Browsing Doctoral Dissertations by Title
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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 ) -
Ognjanović, Zoran (Kragujevac)[more][less]
Abstract: 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 Files in this item: 1
phdZoranOgnjanovic.pdf ( 1.259Mb ) -
Knežević, Zoran (Belgrade)[more][less]
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Shkheam, Abejela (, 2013)[more][less]
Abstract: 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 Files in this item: 1
phd_Shkheam_Abejela.pdf ( 650.6Kb ) -
Tepavčević, Andreja (Novi Sad)[more][less]
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Bulatović, Jelena (Belgrade)[more][less]
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Borovićanin, Bojana (Kragujevac, Serbia , 2008)[more][less]
Abstract: 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 Files in this item: 1
disertacija_Bojana Borovicanin.pdf ( 1.939Mb ) -
Jovanović, Irena (Beograd , 2014)[more][less]
Abstract: 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 Files in this item: 1
Jovanović_Irena.pdf ( 1.138Mb ) -
Lalović, Ana (Beograd , 2016)[more][less]
Abstract: The goal of this thesis is to reduce multidimensional space of galactic properties to the smallest number of dimensions su cient to describe them. For this purpose, the statistical analysis is applied over the parameters that describe fundamental galactic properties on the morphologically representative sample of 2180 galaxies. The sample of galaxies used in this thesis is based on the Arecibo Legacy Fast ALFA (Alfalfa) blind HI survey. The importance of an HI blind survey lies in the fact that galaxies are chosen on the basis of their gas content (HI) solely, thus free of optical selection e ects. From the initial sample counting 10000 galaxies, 2180 of them were chosen, since for this subsample the optical spectroscopy from the Sloan Digital Sky Survey (SDSS) was available and moreover the photometry in the UV (Galaxy Evolution Explorer, GALEX), and optical (SDSS) to the near-infrared (Two Micron All Sky Survey, 2MASS). Parameters are selected according to the previously established correlations between fundamental galactic properties, relying on the previous work. They are extensively tested and confronted between each other to be chosen from the larger parametric space. To select parameters, we rst measured stellar kinematics using publicly available code (pPXF), and tested both empirical and synthetic stellar libraries. In particular, we have measured the velocity dispersion and the higher moments of the line-of-sight velocity distribution function. This is the largest galaxy sample created so far with detailed stellar kinematics measured including higher moments of the line-of-sight velocity distribution function. The sample size allows statistical tests to be applied to the higher moment of the velocity distribution function (h4), with respect to the di erent groups of morphological galaxy types. Various tests agree with the previous indication that elliptical and lenticular galaxies have the same origin. Further, we have measured the line strength indices for several absorption lines (Lick indices), since some of them are good proxies to galaxy ages and metallicity, also the fundamental galactic properties. In the nal statistical analysis, metallicity proves to be of no importance, but the inclusion of galaxy ages in the analysis, the results change signi cantly. The last step in the parameter selection is the modelling of the galaxies' surface brightness pro les with the Sersic pro le, that is performed in this thesis with the Gal t code. The velocity dispersion measured, along with the Sersic index and effective radius of the Sersic pro le takes the role in the dynamical mass calculation, being the fundamental galactic property and hence used in the nal statistical analysis. Finally, we have taken the mass of the gas component and maximal rotational velocity from the radio-spectroscopy and Kron magnitudes (i.e. colours) from the ultraviolet/ optical/nearinfrared photometry (GALEX/SDSS/2MASS databases). After extensive testing, we have chosen the colour calculated from ultraviolet and optical magnitudes (NUV r colour), for the nal statistical analysis. It is worth noting that previous analysis of the galactic properties lack velocity dispersion, as well as the colour with the ultraviolet component, although it is a direct proxy to the speci c star formation rate in the galaxy. This particular colour makes correlations among analysed parameters stronger and proves to be more important than optical colours. Finally, when the proper parametric space of galactic properties is formed (velocity dispersion, colour, luminosity, Petrosian radii R50 and R90, dynamical, HI and stellar masses, maximal rotational velocity and the galaxy ages), the correlation analysis is performed to inspect correlations between parameters. This analysis con rms relations that are already known to hold. Then the principal component analysis is done with the purpose of nding and identifying the smallest number of galactic properties responsible for the nal products of galaxy evolution, as we see today, in the local Universe. The results of the corresponding analysis are the following: there are at least three statistically important, independent components. The rst and the most important component cannot be identi ed with either galactic property, but presents the mixture of several properties: dynamical mass, mass of the stellar and gas component, luminosity and Petrosian radii R50 and R90. Relaying on the previous work, this component may be identi ed with the "size" of the galaxies. The second component, mostly in uenced by the galactic colour, may be identi ed with the "aspect" of the galaxies. The colour was not found to be important in previous work. The galaxy ages can be identi ed with the third principal component. There is a hint on the fourth component, dominated by the maximal rotational velocity that can be identi ed with the speci c angular momentum of galaxies. Although not proven to be statistically important, it may become so in the larger sample of galaxies which will provide the information of the true peak of the galaxies' rotational curves, since the single-beam HI spectra may show the single maximum and this may not be the true maximum. Also, the rotational velocity includes the inclination correction, another questionable parameter in the analysis. To conclude: there are at least three, and possibly four dimensions of the multidimensional galactic space, as we see today. URI: http://hdl.handle.net/123456789/4446 Files in this item: 1
Lalovic_Ana3.pdf ( 11.44Mb ) -
Adamović, Dušan (Belgrade , 1965)[more][less]
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Algali, Khola (Beograd , 2019)[more][less]
Abstract: In this thesis we give some new asymptotic formulas for mean values of multiplicative functions of several variables depending on GCD and LCM of arguments. We obtain an asymptotic formula with a power saving error term for the summation function of a family of generalized least common multiple and greatest common divisor functions of several integer variables. Xn 1,...,nk+`≤x [n1,...,nk]a (n1,...,nk)c , [nk+1,...,nk+`]b (nk+1,...,nk+`)d = Ck,a,c;`,b,d (a + 1)k(b + 1)` xk(a+1)+`(b+1) + O xk(a+1)+`(b+1)−1 2+ and Xn 1,...,nk+`≤x [n1,...,nk]a (n1,...,nk)c , [nk+1,...,nk+`]b (nk+1,...,nk+`)d (n1 ...nk)a(nk+1 ...nk+`)b = Ck,a,c;`,b,d xk+` + O xk+`−1 2+ . Also we obtain an asymptotic formula with a power saving error term for the summation function of Euler phi-function evaluated at iterated and generalized least common multiples of four integer variables. Xn 1,n2,n3,n4≤x ϕ [n1,n2]a (n1,n2)c , [n3,n4]b (n3,n4)d = Ca,c;b,d (a + 1)2(b + 1)2 x2a+2b+4 + O x2a+2b+7 2+ . URI: http://hdl.handle.net/123456789/4820 Files in this item: 1
khola_phd_new_ver.pdf ( 665.4Kb ) -
Branković, Velimir (Beograd , 1985)[more][less]