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179 items
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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)
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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)
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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 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 polynomials... million, n ≈ one hundred million suggest that these limits exist and that they are both equal to 0.20885. 4. Extension of Mahler measure The definition of the Mahler measure could be extended to polynomials in several variables. We recall Jensen’s formula which states that 1 2π ∫2π 0 log |P (e iθ)|dθ ...
... of million, n ~ one hundred million suggest that these limits exist and that they are both equal to 0.20885. 4. Extension of Mahler measure The definition of the Mahler measure could be extended to polynomials in several variables. We recall Jensen’s formula which states that x ri log |P(e!®)|d = loglag|+D7_ ...
... mesure de Mahler. Funding. Partially supported by Serbian Ministry of Education and Science, Project 174032. Manuscript received 5th December 2019, accepted 26th February 2020. 1. Introduction If P (x) = ad xd +ad−1xd−1+·· ·+a1x+a0 (ad 6= 0) has zeros α1,α2, . . . ,αd then the Mahler measure of P (x) ...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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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 polynomials... Algebraic integer; the house of algebraic integer; maximal modulus; reciprocal polynomial; primitive polynomial, Schinzel-Zassenhaus conjecture; Mahler measure; method of least squares; cyclotomic polynomials 2010MATHEMATICS SUBJECT CLASSIFICATION 11C08, 11R06, 11Y40 1. Introduction Let α be an algebraic ...
... of degree d, with conjugates α = α1,α2, . . . ,αd and minimal polynomial P. The house of α (and of P) is de�ned by: α = max 1≤i≤d |αi|. The Mahler measure of α isM(α) = ∏d i=1max(1, |αi|). Clearly, α > 1, and a theorem of Kronecker tells us that α = 1 if and only if α is a root of unity. In 1965 ...
... integer can be written as a factor of a reciprocal polynomial with at most eight monomials. The same fact is valid for many polynomials having Mahler measure less than 1.3 and has been used for creation of Mossingho� ’s list of such polynomials [11]. We have used here this idea to search for extremal ...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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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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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)
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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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Indexing of textual databases based on lexical resources: A case study for Serbian
In this paper we describe an approach to improvement of information retrieval results for large textual databases by pre-indexing documents using bag-of-words and Named Entity Recognition. The approach was applied on a database of geological projects financed by the Republic of Serbia in the last half century. Each document within this database is described by metadata, consisting of several fields such as title, domain, keywords, abstract, geographical location and the like. A bag of words was produced from these ...Ranka Stanković, Cvetana Krstev, Ivan Obradović, Olivera Kitanović. "Indexing of textual databases based on lexical resources: A case study for Serbian" in Semantic Keyword-based Search on Structured Data Sources : First COST Action IC1302 International KEYSTONE Conference, IKC 2015, Coimbra, Portugal, September 8-9, 2015. Revised Selected Papers, Springer (2015). https://doi.org/10.1007/978-3-319-27932-9_15
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Comparative analysis of correlation coefficients in mineralogical and geophysical data from the mine tailing site “Rudnik” (Serbia)
Vesna Cvetkov, Filip Arnaut, Dragana Životić. "Comparative analysis of correlation coefficients in mineralogical and geophysical data from the mine tailing site “Rudnik” (Serbia)" in 5th Congress Geologists of the Republic of North Macedonia, Ohrid, 28-29. 10. 2024, Македонско геолошко друштво (2024)
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Prioritization of strategic measures for strengthening the security of supply of the Serbian natural gas sector
To strengthen the security of supply of the Serbian gas sector, it is necessary to analyze the impact of planned strategic measures. The analysis involves the identification of the most influential threats to the security of natural gas supply and prioritization of the strategic measures for overcoming the consequences of threats. The proposed methodology is based on Fuzzy Analytic Hierarchy Process. The obtained weights for the identified threats and strategic measures are formed according to experts' judgments. The results ...Sigurnost snabdevanja, Donošenje odluka, Snabdevanje prirodnim gasom, Fazi AHP, Energetski indikatori... are termination of supply at the border with Hungary, termination of supply from Russia, and termination of supply from gas storage. The strategic measure with the highest priority is the so-called “Turkish Stream” project. Two additional strategic measures (gas interconnection Serbia – Bulgaria and ...
... contain the evaluation of likelihoods and severities of identified threats, nor the effectiveness and the individual contribution of each strategic measure to the improvement of the security of natural gas supply. The objective of this work is to analyze the key threats and strategic * Corresponding ...
... case of disrup- tion of the single largest part of the infrastructure on a day of excep- tionally high gas demand (GNI, 2018). The HHI represents the measure of concentration and diversity of gas supply (Chang, 2007). The paper is organized as follows. Section 2 presents the model which is used for analyzing ...Boban Pavlović, Dejan Ivezić, Marija Živković. "Prioritization of strategic measures for strengthening the security of supply of the Serbian natural gas sector" in Energy Policy, Elsevier BV (2020). https://doi.org/10.1016/j.enpol.2020.111936
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On the compatibility of lexical resources for NooJ
Lexical resources for many languages are provided for the NooJ linguistic development environment. Meta-data descriptions of morphosyntactic and semantic properties of these languages and their resources are a mandatory part of each language module. In this paper we analyze how well the meta-data actually describe resources for a chosen subset of languages and to what extent are they compatible across languages to support multilingual processing. We show that there is place for improvement in both directions.Ranka Stanković, Miloš Utvić, Duško Vitas, Cvetana Krstev, Ivan Obradović. "On the compatibility of lexical resources for NooJ" in Automatic Processing of Various Levels of Linguistic Phenomena: Selected Papers from the 2011 International Nooj Conference, Cambridge Scholars Publishing (2012): 96-108
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Transformer-Based Composite Language Models for Text Evaluation and Classification
Parallel natural language processing systems were previously successfully tested on the tasks of part-of-speech tagging and authorship attribution through mini-language modeling, for which they achieved significantly better results than independent methods in the cases of seven European languages. The aim of this paper is to present the advantages of using composite language models in the processing and evaluation of texts written in arbitrary highly inflective and morphology-rich natural language, particularly Serbian. A perplexity-based dataset, the main asset for the ...Mihailo Škorić, Miloš Utvić, Ranka Stanković. "Transformer-Based Composite Language Models for Text Evaluation and Classification" in Mathematics, MDPI AG (2023). https://doi.org/10.3390/math11224660
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Mapping and classifying large deformation from digital imagery: application to analogue models of lithosphere deformation
kontinentalna tektonika: kompresija, kontinentalna tektonika: ekstenzija, kontinentalna tektonika: transkurentni i transformni rasedi, pukotine, rasedi, zone snažnih deformacija, kinematika deformacija kore i omotača, teorijska mehanika, modelovanjeTaco Broerse, Nemanja Krstekanić, Cor Kasbergen, Ernst Willingshofer. "Mapping and classifying large deformation from digital imagery: application to analogue models of lithosphere deformation" in Geophysical Journal International, Oxford University Press (OUP) (2021). https://doi.org/10.1093/gji/ggab120
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Topic Modeling of the SrpELTeC Corpus: A Comparison of NMF, LDA, and BERTopic
Modeliranje tema je efikasan način da se dobije uvid u velike količine podataka. Neki od najčešće korišćenih metoda za modeliranje tema su Latentna Dirihleova alokacija (LDA) i faktorizacija nenegativne matrice (NMF). Međutim, sa porastom modela samopažnje i unapred obučenih jezičkih modela, pojavili su se novi načini za ekstrakcju tema. BERTopic predstavlja novi pristup modeliranju tema. U ovom radu smo uporedili performanse LDA, NMF i BERTopic na književnim tekstovima na srpskom, merenjem koherentnosti tema i raznovrsnosti tema, kao i kvalitativnom ...Teodora Mihajlov, Milica Ikonić Nešić, Ranka Stanković, Olivera Kitanović. "Topic Modeling of the SrpELTeC Corpus: A Comparison of NMF, LDA, and BERTopic" in Annals of Computer Science and Information Systems, IEEE (2024). https://doi.org/10.15439/2024F1593
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The Impact Assessment of NO2 Emission from District Heating Plant on Local Air Quality, the Case of Zemun, Belgrade
The Belgrade district heating system relies on fossil fuels in heat production, where natural gas has the largest share of around 95% and fuel oil with around 4.4%. The Zemun heating plant is completely fueled with fuel oil. Currently, it is the largest plant that is not fueled with natural gas. The objective of this paper is to assess the impact of NO2 from the Zemun heating plant on local air quality by analyzing and comparing the concentration of ...NO2, Zagađenje vazduha, Kvalitet vazduh na lokalnom nivou, Model disperzije, AERMOD, Daljinsko grejanje, BeogradBoban Pavlović, Uroš Pantelić, Marija Živković, Dejan Ivezić. "The Impact Assessment of NO2 Emission from District Heating Plant on Local Air Quality, the Case of Zemun, Belgrade" in Conference on Sustainable Development of Energy, Water and Environment Systems, Dubrovnik, 10.10.-15.10.2021., University of Zagreb, Zagreb, Croatia; Instituto Superior Técnico, Lisbon, Portugal (2021)
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Concepts for Improving Machine Learning Based Landslide Assessment
... thresholds (Fig. 13b). The AUC is used as a single measure of model evaluation, approaching a value of 1 for good models, while a value of 0.5 denotes a random guess model (Bradley 1997). The common and well-established raster map comparison measure is kappa statistic. The kappa statistic measures ...
... results are presented in Table 8. Some of the advantages of the accuracy measure are that it is very easy to interpret and is simple to calculate, which are the main reasons why it is very popular. Nevertheless, this measure does not consider the distribution/proportion of each class in the dataset ...
... Witten et al. (2011), Mitchel (1997), and Hastie et al. (2009), wherein most of these are explained in detail. The obtained values of the overlay measure (AUC) indicate a good performance for all four models with slight differences (Table 3 and Fig. 7). The values of TP (true positive) rate indicate ...Miloš Marjanović, Mileva Samardžić Petrović, Biljana Abolmasov, Uroš Đurić. "Concepts for Improving Machine Learning Based Landslide Assessment" in Natural Hazards GIS-based Spatial Modeling Using Data Mining Techniques, Advances in Natural and Technological Hazards Research, volume 48, Springer Nature Switzerland AG 2019 (2019). https://doi.org/10.1007/978-3-319-73383-8_2
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A comparison between ARIMA, LSTM, ARIMA-LSTM and SSA for cross-border rail freight traffic forecasting: the case of Alpine-Western Balkan Rail Freight Corridor
Miloš Milenković, Miloš Gligorić, Nebojša Bojović, Zoran Gligorić. "A comparison between ARIMA, LSTM, ARIMA-LSTM and SSA for cross-border rail freight traffic forecasting: the case of Alpine-Western Balkan Rail Freight Corridor" in Transportation Planning and Technology, Informa UK Limited (2023). https://doi.org/10.1080/03081060.2023.2245389
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Ground surface subsidence monitoring using sentinel-1 in the “Kostolac” open pit coal mine
Zoran Gojković, Milan Kilibarda, Ljiljana Brajović, Miloš Marjanović, Aleksandar Milutinović, Aleksandar Ganić (2023)Open pit coal mining affects surrounding populated areas, resulting in terrain surface deformation. Surface deformation should be monitored as often as possible to control deformations and prevent potential incidents. This paper analyzes time series deformation estimated from the Sentinel-1 satellite images using the Persistent Scatterer Interferometry method to monitor subsidence rates caused by open pit mining activities. It is possible to measure deformations using classical geodetic methods, but those are rarely used in practice because they are time-consuming and ...Zoran Gojković, Milan Kilibarda, Ljiljana Brajović, Miloš Marjanović, Aleksandar Milutinović, Aleksandar Ganić. "Ground surface subsidence monitoring using sentinel-1 in the “Kostolac” open pit coal mine" in Remote Sensing (2023). https://doi.org/10.3390/rs15102519
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Improving Document Retrieval in Large Domain Specific Textual Databases Using Lexical Resources
Large collections of textual documents represent an example of big data that requires the solution of three basic problems: the representation of documents, the representation of information needs and the matching of the two representations. This paper outlines the introduction of document indexing as a possible solution to document representation. Documents within a large textual database developed for geological projects in the Republic of Serbia for many years were indexed using methods developed within digital humanities: bag-of-words and named ...Ranka Stanković, Cvetana Krstev, Ivan Obradović, Olivera Kitanović. "Improving Document Retrieval in Large Domain Specific Textual Databases Using Lexical Resources" in Trans. Computational Collective Intelligence - Lecture Notes in Computer Science 26, Springer (2017). https://doi.org/10.1007/978-3-319-59268-8_8