Auflistung Doctoral Dissertations nach Titel
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Šegan-Radonjić, Marija (University of Belgrade , 2019)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
MarijaSeganDoktorat.pdf ( 29.70Mb ) -
Tsirvoulis, Georgios (Beograd , 2019)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
Tsirvoulis_Georgios.pdf ( 76.51Mb ) -
Borisavljević, Mirjana (Beograd , 1997)[more][less]
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Bakić, Radoš (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/184 Dateien zu dieser Ressource: 1
phdRadosBakic.pdf ( 1.659Mb ) -
Mijajlović, Ivana (London)[more][less]
URI: http://hdl.handle.net/123456789/314 Dateien zu dieser Ressource: 1
phdIvanaMijajlovic.pdf ( 760.3Kb ) -
Pavlović, Aleksandar (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/295 Dateien zu dieser Ressource: 1
PhdAleksandarPavlovic.pdf ( 7.226Mb ) -
Đokić, Dragan (Beograd , 2022)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
dragan_djokic_teza.pdf ( 867.8Kb ) -
Urošević, Dejan (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/122 Dateien zu dieser Ressource: 1
phdDejanUrosevic.pdf ( 7.815Mb ) -
Ćatović, Zlatko (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/134 Dateien zu dieser Ressource: 1
phdZlatkoCatovic.pdf ( 4.531Mb ) -
Mitrašinović, Ana (Beograd , 2022)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
mitrasinovic_ana.pdf ( 5.370Mb ) -
Pogany, Tibor (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/75 Dateien zu dieser Ressource: 1
phdTiborPogany.pdf ( 2.324Mb ) -
Todorović, Petar (Belgrade , 1961)[more][less]
URI: http://hdl.handle.net/123456789/74 Dateien zu dieser Ressource: 1
phdPetarTodorovic.pdf ( 2.191Mb ) -
Ikodinović, Nebojša (Kragujevac)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
phdNebojsaIkodinovic.pdf ( 3.008Mb ) -
Ognjanović, Zoran (Kragujevac)[more][less]
Zusammenfassung: The thesis consists of seven chapters and two appendixes. The Chapter 1 and the appendixes contain known notions and properties from probability logics. In Chapter 2 some propositional probability logics are introduced and their languages, models, satisfiability relations, and (in)finitary axiomatic systems are given. Object languages are countable, formulas are finite, while only proofs are allowed to be infinite. The considered languages are obtained by adding unary probabilistic operators of the form P≥s. Decidability of the logics is proved. In Chapter 3 some first order probability logics are considered while in Chapter 4 new types of probability operators are introduced. The new operators are suitable for describing events in discrete sample spaces. It is shown that they are not definable in languages of probability logics that have been used so far. A propositional and a first-order logic for reasoning about discrete linear time and finitely additive probability are given in Chapter 5. Sound and complete infinitary axiomatizations for the logics are provided as well. In Chapter 6 a probabilistic extension of modal logic is studied and it is shown that those logics are closely related, but that modal necessity is a stronger notion than probability necessity. In Chapter 7 decidability of these logics is shown by reducing the corresponding satisfiability problem to the linear programming problem. Finally, two automated theorems provers based on that idea are described. URI: http://hdl.handle.net/123456789/197 Dateien zu dieser Ressource: 1
phdZoranOgnjanovic.pdf ( 1.259Mb ) -
Knežević, Zoran (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/135 Dateien zu dieser Ressource: 1
phdZoranKnezevic.pdf ( 42.64Mb ) -
Shkheam, Abejela (, 2013)[more][less]
Zusammenfassung: This thesis has been written under the supervision of my mentor, Prof. dr. Milo s Arsenovi c at the University of Belgrade academic, and my co-mentor dr. Vladimir Bo zin in year 2013. The thesis consists of three chapters. In the rst chapter we start from de nition of harmonic functions (by mean value property) and give some of their properties. This leads to a brief discussion of homogeneous harmonic polynomials, and we also introduce subharmonic functions and subharmonic behaviour, which we need later. In the second chapter we present a simple derivation of the explicit formula for the harmonic Bergman reproducing kernel on the ball in euclidean space and give a proof that the harmonic Bergman projection is Lp bounded, for 1 < p < 1, we furthermore discuss duality results. We then extend some of our previous discussion to the weighted Bergman spaces. In the last chapter, we investigate the Bergman space for harmonic functions bp, 0 < p < 1 on RnnZn. In the planar case we prove that bp 6= f0g for all 0 < p < 1. Finally we prove the main result of this thesis bq bp for n=(k + 1) q < p < n=k, (k = 1; 2; :::). This chapter is based mainly on the published paper [44]. M. Arsenovi c, D. Ke cki c,[5] gave analogous results for analytic functions in the planar case. In the plane the logarithmic function log jxj, plays a central role because it makes a di erence between analytic and harmonic case, but in the space the function jxj2n; n > 2 hints at the contrast between harmonic function in the plane and in higher dimensions. URI: http://hdl.handle.net/123456789/3053 Dateien zu dieser Ressource: 1
phd_Shkheam_Abejela.pdf ( 650.6Kb ) -
Tepavčević, Andreja (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/185 Dateien zu dieser Ressource: 1
phdAndrejaTepavcevic.pdf ( 3.351Mb ) -
Bulatović, Jelena (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/332 Dateien zu dieser Ressource: 1
phdJelenaBulatovic.pdf ( 5.039Mb ) -
Borovićanin, Bojana (Kragujevac, Serbia , 2008)[more][less]
Zusammenfassung: Different spectral characterizations of certain classes of graphs are considered in this dissertation. The large number of papers concerning this topic, indicates that problems of this kind are very interesting in spectral graph theory. This dissertation, beside Preface and References with 46 items, consists of two chapters: 1. Harmonic graphs, 2. Graphs with maximal index. Harmonic graphs are introduced and studied in details in Chapter 1. This chapter consists of four sections. In section 1.1 the definition of harmonic graphs, as well as their basic properties, are given. Harmonic trees are discussed in section 1.2. In section 1.3 we characterize harmonic graphs with small number of cycles; in particular, all unicyclic, bicyclic, tricyclic and tetracyclic graphs are determined. Finally, in section 1.4, we determine all connected 3-harmonic graphs with integral spectrum. The solution of maximal index problem in certain classes of graphs is given in Chapter 2. This chapter consists of four sections. In sections 2.1 and 2.2 we review some results related to the index of a graph. The emphasis is on graphs with given number of both vertices and edges; in particular we discuss graphs having the fixed number of pendant edges, too. In section 2.3 we give the solution of maximal index problem in the class of connected tricyclic graphs with n vertices and k pendant edges. Finally, in section 2.4, we determine graphs with maximal index among all connected cactuses with n vertices. URI: http://hdl.handle.net/123456789/1834 Dateien zu dieser Ressource: 1
disertacija_Bojana Borovicanin.pdf ( 1.939Mb ) -
Jovanović, Irena (Beograd , 2014)[more][less]
Zusammenfassung: Spectral graph theory is a mathematical theory where graphs are considered by means of the eigenvalues and the corresponding eigenvectors of the matrices that are assigned to them. The spectral recognition problems are of particular interest. Between them we can distinguish: characterizations of graphs with a given spectrum, exact or approximate constructions of graphs with a given spectrum, similarity of graphs and perturbations of graphs. In this dissertation we are primarily interested for the similarity of graphs, where graphs with the same number of vertices and graphs of different orders are considered. Similarity of graphs of equal orders can be established by computation of the spectral distances between them, while for graphs with different number of vertices the measures of similarity are introduced. In that case, graphs under study are usually very large and they are denoted as networks, while the measures of similarity can be spectraly based. Some mathematical results on the Manhattan spectral distance of graphs based on the adjacency matrix, Laplacian and signless Laplacian matrix are given in this dissertation. A new measure of similarity for the vertices of the networks under study is proposed. It is based on the difference of the generating functions for the numbers of closed walks in the vertices of networks. These closed walks are calculated according to the new spectral formula which enumerates the numbers of spanning closed walks in the graphlets of the corresponding graphs. The problem of the characterization of a digraph with respect to the spectrum of AAT , apropos ATA, where A is the adjacency matrix of a digraph, is introduced. The notion of cospectrality is generalized, and so the cospectrality between some particular digraphs with respect to the matrix AAT and multigraphs with respect to the signless Laplacian matrix is considered. URI: http://hdl.handle.net/123456789/4233 Dateien zu dieser Ressource: 1
Jovanović_Irena.pdf ( 1.138Mb )