Претрага
9 items
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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
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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
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The Reciprocal Algebraic Integers Having Small House
Dragan Stankov (2021)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 Reciprocal Algebraic Integers Having Small House" in Experimental Mathematics (2021). https://doi.org/ 10.1080/10586458.2021.1982425
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A necessary and sufficient condition for an algebraic integer to be a Salem number
Dragan Stankov (2019)We present a necessary and sufficient condition for a root greater than unity of a monic reciprocal polynomial of an even degree at least four, with integer coefficients, to be a Salem number. This condition requires that the minimal polynomial of some power of the algebraic integer has a linear coefficient that is relatively large. We also determine the probability that an arbitrary power of a Salem number, of certain small degrees, satisfies this condition.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. "A necessary and sufficient condition for an algebraic integer to be a Salem number" in Journal de theorie des nombres de Bordeaux (2019). https://doi.org/10.5802/jtnb.1076
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On the distribution modulo 1 of the sum of powers of a Salem number
Dragan Stankov (2016)It is well known that the sequence of powers of a Salem number θ, modulo 1, is dense in the unit interval, but is not uniformly distributed. Generalizing a result of Dupain, we determine, explicitly, the repartition function of the sequence , where P is a polynomial with integer coefficients and θ is quartic. Also, we consider some examples to illustrate the method of determination.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. "On the distribution modulo 1 of the sum of powers of a Salem number" in Comptes rendus Mathematique (2016). https://doi.org/10.1016/j.crma.2016.03.012
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On Linear Combinations of the Chebyshev Polynomials
Stankov Dragan (2015)Stankov Dragan. "On Linear Combinations of the Chebyshev Polynomials" in Publications de lInstitut Mathématique 111 no. 97, Beograd:Matematički institut SANU (2015): 57-67. https://doi.org/DOI: 10.2298/PIM150220001S
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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
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A Model for Determining Fuzzy Evaluations of Partial Indicators of Availability for High-Capacity Continuous Systems at Coal Open Pits Using a Neuro-Fuzzy Inference System
This paper presents a model for determining fuzzy evaluations of partial indicators of the availability of continuous systems at coal open pits using a neuro-fuzzy inference system. The system itself is a combination of fuzzy logic and artificial neural networks. The system availability is divided into partial indicators. By combining the fuzzy logic and artificial neural networks, a model is obtained that has the ability to learn and uses expert judgment for that learning. This paper deals with the ...системи, континуални системи експлоатације (роторни багер-транспортер-дробилично постројење), рударство, расположивост, меко рачунарство, фази логика, ANN, ANFISMiljan Gomilanović, Miloš Tanasijević, Saša Stepanović, Filip Miletić. "A Model for Determining Fuzzy Evaluations of Partial Indicators of Availability for High-Capacity Continuous Systems at Coal Open Pits Using a Neuro-Fuzzy Inference System" in Energies, MDPI AG (2023). https://doi.org/10.3390/en16072958
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Споменица 1991. – 2015. година: 135 година геологије и 70 година рударства на Универзитету у Београду
... gradual shift in magma composition?, Journal of Volcanology and Geothermal Research, 2015. 357. Stankov D.: On Linear Combinations of the Chebyshev Polynomials, Publi- cations de l"Institut Mathématique, 2015. 358. Prelević D., Brügmann G., Barth M., Božović M., Cvetković V., Foley S., Maksimović Z.: ...главни и одговорни уредник Душан Поломчић. Споменица 1991. – 2015. година: 135 година геологије и 70 година рударства на Универзитету у Београду, Београд : Универзитет у Београду, Рударско-геолошки факултет, 2016