18 items

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  Software for teaching math and preparing tests cite

  Stankov Dragan (2012)

  Stankov Dragan. "Software for teaching math and preparing tests" in Zbornik radova / Simpozijum Matematika i primene, Beograd 27. i 28. maj 2011, Beograd:Matematički fakultet (2012)

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  Roots of trinomials of bounded height cite

  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

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  Powers of Salem Numbers and Distribution Modulo 1 cite

  Stankov Dragan (2015)

  Stankov Dragan. "Powers of Salem Numbers and Distribution Modulo 1" in 29th Journées Arithmétiques, Debrecen:Debrecen Egyetem (2015): 83-83

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  Distribution Modulo One of the Sum of Powers of a Salem Nubmer cite

  Stankov Dragan (2015)

  Stankov Dragan. "Distribution Modulo One of the Sum of Powers of a Salem Nubmer" in Šesti simpozijum Matematika i primene zbornik radova, Beograd:Univerzitet u Beogradu Matematički fakultet (2015)

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  Savršeni brojevi - nasjtariji nerešeni matematički problem cite

  Stankov Dragan (2015)

  Stankov Dragan. "Savršeni brojevi - nasjtariji nerešeni matematički problem" in Noć istraživača, Zrenjanin:Visoka tehnička škola (2015)

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  On spectar of neither pisot nor salem algebraic integrated cite

  Stankov Dragan (2010)

  Stankov Dragan. "On spectar of neither pisot nor salem algebraic integrated" in Monatshefte Fur Mathematik 159 no. 01-Feb, Vienna:Springer (2010): 115-131. https://doi.org/10.1007/s00605-008-0048-0

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  On Linear Combinations of the Chebyshev Polynomials cite

  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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  The number of unimodular roots of some reciprocal polynomials cite

  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 polynomials

  Dragan 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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  A necessary and sufficient condition for an algebraic integer to be a Salem number cite

  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 polynomials

  Dragan 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 cite

  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 polynomials

  Dragan 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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  The Reciprocal Algebraic Integers Having Small House cite

  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 polynomials

  Dragan Stankov. "The Reciprocal Algebraic Integers Having Small House" in Experimental Mathematics (2021). https://doi.org/ 10.1080/10586458.2021.1982425

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  Збирка решених задатака из Mатематике I cite

  Драган Станков (2016)

  линеарна алгебра, аналитичка геометрија, векторски рачун

  Драган Станков. Збирка решених задатака из Mатематике I, Београд : Универзитет у Београду, Рударско-геолошки факултет, 2016

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  Математика 2 cite

  Драган Станков (2020)

  математичка анализа

  Драган Станков. Математика 2, Београд : Универзитет у Београду, Рударско-геолошки факултет, 2020

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  The number of nonunimodular roots of a reciprocal polynomial cite

  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 polynomials

  Dragan 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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  Creation of a Training Dataset for Question-Answering Models in Serbian cite

  Ranka Stanković, Jovana Rađenović, Maja Ristić, Dragan Stankov (2024)

  Razvoj i primena veštačke inteligencije u jezičkim tehnologijama značajno su napredovali poslednjih godina, posebno u domenu zadatka odgovaranja na pitanja (Question Answering - QA). Dok su postojeći resursi za QA zadatke razvijeni za glavne svetske jezike, srpski jezik je relativno zanemaren u ovoj oblasti. Ovaj rad predstavlja inicijativu za kreiranje obimnog i raznovrsnog skupa podataka za obučavanje modela za odgovaranje na pitanja na srpskom jeziku, koji će doprineti unapređenju jezičkih tehnologija za srpski jezik. Pored brojnih istraživanja o jezičkim modelima ...

  veštačka inteligencija, obrada prirodnog jezika, jezički resursi, anotirani skupovi, ekstrakcija informacija, odgovaranje na pitanja

  Ranka Stanković, Jovana Rađenović, Maja Ristić, Dragan Stankov. "Creation of a Training Dataset for Question-Answering Models in Serbian" in South Slavic Languages in the Digital Environment JuDig Book of Abstracts, University of Belgrade - Faculty of Philology, Serbia, November 21-23, 2024, University of Belgrade - Faculty of Philology (2024)

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  The alternative to Mahler measure of polynomials in several variables cite

  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. ...

  mahler measure, argument principle, Boyd-Lawton limit formula

  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)

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  Approximation of the number of roots that do not lie on the unit circle of a self-reciprocal polynomial cite

  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 ...

  reciprocal polynomial, envelope, unimodular roots

  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)

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  An alternative to Mahler Measure of polynomials cite

  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 ...

  mahler measure, argument principle, limit ratio

  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)