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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> 1319</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: rational trigonometric Bézier curves</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1319</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/abstracts/search?q=Maria%20Hussin">Maria Hussin</a>, <a href="https://publications.waset.org/abstracts/search?q=Malik%20Zawwar%20Hussain"> Malik Zawwar Hussain</a>, <a href="https://publications.waset.org/abstracts/search?q=Mubashrah%20Saddiqa"> Mubashrah Saddiqa</a> </p> <p class="card-text"><strong>Abstract:</strong></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 class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=control%20points" title="control points">control points</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20trigonometric%20B%C3%A9zier%20curves" title=" rational trigonometric Bézier curves"> rational trigonometric Bézier curves</a>, <a href="https://publications.waset.org/abstracts/search?q=radius%20error" title=" radius error"> radius error</a>, <a href="https://publications.waset.org/abstracts/search?q=shape%20measure" title=" shape measure"> shape measure</a>, <a href="https://publications.waset.org/abstracts/search?q=weight%20functions" title=" weight functions"> weight functions</a> </p> <a href="https://publications.waset.org/abstracts/15444/circular-approximation-by-trigonometric-bezier-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15444.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">480</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">1318</span> Monotone Rational Trigonometric Interpolation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Uzma%20Bashir">Uzma Bashir</a>, <a href="https://publications.waset.org/abstracts/search?q=Jamaludin%20Md.%20Ali"> Jamaludin Md. Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study is concerned with the visualization of monotone data using a piece-wise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left-free. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20splines" title="trigonometric splines">trigonometric splines</a>, <a href="https://publications.waset.org/abstracts/search?q=monotone%20data" title=" monotone data"> monotone data</a>, <a href="https://publications.waset.org/abstracts/search?q=shape%20preserving" title=" shape preserving"> shape preserving</a>, <a href="https://publications.waset.org/abstracts/search?q=C1%20monotone%20interpolant" title=" C1 monotone interpolant"> C1 monotone interpolant</a> </p> <a href="https://publications.waset.org/abstracts/5079/monotone-rational-trigonometric-interpolation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5079.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">275</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">1317</span> Curve Fitting by Cubic Bezier Curves Using Migrating Birds Optimization Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mitat%20Uysal">Mitat Uysal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new met heuristic optimization algorithm called as Migrating Birds Optimization is used for curve fitting by rational cubic Bezier Curves. This requires solving a complicated multivariate optimization problem. In this study, the solution of this optimization problem is achieved by Migrating Birds Optimization algorithm that is a powerful met heuristic nature-inspired algorithm well appropriate for optimization. The results of this study show that the proposed method performs very well and being able to fit the data points to cubic Bezier Curves with a high degree of accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algorithms" title="algorithms">algorithms</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=heuristic%20optimization" title=" heuristic optimization"> heuristic optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=migrating%20birds%20optimization" title=" migrating birds optimization"> migrating birds optimization</a> </p> <a href="https://publications.waset.org/abstracts/78026/curve-fitting-by-cubic-bezier-curves-using-migrating-birds-optimization-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78026.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">346</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">1316</span> Weighted G2 Multi-Degree Reduction of Bezier Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salisu%20ibrahim">Salisu ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdalla%20Rababah"> Abdalla Rababah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this research, we use Weighted G2-Multi-degree reduction of Bezier curve of degree n to a Bezier curve of degree m, m < n. The degree reduction of Bezier curves is used to represent a given Bezier curve of n by a Bezier curve of degree m, m < n. Exact degree reduction is not possible, and degree reduction is approximate process in nature. We derive a weighted degree reducing method that is geometrically continuous at the end points. Different norms will be considered, several error minimizations will be given. The proposed methods produce error function that are less than the errors of existing methods. <p class="card-text"><strong>Keywords:</strong> <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=multiple%20degree%20reduction" title=" multiple degree reduction"> multiple degree reduction</a>, <a href="https://publications.waset.org/abstracts/search?q=geometric%20continuity" title=" geometric continuity"> geometric continuity</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20function" title=" error function"> error function</a> </p> <a href="https://publications.waset.org/abstracts/18669/weighted-g2-multi-degree-reduction-of-bezier-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18669.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">492</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">1315</span> Approximating Maximum Speed on Road from Curvature Information of Bezier Curve</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Yushalify%20Misro">M. Yushalify Misro</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Ramli"> Ahmad Ramli</a>, <a href="https://publications.waset.org/abstracts/search?q=Jamaludin%20M.%20Ali"> Jamaludin M. Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, the curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use the different approach to finding the best approximation for the curve so that it will resemble highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first the Bezier curve estimates the real shape of the curve which can be verified visually. Even, though, the fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed is acceptable. We verified our result with the manual calculation of the curvature from the map. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=speed%20estimation" title="speed estimation">speed estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=path%20constraints" title=" path constraints"> path constraints</a>, <a href="https://publications.waset.org/abstracts/search?q=reference%20trajectory" title=" reference trajectory"> reference trajectory</a>, <a href="https://publications.waset.org/abstracts/search?q=Bezier%20curve" title=" Bezier curve"> Bezier curve</a> </p> <a href="https://publications.waset.org/abstracts/36228/approximating-maximum-speed-on-road-from-curvature-information-of-bezier-curve" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36228.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">377</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">1314</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">280</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">1313</span> High Accuracy Analytic Approximation for Special Functions Applied to Bessel Functions J₀(x) and Its Zeros</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass">Fernando Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin"> Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20approximations" title="analytic approximations">analytic approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20approximations" title=" asymptotic approximations"> asymptotic approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=Bessel%20functions" title=" Bessel functions"> Bessel functions</a>, <a href="https://publications.waset.org/abstracts/search?q=quasirational%20approximations" title=" quasirational approximations"> quasirational approximations</a> </p> <a href="https://publications.waset.org/abstracts/92867/high-accuracy-analytic-approximation-for-special-functions-applied-to-bessel-functions-j0x-and-its-zeros" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/92867.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">259</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">1312</span> Closed Forms of Trigonometric Series Interms of Riemann’s ζ Function and Dirichlet η, λ, β Functions or the Hurwitz Zeta Function and Harmonic Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Slobodan%20B.%20Tri%C4%8Dkovi%C4%87">Slobodan B. Tričković</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dirichlet%20eta%20lambda%20beta%20functions" title="Dirichlet eta lambda beta functions">Dirichlet eta lambda beta functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Riemann%27s%20zeta%20function" title=" Riemann's zeta function"> Riemann's zeta function</a>, <a href="https://publications.waset.org/abstracts/search?q=Hurwitz%20zeta%20function" title=" Hurwitz zeta function"> Hurwitz zeta function</a>, <a href="https://publications.waset.org/abstracts/search?q=Harmonic%20numbers" title=" Harmonic numbers"> Harmonic numbers</a> </p> <a href="https://publications.waset.org/abstracts/167649/closed-forms-of-trigonometric-series-interms-of-riemanns-z-function-and-dirichlet-i-l-v-functions-or-the-hurwitz-zeta-function-and-harmonic-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167649.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">108</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">1311</span> Adaptive Motion Planning for 6-DOF Robots Based on Trigonometric Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jincan%20Li">Jincan Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Mingyu%20Gao"> Mingyu Gao</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhiwei%20He"> Zhiwei He</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuxiang%20Yang"> Yuxiang Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhongfei%20Yu"> Zhongfei Yu</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuanyuan%20Liu"> Yuanyuan Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=kinematic%20constraints" title="kinematic constraints">kinematic constraints</a>, <a href="https://publications.waset.org/abstracts/search?q=motion%20planning" title=" motion planning"> motion planning</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20function" title=" trigonometric function"> trigonometric function</a>, <a href="https://publications.waset.org/abstracts/search?q=6-DOF%20robots" title=" 6-DOF robots"> 6-DOF robots</a> </p> <a href="https://publications.waset.org/abstracts/87082/adaptive-motion-planning-for-6-dof-robots-based-on-trigonometric-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/87082.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">278</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">1310</span> Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shazalina%20Mat%20Zin">Shazalina Mat Zin</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Abd.%20Majid"> Ahmad Abd. Majid</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Izani%20Md.%20Ismail"> Ahmad Izani Md. Ismail</a>, <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Abbas"> Muhammad Abbas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature. <p class="card-text"><strong>Keywords:</strong> <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=cubic%20trigonometric%20B-spline" title=" cubic trigonometric B-spline"> cubic trigonometric B-spline</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference" title=" finite difference"> finite difference</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20equation" title=" wave equation"> wave equation</a> </p> <a href="https://publications.waset.org/abstracts/10136/cubic-trigonometric-b-spline-approach-to-numerical-solution-of-wave-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10136.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">548</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">1309</span> L1-Convergence of Modified Trigonometric Sums</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sandeep%20Kaur%20Chouhan">Sandeep Kaur Chouhan</a>, <a href="https://publications.waset.org/abstracts/search?q=Jatinderdeep%20Kaur"> Jatinderdeep Kaur</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20S.%20Bhatia"> S. S. Bhatia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20Dirichlet%20kernel" title="conjugate Dirichlet kernel">conjugate Dirichlet kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=Dirichlet%20kernel" title=" Dirichlet kernel"> Dirichlet kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=L1-convergence" title=" L1-convergence"> L1-convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20sums" title=" modified sums"> modified sums</a> </p> <a href="https://publications.waset.org/abstracts/44182/l1-convergence-of-modified-trigonometric-sums" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44182.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">360</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1308</span> Optimized and Secured Digital Watermarking Using Fuzzy Entropy, Bezier Curve and Visual Cryptography</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Rama%20Kishore">R. Rama Kishore</a>, <a href="https://publications.waset.org/abstracts/search?q=Sunesh"> Sunesh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recent development in the usage of internet for different purposes creates a great threat for the copyright protection of the digital images. Digital watermarking can be used to address the problem. This paper presents detailed review of the different watermarking techniques, latest trends in the field of secured, robust and imperceptible watermarking. It also discusses the different optimization techniques used in the field of watermarking in order to improve the robustness and imperceptibility of the method. Different measures are discussed to evaluate the performance of the watermarking algorithm. At the end, this paper proposes a watermarking algorithm using (2, 2) share visual cryptography and Bezier curve based algorithm to improve the security of the watermark. The proposed method uses fractional transformation to improve the robustness of the copyright protection of the method. The algorithm is optimized using fuzzy entropy for better results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=digital%20watermarking" title="digital watermarking">digital watermarking</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20transform" title=" fractional transform"> fractional transform</a>, <a href="https://publications.waset.org/abstracts/search?q=visual%20cryptography" title=" visual cryptography"> visual cryptography</a>, <a href="https://publications.waset.org/abstracts/search?q=Bezier%20curve" title=" Bezier curve"> Bezier curve</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20entropy" title=" fuzzy entropy"> fuzzy entropy</a> </p> <a href="https://publications.waset.org/abstracts/89843/optimized-and-secured-digital-watermarking-using-fuzzy-entropy-bezier-curve-and-visual-cryptography" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89843.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">371</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">1307</span> Derivation of Trigonometric Identities and Solutions through Baudhayan Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rakesh%20Bhatia">Rakesh Bhatia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Students often face significant challenges in understanding and applying trigonometric identities, primarily due to the overwhelming need to memorize numerous formulas. This often leads to confusion, frustration, and difficulty in effectively using these formulas across diverse types of problems. Traditional methods of learning trigonometry demand considerable time and effort, which can further hinder comprehension and application. Vedic Mathematics offers an innovative and simplified approach to overcoming these challenges. This paper explores how Baudhayan Numbers, can be used to derive trigonometric identities and simplify calculations related to height and distance. Unlike conventional approaches, this method minimizes the need for extensive paper-based calculations, promoting a conceptual understanding. Using Vedic Mathematics Sutras such as Anurupyena and Vilokanam, this approach enables the derivation of over 100 trigonometric identities through a single, unified approach. The simplicity and efficiency of this technique not only make learning trigonometry more accessible but also foster computational thinking. Beyond academics, the practical applications of this method extend to engineering fields such as bridge design and construction, where precise trigonometric calculations are critical. This exploration underscores the potential of Vedic Mathematics to revolutionize the learning and application of trigonometry by offering a streamlined, intuitive, and versatile framework. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=baudhayan%20numbers" title="baudhayan numbers">baudhayan numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=anurupyena" title=" anurupyena"> anurupyena</a>, <a href="https://publications.waset.org/abstracts/search?q=vilokanam" title=" vilokanam"> vilokanam</a>, <a href="https://publications.waset.org/abstracts/search?q=sutras" title=" sutras"> sutras</a> </p> <a href="https://publications.waset.org/abstracts/194925/derivation-of-trigonometric-identities-and-solutions-through-baudhayan-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/194925.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">20</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">1306</span> Degree of Approximation of Functions Conjugate to Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=signals" title="signals">signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20fourier%20approximation" title=" trigonometric fourier approximation"> trigonometric fourier approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=class%20W%28L%5Er" title=" class W(L^r"> class W(L^r</a>, <a href="https://publications.waset.org/abstracts/search?q=%5Cxi%28t%29" title="\xi(t)">\xi(t)</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20fourier%20series" title=" conjugate fourier series"> conjugate fourier series</a> </p> <a href="https://publications.waset.org/abstracts/20996/degree-of-approximation-of-functions-conjugate-to-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20996.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">402</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">1305</span> The Conceptual and Procedural Knowledge of Rational Numbers in Primary School Teachers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20M.%20Kashim">R. M. Kashim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conceptual%20knowledge" title="conceptual knowledge">conceptual knowledge</a>, <a href="https://publications.waset.org/abstracts/search?q=primary%20school%20teachers" title=" primary school teachers"> primary school teachers</a>, <a href="https://publications.waset.org/abstracts/search?q=procedural%20knowledge" title=" procedural knowledge"> procedural knowledge</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20numbers" title=" rational numbers"> rational numbers</a> </p> <a href="https://publications.waset.org/abstracts/44950/the-conceptual-and-procedural-knowledge-of-rational-numbers-in-primary-school-teachers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44950.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">1304</span> Box Counting Dimension of the Union L of Trinomial Curves When α ≥ 1</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kaoutar%20Lamrini%20Uahabi">Kaoutar Lamrini Uahabi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Atounti"> Mohamed Atounti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=feasible%20angles" title="feasible angles">feasible angles</a>, <a href="https://publications.waset.org/abstracts/search?q=fractal%20dimension" title=" fractal dimension"> fractal dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=Minkowski%20sausage" title=" Minkowski sausage"> Minkowski sausage</a>, <a href="https://publications.waset.org/abstracts/search?q=trinomial%20curves" title=" trinomial curves"> trinomial curves</a>, <a href="https://publications.waset.org/abstracts/search?q=trinomial%20equation" title=" trinomial equation"> trinomial equation</a> </p> <a href="https://publications.waset.org/abstracts/87207/box-counting-dimension-of-the-union-l-of-trinomial-curves-when-a-1" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/87207.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">196</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">1303</span> Approximation of Intersection Curves of Two Parametric Surfaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Misbah%20Irshad">Misbah Irshad</a>, <a href="https://publications.waset.org/abstracts/search?q=Faiza%20Sarfraz"> Faiza Sarfraz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The problem of approximating surface to surface intersection is considered to be very important in computer aided geometric design and computer aided manufacturing. Although it is a complex problem to handle, its continuous need in the industry makes it an active topic in research. A technique for approximating intersection curves of two parametric surfaces is proposed, which extracts boundary points and turning points from a sequence of intersection points and interpolate them with the help of rational cubic spline functions. The proposed approach is demonstrated with the help of examples and analyzed by calculating error. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximation" title="approximation">approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=parametric%20surface" title=" parametric surface"> parametric surface</a>, <a href="https://publications.waset.org/abstracts/search?q=spline%20function" title=" spline function"> spline function</a>, <a href="https://publications.waset.org/abstracts/search?q=surface%20intersection" title=" surface intersection"> surface intersection</a> </p> <a href="https://publications.waset.org/abstracts/52667/approximation-of-intersection-curves-of-two-parametric-surfaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52667.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">277</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">1302</span> Primary School Teachers’ Conceptual and Procedural Knowledge of Rational Number and Its Effects on Pupils’ Achievement in Rational Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20M.%20Kashim">R. M. Kashim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study investigated primary school teachers’ conceptual and procedural knowledge of rational numbers and its effects on pupil’s achievement in rational numbers. Specifically, primary school teachers’ level of conceptual knowledge about rational numbers, primary school teachers’ level of procedural knowledge about rational numbers, and the effects of teachers conceptual and procedural knowledge on their pupils understanding of rational numbers in primary schools is investigated. The study was carried out in Bauchi metropolis in the Bauchi state of Nigeria. The design of the study was a multi-stage design. The first stage was a descriptive design. The second stage involves a pre-test, post-test only quasi-experimental design. Two instruments were used for the data collection in the study. These were Conceptual and Procedural knowledge test (CPKT) and Rational number achievement test (RAT), the population of the study comprises of three (3) mathematics teachers’ holders of Nigerian Certificate in Education (NCE) teaching primary six and 210 pupils in their intact classes were used for the study. The data collected were analyzed using mean, standard deviation, analysis of variance, analysis of covariance and t- test. The findings indicated that the pupils taught rational number by a teacher that has high conceptual and procedural knowledge understand and perform better than the pupil taught by a teacher who has low conceptual and procedural knowledge of rational number. It is, therefore, recommended that teachers in primary schools should be encouraged to enrich their conceptual knowledge of rational numbers. Also, the superiority performance of teachers in procedural knowledge in rational number should not become an obstruction of understanding. Teachers Conceptual and procedural knowledge of rational numbers should be balanced so that primary school pupils will have a view of better teaching and learning of rational number in our contemporary schools. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conceptual" title="conceptual">conceptual</a>, <a href="https://publications.waset.org/abstracts/search?q=procedural%20knowledge" title=" procedural knowledge"> procedural knowledge</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20number" title=" rational number"> rational number</a>, <a href="https://publications.waset.org/abstracts/search?q=pupils" title=" pupils"> pupils</a> </p> <a href="https://publications.waset.org/abstracts/24016/primary-school-teachers-conceptual-and-procedural-knowledge-of-rational-number-and-its-effects-on-pupils-achievement-in-rational-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24016.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">461</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">1301</span> Symbolic Computation and Abundant Travelling Wave Solutions to Modified Burgers' Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Younis">Muhammad Younis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=traveling%20wave%20solutions" title="traveling wave solutions">traveling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=NLPDE" title=" NLPDE"> NLPDE</a>, <a href="https://publications.waset.org/abstracts/search?q=computation" title=" computation"> computation</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability" title=" integrability"> integrability</a> </p> <a href="https://publications.waset.org/abstracts/48762/symbolic-computation-and-abundant-travelling-wave-solutions-to-modified-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48762.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">439</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">1300</span> Primary School Teachers’ Conceptual and Procedural Knowledge of Rational Numbers and Its Effects on Pupils Achievement of Rational Numbers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Raliatu%20Mohammed%20Kashim">Raliatu Mohammed Kashim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study investigated primary school teachers conceptual and procedural knowledge of rational numbers to determine how it effects on pupil’s achievement on rational number. Specifically, primary school teachers’ level of conceptual and procedural knowledge about rational number and its effects on their pupils understanding of rational number in primary school was explored. The study was carried out in Bauchi state of Nigeria, Using a multistage design. The first stage was a descriptive design. The second stage involves a pre-test post-test only quasi experiment design. The population of the study comprises of six mathematics teachers holding the Nigerian Certificate in Education (NCE) teaching primary six and their two hundred and ten pupils in intact class. Two instrument namely Conceptual and Procedural knowledge Test (CPKT) and Rational number Achievement Test (RAT) were used for data collection. Data collected was analyzed using ANCOVA and Scheffe’s Test. The result revealed a significant differences between pupils taught by teachers with high conceptual and procedural knowledge and those target by teachers with low conceptual and procedural knowledge. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conceptual%20knowledge" title="conceptual knowledge">conceptual knowledge</a>, <a href="https://publications.waset.org/abstracts/search?q=procedural%20knowledge" title=" procedural knowledge"> procedural knowledge</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20numbers" title=" rational numbers"> rational numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=multistage%20design" title=" multistage design "> multistage design </a> </p> <a href="https://publications.waset.org/abstracts/12443/primary-school-teachers-conceptual-and-procedural-knowledge-of-rational-numbers-and-its-effects-on-pupils-achievement-of-rational-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12443.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">396</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">1299</span> Modeling and Computational Validation of Dispersion Curves of Guide Waves in a Pipe Using ANSYS</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Perdomo">A. Perdomo</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20R.%20Bacca"> J. R. Bacca</a>, <a href="https://publications.waset.org/abstracts/search?q=Q.%20E.%20Jabid"> Q. E. Jabid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In recent years, technological and investigative progress has been achieved in the area of monitoring of equipment and installation as a result of a deeper understanding of physical phenomenon associated with the non-destructive tests (NDT). The modal analysis proposes an efficient solution to determine the dispersion curves of an arbitrary waveguide cross-sectional. Dispersion curves are essential in the discontinuity localization based on guided waves. In this work, an isotropic hollow cylinder is dynamically analyzed in ANSYS to obtain resonant frequencies and mode shapes all of them associated with the dispersion curves. The numerical results provide the relation between frequency and wavelength which is the foundation of the dispersion curves. Results of the simulation process are validated with the software GUIGW. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ansys%20APDL" title="ansys APDL">ansys APDL</a>, <a href="https://publications.waset.org/abstracts/search?q=dispersion%20curves" title=" dispersion curves"> dispersion curves</a>, <a href="https://publications.waset.org/abstracts/search?q=guide%20waves" title=" guide waves"> guide waves</a>, <a href="https://publications.waset.org/abstracts/search?q=modal%20analysis" title=" modal analysis"> modal analysis</a> </p> <a href="https://publications.waset.org/abstracts/108272/modeling-and-computational-validation-of-dispersion-curves-of-guide-waves-in-a-pipe-using-ansys" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/108272.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">263</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">1298</span> Regionalization of IDF Curves with L-Moments for Storm Events</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Noratiqah%20Mohd%20Ariff">Noratiqah Mohd Ariff</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Aziz%20Jemain"> Abdul Aziz Jemain</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohd%20Aftar%20Abu%20Bakar"> Mohd Aftar Abu Bakar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The construction of Intensity-Duration-Frequency (IDF) curves is one of the most common and useful tools in order to design hydraulic structures and to provide a mathematical relationship between rainfall characteristics. IDF curves, especially those in Peninsular Malaysia, are often built using moving windows of rainfalls. However, these windows do not represent the actual rainfall events since the duration of rainfalls is usually prefixed. Hence, instead of using moving windows, this study aims to find regionalized distributions for IDF curves of extreme rainfalls based on storm events. Homogeneity test is performed on annual maximum of storm intensities to identify homogeneous regions of storms in Peninsular Malaysia. The L-moment method is then used to regionalized Generalized Extreme Value (GEV) distribution of these annual maximums and subsequently. IDF curves are constructed using the regional distributions. The differences between the IDF curves obtained and IDF curves found using at-site GEV distributions are observed through the computation of the coefficient of variation of root mean square error, mean percentage difference and the coefficient of determination. The small differences implied that the construction of IDF curves could be simplified by finding a general probability distribution of each region. This will also help in constructing IDF curves for sites with no rainfall station. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=IDF%20curves" title="IDF curves">IDF curves</a>, <a href="https://publications.waset.org/abstracts/search?q=L-moments" title=" L-moments"> L-moments</a>, <a href="https://publications.waset.org/abstracts/search?q=regionalization" title=" regionalization"> regionalization</a>, <a href="https://publications.waset.org/abstracts/search?q=storm%20events" title=" storm events"> storm events</a> </p> <a href="https://publications.waset.org/abstracts/42876/regionalization-of-idf-curves-with-l-moments-for-storm-events" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42876.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">534</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">1297</span> Life Prediction Method of Lithium-Ion Battery Based on Grey Support Vector Machines</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiaogang%20Li">Xiaogang Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Jieqiong%20Miao"> Jieqiong Miao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> As for the problem of the grey forecasting model prediction accuracy is low, an improved grey prediction model is put forward. Firstly, use trigonometric function transform the original data sequence in order to improve the smoothness of data , this model called SGM( smoothness of grey prediction model), then combine the improved grey model with support vector machine , and put forward the grey support vector machine model (SGM - SVM).Before the establishment of the model, we use trigonometric functions and accumulation generation operation preprocessing data in order to enhance the smoothness of the data and weaken the randomness of the data, then use support vector machine (SVM) to establish a prediction model for pre-processed data and select model parameters using genetic algorithms to obtain the optimum value of the global search. Finally, restore data through the "regressive generate" operation to get forecasting data. In order to prove that the SGM-SVM model is superior to other models, we select the battery life data from calce. The presented model is used to predict life of battery and the predicted result was compared with that of grey model and support vector machines．For a more intuitive comparison of the three models, this paper presents root mean square error of this three different models .The results show that the effect of grey support vector machine (SGM-SVM) to predict life is optimal, and the root mean square error is only 3.18%. Keywords: grey forecasting model, trigonometric function, support vector machine, genetic algorithms, root mean square error <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Grey%20prediction%20model" title="Grey prediction model">Grey prediction model</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20functions" title=" trigonometric functions"> trigonometric functions</a>, <a href="https://publications.waset.org/abstracts/search?q=support%20vector%20machines" title=" support vector machines"> support vector machines</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithms" title=" genetic algorithms"> genetic algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=root%20mean%20square%20error" title=" root mean square error"> root mean square error</a> </p> <a href="https://publications.waset.org/abstracts/29370/life-prediction-method-of-lithium-ion-battery-based-on-grey-support-vector-machines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29370.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">468</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">1296</span> Centrifuge Modeling of Monopiles Subjected to Lateral Monotonic Loading</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20R.%20Khodaei">H. R. Khodaei</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Moradi"> M. Moradi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20H.%20Tajik"> A. H. Tajik</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The type of foundation commonly used today for berthing dolphins is a set of tubular steel piles with large diameters, which are known as monopiles. The design of these monopiles is based on the theories related with laterally loaded piles. One of the most common methods to analyze and design the piles subjected to lateral loads is the p-y curves. In the present study, centrifuge tests are conducted in order to obtain the p-y curves. Series of tests were designed in order to investigate the scaling laws in the centrifuge for monotonic loading. Also, two important parameters, the embedded depth L of the pile in the soil and free length e of the pile, as well as their ratios were studied via five experimental tests. Finally, the p-y curves of API are presented to be compared with the curves obtained from the tests so that the differences could be demonstrated. The results show that the p-y curves proposed by API highly overestimate the lateral load bearing capacity. It suggests that these curves need correction and modification for each site as the soil conditions change. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=centrifuge%20modeling" title="centrifuge modeling">centrifuge modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=monopile" title=" monopile"> monopile</a>, <a href="https://publications.waset.org/abstracts/search?q=lateral%20loading" title=" lateral loading"> lateral loading</a>, <a href="https://publications.waset.org/abstracts/search?q=p-y%20curves" title=" p-y curves"> p-y curves</a> </p> <a href="https://publications.waset.org/abstracts/84252/centrifuge-modeling-of-monopiles-subjected-to-lateral-monotonic-loading" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/84252.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">253</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">1295</span> High Accuracy Analytic Approximations for Modified Bessel Functions I₀(x)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pablo%20Martin">Pablo Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Olivares"> Jorge Olivares</a>, <a href="https://publications.waset.org/abstracts/search?q=Fernando%20Maass"> Fernando Maass</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20approximations" title="analytic approximations">analytic approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical-physics%20applications" title=" mathematical-physics applications"> mathematical-physics applications</a>, <a href="https://publications.waset.org/abstracts/search?q=quasi-rational%20functions" title=" quasi-rational functions"> quasi-rational functions</a>, <a href="https://publications.waset.org/abstracts/search?q=special%20functions" title=" special functions"> special functions</a> </p> <a href="https://publications.waset.org/abstracts/77484/high-accuracy-analytic-approximations-for-modified-bessel-functions-i0x" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77484.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">257</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">1294</span> Generating Arabic Fonts Using Rational Cubic Ball Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fakharuddin%20Ibrahim">Fakharuddin Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Jamaludin%20Md.%20Ali"> Jamaludin Md. Ali</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Ramli"> Ahmad Ramli </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G<sup>1</sup> continuity. The conditions considered are known as the G<sup>1</sup> Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=data%20interpolation" title="data interpolation">data interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20ball%20curve" title=" rational ball curve"> rational ball curve</a>, <a href="https://publications.waset.org/abstracts/search?q=hermite%20condition" title=" hermite condition"> hermite condition</a>, <a href="https://publications.waset.org/abstracts/search?q=continuity" title=" continuity"> continuity</a> </p> <a href="https://publications.waset.org/abstracts/44202/generating-arabic-fonts-using-rational-cubic-ball-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44202.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">433</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">1293</span> Regionalization of IDF Curves, by Interpolating Intensity and Adjustment Parameters - Application to Boyacá, Colombia</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pedro%20Mauricio%20Acosta">Pedro Mauricio Acosta</a>, <a href="https://publications.waset.org/abstracts/search?q=Carlos%20Andr%C3%A9s%20Caro"> Carlos Andrés Caro</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research presents the regionalization of IDF curves for the department of Boyacá, Colombia, which comprises 16 towns, including the provincial capital, Tunja. For regionalization adjustment parameters (U and alpha) of the IDF curves stations referred to in the studied area were used. Similar regionalization is used by the interpolation of intensities. In the case of regionalization by parameters found by the construction of the curves intensity, duration and frequency estimation methods using ordinary moments and maximum likelihood. Regionalization and interpolation of data were performed with the assistance of Arcgis software. Within the development of the project the best choice to provide a level of reliability such as to determine which of the options and ways to regionalize is best sought. The resulting isolines maps were made in the case of regionalization intensities, each map is associated with a different return period and duration in order to build IDF curves in the studied area. In the case of the regionalization maps parameters associated with each parameter were performed last. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=intensity%20duration" title="intensity duration">intensity duration</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20curves" title=" frequency curves"> frequency curves</a>, <a href="https://publications.waset.org/abstracts/search?q=regionalization" title=" regionalization"> regionalization</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrology" title=" hydrology"> hydrology</a> </p> <a href="https://publications.waset.org/abstracts/33615/regionalization-of-idf-curves-by-interpolating-intensity-and-adjustment-parameters-application-to-boyaca-colombia" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33615.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">331</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">1292</span> A Comparison between Empirical and Theoretical OC Curves Related to Acceptance Sampling for Attributes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Encarnacion%20Alvarez">Encarnacion Alvarez</a>, <a href="https://publications.waset.org/abstracts/search?q=Noem%C4%B1%20Hidalgo-Rebollo"> Noemı Hidalgo-Rebollo</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20F.%20Munoz"> Juan F. Munoz</a>, <a href="https://publications.waset.org/abstracts/search?q=Francisco%20J.%20Blanco-Encomienda"> Francisco J. Blanco-Encomienda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many companies use the technique named as acceptance sampling which consists on the inspection and decision making regarding products. According to the results derived from this method, the company takes the decision of acceptance or rejection of a product. The acceptance sampling can be applied to the technology management, since the acceptance sampling can be seen as a tool to improve the design planning, operation and control of technological products. The theoretical operating characteristic (OC) curves are widely used when dealing with acceptance sampling. In this paper, we carry out Monte Carlo simulation studies to compare numerically the empirical OC curves derived from the empirical results to the customary theoretical OC curves. We analyze various possible scenarios in such a way that the differences between the empirical and theoretical curves can be observed under different situations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=single-sampling%20plan" title="single-sampling plan">single-sampling plan</a>, <a href="https://publications.waset.org/abstracts/search?q=lot" title=" lot"> lot</a>, <a href="https://publications.waset.org/abstracts/search?q=Monte%20Carlo%20simulation" title=" Monte Carlo simulation"> Monte Carlo simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=quality%20control" title=" quality control"> quality control</a> </p> <a href="https://publications.waset.org/abstracts/19429/a-comparison-between-empirical-and-theoretical-oc-curves-related-to-acceptance-sampling-for-attributes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19429.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">478</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">1291</span> Cryptography Over Sextic Extension with Cubic Subfield</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Chillali">A. Chillali</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Sahmoudi"> M. Sahmoudi </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we will give a method for encoding the elements of the ring of integers of sextic extension, namely L = Q(a,b) which is a rational quadratic over cubic field K =Q(a) where a^{2} is a rational square free integer and b is a root of irreducible polynomiale of degree 3. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coding" title="coding">coding</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20bases" title=" integral bases"> integral bases</a>, <a href="https://publications.waset.org/abstracts/search?q=sextic" title=" sextic"> sextic</a>, <a href="https://publications.waset.org/abstracts/search?q=quadratic" title=" quadratic"> quadratic</a> </p> <a href="https://publications.waset.org/abstracts/24264/cryptography-over-sextic-extension-with-cubic-subfield" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24264.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">302</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">1290</span> Improvement of the Numerical Integration's Quality in Meshless Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahlem%20Mougaida">Ahlem Mougaida</a>, <a href="https://publications.waset.org/abstracts/search?q=Hedi%20Bel%20Hadj%20Salah"> Hedi Bel Hadj Salah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20methods" title="adaptive methods">adaptive methods</a>, <a href="https://publications.waset.org/abstracts/search?q=meshless" title=" meshless"> meshless</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20integration" title=" numerical integration"> numerical integration</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20quadrature" title=" rational quadrature"> rational quadrature</a> </p> <a href="https://publications.waset.org/abstracts/46442/improvement-of-the-numerical-integrations-quality-in-meshless-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46442.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">369</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=rational%20trigonometric%20B%C3%A9zier%20curves&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=rational%20trigonometric%20B%C3%A9zier%20curves&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=rational%20trigonometric%20B%C3%A9zier%20curves&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=rational%20trigonometric%20B%C3%A9zier%20curves&page=5">5</a></li> <li class="page-item"><a class="page-link" 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