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Research ArticleOpen accessEvery word in the titleMathematical Sophistication and Differentiated Emotions during Mathematical Problem SolvingBradford D. Allen, James CarifioGeorge Polya, author of Mathematical Discovery and the enduring best seller How to Solve It: A New Aspect of Mathematical Method, claims that more sophisticated people experience more differentiated emotion during mathematical problem solving, a claim that has been untested for nearly fifty years. Using instruments that measure ongoing evaluations and emotion in real time, and traits that reflect mathematical … …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 7,575 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA Secure Key Authentication Scheme Based on the Hardness of Solving Elliptic Curve Discrete Logarithm ProblemIzzmier Izzuddin Zulkepli, Eddie Shahril IsmailA key authentication scheme is a scheme that protects a user’s public key from modification and counterfeiting by an adversary. The new development and improvement of key authentication schemes should be made continuously so that the systems are safe and practical to be used. To the best of our knowledge, there is no key authentication using the elliptic curve so … …Journal of Computer Science, Vol. 16, Issue 5 · 15 May 2020 · 7,435 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph ColoringHaridas Kumar Das, Nasim RezaThis paper is based on the analytic and computational solution procedures of Gröbner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 27 Jun 2018 · 8,591 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleSolving School Bus Routing Problem by Intelligent Water Drops AlgorithmAmeera Saleh Jaradat, Mohammed Qassim ShatnawiThe School Bus Routing Problem (SBRP) is an essential subject in the development of transportation. Solving the problem will have a great impact on the transportation systems by improving the quality of the provided service and reducing the operations costs. SBRP tries to find an efficient school buses plan where each bus takes up students from different bus stops and … …Journal of Computer Science, Vol. 16, Issue 1 · 11 Jan 2018 · 8,587 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 titleExplicit Direct Integrators of RK Type for Solving Special Fifth-Order Ordinary Differential EquationsMohammed S. Mechee, Murtaza A. KadhimThe main contribution of this paper is the development of direct explicit methods of Runge-Kutta (RK) type for solving special fifth-Order Ordinary Differential Equations (ODEs). For this purpose, we have generalized RKD and RKT methods of special third and fourth-order ODEs. Using Taylor expansion, we have derived the algebraic equations of algebraic equations of order conditions for the proposed RKM … …American Journal of Applied Sciences, Vol. 13, Issue 12 · 26 Dec 2016 · 7,940 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA Successive Admissible Cell Method for Solving Large Scale Linear Assignment Problem with Dense Cost MatrixWarut Boonphakdee, Peerayuth CharnsethikulNormally, the Linear Assignment Problem (LAP) has been solved by successful algorithms such as Lapjv and Munkres programmed as MATLAB codes. This study presented an improved algorithm for solving large scale LAP. A preprocessing (PP) algorithm was proposed to apply for constructing the kth transferred reduced cost matrix then this matrix was solved by Lapjvalgorithm. Performances of PP-Lapjvalgorithm were faster … …Journal of Computer Science, Vol. 12, Issue 8 · 16 Nov 2016 · 6,948 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleFitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value ProblemsAsad Freihat, Radwan Abu-Gdairi, Hammad Khalil et al.In this article, the reproducing kernel Hilbert space W24 [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The … …American Journal of Applied Sciences, Vol. 13, Issue 5 · 11 May 2016 · 7,647 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleA Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE SystemsE.R. El-Zahar, H.M. Habib, M.M. Rashidi, I.M. El-DesokyIn this study, a comparison among three semi-analytical numerical integration algorithms for solving stiff ODE systems is presented. The algorithms are based on Differential Transform Method (DTM) which are Multiple-Step DTM (MsDTM), Enhanced MsDTM (E-MsDTM) and MsDTM with Padé approximants (MsDTM-P). These methods can be classified as explicit one step semi-analytical numerical integration methods. The error and stability analysis of … …American Journal of Applied Sciences, Vol. 12, Issue 5 · 26 Jun 2015 · 6,955 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleLOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITHIN LOCAL FRACTIONAL OPERATORSAmmar Ali NeamahThe paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations. …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 9 Oct 2014 · 6,511 accessesView PDFCite