Претрага
10 items
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Approximation of the number of roots that do not lie on the unit circle of a self-reciprocal polynomial
Dragan Stankov (2024)We introduce the ratio of the number of roots not equal to 1 in modulus of a reciprocal polynomial Rd(x) to its degree d. For some sequences of reciprocal polynomials we show that the ratio has a limit L when d tends to infinity. Each of these sequences is defined using a two variable polynomial P(x,y) so that Rd(x) = P(x,xn). For P(x,y) we present the theorem for the limit ratio which is analogous to the Boyd-Lawton limit formula ...Dragan Stankov. "Approximation of the number of roots that do not lie on the unit circle of a self-reciprocal polynomial" in The book of abstracts XIV symposium "mathematics and applications” Belgrade, Serbia, December, 6–7, 2024 , Univerzitet u Beogradu, Matematički fakultet (2024) М64
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Roots of trinomials of bounded height
Stankov Dragan (2014)Stankov Dragan. "Roots of trinomials of bounded height" in International Conference. 13th Serbian Mathematical Congress, Maj, 22-25, 2014, Vrnjačka Banja, Serbia : Book of Abstracts, Niš:Faculty of Sciences and Mathematics (2014): 11 M63
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On the optimality of some multi-point methods for finding multiple roots of nonlinear equation
Ralević Nebojša, Ćebić Dejan (2016)Ralević Nebojša, Ćebić Dejan. "On the optimality of some multi-point methods for finding multiple roots of nonlinear equation" in Nonlinear Analysis: Modelling and Control 21 no. 1 (2016): 121-134 M22
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The third order mean-based Jarratt-type method for finding simple roots of nonlinear equation
Ralević Nebojša, Ćebić Dejan, Pavkov Ivan. "The third order mean-based Jarratt-type method for finding simple roots of nonlinear equation" in IEEE 13th International Symposium on Intelligent Systems and Informatics (SISY) (2015): 123-126. https://doi.org/10.1109/SISY.2015.7325364 M33
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A variant of McDougall-Wotherspoon method for finding simple roots of nonlinear equations
Glišović Nataša, Ralević Nebojša, Ćebić Dejan. "A variant of McDougall-Wotherspoon method for finding simple roots of nonlinear equations" in Scientific Publications of the State University of Novi Pazar, Series A: Applied Mathematics, Informatics and Mechanics 10 no. 1 (2018): 55-61 M52
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Mean-based iterative methods for finding multiple roots in nonlinear chemistry problems
Dejan Ćebić, Nebojša M. Ralević (2021)Dejan Ćebić, Nebojša M. Ralević. "Mean-based iterative methods for finding multiple roots in nonlinear chemistry problems" in Journal of Mathematical Chemistry, Springer Science and Business Media LLC (2021). https://doi.org/10.1007/s10910-021-01253-3 М22
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The number of unimodular roots of some reciprocal polynomials
Dragan Stankov (2020)We introduce a sequence P2n of monic reciprocal polynomials with integer coefficients having the central coefficients fixed. We prove that the ratio between number of nonunimodular roots of P2n and its degree d has a limit when d tends to infinity. We present an algorithm for calculation the limit and a numerical method for its approximation. If P2n is the sum of a fixed number of monomials we determine the central coefficients such that the ratio has the minimal limit. ...Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, Schinzel-Zassenhaus conjecture, Mahler measure, method of least squares, cyclotomic polynomialsDragan Stankov. "The number of unimodular roots of some reciprocal polynomials" in Cmptes rendus mathematique (2020). https://doi.org/10.5802/crmath.28 М23
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The number of nonunimodular roots of a reciprocal polynomial
Dragan Stankov (2023)We introduce a sequence Pd of monic reciprocal polynomials with integer coefficients having the central coefficients fixed as well as the peripheral coefficients. We prove that the ratio of the number of nonunimodular roots of Pd to its degree d has a limit L when d tends to infinity. We show that if the coefficients of a polynomial can be arbitrarily large in modulus then L can be arbitrarily close to 0. It seems reasonable to believe that if ...Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, Schinzel-Zassenhaus conjecture, Mahler measure, method of least squares, cyclotomic polynomialsDragan Stankov. "The number of nonunimodular roots of a reciprocal polynomial" in Comptes rendus mathematique, Elsevier France Editions Scientifiques et Medicales (2023). https://doi.org/10.5802/crmath.422 М23
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An alternative to Mahler Measure of polynomials
Dragan Stankov (2024)We introduce the ratio of the number of roots of a polynomial Pd, greater than one in modulus, to its degree d as an alternative to Mahler measure. We investigate some properties of the limit ratio. We generalise this definition for a two variable polynomial P(x,y) using the Cauchy’s argument principle. We present an algorithm for calculating the limit ratio and a numerical method for its approximation. We estimated the limit ratio for some families of polynomials. Some examples ...Dragan Stankov. "An alternative to Mahler Measure of polynomials" in The book of abstracts XV serbian mathematical congress, Belgrade, Serbia, june, 19–22, 2024, Univerzitet u Beogradu, Matematički fakultet (2024) М34
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The alternative to Mahler measure of polynomials in several variables
Dragan Stankov (2024)We introduce the ratio of the number of roots of a polynomial Pd, greater than one in modulus, to its degree d as an alternative to Mahler measure. We investigate some properties of the alternative. We generalise this definition for a polynomial in several variables using Cauchy’s argument principle. If a polynomial in two variables do not vanish on the torus we prove the theorem for the alternative which is analogous to the Boyd-Lawton limit formula for Mahler measure. ...Dragan Stankov. "The alternative to Mahler measure of polynomials in several variables" in The book of abstracts XIV symposium "mathematics and applications” Belgrade, Serbia, December, 6–7, 2024 , Univerzitet u Beogradu, Matematički fakultet (2024) М64