Browsing Doctoral Dissertations by Title
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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 ) -
Stojadinović, Mirko (Beograd , 2016)[more][less]
Abstract: Many real-world problems can be modeled as constraint satisfaction problems (CSPs) and then solved by one of many available techniques for solving these problems. One of the techniques is reduction to SAT, i.e. Boolean Satisfiability Problem. Variables and constraints of CSP are translated (encoded) to SAT instance, that is then solved by state-of-the-art SAT solvers and solution, if exists, is translated to the solution of the original CSP. The main aim of this thesis is to improve CSP solving techniques that are using reduction to SAT. Two new hybrid encodings of CSPs to SAT are presented and they combine good sides of the existing encodings. We give the proof of correctness of one encoding that did not exist in literature. We developed system meSAT that enables reduction of CSPs to SAT by using 4 basic and 2 hybrid encodings. The system also enables solving of CSPs by reduction to two problems related to SAT, SMT and PB. We developed a portfolio for automated selection of encoding/solver to be used on some new instance that needs to be solved. The developed portfolio is comparable with the state-of-the-art portfolios. We developed a hybrid approach based on short solving timeouts with the aim of significantly reducing the preparation time of a portfolio. By using this approach, we got results comparable to the ones obtained by using preparation time of usual length. We made comparison between several machine learning techniques with the aim to find out which one is the best suited for the short training approach. The problem of assigning air traffic controllers to shifts is described and three models of this problem are presented. We used a large number of different solving methods and a diverse set of solvers for solving this problem. We developed optimization techniques that aim to find optimal solutions of the problem. A hybrid technique combining reduction to SAT and local search is shown to be the most efficient one. We also considered sudoku puzzles and the existing techniques of solving the puzzles of greater size than 9 9. Amongst the used techniques, the existing reduction to SAT is the most efficient in solving these puzzles. We improved the existing algorithm for generating large sudoku puzzles. It is shown that simple preprocessing rules additionally improve speed of generating large sudokus. URI: http://hdl.handle.net/123456789/4427 Files in this item: 1
MirkoStojadinovicTeza.pdf ( 2.030Mb ) -
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 ) -
Tsirvoulis, Georgios (Beograd , 2019)[more][less]
Abstract: Asteroid families are populations of asteroids in the Main Belt that share a common origin, that is they are the fragments of energetic collisions between two asteroids. Their study over the years has produced a number of important results concerning the collisional and dynamical evolution of the Main Belt, the physical properties of the primordial bodies of the Solar System and the physics of energetic collisions, to name a few. The contribution of the present thesis can be summarized into two main topics: The first is the discovery of a new mechanism that leads to significant perturbations on the orbits of asteroids, and consequently on the evolution of asteroid families affected by it, and the second is the discovery of a couple of new families, each with its own peculiarities. The first part of this thesis was initially motivated by the irregular shape of the (1726) Hoffmeister asteroid family. In an effort to explain this peculiarity we carried out a thorough dynamical analysis of its past evolution and found out that none of the mechanisms known to affect the orbits of asteroids could explain it. Investigating further we discovered that the linear nodal secular resonance with the most massive asteroid (1) Ceres, is the mechanism responsible for the anisotropic inclination distribution of Hoffmeister family members. Having established the importance of the nodal secular resonance with Ceres, we sought to expand on the subject with the study of all linear secular resonances, nodal and periapsidal, involving not only (1) Ceres, but (4) Vesta, the second most massive asteroid, as well. To do so we utilized numerical integrations of test particles across the whole Main Belt, and evaluated the impact of these resonances on their orbits. Furthermore we identified all asteroid families crossed by one or more of these resonances. Two of these cases, the families of (1251) Seinajoki and (1128) Astrid were then studied in more detail, confirming the importance of the previously ignored secular resonances with massive asteroids. The second part details the discovery of two new asteroid families. The first one, that of (326) Tamara family, was motivated by the unexpectedly high number of dark asteroids in the Phocaea region, a part of the inner Main Belt which is expected to consist mostly of bright ones. Using all available physical data we were able to show that most of the dark asteroids therein belong to a single dynamical family, which we then further analyzed finding that it is 264 ± 43 Myrs old and that it could have a significant contribution to the influx of small dark asteroids toward the Near Earth region. The second discovered family, that of (633) Zelima, is a small cluster, sub-family of the large (221) Eos family. After identifying its members, we derived the age of the Zelima family, which turned out to be only about 3.66 Myrs. URI: http://hdl.handle.net/123456789/4752 Files in this item: 1
Tsirvoulis_Georgios.pdf ( 76.51Mb ) -
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 ) -
Urošević, Dejan (Belgrade)[more][less]
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Ćatović, Zlatko (Belgrade)[more][less]
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Mitrašinović, Ana (Beograd , 2022)[more][less]
Abstract: The subject of this dissertation is to study the effects of galaxy flybys on the structural evolution of galaxies. Galaxy flybys are very close interactions that do not result in a merger. With the high frequency in the late Universe, their role in the evolution of galaxies is significant. Earlier studies focused on equal-mass flybys, which are extremely rare. We focus on typical flybys with a lower mass ratio. We aim to explore the structure and evolution of galaxies in greater detail and demonstrate that these flybys are just as important as equal-mass ones. We performed a series of N body simulations of typical flybys with varying impact para- meters. We demonstrated the applicability and importance of isolated N body simulations and developed an efficient method for reliable bar detection in galaxy discs. For the first time, we examined the evolution of the secondary galaxy, focusing on its dark matter mass loss. The results show that the leftover mass follows logarithmic growth law with impact parameter and suggest that flybys contribute to the formation of dark matter-deficient galaxies. The primary galaxy is affected in a similar way as in equal-mass flybys. Bars form in closer flybys, two-armed spirals form during all flybys, and the dark matter halo spins up. Most of the parameters of these structures are correlated or anti-correlated with the impact parameter. We also noticed that a double bar could form as evolving spirals wrap around the early-formed bar. We successfully demonstrated that frequent, typical flybys with lower mass ratios signifi- cantly affect the evolution of galaxies, producing various observed effects. Our results should serve as a warning not to disregard these interactions in future studies. URI: http://hdl.handle.net/123456789/5441 Files in this item: 1
mitrasinovic_ana.pdf ( 5.370Mb ) -
Pogany, Tibor (Belgrade)[more][less]
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Todorović, Petar (Belgrade , 1961)[more][less]
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Ikodinović, Nebojša (Kragujevac)[more][less]
Abstract: The thesis is devoted to logics which are applicable in different areas of mathematics (such as topology and probability) and computer sciences (reasoning with uncertainty). Namely, some extensions of the classical logic, which are either model-theoretical or non-classical, are studied. The thesis consists of three chapters: an introductory chapter and two main parts (Chapter 2 and Chapter 3). In the introductory chapter of the thesis the well-known notions and properties from extensions of the first order logic and nonclassical logics are presented. Chapter 2 of the thesis is related to logics for topological structures, particularly, topological class spaces (topologies on proper classes). One infinite logic with new quantifiers added is considered as the corresponding logic. Methods of constructing models, which can be useful for many others similar logics, are used to prove the completeness theorem. A number of probabilistic logic suitable for reasoning with uncertainty are investigated in Chapter 3. Especially, some ways of incorporation into the realm of logic conditional probability understood in different ways (in the sense of Kolmogorov or De Finnety) are given. For all these logics the corresponding axiomatizations are given and the completeness for each of them is proved. The decidability for all these logics is discussed too. URI: http://hdl.handle.net/123456789/194 Files in this item: 1
phdNebojsaIkodinovic.pdf ( 3.008Mb )