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trigonometric</title> <meta name="description" content="Search results for: trigonometric"> <meta name="keywords" content="trigonometric"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/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="trigonometric"> <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> 39</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: trigonometric</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">39</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">271</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">38</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">475</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">37</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">103</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">36</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">271</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">35</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">541</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">34</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">354</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">33</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">6</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">32</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">397</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">31</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">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">30</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">251</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">29</span> Active Contours for Image Segmentation Based on Complex Domain Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sajid%20Hussain">Sajid Hussain</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The complex domain approach for image segmentation based on active contour has been designed, which deforms step by step to partition an image into numerous expedient regions. A novel region-based trigonometric complex pressure force function is proposed, which propagates around the region of interest using image forces. The signed trigonometric force function controls the propagation of the active contour and the active contour stops on the exact edges of the object accurately. The proposed model makes the level set function binary and uses Gaussian smoothing kernel to adjust and escape the re-initialization procedure. The working principle of the proposed model is as follows: The real image data is transformed into complex data by iota (i) times of image data and the average iota (i) times of horizontal and vertical components of the gradient of image data is inserted in the proposed model to catch complex gradient of the image data. A simple finite difference mathematical technique has been used to implement the proposed model. The efficiency and robustness of the proposed model have been verified and compared with other state-of-the-art models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=image%20segmentation" title="image segmentation">image segmentation</a>, <a href="https://publications.waset.org/abstracts/search?q=active%20contour" title=" active contour"> active contour</a>, <a href="https://publications.waset.org/abstracts/search?q=level%20set" title=" level set"> level set</a>, <a href="https://publications.waset.org/abstracts/search?q=Mumford%20and%20Shah%20model" title=" Mumford and Shah model"> Mumford and Shah model</a> </p> <a href="https://publications.waset.org/abstracts/161606/active-contours-for-image-segmentation-based-on-complex-domain-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/161606.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">114</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">28</span> Enhancing Embedded System Efficiency with Digital Signal Processing Cores</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anil%20H.%20Dhanawade">Anil H. Dhanawade</a>, <a href="https://publications.waset.org/abstracts/search?q=Akshay%20S."> Akshay S.</a>, <a href="https://publications.waset.org/abstracts/search?q=Harshal%20M.%20Lakesar"> Harshal M. Lakesar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a comprehensive analysis of the performance advantages offered by DSP (Digital Signal Processing) cores compared to traditional MCU (Microcontroller Unit) cores in the execution of various functions critical to real-time applications. The focus is on the integration of DSP functionalities, specifically in the context of motor control applications such as Field-Oriented Control (FOC), trigonometric calculations, back-EMF estimation, digital filtering, and high-resolution PWM generation. Through comparative analysis, it is demonstrated that DSP cores significantly enhance processing efficiency, achieving faster execution times for complex mathematical operations essential for precise torque and speed control. The study highlights the capabilities of DSP cores, including single-cycle Multiply-Accumulate (MAC) operations and optimized hardware for trigonometric functions, which collectively reduce latency and improve real-time performance. In contrast, MCU cores, while capable of performing similar tasks, typically exhibit longer execution times due to reliance on software-based solutions and lack of dedicated hardware acceleration. The findings underscore the critical role of DSP cores in applications requiring high-speed processing and low-latency response, making them indispensable in the automotive, industrial, and robotics sectors. This work serves as a reference for future developments in embedded systems, emphasizing the importance of architecture choice in achieving optimal performance in demanding computational tasks. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CPU%20core" title="CPU core">CPU core</a>, <a href="https://publications.waset.org/abstracts/search?q=DSP" title=" DSP"> DSP</a>, <a href="https://publications.waset.org/abstracts/search?q=assembly%20code" title=" assembly code"> assembly code</a>, <a href="https://publications.waset.org/abstracts/search?q=motor%20control" title=" motor control"> motor control</a> </p> <a href="https://publications.waset.org/abstracts/193351/enhancing-embedded-system-efficiency-with-digital-signal-processing-cores" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/193351.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">16</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">27</span> Study on Accurate Calculation Method of Model Attidude on Wind Tunnel Test</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jinjun%20Jiang">Jinjun Jiang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lianzhong%20Chen"> Lianzhong Chen</a>, <a href="https://publications.waset.org/abstracts/search?q=Rui%20Xu"> Rui Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The accurate of model attitude angel plays an important role on the aerodynamic test results in the wind tunnel test. The original method applies the spherical coordinate system transformation to obtain attitude angel calculation.The model attitude angel is obtained by coordinate transformation and spherical surface mapping applying the nominal attitude angel (the balance attitude angel in the wind tunnel coordinate system) indicated by the mechanism. First, the coordinate transformation of this method is not only complex but also difficult to establish the transformed relationship between the space coordinate systems especially after many steps of coordinate transformation, moreover it cannot realize the iterative calculation of the interference relationship between attitude angels; Second, during the calculate process to solve the problem the arc is approximately used to replace the straight line, the angel for the tangent value, and the inverse trigonometric function is applied. Therefore, in the calculation of attitude angel, the process is complex and inaccurate, which can be solved approximately when calculating small attack angel. However, with the advancing development of modern aerodynamic unsteady research, the aircraft tends to develop high or super large attack angel and unsteadyresearch field.According to engineering practice and vector theory, the concept of vector angel coordinate systemis proposed for the first time, and the vector angel coordinate system of attitude angel is established.With the iterative correction calculation and avoiding the problem of approximate and inverse trigonometric function solution, the model attitude calculation process is carried out in detail, which validates that the calculation accuracy and accuracy of model attitude angels are improved.Based on engineering and theoretical methods, a vector angel coordinate systemis established for the first time, which gives the transformation and angel definition relations between different flight attitude coordinate systems, that can accurately calculate the attitude angel of the corresponding coordinate systemand determine its direction, especially in the channel coupling calculation, the calculation of the attitude angel between the coordinate systems is only related to the angel, and has nothing to do with the change order s of the coordinate system, whichsimplifies the calculation process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=attitude%20angel" title="attitude angel">attitude angel</a>, <a href="https://publications.waset.org/abstracts/search?q=angel%20vector%20coordinate%20system" title=" angel vector coordinate system"> angel vector coordinate system</a>, <a href="https://publications.waset.org/abstracts/search?q=iterative%20calculation" title=" iterative calculation"> iterative calculation</a>, <a href="https://publications.waset.org/abstracts/search?q=spherical%20coordinate%20system" title=" spherical coordinate system"> spherical coordinate system</a>, <a href="https://publications.waset.org/abstracts/search?q=wind%20tunnel%20test" title=" wind tunnel test"> wind tunnel test</a> </p> <a href="https://publications.waset.org/abstracts/159541/study-on-accurate-calculation-method-of-model-attidude-on-wind-tunnel-test" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/159541.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">146</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">26</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">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">25</span> Analytical Modeling of Globular Protein-Ferritin in α-Helical Conformation: A White Noise Functional Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vernie%20C.%20Convicto">Vernie C. Convicto</a>, <a href="https://publications.waset.org/abstracts/search?q=Henry%20P.%20Aringa"> Henry P. Aringa</a>, <a href="https://publications.waset.org/abstracts/search?q=Wilson%20I.%20Barredo"> Wilson I. Barredo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study presents a conformational model of the helical structures of globular protein particularly ferritin in the framework of white noise path integral formulation by using Associated Legendre functions, Bessel and convolution of Bessel and trigonometric functions as modulating functions. The model incorporates chirality features of proteins and their helix-turn-helix sequence structural motif. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=globular%20protein" title="globular protein">globular protein</a>, <a href="https://publications.waset.org/abstracts/search?q=modulating%20function" title=" modulating function"> modulating function</a>, <a href="https://publications.waset.org/abstracts/search?q=white%20noise" title=" white noise"> white noise</a>, <a href="https://publications.waset.org/abstracts/search?q=winding%20probability" title=" winding probability"> winding probability</a> </p> <a href="https://publications.waset.org/abstracts/29779/analytical-modeling-of-globular-protein-ferritin-in-a-helical-conformation-a-white-noise-functional-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29779.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">477</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">24</span> A Superposition Method in Analyses of Clamped Thick Plates</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexander%20Matrosov">Alexander Matrosov</a>, <a href="https://publications.waset.org/abstracts/search?q=Guriy%20Shirunov"> Guriy Shirunov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=general%20solution" title="general solution">general solution</a>, <a href="https://publications.waset.org/abstracts/search?q=method%20of%20initial%20functions" title=" method of initial functions"> method of initial functions</a>, <a href="https://publications.waset.org/abstracts/search?q=superposition%20method" title=" superposition method"> superposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=thick%20isotropic%20plates" title=" thick isotropic plates "> thick isotropic plates </a> </p> <a href="https://publications.waset.org/abstracts/23971/a-superposition-method-in-analyses-of-clamped-thick-plates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23971.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">598</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">23</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">22</span> Coefficients of Some Double Trigonometric Cosine and Sine Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jatinderdeep%20Kaur">Jatinderdeep Kaur</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results. <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=conjugate%20fejer%20kernel" title=" conjugate fejer kernel"> conjugate fejer kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20series" title=" fourier series"> fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=semi-convexity" title=" semi-convexity"> semi-convexity</a> </p> <a href="https://publications.waset.org/abstracts/32156/coefficients-of-some-double-trigonometric-cosine-and-sine-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32156.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">21</span> Efficient Alias-Free Level Crossing Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Negar%20Riazifar">Negar Riazifar</a>, <a href="https://publications.waset.org/abstracts/search?q=Nigel%20G.%20Stocks"> Nigel G. Stocks</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to an alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=alias-free" title="alias-free">alias-free</a>, <a href="https://publications.waset.org/abstracts/search?q=level%20crossing%20sampling" title=" level crossing sampling"> level crossing sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=spectrum" title=" spectrum"> spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20polynomial" title=" trigonometric polynomial"> trigonometric polynomial</a> </p> <a href="https://publications.waset.org/abstracts/136144/efficient-alias-free-level-crossing-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/136144.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">209</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">20</span> High Speed Image Rotation Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hee-Choul%20Kwon">Hee-Choul Kwon</a>, <a href="https://publications.waset.org/abstracts/search?q=Hyungjin%20Cho"> Hyungjin Cho</a>, <a href="https://publications.waset.org/abstracts/search?q=Heeyong%20Kwon"> Heeyong Kwon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Image rotation is one of main pre-processing step in image processing or image pattern recognition. It is implemented with rotation matrix multiplication. However it requires lots of floating point arithmetic operations and trigonometric function calculations, so it takes long execution time. We propose a new high speed image rotation algorithm without two major time-consuming operations. We compare the proposed algorithm with the conventional rotation one with various size images. Experimental results show that the proposed algorithm is superior to the conventional rotation ones. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=high%20speed%20rotation%20operation" title="high speed rotation operation">high speed rotation operation</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20processing" title=" image processing"> image processing</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20rotation" title=" image rotation"> image rotation</a>, <a href="https://publications.waset.org/abstracts/search?q=pattern%20recognition" title=" pattern recognition"> pattern recognition</a>, <a href="https://publications.waset.org/abstracts/search?q=transformation%20matrix" title=" transformation matrix"> transformation matrix</a> </p> <a href="https://publications.waset.org/abstracts/25258/high-speed-image-rotation-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25258.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">506</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">19</span> Approximation of Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means of Fourier Series</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>, <a href="https://publications.waset.org/abstracts/search?q=Uaday%20Singh"> Uaday Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lipschitz%20classes" title="Lipschitz classes">Lipschitz classes</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20matrix%20operator" title=" product matrix operator"> product matrix operator</a>, <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> </p> <a href="https://publications.waset.org/abstracts/4757/approximation-of-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means-of-fourier-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4757.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">477</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">18</span> Image Rotation Using an Augmented 2-Step Shear Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hee-Choul%20Kwon">Hee-Choul Kwon</a>, <a href="https://publications.waset.org/abstracts/search?q=Heeyong%20Kwon"> Heeyong Kwon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Image rotation is one of main pre-processing steps for image processing or image pattern recognition. It is implemented with a rotation matrix multiplication. It requires a lot of floating point arithmetic operations and trigonometric calculations, so it takes a long time to execute. Therefore, there has been a need for a high speed image rotation algorithm without two major time-consuming operations. However, the rotated image has a drawback, i.e. distortions. We solved the problem using an augmented two-step shear transform. We compare the presented algorithm with the conventional rotation with images of various sizes. Experimental results show that the presented algorithm is superior to the conventional rotation one. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=high-speed%20rotation%20operation" title="high-speed rotation operation">high-speed rotation operation</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20rotation" title=" image rotation"> image rotation</a>, <a href="https://publications.waset.org/abstracts/search?q=transform%20matrix" title=" transform matrix"> transform matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20processing" title=" image processing"> image processing</a>, <a href="https://publications.waset.org/abstracts/search?q=pattern%20recognition" title=" pattern recognition"> pattern recognition</a> </p> <a href="https://publications.waset.org/abstracts/64167/image-rotation-using-an-augmented-2-step-shear-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64167.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">17</span> Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ranajay%20Bhowmick">Ranajay Bhowmick</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cubic%20equation" title="cubic equation">cubic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=stress%20invariant" title=" stress invariant"> stress invariant</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric" title=" trigonometric"> trigonometric</a>, <a href="https://publications.waset.org/abstracts/search?q=explicit%20solution" title=" explicit solution"> explicit solution</a>, <a href="https://publications.waset.org/abstracts/search?q=principal%20stress" title=" principal stress"> principal stress</a>, <a href="https://publications.waset.org/abstracts/search?q=failure%20criterion" title=" failure criterion"> failure criterion</a> </p> <a href="https://publications.waset.org/abstracts/128515/solution-of-s3-problem-of-deformation-mechanics-for-a-definite-condition-and-resulting-modifications-of-important-failure-theories" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/128515.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">137</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">16</span> Encephalon-An Implementation of a Handwritten Mathematical Expression Solver</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shreeyam">Shreeyam</a>, <a href="https://publications.waset.org/abstracts/search?q=Ranjan%20Kumar%20Sah"> Ranjan Kumar Sah</a>, <a href="https://publications.waset.org/abstracts/search?q=Shivangi"> Shivangi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recognizing and solving handwritten mathematical expressions can be a challenging task, particularly when certain characters are segmented and classified. This project proposes a solution that uses Convolutional Neural Network (CNN) and image processing techniques to accurately solve various types of equations, including arithmetic, quadratic, and trigonometric equations, as well as logical operations like logical AND, OR, NOT, NAND, XOR, and NOR. The proposed solution also provides a graphical solution, allowing users to visualize equations and their solutions. In addition to equation solving, the platform, called CNNCalc, offers a comprehensive learning experience for students. It provides educational content, a quiz platform, and a coding platform for practicing programming skills in different languages like C, Python, and Java. This all-in-one solution makes the learning process engaging and enjoyable for students. The proposed methodology includes horizontal compact projection analysis and survey for segmentation and binarization, as well as connected component analysis and integrated connected component analysis for character classification. The compact projection algorithm compresses the horizontal projections to remove noise and obtain a clearer image, contributing to the accuracy of character segmentation. Experimental results demonstrate the effectiveness of the proposed solution in solving a wide range of mathematical equations. CNNCalc provides a powerful and user-friendly platform for solving equations, learning, and practicing programming skills. With its comprehensive features and accurate results, CNNCalc is poised to revolutionize the way students learn and solve mathematical equations. The platform utilizes a custom-designed Convolutional Neural Network (CNN) with image processing techniques to accurately recognize and classify symbols within handwritten equations. The compact projection algorithm effectively removes noise from horizontal projections, leading to clearer images and improved character segmentation. Experimental results demonstrate the accuracy and effectiveness of the proposed solution in solving a wide range of equations, including arithmetic, quadratic, trigonometric, and logical operations. CNNCalc features a user-friendly interface with a graphical representation of equations being solved, making it an interactive and engaging learning experience for users. The platform also includes tutorials, testing capabilities, and programming features in languages such as C, Python, and Java. Users can track their progress and work towards improving their skills. CNNCalc is poised to revolutionize the way students learn and solve mathematical equations with its comprehensive features and accurate results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=AL" title="AL">AL</a>, <a href="https://publications.waset.org/abstracts/search?q=ML" title=" ML"> ML</a>, <a href="https://publications.waset.org/abstracts/search?q=hand%20written%20equation%20solver" title=" hand written equation solver"> hand written equation solver</a>, <a href="https://publications.waset.org/abstracts/search?q=maths" title=" maths"> maths</a>, <a href="https://publications.waset.org/abstracts/search?q=computer" title=" computer"> computer</a>, <a href="https://publications.waset.org/abstracts/search?q=CNNCalc" title=" CNNCalc"> CNNCalc</a>, <a href="https://publications.waset.org/abstracts/search?q=convolutional%20neural%20networks" title=" convolutional neural networks"> convolutional neural networks</a> </p> <a href="https://publications.waset.org/abstracts/165164/encephalon-an-implementation-of-a-handwritten-mathematical-expression-solver" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165164.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">122</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">15</span> FPGA Implementation of Novel Triangular Systolic Array Based Architecture for Determining the Eigenvalues of Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soumitr%20Sanjay%20Dubey">Soumitr Sanjay Dubey</a>, <a href="https://publications.waset.org/abstracts/search?q=Shubhajit%20Roy%20Chowdhury"> Shubhajit Roy Chowdhury</a>, <a href="https://publications.waset.org/abstracts/search?q=Rahul%20Shrestha"> Rahul Shrestha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have presented a novel approach of calculating eigenvalues of any matrix for the first time on Field Programmable Gate Array (FPGA) using Triangular Systolic Arra (TSA) architecture. Conventionally, additional computation unit is required in the architecture which is compliant to the algorithm for determining the eigenvalues and this in return enhances the delay and power consumption. However, recently reported works are only dedicated for symmetric matrices or some specific case of matrix. This works presents an architecture to calculate eigenvalues of any matrix based on QR algorithm which is fully implementable on FPGA. For the implementation of QR algorithm we have used TSA architecture, which is further utilising CORDIC (CO-ordinate Rotation DIgital Computer) algorithm, to calculate various trigonometric and arithmetic functions involved in the procedure. The proposed architecture gives an error in the range of 10−4. Power consumption by the design is 0.598W. It can work at the frequency of 900 MHz. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coordinate%20rotation%20digital%20computer" title="coordinate rotation digital computer">coordinate rotation digital computer</a>, <a href="https://publications.waset.org/abstracts/search?q=three%20angle%20complex%20rotation" title=" three angle complex rotation"> three angle complex rotation</a>, <a href="https://publications.waset.org/abstracts/search?q=triangular%20systolic%20array" title=" triangular systolic array"> triangular systolic array</a>, <a href="https://publications.waset.org/abstracts/search?q=QR%20algorithm" title=" QR algorithm "> QR algorithm </a> </p> <a href="https://publications.waset.org/abstracts/40252/fpga-implementation-of-novel-triangular-systolic-array-based-architecture-for-determining-the-eigenvalues-of-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40252.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">14</span> ANN Based Simulation of PWM Scheme for Seven Phase Voltage Source Inverter Using MATLAB/Simulink</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Arif%20Khan">Mohammad Arif Khan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper analyzes and presents the development of Artificial Neural Network based controller of space vector modulation (ANN-SVPWM) for a seven-phase voltage source inverter. At first, the conventional method of producing sinusoidal output voltage by utilizing six active and one zero space vectors are used to synthesize the input reference, is elaborated and then new PWM scheme called Artificial Neural Network Based PWM is presented. The ANN based controller has the advantage of the very fast implementation and analyzing the algorithms and avoids the direct computation of trigonometric and non-linear functions. The ANN controller uses the individual training strategy with the fixed weight and supervised models. A computer simulation program has been developed using Matlab/Simulink together with the neural network toolbox for training the ANN-controller. A comparison of the proposed scheme with the conventional scheme is presented based on various performance indices. Extensive Simulation results are provided to validate the findings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=space%20vector%20PWM" title="space vector PWM">space vector PWM</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20harmonic%20distortion" title=" total harmonic distortion"> total harmonic distortion</a>, <a href="https://publications.waset.org/abstracts/search?q=seven-phase" title=" seven-phase"> seven-phase</a>, <a href="https://publications.waset.org/abstracts/search?q=voltage%20source%20inverter" title=" voltage source inverter"> voltage source inverter</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-phase" title=" multi-phase"> multi-phase</a>, <a href="https://publications.waset.org/abstracts/search?q=artificial%20neural%20network" title=" artificial neural network"> artificial neural network</a> </p> <a href="https://publications.waset.org/abstracts/46867/ann-based-simulation-of-pwm-scheme-for-seven-phase-voltage-source-inverter-using-matlabsimulink" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46867.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">13</span> Design and Validation of Different Steering Geometries for an All-Terrain Vehicle</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prabhsharan%20Singh">Prabhsharan Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Rahul%20Sindhu"> Rahul Sindhu</a>, <a href="https://publications.waset.org/abstracts/search?q=Piyush%20Sikka"> Piyush Sikka</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The steering system is an integral part and medium through which the driver communicates with the vehicle and terrain, hence the most suitable steering geometry as per requirements must be chosen. The function of the chosen steering geometry of an All-Terrain Vehicle (ATV) is to provide the desired understeer gradient, minimum tire slippage, expected weight transfer during turning as these are requirements for a good steering geometry of a BAJA ATV. This research paper focuses on choosing the best suitable steering geometry for BAJA ATV tracks by reasoning the working principle and using fundamental trigonometric functions for obtaining these geometries on the same vehicle itself, namely Ackermann, Anti- Ackermann, Parallel Ackermann. Full vehicle analysis was carried out on Adams Car Analysis software, and graphical results were obtained for various parameters. Steering geometries were achieved by using a single versatile knuckle for frontward and rearward tie-rod placement and were practically tested with the help of data acquisition systems set up on the ATV. Each was having certain characteristics, setup, and parameters were observed for the BAJA ATV, and correlations were created between analytical and practical values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=all-terrain%20vehicle" title="all-terrain vehicle">all-terrain vehicle</a>, <a href="https://publications.waset.org/abstracts/search?q=Ackermann" title=" Ackermann"> Ackermann</a>, <a href="https://publications.waset.org/abstracts/search?q=Adams%20car" title=" Adams car"> Adams car</a>, <a href="https://publications.waset.org/abstracts/search?q=Baja%20Sae" title=" Baja Sae"> Baja Sae</a>, <a href="https://publications.waset.org/abstracts/search?q=steering%20geometry" title=" steering geometry"> steering geometry</a>, <a href="https://publications.waset.org/abstracts/search?q=steering%20system" title=" steering system"> steering system</a>, <a href="https://publications.waset.org/abstracts/search?q=tire%20slip" title=" tire slip"> tire slip</a>, <a href="https://publications.waset.org/abstracts/search?q=traction" title=" traction"> traction</a>, <a href="https://publications.waset.org/abstracts/search?q=understeer%20gradient" title=" understeer gradient"> understeer gradient</a> </p> <a href="https://publications.waset.org/abstracts/121416/design-and-validation-of-different-steering-geometries-for-an-all-terrain-vehicle" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/121416.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">154</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">12</span> Efficient High Fidelity Signal Reconstruction Based on Level Crossing Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Negar%20Riazifar">Negar Riazifar</a>, <a href="https://publications.waset.org/abstracts/search?q=Nigel%20G.%20Stocks"> Nigel G. Stocks</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide high fidelity signal reconstruction for speech signals; these strategies circumvent the problem of exponentially increasing number of samples as the bit-depth is increased and hence are highly efficient. Specifically, the results indicate that the distribution of the intervals between samples is one of the key factors in the quality of signal reconstruction; including samples with short intervals do not improve the accuracy of the signal reconstruction, whilst samples with large intervals lead to numerical instability. The proposed sampling method, termed reduced conventional level crossing (RCLC) sampling, exploits redundancy between samples to improve the efficiency of the sampling without compromising performance. A reconstruction technique is also proposed that enhances the numerical stability through linear interpolation of samples separated by large intervals. Interpolation is demonstrated to improve the accuracy of the signal reconstruction in addition to the numerical stability. We further demonstrate that the RCLC and interpolation methods can give useful levels of signal recovery even if the average sampling rate is less than the Nyquist rate. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=level%20crossing%20sampling" title="level crossing sampling">level crossing sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20stability" title=" numerical stability"> numerical stability</a>, <a href="https://publications.waset.org/abstracts/search?q=speech%20processing" title=" speech processing"> speech processing</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20polynomial" title=" trigonometric polynomial"> trigonometric polynomial</a> </p> <a href="https://publications.waset.org/abstracts/134973/efficient-high-fidelity-signal-reconstruction-based-on-level-crossing-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/134973.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">146</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">11</span> Measurement System for Human Arm Muscle Magnetic Field and Grip Strength</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shuai%20Yuan">Shuai Yuan</a>, <a href="https://publications.waset.org/abstracts/search?q=Minxia%20Shi"> Minxia Shi</a>, <a href="https://publications.waset.org/abstracts/search?q=Xu%20Zhang"> Xu Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jianzhi%20Yang"> Jianzhi Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Kangqi%20Tian"> Kangqi Tian</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuzheng%20Ma"> Yuzheng Ma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The precise measurement of muscle activities is essential for understanding the function of various body movements. This work aims to develop a muscle magnetic field signal detection system based on mathematical analysis. Medical research has underscored that early detection of muscle atrophy, coupled with lifestyle adjustments such as dietary control and increased exercise, can significantly enhance muscle-related diseases. Currently, surface electromyography (sEMG) is widely employed in research as an early predictor of muscle atrophy. Nonetheless, the primary limitation of using sEMG to forecast muscle strength is its inability to directly measure the signals generated by muscles. Challenges arise from potential skin-electrode contact issues due to perspiration, leading to inaccurate signals or even signal loss. Additionally, resistance and phase are significantly impacted by adipose layers. The recent emergence of optically pumped magnetometers introduces a fresh avenue for bio-magnetic field measurement techniques. These magnetometers possess high sensitivity and obviate the need for a cryogenic environment unlike superconducting quantum interference devices (SQUIDs). They detect muscle magnetic field signals in the range of tens to thousands of femtoteslas (fT). The utilization of magnetometers for capturing muscle magnetic field signals remains unaffected by issues of perspiration and adipose layers. Since their introduction, optically pumped atomic magnetometers have found extensive application in exploring the magnetic fields of organs such as cardiac and brain magnetism. The optimal operation of these magnetometers necessitates an environment with an ultra-weak magnetic field. To achieve such an environment, researchers usually utilize a combination of active magnetic compensation technology with passive magnetic shielding technology. Passive magnetic shielding technology uses a magnetic shielding device built with high permeability materials to attenuate the external magnetic field to a few nT. Compared with more layers, the coils that can generate a reverse magnetic field to precisely compensate for the residual magnetic fields are cheaper and more flexible. To attain even lower magnetic fields, compensation coils designed by Biot-Savart law are involved to generate a counteractive magnetic field to eliminate residual magnetic fields. By solving the magnetic field expression of discrete points in the target region, the parameters that determine the current density distribution on the plane can be obtained through the conventional target field method. The current density is obtained from the partial derivative of the stream function, which can be represented by the combination of trigonometric functions. Optimization algorithms in mathematics are introduced into coil design to obtain the optimal current density distribution. A one-dimensional linear regression analysis was performed on the collected data, obtaining a coefficient of determination R2 of 0.9349 with a p-value of 0. This statistical result indicates a stable relationship between the peak-to-peak value (PPV) of the muscle magnetic field signal and the magnitude of grip strength. This system is expected to be a widely used tool for healthcare professionals to gain deeper insights into the muscle health of their patients. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=muscle%20magnetic%20signal" title="muscle magnetic signal">muscle magnetic signal</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetic%20shielding" title=" magnetic shielding"> magnetic shielding</a>, <a href="https://publications.waset.org/abstracts/search?q=compensation%20coils" title=" compensation coils"> compensation coils</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20functions." title=" trigonometric functions."> trigonometric functions.</a> </p> <a href="https://publications.waset.org/abstracts/171772/measurement-system-for-human-arm-muscle-magnetic-field-and-grip-strength" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171772.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">57</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">10</span> Analytical Formulae for the Approach Velocity Head Coefficient</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdulrahman%20Abdulrahman">Abdulrahman Abdulrahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=broad%20crested%20weir" title="broad crested weir">broad crested weir</a>, <a href="https://publications.waset.org/abstracts/search?q=combined%20control%20meter" title=" combined control meter"> combined control meter</a>, <a href="https://publications.waset.org/abstracts/search?q=control%20structures" title=" control structures"> control structures</a>, <a href="https://publications.waset.org/abstracts/search?q=critical%20flow" title=" critical flow"> critical flow</a>, <a href="https://publications.waset.org/abstracts/search?q=discharge%20measurement" title=" discharge measurement"> discharge measurement</a>, <a href="https://publications.waset.org/abstracts/search?q=flow%20control" title=" flow control"> flow control</a>, <a href="https://publications.waset.org/abstracts/search?q=hydraulic%20engineering" title=" hydraulic engineering"> hydraulic engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=hydraulic%20structures" title=" hydraulic structures"> hydraulic structures</a>, <a href="https://publications.waset.org/abstracts/search?q=open%20channel%20flow" title=" open channel flow"> open channel flow</a> </p> <a href="https://publications.waset.org/abstracts/71803/analytical-formulae-for-the-approach-velocity-head-coefficient" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71803.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> <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" 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