Auflistung Doctoral Dissertations nach Titel
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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 ) -
Lalović, Ana (Beograd , 2016)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
Lalovic_Ana3.pdf ( 11.44Mb ) -
Adamović, Dušan (Belgrade , 1965)[more][less]
URI: http://hdl.handle.net/123456789/217 Dateien zu dieser Ressource: 1
phdDusanAdamovicS.pdf ( 2.452Mb ) -
Algali, Khola (Beograd , 2019)[more][less]
Zusammenfassung: 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 Dateien zu dieser Ressource: 1
khola_phd_new_ver.pdf ( 665.4Kb ) -
Branković, Velimir (Beograd , 1985)[more][less]
URI: http://hdl.handle.net/123456789/4098 Dateien zu dieser Ressource: 1
Stabilnost_kretanja.PDF ( 3.236Mb ) -
Bakša, Aleksandar (Belgrade , 1976)[more][less]
URI: http://hdl.handle.net/123456789/284 Dateien zu dieser Ressource: 1
phdAleksandarBaksa.pdf ( 3.142Mb ) -
Ranković, Dragana (Beograd , 2011)[more][less]
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Alidema, Rašit (Belgrade , 1980)[more][less]
URI: http://hdl.handle.net/123456789/355 Dateien zu dieser Ressource: 1
phdRasitAlidema.pdf ( 2.021Mb ) -
Đukić, Đorđe (Beograd , 1971)[more][less]
URI: http://hdl.handle.net/123456789/4102 Dateien zu dieser Ressource: 1
Stacionarni_ravanski.PDF ( 2.322Mb ) -
Đukić, Đorđe (Belgrade , 1971)[more][less]
URI: http://hdl.handle.net/123456789/261 Dateien zu dieser Ressource: 1
phdDjordjeDjukic.pdf ( 4.861Mb ) -
Nikolić, Nebojša (Beograd , 2015)[more][less]
Zusammenfassung: A Steiner system S(t; k; v) is a set which contains v elements (v-set) and a family of k-subsets (blocks), such that each t-subset appears in exactly one block (v > k > t > 1; v; k; t 2 N). In the case of a (v; k; t)¡covering, each t-subset appears in at least one block of a given family. A Steiner system S(t; k; v) exists if and only if C(v; k; t) = ¡v t ¢±¡k t ¢ , where C(v; k; t) is the cardinality of minimal (v; k; t)¡covering. As the existence of Steiner system S(t; k; v) and the determination of the minimal (v; k; t)¡covering are still open problems, their solutions are known only in some special cases. Besides the review of the previous results related to the problem of the existence of Steiner systems and the problem of determining the minimal (v; k; t)¡covering, several new constructions of (v; k; t)¡covering are given in this paper. Since the number of blocks in (v; k; t)¡covering represents the upper bound on C(v; k; t), a large number of upper bounds are also obtained by using these constructions. In many cases, the obtained upper bounds are better than the best known upper bounds on C(v; k; t). This dissertation gives a new combinatorial construction of minimal (v; 3; 2)¡ coverings, which represents a generalization of Bose and Skolem constructions of the Steiner triple systems STS(6n + 3) and STS(6n + 1). In each of the 6 cases (v = 6n; : : : ; 6n+5), (v; 3; 2)¡covering is obtained by applying certain permutation p to the initial set of blocks. The obtained construction also represents a new proof of the statement that the values of C(v; 3; 2) are equal to SchÄonheim lower bound L(v; 3; 2). Other constructions of (v; k; t)¡coverings, given in this paper, are heuristic. First, we give improved implementation of the well known greedy algorithm. Then, a new greedy algorithm, as well as the theorem which provides a su±cient con- dition for equality of greedy lex and greedy colex coverings are given. Finally, by v using so called LR procedure, three other heuristics are developed and implemented: Large neighbourhood search, Variable neighborhood descent and General variable neighborhood search. Large neighbourhood search is the procedure of alternately destroying and re- pairing a solution in order to improve the incumbent solution. In the proposed algorithm, this is the procedure for systematic removing and adding blocks to the covering, based on LR procedure. By using LR procedure, the blocks which exclu- sively cover the minimal number of t-subsets are removed from (v; k; t)¡covering, and then the uncovered t-subsets are covered with as few blocks as possible. The greedy algorithm is used for the covering of the uncovered t-subsets. Variable neighborhood search is based on the idea of systematic change of neigh- borhood within a local search algorithm in order to avoid the convergence to a local minimum. A variant of the method where changes of neighborhood is performed in a deterministic way is called Variable neighborhood descent. A variant where the local search procedure is replaced by the Variable neighborhood descent method is General variable neighborhood search. The basis of the local search procedure applied in these two heuristics is also LR procedure. Regarding quality of the obtained results and the performance of the methods, Large neighbourhood search, Variable neighborhood descent, and General variable neighborhood search overcome two heuristics for solving the problem of minimal (v; k; t)¡covering known from the literature: Simulated annealing and Tabu search. Unlike the existing heuristics, the proposed heuristics are applicable to arbitrarily (v; k; t)¡covering. By applying aforementioned heuristics, 23 new best known upper bounds on C(v; k; t) are established. URI: http://hdl.handle.net/123456789/4285 Dateien zu dieser Ressource: 1
phdNikolic_Nebojsa.pdf ( 851.1Kb ) -
Popović, Luka (Belgrade)[more][less]
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Đorić, Dragan (Beograd , 2002)[more][less]
URI: http://hdl.handle.net/123456789/4136 Dateien zu dieser Ressource: 1
Statisticka_analiza.PDF ( 3.153Mb ) -
Jevremović, Vesna (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/95 Dateien zu dieser Ressource: 1
phdVesnaJevremovic.pdf ( 2.648Mb )