Browsing Doctoral Dissertations by Title

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 nonsingular 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 nontrivial 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 4manifolds. 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 4manifolds 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 4manifolds, including CP2, CP2♯CP2, S2×S2, etc. In Chapter 5 we calculate the StiefelWhitney 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 ndimensional 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]

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 nonlocal thermodynamic equilibrium (NLTE), which, in turn requires selfconsistent 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 highresolution 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 nonLTE 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 nonlocal 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 GaussSeidel iteration and “Sweepbysweep” implicit lambda iteration, latter one being based on “Forthandback” 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). “Sweepbysweep” 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 GaussSeidel iteration on problems with periodic boundary conditions. Also, it turns out that “Sweepbysweep” 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 nonLTE problem (Generalization to other iterative schemes is given in appendix A). This method allows for the selfconsistent 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 sixvectors 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 selfemitting 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 selfemitting disks dramatically changes not only intensity, but also polarized spectral lines pro files. Interplay of nonLTE, multidimensional effects and rotation results in very complicated line profiles which are nontrivial 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 doublelobed 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]

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 populationbased 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 wellknown practical problems. Comparative analysis with the stateoftheart 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]

MadarasSilađi, 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]

Jovanović, Milan (Belgrade)[more][less]

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 ontologyeditors 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 semiautomatic procedure to create ontologies for different natural languages. The approach utilizes various software tools that are available on the Internet, most notably DODDLEOWL 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 ) 
Nikolić, Mladen (Belgrade , 2013)[more][less]
Abstract: In this thesis the problem of guiding search in automated theorem proving is considered. The thesis consists of two parts that have the CDCL search system, the system intensively used by modern SAT solvers, as their common topic. In the rst part of the thesis a simple approach to guiding search is considered  guiding by the selection of the solver, its heuristics, and their parameters, based on the properties of an instance to be solved. The basis of the proposed methods for algorithm selection is syntactical similarity of formulae which is re ected in their graph structure. This graph similarity is established and analyzed by using an original graph similarity measure (which turned out to be useful in other contexts, too). Yet, practical approaches to measuring similarity of formulae are based on their numerical features due to the computational complexity issues. Two simple methods for algorithm selection, based on k nearest neighbors, were proposed. The rst technique, ArgoSmArT is based on classi cation of instance in one of the prede ned families for which the e cient algorithms are known. The instance is solved by algorithm corresponding to the family to which the instance was classi ed. The second technique, ArgoSmArT kNN is based on nding several similar instances in the training set for which the solving times by all considered algorithms are known. The instance is solved by the algorithm that behaves the best on those instances. ArgoSmArT technique is better suited for con guration selection of a SAT solver, and ArgoSmArT kNN for SAT solver selection. ArgoSmArT kNN technique showed to be more e cient than the most important and very complex system for SAT solver selection  SATzilla system. Apart from CNF SAT solver selection, the problem of nonCNF SAT solver selection is considered. The focus was not on solver selection techniques, since the proposed techniques are directly applicable, but on the attributes that can be used to describe nonCNF SAT instances, which have not been proposed earlier. The results in this domain are positive, but still limited. The main reason for that is the lack of greater number of nonCNF SAT solver of di erent behaviour, which is not surprising, having in mind that this kind of solvers is in its early stage of development. Apart from construction of e cient SAT solver selection system, the methodology of SAT solver comparison, based on statistical hypothesis testing is proposed. The need for such a methodology comes from great run time variations of single instance solving by a solver, which can result in di erent SAT solver orderings when one tries to compare their performance or rank them, as experimentally demonstrated. The proposed methodology gives the estimate of statistical signi cance of the performed test and the estimate of the e ect size, for instance the probability of a solver being faster than another. The second part of the thesis is concerned with generalizing CDCL search system to fragments of rst order logic. The proposed system can be used as a basis for e cient proving in some fragment if the rules of resolution and factoring are speci ed for that fragment. These rules are de ned for an extension of coherent logic. The soundness and completeness of the system are proved. The system has several distinguishing features which are a consequence of previously performed analysis of challenges in coherent logic theorem proving. The system enables rst order reasoning, instead of ground one characteristic for all existing coherent logic provers. Moreover, it introduces backjumps and lemma learning. The special attention in system design was paid to the possibility of generating readable proofs by the prover implementing the system. This possibility is one of the greatest qualities of coherent logic, but it is not easy to achieve if CDCL search system is used. One of the properties of the system that came from the need for generation of readable proofs is preservation of quanti ers in proving process which is rather unusual for existing CDCL systems. Another advantage of the proposed CDCL system is the possibility of transfer of heuristics which are already successfully employed in SAT solving to other domains. Based on the proposed system, the proof procedure Calypso for extended coherent logic was de ned which can also be used in standard coherent logic. The extension of Rete algorithm which enables detection of con icts and literals to be propagated or decided is proposed. Procedure Claypso is implemented in C++. It was evaluated on a representative coherent logic problems and it showed superior to other coherent logic provers and also the prover Vampire, the most e cient prover for rst order logic. Based on the results presented in this thesis, it can be concluded that the main hypothesis of this work, that the search system used in CDCL SAT solvers can be signi cantly improved by simple guiding and that it can be successfully formulated for fragments of rst order logic such as coherent logic, was con rmed and that the concrete answers on how to do that were provided. URI: http://hdl.handle.net/123456789/2584 Files in this item: 1
nikolic_mladen.pdf ( 1.448Mb ) 
Jovanović, Predrag (Belgrade , 2005)[more][less]

Dimovski, Igor (Novi Sad , 2011)[more][less]
Abstract: A comprehensive pedagogical research regarding teaching mathematics at a tertiary, university level has been presented in the PhD dissertation. The educational resources tailored in an electronic form using the programme package Matlab are integrated in the learning process. The impact of ICT use to the essential knowledge that refers to multivariate calculus (functions of several variables, vectorvalued functions and the threedimensional analytical geometry) has been statistically explored by intensive use of 3D static and dynamic visual tools. Part of the students who have participated in the research have developed Matlab programmes all by their own. One part of the research has been focused on probable impact of the programming skills on learning mathematical concepts. URI: http://hdl.handle.net/123456789/3874 Files in this item: 1
PhD_I_Dimovski.pdf ( 5.423Mb ) 
MilanovićLazarević, Smilja (Belgrade , 1987)[more][less]
URI: http://hdl.handle.net/123456789/248 Files in this item: 1
phdSmiljaMilanovicLazarevic.PDF ( 4.155Mb ) 
Dimitrijević, Milan (Belgrade)[more][less]
Abstract: A detailed analysis of the motion of a charged particle under the influence of Coulomb, polarization, and quadrupolar potential has been performed, and analytical expressions for particle path parameters have been obtained. Also, conditions for existence of a critical impact parameter, which separates paths ending in the atom from those going to infinity, have been examined, and methods for its determination have been elaborated. Results of this investigations have been applied to the theory of Stark broadening (broadening of spectral lines under the influence of collisions with charged particles), where a special attention has been paid to the adiabatic limit, and to quasistatic and impact approximations. Modification of Stark broadening functions has been performed and it has been demonstrated that the biggest influence of path curvature on them, is in the vicinity of the critical impact parameter, which separates paths ending in the atom from those going to infinity. The change in the values of the Stark broadening functions will have the largest influence on Stark broadening parameters for lines for which, at the most probable velocity, influence of the contribution of inelastic collisions is dominant and effective polarizability large. The application of semiempirical approximative approach for calculation of Stark broadening parameters for multiply charged emitters, has been analyzed as well, and the modification of semiclassical theory has been performed. The averaged ratio of experimental and theoretical results is 0.75 for semiempirical, 1.47 for semiclassical, and 1.04 for modified semiclassical approach.У раду је извршена детаљна анализа кретања наелектрисане честице под утицајем Кулоновог, поларизационог и квадруполног потенцијала и добијени су аналитички изрази за параметре путање честице. Такође су испитани услови за егзистенцију критичног сударног параметра, који раздваја путање које завршавају у атому од оних које одлазе у бесконачност, и разрађене методе за његово налажење. Резултати овог испитивања су примењени на теорију Штарковог ширења (ширења спектралних линија под утицајем судара са наелектрисаним честицама), при чему је посебна пажња посвећена адијабатској граници и квазистатичкој и сударној апроксимацији. Изведена је модификација функција Штарковог ширења и показано је да је највећи утицај закривљености путање на њих, у близини критичног сударног параметра, који раздваја путање које завршавају у атому од оних које одлазе у бесконачност. Промена у величини функција Штарковог ширења ће највише утицати на параметре Штарковог ширења код линија за које је, при највероватнијој брзини, утицај доприноса нееластичних судара доминантан а ефективна поларизабилност велика. Такође је анализирана примена семиемпиријског апроксимативног прилаза за израчунавање параметара Штарковог ширења за вишеструко наелектрисане емитере, при чему је извршена модификација семикласичне теорије. Усредњени однос експерименталних и теоријских резултата је 0.75 за семиемпиријски, 1.47 за семикласични а 1.04 за модификовани семикласични прилаз. URI: http://hdl.handle.net/123456789/77 Files in this item: 1
Dimitrijevic.pdf ( 6.262Mb ) 
Vince, Ištvan (Belgrade)[more][less]