Browsing Mathematics by Title
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Louka, Hana Almoner (Beograd , 2016)[more][less]
Abstract: This thesis has been written under the supervision of my mentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 2016. The topic of this thesis is quantum information theory, with special attention to quantum contract signing protocols. The thesis is divided into four chapters. Chapter 1 gives introduction to Quantum mechanics and necessary mathematical background. Chapter 2 is about quantum information theory. Quantum algorithms, including Schor's and Grover's, are described. Chapter 3 deals with classical contract signing, and cryptography. Also discussed is the RSA algorithm and BB84 quantum key distribution. Chapter 4 describes quantum signing protocol, and proves, among other things, asymptotic behavior for probability of cheating. URI: http://hdl.handle.net/123456789/4342 Files in this item: 1
hana-thesis2-1.pdf ( 711.2Kb ) -
Davidović, Tatjana (Belgrade , 2006)[more][less]
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Baranović, Nives (Beograd , 2022)[more][less]
Abstract: Future primary education teachers should acquire appropriate mathematical knowledge, skills, and abilities to provide a suitable environment for developing their prospective students' responding knowledge, skills, and abilities. Various studies in education show that students of all ages have difficulties mastering geometric concepts and making functional connections between them, especially at the transition from school to university level. Therefore, a quasi-experimental study was conducted with non-equivalent groups of future primary education teachers. The study aimed to determine a particular teaching method's effectiveness for developing visualization skills, geometric thinking, and optimizing geometry learning outcomes. Three tests were used before and after teaching to collect data on the characteristics of the research participants. The tests were: the VH test to measure the level of geometric thinking, the GEO test to gain insight into geometric knowledge and visual skills, and the SPAC test to measure the unique visual-spatial ability to establish connections between 3D figures and their networks. In the experimental group, a specific teaching approach was applied. The teaching approach is based on the visual-analytical method and directed observation and balancing of three ways of expression: linguistic, visual, and symbolic. Van Hiele's five stages of learning were used in the structuring and selecting of teaching activities. The pre-test results confirmed the relatively weak prior knowledge, visualization skills, and level of geometric thinking of all participants, and the possession of appropriate visual-spatial abilities that predict possible success. The t-test confirmed no statistically significant difference between the participants at the beginning of the teaching. The Spearman correlation coefficient determined a positive, statistically significant correlation between all three tests, indicating a possibility for mutual development. The post-test results confirmed the effectiveness of the applied strategies and teaching methods in achieving better geometry learning outcomes, developing visual literacy, and progress in the levels of geometric thinking of the participants in the experimental group. The experimental group participants had statistically significantly better results on the post-test than the results they achieved on the pre-test compared to the results achieved by the control group participants who were taught more traditionally. Participants in the control group also improved, but these improvements were not statistically significant. The above confirmed that it is possible to develop geometry and visual literacy through systematic learning and teaching at different levels of the educational system. URI: http://hdl.handle.net/123456789/5453 Files in this item: 1
Doktorat _Baranovic 2022 Final NB.pdf ( 7.954Mb ) -
Vidović, Zoran (Beograd , 2020)[more][less]
Abstract: From a sequence of observations, the ones that exceed previous ones in a time seriesare called records. The pioneer paper of record theory is considered to be Chandler [39]. Thistheory gained its popularity doe to significant public interest towards records. As a result, largenumber of papers are published on this topic.Record values are very important in statistics. Record values are applied in parameterestimation issues, characterization issues, hypothesis and stationarity tests, etc. Also, theirusefulness in probability theory and in theory of random process is tremendous.This dissertation discusses applications of records through numerical evaluations of maximumlikelihood estimators of parameters of the three-parameter extensions of Weibull distributionfamily, new recurrence relations of record moments, records in Bayesian inference, applicationsof records in characterization issues for random chord length distributions as well with theasymptotic behaviour of extremes of random chord lengths. This dissertation consists on sixchapters.Several examples of records are presented in the first chapter.Second chapter discusses the strict formulations of records from a sequence of independentand identically distributed random variables. Their application and their extensions from thesame model are presented, as well with several interesting results.The problem of existence and uniqueness of maximum likelihood estimators based on recordsis elaborated in the third chapter. In this chapter, we present sufficient conditions that confirmthe existence and uniqueness of maximum likelihood estimators for a three-parameter extensionsof Weibull distributions. Also, several well known results are presented as examples. Severalresults from this chapter could be found in [135].The fourth chapter is dedicated to moment recurrence relations of a three-parameter ex-tension of Weibull distribution based on records with possible applications. These results arepublished in [136].Fifth chapter deals with Bayesian prediction of order statistics based on record values. Here,we expand the applicability of records in real problems and provide a better understanding oftheir significance. Several results presented in this chapter could be found in [136].In the sixth chapter the random chord length issue is considered through the record valuetheory. A new generation method of random chords is presented. The study of limit behaviourof maximum length of random chords for all cases of generation is also conducted. Character-ization results for random chord length distributions based on record moments are obtained. Several results presented in this chapter could be found in [134]. URI: http://hdl.handle.net/123456789/5089 Files in this item: 1
disertacija_Z_Vidovic.pdf ( 2.262Mb ) -
Banković, Dragić (Belgrade , 1980)[more][less]
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Savić, Branko (Belgrade)[more][less]
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Pantić, Dražen (Belgrade)[more][less]
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Lepović, Mirko (Beograd , 1991)[more][less]
URI: http://hdl.handle.net/123456789/4138 Files in this item: 1
Spektralna_teorija_grafova.PDF ( 4.283Mb ) -
Marić, Miroslav (Belgrade)[more][less]
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Lazić, Mirjana (Kragujevac, Serbia , 2011)[more][less]
Abstract: This doctoral dissertation belongs to the Spectral theory of finite and infinite graphs, which joins elements of Graph theory and Linear algebra. The dissertation, beside Preface and References with 24 items, consists of four chapters divided in sections and Appendix. In Chapter 1 some results on the reduced energy of graphs are given. All connected graphs whose reduced energy does not exceed 3 are described. In Chapter 2 all finite and infinite graphs with seven nonzero eigenvalues are determined. Some results on integral graphs are given in Chapter 3. Finally, Chapter 4 contains some results on symmetric double starlike trees. The definitions of starlike tree and double starlike tree are given and we proved that there exist no two cospectral non-isomorphic symmetric double starlike trees. URI: http://hdl.handle.net/123456789/1879 Files in this item: 1
dokdis.pdf ( 713.4Kb ) -
Matić, Dragan (Beograd , 2013)[more][less]
Abstract: In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and p-ary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving p-ary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science. URI: http://hdl.handle.net/123456789/4229 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) -
Matić, Dragan (Beograd , 2013)[more][less]
Abstract: In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and p-ary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving p-ary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science. URI: http://hdl.handle.net/123456789/3050 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) -
Todorčević, Stevo (Belgrade)[more][less]
Abstract: The thesis consists of four chapters and one appendix. The relation between trees and ordering types, especially the relation between tree-subtree and the type-subtype are considered in Chapter 1. By using Jensens’s principle, Aronszajn’s tree which does not contain any Aronszajn’s subtree and Cantor’s subtree are constructed. Moreover, it is shown that in the model ZFC+GCH each ω_2- Aronszajn’s tree contains Aronszajn’s and Cantor’s subtree. In the first part of Chapter 2 the problem of the existence of Boolean algebras which have non-trivial automorphisms and endomorptisms are studied. It is shown that for each cardinal k, k>ω, there are exactly 2^k types of isomorphic Boolean algebras without non-trivial automorphisms. In the second part of that chapter the problem of isomorphism and automorhism of ω_1-trees is studied. It is shown that there are 2^ω1 types of isomorphic total rigid Aronszajn’s trees, so one Aronszajn’s tree does not have any nontrivial automorphism. Several problems of the partition relations of cardinal numbers are solved in Chapter 3. The appendix contains the proof of the property that in ZFC the σ-dense partial ordered set of power ω_1 does not exist. It is shown that in ZFC there is not any linearly ordered topological space with weight less or equal ω_1 which satisfies Kurepa’s generalization of the notion of separable topological space. It is also shown that if ¬ω Kurepa’s hypothesis + Martin’s axiom + ¬Continuum hypothesis is assumed, then each perfect normal non - Arhimedian space whose weight is ω1 is measurable. URI: http://hdl.handle.net/123456789/316 Files in this item: 1
phdStevoTodorcevic.pdf ( 18.19Mb ) -
Dragović, Vladimir (Beograd , 1992)[more][less]
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Šegan-Radonjić, Marija (University of Belgrade , 2019)[more][less]
Abstract: Предмет докторске дисертације је израда оквира за дигитално архивирање у циљу очувања, представљања и омогућавања доступности дигитализованог и дигиталног садржаја за потребе историјских и других истраживања. Предложени оквир заснива се на концепту ,,тематских колекција“ и намењен је истраживачима који желе да креирају сопствене дигиталне збирке историјских извора и текстова како би ширу научну заједницу упознали са својим истраживањем, повезали га са ширим контекстом и створили услове за умрежавање и сарадњу. Оквир, на примеру дигитализације архивског материјала Математичког института САНУ и у складу са актуелним препорукама и прописима за дигитализацију културног наслеђа у Републици Србији, нуди смернице за: 1) економичан поступак превођења у дигитални облик ради добијања оперативних копија за представљање на вебу, 2) каталогизацију и опис дигиталних докумената помоћу Dublin Core скупа елемената, 3) креирање дигиталног архива помоћу Omeka Classic платформе, 4) израду упутства за архивско истраживање одређених историјских тема и 5) састављање историјских есеја у дигиталном окружењу. Посебни циљ докторске дисертације је примена предложеног оквира у историјским и другим истраживањима, конкретно у проучавању развоја Математичког института у периоду од његовог успостављања у крилу Српске академије наука 1946. године до његовог осамостаљивања 1961. године. Резултати рада су: 1) систематски обрађено питање прошлости Математичког института САНУ у поменутом хронолошком оквиру, 2) дигитална колекција посвећена историји математике и сродних наука у Србији и југоисточној Европи и 3) предлог оквира за дигитално архивирање дигиталног и дигитализованог садржаја за потребе историјских и других истраживања. URI: http://hdl.handle.net/123456789/4855 Files in this item: 1
MarijaSeganDoktorat.pdf ( 29.70Mb ) -
Borisavljević, Mirjana (Beograd , 1997)[more][less]
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Bakić, Radoš (Belgrade)[more][less]
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Mijajlović, Ivana (London)[more][less]
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Pavlović, Aleksandar (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/295 Files in this item: 1
PhdAleksandarPavlovic.pdf ( 7.226Mb ) -
Đokić, Dragan (Beograd , 2022)[more][less]
Abstract: The distribution of primes is determined by the distribution of zeros of Riemann zeta function, and indirectly by the distribution of magnitude of this function on the critical line <s = 1 2 . Similarly, in order to consider the distribution of primes in arithmetic progressions, Dirichlet introduced L-functions as a generalization of Riemann zeta function. Generalized Riemann hypothesis, the most important open problem in mathematics, predicts that all nontrivial zeros of Dirichlet L-function are located on the critical line. Therefore, one of the main goals in Analytic Number Theory is to consider the moments of Dirichlet L-functions (according to a certain well defined family). The relation with the characteristic polynomials of random unitary matrices is one of the fundamental tools for heuristic understanding of L-functions and derivation hypotheses about asymptotic formulae for their moments. Asymptotics for even moments 1 T Z T 0 ζ 1 2 + it 2k dt, as T → ∞, is still an open question (except for k = 1, 2), and it is related to the Lindelöf Hypothesis. In this dissertation we consider the sixth moment of Dirichlet L-functions over rational function fields Fq(x), where Fq is a finite field. We will present the asymptotic formula for the sixth moment with the triple average X Q monic deg Q=d X χ (mod Q) χ odd primitive 2π Z log q 0 L 1 2 + it, χ 6 dt 2π log q as d → ∞. All additional averaging is currently necessary to obtain the asymptotics. The summation over Dirichlet characters and their moduli is motivated by Bombieri-Vinogradov Theorem. Our result is a function field analogue of the paper [25] for the corresponding family and averaging over field Q. Also, our main term confirms the existing Random matrix theory predictions. URI: http://hdl.handle.net/123456789/5531 Files in this item: 1
dragan_djokic_teza.pdf ( 867.8Kb )