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interpolating polynomial</title> <meta name="description" content="Search results for: interpolating polynomial"> <meta name="keywords" content="interpolating 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 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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="interpolating 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> 267</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: interpolating polynomial</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">267</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">266</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">265</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">264</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">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> 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">261</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">260</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">259</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">258</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">257</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">256</span> Improving Temporal Correlations in Empirical Orthogonal Function Expansions for Data Interpolating Empirical Orthogonal Function Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ping%20Bo">Ping Bo</a>, <a href="https://publications.waset.org/abstracts/search?q=Meng%20Yunshan"> Meng Yunshan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Satellite-derived sea surface temperature (SST) is a key parameter for many operational and scientific applications. However, the disadvantage of SST data is a high percentage of missing data which is mainly caused by cloud coverage. Data Interpolating Empirical Orthogonal Function (DINEOF) algorithm is an EOF-based technique for reconstructing the missing data and has been widely used in oceanographic field. The reconstruction of SST images within a long time series using DINEOF can cause large discontinuities and one solution for this problem is to filter the temporal covariance matrix to reduce the spurious variability. Based on the previous researches, an algorithm is presented in this paper to improve the temporal correlations in EOF expansion. Similar with the previous researches, a filter, such as Laplacian filter, is implemented on the temporal covariance matrix, but the temporal relationship between two consecutive images which is used in the filter is considered in the presented algorithm, for example, two images in the same season are more likely correlated than those in the different seasons, hence the latter one is less weighted in the filter. The presented approach is tested for the monthly nighttime 4-km Advanced Very High Resolution Radiometer (AVHRR) Pathfinder SST for the long-term period spanning from 1989 to 2006. The results obtained from the presented algorithm are compared to those from the original DINEOF algorithm without filtering and from the DINEOF algorithm with filtering but without taking temporal relationship into account. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=data%20interpolating%20empirical%20orthogonal%20function" title="data interpolating empirical orthogonal function">data interpolating empirical orthogonal function</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20reconstruction" title=" image reconstruction"> image reconstruction</a>, <a href="https://publications.waset.org/abstracts/search?q=sea%20surface%20temperature" title=" sea surface temperature"> sea surface temperature</a>, <a href="https://publications.waset.org/abstracts/search?q=temporal%20filter" title=" temporal filter"> temporal filter</a> </p> <a href="https://publications.waset.org/abstracts/64675/improving-temporal-correlations-in-empirical-orthogonal-function-expansions-for-data-interpolating-empirical-orthogonal-function-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64675.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">324</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> 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">254</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">253</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">252</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">251</span> Optimizing Fermented Paper Production Using Spyrogira sp. Interpolating with Banana Pulp</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hadiatullah">Hadiatullah</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20S.%20D.%20Desak%20Ketut"> T. S. D. Desak Ketut</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20A.%20Ayu"> A. A. Ayu</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20N.%20Isna"> A. N. Isna</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20P.%20Ririn"> D. P. Ririn </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Spirogyra sp. is genus of microalgae which has a high carbohydrate content that used as a best medium for bacterial fermentation to produce cellulose. This study objective to determine the effect of pulp banana in the fermented paper production process using Spirogyra sp. and characterizing of the paper product. The method includes the production of bacterial cellulose, assay of the effect fermented paper interpolating with banana pulp using Spirogyra sp., and the assay of paper characteristics include gram-mage paper, water assay absorption, thickness, power assay of tensile resistance, assay of tear resistance, density, and organoleptic assay. Experiments were carried out with completely randomized design with a variation of the concentration of sewage treatment in the fermented paper production interpolating banana pulp using Spirogyra sp. Each parameter data to be analyzed by Anova variance that continued by real difference test with an error rate of 5% using the SPSS. Nata production results indicate that different carbon sources (glucose and sugar) did not show any significant differences from cellulose parameters assay. Significantly different results only indicated for the control treatment. Although not significantly different from the addition of a carbon source, sugar showed higher potency to produce high cellulose. Based on characteristic assay of the fermented paper showed that the paper gram-mage indicated that the control treatment without interpolation of a carbon source and a banana pulp have better result than banana pulp interpolation. Results of control gram-mage is 260 gsm that show optimized by cardboard. While on paper gram-mage produced with the banana pulp interpolation is about 120-200 gsm that show optimized by magazine paper and art paper. Based on the density, weight, water absorption assays, and organoleptic assay of paper showing the highest results in the treatment of pulp banana interpolation with sugar source as carbon is 14.28 g/m2, 0.02 g and 0.041 g/cm2.minutes. The conclusion found that paper with nata material interpolating with sugar and banana pulp has the potential formulation to produce super-quality paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cellulose" title="cellulose">cellulose</a>, <a href="https://publications.waset.org/abstracts/search?q=fermentation" title=" fermentation"> fermentation</a>, <a href="https://publications.waset.org/abstracts/search?q=grammage" title=" grammage"> grammage</a>, <a href="https://publications.waset.org/abstracts/search?q=paper" title=" paper"> paper</a>, <a href="https://publications.waset.org/abstracts/search?q=Spirogyra%20sp." title=" Spirogyra sp."> Spirogyra sp.</a> </p> <a href="https://publications.waset.org/abstracts/32790/optimizing-fermented-paper-production-using-spyrogira-sp-interpolating-with-banana-pulp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32790.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">333</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> 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">249</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">248</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">247</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> </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> A Study of Chromatic Uniqueness of W14</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zainab%20Yasir%20Al-Rekaby">Zainab Yasir 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> Coloring 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 W14 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/20242/a-study-of-chromatic-uniqueness-of-w14" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20242.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">414</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> A Generalization of Planar Pascal’s Triangle to Polynomial Expansion and Connection with Sierpinski Patterns</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wajdi%20Mohamed%20Ratemi">Wajdi Mohamed Ratemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The very well-known stacked sets of numbers referred to as Pascal’s triangle present the coefficients of the binomial expansion of the form (x+y)n. This paper presents an approach (the Staircase Horizontal Vertical, SHV-method) to the generalization of planar Pascal’s triangle for polynomial expansion of the form (x+y+z+w+r+⋯)n. The presented generalization of Pascal’s triangle is different from other generalizations of Pascal’s triangles given in the literature. The coefficients of the generalized Pascal’s triangles, presented in this work, are generated by inspection, using embedded Pascal’s triangles. The coefficients of I-variables expansion are generated by horizontally laying out the Pascal’s elements of (I-1) variables expansion, in a staircase manner, and multiplying them with the relevant columns of vertically laid out classical Pascal’s elements, hence avoiding factorial calculations for generating the coefficients of the polynomial expansion. Furthermore, the classical Pascal’s triangle has some pattern built into it regarding its odd and even numbers. Such pattern is known as the Sierpinski’s triangle. In this study, a presentation of Sierpinski-like patterns of the generalized Pascal’s triangles is given. Applications related to those coefficients of the binomial expansion (Pascal’s triangle), or polynomial expansion (generalized Pascal’s triangles) can be in areas of combinatorics, and probabilities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pascal%E2%80%99s%20triangle" title="pascal’s triangle">pascal’s triangle</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20pascal%E2%80%99s%20triangle" title=" generalized pascal’s triangle"> generalized pascal’s triangle</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20expansion" title=" polynomial expansion"> polynomial expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=sierpinski%E2%80%99s%20triangle" title=" sierpinski’s triangle"> sierpinski’s triangle</a>, <a href="https://publications.waset.org/abstracts/search?q=combinatorics" title=" combinatorics"> combinatorics</a>, <a href="https://publications.waset.org/abstracts/search?q=probabilities" title=" probabilities"> probabilities</a> </p> <a href="https://publications.waset.org/abstracts/37988/a-generalization-of-planar-pascals-triangle-to-polynomial-expansion-and-connection-with-sierpinski-patterns" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37988.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">367</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> Frobenius Manifolds Pairing and Invariant Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zainab%20Al-Maamari">Zainab Al-Maamari</a>, <a href="https://publications.waset.org/abstracts/search?q=Yassir%20Dinar"> Yassir Dinar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=invariant%20ring" title="invariant ring">invariant ring</a>, <a href="https://publications.waset.org/abstracts/search?q=Frobenius%20manifold" title=" Frobenius manifold"> Frobenius manifold</a>, <a href="https://publications.waset.org/abstracts/search?q=inversion" title=" inversion"> inversion</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20theory" title=" representation theory"> representation theory</a> </p> <a href="https://publications.waset.org/abstracts/143099/frobenius-manifolds-pairing-and-invariant-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143099.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">98</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">243</span> A Comparative Study on Sampling Techniques of Polynomial Regression Model Based Stochastic Free Vibration of Composite Plates</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Dey">S. Dey</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20Mukhopadhyay"> T. Mukhopadhyay</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Adhikari"> S. Adhikari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an exhaustive comparative investigation on sampling techniques of polynomial regression model based stochastic natural frequency of composite plates. Both individual and combined variations of input parameters are considered to map the computational time and accuracy of each modelling techniques. The finite element formulation of composites is capable to deal with both correlated and uncorrelated random input variables such as fibre parameters and material properties. The results obtained by Polynomial regression (PR) using different sampling techniques are compared. Depending on the suitability of sampling techniques such as 2k Factorial designs, Central composite design, A-Optimal design, I-Optimal, D-Optimal, Taguchi’s orthogonal array design, Box-Behnken design, Latin hypercube sampling, sobol sequence are illustrated. Statistical analysis of the first three natural frequencies is presented to compare the results and its performance. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=composite%20plate" title="composite plate">composite plate</a>, <a href="https://publications.waset.org/abstracts/search?q=natural%20frequency" title=" natural frequency"> natural frequency</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20regression%20model" title=" polynomial regression model"> polynomial regression model</a>, <a href="https://publications.waset.org/abstracts/search?q=sampling%20technique" title=" sampling technique"> sampling technique</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertainty%20quantification" title=" uncertainty quantification"> uncertainty quantification</a> </p> <a href="https://publications.waset.org/abstracts/24714/a-comparative-study-on-sampling-techniques-of-polynomial-regression-model-based-stochastic-free-vibration-of-composite-plates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24714.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">513</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> 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">241</span> Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reza%20Mohammadi">Reza Mohammadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdieh%20Sahebi"> Mahdieh Sahebi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourth-order%20parabolic%20equation" title="fourth-order parabolic equation">fourth-order parabolic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient" title=" variable coefficient"> variable coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20quintic%20spline" title=" polynomial quintic spline"> polynomial quintic spline</a>, <a href="https://publications.waset.org/abstracts/search?q=off-step%20points" title=" off-step points"> off-step points</a> </p> <a href="https://publications.waset.org/abstracts/51758/quintic-spline-solution-of-fourth-order-parabolic-equations-arising-in-beam-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51758.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">352</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">240</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">239</span> Estimating X-Ray Spectra for Digital Mammography by Using the Expectation Maximization Algorithm: A Monte Carlo Simulation Study</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chieh-Chun%20Chang">Chieh-Chun Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Cheng-Ting%20Shih"> Cheng-Ting Shih</a>, <a href="https://publications.waset.org/abstracts/search?q=Yan-Lin%20Liu"> Yan-Lin Liu</a>, <a href="https://publications.waset.org/abstracts/search?q=Shu-Jun%20Chang"> Shu-Jun Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jay%20Wu"> Jay Wu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With the widespread use of digital mammography (DM), radiation dose evaluation of breasts has become important. X-ray spectra are one of the key factors that influence the absorbed dose of glandular tissue. In this study, we estimated the X-ray spectrum of DM using the expectation maximization (EM) algorithm with the transmission measurement data. The interpolating polynomial model proposed by Boone was applied to generate the initial guess of the DM spectrum with the target/filter combination of Mo/Mo and the tube voltage of 26 kVp. The Monte Carlo N-particle code (MCNP5) was used to tally the transmission data through aluminum sheets of 0.2 to 3 mm. The X-ray spectrum was reconstructed by using the EM algorithm iteratively. The influence of the initial guess for EM reconstruction was evaluated. The percentage error of the average energy between the reference spectrum inputted for Monte Carlo simulation and the spectrum estimated by the EM algorithm was -0.14%. The normalized root mean square error (NRMSE) and the normalized root max square error (NRMaSE) between both spectra were 0.6% and 2.3%, respectively. We conclude that the EM algorithm with transmission measurement data is a convenient and useful tool for estimating x-ray spectra for DM in clinical practice. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=digital%20mammography" title="digital mammography">digital mammography</a>, <a href="https://publications.waset.org/abstracts/search?q=expectation%20maximization%20algorithm" title=" expectation maximization algorithm"> expectation maximization algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=X-Ray%20spectrum" title=" X-Ray spectrum"> X-Ray spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=X-Ray" title=" X-Ray"> X-Ray</a> </p> <a href="https://publications.waset.org/abstracts/3616/estimating-x-ray-spectra-for-digital-mammography-by-using-the-expectation-maximization-algorithm-a-monte-carlo-simulation-study" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3616.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">730</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">238</span> Spatial Interpolation Technique for the Optimisation of Geometric Programming Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Debjani%20Chakraborty">Debjani Chakraborty</a>, <a href="https://publications.waset.org/abstracts/search?q=Abhijit%20Chatterjee"> Abhijit Chatterjee</a>, <a href="https://publications.waset.org/abstracts/search?q=Aishwaryaprajna"> Aishwaryaprajna</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=geometric%20programming%20problem" title="geometric programming problem">geometric programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20optimisation%20technique" title=" multivariate optimisation technique"> multivariate optimisation technique</a>, <a href="https://publications.waset.org/abstracts/search?q=posynomial" title=" posynomial"> posynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=spatial%20interpolation" title=" spatial interpolation"> spatial interpolation</a> </p> <a href="https://publications.waset.org/abstracts/70385/spatial-interpolation-technique-for-the-optimisation-of-geometric-programming-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70385.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">371</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=interpolating%20polynomial&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=interpolating%20polynomial&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=interpolating%20polynomial&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=interpolating%20polynomial&page=5">5</a></li> <li class="page-item"><a class="page-link" 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