Претрага
11 items

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, SchinzelZassenhaus 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

The Reciprocal Algebraic Integers Having Small House
Dragan Stankov (2021)Algebraic integer, the house of algebraic integer, maximal modulus, reciprocal polynomial, primitive polynomial, SchinzelZassenhaus 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

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, SchinzelZassenhaus 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

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, SchinzelZassenhaus 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

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, SchinzelZassenhaus 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

Nonequilibrium athermal randomfield Ising model on hexagonal lattices
Svetislav Mijatović, Dragutin Jovković, Đorđe Spasojević. "Nonequilibrium athermal randomfield Ising model on hexagonal lattices" in Physical Review E, American Physical Society (APS) (2021). https://doi.org/10.1103/PhysRevE.103.032147

Quantitative analysis of syllable properties in Croatian, Serbian, Russian, and Ukrainian
Biljana Rujević, Marija Kaplar, Sebastijan Kaplar, Ranka Stanković, Ivan Obradović, Jan Mačutek (2021)Biljana Rujević, Marija Kaplar, Sebastijan Kaplar, Ranka Stanković, Ivan Obradović, Jan Mačutek. "Quantitative analysis of syllable properties in Croatian, Serbian, Russian, and Ukrainian" in Language and Text: Data, models, information and applications, John Benjamins Publishing Company (2021). https://doi.org/10.1075/cilt.356.04ruj

An Efficient Class of Iterative RootFinding Methods with Applications
Dejan Ćebić, Nebojša Ralević (2021)Dejan Ćebić, Nebojša Ralević. "An Efficient Class of Iterative RootFinding Methods with Applications" in 2021 IEEE 19th International Symposium on Intelligent Systems and Informatics (SISY), IEEE (2021). https://doi.org/10.1109/SISY52375.2021.9582495

Frequency and Length of Syllables in Serbian
Marija Radojičić, Biljana Lazić, Sebastijan Kaplar, Ranka Stanković, Ivan Obradović, Ján Mačutek, Lívia Leššová (2019)Basic analyses of several properties of syllables (the rankfrequency distribution, the distribution of length, and the relation between length and frequency) in Serbian is presented. The syllabification algorithm used combines the maximum onset principle and the sonority hierarchy. Results indicate that syllables behave similarly to words as far as mathematical models are concerned, but values of parameters in models for syllables are quite different from those for words.... Croatian, a language which is close to Serbian. No other language in their study achieves a stronger correlation. This fact tempts us to formulate a conjecture (which, of course, must be corroborated on many other languages) that the correlation between frequency and length of syllables is stronger than ...Marija Radojičić, Biljana Lazić, Sebastijan Kaplar, Ranka Stanković, Ivan Obradović, Ján Mačutek, Lívia Leššová. "Frequency and Length of Syllables in Serbian" in Glottometrics (2019)

An optimal sixteenth order family of methods for solving nonlinear equations and their basins of attraction
Dejan Ćebić, Nebojša Ralević, Marina Marčeta. "An optimal sixteenth order family of methods for solving nonlinear equations and their basins of attraction" in Mathematical Communications (2020)

Critical disorder and critical magnetic field of the nonequilibrium athermal randomfield Ising model in thin systems
Svetislav Mijatović, Dragutin Jovković, Sanja Janićević, Đorđe Spasojević. "Critical disorder and critical magnetic field of the nonequilibrium athermal randomfield Ising model in thin systems" in Physical Review E, American Physical Society (APS) (2019). https://doi.org/10.1103/PhysRevE.100.032113