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18 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

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

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

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

Analyses of Landslide Hazard Evaluation Factors Using Polynomial Interpolation
Jovanovski Milorad, Abolmasov Biljana, Peshevski Igor. "Analyses of Landslide Hazard Evaluation Factors Using Polynomial Interpolation" in Landslide Science and Practice, Volume 1: Landslide Inventory and Susceptibility and hazard Zoning 1, :Springer Verlag Berlin Heidlelberg (2013): 561566. https://doi.org/10.1007/9783642313257_73

Linearization of Input Signal as a Necessary Tool in Stochastic Modeling of Karst Groundwater
Veljko Marinović (2021)Modelling of karst hydrogeological systems is a very complicated task, bearing in mind that for a deterministic model one should know the internal physical processes of precipitation transformation into discharge, while for a stochastic model nonlinear dynamic systems such as karst should be simulated by linear regression equations. Stochastic models need linearization of input time series due to often large residual in the recession period. This occur because the model is not able to absorb single rain episodes, which ...Veljko Marinović. "Linearization of Input Signal as a Necessary Tool in Stochastic Modeling of Karst Groundwater" in Karst: From Top to Bottom, Belgrade, 6.6.2021., Belgrade : Centre for Karst Hydrogeology (2021)

Advantages and Disadvantages of a Parallel and Zigzag Method of Acquisition in Walking Mode in Magnetometric Archeological Research
магнетометријска испитивања, цикцак и паралелна аквизиција у ходајућем моду, линеарне аномалије, археологија... in the direc tion perpendicular to the direction of acquisition (Figure 10.a.). Figure 10 The same data was gridded using a nonlinear local polynomial method, and it was observed that there was an absence of linear anomalies, which supports the hypothesis that the process of linear interpolation ...
... .(93110) Figure 10. Contour map shown in Figure 8. a. Filtered by moving average fi lter in two direction; b. interpolated by nonlinear local polynomial method. Fig. 11 Contour map of vertical gradient of TMI in last one case with fl ecked anomaly due to the large error of GPS. 107 Archaeology ...
... direction of acquisition. Also, the absence of linear anoma lies is observed using the nonlinear interpolation method. In this case, the local polynomial method proved to be the best. In order to avoid linear anomalies it is neces sary to apply a parallel method of data acquisition in the walking ...Mirko Petković, Vesna Cvetkov, Branislav Sretenović. "Advantages and Disadvantages of a Parallel and Zigzag Method of Acquisition in Walking Mode in Magnetometric Archeological Research" in Arheologija i prirodne nauke (2014)

Preliminary regional landslide susceptibility assessment using limited data
Igor Peshevski, Milorad Jovanovski, Biljana Abolmasov, Jovan Papic, Uroš Đurić, Miloš Marjanović, Ubydul Haque, Natasha Nedelkovska (2019)In this paper a heuristic approach for preliminary regional landslide susceptibility assessment using limited amount of data is presented. It is called arbitrary polynomial method and takes into account 5 landslide conditioning parameters: lithology, slope inclination, average annual rainfall, land use and maximum expected seismic intensity. According to the method, in the first stage, a gradation is performed for each of the carefully selected conditioning parameters by assigning so called rating points to the grid cells on which the ...... heuristic approach for preliminary regional landslide susceptibility assessment using limited amount of data is presented. It is called arbitrary polynomial method and takes in to account 5 landslide conditioning parameters: lithology, slope inclination, average annual rain fall, land use and maximum ...
... accepted October 26, 2018 Available online February 15, 2019 Keywords: regional landslide susceptibility, arbitrarypolynomial method, conditioning parameters, sensitivity, Polog region G eo lo g ia C ro a ti ca Geologia Croatica 72/182 have proven to be a reliable ...
... a region by using a limited amount of datasets due to the previously mentioned constraints, a specific heuristic approach called the arbitrarypolynomial method is presented here. The approach takes into account the findings of past research (e.g. by ABOLMASOV & STOJKOV 1994, ABOLMASOV & STOJKOV ...Igor Peshevski, Milorad Jovanovski, Biljana Abolmasov, Jovan Papic, Uroš Đurić, Miloš Marjanović, Ubydul Haque, Natasha Nedelkovska. "Preliminary regional landslide susceptibility assessment using limited data" in Geologica Croatica , Croatian Geological Society (2019). https://doi.org/10.4154/gc.2019.03

Meanbased iterative methods for finding multiple roots in nonlinear chemistry problems
Dejan Ćebić, Nebojša M. Ralević (2021)Dejan Ćebić, Nebojša M. Ralević. "Meanbased 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/s10910021012533

Simple 2D Gravitydensity inversion for modeling of the sedimentary basin basement
Ivana Vasiljević, Snežana Ignjatović, Dragana Đurić,. "Simple 2D Gravitydensity inversion for modeling of the sedimentary basin basement" in International scientific conference Challenges in Applied Geology and Geophysics: 100th Anniversary of Applied Geology at AGH University of Science and Technology, Book of abstracts, Kraków, Poland, 1013. Sep. 2019, Kraków, Poland : AGH University of Science and Technology (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)

Simple 2D gravity–density inversion for the modeling of the basin basement: example from the Banat area, Serbia
We have developed a technique to calculate lateral density distribution of the sedimentary basin basement by combining linear gravity–density inversion and 2D forward modeling. The procedure requires gravity anomaly data, depthtobasement data and density data for the sediments (density–depth distribution). Gravity efect of density variations in the basement was extracted from the total gravity anomaly by removing the joint efect of the sediments with vertical density variations and homogeneous basement of average density contrast (calculated by 2D modeling). Gravity ...Ivana Vasiljević, Snežana Ignjatović, Dragana Đurić. "Simple 2D gravity–density inversion for the modeling of the basin basement: example from the Banat area, Serbia" in Acta Geophysica, Springer (2019). https://doi.org/10.1007/s11600019003289

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

Correlation Between Dynamic CBR and Compaction and Bearing Capacity of Pavement Foundation Layers
This paper presents a dynamic California Bearing Ratio (CBRd) device that can be used on a prepared pavement foundation layer to obtain a certain parameter of the tested material in the laboratory and in situ in a direct and fast way. For the selected natural material (gravel), it is shown that the laboratory CBRd can be used to estimate the compaction and bearing capacity, because it correlates well with the parameters of the standard and modifed Proctor compaction tests. ...korelacija parametara, donji slojevi saobraćajnica, laboratorijska i terenska ispitivanja, dinamički kalifornijski indeks nosivosti CBRd... decreasing trend for the measured CBR,„, values. The impact of the water content for the formation of CBR, , was successfully predicted using polynomial functions: CBR, (SP)=0.2216w* +3.8763w" —12.611w+28.471, R* =0.9581, (5) CBR,, (MP)=0.1547w* +2.5276w" —7.9066w+50.122, R* =0.8999, (4) where ...Milan Bogdanović, Snežana Bogdanović, Dragoslav Rakić, Irena Basarić Ikodinović. "Correlation Between Dynamic CBR and Compaction and Bearing Capacity of Pavement Foundation Layers" in Soil Mechanics and Foundation Engineering, Springer Science and Business Media LLC (2024). https://doi.org/10.1007/s1120402409939x

Properties of fly ash and slag from the power plants
This paper describes the physical, chemical and mineral properties of ash and slag, which were taken from thermal power plants Nikola Tesla A, Nikola Tesla B, Kostolac A and Kostolac B. The knowledge of the mineralogical material composition is important because the type of minerals directly determines the properties of the fly ash and slag and their possible application. Laboratory tests showed that ash and slag samples consist of the following minerals: amorphous materials, quartz, feldspar, mullite, melilite, cristobalite, ...fly ash, slag, physical composition, chemical composition, mineral composition, Xray diffraction method... which certain correlation co efficients were determined and compared between the ash and slag. Dependence for all the samples was done using polynomial functions, because only this function gave the best correlation results. Results of the correlation coefficient, as a relationship and a correlation ...Miloš Šešlija, Aleksandra Rosić, Nebojša Radović, Milinko Vasić, Mitar Đogo, Milovan Jotić. "Properties of fly ash and slag from the power plants" in Geologia Croatica, Zagreb : Croatian Geological Survey (2016). https://doi.org/10.4154/gc.2016.26

A KnowledgeBased Approach to Mine Ventilation Planning in Yugoslav Mining Practice
Ventilation system analysis is a complex process based on the calculation and analysis of numerous parameters. These problems can be successfully solved by the SimVent numerical package, but a full understanding and use of the obtained results require the involvement of an experienced specialist in the ventilation field. The solution was found in the creation of a hybrid system INVENTS, whose knowledge base represents a formalization of the expert knowledge in the mine ventilation field. In this paper, we ...... (branches 1, 3, 5, 7, 9, 14, 15, 16). The pressure of the main fan is represented by the characteristic working curve of the fan, approximated by a polynomial giving the dependence of the fan depression from air flow. The SimVent simulator of complex mine ventilation networks based on the HardyCross ...Nikola Lilić, Ivan Obradović, Ranka Stanković. "A KnowledgeBased Approach to Mine Ventilation Planning in Yugoslav Mining Practice" in Mineral Resources Engineering 11 no. 4, Imperial College Press (2002): 361382. https://doi.org/10.1142/S0950609802001014

Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules
The stability analysis of homogeneous rock slope following the Hoek–Brown failure criterion under the hypothesis of different flow rules is performed based on limit equilibrium and finite element methods. The applied failure criterion is the generalized Hoek–Brown that can be introduced as a shear/normal function in analysis applying different flow rules. The results are compared with those obtained by the application of equivalent shear strength parameters of the Mohr–Coulomb criterion, considering that this is still the most widely used ...Kružna klizna površ, HukBraunov kriterijum loma, Kriterijum popuštanja, Smičuća/normalna funkcija, Nivo napona, Verovatnoća i parametarska analizaSvetlana Melentijević, Zoran Berisavljević, Dušan Berisavljević, Claudio Olalla Marañón . "Rock slope stability analysis under Hoek–Brown failure criterion with different flow rules" in Bulletin of Engineering Geology and the Environment , Springer (2024). https://doi.org/10.1007/s10064024036670