Browsing Doctoral Dissertations by Title
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Golubović, Zoran (Belgrade , 1984)[more][less]
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Cuparić, Marija (Beograd , 2021)[more][less]
Abstract: The goal of this dissertation is the construction of new goodness-of-fit tests,analysis of their properties, as well as to obtain new theoretical findings regarding the limitingdistributions of weakly degeneratedV−statistics with estimated parameters. New goodness-of-fit tests are based on equidistributional type characterizations of two sample functions.Test statistics are formed asL2distances betweenV−empirical distribution functions ofstatistics from characterization, and also asL2andL∞distances betweenV−empiricalLaplace transformations of those statistics. In the latter case, resulting test statistics can beobserved asV−statistics with an estimated parameter or as functions of those statistics.Until now, limiting results were known for non-degenerateV−statistics with estimatedparameters, as well as for weakly degenerateV−statistics of degree two with estimatedparameters. Limiting results for the appropriate class of weakly degenerateV−statistics withan estimated parameter of degreem, wheremis even number, are derived in this dissertation.Owing to these results, asymptotic properties for presented tests are determined. To assessthe quality of these tests, empirical powers were determined using Monte Carlo simulations, aswell as approximate Bahadur efficiency. New results are presented regarding the approximateBahadur efficiency in case of close alternatives, which is applicable also when the limitingdistribution of statistics under the null hypothesis is not normal. In this sense, the comparisonbetween many tests is performed, both classical tests and recently developed tests.All previously mentioned results were obtained for complete samples. Additional, modifi-cation of previously introduced tests for randomly censored data was also proposed. In sucha case, the new theoretically justified bootstrap method is proposed for the approximation ofp−value. URI: http://hdl.handle.net/123456789/5212 Files in this item: 1
marijacuparicdr.pdf ( 1.771Mb ) -
Nešić, Slobodan (Belgrade , 1980)[more][less]
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Baralić, Đorđe (Beograd , 2013)[more][less]
Abstract: The main objects studied in this doctoral thesis are quasitoric manifolds and spaces arising as the images of polyhedral product functors. Quasitoric manifolds are particularly interesting as topological generalization of non-singular toric varieties. They are a research topic of many mathematical disciplines including toric geometry, symplectic geometry, toric topology, algebraic geometry, algebraic topology, theory of convex polytopes, and topological combinatorics. These objects have already found numerous applications in mathematics and sciences and they continue to be intensively studied. In this thesis we put some emphasis on combinatorial methods, focusing on the interaction of the geometry of toric actions and combinatorics of simple polytopes. This connection of geometry and combinatorics is based on the fundamental observation that convex polytopes naturally arise as orbit spaces of toric actions on quasitoric manifolds. Our main original contributions in this thesis are related to classical topological questions about degrees of maps between manifolds as well as their embeddings and immersions into Euclidean spaces. We follow the general scheme characteristic for Algebraic Topology where a topological problem is reduced, often by non-trivial reductions, to a question of arithmetical, algebraic, or combinatorial nature. We believe that the novel applications of this scheme developed in the thesis, especially the new techniques and calculations, have a potential to be applied on other problems about quasitoric manifods. Here is a summary of the content of the thesis. For the reader’s convenience and for completeness, in the first three chapters we give an elementary exposition of the basic theory of simplicial complexes, convex polytopes, toric varieties and quasitoric manifolds. The emphasis is on the fundamental constructions and central results, however the combinatorial approach, utilized in the thesis, allows us present the theory in a direct and concrete way, with a minimum of topological prerequisites. The mapping degrees of maps between quasitoric manifolds are studied in Chapter 4 with a particular emphasis on quasitoric 4-manifolds. Utilizing the technique pioneered by Haibao Duan and Shicheng Wang, which is based on the intersection form and the cohomology ring calculations, we demonstrate that a complete information about mapping degrees can be obtained in many concrete situations. The theorems and the corresponding criteria for the existence of mapping degrees are formulated in the language of elementary number theory. It is amusing that the question whether a number appears as a mapping degree between concrete 4-manifolds is directly linked with classical results from number theory such as whether a number can be expressed as a sum of two or three squares, etc. This approach allows us to analyze many concrete 4-manifolds, including CP2, CP2♯CP2, S2×S2, etc. In Chapter 5 we calculate the Stiefel-Whitney classes of some concrete quasitoric manifolds and their duals. This information is used to determine cohomological obstructions to embeddings and immersions of these manifolds in Euclidean spaces. As an initial observation we showed that the calculations are highly dependent on the action of torus. Indeed, there are examples of quasitoric manifolds over the same polytope which exhibit a very different behavior and different complexity of the associated characteristic classes. Focusing on the quasitoric manifolds over the n-dimensional cube, we are able to produce quasitoric manifolds which are very complex in the sense that they almost attain the theoretical minimum dimension for their embedding or (totally skew) immersion in Euclidean spaces. The thesis ends with an appendix with an outline of the theory of group actions and equivariant topology. URI: http://hdl.handle.net/123456789/4232 Files in this item: 1
phdDjordjeBaralic.pdf ( 8.102Mb ) -
Andrijević, Dimitrije (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/37 Files in this item: 1
phdDimitrijeAndrijevic.pdf ( 3.211Mb ) -
Dimitrijević, Radoslav (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/312 Files in this item: 1
phdRadoslavDimitrijevic.pdf ( 11.78Mb ) -
Cvetković, Dragoljub (Beograd , 1985)[more][less]
URI: http://hdl.handle.net/123456789/4101 Files in this item: 1
Trajektorije_pramenova.PDF ( 8.497Mb ) -
Cvetković, Dragoljub (Belgrade , 1985)[more][less]
URI: http://hdl.handle.net/123456789/249 Files in this item: 1
phdDragoljubCvetkovic.PDF ( 18.28Mb ) -
Predić, Bogoljub (Belgrade , 1984)[more][less]
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Milić, Ivan (, 2014)[more][less]
Abstract: Multidimensional radiative transfer is an essential ingredient of modern ap- proach to modeling of astrophysical objects. Realistic modeling calls for the as- sumption of non-local thermodynamic equilibrium (NLTE), which, in turn requires self-consistent solution of coupled equations of radiative transfer statistical equilib- rium. This approach allows us to compute emergent spectrum from a given model of the object, which is, in principle, a necessary step in interpretation of observational results. Thanks to the high-resolution and high signal to noise observations, it is often possible to measure not only intensity of the light but also its state of po- larization. For interpretation of such observations it is necessary to solve radiative transfer problem for polarized radiation. This thesis deals with non-LTE transfer of (generally polarized) radiation in two- dimensional media. Thesis can be divided in two parts. In the first part, we present a numerical method for the formal solution of the radiative transfer equation in 2D Cartesian coordinate system. This method allows us to explicitly account for the contribution of non-local source functions to the local specific intensity, and, hence, to the local scattering integral. The knowledge of these contributions is necessary for an iterative solution of coupled equations of radiative transfer and statistical equilibrium. Based on this formal solution we introduce two novel schemes for multidimensional NLTE radiative transfer which have so far been used only in 1D geometry: symmetric Gauss-Seidel iteration and “Sweep-by-sweep” implicit lambda iteration, latter one being based on “Forth-and-back” implicit lambda iteration. Both methods utilize implicit use of the local source function and the source func- tion corrections each sweep of the computational grid (four times per iteration). “Sweep-by-sweep” implicit lambda iteration also uses the idea of iteration factors and achieves acceleration of about factor of seven with respect to the referent Ja- cobi method. Both new methods also significantly surpass both Jacobi iteration and Gauss-Seidel iteration on problems with periodic boundary conditions. Also, it turns out that “Sweep-by-sweep” implicit lambda iteration scales with grid resolu- tion better than the Jacobi iteration. The second part of the thesis deals with numerical polarized radiative transfer on 2D cylindrical grids. The method is based on the second order short characteristics for the formal solution and uses standard Jacobi iteration with Ng acceleration to solve the polarized non-LTE problem (Generalization to other iterative schemes is given in appendix A). This method allows for the self-consistent solution of coupled equations of radiative transfer and statistical equilibrium equation for a two level atom model for polarized radiation. The method employs reduced intensity basis where intensity and source function are written as six-vectors and source function does not depend on direction which allows for significant saving in memory and computing time. It is applicable for modeling of axisymmetric objects such as as- trophysical disks. The method has been tested on simple models of circumstellar and self-emitting disks. The most important conclusion of these computations is that the presence of the disk in the system introduces a significant degree of linear polarization due to the scattering processes and that one is able to model it in detail using our approach. Also, it is shown that the presence of rotation in self-emitting disks dramatically changes not only intensity, but also polarized spectral lines pro- files. Interplay of non-LTE, multidimensional effects and rotation results in very complicated line profiles which are non-trivial for interpretation. However, the main effect is that the rotation decreases the amount of Stokes Q component and, de- pending on the rotation velocity causes appearance of double-lobed U polarization profile. If these effects can be observed, this kind of modeling provides a useful tool for interpretation of the spectropolarimetric observations. URI: http://hdl.handle.net/123456789/4757 Files in this item: 1
IvanMilic_teza.pdf ( 1.075Mb ) -
Popović, Nikola (Belgrade)[more][less]
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Zeković, Vladimir (Beograd , 2020)[more][less]
Abstract: In the disertation, by the linear plasma theory we show that resonant electromagnetic (EM)micro-instabilities are excited by the two colliding plasmas which are interpenetrating eachother with the super-Alfv ́enic velocity, in the direction quasi-parallel to the magnetic field.The expected Rankine-Hugoniot shock conditions, naturally arise as a consequence of a highlyresonant interaction of ions with the instability. By using kinetic simulations, we find herethat such resonant instabilities appear in the linear stage, and we show how these instabilitiestrigger the shock formation during the non-linear stage.By theoretical modeling, we show how a magnetosonic soliton forms and leads to the periodicshock reformation and initiation of the return current of ions, which drives the EM upstreaminstability. We find that ions are being pre-accelerated by the upstream and shock instabilities ina mechanism that is similar to the diffusive shock acceleration (DSA). By our EM test particlesimulation runs we show that at quasi-parallel shocks, EM instabilities highly contribute toelectron pre-acceleration, leading to the formation of a power-law electron spectra through theFermi-like mechanism.By very long kinetic simulation runs, in this disertation we find that ions and electronsenter DSA in a similar number which is further applied in a model of non-linear DSA. Withinthis model, we obtain the theoretical particle spectra and we find the electron-to-proton ratioat high energies for the different Mach numbers. We show that the spectra of quasi-thermalparticles at the shock can be represented by a non-equilibriumκ-distribution. We find thatthe level of modification decreases andκ-index increases behind the shock, implying that theparticle distribution tends to become a Maxwellian. URI: http://hdl.handle.net/123456789/5094 Files in this item: 1
ZekovicVladimir.pdf ( 56.60Mb ) -
Bačanin Džakula, Nebojša (Beograd , 2015)[more][less]
Abstract: Hard optimization problems that cannot be solved within acceptable computational time by deterministic mathematical methods have been successfully solved in recent years by population-based stochastic metaheuristics, among which swarm intelligence algorithms represent a prominent class. This thesis investigates improvements of the swarm intelligence metaheuristics by hybridization. During analysis of the existing swarm intelligence metaheuristics in some cases de ciencies and weaknesses in the solution space search mechanisms were observed, primarily as a consequence of the mathematical model that simulates natural process as well as inappropriate balance between intensi cation and diversi cation. The thesis examines whether existing swarm intelligence algorithms for global optimization could be improved (in the sense of obtaining better results, faster convergence, better robustness) by hybridization with other algorithms. A number of hybridized swarm intelligence metaheuristics were developed and implemented. Considering the fact that good hybrids are not created as a random combination of individual functional elements and procedures from di erent algorithms, but rather established on comprehensive analysis of the functional principles of the algorithms that are used in the process of hybridization, development of the hybrid approaches was preceded by thorough research of advantages and disadvantages of each involved algorithm in order to determine the best combination that neutralizes disadvantages of one approach by incorporating the strengths of the other. Developed hybrid approaches were veri ed by testing on standard benchmark sets for global optimization, with and without constraints, as well as on well-known practical problems. Comparative analysis with the state-of-the-art algorithms from the literature demonstrated quality of the developed hybrids and con rmed the hypothesis that swarm intelligence algorithms can be successfully improved by hybridization. URI: http://hdl.handle.net/123456789/4245 Files in this item: 1
phdBacaninNebojsa.pdf ( 3.813Mb ) -
Lučić, Zoran (Belgrade , 1985)[more][less]
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Madaras-Silađi, Rozalija (Novi Sad)[more][less]
URI: http://hdl.handle.net/123456789/193 Files in this item: 1
phdRozalijaMadarasSiladji.pdf ( 3.002Mb ) -
Vujošević, Luka (Belgrade , 1964)[more][less]
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Jovanović, Milan (Belgrade)[more][less]
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Lazarević, Ivan (Beograd , 2022)[more][less]
Abstract: In this doctoral thesis we obtained some results in graph theory and its applica tions. In the rst chapter, we give the review of basic notions and theorems of combinatorial theory of graphs, spectral theory of graphs, random graphs and distribution of their eigenvalues. The most detailed consideration is given to adjacency matrix and properties of its spectrum. In particular, in this dissertation we study Energy of graphs and generalizations of it. Energy of graph is the sum of absolute values of eigenvalues of a graph. Schatten norms of graphs represent p-th degree norm of singular values of graph, and the special cases of this norm for p = 1 corresponds to the Energy of graph. In chapter three of this dissertation we are given the most original scienti c contribution. We prove the conjecture of Nikiforov about Schatten norms of graphs when p > 2. First we prove that conjecture is true for some special classes of graph (for trees and strongly regular graph with maximal energy). After that, we prove the conjecture in the general case. Auxiliary theorem obtained in the proof of this conjecture is also an original result which gives a sharp upper bound of sum of quadratic of the largest k singular values of graph. A corollary of this theorem which gives an upper bound for sum of squares of the biggest two singular values of graph can be useful in further research. In the subsection 3.3 we give an original theorem about asymptotic properties of spectrum and thus energy of complement graph for a large values of n. In the subsection 3.4 we calculate a mean of p-th degree of singular values and upper bound of geometric mean of almost all graphs. The last chapter shows relation between combinatorial theory of graphs with universal universal algebra and mathematical logic. The central part of this chapter is original and shorter proof of an important theorem which solves a dichotomy conjecture for CSP problem on undirected graphs. URI: http://hdl.handle.net/123456789/5371 Files in this item: 1
Ivan_teza20042022.pdf ( 1.428Mb ) -
Alatrash, Emhimed Salem (Beograd , 2015)[more][less]
Abstract: Ontologies, often defined as an explicit specification of conceptualization, are necessary for knowledge representation and knowledge exchange. This means that ontology describes concepts and relations that exist in a domain. To enable knowledge exchange, it is necessary to describe these concepts and relations in a better way than just ordering them in taxonomy. A computational ontology consists of a number of different components, such as Concepts, Instances, Individuals or Facts, Relations and Attributes. The present research is intended to consider different software tools related to Semantic web, and achieve a kind of comparison among them. In fact, five ontology-editors are described and compared. They are: Apollo, Onto Studio, Protégé, Swoop and TopBraid Composer Free Edition. The structure and basic features of these editors as well as the way of using them are described. The main criterion used in the process of comparing these editors lies in their convenience for the user, and the possibility to apply them in different kinds of application. The main goal of the work is to introduce a method for ontology construction of a certain domain in applying the Semantic web. A number of software tools adapted to build up the domain ontologies of most wide–spread natural languages are available; however accomplishing that for any given natural language presents a challenge. This research proposes a semi-automatic procedure to create ontologies for different natural languages. The approach utilizes various software tools that are available on the Internet, most notably DODDLE-OWL which is a domain ontology development tool implemented for English and Japanese languages. Through this tool, WordNet, Protégé and XSLT transformations, the researcher proposes a general procedure to construct domain ontology for any natural language. URI: http://hdl.handle.net/123456789/4266 Files in this item: 1
phdEmhimedAlatrash.pdf ( 2.171Mb ) -
Jović, Aleksandar (Beograd , 2021)[more][less]
Abstract: The continuous-time programming problem consists in minimizing an integral functional, with phase constraints of different types. The subject of this doctoral dissertation is to establish extremum conditions as well as duality theorems for a class of convex and smooth continuous-time programming problems, with phase constraints of the inequality type. Unfortunately, some of the results in this field are not valid, which is confirmed in 2019. In this paper, new optimality conditions for the aforementioned class of problems are ob tained. The theorems of weak and strong duality are proved. The main tool for deriving these results is a new theorem of the alternative for a convex system of strict and nonstrict inequal ities in infinite dimensional spaces. In order to apply the aforementioned theorem, a suitable regularity condition must be satisfied. Some optimality conditions are obtained with additional constraint regularity qualification. Theoretical results are confirmed by practical examples. URI: http://hdl.handle.net/123456789/5298 Files in this item: 1
A.Jovic_doktorska_disertacija.pdf ( 1.280Mb )