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approximation</title> <meta name="description" content="Search results for: polynomial approximation"> <meta name="keywords" content="polynomial approximation"> <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 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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="polynomial approximation"> <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> 753</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: polynomial approximation</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">753</span> Polynomially Adjusted Bivariate Density Estimates Based on the Saddlepoint Approximation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20B.%20Provost">S. B. Provost</a>, <a href="https://publications.waset.org/abstracts/search?q=Susan%20Sheng"> Susan Sheng</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An alternative bivariate density estimation methodology is introduced in this presentation. The proposed approach involves estimating the density function associated with the marginal distribution of each of the two variables by means of the saddlepoint approximation technique and applying a bivariate polynomial adjustment to the product of these density estimates. Since the saddlepoint approximation is utilized in the context of density estimation, such estimates are determined from empirical cumulant-generating functions. In the univariate case, the saddlepoint density estimate is itself adjusted by a polynomial. Given a set of observations, the coefficients of the polynomial adjustments are obtained from the sample moments. Several illustrative applications of the proposed methodology shall be presented. Since this approach relies essentially on a determinate number of sample moments, it is particularly well suited for modeling massive data sets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=density%20estimation" title="density estimation">density estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=empirical%20cumulant-generating%20function" title=" empirical cumulant-generating function"> empirical cumulant-generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=moments" title=" moments"> moments</a>, <a href="https://publications.waset.org/abstracts/search?q=saddlepoint%20approximation" title=" saddlepoint approximation"> saddlepoint approximation</a> </p> <a href="https://publications.waset.org/abstracts/72664/polynomially-adjusted-bivariate-density-estimates-based-on-the-saddlepoint-approximation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72664.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">280</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">752</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">459</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">751</span> Nonparametric Copula Approximations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Serge%20Provost">Serge Provost</a>, <a href="https://publications.waset.org/abstracts/search?q=Yishan%20Zang"> Yishan Zang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=copulas" title="copulas">copulas</a>, <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomial%20approximation" title=" Bernstein polynomial approximation"> Bernstein polynomial approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=least-squares%20polynomial%20approximation" title=" least-squares polynomial approximation"> least-squares polynomial approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=kernel%20density%20estimation" title=" kernel density estimation"> kernel density estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=density%20approximation" title=" density approximation"> density approximation</a> </p> <a href="https://publications.waset.org/abstracts/170324/nonparametric-copula-approximations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/170324.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">74</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">750</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">749</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">748</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">747</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">746</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">745</span> Approximation by Generalized Lupaş-Durrmeyer Operators with Two Parameter α and β</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Preeti%20Sharma">Preeti Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the Stancu type generalization of Lupaş-Durrmeyer operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, 1]. Also, Voronovskaja type theorem is studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lupas-Durrmeyer%20operators" title="Lupas-Durrmeyer operators">Lupas-Durrmeyer operators</a>, <a href="https://publications.waset.org/abstracts/search?q=polya%20distribution" title=" polya distribution"> polya distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=weighted%20approximation" title=" weighted approximation"> weighted approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=rate%20of%20convergence" title=" rate of convergence"> rate of convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=modulus%20of%20continuity" title=" modulus of continuity"> modulus of continuity</a> </p> <a href="https://publications.waset.org/abstracts/47660/approximation-by-generalized-lupas-durrmeyer-operators-with-two-parameter-a-and-v" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47660.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">744</span> Optimal Image Representation for Linear Canonical Transform Multiplexing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Navdeep%20Goel">Navdeep Goel</a>, <a href="https://publications.waset.org/abstracts/search?q=Salvador%20Gabarda"> Salvador Gabarda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4x4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4*4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4*4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chirp%20signals" title="chirp signals">chirp signals</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20multiplexing" title=" image multiplexing"> image multiplexing</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20transformation" title=" image transformation"> image transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20canonical%20transform" title=" linear canonical transform"> linear canonical transform</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20approximation" title=" polynomial approximation"> polynomial approximation</a> </p> <a href="https://publications.waset.org/abstracts/35260/optimal-image-representation-for-linear-canonical-transform-multiplexing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35260.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">412</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">743</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">742</span> The Bernstein Expansion for Exponentials in Taylor Functions: Approximation of Fixed Points</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tareq%20Hamadneh">Tareq Hamadneh</a>, <a href="https://publications.waset.org/abstracts/search?q=Jochen%20Merker"> Jochen Merker</a>, <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Al-Zoubi"> Hassan Al-Zoubi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Bernstein's expansion for exponentials in Taylor functions provides lower and upper optimization values for the range of its original function. these values converge to the original functions if the degree is elevated or the domain subdivided. Taylor polynomial can be applied so that the exponential is a polynomial of finite degree over a given domain. Bernstein's basis has two main properties: its sum equals 1, and positive for all x 2 (0; 1). In this work, we prove the existence of fixed points for exponential functions in a given domain using the optimization values of Bernstein. The Bernstein basis of finite degree T over a domain D is defined non-negatively. Any polynomial p of degree t can be expanded into the Bernstein form of maximum degree t ≤ T, where we only need to compute the coefficients of Bernstein in order to optimize the original polynomial. The main property is that p(x) is approximated by the minimum and maximum Bernstein coefficients (Bernstein bound). If the bound is contained in the given domain, then we say that p(x) has fixed points in the same domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bernstein%20polynomials" title="Bernstein polynomials">Bernstein polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Stability%20of%20control%20functions" title="Stability of control functions">Stability of control functions</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20optimization" title="numerical optimization">numerical optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%20function" title="Taylor function">Taylor function</a> </p> <a href="https://publications.waset.org/abstracts/149910/the-bernstein-expansion-for-exponentials-in-taylor-functions-approximation-of-fixed-points" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/149910.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">135</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">741</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">550</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">740</span> Approximation Property Pass to Free Product</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kankeyanathan%20Kannan">Kankeyanathan Kannan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximation%20property" title="approximation property">approximation property</a>, <a href="https://publications.waset.org/abstracts/search?q=weakly%20amenable" title=" weakly amenable"> weakly amenable</a>, <a href="https://publications.waset.org/abstracts/search?q=strong%20invariant%20approximation%20property" title=" strong invariant approximation property"> strong invariant approximation property</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20approximation%20property" title=" invariant approximation property"> invariant approximation property</a> </p> <a href="https://publications.waset.org/abstracts/44414/approximation-property-pass-to-free-product" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44414.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">675</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">739</span> Polynomial Chaos Expansion Combined with Exponential Spline for Singularly Perturbed Boundary Value Problems with Random Parameter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=W.%20K.%20Zahra">W. K. Zahra</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20El-Beltagy"> M. A. El-Beltagy</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20R.%20Elkhadrawy"> R. R. Elkhadrawy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20problem" title="singular perturbation problem">singular perturbation problem</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20chaos%20expansion" title=" polynomial chaos expansion"> polynomial chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=Shishkin%20mesh" title=" Shishkin mesh"> Shishkin mesh</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20small%20parameters" title=" two small parameters"> two small parameters</a>, <a href="https://publications.waset.org/abstracts/search?q=exponential%20spline" title=" exponential spline"> exponential spline</a> </p> <a href="https://publications.waset.org/abstracts/100441/polynomial-chaos-expansion-combined-with-exponential-spline-for-singularly-perturbed-boundary-value-problems-with-random-parameter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/100441.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">160</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">738</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">531</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">737</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">736</span> Modified Approximation Methods for Finding an Optimal Solution for the Transportation Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20Guruprasad">N. Guruprasad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computation" title="computation">computation</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20cost" title=" modified cost"> modified cost</a>, <a href="https://publications.waset.org/abstracts/search?q=Russell%E2%80%99s%20approximation%20method" title=" Russell’s approximation method"> Russell’s approximation method</a>, <a href="https://publications.waset.org/abstracts/search?q=transportation" title=" transportation"> transportation</a>, <a href="https://publications.waset.org/abstracts/search?q=Vogel%E2%80%99s%20approximation%20method" title=" Vogel’s approximation method"> Vogel’s approximation method</a> </p> <a href="https://publications.waset.org/abstracts/19162/modified-approximation-methods-for-finding-an-optimal-solution-for-the-transportation-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19162.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">547</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">735</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">734</span> A Hybrid Adomian Decomposition Method in the Solution of Logistic Abelian Ordinary Differential and Its Comparism with Some Standard Numerical Scheme</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20J.%20Adeyeye">F. J. Adeyeye</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20Eni"> D. Eni</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20M.%20Okedoye"> K. M. Okedoye</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adomian%20decomposition%20method" title="Adomian decomposition method">Adomian decomposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20part" title=" nonlinear part"> nonlinear part</a>, <a href="https://publications.waset.org/abstracts/search?q=one-step%20method" title=" one-step method"> one-step method</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%20series%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20approximation" title=" Taylor series approximation"> Taylor series approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20of%20Adomian%20polynomial" title=" hybrid of Adomian polynomial"> hybrid of Adomian polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=logistic%20problem" title=" logistic problem"> logistic problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Malthusian%20parameter" title=" Malthusian parameter"> Malthusian parameter</a>, <a href="https://publications.waset.org/abstracts/search?q=Verhulst%20Model" title=" Verhulst Model"> Verhulst Model</a> </p> <a href="https://publications.waset.org/abstracts/36872/a-hybrid-adomian-decomposition-method-in-the-solution-of-logistic-abelian-ordinary-differential-and-its-comparism-with-some-standard-numerical-scheme" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36872.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">400</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">733</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">526</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">732</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">731</span> Constant Factor Approximation Algorithm for p-Median Network Design Problem with Multiple Cable Types</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chaghoub%20Soraya">Chaghoub Soraya</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhang%20Xiaoyan"> Zhang Xiaoyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximation%20algorithms" title="approximation algorithms">approximation algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=buy-at-bulk" title=" buy-at-bulk"> buy-at-bulk</a>, <a href="https://publications.waset.org/abstracts/search?q=combinatorial%20optimization" title=" combinatorial optimization"> combinatorial optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=network%20design" title=" network design"> network design</a>, <a href="https://publications.waset.org/abstracts/search?q=p-median" title=" p-median"> p-median</a> </p> <a href="https://publications.waset.org/abstracts/127337/constant-factor-approximation-algorithm-for-p-median-network-design-problem-with-multiple-cable-types" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127337.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">203</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">730</span> Approximation of the Time Series by Fractal Brownian Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Valeria%20Bondarenko">Valeria Bondarenko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20Brownian%20motion" title="fractional Brownian motion">fractional Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=Gausssian%20processes" title=" Gausssian processes"> Gausssian processes</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation" title=" approximation"> approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20series" title=" time series"> time series</a>, <a href="https://publications.waset.org/abstracts/search?q=estimation%20of%20properties%20of%20the%20model" title=" estimation of properties of the model"> estimation of properties of the model</a> </p> <a href="https://publications.waset.org/abstracts/4285/approximation-of-the-time-series-by-fractal-brownian-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4285.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">376</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">729</span> Approximation of Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means of Fourier Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a>, <a href="https://publications.waset.org/abstracts/search?q=Uaday%20Singh"> Uaday Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lipschitz%20classes" title="Lipschitz classes">Lipschitz classes</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20matrix%20operator" title=" product matrix operator"> product matrix operator</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20Fourier%20approximation" title=" trigonometric Fourier approximation"> trigonometric Fourier approximation</a> </p> <a href="https://publications.waset.org/abstracts/4757/approximation-of-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means-of-fourier-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4757.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">477</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">728</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">727</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">418</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">726</span> High-Pressure Calculations of the Elastic Properties of ZnSx Se 1−x Alloy in the Virtual-Crystal Approximation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20Lebga">N. Lebga</a>, <a href="https://publications.waset.org/abstracts/search?q=Kh.%20Bouamama"> Kh. Bouamama</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Kassali"> K. Kassali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We report first-principles calculation results on the structural and elastic properties of ZnS x Se1−x alloy for which we employed the virtual crystal approximation provided with the ABINIT program. The calculations done using density functional theory within the local density approximation and employing the virtual-crystal approximation, we made a comparative study between the numerical results obtained from ab-initio calculation using ABINIT or Wien2k within the Density Functional Theory framework with either Local Density Approximation or Generalized Gradient approximation and the pseudo-potential plane-wave method with the Hartwigzen Goedecker Hutter scheme potentials. It is found that the lattice parameter, the phase transition pressure, and the elastic constants (and their derivative with respect to the pressure) follow a quadratic law in x. The variation of the elastic constants is also numerically studied and the phase transformations are discussed in relation to the mechanical stability criteria. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=density%20functional%20theory" title="density functional theory">density functional theory</a>, <a href="https://publications.waset.org/abstracts/search?q=elastic%20properties" title=" elastic properties"> elastic properties</a>, <a href="https://publications.waset.org/abstracts/search?q=ZnS" title=" ZnS"> ZnS</a>, <a href="https://publications.waset.org/abstracts/search?q=ZnSe" title=" ZnSe"> ZnSe</a>, <a href="https://publications.waset.org/abstracts/search?q=" title=" "> </a> </p> <a href="https://publications.waset.org/abstracts/33371/high-pressure-calculations-of-the-elastic-properties-of-znsx-se-1x-alloy-in-the-virtual-crystal-approximation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33371.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">574</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">725</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">724</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 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