respective image and finally doing some post-processing like rotation, scaling, shift, noise, etc. Consequently, pseudo Zernike moment is used as a features extraction method for matching image blocks and as a primary factor on which performance of detection algorithms depends. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=copy-move%20image%20forgery" title="copy-move image forgery">copy-move image forgery</a>, <a href="https://publications.waset.org/abstracts/search?q=digital%20forensics" title=" digital forensics"> digital forensics</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20forensics" title=" image forensics"> image forensics</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20forgery" title=" image forgery"> image forgery</a> </p> <a href="https://publications.waset.org/abstracts/49539/analysis-of-various-copy-move-image-forgery-techniques-for-better-detection-accuracy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/49539.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">288</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Zernike%20%E2%80%8Epolynomials&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Zernike%20%E2%80%8Epolynomials&page=3">3</a></li> <li class="page-item"><a class="page-link" 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