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polynomial</title> <meta name="description" content="Search results for: Legendre polynomial"> <meta name="keywords" content="Legendre polynomial"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Legendre polynomial"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 271</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Legendre polynomial</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">271</span> Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sachin%20Kumar">Sachin Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20PDE" title="fractional PDE">fractional PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20valued%20function" title=" fuzzy valued function"> fuzzy valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20polynomial" title=" Legendre polynomial"> Legendre polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/125273/operational-matrix-method-for-fuzzy-fractional-reaction-diffusion-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125273.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">201</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">270</span> A Method for solving Legendre's Conjecture</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hashem%20Sazegar">Hashem Sazegar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bertrand-chebyshev%20theorem" title="bertrand-chebyshev theorem">bertrand-chebyshev theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=landau%E2%80%99s%20problems" title=" landau’s problems"> landau’s problems</a>, <a href="https://publications.waset.org/abstracts/search?q=goldbach%E2%80%99s%20conjecture" title=" goldbach’s conjecture"> goldbach’s conjecture</a>, <a href="https://publications.waset.org/abstracts/search?q=twin%20prime" title=" twin prime"> twin prime</a>, <a href="https://publications.waset.org/abstracts/search?q=ramanujan%20proof" title=" ramanujan proof"> ramanujan proof</a> </p> <a href="https://publications.waset.org/abstracts/30842/a-method-for-solving-legendres-conjecture" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30842.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">360</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">269</span> Chebyshev Polynomials Relad with Fibonacci and Lucas Polynomials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vandana%20N.%20Purav">Vandana N. Purav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=" title=""></a> </p> <a href="https://publications.waset.org/abstracts/24133/chebyshev-polynomials-relad-with-fibonacci-and-lucas-polynomials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24133.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">368</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">268</span> Transformations between Bivariate Polynomial Bases</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dimitris%20Varsamis">Dimitris Varsamis</a>, <a href="https://publications.waset.org/abstracts/search?q=Nicholas%20Karampetakis"> Nicholas Karampetakis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bivariate%20interpolation%20polynomial" title="bivariate interpolation polynomial">bivariate interpolation polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20basis" title=" polynomial basis"> polynomial basis</a>, <a href="https://publications.waset.org/abstracts/search?q=transformations" title=" transformations"> transformations</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolating%20polynomial" title=" interpolating polynomial"> interpolating polynomial</a> </p> <a href="https://publications.waset.org/abstracts/14542/transformations-between-bivariate-polynomial-bases" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14542.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">405</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">267</span> Optimal Control of Volterra Integro-Differential Systems Based on Legendre Wavelets and Collocation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khosrow%20Maleknejad">Khosrow Maleknejad</a>, <a href="https://publications.waset.org/abstracts/search?q=Asyieh%20Ebrahimzadeh"> Asyieh Ebrahimzadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20wavelet" title=" Legendre wavelet"> Legendre wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integro-differential%20equation" title=" Volterra integro-differential equation"> Volterra integro-differential equation</a> </p> <a href="https://publications.waset.org/abstracts/5005/optimal-control-of-volterra-integro-differential-systems-based-on-legendre-wavelets-and-collocation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5005.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">388</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">266</span> From Convexity in Graphs to Polynomial Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ladznar%20S.%20Laja">Ladznar S. Laja</a>, <a href="https://publications.waset.org/abstracts/search?q=Rosalio%20G.%20Artes"> Rosalio G. Artes</a>, <a href="https://publications.waset.org/abstracts/search?q=Jr."> Jr.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20subgraph" title="convex subgraph">convex subgraph</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20index" title=" convex index"> convex index</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20function" title=" generating function"> generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a> </p> <a href="https://publications.waset.org/abstracts/9019/from-convexity-in-graphs-to-polynomial-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9019.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">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">265</span> Introduction to Paired Domination Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Puttaswamy">Puttaswamy</a>, <a href="https://publications.waset.org/abstracts/search?q=Anwar%20Alwardi"> Anwar Alwardi</a>, <a href="https://publications.waset.org/abstracts/search?q=Nayaka%20S.%20R."> Nayaka S. R.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=domination%20polynomial" title="domination polynomial">domination polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20dominating%20set" title=" paired dominating set"> paired dominating set</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20number" title=" paired domination number"> paired domination number</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20polynomial" title=" paired domination polynomial"> paired domination polynomial</a> </p> <a href="https://publications.waset.org/abstracts/52964/introduction-to-paired-domination-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52964.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">232</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">264</span> Medical Image Classification Using Legendre Multifractal Spectrum Features</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Korchiyne">R. Korchiyne</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Sbihi"> A. Sbihi</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20M.%20Farssi"> S. M. Farssi</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Touahni"> R. Touahni</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Tahiri%20Alaoui"> M. Tahiri Alaoui</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Trabecular bone structure is important texture in the study of osteoporosis. Legendre multifractal spectrum can reflect the complex and self-similarity characteristic of structures. The main objective of this paper is to develop a new technique of medical image classification based on Legendre multifractal spectrum. Novel features have been developed from basic geometrical properties of this spectrum in a supervised image classification. The proposed method has been successfully used to classify medical images of bone trabeculations, and could be a useful supplement to the clinical observations for osteoporosis diagnosis. A comparative study with existing data reveals that the results of this approach are concordant. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multifractal%20analysis" title="multifractal analysis">multifractal analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=medical%20image" title=" medical image"> medical image</a>, <a href="https://publications.waset.org/abstracts/search?q=osteoporosis" title=" osteoporosis"> osteoporosis</a>, <a href="https://publications.waset.org/abstracts/search?q=fractal%20dimension" title=" fractal dimension"> fractal dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20spectrum" title=" Legendre spectrum"> Legendre spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=supervised%20classification" title=" supervised classification"> supervised classification</a> </p> <a href="https://publications.waset.org/abstracts/15795/medical-image-classification-using-legendre-multifractal-spectrum-features" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15795.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">514</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">263</span> On the Zeros of the Degree Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20R.%20Nayaka">S. R. Nayaka</a>, <a href="https://publications.waset.org/abstracts/search?q=Putta%20Swamy"> Putta Swamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=degree%20polynomial" title="degree polynomial">degree polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=regular%20graph" title=" regular graph"> regular graph</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20and%20maximum%20degree" title=" minimum and maximum degree"> minimum and maximum degree</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operations" title=" graph operations"> graph operations</a> </p> <a href="https://publications.waset.org/abstracts/56602/on-the-zeros-of-the-degree-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56602.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">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">262</span> A Dynamical Study of Fractional Order Obesity Model by a Combined Legendre Wavelet Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hakiki%20Kheira">Hakiki Kheira</a>, <a href="https://publications.waset.org/abstracts/search?q=Belhamiti%20Omar"> Belhamiti Omar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title="Caputo derivative">Caputo derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=epidemiology" title=" epidemiology"> epidemiology</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20wavelet%20method" title=" Legendre wavelet method"> Legendre wavelet method</a>, <a href="https://publications.waset.org/abstracts/search?q=obesity" title=" obesity "> obesity </a> </p> <a href="https://publications.waset.org/abstracts/42731/a-dynamical-study-of-fractional-order-obesity-model-by-a-combined-legendre-wavelet-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42731.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">420</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">261</span> Superconvergence of the Iterated Discrete Legendre Galerkin Method for Fredholm-Hammerstein Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Payel%20Das">Payel Das</a>, <a href="https://publications.waset.org/abstracts/search?q=Gnaneshwar%20Nelakanti"> Gnaneshwar Nelakanti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hammerstein%20integral%20equations" title="hammerstein integral equations">hammerstein integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20galerkin" title=" discrete galerkin"> discrete galerkin</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%0D%0Aquadrature" title=" numerical quadrature"> numerical quadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=superconvergence" title=" superconvergence"> superconvergence</a> </p> <a href="https://publications.waset.org/abstracts/22260/superconvergence-of-the-iterated-discrete-legendre-galerkin-method-for-fredholm-hammerstein-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22260.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">469</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">260</span> Generic Polynomial of Integers and Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nidal%20Ali">Nidal Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Consider an algebraic number field K of degree n, A0 K is its ring of integers and a prime number p inert in K. Let F(u1, . . . , un, x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in Fp[x] of degree d dividing n. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generic%20polynomial" title="generic polynomial">generic polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=irreducibility" title=" irreducibility"> irreducibility</a>, <a href="https://publications.waset.org/abstracts/search?q=iteration" title=" iteration"> iteration</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=inert%20prime" title=" inert prime"> inert prime</a>, <a href="https://publications.waset.org/abstracts/search?q=totally%20ramified" title=" totally ramified"> totally ramified</a> </p> <a href="https://publications.waset.org/abstracts/16820/generic-polynomial-of-integers-and-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16820.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">346</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">259</span> Application of Wavelet Based Approximation for the Solution of Partial Integro-Differential Equation Arising from Viscoelasticity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Somveer%20Singh">Somveer Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Vineet%20Kumar%20Singh"> Vineet Kumar Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=legendre%20wavelets" title="legendre wavelets">legendre wavelets</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrices" title=" operational matrices"> operational matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20integro-differential%20equation" title=" partial integro-differential equation"> partial integro-differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=viscoelasticity" title=" viscoelasticity"> viscoelasticity</a> </p> <a href="https://publications.waset.org/abstracts/57515/application-of-wavelet-based-approximation-for-the-solution-of-partial-integro-differential-equation-arising-from-viscoelasticity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57515.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">448</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">258</span> The K-Distance Neighborhood Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soner%20Nandappa%20D.">Soner Nandappa D.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Mohammed%20Naji"> Ahmed Mohammed Naji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vertex%20degrees" title="vertex degrees">vertex degrees</a>, <a href="https://publications.waset.org/abstracts/search?q=distance%20in%20graphs" title=" distance in graphs"> distance in graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operation" title=" graph operation"> graph operation</a>, <a href="https://publications.waset.org/abstracts/search?q=Nk-polynomials" title=" Nk-polynomials"> Nk-polynomials</a> </p> <a href="https://publications.waset.org/abstracts/52946/the-k-distance-neighborhood-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52946.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">549</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">257</span> Effect of Temperature on the Binary Mixture of Imidazolium Ionic Liquid with Pyrrolidin-2-One: Volumetric and Ultrasonic Study</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20Srinivasa%20Krishna">T. Srinivasa Krishna</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Narendra"> K. Narendra</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Thomas"> K. Thomas</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20S.%20Raju"> S. S. Raju</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Munibhadrayya"> B. Munibhadrayya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The densities, speeds of sound and refractive index of the binary mixture of ionic liquid (IL) 1-Butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([BMIM][Imide]) and Pyrrolidin-2-one(PY) was measured at atmospheric pressure, and over the range of temperatures T= (298.15 -323.15)K. The excess molar volume, excess isentropic compressibility, excess speed of sound, partial molar volumes, and isentropic partial molar compressibility were calculated from the values of the experimental density and speed of sound. From the experimental data excess thermal expansion coefficients and isothermal pressure coefficient of excess molar enthalpy at 298.15K were calculated. The results were analyzed and were discussed from the point of view of structural changes. Excess properties were calculated and correlated by the Redlich–Kister and the Legendre polynomial equation and binary coefficients were obtained. Values of excess partial volumes at infinite dilution for the binary system at different temperatures were calculated from the adjustable parameters obtained from Legendre polynomial and Redlich–Kister smoothing equation. Deviation in refractive indices ΔnD and deviation in molar refraction, ΔRm were calculated from the measured refractive index values. Equations of state and several mixing rules were used to predict refractive indices of the binary mixtures and compared with the experimental values by means of the standard deviation and found to be in excellent agreement. By using Prigogine–Flory–Patterson (PFP) theory, the above thermodynamic mixing functions have been calculated and the results obtained from this theory were compared with experimental results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=density" title="density">density</a>, <a href="https://publications.waset.org/abstracts/search?q=refractive%20index" title=" refractive index"> refractive index</a>, <a href="https://publications.waset.org/abstracts/search?q=speeds%20of%20sound" title=" speeds of sound"> speeds of sound</a>, <a href="https://publications.waset.org/abstracts/search?q=Prigogine-Flory-Patterson%20theory" title=" Prigogine-Flory-Patterson theory"> Prigogine-Flory-Patterson theory</a> </p> <a href="https://publications.waset.org/abstracts/36516/effect-of-temperature-on-the-binary-mixture-of-imidazolium-ionic-liquid-with-pyrrolidin-2-one-volumetric-and-ultrasonic-study" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36516.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">408</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">256</span> Hosoya Polynomials of Zero-Divisor Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Jalil%20M.%20Khalaf">Abdul Jalil M. Khalaf</a>, <a href="https://publications.waset.org/abstracts/search?q=Esraa%20M.%20Kadhim"> Esraa M. Kadhim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hosoya%20polynomial" title="Hosoya polynomial">Hosoya polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=wiener%20index" title=" wiener index"> wiener index</a>, <a href="https://publications.waset.org/abstracts/search?q=Hyper-Wiener%20index" title=" Hyper-Wiener index"> Hyper-Wiener index</a>, <a href="https://publications.waset.org/abstracts/search?q=zero-divisor%20graphs" title=" zero-divisor graphs"> zero-divisor graphs</a> </p> <a href="https://publications.waset.org/abstracts/27159/hosoya-polynomials-of-zero-divisor-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27159.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">530</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">255</span> Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Suparman">Suparman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=piecewise%20regression" title="piecewise regression">piecewise regression</a>, <a href="https://publications.waset.org/abstracts/search?q=bayesian" title=" bayesian"> bayesian</a>, <a href="https://publications.waset.org/abstracts/search?q=reversible%20jump%20MCMC" title=" reversible jump MCMC"> reversible jump MCMC</a>, <a href="https://publications.waset.org/abstracts/search?q=segmentation" title=" segmentation"> segmentation</a> </p> <a href="https://publications.waset.org/abstracts/46201/segmentation-of-piecewise-polynomial-regression-model-by-using-reversible-jump-mcmc-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46201.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">373</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">254</span> An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haniye%20Dehestani">Haniye Dehestani</a>, <a href="https://publications.waset.org/abstracts/search?q=Yadollah%20Ordokhani"> Yadollah Ordokhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title=" fractional partial differential equations"> fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=legendre-laguerre%20functions" title=" legendre-laguerre functions"> legendre-laguerre functions</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-operational%20matrix%20of%20integration" title=" pseudo-operational matrix of integration"> pseudo-operational matrix of integration</a> </p> <a href="https://publications.waset.org/abstracts/97195/an-efficient-collocation-method-for-solving-the-variable-order-time-fractional-partial-differential-equations-arising-from-the-physical-phenomenon" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97195.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">166</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">253</span> Modeling and Simulation of a CMOS-Based Analog Function Generator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Madina%20Hamiane">Madina Hamiane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modelling%20and%20simulation" title="modelling and simulation">modelling and simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=analog%20function%20generator" title=" analog function generator"> analog function generator</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20approximation" title=" polynomial approximation"> polynomial approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=CMOS%20transistors" title=" CMOS transistors"> CMOS transistors</a> </p> <a href="https://publications.waset.org/abstracts/7108/modeling-and-simulation-of-a-cmos-based-analog-function-generator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7108.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">458</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">252</span> Brinkman Flow Past an Impervious Spheroid under Stokesian Assumption</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=D.%20Satish%20Kumar">D. Satish Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20K.%20V.%20Iyengar"> T. K. V. Iyengar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study the Brinkman flow, under Stokesian assumption, past an impervious prolate spheroid and obtain the expressions for the velocity and pressure fields in terms of Legendre functions, Associated Legendre functions, prolate radial and angular spheroidal wave functions. We further obtain an expression for the drag experienced by the spheroid and numerically study its variation with respect to the flow parameters and display the results through graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=prolate%20spheoid" title="prolate spheoid">prolate spheoid</a>, <a href="https://publications.waset.org/abstracts/search?q=porous%20medium" title=" porous medium"> porous medium</a>, <a href="https://publications.waset.org/abstracts/search?q=stokesian%20assumption" title=" stokesian assumption"> stokesian assumption</a>, <a href="https://publications.waset.org/abstracts/search?q=brinkman%20model" title=" brinkman model"> brinkman model</a>, <a href="https://publications.waset.org/abstracts/search?q=velocity" title=" velocity"> velocity</a>, <a href="https://publications.waset.org/abstracts/search?q=pressure" title=" pressure"> pressure</a>, <a href="https://publications.waset.org/abstracts/search?q=drag" title=" drag"> drag</a> </p> <a href="https://publications.waset.org/abstracts/24084/brinkman-flow-past-an-impervious-spheroid-under-stokesian-assumption" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24084.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">536</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">251</span> Stabilization Control of the Nonlinear AIDS Model Based on the Theory of Polynomial Fuzzy Control Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shahrokh%20Barati">Shahrokh Barati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=polynomial%20fuzzy" title="polynomial fuzzy">polynomial fuzzy</a>, <a href="https://publications.waset.org/abstracts/search?q=AIDS" title=" AIDS"> AIDS</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20AIDS%20model" title=" nonlinear AIDS model"> nonlinear AIDS model</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20control%20systems" title=" fuzzy control systems"> fuzzy control systems</a> </p> <a href="https://publications.waset.org/abstracts/36231/stabilization-control-of-the-nonlinear-aids-model-based-on-the-theory-of-polynomial-fuzzy-control-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36231.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">468</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">250</span> On CR-Structure and F-Structure Satisfying Polynomial Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manisha%20Kankarej">Manisha Kankarej</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CR-submainfolds" title="CR-submainfolds">CR-submainfolds</a>, <a href="https://publications.waset.org/abstracts/search?q=CR-structure" title=" CR-structure"> CR-structure</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability%20condition" title=" integrability condition"> integrability condition</a>, <a href="https://publications.waset.org/abstracts/search?q=Nijenhuis%20tensor" title=" Nijenhuis tensor"> Nijenhuis tensor</a> </p> <a href="https://publications.waset.org/abstracts/63709/on-cr-structure-and-f-structure-satisfying-polynomial-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63709.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">525</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">249</span> Implicit Off-Grid Block Method for Solving Fourth and Fifth Order Ordinary Differential Equations Directly</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Olusola%20Ezekiel%20Abolarin">Olusola Ezekiel Abolarin</a>, <a href="https://publications.waset.org/abstracts/search?q=Gift%20E.%20Noah"> Gift E. Noah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problem" title="initial value problem">initial value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equation" title=" ordinary differential equation"> ordinary differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=implicit%20off-grid%20block%20method" title=" implicit off-grid block method"> implicit off-grid block method</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a> </p> <a href="https://publications.waset.org/abstracts/171485/implicit-off-grid-block-method-for-solving-fourth-and-fifth-order-ordinary-differential-equations-directly" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171485.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">84</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">248</span> Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tsun-Hui%20Huang">Tsun-Hui Huang</a>, <a href="https://publications.waset.org/abstracts/search?q=Shyue-Cheng%20Yang"> Shyue-Cheng Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Chiou-Fen%20Shieha"> Chiou-Fen Shieha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=polynomial%20constitutive%20equation" title="polynomial constitutive equation">polynomial constitutive equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary" title=" solitary"> solitary</a>, <a href="https://publications.waset.org/abstracts/search?q=stress%20solitary%20waves" title=" stress solitary waves"> stress solitary waves</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20constitutive%20law" title=" nonlinear constitutive law"> nonlinear constitutive law</a> </p> <a href="https://publications.waset.org/abstracts/10185/stress-solitary-waves-generated-by-a-second-order-polynomial-constitutive-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10185.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">497</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">247</span> Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zuhier%20Altawallbeh">Zuhier Altawallbeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hochschild%20homology" title="hochschild homology">hochschild homology</a>, <a href="https://publications.waset.org/abstracts/search?q=homotopic%20function" title=" homotopic function"> homotopic function</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20and%20projective%20modules" title=" free and projective modules"> free and projective modules</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20resolution" title=" free resolution"> free resolution</a>, <a href="https://publications.waset.org/abstracts/search?q=exterior%20algebra" title=" exterior algebra"> exterior algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20algebra" title=" symmetric algebra"> symmetric algebra</a> </p> <a href="https://publications.waset.org/abstracts/20251/explicit-chain-homotopic-function-to-compute-hochschild-homology-of-the-polynomial-algebra" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20251.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">405</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">246</span> Forward Stable Computation of Roots of Real Polynomials with Only Real Distinct Roots</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nevena%20Jakov%C4%8Devi%C4%87%20Stor">Nevena Jakovčević Stor</a>, <a href="https://publications.waset.org/abstracts/search?q=Ivan%20Slapni%C4%8Dar"> Ivan Slapničar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=roots%20of%20polynomials" title="roots of polynomials">roots of polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20decomposition" title=" eigenvalue decomposition"> eigenvalue decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=arrowhead%20matrix" title=" arrowhead matrix"> arrowhead matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20relative%20accuracy" title=" high relative accuracy"> high relative accuracy</a> </p> <a href="https://publications.waset.org/abstracts/40100/forward-stable-computation-of-roots-of-real-polynomials-with-only-real-distinct-roots" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40100.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">417</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">245</span> Identification of Nonlinear Systems Structured by Hammerstein-Wiener Model </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Brouri">A. Brouri</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Giri"> F. Giri</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Mkhida"> A. Mkhida</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Elkarkri"> A. Elkarkri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20L.%20Chhibat"> M. L. Chhibat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the linear subsystem is allowed to be parametric or not, continuous- or discrete-time. The input and output nonlinearities are polynomial and may be noninvertible. A two-stage identification method is developed such the parameters of all nonlinear elements are estimated first using the Kozen-Landau polynomial decomposition algorithm. The obtained estimates are then based upon in the identification of the linear subsystem, making use of suitable pre-ad post-compensators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20system%20identification" title="nonlinear system identification">nonlinear system identification</a>, <a href="https://publications.waset.org/abstracts/search?q=Hammerstein-Wiener%20systems" title=" Hammerstein-Wiener systems"> Hammerstein-Wiener systems</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20identification" title=" frequency identification"> frequency identification</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20decomposition" title=" polynomial decomposition"> polynomial decomposition</a> </p> <a href="https://publications.waset.org/abstracts/7969/identification-of-nonlinear-systems-structured-by-hammerstein-wiener-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7969.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">511</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">244</span> Application of Chinese Remainder Theorem to Find The Messages Sent in Broadcast</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayubi%20Wirara">Ayubi Wirara</a>, <a href="https://publications.waset.org/abstracts/search?q=Ardya%20Suryadinata"> Ardya Suryadinata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Improper application of the RSA algorithm scheme can cause vulnerability to attacks. The attack utilizes the relationship between broadcast messages sent to the user with some fixed polynomial functions that belong to each user. Scheme attacks carried out by applying the Chinese Remainder Theorem to obtain a general polynomial equation with the same modulus. The formation of the general polynomial becomes a first step to get back the original message. Furthermore, to solve these equations can use Coppersmith's theorem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=RSA%20algorithm" title="RSA algorithm">RSA algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=broadcast%20message" title=" broadcast message"> broadcast message</a>, <a href="https://publications.waset.org/abstracts/search?q=Chinese%20Remainder%20Theorem" title=" Chinese Remainder Theorem"> Chinese Remainder Theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=Coppersmith%E2%80%99s%20theorem" title=" Coppersmith’s theorem"> Coppersmith’s theorem</a> </p> <a href="https://publications.waset.org/abstracts/9543/application-of-chinese-remainder-theorem-to-find-the-messages-sent-in-broadcast" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9543.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">341</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">243</span> Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ogunrinde%20Roseline%20Bosede">Ogunrinde Roseline Bosede</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title="differential equations">differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical" title=" numerical"> numerical</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial" title=" polynomial"> polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problem" title=" initial value problem"> initial value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a> </p> <a href="https://publications.waset.org/abstracts/23505/inverse-polynomial-numerical-scheme-for-the-solution-of-initial-value-problems-in-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23505.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">447</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">242</span> On Chromaticity of Wheels</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zainab%20Yasir%20Abed%20Al-Rekaby">Zainab Yasir Abed Al-Rekaby</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Jalil%20M.%20Khalaf"> Abdul Jalil M. Khalaf</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chromatic%20polynomial" title="chromatic polynomial">chromatic polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=chromatically%20equivalent" title=" chromatically equivalent"> chromatically equivalent</a>, <a href="https://publications.waset.org/abstracts/search?q=chromatically%20unique" title=" chromatically unique"> chromatically unique</a>, <a href="https://publications.waset.org/abstracts/search?q=wheel" title=" wheel"> wheel</a> </p> <a href="https://publications.waset.org/abstracts/12874/on-chromaticity-of-wheels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12874.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">431</span> 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