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120 articles for “Polynomial”
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Research ArticleOpen accessEvery word in the titleGroup Re-keying Protocol Based on Modular Polynomial Arithmetic Over Galois Field GF(2n)Sundaram Sudha, Azman Samsudin, Mohammad Ahmad AliaProblem statement: In this study we propose a group re-keying protocol based on modular polynomial arithmetic over Galois Field GF(2n). Common secure group communications requires encryption/decryption for group re-keying process, especially when a group member is leaving the group. Approach: This study proposes secret keys multiplication protocol based on modular polynomial arithmetic (SKMP), which eliminates the need for the encryption/decryption … …American Journal of Applied Sciences, Vol. 6, Issue 9 · 30 Sep 2009 · 7,165 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Discrete Least Squares Polynomial Fit, Linear Spaces and Data ClassificationFrançois Dubeau, Youness MirThe best discrete least squares polynomial fit to a data set is revisited. We point out some properties related to the best polynomial and precise the dimension of vector spaces encountered to solve the problem. Finally, we suggest a basic classification of data sets based on their increasing or decreasing trend, and on their convexity or concavity form. …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 6,865 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleClosed Form Solution to an Optimal Control Problem by Orthogonal Polynomial ExpansionMohammad Ali Tavallaei, Behrouz TousiIn this study the use of orthogonal polynomials for obtaining a close form solution to optimal control problems with a weighed quadratic cost function, is proposed. The method consists of using the Orthogonal Polynomials for the expansion of the state variables and the control signal. This expansion results in a set of linear equations, from which the closed form solution … …American Journal of Engineering and Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2008 · 7,326 accessesView PDFCite
EditorialOpen accessEvery word in the titleOn Matrix Representation of Bernstein Polynomials for Triple SequencesArulmani Indumathi, Ayhan Esi, Nagarajan SubramanianIn this article, we give an overview of other commonly used basis for the triple sequence space of Bernstein polynomials, the Bernstein basis and put forward a matrix representation of Bernstein polynomials for the triple sequence space and its many useful properties. …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 21 Aug 2020 · 6,356 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Generalized Some (p, q)-Special PolynomialsUgur Duran, Mehmet Acikgoz, Serkan AraciIn this study, we introduce a new class of generalized (p, q)-Bernoulli, (p, q)-Euler and (p, q)-Genocchi polynomials and investigate their some properties. We derive (p, q)-generalizations of some familiar formulae belonging to classical Bernoulli, Euler and Genocchi polynomials. We also obtain a (p, q)-extension of the Srivastava-Pintér addition theorem. …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 18 May 2018 · 7,437 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleApplications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli PolynomialsMehmet Acikgoz, Resul Ates, Ugur Duran, Serkan AraciThis article aims to identify the generating function of modified Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modified Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 4 Jan 2018 · 8,182 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA Computational Method Based on Bernstein Polynomials for Solving FredholmIntegro-Differential Equations under Mixed ConditionsMiloud Moussai, Lakhdar ChiterIn this study, a computational method for solving linear FredholmIntegro-Differential Equation (FIDE) of the first order under the mixed conditions using the Bernstein polynomials. First, we present some properties of these polynomials and the method is explained. These properties are then used to convert the integro-differential equation to a system of linear algebraic equations with unknown Bernstein coefficients. Using Galerkin … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 27 Feb 2017 · 7,142 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA Note on the Bivariate Lagrange Interpolation PolynomialsDan BărbosuThe focus of the research is to obtain reccurence formulas for the bivariate Lagrange interpolation polynomials, similar to the reccurence formulas verified by the univariate Lagrange interpolation polynomials. …American Journal of Applied Sciences, Vol. 5, Issue 12 · 31 Dec 2008 · 6,697 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Asymptotics of Lp Extremal Polynomials on a Complex Curve Plus an Infinite Number of PointsYamina Laskri, Rachid BenzineWe study, for all p>0 and under certain conditions the asymptotic behavior of Lp extremal polynomials with respect to the measure α=β+Y. Where, β denotes a positive Szegö measure on the closed rectifiable Jordan curve E in the complex plane and γ has an infinity of masses in the region exterior to the curve E. …Journal of Mathematics and Statistics, Vol. 1, Issue 3 · 30 Sep 2005 · 5,986 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleDSP-128:Stream Cipher Based On Discrete Log Problem And Polynomial ArithmeticKhaled M. Suwais, Azman SamsudinDSP-128 is a new multithreaded stream cipher based on the intractability of the Discrete Logarithm Problem (DLP) with key size of 128-bit. The design of DSP-128 is divided into three stages: Initialization Stage, Keystream Generation Stage, and Encryption Stage. The design goal of DSP-128 is to come up with a secure stream cipher with good performance for data encryption. The … …American Journal of Applied Sciences, Vol. 5, Issue 7 · 31 Jul 2008 · 7,396 accessesView PDFCite