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equation</title> <meta name="description" content="Search results for: Lagrange equation"> <meta name="keywords" content="Lagrange equation"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1136</span> Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Watcharakorn%20Thongchuay">Watcharakorn Thongchuay</a>, <a href="https://publications.waset.org/search?q=Puntip%20Toghaw"> Puntip Toghaw</a>, <a href="https://publications.waset.org/search?q=Montri%20Maleewong"> Montri Maleewong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Wavelet-Galerkin finite element method for solving the one-dimensional heat equation is presented in this work. Two types of basis functions which are the Lagrange and multi-level wavelet bases are employed to derive the full form of matrix system. We consider both linear and quadratic bases in the Galerkin method. Time derivative is approximated by polynomial time basis that provides easily extend the order of approximation in time space. Our numerical results show that the rate of convergences for the linear Lagrange and the linear wavelet bases are the same and in order 2 while the rate of convergences for the quadratic Lagrange and the quadratic wavelet bases are approximately in order 4. It also reveals that the wavelet basis provides an easy treatment to improve numerical resolutions that can be done by increasing just its desired levels in the multilevel construction process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Galerkin%20finite%20element%20method" title="Galerkin finite element method">Galerkin finite element method</a>, <a href="https://publications.waset.org/search?q=Heat%20equation" title=" Heat equation "> Heat equation </a>, <a href="https://publications.waset.org/search?q=Lagrange%20basis%20function" title=" Lagrange basis function"> Lagrange basis function</a>, <a href="https://publications.waset.org/search?q=Wavelet%20basis%20function." title=" Wavelet basis function."> Wavelet basis function.</a> </p> <a href="https://publications.waset.org/7279/lagrange-and-multilevel-wavelet-galerkin-with-polynomial-time-basis-for-heat-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7279/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7279/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7279/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7279/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7279/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7279/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7279/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7279/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7279/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7279/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7279.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">1729</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1135</span> Lagrange-s Inversion Theorem and Infiltration</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Pushpa%20N.%20Rathie">Pushpa N. Rathie</a>, <a href="https://publications.waset.org/search?q=Prabhata%20K.%20Swamee"> Prabhata K. Swamee</a>, <a href="https://publications.waset.org/search?q=Andr%C3%A9%20L.%20B.%20Cavalcante"> André L. B. Cavalcante</a>, <a href="https://publications.waset.org/search?q=Luan%20Carlos%20de%20S.%20M.%20Ozelim"> Luan Carlos de S. M. Ozelim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Green-Ampt%20Equation" title="Green-Ampt Equation">Green-Ampt Equation</a>, <a href="https://publications.waset.org/search?q=Lagrange%27s%20Inversion%0D%0ATheorem" title=" Lagrange's Inversion Theorem"> Lagrange's Inversion Theorem</a>, <a href="https://publications.waset.org/search?q=Talsma-Parlange%20Equation" title=" Talsma-Parlange Equation"> Talsma-Parlange Equation</a>, <a href="https://publications.waset.org/search?q=Three-Parameter%20Infiltration%0D%0AEquation" title=" Three-Parameter Infiltration Equation"> Three-Parameter Infiltration Equation</a> </p> <a href="https://publications.waset.org/9410/lagrange-s-inversion-theorem-and-infiltration" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9410/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9410/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9410/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9410/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9410/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9410/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9410/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9410/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9410/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9410/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9410.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">1888</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1134</span> Element-Independent Implementation for Method of Lagrange Multipliers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Gil-Eon%20Jeong">Gil-Eon Jeong</a>, <a href="https://publications.waset.org/search?q=Sung-Kie%20Youn"> Sung-Kie Youn</a>, <a href="https://publications.waset.org/search?q=K.%20C.%20Park"> K. C. Park</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Treatment for the non-matching interface is an important computational issue. To handle this problem, the method of Lagrange multipliers including classical and localized versions are the most popular technique. It essentially imposes the interface compatibility conditions by introducing Lagrange multipliers. However, the numerical system becomes unstable and inefficient due to the Lagrange multipliers. The interface element-independent formulation that does not include the Lagrange multipliers can be obtained by modifying the independent variables mathematically. Through this modification, more efficient and stable system can be achieved while involving equivalent accuracy comparing with the conventional method. A numerical example is conducted to verify the validity of the presented method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Element-independent%20formulation" title="Element-independent formulation">Element-independent formulation</a>, <a href="https://publications.waset.org/search?q=non-matching%20interface" title=" non-matching interface"> non-matching interface</a>, <a href="https://publications.waset.org/search?q=interface%20coupling" title=" interface coupling"> interface coupling</a>, <a href="https://publications.waset.org/search?q=methods%20of%20Lagrange%20multipliers." title=" methods of Lagrange multipliers."> methods of Lagrange multipliers.</a> </p> <a href="https://publications.waset.org/10006394/element-independent-implementation-for-method-of-lagrange-multipliers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006394/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006394/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006394/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006394/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006394/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006394/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006394/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006394/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006394/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006394/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006394.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">1183</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1133</span> Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Taweechai%20Nuntawisuttiwong">Taweechai Nuntawisuttiwong</a>, <a href="https://publications.waset.org/search?q=Natasha%20Dejdumrong"> Natasha Dejdumrong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Newton-Lagrange Interpolations are widely used in numerical analysis. However, it requires a quadratic computational time for their constructions. In computer aided geometric design (CAGD), there are some polynomial curves: Wang-Ball, DP and Dejdumrong curves, which have linear time complexity algorithms. Thus, the computational time for Newton-Lagrange Interpolations can be reduced by applying the algorithms of Wang-Ball, DP and Dejdumrong curves. In order to use Wang-Ball, DP and Dejdumrong algorithms, first, it is necessary to convert Newton-Lagrange polynomials into Wang-Ball, DP or Dejdumrong polynomials. In this work, the algorithms for converting from both uniform and non-uniform Newton-Lagrange polynomials into Wang-Ball, DP and Dejdumrong polynomials are investigated. Thus, the computational time for representing Newton-Lagrange polynomials can be reduced into linear complexity. In addition, the other utilizations of using CAGD curves to modify the Newton-Lagrange curves can be taken. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Newton%20interpolation" title="Newton interpolation">Newton interpolation</a>, <a href="https://publications.waset.org/search?q=Lagrange%20interpolation" title=" Lagrange interpolation"> Lagrange interpolation</a>, <a href="https://publications.waset.org/search?q=linear%0D%0Acomplexity." title=" linear complexity."> linear complexity.</a> </p> <a href="https://publications.waset.org/10010689/fast-and-efficient-algorithms-for-evaluating-uniform-and-nonuniform-lagrange-and-newton-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010689/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010689/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010689/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010689/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010689/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010689/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010689/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010689/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010689/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010689/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010689.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">617</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1132</span> Lagrangian Geometrical Model of the Rheonomic Mechanical Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Camelia%20Frigioiu">Camelia Frigioiu</a>, <a href="https://publications.waset.org/search?q=Katica%20%28Stevanovic%29%20Hedrih"> Katica (Stevanovic) Hedrih</a>, <a href="https://publications.waset.org/search?q=Iulian%20Gabriel%20Birsan"> Iulian Gabriel Birsan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lagrange%27s%20equations" title="Lagrange's equations">Lagrange's equations</a>, <a href="https://publications.waset.org/search?q=mechanical%20system" title=" mechanical system"> mechanical system</a>, <a href="https://publications.waset.org/search?q=non-linear%20connection" title=" non-linear connection"> non-linear connection</a>, <a href="https://publications.waset.org/search?q=rheonomic%20Lagrange%20space." title=" rheonomic Lagrange space."> rheonomic Lagrange space.</a> </p> <a href="https://publications.waset.org/2858/lagrangian-geometrical-model-of-the-rheonomic-mechanical-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/2858/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/2858/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/2858/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/2858/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/2858/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/2858/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/2858/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/2858/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/2858/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/2858/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/2858.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">1677</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1131</span> Quasilinearization–Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Alireza%20Rezaei">Alireza Rezaei</a>, <a href="https://publications.waset.org/search?q=Fatemeh%20Baharifard"> Fatemeh Baharifard</a>, <a href="https://publications.waset.org/search?q=Kourosh%20Parand"> Kourosh Parand</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Quasilinearization%20method" title="Quasilinearization method">Quasilinearization method</a>, <a href="https://publications.waset.org/search?q=Barycentric%20lagrange%20interpolation" title=" Barycentric lagrange interpolation"> Barycentric lagrange interpolation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20ODE" title=" nonlinear ODE"> nonlinear ODE</a>, <a href="https://publications.waset.org/search?q=fin%20problem" title=" fin problem"> fin problem</a>, <a href="https://publications.waset.org/search?q=heat%20transfer." title=" heat transfer."> heat transfer.</a> </p> <a href="https://publications.waset.org/7635/quasilinearization-barycentric-approach-for-numerical-investigation-of-the-boundary-value-fin-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7635/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7635/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7635/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7635/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7635/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7635/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7635/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7635/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7635/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7635/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7635.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">1874</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1130</span> Single Image Defogging Method Using Variational Approach for Edge-Preserving Regularization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Wan-Hyun%20Cho">Wan-Hyun Cho</a>, <a href="https://publications.waset.org/search?q=In-Seop%20Na"> In-Seop Na</a>, <a href="https://publications.waset.org/search?q=Seong-ChaeSeo"> Seong-ChaeSeo</a>, <a href="https://publications.waset.org/search?q=Sang-Kyoon%20Kim"> Sang-Kyoon Kim</a>, <a href="https://publications.waset.org/search?q=Soon-Young%20Park"> Soon-Young Park</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we propose the variational approach to solve single image defogging problem. In the inference process of the atmospheric veil, we defined new functional for atmospheric veil that satisfy edge-preserving regularization property. By using the fundamental lemma of calculus of variations, we derive the Euler-Lagrange equation foratmospheric veil that can find the maxima of a given functional. This equation can be solved by using a gradient decent method and time parameter. Then, we can have obtained the estimated atmospheric veil, and then have conducted the image restoration by using inferred atmospheric veil. Finally we have improved the contrast of restoration image by various histogram equalization methods. The experimental results show that the proposed method achieves rather good defogging results.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Image%20defogging" title="Image defogging">Image defogging</a>, <a href="https://publications.waset.org/search?q=Image%20restoration" title=" Image restoration"> Image restoration</a>, <a href="https://publications.waset.org/search?q=Atmospheric%0D%0Aveil" title=" Atmospheric veil"> Atmospheric veil</a>, <a href="https://publications.waset.org/search?q=Transmission" title=" Transmission"> Transmission</a>, <a href="https://publications.waset.org/search?q=Variational%20approach" title=" Variational approach"> Variational approach</a>, <a href="https://publications.waset.org/search?q=Euler-Lagrange%20equation" title=" Euler-Lagrange equation"> Euler-Lagrange equation</a>, <a href="https://publications.waset.org/search?q=Image%20enhancement." title=" Image enhancement."> Image enhancement.</a> </p> <a href="https://publications.waset.org/11198/single-image-defogging-method-using-variational-approach-for-edge-preserving-regularization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/11198/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/11198/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/11198/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/11198/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/11198/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/11198/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/11198/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/11198/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/11198/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/11198/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/11198.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">2941</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1129</span> On the Integer Solutions of the Pell Equation x2 - dy2 = 2t</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Bet%C3%BCl%20Gezer"> Betül Gezer</a>, <a href="https://publications.waset.org/search?q=Osman%20Bizim"> Osman Bizim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=Diophantine%20equation." title=" Diophantine equation."> Diophantine equation.</a> </p> <a href="https://publications.waset.org/423/on-the-integer-solutions-of-the-pell-equation-x2-dy2-2t" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/423/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/423/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/423/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/423/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/423/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/423/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/423/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/423/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/423/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/423/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/423.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">2387</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1128</span> The Lower and Upper Approximations in a Group</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Zhaohao%20Wang">Zhaohao Wang</a>, <a href="https://publications.waset.org/search?q=Lan%20Shu"> Lan Shu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagranges Theorem.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lower%20approximations" title="Lower approximations">Lower approximations</a>, <a href="https://publications.waset.org/search?q=Upper%20approximations" title=" Upper approximations"> Upper approximations</a>, <a href="https://publications.waset.org/search?q=Rough%20sets" title=" Rough sets"> Rough sets</a>, <a href="https://publications.waset.org/search?q=Rough%20groups" title=" Rough groups"> Rough groups</a>, <a href="https://publications.waset.org/search?q=Lagrange" title=" Lagrange"> Lagrange</a> </p> <a href="https://publications.waset.org/9259/the-lower-and-upper-approximations-in-a-group" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9259/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9259/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9259/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9259/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9259/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9259/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9259/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9259/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9259/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9259/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9259.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">2218</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1127</span> Control of Pendulum on a Cart with State Dependent Riccati Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=N.%20M.%20Singh">N. M. Singh</a>, <a href="https://publications.waset.org/search?q=Jayant%20Dubey"> Jayant Dubey</a>, <a href="https://publications.waset.org/search?q=Ghanshyam%20Laddha"> Ghanshyam Laddha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> State Dependent Riccati Equation (SDRE) approach is a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP modeling is based on Euler-Lagrange equations. A procedure is developed for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=State%20Dependent%20Riccati%20Equation%20%28SDRE%29" title="State Dependent Riccati Equation (SDRE)">State Dependent Riccati Equation (SDRE)</a>, <a href="https://publications.waset.org/search?q=Single%20Inverted%20Pendulum%20%28SIP%29" title=" Single Inverted Pendulum (SIP)"> Single Inverted Pendulum (SIP)</a>, <a href="https://publications.waset.org/search?q=Linear%20Quadratic%20Regulator%20%28LQR%29" title=" Linear Quadratic Regulator (LQR)"> Linear Quadratic Regulator (LQR)</a> </p> <a href="https://publications.waset.org/1812/control-of-pendulum-on-a-cart-with-state-dependent-riccati-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1812/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1812/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1812/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1812/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1812/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1812/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1812/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1812/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1812/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1812/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1812.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">3086</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1126</span> The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Armend%20Sh.%20Shabani">Armend Sh. Shabani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%27s%20equation" title="Pell's equation">Pell's equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%27s%20equation." title=" solutions of Pell's equation."> solutions of Pell's equation.</a> </p> <a href="https://publications.waset.org/14954/the-proof-of-two-conjectures-related-to-pell-s-equation-x2-dy2-4" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14954/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/14954/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/14954/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/14954/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/14954/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/14954/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/14954/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/14954/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/14954/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/14954/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/14954.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">1238</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1125</span> Dynamic Analysis of Offshore 2-HUS/U Parallel Platform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Xie%20Kefeng">Xie Kefeng</a>, <a href="https://publications.waset.org/search?q=Zhang%20He"> Zhang He</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=2-HUS%2FU%20platform" title="2-HUS/U platform">2-HUS/U platform</a>, <a href="https://publications.waset.org/search?q=Dynamics" title=" Dynamics"> Dynamics</a>, <a href="https://publications.waset.org/search?q=Lagrange" title=" Lagrange"> Lagrange</a>, <a href="https://publications.waset.org/search?q=Parallel%20platform." title=" Parallel platform."> Parallel platform.</a> </p> <a href="https://publications.waset.org/10006236/dynamic-analysis-of-offshore-2-husu-parallel-platform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006236/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006236/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006236/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006236/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006236/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006236/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006236/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006236/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006236/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006236/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006236.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">972</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1124</span> An Analytical Method for Solving General Riccati Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Y.%20Pala">Y. Pala</a>, <a href="https://publications.waset.org/search?q=M.%20O.%20Ertas"> M. O. Ertas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Riccati%20Equation" title="Riccati Equation">Riccati Equation</a>, <a href="https://publications.waset.org/search?q=ordinary%20differential%20equation" title=" ordinary differential equation"> ordinary differential equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20differential%20equation" title=" nonlinear differential equation"> nonlinear differential equation</a>, <a href="https://publications.waset.org/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/search?q=proper%20solution." title=" proper solution."> proper solution.</a> </p> <a href="https://publications.waset.org/10006683/an-analytical-method-for-solving-general-riccati-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006683/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006683/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006683/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006683/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006683/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006683/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006683/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006683/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006683/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006683/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006683.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">2024</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1123</span> The Pell Equation x2 − Py2 = Q</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Canan%20Kocap%C4%B1nar"> Canan Kocapınar</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Pell%20equation" title="Pell equation">Pell equation</a>, <a href="https://publications.waset.org/search?q=solutions%20of%20Pell%20equation." title=" solutions of Pell equation."> solutions of Pell equation.</a> </p> <a href="https://publications.waset.org/7822/the-pell-equation-x2-py2-q" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/7822/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/7822/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/7822/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/7822/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/7822/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/7822/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/7822/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/7822/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/7822/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/7822/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/7822.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">2106</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1122</span> Time/Temperature-Dependent Finite Element Model of Laminated Glass Beams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Alena%20Zemanov%C3%A1">Alena Zemanová</a>, <a href="https://publications.waset.org/search?q=Jan%20Zeman"> Jan Zeman</a>, <a href="https://publications.waset.org/search?q=Michal%20%C5%A0ejnoha"> Michal Šejnoha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The polymer foil used for manufacturing of laminated glass members behaves in a viscoelastic manner with temperature dependance. This contribution aims at incorporating the time/temperature-dependent behavior of interlayer to our earlier elastic finite element model for laminated glass beams. The model is based on a refined beam theory: each layer behaves according to the finite-strain shear deformable formulation by Reissner and the adjacent layers are connected via the Lagrange multipliers ensuring the inter-layer compatibility of a laminated unit. The time/temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams, Landel, and Ferry. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, we demonstrate that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Laminated%20glass" title="Laminated glass">Laminated glass</a>, <a href="https://publications.waset.org/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/search?q=finite-strain%0D%0AReissner%20model" title=" finite-strain Reissner model"> finite-strain Reissner model</a>, <a href="https://publications.waset.org/search?q=Lagrange%20multipliers" title=" Lagrange multipliers"> Lagrange multipliers</a>, <a href="https://publications.waset.org/search?q=generalized%20Maxwell%20model" title=" generalized Maxwell model"> generalized Maxwell model</a>, <a href="https://publications.waset.org/search?q=Williams-Landel-Ferry%20equation" title=" Williams-Landel-Ferry equation"> Williams-Landel-Ferry equation</a>, <a href="https://publications.waset.org/search?q=Newton%20method." title=" Newton method."> Newton method.</a> </p> <a href="https://publications.waset.org/10001528/timetemperature-dependent-finite-element-model-of-laminated-glass-beams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10001528/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10001528/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10001528/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10001528/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10001528/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10001528/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10001528/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10001528/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10001528/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10001528/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10001528.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">1685</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1121</span> Development of a Three-Dimensional-Flywheel Robotic System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Chung-Chun%20Hsiao">Chung-Chun Hsiao</a>, <a href="https://publications.waset.org/search?q=Yu-Kai"> Yu-Kai</a>, <a href="https://publications.waset.org/search?q=Ting"> Ting</a>, <a href="https://publications.waset.org/search?q=Kai-Yuan%20Liu"> Kai-Yuan Liu</a>, <a href="https://publications.waset.org/search?q=Pang-Wei%20Yen"> Pang-Wei Yen</a>, <a href="https://publications.waset.org/search?q=Jia-Ying%20Tu"> Jia-Ying Tu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, a new design of spherical robotic system based on the concepts of gimbal structure and gyro dynamics is presented. Robots equipped with multiple wheels and complex steering mechanics may increase the weight and degrade the energy transmission efficiency. In addition, the wheeled and legged robots are relatively vulnerable to lateral impact and lack of lateral mobility. Therefore, the proposed robotic design uses a spherical shell as the main body for ground locomotion, instead of using wheel devices. Three spherical shells are structured in a similar way to a gimbal device and rotate like a gyro system. The design and mechanism of the proposed robotic system is introduced. In addition, preliminary results of the dynamic model based on the principles of planar rigid body kinematics and Lagrangian equation are included. Simulation results and rig construction are presented to verify the concepts.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Gyro" title="Gyro">Gyro</a>, <a href="https://publications.waset.org/search?q=gimbal" title=" gimbal"> gimbal</a>, <a href="https://publications.waset.org/search?q=Lagrange%20equation" title=" Lagrange equation"> Lagrange equation</a>, <a href="https://publications.waset.org/search?q=spherical%20robots." title=" spherical robots."> spherical robots.</a> </p> <a href="https://publications.waset.org/10001039/development-of-a-three-dimensional-flywheel-robotic-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10001039/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10001039/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10001039/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10001039/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10001039/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10001039/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10001039/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10001039/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10001039/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10001039/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10001039.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">2060</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1120</span> The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Ahmet%20Tekcan">Ahmet Tekcan</a>, <a href="https://publications.waset.org/search?q=Arzu%20%C3%96zko%C3%A7"> Arzu Özkoç</a>, <a href="https://publications.waset.org/search?q=Hatice%20Alkan"> Hatice Alkan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Diophantine%20equation" title="Diophantine equation">Diophantine equation</a>, <a href="https://publications.waset.org/search?q=Pell%20equation" title=" Pell equation"> Pell equation</a>, <a href="https://publications.waset.org/search?q=quadratic%20form." title=" quadratic form."> quadratic form.</a> </p> <a href="https://publications.waset.org/6133/the-diophantine-equation-y2-2yx-3-0-and-corresponding-curves-over-fp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/6133/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/6133/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/6133/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/6133/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/6133/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/6133/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/6133/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/6133/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/6133/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/6133/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/6133.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">1266</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1119</span> Solution of The KdV Equation with Asymptotic Degeneracy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Tapas%20Kumar%20Sinha">Tapas Kumar Sinha</a>, <a href="https://publications.waset.org/search?q=Joseph%20Mathew"> Joseph Mathew</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=KdV%20equation" title="KdV equation">KdV equation</a>, <a href="https://publications.waset.org/search?q=Asymptotic%20Degeneracy" title=" Asymptotic Degeneracy"> Asymptotic Degeneracy</a>, <a href="https://publications.waset.org/search?q=Solitons" title=" Solitons"> Solitons</a>, <a href="https://publications.waset.org/search?q=Inverse%20Scattering" title=" Inverse Scattering"> Inverse Scattering</a> </p> <a href="https://publications.waset.org/1871/solution-of-the-kdv-equation-with-asymptotic-degeneracy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1871/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1871/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1871/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1871/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1871/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1871/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1871/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1871/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1871/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1871/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1871.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">1620</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1118</span> Hydrodynamic Simulation of Co-Current and Counter Current of Column Distillation Using Euler Lagrange Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=H.%20Troudi">H. Troudi</a>, <a href="https://publications.waset.org/search?q=M.%20Ghiss"> M. Ghiss</a>, <a href="https://publications.waset.org/search?q=Z.%20Tourki"> Z. Tourki</a>, <a href="https://publications.waset.org/search?q=M.%20Ellejmi"> M. Ellejmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Packed columns of liquefied petroleum gas (LPG) consists of separating the liquid mixture of propane and butane to pure gas components by the distillation phenomenon. The flow of the gas and liquid inside the columns is operated by two ways: The co-current and the counter current operation. Heat, mass and species transfer between phases represent the most important factors that influence the choice between those two operations. In this paper, both processes are discussed using computational CFD simulation through ANSYS-Fluent software. Only 3D half section of the packed column was considered with one packed bed. The packed bed was characterized in our case as a porous media. The simulations were carried out at transient state conditions. A multi-component gas and liquid mixture were used out in the two processes. We utilized the Euler-Lagrange approach in which the gas was treated as a continuum phase and the liquid as a group of dispersed particles. The heat and the mass transfer process was modeled using multi-component droplet evaporation approach. The results show that the counter-current process performs better than the co-current, although such limitations of our approach are noted. This comparison gives accurate results for computations times higher than 2 s, at different gas velocity and at packed bed porosity of 0.9.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Co-current" title="Co-current">Co-current</a>, <a href="https://publications.waset.org/search?q=counter%20current" title=" counter current"> counter current</a>, <a href="https://publications.waset.org/search?q=Euler%20Lagrange%20model" title=" Euler Lagrange model"> Euler Lagrange model</a>, <a href="https://publications.waset.org/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/search?q=mass%20transfer." title=" mass transfer."> mass transfer.</a> </p> <a href="https://publications.waset.org/10006393/hydrodynamic-simulation-of-co-current-and-counter-current-of-column-distillation-using-euler-lagrange-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10006393/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10006393/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10006393/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10006393/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10006393/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10006393/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10006393/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10006393/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10006393/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10006393/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10006393.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">1366</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1117</span> Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Said%20Laachir">Said Laachir</a>, <a href="https://publications.waset.org/search?q=Aziz%20Laaribi"> Aziz Laaribi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Helmholtz%20equation" title="Helmholtz equation">Helmholtz equation</a>, <a href="https://publications.waset.org/search?q=Nikiforov-Uvarov%20method" title=" Nikiforov-Uvarov method"> Nikiforov-Uvarov method</a>, <a href="https://publications.waset.org/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/search?q=eigenfunctions." title=" eigenfunctions."> eigenfunctions.</a> </p> <a href="https://publications.waset.org/9996665/exact-solutions-of-the-helmholtz-equation-via-the-nikiforov-uvarov-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/9996665/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/9996665/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/9996665/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/9996665/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/9996665/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/9996665/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/9996665/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/9996665/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/9996665/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/9996665/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/9996665.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">3003</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1116</span> Study of Cahn-Hilliard Equation to Simulate Phase Separation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nara%20Guimar%C3%A3es">Nara Guimarães</a>, <a href="https://publications.waset.org/search?q=Marcelo%20Aquino%20Martorano"> Marcelo Aquino Martorano</a>, <a href="https://publications.waset.org/search?q=Douglas%20Gouv%C3%AAa"> Douglas Gouvêa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Cahn-Hilliard%20equation" title="Cahn-Hilliard equation">Cahn-Hilliard equation</a>, <a href="https://publications.waset.org/search?q=miscibility%20gap" title=" miscibility gap"> miscibility gap</a>, <a href="https://publications.waset.org/search?q=phase%0D%0Aseparation." title=" phase separation."> phase separation.</a> </p> <a href="https://publications.waset.org/10000644/study-of-cahn-hilliard-equation-to-simulate-phase-separation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10000644/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10000644/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10000644/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10000644/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10000644/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10000644/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10000644/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10000644/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10000644/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10000644/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10000644.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">2053</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1115</span> Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hidetoshi%20Konno"> Hidetoshi Konno</a>, <a href="https://publications.waset.org/search?q=Akio%20Suzuki"> Akio Suzuki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Transient%20population%20dynamics" title=" Transient population dynamics"> Transient population dynamics</a>, <a href="https://publications.waset.org/search?q=Phase%20singularity" title=" Phase singularity"> Phase singularity</a>, <a href="https://publications.waset.org/search?q=Birth-death%20process" title=" Birth-death process"> Birth-death process</a>, <a href="https://publications.waset.org/search?q=Non-stationary%20Master%20equation" title=" Non-stationary Master equation"> Non-stationary Master equation</a>, <a href="https://publications.waset.org/search?q=nonlinear%20Langevin%20equation" title=" nonlinear Langevin equation"> nonlinear Langevin equation</a>, <a href="https://publications.waset.org/search?q=generalized%20Logistic%20equation." title=" generalized Logistic equation."> generalized Logistic equation.</a> </p> <a href="https://publications.waset.org/16095/transient-population-dynamics-of-phase-singularities-in-2d-beeler-reuter-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16095/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16095/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16095/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16095/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16095/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16095/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16095/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16095/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16095/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16095/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16095.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">1593</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1114</span> Using Lagrange Equations to Study the Relative Motion of a Mechanism</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=R.%20A.%20Petre">R. A. Petre</a>, <a href="https://publications.waset.org/search?q=S.%20E.%20Nichifor"> S. E. Nichifor</a>, <a href="https://publications.waset.org/search?q=A.%20Craifaleanu"> A. Craifaleanu</a>, <a href="https://publications.waset.org/search?q=I.%20Stroe"> I. Stroe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Lagrange%20equations" title="Lagrange equations">Lagrange equations</a>, <a href="https://publications.waset.org/search?q=relative%20motion" title=" relative motion"> relative motion</a>, <a href="https://publications.waset.org/search?q=inertial%20or%20non-inertial%20reference%20frame." title=" inertial or non-inertial reference frame. "> inertial or non-inertial reference frame. </a> </p> <a href="https://publications.waset.org/10011475/using-lagrange-equations-to-study-the-relative-motion-of-a-mechanism" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10011475/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10011475/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10011475/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10011475/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10011475/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10011475/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10011475/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10011475/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10011475/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10011475/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10011475.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">580</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1113</span> Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nisha%20Goyal">Nisha Goyal</a>, <a href="https://publications.waset.org/search?q=R.K.%20Gupta"> R.K. Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Sawada-Kotera-Kadomtsev-Petviashivili%20equation" title="Sawada-Kotera-Kadomtsev-Petviashivili equation">Sawada-Kotera-Kadomtsev-Petviashivili equation</a>, <a href="https://publications.waset.org/search?q=Bogoyavlensky-Konoplechenko%20equation" title=" Bogoyavlensky-Konoplechenko equation"> Bogoyavlensky-Konoplechenko equation</a>, <a href="https://publications.waset.org/search?q=" title=" "> </a> </p> <a href="https://publications.waset.org/15030/traveling-wave-solutions-for-the-sawada-kotera-kadomtsev-petviashivili-equation-and-the-bogoyavlensky-konoplechenko-equation-by-gg-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/15030/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/15030/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/15030/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/15030/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/15030/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/15030/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/15030/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/15030/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/15030/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/15030/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/15030.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">1617</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1112</span> Stability of Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Lane-Emden%20equation" title=" Lane-Emden equation"> Lane-Emden equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%20integral%20equation." title=" Volterra integral equation."> Volterra integral equation.</a> </p> <a href="https://publications.waset.org/16803/stability-of-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16803/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16803/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16803/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16803/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16803/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16803/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16803/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16803/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16803/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16803/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16803.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">3717</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1111</span> Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Anjali%20Verma">Anjali Verma</a>, <a href="https://publications.waset.org/search?q=Ram%20Jiwari"> Ram Jiwari</a>, <a href="https://publications.waset.org/search?q=Jitender%20Kumar"> Jitender Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shallow%20water%20wave%20equation" title="Shallow water wave equation">Shallow water wave equation</a>, <a href="https://publications.waset.org/search?q=Exact%20solutions" title=" Exact solutions"> Exact solutions</a>, <a href="https://publications.waset.org/search?q=%02%28G%27%2FG%29%20expansion%20method." title=" (G'/G) expansion method."> (G'/G) expansion method.</a> </p> <a href="https://publications.waset.org/16740/traveling-wave-solutions-for-shallow-water-wave-equation-by-gg-expansion-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/16740/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/16740/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/16740/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/16740/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/16740/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/16740/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/16740/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/16740/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/16740/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/16740/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/16740.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">1839</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1110</span> Using Divergent Nozzle with Aerodynamic Lens to Focus Nanoparticles</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Hasan%20Jumaah%20Mrayeh">Hasan Jumaah Mrayeh</a>, <a href="https://publications.waset.org/search?q=Fue-Sang%20Lien"> Fue-Sang Lien</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>ANSYS Fluent will be used to simulate Computational Fluid Dynamics (CFD) for an efficient lens and nozzle design which will be explained in this paper. We have designed and characterized an aerodynamic lens and a divergent nozzle for focusing flow that transmits sub 25 nm particles through the aerodynamic lens. The design of the lens and nozzle has been improved using CFD for particle trajectories. We obtained a case for calculating nanoparticles (25 nm) flowing through the aerodynamic lens and divergent nozzle. Nanoparticles are transported by air, which is pumped into the aerodynamic lens through the nozzle at 1 atmospheric pressure. We have also developed a computational methodology that can determine the exact focus characteristics of aerodynamic lens systems. Particle trajectories were traced using the Lagrange approach. The simulation shows the ability of the aerodynamic lens to focus on 25 nm particles after using a divergent nozzle.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Aerodynamic%20lens%20AL" title="Aerodynamic lens AL">Aerodynamic lens AL</a>, <a href="https://publications.waset.org/search?q=divergent%20nozzle%20DN" title=" divergent nozzle DN"> divergent nozzle DN</a>, <a href="https://publications.waset.org/search?q=ANSYS%20Fluent" title=" ANSYS Fluent"> ANSYS Fluent</a>, <a href="https://publications.waset.org/search?q=Lagrange%20approach." title=" Lagrange approach."> Lagrange approach.</a> </p> <a href="https://publications.waset.org/10010283/using-divergent-nozzle-with-aerodynamic-lens-to-focus-nanoparticles" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10010283/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10010283/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10010283/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10010283/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10010283/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10010283/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10010283/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10010283/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10010283/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10010283/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10010283.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">1000</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1109</span> Existence of Iterative Cauchy Fractional Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Rabha%20W.%20Ibrahim">Rabha W. Ibrahim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Fractional%20calculus" title="Fractional calculus">Fractional calculus</a>, <a href="https://publications.waset.org/search?q=fractional%20differential%20equation" title=" fractional differential equation"> fractional differential equation</a>, <a href="https://publications.waset.org/search?q=Cauchy%20equation" title=" Cauchy equation"> Cauchy equation</a>, <a href="https://publications.waset.org/search?q=Riemann-Liouville%20fractional%20operators" title=" Riemann-Liouville fractional operators"> Riemann-Liouville fractional operators</a>, <a href="https://publications.waset.org/search?q=Volterra%0D%0Aintegral%20equation" title=" Volterra integral equation"> Volterra integral equation</a>, <a href="https://publications.waset.org/search?q=non-expansive%20mapping" title=" non-expansive mapping"> non-expansive mapping</a>, <a href="https://publications.waset.org/search?q=iterative%20differential%20equation." title=" iterative differential equation."> iterative differential equation.</a> </p> <a href="https://publications.waset.org/17037/existence-of-iterative-cauchy-fractional-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/17037/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/17037/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/17037/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/17037/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/17037/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/17037/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/17037/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/17037/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/17037/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/17037/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/17037.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">2684</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1108</span> A Meshfree Solution of Tow-Dimensional Potential Flow Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=I.%20V.%20Singh">I. V. Singh</a>, <a href="https://publications.waset.org/search?q=A.%20Singh"> A. Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.</p> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Meshless" title="Meshless">Meshless</a>, <a href="https://publications.waset.org/search?q=EFG%20method" title=" EFG method"> EFG method</a>, <a href="https://publications.waset.org/search?q=potential%20flow" title=" potential flow"> potential flow</a>, <a href="https://publications.waset.org/search?q=Lagrange%20multiplier%20method" title=" Lagrange multiplier method"> Lagrange multiplier method</a>, <a href="https://publications.waset.org/search?q=penalty%20method" title=" penalty method"> penalty method</a>, <a href="https://publications.waset.org/search?q=penalty%20parameter%20and%20scaling%20parameter" title=" penalty parameter and scaling parameter"> penalty parameter and scaling parameter</a> </p> <a href="https://publications.waset.org/1478/a-meshfree-solution-of-tow-dimensional-potential-flow-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/1478/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/1478/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/1478/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/1478/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/1478/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/1478/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/1478/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/1478/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/1478/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/1478/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/1478.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">1504</span> </span> </div> </div> <div class="card publication-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1107</span> Ginzburg-Landau Model for Curved Two-Phase Shallow Mixing Layers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Irina%20Eglite">Irina Eglite</a>, <a href="https://publications.waset.org/search?q=Andrei%20A.%20Kolyshkin"> Andrei A. Kolyshkin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Method of multiple scales is used in the paper in order to derive an amplitude evolution equation for the most unstable mode from two-dimensional shallow water equations under the rigid-lid assumption. It is assumed that shallow mixing layer is slightly curved in the longitudinal direction and contains small particles. Dynamic interaction between carrier fluid and particles is neglected. It is shown that the evolution equation is the complex Ginzburg-Landau equation. Explicit formulas for the computation of the coefficients of the equation are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Shallow%20water%20equations" title="Shallow water equations">Shallow water equations</a>, <a href="https://publications.waset.org/search?q=mixing%20layer" title=" mixing layer"> mixing layer</a>, <a href="https://publications.waset.org/search?q=weakly%0Anonlinear%20analysis" title=" weakly nonlinear analysis"> weakly nonlinear analysis</a>, <a href="https://publications.waset.org/search?q=Ginzburg-Landau%20equation" title=" Ginzburg-Landau equation"> Ginzburg-Landau equation</a> </p> <a href="https://publications.waset.org/14646/ginzburg-landau-model-for-curved-two-phase-shallow-mixing-layers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/14646/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a 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