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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="fourth order compact"> <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> 14579</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: fourth order compact</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14579</span> Compact Finite Difference Schemes for Fourth Order Parabolic Partial Differential Equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sufyan%20Muhammad">Sufyan Muhammad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=central%20finite%20differences" title="central finite differences">central finite differences</a>, <a href="https://publications.waset.org/abstracts/search?q=compact%20schemes" title=" compact schemes"> compact schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernoulli%27s%20equations" title=" Bernoulli's equations"> Bernoulli's equations</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20differences" title=" finite differences"> finite differences</a> </p> <a href="https://publications.waset.org/abstracts/55343/compact-finite-difference-schemes-for-fourth-order-parabolic-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55343.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">288</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14578</span> New High Order Group Iterative Schemes in the Solution of Poisson Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sam%20Teek%20Ling">Sam Teek Ling</a>, <a href="https://publications.waset.org/abstracts/search?q=Norhashidah%20Hj.%20Mohd.%20Ali"> Norhashidah Hj. Mohd. Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=explicit%20group%20iterative%20method" title="explicit group iterative method">explicit group iterative method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference" title=" finite difference"> finite difference</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth%20order%20compact" title=" fourth order compact"> fourth order compact</a>, <a href="https://publications.waset.org/abstracts/search?q=Poisson%20equation" title=" Poisson equation"> Poisson equation</a> </p> <a href="https://publications.waset.org/abstracts/1329/new-high-order-group-iterative-schemes-in-the-solution-of-poisson-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1329.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">432</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">14577</span> New Fourth Order Explicit Group Method in the Solution of the Helmholtz Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Norhashidah%20Hj%20Mohd%20Ali">Norhashidah Hj Mohd Ali</a>, <a href="https://publications.waset.org/abstracts/search?q=Teng%20Wai%20Ping"> Teng Wai Ping</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=explicit%20group%20method" title="explicit group method">explicit group method</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference" title=" finite difference"> finite difference</a>, <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title=" Helmholtz equation"> Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=five-point%20formula" title=" five-point formula"> five-point formula</a>, <a href="https://publications.waset.org/abstracts/search?q=nine-point%20formula" title=" nine-point formula"> nine-point formula</a> </p> <a href="https://publications.waset.org/abstracts/17278/new-fourth-order-explicit-group-method-in-the-solution-of-the-helmholtz-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17278.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">500</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">14576</span> Optimization of Fourth Order Discrete-Approximation Inclusions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elimhan%20N.%20Mahmudov">Elimhan N. Mahmudov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=difference" title="difference">difference</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth" title=" fourth"> fourth</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation" title=" approximation"> approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=transversality" title=" transversality"> transversality</a> </p> <a href="https://publications.waset.org/abstracts/25199/optimization-of-fourth-order-discrete-approximation-inclusions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25199.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">374</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">14575</span> An Optimal and Efficient Family of Fourth-Order Methods for Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Parshanth%20Maroju">Parshanth Maroju</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramandeep%20Behl"> Ramandeep Behl</a>, <a href="https://publications.waset.org/abstracts/search?q=Sandile%20S.%20Motsa"> Sandile S. Motsa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=basins%20of%20attraction" title="basins of attraction">basins of attraction</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20equations" title=" nonlinear equations"> nonlinear equations</a>, <a href="https://publications.waset.org/abstracts/search?q=simple%20roots" title=" simple roots"> simple roots</a>, <a href="https://publications.waset.org/abstracts/search?q=Newton%27s%20method" title=" Newton's method"> Newton's method</a> </p> <a href="https://publications.waset.org/abstracts/57597/an-optimal-and-efficient-family-of-fourth-order-methods-for-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57597.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">312</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">14574</span> Study on a Family of Optimal Fourth-Order Multiple-Root Solver</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Young%20Hee%20Geum">Young Hee Geum</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=basin%20of%20attraction" title="basin of attraction">basin of attraction</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugacy" title=" conjugacy"> conjugacy</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth-order" title=" fourth-order"> fourth-order</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple-root%20finder" title=" multiple-root finder"> multiple-root finder</a> </p> <a href="https://publications.waset.org/abstracts/74099/study-on-a-family-of-optimal-fourth-order-multiple-root-solver" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74099.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">14573</span> Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reza%20Mohammadi">Reza Mohammadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdieh%20Sahebi"> Mahdieh Sahebi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourth-order%20parabolic%20equation" title="fourth-order parabolic equation">fourth-order parabolic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient" title=" variable coefficient"> variable coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20quintic%20spline" title=" polynomial quintic spline"> polynomial quintic spline</a>, <a href="https://publications.waset.org/abstracts/search?q=off-step%20points" title=" off-step points"> off-step points</a> </p> <a href="https://publications.waset.org/abstracts/51758/quintic-spline-solution-of-fourth-order-parabolic-equations-arising-in-beam-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51758.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">352</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">14572</span> Quintic Spline Method for Variable Coefficient Fourth-Order Parabolic Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reza%20Mohammadi">Reza Mohammadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdieh%20Sahebi"> Mahdieh Sahebi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourth-order%20parabolic%20equation" title="fourth-order parabolic equation">fourth-order parabolic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient" title=" variable coefficient"> variable coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20quintic%20spline" title=" polynomial quintic spline"> polynomial quintic spline</a>, <a href="https://publications.waset.org/abstracts/search?q=off-step%20points" title=" off-step points"> off-step points</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20analysis" title=" stability analysis"> stability analysis</a> </p> <a href="https://publications.waset.org/abstracts/47781/quintic-spline-method-for-variable-coefficient-fourth-order-parabolic-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47781.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">366</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">14571</span> A Hybrid Block Multistep Method for Direct Numerical Integration of Fourth Order Initial Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adamu%20S.%20Salawu">Adamu S. Salawu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ibrahim%20O.%20Isah"> Ibrahim O. Isah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomial" title="Chebyshev polynomial">Chebyshev polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20multistep%20method" title=" hybrid multistep method"> hybrid multistep method</a>, <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problems" title=" initial value problems"> initial value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a> </p> <a href="https://publications.waset.org/abstracts/113723/a-hybrid-block-multistep-method-for-direct-numerical-integration-of-fourth-order-initial-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113723.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">122</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14570</span> On the Fourth-Order Hybrid Beta Polynomial Kernels in Kernel Density Estimation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benson%20Ade%20Eniola%20Afere">Benson Ade Eniola Afere</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduces a family of fourth-order hybrid beta polynomial kernels developed for statistical analysis. The assessment of these kernels' performance centers on two critical metrics: asymptotic mean integrated squared error (AMISE) and kernel efficiency. Through the utilization of both simulated and real-world datasets, a comprehensive evaluation was conducted, facilitating a thorough comparison with conventional fourth-order polynomial kernels. The evaluation procedure encompassed the computation of AMISE and efficiency values for both the proposed hybrid kernels and the established classical kernels. The consistently observed trend was the superior performance of the hybrid kernels when compared to their classical counterparts. This trend persisted across diverse datasets, underscoring the resilience and efficacy of the hybrid approach. By leveraging these performance metrics and conducting evaluations on both simulated and real-world data, this study furnishes compelling evidence in favour of the superiority of the proposed hybrid beta polynomial kernels. The discernible enhancement in performance, as indicated by lower AMISE values and higher efficiency scores, strongly suggests that the proposed kernels offer heightened suitability for statistical analysis tasks when compared to traditional kernels. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=AMISE" title="AMISE">AMISE</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth-order%20Kernels" title=" fourth-order Kernels"> fourth-order Kernels</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20Kernels" title=" hybrid Kernels"> hybrid Kernels</a>, <a href="https://publications.waset.org/abstracts/search?q=Kernel%20density%20estimation" title=" Kernel density estimation"> Kernel density estimation</a> </p> <a href="https://publications.waset.org/abstracts/171464/on-the-fourth-order-hybrid-beta-polynomial-kernels-in-kernel-density-estimation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171464.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">70</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14569</span> Implicit Off-Grid Block Method for Solving Fourth and Fifth Order Ordinary Differential Equations Directly</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Olusola%20Ezekiel%20Abolarin">Olusola Ezekiel Abolarin</a>, <a href="https://publications.waset.org/abstracts/search?q=Gift%20E.%20Noah"> Gift E. Noah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problem" title="initial value problem">initial value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equation" title=" ordinary differential equation"> ordinary differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=implicit%20off-grid%20block%20method" title=" implicit off-grid block method"> implicit off-grid block method</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a> </p> <a href="https://publications.waset.org/abstracts/171485/implicit-off-grid-block-method-for-solving-fourth-and-fifth-order-ordinary-differential-equations-directly" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171485.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">84</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">14568</span> Wavelet Method for Numerical Solution of Fourth Order Wave Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20H.%20Choudhury">A. H. Choudhury</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hyperbolic%20problem" title="hyperbolic problem">hyperbolic problem</a>, <a href="https://publications.waset.org/abstracts/search?q=semidiscrete%20approximations" title=" semidiscrete approximations"> semidiscrete approximations</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=Wavelet-Galerkin%20Method" title=" Wavelet-Galerkin Method"> Wavelet-Galerkin Method</a> </p> <a href="https://publications.waset.org/abstracts/76873/wavelet-method-for-numerical-solution-of-fourth-order-wave-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76873.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">315</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">14567</span> Under the ‘Fourth World’: A Discussion to the Transformation of Character-Settings in Chinese Ethnic Minority Films</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sicheng%20Liu">Sicheng Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Based on the key issue of the current fourth world studies, the article aims to analyze the features of character-settings in Chinese ethnic minority films. As a generalizable transformation, this feature progresses from a microcosmic representation. It argues that, as the mediation, films note down the current state of people and their surroundings, while the ‘fourth world’ theorization (or the fourth cinema) provides a new perspective to ethnic minority topics in China. Like the ‘fourth cinema’ focusing on the depiction of indigeneity groups, the ethnic minority films portrait the non-Han nationalities in China. Both types possess the motif of returning history-writing to the minority members’ own hand. In this article, the discussion entirely involves three types of cinematic role-settings in Chinese minority themed films, which illustrates that, similar to the creative principle of the fourth film, the themes and narratives of these films are becoming more individualized, with more concern to minority grassroots. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%27fourth%20world%27" title="'fourth world'">'fourth world'</a>, <a href="https://publications.waset.org/abstracts/search?q=Chinese%20ethnic%20minority%20films" title=" Chinese ethnic minority films"> Chinese ethnic minority films</a>, <a href="https://publications.waset.org/abstracts/search?q=ethnicity%20and%20culture%20reflection" title=" ethnicity and culture reflection"> ethnicity and culture reflection</a>, <a href="https://publications.waset.org/abstracts/search?q=%27mother%20tongue%27%20%28muyu%29" title=" 'mother tongue' (muyu)"> 'mother tongue' (muyu)</a>, <a href="https://publications.waset.org/abstracts/search?q=highlighting%20to%20individual%20spiritual" title=" highlighting to individual spiritual "> highlighting to individual spiritual </a> </p> <a href="https://publications.waset.org/abstracts/110904/under-the-fourth-world-a-discussion-to-the-transformation-of-character-settings-in-chinese-ethnic-minority-films" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110904.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">187</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">14566</span> Design Optimization of a Compact Quadrupole Electromagnet for CLS 2.0</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Md.%20Armin%20Islam">Md. Armin Islam</a>, <a href="https://publications.waset.org/abstracts/search?q=Les%20Dallin"> Les Dallin</a>, <a href="https://publications.waset.org/abstracts/search?q=Mark%20Boland"> Mark Boland</a>, <a href="https://publications.waset.org/abstracts/search?q=W.%20J.%20Zhang"> W. J. Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper reports a study on the optimal magnetic design of a compact quadrupole electromagnet for the Canadian Light Source (CLS 2.0). The nature of the design is to determine a quadrupole with low relative higher order harmonics and better field quality. The design problem was formulated as an optimization model, in which the objective function is the higher order harmonics (multipole errors) and the variable to be optimized is the material distribution on the pole. The higher order harmonics arose in the quadrupole due to truncating the ideal hyperbola at a certain point to make the pole. In this project, the arisen harmonics have been optimized both transversely and longitudinally by adjusting material on the poles in a controlled way. For optimization, finite element analysis (FEA) has been conducted. A better higher order harmonics amplitudes and field quality have been achieved through the optimization. On the basis of the optimized magnetic design, electrical and cooling calculation has been performed for the magnet. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=drift" title="drift">drift</a>, <a href="https://publications.waset.org/abstracts/search?q=electrical" title=" electrical"> electrical</a>, <a href="https://publications.waset.org/abstracts/search?q=and%20cooling%20calculation" title=" and cooling calculation"> and cooling calculation</a>, <a href="https://publications.waset.org/abstracts/search?q=integrated%20field" title=" integrated field"> integrated field</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetic%20field%20gradient" title=" magnetic field gradient"> magnetic field gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=multipole%20errors" title=" multipole errors"> multipole errors</a>, <a href="https://publications.waset.org/abstracts/search?q=quadrupole" title=" quadrupole"> quadrupole</a> </p> <a href="https://publications.waset.org/abstracts/106773/design-optimization-of-a-compact-quadrupole-electromagnet-for-cls-20" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/106773.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">143</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">14565</span> Dual Band Antenna Design with Compact Radiator for 2.5/5.2/5.8 Ghz Wlan Application Using Genetic Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramnath%20Narhete">Ramnath Narhete</a>, <a href="https://publications.waset.org/abstracts/search?q=Saket%20Pandey"> Saket Pandey</a>, <a href="https://publications.waset.org/abstracts/search?q=Puran%20Gour"> Puran Gour</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents of dual-band planner antenna with a compact radiator for 2.4/5.2/5.8 proposed by optimizing its resonant frequency, Bandwidth of operation and radiation frequency using the genetic algorithm. The antenna consists L-shaped and E-shaped radiating element to generate two resonant modes for dual band operation. The above techniques have been successfully used in many applications. Dual band antenna with the compact radiator for 2.4/5.2/5.8 GHz WLAN application design and radiator size only width 8mm and a length is 11.3 mm. The antenna can we used for various application in the field of communication. Genetic algorithm will be used to design the antenna and impedance matching network. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title="genetic algorithm">genetic algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=dual-band%20E" title=" dual-band E"> dual-band E</a>, <a href="https://publications.waset.org/abstracts/search?q=dual-band%20L" title=" dual-band L"> dual-band L</a>, <a href="https://publications.waset.org/abstracts/search?q=WLAN" title=" WLAN"> WLAN</a>, <a href="https://publications.waset.org/abstracts/search?q=compact%20radiator" title=" compact radiator"> compact radiator</a> </p> <a href="https://publications.waset.org/abstracts/28512/dual-band-antenna-design-with-compact-radiator-for-255258-ghz-wlan-application-using-genetic-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28512.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">579</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">14564</span> Impact of Lifestyle and User Expectations on the Demand of Compact Living Spaces in the Home Interiors in Indian Cities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Velly%20Kapadia">Velly Kapadia</a>, <a href="https://publications.waset.org/abstracts/search?q=Reenu%20Singh"> Reenu Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This report identifies the long-term driving forces behind urbanization and the impact of compact living on both society and the home and proposes a concept to create smarter and more sustainable homes. Compact living has been trending across India as a sustainable housing solution, and the reality is that India is currently facing a housing shortage in urban areas of around 10 million units. With the rising demand for housing, urban land prices have been rising and the cost of homes. The paper explores how and why the interior design of the homes can be improved to relieve the housing demand in an environmentally, socially and economically sustainable manner. A questionnaire survey was conducted to determine living patterns, area requirements, ecological footprints, energy consumption, purchasing patterns, and various pro-environmental behaviors of people who downsize to compact homes. Quantitative research explores sustainable material choices, durability, functionality, cost, and reusability of furniture. Besides addressing the need for smart and sustainable designed compact homes, a conceptual model is proposed, including options of ideal schematic layouts for homes in urban areas. In the conclusions, suggestions to improve space planning and suitable interior entities have been made to support the fact that compact homes are an eminently practical and sensible solution for the urban citizen. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compact%20living" title="compact living">compact living</a>, <a href="https://publications.waset.org/abstracts/search?q=housing%20shortage" title=" housing shortage"> housing shortage</a>, <a href="https://publications.waset.org/abstracts/search?q=lifestyle" title=" lifestyle"> lifestyle</a>, <a href="https://publications.waset.org/abstracts/search?q=sustainable%20interior%20design" title=" sustainable interior design"> sustainable interior design</a> </p> <a href="https://publications.waset.org/abstracts/135070/impact-of-lifestyle-and-user-expectations-on-the-demand-of-compact-living-spaces-in-the-home-interiors-in-indian-cities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/135070.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">202</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">14563</span> Design of a Rectifier with Enhanced Efficiency and a High-gain Antenna for Integrated and Compact-size Rectenna Circuit</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rawaa%20Maher">Rawaa Maher</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Allam"> Ahmed Allam</a>, <a href="https://publications.waset.org/abstracts/search?q=Haruichi%20Kanaya"> Haruichi Kanaya</a>, <a href="https://publications.waset.org/abstracts/search?q=Adel%20B.%20Abdelrahman"> Adel B. Abdelrahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a compact, high-efficiency integrated rectenna is presented to operate in the 2.45 GHz band. A comparison between two rectifier topologies is performed to verify the benefits of removing the matching network from the rectifier. A rectifier high conversion efficiency of 74.1% is achieved. To complete the rectenna system, a novel omnidirectional antenna with high gain (3.72 dB) and compact size (25 mm * 29 mm) is designed and fabricated. The same antenna is used with a reflector for raising the gain to nearly 8.3 dB. The simulation and measurement results of the antenna are in good agreement. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=internet%20of%20things" title="internet of things">internet of things</a>, <a href="https://publications.waset.org/abstracts/search?q=integrated%20rectenna" title=" integrated rectenna"> integrated rectenna</a>, <a href="https://publications.waset.org/abstracts/search?q=rectenna" title=" rectenna"> rectenna</a>, <a href="https://publications.waset.org/abstracts/search?q=RF%20energy%20harvesting" title=" RF energy harvesting"> RF energy harvesting</a>, <a href="https://publications.waset.org/abstracts/search?q=wireless%20sensor%20networks%28WSN%29" title=" wireless sensor networks(WSN)"> wireless sensor networks(WSN)</a> </p> <a href="https://publications.waset.org/abstracts/146075/design-of-a-rectifier-with-enhanced-efficiency-and-a-high-gain-antenna-for-integrated-and-compact-size-rectenna-circuit" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146075.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">182</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">14562</span> Impact of the Fourth Industrial Revolution on Food Security in South Africa</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fiyinfoluwa%20Giwa">Fiyinfoluwa Giwa</a>, <a href="https://publications.waset.org/abstracts/search?q=Nicholas%20Ngepah"> Nicholas Ngepah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper investigates the relationship between the Fourth Industrial Revolution and food security in South Africa. The Ordinary Least Square was adopted from 2012 Q1 to 2021 Q4. The study used artificial intelligence investment and the food production index as the measure for the fourth industrial revolution and food security, respectively. Findings reveal a significant and positive coefficient of 0.2887, signifying a robust statistical relationship between AI adoption and the food production index. As a policy recommendation, this paper recommends the introduction of incentives for farmers and agricultural enterprises to adopt AI technologies -and the expansion of digital connectivity and access to technology in rural areas. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fourth%20Industrial%20Revolution" title="Fourth Industrial Revolution">Fourth Industrial Revolution</a>, <a href="https://publications.waset.org/abstracts/search?q=food%20security" title=" food security"> food security</a>, <a href="https://publications.waset.org/abstracts/search?q=artificial%20intelligence%20investment" title=" artificial intelligence investment"> artificial intelligence investment</a>, <a href="https://publications.waset.org/abstracts/search?q=food%20production%20index" title=" food production index"> food production index</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20least%20square" title=" ordinary least square"> ordinary least square</a> </p> <a href="https://publications.waset.org/abstracts/171855/impact-of-the-fourth-industrial-revolution-on-food-security-in-south-africa" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171855.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">75</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">14561</span> An Implicit High Order Difference Scheme for the Solution of 1D Pennes Bio-Heat Transfer Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Swarn%20Singh">Swarn Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Suruchi%20Singh"> Suruchi Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme. In this paper we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convergence" title="convergence">convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20scheme" title=" finite difference scheme"> finite difference scheme</a>, <a href="https://publications.waset.org/abstracts/search?q=Pennes%20bio-heat%20equation" title=" Pennes bio-heat equation"> Pennes bio-heat equation</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability "> stability </a> </p> <a href="https://publications.waset.org/abstracts/22704/an-implicit-high-order-difference-scheme-for-the-solution-of-1d-pennes-bio-heat-transfer-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22704.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">471</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">14560</span> A Compact Wearable Slot Antenna for LTE and WLAN Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haider%20K.%20Raad">Haider K. Raad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a compact wide-band, ultra-thin and flexible slot antenna intended for wearable applications is presented. The presented antenna is designed to provide Wireless Local Area Network (WLAN) and Long Term Evolution (LTE) connectivity. The presented design exhibits a relatively wide bandwidth (1600-3500 MHz below -6 dB impedance bandwidth limit). The antenna is positioned on a 33 mm x 30 mm flexible substrate with a thickness of 50 µm. Antenna properties, such as the far-field radiation patterns, scattering parameter <em>S</em><sub>11</sub> are provided. The presented compact, thin and flexible design along with excellent radiation characteristics are deemed suitable for integration into flexible and wearable devices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=wearable%20electronics" title="wearable electronics">wearable electronics</a>, <a href="https://publications.waset.org/abstracts/search?q=slot%20Antenna" title=" slot Antenna"> slot Antenna</a>, <a href="https://publications.waset.org/abstracts/search?q=LTE" title=" LTE"> LTE</a>, <a href="https://publications.waset.org/abstracts/search?q=WLAN" title=" WLAN"> WLAN</a> </p> <a href="https://publications.waset.org/abstracts/56808/a-compact-wearable-slot-antenna-for-lte-and-wlan-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56808.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">234</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14559</span> System Analysis on Compact Heat Storage in the Built Environment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wilko%20Planje">Wilko Planje</a>, <a href="https://publications.waset.org/abstracts/search?q=Remco%20Poll%C3%A9"> Remco Pollé</a>, <a href="https://publications.waset.org/abstracts/search?q=Frank%20van%20Buuren"> Frank van Buuren</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An increased share of renewable energy sources in the built environment implies the usage of energy buffers to match supply and demand and to prevent overloads of existing grids. Compact heat storage systems based on thermochemical materials (TCM) are promising to be incorporated in future installations as an alternative for regular thermal buffers. This is due to the high energy density (1 – 2 GJ/m3). In order to determine the feasibility of TCM-based systems on building level several installation configurations are simulated and analyzed for different mixes of renewable energy sources (solar thermal, PV, wind, underground, air) for apartments/multistore-buildings for the Dutch situation. Thereby capacity, volume and financial costs are calculated. The simulation consists of options to include the current and future wind power (sea and land) and local roof-attached PV or solar-thermal systems. Thereby, the compact thermal buffer and optionally an electric battery (typically 10 kWhe) form the local storage elements for energy matching and shaving purposes. Besides, electric-driven heat pumps (air / ground) can be included for efficient heat generation in case of power-to-heat. The total local installation provides both space heating, domestic hot water as well as electricity for a specific case with low-energy apartments (annually 9 GJth + 8 GJe) in the year 2025. The energy balance is completed with grid-supplied non-renewable electricity. Taking into account the grid capacities (permanent 1 kWe/household), spatial requirements for the thermal buffer (< 2.5 m3/household) and a desired minimum of 90% share of renewable energy per household on the total consumption the wind-powered scenario results in acceptable sizes of compact thermal buffers with an energy-capacity of 4 - 5 GJth per household. This buffer is combined with a 10 kWhe battery and air source heat pump system. Compact thermal buffers of less than 1 GJ (typically volumes 0.5 - 1 m3) are possible when the installed wind-power is increased with a factor 5. In case of 15-fold of installed wind power compact heat storage devices compete with 1000 L water buffers. The conclusion is that compact heat storage systems can be of interest in the coming decades in combination with well-retrofitted low energy residences based on the current trends of installed renewable energy power. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compact%20thermal%20storage" title="compact thermal storage">compact thermal storage</a>, <a href="https://publications.waset.org/abstracts/search?q=thermochemical%20material" title=" thermochemical material"> thermochemical material</a>, <a href="https://publications.waset.org/abstracts/search?q=built%20environment" title=" built environment"> built environment</a>, <a href="https://publications.waset.org/abstracts/search?q=renewable%20energy" title=" renewable energy"> renewable energy</a> </p> <a href="https://publications.waset.org/abstracts/91128/system-analysis-on-compact-heat-storage-in-the-built-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91128.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">244</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">14558</span> Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Triki">H. Triki</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Hamaizi"> Y. Hamaizi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20El-Akrmi"> A. El-Akrmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schr%C3%B6dinger%20equation" title="nonlinear Schrödinger equation">nonlinear Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=high-order%20effects" title=" high-order effects"> high-order effects</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20solution" title=" soliton solution"> soliton solution</a> </p> <a href="https://publications.waset.org/abstracts/11564/soliton-solutions-of-the-higher-order-nonlinear-schrodinger-equation-with-dispersion-effects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11564.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">635</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">14557</span> Compact Settlement: The Direction of Chinese Future Urban Residential Area Sustainable Development</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yajing%20Jiang">Yajing Jiang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jing%20Wu"> Jing Wu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Residential area construction links many problems such as population resources, ecology, social values, public services and transportation in the city. After Chinese housing reform, a large number of residential area development accompanied by the loss of agricultural and ecological land. To explore the future of Chinese urban residential area, this article concentrates on how the 'Compact Settlement' behaves in improving the living environment and saving the resources. Through the research of residential area in Hangzhou, there are some determines that increasing the development intensity of the area can indeed bring some improvement in the overall environment. In conclusion, possible design alternatives are discussed for leading Chinese urban development towards a more sustainable path. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=compact%20city%20development" title="compact city development">compact city development</a>, <a href="https://publications.waset.org/abstracts/search?q=environmental%20sustainability" title=" environmental sustainability"> environmental sustainability</a>, <a href="https://publications.waset.org/abstracts/search?q=residential%20area" title=" residential area"> residential area</a>, <a href="https://publications.waset.org/abstracts/search?q=Hangzhou" title=" Hangzhou"> Hangzhou</a> </p> <a href="https://publications.waset.org/abstracts/72634/compact-settlement-the-direction-of-chinese-future-urban-residential-area-sustainable-development" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72634.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">316</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">14556</span> Indian Business-Papers in Industrial Revolution 4.0: A Paradigm Shift</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Disha%20Batra">Disha Batra</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Industrial Revolution 4.0 is quite different, and a paradigm shift is underway in the media industry. With the advent of automated journalism and social media platforms, newspaper organizations have changed the way news was gathered and reported. The emergence of the fourth industrial revolution in the early 21st century has made the newspapers to adapt the changing technologies to remain relevant. This paper investigates the content of Indian business-papers in the era of the fourth industrial revolution and how these organizations have emerged in the time of convergence. The study is the content analyses of the top three Indian business dailies as per IRS (Indian Readership Survey) 2017 over a decade. The parametric analysis of the different parameters (source of information, use of illustrations, advertisements, layout, and framing, etc.) have been done in order to come across with the distinct adaptations and modifications by these dailies. The paper significantly dwells upon the thematic analysis of these newspapers in order to explore and find out the coverage given to various sub-themes of EBF (economic, business, and financial) journalism. Further, this study reveals the effect of high-speed algorithm-based trading, the aftermath of the fourth industrial revolution on the creative and investigative aspect of delivering financial stories by these respective newspapers. The study indicates a change heading towards an ongoing paradigm shift in the business newspaper industry with an adequate change in the source of information gathering along with the subtle increase in the coverage of financial news stories over the time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=business-papers" title="business-papers">business-papers</a>, <a href="https://publications.waset.org/abstracts/search?q=business%20news" title=" business news"> business news</a>, <a href="https://publications.waset.org/abstracts/search?q=financial%20news" title=" financial news"> financial news</a>, <a href="https://publications.waset.org/abstracts/search?q=industrial%20revolution%204.0." title=" industrial revolution 4.0."> industrial revolution 4.0.</a> </p> <a href="https://publications.waset.org/abstracts/112299/indian-business-papers-in-industrial-revolution-40-a-paradigm-shift" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/112299.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">115</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">14555</span> Hyperelastic Formulation for Orthotropic Materials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Daniel%20O%27Shea">Daniel O'Shea</a>, <a href="https://publications.waset.org/abstracts/search?q=Mario%20M.%20Attard"> Mario M. Attard</a>, <a href="https://publications.waset.org/abstracts/search?q=David%20C.%20Kellermann"> David C. Kellermann</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a hyperelastic strain energy function that maps isotopic hyperelastic constitutive laws for the use of orthotropic materials without the use of structural tensors or any kind of fiber vector, or the use of standard invariants. In particular, we focus on neo-Hookean class of models and represent them using an invariant-free formulation. To achieve this, we revise the invariant-free formulation of isotropic hyperelasticity. The formulation uses quadruple contractions between fourth-order tensors, rather than scalar products of scalar invariants. We also propose a new decomposition of the orthotropic Hookean stiffness tensor into two fourth-order Lamé tensors that collapse down to the classic Lamé parameters for isotropic continua. The resulting orthotropic hyperelastic model naturally maintains all of the advanced properties of the isotropic counterparts, and similarly collapse back down to their isotropic form by nothing more than equality of parameters in all directions (isotropy). Comparisons are made with large strain experimental results for transversely isotropic rubber type materials under tension. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20strain" title="finite strain">finite strain</a>, <a href="https://publications.waset.org/abstracts/search?q=hyperelastic" title=" hyperelastic"> hyperelastic</a>, <a href="https://publications.waset.org/abstracts/search?q=invariants" title=" invariants"> invariants</a>, <a href="https://publications.waset.org/abstracts/search?q=orthotropic" title=" orthotropic"> orthotropic</a> </p> <a href="https://publications.waset.org/abstracts/79452/hyperelastic-formulation-for-orthotropic-materials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79452.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">446</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">14554</span> A Novel Design of Inset Feed Patch Antenna for Ultra Wide Band Application </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Priyanka%20Aggarwal">Priyanka Aggarwal</a>, <a href="https://publications.waset.org/abstracts/search?q=Priyanka%20Mangla"> Priyanka Mangla</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work has focused on the aspect of UWB antenna design, which is very suitable for portable UWB applications. The design of new UWB antenna faces some challenges. The antenna should be compact, preferably conformal, and low cost for manufacture, and have good electrical performance, such as good matching, directional radiation performance over a wide band, good time response, etc. Keeping these goals in mind a compact and directional compact open-slot antenna was built. The antenna radiating structure is in the form of two exponentially tapered arms that lie on the opposite sides of the substrate. The antenna operates over the frequency band from 2.95 GHz to more than 12.1 GHz. It exhibits a directive radiation performance with a peak gain which is between 5.4 dBi and 8.3 dBi in the specified band. The antenna has linear phase response over the entire UWB frequency range and hence constant group delay which is vital for transmission and reception of sub-nanosecond pulses. Due to its planar profile, physically compact size, wide impedance bandwidth, directive performance over a wide bandwidth proposed antenna is a good candidate for portable UWB applications and other UWB integrated circuits. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inset%20feed%20patch%20antenna" title="inset feed patch antenna">inset feed patch antenna</a>, <a href="https://publications.waset.org/abstracts/search?q=ultra%20wide%20band" title=" ultra wide band"> ultra wide band</a>, <a href="https://publications.waset.org/abstracts/search?q=radiation%20performance" title=" radiation performance"> radiation performance</a>, <a href="https://publications.waset.org/abstracts/search?q=geometry" title=" geometry"> geometry</a>, <a href="https://publications.waset.org/abstracts/search?q=antenna" title=" antenna"> antenna</a> </p> <a href="https://publications.waset.org/abstracts/33469/a-novel-design-of-inset-feed-patch-antenna-for-ultra-wide-band-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33469.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">437</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">14553</span> Comparing Numerical Accuracy of Solutions of Ordinary Differential Equations (ODE) Using Taylor's Series Method, Euler's Method and Runge-Kutta (RK) Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Palwinder%20Singh">Palwinder Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Munish%20Sandhir"> Munish Sandhir</a>, <a href="https://publications.waset.org/abstracts/search?q=Tejinder%20Singh"> Tejinder Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ordinary%20differential%20equations%20%28ODE%29" title="Ordinary differential equations (ODE)">Ordinary differential equations (ODE)</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%E2%80%99s%20Series%20Method" title=" Taylor’s Series Method"> Taylor’s Series Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler%E2%80%99s%20Method" title=" Euler’s Method"> Euler’s Method</a>, <a href="https://publications.waset.org/abstracts/search?q=Runge-Kutta%20Fourth%20Order%20Method" title=" Runge-Kutta Fourth Order Method"> Runge-Kutta Fourth Order Method</a> </p> <a href="https://publications.waset.org/abstracts/56685/comparing-numerical-accuracy-of-solutions-of-ordinary-differential-equations-ode-using-taylors-series-method-eulers-method-and-runge-kutta-rk-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56685.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">358</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">14552</span> Voltage Controlled Ring Oscillator for RF Applications in 0.18 µm CMOS Technology</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Arif%20Sobhan%20Bhuiyan">Mohammad Arif Sobhan Bhuiyan</a>, <a href="https://publications.waset.org/abstracts/search?q=Zainal%20Abidin%20Nordin"> Zainal Abidin Nordin</a>, <a href="https://publications.waset.org/abstracts/search?q=Mamun%20Bin%20Ibne%20Reaz"> Mamun Bin Ibne Reaz</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A compact and power efficient high performance Voltage Controlled Oscillator (VCO) is a must in analog and digital circuits especially in the communication system, but the best trade-off among the performance parameters is a challenge for researchers. In this paper, a design of a compact 3-stage differential voltage controlled ring oscillator (VCRO) with low phase noise, low power and higher tuning bandwidth is proposed in 0.18 µm CMOS technology. The VCRO is designed with symmetric load and positive feedback techniques to achieve higher gain and minimum delay. The proposed VCRO can operate at tuning range of 3.9-5.0 GHz at 1.6 V supply voltage. The circuit consumes only 1.0757 mW of power and produces -129 dbc/Hz. The total active area of the proposed VCRO is only 11.74 x 37.73 µm2. Such a VCO can be the best choice for compact and low-power RF applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CMOS" title="CMOS">CMOS</a>, <a href="https://publications.waset.org/abstracts/search?q=VCO" title=" VCO"> VCO</a>, <a href="https://publications.waset.org/abstracts/search?q=VCRO" title=" VCRO"> VCRO</a>, <a href="https://publications.waset.org/abstracts/search?q=oscillator" title=" oscillator"> oscillator</a> </p> <a href="https://publications.waset.org/abstracts/2797/voltage-controlled-ring-oscillator-for-rf-applications-in-018-m-cmos-technology" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2797.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">474</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">14551</span> Salinity Effects on Germination of Malaysian Rice Varieties and Weedy Rice Biotypes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Kamal%20Uddin">M. Kamal Uddin</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Mohd%20Dandan"> H. Mohd Dandan</a>, <a href="https://publications.waset.org/abstracts/search?q=Ame%20H.%20Alidin"> Ame H. Alidin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Germination and seedling growth of plant species are reduced in saline due to an external osmotic potential. An experiment was conducted at the laboratory, Faculty of Sustainable Agriculture, Universiti Malaysia Sabah, to compare the salt effect on seed germination and growth of weedy rice and cultivated rice. Seeds (10 in each) were placed in petri dishes. Five salinity levels 0 (distilled water), 4, 8, 12 and 16 dSm-1 (NaCl) were applied. The number of germinated seeds was recorded daily. The final germination percentage, germination index (GI), seedling vigour index (SVI) mean germination time (MGT), shoot and root dry weight were estimated. At highest salinity (16 dSm-1) germination percentage was higher (100%) in weedy rice awn and weedy rice compact. Lowest germination percentage was in MR219 and TQR-8 (50-60%). Mean germination time (MGT) was found higher in all weedy rice biotypes compared to cultivated rice. At highest salinity (16dSm-1) weedy rice open produced the highest MGT (9.92) followed by weedy rice compact (9.73) while lowest MGT was in MR219 (9.48). At highest salinity (16dSm-1) germination index was higher in weedy rice awn (11.71) and compact type (9.62). Lowest germination index was in MR219 (5.90) and TQR-8 (8.94). At the highest salinity (16 dSm−1), seedling vigor index was highest in weedy rice awn (6.06) followed by weedy rice compact (5.26); while lowest was in MR219 (2.11) followed by MR269 (3.82).On the basis of Germination index, seedling vigor index and growth related results it could be concluded that weedy rice awn, compact and open biotypes were more salt tolerant compared to other cultivated rice MR219, MR269, and TQR-8. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=germination" title="germination">germination</a>, <a href="https://publications.waset.org/abstracts/search?q=salinity" title="salinity">salinity</a>, <a href="https://publications.waset.org/abstracts/search?q=rice%20and%20weedy%20rice" title="rice and weedy rice">rice and weedy rice</a>, <a href="https://publications.waset.org/abstracts/search?q=sustainable%20agriculture" title=" sustainable agriculture"> sustainable agriculture</a> </p> <a href="https://publications.waset.org/abstracts/21509/salinity-effects-on-germination-of-malaysian-rice-varieties-and-weedy-rice-biotypes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21509.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">491</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">14550</span> Urban Compactness and Sustainability: Beijing Experience</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xilu%20Liu">Xilu Liu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ameen%20Farooq"> Ameen Farooq</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Beijing has several compact residential housing settings in many of its urban districts. The study in this paper reveals that urban compactness, as predictor of density, may carry an altogether different meaning in the developing world when compared to the U.S for achieving objectives of urban sustainability. Recent urban design studies in the U.S are debating for compact and mixed-use higher density housing to achieve sustainable and energy efficient living environments. While the concept of urban compactness is widely accepted as an approach in modern architectural and urban design fields, this belief may not directly carry well into all areas within cities of developing countries. Beijing’s technology-driven economy, with its historic and rich cultural heritage and a highly speculated real-estate market, extends its urban boundaries into multiple compact urban settings of varying scales and densities. The accelerated pace of migration from the countryside for better opportunities has led to unsustainable and uncontrolled buildups in order to meet the growing population demand within and outside of the urban center. This unwarranted compactness in certain urban zones has produced an unhealthy physical density with serious environmental and ecological challenging basic living conditions. In addition, crowding, traffic congestion, pollution and limited housing surrounding this compactness is a threat to public health. Several residential blocks in close proximity to each other were found quite compacted, or ill-planned, with residential sites due to lack of proper planning in Beijing. Most of them at first sight appear to be compact and dense but further analytical studies revealed that what appear to be dense actually are not as dense as to make a good case that could serve as the corner stone of sustainability and energy efficiency. This study considered several factors including floor area ratio (FAR), ground coverage (GSI), open space ratio (OSR) as indicators in analyzing urban compactness as a predictor of density. The findings suggest that these measures, influencing the density of residential sites under study, were much smaller in density than expected given their compact adjacencies. Further analysis revealed that several residential housing appear to support the notion of density in its compact layout but are actually compacted due to unregulated planning marred by lack of proper urban design standards, policies and guidelines specific to their urban context and condition. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Beijing" title="Beijing">Beijing</a>, <a href="https://publications.waset.org/abstracts/search?q=density" title=" density"> density</a>, <a href="https://publications.waset.org/abstracts/search?q=sustainability" title=" sustainability"> sustainability</a>, <a href="https://publications.waset.org/abstracts/search?q=urban%20compactness" title=" urban compactness"> urban compactness</a> </p> <a href="https://publications.waset.org/abstracts/35397/urban-compactness-and-sustainability-beijing-experience" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35397.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">424</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourth%20order%20compact&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourth%20order%20compact&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourth%20order%20compact&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourth%20order%20compact&page=5">5</a></li> <li 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