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functions</title> <meta name="description" content="Search results for: airy functions"> <meta name="keywords" content="airy functions"> <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="airy functions"> <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> 2504</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: airy functions</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2504</span> Visualization of Energy Waves via Airy Functions in Time-Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20Sener">E. Sener</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20Isik"> O. Isik</a>, <a href="https://publications.waset.org/abstracts/search?q=E.%20Eroglu"> E. Eroglu</a>, <a href="https://publications.waset.org/abstracts/search?q=U.%20Sahin"> U. Sahin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=airy%20functions" title="airy functions">airy functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Klein-Gordon%20Equation" title=" Klein-Gordon Equation"> Klein-Gordon Equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%E2%80%99s%20equations" title=" Maxwell’s equations"> Maxwell’s equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Surplus%20of%20energy" title=" Surplus of energy"> Surplus of energy</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20boundary%20operators" title=" wave boundary operators"> wave boundary operators</a> </p> <a href="https://publications.waset.org/abstracts/42403/visualization-of-energy-waves-via-airy-functions-in-time-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42403.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">2503</span> Airy Wave Packet for a Particle in a Time-Dependant Linear Potential </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Berrehail">M. Berrehail</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Benamira"> F. Benamira</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=airy%20wave%20packet" title="airy wave packet">airy wave packet</a>, <a href="https://publications.waset.org/abstracts/search?q=ivariant" title=" ivariant"> ivariant</a>, <a href="https://publications.waset.org/abstracts/search?q=time-dependent%20linear%20potential" title=" time-dependent linear potential"> time-dependent linear potential</a>, <a href="https://publications.waset.org/abstracts/search?q=unitary%20transformation" title=" unitary transformation"> unitary transformation</a> </p> <a href="https://publications.waset.org/abstracts/31077/airy-wave-packet-for-a-particle-in-a-time-dependant-linear-potential" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31077.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">2502</span> Effect of the Applied Bias on Miniband Structures in Dimer Fibonacci Inas/Ga1-Xinxas Superlattices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Z.%20Aziz">Z. Aziz</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Terkhi"> S. Terkhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Sefir"> Y. Sefir</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Djelti"> R. Djelti</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Bentata"> S. Bentata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The effect of a uniform electric field across multibarrier systems (InAs/InxGa1-xAs) is exhaustively explored by a computational model using exact airy function formalism and the transfer-matrix technique. In the case of biased DFHBSL structure a strong reduction in transmission properties was observed and the width of the miniband structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the miniband structure, which becomes increasingly important (Wannier-Stark Effect). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dimer%20fibonacci%20height%20barrier%20superlattices" title="dimer fibonacci height barrier superlattices">dimer fibonacci height barrier superlattices</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20extended%20state" title=" singular extended state"> singular extended state</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20airy%20function" title=" exact airy function"> exact airy function</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix%20formalism" title=" transfer matrix formalism"> transfer matrix formalism</a> </p> <a href="https://publications.waset.org/abstracts/3930/effect-of-the-applied-bias-on-miniband-structures-in-dimer-fibonacci-inasga1-xinxas-superlattices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3930.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">307</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">2501</span> Effect of the Applied Bias on Mini-Band Structures in Dimer Fibonacci InAs/Ga1-XInXAs Superlattices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Z.%20Aziz">Z. Aziz</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Terkhi"> S. Terkhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Sefir"> Y. Sefir</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Djelti"> R. Djelti</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Bentata"> S. Bentata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The effect of a uniform electric field across multi-barrier systems (InAs/InxGa1-xAs) is exhaustively explored by a computational model using exact Airy function formalism and the transfer-matrix technique. In the case of biased DFHBSL structure a strong reduction in transmission properties was observed and the width of the mini-band structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the mini-band structure, which becomes increasingly important (Wannier-Stark Effect). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dimer%20fibonacci%20height%20barrier%20superlattices" title="dimer fibonacci height barrier superlattices">dimer fibonacci height barrier superlattices</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20extended%20state" title=" singular extended state"> singular extended state</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20Airy%20function%20and%20transfer%20matrix%20formalism" title=" exact Airy function and transfer matrix formalism"> exact Airy function and transfer matrix formalism</a>, <a href="https://publications.waset.org/abstracts/search?q=bioinformatics" title=" bioinformatics"> bioinformatics</a> </p> <a href="https://publications.waset.org/abstracts/2231/effect-of-the-applied-bias-on-mini-band-structures-in-dimer-fibonacci-inasga1-xinxas-superlattices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2231.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">289</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">2500</span> Formation of Miniband Structure in Dimer Fibonacci GaAs/Ga1-XAlXAs Superlattices </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Aziz%20Zoubir">Aziz Zoubir</a>, <a href="https://publications.waset.org/abstracts/search?q=Sefir%20Yamina"> Sefir Yamina</a>, <a href="https://publications.waset.org/abstracts/search?q=Djelti%20Redouan"> Djelti Redouan</a>, <a href="https://publications.waset.org/abstracts/search?q=Bentata%20Samir"> Bentata Samir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The effect of a uniform electric field across multibarrier systems (GaAs/AlxGa1-xAs) is exhaustively explored by a computational model using exact Airy function formalism and the transfer-matrix technique. In the case of biased Dimer Fibonacci Height Barrier superlattices (DFHBSL) structure a strong reduction in transmission properties was observed and the width of the miniband structure linearly decreases with the increase of the applied bias. This is due to the confinement of the states in the miniband structure, which becomes increasingly important (Wannier-Stark effect). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dimer%20Fibonacci%20Height%20Barrier%20superlattices" title="Dimer Fibonacci Height Barrier superlattices">Dimer Fibonacci Height Barrier superlattices</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20extended%20states" title=" singular extended states"> singular extended states</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20Airy%20function" title=" exact Airy function"> exact Airy function</a>, <a href="https://publications.waset.org/abstracts/search?q=transfer%20matrix%20formalism" title=" transfer matrix formalism"> transfer matrix formalism</a> </p> <a href="https://publications.waset.org/abstracts/14193/formation-of-miniband-structure-in-dimer-fibonacci-gaasga1-xalxas-superlattices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14193.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">509</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">2499</span> Some Results on Generalized Janowski Type Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuad%20Al%20Sarari">Fuad Al Sarari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convolution%20conditions" title="convolution conditions">convolution conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=subordination" title=" subordination"> subordination</a>, <a href="https://publications.waset.org/abstracts/search?q=Janowski%20functions" title=" Janowski functions"> Janowski functions</a>, <a href="https://publications.waset.org/abstracts/search?q=starlike%20functions" title=" starlike functions"> starlike functions</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20functions" title=" convex functions"> convex functions</a> </p> <a href="https://publications.waset.org/abstracts/170335/some-results-on-generalized-janowski-type-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/170335.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">67</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">2498</span> The Behavior of The Zeros of Bargmann Analytic Functions for Multiple-Mode Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muna%20Tabuni">Muna Tabuni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper contains an investigation of the behavior of the Zeros of Bargmann functions for one and two-mode systems. A brief introduction to Harmonic oscillator formalism for one and two-mode is given. The Bargmann analytic representation for one and two-mode has been studied. The zeros of Bargmann analytic function for one-mode are considered. The Q Husimi functions are introduced. The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros are discussed. The zeros of Bargmann analytic functions for two-mode are introduced. Various examples have been given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bargmann%20functions" title="Bargmann functions">Bargmann functions</a>, <a href="https://publications.waset.org/abstracts/search?q=two-mode" title=" two-mode"> two-mode</a>, <a href="https://publications.waset.org/abstracts/search?q=zeros" title=" zeros"> zeros</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20oscillator" title=" harmonic oscillator"> harmonic oscillator</a> </p> <a href="https://publications.waset.org/abstracts/20682/the-behavior-of-the-zeros-of-bargmann-analytic-functions-for-multiple-mode-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20682.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">570</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">2497</span> Derivatives Formulas Involving I-Functions of Two Variables and Generalized M-Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gebreegziabher%20Hailu%20Gebrecherkos">Gebreegziabher Hailu Gebrecherkos</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study explores the derivatives of functions defined by I-functions of two variables and their connections to generalized M-series. We begin by defining I-functions, which are generalized functions that encompass various special functions, and analyze their properties. By employing advanced calculus techniques, we derive new formulas for the first and higher-order derivatives of I-functions with respect to their variables; we establish some derivative formulae of the I-function of two variables involving generalized M-series. The special cases of our derivatives yield interesting results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=I-function" title="I-function">I-function</a>, <a href="https://publications.waset.org/abstracts/search?q=Mellin-Barners%20control%20integral" title=" Mellin-Barners control integral"> Mellin-Barners control integral</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20M-series" title=" generalized M-series"> generalized M-series</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20order%20derivative" title=" higher order derivative"> higher order derivative</a> </p> <a href="https://publications.waset.org/abstracts/192292/derivatives-formulas-involving-i-functions-of-two-variables-and-generalized-m-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192292.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">18</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2496</span> Some Inequalities Related with Starlike Log-Harmonic Mappings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Melike%20Aydo%C4%9Fan">Melike Aydoğan</a>, <a href="https://publications.waset.org/abstracts/search?q=D%C3%BCrdane%20%C3%96zt%C3%BCrk"> Dürdane Öztürk</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=starlike%20log-harmonic%20functions" title="starlike log-harmonic functions">starlike log-harmonic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=univalent%20functions" title=" univalent functions"> univalent functions</a>, <a href="https://publications.waset.org/abstracts/search?q=distortion%20theorem" title=" distortion theorem"> distortion theorem</a> </p> <a href="https://publications.waset.org/abstracts/22032/some-inequalities-related-with-starlike-log-harmonic-mappings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22032.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">526</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">2495</span> RAFU Functions in Robotics and Automation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alicia%20C.%20Sanchez">Alicia C. Sanchez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=automatic%20navigation%20control" title="automatic navigation control">automatic navigation control</a>, <a href="https://publications.waset.org/abstracts/search?q=lateral%20control" title=" lateral control"> lateral control</a>, <a href="https://publications.waset.org/abstracts/search?q=lane-keeping%20control" title=" lane-keeping control"> lane-keeping control</a>, <a href="https://publications.waset.org/abstracts/search?q=RAFU%20approximation" title=" RAFU approximation"> RAFU approximation</a> </p> <a href="https://publications.waset.org/abstracts/138558/rafu-functions-in-robotics-and-automation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138558.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">2494</span> Subclasses of Bi-Univalent Functions Associated with Hohlov Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rashidah%20Omar">Rashidah Omar</a>, <a href="https://publications.waset.org/abstracts/search?q=Suzeini%20Abdul%20Halim"> Suzeini Abdul Halim</a>, <a href="https://publications.waset.org/abstracts/search?q=Aini%20Janteng"> Aini Janteng</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function <em>f </em>ϵ<em> A </em>is said to be bi-univalent in the open unit disk <em>D</em> if both <em>f </em>and <em>f<sup>-1</sup></em> are univalent in <em>D</em>. The symbol <em>A</em> denotes the class of all analytic functions <em>f</em> in <em>D</em> and it is normalized by the conditions <em>f</em>(0) = <em>f’</em>(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function <em>f</em> is subordinate to an analytic function <em>g</em> if there is an analytic function <em>w</em> defined on <em>D</em> with <em>w</em>(0) = 0 and |<em>w</em>(z)| < 1 satisfying <em>f</em>(<em>z</em>) = <em>g</em>[<em>w</em>(<em>z</em>)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20functions" title="analytic functions">analytic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=bi-univalent%20functions" title=" bi-univalent functions"> bi-univalent functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Hohlov%20operator" title=" Hohlov operator"> Hohlov operator</a>, <a href="https://publications.waset.org/abstracts/search?q=subordination" title=" subordination"> subordination</a> </p> <a href="https://publications.waset.org/abstracts/72671/subclasses-of-bi-univalent-functions-associated-with-hohlov-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72671.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">293</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">2493</span> Geometric Properties of Some q-Bessel Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=%C4%B0brahim%20Akta%C5%9F">İbrahim Aktaş</a>, <a href="https://publications.waset.org/abstracts/search?q=%C3%81rp%C3%A1d%20Baricz"> Árpád Baricz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bessel%20function" title="bessel function">bessel function</a>, <a href="https://publications.waset.org/abstracts/search?q=lommel%20function" title=" lommel function"> lommel function</a>, <a href="https://publications.waset.org/abstracts/search?q=radius%20of%20starlikeness%20and%20convexity" title=" radius of starlikeness and convexity"> radius of starlikeness and convexity</a>, <a href="https://publications.waset.org/abstracts/search?q=Struve%20function" title=" Struve function"> Struve function</a> </p> <a href="https://publications.waset.org/abstracts/63119/geometric-properties-of-some-q-bessel-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63119.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">276</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">2492</span> Approximation of Analytic Functions of Several Variables by Linear K-Positive Operators in the Closed Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tulin%20Coskun">Tulin Coskun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20functions" title="analytic functions">analytic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation%20of%20analytic%20functions" title=" approximation of analytic functions"> approximation of analytic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Linear%20k-positive%20operators" title=" Linear k-positive operators"> Linear k-positive operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Korovkin%20type%20theorems" title=" Korovkin type theorems"> Korovkin type theorems</a> </p> <a href="https://publications.waset.org/abstracts/53219/approximation-of-analytic-functions-of-several-variables-by-linear-k-positive-operators-in-the-closed-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53219.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">338</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">2491</span> Unconventional Calculus Spreadsheet Functions </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chahid%20K.%20Ghaddar">Chahid K. Ghaddar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=calculus" title="calculus">calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20algebraic%20equations" title=" differential algebraic equations"> differential algebraic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=solvers" title=" solvers"> solvers</a>, <a href="https://publications.waset.org/abstracts/search?q=spreadsheet" title=" spreadsheet"> spreadsheet</a> </p> <a href="https://publications.waset.org/abstracts/46198/unconventional-calculus-spreadsheet-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46198.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">362</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">2490</span> Fuzzy Control and Pertinence Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Luiz%20F.%20J.%20Maia">Luiz F. J. Maia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=control%20surface" title="control surface">control surface</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20control" title=" fuzzy control"> fuzzy control</a>, <a href="https://publications.waset.org/abstracts/search?q=Inverted%20pendulum" title=" Inverted pendulum"> Inverted pendulum</a>, <a href="https://publications.waset.org/abstracts/search?q=pertinence%20functions" title=" pertinence functions"> pertinence functions</a> </p> <a href="https://publications.waset.org/abstracts/2467/fuzzy-control-and-pertinence-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2467.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">449</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">2489</span> A New Approach for Generalized First Derivative of Nonsmooth Functions Using Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Mehdi%20Mazarei">Mohammad Mehdi Mazarei</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20Asghar%20Behroozpoor"> Ali Asghar Behroozpoor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=general%20derivative" title="general derivative">general derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming"> linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a>, <a href="https://publications.waset.org/abstracts/search?q=smooth%20and%20nonsmooth%20functions" title=" smooth and nonsmooth functions"> smooth and nonsmooth functions</a> </p> <a href="https://publications.waset.org/abstracts/19425/a-new-approach-for-generalized-first-derivative-of-nonsmooth-functions-using-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19425.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">557</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">2488</span> Non-Linear Load-Deflection Response of Shape Memory Alloys-Reinforced Composite Cylindrical Shells under Uniform Radial Load</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Behrang%20Tavousi%20Tehrani">Behrang Tavousi Tehrani</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad-Zaman%20Kabir"> Mohammad-Zaman Kabir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Shape memory alloys (SMA) are often implemented in smart structures as the active components. Their ability to recover large displacements has been used in many applications, including structural stability/response enhancement and active structural acoustic control. SMA wires or fibers can be embedded with composite cylinders to increase their critical buckling load, improve their load-deflection behavior, and reduce the radial deflections under various thermo-mechanical loadings. This paper presents a semi-analytical investigation on the non-linear load-deflection response of SMA-reinforced composite circular cylindrical shells. The cylinder shells are under uniform external pressure load. Based on first-order shear deformation<em> shell theory (FSDT),</em> the equilibrium equations of the structure are derived. One-dimensional simplified Brinson’s model is used for determining the SMA recovery force due to its simplicity and accuracy. Airy stress function and Galerkin technique are used to obtain non-linear load-deflection curves. The results are verified by comparing them with those in the literature. Several parametric studies are conducted in order to investigate the effect of SMA volume fraction, SMA pre-strain value, and SMA activation temperature on the response of the structure. It is shown that suitable usage of SMA wires results in a considerable enhancement in the load-deflection response of the shell due to the generation of the SMA tensile recovery force. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=airy%20stress%20function" title="airy stress function">airy stress function</a>, <a href="https://publications.waset.org/abstracts/search?q=cylindrical%20shell" title=" cylindrical shell"> cylindrical shell</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20technique" title=" Galerkin technique"> Galerkin technique</a>, <a href="https://publications.waset.org/abstracts/search?q=load-deflection%20curve" title=" load-deflection curve"> load-deflection curve</a>, <a href="https://publications.waset.org/abstracts/search?q=recovery%20stress" title=" recovery stress"> recovery stress</a>, <a href="https://publications.waset.org/abstracts/search?q=shape%20memory%20alloy" title=" shape memory alloy"> shape memory alloy</a> </p> <a href="https://publications.waset.org/abstracts/96718/non-linear-load-deflection-response-of-shape-memory-alloys-reinforced-composite-cylindrical-shells-under-uniform-radial-load" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/96718.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">188</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">2487</span> Generalization of Tsallis Entropy from a Q-Deformed Arithmetic</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Juan%20Pe%C3%B1a">J. Juan Peña</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Morales"> J. Morales</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Garc%C3%ADa-Ravelo"> J. García-Ravelo</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Garc%C3%ADa-Mart%C3%ADnez"> J. García-Martínez</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sᵩ is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=q-calculus" title="q-calculus">q-calculus</a>, <a href="https://publications.waset.org/abstracts/search?q=q-deformed%20arithmetic" title=" q-deformed arithmetic"> q-deformed arithmetic</a>, <a href="https://publications.waset.org/abstracts/search?q=entropy" title=" entropy"> entropy</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20functions" title=" exponential functions"> exponential functions</a>, <a href="https://publications.waset.org/abstracts/search?q=thermodynamic%20functions" title=" thermodynamic functions"> thermodynamic functions</a> </p> <a href="https://publications.waset.org/abstracts/181635/generalization-of-tsallis-entropy-from-a-q-deformed-arithmetic" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181635.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">78</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">2486</span> Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khosrow%20Maleknejad">Khosrow Maleknejad</a>, <a href="https://publications.waset.org/abstracts/search?q=Yaser%20Rostami"> Yaser Rostami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%C4%B1ntegro-differential%20equations" title="ıntegro-differential equations">ıntegro-differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20B-spline%20wavelet" title=" quartic B-spline wavelet"> quartic B-spline wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrices" title=" operational matrices"> operational matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=dual%20functions" title=" dual functions"> dual functions</a> </p> <a href="https://publications.waset.org/abstracts/5002/numerical-solution-for-integro-differential-equations-by-using-quartic-b-spline-wavelet-and-operational-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5002.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">456</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">2485</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">252</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">2484</span> A Qualitative Case Study Exploring Zambian Mathematics Teachers' Content Knowledge of Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Priestly%20Malambo">Priestly Malambo</a>, <a href="https://publications.waset.org/abstracts/search?q=Sonja%20Van%20Putten"> Sonja Van Putten</a>, <a href="https://publications.waset.org/abstracts/search?q=Hanlie%20Botha"> Hanlie Botha</a>, <a href="https://publications.waset.org/abstracts/search?q=Gerrit%20Stols"> Gerrit Stols</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=secondary%20school" title="secondary school">secondary school</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20reasoning" title=" mathematical reasoning"> mathematical reasoning</a>, <a href="https://publications.waset.org/abstracts/search?q=student-teachers" title=" student-teachers"> student-teachers</a>, <a href="https://publications.waset.org/abstracts/search?q=functions" title=" functions"> functions</a> </p> <a href="https://publications.waset.org/abstracts/75944/a-qualitative-case-study-exploring-zambian-mathematics-teachers-content-knowledge-of-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/75944.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">255</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">2483</span> Bernstein Type Polynomials for Solving Differential Equations and Their Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yilmaz%20Simsek">Yilmaz Simsek</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generating%20functions" title="generating functions">generating functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20basis%20functions" title=" Bernstein basis functions"> Bernstein basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomials" title=" Bernstein polynomials"> Bernstein polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Bezier%20curves" title=" Bezier curves"> Bezier curves</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a> </p> <a href="https://publications.waset.org/abstracts/67937/bernstein-type-polynomials-for-solving-differential-equations-and-their-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67937.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">274</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2482</span> Hypergeometric Solutions to Linear Nonhomogeneous Fractional Equations with Spherical Bessel Functions of the First Kind</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> The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=caputo%20fractional%20derivatives" title="caputo fractional derivatives">caputo fractional derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric%20functions" title=" hypergeometric functions"> hypergeometric functions</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20differential%20equations" title=" linear differential equations"> linear differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=spherical%20Bessel%20functions" title=" spherical Bessel functions"> spherical Bessel functions</a> </p> <a href="https://publications.waset.org/abstracts/91343/hypergeometric-solutions-to-linear-nonhomogeneous-fractional-equations-with-spherical-bessel-functions-of-the-first-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91343.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">325</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">2481</span> Exact Formulas of the End-To-End Green’s Functions in Non-hermitian Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haoshu%20Li">Haoshu Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Shaolong%20Wan"> Shaolong Wan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-Hermitian" title="non-Hermitian">non-Hermitian</a>, <a href="https://publications.waset.org/abstracts/search?q=Green%27s%20function" title=" Green's function"> Green's function</a>, <a href="https://publications.waset.org/abstracts/search?q=non-Hermitian%20skin%20effect" title=" non-Hermitian skin effect"> non-Hermitian skin effect</a>, <a href="https://publications.waset.org/abstracts/search?q=signal%20amplification" title=" signal amplification"> signal amplification</a> </p> <a href="https://publications.waset.org/abstracts/149780/exact-formulas-of-the-end-to-end-greens-functions-in-non-hermitian-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/149780.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">142</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">2480</span> Certain Results of a New Class of Meromorphic Multivalent Functions Involving Ruscheweyh Derivative</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kassim%20A.%20Jassim">Kassim A. Jassim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=meromorphic%20multivalent%20function" title="meromorphic multivalent function">meromorphic multivalent function</a>, <a href="https://publications.waset.org/abstracts/search?q=Ruscheweyh%20derivative" title=" Ruscheweyh derivative"> Ruscheweyh derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=hadamard%20product" title=" hadamard product"> hadamard product</a> </p> <a href="https://publications.waset.org/abstracts/43208/certain-results-of-a-new-class-of-meromorphic-multivalent-functions-involving-ruscheweyh-derivative" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43208.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">337</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">2479</span> Nonhomogeneous Linear Fractional Differential Equations Will Bessel Functions of the First Kind Giving Hypergeometric Functions Solutions</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> Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo" title="Caputo">Caputo</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20calculation" title=" fractional calculation"> fractional calculation</a>, <a href="https://publications.waset.org/abstracts/search?q=hypergeometric" title=" hypergeometric"> hypergeometric</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20differential%20equations" title=" linear differential equations"> linear differential equations</a> </p> <a href="https://publications.waset.org/abstracts/91373/nonhomogeneous-linear-fractional-differential-equations-will-bessel-functions-of-the-first-kind-giving-hypergeometric-functions-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91373.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">198</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">2478</span> Some Integral Inequalities of Hermite-Hadamard Type on Time Scale and Their Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Artion%20Kashuri">Artion Kashuri</a>, <a href="https://publications.waset.org/abstracts/search?q=Rozana%20Liko"> Rozana Liko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20functions" title="convex functions">convex functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Hermite-Hadamard%20inequality" title=" Hermite-Hadamard inequality"> Hermite-Hadamard inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=special%20means" title=" special means"> special means</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20scale" title=" time scale"> time scale</a> </p> <a href="https://publications.waset.org/abstracts/133550/some-integral-inequalities-of-hermite-hadamard-type-on-time-scale-and-their-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/133550.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">150</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">2477</span> Duality in Multiobjective Nonlinear Programming under Generalized Second Order (F, b, φ, ρ, θ)− Univex Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meraj%20Ali%20Khan">Meraj Ali Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Falleh%20R.%20Al-Solamy"> Falleh R. Al-Solamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=duality" title="duality">duality</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20programming" title=" multiobjective programming"> multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=univex%20functions" title=" univex functions"> univex functions</a>, <a href="https://publications.waset.org/abstracts/search?q=univex" title=" univex"> univex</a> </p> <a href="https://publications.waset.org/abstracts/4320/duality-in-multiobjective-nonlinear-programming-under-generalized-second-order-f-b-f-r-th-univex-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4320.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">2476</span> Multi-Objective Optimal Threshold Selection for Similarity Functions in Siamese Networks for Semantic Textual Similarity Tasks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kriuk%20Boris">Kriuk Boris</a>, <a href="https://publications.waset.org/abstracts/search?q=Kriuk%20Fedor"> Kriuk Fedor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a comparative study of fundamental similarity functions for Siamese networks in semantic textual similarity (STS) tasks. We evaluate various similarity functions using the STS Benchmark dataset, analyzing their performance and stability. Additionally, we introduce a multi-objective approach for optimal threshold selection. Our findings provide insights into the effectiveness of different similarity functions and offer a straightforward method for threshold selection optimization, contributing to the advancement of Siamese network architectures in STS applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=siamese%20networks" title="siamese networks">siamese networks</a>, <a href="https://publications.waset.org/abstracts/search?q=semantic%20textual%20similarity" title=" semantic textual similarity"> semantic textual similarity</a>, <a href="https://publications.waset.org/abstracts/search?q=similarity%20functions" title=" similarity functions"> similarity functions</a>, <a href="https://publications.waset.org/abstracts/search?q=STS%20benchmark%20dataset" title=" STS benchmark dataset"> STS benchmark dataset</a>, <a href="https://publications.waset.org/abstracts/search?q=threshold%20selection" title=" threshold selection"> threshold selection</a> </p> <a href="https://publications.waset.org/abstracts/187407/multi-objective-optimal-threshold-selection-for-similarity-functions-in-siamese-networks-for-semantic-textual-similarity-tasks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/187407.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">39</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">2475</span> The Role of Eclectic Approach to Teach Communicative Function at Secondary Level</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fariha%20Asif">Fariha Asif</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main purpose of this study was to investigate the effectiveness of eclectic approach in teaching of communicative functions. The objectives of the study were to get the information about the use of communicative functions through eclectic approach and to point out the most effective way of teaching functional communication and social interaction with the help of communicative activities through eclectic approach. The next step was to select sample from the selected population. As the research was descriptive so a questionnaire was developed on the basis of hypothesis and distributed to different selected schools of Lahore, Pakistan. Then data was tabulated, analyzed and interpreted through computer by finding percentages of different responses given by teachers to see the results. It was concluded that eclectic approach is effective in teaching communicative functions and communicative functions are better when taught through eclectic approach and communicative activities are more appropriate way of teaching communicative functions. It was found those teachers who were qualified in ELT gave better opinions as compare to those who did not have this degree. Techniques like presentations, dialogues and roleplay proved to be effective for teaching functional communication through communicative activities and also motivate the students not only in learning rules but also in using them to communicate with others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=methodology" title="methodology">methodology</a>, <a href="https://publications.waset.org/abstracts/search?q=functions" title=" functions"> functions</a>, <a href="https://publications.waset.org/abstracts/search?q=teaching" title=" teaching"> teaching</a>, <a href="https://publications.waset.org/abstracts/search?q=ESP" title=" ESP"> ESP</a> </p> <a href="https://publications.waset.org/abstracts/19494/the-role-of-eclectic-approach-to-teach-communicative-function-at-secondary-level" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19494.pdf" target="_blank" class="btn btn-primary 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