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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> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Bernstein basis functions</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info"></span> Bernstein Type Polynomials for Solving Differential Equations and Their Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yilmaz%20Simsek">Yilmaz Simsek</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generating%20functions" title="generating functions">generating functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20basis%20functions" title=" Bernstein basis functions"> Bernstein basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomials" title=" Bernstein polynomials"> Bernstein polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Bezier%20curves" title=" Bezier curves"> Bezier curves</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a> </p> <a href="https://publications.waset.org/abstracts/67937/bernstein-type-polynomials-for-solving-differential-equations-and-their-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67937.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">280</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info"></span> The Bernstein Expansion for Exponentials in Taylor Functions: Approximation of Fixed Points</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tareq%20Hamadneh">Tareq Hamadneh</a>, <a href="https://publications.waset.org/abstracts/search?q=Jochen%20Merker"> Jochen Merker</a>, <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Al-Zoubi"> Hassan Al-Zoubi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain. <p class="card-text"><strong>Keywords:</strong> <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=Stability%20of%20control%20functions" title="Stability of control functions">Stability of control functions</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20optimization" title="numerical optimization">numerical optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%20function" title="Taylor function">Taylor function</a> </p> <a href="https://publications.waset.org/abstracts/149910/the-bernstein-expansion-for-exponentials-in-taylor-functions-approximation-of-fixed-points" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/149910.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">139</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"></span> Durrmeyer Type Modification of q-Generalized Bernstein Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ruchi">Ruchi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Acu"> A. M. Acu</a>, <a href="https://publications.waset.org/abstracts/search?q=Purshottam%20N.%20Agrawal"> Purshottam N. Agrawal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper to introduce the Durrmeyer type modification of q-generalized-Bernstein operators which include the Bernstein polynomials in the particular α = 0. We investigate the rate of convergence by means of the Lipschitz class and the Peetre’s K-functional. Also, we define the bivariate case of Durrmeyer type modification of q-generalized-Bernstein operators and study the degree of approximation with the aid of the partial modulus of continuity and the Peetre’s K-functional. Finally, we introduce the GBS (Generalized Boolean Sum) of the Durrmeyer type modification of q- generalized-Bernstein operators and investigate the approximation of the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=B%C3%B6gel%20continuous" title="Bögel continuous">Bögel continuous</a>, <a href="https://publications.waset.org/abstracts/search?q=B%C3%B6gel%20differentiable" title=" Bögel differentiable"> Bögel differentiable</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20Boolean%20sum" title=" generalized Boolean sum"> generalized Boolean sum</a>, <a href="https://publications.waset.org/abstracts/search?q=Peetre%E2%80%99s%20K-functional" title=" Peetre’s K-functional"> Peetre’s K-functional</a>, <a href="https://publications.waset.org/abstracts/search?q=Lipschitz%20class" title=" Lipschitz class"> Lipschitz class</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20modulus%20of%20smoothness" title=" mixed modulus of smoothness"> mixed modulus of smoothness</a> </p> <a href="https://publications.waset.org/abstracts/79175/durrmeyer-type-modification-of-q-generalized-bernstein-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79175.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">219</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"></span> Bivariate Generalization of q-α-Bernstein Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tarul%20Garg">Tarul Garg</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20N.%20Agrawal"> P. N. Agrawal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=B%C3%B6gel%20continuous" title="Bögel continuous">Bögel continuous</a>, <a href="https://publications.waset.org/abstracts/search?q=B%C3%B6gel%20differentiable" title=" Bögel differentiable"> Bögel differentiable</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20Boolean%20sum" title=" generalized Boolean sum"> generalized Boolean sum</a>, <a href="https://publications.waset.org/abstracts/search?q=K-functional" title=" K-functional"> K-functional</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20modulus%20of%20smoothness" title=" mixed modulus of smoothness"> mixed modulus of smoothness</a> </p> <a href="https://publications.waset.org/abstracts/79181/bivariate-generalization-of-q-a-bernstein-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79181.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">386</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"></span> I Feel Pretty: Using Discretization to Unpack Gender Disparity in Musical Theatre - A Study of Leonard Bernstein’s West Side Story</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Erin%20McKellar">Erin McKellar</a>, <a href="https://publications.waset.org/abstracts/search?q=Narelle%20Yeo"> Narelle Yeo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Gender disparity can be found in the representation of the female characters in Leonard Bernstein’s musical West Side Story. As a postmodern composer, Bernstein was open about his social activism, yet did not consider his compositional portrayal of female characters as part of that activism. Using discretization as an analysis tool, this thesis explores the melodic contours of male and female songs in West Side Story to show differences in complexity between male and female characterisation. The analysis explores the intervallic relationship between the vocal line and melodic color in relation to the accompaniment harmony, taking into consideration the use of consonance and dissonance. West Side Story is commonly known for its distinct use of the tritone motif and its inherent dissonance. It is evident when reviewing the findings of this study that there is a distinct disparity between male-led and female-led music. The male-led numbers consistently adhere to a dissonant aesthetic with the tritone motif implemented in all of the extracted songs. By contrast, the female songs remain consonant with simple intervallic movements. By examining the results of this study through the lens of Equality Feminism, this thesis finds that Bernstein has simplified the characterisations of the female leads. The thesis further proposes that without cognisant consideration of the compositional portrayal of women, the musical theatre will continue to reinforce gender stereotypes, as evident through this study of Bernstein’s West Side Story. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=music%20theatre" title="music theatre">music theatre</a>, <a href="https://publications.waset.org/abstracts/search?q=gender%20bias" title=" gender bias"> gender bias</a>, <a href="https://publications.waset.org/abstracts/search?q=composition" title=" composition"> composition</a>, <a href="https://publications.waset.org/abstracts/search?q=Leonard%20Bernstein" title=" Leonard Bernstein"> Leonard Bernstein</a> </p> <a href="https://publications.waset.org/abstracts/144878/i-feel-pretty-using-discretization-to-unpack-gender-disparity-in-musical-theatre-a-study-of-leonard-bernsteins-west-side-story" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/144878.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">165</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"></span> MHD Equilibrium Study in Alborz Tokamak</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Maryamosadat%20Ghasemi">Maryamosadat Ghasemi</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Amrollahi"> Reza Amrollahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Plasma equilibrium geometry has a great influence on the confinement and magnetohydrodynamic stability in tokamaks. The poloidal field (PF) system of a tokamak should be able to support this plasma equilibrium geometry. In this work the prepared numerical code based on radial basis functions are presented and used to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibrium of tokamak plasma. The radial basis functions (RBFs) which is a kind of numerical meshfree method (MFM) for solving partial differential equations (PDEs) has appeared in the last decade and is developing significantly in the last few years. This technique is applied in this study to obtain the equilibrium configuration for Alborz Tokamak. The behavior of numerical solution convergences show the validation of this calculations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=equilibrium" title="equilibrium">equilibrium</a>, <a href="https://publications.waset.org/abstracts/search?q=grad%E2%80%93shafranov" title=" grad–shafranov"> grad–shafranov</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20functions" title=" radial basis functions"> radial basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Alborz%20Tokamak" title=" Alborz Tokamak"> Alborz Tokamak</a> </p> <a href="https://publications.waset.org/abstracts/30952/mhd-equilibrium-study-in-alborz-tokamak" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30952.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">481</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"></span> Energy-Level Structure of a Confined Electron-Positron Pair in Nanostructure</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tokuei%20Sako">Tokuei Sako</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul-Antoine%20Hervieux"> Paul-Antoine Hervieux</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The energy-level structure of a pair of electron and positron confined in a quasi-one-dimensional nano-scale potential well has been investigated focusing on its trend in the small limit of confinement strength ω, namely, the Wigner molecular regime. An anisotropic Gaussian-type basis functions supplemented by high angular momentum functions as large as l = 19 has been used to obtain reliable full configuration interaction (FCI) wave functions. The resultant energy spectrum shows a band structure characterized by ω for the large ω regime whereas for the small ω regime it shows an energy-level pattern dominated by excitation into the in-phase motion of the two particles. The observed trend has been rationalized on the basis of the nodal patterns of the FCI wave functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=confined%20systems" title="confined systems">confined systems</a>, <a href="https://publications.waset.org/abstracts/search?q=positron" title=" positron"> positron</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20function" title=" wave function"> wave function</a>, <a href="https://publications.waset.org/abstracts/search?q=Wigner%20molecule" title=" Wigner molecule"> Wigner molecule</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20dots" title=" quantum dots"> quantum dots</a> </p> <a href="https://publications.waset.org/abstracts/4205/energy-level-structure-of-a-confined-electron-positron-pair-in-nanostructure" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4205.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">391</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"></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">74</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"></span> Local Radial Basis Functions for Helmholtz Equation in Seismic Inversion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hebert%20Montegranario">Hebert Montegranario</a>, <a href="https://publications.waset.org/abstracts/search?q=Mauricio%20Londo%C3%B1o"> Mauricio Londoño </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title="Helmholtz equation">Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=meshless%20methods" title=" meshless methods"> meshless methods</a>, <a href="https://publications.waset.org/abstracts/search?q=seismic%20imaging" title=" seismic imaging"> seismic imaging</a>, <a href="https://publications.waset.org/abstracts/search?q=wavefield%20inversion" title=" wavefield inversion"> wavefield inversion</a> </p> <a href="https://publications.waset.org/abstracts/33679/local-radial-basis-functions-for-helmholtz-equation-in-seismic-inversion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33679.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">552</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"></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">377</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info"></span> Poor Cognitive Flexibility as Suggested Basis for Learning Difficulties among Children with Moderate-INTO-Severe Asthma: Evidence from WCSTPerformance</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haitham%20Taha">Haitham Taha </a> </p> <p class="card-text"><strong>Abstract:</strong></p> The cognitive flexibility of 27 asthmatic children with learning difficulties was tested by using the Wisconsin card sorting test (WCST) and compared to the performances of 30 non-asthmatic children who have persistence learning difficulties also. The results revealed that the asthmatic group had poor performance through all the WCST psychometric parameters and especially the preservative errors one. The results were discussed in light of the postulation that poor executive functions and specifically poor cognitive flexibility are in the basis of the learning difficulties of asthmatic children with learning difficulties. Neurophysiologic framework was suggested for explaining the etiology of poor executive functions and cognitive flexibility among children with moderate into severe asthma. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asthma" title="asthma">asthma</a>, <a href="https://publications.waset.org/abstracts/search?q=learning%20disabilities" title=" learning disabilities"> learning disabilities</a>, <a href="https://publications.waset.org/abstracts/search?q=executive%20functions" title=" executive functions"> executive functions</a>, <a href="https://publications.waset.org/abstracts/search?q=cognitive%20flexibility" title=" cognitive flexibility"> cognitive flexibility</a>, <a href="https://publications.waset.org/abstracts/search?q=WCST" title=" WCST "> WCST </a> </p> <a href="https://publications.waset.org/abstracts/13405/poor-cognitive-flexibility-as-suggested-basis-for-learning-difficulties-among-children-with-moderate-into-severe-asthma-evidence-from-wcstperformance" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13405.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">507</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"></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 btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">571</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"></span> Collocation Method for Coupled System of Boundary Value Problems with Cubic B-Splines </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20N.%20S.%20Kasi%20Viswanadham">K. N. S. Kasi Viswanadham </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the 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=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=cubic%20b-splines" title=" cubic b-splines"> cubic b-splines</a>, <a href="https://publications.waset.org/abstracts/search?q=mesh%20points" title=" mesh points"> mesh points</a> </p> <a href="https://publications.waset.org/abstracts/54713/collocation-method-for-coupled-system-of-boundary-value-problems-with-cubic-b-splines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54713.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">217</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"></span> Nonparametric Copula Approximations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Serge%20Provost">Serge Provost</a>, <a href="https://publications.waset.org/abstracts/search?q=Yishan%20Zang"> Yishan Zang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=copulas" title="copulas">copulas</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomial%20approximation" title=" Bernstein polynomial approximation"> Bernstein polynomial approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=least-squares%20polynomial%20approximation" title=" least-squares polynomial approximation"> least-squares polynomial approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=kernel%20density%20estimation" title=" kernel density estimation"> kernel density estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=density%20approximation" title=" density approximation"> density approximation</a> </p> <a href="https://publications.waset.org/abstracts/170324/nonparametric-copula-approximations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/170324.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">80</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"></span> Strongly Coupled Finite Element Formulation of Electromechanical Systems with Integrated Mesh Morphing Using Radial Basis Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=David%20Kriebel">David Kriebel</a>, <a href="https://publications.waset.org/abstracts/search?q=Jan%20Edgar%20Mehner"> Jan Edgar Mehner</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper introduces a method to efficiently simulate nonlinear changing electrostatic fields occurring in micro-electromechanical systems (MEMS). Large deflections of the capacitor electrodes usually introduce nonlinear electromechanical forces on the mechanical system. Traditional finite element methods require a time-consuming remeshing process to capture exact results for this physical domain interaction. In order to accelerate the simulation process and eliminate the remeshing process, a formulation of a strongly coupled electromechanical transducer element will be introduced, which uses a combination of finite-element with an advanced mesh morphing technique using radial basis functions (RBF). The RBF allows large geometrical changes of the electric field domain while retaining the high element quality of the deformed mesh. Coupling effects between mechanical and electrical domains are directly included within the element formulation. Fringing field effects are described accurately by using traditional arbitrary shape functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=electromechanical" title="electromechanical">electromechanical</a>, <a href="https://publications.waset.org/abstracts/search?q=electric%20field" title=" electric field"> electric field</a>, <a href="https://publications.waset.org/abstracts/search?q=transducer" title=" transducer"> transducer</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=modeling" title=" modeling"> modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=finite-element" title=" finite-element"> finite-element</a>, <a href="https://publications.waset.org/abstracts/search?q=mesh%20morphing" title=" mesh morphing"> mesh morphing</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20function" title=" radial basis function"> radial basis function</a> </p> <a href="https://publications.waset.org/abstracts/135652/strongly-coupled-finite-element-formulation-of-electromechanical-systems-with-integrated-mesh-morphing-using-radial-basis-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/135652.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"></span> Electron Bernstein Wave Heating in the Toroidally Magnetized System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Johan%20Buermans">Johan Buermans</a>, <a href="https://publications.waset.org/abstracts/search?q=Kristel%20Cromb%C3%A9"> Kristel Crombé</a>, <a href="https://publications.waset.org/abstracts/search?q=Niek%20Desmet"> Niek Desmet</a>, <a href="https://publications.waset.org/abstracts/search?q=Laura%20Dittrich"> Laura Dittrich</a>, <a href="https://publications.waset.org/abstracts/search?q=Andrei%20Goriaev"> Andrei Goriaev</a>, <a href="https://publications.waset.org/abstracts/search?q=Yurii%20Kovtun"> Yurii Kovtun</a>, <a href="https://publications.waset.org/abstracts/search?q=Daniel%20L%C3%B3pez-Rodriguez"> Daniel López-Rodriguez</a>, <a href="https://publications.waset.org/abstracts/search?q=S%C3%B6ren%20M%C3%B6ller"> Sören Möller</a>, <a href="https://publications.waset.org/abstracts/search?q=Per%20Petersson"> Per Petersson</a>, <a href="https://publications.waset.org/abstracts/search?q=Maja%20Verstraeten"> Maja Verstraeten</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The International Thermonuclear Experimental Reactor (ITER) will rely on three sources of external heating to produce and sustain a plasma; Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRH), and Electron Cyclotron Resonance Heating (ECRH). ECRH is a way to heat the electrons in a plasma by resonant absorption of electromagnetic waves. The energy of the electrons is transferred indirectly to the ions by collisions. The electron cyclotron heating system can be directed to deposit heat in particular regions in the plasma (https://www.iter.org/mach/Heating). Electron Cyclotron Resonance Heating (ECRH) at the fundamental resonance in X-mode is limited by a low cut-off density. Electromagnetic waves cannot propagate in the region between this cut-off and the Upper Hybrid Resonance (UHR) and cannot reach the Electron Cyclotron Resonance (ECR) position. Higher harmonic heating is hence preferred in heating scenarios nowadays to overcome this problem. Additional power deposition mechanisms can occur above this threshold to increase the plasma density. This includes collisional losses in the evanescent region, resonant power coupling at the UHR, tunneling of the X-wave with resonant coupling at the ECR, and conversion to the Electron Bernstein Wave (EBW) with resonant coupling at the ECR. A more profound knowledge of these deposition mechanisms can help determine the optimal plasma production scenarios. Several ECRH experiments are performed on the TOroidally MAgnetized System (TOMAS) to identify the conditions for Electron Bernstein Wave (EBW) heating. Density and temperature profiles are measured with movable Triple Langmuir Probes in the horizontal and vertical directions. Measurements of the forwarded and reflected power allow evaluation of the coupling efficiency. Optical emission spectroscopy and camera images also contribute to plasma characterization. The influence of the injected power, magnetic field, gas pressure, and wave polarization on the different deposition mechanisms is studied, and the contribution of the Electron Bernstein Wave is evaluated. The TOMATOR 1D hydrogen-helium plasma simulator numerically describes the evolution of current less magnetized Radio Frequency plasmas in a tokamak based on Braginskii’s legal continuity and heat balance equations. This code was initially benchmarked with experimental data from TCV to determine the transport coefficients. The code is used to model the plasma parameters and the power deposition profiles. The modeling is compared with the data from the experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=electron%20Bernstein%20wave" title="electron Bernstein wave">electron Bernstein wave</a>, <a href="https://publications.waset.org/abstracts/search?q=Langmuir%20probe" title=" Langmuir probe"> Langmuir probe</a>, <a href="https://publications.waset.org/abstracts/search?q=plasma%20characterization" title=" plasma characterization"> plasma characterization</a>, <a href="https://publications.waset.org/abstracts/search?q=TOMAS" title=" TOMAS"> TOMAS</a> </p> <a href="https://publications.waset.org/abstracts/163243/electron-bernstein-wave-heating-in-the-toroidally-magnetized-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163243.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">98</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"></span> Performance of Neural Networks vs. Radial Basis Functions When Forming a Metamodel for Residential Buildings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Philip%20Symonds">Philip Symonds</a>, <a href="https://publications.waset.org/abstracts/search?q=Jon%20Taylor"> Jon Taylor</a>, <a href="https://publications.waset.org/abstracts/search?q=Zaid%20Chalabi"> Zaid Chalabi</a>, <a href="https://publications.waset.org/abstracts/search?q=Michael%20Davies"> Michael Davies</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With the world climate projected to warm and major cities in developing countries becoming increasingly populated and polluted, governments are tasked with the problem of overheating and air quality in residential buildings. This paper presents the development of an adaptable model of these risks. Simulations are performed using the EnergyPlus building physics software. An accurate metamodel is formed by randomly sampling building input parameters and training on the outputs of EnergyPlus simulations. Metamodels are used to vastly reduce the amount of computation time required when performing optimisation and sensitivity analyses. Neural Networks (NNs) are compared to a Radial Basis Function (RBF) algorithm when forming a metamodel. These techniques were implemented using the PyBrain and scikit-learn python libraries, respectively. NNs are shown to perform around 15% better than RBFs when estimating overheating and air pollution metrics modelled by EnergyPlus. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=neural%20networks" title="neural networks">neural networks</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20functions" title=" radial basis functions"> radial basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=metamodelling" title=" metamodelling"> metamodelling</a>, <a href="https://publications.waset.org/abstracts/search?q=python%20machine%20learning%20libraries" title=" python machine learning libraries"> python machine learning libraries</a> </p> <a href="https://publications.waset.org/abstracts/36155/performance-of-neural-networks-vs-radial-basis-functions-when-forming-a-metamodel-for-residential-buildings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36155.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">454</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"></span> Handwriting Velocity Modeling by Artificial Neural Networks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Aymen%20Slim">Mohamed Aymen Slim</a>, <a href="https://publications.waset.org/abstracts/search?q=Afef%20Abdelkrim"> Afef Abdelkrim</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Benrejeb"> Mohamed Benrejeb</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The handwriting is a physical demonstration of a complex cognitive process learnt by man since his childhood. People with disabilities or suffering from various neurological diseases are facing so many difficulties resulting from problems located at the muscle stimuli (EMG) or signals from the brain (EEG) and which arise at the stage of writing. The handwriting velocity of the same writer or different writers varies according to different criteria: age, attitude, mood, writing surface, etc. Therefore, it is interesting to reconstruct an experimental basis records taking, as primary reference, the writing speed for different writers which would allow studying the global system during handwriting process. This paper deals with a new approach of the handwriting system modeling based on the velocity criterion through the concepts of artificial neural networks, precisely the Radial Basis Functions (RBF) neural networks. The obtained simulation results show a satisfactory agreement between responses of the developed neural model and the experimental data for various letters and forms then the efficiency of the proposed approaches. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Electro%20Myo%20Graphic%20%28EMG%29%20signals" title="Electro Myo Graphic (EMG) signals">Electro Myo Graphic (EMG) signals</a>, <a href="https://publications.waset.org/abstracts/search?q=experimental%20approach" title=" experimental approach"> experimental approach</a>, <a href="https://publications.waset.org/abstracts/search?q=handwriting%20process" title=" handwriting process"> handwriting process</a>, <a href="https://publications.waset.org/abstracts/search?q=Radial%20Basis%20Functions%20%28RBF%29%20neural%20networks" title=" Radial Basis Functions (RBF) neural networks"> Radial Basis Functions (RBF) neural networks</a>, <a href="https://publications.waset.org/abstracts/search?q=velocity%20modeling" title=" velocity modeling"> velocity modeling</a> </p> <a href="https://publications.waset.org/abstracts/10496/handwriting-velocity-modeling-by-artificial-neural-networks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10496.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">445</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info"></span> Extended Arithmetic Precision in Meshfree Calculations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edward%20J.%20Kansa">Edward J. Kansa</a>, <a href="https://publications.waset.org/abstracts/search?q=Pavel%20Holoborodko"> Pavel Holoborodko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title="partial differential equations">partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Meshfree%20radial%20basis%20functions" title=" Meshfree radial basis functions"> Meshfree radial basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=" title=""></a>, <a href="https://publications.waset.org/abstracts/search?q=no%20restrictions%20on%20spatial%20dimensions" title=" no restrictions on spatial dimensions"> no restrictions on spatial dimensions</a>, <a href="https://publications.waset.org/abstracts/search?q=Extended%20arithmetic%20precision." title=" Extended arithmetic precision."> Extended arithmetic precision.</a> </p> <a href="https://publications.waset.org/abstracts/117617/extended-arithmetic-precision-in-meshfree-calculations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/117617.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">159</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"></span> On the Basis Number and the Minimum Cycle Bases of the Wreath Product of Paths with Wheels</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20M.%20M.%20Jaradat">M. M. M. Jaradat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For a given graph G, the set Ԑ of all subsets of E(G) forms an |E(G)| dimensional vector space over Z2 with vector addition X⊕Y = (X\Y ) [ (Y \X) and scalar multiplication 1.X = X and 0.X = Ø for all X, Yϵ Ԑ. The cycle space, C(G), of a graph G is the vector subspace of (E; ⊕; .) spanned by the cycles of G. Traditionally there have been two notions of minimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimum cycle basis (MCB) if its total length Σ BϵB |B| is minimum among all bases of C(G). The lexicographic product GρH has the vertex set V (GρH) = V (G) x V (H) and the edge set E(GρH) = {(u1, v1)(u2, v2)|u1 = u2 and v1 v2 ϵ E(H); or u1u2 ϵ E(G) and there is α ϵ Aut(H) such that α (v1) = v2}. In this work, a construction of a minimum cycle basis for the wreath product of wheels with paths is presented. Also, the length of the longest cycle of a minimum cycle basis is determined. Moreover, the basis number for the wreath product of the same is investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cycle%20space" title="cycle space">cycle space</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20cycle%20basis" title=" minimum cycle basis"> minimum cycle basis</a>, <a href="https://publications.waset.org/abstracts/search?q=basis%20number" title=" basis number"> basis number</a>, <a href="https://publications.waset.org/abstracts/search?q=wreath%20product" title=" wreath product"> wreath product</a> </p> <a href="https://publications.waset.org/abstracts/2144/on-the-basis-number-and-the-minimum-cycle-bases-of-the-wreath-product-of-paths-with-wheels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2144.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">285</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"></span> Numerical Wave Solutions for Nonlinear Coupled Equations Using Sinc-Collocation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nonlinear%20coupled%20KdV%20equations" title="Nonlinear coupled KdV equations">Nonlinear coupled KdV equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Soliton%20solutions" title=" Soliton solutions"> Soliton solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Sinc-collocation%20method" title=" Sinc-collocation method"> Sinc-collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Sinc%20functions" title=" Sinc functions"> Sinc functions</a> </p> <a href="https://publications.waset.org/abstracts/23564/numerical-wave-solutions-for-nonlinear-coupled-equations-using-sinc-collocation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23564.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">528</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"></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">578</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"></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">36</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"></span> Theorising Chinese as a Foreign Language Curriculum Justice in the Australian School Context</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wen%20Xu">Wen Xu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The expansion of Confucius institutes and Chinese as a Foreign Language (CFL) education is often considered as cultural invasion and part of much bigger, if not ambitious, Chinese central government agenda among Western public opinion. The CFL knowledge and teaching practice inherent in textbooks are also harshly critiqued as failing to align with Western educational principles. This paper takes up these concerns and attempts to articulate that Confucius’s idea of ‘education without discrimination’ appears to have become synonymous with social justice touted in contemporary Australian education and policy discourses. To do so, it capitalises on Bernstein's conceptualization of classification and pedagogic rights to articulate CFL curriculum's potential of drawing in and drawing out curriculum boundaries to achieve educational justice. In this way, the potential useful knowledge of CFL constitutes a worthwhile tool to engage in a peripheral Western country’s education issues, as well as to include disenfranchised students in the multicultural Australian society. It opens spaces for critically theorising CFL curricular justice in Australian educational contexts, and makes an original contribution to scholarly argumentation that CFL curriculum has the potential of including socially and economically disenfranchised students in schooling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=curriculum%20justice" title="curriculum justice">curriculum justice</a>, <a href="https://publications.waset.org/abstracts/search?q=Chinese%20as%20a%20Foreign%20Language%20curriculum" title=" Chinese as a Foreign Language curriculum"> Chinese as a Foreign Language curriculum</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein" title=" Bernstein"> Bernstein</a>, <a href="https://publications.waset.org/abstracts/search?q=equity" title=" equity"> equity</a> </p> <a href="https://publications.waset.org/abstracts/118725/theorising-chinese-as-a-foreign-language-curriculum-justice-in-the-australian-school-context" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/118725.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">147</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"></span> Inverse Cauchy Problem of Doubly Connected Domains via Spectral Meshless Radial Point Interpolation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elyas%20Shivanian">Elyas Shivanian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in doubly connected domains. It is obtained the unknown data on the inner boundary of the domain while overspecified boundary data are imposed on the outer boundary of the domain by using the SMRPI. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high order convergence rate. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and it is revealed the SMRPI is more accurate and stable by adding strong perturbations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cauchy%20problem" title="cauchy problem">cauchy problem</a>, <a href="https://publications.waset.org/abstracts/search?q=doubly%20connected%20domain" title=" doubly connected domain"> doubly connected domain</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20basis%20function" title=" radial basis function"> radial basis function</a>, <a href="https://publications.waset.org/abstracts/search?q=shape%20function" title=" shape function"> shape function</a> </p> <a href="https://publications.waset.org/abstracts/56408/inverse-cauchy-problem-of-doubly-connected-domains-via-spectral-meshless-radial-point-interpolation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56408.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">280</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info"></span> Decentralized Control of Interconnected Systems with Non-Linear Unknown Interconnections</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haci%20Mehmet%20Guzey">Haci Mehmet Guzey</a>, <a href="https://publications.waset.org/abstracts/search?q=Levent%20Acar"> Levent Acar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a novel decentralized controller is developed for linear systems with nonlinear unknown interconnections. A model linear decoupled system is assigned for each system. By using the difference actual and model state dynamics, the problem is formulated as inverse problem. Then, the interconnected dynamics are approximated by using Galerkin’s expansion method for inverse problems. Two different sets of orthogonal basis functions are utilized to approximate the interconnected dynamics. Approximated interconnections are utilized in the controller to cancel the interconnections and decouple the systems. Subsequently, the interconnected systems behave as a collection of decoupled systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=decentralized%20control" title="decentralized control">decentralized control</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20problems" title=" inverse problems"> inverse problems</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20scale%20systems" title=" large scale systems"> large scale systems</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20interconnections" title=" nonlinear interconnections"> nonlinear interconnections</a>, <a href="https://publications.waset.org/abstracts/search?q=basis%20functions" title=" basis functions"> basis functions</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20identification" title=" system identification"> system identification</a> </p> <a href="https://publications.waset.org/abstracts/20511/decentralized-control-of-interconnected-systems-with-non-linear-unknown-interconnections" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20511.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">537</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"></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">532</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"></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">311</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"></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">299</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"></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">281</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">« Previous</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Bernstein%20basis%20functions&page=2" rel="next">Next »</a></li> </ul> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div 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